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MANUAL ON STREAM GAUGING - E-Library - WMO

QualityManagementFramework**MANUAL** **ON****STREAM** **GAUGING**VOLUME II – Computation of discharge**WMO**-No. 1044

Manual onStream GaugingVolume II – Computation of Discharge**WMO**-No. 10442010

**WMO**-No. 1044© World Meteorological Organization, 2010The right of publication in print, electronic and any other form and in any language is reserved by**WMO**. Short extracts from **WMO** publications may be reproduced without authorization, providedthat the complete source is clearly indicated. Editorial correspondence and requests to publish,reproduce or translate this publication in part or in whole should be addressed to:Chairperson, Publications BoardWorld Meteorological Organization (**WMO**)7 bis, avenue de la Paix Tel.: +41 (0) 22 730 84 03P.O. Box No. 2300 Fax: +41 (0) 22 730 80 40CH-1211 Geneva 2, SwitzerlandE-mail: publications@wmo.intISBN 978-92-63-11044-2NOTEThe designations employed in **WMO** publications and the presentation of material in this publication do notimply the expression of any opinion whatsoever on the part of the Secretariat of **WMO** concerning the legalstatus of any country, territory, city or area, or of its authorities, or concerning the delimitation of its frontiersor boundaries.Opinions expressed in **WMO** publications are those of the authors and do not necessarily reflect those of **WMO**.The mention of specific companies or products does not imply that they are endorsed or recommended by **WMO**in preference to others of a similar nature which are not mentioned or advertised.

contentsPageForeword.................................................................................................................................................PREFACE......................................................................................................................................................SUMMARY (English, French, Russian, Spanish) ...........................................................................................INTRODUCTI**ON**.........................................................................................................................................viiixxixvii1.1 Streamflow records.......................................................................................................................... xvii1.2 General stream-gauging procedures................................................................................................ xvii1.3 Definitions....................................................................................................................................... xviiiChapter 1. Discharge ratings using simple stage-discharge relations ..............................II.1-11.1 Introduction.................................................................................................................................... II.1-11.2 Stage-discharge controls.................................................................................................................. II.1-11.2.1 Section control................................................................................................................ II.1-21.2.2 Channel control.............................................................................................................. II.1-21.2.3 Combination or compound controls............................................................................... II.1-21.3 Governing hydraulic equations........................................................................................................ II.1-21.4 Complexities of stage-discharge relations......................................................................................... II.1-31.5 Graphical plotting of rating curves................................................................................................... II.1-31.5.1 List of discharge measurements....................................................................................... II.1-31.5.2 Use of inside and outside gauge readings........................................................................ II.1-51.5.3 Arithmetic plotting scales................................................................................................ II.1-51.5.4 Logarithmic plotting scales.............................................................................................. II.1-61.5.5 Computer plotting of discharge measurements and rating curves................................... II.1-81.5.6 Analysis of rating curves.................................................................................................. II.1-81.6 Ratings for artificial section controls................................................................................................. II.1-91.6.1 Notched flat-crested rectangular weir...................................................................................... II.1-91.6.2 Trenton-type control....................................................................................................... II.1-101.6.3 Columbus-type control................................................................................................... II.1-111.7 Ratings for natural section controls.................................................................................................. II.1-111.8 Ratings for natural compound section controls................................................................................ II.1-121.9 Ratings for stable channel controls .................................................................................................. II.1-121.10 Ratings for compound controls involving section and channel control............................................. II.1-131.11 Extrapolation of rating curves.......................................................................................................... II.1-141.11.1 Low flow extrapolation.................................................................................................... II.1-141.11.2 High flow extrapolation................................................................................................... II.1-141.12 Shifts in the discharge rating............................................................................................................ II.1-191.12.1 Detection of shifts in the rating....................................................................................... II.1-191.12.2 Statistical analysis of the stage-discharge relation............................................................ II.1-201.12.3 Rating shifts for artificial controls..................................................................................... II.1-201.12.4 Rating shifts for natural section controls.......................................................................... II.1-221.12.5 Rating shifts for channel control...................................................................................... II.1-231.13 Effect of ice formation on discharge ratings..................................................................................... II.1-261.13.1 General........................................................................................................................... II.1-26

ivmanual on stream gauging1.13.2 Frazil............................................................................................................................... II.1-271.13.3 Anchor ice....................................................................................................................... II.1-271.13.4 Surface ice...................................................................................................................... II.1-281.13.5 Computation of discharge during periods of backwater from anchor ice......................... II.1-291.13.6 Computation of discharge during periods of backwater from surface ice......................... II.1-301.14 Sand channel streams...................................................................................................................... II.1-351.14.1 Bed configuration........................................................................................................... II.1-351.14.2 Relation of mean depth to discharge............................................................................... II.1-361.14.3 Development of discharge rating.................................................................................... II.1-371.14.4 Evidence of bed forms..................................................................................................... II.1-391.14.5 Shifting controls.............................................................................................................. II.1-391.14.6 Artificial controls for sand channels................................................................................. II.1-40PageChapter 2. Discharge Ratings using the velocity index method............................................II.2-12.1 Introduction.................................................................................................................................... II.2-12.2 Basics of the velocity index method................................................................................................. II.2-12.3 Stage-area rating development........................................................................................................ II.2-22.4 Velocity index rating development................................................................................................... II.2-32.5 Discharge computation................................................................................................................... II.2-42.5.1 General........................................................................................................................... II.2-42.5.2 Mean discharge at tidally affected sites........................................................................... II.2-52.5.3 Discharge records during ice-affected periods................................................................. II.2-62.6 Example ADVM velocity-index site................................................................................................... II.2-72.6.1 Development of stage-area rating................................................................................... II.2-82.6.2 Development of velocity-index rating.................................................................................. II.2-92.7 Velocity index error sources.............................................................................................................. II.2-10Chapter 3. DISCHARGE RATINGS USING SLOPE AS A PARAMETER........................................................II.3-13.1 General considerations..................................................................................................................... II.3-13.2 Theoretical considerations................................................................................................................ II.3-13.3 Variable slope caused by variable backwater.................................................................................... II.3-23.3.1 Constant-fall method...................................................................................................... II.3-43.3.2 Variable fall method........................................................................................................ II.3-73.4 Variable slope caused by changing discharge................................................................................... II.3-133.4.1 Theoretical considerations............................................................................................... II.3-133.4.2 Methods of rating adjustment for changing discharge.................................................... II.3-143.5 Variable slope caused by a combination of variable backwater and changing discharge................... II.3-193.6 Shifts in discharge ratings where slope is a factor............................................................................. II.3-193.7 Computer methods for analysis and computation of slope affected ratings...................................... II.3-19Chapter 4. FLOW COMPUTATI**ON** MODELS FOR UPLAND, BRANCHED AND TIDAL **STREAM**S............4.1 General............................................................................................................................................ II.4-14.2 Terminology.................................................................................................................................... II.4-24.3 One-dimensional unsteady flow equations....................................................................................... II.4-24.4 Model formulation........................................................................................................................... II.4-24.5 Boundary conditions........................................................................................................................ II.4-34.6 Model applications.......................................................................................................................... II.4-34.6.1 Columbia River reach at Rocky Reach Dam near Wenatchee, Washington,United States................................................................................................................... II.4-5II.4-1

contents4.6.2 Potomac River near Washington, D.C., United States...................................................... II.4-54.7 Empirical methods........................................................................................................................... II.4-74.7.1 Method of cubatures....................................................................................................... II.4-74.7.2 Rating-fall method ......................................................................................................... II.4-84.7.3 Tide-correction method.................................................................................................. II.4-84.7.4 Coaxial rating-curve method........................................................................................... II.4-9PageChapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIES.................................II.5-15.1 Introduction.................................................................................................................................... II.5-15.2 Dams with movable gates................................................................................................................ II.5-15.2.1 General........................................................................................................................... II.5-15.2.2 Drum gates..................................................................................................................... II.5-25.2.3 Radial or Tainter gates..................................................................................................... II.5-85.2.4 Vertical lift gates.............................................................................................................. II.5-125.2.5 Roller gates..................................................................................................................... II.5-125.2.6 Movable dams................................................................................................................ II.5-135.2.7 Flashboards..................................................................................................................... II.5-155.2.8 Stop logs and needles..................................................................................................... II.5-165.3 Navigation locks.............................................................................................................................. II.5-165.4 Pressure conduits............................................................................................................................. II.5-205.4.1 General........................................................................................................................... II.5-205.4.2 Metering devices for pressure-conduit flow..................................................................... II.5-215.4.3 Discharge-measurement methods for meter calibration.................................................. II.5-255.4.4 Calibration of turbines, pumps, gates and valves............................................................. II.5-295.5 Urban storm drains.......................................................................................................................... II.5-305.5.1 United States Geological Survey sewer flow-meter.......................................................... II.5-305.5.2 Wenzel asymmetrical and symmetrical flow-meters......................................................... II.5-325.6 Automated computation of flow through water control structures................................................... II.5-325.6.1 General description of Program DAMFLO.2..................................................................... II.5-325.6.2 Time-varying input data.................................................................................................. II.5-335.6.3 Fixed input data.............................................................................................................. II.5-335.6.4 Program output data....................................................................................................... II.5-34Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using .electronic methods.......................................................................................................II.6-16.1 General............................................................................................................................................ II.6-16.2 Surface water data and information................................................................................................. II.6-26.3 Establishing a site in the electronic processing system...................................................................... II.6-36.4 Entry of field data to the electronic processing system..................................................................... II.6-36.4.1 Unit value data................................................................................................................ II.6-36.4.2 Sources of unit value data............................................................................................... II.6-46.4.3 Unit value recording time interval................................................................................... II.6-56.4.4 Time system requirements............................................................................................... II.6-56.4.5 Standard format.............................................................................................................. II.6-56.4.6 Field measurement data.................................................................................................. II.6-56.5 Verification and editing of unit values.............................................................................................. II.6-76.5.1 Times and dates.............................................................................................................. II.6-76.5.2 Time corrections and adjustments................................................................................... II.6-76.5.3 Parameter value verifications........................................................................................... II.6-8

vimanual on stream gauging6.5.4 Parameter value corrections............................................................................................ II.6-116.6 Verification and analysis of field measurements................................................................................ II.6-146.6.1 Discharge measurement checking................................................................................... II.6-146.6.2 Special checking procedures for other types of discharge measurements......................... II.6-166.6.3 Rounding and significant figures..................................................................................... II.6-206.6.4 Summary of discharge measurements............................................................................. II.6-206.7 Entry of rating curves to the electronic processing system................................................................ II.6-206.7.1 Tabular entry................................................................................................................... II.6-206.7.2 Equation entry................................................................................................................ II.6-216.7.3 Graphical entry............................................................................................................... II.6-226.8 Rating tables.................................................................................................................................... II.6-226.8.1 Interpolation methods..................................................................................................... II.6-226.8.2 Rating table smoothness analysis..................................................................................... II.6-236.8.3 Other rating table information........................................................................................ II.6-236.9 Rating curve plots............................................................................................................................ II.6-236.9.1 Linear scale plots............................................................................................................. II.6-236.9.2 Logarithmic scale plots.................................................................................................... II.6-246.9.3 Rating curve shaping....................................................................................................... II.6-256.9.4 Computer development of rating curves......................................................................... II.6-256.10 Discharge measurement shift adjustments....................................................................................... II.6-286.10.1 Shifts for stage-discharge ratings..................................................................................... II.6-296.10.2 Shifts for slope ratings..................................................................................................... II.6-296.10.3 Shifts for rate-of-change-in-stage ratings......................................................................... II.6-306.10.4 Shifts for stations............................................................................................................. II.6-306.11 Application of shift adjustments....................................................................................................... II.6-316.11.1 Shift-adjustment variation diagrams................................................................................ II.6-326.11.2 Unit value graphical comparison of shifts........................................................................ II.6-346.12 Primary computations...................................................................................................................... II.6-356.12.1 Unit value computations................................................................................................. II.6-356.12.2 Daily value computations................................................................................................ II.6-416.12.3 Summary of primary computations................................................................................. II.6-436.13 Hydrograph plots............................................................................................................................. II.6-466.13.1 Unit value hydrographs................................................................................................... II.6-466.13.2 Daily value hydrographs.................................................................................................. II.6-466.14 Computation of extremes................................................................................................................ II.6-466.14.1 Annual peak stage and discharge.................................................................................... II.6-476.14.2 Secondary peak stages and discharges............................................................................ II.6-476.14.3 Annual minimum discharge............................................................................................ II.6-476.15 Estimating missing records............................................................................................................... II.6-476.15.1 Hydrographic and climatic comparison method.............................................................. II.6-486.15.2 Discharge ratio method................................................................................................... II.6-486.15.3 Regression method......................................................................................................... II.6-486.15.4 Water-budget method.................................................................................................... II.6-496.15.5 Mathematical translation method................................................................................... II.6-496.15.6 Flow routing methods..................................................................................................... II.6-496.16 Monthly and annual value computations......................................................................................... II.6-506.16.1 Monthly and annual values of stage................................................................................ II.6-506.16.2 Monthly and annual values of discharge.......................................................................... II.6-506.16.3 Monthly and annual values for reservoirs......................................................................... II.6-516.16.4 Monthly and annual values for tidal stations.................................................................... II.6-516.17 Station analysis documentation........................................................................................................ II.6-51Page

ForewordIncreasing pressures on our vital water resourcessignify that confidence in the quality of streamflowrecords is today, more than ever, an essentialprerequisite for the sustainable management ofthese critical resources.The Manual on Stream Gauging (**WMO**-No. 519)was first released in 1980. Since then, however,there have been significant advances both in theapproach and the methodologies employed.Consequently, at its twelfth session (Geneva,October 2004), the **WMO** Commission forHydrology (CHy) decided to meet the identifiedneeds of the National Hydrological Services byrevising the Manual to include the newertechnologies that have been introduced over theperiod and are currently employed in this crucialfield.In this context, Volume I of the Manual on StreamGauging encompasses the topics of gauge heightmeasurement, stream velocity and streamdischarge, whilst Volume II focuses on thedischarge rating relationship.On behalf of **WMO**, I wish to commend bothvolumes of this Manual and to express myappreciation to all who contributed to this keyupdate.(M. Jarraud)Secretary-General

PREFACEWith the adoption by the **WMO** Commissionfor Hydrology of the Quality ManagementFramework – Hydrology (QMF-H) at its thirteenthsession, the Commission demonstrated theimportance that National Hydrological Servicesplace on the efficiency, quality and effectivenesswith which they perform their functions. Thestream gauging programme is one of thefundamental building blocks of the operations ofany hydrological service and therefore it is onlynatural that a thorough revision and update of the**WMO** Manual on Stream Gauging would be amongthe initial publications to be labeled as a componentof QMF-H. For this reason, it is particularlygratifying for me to be able to introduce thisimportant contribution from the Commission tothe international hydrological community.The preparation of the Manual was led by Mr PaulPilon (Canada), then member of the advisoryworking group of the Commission for Hydrology.Mr Vernon B. Sauer made the revisions to theManual. The reviewers of the draft text wereMichael Nolan, Larry Bohman and Scott Morlock(United States of America); Stewart Child, JamesWaters and Reginald Herschy (United Kingdom ofGreat Britain and Northern Ireland); Pavel Polcar(Czech Republic); Kimmo Ristolainen (Finland);Svein Harsten (Norway); and Julio Llinas(Dominican Republic). The draft was edited byJames Biesecker (United States).The activities were carried out in association withthe Open Panel of CHy Experts (OPACHE) on BasicSystems (Hydrometry and Hydraulics).I express my gratitude to the original authors ofthe Manual on Stream Gauging (Mr R.W. Herschyand Mr S.E. Rantz), the author of this revision(Mr Sauer) and the reviewers for their contributionsto the preparation of the revised Manual.The Commission for Hydrology is planning toorganize courses in various regions to trainhydrological personnel in its use. The translationof the Manual into other languages will beconsidered soon by the Commission.(Bruce Stewart)President, Commission for Hydrology

SUMMARYxiiiindirecte des débits de pointe) – donne unedescription générale des procédures appliquées pourrecueillir des données sur le terrain et calculer lesdébits de pointe par différentes méthodes indirectesaprès une crue. Le chapitre 10 – Uncertainty ofDischarge Measurements (Incertitude des mesures dedébit) – traite des incertitudes afférentes aux diversesméthodes évoquées précédemment.Le Volume II – Computation of Discharge (Calcul desdébits) – traite principalement du calcul de larelation hauteur-débit et du débit journalier moyen.Il est destiné principalement aux jeunes ingénieursayant reçu une formation de base en hydraulique etcomprend six chapitres. Le chapitre 1 – DischargeRatings Using Simple Stage-Discharge Relations(Étalonnage des débits sur la base d’une simplerelation hauteur-débit) – analyse les cas où le débitne dépend que de la hauteur. Il expose les questionssuivantes: contrôles de la relation hauteur-débit,équations hydrauliques de base, complexité de larelation hauteur-débit, pointage des courbes detarage, sections de contrôle naturelles et artificielles,tronçons de contrôle, extrapolation des courbes detarage, détarage, effets de la formation de glacesur le tarage et cours d’eau à lit sablonneux. Lechapitre 2 – Discharge Ratings Using Velocity IndexMethod (Étalonnage des débits la méthode fondéesur l’indice de vitesse) – présente les principes debase de cette méthode, l’établissement des courbeshauteur – superficie et des courbes basées sur l’indicede vitesse, puis aborde le calcul du débit en fonctionde l’indice de vitesse basé sur le moulinet acoustiqueà effet doppler, à titre d’exemple. Le chapitre 3 –Discharge Ratings Using Slope as a Parameter(Étalonnage des débits utilisant la pente commeparamètre) – porte sur les questions suivantes: pentevariable due à des remous variables, à un débitchangeant ou à une combinaison des deux facteurs,détarage lorsque la pente entre en ligne de compteet méthode de calcul des relevés de débit pour lesstations avec une pente marquée. Le chapitre 4 –Flow Computation Models for Upland, Branched, andTidal Streams (Modèles de calcul de l’écoulementpour les cours d’eau supérieurs, ramifiés et àmarée) – porte sur la formulation des modèles etles conditions aux limites, les applications demodèles et d’autres méthodes empiriques.Le chapitre 5 – Discharge Ratings for MiscellaneousHydraulic Facilities (Étalonnage des débits pourdiverses installations hydrauliques) – porte sur lesbarrages à vannes mobiles, les écluses de navigation,les conduites en charge, les canaux de drainageurbains et le calcul automatique de l’écoulementpar des ouvrages hydrauliques. Enfin, le chapitre 6 –Analysis and Computation of Discharge Records UsingElectronic Methods (Analyse et calcul des relevés dedébit par des moyens électroniques) – aborde lesdifférents problèmes liés à l’analyse et au calculélectroniques des relevés de débit tels quel’introduction des données de terrain dans lesystème de traitement électronique, la vérificationet l’ajustement des valeurs unitaires, la vérificationet l’analyse des mesures effectuées sur le terrain,l’introduction des courbes de tarage dans le systèmede traitement électronique, les barèmes et lescourbes d’étalonnage, les corrections apportées à ladérive des mesures du débit, les calculs primaires,les hydrogrammes, le calcul des extrêmes,l’évaluation des relevés manquants, le calcul desvaleurs mensuelles et annuelles ainsi que ladocumentation sur l’analyse des données recueilliesaux stations.РЕЗЮМЕТридцать лет спустя после опубликования своегопервого Наставления по измерению расхода водыВМО публикует это переработанное издание, вкотором нашли отражение новые технологии, появившиесяпосле 1980 г. Наставление, как и в предыдущемслучае, будет издано двумя отдельнымитомами (том I: Полевые работы, и том II: Вычислениерасхода воды), с тем чтобы сохранить концепцию«рабочего наставления». Том I, который предназначенглавным образом для техников-гидрологов,состоит из десяти глав. В этом томе обсуждаются триосновные темы: выбор мест расположения гидрометрическихстворов, измерение уровня воды иизмерение расхода воды. Глава 1 содержит введениеи краткое описание данных наблюдений за речнымстоком и процедур измерения стока воды; она такжевключает некоторые предварительные определениятерминов, используемых в Наставлении. В главе 2 —Выбор мест расположения гидрометрических створов,рассматриваются общие аспекты проектированиясети гидрометрических станций с учетомосновной цели, для которой создается сеть (например,паводки или исследования повторяемостинизкого стока), а также аспекты гидравлики, которыеследует учитывать при выборе места расположенияконкретного створа. Раздел, посвященныйпроектированию сетей гидрометрических станций,по сути, предназначен для опытных гидрологов,

xiv**MANUAL** **ON** **STREAM** **GAUGING**которые занимаются планированием таких сетей.Глава 3 — Инспекция гидрометрических станций,содержит обзор видов контроля, характеристикудовлетворительного контроля и искусственныхконтрольных сечений, а также критерии выбора ипроектирования искусственных контрольных сечений.В главе 4 — Измерение уровня воды, рассматриваютсяосновные требования к сбору данных обуровне воды, водомерным сооружениям и приборам,типичной конфигурации приборов на водомерныхпостах, извлечению данных и их преобразованию,проектированию новых станций измерения уровнейводы и функционированию станций измеренияуровней воды, а также соображения безопасностипри оперативном измерении расхода воды. Глава 5— Измерение расхода воды методами, при которыхиспользуются гидрометрические вертушки, содержитобщее описание обычного измерения расхода воды,приборов и оборудования, измерения скорости иглубины и процедуры измерения расхода воды спомощью обычных вертушек. В главе 6 — Измерениярасхода воды с помощью акустического и электромагнитногометодов, дается описание трех методовизмерения, представленных в первом издании ишироко используемых для измерений расхода воды,а именно: метода измерения с движущегося судна сиспользованием акустических профилометров Доплерадля измерения течения (ADCPs), ультразвуковогометода измерения скорости течения (AVM) иэлектромагнитного метода. Рассматривается и четвертыйметод, который предполагает использованиеакустического доплеровского измерителя скорости(ADVM). Глава 7 — Измерения расхода воды с помощьюгидрометрических сооружений, посвященастандартным сооружениям. Методы, изложенные вглаве 8 — Измерения расходов воды разными методами,включают в себя методы скорость-индекс;измерения с помощью поплавков; объемные измерения;измерения с помощью переносных водосливовили лотков Паршаля; измерения неустойчивогопотока для боковых волн или пробковых потоков;метод разбавления с использованием трассеров; измеренияс помощью дистанционного зондированияи с самолета, а также радиолокационные методыизмерения расхода. Глава 9 — Косвенное определениемаксимального расхода воды, дает общее описаниепроцедур, используемых при сборе данныхполевых измерений и при вычислениях максимальногорасхода с помощью различных косвенныхметодов после прохождения паводка. В главе 10 —Неопределенность измерений расхода, рассматриваетсянеопределенность, связанная с различнымиметодами, представленными выше.Том II — Вычисление расхода воды, рассматриваетглавным образом вычисление зависимости расходаот уровня и вычисление среднего суточного расхода.Он предназначен для младших техников, знакомых сосновами гидравлики. Том II состоит из шести глав.В главе I — Кривые расхода воды на примере простойзависимости расходов от уровня, рассматриваютсякривые, в которых расход ставится в зависимостьтолько от уровня. В ней описываются контрольныесечения для измерения уровня и расхода; основныеуравнения гидравлики; сложности, связанные сзависимостью расхода от уровня; графическое построениекривых расхода; кривые расхода для искусственныхи естественных контрольных сечений;контрольное русло; экстраполяция кривых расхода;смещения кривых расхода; влияние образованияльда на кривые расхода и деформацию русла. Глава 2— Кривые расхода воды с использованием методаскорость-индекс, описывает основы метода скоростьиндекс;построение кривой уровень-площадь икривой скорость-индекс; а также рассматривает вычислениерасхода воды с помощью индекса скоростиADVM в качестве примера. В главе 3 — Кривыерасхода воды на примере использования уклонаводной поверхности в качестве параметра, рассматриваетсяпеременный уклон, вызванный меняющимсяподпором, изменением расхода и сочетаниемтого и другого, а также смещения кривых расхода,в которых уклон является коэффициентом. В нейтакже представлен подход к вычислению расхода настанциях, измеряющих уклон. Глава 4 — Моделирасчета потока воды для нагорных, разветвленных иприливно-отливных течений, начиная с одномерныхуравнений неустановившегося потока, посвященаформулированию модели и граничных условий,применениям моделей и другим эмпирическимметодам. Глава 5 — Кривые расхода воды для различныхгидротехнических сооружений, рассматриваетдамбы с раздвижными шлюзами, навигационныешлюзы, напорные водоотводные каналы, городскиеводостоки, а также автоматическое вычислениепотока через водорегулирующие сооружения. Наконец,в главе 6 — Анализ и вычисление расхода водыс использованием электронных методов, рассматриваютсяразличные проблемы, связанные с электронныманализом и вычислением расходов, такиекак введение данных полевых измерений в электроннуюсистему обработки данных; верификация иредактирование единичных значений; верификацияи редактирование данных полевых измерений;внесение кривых расходов в электронную системуобработки данных; таблицы и графики кривых расхода;поправки на смещение в измерениях расхода;первичные вычисления; графики, представляющиегидрографические данные; вычисления экстремальныхзначений; расчет недостающих данных;вычисления ежемесячных и годовых значений идокументация с результатами анализа данных наблюденийна станции.

SUMMARYxvRESUMENTreinta años después de la primera publicación delManual on Stream Gauging (Manual sobre aforo decaudales), la OMM presenta una edición actualizadadel mismo para incluir las nuevas tecnologías quehan ido apareciendo desde 1980. De nuevo, y paraseguir con el concepto de “manual de trabajo”, estapublicación se divide en dos volúmenes (Volumen I“Trabajos sobre el terreno” y Volumen II “Cálculodel caudal”). El Volumen I “Trabajos sobre elterreno” está destinado esencialmente a los técnicosen hidrología y consta de diez capítulos. En dichoVolumen se abordan tres cuestiones principales, asaber: la selección del emplazamiento de lasestaciones de aforo, la medición del nivel y lamedición del caudal. En el capítulo 1 “Introducción”se exponen brevemente los registros del flujo de lacorriente y los métodos de aforo generalmenteutilizados, ofreciéndose además algunas definicionespreliminares de la terminología utilizada en elManual. El capítulo 2 “Selección del emplazamientode las estaciones de aforo” trata de los aspectosgenerales del diseño de redes de estaciones de aforo,teniendo en cuenta el objetivo buscado con elestablecimiento de dichas redes (por ejemplo,estudios sobre la frecuencia de crecidas o períodosde estiaje) y los factores hidráulicos que han detenerse en cuenta en la selección de un sitiodeterminado. La sección dedicada al diseño de redesde estaciones de aforo está destinada, naturalmente,a los hidrólogos experimentados que elaboran losplanes de este tipo de redes. El capítulo 3 “Controlesen las estaciones de aforo” estudia los distintos tiposde control, las características que deben reunir loscontroles naturales satisfactorios y los artificiales,así como los criterios para seleccionar y diseñar loscontroles artificiales. El capítulo 4 “Medición delnivel” analiza los requisitos básicos para larecopilación de datos sobre el nivel de las aguas, lasestructuras e instrumentos de medición, lasconfiguraciones típicas de los instrumentos de lasestaciones de aforo, la recuperación y conversión dedatos, el diseño de las nuevas estaciones de nivel yel funcionamiento de las estaciones de medicióndel nivel, así como las cuestiones relacionadas conla seguridad durante las operaciones de aforo delcaudal. El capítulo 5 “Medición del caudal por elmétodo clásico del molinete” facilita una descripcióngeneral de las mediciones del caudal efectuadas conmolinete, de los instrumentos y equipo necesarios,de los métodos para medir la velocidad y laprofundidad, y de los procedimientos de medicióndel caudal con el método clásico del molinete. En elcapítulo 6 “Medición del caudal por métodosacústicos y electromagnéticos” se exponen tresmétodos de aforo del caudal introducidos en laprimera edición y cuyo uso se ha generalizado, asaber: el método del bote móvil dotado deperfiladores de corriente de efecto Doppler (ADCP),el método de los medidores ultrasónicos (acústicos)de velocidad (AVM) y el método electromagnético.En este capítulo se presenta además un cuartométodo basado en medidores acústicos de velocidadde efecto Doppler (ADVM). El capítulo 7 “Medicióndel caudal por medio de estructuras de mediciónprecalibradas” se centra en las estructuras demedición normalizadas. El capítulo 8 “Otrosmétodos de medición del caudal” pasa revista avarios métodos como son los índices de velocidad,las mediciones con flotadores, los métodosvolumétricos, los vertederos de aforo portátiles y losmedidores Parshall, las mediciones de los flujosinestables de las ondas abruptas de traslación (rollwaves), los métodos de dilución de trazadores, lasmediciones realizadas por teledetección o desdeaeronaves y los métodos para medir el caudalmediante radares. El capítulo 9 “Determinaciónindirecta de caudales máximos instantáneos” ofreceun estudio general de los procedimientos indirectosutilizados para la recopilación de datos sobre elterreno y para el cálculo de caudales máximosinstantáneos después de una crecida. El capítulo 10“Incertidumbre de las mediciones del caudal”analiza las incertidumbres relacionadas con losdiversos métodos anteriormente mencionados.El Volumen II “Cálculo del caudal” se ocupaprincipalmente del cálculo de la relación alturacaudaly del caudal medio diario. Está destinadoprincipalmente a los ingenieros noveles que tienenconocimientos básicos en hidráulica y consta deseis capítulos. El capítulo 1 “Calibración del caudalmediante una simple relación altura-caudal” analizalos casos en que el caudal se relaciona únicamentecon la altura. En este capítulo se abordan cuestionescomo los controles de la relación altura-caudal, lasecuaciones fundamentales de la hidráulica, lascomplejidades de la relación altura-caudal, latrascripción gráfica de las curvas de gasto, el aforoen los controles de las secciones artificiales ynaturales, el control del canal, la extrapolación delas curvas de gasto, las fluctuaciones del caudal, losefectos de la formación de hielo en el caudal y losríos de lecho arenoso. En el capítulo 2 “Calibracióndel caudal mediante el método del índice develocidad” se exponen los principios básicos delmétodo del índice de velocidad y del establecimientode curvas de gasto fundamentadas en la relaciónaltura-superficie y en el índice de velocidad. Además,

xvi**MANUAL** **ON** **STREAM** **GAUGING**se presenta el cálculo del caudal utilizando comoejemplo el índice de velocidad ADVM. El capítulo 3“Calibración del caudal utilizando la pendientecomo parámetro” trata de las cuestiones siguientes:pendiente variable debida a remansos variables, aun caudal variable o a una combinación de ambos,y fluctuación de las curvas de gasto cuando lapendiente constituye un factor. Asimismo, presentaun método de cálculo de los registros del caudalpara la estaciones en pendiente. El capítulo 4“Modelos de cálculo del caudal aguas arriba y enríos ramificados y con mareas a partir de ecuacionesunidimensionales de flujos variables” estudia laformulación de modelos y condiciones de contorno,así como las aplicaciones de los modelos y otrosmétodos empíricos. El capítulo 5 “Calibración delcaudal en diversas instalaciones hidráulicas” abordalas cuestiones relacionadas con las presas concompuertas móviles, las esclusas de navegación, lastuberías de carga, los canales de drenaje urbano y elcálculo automático de la corriente medianteestructuras de control del agua. Finalmente, elcapítulo 6 “Análisis y cálculo de registro del caudalmediante métodos electrónicos” examina diferentesproblemas relacionados con el análisis y el cálculode los registros del caudal como son: la introducciónde datos de campo en un sistema de procesamientoelectrónico, la verificación y ajuste de valoresunitarios, la verificación y análisis de medicionessobre el terreno, la introducción de curvas de gastoen el sistema de procesamiento electrónico, latranscripción gráfica de curvas y tablas de gasto, losajustes aportados a las desviaciones de las medicionesdel caudal, los cálculos primarios, los hidrográmas,el cálculo de extremos, la estimación de los registrosfaltantes, los cálculos de valores mensuales yanuales, y los documentos de análisis de laestación.

INTRODUCTI**ON**1.1 Streamflow recordsStreamflow serves man in many ways. It supplieswater for domestic, commercial and industrial use;irrigation water for crops; dilution and transportof wastes; energy for hydroelectric power; transportchannels for commerce; and a medium forrecreation. Records of streamflow are the basicdata used in developing reliable surface watersupplies because the records provide informationon the availability of streamflow and its variabilityin time and space. The records are therefore usedin the planning and design of surface water relatedprojects, and they are also used in the managementor operation of such projects after the projectshave been completed. Streamflow records are alsoused for calibrating hydrological models, whichare used for forecasting, such as flood forecasting.Streamflow, when it occurs in excess, can create ahazard – floods cause extensive damage andhardship. Records of flood events obtained atgauging stations serve as the basis for the designof bridges, culverts, dams and flood controlreservoirs, and for flood plain delineation andflood warning systems. Likewise, extreme lowflow and drought conditions occur in naturalstreams, and should be documented with reliablestreamflow records to provide data for design ofwater supply systems. It is therefore essential tohave valid records of all variations in streamflow.The streamflow records referred to above areprimarily continuous records of discharge atstream-gauging stations; a gauging station being astream site instrumented and operated so that acontinuous record of stage and discharge can beobtained. Networks of stream-gauging stations aredesigned to meet the various demands forstreamflow information including an inventory ofthe total water resources of a geographic area. Thenetworks of continuous record stations, however,are often augmented by auxiliary networks ofpartial record stations to fill a particular need forstreamflow information at relatively low cost. Forexample, an auxiliary network of sites, instrumentedand operated to provide only instantaneous peakdischarge data, is often established to obtain basicinformation for use in regional flood frequencystudies. An auxiliary network of un-instrumentedsites for measuring low flow only is oftenestablished to provide basic data for use in regionalstudies of drought and of fish and wildlifemanagement.This Manual is a revision of the previouslypublished Manual on Stream Gauging (**WMO**-No. 519), Volumes I and II, 1980. Much of theoriginal material is used in this manual whereprocedures and equipment are still relevant.Likewise, material from a similar 2-volume manualby Rantz (1982) is also used. In many cases, thetwo manuals are identical.1.2 General stream-gaugingproceduresOnce the general location of a gauging station hasbeen determined from a consideration of the needfor streamflow data, its precise location is selectedto take advantage of the best locally availableconditions for stage and discharge measurementand for developing a stable stage-discharge relation,also called a “discharge rating”, or simply a“rating”.A continuous record of stage is obtained byinstalling instruments that sense and record thewater surface elevation in the stream. Dischargemeasurements are initially made at various stagesto define the relation between stage and discharge.Discharge measurements are then made at periodicintervals, usually monthly, to verify the stagedischargerelation or to define any change in therelation caused by changes in channel geometryand/or channel roughness.Artificial controls such as low weirs or flumes areconstructed at some stations to stabilize the stagedischargerelations in the low flow range. Thesecontrol structures are calibrated by stage anddischarge measurements in the field.In recent years, it is increasingly common to havereal-time, automatic, transfer of data from gaugingstations to hydrological analysis centres. Duringcertain events, such as imminent flood threats,real-time data are used as input to hydrologicalmodels to simulate water behaviour and provideflood forecasts for authorities. Real-time data are

xviii**MANUAL** **ON** **STREAM** **GAUGING**frequently published on internet sites forimmediate use by the general public. Real-timedata are used for several purposes and users shouldbe made aware that real-time data are alwaysconsidered preliminary and have not been qualitycontrolled.Data obtained at the gauging stations are reviewedand analyzed by engineering personnel throughoutthe water year. Discharge ratings are established,either by graphical methods or by computermethods. Unit values of recorded gauge heightsare used to compute unit and daily values of gaugeheight and discharge. The mean discharge for eachday and extremes of discharge for the year arecomputed. The data are then prepared forpublication and are considered final.1.3 DefinitionsA few common terms as defined by Sauer (2002)that are used throughout this Manual (Volumes Iand II) will be defined in this section. This is notintended to define all stream gauging terms.Additional definitions will be given as needed inother sections of the Manual.Gauge height, stage, and elevation are interchangeableterms used to define the height of the surface of awater feature, such as a stream, reservoir, lake, orcanal. For a stream gauging station, gauge heightis the more appropriate terminology, but themore general term “stage” is sometimes usedinterchangeably. For lakes, reservoirs and tidalstreams, the height of the water surface usually isreferred to as elevation. Gauge height (also stage)is measured above an arbitrary gauge datum,whereas elevation is measured above an establishedvertical datum, such as mean sea level. Gaugeheights and elevations are principal data elementsin the collection, processing, and analysis ofsurface-water data and information. Gauge heightsand elevations are measured in various ways, suchas by direct observation of a gauging device, or byautomatic sensing through the use of floats,transducers, gas-bubbler manometers and acousticmethods. Gauge heights and elevations should bemeasured and stored as instantaneous unit values.Subsequent data processing and analysis willprovide the means for any required analysis, suchas averaging.Stream velocity is another data element in a streamgauging system. Unit values of stream velocityare measured at some sites for the purpose ofcomputing stream discharge. This is done mostcommonly where variable backwater conditionsare present. Unit values of stream velocity aremeasured at some sites where variable backwateris not present to improve the calculation ofdischarge. The three principal instruments formeasuring stream velocity are the deflection vanegauge, the electromagnetic velocity meter andthe acoustic (ultrasonic or Doppler) velocitymeters.Stream discharge is a very important element, andfrequently the ultimate goal in stream gauging.Discharge cannot be measured directly, but mustbe computed from other measured variables suchas gauge height, stream depth, stream width, andstream velocity. Daily mean values of discharge areusually computed from instantaneous unit valuesof discharge, using computer methods. This differsfrom some of the methods used in the past wheredaily mean values of discharge were computedfrom daily mean values of gauge height. It alsodiffers from procedures where mean values ofgauge height for subdivided parts of a day wereused to compute discharge.The term unit value is used to denote a measured orcomputed value of a variable parameter that isassociated with a specified instantaneous time anddate. In addition, unit values generally are part ofa time-series data set. For surface-water records,unit values for all parameters always should beinstantaneous values. Some parameters, such asvelocity, tend to fluctuate rapidly and a trueinstantaneous value would be difficult to use inthe analysis and processing of the records. Someinstruments are designed to take frequent (forexample, every second) readings, temporarily storethese readings, and then compute and store amean value for a short time period. For thesesituations, the field instruments are programmedto record mean unit values for very short timeintervals (1 to 2 minutes) so they can be consideredfor practical purposes to be instantaneous unitvalues. Data recorded for very short time intervalsare sometimes referred to as high time-resolutiondata.Daily values are measured or computed values of aparameter for a specific date. The time of the dailyvalue is not required, although for certain dailyvalues, time sometimes is stated. Examples of dailyvalues are daily mean value, maximum instantaneousvalue for a day, and minimum instantaneous valuefor a day. In the case of maximum and minimuminstantaneous values for a day, the time of the valueusually is stated.

INTRODUCTI**ON**xixReferencesHerschy, Reginald W., 1995: Streamflow measurement,Second edition: Taylor and Francis, 524 p.International Organization for Standardization, 1995:Liquid flow measurement in open channels –Establishment and operation of a gauging station.ISO 1100-1, Geneva.International Organization for Standardization, 1998:Liquid flow measurement in open channels – Determinationof the stage-discharge relation. ISO 1100-2, Geneva.International Organization for Standardization, 1995:Liquid flow measurement in open channels – Water-levelmeasuring devices. ISO 4373, Geneva.Rantz, S.E., and others, 1982: Measurement andcomputation of streamflow. Volume 1 – Measurementof stage and discharge. United States GeologicalSurvey Water Supply Paper 2175, pp. 1-284.Rantz, S.E., and others, 1982: Measurement andcomputation of streamflow. Volume 2 – Computationof discharge. United States Geological Survey WaterSupply Paper 2175, pp 285-631.Sauer, V.B., 2002: Standards for the analysis andprocessing of surface-water data and informationusing electronic methods. United States GeologicalSurvey Water-Resources Investigations Report01-4044, pp. 2-4.World Meteorological Organization, 1980: Manualon Stream Gauging (**WMO**-No. 519). Volume I:Fieldwork, 308 pp.World Meteorological Organization, 1980: Manual onStream Gauging (**WMO**-No. 519). Volume II:Computation of Discharge, 258 pp.World Meteorological Organization, 2008: Guide toHydrological Practices (**WMO**-No. 168), Sixth edition.Volume I: Hydrology – From Measurement toHydrological Information, 296 pp., Geneva.World Meteorological Organization, 2009: Guide toHydrological Practices (**WMO**-No. 168), Sixth edition.Volume II: Management of Water Resources andApplication of Hydrological Practices, 302 pp.,Geneva.

Chapter 1Discharge ratings using simple stage-discharge relations1.1 IntroductionContinuous records of discharge at gaugingstations are computed by applying the dischargerating for the stream to records of stage. Dischargeratings may be simple or complex, depending onthe number of variables needed to define the stagedischargerelation. This chapter is concerned withratings in which the discharge can be related tostage alone. The terms rating, rating curve, stationrating, and stage-discharge relation are synonymousand are used interchangeably in this Manual. Partsof this chapter are based on ISO standard 1100-2(1998), with some sections taken directly from theISO standard.Discharge ratings for gauging stations are usuallydetermined empirically by means of dischargemeasurements made in the field. Notableexceptions are the pre-calibrated ratings used inseveral countries for the special weirs and flumesdiscussed in Volume I, Chapter 7. However, evenat sites where a weir or flume is used, it is advisableto make some current meter measurements for thepurpose of confirming the pre-calibrated rating.Common practice is to measure the discharge of thestream periodically, usually by current meter, and tonote the concurrent stage. Measured discharge isthen plotted against concurrent stage on graph paperto define the rating curve. At a new station manydischarge measurements are needed to define thestage discharge relation throughout the entire rangeof stage. Periodic measurements are needed thereafterto either confirm the stability of the rating or tofollow changes (shifts) in the rating. A minimum often discharge measurements per year is recommended,unless it has been demonstrated that the stagedischargerelation is completely unvarying withtime. In that event the frequency of measurementsmay be reduced. It is of prime importance that thestage-discharge relation be defined for floodconditions, for extreme low flow conditions and forperiods when the rating is subject to shifts as a resultof ice formation or as a result of the variable channeland control conditions. It is essential that the streamgauging programme provides for the non-routinemeasurement of discharge at those times.If the discharge measurements cover the entirerange of stage experienced during a period of timewhen the stage-discharge relation is stable, there islittle problem in defining the discharge rating forthat period. On the other hand, if, there are nodischarge measurements to define the upper end ofthe rating the defined lower part of the rating curvemust be extrapolated to the highest stageexperienced. Such extrapolations are always subjectto error, but the error may be minimized if theanalyst has knowledge of the principles that governthe shape of rating curves. Much of the material inthis Chapter is directed toward a discussion ofthose principles so that when the hydrologist isfaced with the problem of extending the high waterend of a rating curve he or she can decide whetherthe extrapolation should be a straight line orwhether it should be concave upward or concavedownward.The problem of extrapolation can be circumvented,of course, if the unmeasured peak discharge isdetermined by use of the indirect methods discussedin Volume I, Chapter 9. In the absence of such peakdischarge determinations, some of the uncertaintyin extrapolating the rating may be reduced by theuse of one or more of several methods of estimatingthe discharge corresponding to high values of stage.Four such methods are discussed in a subsequentsection of this chapter.In some cases the lower end of the rating curve mayalso need extrapolation. Procedures for low-waterextrapolation are discussed in subsequent sectionsof this Manual. A most important method involvesuse of the gauge height of zero flow which will bediscussed in detail.1.2 Stage-discharge controlsThe subject of stage-discharge controls was discussedin detail in Volume I, Chapter 3, but a brief summaryat this point is appropriate.The stage-discharge relation for open-channel flowat a gauging station is governed by channelconditions downstream from the gauge, referred toas a control. Two types of controls can exist,depending on channel and flow conditions. Lowflows are usually controlled by a section controlwhereas high flows are usually controlled by a

II.1-2manual on stream gaugingchannel control. Medium flows may be controlledby either type of control. At extreme high stages,particularly where significant flow is conveyed inoverbanks or flows through multiple roadwaybridges, the control will include the influence ofthese features. At some stages a combination ofsection and channel control may occur. These aregeneral rules and exceptions can and do occur.Knowledge of the channel features that control thestage-discharge relation is important. Thedevelopment of stage-discharge curves where morethan one control is effective, where control featureschange and where the number of measurements islimited, usually requires judgment in interpolatingbetween measurements and in extrapolatingbeyond the highest or lowest measurements. This isparticularly true where the controls are notpermanent and tend to shift from time to time,resulting in changes in the positioning of segmentsof the stage-discharge relation.1.2.1 Section controlA section control is a specific cross-section of astream channel, located downstream from a waterlevelgauge that controls the relation between gaugeheight and discharge at the gauge. A section controlcan be a natural feature such as a rock ledge, a sandbar, a severe constriction in the channel or anaccumulation of debris. Likewise, a section controlcan be a manmade feature such as a small dam, aweir, a flume, or an overflow spillway. Sectioncontrols can frequently be visually identified in thefield by observing a riffle, or pronounced drop in thewater surface, as the flow passes over the control.Frequently, as gauge height increases because ofhigher flows, the section control will becomesubmerged to the extent that it no longer controlsthe relation between gauge height and discharge. Atthis point, the riffle is no longer observable, and flowis then regulated either by another section controlfurther downstream or by the hydraulic geometryand roughness of the channel downstream (channelcontrol).1.2.2 Channel controlA channel control consists of a combination offeatures throughout a reach downstream from agauge. These features include channel size, shape,curvature, slope and channel roughness. The lengthof channel reach that controls a stage-dischargerelation varies. The stage-discharge relation for arelatively steep channel may be controlled by arelatively short channel reach whereas the relationfor a relatively flat channel may be controlled by amuch longer channel reach. In addition, the lengthof a channel control will vary depending on themagnitude of flow. Precise definition of the length ofa channel-control reach is usually neither possiblenor necessary.1.2.3 Combination or compoundcontrolsAt some stages the stage-discharge relation may begoverned by a combination of section and channelcontrols, sometimes referred to as compoundcontrols. This usually occurs for a short range instage between section-controlled and channelcontrolledsegments of the rating. This part of therating is commonly referred to as a transition zoneof the rating and represents the change from sectioncontrol to channel control. In other instances, acombination control may consist of two sectioncontrols, where each has partial controlling effect.More than two controls acting simultaneously arerare. In any case, combination controls, and/ortransition zones, occur for very limited parts of astage-discharge relation and can usually be definedby plotting procedures. Transition zones inparticular represent changes in the slope or shapeof a stage-discharge relation.1.3 Governing hydraulicequationsStage-discharge relations are hydraulic relationsthat can be defined according to the type of controlthat exists. Section controls, either natural ormanmade, are governed by some form of the weiror flume equations. In a very general and basicform, these equations are expressed as:Q = C BHDβ(1.1)where Q is discharge, in cubic metres per second(m 3 s -1 ); C Dis a coefficient of discharge and mayinclude several factors; B is cross-section width,in metres (m); H is hydraulic head, in metres, andβ is an exponent depending on the shape of thecontrol (for example for V-shaped, β = 2.5 and forrectangular, β = 1.5).Stage-discharge relations for channel controls withuniform flow are governed by the Manning orChezy equation, as it applies to the reach ofcontrolling channel downstream from a gauge. TheManning equation is:Q = 1 2/3 1/2AR S(1.2)n

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-3where A is cross-section area, in square metres (m 2 );R is hydraulic radius, in metres (m); S is frictionslope, and n is channel roughness.The Chezy equation is:1/2 1/2Q = CAR S(1.3)where C is the Chezy form of channel roughness.The above equations are generally applicable forgradually varied, uniform flow. For highly varied,non-uniform flow, equations such as the Saint-Venant unsteady flow equations would beappropriate. However, these are seldom used in thedevelopment of stage-discharge relations, and arenot described in this Manual.1.4 Complexities of stage-dischargerelationsStage-discharge relations for stable controls such asa rock outcrop and manmade structures such asweirs, flumes and small dams usually present fewproblems in their calibration and maintenance.However, complexities can arise when controls arenot stable and/or when variable backwater occurs.For unstable controls, segments of a stage-dischargerelation may change position occasionally, or evenfrequently. This is usually a temporary conditionwhich can be accounted for through the use of theshifting-control method.Variable backwater can affect a stage-dischargerelation, both for stable and unstable channels.Sources of backwater can be downstream reservoirs,tributaries, tides, ice, dams and other obstructionsthat influence the flow at the gauging stationcontrol. Methods of developing complex ratings forvariable backwater conditions will be discussed inChapters 2 and 3 of this Manual.Another complexity that exists for some streams ishysteresis, which results when the water surfaceslope changes due to either rapidly rising or rapidlyfalling water levels in a channel control reach.Hysteresis ratings are sometimes referred to as loopratings, and are most pronounced in relatively flatsloped streams. On rising stages the water surfaceslope is significantly steeper than for steady flowconditions, resulting in greater discharge thanindicated by the steady flow rating. The reverse istrue for falling stages. Details on hysteresis ratingswill be discussed in a subsequent section of thischapter.1.5 Graphical plotting of ratingcurvesThe relation between stage and discharge is definedby plotting measurements of discharge withcorresponding observations of stage, taking intoaccount whether the discharge is steady, increasingor decreasing and also noting the rate of change instage. This may be done manually by plotting onpaper or by using computerized plotting techniques.A choice of two types of plotting scale are available,either an arithmetic scale or a logarithmic scale.Each has certain advantages and disadvantages, asexplained in subsequent paragraphs. It is customaryto plot the stage as ordinate and the discharge asabscissa, although when using the stage-dischargerelation to derive discharge from a measured valueof stage, the stage is treated as the independentvariable.1.5.1 List of discharge measurementsThe first step before making a plot of stage versusdischarge is to prepare a list of dischargemeasurements that will be used for the plot. At aminimum this list should include at least 12 to 15measurements, all made during the period ofanalysis. If the rating is segmented then moremeasurements may be required. These measurementsshould be well distributed over the range in gaugeheights experienced. It should also include low andhigh measurements from other times that might beuseful in defining the correct shape of the ratingand for extrapolating the rating. Extreme low andhigh measurements should be included whereverpossible.For each discharge measurement in the list it isimportant that at least the following items areincluded:(a) Unique identification number;(b) Date of measurement;(c) Gauge height of measurement. If there is adifference between inside and outside gaugereadings, list both readings;(d) Total discharge;(e) Accuracy of measurement;(f) Rate-of-change in stage during measurement, aplus sign indicating rising stage and a minussign indicating falling stage.Other information might be included in the list ofmeasurements but is not mandatory. For instance,names of hydrographers making the measurement,time of measurement, difference between insideand outside gauge readings (if any), location ofmeasurement, method of measurement and notes

II.1-4manual on stream gaugingTable II.1.1. Typical list of discharge measurementsid number Date Made by Width Area MeanvelocityGaugeheightEffectivedepthDischarge Method NumberverticalsGauge heightchangeRatedm m 2 m/s m m m 3 /s m/h12 08/04/38 MEF 36.27 77.94 1.272 2.682 2.082 99.12 0.2/0.8 22 – 0.082 GOOD183 06/02/55 GTC 33.53 78.41 1.405 2.786 2.186 11.02 0.6/0.2/0.8 22 – 0.047 GOOD201 04/02/57 AJB 28.96 21.92 1.511 2.002 1.402 33.13 0.6/0.2/0.8 21 – 0.013 POOR260 13/03/63 GMP 26.52 21.46 1.400 1.981 1.381 30.02 0.6 22 – 0.020 GOOD313 24/08/66 HFR 30.18 42.08 1.602 2.374 1.774 67.40 0.6/0.2/0.8 22 + 0.006 GOOD366 21/08/73 MAF 28.96 14.86 0.476 1.557 0.957 7.080 0.6 21 0 GOOD367 10/10/73 MAF 28.96 13.66 0.361 1.490 0.890 4.928 0.6 21 0 GOOD368 26/11/73 MAF 29.26 14.21 0.373 1.509 0.909 5.296 0.6 18 0 GOOD369 19/02/74 MAF 29.87 16.26 1.291 1.838 1.238 20.99 0.6 21 0 GOOD370 09/04/74 MAF 29.26 21.27 0.805 1.780 1.180 17.13 0.6/0.2/0.8 21 0 GOOD371 29/05/74 MAF 29.57 19.69 0.688 1.710 1.110 13.54 0.6 21 0 GOOD372 10/07/74 MAF 28.96 16.81 0.458 1.573 0.973 7.703 0.6 21 0 GOOD373 22/08/74 MAF 29.26 15.79 0.481 1.570 0.970 7.590 0.6 21 0 GOOD374 01/10/74 MAF 29.26 13.19 0.264 1.414 0.814 3.483 0.6 21 0 GOOD375 11/11/74 MAJ 28.96 11.71 0.283 1.396 0.796 3.313 0.6 21 0 GOOD382 01/10/75 MAF 30.48 43.76 1.598 2.432 1.832 69.95 0.2/0.8 21 + 0.017 GOOD

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-5about the condition of the control. Table II.1.1shows a typical list of discharge measurements,including a number of items in addition to themandatory items. The discharge measurement listmay be handwritten for use when hand-plotting isdone or the data may be a computer list where acomputerized plot is developed.1.5.2 Use of inside and outside gaugereadingsAt some recording gauging stations there is often adifference between recorded (inside) gauge heightsand outside gauge heights during periods of highstage. When that happens, both inside and outsidegauge heights for discharge measurements shouldbe recorded on the form shown in Table II.1.1.When plotting the measurements for rating analysis,the outside gauge readings are used first. The stagedischargerelation is extended to the stage of theoutside high water marks that are observed for eachflood event. The stage-discharge relation is nexttransposed to correspond with the inside gaugeheights obtained from the stage recorder at thetimes of discharge measurement and at flood peaks.The rationale behind this procedure is as follows.The outside gauge readings are used for developingthe rating because the hydraulic principles onwhich the rating is based require the use of the truestage of the stream. The transposition of the ratingto inside (recorded) stages is then made because therecorded stages will be used with the rating todetermine discharge. The recorded stages are usedfor discharge determination because if differencesexist between inside and outside gauge readings,those differences will be known only for those timeswhen the two gauges are read concurrently. If theoutside gauge heights were used with the rating todetermine discharge, variable corrections, eitherknown or assumed, would have to be applied to therecorded gauge heights to convert them to outsidestages. Differences between inside and outsidegauge heights do exist for some stations and mustbe recognized in the development of ratings.However in the discussions that follow nodistinction between the two gauges will be made.1.5.3 Arithmetic plotting scalesThe simplest type of plot uses an arithmeticallydivided plotting scale as shown in Figure II.1.1. Thisplot uses calibration measurements shown inTable II.1.1. Scale subdivisions should be chosen tocover the complete range of gauge height anddischarge expected to occur at the gauging site.Scales should be subdivided in uniform, evenincrements that are easy to read and interpolate.They should also be chosen to produce a ratingcurve that is not unduly steep or flat. Usually thecurve should follow a slope of between 30° and 50°.If the range in gauge height or discharge is large, itmay be necessary to plot the rating curve in two ormore segments to provide scales that are easily readwith the necessary precision. This procedure mayresult in separate curves for low water, mediumwater and high water. Care should be taken to seethat, when joined, the separate curves form asmooth, continuous combined curve.The use of arithmetic co-ordinate paper for ratinganalysis has certain advantages, particularly in thestudy of the pattern of rating shifts in the lowerpart of the rating. A change (shift) in the low-flowrating at many sites results from a change in thegauge height of effective zero flow, which means aconstant shift in gauge height. A shift of that kindis more easily visualized on arithmetic co-ordinatepaper because on that paper the shift curve isparallel to the original rating curve. The two curvesare separated by a vertical distance equal to thechange in the value of the gauge height of zero flow.A further advantage of arithmetic co-ordinate paperis the fact that the gauge height of zero flow can beplotted directly on arithmetic co-ordinate paper,thereby facilitating extrapolation of the low waterend of the rating curve. That cannot be done onlogarithmic paper because zero values cannot beshown on that type of paper.For analytical purposes arithmetic scales havepractically no advantage. For this reason, logarithmicplotting should always be used initially indeveloping the general shape of the rating. Thefinal curve may be displayed on either type of graph(h – e).n2.521.5260370 369371373 3721368367 3663743750.520138231300 50 100 150Discharge Q m 3 /sFigure II.1.1. Arithmetic plot of stage-dischargerelation12183

II.1-6manual on stream gaugingpaper and used as a base curve for the analysis ofshifts. A combination of the two types of graphpaper is frequently used with the lower part of therating plotted on an inset of rectangular co-ordinatepaper or on a separate sheet of rectangularco-ordinate paper.1.5.4 Logarithmic plotting scalesMost stage-discharge relations, or segments thereof,are best analyzed graphically through the use oflogarithmic plotting paper. To utilize fully thisprocedure, gauge height should be transformed toeffective depth of flow on the control by subtractingfrom it the effective gauge height of zero discharge.Using these conditions, the slope of the rating willOriginalscale109876543210.90.80.70.60.50.40.30.20.12 x originalscale20181614121086421.81.61.41.210.80.60.40.2Figure II.1.2. Example showing how the logarithmicscale of graph paper may be transposedconform to the type of control (section or channel),thereby providing valuable information to shapecorrectly the rating curve segment. In addition, thisfeature allows the analyst to calibrate the stagedischargerelation with fewer dischargemeasurements. The slope of a rating curve is theratio of the horizontal distance to the verticaldistance. This non-standard way of measuring slopeis necessary because the dependent variable(discharge) is always plotted as the abscissa.The measured distance between any two abscissason logarithmic graph paper, whose values areprinted or indicated on the sheet by the manufacturerof the paper, represents the difference between thelogarithms of those values. Consequently, themeasured distance is related to the ratio of the twovalues. Therefore, the distance between pairs ofnumbers such as 1 and 2, 2 and 4, 3 and 6, 5 and 10,are all equal because the ratios of the various pairsare identical. Thus the logarithmic scale of eitherthe ordinates or the abscissas is maintained if allprinted numbers on the scale are multiplied ordivided by a constant. This property of the paperhas practical value. For example, assume that thelogarithmic plotting paper available has 2 cycles, asshown in figure 1.2 and that ordinates ranging from0.3 to 15.0 are to be plotted. If the printed scale ofordinates is used and the bottom line is called 0.1,the top line of the paper becomes 10.0, and valuesbetween 10.0 and 15.0 cannot be accommodated.However, the logarithmic scale will not be distortedif all values are multiplied by a constant. For thisparticular problem, 2 is the constant used inFigure II.1.2, and now the desired range of 0.3 to15.0 can be accommodated. Examination ofFigure II.1.2 shows that the change in scale has notchanged the distance between any given pair orordinates; the position of the ordinate scale hasmerely been transposed.A rating curve that plots as a straight line onlogarithmic paper has the equation:Q = C ( h − e ) β (1.4)where Q is discharge; h is gauge height of the watersurface; e is gauge height of zero flow for a controlof regular shape, or of effective zero flow for acontrol of irregular shape; (h – e) is head or depth ofwater on the control. This value is indicated by theordinate scale printed by the manufacturer or bythe ordinate scale that has been transposed, asexplained in the preceding paragraph; C is thedischarge when the head (h – e) equals 1.0; β is slopeof the rating curve. Slope in equation 1.4 is the ratioof the horizontal distance to the vertical distance.

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-7a = 2a = 1.5a = 1a = 012 11.5 11 109 8.5 8 7GAUGE HEIGHT, IN METRES7 6.5 6 55 4.5 4 34 3.5 3 23 2.5 2 12.7 2.2 0.72.5 2 0.52.3 0.32.2 0.2a = 0a = 1 (concave up)a = 1.5 (straight line)a = 2 (concave down)Note – All curves representthe same rating. The truevalue of “a” is 1.5.2.1 00.1 0.2 0.3 0.4 0.7 1 2 3 5 7 10 20 30 50DISCHARGE, IN CUBIC METRES PER SEC**ON**DFigure II.1.3. Rating curve shapes resulting from the use of differing values of effective zero-flowChanges to the control will have predictable resultson the logarithmic rating plot. If the width of thecontrol increases, C increases and the new ratingwill be parallel to and to the right of the originalrating. If the width of the control decreases, theopposite effect occurs; C decreases and the newrating will be parallel to and to the left of theoriginal rating. If the control scours, e decreases andthe depth (h – e) for a given gauge height increases;the new rating moves to the right and will no longerbe a straight line but will be a curve that is concavedownward. If the control becomes built up bydeposition, e increases and the depth (h – e) for agiven gauge height decreases; the new rating movesto the left and is no longer linear, but is a curve thatis concave upward.When discharge measurements are originallyplotted on logarithmic paper no consideration isusually given to values of e. The gauge height ofeach measurement is plotted using the ordinatescale provided by the manufacturer or, if necessary,an ordinate scale that has been transposed asillustrated in Figure II.1.2. Referring to Figure II.1.3,the inside scale (e = 0) is the scale printed by thepaper manufacturer. Assume that the dischargemeasurements have been plotted to that scale andthat they define the curvilinear relation betweengauge height h, and discharge Q, that is shown inthe topmost curve. For the purpose of extrapolatingthe relation, a value of e is sought, which whenapplied to h, will result in a linear relation between(h – e) and Q. For a section control of regular shape,the value of e will be known; it will be the gaugeheight of the lowest point of the control (gaugeheight of zero flow). For a channel control or sectioncontrol of irregular shape, the value of e is the gaugeheight of effective zero flow; that may be determinedby successive approximations.In successive trials, the ordinate scale in Figure II.1.3is varied for e values of 1 m, 1.5 m and 2 m, each ofwhich results in a different curve, but each newcurve still represents the same rating as the topcurve. For example, a discharge of 3 m 3 s -1corresponds to a gauge height h of 4 m on all fourcurves. The true value of e is 1.5 m, and thus therating plots as a straight line if the ordinate scalenumbers are increased by that value. In other words,while even on the new scale a discharge of 3 m 3 s -1corresponds to a gauge height h of 4 m, the head ordepth on the control for a discharge of 3 m 3 s -1 is(h – e), or 2.5 m; the linear rating marked e = 1.5 mcrosses the ordinate for 3 m 3 s -1 at 4 m on the new

II.1-8manual on stream gaugingscale and at 2.5 m on the manufacturer’s, or insidescale. If values of e smaller than the true value of1.5 m are used, rating curve will be concave upward;if values of e greater than 1.5 m are used, curve willbe concave downward. The value of e to be used fora rating curve, or a segment of a rating curve, canthus be determined by adding or subtracting trialvalues of e to the numbered scales on the logarithmicplotting paper until a value is found that results ina straight line plot of the rating. It is important tonote that if the logarithmic ordinate scale must betransposed by multiplication or division toaccommodate the range of stage to be plotted, thattransposition must be made before the ordinatescale is manipulated for values of e.1.5.5 Computer plotting of dischargemeasurements and rating curvesPlotting of discharge measurements and ratingcurves, either arithmetic plots or logarithmic plots,is best done by computer. These plots can be viewedon the computer monitor and/or plotted on paperforms. Advantages of computer plots are:(a) Selection of measurements for plotting can bemade quickly and easily;(b) Scale changes can be made and measurementsreplotted quickly;(c) Various values of e can be easily tried for thepurpose of defining a straight-line rating onlogarithmic plots;(d) Separate rating segments, representing differentcontrol conditions, can be easily and quicklyplotted;(e) Rating analysis, as described in the subsequentsection, is accomplished easily;(f) Plotting errors are virtually eliminated.Logarithmic plots of rating curves must meet therequirement that the log cycles are square. That is,the linear measurement of a log cycle, bothhorizontally and vertically, must be equal.Otherwise, it is impossible to hydraulically analyzethe resulting plot of the rating. This requirementfor square log cycles should always be tested becausesome computer programs do not include this as anautomatic feature.1.5.6 Analysis of rating curvesRating curves for section controls such as a weir orflume conform to equation 1.1, and when plottedlogarithmically the slope will be 1.5 or greaterdepending on control shape, velocity of approachand minor variations of the coefficient of discharge.Logarithmic rating curves for most weir shapes willplot with a slope of 2 or greater. An exception is thesharp-crested rectangular weir, which plots with aslope slightly greater than 1.5. Logarithmic ratingsfor section controls in natural channels will almostalways have a slope of 2 or greater. This characteristicslope of 2 or greater for most section controls allowsthe analyst to identify easily the existence of sectioncontrol conditions simply by plotting dischargeversus effective depth, (h – e), on logarithmicplotting paper.Rating curves for channel controls, on the otherhand, are governed by equation 1.2 or 1.3, andwhen plotted as effective depth versus dischargethe slope will usually be less than 2. Variations inthe slope of the rating when channel control existsare the result of changes in channel roughness andfriction slope as depth changes.The above discussion applies to control sections ofregular shape (triangular, trapezoidal and parabolic).When a significant change in shape occurs, such asa trapezoidal section control with a small V-notchfor extreme low water, there will be a change in therating curve slope at the point where the controlshape changes. Likewise, when the control changesfrom section control to channel control, thelogarithmic plot will show a change in slope. Thesechanges are usually defined by short curvedsegments of the rating, referred to as transitions.This kind of knowledge about the plottingcharacteristics of a rating curve is extremely valuablein the calibration and maintenance of the rating,and in later analysis of shifting control conditions.By knowing the kind of control (section or channel)and the shape of the control, the analyst can moreprecisely define the correct hydraulic shape of therating curve. In addition, these kinds of informationallow the analyst to extrapolate accurately a ratingcurve, or conversely, know when extrapolation islikely to lead to significant errors.Figure II.1.4 gives examples of a hypothetical ratingcurve showing the logarithmic plottingcharacteristics for channel and section controls andfor cross-section shape changes. Insert A inFigure II.1.4 shows a trapezoidal channel with noflood plain and with channel control conditions.The corresponding logarithmic plot of the ratingcurve, when plotted with an effective gauge heightof zero flow e that results in a straight line rating,has a slope less than 2. In insert B a flood plain hasbeen added which is also channel control. This is achange to the shape of the control cross section andresults in a change in the shape of the rating curveabove bankfull stage. If the upper segment (abovethe transition curve) were re-plotted to the correctvalue of effective gauge height of zero flow, it too

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-9would have a slope less than 2. In the third plot,insert C, a section control for low flow has beenadded. This results in a change in rating curve shapebecause of the change in control. For the low waterpart of the rating, the slope will usually be greaterthan 2.Figure II.1.5 is a logarithmic plot of an actualrating curve, using the measurements showninTable II.1.1. This rating is for a real stream wheresection control exists throughout the range offlow, including the high flow measurements. Theeffective gauge height of zero flow e for this streamis 0.6 metres, which is subtracted from the gaugeheight of the measurements to define the effectivedepth of flow at the control. The slope of the ratingbelow 1.4 m is about 4.3, which is greater than(a)Channel shapeRating shape2 and conforms to a section control. Above 1.5 m,the slope is 2.8, which also conforms to a sectioncontrol. The change in slope of the rating aboveabout 1.5 m is caused by a change in the shape ofthe control cross-section. Below about 1.4 m thecontrol section is essentially a triangular shape. Inthe range of 1.4 to 1.5 m the control shape ischanging to trapezoidal, resulting in the transitioncurve of the rating. And above about 1.5 m thecontrol cross-section is basically trapezoidal.The examples of Figures II.1.4 and II.1.5 are intendedto illustrate some of the principals of logarithmicplotting. The analyst should try to use theseprincipals to the best extent possible, but shouldalways be aware that there are probably exceptionsand differences that occur at some sites.Mathematical derivation and additional examplesof rating analysis is given in subsequent sections ofthis chapter.Channel control(no flood plain,no section control)Log (h – e)Channel controlrating– 21(b)Log Q1.6 Ratings for artificial sectioncontrols(h – e).n(c)Flood plainChannel control(no section control)Flood plainChannel controlSection control41Flood plainFlood plainLog (h – e)Flood plain ratingChannel controlrating1– 2Log QLog (h – e)Transition curveFlood plain ratingTransition curveChannel control 1Section– 2controlTransition curve1– 2Log QFigure II.1.4. Relation of channel andcontrol properties to rating curve shape374375382368 366 372 371 370 260 313201369367 3730.11 10 100 200Discharge, Qm 3 /sFigure II.1.5. Logarithmic plot ofstage-discharge relation18312Knowledge of the rating characteristics of artificialsection controls of standard shape is necessary foran understanding of the rating characteristics ofnatural controls, almost all of which have irregularshape. The structures detailed in Volume I,Chapter 7 may be used as controls for velocity areastations, the low or medium flows being measuredby the structure using the laboratory rating, themedium and high flows being measured by currentmeter. For such dual purpose stations the laboratoryrating is used up to the modular limit and the ratingcontinued by current meter. For structures such asthe Crump weir or Flat-V weir where a crest tappingis used the range of the structure is increased intothe non-modular region until complete drowningtakes place. Flows above this limit will be dependenton a downstream control or a channel control.If the weirs described in Volume I, Chapter 7 arecompounded without divide walls beingincorporated in the design a loss of accuracy willoccur if the laboratory ratings are used. This loss ofaccuracy may not be serious but it is recommendedthat all such non-standard variations be fieldcalibrated. The calibration of a non standard broadcrestedweir follows.1.6.1 Notched flat-crested rectangular weirFigure II.1.6 shows the notched flat-crestedrectangular weir that is the control for a gauging

II.1-10manual on stream gaugingGAUGE HEIGHT, IN METRESa = 0.2a = 0.02.2 2.01.2 1.00.9 0.70.7 0.50.5 0.30.4 0.20.3 0.10.27 0.070.25 0.050.23 0.031.22 mTangent a - 0.02.5Concave down113.7 ma - 0.2G.H. = 0.0 mG.H. = 0.43Concave upTangent0.22 0.020.8 0.1 0.2 0.4 0.5 0.7 1.0 2 4 5 7 10 20 30DISCHARGE, IN CUBIC METRES PER SEC**ON**DFigure II.1.6. Rating curve for a notchedbroad-crested controlstation on Great Trough Creek near Marklesburg,Pennsylvania, United States of America. Becausethere is a sharp break in the cross-section at gaugeheight 0.43 m a break occurs in the slope of therating curve at that stage. The gauge height of zeroflow for stages between 0.0 and 0.43 m is 0.0 m; forstages above 0.43 m the effective gauge height ofzero flow is at some point between 0.0 and 0.43 m.If the low end of the rating is made a tangent, thegauge height of zero flow (e) is 0.0 m and the slopeof this tangent turns out to be 2.5, which, as nowexpected, is greater than the theoretical slope of1.5. The upper part of this rating curve is concaveupward because the value of e used (0.0 m) is lowerthan the effective value of zero flow for highstages.If the upper end of the rating is made a tangent, itis found that the value of e, or effective zero flow,must be increased to 0.2 m. Because we have raisedthe value of e, this will make the low water end ofthe curve concave downward. The high watertangent of the curve, principally because ofincreased rate of change of velocity of approach,will have a slope that is greater than that of the lowwater tangent of the curve previously described. Itsslope is found to have a value of 3.0.The low water tangent for the notched control,which is defined by discharge measurements,warrants further discussion. Its slope of 2.5 is higherthan one would normally expect for a simple flatcrestedrectangular notch. Reasons for this may be:(a) The velocity of approach factor is included inthe rating;31(b) A thin-plate weir is fixed to the downstreamedge of the notch with its elevation about0.03 m above the base of the notch;(c) Probably more important, the width of thenotch is small compared to the total width of thecontrol; this may alter the flow characteristicsto the extent that the notch may in fact beoperating between rectangular and v-notchconditions.These observations are mentioned here only towarn the reader not to expect a slope as great as 2.5in the rating for a simple flat-crested rectangularnotch. In fact, the sole purpose here of discussingthe low water tangent of the rating curve is todemonstrate the effect exerted in the curve byvarying the applied values of e. It should also benoted that the slope of the rating for section controlswill almost always be greater than 2, as discussed inprevious sections of this chapter.The low water end of a rating curve is usually welldefined by discharge measurements. If it is necessaryto extrapolate the rating downward it is best doneby re-plotting the low water end of the curve onarithmetic coordinate graph paper and extrapolatingthe curve down to the point of zero discharge.1.6.2 Trenton-type controlThe so-called Trenton-type control is a concreteweir that is popular in the United States. Thedimensions of the cross-section of the crest areshown in Figure II.1.7. The crest may be constructedso as to be horizontal for its entire length across thestream or for increased low flow sensitivity the crestmay be given the shape of an extremely flat V. For ahorizontal crest, the equation of the stage dischargerelation, as obtained from a logarithmic plot of thedischarge measurements, is commonly of the orderof:Q = 2.31 bh1.65 (1.5)where b = top width of water surface, in metres.The precise values of the constants will vary withthe height of the weir above the stream-bed becausethat height affects the velocity of approach. Theconstants of the equation are greater than those fora flat-crested rectangular weir (see Volume I,Chapter 7) because the cross-sectional shape of theTrenton-type control is more efficient than arectangle, with regard to the flow of water.When the Trenton-type control is built with itscrest in the shape of a flat V, the exponent of h in

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-11the discharge equation is usually 2.5 or more, asexpected for a triangular notch where velocity ofapproach is significant. The precise values of theconstants in the discharge equation are dependenton the geometry of the installation.1.6.3 Columbus-type controlOne of the most widely used controls in the UnitedStates is the Columbus-type control, as shown inFigure II.1.8. This control is a concrete weir with aparabolic notch that is designed to give accuratemeasurements of a wide range of flows.The notch accommodates low flows; the mainsection, whose crest has a flat upward slope awayfrom the notch, accommodates higher flows. Thethroat of the notch is convex along the axis of flowto permit the passage of debris. For stages above ahead of 0.2 m, which is the elevation of the top ofthe notch, the elevation of effective zero flow is0.06 m, and the equation of discharge isapproximately:( ) (1.6)Q = 12.14 h − 0.061 3.3The precise values of the constants in the equationwill vary with conditions for each installation. Theshape of the crest above a stage of 0.2 m is essentiallya flat V, for which the theoretical exponent of headis 2.5 in the discharge equation. However, the actualvalue of the exponent is greater than 2.5 principallybecause of the increase of velocity of approach withstage.FLOW914241 127 5461.7 Ratings for natural sectioncontrolsDimensions in mm150203R203R1:1 slope457Natural section controls, listed in order ofpermanence, are usually a rock ledge outcrop acrossthe channel, a riffle composed of loose rock, cobblesand gravel or a gravel bar. Less commonly, thesection control is a natural constriction in width ofthe channel, or is a sharp break in channel slope, asat the head of a cascade or brink of a falls. Theequation for ratings of natural section controlsfollows the form of equation 1.4.Figure II.1.7. Cross section of Trenton-type control0.610 0.610 0.6100.305Slope = 1:10Slope = 1:10Slope = 1:5Y Slope = 1:5N0.214X NStreambedProfile of weir crest and notchCoordination of notch profile,in metresFlowX N Y N0.00 0.000.7620.0137 0.030.0322 0.060.0573 0.090.0894 0.120.135 0.15Coordinates of cross sectionY0.195 0.18of weir crest, in metres 0.293 0.21X Y70.00 0.0380.02 0.018120.04 0.0060.06 0.0020.08 0.000X0.10 0.0000.12 0.0020.15 0.0080.20 0.024Cross section of weir0.25 0.0460.30 0.0750.35 0.1090.40 0.1490.45 0.1950.50 0.2460.60 0.3600.76 0.6000.597Figure II.1.8. Dimensions of Columbus-type controlWhere the control is a rock outcrop, riffle or gravelbar, the stage-discharge relation, when plotted onlogarithmic paper, conforms to the generalprinciples discussed for broad-crested artificialcontrols. If the natural control is essentiallyhorizontal for the entire width of the control thehead on the control is the difference between thegauge heights of the water surface and the crest ofthe control. The exponent β of the head in theequation of discharge, (equation 1.4) will be greaterthan the theoretical value 1.5 primarily because ofthe increase in velocity of approach with stage. Ifthe crest of the control has a roughly parabolicprofile, as most natural controls have (greaterdepths on the control near midstream), theexponent β will be even larger because of theincrease in width of the stream with stage, as well asthe increase in velocity of approach with stage. Thevalue of β will almost always exceed 2.0 and a rangeof β from 1 to 4 is common for natural controls. Ifthe control is irregularly notched, as is often thecase, the gauge height of effective zero flow e for allbut the lowest stages will be somewhat greater thanthat for the lowest point in the notch.

II.1-12manual on stream gaugingThe above principles are also roughly applicable tothe discharge equations for an abrupt widthcontraction or an abrupt steepening of bed slope.The exponent and the gauge height of effective zeroflow are influenced by the transverse profile of thestream-bed at the control cross-section.1.8 Ratings for natural compoundsection controlsIf a natural control section is a local rise in thestream-bed, such as at a rock outcrop riffle or gravelbar, that cross-section is invariably a control only forlow flows. The gauging station in that circumstancehas a compound control with the high flows beingsubject to channel control. Occasionally there is asecond outcrop or riffle down stream from the lowwater riffle that acts as a section control for flows ofintermediate magnitude. When the control forintermediate stages is effective it causes submergenceof the low water control. At high flows the sectioncontrol for intermediate stages is in turn submergedwhen channel control becomes effective. An exampleof a compound control involving two sectioncontrols is shown in Figure II.1.9.Figure II.1.8 shows the rating for the compoundsection control at the gauging station on MuncyCreek near Sonestown, Pennsylvania, United States.The control consists of two rock riffles, effectiveGAUGE HEIGHT, IN METRESa = 0.40a = 0.371.40 1.371.20 1.271.00 0.970.90 0.870.80 0.770.70 0.670.60 0.57High stageLow stageBedG.H. = 0.37Concave up Transition a = 0.37 Tangent0.50 0.4710.48 0.452.20.46 0.430.45 0.420.05 0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 2 3 4 5 6 8 10 20Tangenta = 0.40 Concave downDISCHARGE, IN CUBIC METRES PER SEC**ON**DG.H. = 0.40Figure II.1.9. Rating curve for a compound sectioncontrol at Muncy Creek near Sonestown,Pennsylvania, United States12.9zero flow e for very low stages being at gauge height0.40 m and for higher stages at gauge height0.37 m. If the low end of the rating is made atangent it means that too large a value of e is usedfor the high end of the rating (0.40 m versus 0.37 m)and the high water end of the curve becomesconcave downward. Conversely, if the high end ofthe curve is made a tangent, the low water end ofthe curve becomes concave upward. The high watertangent of the one curve has a greater value of βthan the low water tangent of the other curve. Thisdifference in the values of β reflects the effect ofdifferences in the geometries of the two controls aswell as the effect of increased rate of change ofapproach velocities at the higher stages. The slopesof the two tangents are 2.9 and 2.2, both valuesbeing greater than the theoretical slope of 1.5.1.9 Ratings for stable channelcontrolsThe term stable channel, as used in this Manual is arelative term. Virtually all natural channels aresubject to at least occasional change as a result ofscour, deposition or the growth of vegetation. Butsome alluvial channels, notably those whose bedand banks are composed of sand, have movableboundaries that change almost continuously, as dotheir stage-discharge relations. For the purpose ofthis manual stable channels include all but sandchannels. Sand channels are discussed insection 1.14, Sand Chanel Streams.Almost all streams that are unregulated by manhave channel control at the higher stages. Amongthose with stable channels, all but the largest rivershave section control at low stages. Because thissection of the manual discusses only stable channelsthat have channel control for the entire range ofstage experienced, the discussion is limited to thenatural channels of extremely large rivers and toartificial channels constructed without sectioncontrols. The artificial channels may be concretelined, partly lined, rip-rapped or unlined. Streamsthat have compound controls involving channelcontrol are discussed in section 1.10.The discharge equation for the condition of channelcontrol is the Manning equation, as discussed inVolume I, Chapter 9, and is shown as equation 1.2in this Volume. In analyzing an artificial channel ofregular shape, whose dimensions are fixed, flow atthe gauge is first assumed to be at uniform depth.Consequently for any stage all dimensions on theright side of the equations are known except n.

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-13A value of n can be computed for a single dischargemeasurement or an average value of n can becomputed from a pair of discharge measurements.Thus a preliminary rating curve for the artificialchannel can be computed for the entire range ofstage from the results of a pair of dischargemeasurements. If subsequent dischargemeasurements depart from the computed ratingcurve it is likely that the original assumption offlow at uniform depth was erroneous. That meansthat the energy slope, S, is not parallel to the bedslope but varies with stage, and that the value of n,which was computed on the basis of bed slope, isalso in error. The rating curve must be revised to fitthe plotted discharge measurements, but thepreliminary rating curve may be used as a guide inshaping the required extrapolation of the ratingcurve. The extrapolation should also be checked byapplication of the conveyance-slope method ofrating extrapolation, which is described insection 1.11.2.To understand the principles that underlie thestage-discharge relation of channel control in anatural channel of irregular shape assume, that theroughness coefficient, n, in the Manning equationis a constant at the higher stages and that the energyslope, S, tends to become constant. Furthermore,area, A, is approximately equal to depth, H, timeswidth, W. By making the substitution for A in theequation 1.7 and 1.8, and by expressing S 1 2 n as aconstant, C 1, the following equation is obtained:Q = C 1HWR2/3 (approx) (1.7)If the hydraulic radius, R, is considered equal to Hand W is considered a constant the equationbecomes:Q = CH = C h − e( ) (approx) (1.8)1.67 1.67However, unless the stream is exceptionally wide, Ris appreciably smaller than H. This has the effect ofreducing the exponent in the last equation,although this reduction may be offset by an increaseof S or W with discharge. Changes in roughnesswith stage will also affect the value of the exponent.The net result of all these factors is a dischargeequation of the form:Q = C ( h − e ) β (1.9)where β will commonly vary between 1.3 and 1.8and seldom reach a value as high 2.0.An example of a discharge rating for channelcontrol in a natural stream is in the followingsection, where compound controls that involvechannel control are discussed.1.10 Ratings for compound controlsinvolving section and channelcontrolA compound control of the stage-discharge relationusually exists in natural channels. Section controlsare more effective for the lower stages and channelcontrol are more effective for the higher stages. Anexample of that situation is given in Figure II.1.10,the rating curve for the Susquehanna River atHarrisburg, Pennsylvania, United States. The lowwater control is a low weir with zero flow at gaugeheight 0.67 m. At a stage of 1.19 m this controlstarts to drown out and channel control becomeseffective. If the low end of the rating is made atangent, a value of e = 0.67 m must be used. Becausethe value of e for the upper end of the rating issomething less than 0.67 m, the high end becomesconcave downward. If the high end of the curve ismade a tangent, the effective value of e is found tobe 0.0 m. Because this is too low a value of e for thelower end of the curve, the low end becomesconcave upward.Where the rating for a section control (low end ofthe curve) is a tangent, the value of β is expectedto be greater than 2.0. In this example β = 2.3.Where the rating for a channel control (high endof the curve) is a tangent, the value of β is expectedto be less than 2.0 and probably between 1.3 and1.8. In this example β = 1.3. Should overbankflow occur the rating curve will bend to the right.It can be demonstrated, non-rigorously, thatstraight line rating curves for section controlsGAUGE HEIGHT, IN METRESa = 0.67a = 0.06.67 55.67 43.67 32.67 21.67 11.47 0.81.27 0.61.17 0.51.07 0.40.97 0.3Compound control{Section control at low stage (a = 0.67 m)Channel control at high stages (a = 0.0 m)Concave up a = 0.0Tangent a = 0.672.31TangentConcave down0.87 0.20.05 0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1 2 3 4 5 6 8 10DISCHARGE, IN CUBIC METRES PER SEC**ON**DFigure II.1.10. Rating curve for a compoundcontrol at Susquehanna River at Harrisburg,Pennsylvania, United States11.3

II.1-14manual on stream gaugingalmost always have a slope greater than 2.0 andthat those for channel controls have a slope lessthan 2.0. This was mentioned in the beginning ofthis Chapter in the section on logarithmic plottingof rating curves.0.130.120.110.100.09Defined1.11 Extrapolation of rating curvesMore often than not, rating curves must beextrapolated beyond the range of measureddischarges. The preceding material in thisChapter explained the principles governing theshape of logarithmic rating curves to guide thehydrologist in shaping the extrapolated segmentof a rating. However, even with knowledge ofthose principles, an element of uncertainty existsin the extrapolation. The purpose of this sectionof the manual is to describe methods of analysisthat will reduce the degree of uncertainty.GAUGE HEIGHT, IN METRES0.080.070.060.050.040.030.020.010Gauge heightof zero flowExtrapolatedDischarge measurement0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5DISCHARGE, IN CUBIC METRES PER SEC**ON**DFigure II.1.11. Example of low-flowextrapolation on arithmetic-coordinategraph paper1.11.1 Low flow extrapolationLow flow extrapolation is best performed onarithmetic coordinate graph paper because thecoordinates of zero flow can be plotted on suchpaper. Zero discharge cannot be plotted onlogarithmic graph paper. An example of suchextrapolation is shown in Figure II.1.11, where thecircled points represent discharge measurementsplotted on the coordinate scales of gauge heightversus discharge. The rating in the example isdefined by the measurements down to a gaugeheight of 0.090 m, but an extrapolation to a gaugeheight of 0.040 m is required. Field observationhas shown the low point on the control (gaugeheight of zero flow) to be at gauge height0.027 m.The method of extrapolation in Figure II.1.11 isself-evident. A curve has been drawn betweenthe plotted points at gauge heights 0.027 mand 0.090 m, to merge smoothly with therating curve above 0.090 m. There is no assurancethat the extrapolation is precise. Low flowdischarge measurements are required for thatassurance but the extrapolation shown is areasonable one.The weir equation 1.1 will apply to low-waterextrapolations where section control exists.Values of the discharge coefficient, C, can becalculated from discharge measurements andcross-section data of the control and thenextrapolated to the range of interest below thelowest discharge measurement. This is a goodtechnique for defining the shape of the ratingcurve in the range where discharge measurementsare not available.1.11.2 High flow extrapolationAs mentioned in a previous section of this chapter,the problem of high flow extrapolation can beavoided if the unmeasured peak discharge for therating is determined by the use of the indirectmethods discussed in Volume I, Chapter 9. In theabsence of such peak discharge determinations,estimates of the discharges corresponding to highvalues of stage may be made by using one or moreof the following four techniques:(a) Conveyance slope method;(b) Areal comparison of peak runoff rates;(c) Flood routing;(d) Step backwater method using models such asHEC-2 or WSPRO.The knowledgeable reader of this Manual maynotice the absence from the above list of twotechniques that were once standard practice:1 2the velocity-area method and Q vs Ad method.1 2The Q vs Ad method was superior to thevelocity-area method and largely supplantedit. Similarly, the conveyance-slope method,because of its superiority, has largely supplanted s1 2Q vs Ad method. Of the three somewhatsimilar methods only the conveyanceslopemethod is described here because adescription of the two earlier methods (Corbett,1945) would have only academic rather thanpractical value.

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-15Conveyance slope methodThe conveyance slope method is based on equationsof steady flow, such as the Chezy or Manningequation. In those equations:Q = KS 1/2 (1.10)In the Chezy equation:K = CAR 1/2and in the Manning equation:1 2/3K = AR n(1.11)(metric units) (1.12)Values of cross section area, A, and hydraulic radius,R, corresponding to any stage can be obtained froma field survey of the discharge measurement crosssection.Values of the coefficient C or n can beestimated in the field. Thus, the value of K, whichembodies all the elements that can be measured orestimated, can be computed for any given stage. Itcan also be shown that errors in estimating C or nare usually not critical. Values of gauge height vs K,covering the complete range of stage up to therequired peak gauge height, are computed andplotted on arithmetic graph paper. A smooth curveis fitted to the plotted points.Values of slope, S, which is actually the energygradient, are usually not available even for measureddischarges. However for the measured discharges,S 1/2 can be computed by dividing each measureddischarge by its corresponding K value. Slope, S, isthen obtained by squaring the resulting value ofS 1/2 . Values of gauge height versus S for measureddischarges are plotted on arithmetic graph paperand a curve is fitted to the plotted points. The curveis extrapolated to the required peak gauge height.The extrapolation is guided by the knowledge thatS tends to become constant at the higher stages.That constant slope is the normal slope, or slope ofthe streambed. The upper end of the defined part ofthe curve of gauge height versus S indicates that aconstant or near constant value of S has beenattained and the extrapolation of the curve can bemade with confidence. The discharge for anyparticular gauge height will be obtained bymultiplying the corresponding value of K from theK curve by the corresponding value of S 1/2 from theS curve. We see that errors in estimating n will havea minor effect because the resulting percentageerror in computing K is compensated by a similarpercentage error in the opposite direction incomputing S 1/2 . In other words, the constancy of Sis unaffected, but if K is, say, 10 per cent high, S 1/2will be 10 per cent low and the two discrepanciesare cancelled when multiplication is performed.However, if the upper end of the define part of thecurve of gauge height versus S has not reached thestage where S has a near constant value, theextrapolation of the curve will be subject touncertainty. In that situation the general slope ofthe streambed, as determined from a topographicmap, provides a guide to the probable constantvalue of S that should be attained at high stages.As mentioned in the preceding paragraph, thedischarge for any particular gauge height is obtainedby the multiplication of appropriate values of K andS 1/2 , and in that manner the upper end of the stagedischargerelation is constructed.Figure II.1.12 provides an example of the slopeconveyance method, as used for rating curveextrapolation at the gauging station on KlamathRiver at Somes Bar California, United States. Theconveyance curve is based on values of K computedfrom the geometry of the measurement crosssection.The slope curve is defined to a gauge heightof 9 m by discharge measurements (circled points)and extrapolated as the solid line to the peak gaugeheight of 20 m. It appears highly unlikely that theslope curve at a gauge height of 20 m will falloutside the limiting dashed curves shown inFigure II.1.12. In other words, it is highly unlikelythat the value of S at 20 m (0.00095) is in error bymore than ± 10 per cent. If that is true, when thesquare root of S is computed and then used in acomputation of peak discharge, the error for bothS 1/2 and Q reduces to ± 5 per cent. One can placeGAUGE HEIGHT (G), IN METRES191817161514131211109876543Conveyance curveSlope curve– 10% + 10%1 2 3 4 5 6 7 5 6 7 8 9 10C**ON**VEYANCE (K), IN MILLI**ON**SSLOPE (S), IN TEN-THOUSANDTHSFigure II.1.12. High-flow extrapolation by use ofconveyance-slope method, Klamath Riverat Somes Bar, California, United States

II.1-16manual on stream gaugingPEAK DISCHARGE (Q) IN CUBIC METRES PER SEC**ON**DPER SQUARE KILOMETRE1008060504030201086543210.80.60.50.40.31008026024022020018016014012040+Maximum 24-hour basinwide precipitation (P),in millimeters+45Q = 4.808 x 10 6 A –0.255 p 2.816 735xNumeral above each plotted pointrepresents station numberSymbols below refer to maximum24-hour basinwide precipitation78.7 mm 178 mm102 mm 203 mm137 mm 229 mm152 mm 254 mm+xx x x xxx25 4827 22233236 15 31 4428 142942 2118 39 9 19 3346 2 102038 124151737313 8342411x26 30x0.20.10.2 0.3 0.4 0.5 0.6 0.8 1 2 3 4 5 6 8 10 20 30 40 50 60 80 100 200 300 500 800 1000 2000 4000 10000DRAINAGE AREA (A), IN SQUARE KILOMETRESFigure II.1.13. Relation of peak discharge to drainage area and maximum 24-hour basin-wideprecipitation in north coastal California, United States, December 1964considerable confidence in the discharge computedfor a gauge height of 20 m in this example. It shouldbe mentioned here that the likelihood of a decreasein slope at high stages, as shown by the dashedcurve on the left of the slope curve, is greatest whenoverbank flows occurs.In the above example, conditions were ideal forapplication of the conveyance-slope method andmay be misleading with regard to the generalaccuracy of the method. The conveyance-slopemethod assumes first that the geometry of the crosssectionused for discharge measurements is fairlyrepresentative of that of a long reach of downstreamchannel. The need to meet this assumptionimmediately eliminates from consideration thosegauging stations where discharge measurements aremade at constricted cross sections, such as occur atmany bridges and cableways.The conveyance-slope method also assumes thatslope tends to become constant at the higher stages.That is strictly true only for long, straight channelsof uniform cross section but natural channels thatmeet that description are virtually nonexistent.Consequently, the slope-stage relation may beanything but a vertical line at the upper stages. Insummary, the conveyance-slope method is a helpfuladjunct in extrapolating rating curves but itslimitations must be understood so that it is notmisused.Areal comparison of peak runoff ratesWhen flood stages are produced over a large areaby an intense general storm, the peak dischargescan often be estimated at gauging stations wherethey are lacking from the known peak dischargesat surrounding stations. Usually each known peakdischarge is converted to peak discharge per unitof drainage area before making the analysis. Inother words, peak discharge is expressed in termsof cubic metres per second per square kilometre.If there has been relatively little difference instorm intensity over the area affected, peakdischarge per unit area may be correlated withdrainage area alone. If storm intensity has beenvariable, as in mountainous terrain, the correlationwill require the use of some index ofstorm intensity as a third variable. Figure II.1.13illustrates a multiple correlation of that typewhere the independent variables used weredrainage area and maximum 24-hour basin-wideprecipitation during the storm of December 1964in north coastal California, United States.The peak discharges estimated by the abovemethod should be used only as a guide inextrapolating the rating curve at a gaugingstation. The basic principles underlying theextrapolation of logarithmic rating curves are notto be violated to accommodate peak discharge

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-17values that are relatively gross estimates, but theestimated discharges should be given properconsideration in the extrapolation process.Step backwater methodThe step backwater method is a technique in whichwater surface profiles for selected discharges arecomputed by successive approximations, asdescribed by Davidian (1984). Computer programssuch as HEC-2 or WSPRO by Sherman (1990) areavailable for making the step backwatercomputations. Although the computations canbe made by hand it is advisable to use a standardcomputer program designed for this purpose.The computations are very detailed and tedious,involving trial-and-error methods that canbe performed quickly and efficiently bycomputer. This section will describe the datarequirements and general procedure for evaluatingthe results.The computations start at a cross-section where thestage-discharge relation is known or assumed andthey proceed to the study site, which is the gaugesite whose rating requires definition or extrapolation.If flow is in the sub-critical regime, as it usually is innatural streams, the computations must proceed inthe upstream direction. Computations proceed inthe downstream direction where flow is in thesupercritical regime. In the discussion that follows,the usual situation of sub-critical flow will beassumed. Water surface profile computations arebased on equation 1.2 (Manning equation) orequation 1.3 (Chezy equation). Irregular crosssectionshape, roughness coefficients that varylaterally and vertically and velocity head adjustmentscan be properly accounted for in the computerprograms.Under conditions of sub-critical flow, water surfaceprofiles converge upstream to a common profile.For example, the stage for a given discharge at agated dam may have a wide range of valuesdepending on the position of the gates. At a studysite far enough upstream to be out of the influenceof the dam, the stage for that discharge will beunaffected by the gate operations. Consequently,when the water surface profile is computed for agiven discharge in the reach between the dam andthe study site, the segment of the computed profilein the vicinity of the study site will be unaffected bythe value of stage that exists at the dam. However,it will be necessary that the computations start atthe dam and proceed upstream, subreach bysubreach (in steps). It follows, therefore, that if aninitial cross-section for the computation of thewater surface profile is selected far enoughdownstream from the study site, the computedwater surface elevation at the study site,corresponding to any given discharge, will have asingle value regardless of the stage selected for theinitial site.A guide for determining the required distance, L,between the study site and the initial section isfound in the dimensionless graph in Figure II.1.14.The graph defined by Bailey and Ray (1966), has forits equation:LSd0.90.80.70.60.5LS 0______––d 0.40.30.20.100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4S 0C 2______gFigure II.1.14. Dimensionless relation fordetermining distance required for backwaterprofiles to convergeS C= 0.86 − 0.64(1.13)g0 0 2where L = the distance required for convergence;S 0= bed slope; d = mean depth for the smallestdischarge to be considered; g = acceleration ofgravity, and C = the Chezy coefficient.If a rated cross-section is available downstreamfrom the study site, that cross-section would beused as the initial section and there would be noneed to be concerned with the above computationof L. As a general rule, it can be said that thesteeper the water surface slope the shorter thereach length required for profile convergence.Conversely, very flat sloped streams requirerelatively long reaches of channel to obtain watersurface profile convergence.After the initial site is selected the next step is todivide the study reach, that is, the reach betweenthe initial section and the study site, into subreaches.That is done by selecting cross-sectionswhere major breaks in the high water profilewould be expected to occur because of changes in

II.1-18manual on stream gaugingchannel geometry or roughness. Those crosssectionsare the end sections of the sub-reaches.The cross-sections are surveyed to a commondatum and roughness coefficients are selected foreach sub-reach. That completes the field work forthe study.The first step in the computations is to select adischarge, Q, for study, and obtain a stage at theinitial section for use with that value of discharge.If the initial section is a rated cross-section, thatstage will be known. If the initial section is not arated cross section, an estimated stage can becomputer using the Chezy or Manning equationsusing the cross section properties and an estimatedwater surface slope. A technique such as theconveyance slope method can be used, as describedin a previous section of this Manual.Step backwater computations begin at the subreachfarthest downstream using a known or estimatedstage at the most downstream cross section for thevalue of discharge being studied. The stage at theupstream end of the subreach is computed bybalancing the energy equation between the twocross sections at each end of the subreach. Thecomputations proceed from subreach to subreachuntil the uppermost cross section is reached. Whendoing these computations by hand it is a trial-anderrorprocedure. Computer programs performthese computations quickly and virtually eliminatethe possibility of mathematical errors which arecommon in step backwater computationsperformed by hand. Profiles for several differentdischarges and starting elevations can be computedquickly and easily to analyze several points on arating curve.If the stage corresponding to the study dischargeat the initial (downstream) cross section wasknown, the stage computed for the upstreamstudy site is satisfactory. If the stage at the initialcross section was estimated it is necessary to repeatthe computations using other values of stage atthe initial cross section for the same discharge.This is done to assure convergence of the watersurface profiles at the study site. Most computerprograms, such as WSPRO by Shearman (1990),will allow entry of several starting elevations for agiven discharge, thus providing several profilecomputations simultaneously. All sets ofcomputations for a given discharge should resultin almost identical values of stage at the studysite. If they do not, the reach should be extendedin the downstream direction, which will involveinclusion of one or more new cross sections. Allcomputations previously described must berepeated for the longer reach. The entire procedurecan be repeated for other discharges until enoughdata are obtained to define the high water ratingfor the study site.The step backwater method can be used to prepare apreliminary rating for a gauging station before asingle discharge measurement is made. A smoothcurve is fitted to the logarithmic plot of the dischargevalues that are studied. The preliminary rating canbe revised, as necessary, when subsequent dischargemeasurements indicate the need for such revision. Ifthe step backwater method is used to define the highwater end of an existing rating curve, the dischargevalues investigated should include one or more ofthe highest discharges previously measured. Bydoing so, selected roughness coefficients can beverified, or can be modified so that step backwatercomputations for the measured discharges providestages at the study site that are in agreement withthose observed. The computations for the high waterend of the rating can then be made with moreconfidence, in the knowledge that reasonable valuesof the roughness coefficients are being used. Therewill also be assurance of continuity between thedefined lower part of the rating and the computedupper part.Flood routingFlood-routing techniques may be used to test andimprove the overall consistency of records ofdischarge during major floods in a river basin. Thenumber of direct observations of discharge duringsuch flood periods is generally limited by the shortduration of the flood and the inaccessibility ofcertain stream sites. Through the use of floodroutingtechniques, all observations of dischargeand other hydrological events in a river basin maybe combined and used to evaluate the dischargehydrograph at a single site. The resulting dischargehydrograph can then be used with the stagehydrograph for that gauge site to construct thestage-discharge relation for the site; or, if only apeak stage is available at the site, the peak stagemay be used with the peak discharge computed forthe hydrograph to provide the end point for a ratingcurve extrapolation.Flood-routing techniques, of which there aremany, are based on the principle of theconservation of mass, where inflow plus or minuschange in storage equals outflow. It is beyond thescope of a stream gauging manual to treat thesubject of flood routing. It is discussed in moststandard hydrology text books such as Linsley,Kohler, and Paulhus, 1949, and Chow, 1964.

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-191.12 Shifts in the discharge ratingShifts in the discharge rating reflect the fact thatstage-discharge relations are not permanent butvary from time to time, either gradually orabruptly, because of changes in the physicalfeatures that form the control for the station. If aspecific change in the rating stabilizes to theextent of lasting for more than a month or two, anew rating curve is usually prepared for the periodof time during which the new stage-dischargerelation is effective. If the effective period of aspecific rating change is of shorter duration, theoriginal rating curve is usually kept in effect, butduring that period shifts or adjustments areapplied to the recorded stage, so that the newdischarge corresponding to a recorded stage isequal to the discharge from the original ratingthat corresponds to the adjusted stage. Forexample, assume that vegetal growth on thecontrol has shifted the rating curve to the left(minus shift), so that in a particular range ofdischarge, stages are 0.015 m higher than theyoriginally had been. To obtain the dischargecorresponding to a recorded stage of, say, 0.396 mthe original rating is entered with a stage of0.381 m (0.396 – 0.015) and the correspondingdischarge is read. The period of time during whichsuch stage adjustments are used is known as aperiod of shifting control.Frequent discharge measurements should be madeduring a period of shifting control to define thestage-discharge relation, or magnitude(s) of shifts,during that period. However, even with infrequentdischarge measurements the stage-dischargerelation can be estimated during the period ofshifting control if the few available measurementsare supplemented with knowledge of shiftingcontrol behaviour. This section of the Manualdiscusses such behaviour.That part of the discussion that deals with channelcontrol shifts does not include alluvial channels,such as sand channels, whose boundaries changealmost continuously. Sand channels are discussedin a subsequent section. Likewise, the formationof ice in the stream and on section controls causesshifts in the discharge rating. Ice is discussedseparately in a subsequent section.1.12.1 Detection of shifts in the ratingStage-discharge relations are usually subject tominor random fluctuations resulting from thedynamic force of moving water and from thecollection of debris or aquatic vegetation onsection controls. Because it is virtually impossibleto sort out those minor fluctuations, a rating curvethat averages the measured discharges withinclose limits is considered adequate. Furthermore,it is recognized that discharge measurements arenot error free, and consequently an average curvedrawn to fit a group of measurements is probablymore accurate than any single measurement thatis used to define the average curve. If a group ofconsecutive measurements subsequently plot tothe right or left of the average rating curve it isusually clearly evident that a shift in the ratinghas occurred. An exception to that statementoccurs where the rating curve is poorly defined orundefined in the range of discharge covered bythe subsequent measurements. In thatcircumstance the indication is that the originalrating curve was in error and requires revision. If,however, only one or two measurements departsignificantly from a defined segment of the ratingcurve, there may be no unanimity of opinion onwhether a shift in the rating has actually occurred,or whether the departure of the measurement(s)results from random error that is to be expectedoccasionally from measurements.Two schools of thought exist with regard toidentifying periods of shifting control. In somecountries, notably the United States, a pragmaticapproach is taken that is based on certainguidelines and on the judgment of the analyst. Inother countries, notably the United Kingdom ofGreat Britain and Northern Ireland, the approachused is based on statistical theory. It is reiteratedthat the discussion that follows excludes theconstantly shifting alluvial channels that arediscussed in a subsequent section.In the United States, if the random departure of adischarge measurement from a defined segmentof the rating curve is within ± 5 per cent of thedischarge value indicated by the rating, themeasurement is considered to be a verification ofthe rating curve. If several consecutivemeasurements meet the 5 per cent criterion, but ifthey all plot on the same side of the definedsegment of the rating curve, they may beconsidered to define a period of shifting control.It should be mentioned that when a dischargemeasurement is made, the measurement iscomputed before the hydrologist leaves thegauging station and the result is plotted on arating curve that shows all previous dischargemeasurements. If the discharge measurement doesnot check a defined segment of the rating curveby 5 per cent or less, or if the dischargemeasurement does not check the trend of

II.1-20manual on stream gaugingdepartures shown by recent measurements, thehydrologist is expected to repeat the dischargemeasurement. In other words, make a checkmeasurement.In making a check measurement, the possibilityof systematic error is eliminated by changing themeasurement conditions as much as possible. Themeter and stopwatch are changed, or the stopwatchis checked against the movement of the secondhand of a standard watch. If an Electronic FieldNotebook (EFN) is used for counting and timingmeter revolutions then manual checks should bemade to insure that the EFN is functioning asrequired. If the measurements are being madefrom a bridge, boat or cableway, the measurementverticals are changed by measuring at verticalsbetween those originally used; if wadingmeasurements are being made, a new measurementsection is sought, or the measurement verticals inthe original section are changed. If the checkmeasurement checks the original rating curve orcurrent rating trend by 5 per cent or less, theoriginal discharge measurement will be given noconsideration in the rating, although it is stillentered in the records. If the check measurementchecks the original discharge or the trend of thatmeasurement if the stage has changed, by5 per cent or less, the two measurements areconsidered to be reliable evidence of a new shiftin the stage-discharge relation. If the checkmeasurement fails to check anything that hasgone before, a second check measurement is madeand the most consistent two of the threemeasurements are used for rating analysis. Theneed for a second check measurement is a rarity,but may possibly occur.Thus, in the United States, a single dischargemeasurement and its check measurement, even ifunsupported by later measurements, may mark aperiod of shifting control. The engineer whoanalyses the rating does have the responsibility ofexplaining the reason for the short-lived shift. Itcan often be explained as having started as a resultof fill (or scour) on a preceding stream rise and ashaving ended as a result of scour (or fill) on therecession or on a following rise.In the United Kingdom, the analysis of the ratingstarts in the usual way. The chronologicallynumbered discharge measurements are plotted onlogarithmic graph paper and are fitted by eye witha smooth curve and the rating equationsestablished by computer. Where compoundcontrols exist there may be one or more points ofinflection in the curve. In the statistical analysisthat follows, each segment of the rating curvebetween inflection points is treated separately.1.12.2 Statistical analysis of the stagedischargerelationThe stage discharge relation, being a line of best fit,should be more accurate than any of the individualdischarge measurements. The equation of therelation may be computed by the method of leastsquares, or regression analysis, which assumes thatthe relation plots as a straight line on logarithmicpaper. Computer programs are readily available forperforming these computations.In the United States the above statistical approachis not favored for several reasons. First, it is felt thatthe limiting criteria of 2 S eper cent will usuallyexceed the 5 per cent criteria preferred in the UnitedStates. Second, any statistical approach gives equalweight to all discharge measurements used in theanalysis. In theUnited States, hydrologists rate theprobable accuracy of the measurements they makeon the basis of measuring conditions at the time,without reference to how closely the measurementsplot on the rating curve. The feeling in the UnitedStates is that more weight in the analysis should begiven to measurements rated good to excellent thanto measurements rated fair to poor. Third, while itis agreed that in general an average curve drawn tofit a group of measurements is probably moreaccurate than any single measurement that is usedto define the average curve, it is also felt in theUnited States that any subsequent measurementthat is verified by a check measurement is moreaccurate than the rating curve value of discharge,particularly at a station that is historically knownto have rating curve shifts.1.12.3 Rating shifts for artificial controlsWeirsArtificial controls are not subject to scour and fill byhigh flows, but the stream-bed immediatelyupstream from the weir may be so affected. If scouroccurs in the pool formed by the weir, the pool isdeepened and velocity of approach decreases. Thenet result is a smaller discharge for a given stagethan under pre-scour conditions. That is, the ratingcurve for the period of scour will shift to the left ofthe rating curve for pre-scour conditions. Theconverse occurs if the weir pool has been subjectedto deposition or fill.The effect of such scour and fill on the stagedischargerelation is usually relatively minor and

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-21usually can be expressed by a parallel shift of mostof the section control portion of the rating curvethat is plotted as a straight line on logarithmicgraph paper. If only a single discharge measurementis available for defining the parallel shift curve, theshift curve is drawn to pass through thatmeasurement. If more than one dischargemeasurement is available, and there is no evidenceof a progressive rating shift with time, the parallelshift curve is drawn to average the dischargemeasurements. If the discharge measurementsindicate a progressive rating shift with time, shiftsare prorated with time. However, what may appearto be a gradually progressive shift may in fact beseveral discrete shifts caused by individual peakflows whose occurrences are not widely separatedin time. The shift in stage to be applied to recordedgauge heights during the period of shifting controlis determined from the vertical spacing betweenthe original rating curve and the shift curve.The shift, if attributable to fill, is considered to startafter the peak discharge of a stream rise thatpreceded the first of the variant dischargemeasurements. Shift adjustments are thereforestarted on the recession of that rise. The shift, ifattributable to scour, is considered to start duringthe high stages of a stream rise that preceded thefirst of the variant discharge measurements. Becausethose high stages generally occur when the sectioncontrol is drowned out by channel control, the shiftin the section control segment of the rating is againcommonly first applied after the peak discharge ofthe rise. The shifts are ended on a stream rise thatfollows the last variant discharge measurement,using the general principle that scour in the gaugepool usually occurs during high stages and fillusually occurs during the recession of a streamrise.The parallel shift discussed in a preceding paragraphrequires some elaboration. A parallel shift of therating curve on logarithmic graph paper indicatesthat for all stages the discharge changes by a fixedpercentage and that the difference in stage betweenthe two lines increases with stage. However, it is notquite true that the discharge changes by a fixedpercentage when the weir pool has scour or fill. Atextremely low flows there will be no effect becausevelocity of approach is negligible; that section ofthe original rating has a break in slope and thelower end of the parallel shift curve above the breakin slope should be smoothly merged with theextreme low water curve. The effect of scour or fillon the percentage change in discharge increasesrapidly with stage to a maximum value and thenslowly decreases to a per cent change that does notdiffer greatly from the maximum percentage. Theparallel shift drawn through the available dischargemeasurement(s) will adequately fit those relativelylarge percentage changes in discharge at the higherstages. The merged section of the shift curve at thelower stages will adequately fit the rapidly increasingpercentage change in discharge at those lowerstages. Figure II.1.15 illustrates the abovediscussion.It has been mentioned frequently in this manualthat section controls are usually submerged at highstages as a result of channel control becomingeffective. The parallel shift curve described aboveshould be extended to the stage where it eitherintersects the actual rating for channel control (inthe case of scour in the weir pool) or can be smoothlymerged into the rating for channel control (in thecase of fill in the weir pool). If a shift has occurredsimultaneously in the channel control, the shiftcurves for the section control and channel controlsegments of the rating are drawn to form acontinuous curve.The preceding paragraphs discuss changes in thevelocity of approach that are caused only by scourand fill in the weir pool. The velocity of approachmay also be affected by aquatic vegetation growingin the weir pool. Usually such an occurrence willreduce the velocity of approach by greatly increasingthe friction loss, and the rating curve will shift tothe left. However, the shift will not be abrupt, butwill gradually increase as the growing seasonprogresses. The aquatic growth in the pool may alsoencroach on the weir to the extent that the effectivelength, b, of the weir is reduced. The effect of areduction in effective length of the weir is a parallelshift of the rating to the left when plotted onlogarithmic graph paper. At all stages the dischargewill be reduced by a percentage that is equal to thepercentage change in effective length of the weir.The shift will either decrease gradually as thevegetation dies in the dormant season, or the shiftmay terminate abruptly if the vegetation is washedout by a stream rise.Aquatic vegetation may sometimes attach itself to aweir crest and thereby reduce the effective head onthe weir for any given gauge height, h. The effectivehead will be reduced by a constant value that isequal to the thickness of the growth. In other words,the effective head, (h – e), is reduced because thevalue of e is increased by the thickness of thegrowth. The reduction in effective head causes therating to shift to the left, it being displaced verticallyby an amount equal to the thickness of the growth.It the shift rating is plotted on arithmetic coordinate

II.1-22manual on stream gauging2.31.8GAUGE HEIGHT (G), IN METRES1.31.100.900.800.700.600.500.400.380.360.350.34Shift curve for scour in weir poolOriginal rating curveShift curve for fill in weir pool0.330.05 0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1 2 3 4 5 6 8 10 20 30DISCHARGE (Q), IN CUBIC METRES PER SEC**ON**DFigure II.1.15. Rating curve for hypothetical rectangular thin-plate weir with shift curves forscour and fill in the weir poolgraph paper it will be parallel to the original rating.If the shift rating is plotted on logarithmic graphpaper, it will be a curve that is concave upward andasymptotic to the original linear rating curve at thehigher stages. The aquatic vegetation on the weirshould be removed with a wire brush before itbecomes heavy enough to affect the stage-dischargerelation. The effect of the shift caused by the algaegrowth disappears during stages when channelcontrol becomes effective.FlumesShifts in the stage-discharge relation for flumes aremost commonly caused by changes in the approachsection, either in the channel immediately upstreamfrom the flume or in the contracting section of theflume upstream from the throat. In either event thechange is caused by the deposition of rocks andcobbles that are too large to pass through the flume.The flume is self cleaning with regard to sediment ofsmaller size. Manual removal of the large debrisshould restore the original discharge rating of theflume.The deposition of rocks and debris upstream fromthe flume may divert most of the flow to the gaugeside of the flume and the build up of water at thegauge will result in a shift of the discharge rating tothe left. Conversely, if most of the flow is divertedto the side of the flume opposite the gauge, thedischarge rating will shift to the right. If rocks andcobbles are deposited at the entrance to the throatof the flume, they will cause the discharge rating toshift to the left, because the stage at the gauge willbe raised higher than normal for any givendischarge. A similar backwater effect will result fromthe growth of aquatic vegetation at the entrance tothe throat.The backwater effect, or decrease in head for a givengauge height, caused by deposition or algal growthat the entrance to the throat of the flume, has theeffect of increasing the value of e in a linearlogarithmic plot of the rating. The shifted rating onlogarithmic graph paper will be a curve that isconcave upward and asymptotic to the originallinear rating curve at the higher stages. The depositionor rocks and debris will usually be associated with ahigh water event, whereas the growth of aquaticvegetation will increase gradually with time. It istherefore essential that measuring structures be wellmaintained and kept free of debris and accretion.1.12.4 Rating shifts for natural sectioncontrolsThe primary cause of changes in natural sectioncontrols is the high velocity associated with highdischarge. Of those controls, a rock ledge outcrop

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-23will be unaffected by high velocities, but boulder,gravel and sand bar riffles are likely to shift, boulderriffles being the most resistant to movement andsand bars the least resistant. After a flood the rifflesare often altered so drastically as to bear noresemblance to their pre-flood state, and a newstage-discharge relation must be defined. Minorstream rises usually move and sort the materialscomposing the riffle, and from the standpoint ofthe rating curve the greatest effect is usually achange in the gauge height of effective zero flow, e.The shift curve ideally should be defined by currentmeter discharge measurements. However, if onlyone or two measurements are available for thepurpose they are examined and the gauge heightshift that they indicate is applied to the sectioncontrol segment of the original rating curve. If theshift rating is plotted on arithmetic paper it willtend to be parallel to the original rating. Theextreme low water end of the curve can beextrapolated to the actual gauge height of zero flow,as determined in the field when low water dischargemeasurements are made. If the shift rating is plottedon logarithmic graph paper, it will be a curve that iseither concave upward or downward, depending onwhether the shift is to the left (increase in e) or theright (decrease in e). The shift curve will tend to beasymptotic to the linear rating at the higher stagesof section control, but its precise slope in the rangeof stage where channel control is beginning to exertan effect will depend on whether or not a shift hasoccurred in the channel control segment of therating curve.Vegetal growth in the approach channel of thecontrol or on the control itself will affect thestage-discharge relation. Aquatic vegetation in theapproach channel will affect the velocity ofapproach, and if the channel growth encroacheson the control it may reduce the effective lengthof the control. Aquatic growth on the controlitself will reduce the discharge corresponding toany given stage by reducing the effective head onthe weir and increasing the resistance of flow and/or by reducing the effective length of the control.The shifts associated with vegetal growth arecyclic and therefore change with time. The growthincreases as the growing season progresses anddeclines during the dormant season, but shiftsmay terminate abruptly if the vegetation is washedout by a stream rise.In temperate climates, accumulations of waterloggedfallen leaves on section controls eachautumn clog the interstices and raise the effectiveelevation of all section controls. The effect of anincrease in the gauge height of effective zero flow, e,has already been explained. The build up of waterloggedleaves is progressive starting with the firstkilling frost (usually in October in the northernhemisphere) and reaching a maximum when thetrees are bare of leaves. The first ensuing stream riseof any significance usually clears the control offallen leaves.Two other causes of backwater (increased gaugeheight for a given discharge), unassociated withhydrological events, also warrant discussion.Holiday-makers in the summer often use thegauge pool for swimming and they will often pilerocks on the control to create a deeper pool. Thischange in the height of the control manifestsitself in the record of stage as an abrupt increasein gauge height, usually during a rainless period,without any corresponding decline in stage thatwould be associated with the passage of a streamrise. The abrupt rise in stage fixes the time whenthe shift in the rating occurred. The magnitude ofthe change in stage is a measure of the change inthe value of e. In some regions of the worldanother cause of backwater is the construction ofdams by beavers. These dams are built of boughs,logs, stones and mud to create a pool that is partof the beaver’s habitat. Again, the time ofoccurrence and the effect on the stage of thestream can be detected in the gauge height recordwhich will show a gradual rise, usually over aperiod of a few days as the dam is being built,without the corresponding decline in stage thatwould be associated with a stream rise. The beaverdams usually remain in place until washed out bya high discharge.A recent technique for documenting changes of thecontrol is the use of inexpensive digital cameras. Adigital camera can be mounted in a protectiveenclosure with a clear glass or lexan window, andfocused on the control section of the stream. Thecamera is programmed to automatically take aphotograph periodically, for example every hour.These photos are very helpful in evaluating shiftapplication, particularly during periods of leafshifts, debris accumulation, ice effects or whensomeone piles rocks on the control. Web cams arealso being used in some places to allow thehydrographer an opportunity to remotely reviewconditions of the control on a daily or more frequentbasis.1.12.5 Rating shifts for channel controlAs mentioned earlier, most natural streams havecompound controls, that is, a section control forlow stages and channel control for high stages. The

II.1-24manual on stream gaugingshifts in section control that were described on thepreceding pages are commonly accompanied byshifts in channel control.The most common cause of a shifting channelcontrol, in a relatively stable channel, is scour or fillof the stream-bed caused by high velocity flow. Thescour usually occurs during a stream rise and fillusually occurs on the recession, but that statementis an over simplification of the highly complexprocess of sediment transport. The degree of scourin a reach is dependent not only on the magnitudeof the discharge and velocity, but also on thesediment load coming into the reach. On somestreams it has been found that when scour isoccurring in a pool at a meander bend there issimultaneous filling on the bar or riffle at thecrossover, or point of inflection between successivemeander bends. On other streams scour has beenfound to take place simultaneously throughrelatively long reaches of channel, both on poolsand over bars. A further complication is the factthat the length of channel that is effective as acontrol is not constant, but increases withdischarge.From the preceding discussion it should be apparentthat there is no really satisfactory substitute fordischarge measurements in defining shifts in thechannel control segment of the rating. Of particularimportance are measurements made at or near thepeak stage that occurs during periods of shiftingcontrol. However, in the usual situation a few (orpossibly only one or two) measurements made atmedium stages are the only ones available foranalyzing channel control shifts, and the shiftsmust be extrapolated to peak stages. However, if itis known that the peak stage results in significantover bank flows, it is probable that a break in therating slope will occur and that therefore theextrapolation is more likely to be in error – henceincreasing the importance of measuring the peakdischarge. The assumptions usually made in thestation analysis are those discussed below. Theresults are accepted unless they are shown to beinvalid by a determination of peak discharge asdescribed in Volume I, Chapter 9, or are shown tobe invalid by use of one or more of the methods ofrating curve extrapolation described in previoussections of this Volume.If a single predominantly large stream rise occurredshortly before the first measurement that indicateda shift, the shifts are assumed to have been causedsolely by that rise. If more than one large streamrise occurred shortly before the first shiftmeasurement, the shift curve may be proratedGAUGE HEIGHTGAUGE HEIGHTZero shiftShift curvefor channel fill212SHIFTShift curvefor channel scourDISCHARGEShift determined fromdischarge measurementOriginalratingbetween rises. For example, if two rises of almostequal magnitude occurred just before the first shiftmeasurement, and if the shift curve indicates a shiftof 0.090 m at a given stage, the shift to be usedduring the period between the two rises would be0.045 m at the given stage. It is often helpful to plotthe shifts indicated by the discharge measurementsagainst the observed stage of those measurementsto obtain the trend of the shifts.The pattern of scour and fill in the control channeldetermines whether the shift will increase withstage, decrease with stage, or be relatively constantat all stages. Figure II.1.16, graph (a), illustrates acommon situation where the shifts, either plus inthe case of scour or minus in the case of fill,increase as stage decreases. The highest value ofthe shift is assumed to be only slightly greaterthan the maximum value observed in order toavoid overcorrecting the original rating. Graph(b) of Figure II.1.16 shows the shifted ratingscorresponding to measurements No. 1 and 2. Theratings have been plotted on arithmetic coordinate112(a)Discharge measurement(b)Figure II.1.16. First example of a stage-shiftrelation and the corresponding stage-dischargerelation caused by scour or fill in thecontrol channel

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-25graph paper because the shifts are more easilyvisualized, at least by the inexperiencedhydrologist, on that type of plotting paper. Thestage shift curve is usually plotted on arithmeticcoordinate paper, but the rating curves are usuallyplotted on logarithmic graph paper. On logarithmicpaper the shift curves in this example wouldconverge more rapidly toward the original ratingcurve at high stages. The shift curves at low stageswould be shaped to merge smoothly with the shiftcurve for section control. The period for applyingthe shifts would be terminated on the stream risefollowing the last shift measurement; the originalrating would be used on the recession from thatrise.GAUGE HEIGHTZero shift1SHIFT2Shift determined fromdischarge measurement2(a)In analyzing shifts there is no substitute forexperience with a given stream because the shiftpattern can often be interpreted logically in morethan one way. For example, refer to the shift curvefor channel fill in graph (b) of Figure II.1.16. Assumethat measurements No. 1 and 2 were made on astream recession and that measurement No. 1 wasmade a few days before measurement No. 2.Measurement No. 2 shows the effect of greater fillthan measurements No. 1. Fill usually occurs on arecession, therefore it is possible that the shiftsshould have been made to vary with time or to varywith time and stage, rather than with stage alone asshown in Figure II.1.16. In the absence of additionalknowledge the simplest interpretation is generallymade, as was done here. Given more dischargemeasurements or a better knowledge of thebehaviour of the particular stream, a more accurateanalysis can be made.Figure II.1.17, graph (a), illustrates a less commonsituation where the shifts increase as stage increases.Again the highest value of shift is assumed to beonly slightly greater than the maximum valueobserved in order to prevent overcorrecting theoriginal rating. Graph (b) of Figure II.1.17 showsthe shift ratings corresponding to measurementsNo. 1 and 2. The period for applying shifting controlcorrections would be terminated on the stream risefollowing the last shift measurement; the originalrating would be used on the rising limb of that rise.As in the case of Figure II.1.16, in the absence ofadditional knowledge more than one interpretationcan be given to shifts shown by measurementsNo. 1 and 2, depending on the relative times whenthe measurements were made and the fact thatscour generally occurs on stream rises and fillgenerally occurs on stream recessions.If there had been an additional major rise, one thatoccurred between the pairs of measurements shownGAUGE HEIGHT11Original ratingShift curvefor channel fillShift curvefor channel scourDISCHARGEDischarge measurement(b)Figure II.1.17. Second example of a stage-shiftrelation and the corresponding stage-dischargesrelation caused by scour or fill in thecontrol channelin Figures II.1.16 and II.1.17, other courses of actionwould be available. If the analyst had no additionaldata on which to base a judgment, he or she couldassume that two separate shift events occurred,each attributable to the rise that preceded adischarge measurement. For each shift period he orshe could use a constant shift, equal to that shownby the discharge measurement made during thatshift period. If, however, the analyst has hadexperience in the past with shifting control at thestation caused by scour and fill in the controlchannel and if that experience had shown thatshifts tend to vary with stage, another course ofaction would suggest itself. For each of the stageperiods the analyst could use a stage shift relationof average shape that passed through the shift valueshown by the appropriate discharge measurement.The above discussion would also apply to thesituation of a single shift period and the availabilityof only a single discharge measurement madeduring that period. It is assumed that the singledischarge measurement would include a checkmeasurement to verify its accuracy, as discussedpreviously.2

II.1-26manual on stream gaugingIf during a period of shifting control severalmeasurements had been made, but few of themcould be fitted with a smooth shift curve, it wouldthen be necessary to prorate the shifts with bothtime and stage, or possibly with time alone, basedon the average shape of a stage shift relation.As mentioned earlier, scour in the control channelcauses a plus shift because depth, and thereforedischarge, is increased for a given gauge height.Deposition or fill in the approach channel causesa minus shift, because depth, and thereforedischarge, is decreased for a given gauge height.Thus the effect on the discharge of scour or fill ina channel control is opposite to that of scour andfill in a weir pool, which affects only the velocityof approach. Therefore, where a permanent weir ispart of a compound control, scour in both theweir pool and in the channel control will cause aminus shift in the rating for section control and aplus shift in the rating for channel control. Theconverse is true when fill occurs in both the weirpool and the channel control. That situation iscompatible with the stage shift relation shown inFigure II.1.17, where a further decrease in stagewould change the sign of the shifts. Where thesection control is a natural riffle, that riffle is likelyto scour when the channel scours and fill whenthe channel fills, a situation that is compatiblewith the stage shift reaction shown in Figure II.1.16.In any event, the shift curves for low stages ofchannel control should be shaped to joinsmoothly with the shift curves for high ages ofsection control, where a compound controlexists.Up to now the discussion of channel control shiftshas been confined to shifts caused by stream-bedscour and deposition. Shifts may also be caused bychanges in the width of the channel. Even in arelatively stable channel the width of the channelmay be increased during intense floods bywidespread bank cutting, and in some areas (forexample, north coastal California, United States)channel widths may be constricted by widespreadlandslides that occur when steep stream-banks areundercut. In meandering streams changes inchannel width occur as point bars are built up bydeposition and later eroded by flood flows. Theeffect of a change in channel width on the stagedischarge relation, unaccompanied by a change instream-bed elevation, is to change the discharge,for a given gauge height, by a fixed percentage.When the original rating curve for channel controlis plotted linearly on logarithmic graph paper, inaccordance with equation 1.4 the value of Cincreases with an increase in width and decreaseswith a decrease in width. The shift curve for achange in width alone will therefore plot onlogarithmic paper as a straight line that is parallelto the original linear rating curve. Under thoseconditions a single discharge measurement issufficient for constructing a shift curve for channelcontrol.When a change in channel width occursconcurrently with a change in stream-bedelevation the effects of the two changes arecompounded. The resulting shift curve is complexand requires at least several dischargemeasurements for its definition. The growth ofvegetation in a stream channel will affect the stagedischarge relation by reducing the discharge for agiven gauge height. The shift rating will thereforeplot to the left (minus shift) of the original rating.The vegetation will increase the roughnesscoefficient of the channel and will tend to constrictthe effective or unobstructed width of the channel.Both of those factors reduce the value of C inequation 1.4, and if the changes in roughnesscoefficient and effective width are unvarying withstage, the shift curve will be parallel to, and to theleft of, the original rating curve that has beenplotted linearly on logarithmic graph paper.However, the changes are not usually independentof stage. If the growth consists of aquatic weeds,the weeds will be overtopped and bent over byhigh water. If the growth consists of alders andwillows, the backwater effect will be greater athigher stages when the tree crowns as well aswhen the tree trunks are submerged. The ratingshift caused by channel vegetation is, of course,variable with time as the aquatic vegetationspreads and increases in size.1.13 Effect of ice formation ondischarge ratings1.13.1 GeneralThe formation of ice in stream channels or onsection controls affects the stage- discharge relationby causing backwater that varies in effect with thequantity and nature of the ice, as well as with thedischarge. Because of the variability of thebackwater effect, discharge measurements shouldbe made as frequently as is feasible when thestream is under ice cover, particularly during freezeup and break-up periods when flow is highlyvariable. Procedures for making measurementsunder ice cover are described in Volume I,Chapter 5.

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-27In midwinter the frequency of measurements willdepend on climate, accessibility, size of stream,winter runoff characteristics and required accuracyof the discharge record. As a general rule, twomeasurements per month is the recommendedfrequency. At stations below power plants that carrya variable load, it may be necessary to make twomeasurements during each winter visit, one at thehigh stage of the regulated flow and the other at thelow stage. The backwater effects may be markedlydifferent at the two stages. In very cold climateswhere winter ice cover persists and winter dischargeshows a relatively smooth recession, fewer wintermeasurements are needed than in a climate thatpromotes the alternate freezing and thawing ofriver ice.Knowledge of the three types of ice formation –frazil, anchor and surface ice – and their possibleeffects, is helpful in analyzing streamflow recordsfor ice- affected periods. With regard to the typeof stage gauge that is preferred for use at iceaffectedstations, the graphic recorder (Volume I,Chapter 4) is by far the best, because the recordergraph generally provides dependable evidence ofthe presence and type of ice formation. However,many stations now use Electronic Data Loggers(EDL) or transmitters that do not directly producea graph of the gauge height record. It is highlyadvisable, therefore, to use these records to plot agraph for periods when ice is probable, and toexamine these graphs for evidence of iceformations.1.13.2 FrazilFrazil is ice in the form of fine elongated needles,thin sheets, or cubical crystals, formed at thesurface of turbulent water, as at riffles. Theturbulence prevents the ice crystals from coalescingto form sheet ice. The crystals may form insufficient numbers to give the water a milkyappearance. When the crystals float into slowerwater they come together to coalesce into massesof floating slush. When the current carries slushice under a sheet of downstream surface ice, theslush may become attached to the underside ofthe surface ice, thereby increasing the effectivedepth of the surface ice. Most of the slush thatadheres to the surface ice does so near the upstreamend of the ice sheet. Frazil or floating slush has noeffect on the stage-discharge relation but mayinterfere with the operation of a current meter. Itis particularly troublesome to operators ofhydroelectric plants. By adhering and building upon trash racks the ice may effectively reduce theflow to the turbines.1.13.3 Anchor iceAnchor ice is an accumulation of spongy ice orslush adhering to the rocks of a stream-bed. Informer years the theory was held that the iceresulted from loss of heat by long-wave radiationfrom streambed to outer space, because anchor icegenerally formed on clear cold nights on thestreambeds of open reaches of river. This theory hasbeen shown to be invalid because all of the longwaveradiation that can be lost from the bed of astream at 0°C would be absorbed in less than 1 cmof water. Anchor ice is now commonly believed tobe either:(a) Frazil that turbulent currents have carried tothe streambed where the ice adhered to therocks; or(b) The result of super-cooled water finding nucleatingagents on the streambed on which toform as ice.The ice first formed on the rocks acts as anucleating agent for the continued growth of theice mass.Regardless of how anchor ice forms it cannot formor exist when the rocks are warmed by short-waveradiation from the sun which penetrates the water.When the morning sun strikes anchor ice that hadformed the night before, and the streambed iswarmed by the incoming solar radiation, the anchorice is released and floats to the surface, oftencarrying small stones that it has picked up from thebed. For the next few hours the stream will be fullof floating slush released in a similar mannerupstream.Anchor ice on the streambed or on the sectioncontrol may build up the bed and/or control tothe extent that a higher than normal stage resultsfrom a given discharge. The solid line graph inFigure II.1.18 shows a typical effect of anchor iceon a water stage recorder graph. The rise starts inlate evening or early morning, many hours afterGAUGE HEIGHT, IN METRES0.60.50.40.30.20.1NORTH FORK BEAVER CREEK NEAR PAULINA, OREG**ON** (United States)Dashed line representseffective gauge height21 Feb. 1953 22 Feb. 1953 23 Feb. 1953Figure II.1.18. Typical anchor-ice rises

II.1-28manual on stream gaugingthe sun has set, when ice begins to adhere to therocks and raise the water level. By 10 a.m. the sunhas warmed the streambed sufficiently to releasethe ice and the stage starts to fall. The distinguishingfeature of the anchor ice hump is that the rise isslow compared to the fall, whereas an actualincrease in streamflow would occur in the oppositesequence, or at least the rise would be as rapid asthe fall. The small rises in actual discharge in thelate afternoon, shown by the short dashed lines inFigure II.1.18 probably result from water beingreleased from channel storage when anchor iceupstream goes out. There may also be some runofffrom the melting of snow and ice during thewarmer part of the day.1.13.4 Surface iceAs the name implies, surface ice forms on thesurface, first as a fringe of shore ice, which then, ifthe stream is not too turbulent, spreads to form acontinuous ice cover spanning the stream frombank to bank. A description of the formation ofsurface ice follows.Formation of ice coverWith the onset of cold weather the water in a streamis gradually cooled. Along the banks where thewater is quiescent, temperature stratification occurs,as in a lake. Because depths near the bank are usuallyvery shallow, temperatures reach the freezing pointmore quickly there. Ice crystals form and adhere tothe banks, twigs and projecting rocks, and a thin icesheet forms. In the open part of the channeltemperature stratification is generally absentbecause of turbulent mixing and the entire waterbody must reach 0°C before any freezing will occur.In the absence of nuclei or foreign material onwhich the ice crystals may form, there may be slightsuper-cooling of the surface layer before any icecrystals are produced.The ice sheet builds out from the shore as supercooledwater, or water carrying ice crystals, impingeson the already formed shore ice, and the transportedor newly formed ice crystals adhere to the sheet. Inthe centre of the stream, turbulence preventscoalescence of the ice crystals (frazil) that form. Inthe less turbulent areas, groups of crystals coalesceto form small pans of floating slush. These pansand/or individual ice crystals are carried by thecurrents until they too impinge and adhere toexisting ice sheets. In this manner an ice sheetfinally forms across the entire stream. The ensuingincrease in thickness of the ice sheet occurs almostentirely at the interface of ice and water.On a fairly wide stream there is no great build up ofpressure as a result of the ice cover because the iceis, to a large degree, in floatation. Ice is weak intension. If the stage rises, or if the ice thickensconsiderably, the increased upward force of thewater causes tension cracks to appear at the banks.The ice floats up to a position in equilibrium withthe water, and water fills the tension cracks andfreezes. The result is again a solid sheet in equilibriumwith the river. If the stage drops, the unsupportedweight of the ice again causes tension cracks,especially at the banks, and the ice drops to anequilibrium position with respect to the water.Water again fills the tension cracks, freezes, andagain a solid sheet of ice results.On narrow streams the ice may be in floatation,bridged or under pressure. If the stream is so narrowor the ice so thick that the ice can resist the tensilestress placed on it by changes in stage, the ice willnot change position regardless of change in stage.At high stages the stream, in effect, will be flowingin a pressure conduit; at low stages the ice sheet willbe bridged so that it makes no contact with thewater. This is particularly true when there are largeboulders in the stream to which the ice is frozen,thereby reducing the length of the unsupportedfree span.Effect of surface ice on stream hydraulicsSurface ice when in contact with the stream may, ineffect, change streamflow from open channel flow toclosed conduit flow. Frictional resistance is increasedbecause a water-ice interface replaces the water-airinterface, hydraulic radius is decreased because ofthe additional wetter perimeter of the ice, and thecross-sectional area is decreased by the thickness ofthe ice. The stage will therefore increase for a givendischarge. Figure II.1.19 shows the water stagerecorder graph for a gauging station as the formationof surface ice begins to cause backwater effect.In this example, daily mean discharge remainedabout the same as before the freeze-up, althoughthe discharge undoubtedly fluctuated somewhatduring each day. It can be seen from Figure II.1.19that surface ice can cause much uncertaintyregarding the discharge because the stage-dischargerelation becomes indeterminate. It is evident inFigure II.1.19 that backwater effect exists and isincreasing, because the rise looks very unnatural,but the amount of backwater effect cannot bedetermined directly from the recorder chart.Surface ice can also cause siphon action when itforms on a section control, but that effect is not

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-29GAUGE HEIGHT, IN METRES8640.2NORTH FORK CROOKED RIVER BELOW DEEP CREEK, OREG**ON** (United States)Cross-sectional view of weir showing extent of ice cover, 4-5 Jan. 1940ICE0– 0.152Gauge height in metres+ 0.152G.H. = – 0.085 mStream bedDashed line represents effective gauge height on a dailybasis only (probable minor daily fluctutations not shown)29 Nov. 1952 30 Nov. 1952 1 Dec. 1952Figure II.1.19. Typical rise as complete ice coverforms (after Moore, 1957)WEIRGauge height record for period 4-5 Jan. 1940G.H. = 0.055 mG.H. = – 0.085 m4 Jan. 5 Jan.G.H. = + 0.055 mG.H. = + 0.006 m (zero flow)Zero flow =+ 0.006 mFigure II.1.20. Effect of siphon action atartificial control in Sugar Run at Pymatuning,Pennsylvania, United States,4-5 January 1940very common. In Figure II.1.20, when water filledthe entire space between control and ice, siphonaction began and water flowed over the controlfaster than it entered the gauge pool. The gaugepool was pulled down 0.100 m below the gaugeheight of zero flow when air entered the systemand broke up the siphon action. Discharge ceasedand then became a trickle while the inflow againfilled the gauge pool. When the entire spacebetween control and ice was filled once more,siphon action began again. Siphon action is easilyrecognizable from the rapid fluctuations of thestage record. If the gauging station is visited atthat time, the discharge measurement should bemade far enough upstream from the gauge poolto be beyond the effect of the fluctuating poollevel.If the section control is open and the gauge is nottoo far removed from the control, there willprobably be no backwater effect even though theentire pool is ice covered. The only effect of the icecover will be to slow up the velocity of approachand this effect will probably be minor. If the gauge,however, is a considerable distance upstream fromthe riffle, surface ice on the pool may causebackwater as the covered reach of pool becomes apartial channel control. Ice forming below an opensection control may jam and raise the water levelsufficiently to introduce backwater effect at thecontrol.1.13.5 Computation of dischargeduring periods of backwaterfrom anchor iceDischarge measurements are usually not madewhen anchor ice is present, for the followingreasons. First, adjustment of the stage record forthe effect of anchor ice can be made quickly andreliably. Second, a discharge measurement made atthat time is of little help in the analysis becausedischarge is highly variable with time as a result ofwater entering or leaving channel storage.Anchor ice rises are clearly recognizable on therecorder chart. In computing discharge for periodsof anchor ice effect, adjustments to gauge heightare made directly on the gauge height graph. InFigure II.1.18, the long dashed line connecting thelow points of the anchor ice hump is the effectivegauge height to use during the hours when thehump was recorded. Actually, the true effectivegauge height is shown by the short dashed line. Asthe anchor ice builds up, the flow decreases fasterthan the normal recession shown by the longdashed line, because some of the flow is going intoa storage as a result of the increased stage.When the anchor ice goes out at about 9 or 10 a.m.,a slug of water is released from storage and the trueeffective gauge height rises. It can be seen, however,that the areas formed by the short dashed linesabove and below the long dashed line balance andwe should get nearly identical results from use ofeither of the dashed lines. The rule then forobtaining effective gauge height during anchor ice

II.1-30manual on stream gaugingperiods is to cut off the hump with a straight lineconnecting the low points.654b Backwater from ice141.13.6 Computation of discharge duringperiods of backwater fromsurface iceFigure II.1.21 is an example of how dischargemeasurements (Nos. 5, 37 and 38), made duringperiods of ice effect, plot on a rating curve.Figure II.1.19 is an example of a gauge height graphas complete ice cover forms. It is apparent fromFigure II.1.19 that the backwater effect from surfaceice cannot be determined directly from the recorderchart or plot of the gauge readings. The recorderchart or gauge height graph is very helpful, however,in determining which periods during the winterthat are ice affected.Complete notes describing ice conditions at thetimes the station was visited are also very valuable.Most important of all are discharge measurementsmade during ice-affected periods. A dischargemeasurement gives a definite point on a hydrographplot of daily mean discharge versus dateFigure II.1.22), through which the graph ofestimated true daily discharge must pass. If littlechange in stage occurred during the day thedischarge measurement was made, the measureddischarge is considered to be the daily meandischarge. If a significant change in stage occurredthat day, the daily mean discharge, Q, is computedfrom the formula:Q = Q Q aQmr(1.14)where Q ais the discharge from the open water (icefree) rating curve corresponding to the daily meangauge height; Q mis the measured discharge, andQ ris the discharge from the open water rating curvecorresponding to the gauge height of the dischargemeasurement.Several methods of correcting open water dischargefor ice effect are in use. The term open waterdischarge, as used in this section of the Manual,refers to the discharge for ice-free conditions,obtained by applying the gauge height record tothe rating or shift curve that was in use immediatelybefore the start of the ice-affected period. Themethods are:(a) Discharge ratio method (sometimes known inthe United States as the Lithuanian method);(b) Shifting control method or Stout method;(c) Direct discharge interpolation method;(d) Hydrographic and climatic comparison method.GAUGE HEIGHT, IN METRES321.00.80.6DISCHARGE, IN CUBIC METRES PER SEC**ON**D1 00080060050040030020010030605040302010865432129223534b 5b 32b 3720Daily-discharge hydrograph for MissouriRiver near Wolf Point, Montana, United StatesDischarge ratio computed onbasis of measured dischargeNOVEMBER–DECEMBER19373031362624Measured dischargeJANUARY193887632Open waterdischarge(from rating)Estimated truedischargeDischarge ratioFEBRUARY1938MARCH193810.800.600.500.40Figure II.1.22. Example of discharge-ratio methodfor correcting discharge record for ice effectSome of the methods are somewhat similar, andvary mainly in how they are applied. Thereliability of each of the methods varies almostdirectly with the number of dischargemeasurements that were made during the iceaffectedperiod that is being studied. Regardlessof the method used, the corrected hydrograph ofdaily discharge, if possible, should be checked forconsistency with other records. Or in some cases,two or more of the above methods may be used1523271 Oct. 1951 to0.520 30 40 50 60 80 100 200 300 400 500 600 800 1000DISCHARGE, IN CUBIC METRES PER SEC**ON**DFigure II.1.21. Rating curve for MenomineeRiver near Pembine, Wisconsin, United States179100.300.200.10DISCHARGE RATIO

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-31for comparison purposes. The method that ismost consistent with information from othersources would then be used. If the station beingstudied is on a stream that carries natural flow(flow not significantly affected by man-madedevelopment) its corrected record is comparedwith those for nearby streams that likewise carrynatural flow. Particularly useful for that purposeare the hydrographs of streams that are unaffectedby ice. If the station being studied is on a regulatedstream, its corrected hydrograph is comparedwith the record of upstream reservoir releases orupstream hydroelectric generation, expressedeither in units of discharge or in units of poweroutput.Discharge ratio methodIn the discharge ratio method which is used inmany European countries, the open water dailymean discharge is multiplied by a variable factor Kto give the corrected discharge during periods of icecover. A value of K is computed for each dischargemeasurement as the ratio of measured discharge(Q m) to the open water discharge (Q r). Because Kvaries during the winter with time, as changes occurin the ice cover, the value of K for use on any givenday is obtained by interpolation, on the basis oftime, between K values computed for consecutivedischarge measurements. Meteorological data aregenerally used to modify the simple interpolationbetween K values for consecutive dischargemeasurements; for example, during a period ofextremely low temperatures the values of K indicatedby simple interpolation would be reduced becausethe discharge usually decreases sharply at suchtimes. The dates on which ice effect begins andends are based on the observed or deducedbeginning and end of ice cover.An example of the discharge ratio method is shownin Figure II.1.22. Note that discharge is plotted ona logarithmic scale. The upper daily hydrographshows open water discharges and the solid circlesare discharge measurements. The lower graphshows the K values obtained from dischargemeasurements (open circles) and the interpolationbetween those values; the middle graph is thehydrograph of estimated true daily discharges,obtained by multiplying concurrent values fromthe upper and lower graphs. The nonlinearinterpolations for K values during the periods9-23 November, 18 January to 19 February, and24 February to 20 March, were based on theobserver’s notes concerning ice conditions and ontemperature and precipitation records (not shownin Figure II.1.22).Shifting control methodThe shifting control method, at one time thestandard method used in the United States, isseldom used there now but is still used in othercountries. In the shifting control method,recorded gauge heights are reduced by a variablebackwater value to obtain the effective dailygauge heights (sometimes called the equivalentgauge height). The effective gauge heights arethen applied to the open water rating to obtainestimated true daily discharges. The backwatercorrection on days when discharge measurementsare made is computed as the difference betweenthe actual gauge height and the effective gaugeheight, effective gauge height being the gaugeheight from the open water rating that correspondsto the measured discharge. The backwatercorrection for use on any given day is obtainedby interpolation, on the basis of time, betweenthe backwater corrections computed forconsecutive discharge measurements. As in thedischarge ratio method, the interpolation issubject to modification on the basis ofmeteorological records and the dates on whichice effect begins and ends are based on theobserved or deduced beginning and end of icecover.An example of the shifting control method isshown in Figure II.1.23 for the same gaugingstation used in the example in Figure II.1.22.Note that an arithmetic (not logarithmic) scale isused in Figure II.1.23. The upper daily hydrographin Figure II.1.23 shows recorded gauge heightsand the solid circles are the effective gauge heightsfor discharge measurements. The lower graphshows the backwater corrections obtained fromdischarge measurements (open circles) and theinterpolation between those values. The middlegraph is the hydrograph of effective gauge heightobtained by subtracting values on the lower graphfrom concurrent values on the upper graph. Thenonlinear interpolations for backwater correctionsduring various periods were based on theobserver’s notes concerning ice conditions andon temperature and precipitation records (notshown in Figure II.1.23). As mentioned in thepreceding paragraph the effective gauge heights(middle graph) are applied to the rating curve toobtain estimated true daily discharges.Direct discharge interpolation methodDaily mean discharges can be determined by directinterpolation between discharge measurements,usually linear or log-linear, during periods when it

II.1-32manual on stream gaugingGAUGE HEIGHT,IN METRES43.532.52Daily-discharge hydrograph for MissouriRiver near Wolf Point, Montana, United StatesEffective gauge height ofdischarge measurementsRecorded daily gauge heightthe true daily discharge directly on the hydrographsheet and that is done on the basis of threecomparisons:(a) Comparison with records for nearby gaugingstations;(b) Comparison with weather records;(c) Comparison with base flow recession curve.Comparison with records for nearby gaugingstationsBACKWATER CORRECTI**ON**S,IN METRES1.510.500.90.50NOVEMBER–DECEMBER1937Effective daily gauge heightBackwater computed on basisof computed dischargeBackwater correctionsJANUARY1938is believed that discharge changes are fairly uniform.The interpolation procedure can be modified attimes when the air temperature and stage recordsindicate significant changes.Hydrographic and climatic comparisonmethodFEBRUARY1938MARCH1938Figure II.1.23. Example of shifting-control methodfor adjusting stage record for ice effectThe method of hydrographic and climaticcomparison has been favored in the United Statesfor many years. The mechanics of the method differfrom those of the discharge ratio method, but bothmethods basically correct the daily open waterdischarge by a variable percentage.The first step is to compute the station dischargerecord for the entire year as though there were noice effect at any time. The daily hydrograph of openwater discharge and the discharge measurementsare then plotted, using a logarithmic dischargescale, and notes concerning ice conditions areentered on the graph. At this point the hydrographsheet resembles the upper graph in Figure II.1.22.Where a measurement of ice affected discharge isnot representative of the daily mean discharge,because of changing stage during the day, the dailymean discharge, as computed by equation 1.15, isalso plotted. All is then in readiness for estimatingComparison with other discharge records is themost important basis for determining the probabledischarge for periods between dischargemeasurements. Even though the record used forcomparison may also have been corrected for iceeffect, its use provides an additional independentset of basic data, that is, another stage record andanother set of current meter measurements. Withouta nearby record that compares well with the recordbeing studied, the accuracy of the daily dischargesestimated between the dates of dischargemeasurements may be greatly reduced. However,hydrographic comparisons are not infallible becausethe relation between the flow of two streams mayvary significantly during the year; hence theimportance of making many dischargemeasurements during ice-affected periods.In making the hydrographic comparison, thenearby station with the most reliable winter streamflowrecord is selected for use as a reference station.The reliability of the reference station may havebeen established by the fact that its discharge isunaffected by ice or is affected by ice for only arelatively short period, or by the fact that manywinter measurements have been made at the stationand the true discharge between the dates ofmeasurement can be estimated from weatherrecords. (See discussion below on use of weatherrecords.) A hydrograph of daily discharge, correctedfor ice effect if necessary, is prepared for the referencestation on a separate sheet of graph paper, similarto that used for plotting the daily hydrograph forthe station being studied.A light table is used in comparing the twohydrographs or they are graphically compared by acomputer plotting program; for example, theUnited States Geological Survey (USGS) uses agraphic program that allows one daily dischargehydrograph to be moved on the screen to overlayanother hydrograph. Whether using a light table orcomputer program, the reference station hydrographis used. The hydrograph for the study station issuperposed on that of the reference station andpositioned laterally so that the date lines of the two

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-33hydrographs coincide. The period preceding thefirst measurement (No. 1) that showed ice effect atthe study station is the period first selected forconsideration. The hydrograph for the study stationis positioned vertically so that hydrographs for thetwo stations roughly coincide for the periodimmediately preceding the day or days when thestart of ice effect is suspected. A comparison of thehydrographs and an inspection of the weatherrecords should fix the date when ice effect started.That date will be preceded by a period of subfreezingweather, and on that date, usually a rainless day,the hydrograph for the study station will start agradual rise not shown by the hydrograph for thereference station. For an appreciable periodthereafter the hydrograph for the study station willremain above that of the reference station.After the starting date, A, of ice effect at the studystation has been selected, the vertical position ofthe hydrograph for the study station is changedslightly, if necessary, to make the two hydrographscoincide on that date. If that positioning causesmeasurement No. 1 to fall directly on the hydrographfor the reference station, the hydrograph for thereference station between date A and measurementNo. 1 is traced with dashed lines on the hydrographsheet for the study station. The daily dischargesindicated by the dashed lines are the estimated truedischarges at the study station during the periodbetween date A and measurement No. 1.However, it is a rare situation where measurementNo. 1 coincides with the reference hydrographwhen discharges at the two stations are made tocoincide on date A. Measurement No. 1 will usuallylie above or below the hydrograph for the referencestation. In that situation, as discharges from thereference hydrograph are being transferred to thesheet bearing the study hydrograph, the study sheetwill in effect be moved up or down, as the case maybe, so that when the transfer of discharge pointsreaches measurement No 1, measurement No. 1will coincide exactly with the reference hydrograph.If the temperature record shows no great fluctuationfrom day to day during the period between date Aand measurement No. 1, the vertical displacementof the sheet bearing the study hydrograph will bemade uniformly during the transfer process. If thetemperature record does fluctuate from day to dayduring the period, the vertical displacement will bemade at a variable rate to reflect the fact that theratio of true discharge to open water dischargeusually decreases during sharp drops in temperature;the ratio increases during sharp rises in temperature.In other words, the vertical distance between openwater discharge and true discharge will increase onthe study hydrograph sheet during sharp drops intemperature. The vertical distance decreases duringsharp rises in temperature. Observer’s notesconcerning major changes in the ice cover,particularly where complete cover is intermittentduring the winter, are also very helpful in estimatingthe degree of ice effect.After correcting the discharge between date A andmeasurement No. 1, the process is repeated for theperiod between discharge measurement No. 1 andthe next successive discharge measurement (No. 2).The two hydrographs are made to coincide atmeasurement No. 1 and the transfer of dischargepoints to the study hydrograph proceeds tomeasurement No. 2. In that manner the open waterdischarge for the study station is corrected until thedate is reached when ice effect ceases.Comparison with weather recordsRecords of air temperature and precipitation are amost valuable aid in making corrections for iceeffect. The temperature record helps the hydrologistdecide whether the precipitation is rain or snow.Snow will have no immediate effect on the runoff.The temperature record also helps the hydrologistdecide whether ice cover is forming, increasing ordissipating. For stations for which there are nonearby discharge records for comparison and forwhich the recorder chart does not providedependable clues to the fluctuation of discharge, itmay be necessary to correct open water dischargesfor ice effect almost solely on the basis of weatherrecords and available measurements of discharge.Discharge usually follows closely the ups-anddownsof the air temperature record and thedischarge measurements help fix, within reasonablelimits, the estimated rises and falls of the truedischarge hydrograph. An exception to thatstatement is found in regions of extreme cold, suchas the Arctic, that become blanketed with a heavysnow cover. The snow acts as an insulator for theunderlying ground and it then requires a prolongedchange in temperature to significantly change theslow uniform recession of streamflow during thewinter.It should be mentioned here that a water temperaturerecorder is a helpful adjunct to a gauging station.When the water temperature is above the freezinglevel there is little likelihood of ice effect.Comparison with base flow recession curvesDuring periods of sub-freezing weather virtually allthe flow in a stream is base flow; that is, water that

II.1-34manual on stream gaugingcomes out of ground-water storage to sustain theflow of the stream during periods when there is nosurface runoff. It will often be found that duringcold ice affected periods, the flow of the stream willbe declining at a rate similar to the rate of recessionshown by that stream during ice free periods. Forexample, consider a situation where a discharge of0.56 m 3 s -1 is measured on a specific day during theice affected period, and an estimate of dailydischarge is required for the next ten days, all ofwhich were free of rain or snowmelt. An ice freeperiod elsewhere in the record is then selected forthe study station when there was no surface runoff,and one day during that period had a discharge of0.56 m 3 s -1 . The receding values of discharge for thefollowing ten days of that ice free period are thenused for the ten days to be estimated. The ice freeperiod that is used for an index should preferablybe in the non-growing season because the use ofwater by vegetation affects the rate of base flowrecession.It is possible that daily discharges estimated fromthe base flow recession may be somewhat highbecause extremely cold weather reduces the rateat which water percolates through the ground andbecause some of the water that does reach thestream may go into storage behind ice dams.Nevertheless a standard base flow recession curveprovides a valuable guide to the probable flowduring recession periods when the stream is icecovered. Because the discharge during periods ofbase flow originates as groundwater, a record ofthe fluctuations of groundwater levels of wells inthe area can be useful as an index for estimatingthe true discharge during those periods.Example of hydrographic and climatic comparisonmethod.An example of the application of the hydrographicand climatic comparison methods is illustrated inFigures II.1.24 and II.1.25. Figure II.1.24 shows aportion of a plotted hydrograph of daily meandischarge for the gauging station on North ForkJohn Day River at Monument, Oregon, UnitedStates. The solid line represents open waterdischarge obtained by applying recorded gaugeheights to the rating curve, and the open waterdischarge on 26 January corresponds to the gaugeheight of discharge measurement C made on thatdate. Note that the open water discharge is almostten times as great as the measured discharge on26 January. The dashed line on Figure II.1.24represents the estimated true daily dischargeobtained by comparison with the hydrograph ofdaily mean discharge for John Day River at ServiceDISCHARGE, IN CUBIC METRES PER SEC**ON**D150908060504030201086543NORTH FORK OF THE JOHN DAY RIVER AT M**ON**UMENT,OREG**ON**, UNITED STATESJOHN DAY RIVER ATSERVICE CREEK,OREG**ON** (U.S.)NORTH FORK OF THEJOHN DAY RIVER ATM**ON**UMENT, OREG**ON** (U.S.)4510MAXIMUM AND MINIMUM 5DAILY TEMPERATURES ATDAYVILLE, OREG**ON** (U.S.), 0IN °C5– 10– 15ABDISCHARGE COMPARIS**ON** AND AIR TEMPERATURES (°C)6050(Circles indicate discharge measurements)403020108Discharge measurementsDec. 1948 Jan. 1949 Feb. 1949Engineer’s notes: A = Control clear; B = Bank ice, slush ice, no effect water 0.56°C;C = Backwater from ice cover downstream water 0°C.Dischargeobtained fromrating curveAdjusteddischargeFigure II.1.24. Daily hydrographs for open-waterdischarge and for discharge corrected forice effect (after Moore, 1957)Dec. 1948 Jan. 1949 Feb. 1949Figure II.1.25. Comparison of daily winterdischarge at two gauging stations showingtheir response to air-temperature fluctuations(after Moore, 1957)Creek, Oregon, and by comparison with the recordof daily maximum and minimum temperature atDayville, Oregon, United States. The referencehydrograph and temperature record used for thecomparison are shown in Figure II.1.25. Actuallythe precipitation record at Dayville was alsoconsidered, but because all precipitation duringthe study period occurred as snow and thereforehad no immediate effect on the runoff, theprecipitation record is not shown inFigure II.1.25.The corrected hydrograph for the study station onNorth Fork John Day River at Monument is alsoshown on Figure II.1.25. The hydrograph of openC

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-35water discharge at that station has been omittedto reduce clutter in the illustration. The dischargefor the reference station on John Day River atService Creek was unaffected by ice. The shapes ofthe two hydrographs are not identical, but a usefulcomparison between the hydrographs for twostations does not require that their shapes beidentical, as long as their discharge trends aresimilar. It can be seen on Figure II.1.25 that bothhydrographs respond to the effect of airtemperature fluctuations during the winterperiod.In applying the method of hydrographic andclimatic comparison, the hydrograph of true dailydischarge, plotted on a logarithmic scale, wasdisplaced from the open water hydrograph by avariable vertical distance. That means, in effect,that discharge ratios, variable with time, wereapplied to the open water discharges, and thereforea basic similarity exists between the hydrographiccomparison method and the discharge ratiomethod. Application of the hydrographiccomparison method would be greatly facilitated ifthe hydrograph of open water discharge for thestudy station were first adjusted by the dischargeratio method because application of that methodis relatively simple. The adjusted hydrographwould then be refined by using it, rather than theopen water hydrograph, in the hydrographiccomparison method. It is much simpler to applythe hydrographic comparison method for refiningdischarge estimates than it is to apply that methodfor making original discharge estimates.Use of Acoustic Doppler Velocity Meters forice-affected periodsIn making the hydrographic comparisons duringice-affected periods, the nearby station with themost reliable winter streamflow record is selectedfor use as a reference station. Discharge recordsgenerated using Acoustic Doppler Velocity Meters(ADVM) have the potential to produce reliablerecords of discharge during ice periods, even whenthe surface is totally ice covered (Morlock andothers, 2002). The implications from this potentialare: (a) installation of an ADVM at a station whereinstallation is feasible (ADVM installationconsiderations are discussed in Volume I, Chapter 5)may provide an improved estimate of dischargeduring ice periods; and (b) A station equipped withan ADVM may provide an ideal station forhydrographic comparisons for stations not equippedwith an ADVM but requiring ice estimates. Use ofADVMs to produce discharge records are discussedin more detail in Chapter 2 of this Volume.1.14 Sand channel streamsIn fixed channels well-defined stage dischargerelations can usually be developed that show onlyminor shifting at low flow. In sand channel streams,however, stage-discharge relations are continuallychanging with time, because of scour and fill, andbecause of changes in the configuration of thechannel bed. These changes cause the shape andposition of the stage-discharge relation to vary fromtime to time and flood to flood, and it becomes verydifficult to explain the apparent haphazard scatterof discharge measurements available to define therating. Familiarity with the results of researchstudies as reported by Colby (1960), Dawdy (1961),Simons and Richardson (1962), Beckman andFurness (1962) and Culbertson and Dawdy (1964)will greatly assist the analyst in defining thedischarge rating.1.14.1 Bed configurationOn the basis of laboratory investigation, Simonsand Richardson (1962) described the bedconfiguration of sand channel streams as ripples,dunes, plane bed, standing waves and antidunes.This sequence of bed configurations occurs withincreasing discharge. When the dunes wash out,and the sand is rearranged to form a plane bed,there is a marked decrease in resistance to flowwhich may result in an abrupt discontinuity in thestage-discharge relation. The forms of bedroughness, as shown in Figure II.1.26 and describedin Table II.1.2, are grouped according to the twoseparate conditions of depth-discharge relationshipthat are evident in a given channel. The sequenceof configurations described in Table II.1.2 isdeveloped by continually increasing discharge.The lower regime occurs with lower discharges andthe upper regime with higher discharges. Anunstable discontinuity in the depth dischargerelationship appears between these two morestable regimes.The presence of fine sediment in the flow influencesthe configurations of the sand bed, and thus theresistance to flow. It has been found by Simons andRichardson (1962) that with concentrations on theorder of 40 000 milligrams per litre of fine material,resistance to flow in the dune range is reduced asmuch as 40 per cent. The effect is less pronouncedin the upper regime but fine sediment may changea standing wave condition into a breaking antidunewhich will increase the resistance to flow. Thus thestage-discharge relationship for a stream may varywith sediment concentration if the flow is heavilyladen with fine sediment.

II.1-36manual on stream gaugingType of configurationTable II.1.2. Surface and bed descriptions for the various flow regimesBedDescriptionLower regime flow:Plane bed Plane; no sediment movement Plane surface; little turbulenceRipplesSmall uniform waves; no sedimentPlane surface; little turbulencemovementDunesLarge, irregular, saw-toothed waves formed Very turbulent; large boilsby sediment moving downstream; wavesmove slowly downstreamUper regime of flow:Plane bed Dunes smoothed out to plane bed Plane surface; little turbulenceStanding waves Smooth sinusoidal waves in fixed position Standing sinusoidal waves in phase with bedwaves; termed “sand waves”AntidunesSymmetrical sinusoidal waves progressingupstream and increasing in amplitude;suddenly collapse into suspension thengradually reformSymmetrical sand waves progressingupstream in phase with bed waves;amplitude increases until wave breaks, wholesystem collapses then gradually reformsFlowLOWER FLOW REGIMEUPPER FLOW REGIMEFlow is from left to rightPlane-bed regime prior to movementRipple regimeDune regimePlane-bed transition regimeStanding-wave regimeAntidune regimeFigure II.1.26. Idealized diagram of bed andwater surface configuration of a fluvial streamswith various regimes of flowChanges in temperature can also alter the form ofbed roughness, and, hence, the resistance to flow.Lowering the temperature increases the viscosity ofthe water and increases the mobility of the sand. If,for example, the form of bed roughness is near to orin transition, and there is a reduction in thetemperature of the water, the increased mobility ofINCREASING VELOCITYthe sand may cause the dunes to wash out, and thebed to become plane. This phenomenon isreversible.Changes in bed forms do not occur instantaneouslywith increasing or decreasing discharge. The timelag between change in bed form and change indischarge may result in loop rating curves. Forexample, if the bed configuration is initially dunes,the dunes will persist on rising stages to a dischargethat is greater than the discharge at which thedunes will reform on falling stages. Thus at a givenstage, the discharge may be greater when the stageis falling. Because the form of each loop curvedepends on the initial condition of bed configurationand the rate of change of discharge, an infinitenumber of different loop curves, and even multipleloopcurves, may occur for a given reach of channelacross the transition from dunes to plane bed. Thestage-discharge relation within the transition bandmay be indeterminate. An example of a loop curve,typical of some sand channels, is shown inFigure II.1.27.1.14.2 Relation of mean depth todischargeA plot of stage against discharge in sand channelstreams often obscures any underlying hydraulicrelationship because neither the bottom nor sidesof these streams are fixed. Figure II.1.28 shows asan extreme example of the stage-discharge plot forHuerfano River near Undercliffe, Colorado, UnitedStates for 1941 and 1942. The relation betweenstage and discharge is indeterminate. However, the

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-37Ripples and dunesTransitionPlane bed, standing wavesand antidunes32STAGEFallingstageRisingstage(GAUGE HEIGHT + 0.3), IN METRES10.80.70.60.50.40.30.21.5 2 3 4 5 6 7 8 10 20 30 40 50 60 80DISCHARGEDISCHARGE, IN CUBIC METRES PER SEC**ON**DFigure II.1.27. Typical loop curve of stageversus discharge for a single flood-event ina sand channel (after Stepanich, Simons andRichardson, 1964)Figure II.1.28. Stage-discharge relationfor Huerfano River near Undercliffe,Colorado, United States.From Dawdy (1961)underlying hydraulic relation may be revealed bya change in variables. The effect of variation inbottom elevation is eliminated by replacing stageby mean depth or hydraulic radius. The effect ofvariation in width is eliminated by using meanvelocity. Figure II.1.29 shows most of the samemeasurements for Huerfano River as were plottedin Figure II.1.28, replotted on the basis of velocityand hydraulic radius. Measurements for this streamwith a hydraulic radius greater than 0.3 metresdefine a single curve with bed forms correspondingto the upper regime. Measurements in thetransition range from dunes to plane bed scatterwildly as would be expected from the previousdiscussion.The discontinuity in the depth discharge relation isfurther illustrated in Figure II.1.30 which shows aplot of hydraulic radius against velocity forRio Grande near Bernalillo, New Mexico, UnitedStates. The measurements plotted on the left representbed configurations of ripples and dunes and thecurve on the right represents bed configurations ofplane bed, standing waves or antidunes.According to Dawdy (1961) the curve representingthe upper regime in a true sand bed stream usuallyfits the following relation:HYDRAULIC RADIUS, IN METRES10.80.70.60.50.40.30.20.10.3 0.4 0.5 0.6 0.7 0.8 1 2 3VELOCITY, IN METRES PER SEC**ON**DFigure II.1.29. Relation of velocity to hydraulicradius for Huerfano River near Undercliffe,Colorado, United States.From Dawdy (1961)shown that the exponent of R ranges from 2/3 as inthe Manning equation, to 1/2, the larger exponentsbeing associated with the coarser grain sizes.V = kR 1/2 (1.15)where V is the mean velocity; k is a constant andR is the hydraulic radius.He found this relation to be applicable for 26 of the27 streams used in his study. More recent study has1.14.3 Development of discharge ratingPlots of mean depth or hydraulic radius againstmean velocity or discharge per foot of width arevaluable in the analysis of stage-discharge relations.These plots clearly identify the regimes of bedconfiguration and assist in the identification of

II.1-38manual on stream gaugingHYDRAULIC RADIUS, IN METRES210.80.60.50.40.3Standing waves or antidunes0.20.3 0.4 0.5 0.6 0.8 1 2 3VELOCITY, IN METRES PER SEC**ON**DFigure II.1.30. Relation of velocity to hydraulicradius for Rio Grande near Bernalillo,New Mexico, United States. From Dawdy (1961)the conditions represented by individual dischargemeasurements. For example, only thosemeasurements identified with the upper regimeshould be used to define the position and slope ofthe upper portion of the stage-discharge curve.Similarly, only those measurements identified withthe lower regime should be used to define thelower portion of the stage-discharge curve.Measurements made in the transition zone may beexpected to scatter widely but do not necessarilyrepresent shifts in more stable portions of therating.Plots of stage against mean depth and stage againstwidth are also helpful in developing a mean stagedischargerelation and in analyzing the cause ofshifts from the mean relation. In the upper regimethe use of these plots in conjunction with the plotof velocity versus mean depth or hydraulic radiusraised to the 1.5 to 2/3 power, (depending on grainsize) may be useful in establishing a reasonableslope to the upper portion of the stage-dischargerelation.The stage-discharge relation developed by Colby(1960) for Pigeon Roost Creek, Mississippi, UnitedStates, is shown in Figure II.1.31. This stream isabout 22.86 m wide, the banks are relatively stableand the median size of the bed material is 0.4 mm.The mean elevation of the channel bed does notchange appreciably with time or discharge. Thediscontinuity in the stage-discharge relation is veryabrupt. Discharges from 25 to 50 m 3 s -1 may occurat a stage of 1.6 m.According to Colby (1960), stage-discharge relationsmay be expected to have a discontinuityprovided the reach has all of the followingcharacteristics:(a) A bed of uniform and readily shiftingsediment which does not form distinct poolsand riffles;(b) At some flows almost all of the stream-bed iscovered with loose sand dunes;(c) At higher flows the bed of the stream is mostlyplane or has antidunes;(d) The depth of flow at the point of discontinuitymust be great enough so that changes in thestage-discharge relation at the discontinuitycan be distinguished from changes caused bysmall local shifts of the channel bottom;(e) The lateral distribution of depths and velocitiesmust be sufficiently uniform for the bedconfiguration to change across most of thestream-bed in a relatively short time.The above conditions are very restrictive. Manystreams with sand beds have well-developed poolsand riffles at the stage where the discontinuitymight otherwise occur. Streams do not generallyhave uniform sediment sizes; many have largesorting coefficients. A few streams having suitablebed material may never show the discontinuitybecause dunes exist even at the highest flow rates.Others may have such high slopes that the lowerregime cannot be defined by dischargemeasurements because of the shallow depths atwhich the discontinuity occurs. Winding streamsseldom have uniform lateral distribution ofGAUGE HEIGHT, IN METRES3210.90.80.70.60.50.40.3 0.4 0.5 0.6 0.8 1 2 3 4 5 6 8 10 20 30 40 50 100 200 300DISCHARGE, IN CUBIC METRES PER SEC**ON**DFigure II.1.31. Stage-discharge relation forstation 34 on Pigeon Roost Creek, Mississippi,United States. After Colby (1960)

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-39velocity and depths. Some streams have suchgradual or inconsistent transitions between dunesand plane bed that the discontinuity may bedifficult if not impossible to define. Dunes mayexist near the banks at the same time that a planebed exists near the centre of the stream. Thetransition in this case may occur so gradually withincreasing stage that the discontinuity in rating iseliminated. However, at any station where dunesexist at low flows and a plane bed exists at higherflows, there is a major change in bed roughness.Knowledge of the bed forms that exist at each stageor discharge can be very helpful in developing thedischarge rating.1.14.4 Evidence of bed formsEvidence of the bed forms that exist at a given timeat a particular station can be obtained in severalways, a listing of which follows:(a) Visual observation of the water surface willreveal one of several conditions: large boils oreddies, which indicate dunes; a very smoothwater surface, which indicates a plane bed;standing waves, which indicate smooth bedwaves in phase with the surface waves; orbreaking waves, which indicate antidunes.Visual observations of the water surface shouldbe recorded on each discharge measurement;(b) Noting whether the sand in the bed is soft orfirm. A soft bed often indicates lower regimeconditions. The stream-bed during upper regimeflow will usually be firm;(c) Measurements of bed elevations in a crosssection will usually indicate the type of bedforms. A large variation in depths indicatesdunes and a small variation in depths a planebed. The small variation in depths for a planebed(upper-regime) configuration should not beconfused with small variations caused by ripplesor by small dunes, both of which are definitelylower-regime configurations. A large variation inbed elevation at a particular point in the crosssectionduring a series of discharge measurementsindicates the movement of dunes;(d) The amount of surge on a recorder chart mayalso indicate the configuration of the channelbed. Medium surge may indicate dunes, little orno surge may indicate a plane bed, and violentsurge may indicate standing waves or antidunes.The transition from plane bed to dunesduring a recession of discharges may cause asecondary hump on the gauge height trace ifthe transition occurs over a short time period;(e) Relationships which define the occurrence ofbed forms as a function of hydraulic radius,R, in metres, slope, S, mean velocity, V, inmetres per second and median grain size, inmillimeters, are useful in developing dischargeratings. A relationship of this type presentedby Simons and Richardson (1962) is shown inFigure II.1.32.Recent studies suggest that the lower regime of bedforms will occur when the ratio:g2VD41 2d3 250is less than 1 x 10 3 , that the upper regime of bedforms will occur when the ratio is greater than4 x 10 3 and that the bed will be in transition if theratio is between these values. In the ratio, V is themean velocity in metres per second, g is theacceleration of gravity in metres per second, D isthe mean depth in metres and d 50is the mediangrain size in metres.1.14.5 Shifting controlsThe upper part of the stage-discharge relation isrelatively stable if it represents the upper regime ofbed forms. Rating shifts that occur in upper regimeflow can be analyzed in accordance with themethods or principles discussed in previous sectionson rating curve shifts. However, the shift ratingsafter minor stream rises will generally have a strongtendency to parallel the base rating when plottedon arithmetic coordinate graph paper. That is, theequation for each shift curve will differ from that ofthe base rating by a change in the value of e inequation 1.4. The shifts will change on stream risesand will often vary with time between rises. Majorstream rises may also change the value of C inequation 1.4.**STREAM** POWER, 62 RSV43210.80.60.40.30.2Upper regimeDunesTransition0.10 0.2 0.4 0.6 0.8 1.0 1.2MEDIAN GRAIN SIZE IN MILLIMETERSFigure II.1.32. Relation of stream power andmedian grain size to form of bed roughness

II.1-40manual on stream gaugingThe lower part of the rating is usually in the duneregime and the stage-discharge relation variesalmost randomly with time. Frequent dischargemeasurements are necessary to define the stagedischargerelation and for some streams they arenecessary to determine the variation of dischargewith time in the absence of any usable relationbetween stage and discharge. A frequency of threedischarge measurements per week is oftenrecommended, but for some streams even dailymeasurements barely suffice.A mean curve for the lower regime is frequentlyused with shifts as defined by dischargemeasurements. In some instances the shift definedby a single discharge measurement represents onlythe temporary position of a dune moving over apartial section control. A series of dischargemeasurements made at short time intervals overthe period of a day may define a pattern of shiftscaused by dune movement. When discharge isconstant but the stage fluctuates, the changinggauge height trace generally reflects dunemovement.Continuous definition of the stage-dischargerelation in a sand channel stream at low flow is avery difficult problem. The installation of a controlstructure should be considered if at all feasible.1.14.6 Artificial controls for sand channelsWhen conventional weirs are installed in sandchannels they are seldom satisfactory, even whendesigned to be self-cleaning. The principle difficultyis that for such weirs in a sand channel, discharge isdependent not only on water surface elevation, butalso on the bed elevation and flow regime upstreamfrom the structure. A satisfactory weir is one whosestage-discharge relation is unaffected by bedconfiguration. A few successful low water controlshave been designed for use in sand channels. Oneexample is the weir designed for the gauging stationon the Rio Grande conveyance channel nearBernardo, New Mexico, United States (Richardsonand Harris, 1962). That structure will not bedescribed here because generalizations concerningweir shape are meaningless. Each control structuremust be individually designed for compatibilitywith channel and flow conditions that exist at theproposed site for the control. A laboratory modelstudy involving a reach of channel is thereforeneeded for each site investigated. Efforts continueto design low water controls that are both relativelycheap and that have satisfactory operatingcharacteristics when installed in sand channels(Stepanich et al., 1964).ReferencesBailey, J.F., and Ray, H.A., 1966: Definition ofstage-discharge relation in natural channels by stepbackwater analysis. United States Geological SurveyWater-Supply Paper 1869-A, 24 pp.Beckman, E.W., and Furness, L.W., 1962: Flowcharacteristics of Elkhorn River near Waterloo, Nebraska:United States Geological Survey Water-Supply Paper1498-B, 34 pp.Chow, Ven Te, 1964: Handbook of applied hydrology.McGraw Hill Book Company.Colby, B.R., 1960: Discontinuous rating curves for PigeonRoost and Cuffawa Creeks in Northern Mississippi.United States Department of Agriculture.ARS 41.36, 31 pp.Corbett, D.M., et al., 1945: Stream-gauging procedure.United States Geological Survey Water-SupplyPaper 888, 245 pp.Culbertson, J.K., and Dawdy, D.R., 1964: A study offluvial characteristics and hydraulic variables. MiddleRio Grande, New Mexico. United States GeologicalSurvey Water-Supply Paper 1498-F, 74pp.Davidian, Jacob, 1984: Computation of water-surface profilesin open channels. United States Geological SurveyTechniques of Water-Resources Investigations,book 3, Chapter A15, 48 pp.Dawdy, D.R., 1961: Depth-discharge relations of alluvialstreams – Discontinuous rating curves. United StatesGeological Survey Water-Supply Paper 1498-C,16 pp.International Organization for Standardization, 1998:Measurement of liquid flow in open channels –Part 2: Determination of the stage-dischargerelation. ISO 1100-2.Kennedy, E.J. 1984: Discharge ratings a gauging stations.United States Geological Survey Techniques of WaterResources Investigations. Book 3, Chapter A10, 59 pp.Linsley, R.K., Kohler, M.A., and Paulhus, J.L.H., 1949:Applied hydrology. New York, McGraw Hill Book Co.,689 pp.Moore, A.M., 1957: Measuring streamflow under iceconditions. American Society Civil Engineers Proc.Paper 1162, Journal of the Hydraulics Division,Volume 83, No. HY1, pp. 1.12, February 1957.Morlock, S.E., Nguyen, H.T., and Ross, Jerry H., 2002:Feasibility of Acoustic Doppler Velocity Meters for theproduction of discharge records from United StatesGeological Survey streamflow-gaging stations.United States Geological Survey Water ResourcesInvestigations Report 01.4157.Rantz and others, 1982: Measurement and computationof streamflow. Volume 1 – Measurement of stage anddischarge. United States Geological Survey WaterSupply Paper 2175, pp 1.284.Rantz and others, 1982: Measurement and computationof streamflow. Volume 2 – Computation of discharge.

Chapter 1. Discharge ratings using simple stage-discharge relationsII.1-41United States Geological Survey Water SupplyPaper 2175, pp 285-631.Richardson, E.V., and Harris, D.D., 1962: A control structurefor measuring water discharge and sediment load. UnitedStates Geological Prof. Paper 450-D, pp. 182-184.Shearman, J.O., 1990: User’s Manual for WSPRO –A computer model for water surface profile computations.Federal Highway Administration PublicationNo. FHWA-IP-89-027, 177 pp.Simons, D.B., and Richardson, E.V., 1962: The effect ofbed roughness on depth-discharge relations in alluvialchannels. United States Geological SurveyWater-Supply Paper 1498-E, 26 pp.Stepanich, F.C., Simons, D.B., and Richardson, E.V.,1964: Control structures for sand-bed channels.ASCE Proc. Paper 3895, Waterways and HarboursDivision Journal, Volume 90, No. WW2, pp. 1.18,May 1964.

Chapter 2Discharge Ratings using the velocity index method2.1 IntroductionDischarge ratings using the velocity-index methodhave been used for many years on streams wherevariable backwater hinders or prohibits the use of asimple stage-discharge rating to compute streamdischarge. The first applications were used with adeflection (vane) gauge, or in some cases a mechanicalcurrent meter, to determine a continuous record of avelocity index at a point in the stream. Laterapplications used electronic devices such as anultrasonic point velocity meter or electromagneticpoint velocity meter. Each of these methods ofobtaining a continuous record of an index of meanstream velocity at a point are described in Chapter 8of Volume I and will not be repeated in this chapter.In recent years, the velocity-index method of creatingratings and computing records of stream dischargehas become more prevalent, due to the increase inuse of hydroacoustic current meters installed atgauging stations. While the method is discussedmainly in the context of acoustic meters, the methodcould in theory be applied to any instrumentationthat measures water velocities, including deflectionvanes, impellor-type fixed meters and electromagneticmeters. This chapter will illustrate the use ofhydroacoustic current meters where the velocityindex for a segment of the stream is recorded. Thedevelopment of the velocity-index rating is basicallythe same for all methods, and that is the primarypurpose of this chapter. In addition, this chapter willprovide an illustrative example of the method andpresent some considerations for using the method,such as sources of error.2.2 Basics of the velocityindex methodIn the velocity-index method, the water velocitymeasured by a hydroacoustic current meter in aportion of a river can be used as an index for themean-channel velocity. Mean-channel velocitiescomputed using velocity-index methods togetherwith the cross-sectional area of the channel can beused to generate records of river streamflow.Hydroacoustic current meters commonly used forvelocity-index applications include Acousticvelocity meters (AVMs), Acoustic Doppler VelocityMeters (ADVM) and Acoustic Doppler Profilers(ADP). Chapter 6 in Volume I contains moredetailed descriptions of these instruments and thetheory of their operation. The velocity that ismeasured by the instrument and used as anindependent parameter in the velocity-index ratingis called the velocity-index. This chapter willillustrate the method by using the ADVM as theinstrument for measuring the velocity index.The velocity-index method can be summarized asfollows:(a) A hydroacoustic current meter is installed ina river where it measures water velocity on acontinuous basis for a portion of the channel:(i) AVMs measure velocity that can be theline velocity from one acoustic path orfrom multiple acoustic paths. For example,if the horizontal angle of flow in thechannel is constant, the AVM line velocityfrom one acoustic path may be sufficientto accurately index mean velocity. If thehorizontal angle of flow in the channelchanges over time, using the average ofAVM line velocities from both acousticpaths of a cross-path configuration maybe a more accurate index of mean velocitythan the velocity from a single path;(ii) ADVMs measure velocities in a samplevolume. The ADVM-measured velocityused to index mean velocity is usually thesample volume downstream componentof velocity. If an ADVM is equipped withmultiple sample volumes, the averagedownstream component of velocity frommore than one sample volume can beused to index mean velocity;(iii) Profilers measure velocities in uniformlysizedcells or bins along the acousticbeams. By measuring velocities in anumber of bins across a channel orvertically through the water column,these instruments produce horizontalor vertical water velocity profiles, hencethe designation profiler. The profilermeasuredvelocity used to index meanvelocity can be the velocity measured inone or multiple bins.(b) Velocity and various current meter performanceand quality-assurance data are recorded by the

II.2-2manual on stream gaugingcurrent meter in internal memory or are loggedby an Electronic Data Logger (EDL). Somehydroacoustic current meters can measurestage acoustically, or stage can be measured bya separate stage sensor;(c) A cross-section, called a standard cross-sectionis surveyed near the current meter installation.The standard cross-section is used to developa relation between stage and channel area,called a stage-area rating. The channel areacomputed from the stage-area rating will beused, with mean-channel velocity, to computedischarge;(d) Discharge measurements are made while stageand velocity-index are measured and recorded.The average stage and average index-velocityare computed for each discharge measurement.The stage-area rating is used to computechannel area (A) from the average stage (S). Themeasured discharge divided by the channelarea computed from the stage-area rating yieldsaverage mean velocity (V) for the dischargemeasurement. The channel area is alwayscomputed for the standard cross-section, usingthe stage-area rating;(e) Each discharge measurement produces a meanchannel velocity (V) and velocity-index (V i).After multiple measurements have been made,a relation between V and V iis developed;the relation is called a velocity-index rating.Velocity-index ratings are commonly developedby first creating scatter plots with V as theordinate (y axis) variable and V ias the abscissa(x axis) variable. A line or curve is fitted to theplotted points. The line or curve is the velocityindexrating. Many velocity-index ratings canbe represented as a mathematical formula (theequation of the plotted line or curve). Singleparameterratings have one independentvariable (V i) used to compute V. Velocityindexratings can also have more than oneindependent variable (such as V iand S) and arecalled multi-parameter or complex ratings;(f) Discharge (Q) is computed from the equationQ = VA. V is computed from application of thevelocity-index rating to V iand A is computedfrom application of the stage-area rating to S.Some countries have been using a similar method,in which one of the two verticals (one on each sideof the cross-section) where, based on previousmeasurements, the average velocity in the verticalis known to be approximately equivalent to theaverage velocity in the whole section, is identified.Once the average velocity in this vertical iscalculated, by simply multiplying its value by thearea of the cross section, a good estimate of thedischarge passing through the cross-section can beobtained.2.3 Stage-area rating developmentA stage-area rating is one of the two ratings neededfor computing discharge records using the velocityindexmethod. The stage-area rating is used toobtain a rated area for a given stage at the streamgauging station. It should be developed based ondata collected at a fixed cross-section in the stream(also referred to as the standard cross-section). Thestandard cross-section should be located near thevelocity-index gauge, if possible, and it should be areasonably stable cross section. Periodic surveys ofthe standard cross section should be made to checkfor changes in channel geometry and therefore thestage-area rating.Several different instruments may be used forsurveying the standard cross-section, including:(a) Level and stadia rod;(b) Tagline;(c) Depth soundings with a sounding rod orsounding weight;(d) Echo sounder with surveying software;(e) Acoustic Doppler Current Profiler (ADCP).ADCPs are convenient for surveying channeldepths, however they were not designed as echosounders and can be difficult to calibrate for precisedepth soundings. Use a tagline if possible, to providetransects that are approximately perpendicular tothe flow. Make the ADCP transect straight acrossthe channel. Calibrated echo sounders used inconjunction with differential GPS and hydrographicsurveying software are useful for obtaining accuratechannel geometry.Important considerations include the following:(a) The cross-section must be referenced to stage atgage datum;(b) Make sure that the survey extends above themaximum expected stage;(c) Periodically check for channel changes – evenupstream or downstream of the standard crosssection. When computing mean channelvelocity (V) for a discharge measurement fordevelopment or checking of a velocity-indexrating, always compute V using the area fromthe stage-area rating.Stage-area ratings can also be developed by plottingstage versus area and then fitting a curve to thestage-area points. The curve can be fitted by multiple

Chapter 2. Discharge Ratings using the velocity index methodII.2-3or curvilinear regression techniques or drawn byeye. The resulting stage-area rating curve can berepresented in a discharge processing program as atable or an equation of the curve.2.4 Velocity index ratingdevelopmentA velocity-index rating represents the relationbetween the velocity-index and concurrent meanvelocity of discharge in the standard cross section.It is important to note that the mean velocity of thedischarge measurement is computed using thecross-section area from the standard cross section,and not the cross-section area of the dischargemeasurement. In the following paragraphs this willbe referred to as mean velocity. Also note that inthe following paragraphs the ADVM is referred to asthe instrument for measuring the velocity-index.This is just for convenience. The velocity-index canbe obtained from other instruments such as theAVM or velocity profiler.A number of discharge measurements throughoutthe expected range in stage are required to developa velocity-index rating. This rating provides themethod for computing mean velocities from theindex velocities recorded at a station.Various methods can be used to develop a velocityindexrating. For example, a velocity-index ratingcould be a single coefficient to relate velocity-indexto mean velocity, provided the range in stage at thestation is not large. Other ratings could be morecomplex, particularly at stations with bidirectionalflow or a large range of stage. For stations with alarge range of stage, stage may be a factor in thecomputation of mean velocities from indexvelocities. The velocity-index rating must bedeveloped individually for each station based onmeasured data.Common practice in developing velocity-indexratings is to plot the mean velocity and ADVMvelocity-index from a series of measurements on anx-y plot, where the y-axis represents mean velocityand the x-axis represents ADVM velocity-index.This plot is the start of the analysis of the relationbetween mean velocity and ADVM velocity-index.With this plot and knowledge of the hydraulics atthe station, a velocity-index rating can be developed.For some stations, the relation may be linear. Forothers, the relation may best be described ascurvilinear or as a compound curve. The relationbetween ADVM velocity-index and mean streamvelocity can be used simply as a graphical rating oras a tabular rating.If the relation between mean velocity and ADVMvelocity-index is linear, it can be defined by a linearequation as shown in equation 2.1:V = C V + C1 i 2 (2.1)where V is the mean velocity at the standard crosssection; V iis the velocity-index measured by theADVM, and C 1and C 2are constants.If the relation between mean velocity and ADVMvelocity-index is curvilinear, a second orderequation of the following form may be used:2V = C V + C V + C3 i 4 i 5where C 3, C 4, and C 5are constants.(2.2)If enough data are available equation 2.2 can bedefined by a least squares solution. In some cases,stage may also be a factor in the relation betweenADVM velocity-index and mean velocity. If this isthe case, a multiple linear regression can be used todefine the relation. However, a considerable amountof data will be required throughout the full range ofstage and velocity to define a significant equation.The equation for a multiple linear regressionequation where velocity index (V i) and stage (S) areindependent variables will take the form shown inequation 2.3:V = C V + C SV + C6 i 7 i 8 (2.3)where C 6, C 7, and C 8are constants.The basic process of developing the rating can besummarized as follows:(a) Create a table summarizing the measurementdata, including measurement number, date,mean gage height, discharge, the rated area (A)from the stage-area rating, mean velocity (V),and velocity index (V i) for each measurementand any remarks. A computer spreadsheetprogram is a convenient tool for listing, plottingand analyzing the data;(b) Plot the data. Create plots of mean channelvelocity (V) and the velocity index (V i) forevaluating the velocity-index relation forlinearity. Plot V on the ordinate and V ionthe abscissa. If the only independent variablerequired to accurately compute mean velocityis velocity-index, a single parameter equationsuch as equation 2.1 may be used. If the velocityindexrelation is not linear then a graphical or

II.2-4manual on stream gaugingtabular method may be used to compute meanvelocity;(c) If the plot indicates that stage (S) or other variablemight be a significant variable, then least-squaresmultiple linear regression can be used to define theequation, similar to equation 2.3 (Sloat and Gain,1995). Additionally, the residuals (unexplainederror) from the resulting regression equationcan be evaluated to determine if a significantrelation exists between the response variable(mean velocity) and independent variable(s) andif the response variable is adequately estimated.Least-squares multiple linear regression and theanalysis of residuals are described, for instance,by Draper and Smith (1982);(d) Assess the linear regressions defined in steps 2or 3 using the following:(i) Correlation coefficient (R-square). TheR-square should be about 0.95 or greater.If R-square is approximately 0.90 or less,determine whether a multi-parametervelocity-index rating with V iand stage (S)improves the velocity-index rating;(ii) Standard error (SE). The SE is an overallindicator of the error of the velocityindexrating. The lower the SE, the moreaccurate the rating;(iii) Residual plots. Plots of the regressionresiduals should be approximately random,indicating no patterns or trends. Outlierson these plots should be checked carefullyfor measurement errors or irregularities invelocity-index data.(e) At the stage (water surface elevation) where flowgoes over bank, the rating will likely change. Inthis case a compound rating may be necessary(that is one equation for flows within thechannel and a separate equation for over bankflow). It will likely be necessary to input such arating in tabular form in discharge processingsoftware.Experience has shown that the single or multiplelinear relations are often applicable for velocityindexratings. Velocity-index ratings documentedin Sloat and Gain (1995) and Morlock and others(2002) were all linear. Ruhl and Simpson (2005)stated that a wide range of relations have beendeveloped in the San Francisco Bay and Delta regionmost of which are linear (Figure II.2.1(a)). However,Ruhl and Simpson (2005) found that more complexratings also are possible. They documented severalhigher-order polynomial ratings (Figure II.2.1(b));loop ratings that are indicative of ebb-floodasymmetries in the current structures at themeasurement location causing a different relationbetween the flood-to-ebb transition versus theebb-to-flood transition (Figure II.2.1(c)) andoccasionally a bimodal relation (Figure II.2.1(d)).While a single parameter linear velocity-indexrating would be easy to input as an equation in adischarge processing program, multiple parameterlinear ratings or complex ratings such as thosedescribed by Ruhl and Simpson (2005) may presenta greater challenge. In these instances ratings mightbe input by using tables, approximated usingsimpler equations or processed outside of theprocessing program using spreadsheets ormathematical processing programs. The output ofthese programs, mean velocity, could then be inputinto the discharge processing software so thatdischarge can be computed.2.5 Discharge computation2.5.1 GeneralDischarge (Q) is computed from the equationQ = VA in the following manner:(a) Recorded values of stage are quality assuredand appropriate corrections are made asdocumented in Section 6.5 of this Manual. Thecomputed stages are then input to the stagearearating to compute area, A;(b) Recorded values of velocity-index are qualityassured, appropriate corrections are made, andthe values are then input to the velocity-indexrating (stage may also be a input parameter formultiple parameter ratings). The output fromthe velocity-index rating is mean velocity, V;(c) For each recorded (unit) value of stage andcorresponding velocity-index, a computed unitvalue discharge, Q, is produced by multiplyingthe area, A, times the mean velocity, V. Dailymeandischarges are computed from the meanof the unit value discharges in a one dayperiod.The records of stage and velocity data are verifiedand edited as described in Section 6.5 of thisManual. Unit value plots are very useful foranalyzing the velocity data, as are various instrumentquality assurance parameters such as ADVM signalstrength. The instrument quality assuranceparameters vary from instrument to instrument;the instrument manuals should be consulted todetermine the availability and use of qualityassurance and diagnostic parameters.Common experience has found that it is usuallydifficult or impossible to correct velocity data from

Chapter 2. Discharge Ratings using the velocity index methodII.2-52.521.510.5(a)Number of data points = 365Correlation coefficient = 0.999Squared correlation coefficient = 0.998Regression significant at < 0.001 levely = 0.8054* x + 0.0265RMS error of prediction = 0.06633210(b)Number of data points = 136Correlation coefficient = 0.998Squared correlation coefficient = 0.997Regression significant at < 0.001 levely = 0.06238* x 2 + 2.088* x + 0.1464RMS error of prediction = 0.09180– 1Mean velocity, in feet per second– 0.5– 1– 1.5– 2– 2.5– 4 – 3 – 2 – 1 0 1 2 33210– 1– 2– 3(c)RATING A-FLOOD TO EBB:Number of data points = 74Correlation coefficient = 0.999Squared correlation coefficient = 0.999Regression significant at < 0.001 levely = – 0.0374* x 2 + 0.9241* x – 0.0177RMS error of prediction = 0.0571Note: Use Flood to Ebbrating for index velocitiesgreater than: 2.428less than: – 1.097RATING B-EBB TO FLOOD:Number of data points = 60Correlation coefficient = 0.999Squared correlation coefficient = 0.999Regression significant at < 0.001 levely = – 0.0179* x 4 + 0.0354* x 3 +0.0987* x 2 + 0.7551* x – 0.2943RMS error of prediction = 0.0603– 3 – 2 – 1 0 1 2 3 4– 2– 3– 4– 5– 2.5 – 2 – 1.5 – 1 – 0.5 0 0.5 110.80.60.40.20– 0.2– 0.4– 0.6(d)UPPER RATING:Number of data points = 41Correlation coeffcient = 0.978Squared correlation coefficient = 0.957Regression significant at < 0.001 levely = 0.6532* x + 0.0474RMS error of prediction = 0.0553Intersection: – 0.0326LOWER RATING:Number of data points = 66Correlation coefficent = 0.968Squared correlation coefficient = 0.937Regression significant at < 0.001 levely = 1.9326* x + 0.0891RMS error of prediction = 0.0503– 0.8– 0.6 – 0.4 – 0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4Index velocity, in feet per secondRegression curveCalibration dataFigure II.2.1. Examples of velocity-index versus mean velocity ratings: (a) simple linear rating;(b) quadratic rating; (c) loop rating and (d) bi-modal ratingADVMs. A common example is a low-velocity biascaused by a fixed object in the ADVM samplevolume. The resultant velocity error is not usually aconsistent bias error that could be fixed with theapplication of a simple velocity correction or shift,but instead the error shows a random pattern. Shiftapplications are however possible for the velocityindexmethod. For example, a change in channelgeometry can change the stage-area and velocityindexratings. If this condition is temporary, it canbe handled by a shift adjustment. It is commonpractice to represent the adjustment as a velocityshift (rather than a stage shift that would cause ashifted area computation). The shift used in thisexample should only be used until the channel isresurveyed at the standard cross section. At thattime, a new stage area rating and velocity-indexrating should be developed. Section 6.10 discussesthe application of shifts for velocity-indexmethods.2.5.2 Mean discharge at tidally affectedsitesVelocity-index rating methods are often used atcoastal gages where flow is affected by tidalfluctuations. Individual unit values of discharge arecomputed just as described in the precedingparagraphs. However, tidal affects need to be takeninto account when computing mean daily discharges.Ruhl and Simpson (2005) discuss these considerationsfor several stations in the San Francisco Bay and

II.2-6manual on stream gaugingDelta, United States of America where the velocityindexmethod was used to compute discharges attidally affected gauges.Calculating daily discharge in a tidally influencedenvironment cannot be accomplished simply byaveraging all of the values collected during a24-hour period. Simple averaging causes cyclicalvariations, or aliasing, in the data that are spuriousand are a function of the averaging scheme, not thedata. Therefore, a low-pass filter is used to removefrequencies that have periods less than 30 hours.The most energetic variations removed in thisprocess are the astronomical tides (typically withperiods at or around 12 and 24 hours); however,other variations (meteorological, hydrologic oroperational) that have periods less than 30 hoursalso are removed. A number of filters are availableincluding the Godin filter (Godin, 1972), a Fouriertransform filter (Walters and Heston, 1982; Burauand others, 1993) or a Butterworth filter (Robertsand Roberts, 1978). All of these filters have beenused in the San Francisco Bay and Delta Programfor a variety of purposes, however, published dailydischarge values, as shown by the red lines inFigure II.2.2 are calculated using a Butterworth filterwith a 30-hour stop period and a 40-hour passperiod. Note that tidal variations with periodsgreater than 30 hours, such as spring/neap cycleeffects, will remain in the resulting tidally averageddata (Roberts and Roberts, 1978). In addition,approximately 2 days of filtered data at thebeginning and end of the time-series or adjacent toany gap in the time-series are erroneous due to filterringing and are not used. The daily discharge iscalculated as the 24-hour daily average of the tidallyfiltered data, as shown by the black line with opencircles (Plot B) in Figure II.2.2.2.5.3 Discharge records duringice-affected periodsDuring ice-affected periods, a simple stage-dischargerating often is not reliable because the ice will causestages to rise without a corresponding rise indischarge. During such periods, the discharge recordis usually estimated using methods described inChapter 1. The estimation is aided if one or moredischarge measurements were made during theperiod. Otherwise, comparisons with thehydrographs of other stations in conjunction withweather data must be used to estimate the record.Estimated records during ice periods are subjectiveand usually are rated poor.ADVMs may allow for less-subjective estimates ofdischarge during ice-affected periods. TheDischarge, in cubic feet per second30 00020 00010 0000– 10 000– 20 000– 30 000– 40 0000– 1 000– 2 000– 3 000– 4 000– 5 000(a)(b)Tidal dischargeCalculated daily dischargeFebruary 2003Filtered dischargeFiltered dischargeFigure II.2.2. Example of tidal discharge record.Plot (a) is tidal discharge (blue) and filtereddischarge (red). Plot (b) is daily average discharge(black) and filtered discharge (red)Note: These plots are from Ruhl and Simpson (2005)and are in English units.following example was taken from Morlock andothers (2002). An ADVM discharge was computedduring a discharge measurement made at theIroquois River gauging station when the river wastotally ice covered. The measurement yielded adischarge of 1.119 m 3 s -1 . The ADVM computeddischarge during the measurement period was1.444 m 3 s -1 , a difference of 29 per cent.Measurement notes indicated the average icethickness was 0.15 m, and when holes werechopped in the ice to make the measurement, thewater level came to the top of the ice. This resultmeans that the river was under pressure and thatthe channel area used to compute the ADVMdischarge was based on a stage that was about0.15 m high. When the channel area wasrecomputed manually for a 0.15 m lower stage,the ADVM discharge for the measurement periodwas recomputed at 1.206 m 3 s -1 , 7.8 per centhigher than the measurement discharge. Becauseof the rough underside of the ice, the velocityprofile usually is different than when the surfaceis free of ice. Rantz and others (1982) recommendthat for velocities sampled at 60 per cent of thedistance from the bottom of ice to streambed, acoefficient of 0.92 should be applied to estimatethe mean velocity. By adjusting the ADVMmeasured velocity by multiplication of 0.92 adischarge of 1.110 m 3 s -1 was computed, which iswithin 1 per cent of the measured discharge.

Chapter 2. Discharge Ratings using the velocity index methodII.2-7A more rigorous approach to estimates of dischargeduring ice-affected periods is described by Wang(2000). Flow-distribution models for derivingstation-specific equations are used to computedischarges from AVM velocities during periods ofchannel ice cover. In this approach, bed-roughnessand ice-roughness parameters are estimated fromvelocity profiles collected at a station. A hydraulicparameter is determined from cross-section areaand locations of the AVM transducers. A betacoefficient is computed from the roughness andhydraulic parameters. The AVM velocity ismultiplied by the beta coefficient which yields adischarge for a particular stage. The beta coefficientcan be expressed as a function of stage through aregression analysis. Thus, discharge becomes afunction of stage and AVM velocity. Dischargescomputed from this method compared closely todischarge measurements made at AVM stations inCanada during ice periods (Wang, 2000). Dischargescomputed from Wang’s methods, althoughdeveloped for AVM stations, can be applied directlyto ADVMs as well. Whether using a simplecoefficient or Wang’s approach, the stage of thebottom of the ice needs to be known. One way toestimate the stage of the bottom of the ice is to usean ADVM equipped with an upward looking stagetransducer.in the station instrument shelter. The cable allowedthe ADVM to be interfaced for programming andallowed the EDL and ADVM to communicate, usingView, looking upstreamFlow2.6 Example ADVM velocity-indexsiteThis example of an ADVM velocity-index station isbased on a report by Morlock and others (2002) forthe United States gauging station Iroquois Rivernear Foresman, Indiana. Tables and illustrationswere taken directly from Morlock’s report whichwas published in English units of measurement,which are retained for this Manual. An Argonaut-SLADVM was installed at the gauging station inSeptember 1999. The range of expected flows wouldbe contained by the main channel where the ADVMsamples velocities. Figure II.2.3 shows a photographof the gauging site and a sketch of the instrumentlayout. Selected river characteristics are given inTable II.2.1.A custom mount for the ADVM was constructedand attached to a downstream highway bridge pierfor protection from debris. The ADVM was mountedat a depth of about 1 metre (at median flow) on agalvanized steel and aluminum frame designed forstrength and weather resistance. The mount wasdesigned so that the ADVM could be pulled up formaintenance and was connected by cable to an EDLADVMAcoustic beamSamplevolumeHighway bridgeInstrumentShelterPierNot to scaleFigure II.2.3. Photograph and site sketch ofIroquois River near Foresman, Indiana,United States, ADVM velocity-index stationTable II.2.1. Selected river characteristics for theIroquois River near Foresman, Indiana,United StatesMean discharge, m 3 s -1 11.61Median discharge, m 3 s -1 5.61Maximum discharge, m 3 s -1 167.9Discharge range, m 3 s -1 167.8Peak stage, m 6.4Stage range, m 6.4Channel width, m 23.8Mean channel depth, m 1.829

II.2-8manual on stream gaugingVELOCITY IN FEET PER SEC**ON**D1.301.251.201.151.101.051.000.501 minute a.i. 10 minute a.i.Figure II.2.4. ADVM velocity unit values showingthe effect of increasing the ADVM averaginginterval from 1 to 10 minutesthe SDI-12 communications protocol. The EDL alsologged stage data from a separate stage sensor.Following installation, the ADVM software wasused to examine signal strengths for spikes so thesample volume end could be programmed. Thesample volume or cell size was programmed so thatno known obstacles were in the sample volume orcell and so that the end of the sample volume waspositioned in such a way that signal strength was atleast five counts above the instrument-noise level.The start and end distances for the sample volume,as measured from the ADVM transducer, was 1 and8 metres, respectively. The start of the samplevolume was beyond the estimated extent of thebridge-pier wake-turbulence zone.After installation, the velocity-averaging intervalwas programmed at 1 minute. The EDL wasprogrammed with a sampling interval of15 minutes; that is, every 15 minutes the EDLwould command the ADVM to sample. Uponcompletion of the ADVM-averaging interval, theEDL was programmed to log ADVM parameterssuch as velocities, beam amplitudes and qualityindicators. Thus, an ADVM velocity was the1-minute average velocity measured by the ADVMlogged every 15 minutes.The velocity-averaging interval was later increasedfrom 1 to 10 minutes. This interval increased thetime that velocities were being sampled from 7 to67 per cent. Increasing the sampling time loweredrandom ADVM velocity variations from sample tosample by as much as 100 per cent, as shown inFigure II.2.4. Because velocity unit-value variationswere reduced and velocities were being sampled agreater percentage of the time, velocity anddischarge uncertainties from short-time scalefluctuations were reduced.2.6.1 Development of stage-area ratingThe stage-area rating was developed by firstsurveying the cross section at the downstream sideof the bridge where the ADVM was attached. Thecross section was a trapezoid in which all flows werecontained. The cross-section survey was completedusing a steel measurement tape referenced to thelow chord of the bridge to measure elevations and asteel tape for distance measurement. The resultingsurveyed cross section had an irregular bottom andsloping sides; from this surveyed cross section, thestandard cross section was developed as shown inFigure II.2.5. A tabular rating was developed for astage range of 2 to 24 ft at shown in Table II.2.2.Linear interpolation was used between the recordedvalues.Table II.2.2. Stages and computed channel areas for the ADVM station,Iroquois River near Foresman, Indiana, United StatesStagemChannelArea, m 2StagemChannelArea, m 2StagemChannelArea, m 20.610 3.99 3.048 54.53 5.486 138.40.914 8.45 3.353 63.17 5.791 151.21.219 13.47 3.658 72.37 6.096 164.61.524 19.04 3.962 82.12 6.401 178.51.829 25.08 4.267 92.34 6.716 192.92.134 31.68 4.572 103.0 7.010 207.82.438 38.74 4.877 114.4 7.315 223.22.743 46.36 5.182 126.2 – –

Chapter 2. Discharge Ratings using the velocity index methodII.2-9Stage in feet stationLeft hand2624222018161412108642Right hand00 20 40 60 80 100 120 140 160 180Station in feetFigure II.2.5. Surveyed and standard crosssections for Iroquois River near Foresman,Indiana, United States2.6.2 Development of velocity-index ratingEighteen discharge measurements, 521 to 544, weremade at the Iroquois River evaluation station.Fourteen of the measurements shown in Table II.2.3,were used to construct an index velocity rating.Measurement 523 was not used to construct therating because the river was ice covered when themeasurement was made; measurement 527 was notused because pertinent measurement data were notavailable at the time the rating was created. For the14 measurements, stages ranged from 4.23 to12.24 feet (1.289 to 3.731 metres) and measurementdischarges ranged from 25.3 to 988 ft 3 s -1 (0.716 to27.98 m 3 s -1 ). Mean channel velocities computedfrom the measurements ranged from 0.27 to1.48 ft s -1 (0.082 to 0.451 m s -1 ). The Argonaut-SLx- component of velocity was used for developmentof the index velocity rating.Plotting ADVM and mean velocities indicated thata well-defined linear relation between ADVMmeasuredvelocities and mean velocities is presentwithin the range of stages and discharges representedby measurements 521 to 536 (Figure II.2.6). As aresult, the relation between ADVM-measuredvelocities and mean velocities could be representedby fitting a straight line to the data.A linear regression was performed in which the14 mean channel velocities, V, computed from the14 discharge measurements were regressed againstthe corresponding ADVM index velocities, V i. Allmeasurements were weighted equally in theanalysis. The equation of the line is:V = 0.97 V i− 0.10(2.4)The r 2 for the regression was 0.98, and the standarderror was 0.05 ft s -1 , which is 5.9 per cent of theTable II.2.3. Summary of discharge measurements for the Iroquois River near Foresman,Indiana, United StatesMeasurementsStage Discharge Mean VelocityDateRatedNumbermm 3 s -1m s -1521 15/10/1999 Fair 1.289 0.716 0.082522 16/12/1999 Poor 1.676 2.688 0.155523 2/2/2000 Fair 1.475 1.119 –524 1/3/2000 Good 2.499 9.006 0.268525 6/4/2000 Fair 1.753 3.172 0.192526 24/4/1999 Good 3.264 16.029 0.268527 9/5/2000 – 2.121 5.749 –528 10/5/2000 Fair 3.280 20.305 0.399529 10/5/2000 Fair 3.328 21.013 0.381530 11/5/2000 Fair 3.359 19.767 0.351531 11/5/2000 Fair 3.353 20.390 0.347532 11/5/2000 Fair 3.331 18.266 0.335533 11/5/2000 Fair 3.313 18.238 0.332534 7/6/2000 Good 2.530 9.884 0.287535 21/6/2000 Fair 3.511 27.980 0.451536 26/6/2000 Fair 3.731 21.891 0.335

II.2-10manual on stream gaugingMEAN VELOCITY, IN FEET PER SEC**ON**D21.81.61.41.210.80.60.40.2Index velocity rating from least squares regression+ 525 Discharge-measurement number+521++525522526+++00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2ADVM VELOCITY, IN FEET PER SEC**ON**Daverage of the mean velocities (0.85 ft s -1 ) computedfrom the 14 measurements used in the regressionanalysis. The r 2 of 0.98 indicated that 98 per cent ofthe variation in mean velocities was accounted forin variations of the ADVM velocities. Therefore itwas assumed that, within the range of dischargemeasurements used to produce equation 2.4, stagewas not a factor. The residual plot from the regressionanalysis did not indicate nonlinearity, non-constantvariances, or large outliers. Equation 2.4 was foundto be an adequate fit of the measurement data andbecame the velocity-index rating.Computed discharges and measured discharges forthe 14 discharge measurements used to develop theratings are compared in Table II.2.4. Also, measureddischarges and ADVM discharges for four dischargemeasurements (537 to 540) made after the ratingswere developed are compared in Table II.2.4. Exceptfor measurements 525 and 526, all 18 dischargemeasurements were within 10 per cent of theADVM discharges.2.7 Velocity index error sources524529+ 531 +528530533 + ++ 532 and 536Figure II.2.6. Index velocity rating for an ADVMat gauging station for the Iroquois River nearForesman, Indiana, United StatesAs in any method of discharge computation,velocity-index methods have associated errorsources that subsequently affect the quality of the534+535discharges computed with the methods. Sloat andGain, 1995 analyzed error for velocity-indexmethods and found that:(a) Uncertainty in estimates of instantaneous andmean daily discharge is produced by randomand systematic errors. Three principal sourcesof error in the estimated discharge can beidentified:(i) Instrumental errors associated withmeasurement of area and velocity-index;(ii) Biases in the representation of meandaily stage and velocity due to naturalvariability in these over time and space;(iii) Errors in cross-sectional area and meanvelocityratings based on stage andvelocity-index;(b) In practice, instrumental errors in stage andvelocity measurements tend to be small andappear to be randomly distributed;(c) Errors in sample representation tend to beperiodic and may induce bias in dischargecomputations over short periods of time, butincreasing the number of observations and thelength of the computational period tend toimprove representation;(d) The errors in cross-sectional area ratingsgenerally are relatively small because stageand cross-sectional area are relatively easy tomeasure and verify on a consistent basis;(e) The largest single source of error remaining indischarge computations is uncertainty in thevelocity-index rating.Ruhl and Simpson (2005) discuss the importance ofand potential errors associated with the collectionof field data for velocity-index rating development.It is particularly critical in tidal systems where thetidally averaged flows are desired. Often tidallyaveraged flows are several orders of magnitudesmaller than instantaneous tidal flows; therefore, arelatively small bias in the tidal flows can become asubstantial error in the tidally averaged data. Clocksynchronization, channel-bottom movement, boatpositioning, discharge measurement duration (toofast or too slow), configuration file settings andequipment positioning all can affect the resultingdata. Attention to detail is critical in minimizingproblems during data collection.Duncker and others (2006) applied a first-ordererror analysis to Acoustic Velocity Meter (AVM)data, stage-area, and velocity-index ratings at eachgauging station. The error analysis results indicatethat the uncertainty is sensitive to the value ofuncertainty associated with Acoustic DopplerCurrent Profiler (ADCP) discharge measurementdata. ADCPs are often used for velocity-index rating

Chapter 2. Discharge Ratings using the velocity index methodII.2-11Table II.2.4. Comparison of discharges computed from ADVM to measured discharges forthe Iroquois River near Foresman, Indiana, United StatesDischarge Measurement ADVM Computed PercentNumber Date RatedDischargem 3 s -1Dischargem 3 s -1Difference521 15/10/1999 Fair 0.716 0.651 – 9.1522 16/12/1999 Poor 2.688 2.625 –2.3523 02/02/2000 Fair 1.119 – –524 01/03/2000 Good 9.006 9.176 1.9525 06/04/2000 Fair 3.172 3.653 15.2526 24/04/1999 Good 16.029 13.990 – 12.7527 09/05/2000 – 5.749 – –528 10/05/2000 Fair 20.305 21.750 7.1529 10/05/2000 Fair 21.013 21.212 0.9530 11/05/2000 Fair 19.767 19.654 – 0.6531 11/05/2000 Fair 20.390 19.371 – 5.0532 11/05/2000 Fair 18.266 18.351 0.5533 05/11/2000 Fair 18.238 18.380 0.8534 07/06/2000 Good 9.884 10.110 2.3535 21/06/2000 Fair 27.980 27.527 – 1.6536 26/06/2000 Fair 21.891 21.920 0.1537 12/07/2000 Fair 36.816 36.533 – 0.8538 13/10/2000 Fair 1.020 1.048 2.8539 15/11/2000 Fair 3.427 3.172 – 7.4540 12/02/2001 Fair 59.189 59.189 0.0development and verification because of theunsteady flow condition at many velocity-indexsites. Duncker and others’ findings emphasize theimportance of following recommended proceduressuch as those documented in Volume I whenmaking ADCP measurements.Morlock and others (2002) provides a detaileddiscussion of stage-area and velocity-index ratingsfor three ADVM-equipped gauging stations, one ofwhich is used in the preceding example. Ruhl andSimpson (2005) provide an excellent summary ofall aspects of velocity-index rating development,through examples of real stations and data. Dunckerand others (2006), Sloat and Gain (1995) and Ruhland Simpson (2005) provide more detaileddiscussions of error analysis including equations forestimating errors.ReferencesBurau, J.R., Simpson, M.R, and Cheng, R.T., 1993: Tidaland residual currents measured by an AcousticDoppler Current profiler at the west end ofCarquinez Strait, San Francisco Bay, California,March to November 1988: United States GeologicalSurvey Water-Resources Investigations Report92.4064, 76 p.Draper, N.R., and Smith, Harry, 1982: Applied regressionanalysis. New York, John Wiley & Sons, p. 141–210.Duncker, J.J., Over, T.M. and Gonzalez, J.A., 2006:Computation and error analysis of discharge for theLake Michigan Diversion Project in Illinois: 1997/99Water Years: United States Geological SurveyScientific Investigations Report 2006-5018, 70 p.Godin, P., 1972: The analysis of tides. University ofToronto Press, 264 p.

II.2-12manual on stream gaugingMorlock, S.E., Nguyen, H.T. and Ross, Jerry H., 2002:Feasibility of Acoustic Doppler Velocity Meters for theproduction of discharge records from United StatesGeological Survey streamflow-gaging stations.United States Geological Survey Water ResourcesInvestigations Report 01-4157.Rantz, S.E. and others, 1982: Measurement andComputation of Streamflow. Volume 1 – Measurementof Stage and Discharge. United States GeologicalSurvey Water Supply Paper 2175.Roberts, J., and Roberts, T.D., 1978: Use of the Butterworthlow-pass filter for oceanographic data. Journal ofGeophysical Research, Volume 83, No. C11,p. 5510–5514.Ruhl, C.A., and Simpson, M.R., 2005: Computation ofdischarge using the index-velocity method in tidallyaffected areas. United States Geological SurveyScientific Investigations Report 2005-5004, 31 p.Sloat, J.V., and Gain, S.W., 1995: Application of AcousticVelocity Meters For Gaging Discharge of Three Low-Velocity Tidal Streams in the St. Johns River Basin,Northeast Florida, United States Geological SurveyWater-Resources Investigations Report 95–4230, 26 p.Walters, R.A., and Heston, Cynthia, 1982: Removing tidalperiod variations from time-series data using low-passdigital filters. Journal of Physical Oceanography,Volume 12, No. 1, p. 112–115.Wang, Dapei, 2000: Discharge calculation of naturalchannel flows with AFM data. Proceedings ofthe American Society of Civil Engineers 2000Joint Water Resources Conference, Minneapolis,Minnesota, United States, 10 p.

Chapter 3DISCHARGE RATINGS USING SLOPE AS A PARAMETER3.1 General considerationsIf variable backwater or highly unsteady flow existsat a gauging station, the energy slope is variable ata given stage and the discharge rating cannot bedefined by stage alone. Variable backwater is mostcommonly caused by variable stage at a downstreamconfluence for a given discharge upstream, or bythe manipulation of gates at a downstream dam.The discharge under those conditions is a functionof both stage and the slope of the energy gradient.Where the rate of change of stage is sufficientlygreat, the acceleration head must also be considered,but this chapter deals only with situations wherethe acceleration head is insignificant and can beneglected.The unsteady-flow situation treated in this chapteris that of a natural flood wave, in which the flowmaintains a stable wave profile as it moves downthe channel. That type of wave is known as auniformly progressive wave and it often producesa loop rating at the gauging station. That is, for agiven stage the discharge is greater when thestream is rising than it is when the stream is falling.The difference between the two discharges issignificant only when the flow is highly unsteady.The term highly unsteady, when associated onlywith the property of producing loop ratings, is arelative term, because channel slope is of equalimportance in determining whether or not loopratings will occur. A flood wave in a steep mountainchannel will have a simple stage-discharge relation.That same flood wave in a flat valley channel mayhave a loop rating. The sections of this chapterthat deal with unsteady flow are concerned onlywith loop ratings whose definition requires the useof slope, as well as stage, in a relation withdischarge.When a new gauging station is established, theneed for a slope parameter in the rating can oftenbe anticipated from the rating procedures used forexisting stations nearby in a similar hydrologic andhydraulic environment. At other times the need fora slope parameter is not as evident. However, a plotof a series of discharge measurements made atmedium and high stages will indicate the type ofrating required for the station and will dictatewhether or not an auxiliary gauge is necessary tocontinuously measure water-surfaced slope.If a pair of gauges is needed, the locations of thebase and auxiliary gauges are based on thecharacteristics of the slope reach. The length of thereach should be such that ordinary errors that occurin the determination of gauge heights at stagestations will cause no more than minor error incomputing the fall in the reach. A fall of about0.15 m is desirable but satisfactory records can oftenbe obtained in reaches where the minimum fall isconsiderably less than 0.15 m. Channel slope in thereach should be as uniform as possible. The reachshould be as far upstream from the source ofbackwater as is practicable and inflow between thetwo gauges should be negligible. If possible, reacheswith overbank flow should be avoided, as shouldreaches with sharp bends or unstable channelconditions. If the reach includes a natural controlfor low stages, the upstream (base) gauge should belocated just upstream from that control so that asimple stage-discharge relation will apply at lowstages. Rarely will a slope reach be found that hasall of the above attributes, but they should beconsidered in making a selection from the reachesthat are available for stage sites.3.2 Theoretical considerationsVariable slopes that affect flow in open channels arecaused by variable backwater, changing dischargeor variable backwater in conjunction with changingdischarge. The pair of differential equations givenbelow provides a general solution to both graduallyvaried and unsteady flow:QK22∂H1 ∂V= − −∂xg ∂t(3.1)Q ∂h= −B(3.2)x ∂tIn the above equations, Q is the discharge; K is theconveyance of the cross section; H is the totalenergy head; x is the distance along the channel;g is the acceleration of gravity; V is the meanvelocity; t is the time; B is the top width of thechannel, and h is the water-surface elevation.A solution to these equations in uniform channelsmay be obtained by approximate step methods

II.3-2manual on stream gaugingafter the conveyance term has been evaluated bydischarge measurements.In those practical problems of determining flow inopen channels that require application ofequation 3.1, the increment of slope due to theacceleration head:1 ∂Vg ∂tis, in general, so small with respect to the other twoterms that its effect may be neglected. Thus, inequation 3.1, the terms that remain in addition todischarge Q, are conveyance K which is a functionof stage, and energy gradient H/x which is related towater-surface slope. At those sites where tidal actionor variation in power production cause theacceleration head to be large, an approximatemethod of integration of equations 3.1 and 3.2 isused in computer models of unsteady flow, such asthose that are discussed in Chapter 4.The discussion of stage-fall-discharge ratingspresented in the following sections draws heavilyon previously published reports. The three primaryreferences used are Corbett and others (1945),Eisenlohr (1964), Mitchell (1954), Rantz (1982),Kennedy (1984) and ISO 9123 (2001).3.3 Variable slope caused byvariable backwaterThe stage at a gauging station for a given discharge,under the usual sub-critical flow conditions, isinfluenced by downstream control elements. Thestage at the station attributable to the control elementsis known to the hydrographer as backwater. As long asthe control elements are stable, the backwater for agiven discharge is unvarying, and the discharge is afunction of stage only. The slope of the water surfaceat that stage is also unvarying. If some of the controlelements are variable, such as movable gates at adownstream dam or the varying stage at a downstreamstream confluence, then for any given discharge thestage at the station and the slope are likewise variable.In the preceding section it was demonstrated that forthe above variable conditions, discharge can be relatedto slope and stage. Because the slope between twofixed points is measured by the fall between thosepoints, it is more convenient to express discharge as afunction of stage and fall.Stage-fall-discharge ratings are usually determinedempirically from observations of (a) discharge,(b) stage at the base gauge, which is usually theupstream gauge and (c) the fall of the water surfacebetween the base gauge and an auxiliary gauge. Thegeneral procedure used in developing the ratings isas follows:(a) A base relation between stage and dischargefor uniform flow or a fixed backwater conditionis developed from the observations. Thedischarge from that relation is defined as therating discharge, Q r;(b) The corresponding relation between stage andfall for conditions of uniform flow or fixedbackwater is developed. The fall defined by thisrelation is defined as rating fall, F r. Figure II.3.1shows schematically three forms the stage fallrelation may have;(c) The ratios of discharge, Q m, measured underconditions of variable backwater, to Q r, arecorrelated with the ratios of the measured fallF mto the rating fall F r. Thus:QQmr⎛ F= f⎜⎝ Fmr⎞⎟⎠(3.3)The form of the relation depends primarily on thechannel features that control the stage-dischargerelation. The relation commonly takes the form:QQnm⎛ Fm⎞= ⎜rF⎟(3.4)r⎝⎠where n varies from 0.4 to 0.6, the theoretical valueof n being 0.5. Generally speaking, the stage-falldischargerating can be extrapolated with moreconfidence when equation 3.4 is used with thetheoretical exponent of 0.5.The fall between the base and auxiliary gauge sites,as determined from recorded stages at the twogauges, may not provide a true representation ofthe slope of the water surface between the two sites.That situation may result from the channel andgauging conditions that are described below.First, the water surface in any reach affected bybackwater is not a plane surface between points in thereach, as sinuosity of the channel will producevariations in the height of the water surface, bothacross and along the reach; variations in channelcross-section and the effects of backwater also tend toproduce curvature of the water surface. The slopedetermined from observed differences in stages is thatof a chord connecting the water-surface elevations atpoints at the ends of a reach. It may not represent theslope of the water surface at either end of the reach,but may be parallel to a line that is tangent to thewater surface at some point in the reach.

Chapter 3. DISCHARGE RATINGS USING SLOPE AS A PARAMETERII.3-3GAUGE HEIGHT, METRES(a)Second, no reach of a natural stream selected forthe determination of slope is completely uniform.The area of the cross section may vary considerablyfrom point to point in the reach, but more importantis the effect that shoals, riffles, rapids or bends inthe stream channel within the reach may have onthe slope of the water surface, as well as on theenergy gradient.Third, the positions of the gauges at the ends ofthe reach with respect to the physical features ofthe channel may have a material effect on therecorded gauge heights, and hence on the indicatedslope. For example, if one gauge is on the inside ofa rather sharp bend and the other on the outsideof a similar bend, the slope computed from recordsof stages at those gauges may be widely differentfrom the actual slope of the water surface. Also, ifone gauge is attached to a bridge pier wheredrawdown around the pier affects the recordedstages in amounts that vary with the velocity pastthe pier, and the other gauge is on the bank or at asection of different velocity conditions, the recordsobtained from these gauges may not be true indicesof the slope. There may be a drawdown effect onthe intake pipe to a gauge well so that effectssimilar to those described above may beproduced.Fourth, both gauges may not be set to exactly thesame datum, the difference in datum possibly beinga large percentage of the total fall if the fall is verysmall. The slope determined from gauges not set tothe same datum would not indicate the true watersurfaceslope but would include in it the quantityy/L, in which y is the difference in datum and L thelength of the reach.(b)RATING FALL, F r, METRESFigure II.3.1. Schematic representation oftypical stage-fall relations. Curve (a), rating fallconstant: curve (b), rating fall a linear functionwith stage: curve (c), rating fall a complexfunction of stage(c)Because of those conditions, theoretical relationsbetween stage, fall and discharge cannot be directlyapplied, and the relations must be empiricallydefined by discharge measurements madethroughout the range of backwater conditions.Thus the best value of the exponent of F m/F rinequation 3.4 will often be in the range from 0.4 to0.6, rather than having the theoretical value of 0.5.Sometimes it may even be necessary to depart froma pure exponential curve in order to fit the plottedpoints satisfactorily. At other times the substitutionof a term F + y, for F values in equation 3.4 willimprove the discharge relation. The use of aconstant, y, whose best value is determined by trialcomputations, compensates in part for theinaccuracies in the value of F that were discussedabove.It is convenient to classify stage-fall-dischargeratings according to the type of relation that maybe developed between stage and rating fall. The twotypes are:(a) Constant-fall method:This type of relation (curve a in Figure II.3.1)may be developed for channels which tend tobe uniform in nature and for which the watersurfaceprofile between gauges does not haveappreciable curvature. A special case of theconstant-fall method is the unit-fall method;(b) Variable-fall method:This type of relation (curves b and c inFigure II.3.1) may be developed where any ofthe following conditions exist:(i) Appreciable curvature occurs in the watersurfaceprofile between gauges;(ii) The reach is non-uniform;(iii) A submerged section control exists in thereach between gauges, but the controldoes not become completely drowned bychannel control even at high discharges;(iv) A combination of some of the conditionslisted above.It is not uncommon for variable backwater to beeffective only part of the time. That follows fromthe two general principles that apply to backwatereffect. First, for a given stage at the variable controlelement, backwater effect decreases at the basegauge as discharge increases. Second, for a givendischarge, backwater effect decreases at the basegauge as stage decreases at the variable controlelement. Thus there are many possiblecombinations of stage at the variable controlelement and of discharge that will result innegligible backwater effect at the base gauge. Forexample, high flows may be free of variablebackwater in a long gauging reach of relatively

II.3-4manual on stream gaugingsteep slope. On the other hand, low flows may befree of variable backwater if the upstream (base)gauge has a section control that is not submergedby low stages at the variable control elementdownstream.Other basic principles and detailed procedures usedin defining stage-fall-discharge ratings are discussedin the pages that follow. The discussions arearranged in accordance with the precedingclassification of stage-fall-discharge relations.Knowledge of the hydraulic principles applicable toa given slope is essential as a guide to the empiricalanalyses of the data.GAUGE HEIGHT, IN METRESMeasured fall. F m 0.10.20.30.4DISCHARGE, IN CUBIC METRES PER SEC**ON**D3.3.1 Constant-fall methodIn uniform channels the water-surface profile isparallel to the bed. The water-surface slope, andthus, the fall between gauges, is the same for alldischarges. The rating fall, F r, for the condition ofno variable backwater (open-water condition)would be the same at any stage. The stage-dischargerelation with no backwater could be described bythe Chezy equation:Q = CA R S(3.5)oooowhere the subscripts denote uniform flow, or by:Qr = CA RFrL(3.6)where the subscripts denote the base ratingconditions.If variable backwater is imposed on the reach bya downstream tributary, the measured fall, F m,and measured discharge, Q m, would be less at agiven stage than indicated by the open-waterrating. If the slope or fall, as measured, trulyrepresents the slope at the base gauge, thosemeasurements would define, as shown inFigure II.3.2, a family of stage-discharge curves,each for a constant but different value of fall. Therelation of each curve in the family to the curvefor base rating conditions, according toequation 3.6, is expressed by:Q F = (3.7)QrF rThe discharge under variable backwater conditionsmay be computed as the product of the discharge,Q r, from the base rating and the square root of theratio of the measured fall to the constant-valuerating fall.Figure II.3.2. Schematic representation of familyof stage-discharge curves, each for a constantbut different value of fallA constant rating fall may also exist at sites wherethe base rating is controlled by a dam downstreamfrom the reach in which fall is measured. If thecurvature in the backwater profile is not significantand if the channel is uniform, the water-surfaceprofile will be approximately parallel to the channelbed at all discharges. For example, the curve inFigure II.3.2 for a constant fall of 0.36 m may betaken to represent the base stage-discharge relationfor a fixed or stable control element. The curves forlesser falls which might result from variablesubmergence of the dam are theoretically related tothis base curve by the square root of the fall ratiosas described above.Quite commonly a constant value of 1.0 is used forF rin equation 3.7. That special case of the constantfallmethod is usually referred to as the unit-fallmethod, which simplifies the computations becauseequation 3.7 then reduces to:QQ r= (3.8)1 2FA constant rating fall is not the usual caseencountered in natural streams. However, ifdischarge measurements cover the entire range offlow conditions and if such measurements conformto a constant rating fall, there is no need to use amore complicated technique. If profile curvatureand velocity-head increments are truly negligiblethe relation between the discharge ratio and fallratio should resolve into a single curve. Otherwisethis relation may be a family of curves with stage asa third variable.

Chapter 3. DISCHARGE RATINGS USING SLOPE AS A PARAMETERII.3-5Procedure for establishing a constant-fall ratingThe general procedure used in establishing a stagefall-dischargerating with a constant rating fall isoutlined as follows:1. Plot all discharge measurements using stageat the base gauge as ordinate and dischargesas abscissa, and note the measured fall, F m,beside each plotted point. If the informationon this plot indicates a family of curves, eachcorresponding to a constant value of fall(Figure II.3.2), the use of a constant rating fallshould be investigated;2. The most satisfactory type of constant-fallrating, from the standpoint of high-waterextrapolation, is one whose discharge ratiofallratio relation is a pure parabolic relation,as in equation 3.7, with the exponent equalto, or nearly equal to 0.5. If such a relationfits the measured discharges, the results areunaffected by whatever value of constant fall,F ris used. For convenience unit fall is used, asin equation 3.8;3. For each discharge measurement, Q m, computeQ rby use of the equation:Q = QrmF0.5m4. Plot values of gauge height versus Q rfor eachdischarge measurement and fit a curve to theplotted points to define the Q rrating curve.Determine values of rating discharges from theQ rrating curve;5. Compute and tabulate the percentagedepartures of the plotted Q rdischarges fromthe Q rrating curve;6. Repeat steps 3-5, using exponents of F motherthan, but close to 0.5. Try exponents equal to0.40, 0.45, 0.55 and 0.60;7. Compare the five Q rrating curves and selectthe curve that best fits the plotted points. Insteps 8 and 9 that follow, the discharges fromthat best rating curve will be referred to as Q rd,and the corresponding exponent of F mwill bereferred to as d;8. If the plotted discharges closely fit the Q rdrating curve, that curve and the relation of Q m/Q rdto F mare accepted for use;9. If the plotted discharges do not closely fit theQ rdrating curve repeat steps 3-5, using theexponent d but substituting the term (F m+ y)for F m. Several values of y, a small quantity thatmay be either positive or negative, are tried toobtain a Q rrating curve that closely fits theplotted discharge;10. Compare the various Q rrating curves obtainedfrom step 9 and select the curve that best fitsthe plotted points used to define it. If theplotted discharges closely fit that Q rratingcurve, that rating curve and the correspondingrelation of (Q m/Q r) to (F m+ y) are accepted foruse. If the fit is not considered to be sufficientlyclose, the use of a pure parabolic relation, suchas equation 3.8, is abandoned and the strictlyempirical approach described in the followingsteps is used;11. From the family of stage-discharge curvesdiscussed in step 1, select one as the base Q rcurve and use the constant fall for this curve asF r;12. Compute the ratios Q m/Q rand F m/F r, plotthe discharge ratios as ordinates and thefall ratios as abscissas and draw an averagecurve through the plotted points that passesthrough the point whose coordinates are (1.0and 1.0);13. Adjust each measured discharge by dividingit by the discharge ratio corresponding tothe fall ratio on the above curve. Plot thesecomputed values of Q ragainst stage anddraw an average curve (Q rcurve) through thepoints;14. Repeat steps 11-13 using alternative constantvalues of F runtil the best relation betweenstage, fall and discharge is established;15. If the best relation derived from the applicationof steps 11-14 is still unsatisfactory use themore flexible variable-fall method describedsubsequently.Example of a constant-fall ratingA typical stage-fall-discharge rating is presented inFigure II.3.3 as an example of a rating with constantrating fall. The upper gauge is a water-stage recorderinstalled in a well attached to a pier of a highwaybridge. The lower gauge is a water-stage recorderinstalled on the right bank 13 300 m below theupper gauge and 1 000 m above a dam.The channel conditions in this reach are reasonablyuniform. Variable backwater is caused by theoperations at the dam.A satisfactory relation between stage, fall anddischarge could not be established for the upper(base) gauge by use of the procedure for a pureparabolic fall-ratio curve as described in steps 1-10earlier. The empirical approach described in steps11-14 was therefore used. The best rating wasobtained by using a value of F requal to 0.457. Thefall-ratio curve in Figure II.3.3 approximately fitsequation 3.7 for all fall ratios no greater than 1.0.For fall ratios greater than 1.0 the curve is flatterthan a parabola defined by equation 3.7.

II.3-6manual on stream gaugingGAUGE HEIGHT AT UPPER GAGE, IN METRES0 1 2 3 4 51098765432Measured dischargeAdjusted dischargeX Measured dischargefall relationAdjusted dischargeplottedADJUSTED DISCHARGE, IN THOUSANDS OF CUBIC METRES PER SEC**ON**DMeasured dischargeplottedFall0.457 metre73 4 5 6MEASURED DISCHARGE, IN THOUSANDSOF CUBIC METRES PER SEC**ON**D1.6Fall-ratio curve forrating fall of0.457 metre10981.41.21.00.80.60.40.2DISCHARGE RATIO Q m/Q r10 1 2DISCHARGE, IN THOUSANDS OF CUBIC METRES PER SEC**ON**D00.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4FALL RATIO F m/F rFigure II.3.3. Stage-fall-discharge relation for Tennessee River at Guntersville, Ala, United States1.220 22 24 26 2830DISCHARGE RATIO, Q m /Q r1.00.80.60.4Fall-ratio curveQ mQ r–( ) 0.5F mF r1.01.21.4 1.629280.20.4 0.6 0.827026FALL RATIO, F m /F r0.226STAGE, IN METRES252423Q r Rating curveMeasured distanceAdjusted dischargeRating-fallcurve252423GAUGE HEIGHT, IN METRES22220 2 4 6 8 10 12 14 0 0.4 0.8 1.2 1.6 2.0DISCHARGE, IN THOUSANDS OF CUBIC METRES PER SEC**ON**DFALL IN METRESFigure II.3.4. Stage-fall-discharge relations for Columbia River at The Dalles, Oregon, United States

Chapter 3. DISCHARGE RATINGS USING SLOPE AS A PARAMETERII.3-72120191817161530 40 50 60 70Q rrating curveAdjusted dischargeMeasured discharge-fall relation21201918171615GAUGE HEIGHT, IN METRES14131211109876543DISCHARGE RATIO Q m /Q r1.2Fall-ratio curve1.00.80.40.30.20 0.2 0 .4 0.6 0.8 1.0 1.1Rating fall curve14131211109876543GAUGE HEIGHT, IN METRES2FALL RATIO F m /F r5 15 20DISCHARGE, IN THOUSANDS OF CUBIC METRES PER SEC**ON**D21.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0RATING FALL, IN METRESFigure II.3.5. Stage-fall-discharge relations for Ohio River at Metropolis, Illinois, United States(from Corbett et al.,1945)To plot a rating discharge, Q r, computed from ameasured discharge, Q m, and a measured fall, F m, onthe Q rrating curve, the fall ratio, F m/F ror F m/0.457 isfirst computed. The fall-ratio curve is then enteredwith the computed fall ratio, and the discharge ratio,Q m/Q ris read. Q mis then divided by that value of thedischarge ratio to give the value of Q rto be plotted.To obtain the discharge from Figure II.3.3 for a givengauge height and given fall F m, the fall ratio, F m/0.457,is first computed. The fall-ratio curve is then enteredwith the computed fall ratio and the discharge ratio,Q m/Q r, is read. From the rating curve, the value of Q rcorresponding to the given gauge height is read. Thedesired discharge, Q m, is then obtained by multiplyingQ rby the discharge ratio.3.3.2 Variable fall methodWhere variable backwater is a factor in the dischargerating it will generally be found that fall is a functionof stage. The average relation between fall anddischarge may be linear or fall may be a complexfunction of stage. Rating principles are best discussedby reference to examples.The right-hand graph in Figure II.3.4 is an exampleof a linear relation between stage and fall. The stagedischargerelation at the base gauge is affected byreservoir operations more than 130 km downstream.The auxiliary gauge is located 30 km downstreamfrom the base gauge. Within the range of measureddischarges, fall increases linearly with stage.A much more complex stage-fall relation is shownin the right-hand graph in Figure II.3.5. At thedownstream (auxiliary) gauge, the stage-dischargerelation is affected only at the lower stages by aconstriction, the backwater from which causes fallto decrease with stage in the slope reach. At thehigher stages the constriction has little effect andfall increases with stage.

II.3-8manual on stream gauging1.0DISCHARGE RATIO Q m/Q r0.90.80.70.60.50.40.30.2Q mQ rFall-ratio curve=F(mF rF m0.44when = 0.2F r(0.40.50.60.7Fall ratio F m/F r0.80.91.0100 110 120 130 140 150 160 1708760.10.35GAUGE HEIGHT, IN METRES043210.10.2Q rrating curveMeasured dischargeAdjusted dischargeRating-fall curve4321GAUGE HEIGHT, IN METRES0 10 20 30 40 50 60 70 80 90 100 110 120DISCHARGE, IN CUBIC METRES PER SEC**ON**D0 1 2 3 0FALL, IN METRESFigure II.3.6. Stage-fall-discharge relations for Kelly Bayou near Houston, Louisiana, United StatesAnother example of a complex stage-fall relation isshown in the right-hand graph in Figure II.3.6 for atributary. The base gauge for this rating is about4.3 km upstream from the mouth of the tributary.The auxiliary gauge is on the main river, 6.7 kmdownstream from the base gauge. At low stages, fallincreases with stage; at medium and high stages thebackwater effect from the main river is morepronounced and fall tends to assume a constantvalue.Where a section control exists just downstream fromthe base gauge, it is necessary to identify thosesituations when backwater effect is absent at the basegauge. Obviously there will be no backwater whenthe tailwater at the section control is below the crestof the control. Most artificial controls are broadcrestedand submergence is generally effective onlywhen tailwater rises to a height above the crest thatis equal to or greater than 0.7 times the head on thecontrol. Looked at another way, submergence iseffective only when the fall between the upstreamand downstream stages is equal to or less than0.3 times the head on the control. Thus a straightline of initial submergence may be drawn on thecurve of stage versus fall. The line passes through thecoordinates representing the elevation of the controlcrest and zero fall, with a slope of 1 m of stage per0.3 m of fall. The precise position and slope of theline will depend on the location of the downstreamgauge with respect to the section control. If the gaugeis immediately downstream from the control, theline of initial submergence will have the positionand slope stated above. If the gauge is far downstreamfrom the control, the line on the stage-fall graph willintersect the elevation of the control crest at a valueof fall greater than zero and the slope of the line willdepend on the hydraulic features of the station. Fieldobservation will be necessary to define the graphcoordinates of the line of initial submergence. Allobserved or recorded values of fall that lie below theline of initial submergence indicate free-fall discharge(discharge unaffected by the tailwater elevation). Allobserved or recorded values of fall that lie above the

Chapter 3. DISCHARGE RATINGS USING SLOPE AS A PARAMETERII.3-92.82.6GAUGE HEIGHT (GH), IN METRES2.42.22.01.81.61.41.21.0Measured dischargeAdjusted discharge xQ rrating curve1.20Q r= 655 (G H m= – 0.548) 1.35Q m/Q r1.101.000.900.80xxxxFall-ratio curve= (Q mF mQ rF r0.5(xRating-fall curveBackwater Free fall0.80.700.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30F m/F r0.60 2 4 6 8 10 21 14 16 18 20DISCHARGE (Q), IN HUNDREDS OF CUBIC METRES PER SEC**ON**D0 0.1 0.2 0.3FALL, IN METRESFigure II.3.7. Stage-fall-discharge relations for Colusa weir near Colusa, California, United Statesline of initial submergence indicate discharge affectedby variable backwater. Furthermore, if the tailwatergauge is close to the control, the fall-ratio curve fordischarges affected by backwater should closely fitthe theoretical equation 3.4. If the tailwater gauge isdistant from the control, the fall-ratio curve willdepart from the theoretical equation.The right-hand graph in Figure II.3.7 shows a stagefallrelation where the base gauge for the station isa short distance from an ungated weir which acts asa section control, and the auxiliary gauge is a shortdistance downstream from the control. There is nopool immediately upstream from the weir, thestreambed being at the elevation of the weir crest.There is a drop of about 0.6 m immediatelydownstream from the weir. The line of initialsubmergence shown crossing the lower part of thestage-fall relation has the theoretical position andslope discussed above. The weir is at the downstreamend of a large natural detention basin along the leftbank of river and water that passes over the weirimmediately enters the river. Because the river stagerises faster than the stage of the detention pool, falldecreases with stage at the base gauge, as shown bythe rating-fall curve.The right-hand graph in Figure II.3.8 is a plot ofstage versus fall for a Canadian river. The base gaugefor this section is on the west arm of Kootenay Lakeabout 13 km upstream from Groham Narrows.Downstream from the narrows is the fore bay of theCorra Linn power plant, and in the fore bay is theauxiliary gauge, about 15 km downstream from thebase gauge. Groham Narrows is the control for thebase gauge, but operations of Corra Linn Dam causevariable submergence of the control when the stageof the fore bay is sufficiently high. The line of initialsubmergence, shown as the free-fall curve inFigure II.3.8, was determined from observation anddischarge measurements. Discharge measurementswhose values of fall plot below, or to the right of,the free-fall curve are unaffected by backwater andthose discharges are therefore independent of fall.Discharge measurements whose values of fall plotabove or to the left of, the free-fall curve are affectedby variable backwater. For those measurements thegraph shows no apparent relation between stage

II.3-10manual on stream gauging1.00.90.8{Free-fallmeasurements1.21.31.4DISCHARGE RATIO Q m/Q r0.70.60.50.40.30.20.1Fall-ratio curve1.11.00.93500 4000 4500 50000.818FALL RATIO F m/F r0.7160.6140.5181614GAUGE HEIGHT, IN METRES864200 0.1 0.2 0.3 0.41012Free-fall dischargecurve: Qadj. plotted0 500 1000 1500 2000 2500 3000 3500 4000DISCHARGE, IN CUBIC METRES PER SEC**ON**DBackwater Free fall00 1 2 3 4 5 6 7FALL, IN METRESFree-fall curve;F mplotted121086422GAUGE HEIGHT, IN METRESFigure II.3.8. Stage-fall-discharge relations for: Kootenay River, British Columbia, Canada.Measurements with falls less than 0.12 m not plotted, from Eisenlohr (1964)and fall, and the free-fall curve (the line of initialsubmergence was used as the rating-fall curve forthe measurements affected by variable backwater).The rating for a gauging station whose base gaugehas no section control is analyzed in a mannersimilar to that already described, the principaldifference being that instead of using a constantvalue of rating fall, the rating fall for any stage isobtained from the rating-fall curve. The rating for agauging station whose base gauge has a sectioncontrol is analyzed in two separate steps. The freefallpart of the rating (no variable backwater) isanalyzed as explained in Chapter 1, where simplestage-discharge relations are discussed. That part ofthe rating that is affected by variable backwater isanalyzed as though no section control existed. It isnot necessary to use the free-fall rating curve as thebasis for establishing that part of the rating that isaffected by variable backwater.In view of the many different and complex situationsthat exist in natural channels, it is difficult to givegeneral guidelines for establishing stage-falldischargerelations. The analyst should make everyeffort to acquaint himself with the physicalcharacteristics of the channel and the source ofvariable backwater. The best position of the relationcurves that comprise the discharge rating must bedetermined by trial and error. The complexity ofthese relations determines to a large degree thenumber of discharge measurements necessary todefine the discharge rating. Although the methodsare empirical, experience has shown that there maybe found a stage-discharge relation (the Q rcurve)which, taken in conjunction with its associatedstage-fall relation (the rating-fall curve), will giveclose approximation to the true discharge under allpossible combinations of stage and fall by theapplication of a single-curve relation, Q m/Q rvs F m/F r. It is desirable, but not always possible, to havethat relation fit the theoretical equation 3.4.Procedure for establishing the ratingThe general procedure used in establishing a stagefall-dischargerating with variable fall is outlined asfollows:

Chapter 3. DISCHARGE RATINGS USING SLOPE AS A PARAMETERII.3-111. Plot all discharge measurements using stagesat the base gauge as ordinates and discharges,Q m, as abscissa, and note the measured fall, F m,beside each plotted point;2. On another graph plot the measured fall, F m,for each discharge measurement against stageat the base gauge, using stage as the ordinate;3. If the base gauge has a section control, determinethe position of the line of initial submergenceon the plot of stage versus measured fall. Itsposition is based on discharge measurementsknown to have been made under conditionsof free fall. Those measurements, plottedagainst stage on logarithmic graph paper, arefitted with a free-fall rating curve which isextrapolated in accordance with the principlesdiscussed in Chapter 1. The remainingmeasurements are added to the logarithmicrating plot. Those measurements that plot tothe left of the extrapolation are consideredto be affected by backwater. That knowledge,along with knowledge of the probable degreeof submergence required to cause backwatereffect, enables the analyst to fix the positionof the line of initial submergence. Only thosemeasurements that plot above, or to the leftof, the line of initial submergence are used inthe analysis of the rating for variable backwaterthat is discussed in the steps that follow;4. Fit a curve, (Q rrating curve) to the stagedischargeplot in step 1, and another curve(F rrating-fall curve) to the stage-fall plot instep 2;5. From the curves in step 4 obtain values ofQ rand F rcorresponding to the stage of eachdischarge measurement;6. Compute the ratios Q m/Q rand F m/F rfor eachdischarge measurement;7. Plot Q m/Q ras ordinate against F m/F ras abscissa,and on that graph draw the curve:Q m/Q r= (F m /F r )0.58. On the basis of the scatter of the plotted pointsabout the curve in step 7, adjust the Q randF rcurves (step 4) to obtain revised values ofQ rand F r(step 5), such that the new ratiosof Q m/Q rand F m/F rfit the curve in step 7 asclosely as possible. The adjustments to the Q rand F rcurve should not be so drastic that theadjusted curves are no longer smooth curves;9. Repeat steps 4-8, using exponents of F m/F rotherthan, but close to 0.5. Try exponents equal to0.40, 0.45, 0.55 and 0.60;10. Compare the five plots of Q m/Q rversus F m/F rand select the one which shows the best fitbetween curve and plotted points. (The ratioof plotted values of Q m/Q rto curve values ofQ m/Q ris identical with the ratio of measureddischarge to discharge obtained from thestage-fall-discharge relations.) In steps 11 and12 that follow, the exponent of that best fallratiocurve will be referred to as n;11. If the plotted ratios closely fit the curve (Q m/Q r) = (F m/F r) n , that curve and the correspondingQ rand F rcurves are accepted for use;12. If the plotted ratios do not closely fit the curve(Q m/Q r) = (F m/F r) n , repeat steps 4-8, using theexponent n but substituting the terms (F m+ y)for F mand (F r+ y) for F r. Several values of y, asmall quantity that may be either positive ornegative, are tried to obtain a close fit betweenplotted points and the curve defined by theequation:[ ]( m r ) = ( +m ) ( +r )nQ Q F y / F y(3.9)13. Compare the various plots of the fall-ratiograph obtained from step 12 and select the oneshowing the best fit between curve and plottedpoints. If the fit is satisfactory, that curve andthe corresponding Q rand F rcurves are selectedfor use. If the fit is not considered to be sufficientlyclose, the use of a pure parabolic relation,such as the equation shown in step 11 orthe equation shown in step 12, is abandonedand the strictly empirical approach describedin the following steps is used;14. Select one of the trial Q rand F rcurves, suchas were constructed in step 4, along with thecorresponding values of Q r, F r, Q m/Q rand F m/F r,such as were obtained in steps 5 and 6;15. Plot the discharge ratios as ordinates and thefall ratios as abscissas, and draw an averagecurve through the plotted points that passesthrough the point whose coordinates are (1.0,1.0);16. On the basis of the scatter of the plotted pointsabout the curve in step 15, adjust the Q rand F rcurves (step 14), as well as the fall-ratio curve.The adjusted curves must remain smoothcurves;17. Repeat steps 14-16, using other trial curves ofQ r, F rand fall ratio versus discharge ratio, untilthe best relation is established between stage,fall and discharge. In other words, until a closefit is obtained between plotted points and thefall-ratio curve;18. After having obtained acceptable Q r, F r, andfall-ratio curves, plot adjusted values of thedischarge measurements on the Q rrating curve.The adjusted values are computed as follows:(i) Given a measured discharge, Q m, anda measured fall, F m, enter the F rcurve(stage-fall relation) with the gauge heightof the discharge measurement and readF r;

II.3-12manual on stream gauging(ii) Compute the fall ratio, F m/F r, and enterthe fall-ratio curve to obtain the dischargeratio, Q m/Q r;(iii) Obtain the value Q rto be plotted bydividing Q mby Q m/Q r. The method ofobtaining the discharge corresponding toa given gauge height and a given fall, F m,is explained later.Examples of rating procedureFigures II.3.4 through II.3.8 are examples of stagefall-dischargerelations for slope stations where fallis a function of stage.Figure II.3.4 shows that excellent results wereachieved in the range of discharge that wasmeasured. The linear trend of fall increasing withstage is clearly evident, and the fall-ratio curve notonly is represented by the theoretical equation 3.7,but is closely fitted by the plotted points. Wherethe rating-fall curve (stage versus fall) is so welldefined, the first estimate of the Q rcurve is usuallymade by the use of equation 3.7, in which Q mwouldrepresent the measured discharges. The computedQ rvalues for the discharge measurements wouldthen be plotted against stage, and a curve fitted tothe plotted points would represent the first trial Q rcurve.Figure II.3.5 is an extremely complex example, ascan be seen from the shape of the rating-fall curve.It is not surprising that the fall-ratio curve couldnot be expressed by a simple parabolic equation,such as equations 3.4 or 3.9.Figure II.3.6 shows an example of a station wherethere is relatively minor effect from variablebackwater at low stages. At medium and high stages,the variable stage of the main river causes variablebackwater at the base gauge. The rating-fall usedduring high-water periods has the constant value of10.0. The fall-ratio curve, for values of F m/F rgreaterthan 0.2, has the equation:QQmr= ( F F ) 0.44 (3.10)mrBecause the exponent 0.44 does not differ greatlyfrom its theoretical value of 0.5, the Q rrating curvecan be extrapolated with some confidence.Figure II.3.7 is an example of the stage-fall-dischargerelation for a station whose base gauge has a sectioncontrol. There is no backwater at low flow, as shownby the six discharge measurements that plot belowthe line of initial submergence on the graph of stageversus fall. The remaining 16 dischargemeasurements show the effect of variable backwater.While the fit of adjusted measured discharges to theQ rrating curve is not completely satisfactory, thereis some satisfaction to be derived from the facts thatthe equation of the fall-ratio curve is theoreticallycorrect and the fall-ratio curve balances the plottedpoints.Figure II.3.8 for a station on the Kootenay River isan example of the stage-fall-discharge relation for astation whose base gauge has a control that isunsubmerged at high stages. Of the 59 dischargemeasurements shown, 23 were made under free fallconditions. Those 23 measurements plot below, orto the right of, the line of initial submergence onthe graph of stage versus fall. The remaining 36discharge measurements are affected by variablebackwater and were used in the stage-fall-dischargeanalysis. Because the line of initial submergencewas used as F rin the analysis, the value of F mforany measurement affected by backwater is less thanF r. Consequently the fall-ratio curve fittedempirically to the plotted points and is not expressedby a simple parabolic relation such as equations 3.7or 3.9.Determination of discharge from relation for variablebackwaterAfter the three necessary relations are available(a) stage versus rating fall, F r, (b) stage versus ratingdischarge Q rand (c) Q m/Q rversus F m/F r, then thedetermination of discharge, Q m, for a given stageand a given fall, F m, proceeds as follows:(a) From a stage-fall table determine the ratingfall, F r, for the known stage;(b) Compute the ratio F m/F r;(c) From a table of discharge ratios, Q m/Q r, and fallratios F m/F r, determine the value of the ratioQ m/Q r;(d) From a stage-discharge table, determine therating discharge, Q r, for the known stage;(e) Compute Q mby multiplying the ratio Q m/Q rbythe value of Q r.Much emphasis has been placed on obtaining apurely parabolic function, such as equations 3.7or 3.9, for the relation between fall ratio anddischarge ratio. Such a relation not only permitsthe analyst to extrapolate the Q rcurve with moreconfidence, but it also expedites the computationof discharge. For example equation 3.4 may betransposed to:QrnQ = Fm n m( ( ) (3.11)F )r

Chapter 3. DISCHARGE RATINGS USING SLOPE AS A PARAMETERII.3-13Two tables can be prepared, one giving the valuesof the quantity Q Frn r corresponding to stage, andthe other giving values of F nm corresponding tovalues of F m. The discharge is then computed asthe product of the two values picked from thetables. Equation 3.9 may be transposed in a similarway.3.4 Variable slope caused bychanging discharge3.4.1 Theoretical considerationsWhere channel control is effective, the effect ofchanging discharge on a graph of the stage-dischargerelation is such as to produce a loop curve as shownin Figure II.3.9, on which the discharge for a givenstage is greater when the stream is rising than it iswhen the stream is falling. In other words, given asimple stage-discharge relation for steady flow –that is, a rating that averages all dischargemeasurements – it will be found that themeasurements made on a rising stage plot to theright of the curve and those made on a falling stageplot to the left. The discharge measurements forindividual flood waves will commonly describeindividual loops in the rating. The departure ofmeasurements from the rating curve for steady flowis of significant magnitude only if the slope of theGAUGE HEIGHT IN METRES14121086420 2 4 6 8 10 12DISCHARGE IN THOUSANDSFigure II.3.9. Stage discharge loop ofthe Ohio River at Wheeling, West Virginia,United States, during the flood of14 March 1905stream is relatively flat and the rate of change ofdischarge is rapid. For gauging stations where thisscatter of discharge measurements does occur, thedischarge rating must be developed by theapplication of adjustment factors that relate steadyflow to unsteady flow. Unsteady flow refers todischarge at a site that changes appreciably withtime, as in the passage of a flood wave.The relation between the discharges for steadyand unsteady conditions at the same stage can bederived from the general equations for unsteadyflow (Rouse, 1950). A simplified equation shownbelow may also be derived by neglecting all termsdue to change of velocity head or acceleration:QQcdh= 1+(3.12)S v dtm1cwwhere Q mis the discharge for unsteady flow; Q cisthe discharge for steady flow; S cis the energy slopefor steady flow at the same stage; v wis the wavevelocity, and dh/dt is the rate of change of stagewith respect to time (dh is positive for risingstages).Because equation 3.12 is basic to the methodscommonly used for adjusting discharge ratings forthe effect of changing discharge, it is appropriate toelaborate on its derivation. The ratio of themagnitudes of two discharges that occur at a givenstage is equal to the ratio of the square roots of theirenergy slopes. That principle can be expressed inthe following basic equation, which is similar toequation 3.12. that was used in preceding sectionsof the Manual:Qm =m(3.13)QcSScwhere S mis the energy slope for unsteady flow atthe time of Q mand the remaining terms are definedabove for equation 3.12.During changing discharge, the slope of the watersurface increases or decreases by an increment ofslope (ΔS), where:1 dhΔ S =(3.14)v dtwIf it is assumed that the increment of slope by whichthe energy gradient changes is likewise equal to ΔS,then:Sm1 dh= Sc+ ΔS= Sc+(3.15)v dtw

II.3-14manual on stream gaugingBy combining equations 3.13 and 3.15:1 2⎛ 1 dh ⎞⎜ Sc+ ⎟Qm ⎜ vwdt=⎟(3.16)Q ⎜ ⎟cSc⎜ ⎟⎝ ⎠or1 2Qm ⎛ 1 dh1 ⎟ ⎞= ⎜ +Q ⎝ S v dt(3.17)cc w ⎠The wave velocity v win the above equations may beevaluated by the Sedden principle (Sedden, J.E.,1900):1 dQv w= (3.18)B dhwhere B is the width of the channel at the watersurface, and dQ/dh is the slope of the stage-dischargecurve for constant-flow conditions.From examination of formulae for mean velocityin open channels the ratio of wave velocity tomean velocity may be shown to vary asfollows:Channel type Ratio v w/V mManningChezyTriangular 1.33 1.25Wide rectangular 1.67 1.50Wide parabolic 1.44 1.33Experience seems to indicate that the most probablevalue of the ratio in natural channels is 1.3.Equation 3.14 explains why the effect of changingdischarge is significant only on flat streams duringrapid changes in discharge because that combinationis necessary to make ΔS significantly large. Duringrapid changes in discharge, absolute values (eitherplus or minus) of dh/dt are large. On flat streamswave velocity, v w, is small. The combination of alarge value of dh/dt and a small value of v wresults ina large value of ΔS.3.4.2 Methods of rating adjustment forchanging dischargeThe four methods of adjusting discharge ratings forchanging slope attributable to changing dischargeare:(a) Jones method;(b) Boyer method;(c) Lewis method;(d) Wiggins method.All four methods are based on equation 3.12, or ona modification of that equation. The Jones andLewis methods are rarely used any more and will beonly briefly described here. The Boyer and Wigginsmethods are preferred for use and are described indetail.The Jones method originally used water-surfaceslope rather than energy gradient for the term S cinequation 3.12. Consequently an auxiliary stagegauge was required for measuring slope. A stagesloperelation for steady flow conditions wasobtained from the recorded or observed stages atthe base and auxiliary gauges. In later years acomputed value of the energy gradient, S c, was usedin place of water-surface slope and an auxiliarystage gauge was no longer needed. Dischargemeasurements that had been made during periodsof steady flow were used to evaluate S c, using theManning equation:Sc⎛ Q= ⎜⎝ Kc2⎞⎟⎠(3.19)where K, the conveyance of the channel, is equalto:1 AR2 3nValues of S cwere computed in that manner forseveral stages to provide the data needed for arelation of S cto stage. The term v win equation 3.12was computed for several stages by use of a complexempirical equation that included the term 1.3V m,to provide the data needed for a relation of v wtostage. Equation 3.12 could then be solved for Q c,which is the steady-flow discharge correspondingto the stage of Q m, because Q cthen became the onlyunknown quantity in the equation. In a final step,the computed values of Q cwere used, with theircorresponding stages, to construct the requiredsteady-flow rating curve.The Lewis method is a simplification of the Boyermethod in which the term 1/S cv win equation 3.12is assumed to have a constant value J at all stages.That assumption reduces equation 3.12 to:1 2Qm ⎛ dh ⎞= ⎜1 + J ⎟ (3.20)Q ⎝ dt ⎠cwhere Q mand dh/dt are measured or observedquantities and, Q cand J must be determined bytrial-and-error computations. For that determinationa trial Q crating curve is drawn on the basis of a plotof measured discharge, Q m, versus stage, thepositioning of the curve being influenced also by

Chapter 3. DISCHARGE RATINGS USING SLOPE AS A PARAMETERII.3-15the value of dh/dt for each discharge measurement.The Q ccurve is then adjusted by trial and error untilthe values of J, computed by use of equation 3.20,approximate or scatter about a constant value. TheLewis method is satisfactory only for those gaugingstations were the term 1/(S cv w) varies little withstage.Boyer methodThe Boyer method provides a solution ofequation 3.12 without the necessity for individualevaluation of v wand S c. The method requiresnumerous discharge measurements made under theconditions of rising and falling stage. Measureddischarge, Q m, is plotted against stage in the usualmanner, and beside each plotted point is noted thevalue of dh/dt for the measurement. For conveniencedh/dt is expressed in feet or metres per hour and thealgebraic sign of dh/dt is included in thenotation – plus for rising stage and minus for fallingstage. A trial Q crating curve, representing thesteady-flow condition where dh/dt equals zero, isfitted to the plotted discharge measurements, itsposition being influenced by the values dh/dt notedfor the plotted points. Values of Q cfrom the curvecorresponding to the stage of each dischargemeasurement, are used in equation 3.12, along withthe measured discharge, Q m, and observed changein stage, dh/dt, to compute corresponding values ofthe adjustment factor, 1/S cv w. The computed valuesof 1/S cv ware then plotted against stage and a smoothcurve is fitted to the plotted points. If the plottedvalues of 1/S cv wscatter widely about the curve, theQ ccurve is modified to produce some new values of1/S cv wthat can be better fitted by a smooth curve.The modifications of the curves of Q cand 1/S cv wshould not be so drastic that the modified curvesare no longer smooth curves, nor should themodified shape of the Q crating curve violate theprinciples underlying rating curves, as discussed inChapter 1. Construction of the two curves completesthe rating analysis. Figure II.3.10 is an example ofsuch an analysis.To adjust the value of subsequent dischargemeasurements for plotting on the Q crating curve,the adjustment-factor curve is first entered with thestage of the measurement to obtain the appropriatevalue of the factor, 1/S cv w. Next, the observed valueof dh/dt is used with that factor to compute theterm:0.5⎛ 1 dh1 ⎟ ⎞⎜ +⎝ S cv wdt ⎠That term is then divided into the measureddischarge, Q m, to obtain the required value of Q c.To determine true discharge Q m, based on the Q crating curve and adjustment-factor curve, during aperiod when the stage and rate of change of stageare known, the procedure described above is usedto obtain the value of the term noted above. Thatterm is then multiplied by Q c, which is obtained byentering the Q crating curve with the known stage.The product is the true discharge, Q m.Wiggins methodThe Wiggins method is a modification of the Jonesmethod in which the energy gradient, rather thanthe water-surface slope, is used. The method isconvenient for adjusting measured discharge Q mforthe effect of changing discharge to obtain thecorresponding steady-flow discharge Q c. However,the reverse procedure of computing discharge Q mfor unsteady flow from the steady-flow dischargerating is rather complicated. Consequently theWiggins method is used only for those stationswhere only occasional adjustment of measureddischarge at high stages is required. If the dischargeis affected by changing stage on numerous dayseach year the Boyer method of discharge adjustmentshould be used.The discharge measurements adjusted by theWiggins method are used to develop a steady-flowrating, and that rating is used directly with thegauge-height record to obtain daily values ofdischarge. This course of action is justifiable forthose streams whose discharge is affected bychanging discharge on only a few days each year.For that type of stream it will generally be foundthat the discharge adjustment is less than ten percent. On the affected days, the discharge obtainedfrom the steady flow rating will be underestimatedby a small percentage when the stage is risingrapidly, and overestimated by a small percentagewhen the stage is falling rapidly. The discrepanciesare compensating and if only a few days areinvolved, the streamflow record is not significantlyimpaired. The advantage of applying the adjustmentto discharge measurements made under unsteadyflowconditions is that the scatter of dischargemeasurements on the rating curve is reduced andthe rating curve can therefore be more preciselydefined.Application of the Wiggins method has beensimplified by the preparation of diagrams thateliminate much of the computational labour.Figures II.3.11 to II.3.14 are used to determine theunsteady-flow value of the energy slope, S m, at thetime of the discharge measurement, Q m, forcombinations of values of mean velocity, V mand

II.3-16manual on stream gauging1413121110Stage-dischargerelationQ crating curveRelation between gageheight and adjustementfactor 1/v WS cGAUGE HEIGHT, IN METRES9876Measured dischargeAdjusted discharge byBoyer methodFactor 1/v WS c543Adjustment Factor 1/v WS c20 2 4 6 8 10 0 0.4 0.8 1.2 1.6 1.7DISCHARGE, IN THOUSANDS OF CUBIC METRES PER SEC**ON**DFigure II.3.10. Adjustment of discharge measurements for changing discharge, Ohio River at Wheeling,West Virginia, United States during the period 14-27 March 1905, from Corbett et al. (1945)hydraulic radius, R. The Manning equation wasused in preparing the graphs, and each of the fourgraphs is applicable for a particular value ofManning’s n, as shown in the following tabulation:– Figure II.3.11: n = 0.025 (smooth bed and banks)– Figure II.3.12: n = 0.035 (fairly smooth)– Figure II.3.13: n = 0.050 (rough)– Figure II.3.14: n = 0.080 (very rough)Figure II.3.15 is used to determine the increment ofenergy slope:v w1dhdtattributable to changing discharge, for combinationsof values of flood-wave velocity, v w, and rate of

Chapter 3. DISCHARGE RATINGS USING SLOPE AS A PARAMETERII.3-17change of stage dh/dt. Flood-wave velocity isassumed to equal 1.3V m.Figures II.3.l6 and II.3.l7 are used to determine thefactor to apply to the measured discharge, Q m, toobtain the steady-flow discharge, Q c. The factor,which is equal to:⎡⎛⎢⎜S⎢⎝⎢⎣m1−vSmwdh ⎞⎤⎟⎥dt ⎠⎥⎥⎦0.5is given for combinations of values of S mfromFigures II.3.11 to II.3.14 and of:v w1dhdtfrom Figure II.3.15. Note that the factor differs fromthat given in equation 3.16, because S mis used hereas the base slope, rather than S cas in equation 3.16.Figure II.3.16 is used for rising stages andFigure II.3.17 is used for falling stages.An example of the use of the Wiggins diagramsfollows.Given: A discharge measurement with the followingdata for a stream with a fairly smooth bed(n = 0.035):Q m= 6513 m 3 s -1Area = 5007 m 2Width = 823 mV m= 1.30 m s -1Change in stage = 0.265 m in 1.5 hours(rising).Compute adjusted discharge to be plotted on therating curve.First compute:R = AreaWidth = 5007823 = 6 mv = 1.3V = 1.3 × 1.30 = 1.69 m s -1wmdh change in stage per hour =0.265= 0.177 m / hrdt 1.5Then:(a) Enter Figure II.3.12 with V m= 1.30 and R = 6.0and read S m= 0.00018;(b) Enter Figure II.3.15 with dh/dt = 0.177 andV w= 1.69 and read slope increment equal to0.000029;(c) Enter Figure II.3.16 (rising stage) with S m=0.00018 and slope increment 0.000029 andread factor = 0.915;(d) Compute adjusted discharge = 0.915 × 6513 =5959 m 3 s -1 .Because the stage was rising the unadjusteddischarges would plot to the right of the ratingcurve. The computed adjustment moves themeasurement to the left.5454MEAN VELOCITY, IN METRES PER SEC**ON**D3210.90.80.70.60.50.40.30.20.0050.0040.0030.0020.0010.000800.000600.000400.000300.000200.000150.000100.000050.000040.000030.000020.00001MEAN VELOCITY, IN METRES PER SEC**ON**D3210.90.80.70.60.50.40.30.20.0050.0040.0030.0020.0010.000800.000600.000500.000400.000300.000200.000150.000100.000050.000040.000030.000020.000010.10.3 0.4 0.6 0.8 1 2 3 4 5 6 7 8 9 10 15HYDRAULIC RADIUS, IN METRES0.10.3 0.4 0.5 0.6 0.70.8 0.9 1 2 3 4 5 6 7 8 9 10 15HYDRAULIC RADIUS, IN METRESFigure II.3.11. Diagram for solution of theManning formula to determine S m.Smooth bed and banks, n = 0.025.Figure II.3.12. Diagram for solution of theManning formula to determine S m.Fairly smooth bed, n = 0.035.

II.3-18manual on stream gauging5454MEAN VELOCITY, IN METRES PER SEC**ON**D3210.90.80.70.60.50.40.30.20.0050.0040.0030.0020.0010.000800.000600.000500.000400.000300.000200.000150.000100.000050.000040.000030.000020.00001MEAN VELOCITY, IN METRES PER SEC**ON**D3210.90.80.70.60.50.40.30.20.0050.0040.0030.0020.0010.000800.000600.000500.000400.000300.000200.000150.000100.000050.000040.000030.000020.000010.10.3 0.4 0.5 0.6 0.70.8 0.9 1 2 3 4 5 6 7 8 9 10 150.10.3 0.4 0.5 0.6 0.70.8 0.9 1 2 3 4 5 6 7 8 9 10 15HYDRAULIC RADIUS, IN METRESHYDRAULIC RADIUS, IN METRESFigure II.3.13. Diagram for solution of theManning formula to determine S m.Rough bed, n = 0.050Figure II.3.14. Diagram for solution of theManning formula to determine S m.Very rough bed, n = 0.0800.460.000200.440.000190.420.400.380.360.000180.000170.00016dhRATE OF CHANGE OF STAGE, (METRES PER HOUR)at0.340.320.300.280.260.240.220.200.180.160.140.120.100.080.060.040.020.000100.0000900.0000700.0000800.0000600.0000500.0000450.0000400.0000350.0000300.0000280.0000260.0000240.0000220.0000200.0000180.0000160.0000140.0000120.0000100.0000060.0000040.0000020.00000100 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3VELOCITY OF A FLOOD WAVE, V W(METRES PER SEC**ON**D)SLOPE FROM FIGURE II.3.110.000150.000140.000130.000120.000110.000100.000090.000080.000070.000060.000050.000040.000030.000020.0000109998 96 94 92 90 88 86 84 82 807500.000010.000020.000030.00004700.0000565600.0000655500.00007SLOPE INCREMENT FROM FIGURE II.3.15RISING STAGE0.000080.000090.00010Figure II.3.15. Diagram for determiningslope increment due to changingdischargeFigure II.3.16. Diagram for determining factorto apply to measured discharge duringperiods of rising stage

Chapter 3. DISCHARGE RATINGS USING SLOPE AS A PARAMETERII.3-190.000200.000190.00018(equation 3.13) are similar, but only the fall-ratingmethods are versatile enough to handle thecombined effect of the two factors.0.000170.000160.000150.000143.6 Shifts in discharge ratingswhere slope is a factorSLOPE FROM FIGURE II.3.110.000130.000120.000110.000100.000090.000080.000070.000060.000050.000040.000031.011.021.041.061.081.101.121.141.161.181.201.251.301.351.401.451.50FALLING STAGEChanges in channel geometry, such as scour or fill;and/or changes in flow conditions, such as vegetalgrowth, will cause shifts in the discharge rating0where slope is a factor, just as they cause shifts insimple stage-discharge relations. When dischargemeasurements indicate a shift in the rating for aslope station, the shifts should be applied to the Q rrating curve if the station is affected by variablebackwater, or to the Q crating curve if the station isaffected by changing discharge. Extrapolation ofthe shift curves should be performed in accordancewith the principles discussed in Chapter 1 for shiftsin simple stage-discharge relations.0.000020.00001000.000010.000020.000080.000070.000060.000050.000040.00003SLOPE INCREMENT FROM FIGURE II.3.150.000090.000103.7 Computer methods for analysisand computation of slopeaffected ratingsFigure II.3.17. Diagram for determining factorto apply to measured discharge duringperiods of falling stageBoth the measured discharge, Q m, and adjusteddischarge, Q c, are entered in the list of dischargemeasurements and both are plotted on the ratingcurve. Suitable symbols are used, however, todifferentiate between the measured and adjusteddischarges.3.5 Variable slope caused by acombination of variablebackwater and changingdischargeWhere the rating for a gauging station is affected bya combination of variable backwater and changingdischarge, the rating should be analyzed as thoughit were affected by variable backwater only, usingthe fall-rating methods described in previoussections of this chapter. The basic equation forvariable-backwater adjustments (equation 3.7) andthat for changing-discharge adjustmentsThe preceding sections of this chapter havedescribed the theory and methods of computingdischarge for stream gauging stations where variablebackwater does not allow the use of a simple stagedischargerelation. The methods of computation, asdescribed, are hand methods using calculators andhand-plotted graphs. This is necessary so that theunderlying concepts of slope affected ratings areproperly understood. Today, however, with theadvent of computers it is possible to develop,analyze and apply slope-affected ratings quicklyand easily. The theory has not changed, only themethod of applying that theory.In the past, the development of slope-affectedratings required laborious hand plotting and replottingof ratings to arrive at an acceptablecalibration. Today the ratings can be plotted andreplotted quickly and easily with computerprograms designed for that purpose, thereby givingthe hydrologist more time for the analytical aspectsof the ratings. An additional benefit is that computerplots are much less susceptible to errors.Some ratings for variable backwater conditions maybe better analyzed using theoretical equationsrather than plotted ratings and hand fitted curves.In addition, ratings may, in some cases, be fitted to

II.3-20manual on stream gauginga set of data points using a least squares analysis orother curve-fitting technique. Computer analysisfor such methods provides additional valuableinformation about deviations of individualmeasurements and overall error analysis of therating itself.Computation of discharge records using variableslope as a factor with be described in a subsequentchapter of this manual. Emphasis will be placed oncomputer methods for making these computations.ReferencesCorbett, D.M., et al, 1945: Stream-gauging procedure.United States Geological Survey Water-SupplyPaper 888, pp. 130-167.Eisenlohr, W.S., Jr., 1964: Discharge ratings for streams atsubmerged section controls. United States GeologicalSurvey Water-Supply Paper 1779-1, 32 pp.International Organization for Standardization, 1998:Measurement of liquid flow in open channels. Part 2 –Determination of the stage-discharge relation,ISO 1100-2, 25 pp.International Organization for Standardization, 2001:Measurement of liquid flow in open channels –Stage-fall-discharge relationships, ISO 9123, 14 pp.Kennedy, E.J., 1984: Discharge ratings at gauging stations.United States Geological Survey Techniques of Water-Resources Investigations, Book 3, Chapter A10, 59 pp.Mitchell, W.D., 1954: Stage-fall-discharge relations forsteady flow in prismatic channels. United StatesGeological Survey Water-Supply Paper 1164, 162 pp.Rantz, S.E. and others, 1982: Measurement andcomputation of streamflow. Volume 2 – Computationof discharge. United States Geological Survey Water-Supply Paper 2175, pp 390-428.Rouse, Hunter, 1950: Engineering hydraulics. New York,John Wiley and Sons.Seddon, J.E., 1900: River hydraulics. Transactions of theAmerican Society of Civil Engineers, Volume 43,pp. 179-243.

Chapter 4FLOW COMPUTATI**ON** MODELS FOR UPLAND, BRANCHED ANDTIDAL **STREAM**S4.1 GeneralA discharge rating can sometimes be obtained forupland streams affected by variable backwater andfor tide-affected streams if a velocity index is usedas a parameter in the rating, along with stage. Theultrasonic and Acoustic Doppler Velocity Meters(ADVM), as described in Volume I, Chapter 8, mayin many instances be satisfactory for obtaining acontinuous record of velocity. Another approachfor computation of discharge where variablebackwater exists is through the use of slope ratings,as described in Volume II, Chapter 3. In the past,some empirical methods have also been used;however these are seldom used today and will onlybe described briefly.In situations where ratings and slope ratings are noteasily calibrated, flow computation modelsinvolving the evaluation of the equations ofunsteady flow may be used. Over the past 50 years,investigators in several countries have been involvedin the development and refinement of these models.The descriptions and examples that follow will bebased almost entirely on publications of the UnitedStates Geological Survey (USGS). Publications byAmein and Fang (1970), Baltzer and Lai (1968),Cunge, Holly, and Verwey (1980), Fread (1974), Lai,Baltzer, and Schaffranek (1980), Preissmann (1960),Schaffranek (1982), Schaffranek, Baltzer andGoldberg (1981) and Strelkoff (1969) are examplesof some of the literature available on the subject ofunsteady flow equations and their solution. Inparticular, the report by Schaffranek (1987) will beused extensively in the following discussions. Someparts of that report, including examples ofapplication, are used verbatim.In the past, the utility of numerical-simulationmodeling was often limited by imposition of certainsimplifying assumptions that were both necessaryand justifiable at the time. They were necessarybecause numerical methods and/or computercapacity were deficient and justifiable becauseparametric evaluation techniques and/or equipmentwere lacking or inadequate. Today, for the mostpart, advances in numerical methods, computertechnology and hydrologic instrumentation haveenabled model engineers to reduce the number ofsuch restrictions, thus producing models that aremore nearly formulated on pure hydraulicconsiderations and have a greater potential toprovide more comprehensive flow information.Consequently, the scope and complexity ofhydrodynamic problems that are now tractablehave expanded.This expansion of the role of numerical-simulationmodeling has stimulated the need for rapideconomical and efficient techniques to compileand appraise prototype data and model results.Thus, it is insufficient for a numerical scheme to bedeveloped merely to the state of being a modelprogram. To achieve a state of usefulness as anoperationally oriented investigative tool, the modelprogram must be supported by a comprehensiveuser-oriented data system and must provide a readymeans of presenting output results in variedgraphical forms.In view of this need, the USGS has developed acomprehensive, one-dimensional numericalsimulationmodel that is fully supported by auser-oriented system for modeling. The branchnetworkflow model, as it is called, is capable ofsimulating unsteady flow in a single open-channelreach or throughout a network of reaches composedof simple or multiple connected one-dimensionalflow channels governed by various time-dependentforcing functions and boundary conditions.Operational modeling capability is achieved bylinking the model to a highly efficient storage-andretrievalmodule that accesses a data base containingtime series of boundary values and by including anextensive set of digital graphics routines. Thesefeatures help transform the model into acomprehensive tool for practical use in the conductof hydrologic investigations.Two illustrative applications of the model arepresented. Application to a 274-m reach of PheasantBranch near Middleton, Wisconsin, United Statesof America, demonstrates its capability in computingunsteady flow in short, upland-river reachesthat can be highly responsive to climatologicalconditions. Application to a 25-branchschematization of the 50-km tidal river part of thePotomac Estuary near Washington, D.C., UnitedStates, illustrates its feasibility in simulating tidalflows in estuarine-type network environments thatare frequently subject to extreme freshwater inflowsand variable meteorological influences.

II.4-2manual on stream gauging4.2 TerminologyTo facilitate further discussion of the application ofthe model to either a single riverine channel or asystem of channels, a few definitions are necessary.The terms reach and branch are used somewhatinterchangeably to mean a length of open channel.The primary subdivision of a reach or branch isreferred to as a subreach or segment. A network isdefined as a system of open channels either simplyconnected in treelike fashion or multiple connectedin a configuration that permits more than one flowpath to exist between certain locations in thesystem.4.3 One-dimensional unsteady flowequationsOne-dimensional unsteady flow in open channelscan be described by two partial-differentialequations expressing mass and momentumconservation. These well-known equations,frequently referred to as the unsteady flow, shallowwater or St. Venant equations (Baltzer and Lai, 1968;Dronkers, 1969; Strelkoff, 1969; Yen, 1973) can bewritten:∂Z∂t∂Q+ − q = 0∂xB (4.1)and∂Q∂∂2( βQA)∂Zgk+ + gA +(4.2)4 3t ∂x∂xARQ Q2− qu ʹ − ε B U c acosα= 0in which the momentum coefficient, β, the flowresistancefunction, k, and the wind-resistancecoefficient, ε, are defined as:β = 1 2U Aηk =( ) 1.49andςaε = C d ς∫2u dA (4.3)2(or, in SI units, as2k = η ) (4.4)(4.5)In these equations, formulated using water-surfaceelevation, Z, and flow discharge, Q, as the dependentvariables, distance along the channel thalweg, x,and elapsed time, t, are the independent variables.(Longitudinal distance, x, and flow discharge, Q, arepositive in the downstream direction.) Otherquantities in the preceding equations are defined asfollows: A = area of conveyance part of cross section;B = total top width of cross section; B e= top widthof conveyance part of cross section; C d, = watersurfacedrag coefficient; g = gravitationalacceleration; q = lateral inflow per unit length ofchannel (negative for outflow); R = hydraulic radiusof cross section; u = flow velocity at a point; u’=x-component of lateral flow velocity; U = meanvelocity of flow, = Q/A; U a= wind velocity; α = winddirection measured from positive x-axis; η = flowresistancecoefficient similar to Manning’s n; ς =water density and ς a= atmospheric density.Although hydraulic radius, R, is used in equation 4.2and in subsequent expansions throughout thisdevelopment, the commonly used substitution ofhydraulic depth is employed in the model. Thisapproximation, R = A/B, is assumed valid for shallowwater bodies, that is, channels having a large widthto-depthratio.The momentum coefficient, β, also called theBoussinesq coefficient, is present in the equation ofmotion to account for any non-uniform velocitydistribution (see equation 4.3).Equations 4.1 and 4.2 are, in general, descriptive ofunsteady flow in a channel of arbitrary geometricconfiguration having both conveyance and overflow(or only conveyance) areas and potentially subjectto continuous lateral flow and/or the shear-stresseffects of wind. In their formulation it is assumedthat the water is homogeneous in density,hydrostatic pressure prevails everywhere in thechannel, the channel bottom slope is mild anduniform, the channel bed is fixed (that is noscouring or deposition occurs), the reach geometryis sufficiently uniform to permit characterization inone dimension and frictional resistance is the sameas for steady flow, thus permitting approximationby the Chezy or Manning equation.4.4 Model formulationNumerous varied mathematical methods andcorresponding numerical schemes exist that renderapproximate solutions of the flow equations.However, new methods and alternative schemesthat provide more accurate approximations and areinherently more flexible and efficient are continuallybeing sought. In the branch-network modelformulation, the flow equations are expressed infinite-difference form using a weighted four-point

Chapter 4. FLOW COMPUTATI**ON** MODELS FOR UPLAND, BRANCHED AND TIDAL **STREAM**SII.4-3(box) scheme. This technique, also used by Fread(1974) and by Cunge and others (1980), permits themodel to be applied using unequal segment lengthsand box-centered to fully forward discretizations. Aunique transformation operation is applied to thesegment flow equations in the branch-networkmodel, however, to lower the order of the coefficientmatrices and thereby reduce computer time andstorage requirements. A general matrix solutionalgorithm is used to simultaneously solve theresultant branch-transformation and boundaryconditionequations. The implicit solution methodis employed because of its inherent efficiency andsuperior stability properties. An optional iterationprocedure, controllable by user-defined tolerancespecifications, is additionally provided to permitimproving the accuracy of the computedunknowns.It is beyond the scope of this report to describe themathematical procedures and solution techniquesin detail. Those readers that are interested in thedetailed mathematics involved in the finitedifference technique should refer to Fread (1974),Cunge and others (1980), Schaffranek (1987),Schaffranek, Baltzer, and Goldberg, (1981),Preissmann (1960), Amein and Fang (1970) andBaltzer and Lai (1968).The solution process begins at an initial time by useof specified initial conditions and proceeds inspecified time increments to the end of thesimulation. Gauss elimination using maximumpivot strategy is employed to solve the system ofequations. Iteration within a time step is performedto provide results within user-specified tolerances.The primary effect of iteration is to improve on thequantities taken as local constants within the timestep, which in turn increases the accuracy of thecomputed unknowns. User-defined accuracyrequirements are typically achieved in two or feweriterations per time step.4.5 Boundary conditionsTo solve the branch-transformation equationsimplicitly, boundary conditions must be specifiedat internal junctions located at branch confluenceswithin the network as well as at external junctionslocated at the extremities of branches, for example,where branches physically terminate or aredelimited for modeling purposes. Equationsdescribing the boundary conditions at internaljunctions are automatically generated by the model,whereas boundary-condition equations for externaljunctions are formulated by the model from usersuppliedtime-series data or from user-specifiedfunctions.Various combinations of boundary conditions canbe specified for external junctions. A null dischargecondition (as, for example, at a dead-end channel),known stage or discharge as a function of time, or aknown, unique stage-discharge relationship can beprescribed. Together, the internal and externalboundary conditions provide a sufficient numberof additional equations to satisfy requirements ofthe solution technique.4.6 Model applicationsThe thoroughness of the equation formulation onwhich a model is based largely governs the range ofcomplexity of flows it can accommodate. Thechoice of a numerical computation schemeprimarily determines whether or not the model willbe stable, convergent, accurate and computationallyefficient given that it is correctly and preciselyimplemented. However, for any model to be usefulit must be subsequently transformed into afunctional user-oriented simulation system, and itsaccuracy, reliability and versatility must beadequately proved and demonstrated.The branch-network model is being used to simulatethe time-varying flows of several coastal and uplandwater bodies in the United States, as identified inTable II.4.1. These represent a broad spectrum ofhydrologic field conditions, depicting such diversehydraulic and field situations as hydropower-plantregulatedflows in a single upland-river reach,tide-induced flows in riverine and estuarine reachesand networks, unsteady flow in a residential canalsystem and meteorologically generated seiches andwind tides in a multiply connected network ofchannels joining two large lakes.Four types of model application are identified inTable II.4.1. The simplest of these is the singlebranchtype, which is an application to a singlereach of channel delimited by a pair of externalboundary conditions. The multiple-branch type isan application to a channel, again delimited by apair of external boundary conditions, butschematized as a series of sequentially connectedreaches. The dendritic-network type is an applicationto a channel system composed of branchesconnected in treelike fashion. The multipleconnected network type is likewise an applicationto a channel system, but one in which the branches

II.4-4manual on stream gaugingTable II.4.1. Application of the branch-network flow model in the United StatesState Water body location Application typeAlabamaCoosa River near ChildersburgAlabama River near Montgomery35.2-km multiple branch21-branch multi-connected networkAlaska Knik/Matanuska River Delta near Palmer 20-branch multi-connected networkCaliforniaSacramento River from Sacramento to FreeportSacramento River from Sacramento to HoodSacramento Delta between Sacramento and Rio VistaThreemile Slough near Rio Vista17.4-km single branch34.3-km multiple branch24-branch multi-connected network5.2-km single branchConnecticutConnecticut River near MiddletownConnecticut River downstream from Hartford9.8-km single branch41.2-km multiple branchFloridaCape Coral residential canal systemPeace River from Arcadia to Fort OgdenPeace River from Fort Ogden to Harbour Heights16-branch multi-connected network30-km multiple branch21-branch multi-connected networkIdaho Kootenai River near Porthill 54.8-km multiple branchKentucky Ohio River Downsteam from Greenup Dam 21.7-km single branchLouisianaAtchafalaya River near Morgan CityWax Lake Outlet near CalumetCalcasieu River between Lake Charles and Moss LakeQuachita River form Monroe to ColumbiaVermillion River from Lafayette to PerryLoggy Bayou near NinockMermentan River from Mermetan to Lake Arthur8-branch multi-connected network15-branch multi-connected network13-branch multi-connected network78.9-km multiple branch48.3-km multiple branch9.2-km single branch25.7-km multiple branchMaryland Potomac River near Wahington, D.C. 25-branch multi-connected networkMichiganDetroit River near DetroitSaginaw River near Saginaw12-branch multi-connected network1.4-branch dentritic networkMissouri Osage River near Schell City 2.6-km single branchNew York Hudson River from Albany to Poughkeepsie 9-branch dentritic networkNorth Dakota Red River of the North at Grand Forks 1.3-km single branchSouth CarolinaIntracoastal Waterway near Myrtle BeachCooper River at Diversion CanalCooper River at Lake Moultrie TailraceBack River near Cooper River confluence36.7-km multiple branch6.3-km single branch1.5-km single branch2.2-km single branchSouth Dakota James River near Hecla 8.5-km multiple branchWashington Columbia River dowmstream from Rocky Reach Dam 3.1-km single branchWisconsinPheasant Branch near MiddletonMenomonee River near MilwaukeeMilwaukee Harbor at Milwaukee0.27-km single branch0.61-km single branch12-branch multi-connected network

Chapter 4. FLOW COMPUTATI**ON** MODELS FOR UPLAND, BRANCHED AND TIDAL **STREAM**SII.4-5are interconnected, thereby permitting multipleflow paths between certain locations in the system.To illustrate the diverse capabilities of the model,two applications identified in Table II.4.1 arediscussed briefly herein. These particularapplications were selected to demonstrate theflexibility of the model in accommodating a widerange of hydrologic conditions and field situations.Rocky Reach Dam12-4537 00++MILE473MILE47447°32’304.6.1 Columbia River reach at RockyReach Dam near Wenatchee,Washington, United StatesThe branch-network flow model has been used tocompute the flow of the Columbia River immediatelydownstream from Rocky Reach Dam nearWenatchee, Washington, United States. Thisrelatively short reach (3.1 km) is treated as a singlesegmentbranch in the model schematization. Flowin the reach is highly unsteady owing to regulationcreated by the combined operation of turbines andgates at the dam for the purpose of optimalhydroelectric power generation.Channel geometry data for the model wereabstracted from detailed field surveys, processed bythe cross-sectional geometry program and preparedfor input to the model. The branch network flowmodel treats the reach as a single segment; therefore,stage-area-width tables were produced that definethe upstream and downstream cross sections at theboundary-value data locations.Time series of water-surface elevations are used asboundary conditions for the model application.These data are collected on a continuous basis atthe field station locations (stations numbered 12-4537.00 and 12-4537.01) identified in Figure II.4.1near river miles 471 and 473, respectively. The closeproximity of the boundary-value stationsunderscores the importance of precise synchronizedrecording of the water-surface elevations. Theboundary value data are extracted from the timedependent data base during the simulation asrequired to define the boundary conditions.The highly unsteady nature of the flow is illustratedin the model-generated plot of computed dischargesin Figure II.4.2. As this figure illustrates, the unsteadydischarge can vary as much as 2 000 m 3 s -1 in lessthan 2 hours elapsed time. In fact, the discharge hasbeen observed to vary as much as 1 000 m 3 s -1 in lessthan 0.5 hour. This application amply demonstratesthe ability of the branch-network flow model tosimulate highly varying flow conditions, as may beencountered in regulated upland rivers.120°20’12 4537 01COLUMBIA++RIVER▼MILE469+MILE470MILE47100+MILE472Study AreaWASHINGT**ON**1 MILE1 KILOMETER47°30120°17’30 47°27’30Figure II.4.1. Columbia River reach nearRocky Reach Dam in the State of Washington,United States4.6.2 Potomac River near Washington,D.C., United StatesIn October 1977, the Water Resources Division ofthe USGS instituted a 5-year interdisciplinary studyof the tidal Potomac River and Estuary (Callenderand others, 1984). The research areas undertaken inthis investigation included historical geologicstudies, geochemistry of bottom sediments, nutrientcycling, sediment transport and tributary loading,wetland studies, benthic ecology and hydrodynamics.The objective of the hydrodynamics project was todevise, implement, calibrate and verify a series ofnumerical flow/transport simulation models insupport of the other research efforts. To quantifythe hydrodynamics of the tidal river, the branchnetworkmodel was applied to the 50-km segmentof the Potomac, including its major tributaries andinlets from the head of tide at the fall line inthe northwest quadrant of Washington, D.C., toIndian Head, Maryland, United States, as shown inFigure II.4.3.

II.4-6manual on stream gaugingCOLUMBIA RIVER BELOW ROCKY REACH DAMFLOW COMPUTED BY THE BRANCH NETWORK MODEL **ON** 80/4 /25 10.13.568.577°15’39°00’77°00’1-1 (12-4537.00)1-2 (12-4537.01)CHAIN BRIDGE01-6465.008.07.57.0KEY BRIDGEDAINGERFIELD ISLANDChain Bridge Washington, D.C.Key Bridge01-6476.00Tidal BasinRoosevelt IsChannelMemorialBridgeWashingtonChannelAnacostia River01-6521.00DISCHARGE, IN 10 3 m 3 /s6.56.05.538°45’WILS**ON** BRIDGEHATT**ON**POINTMOUNT VERN**ON**VIRGINIA01-6525.88Hains PointWilson BridgeBroad CreekMARYLAND5.04.5INDIAN HEADDogueCreekAccotinkBayMountVernonPOTOMACRIVERPiscatawayCreek4.0Pohick BayGunstonCove3.52 4 6 8 10 12 14 16 18 20 22 24TIME 76/7 /24Indian Head01-6554.8005 MILES0 5 KILOMETERSFigure II.4.2. Comparison of computed dischargeto observed discharge for the Columbia Rivernear Rocky Reach Dam in the State ofWashington, United StatesFigure II.4.3. Potomac River near Washington, DC.,United StatesThe Potomac River downstream from Chain Bridgeis confined for a short distance (approximately5 km) to a narrow, deep, but gradually expandingchannel bounded by steep rocky banks and highbluffs. Farther downstream the river consists of abroad, shallow, and rapidly expanding channelconfined between banks of low to moderate relief.Seven cross-sectional profiles illustrating thechannel geometry are plotted in Figure II.4.3. Thecross-sectional area and corresponding channelwidth expand more than forty-fold between ChainBridge and Indian Head. In general, the depth variesfrom about 9 m at Chain Bridge to about 12 m atIndian Head.Flow in the upstream portion of the tidal river istypically unidirectional and pulsating. Bidirectionalflow occurs in the broader downstream portion.The location of the transition from one flow patternto the other varies, primarily in response to changinginflow at the head of tide but also to changing tidaland meteorological conditions.The tidal river system is schematized as shown inFigure II.4.4. The network is composed of25 branches (identified by roman numerals) thatjoin or terminate at 25 junction locations (identifiedby numbered boxes). Junctions that do notconstitute tributary or inlet locations in Figure II.4.4were included in the network schematization toaccommodate potential nodal flows (point sourceinflows or outflows such as sewage treatmentoutfalls or pump withdrawals) or to account forabrupt changes in channel characteristics.A total of 66 cross sections were used to depict thechannel geometry in 52 flow segments. Whereasthe coefficient matrix of segment flow equationswould require 15 376 computer words, use ofbranch-transformation equations reduces thematrix size to 10 000 words. The computationaleffort required to affect a solution is alsoproportionally reduced.In the tidal Potomac River model, flow dischargesderived at a rated gauging station (01-6465.00)1.9 km upstream from Chain Bridge are used asboundary values at junction 1. Water-surfaceelevations recorded at a gauging station (01-6554.80) at Indian Head are used as the downstreamboundary values at junction 19. All other externalboundary conditions are fulfilled by specifying that

Chapter 4. FLOW COMPUTATI**ON** MODELS FOR UPLAND, BRANCHED AND TIDAL **STREAM**SII.4-7Chain Bridge101-6465.008zero discharge conditions prevail at the upstreamtidal extent of the particular channel orembayment.Dogue CreekAccotink Bay 25Pohick BayKey BridgeRoosevelt Is.ChannelMemorial Bridge14th St. Bridge2324Hains PointWilson BridgeXXIV22XIXXXVXXIIIXXIIIndian HeadPotomac River23415161718Potomac River19IIIIIITidal BasinXVIIIIVWashingtonChannel20211413XVII91011XV5 12XVIV01-6521.006 Marbury PointVI7 01-6525.88VIIVIIIIXXXIXXXXI01-6476.00Gunston Cove01-6554.80Anacostia RiverBroad CreekXIIXIIIXIVPiscataway CreekFigure II.4.4. Schematization of the tidalPotomac River system for the branch-networkflow modelWater-surface elevations recorded near Key Bridge(station 01-6476.00), near Wilson Bridge (station01-6525.88) and near Hains Point (station 01-6521.00) were used to calibrate and verify the model(see Figures II.4.3 and II.4.4). Model-computeddischarges were also compared with dischargesmeasured for complete tidal cycles at DaingerfieldIsland, Broad Creek and Indian Head.In Figure II.4.5, model-computed discharges areplotted against discharges measured at Indian Headfrom 2015 hours on 3 June to 0830 hours on 4 June,1981. As is evident from the plot, there is excellentagreement between computed and measureddischarges. Computed and measured ebb andflood volume fluxes compare within + 0.6 and– 2.3 per cent, respectively. This application of themodel clearly demonstrates its adaptability to thesimulation of unsteady flow in a network ofinterconnected channels.4.7 Empirical methodsFour empirical methods of rating tidal reaches havebeen in use, all but one of which were developedbefore the use of digital computers becamecommonplace. These methods are no longer ingeneral use for tidal streams today because modelssuch as the branch-network model described in theprevious sections of this chapter are easily appliedwith much better accuracy.The empirical techniques are:(a) Method of cubatures;(b) Rating-fall method;(c) Tide-correction method;(d) Coaxial graphical-correlation method.All of the above methods have their shortcomingswhich are discussed, where appropriate, in thefollowing sections.4.7.1 Method of cubaturesOne of the oldest methods of computing dischargein tidal estuaries is the method of cubatures(Pillsbury, 1956). The method is based on theequation of the conservation of mass, whereoutflow at the study station = inflow ± change instorage.

II.4-8manual on stream gaugingDISCHARGE, IN THOUSANDS OF CUBIC METRES PER SEC**ON**D543210-1-2-3-4ComputedMeasuredstations should be reduced to the same horizontaldatum, preferably taken low enough to make allstages positive.If existing surveys do not afford reliable data on theareas of the water surfaces between the selectedtidal stations, a survey to establish these surfaces isrequired. Usually such surface areas may be taken asincreasing, uniformly from low water to high water,but if there are any considerable tide flats that areexposed at the lower tidal stages, the area at thestage at which such flats are covered should also befound.Freshwater inflow to the reach from tributarystreams is estimated if the tributary flow is relativelysmall. If the tributary streams are large they aregauged upstream from the head of tide to provide acontinuous record of freshwater inflow, just as isdone with the principal inflow stream.The method of cubatures is not only cumbersomefor use but the discharge figures obtained are onlyrough approximations of the true values because ofthe large errors inherent in computing the storagecomponent of the continuity equation.-510 20 22 24 2 4 6 8 10 123 June1981TIME, IN HOURS4 June1981Figure II.4.5. Model-generated plot of computedversus measured discharges for the PotomacRiver at Indian Head, Maryland, United States,on 3-4 June 1981The inflow term in the above equation is thefreshwater discharge measured at a gauging stationat or upstream from the head of tide – that is, agauging station having a simple stage-dischargerelation. The storage term refers to volume of waterin the reach between the inflow gauging stationand the study station on the estuary. Intermediatestage gauges are usually needed for evaluating thestorage term. The gauges are spaced at such distancesthat no significant error is introduced in thecomputations by considering the water surfacesbetween gauges as planes. That requirementordinarily is met by stations some kilometres apart,but suitably placed with regard to marked changesin the cross-section of the waterway. The differencesin the tidal ranges on the opposite shores of a wideestuary may usually be disregarded, but it may benecessary to establish tidal stations on any longtidal tributaries of the main waterway. Forconvenience in the computations, the tides at all4.7.2 Rating-fall methodStage-fall-discharge relations have been usedsuccessfully for rating tide-affected streams whereacceleration head is a minor factor. The rating-fallmethod that is discussed in detail in Chapter 3 isused for that purpose. Acceleration head is often aminor factor where the slope reach is located at theupper end of an estuary near the head of tide.Consequently it is usually only at or near suchlocations that the rating-fall method can be usedsuccessfully.4.7.3 Tide-correction methodThe tide-correction method assumes that a directproportionality exists between the cyclic range instage observed at any two points within a tidalreach. Based on that assumption a relation of meandischarge for a tidal cycle to mean stage for a tidalcycle is developed for the base-gauge site. Incalibrating that relation, the mean discharge for atidal cycle, obtained by averaging several individualmeasurements made one to two hours apartthroughout the cycle, is plotted against adjustedmean stage at the base gauge. The adjustmentapplied to the mean stage at the base gauge isdetermined from the difference, at the secondarygauge, between observed mean stage and the stagewhich is presumed to exist under conditions of

Chapter 4. FLOW COMPUTATI**ON** MODELS FOR UPLAND, BRANCHED AND TIDAL **STREAM**SII.4-9least tide fluctuation. That difference, D, ismultiplied by the ratio of the stage range at thebase gauge to the stage range at the secondarygauge. The product is the stage adjustment requiredat the base gauge. In practice the secondary stageobservations are frequently made at a nearbyocean inlet. Mean sea level is assumed to representthe condition of least tidal fluctuation, andtherefore, if all gauges have their datum’s set tomean sea level, D is always equal to the mean stagefor a tidal cycle at the secondary gauge. Essentiallythe tide-correction method attempts toapproximate the stage which would occur for aparticular steady-flow-discharge under a fixedbackwater condition.The tide-correction method of rating a tide-affectedstream may be used where reverse flows occurduring a part of reach tide cycle because the meandischarge for the cycle is the value used in thecomputation. It is also applicable to a reach oftidal waterway on which both observation stationsare upstream from the mouth of the waterway.Mean-cycle discharge obtained from the ratingcurve can be plotted against mean-cycle time on ahydrograph sheet, and after connecting the pointsby straight lines the daily mean discharges can bedetermined.The tide-correction method has been satisfactory,though cumbersome, for computing the dailydischarge of tide-affected canals in Florida, UnitedStates, but efforts to adopt the method for useelsewhere in the United States have generally beenunsuccessful.4.7.4 Coaxial rating-curve methodThe coaxial method of graphical correlation todetermine discharge in a tidal reach (Rantz, 1963)was developed to fill the need for a simple methodof making reasonably accurate on-the-spotdetermination of streamflow. A method of this kindis required, for example, in the operation of asewage plant discharging its effluent into a tideaffectedstream. The method that was developed,which is basically a graphical method of solving theequations of unsteady flow, fills this need in thatreadings from a pair of stage gauges can be used todetermine momentary discharge directly from a setof rating curves. However, the method is toocumbersome for use in computing a continuousrecord of discharge for a gauging station. Solutionof the theoretical equations of unsteady flow asdescribed in previous sections of this chapter ismuch better for the latter purpose.ReferencesAmein, Michael, and Fang, C.S., 1970: Implicit floodrouting in natural channels. American Society of CivilEngineers Proceedings. Journal of the HydraulicsDivision, Volume 96, No. HY12, p. 2481-2500.Baltzer, R.A., and Lai, Chintu, 1968: Computer simulationof unsteady flows in waterways. American Society ofCivil Engineers Proceedings, Journal of the HydraulicsDivision, Volume 94, No. HY 4, p. 1083-1117.Callender, Edward, Carter, Virginia, Hahl, D.C., Hitt,Kerie, and Schultz, B. I., eds., 1984: A water-qualitystudy of the tidal Potomac River and estuary-Anoverview. United States Geological Survey Water-Supply Paper 2233, 46 p.Cunge, J.A., Holly, F.M., Jr., and Verwey, Adri, 1980:Practical aspects of computational river hydraulics.Marshfield, Mass., Pitman, 420 p.Dronkers, J.J., 1969: Tidal computations for rivers, coastalareas, and seas. American Society of Civil EngineersProceedings, Journal of the Hydraulics Division,Volume 95, No. HYl, p. 29-77.Fread, D.L., 1974: Numerical properties of implicit fourpointfinite-difference equations of unsteady flow.National Oceanic and Atmospheric AdministrationTechnical Memorandum NWS HYDRO-18, 38 p.International Organization for Standardization, 1974:Measurement of flow in tidal channels. ISO 2425,Geneva.Lai, Chintu, Baltzer, R.A., and Schaffranek, R.W., 1980:Techniques and experiences in the utilization of unsteadyopen-channel flow models. American Society of CivilEngineers, Specialty Conference on Computer andPhysical Modeling in Hydraulic Engineering, Chicago,TIl., 6-8 August 1980, Proceedings, p. 177-191.Pillsbury, G.B., 1956: Tidal hydraulics. United States ArmyCorps of Engineers, Waterways Experiment Station,Vicksburg, Mississippi, pp. 220-228.Preissmann, Alexander, 1960: Propagation desintumescences dans les canaux et les rivières:Premier Congrès d’Association française de calcul.(Propagation of translatory waves in channels andrivers: First Congress of the French Association forComputation), Grenoble, France, p. 433-442.Rantz, S.E., 1963: An empirical method of determiningmomentary discharge of tide-affected streams. UnitedStates Geological Survey Water-Supply Paper 1586-D, 28 pp.Regan, R.S., and Schaffranek, R.W., 1985: A computerprogram for analyzing channel geometry. United StatesGeological Survey Water-Resources InvestigationsReport 85-4335, 49 p.Schaffranek, R.W., 1982: A flow model for assessingthe tidal Potomac River. American Society of CivilEngineers, Specialty Conference on ApplyingResearch to Hydraulic Practice, Jackson, Miss.,17-20 August 1982, Proceedings, p. 521-545.

II.4-10manual on stream gaugingSchaffranek, R.W., 1987: Flow model for open-channelreach or network. United States Geological SurveyProfessional Paper 1384, 11 p.Schaffranek, RW., Baltzer, RA., and Goldberg, D.E., 1981:A model for simulation of flow in singular andinterconnected channels. United States GeologicalSurvey Techniques of Water- ResourcesInvestigations, Book 7, Chap. C3, 110 p.Strelkoff, Theodor, 1969: One-dimensional equationsof open-channel flow. American Society of CivilEngineers Proceedings, Journal of the HydraulicsDivision, Volume 95, No. HY3, p. 861-876.Yen, Ben Chie, 1973: Open-channel flow equationsrevisited. American Society of Civil EngineersProceedings, Journal of the Engineering MechanicsDivision, Volume 91, No. EM5, p. 979-1009.

Chapter 5DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIES5.1 IntroductionThis chapter includes specialized problems in establishingdischarge ratings for various hydraulicfacilities, using techniques that are not specificallydescribed in Chapters 1 to 4 . In addition, a generaldescription of a computer program that integratesseveral of the structure ratings into an automatedprogram for computation of flow through a lockand dam structure is presented in this chapter. Thehydraulic facilities and computer program arediscussed under the following principal headings:(a) Dams with movable gates;(b) Navigation locks;(c) Pressure conduits;(d) Urban storm drains;(e) Automated computation of flow through watercontrol structures.5.2 Dams with movable gates5.2.1 GeneralDams are commonly equipped with movable gatesfor better control of pool stage and outflow. As sucha general rule is that are not rated, Instead thechannel downstream is rated by the most practicablemethod. The rating method may be a simple stagedischargerelation (Chapter 1), a velocity-indexrating (Chapter 2), a stage-fall-discharge relation(Chapter 3) or by use of the ultrasonic (acoustic)method (Volume I, Chapter 6). However, in somesituations none of those rating methods may besatisfactory. For example, consider a river controlledby a series of low navigation dams. In that situationthe river profile resembles a huge staircase; successivepools separated by dams. The movable dam crestsnegate the use of a simple stage-discharge relation.The slope of the water surface in the pools may betoo flat for a stage-fall-discharge relation; andvelocities may be too low for accurate evaluation bythe acoustic Doppler or ultrasonic methods. In thatsituation the most practicable method of obtaininga continuous record of discharge is to calibrate theflow through or over the movable gates. If boattraffic is heavy and natural inflow is light, asignificant part of the discharge may be the flowreleased through the navigation locks and thelockages must likewise be calibrated. In some cases,computation of turbine flow may also be required.Calibration of the gates by discharge measurementsduring periods of small releases of water may beextremely difficult. If boat lockages are infrequent,standard current-meter measurements madedownstream by boat, using a low-velocity metermay be adequate. If boat lockages are frequent, thesurges in discharge attributable to the lockages maycause unsteady and non-uniform flow conditionsdownstream. Discharge measurements must thenbe made as rapidly as possible under conditionsthat are not conducive to accurate results. A rapiddischarge measurement may be made by themoving-boat method using the Acoustic DopplerCurrent Profiler (ADCP) as described in Volume I,Chapter 6, or by use of a bank of current metersoperated from a bridge as described in Volume I,Chapter 5. If velocities are too low for accuratemeasurement by either of those two methods and ifonly small quantities of water are being releasedunder the dam-crest gates, the best course of actionmight be to use the volumetric method discussed inVolume I, Chapter 8 for measuring flow over a damcrest. In using the volumetric method, the bargecarrying the calibration tank is kept in place notonly by lines operated from the banks but also byan outboard motor on the barge to keep the bargefrom drifting downstream. The difficulty ofmeasuring low flow under the conditions describedabove is apparent. At those times it may also bedifficult to determine the actual head on the gatesbecause lockages often cause longitudinal seichelikewaves to traverse the gauge pool and thosewaves travel back and forth over the length of thepool for a considerable period of time.The flow at movable dam-crest gates may be placedin two general categories: (a) weir flow over the gateor dam crest and (b) orifice flow under the gate.Each of those types of flow may be either free orsubmerged, depending on the relative elevations ofheadwater, tailwater and pertinent elements of thedam crest or gate. Listed below are the crest gatesthat will be discussed:(a) Drum gates;(b) Radial or Tainter gates;(c) Vertical lift gates;(d) Roller gates;(e) Movable dams:(i) Bear-trap gates;(ii) Hinged-leaf gates;(iii) Wickets;

II.5-2manual on stream gauging(iv) Inflatable dams;(f) Flashboards;(g) Stop logs and needles.A gated dam usually has several gates along its crest.The gates are installed in bays that are separated bypiers. All other conditions being equal, the dischargethrough a single gate, when adjacent gates are open,will be about five per cent greater than the dischargethrough that same gate when adjacent gates areclosed. The various types of gates should becalibrated by discharge measurements. But as anaid to shaping the calibration curves, experimentalratings, where available, are given in the text thatfollows.Discharge measurements for the purpose ofdetermining gate coefficients will almost always bemade in the downstream channel and will includethe flow for all the gates that are open. Furthermore,for given stages upstream and downstream fromthe gates, the gate coefficient will commonly varywith the gate position or opening. Consequently, ifdischarge is to be measured with more than onegate open, arrangements should be made, if possible,for all gates to be positioned identically. If thedifferences in the positioning of the gates are minorand if the gate coefficient does not vary significantlywith its positioning, a discharge measurement maybe made. For computation of the gate coefficient anaverage gate position will be assumed for each ofthe bays carrying flow.5.2.2 Drum gatesA drum gate consists of a segment of a cylinderwhich, in the open or lowered position, fits in arecess in the top of the spillway. When water isadmitted to the recess, the hollow drum gate isforced upward to a closed position. One type ofdrum gate (Figure II.5.1 (a)) is a completely enclosedgate hinged at the upstream edge. Buoyant forcesaid in its lifting. This type of gate is adapted toautomatic operation and also conforms closely tothe shape of the ogee crest when lowered. A secondtype (Figure II.5.1(b)) has no bottom plate and israised by water pressure alone. Because of the largerecess required by drum gates in the loweredposition they do not adapt well to small dams.With regard to its calibration, the drum gateresembles a thin-plate weir with a curved upstreamface over the greater part of its travel. Given anadequate positioning indicator, the drum gate canserve as a satisfactory stream-gauging control. Itsuse for that purpose has been investigated byBradley (1953) and the discussion that follows istaken almost verbatim from Bradley’s paper dealingwith a drum gate of the type shown inFigure II.5.1(a).When the drum gate simulates a thin-plate weir,that is, when a line drawn tangent to the downstreamlip of the gate makes a positive angle with thehorizontal, as shown in Figure II.5.2(a), fourprincipal factors are involved. These factors are H,the total head above the high point of the gate; θ,the angle between the horizontal and a line drawntangent to the downstream lip of the gate; r, theradius of the gate, or an equivalent radius if theshape of the gate is parabolic and C q, the coefficientof discharge in the following equation:Q = C qLH 3/2 (5.1)where Q is discharge (m 3 s -1 ) and L is length of thegate (m) normal to the discharge.The velocity in the approach section was notincluded as a variable because the drum-gateinstallations studied were on high dams whereapproach effects were negligible. It has been shownthat when the approach depth measured below thehigh point of the gate is equal to or greater thanHinge and sealHollow drumSealSealHollow drumHinge and seal(a)(b)Figure II.5.1. Two types of drum gate

Chapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIESII.5-3h ah aHigh pointof gate+θH+θH-θ-θrrrο(a) Positive angle, θ(b) Negative angle, θ(c) Control pointFigure II.5.2. Drum-gate positions (after Bradley, 1953)twice the head on the gate, further increases in theapproach depth produces little change in thecoefficient of discharge. Most drum-gate installationsare on dams that meet the above depth criterion,particularly when the gate is in a raised position.Therefore, in the usual case of adequate approachdepth, the four variables, H, θ, r and C qcompletelydefine the flow over this type of gate when angle θis positive (Figure II.5.2(a)).For negative values of θ (Figure II.5.2(b)) thedownstream lip of the gate no longer controls theflow. In that situation the control point shiftsupstream to the vicinity of the high point of thegate for each setting, as illustrated in Figure II.5.2(c),and flow conditions gradually approach those ofthe free crest as the gate is lowered. Although otherfactors enter the problem, similitude in thecomputation exists down to an angle of about– 15°.Experimentation with eleven drum gates producedthe family of curves for C qshown in Figure II.5.3.The discharge coefficients in the region betweenθ = – 15° and the gate completely down aredetermined by graphical interpolation, a methodthat will be explained in the example that follows.The effect of submergence of the drum gate on C qwas not investigated because drum gates areinvariably used on high dams and the probabilityof submergence is negligible. The data to becontinuously recorded for computing dischargeover rated drum gates are reservoir stage and theindication of drum-gate position for each gate.The method of rating a drum gate on a roundcrestedweir will now be demonstrated using as anexample the plan and spillway cross-section ofBlack Canyon diversion dam in Idaho, United Statesof America (Figures II.5.4 and II.5.5). The first stepis the determination of the design head of the damand the corresponding discharge coefficient for thefree crest. That is done in accordance with thetechnique described under the heading Nappe-fittingmethod in the United States Geological Survey(USGS), Manual on computing peak discharge atdams (Hulsing, 1967, pp. 13-23). If a dischargemeasurement has been made under the conditionof flow over a free crest, the results of themeasurement are used to check the value of designhead and design-head coefficient, using thetechnique described under the heading Indexmeasurementmethod in the previously cited Manualby Hulsing (1967, pp. 23-24). The design head (H 0), in Degreesθ50454035302520151050-5-10Hrh aStraight InclinedWeirs (H= 0)r-150.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Ratio H r-202.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4Discharge Coefficient, C qθRatioHr0.7 0Figure II.5.3. General curves for the determinationof discharge coefficients (after Bradley, 1953)

II.5-4manual on stream gaugingCrest (Gate Up) El. 761.1 m738742740744746748750748746746744740738734733732PAYETTE RIVER728732736734El. 755.29 m1.37 m3.89 mCrest (Gate Down) El. 756.67Center line of Pin El. 756.40 m756.67 mPoint of CompoundCurvature El. 755.36 mEl. 755.35 m19.51 m by 4.42 m Drum Gates19.51 m1.98 m 2.03 m2.44 m 1.52 m 3.12 m6.4 m Radius1 on 17526°50’7327387507287467447427407387347327307307367347407427447467487481 on 1Figure II.5.4. Plan of Black Canyon Diversion Damin Idaho, United States (after Bradley, 1953)Figure II.5.5. Spillway crest details, Black CanyonDam in Idaho, United States (after Bradley, 1953)1.31.21.16RATIO, H H o10.90.80.70.60.50.4Total head above crest (m)54320.30.210.100.7 0.8 0.9 1 1.1RATIO, C qC o01.4 1.5 1.6 1.7 1.8 1.9 2Coefficient C qFigure II.5.6. Diagram for determining coefficientsof discharge for heads other than the design head(after Bradley, 1953)Figure II.5.7. Head coefficient curve, Black CanyonDam, Idaho, United States (after Bradley, 1953)of Black Canyon diversion dam was found to be4.35 m and the corresponding coefficient ofdischarge (C 0) was found to be 1.92 (C d= 0.613).With the coefficient of discharge known for freeflow at the design head, the entire free-flowcoefficient curve can be established by use ofFigure II.5.6. The free-flow coefficient curve for thespillway of Black Canyon diversion dam (H 0= 4.35 m;C 0= 1.91) is constructed by arbitrarily assumingseveral values of H/H 0and reading the correspondingvalues of C/C 0in Figure II.5.6. The method ofcomputation is illustrated in Table II.5.1, and thehead-coefficient curve for free flow (gate down)obtained in that manner is shown in Figure II.5.7.Before considering the rating of the spillway withgates in raised positions it is necessary to constructa diagram, such as that shown in Figure II.5.8, torelate gate elevation to the angle θ for the Black

Chapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIESII.5-5Table II.5.1. Head and discharge computations for a free crest (Black Canyon Dam in Idaho, United States)Total head H,in metresReservoir elevation,in metresRatio a H/H oRatio b C q/C oCoefficient C qQ in cu m per sec. c(1) (2) (3) (4) (5) (6)5.182 761.848 1.172 1.020 1.963 451.654.877 761.543 1.104 1.012 1.944 408.334.420 761.086 1.0 1.0 1.921 348.183.658 760.324 0.827 0.980 1.883 256.893.048 759.714 0.690 0.960 1.844 191.392.438 759.104 0.552 0.940 1.806 134.111.829 758.495 0.414 0.905 1.731 83.511.219 757.885 0.276 0.850 1.633 42.870.914 757.580 0.207 0.815 1.566 26.700.610 757.276 0.138 0.760 1.458 13.54a H = 4.420 m b C o= 1.92cThe discharge for one gate: Q = C qLH 3/2 , in which L = 19.507 mCanyon Dam gate. The tabulation in Figure II.5.8shows the angle θ for corresponding elevations ofthe downstream lip of the gate at intervals of0.6 m.Beginning with the maximum positive angle of thegate, which is 34.883°, the computation may bestarted by choosing a representative number ofreservoir elevations as indicated in column 2 ofTable II.5.2. The difference between the reservoirelevation and the high point of the gate constitutesthe total head on the gate and values of head areEl. Crest 756.666 mEl. Pin 756.401 mEl. 750.265 m5.090 m?37˚19a > 11.25˚El. 758.099 mEl. 757.657 mEl. 757.275 mEl. 756.940 mEl. 756.655 mR = 6.401 mA = 34 .8651.045 1.418 1.637El. 761.086 mEl. 760.476 mEl. 759.866 mEl. 759.257 mEl. 758.647 mEl. 758.037 mEl. 757.428 mEl. 756.818 mEl. 756.401 mEl. 756.209 mEl. 755.355 mθ = 37.317 ˚Elevationhighpoint β θ inof gate sine β in degrees degrees576.666 – 37.317757.657 0.19167 11.050 – 15.017758.100 0.30541 17.783 – 8.264758.647 0.41918 24.783 – 1.284759.257 0.53288 32.200 + 6.133759.866 0.64658 40.292 + 14.225760.476 0.76041 49.500 + 23.433761.056 0.87420 60.950 + 34.883Figure II.5.8. Relation of gate elevation to angle θ(after Bradley, 1953)recorded in column 3. Column 4 shows these sameheads divided by the radius of the gate, which is6.3 m.The discharge coefficients listed in column 5 ofTable II.5.2 of the set of computations designatedA, are obtained by entering the curves in Figure II.5.3with the values in column 4 for θ = + 34.883°. Theremainder of the procedure outlined in columns 6and 7 of Table II.5.2 consists of computing thedischarge for one gate from equation 5.1. A similarcomputation procedure is repeated for otherpositive angles of θ, as in sets B, C and D ofTable II.5.2.For positive values of angle θ the high point of thegate is the downstream lip of the gate. As the angleθ decreases to negative values the high point of thegate is no longer the downstream lip. In determiningthe discharge for negative values of θ between 0°and – 15°, the procedure remains the same as wasused for positive values of θ, but as mentionedabove, the controlling difference between reservoirelevation and high point of the gate is no longerthe head above the downstream lip. (seeFigure II.5.8.) Discharge computations for negativeangles down to – 15.017° are tabulated in sets E, Fand G of Table II.5.2.The plotting of values of discharge, reservoirelevation and gate elevation from Table II.5.2,results in the seven curves in Figure II.5.9 that bearthe plotted points, shown by closed circles. The

II.5-6manual on stream gauging762762761761760RESERVOIR ELEVATI**ON**, IN METRES760759758757759758757756.67Gate completely downElevation of high point of gauge, in metres756Free Crest El. 756.67 m7550 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48DISCHARGE, IN THOUSANDS OF CUBIC METRES PER SEC**ON**DFigure II.5.9. Rating curves for Black Canyon Dam drum spillway in Idaho, United States(after Bradley, 1953)RESERVOIR ELEVATI**ON**, IN METRES762761760759758757Discharge in cubic meters per second for one gate34032030028026024022020012010080604020100180160140Crest El. 756.67 mFree Crest El. 756.67 m756756 757 758 759 760 761 762ELEVATI**ON** OF HIGH POINT OF GATE, IN METRESFigure II.5.10. Cross-plotted initial rating curves,Black Canyon Dam, Idaho, United States(after Bradley, 1953)extreme lower curve, which bears plotted pointsshown by X’s, represents the discharge of the freecrest with the gate completely down. The plottedpoints represent values obtained from Table II.5.1.The discharge values shown in Figure II.5.9 are forone gate only. When more than one gate is inoperation the discharges from the separate gatesmay be totaled, providing the gates are each raisedthe same amount. The experimental models used inthis study had from one to eleven gates operating,so that a reasonable allowance for pier effect on thedischarge is already present in the results.The intervals between the eight curves inFigure II.5.9 that are identified by plotted points aretoo great for rating purposes, particularly the gapbetween gate elevations 757.6 and 756.7 m. Thatdeficiency is remedied by cross-plotting the eightcurves for various constant values of discharge, asshown in Figure II.5.10. Fortunately the result is astraight-line variation for any constant value ofdischarge. The lines in Figure II.5.10 are not quiteparallel and there is no assurance that they will bestraight for every drum gate. Nevertheless, thisuncertainty will not detract appreciably from theaccuracy obtained. Interpolated information fromFigure II.5.10 is then utilized to construct theadditional curves in Figure II.5.9. Figure II.5.9 nowshows the rating for the Black Canyon Dam spillwayfor gate intervals of 0.150 m. For intermediatevalues, straight-line interpolation is permissible.

Chapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIESII.5-7Table II.5.2. Head and discharge computations for drum gates in raised positionsSetReservoirelevation inmetresH in metres a Ratio H-YCoefficient C qH 3/2 in metres Q in m 3 /sec b1 2 3 4 5 6 7gate elevation 760.476; θ = + 34.88°A 761.390 0.305 0.048 2.131 0.168 6.99761.695 0.610 0.095 2.132 0.476 19.79762.000 0.914 0.143 2.130 0.874 36.33gate elevation 760.476; θ = + 23.43°B 760.781 0.305 0.048 2.122 0.168 6.97761.086 0.610 0.095 2.129 0.476 19.76761.390 0.914 0.143 2.127 0.874 36.27761.695 1.219 0.190 2.134 1.346 56.04762.000 1.524 0.238 2.137 1.881 78.44gate elevation 759.866; θ = + 14.22°C 760.171 0.305 0.048 2.036 0.168 6.68760.476 0.610 0.095 2.059 0.476 19.11760.781 0.914 0.143 2.070 0.874 35.31761.390 1.524 0.238 2.098 1.881 76.99762.000 2.134 0.333 2.120 3.117 128.90gate elevation 759.257; θ = + 6.13°D 759.562 0.305 0.048 1.915 0.168 6.29759.866 0.610 0.095 1.937 0.476 17.98760.171 0.914 0.143 1.971 0.874 33.61760.781 1.524 0.235 2.004 1.881 73.54761.390 2.134 0.333 2.043 3.117 124.20762.000 2.743 0.429 2.082 4.543 184.48gate elevation 667.207; θ = – 1.28°E 758.952 0.305 0.048 1.768 0.168 5.80759.257 0.610 0.095 1.812 0.476 16.82759.562 0.914 0.143 1.844 0.874 31.46760.171 1.524 0.228 1.905 1.881 69.91760.781 2.134 0.333 2.957 3.117 118.99761.390 2.743 0.429 2.004 4.543 177.63762.000 3.353 0.524 2.040 6.139 244.29gate elevation 758.0.98; θ = – 8.28°F 758.342 0.244 0.038 1.664 0.120 3.91758.647 0.549 0.086 1.711 0.406 13.56758.952 0.853 0.133 1.749 0.788 26.90759.562 1.463 0.229 1.828 1.770 63.12760.171 2.073 0.324 1.893 2.984 110.21760.781 2.682 0.419 1.937 4.393 166.02761.390 3.292 0.515 1.976 5.973 230.24762.000 3.901 0.610 2.007 7.706 301.66

II.5-8manual on stream gauging(continued)SetReservoirelevation inmetresH in metres a Ratio H-YCoefficient C qH 3/2 in metres Q in m 3 /sec b1 2 3 4 5 6 7gate elevation 757.657; θ = – 15.02°G 758.038 0.381 0.060 1.654 0.235 7.59758.342 0.686 0.107 1.695 0.568 18.77758.647 0.991 0.155 1.739 0.986 33.44759.257 1.600 0.250 1.808 2.024 71.42759.866 2.210 0.315 1.863 3.285 119.38760.476 2.819 0.440 1.913 4.734 176.64761.086 3.429 0.536 1.954 6.350 242.05761.695 4.039 0.631 1.985 8.116 314.23aH is the total head on the gate. b The discharge for one gate: Q = C qLH 3/25.2.3 Radial or Tainter gatesThe damming face of a radial or Tainter gate isessentially a segment of a hollow steel cylinderspanning between piers on the dam crest. Thecylindrical segment is supported on a steelframework that pivots on trunnions embedded inthe downstream part of the piers. The gate israised or lowered by hoisting cables that areattached to each end of the gate. The cables leadto winches on a platform above the gate. In itsclosed position the lower lip of the gate rests onthe dam crest.Radial gates on a horizontal surfaceshown in the three figures, all pertinent elementshave been made dimensionless by using gateradius, r, as a reference. Thus the relative headwaterdepth is h 0/r, the relative tailwater depth is h 2/r,the relative height of opening is b/r and the relativetrunnion height is a/r. Free efflux (flow) occurswhen h 2< b; submerged efflux occurs when h 2> b.Each of the three graphs shows values of thecoefficient of discharge for:(a) Free efflux for three values of b/r;(b) Submerged efflux for two values of b/r when h 2/r = 0.5;(c) Submerged efflux for three values of b/r whenh 2/r = 0.7.Experimental work has been performed to determinedischarge coefficients for radial gates that controlflow along a horizontal surface (Toch, 1953).The results of those experiments are shown inFigures II.5.11 to II.5.14. Figure II.5.11 is a definitionsketch for a radial gate on a horizontal surface. Thedischarge coefficient, C d, is defined as:C dq=b (21/2gh 0)(5.2)V OV O2/2grH LoV 22/2gwhere q is discharge per unit width of the gate, g isacceleration of gravity and h 0and b are elementsshown in the definition sketch (Figure II.5.11).Figures II.5.12 to II.5.14 show values of C dfor threevalues of the ratio, a/r, where a is trunnionelevation and r is gate radius. In the relationsh 0?Vh2h 2iθbC cbFigure II.5.11. Definition sketch of a radial gate ona horizontal surface (after Toch, 1953)V i

Chapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIESII.5-90.80.8b __ = 0.1r0.6Free efflux__ br = 0.10.30.6Free efflux0.30.50.50.3C d0.4b __ = 0.3r0.10.30.1C d0.4b __ = 0.3r0.10.10.50.2Submerged effluxa __ = 0.1r__ h 2= 0.5 0.7r00 0.2 0.4 0.6 0.8 1 1.3 1.4 1.6 1.8h 0/r0.2Submerged efflux__ ah = 0.5___ 20.7r= 0.5r00 0.2 0.4 0.6 0.8 1 1.3 1.4 1.6 1.8h 0/rFigure II.5.12. Coefficient of discharge for free andsubmerged efflux, ra — = 0.1 (after Toch, 1953)Figure II.5.13. Coefficient of discharge for free andsubmerged efflux, ra — = 0.5 (after Toch, 1953)C d0.80.60.40.2b __ = 0.3rFree effluxRadial gates on a curved dam crest or sill0.5b __ = 0.1r0.50.1h__ 2__ a= 0.5= 0.9rr0.700 0.2 0.4 0.6 0.8 1 1.3 1.4 1.6 1.8More commonly radial gates are used to control theflow over a curved dam crest or over a sill. Thedischarge coefficients determined for a radial gateon a horizontal surface cannot be transferred to aradial gate on a curved dam crest or sill because ofdifferences in the pressure distribution. The flowunder radial gates on a curved crest or sill iscontrolled by the geometry of three interrelatedvariables: the crest shape, the gate and the gatesetting. Major factors that influence the dischargerelations are the position of the gate-seal point with0.30.30.1Submerged effluxFigure II.5.14. Coefficient of discharge for free andsubmerged efflux, ra — = 0.9 (after Toch, 1953)h 0/rrespect to the highest point of the spillway crestand the curvature of the upstream face of the gate.Therefore experimentally derived dischargecoefficients for various prototype dams cannot betransferred to other installations unless the severalvariables involved are similar. Consequently, radialgates will invariably require rating by current-meterdischarge measurements.When radial gates control the flow over a sill or acurved dam crest, five flow regimes may occur:(a) Free orifice flow;(b) Submerged orifice flow;(c) Free weir flow;(d) Submerged weir flow;(e) Flow over closed radial gates.Figure II.5.15 is a definition sketch for the discussionsthat follow, all of which are concerned with only asingle gate. As already mentioned, when dischargemeasurements for calibration purposes are madewith several gates open it is highly desirable that allgate openings be identical, unless of course thegates are all raised sufficiently for their lower lips tobe clear of the water. If gate openings are variableunder the condition of orifice flow it will benecessary to use an average gate opening incomputing discharge coefficients for the gates fromthe measured discharge.Definitions of symbols used in the sketch inFigure II.5.15 are: a = elevation difference, trunnioncentreline to sill; c = elevation difference, gatereference point (R.P.) to sill; d = elevation difference,gate R.P. to sill with the gate in a closed position;

II.5-10manual on stream gaugingh 1= static headwater referenced to gate sill;h 3= static tailwater referenced to gate sill;h g= vertical gate opening; r = radius from trunnioncentreline to gate R.P.; R = radius from trunnioncentreline to upstream face of a Tainter gate;R.P. = reference point used as indicator of gateposition; ∆h = h 1– h 3= static head loss throughstructure; θ = included angle between radial linesfrom the trunnion centreline through the R.P. andthrough the lower lip of the gate; φ L= the anglemeasured from horizontal to the radial line fromthe trunnion centreline through the lower lip ofthe gate with the gate in a closed position; andφ U= the angle measured from horizontal to theradial line from the trunnion centreline throughthe gate R.P.Additional symbols used in the text: L = lateral gatelength (normal to flow); Q = discharge for one gate;g = acceleration of gravity.Free orifice flowFree orifice flow occurs when the lower lip of theraised gate is submerged by headwater but is abovethe elevation of tailwater. When the radial gate ison a sill, as in Figure II.5.15, free orifice flow occursunder the gate when h gis less than 2/3/h 1and h 3isless than h g. Discharge for that condition iscomputed from the equation:( ) 1 2Q = ChgL 2gh 1(5.3)The definition of symbols is given in Figure II.5.15.Values of C will vary inversely with h gbecause thechange in slope of the lower lip of the gate, as thegate is raised, progressively decreases the hydraulicefficiency of the orifice. There is also a tendency forC to increase with h 1, particularly at low stages, butthat effect is usually minor compared to the effectof h g. Consequently C can usually be related to h galone. In developing the relation, dischargemeasurements should be made throughout theexpected range of h gand h 1. Values of C are thenplotted against h gand the plotted points are fittedwith a smooth curve. For convenience in latercomputations of discharge, the ordinates of thecurve are put in tabular form.The vertical gate opening, h g, is computed from thefollowing equation based on gate geometry and theposition of the reference point at various gate settings:h g⎛ c − a ⎞= R cosθ⎜ ⎟ + a − R sinθ⎝ r ⎠2⎛ c − a ⎞1 − ⎜ ⎟ ,⎝ r ⎠RrR.P.ϕ Uc∆hθϕ Ladh 1h gGate sillh 3Figure II.5.15. Definition sketch of a radial or Tainter gate on a sill

Chapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIESII.5-11whereθ = ϕL− ϕU= sin−1⎛⎜⎝aR⎞⎟ − sin⎠1⎛⎜⎝−a − drBecause C does not vary linearly with h git is highlydesirable, and often necessary, that all gates bepositioned identically during a dischargemeasurement to avoid the necessity of using anaverage value of h gin the computation of C.Submerged orifice flowSubmerged orifice flow occurs when the lower lip ofthe raised gate is submerged by both headwater andtailwater. When the radial gate is on a sill, as inFigure II.5.15, submerged orifice flow occurs whenh 3is greater than h g, and h gis less than 2/3h 1. Thebasic equation for computing discharge is:( 2gΔh) 1 2Q = C h L(5.4)gsgValues of C gsare determined from dischargemeasurements, and in addition, values of h 3/h gandh 3/h lare computed for each measurement. Forcalibration purposes it is desirable to havemeasurements that cover the range of 1 to 100 forthe ratio h 3/h g, with several in the range of 1 to 2.The value of C gsis a function of h g, h 1and h 3, andthe complexity of that function depends on thegeometry of the hydraulic structure. The geometrymay be such that all computed values of C gsshowlittle variation from a mean value When that occursthe mean value of C gsis used in equation 5.4.However, computed values of C gswill often vary,particularly in the range of 1 to 2 for the ratio h 3/h g.If that occurs three relations involving C gsareplotted graphically and the one that best fits theplotted points is selected for use. The three relationsare: C gsversus h g; C gsversus h 3/h 1, and C gsversush 3/h g.Quite often the last of the three relations will showthe best fit. It will plot as a straight line onlogarithmic graph paper and have the generalequation:( h ) BCgsK3h g= (5.5)When equation 5.5 is substituted in equation 5.4,the result is:B( h h ) h L( gΔ) 1 2Q = K3 g g2 h(5.6)Ordinates of the relation indicated by equation 5.5are put in tabular form for convenience in latercomputations of discharge. Because C gsdoes not⎞⎟⎠vary linearly with h git is highly desirable, and oftennecessary, that all open gates be positionedidentically during a discharge measurement toavoid the necessity of using an average value of h gin the computation of C gsfrom measureddischarge.Free weir flowWeir flow will occur when the lower lip of the gateis above the water surface. When the radial gate ison a sill, as in Figure II.5.15, weir flow will occurwhen h gis greater than 2/3h 1because of drawdownof the water surface at the dam crest. The lower lipof the gate will then be above the water surface.Whether the weir flow is free or submerged willdepend on the relative elevations of h 3and h 1. Freeweir flow will occur when the submergence ratio,h 3/h 1, is less than about 0.5 to 0.7, depending onthe geometry of the weir crest. The dischargeequation is:Q3 2= CwLh 1(5.7)Values of C w, which are dependent on the shape ofthe dam crest, are determined from dischargemeasurements, and the computed values are thenplotted against h l. Approach velocity head is usuallynegligible, but even where it is not, its effect isincluded in the variable coefficient, C w.Measurements should be made at headwater (h 1)intervals of 0.3 to 0.6 m throughout the expectedheadwater range to establish the functional relationbetween C wand h l. Information contained in apreviously cited report by Hulsing (1967) willusually be helpful as a guide to the probable shapeof that relation.Submerged weir flowAs mentioned above, weir flow is submerged whenthe submergence ratio h 3/h 1is greater than about0.5 to 0.7, depending on the geometry of the weircrest. The discharge equation for that condition is:Q3 2= CwCwsLH 1(5.8)where C wis the coefficient previously determinedfrom equation 5.7. Values of C wsmust be determinedfrom discharge measurements and expressed as afunction of h 3/h l. Satisfactory definition of thefunctional relation will probably require 10 to12 discharge measurements well distributed overthe range of h 3/h l. Information contained in theHulsing report (1967) will often be helpful in theanalysis. If the submergence is greater than 0.95 formuch of the time it may be advisable to attempt to

II.5-12manual on stream gaugingdevelop a relation of discharge to tailwater stage foruse during periods of excessive submergence.Flow over closed radial gatesAt extremely high flows the closed radial gate maybe overtopped, at which time the discharge overthe gate is computed from the general weirequation:3 2Q = CLh(5.9)where h is the head on the upper lip of the gate. Thegate itself will act as a thin-plate weir. Values of thedischarge coefficient C will vary primarily with thegeometry of the gate and with h. The geometry ofthe dam crest or sill will have a lesser effect on thevalue of C. Discharge measurements will be requiredto define the rating for flow over the gate, both forunsubmerged flow (tailwater below the upper lip ofthe gate) and for submerged flow (tailwater abovethe upper lip of the gate).Flow over a radial gate can also occur at low stagesif the gate is of the submersible type. A submersiblegate is designed to be lowered to allow flushing ofupstream debris over the top of the gate. When solowered, the bottom lip of the gate drops below thenormal sill elevation. The upper surface of asubmersible gate usually has an ogee or roundedcrest.The principles that govern the rating of radial gateslikewise apply to vertical-lift gates. When theelevation of the lower edge of the raised gate is lessthan two-thirds of the upstream head, orifice flowoccurs. The orifice flow is free if the tail-water isbelow the lower edge of the raised gate. The orificeflow is submerged if the tail-water is above the loweredge. General equations 5.3 and 5.4 apply to thedischarge and values of C and C gsin those equationsmust be determined from discharge measurements.If the elevation of the lower edge of a raised gate isgreater than two-thirds of the upstream head, weirflow over the dam occurs. If the weir flow is free,equation 5.7 applies. If the elevation of the tailwatercauses submergence effect, equation 5.8 applies.The coefficients in the two weir equations areprimarily dependent on the shape of the weir crest.Values of the coefficients are determined fromdischarge measurements, but helpful informationconcerning them is found in a report by Hulsing(1967).When a closed gate is overtopped by headwater, theupper edge of the gate acts as a weir and generalequation 5.9 is applicable. The upper edge of avertical-lift gate commonly has the shape of amodified horizontal broad-crested weir. Coefficientsof discharge are determined from dischargemeasurements. Again helpful information is to befound in the Hulsing report (1967).5.2.4 Vertical lift gatesVertical lift gates are simple rectangular gates ofwood or steel spanning between piers on the damcrest. The gates move vertically in slots in the piers,and all but the smallest gates are mounted on rollersto reduce the friction caused by the hydrostatic forceon the gate. The vertical lift gate, like the radial gate,must be hoisted at both ends, and the entire weightis suspended from the hoisting cables or chains(United States Army Corps of Engineers (USACE),1952). Piers must be extended to a considerableheight above high water to provide guide slots forthe gate in the fully raised position. To reduce theheight of the piers required for operating largevertical lift gates, the large gates are often built intwo horizontal sections so that the upper sectionmay be lifted and placed in another gate slot beforeraising the lower section. This design also reducesthe load on the hoisting mechanism. Discharge mayoccur over either one or both sections of the gate orover the spillway crest. Discharge over the spillwaycrest may occur as weir flow if the gate is raised abovethe water surface or as orifice flow if the raised gatedoes not clear the water surface.5.2.5 Roller gatesA roller (or rolling) gate as shown in Figure II.5.16 isa horizontal, internally braced, metal cylinderspanning between piers. Rings of gear teeth at theends of the cylinder mesh with inclined metal rackssupported by the piers. When a pull is exerted onthe hoisting cable or chain, the gate rolls up therack (Figure II.5.16(a)). The effective dammingheight of the cylinder can be increased by means ofa projecting apron (Figure II.5.16(b)) which rotatesinto contact with the dam crest as the gate rollsdown the inclined racks (USACE, 1952). A similarapron or rounded lip may be added to the top ofthe gate (Figure II.5.16(c)).As in the case of radial and vertical-lift gates, orificeflow will occur under partly raised rolling gates,weir flow over the dam will occur when the gatesare raised sufficiently (two-thirds or more of theheadwater elevation) to be clear of the water surface,and weir flow over the gates will occur when theclosed gates are overtopped by headwater. Theprinciples of rating roller gates are similar to thosediscussed for radial gates and vertical-lift gates.

Chapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIESII.5-13Ring gearand rackDammingheightHoistingchainDammingheight(a) Simple roller gate(b) Roller gate with apron(c) Roller gate with top apronFigure II.5.16. Schematic sketches of roller gates (USACE, 1952)Solid upper leafBuoyant lower leafWater released tolower pool lowers damWater pressure from upper pool raises and holds damFigure II.5.17. Bear-trap gate (USACE, 1952)5.2.6 Movable damsA movable dam consists of a low concrete sill and adamming surface that can be raised above the watersurface to maintain a desired pool level or loweredto the sill at higher discharges so as to offer nointerference to the flow. The most commonly usedgates or damming surfaces are bear-trap gates,hinged-leaf gates, wickets and inflatable dams.Bear-trap gateA bear trap gate (Figure II.5.17) consists of two leavesof timber or steel hinged and sealed to the dam or sill.When water is admitted to the space under the leavesthey are forced upward. The downstream leaf is hollowso that its buoyancy aids the lifting operation. Whenthe dam is collapsed by the release of water fromunder the leaves the leaves lie flat (USACE, 1952).Hinged-leaf gateA hinged-leaf gate (Figure II.5.18) is a rigid flat leafhinged at bearings along its lower edge. In its raisedposition the leaf slopes upward and downstream atan angle of between 20° and 30° from the vertical.When lowered it lies in a nearly horizontal position.The position of the leaf is controlled by a mechanicalhoist or by a counterweight device that causes theleaf to rise or fall automatically with a slightincremental change in headwater level.WicketsA wicket is a shutter held in position against thewater load by a metal prop (Figure II.5.19(a)). It isnot intended that water should flow over the wicketat an appreciable depth because the resultant waterload will shift to a point above the prop and causethe wicket to overturn or vibrate violently (USACE,1952). The metal prop, hinged at mid-length of thewicket, sits against a shoulder on a metal fixture(hurter) embedded in the foundation. The wicket israised by an upstream pull on a hoisting lineattached to the bottom of the wicket. This causesthe prop to fall into its seat, after which the wicketis rotated into position against the sill(Figure II.5.19(b)). The wicket is lowered by pulling

II.5-14manual on stream gaugingupstream on a line attached to the top of the wicket.The base of the prop is pulled away from its seatand falls to one side into a groove in the hurter inwhich it can slide freely downstream. Wickets areraised and lowered by use of a boat operating onthe upstream side of the dam. Figures II.5.19(c) andII.5.19(d) show improved types of wickets. TheBebout wicket (Figure II.5.19(d)) trips automaticallyto permit the passage of high flows.Open positionClosed positionInflatable damsAn inflatable dam, before activation, is a collapsednylon/rubber bladder that occupies the full widthof the stream and is attached to a concrete sill onthe channel bottom. The dam is activated bypumping water into the bladder, thereby inflatingit to form a barrier across the channel. The dam isdeactivated by releasing water from inside theConcrete sillFigure II.5.18. Hinged-leaf gateResultant water loadPull to tripWicketPull to raiseBumper blockPropHorsePropHurter(a) Basic principle ofwicket dam(b) Wooden chanoinewicketPull to raise or lowerWicket tripsautomaticallywhen load risesabove trunnionPush to trip manuallyResultant waterload at full poolHurter(c) Chanoine-Pascaudtwo-position steel wicket(d) Bebout self-trippingwicketFigure II.5.19. Wickets (USACE, 1952)

Chapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIESII.5-15bladder. Inflatable dams are usually used on shallowstreams to maintain a water level in the stream thatis sufficiently high to submerge the intake of adiversion works. When the river stage is high thedam is deflated. The inflation and deflation areoften automatically controlled in response to thechanging stage of the stream. Although it wouldprobably be feasible to determine the rating for aninflatable dam by monitoring both the stream stageand the pressure within the dam bladder, inflatabledams have not been used as gauging-stationcontrols. It is invariably simpler to operate aconventional gauging station on the stream eitherdownstream from the inflatable dam or far enoughupstream to be beyond the influence of backwaterfrom the dam.Discharge characteristics of movable damsThe discharge characteristics of bear-trap gates,hinged-leaf gates and wickets are similar. In theirlowered position they act as broad-crested weirsthat control the stage-discharge relation over alimited range of low-water stage. The stage at whichthey become submerged depends primarily on theheight of the sill on which they rest. Their dischargeratings in the lowered position will resemble thatfor a highway embankment (Hulsing, 1967, pp. 26-27) whose general equation is:3 2Q = CbH(5.10)where Q is discharge; C is the coefficient of discharge;b is the width normal to the flow, and H is the totalhead.The value of C will be dependent on the elevationsof headwater and tailwater, the length of the crestin the direction of flow and the geometry of thecrest. For unsubmerged flow (tailwater ≤ 0.7 timesheadwater) C can be expected to range from about1.43 to 1.71 depending primarily on the ratio ofstatic head, h, to length of sill in the direction offlow, L. For submerged flow, the free-flow value of Cwill be multiplied by a factor that ranges fromalmost zero to almost 1.00, depending on the degreeof submergence.When overtopped in their raised position byheadwater, the three types of movable dams, beartrapgate, hinged-leaf gate and wickets, act asinclined thin-plate rectangular weirs. Figure II.5.20gives values of the discharge coefficient C in thegeneral weir equation (equation 5.10) for variousangles of inclination of such weirs. If the upstreamedge of the crest is rounded, the value of C mayincrease by 5 to 10 per cent.5.2.7 FlashboardsThe usual flashboard installation consists ofhorizontal wooden panels supported by verticalpins placed on the crest of a spillway(Figure II.5.21(a)). Such installations are temporaryand are designed to fail when the water surface inthe reservoir reaches a predetermined level. Acommon design uses steel pipes or rods set looselyin sockets in the crest of the dam and designed tobend and release the flashboards at the desiredwater level. Temporary flashboards of this type havebeen used in heights up to 1.2 or 1.5 m. Becausetemporary flashboards are lost each time thesupports fail, permanent flashboards are moreeconomical for large installations. Permanentflashboards usually consist of horizontal woodenpanels that can be raised or lowered from anoverhead cableway or bridge. The bottom edges ofthe panels are placed in a seat or hinge on thespillway crest, and the panels are supported in theraised position by struts (Figure II.5.21(b)) or byattaching the top edges of the panels to the bridge.To rate the vertical flashboards shown onFigure II.5.21(a), a value of C = 1.83 is usually usedin the general weir equation, equation 5.10.When the permanent flashboards in Figure II.5.21(b)are lowered the value of C that should be used isthat for the free dam crest (no flashboards). Thevalue of C to use when the flashboards are raisedand supported by struts is determined fromFigure II.5.20, which shows C values for variousangles of inclination. If the raised flashboards aresupported in an inclined position by a bridge, so1:1From U.S. Geol. SurveyWater-supply paper200 p. 128From U.S. Bureau ofReclamation Bulletin 32H:3V1H:3VC (when English units are used)3.83.73.63.53..43.33.23.11H:3V2H:3VC= Q ____bH 3/240 30 20 10 0 10 20 30 40 50 60 70 80 90INCLINATI**ON** FROM THE VERTICAL, IN DEGREES50 60 70 80 90 80 70 60 50 40 30 20 10 0INCLINATI**ON** FROM THE HORIZ**ON**TAL, IN DEGREESUP**STREAM**DOWN**STREAM**1:1Peak at slope of about1.6 /H:1V based on pls.10 and 12 in WSP 20012H:1V2H:1V4H:1VFigure II.5.20. Discharge coefficients foran inclined rectangular thin-plate weir

II.5-16manual on stream gaugingthat the top edge of the flashboards is flush withthe upstream edge of the bridge floor, a flat-crestedrectangular weir with inclined upstream face isassumed. The bridge floor acts as the flat weir crestand the flashboards act as the inclined upstreamface of the weir. Discharge is computed by the useof equation 5.10 and the value of C to be used inthat equation can be obtained from Figure II.5.20.5.2.8 Stop logs and needlesStop logs consist of horizontal timbers, similar toflashboards, spanning between vertically slottedpiers on the dam crest. The timbers may be insertedinto or removed from the vertical slots by hand orwith a hoist. There is usually considerable leakagebetween the timbers and considerable time may berequired for their removal if they become jammedin the slots. Stop logs are ordinarily used only forsmall installations where the cost of more elaboratedevices is not warranted or in situations where theremoval or replacement of the stop logs is expectedonly at infrequent intervals.Needles consist of timbers standing on end, withtheir lower ends resting in a keyway in the spillwayand their upper ends supported against the upstreamedge of a bridge floor. Needles are easier to removethan stop logs but are difficult to place in flowingwater. Consequently they are used mainly foremergency bulkheads that are installed duringperiods of low flow.The simple crest shape of stop logs and needlesmakes it easy to determine the theoretical value ofthe discharge coefficient C in the general weirequation 5.10, as given by Hulsing (1967) oncomputing discharge over dams. However, it isusually futile to rate stop logs or needles theoreticallybecause of the appreciable leakage between them.5.3 Navigation locksNavigation locks are required for boat traffic toovercome the difference between headwater andtailwater elevations at a dam. The boat enters theopen gate of the lock and the lock is closed behindthe boat. Valves are used for filling or emptying thelocks, as the case may be, to bring the water level inthe lock to that of the pool ahead of the boat. Theother lock gate is opened and the boat proceeds onits journey. Various lock-filling and lock-emptyingsystems have been devised as a compromise betweentwo conflicting demands: (a) that the filling time beshort so as not to delay traffic and (b) that thedisturbances in the lock chamber do not causestresses in mooring hawsers which might cause theboat or barges to break loose and thereby damageeither the boat or lock structure.The flow through navigation locks is computed asthe total volume of water released during a finitetime interval, usually one day. The volume of waterdischarged for any one lockage is the product of theplan or water-surface area of the lock and thedifference between headwater and tailwater at thetime of lockage. These volumes are summed for theday and divided by 86 400, which is the number ofPins on downstreamside of flashboardsFlashboardsFlashboardsSealFlashboardsStrutDamDam(a) Temporary type (Front view)(b) Permanent type (End view)Figure II.5.21. Flashboards

Chapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIESII.5-17seconds in a day, to obtain the average lockage flowin cubic feet per second or cubic metres per second.Usually it will be sufficiently accurate to computethe daily average lockage discharge, Q L, by use ofthe equation:QLN= A86 400( E − E )ht(5.11)where N is the number of lockages in a day; A is theplan or surface area of the lock; E his the daily meanheadwater elevation, and E tis the daily meantailwater elevation.If appreciable leakage through the lock occursbetween boat lockages, the daily average leakagemust be added to the daily average lockagedischarge.Measurement of leakage through navigationlocksIf the leakage through the closed lock gates is greatit can be measured in the fore-bay with a lowvelocitycurrent meter or Acoustic Doppler CurrentProfiler (ADCP). The leakage will seldom be thatgreat, however, and usually will have to be computedby a volumetric method.If, for considerable periods of time between lockages,the lockmaster keeps the valves and lower gatesclosed and the upper gates open, leakage will occurthrough the lower gates, and it is that leakage, Q Lm,which must be determined. If instead it is the valvesand upper gates that are kept closed and the lowergates that are kept open, leakage will occur throughthe upper gates and it is that leakage, Q Um, whichmust be determined. If all valves and gates are keptclosed it is the equilibrium leakage, Q Le, throughthe lower gate that must be determined.Instructions for determining Q Lm, Q Umand Q Lefollow. Figure II.5.22 is a definition sketch of alock.Definitions:h Um= h Lm– Maximum head on upper or lower gatesfor given headwater and tailwater stages;h U– Head on upper gate;h L– Head on lower gate;Q U– Leakage through upper gate produced by h U;Q Um– Leakage through upper gate produced by h Um;Q L– Leakage through lower gate produced by h L;Q Lm– Leakage through lower gate produced by h Lm;Q n– Rate of storage in lock with both gates closed= Q L– Q U. (When Q nis negative, the water level risesin lock chamber. When Q nis positive, the water levelfalls in lock chamber.);h Ue– Equilibrium head on upper gate when Q U= Q L;h Le– Equilibrium head on lower gate when Q U= Q L;Q Le– Leakage through lower gate produced by h Le;h U+ h L= h Um= h Lm;h Ue+ h Le= h Um= h Lm.Field work(a) Close upper and lower lock gates and open thevalve to fill the lock chamber. When the lockchamber is filled, close the valve and open oneupper gate slightly;Headwaterh Umh UUpper gateWater surface in lock chamberLower gateh Lh LmTailwaterFigure II.5.22. Definition sketch of a lock

II.5-18manual on stream gauging(b) Attach the zero end of a steel tape by a smallstaple to the middle of a long plank. Floatthe plank in a lock chamber against the lockwall after first setting a reference mark on topof the wall for use as an index for reading thetape. A portable electric-tape gauge is evenmore satisfactory for reading stages in the lockchamber (see Volume I, Chapter 4);(c) Record gauge heights in the upper pool andlower pool and the tape reading in the lockchamber;(d) Close the upper gate. Read the tape immediatelyafter the gate is fully closed and seated, andstart a stop watch. Thereafter read the tapeand stop watch at intervals of about 0.150 mas stage decreases in the chamber or at minuteintervals, whichever comes first. Continue forabout ten minutes;(e) Empty the lock chamber by opening the lowergate and then partly close the lower gate; thatis, leave one lower gate slightly open;(f) Record gauge heights in the upper pool andlower pool and the tape reading in the lockchamber;(g) Close the lower gate. Read the tape immediatelyafter the gate is fully closed and seated andstart a stop-watch. Thereafter read the tapeand stop-watch at intervals of about 0.150 mas stage increases in the chamber, or at minuteintervals, whichever comes first. Continue forabout ten minutes;(h) Obtain dimensions of the lock chamber for usein computing volumes of water involved in theleakage. That completes the field work.Computations for Q Lm(a) Use readings obtained when observationswere started with a full lock chamber. Subtractinitial tape reading (made with upper gate openslightly) from all tape readings;(b) Plot adjusted tape readings from step 1 againsttime in seconds. The first reading made afterthe upper gate was fully closed is plotted at zeroseconds. Too much uncertainty usually existsas to when the gate actually seated to use theclosure of the gate as the starting time for thegraph (see Figure II.5.23). The plot should bemade on a large sheet of graph paper;(c) Connect the plotted points with a smoothcurve. A tangent to the curve at any value ofthe abscissa represents the rate of change ofwater-surface elevation at that instant. Therate of change multiplied by the surface areaof the lock chamber gives the instantaneousrate of storage in the lock chamber; that is, thedifference in rate of leakage out of the chamberthrough the lower gate and rate of leakage intothe chamber through the upper gate. At theinstant the upper gate is closed the leakage outof the chamber is at its maximum, Q Lm(fullhead on the lower gate), and the leakage intothe chamber is zero (zero head on the uppergate). As the stage in the chamber falls theleakage out of the chamber decreases becauseof the decreased head on the lower gate andleakage into the chamber increases becauseof the increased head on the upper gate.Eventually the leakage into the lock wouldequal the leakage out of the lock (Q Le) and thestage in the chamber would remain constant;(d) To obtain the rate of storage at any instant fromthe tangent of the curve showing the decreasein lock stage with time, construct a diagramshowing the storage rate (Q n) for varioustangential slopes. The method of constructingthe diagram is demonstrated in Figure II.5.23.The area of the lock chamber is 1183.241 m 2 .If the stage in the chamber dropped 0.6 m, thechange in volume would be 0.6 x 1183.24 or712 m 3 . If Q nwere 5.66 m 3 , the time required fora 0.6 m drop would be 127.5 seconds. A verticalline is drawn at 127.5 seconds on Figure II.5.23and a diagonal line having a drop of 0.6 m isdrawn between the abscissa values of 0 and127.5 seconds. A tangent to the storage curvehaving a similar slope would have a Q nvalue of5.66 m 3 . Diagonals representing other values ofQ nare added as shown;(e) Select two points on the storage curve, onenear the origin (0 seconds) and the other nomore than 0.3 m lower in stage. Draw tangentsto those points and use the slopes of thosetangents with the tangential rate diagramto obtain the two values of Q n. To obtain thetangential slope at a point on the curve, use apair of dividers to lay off short equal distanceson the curve on each side of the selected point.A chord connecting the equidistance pointswill have a slope approximately equal to thatof the tangent;(f) The two values of Q nobtained in the precedingstep will be used to compute Q Lm. No furtheruse will be made of the leakage curve, exceptthat it has value for making a rough check onthe basic assumption that will be made in thecomputations that follow. That assumption isthat the leakage through a gate can be treatedas though it all occurred at an orifice at thebottom of the gate. In other words:QQLLm⎛ h=⎜⎝ hLLm⎞⎟⎠1 2andQQUUm⎛ h=⎜⎝ hUUm⎞⎟⎠1 2(5.12)

Chapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIESII.5-19or1 2⎛ h ⎞LQL= QLm⎜⎟ and⎝ hLm⎠QU= QUm⎛ h⎜⎝ h(g) From Figure II.5.22 and equation 5.12:Qn= QL− QUUUm⎞⎟⎠1 2or (5.13)Qn= QLm⎛ h⎜⎝ hLLm⎞⎟⎠1 2− QUm⎛ h⎜⎝ hUUm⎞⎟⎠1 2For each of the two values of Q n, all valuesin equation 5.13 are known except for thevalues of Q Lmand Q Um. The known values canbe substituted in equation 5.13 to give twosimultaneous equations which can then besolved for the desired value of Q Lm;(h) In the preceding step it would be a simplematter to solve for Q Umbut we do not do so.Our basic assumption of orifice flow may notbe strictly correct and experience has shownthat the desired value of Q Umcan be computedwith much more accuracy by using the fielddata obtained when observations of leakagewere started with an empty lock chamber;(i) To obtain values of leakage through thelower gate, when the upper gate is open, forother values of total head, use the followingequation:1 2⎛ hʹLm⎞Q ʹLm= QLm⎜⎟(5.14)⎝ hLm⎠where Q Lmand h Lmare values obtained from aleakage test as described above, and Q’ Lmis theleakage through the lower gate correspondingto any other value of total head h’ Lm;(j) Prepare a rating table of Q Lmversus h Lm.1.6Q nDECREASE IN WATER-SURFACE ELEVATI**ON** IN LOCK CHAMBERIN METRES, STARTING WITH FULL LOCK CHAMBER1.41.210.80.60.40.287654321LEAKAGE, IN CUBIC METRESPER SEC**ON**DArea of lock chamber = 1183.24 m 200 100 200 300 400 500 600TIME FROM FIRST OBSERVATI**ON**, IN SEC**ON**DSFigure II.5.23. Leakage diagram starting with lock chamber full

II.5-20manual on stream gaugingComputations for Q Um(a) Use readings obtained when observationswere started with an empty lock chamber.Subtract initial tape reading (made withlower gate slightly open) from all tapereadings;(b) Plot adjusted tape readings from step 1against time in seconds;(c) Proceed with computations in a manneranalogous to that used in the computationof Q Lm;(d) Obtain Q nfor two points on the leakage curve,one near the origin (0 seconds) and the otherno more than 0.3 m higher in stage;(e) Use equation 5.13 to solve for the desired valueof Q Um;(f) To obtain values of leakage through theupper gate, when the lower gate is open, forother values of total head, use the followingequation:1 2⎛ hʹUm⎞Q ʹUm= QUm⎜⎟(5.15)⎝ hUm⎠where Q Umand h Umare values obtained froma leakage test as described above, and Q’ Umis the leakage through the upper gate correspondingto any other value of total headh’ Um;(g) Prepare a rating table of Q Umversus h Um.Computations for Q Le(a) Q Leis the leakage through the lower gate whenequilibrium exists; that is, the stage in the lockchamber is constant because Q U= Q L;(b) Starting with the equation, Q Ue= Q Le, it isa simple matter to transform the equationto:[(]2 2h h Q Q ) + 1Le=Lm Lm Um(5.16)All values on the right-hand side ofequation 5.16 are known because in precedingsteps Q Lmand Q Umhad been computed. Solvefor h Le;(c) Obtain the desired value of Q Lefrom theequation:1 2⎛ hLe⎞QLe= QLm⎜⎟(5.17)⎝ hLm⎠(d) Use the rating tables for Q Lmand Q Umwithequations 5.16 and 5.17, to prepare a ratingtable of Q Leversus h Lm.5.4 Pressure conduits5.4.1 GeneralIn one respect the gauging of a pressure conduit issimple in that the cross-sectional area is constantfor all discharges. The calibration of the meteringdevice offers difficulty, however, because thedischarge measurements require specialinstrumentation unless they can be made by currentmeter in the forebay or afterbay of the conduitwhere open-channel conditions exist.The following are the metering devices used forpressure conduits:(a) Mechanical meters:(i) Displacement meter(ii) Inferential meter;(iii) Variable-area meter;(b) Differential-head meters:(i) Constriction meters:a. Venturi meter;b. Flow nozzle;c. Orifice meter;(ii) Bend meter;(iii) Pressure differential in a reach of unalteredconduit;(c) Electromagnetic velocity meter;(d) Ultrasonic (acoustic) velocity meter;(e) Acoustic Doppler Velocity Meter;(f) Laser flow-meter.Changes in the rating of mechanical meters occuronly as a result of wear on the moving parts ofthe meter. Changes in the rating of differentialheadmeters that are kept clean occur only as aresult of changes in perimeter roughness of theconduit with time. The electromagnetic, acousticand laser velocity meters are complex electronicdevices and as such they are subject to theoccasional calibration drift that for variousreasons affect such devices.The various meters must be calibrated when firstinstalled and the calibration must be periodicallychecked thereafter. Methods of measuring dischargefor that purpose include:(a) Pitot-static tubes and pitometers;(b) Salt-velocity method;(c) Gibson method.This section of the Manual closes with a briefdiscussion of discharge ratings for turbines,pumps, gates and valves, all of which areassociated with pressure conduits. In addition, abrief discussion is included that describes acomputer program for computing flow throughwater control structures.

Chapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIESII.5-215.4.2 Metering devices for pressureconduitflowMechanical metersMechanical meters are widely used in waterdistributionsystems because of their low costand small size, but they can only be used tomeasure a relatively narrow range of discharge.They are not suited for the measurement of verylow flow rates because the liquid may pass themeter without moving the mechanical elements.They are seldom used to measure dischargesgreater than 0.28 m 3 s -1 because of high headloss. A large variety of mechanical meters arecommercially available, but only the threegeneral types – displacement, inferential andvariable-area – will be described here (Howe,1950, pp. 210-212).Displacement metersAn elementary form of all displacement metersconsist of a single or multiple piston arrangementin which fluid passing through the meter moves apiston back and forth. The movement of thepiston is readily registered upon a counting devicecalibrated in any desired units to give totalvolume of flow. Such meters can have a fairlylarge capacity and are accurate if no slippageoccurs.Another commonly used displacement meter isthe disk meter which oscillates in a measuringchamber. For each oscillation a known volume ofwater passes the meter. The motion of the diskoperates a gear train which in turn activates acounting mechanism, thereby furnishing ameasure of the total volume of flow. When thedisk is new the meter is accurate to within 1 percent, but the meter may under-register significantlyas the disk becomes worn.Inferential metersInferential meters are in effect small turbines andare called inferential because the rate of flow isinferred from the speed of rotation of thepropeller. An essential element of such meters is aset of guide vanes which may be adjusted tochange the calibration of the meter. However, thecalibration may inadvertently change if thesurface of the propeller blades becomes worn orcoated. Although inferential meters normallyregister only volume of flow, equipment may beadded to the meter to indicate instantaneous rateof discharge.Variable-area meterThe variable-area meter consists of a vertical taperedtube containing a small plunger or float. In someinstruments the plunger is completely immersed ina transparent, graduated tube. In others, a stemprojects through the end of the conical tube andtraverses a scale. In both types the plunger rises asthe rate of flow increases, thereby increasing thearea around it. By calibration, the position of theplunger can be related to the rate of flow. Theseinstruments are restricted to the measurement ofrather small discharges and will not accommodateany great change in viscosity without recalibration.Accuracy within 1 per cent is possible.Differential-head metersThe flow of fluid through a constriction in a pressureconduit results in a lowering of pressure at theconstriction. The drop in piezometric head betweenthe undisturbed flow and the constriction is afunction of the flow rate. The venturi meter, flownozzle and orifice meter (Figure II.5.24) areconstriction meters that make use of this principle.The difference in piezometric head may be measuredwith a differential manometer or pressure gauges.In order that such an installation may functionproperly, a straight length of pipe at least10 diameters long should precede the meter.Straightening vanes may also be installed in theconduit just upstream from the meter to suppressdisturbances in the flow.Venturi metersVenturi meters (Figure II.5.24(a)) are highly accurateand efficient flow meters. They have no movingparts, require little maintenance and cause littlehead loss (United States Bureau of Reclamation,1971). They operate on the principle that flow in agiven closed-conduit system moves more rapidlythrough areas of small cross-section (D2 inFigure II.5.24(a)) than through areas of large crosssection(D1 in Figure II.5.24(a)). The total energy inthe flow, consisting primarily of velocity head andpressure head, is essentially the same at D1 and D2within the meter. Thus the pressure must decreasein the constricted throat, D2, where the velocity ishigher; and conversely the pressure must be greaterat D1, upstream from the throat, where the velocityis lower. This reduction in pressure from the meterentrance to the meter throat is directly related tothe rate of flow passing through the meter, and isthe measurement used to determine flow rate.Tables or diagrams of the head differential versusrate of flow may be prepared, and flow indicators or

II.5-22manual on stream gaugingflow recorders may be used to display the differentialor the rate of flow.The relation of rate of flow, or discharge, to thehead and dimensions of the meter is:QCA2= (5.18)41 − r2ghwhere A 2= cross-sectional area of the throat, in m 2 ;h = difference in pressure head between upstreampressure-measurement section and the downstreampressure-measurement section, in metres; g = 9.81metres per second per second; r = ratio of the throatdiameter to pipe diameter = D 2/D 1and C = coefficientof discharge for the venturi meter.The coefficient of discharge for the venturi meterwill range from an approximate value of 0.935 forsmall throat velocities and diameters, to 0.988 forrelatively large throat velocities and diameters.(See Figure II.5.25.)Flow nozzlesFlow nozzles operate on the same basic principle asventuri meters. In effect, the flow nozzle is a venturimeter that has been simplified and shortened byomitting the long diffuser on the outlet side(Figure II.5.24(b)). The streamlined entrance of thenozzle provides a straight cylindrical jet withoutcontraction so that the coefficient is almost thesame as that for the venturi meter. In the flownozzle the jet is allowed to expand of its own accordand the high degree of turbulence createddownstream from the nozzle causes a greater loss ofhead than occurs in the venturi meter where thelong diffuser suppresses turbulence.The relation of rate of flow to the head and to thedimensions of the flow nozzle is defined byequation 5.18, the same equation as used forventuri meters. The symbols have the samemeaning as for the venturi meter, except that C inequation 5.18 is the coefficient of discharge forthe flow nozzle.D 1FlowHead losshD D23(a) Venturi meterHead losshThe coefficient of discharge for the flow nozzle willrange from 1.0 to 0.97 or less. Inasmuch as the flowconditions at the entrance to the throat are similarto those of the venturi meter, the coefficients shouldbe nearly the same with the same diameter ratio, r.The upstream pressure connection is frequentlymade through a hole in the wall of the conduit at adistance of about 1 pipe diameter upstream fromthe starting point of the flare of the nozzle. Thepressure observed is that of the stream before it hasbegun to turn inward in response to the inletcurvature of the nozzle. The downstream pressureconnection may be made through the pipe wallopposite the end of the nozzle throat.FlowD D 2D 1 FlowD 2D 1(b) Flow nozzlehVena contractaVariable distance(c) Orifice meterHead lossFigure II.5.24. Three types of constrictionmeters for pipe flow (Courtesy of United StatesBureau of Reclamation)Orifice metersA thin-plate orifice inserted across a pipeline canbe used for measuring flow in much the samemanner as a flow nozzle (Figure II.5.24(c)). Theupstream pressure connection is often located at adistance of about 1 pipe diameter upstream fromthe orifice plate. The pressure of the jet rangesfrom a minimum at the vena contracta – thesmallest cross-section of the jet – to a maximum atabout four or five conduit diameters downstreamfrom the orifice plate. The downstream pressureconnection, the centre connection shown inFigure II.5.24(c), is usually made at the venacontracta to obtain a large pressure differentialacross the orifice. The location of the venacontracta may be determined from data providedin standard hydraulic handbooks.

Chapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIESII.5-23The relation of rate of flow to the head anddimensions of the metering section is defined byequation 5.18, the same equation as used for venturiand orifice meters. The symbols have the samemeaning for all three meters, except that C inequation 5.18 is the coefficient of discharge for theflow nozzle.For pressure taps located one pipe diameter upstreamfrom the orifice plate and at the vena contracta, thecoefficient of discharge ranges from 0.599 for an rvalue of 0.20, to 0.620 for an r of 0.71 . The principaldisadvantage of orifice meters, as compared toventuri meters or flow nozzles, is their greater lossof head. On the other hand they are inexpensiveand are capable of producing accurate flowmeasurements.Bend metersAnother type of differential head meter is the bendmeter, which utilizes the pressure differencebetween the inside and outside of a pipe bend. Themeter is simple and inexpensive. An elbow alreadyin the line may be used without causing addedhead loss. For best results a bend meter should becalibrated in place. The meter equation is:Q= C dA 2 gh(5.19)where C dis the coefficient of discharge; h is thedifference in piezometric head between the outsideand inside of the bend at the midsection, and A isthe cross-sectional area of the pipe.For best results it is recommended that the lengthsof straight pipe upstream and downstream from thebend be equal to at least 25 pipe diameters and10 pipe diameters, respectively. Lansford (1936)experimented with 90° bends and concluded that ifcalibration of a 90° bend is not feasible, results atmoderate to high Reynolds numbers that areaccurate to within 10 per cent can be obtained froma simple formula for Q, in which:C d= r 2D(5.20)where D is the pipe diameter and r is the centrelineradius of the bend.0.99COEFFICIENT OF DISCHARGE (C)0.980.970.960.95201510 8 6Throat velocity in metres per second54321.510.90.940.9330 40 50 60 70 80 90 100 150 200 300 400 500 600 800 1000THROAT DIAMETER IN MILLIMETRESFigure II.5.25. Discharge coefficient for Venturi meter, based on throat diameter and throat velocity

II.5-24manual on stream gaugingPressure differential in a reach of unaltered conduitIf a pressure-conduit system has high velocities andlow pressures it may not be practical to install aventuri meter in the line because cavitation willoccur in the throat along with excessive vibration.In that situation the installation of a manometerbetween two piezometer taps in the conduit, severalhundred feet apart, may be the most feasiblemethod of metering the flow. One, but preferablytwo discharge measurements would suffice to ratethe manometer and a third measurement could bemade to check the rating equation which is:Q = K Δh(5.21)where Q = discharge; K = a constant, and Δh = headdifferential.If two discharge measurements are used in theinitial calibration, the two computed K values,which should agree closely, are averaged.In the case of reaction turbines the discharge may bemetered by a manometer that measures the pressuredrop in the scroll case. The scroll case of a reactionturbine has a decreasing diameter, being largest at itsupstream end where it is joined to the penstock. Aset of piezometer taps is installed at each end of thescroll case forming, in effect, a type of venturi section.Discharge is computed by use of equation 5.21 whereK is determined from discharge measurements,preferably made over the complete range of output,and simultaneous observations of the pressure drop.The calibration should remain constant as long asthe turbine efficiency does not change.Summary of differential-head metersDifferential-head meters are very satisfactorymetering devices as long as they are kept clean andthe velocities in the conduit are high enough togive significant pressure differentials between thetwo piezometer taps.Electromagnetic Velocity MeterElectromagnetic velocity meters for measuring flowin pressure conduits are commercially available. Theprinciple of the electromagnetic velocity meter wasexplained in Volume I, Chapter 5, but to repeatbriefly, when a fluid which is an electric conductormoves across a magnetic field at 90° an electromotiveforce is produced in the fluid at right angles to boththe flux of the magnetic field and the velocity of thefluid. The induced voltage is proportional to theaverage velocity of the fluid, V. If the pipe is aconductor, as it usually will be, an insulating linermust be installed in the metering section and theprobes must contact the water. Two or more dischargemeasurements are required to calibrate the meter.Ultrasonic (acoustic) Velocity MeterAcoustic velocity meters for measuring flow inpressure conduits are commercially available. Theprinciple of the ultrasonic (acoustic) method wasexplained in Volume I, Chapter 6, and will not bediscussed further, other than to state that betterresults are apparently obtained with the transducersof the meter in direct contact with the fluid streamthan are obtained with the transducers mounted onthe outside of the conduit walls (Schuster, 1975).The acoustic velocity meter is self calibrated butmay be check calibrated by discharge measurementsif necessary.Acoustic Doppler Velocity MetersCommercially available Acoustic Doppler VelocityMeters (ADVM) could be used for measuring flow inpressure conduits. Classes of instruments for thisapplication include the Acoustic DopplerVelocimeter (ADV) described in Volume I,Section 5.3.8 and the ADVM described in Volume I,Section 6.3. Both instruments use the same basictheory of operation, in that they compute watervelocities using the Doppler shift of soundtransmitted underwater and reflected off movingparticulates suspended in the water. The theory ofoperation is described in more detail in the relevantsections of Volume I and is not discussed furtherhere. The distinguishing feature of the ADV versusthe ADVM is that the ADV measures velocities in asmall volume thus may be considered a point meterwhile an ADVM measures velocities in one or morelarger sample volumes. Instruments with multiplesample volumes provide current profiles in thevertical or horizontal depending on how theinstrument is physically mounted. In theory eitherinstrument could be used in pressure conduits tocompute discharge. Calibration by dischargemeasurements would likely be needed. The mainconsideration for using acoustic Dopplerinstruments is to avoid contamination of theacoustic signal by physical boundaries, namely, thewalls of the conduit. Another consideration is touse a physically small instrument to minimize flowdisturbance in the measured volume.Laser flow-meterLaser (light amplification by stimulated emissionradiation) beams have been used for studying the

Chapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIESII.5-25turbulent characteristics of flowing liquids and fordetermining the velocity of fluid flow (Schuster,1970). The Doppler principle, which involves ameasurable shift in the frequency of the light raysunder the influence of an external velocity imposedon the system, underlies the operation of the laserflow-meter. The flowing water scatters part of abeam of light (laser) directed through it. Bycomparing the frequencies of the scattered andunscattered rays, collected in receiving lenses onthe opposite side of the stream, the velocity of thewater (hence the discharge) can be calculated. Inlaboratory experiments the instrument hasmeasured fluid flows as slow as a few millimetresper second and as fast as 300 m or more per second.The device is commercially available for measuringdischarge in both open channels and pressureconduits.5.4.3 Discharge-measurement methodsfor meter calibrationMeasurement of discharge by pitot-static tubes andpitometersPitot-static tubes and pitometers may be classed asdifferential-head meters, but they are seldom usedfor continuous-flow measurement. Instead they areusually used for calibrating other metering devicesin place and for intermittent measurements. Pitottubes and pitometers indicate the velocity head at apoint in the conduit cross-section.The operation of pitot-static tubes or pitometers isbased on the principle that the increase in head atthe mouth of a bent tube facing upstream is ameasure of the velocity head of the oncoming flow.The most commonly used type of pitot-static tube(Figure II.5.26(a)) consists of two separate,essentially parallel tubes, one for indicating totalhead, P t(sum of static and velocity heads), and theother for indicating only static (pressure) head, P s.Manometers are commonly used to measure theseheads, the velocity head being the differencebetween the static head and the total head. Apressure transducer may also be used instead of themanometer for measuring the differential head.Where pitot-static tubes are used for continuousflowmeasurement, oscillograph or digital recordingof the electrical signal from the transducer providesa continuous record of the changes in head.The general equation for pitot-static tubes andpitometers is:V = C 2gΔh1(5.22)where V = velocity; C 1= coefficient, g = accelerationof gravity and Δh = observed velocity headdifferential.The coefficient C 1will vary with the dimensionsand geometry of the meter, but the instruments areusually individually rated by the manufacturer inthe manner that current meters are rated, and thevalue of C 1is therefore known. For the pitot-statictube shown in Figure II.5.26(a) the value of C 1usually ranges from 0.98 to 1.00.Another commonly used type of pitot device is theCole pitometer (Figure II.5.26(b), which consists oftwo tubes headed in opposite directions. The tubescan be rotated so that the instrument may beinserted through a small bushing in a pipe. WhenTotal head (P t)pressure connectionStatic head (P s)pressure connectionDirection of flowDirection of flow(a)(b)Figure II.5.26. Schematic drawing of (a) pitot-static tube and (b) Cole pitometer

II.5-26manual on stream gaugingin operating position the downstream tube registersa negative pressure because its opening is in thewake of the instrument. The differential of thewater columns is therefore considerably greaterthan V 2 /2g. The value of C 1in equation 5.22 usuallyranges from 0.84 to 0.87.Reinforced pitot tubes and pitometers have beenused successfully in pipes up to five feet in diameterhaving flow velocities of 1.5 to 6 m s -1 (UnitedStates Bureau of Reclamation, 1971). Even largerpipes can be traversed by a pitometer by havingaccess ports on both sides of the pipe and by probingto or past the conduit centreline from each side.The principal disadvantage encountered is thatrelatively large forces push on the tube when flowvelocities are high, making positioning and securingof the instrument difficult. Dynamic instabilitymay also occur, causing the tube to vibrate andproduce erroneous readings. At moderate flowvelocities the measurements are accurate.The most common pressure conduit is the circularpipe. For a constant rate of flow the velocity variesfrom point to point across the stream, graduallyincreasing from the walls to the centre of the pipe.The mean velocity is obtained by dividing the crosssectionalarea of the pipe into a number of concentricequal area rings and a central circle. The standard10-point system is shown in Figure II.5.27(a). Moredivisions may be used if large flow distortions orother unusual flow conditions exist. Observationsare made at specific locations in these sub-areas(Figure II.5.27(a)) and mean velocity is computedfrom the equation:Vmean1 ( g Δhaverage= C 2)()(5.23)The mean velocity in rectangular ducts can bedetermined by first dividing the cross-section intoan even number, at least 16, of equal rectanglesgeometrically similar to the duct cross-section andthen making a pitot-tube observation at the centreof each sub-area (Figure II.5.27(b)). Additionalreadings should be taken in the areas along theperiphery of the cross-section in accordance withthe diagram in Figure II.5.27(c). Mean velocity isthen computed from equation 5.23.When using pitot-static tubes or pitometers it mustbe remembered that at low velocities, headdifferentials are small and errors in reading headdifferentials will seriously affect the results. Also theopenings in the tubes are small and foreign materialin the water, such as sediment or trash, can plug thetubes... + ... + .. + ... + ..0.146D0.082D0.026D. .+ . +.+ ++ +. .+ . +.0.342D0.226DD0.974D0.918D0.854D0.774D0.658D1 2 3 4 5 6 7 8 9 10. + .. + .. + ... + ..(b) System for rectangularconduits, where at least16 divisions must be used(a) Ten-point systemfor circular conduits(c) Additional points for datain areas around peripheryof the rectangular conduitFigure II.5.27. Locations for pitot-tubemeasurements in circular and rectangularconduits. (Reproduced from B.S. 1042,Flow measurement (1943), by permission ofthe British Standards Institution)Measurement of discharge by salt-velocity methodDischarges in conduits flowing full may bedetermined from the known dimensions of theconduit and velocity observations made by the saltvelocitymethod. Basically, the method uses theincreased conductivity of salt water as a means oftiming the travel of a salt solution through a lengthof conduit. A concentrated solution of sodiumchloride is suddenly injected into the conduit at aninjection station. At two downstream stationselectrodes are connected to a recording ammeter.An increase in the recorded electric current occurswhen the prism of water containing the salt passesthe electrodes (Figure II.5.28). The difference intime, t, between the centres of gravity of therecorded salt passage is obtained from the recorderchart as shown in Figure II.5.28. The discharge isequal to the volume of the conduit between thetwo electrodes divided by time, t, in seconds. It isnot necessary that the conduit be uniform.The brine-injection system that is used is quitecomplex (Figures II.5.29 and II.5.30). A turbulencecreatingdevice (turbulator) is also sometimes used154L54W5W5

Chapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIESII.5-271 second time scale+ 55 + 5850-3AFirst curvePassage time = 20.13 secondsTest 50-350-3BBase lineSecond curveFigure II.5.28. Sample record of a salt cloud passing upstream and downstream electrodes in thesalt-velocity method of measuring flows in pipelines. (Courtesy of United States Bureau of Reclamation)From aircompressorAir receiverWater exhaust valveBrine tankRechargeair valveSolenoid valve switch gearInjectionair valveInjectioncontrolAmplifiersRecorderBrine injection lineBrinecylinderConduitpressure lineSalt velocityLimit switchbridgesAir power cylinderPlug valve, closed when charging cylinderFLOW4. Dia.4. Dia. minimumVariableTurbulatorstationBrine injectionstationFirst electrodestationSecond electrodestationFigure II.5.29. General arrangement of salt-velocity equipment for pressure conduits(Courtesy of United States Bureau of Reclamation)to insure adequate mixing of the brine and water bythe time the upstream electrode station is reached.The required equipment and techniques have beendescribed in detail by Thomas and Dexter (1955).Measurement of discharge by the Gibson methodThe Gibson method was developed for computingthe discharge of a conduit or penstock controlledby a valve, turbine or regulating device located atthe downstream end. The pressure conduit mustextend at least 7.5 m and preferably much moreupstream from the valve or regulating device, butthe conduit need not be of uniform cross-sectionalarea. The underlying principle of the method is thatthe pressure rise that results from gradually shuttingoff the flow in a conduit is an indication of theoriginal velocity of the water (Howe, 1950,pp. 209-210).The Gibson apparatus (Figure II.5.31(a)) consistsof:(a) A mercury U-tube connected to the penstockjust upstream from a gate;

II.5-28manual on stream gaugingConduit pressure lineto injection cylinderManholeBrinesupply lineflowPopvalvePop valveScrew jackBraceAnchoredbracketBrineinjectionstationJack blockConduit section at Brineinjection stationDownstream elevation ofBrine injection assemblyFigure II.5.30. Brine injection equipment in conduit (Courtesy of United States Bureau of Reclamation)PenstockTB.t 1t 0t 0DrumSlit inface ofboxLensLightsourcePressure headhV 2f +2gC.A.Pendulum marksFilmPendulumMercuryTime(a)(b)Figure II.5.31. Gibson apparatus and pressure-variation chart (after Howe, 1950).Reprinted by permission of John Wiley and Sons Ltd.(b) A light source behind the U-tube;(c) A pendulum that swings in front of the box;(d) A narrow slit in the box directly behind theU-tube.Light shines through the U-tube and exposes a filmon a rotating drum unless blocked by the pendulumor the mercury in the tube. During a test, the filmtherefore registers the fluctuation of the mercury

Chapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIESII.5-29column and the time intervals indicated by thependulum (Figure II.5.31(b)). The period ofdeceleration, T, terminates when the oscillationsbecome symmetrical (point B, Figure II.5.31(b),where t 1= t 0). An integration of the area ABCA leadsdirectly to the discharge through application of theequation:⎛ πDQ =⎜⎝ 42⎞⎛⎟⎜⎠⎝gL⎟ ⎠⎞( areaABCA)(5.24)in which Q is the discharge, D and L the diameterand length of conduit, and g the gravitationalconstant. The lower boundary of the area AC(practically a straight line) must be located by atrial-and-error process which is somewhat timeconsumingbut which nevertheless gives an accuratelocation of the line.It is generally agreed that the Gibson method isvery accurate. As an application of the momentumprinciple this might be expected. The personnelrequirements are not great because only oneoperator is required to run the instrument. Neitheris cost of the equipment excessive. A series of testsconsumes considerable time, however, because ofthe necessity for alternately shutting down the flowand bringing it back to a steady rate. Nevertheless,it must be concluded that the Gibson method offersa fairly simple and accurate approach to certainmeasurement problems that might otherwise bedifficult.5.4.4 Calibration of turbines, pumps,gates and valvesThe calibration of a reaction turbine by themeasurement of pressure drop in the scroll case hasalready been discussed. However, in some hydraulicsystems it may be desirable, or perhaps necessary, toconsider the turbine, pumps, gates or valvesthemselves as flow-meters for the system. To dothat it is required that the pertinent hydraulicelement be calibrated. The calibration is often donein the laboratory using hydraulic models, but it ispreferable that the hydraulic element be calibratedin place, or check the laboratory-derived calibrationby field measurements of discharge. For fieldcalibration, discharge measurements are made byone of the three methods discussed above, if theycannot be made by current meter in the forebay orafterbay of the system where open-channelconditions exist.In the case of turbines or pumps, relations ofdischarge versus power are generally desired. Theymay be defined by observing the metered poweroutput or input during periods when dischargemeasurements are made for various load conditions.Suitable curves or tables may be developed fromthese test data to show the discharge (Q) that occursfor specific types of operation. Curves or tables mayalso be prepared from model test data, if the testdata can be verified by a few discharge measurements.The calibration will change with time if there is achange in the efficiency of the turbine or pumpresulting from long service or from other factorsthat cause deterioration.If the range of operating conditions for a pump orturbine is narrow the calibration is simplified. Forexample, in such a situation where power input oroutput is metered, a simple relation of dischargeversus power divided by head may be adequate. Fora pump operated by an internal-combustion engine,where power was not metered but rotational speedwas automatically recorded, the followingcalibration scheme has been used. For the mostcommonly used rotational speed, (RPM) r, a baserating of discharge (Q r) versus head was defined bycurrent-meter discharge measurements. To obtainthe discharge (Q m) for other rotational speeds,(RPM) m, an empirical adjustment relation of Q m/Q rversus (RPM) m/(RPM) rwas defined by the dischargemeasurements. (The method of defining the tworelations is similar to that used in the constant-fallmethod of rating open-channel discharges,discussed in Chapter 3.) The use of head in thepump rating is analogous to the use of stage in theopen-channel method. The use of rotational speedof the pump is analogous to the use of fall in theopen-channel method. After the two relations havebeen defined, to obtain the discharge (Q m) for agiven head and a given rotational speed, (RPM) m,the ratio (RPM) mto (RPM) ris first computed. Thatratio is then used in the adjustment relation toobtain the ratio Q m/Q r. The value Q ris the dischargecorresponding to the given head in the base rating.The desired discharge (Q m) is then computed bymultiplying Q rby the ratio Q m/Q r.For gates and valves, relations of discharge versusgate opening for various appropriate heads aredesired. They may be defined by observing thegate or valve openings during periods whendischarge measurements are made for variousoperating heads. Measurements made over the fullrange of gate openings and heads will provide thedata for establishing the required curves or tables.Generally the relations are in the form of discharge(Q) for gate openings expressed as a percentage offull openings, for pertinent operating heads.Curves or tables may also be prepared from modeltest data, if the test data can be verified by a few

II.5-30manual on stream gaugingdischarge measurements. As with turbines andpumps, the calibrations for gates and valves aresubject to change with time as wear or deteriorationoccurs.5.5 Urban storm drainsQuantitative studies of urban storm runoffhave been handicapped by a lack of properinstrumentation for metering the flow in sewers.An ideal sewer flow-meter should have thefollowing characteristics:(a) Capability to operate under both open-channeland full-flow conditions;(b) Known accuracy throughout the range ofmeasurement;(c) Minimum disturbance to the flow or reductionin pipe capacity;(d) Minimum requirement of field maintenance;(e) compatibility with real-time remote datatransmission;(f) Reasonable construction and installationcosts.Over the years many devices have been tested foruse as sewer flow-meters. Wenzel (1968) hasreviewed the methods and devices tested, weirs,depth measurement, depth and point-velocitymeasurements, dilution methods and venturiflumes, and found that all have disadvantages ofone kind or another. Of those devices one of themost favourable was the flat-bottom venturi flumespecifically designed for flow measurements inconduits by Palmer and Bowlus (1936). That flumehas a throat of trapezoidal cross-section, a flatbottom, and upstream and downstream side andbottom transitions. The flat bottom permits debristo flow smoothly through the throat and thetransitions reduce the head loss substantially belowthat which would be caused by a weir, forexample.Wenzel (1968), in his study, concluded that furthereffort in designing some new modifications of aventuri flume offered the greatest promise of successin developing a more satisfactory flow-meteringdevice for urban storm drains. Accordingly threenew variations of a venturi section have beendesigned and laboratory tested in the United States.The three types are briefly described below.In recent years, ADVM have been used on a limitedbasis for sewer flows. These seem to have greatpotential for sewer applications and will no doubtfind success.5.5.1 United States Geological Surveysewer flow-meterThe United States Geological Survey (USGS) meteris a U-shaped constriction made to be inserted in acircular Pipe, as shown in Figure II.5.32. Thesymmetry of the design permits fabrication in twohalf-sections for easy transportation and installation.Moulds are available for fibreglass prototypes inpipe sizes from 0.61 to 1.52 m.The overall length from toe to heel is 1.75 pipediameters. The throat length, equal to one pipediameter, and the approach and getaway apronslopes of 1 on 3, resemble venturi meterspecifications. The constriction, in fact, is a venturiflume for open channel flows. For pressure flows itmay be considered to be a modified venturi meter.For sub-critical open-channel flows, the constrictiondams up the flow, which then passes throughcritical depth as it spills through the throat. If theoncoming flow is supercritical, two conditions arepossible: a hydraulic jump may be forced to form,which then spills through the throat and continuesdownstream as supercritical flow or, on steeperslopes, the oncoming flow may remain supercriticalthroughout the entire constriction. As dischargeincreases the water surface on the upstream siderises, touches the top of the pipe, and fills theupstream pipe, while the downstream side continuesto flow part full. A discharge rating is available foreach of these open-channel conditions.Further increases in discharge trigger full-pipeconditions, which are also well rated. It is for thesepressure-flow conditions that the question of headloss becomes of interest. Head loss, or backwater, istaken to be the increase in the upstream piezometricgrade line caused by the presence of the constrictionin the sewer line. For this constriction shape, thehead loss is expressed as a function of the throatvelocity head, H L:2VH L= 0.04(5.25)2gThe constriction is considered to be self-cleaning.Inasmuch as sewers are generally laid to a selfscouringslope, any silting upstream from theconstriction is expected to flush out on the nextrise. The deposition of silt would have a negligibleeffect on the rating for small discharges, and noeffect for high discharges.The curved floor in the throat, parallel to thecircumference of the pipe rather than beinghorizontal, retains some self-cleaning ability. It is a

Chapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIESII.5-312.25 Dthroat areapipe area= 0.709piezometer tap5/8 D31DD3/8 D3/8 D D3/8 D1/8 DSide viewThroat cross sectionFigure II.5.32. Sketch of United States Geological Survey flow-meter in a sewercompromise between a V-notch base which wouldhave excellent rating sensitivity for small dischargesbut a tendency to clog with small debris, and theother extreme, a horizontal floor as in a Palmer-Bowlus trapezoidal constriction. The floor thickness,one eight of the pipe diameter, provides enoughheight to produce and maintain a stable hydraulicjump and also provides enough constriction (throatarea is 0.709 of pipe area) to produce an adequatepressure drop for full-pipe flows. Yet it is low enoughto maintain open-channel flow for a larger range ofdischarge than would be maintained by a thickerconstriction. By leaving the upper part of the pipeunconstricted, a quick transition from openchannelto full-pipe flow conditions is assured andpressure build-up upstream from the constrictionand head loss are minimized.The pressures in the approach and in the throat ofthe constriction are measured remotely by pressuretransducers. Dry nitrogen gas is bubbled at a constantrate through tubes to the two piezometer openings.The pressure at each opening is reflected to the headof the gas column where the transducer is located.Data from the flow meter are entered into thesystem and converted to two digital numbersproportional to the two pressures measured. Thetwo transducer outputs are applied to a dualanalogue input amplifier that transforms them toanalogue voltage levels, which are then applied toanalogue-to-digital converters. Provisions are madeso that one may compress, expand or shift the rangeat the analogue section.The format under which data are recorded isdependent upon the conditions indicated by thesystem data inputs. The system logic inhibits datarecordings during dry-weather, no-flow conditions.When flow begins in the sewer being monitored bythe system, the pressure at the approach tap willincrease. During the period when this pressureexceeds a preset value, as indicated by thecorresponding analogue voltage exceeding aprogrammed level, recordings will be continuouson a 1-minute cycle. One or more recordingprecipitation gauges and an automatic watersampler are included in the instrumentation forstudying urban storm runoff.It is desirable that the meter be calibrated in placeby current-meter discharge measurements. However,as a guide to the probable meter rating and for useuntil field calibration is completed, the followinglaboratory discharge equations are presented. Thecoefficients shown are for use with S.I. units:(a) Pipe flowing full:QD⎛ Δh⎞1 ⎜ ⎟⎝ d ⎠= . 45535 20.517(5.26)where Q is discharge; D is pipe diameter andΔh is the head differential between piezometerreadings.The constant 1.4553 includes the constantfor the acceleration of gravity. The exponent0.517 fits the laboratory data better than thetheoretical exponent 0.5;(b) Open-channel flow:(i) Supercritical regime:( h ) 1. 585 2Q d = 1.45531d(5.27)where h 1is the depth above pipe invert atthe upstream piezometer.

II.5-32manual on stream gauging(ii) Subcritical regime – slope of culvert < 0.020:For h 1/d ≥ 0.30Qd5 2( h 0.191) 1. 7564= 0.722d −For h 1/d < 0.301( h 0.177) 1. 3784(5.28)5 2Q d = 0.2911d −(5.29)(iii) Subcritical regime slope of culvert:( h ) 2. 7085 2Q ad = 0.2731d(5.30)where[ ]a = 2.15+ ( 9.4943) ( 1011 )( Slope − 0. 008) 6. 7562(5.31)(c) Transitional flow between open-channel flowand full-pipe flow:⎛ 0.590 − h⎜⎝ 0.164d ⎞⎟⎠1 25 22Q d = 2.6 ±(5.32)where h 2is the depth above the flow-meterinvert at the downstream piezometer.processes, such as those described in precedingchapters and in the preceding paragraphs of thischapter. For instance, a lock and dam structure mayhave flow through various types of gates, free-flowover spillways, navigation locks, power generationturbines, pumps, siphons and sluices. Moderncomputer technology has provided the means todevelop programs that compute flow quickly,automatically and simultaneously for each of theseparate structures in a water control system. Onesuch program, entitled DAMFLO.2, has been in useby the USGS for several years. It is beyond the scopeof this Manual to give a complete and detaileddescription of this program, however a generaldescription is given in the following paragraphs.Complete documentation and descriptions of theprogram components can be found in a report bySanders and Feaster (2004). Program DAMFLO.2computes, tabulates and plots flows through sluiceand Tainter gates, crest gates, lock gates, spillways,locks, pumps and siphons using hydraulic equationslike those given in preceding sections of thischapter.5.5.2 Wenzel asymmetrical andsymmetrical flow-metersA generalized drawing of the asymmetrical venturisection devised by Wenzel (1975) is shown inFigure II.5.33. The symmetrical venturi section differsfrom the asymmetrical type shown by having identicalconstrictions on either side of the vertical centrelineof the pipe. The constriction consists of a cylindricalsection, whose radius is greater than that of the pipe,with entrance and exit transitions having a slope of 1on 4. The cylindrical section intersects the pipe wall adistance S from the centreline, thereby maintainingthe invert region free of obstruction so that selfcleaningis facilitated. In all laboratory tests a constantvalue of 0.1 was maintained for S/D, but the ratio r/Dwas varied to provide various ratios of throat area topipe area for testing. A throat length between 2.25Dand 4.0D is recommended. The upstream piezometertap is located approximately D/3 upstream from thebeginning of the entrance transition; the downstreampiezometer tap is located approximately at the centreof the throat. As mentioned earlier, no informationon the field performance of the Wenzel flow-meters isas yet available.5.6 Automated computation of flowthrough water control structuresFlow through a dam and/or water control structurecan involve several different types of computational5.6.1 General description ofProgram DAMFLO.2DAMFLO.2 is a set of programs created usingprocedures and language developed by the SASInstitute (Statistical Analysis System) (1993). The SASsoftware was used because of its integrated plotting,interactive tabling, data entry by forms and variousstatistical, date-time and data-handling programs.DAMFLO.2 is an example of the use of an integratedsoftware package that produces an integrated dataprocessingprogram. The program is integrated inthat all tables and files of computed unit-value anddaily-value flows, as well as data plots, appearautomatically without the need to run severalprograms. Practically all of the tabulated data,including flow types and error flags, are presentedgraphically and by interactive table so that thehydrographer will not have to scan hundreds ofprinted data items.Coefficients and ratings for the hydraulic equationsused in DAMFLO.2 to compute flow through thevarious controls at a dam are calibrated using flowmeasurements. Time-varying data, such as watersurface elevations upstream and downstream of thedam, and gate openings are recorded in the field ator near the dam and are stored in the database in asingle file as sequential groups of data types. Fixeddata that describe the physical features of thevarious structures are stored in a SAS database usingthe SAS forms capability.

Chapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIESII.5-33Upstream measuring sectionS1 2LL 1L 2L 3BThroat measuringsectionArAD2D2DCritical section4 B4Section A–ATransitionsSection B–BFigure II.5.33. Sketch of Wenzel asymmetrical flow-meter in a sewer (after Wenzel, 1975)Programs that compute flow through each outletare executed by separate commands stored in asingle file for each structure. This file is created bythe hydrographer, external to SAS, using a texteditor. DAMFLO.2 is considered modular in thesense that any configuration of outlet structurescan be modeled.Weir, Tainter-gate, sluice-gate, locks and crest-gateflows are computed in DAMFLO.2 usingmethodology documented by Collins (1977),Stuthman and Sanders (1982) and Sanders andFeaster (2004). These methods are, for the mostpart, identical to the hydraulic equations given inthis chapter and other parts of this Manual. Somevariations may be noted. Submerged weir flow iscomputed using the unit-fall method as describedin Chapter 3 of this Manual and as described byKennedy (1984). Methods of adjusting free-weirflow for submergence are used, as described byHulsing (1967). The program also allows negativeweir and orifice flows at low-head dams when thetailwater is higher than the headwater. Flow datacomputed for non-standard outlets can be stored ina separate database, then retrieved, and added toflows computed for the standard outlets byDAMFLO.2.5.6.2 Time-varying input dataTime varying data, such as water surface elevationsand gate openings, are specified in data files atappropriate time intervals such as every 30 minutes,or every 60 minutes and so forth. The programrequires only that the retrieval of the time-varyingdata groups be sequential by type in one file. Forexample, all date, time and gauge-height data wouldbe sequentially filed for a headwater gauge-heightdata type (data group 1), followed by all date, timeand gauge-height data for a tailwater gauge-heightdata type (data-group 2), followed by all date, timeand gate-opening data for the gate-opening datatype for a Tainter gate (data-group 3) and so forth.The order of the data groups within the timevaryingdata file can be specified in any order by thehydrographer.The hydrographer can select time intervals forcomputations that differ from the time intervals ofthe time-varying input data, within certainconstraints. This is especially convenient when thetime-varying input data are recorded at differenttime intervals. Time varying data can be interpolatedby linear or stair-step interpolation. In stair-stepinterpolation, such as would be used for Taintergate data, a preceding input value is held constantuntil changed by a succeeding input value.5.6.3 Fixed input dataPhysical dimensions of the various structures, suchas gate widths, sill elevations, lock dimensions andso forth are provided as fixed data. Ratings andhydraulic coefficients are also provided as fixedinput data. The fixed data are divided into threegroups, stage limits, hydraulic ratings and physicaland hydraulic parameters.The fixed input data for stage (or gauge height)consist of minimum and maximum expected stage,

II.5-34manual on stream gaugingmaximum expected rate of change of stage anddatum corrections. Each set of fixed input data forstage is referenced using a stage-gauge identificationnumber, which should be assigned sequentiallybeginning with 1.The fixed input data for hydraulic ratings consist ofrating type and a set number. The set number refersto the outlets (or outlet) for which the hydraulicrating applies. Hydraulic ratings are available forfive different outlet types: (1) Tainter gates, (2)spillways, (3) pumps, (4) lock gates and (5) crestgates. For example, if the outlet type is a crest gate,the hydraulic ratings available are spillway headversus discharge or head-over-gate versusdischarge.Physical and hydraulic parameter data at a dam arethe data needed to define the physical properties ofthe outlets, such as sill elevations and gate widthsand various hydraulic coefficients and computationalmethods associated with the outlets.5.6.4 Program output dataThe program output allows for three options.Option 1 will provide primary computation tablesand plots, and will send them to a computer screen.Option 2 will send the computations and plots to aprinter. Option 3 will print the primary computationstables, without printing the plots.The unit-value primary computations display inputdata, submergence ratios, computed flows, flowtypes, and warning messages. The hydrographercan specify the time interval for the tabulations.The daily value primary computations display dailyminimum, daily maximum and daily mean statisticsof flow, and summarize warning messages. Dailymeans of all instantaneous flows are computedusing trapezoidal sub-areas of the hydrograph. Thetrapezoidal method is not used for lockage flowsbecause those flows are mean flows over acomputational time interval and are notinstantaneous.Total computed unit-value flows also are plottedwith appropriate warning flags. It is possible to plottailwater elevations against total computed outflowto evaluate the amount of backwater downstreamof the dam, or more specifically, the lack ofbackwater at high stage when the dam outlets aretotally submerged and submergence ratings are nolonger valid. A hydrograph of daily minimum,maximum and mean flows also is produced by theprogram.ReferencesBradley, J.N., 1953: Rating curves for flow over drum gates.American Society of Civil Engineering Proceedings,Hydraulics Division, Volume 79, Separate No. 169,18 pp.Collins, D.L., 1977: Computation of records at controlstructures. United States Geological Survey Water-Resources Investigations Report 77-8, 57 pp.Howe, J.W., 1950: Flow measurement, in Rouse, Hunter,Engineering hydraulics. New York, John Wiley andSons, Ltd., pp. 177-228.Hulsing, Harry, 1967: Measurement of peak dischargeat dams by indirect methods. United States SurveyTechnology. Water-Resources Inv., Book 3,Chapter A5, 29 pp.Kennedy, E.J., 1984: Discharge ratings at gauging stations.United States Geological Survey Techniques ofWater-Resources Investigations, book 3, chap. A10,59 pp.Lansford, W.M., 1936: The use of an elbow in a pipe linefor determining the rate of flow in a pipe. Universityof Illinois Engineering Experiment Station. BulletinNo. 289.Palmer, H.K., and Bowlus, F.D., 1936: Adaptations ofventuri flumes to flow measurements in conduits.Transactions of the American Society of CivilEngineers, Volume 101, pp. 1195.1239.Sanders, Curtis L., Jr., and Feaster, Toby D., 2004:Computation of flow through water-control structuresusing program DAMFLO.2. United States GeologicalSurvey Open File Report 03-473, 99 pp.SAS Institute Inc., 1993: SAS language and procedures(First edition.): SAS Institute Inc., Introduction,Version 6, 124 pp.Schuster, J.C., 1970: Water measurement procedures,irrigation operators workshop. United States Bureau ofReclamation REC - OCE - 70-38, 49 pp.,Schuster, J.C., 1975: Measuring water velocity by ultrasonicflowmeter. American Society of Civil Engineers,Journal of the Hydraulics Division, Volume 101,No. HY12, pp. 1503-1518.Stuthman, N.G., and Sanders, C.L., Jr.: 1982: Instructionsfor processing digital stream flow data collected at dams(Program E466). United States Geological SurveyWATSTORE User’s Guide, Volume 5, chap. 2, 45 pp.Thomas, C.W., and Dexter, R.B., 1955: Modern equipmentfor application of salt-velocity method of dischargemeasurement for performance tests. Proceedings of theSixth General Meeting, International Associationof Hydraulic Research, Volume 2, The Hague,Netherlands, 1955.Toch, Arthur, 1953: Discharge characteristics of Taintergates. American Society of Civil EngineeringProceedings, Hydraulics Division, Volume 79,Separate No. 295, 20 pp.

Chapter 5. DISCHARGE RATINGS FOR MISCELLANEOUS HYDRAULIC FACILITIESII.5-35United States Army Corps of Engineers, 1952:Navigation lock and dam design – navigation dams:Eng. Manual 1110-2-2606, 22 pp.United States Bureau of Reclamation, 1971:Water Measurement Manual (Second edition).Water Resources Technical Publication,pp. 185.212.Wenzel, H.G., 1968: A critical review of methods ofmeasuring discharge within a sewer pipe. AmericanSociety of Civil Engineers Urban Water ResourcesResearch Tech. Memo. No. 4, 20 pp.Wenzel, H.G., 1975: Meter for sewer flow measurement.American Society of Civil Engineers, HydraulicsDivision Journal, Volume 101, No. HYl, pp. 115.133.

Chapter 6Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS usingelectronic methods6.1 GeneralIn many countries streamflow records are publishedannually. The 12-month period used, which isknown as the water year, does not usually coincidewith the calendar year. In the western hemispherethe water year runs from 1 October to 30 Septemberand is designated by the calendar year of the lastnine months. For example the 2006 water year runsfrom 1 October 2005 to 30 September 2006. Thefollowing considerations govern the choice of the12 months that will constitute the water year. The12-month record is essentially an inventory of thewater supply. As with any inventory, it should bemade when the stock on hand (available waterresource) is at a minimum. That is the case in mostof the western hemisphere on 30 September, whenthe growing season is at an end. Not only aregroundwater, soil moisture and surface storage at ornear a minimum on that date as a result of heavywater use during the preceding summer, but thereplenishing rains of autumn have not yet begunand streamflow is also near minimum. In short, the12-month period to be used as the water year isdetermined by the climatic regime of the region.For the publication of data however, some countries,notably the United Kingdom of Great Britain andNorthern Ireland, use the calendar year.A daily record of stage and discharge, along withmomentary values of peak discharge and minimumflow, is computed for the water year from the recordof stage and the discharge rating for the gaugingstation. Prior to the early 1960s, almost allstreamflow data were processed by hand anddesktop calculators. After that time, some of theprocessing steps, such as drawing rating curves,were accomplished by hand methods and transferredto the computer by keying in the necessary data.The type of stage recorder determined whether thecomputations were performed manually or by anelectronic computer. Since the early 1970s, computeranalysis became more prevalent, and today almostall discharge records are computed by automatedmethods. In many instances, rating curves are stillbeing developed by hand plotting methods, andentered to computer programs by keyboard;however, even these are becoming less frequent.Instrumentation for the collection and field recordingof time-series data has attempted to keep pace withcomputer capabilities for processing the data;however, a noticeable lag has resulted. The evolutionof data-collection methods shows a progression fromanalog recorders to digital recorders and finally toElectronic Data Loggers (EDLs) and Data-CollectionPlatforms (DCPs). Even so, many digital recordersstill are in use as primary instruments and graphicrecorders are frequently used as backup instruments.Part of the reason for this is a lag in the acceptance ofelectronic data loggers, which is due to lack of fundsto support a full conversion. With a mixture ofinstrumentation still in use, it becomes importantthat data-processing software be able to accommodatethe various formats of input for time-series data.Field measurements traditionally have been recordedon paper forms. This form is still an accepted modefor these types of measurements. However, electronicdata files from hydroacoustic instruments andelectronic field notebooks have been developed thatmay eventually become the standard for recordingfield notes. Processing software must be able toaccept both types of input: keyboard entry from fieldnotes recorded on paper forms and direct entry fromelectronic data files and field notebooks.In addition to changing instrumentation, increasedcapabilities have developed for the analysis ofstreamflow information. Traditionally, streamflowinformation is produced through the use of stagedischargerelations, with adjustments for shiftingcontrols. For some stations more complexcomputation procedures are used to account forvariable backwater and rate-of-change in stage.Structures such as dams, spillways and turbines, areused at some stations to measure streamflow. Theuse of electromagnetic velocity meters, acousticvelocity meters and Acoustic Doppler Velocity Meters(ADVM) has increased the ability to continuouslymonitor stream velocity, and thereby provide anindex of variable backwater. Unsteady-flow models,such as the Branch-Network Dynamic Flow Model(BRANCH) by Schaffrannek and others (1981), alsohave been accepted as methods to computestreamflow records. An unsteady-flow model usesdetailed hydraulic characteristics of a stream reachand has the capability to provide streamflowinformation at virtually every location in the streamreach. This capability is a distinct advantage over thetraditional gauging station that provides informationat only one location.

II.6-2manual on stream gaugingThere is increasing need for streamflow informationon a real-time, or near-real-time, basis. This has ledto remote sensing and transmitting systems wheredata are received in the office within minutes, or atthe most hours, of the time of occurrence. Thesedata usually are processed immediately uponreception in the office using automated computersystems. In many instances the real-time data aremade available through the internet to almostanyone. Information of this type should be classifiedas operational, having more uncertainty thaninformation that are subjected to verification,interpretation and review. Operational data andinformation should be reviewed before publicationand archiving.Changing technologies of data collection andprocessing require changes in computer software.There is no doubt that this will be a continuingprocess as new and better computer technologiesbecome available. To produce an accurate andconsistent data base, it is important that certainprocedures be standardized. The traditional handmethods, and some of the more recent computermethods, have been described in variouspublications such as Rantz and others (1982),Kennedy (1983), Kennedy (1984), Marsh andStephenson (1976) and World MeteorologicalOrganization (**WMO**) (1971). Many of the field andoffice procedures, as well as the equipment,described in those reports are still valid. In particular,the concepts and theory of surface-water analysisare accepted. However, much of the information inthose reports applies to processing techniqueswhere hand methods are used either totally orpartially. The following sections of this Manualdescribe standards for data analysis and processingthat can be incorporated into computer programs.As a basis for these standards, the report by Sauer(2002) has been used as a major source of informationand many sections of that report are used verbatimin the following sections.In the United States of America, the computerprogram used for computing and processingstreamflow records is known as the AutomatedData Processing System (ADAPS) (Dempster,1990; United States Geological Survey (USGS),2005). Other countries, such as the UnitedKingdom, Canada and France, have developedtheir own versions of automated computerprograms for computing streamflow records.Even though the various international versionsmay be different in respect to procedures orsequence for inputting field-recorded data,computing unit and daily values of streamflow,outputting data tables and other aspects ofanalysis and computation, the end result isessentially the same.6.2 Surface water data andinformationSurface-water data and information are composedof a number of measured and computed variables.The words data and information, as used in thisManual, are intended to have special meanings.The term data is used for the results obtained fromthe measurement of a basic variable, which cannotbe repeated. Data can be accepted, qualified orrejected, but they cannot be modified withoutcompromising their identity. Any change ormodification of a data value converts that valueinto information. For example, if an originalmeasurement of gauge height is corrected for sensorerror (such as drift related to time, gauge height,temperature or other factors), the new value ofgauge height is information. Another examplewould be the use of a gauge-height value and arelation of gauge height to discharge to compute avalue of discharge. The computed discharge value isinformation. Unlike data, information can bemodified, as would be the case if a stage-dischargerelation were revised.The term unit value is used to denote a measuredor computed value that is associated with aspecified instantaneous time. In addition, unitvalues generally are part of a time-series data set.For surface- water records, unit values for allparameters always should be instantaneousvalues. Some parameters, such as velocity, tend tofluctuate rapidly and a true instantaneous valuewould be difficult to use in the analysis andprocessing of the records. Some instruments aredesigned to take frequent (for example, everysecond) readings, temporarily store these readingsand then compute and store a mean value for ashort time period. For these situations, the fieldinstruments should be programmed to recordmean unit values for very short time intervals(one to two minutes) so they can be consideredfor practical purposes to be instantaneous unitvalues.Daily values are measured or computed values of aparameter for a specific date only. The time of thedaily value is not required, although for certaindaily values, time sometimes is stated. Examples ofdaily values are daily mean value, maximuminstantaneous value for a day and minimuminstantaneous value for a day. In the case of

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-3maximum and minimum instantaneous values fora day, the time of the value usually is stated.6.3 Establishing a site in theelectronic processing systemThe processing of field data varies depending onthe type of gauging station, such as field collectionequipment, computational methods, informationoutput requirements and other aspects of eachstation. For instance, there are several types of stagedata collection methods, such as observer data,Analog Digital Recorders (ADR), EDL and DCP.These were described in Chapter 4 of Volume I.Different types of ratings are also possible, such assimple stage-discharge ratings, stage-area ratings,ratings, stage-fall ratings, control structure ratingsand others as described in the first 4 chapters ofVolume II and in Chapters 6 and 7 of Volume I.Various output requirements may also be a factor,although daily values of discharge are usually thefinal result. Other output requirements aresometimes required, such as unit values of stageand discharge, daily values of reservoir surface areaand contents and various tide data.The first step, therefore, is to establish the gaugingstation in the electronic processing system. Eachgauging site must be established to accommodatethe various input, computation methods and outputrequirements specific that station. The specificrequirements for a gauging station may change fromtime to time and the electronic processing systemshould be able to accommodate these changes. Theelectronic processing systems used by most countriesare versatile enough to accommodate most of thecombinations of data input and output.It should be noted that the sequence of steps mayvary from that shown in the following sections. Forinstance, different types of gauging stations mayrequire a different sequence of steps or computations.Also, some steps such as analyzing the data are acontinuing process from the beginning to the endof the water year. The final written document thatsummarizes the station analysis may not be finalizeduntil the end of the water year.6.4 Entry of field data to theelectronic processing systemThe second step required for the processing ofsurface-water data is the entry of field data andinformation to the electronic processing system.This process will include unit value data and fieldmeasurement data and information. Fieldmeasurements can include discharge measurements,gauge-datum leveling data, crest-stage gauge data,channel and control cross-section data and othermiscellaneous data and information.6.4.1 Unit value dataThe recording of unit value data has evolved fromsimple hand written notes (observer data), toanalog recorders, to digital recorders, tosophisticated programmable data loggers and todirect data transmission to the computer. Althoughthe trend today is toward the use of programmabledata loggers and direct data transmission, digitalrecorders still are widely used and some use ofanalog recorders and hand written observerrecords. Therefore, the electronic processingsystem must accommodate each of these types ofdata.Preparation of unit value data for electronicprocessing should follow a basic sequence. However,because different methods are available forcollecting and recording field data, there may beinstances where the preferred sequence cannot befollowed. The following sequence is advised:(a) A copy of the original, unedited unit valuesshould be archived before any editing,conversions or computations are made. Allediting, conversions and computations shouldbe performed using an electronic copy of theoriginal data;(b) The unit values should be translated into astandard format;(c) The unit value times should be corrected forclock errors, if applicable;(d) Conversions to UTC time should be made sothat all unit value data can be related to standardtime or daylight savings time, as required;(e) The unit values prepared in this manner thencan be used for all further computations,analysis and archiving, as described in thisManual.Various types of unit value data can be entered intothe electronic processing system. These data includeunit values of gauge height, velocity or velocityindex, spillway gate opening or index, turbinepressures, navigation lockages and other readingsassociated with structures. For some gauge sites,multiple data sets of unit values may be availablefor a given parameter. For instance, a stream affectedby backwater may have two gauges at differentlocations for the purpose of measuring gauge

II.6-4manual on stream gaugingheight. Unit values of gauge heights or elevationsare required for almost all gauging sites.6.4.2 Sources of unit value dataThe sources of unit value data are described in detailin Chapter 4, Volume I. A brief description of themethods of obtaining, recording and entering unitvalue data to the electronic processing system isgiven in the following paragraphs. Each set of unitvalues must be identified as to the source andmethod of acquisition.Observer dataAt some gauge sites gauge readings are made by anobserver. These readings are recorded, along withdate and time of the reading, on a preprinted form.Such readings may be used as the primary set ofunit values for the station or for backup andverification of another measuring and recordingmethod. The hand written unit values made by anobserver must be entered into the electronicprocessing system by direct keyboard entry. Thedate and time must be entered for each unit valueand the time zone designation must be entered foreach set of unit values.Analog recordersAnalog recorders are frequently used to record thegauge height, or other parameters, as sensed by afloat, pressure system or other device connected tothe recorder. Analog recorders provide a continuoustrace of the measurements on a graphical chart thatis driven by a clock to provide a time scale. Unitvalue data from these charts are entered to theelectronic processing system through the use of anautomatic, or hand operated, digitizer. The digitizerenters unit values from the chart at time intervalsspecified by the hydrographer. Beginning andending dates and times, and the time zonedesignation, must be entered for each segment ofchart that is digitized. Analog records may be usedas the primary unit values for a station, but aremore frequently used for backup and verification ofunit values collected with a different method.Automated digital recordersThe Automated Digital Recorder (ADR) is a devicethat records data on a narrow paper strip bypunching a series of holes that are digitally codedto represent the unit value. The paper strip advancesafter each punch and data are recorded at a specifiedtime interval, commonly 5, 15 or 60 minutes. Othertime intervals may be used but the time interval isuniform for each gauge. Unit value data are enteredto the electronic processing system by passing thepaper strip through a digital tape reader. Startingand ending dates, times, and the time zonedesignation must be entered for each processingperiod. ADRs are frequently used as the primaryrecording instrument for a gauge site but are alsoused as backup and verification for other types ofinstruments.Electronic data loggersVarious types of Electronic Data Loggers (EDLs) arein use for recording unit value data. These devicesreceive data from a sensing instrument and recordthe unit value in electronic memory. Data areextracted from the data logger either by removingthe memory chip or by reading data from thememory into an external storage module or fieldcomputer. Because of the many configurations andtypes of data loggers currently in use, and becausechanges occur frequently, it is not practical toattempt a description in this Manual. The processof entering data from these types of recordersprimarily is electronic. Electronic data loggers havethe advantage over analog recorders and ADRsbecause they can be programmed to sense andrecord according to pre-defined rules. A recordingsystem of this type results in a variable time intervalbetween unit values, and necessitates the recordingof the time and date associated with each unitvalue. If the recording time interval is constant,then most electronic data loggers do not record thetime and date associated with each unit value. Foreither method, variable or constant recordinginterval, the starting and ending date and timemust be entered for the period of record beingprocessed. Electronic data loggers frequently areused for the primary recording instrument but insome cases they may be used only for backup.Data-collection platformsData-Collection Platforms (DCPs) are field systemsthat store data electronically for a relatively shorttime (two to four hours) and then transmit it to anoffice computer. For some types of DCPs, storagemay be comparable to an electronic data logger andthe data can be retrieved in similar fashion. DCPsare frequently operated in conjunction with anelectronic data logger, ADR or analog recorder. Avariety of gauge and recorder configurations ispossible. Where two or more recorders are used,one should be designated the primary instrument;the DCP is frequently given that distinction. Insome instances the DCP is the only instrument usedand the primary record is received directly in the

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-5office. Unit value data transmitted and received bysatellite automatically are tagged with date andtime, which is determined from UniversalCoordinated Time (UTC).OtherUnit value data that are stored on other computersystems can be transferred to the electronicprocessing system by use of card images or otherstandard formats. One of the recorder typesdescribed above usually is designated as the primaryrecorder for computing the primary records ofgauge height, discharge, reservoir contents or otherparameters. A second recorder is frequently operatedin conjunction with the primary recorder and isdesignated the backup recorder. In the event of themalfunction of the primary recorder, the electronicprocessing system should allow the entry of unitvalues from the backup recorder as a substitute forthe primary recorder. These substitute unit valuesshould be identified with a flag as to the source ofthe backup records. These records also should besubject to all further analysis, such as timecorrections, parameter value corrections and others,as described in the following sections.6.4.3 Unit value recording time intervalThe time interval between recorded unit values maybe a constant value or variable. The programmabledata logger allows the recording interval to bevaried according to user-specified rules. The variabletime interval can be based on the value of theparameter being recorded, the time length since thelast recording, the rate of change of the parametervalue being recorded, the value or rate of change ofsome other parameter or some combination ofthese. The electronic processing system should beable to accommodate either method of datarecording, constant or variable time interval.6.4.4 Time system requirementsThe time system used in most field data-collectionsystems is based on the local time at each gauginglocation. For most of the United States, the localtime is a changing time system where the clock isadvanced one hour in the spring, and set back onehour in the fall. The time during the summer periodcommonly is referred to as daylight savings time,and the remainder of the year as standard time. Theadvent of the satellite DCP has required the use ofUTC for DCP field instruments. Additionally, somegauge sites are operated year around on localstandard time without making the change fordaylight savings time. Consequently, there is amixture of time systems being used. The surfacewaterelectronic processing system mustaccommodate the entry of data in any of the timesystems. Therefore, all data entry must include adesignation of the time system at which the datawere recorded.All times, both for time series data and formeasurement, data will automatically be convertedto UTC time for storage in the electronic processingsystem. Therefore, time adjustments for the onehourdaylight savings time offset (as used in theUnited States) automatically will be accounted forwhen times are converted to UTC. The hydrographerwill be able to perform computations, such as fordaily mean values of streamflow, using any specifiedtime system. The electronic processing systemautomatically will make the necessary timeconversions, including changes between standardand daylight savings times, prior to making thecomputations. Likewise, unit values of gauge height,discharge or other parameters would be retrievedusing a time system selected by the hydrographer.6.4.5 Standard formatAll unit value data stored in the electronic processingsystem should conform to a standard unit valueformat. This format essentially means that theelectronic processing system should convert all unitvalues to engineering units and assign times anddates based on the time system used for fieldrecording of data. Time adjustments for the purposeof converting the unit value times to standard UTCtime are made automatically. Time correctionsmade for clock errors should be made after the dataare converted to a standard format. Parameter valuecorrections are made on the basis of hydrographerinstructions after data are entered in the electronicprocessing system. Additional details regardingtime and parameter corrections are described infollowing sections.6.4.6 Field measurement dataVarious types of field measurements are made atsurface-water gauging stations, each providingvarious kinds of data and information. Theseinclude measurements of stream discharge, levelingfor gauge datum checking, crest-stage gaugemeasurements, channel and control cross-sectionmeasurements and other miscellaneous data andinformation. Usually each type of field measurementis recorded on a form designed especially for thattype of measurement. The electronic processingsystem should be able to receive, process and storethe field measurement data and information so the

II.6-6manual on stream gaugingdata can be used in other parts of the electronicprocessing system.Most field data are recorded on paper forms andmust be transferred to the electronic processingsystem by keyboard. Field data and informationthat are recorded electronically in a field computerwill require an interface between the field computerand the office computer to transfer the dataautomatically.Discharge measurementsThe electronic processing system should have thecapability to receive and store essentially all of thedata and information recorded on dischargemeasurement note sheets. This capability shouldinclude the information shown on the front sheetof the notes and the detailed data shown in thebody of the notes. In the case where dischargemeasurements are recorded in electronic fieldcomputers, the electronic processing system wouldreceive the data and information automaticallythrough an interface.Although the electronic processing system shouldbe able to receive all data (front sheet and insidebody) from a discharge measurement recorded onpaper forms, it is not mandatory that the insidebody data and information be entered. This part ofthe measurement is not normally used in theprocessing of daily discharge records. The mainpurpose for entering the data and information fromthe inside body would be for computationalchecking and for special studies.The original measurement is either the data orinformation recorded on paper notes or in anelectronic field notebook. If the measurement wasrecorded on paper, those original paper notes aresaved for archival. If the measurement was recordedelectronically, the first electronic copy entered tothe processing system becomes the archival copy.For this reason it is mandatory that the entiremeasurement recorded in an electronic fieldnotebook, including all of the individual dataelements, be entered in the electronic processingsystem.Discharge measurement entry requirementsDischarge measurement data will be acquired fromone of several different methods as described inChapters 5 through 9 of Volume I. The input formspresented to the user of the electronic processingsystem should be designed to conform to themeasurement method. That is the input form formeasurement summary information for a specificmethod of measurement (for example, a wadingmeasurement with a mechanical current meter)would have input items specific to that method ofmeasurement and would omit input items that arenot applicable to that method. The specificmeasurement data on the inside of the dischargemeasurement, although not mandatory, would beentered on separate input forms.Although separate input formats are used for thevarious types of measurements, all measurements,including indirect measurements, should benumbered consecutively and maintained in one fileof discharge measurements. The numberingsequence should begin with one for the firstdischarge measurement of record, and continueconsecutively throughout the period of record, withall discharge measurements numbered inchronological order. Discharge measurementnumbers may contain alphabetic characters (forexample, 127A, 127B and others) to allow insertionof a measurement in an established sequence.Renumbering of discharge measurements should bediscouraged.The rapid development of new instruments formeasuring discharge, particularly acousticinstruments, has presented a challenge for developersand maintainers of discharge computation dataprocessing programs. For example, the enormousamount of data available from an ADCP measurementmust be distilled into the most important informationfor processing programs to use. Also, it is desirable toidentify the type of instrument being used.Gauge datum levelingLeveling for the purpose of establishing or checkingthe datum of reference marks, benchmarks, staffgauges, wire-weight gauges and other gauge featuresis performed routinely or when problems arise atmost gauging stations, as described in Chapter 4 ofVolume I. Guidelines for leveling procedures asperformed in the United States are described byKennedy (1990). The electronic processing systemshould provide capability to accept leveling dataand should be able to produce an analysis andsummary of the leveling information.Crest-stage gauge dataCrest-stage gauges are special gauges capable ofrecording the highest level of a flood peak. Thesegauges may be operated independently as a partialrecord site, or they may be operated as a continuousrecord site to verify the peak gauge height. A special

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-7note sheet is usually used to record data andinformation for crest-stage gauges. The electronicprocessing system should be able to accept thesedata.performed on a copy of the original data, and not onthe original. This copy will become the work file, andalso will be archived following completion andfinalization of the records.Channel and control cross sectionsData defining cross sections of the stream channeland/or control are useful in rating curve analysis.Unsteady-flow model methods of computing streamdischarge must have cross-section data at intervalsalong the stream reach for which the model isdefined. The electronic processing system shouldallow input of items necessary for defining thecross-section location and the descriptors for eachcross section. In addition Manning coefficients maybe required and should be variable, both horizontallyand vertically. For some cross sections that areconsidered section controls, a weir coefficient (C)should be an optional entry, which also may bevariable with stage. Transverse stationing for crosssections should begin on the left bank of the streamand increase from left to right. If survey data areentered with transverse stationing that increasesfrom right to left, the electronic processing systemshould provide an automatic conversion of the datato the left-to-right format. The electronic processingsystem also should accommodate input of crosssectiondata that were collected and recordedelectronically.Miscellaneous field notesMiscellaneous field notes occasionally are made atmost gauge sites. These may be just a gauge reading,a measurement of some feature or variable, a recordof maintenance or simply written comments. Theelectronic processing system should allow entry ofthese notes.6.5 Verification and editing ofunit valuesUnit values for the various parameters, such as gaugeheight and velocity, must be carefully checked andverified before being used in further analysis.Erroneous or suspicious data may require editing andappending special identification codes (flags) toindividual values. Before any editing is performed, theoriginal unit values should be set aside for archiving.This section of the Manual describes techniques forverification and editing, which includes timecorrections, unit value corrections, datum adjustmentsand various comparisons and cross-checking. Allverification, editing and time corrections must be6.5.1 Times and datesUnit values of gauge height and other streamflowparameters generally are recorded in fieldinstruments at a fixed time interval, such as every15 minutes, one hour and so forth. The time anddate associated with each unit value are not alwaysrecorded, but are determined on the basis of theinitial time and date, and the recording timeinterval. Times and dates are recorded for each unitvalue when field recorders are programmed forvariable time-interval data. Field instrument clocksare fairly reliable, but occasionally clock errors willresult. True times and dates are those noted by thehydrographer using his watch and calendar at thetime the field instrument is serviced. Servicingwould be at the beginning and end of a recordperiod and occasionally at intermediate points of arecord period. The hydrographer should also notethe time-system designation, such daylight savingstime whenever the time and date are noted. Times,dates and time system designations noted byhydrographers will be used as the basis for makingtime corrections, standard and daylight savingstime adjustments and conversion to UTC of theunit value data.Data acquired by satellite DCP installations willhave UTC times and dates assigned automatically.These times and dates are considered accurate anddo not need adjustment or correction.6.5.2 Time corrections and adjustmentsTime corrections to account for clock errors may benecessary for unit value data recorded in the field.In addition, all unit value times must be adjusted toUTC time for purposes of archiving. These timecorrections and adjustments do not apply to datacollected by way of a satellite DCP because thosedata are considered correct as collected.Clock error correctionsThe simplest case of clock error is where thebeginning time and date are correct and the endingtime and date are incorrect by a known amount.Lacking any evidence of intermediate clock orrecorder problems, it usually is assumed that theclock error is a gradual and uniform error. Thecorrection for this type of error should be prorateduniformly throughout the record period.

II.6-8manual on stream gaugingA somewhat more complex case involves a clockor recorder malfunction somewhere in the middleof the record period or where the clock was setwrong at the beginning of a record period. One ormore instances of intermediate clock problemsmay result in some cases. The time-correctionprocedure should allow the hydrographer to assigntime and date values at more than one place withina record period, and the electronic processingsystem should adjust all intervening unit valuetimes accordingly. Occasionally, it may not bepossible to determine why the time for a record isincorrect, or at what point in a record that timingproblems occurred. A hydrographer may need tomake arbitrary time assignments based on theirbest judgment.In some cases intermediate time and date readingsmay be available from discharge measurementnotes or miscellaneous field notes when the gaugewas visited but the record was not removed. Theelectronic processing system should automaticallyretrieve dates and times from the field note entriesfor checking clock performance. This requires thatthe unit value file has been marked in some way sothe hydrographer can identify the place in therecord where the correct times and dates apply.Such readings would be treated the same as describedabove and corrections would be made by linearproration between adjacent readings.Past methods for making time corrections providea method whereby occasional unit values aredropped, or added, in order to account for a timeerror. This method is not considered as good asthe linear proration method and should not beused.The standard time-correction method, or linearproration method, described herein will result inunit values of gauge height (or velocity or otherparameter) that will not be on the even hour, or15 minutes or other even time. This is not considereddetrimental to the record. If unit values of gaugeheight (or other parameter) are needed on the evenhour or other even time interval, they can beobtained by interpolation between the timeadjustedvalues.Time differences caused by a change to or fromdaylight savings time should not be treated thesame as clock error. If a clock error exists during aperiod of record where the time changed because ofdaylight savings time, the clock error should first beprorated by assuming a uniform time designationfor all of the period of record being processed. Theelectronic processing system should adjust timesand dates input from field notes to the same timedesignation. The clock error is then correctedaccording to the hydrographer’s instructions. Afterclock error corrections are made, the record isautomatically converted with the electronicprocessing system to UTC time for storage andarchiving. No unit values would be dropped orartificially added because of the daylight savingstime change.Universal coordinated time (UTC) adjustmentsAll data and information should be stored withUTC. Therefore, following the standard timecorrectionmethod for making clock erroradjustments, the electronic processing systemshould automatically adjust all local times to UTC.This is a simple process of adding the UTC timeoffset to the recorded local times. The recordedlocal times must have a time-zone designation aspart of the input to define the time-zone systemused for recording.Unit values used in other analyses, such ascomputation of daily values, will adjust the UTCtimes to whatever time system is designated by thehydrographer. In this way, the electronic processingsystem can produce records on the basis of anydesignated time system. The time adjustmentsresulting for a period where time changes fromstandard time to daylight savings time and for aperiod where time changes from daylight savingstime to standard time is illustrated in Figure II.6.1.Also shown in this figure are unit values that wouldbe used for computing daily values for days thatchange between standard time and daylight savingstime. Note that all recorded unit values are used inthe computations and none are dropped orartificially added. The day when time changes intodaylight savings time will contain 23 hours and theday when time changes out of daylight savings timewill contain 25 hours.6.5.3 Parameter value verificationsUnit values of gauge height and other parametersthat have been automatically measured andrecorded by field instruments always should becarefully inspected and verified before acceptingthem for further analysis and computations.Various methods are available to make this taskrelatively easy. The most frequently used methodsare threshold comparisons, rating comparisons,direct reading comparisons and graphical methods.Of these, graphical methods are the most versatileand can be easily adapted to any of the othermethods.

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-9Example A. Time changes from standard timeto daylight savings timeExample B. Time changes from daylightsavings time to standard timeUnit Local Local UTC Time Unit Local Local UTC TimeValue Date Time Time Zone Value Date Time Time Zonexxxx 04/03 2300 0400 EST xxxx 10/24 2300 0300 EDSTxxxx 04/03 2400 0500 xxxx 10/24 2400 0400xxxx 04/04 0100 0600 xxxx 10/25 0100 0500 EDSTxxxx 0200 0700 EST xxxx 0100 0600 ESTxxxx 0400 0800 EDST xxxx 0200 0700xxxx 0500 0900 xxxx 0300 0800xxxx 0600 1000 xxxx 0400 0900xxxx 0700 1100 xxxx 0500 1000xxxx 0800 1200 xxxx 0600 1100xxxx 0900 1300 xxxx 0700 1200xxxx 1000 1400 xxxx 0800 1300xxxx 1100 1500 xxxx 0900 1400xxxx 1200 1600 xxxx 1000 1500xxxx 1300 1700 xxxx 1100 1600xxxx 1400 1800 xxxx 1200 1700xxxx 1500 1900 xxxx 1300 1800xxxx 1600 2000 xxxx 1400 1900xxxx 1700 2100 xxxx 1500 2000xxxx 1800 2200 xxxx 1600 2100xxxx 1900 2300 xxxx 1700 2200xxxx 2000 2400 xxxx 1800 2300xxxx 2100 0100 xxxx 1900 2400xxxx 2200 0200 xxxx 2000 0100xxxx 2300 0300 xxxx 2100 0200xxxx 04/04 2400 0400 xxxx 2200 0300xxxx 04/05 0100 0500 xxxx 2300 0400xxxx 0200 0600 xxxx 10/25 2400 0500xxxx 0300 0700 xxxx 10/26 0100 0600xxxx 04/05 0400 0800 EDST xxxx 10/26 0200 0700 EST24 unit values used to compute daily value for4 April26 unit values used to compute daily value for25 OctoberFigure II.6.1. Comparison of time systems where daylight savings time is used. (Coordinated UniversalTime (UTC); United States Eastern Standard Time (EST); Eastern Daylight Savings Time (EDST))

II.6-10manual on stream gaugingThreshold comparisonsA threshold is a minimum or maximum value thatcan help detect unit values that might be erroneous.Thresholds can be compared directly to unit values,or to differences between adjacent unit values.Testing a period of record against a set of thresholdsis performed automatically with the electronicprocessing system. The hydrographer is alertedwhenever a unit value exceeds the threshold value.Thresholds can be established by the hydrographeror they can be automatically computed based on aperiod of record.The set of thresholds should consist of:(a) A high-value threshold;(b) A low-value threshold;(c) A maximum difference threshol;(d) A flat-spot threshold (maximum time forconstant values).Thresholds should be used to detect values that areunusual and outside the normal expected range ofthe data. For instance, an ADR punch recordermalfunctions and punches additional holes in thepaper tape, which translates to unit values outsideof the expected range of values. The threshold checkshould alert the hydrographer to this condition.Maximum and minimum threshold values shouldbe set at or near the maximum and minimum valuesactually experienced during the past three to fiveyears of record. The difference threshold also shouldbe set at or near the largest valid difference duringthe past three to five years.Selection of threshold values should be based, ifpossible, on an analysis of the observed record forthe past three to five years. This analysis should beperformed with the electronic processing systemand should furnish listings of the 20 highest andlowest peak unit values during the period. Theelectronic processing system also should providethe 20 greatest differences between consecutiveunit values, and the 20 longest time periods duringwhich there was no change in unit values. This typeof analysis would provide data for the hydrographerto use in selecting appropriate thresholds and wouldbe performed every three years, or whenever it isdesired to change thresholds.Threshold checking, if used primarily for thepurpose of identifying unit values that are outsidethe range of most experience, is a very valuable toolfor identifying erroneous unit values. However,caution should be exercised if high-value thresholdsare set too low or low-value thresholds set too highso that many unit values within the range ofexperience are identified by the threshold test. Inthis case, the hydrographer always should applyother methods to verify unit values that have failedthe threshold test.An important consideration of unit value verificationis the public display of unit values on World WideWeb pages, which is rapidly becoming moreprevalent. For example, the USGS displays nearreal-time stage and discharge unit-value data frommost of the continuous stream gauges it operates.The USGS uses thresholds that are designed to actas Web filters: data values outside the thresholdlimits are not displayed yet they remain in thedatabase and thus preserved in the event that theyare not erroneous.Rating comparisonsThe rating comparison identifies all unit values thatexceed the high end or fall below the low end of therating currently in use. This comparison can beperformed automatically with the electronicprocessing system because ratings are stored in theelectronic processing system. This test would alertthe hydrographer to possible erroneous unit valuesas well as to the possible need to extend the ratingcurrently in use.Direct reading comparisonsVarious types of direct readings may be available forcomparison and verification of recorded unit values.These include actual gauge readings made by anobserver or hydrographer, readings obtained frommaximum and minimum indicators, high watermark readings and crest gauge readings. All of thesevarious direct readings should be input to theelectronic processing system and automaticallydisplayed to the hydrographer in conjunction withthe unit values being verified.At some gauging stations auxiliary and/or backupgauges are operated in conjunction with the primarygauge. In many cases, the records from these gaugescan be used as an independent check to the primaryrecord.Graphical comparisonsGraphics can be the most important and easily usedmethod to verify a period of unit values. All of themethods described in the previous sections shouldbe incorporated into a graphic system to automaticallyscan and review a period of record for the purpose ofverification. The primary record of unit values shouldbe plotted as a time series, with a unit-values scale

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-11that allows the hydrographer to see each value clearlyand that does not distort the general shape of therecord. The time scale should automatically defaultto the time zone normally used for the station, butthere should be provision for the hydrographer tochange to any other time zone. A basic plot of unitvalues can be used to identify erroneous data by anexperienced hydrographer. With the addition to theplot of thresholds, rating limits, observer andhydrographer gauge readings, high water marks,maximum and minimum indicator readings andauxiliary gauge records, much more can be done toverify the primary record.The recorded unit values should be plotted andconsidered the base plot. The processing systemshould plot all direct gauge readings by observersand hydrographers at the correct time on the baseplot. High and low thresholds, high and low ratinglimits, high-water mark readings, maximum andminimum indicator readings and crest-stage gaugereadings should be plotted at their respectiveelevations as a horizontal line that extendsthroughout the period of record being verified. Thisprocess will allow the hydrographer to comparethese readings to peaks and troughs in the primaryrecord. Auxiliary and backup records should beplotted as a time series for comparison to the primaryrecord. The plotting system should use differentcolors and symbols to easily distinguish the variouscomponents. Unit values that trigger the differencethreshold and the flat spot threshold also should beeasily identified by color or symbol. When evaluatingthe potential for ice-affected periods, stage unit valueplots that include air temperature, precipitation andwater temperature values, if available, are veryhelpful in determining whether or not dischargecomputations should be adjusted for ice effects.6.5.4 Parameter value correctionsThe verification process described in the previoussections will sometimes identify unit values ofgauge height or other parameters that are eithererroneous or suspected of being erroneous. Bydefinition, an erroneous gauge reading resultswhen the recording instrument does not recordthe true parameter value that occurred in thestream, lake or other water body. A base, orreference gauge, usually is used for determiningthe true parameter value.An erroneous gauge reading can result from eitherinstrument errors, datum errors, or both. Instrumenterrors are those errors resulting from a malfunction,incorrect setting, incorrect calibration, or otherproblem with the recording instrument. Aninstrument error usually can be detected bycomparing a recorded parameter value with acorresponding reference gauge reading. Datumerrors, on the other hand, are those errors resultingfrom a change in the reference gauge and applyonly to gauge heights or elevations. A datum errorusually can be detected only by running levels tothe reference gauge, using a stable benchmark ofknown elevation as a reference.Another distinction between datum errors andinstrument errors is that datum errors generallyoccur over many months or years, whereasinstrument errors occur over a few days or weeks.Consequently, corrections for datum errors andinstrument errors usually are made separately.However, correction for datum errors should usethe same methods as those used for instrumenterrors as described below for instrument errorcorrections.When a parameter value, or series of values, hasbeen determined to be erroneous, it may becorrected, or edited, if the hydrographer has asufficient basis for doing so. Editing of individualunit values should be allowed with the electronicprocessing system at any of the verification steps,including the graphical display. In the graphicaldisplay the hydrographer should edit unit valuesdirectly on the graph, or in a supplemental table ofunit values. In addition to correcting and editingunit values, the electronic processing system alsoshould allow the hydrographer to flag unit valuesin such a way that they will not be used in furtheranalysis.Datum adjustments and conversionsThe gauge datum of a gauge site is usually an arbitrarydatum, unique and specifically selected as a convenientworking reference for each gauge site. The datumfrequently is located at a level just below the lowestexpected gauge height or just below the gauge heightof zero flow. For some stations, such as at reservoirsand coastal streams, the gauge datum may not bearbitrary, but is established to be the same as mean sealevel or other common datum. In any case, there aretimes when datum adjustments must be made tocorrect a datum error. Also, there are some stations forwhich it is necessary to convert an arbitrary datum toa known datum, such as mean sea level. These aredescribed in the following sections.Adjustments for gauge datum errorGauge datum adjustments generally are consideredto be corrections applied to recorded gauge heights

II.6-12manual on stream gaugingand water-surface elevations to make themconsistent with the gauge datum. Physicalmovement of a gauge or gauge structure cansometimes occur, causing an error of gauge readingsin relation to the gauge datum. Such a change maybe over a long period of time, such as from settlingor subsidence, or the change may be sudden, suchas from an earthquake, flood damage or accident.Whether the change is gradual or sudden, the resultis the same, in that the gauge no longer recordsgauge heights and elevations that are correct inrelation to the original gauge datum. Gaugemovement, relative to gauge datum, is quantitativelymeasured by leveling from stable reference marksor benchmarks of known elevation. Levelingprocedures for surface- water gauging stations arewell established and are described by Kennedy(1990).Datum errors should be carefully analyzed todetermine the best method to make corrections.Frequently, it cannot be determined when a datumerror occurred and the best method of correction isto prorate it uniformly throughout the period inquestion. If a specific time of occurrence can bedefined then the correction can be made starting atthat time and carrying the correction forward untilthe datum is restored. As a general rule, correctionsfor gauge-datum errors of 0.02 ft, or 0.006 mm, orless are not applied except in cases where smallergauge-datum errors are critical in correctly defininganother parameter, such as for reservoir contentscomputations. Small errors of this kind usually areabsorbed by ratings and rating shifts.Conversion to a common national datumIn addition to making datum adjustments for thepurpose of correcting gauge-height values that areincorrect because of a change of the base gauge, it issometimes necessary to convert recorded gaugeheights to a different datum, such as a nationaldatum. The most common conversion is where therecorded values must be converted to mean sea level.This type of conversion requires that a constantvalue be added to, or subtracted from, the recordedgauge heights throughout the record period. A gaugedatum adjustment for gauge movement also may beneeded at times. In such cases two simultaneousadjustments would be needed.Instrument error correctionsRecording instruments and parameter sensors may,at times, produce erroneous gauge readings for anumber of reasons. For example, float tapes mayslip, recorders may punch incorrectly, gaugedrawdown because of high velocity may occur,stage or velocity sensors may drift because oftemperature and the recorder may even be setwrong by the hydrographer. These, and numerousother causes, will result in erroneous unit values ofgauge height, velocity or other parameters.The electronic processing system must provide easyand quick ways to make corrections when instrumenterrors are identified. Corrections should bepossible through a graphical interface, such as theone described above for review and verification,and also with a tabular format. The hydrographershould be able to make corrections to individualunit values, or to sequences of unit values. Threetypes of corrections should be available for use:(a) Constant value corrections;(b) Parameter (usually stage) variable corrections;(c) Time variable corrections.Constant value correctionsConstant value corrections are simply the additionor subtraction of a constant value from a sequenceof unit values. The hydrographer should be able tospecify the constant value correction to be used andthe dates and times for which the correction is to beapplied. The electronic processing system thenshould apply the correction automatically.Parameter variable correctionsCertain types of parameter errors may vary accordingto the value of the parameter. For instance, for somegauging stations the stage measurements may notreflect actual river stage because of drawdowncaused by high flow velocity near the gauge intake.The resulting stage error is directly related to thevelocity, which in turn is often related to the stage.A relation between stage and stage-correction cansometimes be defined that is reasonably consistentfor long time periods and can be used to determinethe gauge-height correction on the basis of therecorded stage.Parameter variable corrections require a relationbetween the parameter and the correction. Thehydrographer should be able to input this relationto the electronic processing system, along with astarting date and time, and if needed an endingdate and time. The electronic processing systemshould calculate and apply the correctionsautomatically. When a correction relation of thistype is entered, and no ending date and time arespecified, then it should be continued in use untilsuch time that an ending date and time arespecified.

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-13A parameter variable correction relation should bedefined by entering point pairs of parameter andcorresponding corrections for as many points asnecessary through the intended range of correction.The processing system should automaticallyinterpolate corrections that are needed between theinput points. If parameter values occur below thelowest point of the correction relation, then thecorrection value for the lowest point of the relationshould be used for all corrections below this point.Likewise, the correction values above the highestpoint of the correction relation should be the sameas the highest correction value of the relation.Alternatively, the correction relation can be enteredas an equation. Upper and lower limits of the inputparameter should be specified for the equation. Thecorrection values corresponding to these limitsshould be held constant when parameter values areless than the lower limit or greater than the upperlimit.Time variable correctionsTime variable corrections are corrections that aredistributed between specified dates and times. Thistype of correction usually is referred to as timeproration. Time proration should apply to singularcorrection values and to parameter variablecorrection relations. Likewise, time variablecorrections should apply to datum corrections aswell as instrument error corrections.Corrections that do not vary with parameter valueare considered a singular correction for a given pointin time. However, such a correction may vary withtime. For example, at the beginning of a time seriesof unit values, a correction of + 0.15 ft is defined,which does not vary with stage. At a subsequent dateand time, a correction of + 0.10 ft is defined, whichlikewise does not vary with stage. The electronicprocessing system should allow the hydrographer tomake a linear, time proration between these twocorrection values and defined times.Corrections that vary with parameter value (asdefined by a parameter variable correction relation)sometimes gradually may change shape or positionwith time. The electronic processing system shouldallow time proration between two consecutiveparameter variable correction relations. Timeproration between two correction relations shouldbe made on the basis of equal parameter values. Forexample, assume that a correction relation isentered with a date and time. A second correctionrelation is entered with a subsequent date and time.At some intermediate date and time, assume thatthe gauge height is 4.23 ft. Correction values aredetermined from each of the two correctionrelations for a gauge height of 4.23 ft, resulting intwo correction values, one at the start of theproration period and one at the end of the prorationperiod. The correction that applies to theintermediate date and time, for the gauge height of4.23 ft., is determined by time interpolationbetween the two correction values.Additive correctionsSometimes, more than one correction for the sameperiod of unit values may be needed. For instance,a datum correction may be needed during the sameperiod of time that a parameter variable correctionrelation is needed. If both corrections are defined,and the dates and times overlap, the electronicprocessing system automatically should apply bothcorrections simultaneously for the overlappingperiod. In other words, all corrections that aredefined for the same date and time, or for the sametype of correction, become additive. There shouldbe no limit as to the number of corrections that canbe used for a given date and time, but it is not likelythat more than two or three would be required.Flagging of unit valuesCorrections cannot always be determined for unitvalues, and in fact, corrections are not alwaysdesired for unit values. For certain situations it isrecommended that daily values be estimated ratherthan attempting to correct, or estimate, unit values.In these situations, the hydrographer should beable to flag specific unit values to specify the reasonthey are not used. The flags also will be an indicatorin other parts of the electronic processing system,such as the primary computations, to ignore theunit values for certain kinds of computations. Thefollowing flags are recommended:(a) Affected – This flag is for unit values that arecorrect and representative of the true stage (orother parameter), but because of some irregularcondition the rating is severely affected and maynot be applicable. This flag should be used forsevere conditions of backwater from irregulardownstream conditions, backwater from iceand other conditions. The flag should not beused for normal shifting control conditions;(b) Erroneous – This flag is for incorrect unit values.For instance, the float is resting on mud in thestilling well, and the recorded unit values donot represent the stage in the stream;(c) Missing – This flag is reserved for situationswhere unit values were expected, but becauseof some malfunction of equipment where nodata were recorded;

II.6-14manual on stream gauging(d) Estimated – This flag is used for estimated unitvalues. It should be automatically attached to unitvalues that are changed by the hydrographer.The first three types of flags defined above areintended primarily for the original, archivable unitvalues. These flags will document, for historicalpurposes, the evaluation and interpretation of thevalidity of the recorded unit values. They alsoshould be carried forward for the analysis andcomputation of records. In the analysis andcomputations, it may be desirable to estimate unitvalues in certain situations. The fourth type of flagis reserved for estimated values, which may replaceaffected, erroneous or missing data. The estimatedflag only will be used for unit values in data setsgenerated subsequent to the original data set. Unitvalues flagged as affected or erroneous should notbe used in the primary computations.6.6 Verification and analysis offield measurementsField measurement data and information that areentered into the electronic processing systeminclude discharge measurements, gauge datumleveling measurements, crest-stage gauge data,channel and control cross-section data andmiscellaneous field notes. All of these data usuallyare entered by keyboard, except that some dischargemeasurements are entered from electronic fieldcomputers. Various computations and comparisonsshould be made to verify the accuracy and insurethe consistency of the information. The followingsections describe some of the verification,computations and cross checking that should beperformed with the electronic processing system.Errors resulting from data entry and incorrectcomputation should be corrected by thehydrographer.It is important to emphasize that measurement data(that is, depth, width and velocity data) should notbe deleted or erased from the original notes, whichin most cases are the paper note sheets. Editing ofdata that are entered from paper notes to theelectronic processing system is permitted, providedthe data were entered by keyboard. This editingallows for correction of keyboard entry errorswithout compromising the integrity of the originalpaper notes. On the other hand, data enteredelectronically, such as from an electronic fieldcomputer, should not be edited, changed or deletedbecause once they are entered to the electronicprocessing system they become the original copywhich will be used for archiving. It is assumed thatno errors occur during an electronic transfer. Allinformation in measurement notes (for example,computed values such as area, velocity, width,discharge and others) may be edited and changedregardless of the entry method. These values shouldbe arithmetically correct and based on the originaldata.6.6.1 Discharge measurement checkingAll discharge measurements should be checkedwherever possible for arithmetic errors, logic errorsand other inconsistencies with the electronicprocessing system. In addition, the electronicprocessing system should compute the standarderror for regular current meter measurements. If arating is available for the gauging station, theelectronic processing system should compute theshift of the measurement from the rating. The shiftanalysis would apply to stage-discharge, slope andrate-of-change in stage and ratings. Most of thefollowing checking and computation steps applyonly to standard current meter measurements.Arithmetic checkingA summary of the numerical results of a dischargemeasurement is entered to the electronic processingsystem from what usually is referred to as the frontsheet of the measurement. Most of the informationon the front sheet are computed from the fieldmeasurement data that are part of the inside bodyof the measurement. For discharge measurementsrecorded on paper forms, the computations aremade by the hydrographer in the field with acalculator. If an electronic field notebook was usedfor recording the discharge measurement data, thenthe computations were made automatically by thefield notebook and little or no arithmetic checkingis required.When original computations are made on paperforms, the following checks of the inside part of themeasurement should be made with the electronicprocessing system:(a) Subsection width – The width for a subsectionis computed as one-half the distance betweenthe preceding vertical stationing and thesucceeding vertical stationing. For verticals atthe edge of a channel or bridge pier, the subsectionwidth is computed as one-half the distanceto the adjacent vertical;(b) Point velocities – If a current meter rating orequation has been entered for the current meterused in making the discharge measurement,then each point velocity should be checked;

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-15(c) Mean velocity for each vertical – The meanvelocity for each vertical is computed asfollows:(i) For the one-point method, the meanvelocity is equal to the point velocityat the 0.6 depth. If the point velocitywas measured at a depth other than the0.6 depth, then the mean velocity for thevertical is computed by multiplying thepoint velocity by the method coefficient. If amethod coefficient has not been entered forthe vertical, then the electronic processingsystem should warn the hydrographer andprovide an opportunity to enter a methodcoefficient. The hydrographer can chooseto ignore the warning;(ii) For the two-point method, the meanvelocity is equal to a mean of the pointvelocities for the 0.2 and 0.8 depths;(iii) For the three-point method, the meanvelocity is equal to a weighted mean ofthe 0.2 depth velocity, the 0.6 depthvelocity and the 0.8 depth velocity, wherethe 0.6 depth velocity is given doubleweight;(d) Subsection mean velocity – The mean velocityfor each subsection is computed as the productof the mean velocity of the vertical and thehorizontal angle coefficient. If a horizontalangle coefficient is not entered for the vertical,then the electronic processing system shouldassume a value of 1.00;(e) Subsection area – The area for each subsectionis computed as the product of the subsectionwidth and the depth at the vertical;(f) Subsection discharge – The discharge for eachsubsection is computed as the product ofthe subsection area and the subsection meanvelocity;(g) Total width – The total width for each channel iscomputed by summing the subsection widths;(h) Total area – The total area for each channel iscomputed by summing the subsection areas;(i) Total discharge – The total discharge foreach channel is computed by summing thesubsection discharges;(j) Total number of verticals – The total number ofverticals for a measurement is simply a countof the number of verticals, and includes thebeginning and ending points where depthoften is equal to zero;(k) Average velocity – The average velocity foreach channel is computed by dividing the totaldischarge by the total area;(l) Totals for multiple channels – When thedischarge measurement has two or morechannels, such as for a braided stream, or aflood measurement that has a main channeland one or more overflow channels, the grandtotal of width, area, discharge and number ofverticals is computed. These grand totals arethe values used to summarize the dischargemeasurement on the front sheet. The averagevelocity for the measurement is the grand totalof discharge divided by the grand total of area.Logic and consistency checkingInformation entered to the electronic processingsystem from one part of the discharge measurementnotes should be automatically compared and crosschecked with information from other parts of themeasurement to verify that it is logical and consistent.The electronic processing system should alertthe hydrographer when inconsistencies occur andprovide an opportunity to make a change. In addition,when specific information items are entered,the electronic processing system then should limitthe entry of other items so that the choices areconsistent. For instance, if the type of measurementis entered as a wading measurement then thechoices for equipment entry would be limited tothe various types of wading rods. A listing of someof the possible logic and consistency checks aregiven below:(a) Compare measurement sequence number withmeasurement date and time – Measurementnumbers generally are in sequential orderaccording to date and time;(b) Compare measurement mean gauge height(s)to gauge readings – The mean gauge heightshould be a value that falls between the lowestand highest gauge readings recorded during thecourse of making the discharge measurement;(c) Compare gauge-height change to gaugereadings – The gauge-height change should bethe difference between the gauge heights at thestart and end of the discharge measurement;(d) Compare gauge-height change time to startand end time – The gauge-height change timeshould be the difference between the start andend time of the discharge measurement;(e) Compare stream width on summary input tostream width for inside note input – The streamwidth on the summary input should be exactlythe same as the stream width computed andentered for the inside note input. For multiplechannels the stream width should be the sumof individual channel widths;(f) Compare stream area on summary input tostream area for inside note input – The streamarea on the summary input should be exactlythe same as the area computed and entered forthe inside note input. For multiple channels

II.6-16manual on stream gaugingthe stream area should be the sum of the individualchannel areas;(g) Check mean velocity – The mean velocityshould be the checked by dividing the measureddischarge by the stream area;(h) Compare number of sections on summaryinput to number of sections for inside noteinput – The number of sections should be thetotal number of verticals used for making thedischarge measurement. This total includeseach end section of the measurement, eventhough depth and velocity at these points maybe zero. For multiple channels, the number ofsections should be the sum of the sections forindividual channels;(i) Check adjusted discharge – If an adjusteddischarge is entered, the electronic processingsystem should compute an adjusted dischargebased on the adjustment method, if stated.This computed value should be compared tothe entered value;(j) Check average time of point velocities – Theaverage time of point velocities on the summaryinput should agree with the average of the timeof current-meter revolutions entered for theinside note input;(k) Compare gauge height of zero flow to gaugereadings – The gauge height of zero flowshould be less than the mean gauge height ofthe discharge measurement, and less than thegauge heights in the gauge-height table, exceptin the cases of a zero flow measurement.6.6.2 Special checking procedures forother types of dischargemeasurementsSome discharge measurements are made underconditions that require computational proceduresthat are different than the standard open-water,current-meter discharge measurement described inpreceding sections. In some cases the differences areminor but in other cases the measurement method iscompletely different. Also, some measurementmethods use highly specialized equipment andrecording methods that differ entirely from those ofstandard discharge measurements. The followingsections describe some of the verification, editingand computations that should be performed withthe electronic processing system for each of thevarious types of measurements.Ice measurementsIce measurements, in most respects, are the same asstandard open-water discharge measurements. Allof the same arithmetic checking, logic andconsistency checking and shift analysis should beperformed on ice measurements. Differencesbetween computations for a standard dischargemeasurement and an ice measurement are listedbelow:(a) Computation of effective depth – The insidebody of the discharge measurement notesfor ice measurements contain two additionalcolumns of data and information. One of theextra data columns is a field measurement ofthe vertical distance between the free watersurface and the bottom of the ice (solid or slushice). These measurements should be comparedto the total depth for each vertical, and if in anygiven vertical the depth from the water surfaceto the bottom of the ice is found to be greaterthan the total depth, a warning message shouldbe issued by the electronic processing systemto the hydrographer. The second additionalcolumn is effective depth, d e, for each verticaland is computed as the difference between thetotal depth, D, and the vertical distance, d i,between the free water surface and the bottomof the ice. The equation is:d = D −(6.1)ed i(b) Computation of subsection area – The area ofeach subsection is computed by multiplyingthe subsection width times the effective depth,d e, of the vertical;(c) Velocity coefficient – For verticals where the0.6 depth method is used to observe velocity,it is frequently necessary to apply a velocitycoefficient to correct for the ice effect on thevertical velocity distribution. This velocitycoefficient is similar to the use of a methodcoefficient for computing the mean velocity ina vertical, as described in a previous section onarithmetic checking. The mean velocity in thevertical is computed by multiplying the velocitycoefficient times the point velocity observed atthe 0.6 depth. If a velocity coefficient is notgiven, then it should default to 1.00. If the twopointmethod (0.2 depth/0.8 depth) is used toobserve velocity, then no velocity coefficient isnecessary;(d) Shift computations – Shifts are not usuallycomputed for ice measurements, but in somecases may be desired. The hydrographer shouldhave the option to specify if shifts should becomputed, and if so, they should be computedjust as they are for a regular open-watermeasurement;(e) Percent difference from rating curve – Thedifference, in percent, between the measureddischarge and the rating curve should becomputed for all ice measurements, based on

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-17the same method as described for standarddischarge measurements;(f) Discharge ratio – For some gauging stations, thedischarge-ratio method is used for computingice records. The hydrographer should have theoption to specify the computation of the ratioif it is used. The electronic processing systemthen should compute the ratio, K i, for eachice measurement as the ratio of the measureddischarge, Q m, to the open-water ratingdischarge, Q r, that corresponds to the meangauge height of the measurement as:K = Q Q(6.2)imrMeasurements with vertical anglesDepth measurements of deep, swift streams that aremade with cable suspension equipment frombridges, cableways and boats cannot always bemade directly. Frequently, the sounding weight iscarried downstream by the current and consequentlythe observed depth is greater than the true verticaldepth. In such cases corrections must be made tothe observed depth in the field at the time themeasurement is made. The body of the field notesfor these measurements contains additionalcolumns for recording air-line vertical distance,observed depth, vertical angle and computedvertical depth. The corrections, which usually arenot recorded in the field notes, account for an airlinecorrection and a wet-line correction of thesounding cable. In some cases, such as whensounding line tags are used, the air-line correctionmay be eliminated or reduced to a negligibleamount.The electronic processing system should containthe air-line correction table and the wet-line tableso that the computed vertical depth can be checked.These tables are given in Chapter 5 of Volume I,which also provides a detailed description of thecomputation methods. A brief summary of theprocedure is listed below:(a) Determine the air-line correction based on theobserved air-line vertical distance between thesounding equipment and the water surface,the observed vertical angle and the air-linecorrection table;(b) Subtract the air-line correction from theuncorrected observed depth of water. Thissubtraction must be made before determiningthe wet-line correction;(c) Determine the wet-line correction based onthe air-line corrected observed depth, theobserved vertical angle and the table of wetlinecorrections;(d) Compute the true vertical depth by subtractingthe wet-line correction from the air-linecorrected observed depth;(e) Air-line and wet-line corrections should beinterpolated from their respective tables to thenearest tenth of a foot.All other computations and checking are essentiallythe same for measurements with vertical angles asthey are for standard discharge measurements,including the computation of measurementstandard error.Acoustic Doppler Current Profiler moving boatmeasurementsThe Acoustic Doppler Current Profiler (ADCP) isused to define the velocity profile in a stream vertical,as well as depth measurements across the stream.The velocity profile provides a much more accuratemeasure of the mean stream velocity than othertechniques where only one or two measuring pointsare used, and sometimes adjusted by velocitycoefficients. The ADCP moving boat method ofmeasurement has replaced other moving boatmethods and has provided a fast, accurate type ofdischarge measurement for wide and deep streams.This type of measurement is fully computerized withall data collected and computed automatically. Dataand information from the ADCP measurementshould be transferred to the electronic processingsystem through an interface. These data andinformation become the archivable record. Summaryinformation for the measurement is much the sameas for a regular discharge measurement.Special considerations for checking ADCP measurements(Oberg and others, 2005) are as follows:(a) The discharge-measurement note sheets shouldbe complete, clear and legible;(b) All electronic data files associated with themeasurement should be backed up in the fieldand archived on an office server;(c) The number of transects collected should beappropriate for the flow conditions. Transectsshould be collected in reciprocal pairs;(d) Configuration files should be checked for errors,appropriateness for the hydrologic conditionsand for consistency with field notes. ADCPdepth, salinity, edge distances, edge shapes,extrapolation methods and ADCP configurationparameters shown on the field notes shouldmatch those in the configuration file;(e) A moving-bed test should be performed priorto the discharge measurement, recorded,archived and noted on the ADCP measurementnote sheets. If a moving bed was detected,

II.6-18manual on stream gaugingDifferential Global Positioning System (DGPS)should be utilized. If DGPS was not used, themeasured discharges should be adjusted forthe moving bed and the measurement qualityshould be downgraded;(f) The average boat speed for the measurementshould not exceed the average water speedunless it was impractical or unsafe to do so,and the reason documented in the field notesor station file. Boat pitch-and-roll should notbe excessive. Excessive boat speed or pitch-androllmay justify downgrading the measurementquality;(g) The measured edge distances recorded on theADCP measurement note sheet should matchthose electronically logged with each transect.The correct edge shape should be selected and5-10 seconds of data collected at transect stop/start points while the boat was held stationary.If sub-sectioning was used to correct problemswith edges, then the sub-sectioning shouldbe clearly documented on the note sheets. Ifa vertical wall(s) was present, then the startand/or end points of the transect should belocated such that the distance from the wall(s)is equivalent to the water depth at the wall orgreater;(h) There should not be excessive loss of profiles.The loss of more than 10 per cent of profilesin one or more transects may necessitatedowngrading the measurement quality,especially if the missing data are concentratedin one part of the measured cross section.When the missing profiles always occur in thesame part of the cross section, the measurementquality should be downgraded, even when lessthan 10 per cent of the profiles are missing;(i) When more than 25 per cent of the depth cellsin one or more transects are marked invalid ormissing, the quality of the measurement mayneed to be downgraded. This downgrading isnot necessary, however, if the distribution ofthe missing depth cells is more or less uniformthroughout the water column and/or the crosssection measured;(j) The extrapolation method for the top andbottom discharges should be reviewed. Ifreview of the data shows the need for a differentextrapolation method than that chosen for usein the field, the extrapolation method shouldbe corrected and the reasons documented onor attached to the measurement note sheet.Wind and horizontally stratified densitycurrents are common causes for profiles that donot fit well by means of the 1/6th power-lawextrapolation method. In these situations it isusually necessary to use different extrapolationtechniques for the top and bottom areas and/or limit the portion of the profile used for theselected method;(k) Measurement computations, including meandischarge and measurement gage height, mustbe correct.Indirect measurementsIndirect discharge measurements include slope area,contracted opening, critical depth, culvert, stepbackwater and flow over dams and embankments.These types of measurements are almost alwaysmade after a flood event rather than during theflood. Data collection, recording of field notes andcomputation procedures are appreciably differentthan standard measurements made during a floodevent. For most indirect measurements, computerprograms are used for the computations and detailedreports are prepared. Entry of information fromindirect measurements to the electronic processingsystem should include only the summaryinformation. The same entry form can be used as fora standard discharge measurement.Portable weir and flume measurementsMeasurements of low discharge can be made usinga portable weir or flume. Various types of weirs andflumes are available for these measurements andusually are rated in the laboratory so that coefficientsand discharge ratings are defined for each. Fieldsetup and measuring methods are described inChapter 7 of Volume I. After the weir or flume isinstalled and a sufficient period of time is allowedfor streamflow to stabilize, a series of upstream headmeasurements are taken for a period of about threeminutes. The average of these head measurementsis used to determine the discharge, either from arating table (flume measurement) or from anequation (weir measurement). Downstream headmeasurements usually are not taken because theflume or weir is installed so free fall or minimumbackwater conditions exist.Entry of the inside body of the discharge measurementis relatively simple and includes only the weiror flume head data and the determined discharge.Some hydrographers enter this information on thefront sheet of the measurement, rather than in theinside body. Regardless of where these notes arerecorded, the electronic processing system shouldprovide a form for entering the basic data andcomputations and should check the computations.The data and information required are as follows:(a) Head measurements – These are the individualobservations of head. The recommended

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-19number of observations is about seven, oneobservation every 30 seconds for a period ofthree minutes. However, this number can varyand in some cases only one observation willbe recorded. The electronic processing systemshould allow for at least 10 entries;(b) Average head, h – This is an unweighted averageof the individual head observations. Theelectronic processing system should calculatethe average head, h, and compare it to theentered value. If the two values are different,a message to this effect should be noted. Thehydrographer should select the average headvalue for use in computing discharge;(c) Discharge, Q – The discharge should becalculated, either from a rating table or froman equation. Rating tables and/or equations forstandard weirs and flumes should be includedin the electronic processing system. However, ifthey are not directly available, the hydrographershould enter one.Entry of front-sheet information for weir and flumemeasurements greatly is abbreviated from that of astandard discharge measurement.Tracer-dilution measurementsTracer-dilution discharge measurements are highlyspecialized techniques that utilize one of a numberof different tracers, different types of measurementequipment and different measurement methods.Data collection, recording and calculation ofmeasurement information vary depending on themethod and tracer used. Details of each type oftracer-dilution measurement are described inChapter 8, Volume I. The methods are standardizedso details of tracer-dilution measurements do notneed to be entered in the electronic processingsystem. Only summary information is required.Volumetric measurementsLow flows sometimes are measured by diverting theflow into a calibrated container, and measuring thetime required to fill, or partially fill, the container, asdescribed in Chapter 8, Volume I. If the container isfilled completely, the flow volume equals thecontainer volume. If the container is partially filled,the flow volume equals the difference of the endingand starting volume. This procedure usually isrepeated three to four times to improve accuracy ofthe measurement. The discharge is computed bydividing the total volume (sum of the volumemeasurements from each repetitive run) by the totaltime of diversion (sum of the time measurementsfrom each repetitive run), in seconds.Data entry from the inside field notes to theelectronic processing system include the following:(a) Total container volume;(b) Starting volume for each repetitive run – Thisvalue should be equal to or greater than zero,but less than the total container volume;(c) Ending volume for each repetitive run – Thisvalue should be greater than the startingvolume, and equal to or less than the totalcontainer volume;(d) Flow volume for each repetitive run – This isthe difference between the ending volume andthe starting volume, and must be equal to orless than the total container volume;(e) Fill time for each repetitive run;(f) Total volume – This is a summation of theindividual flow volumes of each run;(g) Total time – This is a summation of theindividual fill times of each run;(h) Discharge – This is the total volume divided bythe total time.The electronic processing system should make thechecks and computations indicated above andreport any discrepancies.The procedure described above is used where thetotal flow can be easily collected in a container. Insome cases, such as at a broad-crested weir or dam,the depth may be too shallow to measure usingconventional methods, but volumetricmeasurements may be applicable to small segmentsof the flow. This is the volumetric-incrementalsampling method. In this method, volumetric flowmeasurements are made as described in thepreceding paragraphs at five to 10 subsections alongthe weir or dam. The flow rate of each sample isincreased by the ratio of the subsection width tothe sampled width to obtain a flow rate for eachsubsection. The total flow of the stream is thesummation of the discharge rates of each subsection.The electronic processing system should performthese computations from the input data and reportany discrepancies. Front sheet information is anabbreviated version of the standard dischargemeasurement.Discharge estimatesLow flows sometimes are estimated when nosuitable measuring method is applicable. Varioustechniques for estimating the flow are used whichshould be described in the field notes. It is notrecommended that the details of making theestimate be entered into the electronic processingsystem, because they generally cannot be checkedor verified, and the paper notes are considered the

II.6-20manual on stream gaugingoriginal archivable record. A summary of themeasurement can be entered using the standarddischarge measurement entry form, but abbreviatedconsiderably to accommodate only the pertinentinformation.6.6.3 Rounding and significant figuresAll field data for discharge measurements should beentered to the electronic processing system withthe same precision and significant figures asrecorded in the field notes. Table look-up valuesand calculated values should be rounded to standardsignificant figures, unless specified otherwise by thehydrographer. Exceptions to the standard significantfigures are required for calculations of the subsectionvalues of width, area and discharge in the insidebody of the field notes, as follows:(a) Subsection width – The width of each subsectionshould be used and displayed as an unroundedvalue;(b) Subsection area – Each subsection area shouldbe rounded and displayed with one additionalsignificant figure from that of the expectedtotal area. For instance, if the total area isexpected to be between 10.0 and 99.9 ft 2 , theindividual subsection areas should be roundedand displayed to hundredths of a square foot;(c) Subsection discharge – Each subsectiondischarge should be rounded and displayedwith one additional significant figure overthat of the expected total discharge, similar tothat described above for subsection area. Forinstance, if the total discharge is expected to bebetween 100 and 999 ft 3 /s, then each subsectiondischarge should be rounded and displayed tothe nearest 0.1 ft 3 /s.All summary information for dischargemeasurements should be rounded and displayedwith standard significant figures unless specifiedotherwise by the hydrographer.6.7 Entry of rating curves to theelectronic processing systemRating curves are relations between dependent andindependent variables, and the development ofrating curves has been described in previous sectionsof both Volumes I and II. Rating curves are anintegral part of the computation of most streamflowrecords and should be made a part of the permanentrecords for each station. However, the electronicprocessing system also should allow the entry,development and display of rating curvesindependent of computing streamflow records forspecific gauging stations. That is, the hydrographershould use the rating curve aspects of the electronicprocessing system for entering, editing, developing,refining and experimenting with the rating curves.Rating curve information required for defining therelation between the independent and dependentvariables, such as gauge heights and discharges, canbe entered into the electronic processing systemusing various methods, including tabular, equationand graphical methods. Tabular entry is the use of atable of descriptor data pairs, each representing aspecific location of the rating curve. Equation entryis the use of a mathematical expression to definethe rating curve. Graphical entry is a methodwhereby a series of points are entered directly on arating curve plot displayed on the computermonitor. The electronic processing systemautomatically evaluates the points and connectsthem to display the rating curve.Tabular entry and graphical entry are similar inthat both utilize hydrographer-defined descriptorpoints. The primary difference is that tabular entryis based on descriptor points that are hand pickedfrom a paper rating curve plot, whereas graphicalentry is based on descriptor points defined on thecomputer monitor, thus, negating the need for apaper plot.6.6.4 Summary of dischargemeasurementsDischarge measurement information and data fromall types of discharge measurements should besummarized in chronological order and grouped bywater year to provide a history of the measurements.In addition to the summary of dischargemeasurements, an output format that includes allof the data and information entered for eachmeasurement should be available to thehydrographer. The hydrographer also should beable to define a custom output format that onlywould include selected items.6.7.1 Tabular entryRating curves may be entered to the electronicprocessing system by keyboard as a series ofdescriptor points, sometimes referred to as pointpairs. Each point pair contains the independentvariable and the corresponding dependent variablefor one position on the rating curve. The electronicprocessing system should not limit the number ofpoint pairs that can be entered. Point pairs alwaysshould be entered in ascending order of theindependent variable, starting with the lowest pointon the rating curve. If the hydrographer incorrectlyenters a point pair in which the independent

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-21variable is not ascending the electronic processingsystem immediately should issue a warning messageto alert the hydrographer that an entry error wasmade. This checking method also should be usedfor the dependent variable for those ratings wherethe dependent variable is not allowed to decrease. Asimilar warning message also should be given ifnegative values are entered for ratings where theyare not allowed.Rating curves that are entered as linear scale ratingswill require only the table of point pairs. No otherdescriptive information is needed for either plottingor expanding a linear scale rating.Rating curves entered as logarithmic scale ratingswill require entry of scale offset information inaddition to the table of point pairs. A scale offset isa value that is subtracted from the independentvariable before interpolating between point pairs ofthe rating. It is important that the scale offsetentered at this point is the same as the one used forthe plotted rating curve. If the hydrographer doesnot enter a scale offset for a logarithmic rating, theelectronic processing system should not accept therating and should prompt the hydrographer that anoffset is required.The electronic processing system should allowone, two or three scale offset values for eachlogarithmic rating curve, with each respectiveoffset applicable to a designated range of therating. The offsets should be entered starting withthe lowest rating curve segment and progressingupward, with a defined breakpoint betweensuccessive offsets. The breakpoint is the value(usually gauge height) of the independent variableabove which the succeeding offset should be used.The following combinations of offsets andbreakpoints are allowable:(a) One offset, no breakpoints – In this case, asingle offset is used throughout the range of therating;(b) Two offsets, one breakpoint – In this case,the first offset is used for all values of theindependent variable that are less than or equalto the breakpoint value. The second offset isused for all values of the independent variablethat are equal to or greater than the breakpointvalue;(c) Three offsets, two breakpoints – In this case,the first offset is used for all values of theindependent variable that are less than or equalto the first breakpoint value. The second offsetis used for all values of the independent variablethat are equal to or between the first and thesecond breakpoints. The third offset is used forall values of the independent variable that areequal to or greater than the second breakpointvalue.A point pair entry in the table of point pairs isrequired at each breakpoint of the rating. If thehydrographer omits the point pair correspondingto a breakpoint, the electronic processing systemshould issue a warning message and should notaccept the rating unless this requirement is met.The point pair at each breakpoint is used as theending point for the rating-curve segment belowthe breakpoint, and the beginning point for therating-curve segment above the breakpoint. Thisprocess insures continuity of the rating-curvesegments.6.7.2 Equation entrySome ratings may be easily expressed in equationform, and if so, they may be entered to the electronicprocessing system as a mathematical expression.Such ratings usually are of simple form, consistingof a smooth curve or straight line, with no unusualshapes or sharp bends. For all equation ratings, abasic format as given in equation 6.3 should beused:( X − e) cY = a + b(6.3)where Y = dependent variable (usually discharge);X = independent variable (usually gauge height);a = equation constant (default value is zero);b = multiplier (default value is 1); e = scale offset(default value is zero) and c = exponent (defaultis 1).Equation 6.3 can be used for rating curvesinterpolated either linearly or logarithmically.Other types of equations are not recommended forsurface-water rating curves.Upper and lower equation limits also should berequired as part of the input for equation ratings.These limits should, by default, be in terms of theindependent variable. However, the hydrographershould have the option to specify the limits interms of the dependent variable. When extrapolationof equation ratings is needed, and can be justified,a modification of the approved limits should beallowed. The electronic processing systemautomatically should not extrapolate the equationbeyond the approved specified limits.The electronic processing system should allow upto three equations for the definition of a ratingcurve. Breakpoints, in terms of the independent

II.6-22manual on stream gaugingvariable, between two consecutive equations arerequired to define the exact point of the ending ofone equation and the beginning of the nextequation. Consecutive equations must intersect atthe given breakpoint. The electronic processingsystem should calculate the dependent variable atthe breakpoint by using each equation, and if thetwo calculated values of the dependent variable arenot identical the electronic processing systemshould alert the hydrographer and not accept theequations until appropriate changes are made.These checks and modifications should be made atthe time of equation entry and before applicationof the equations.When multiple equations are used to define a ratingcurve, a lower limit should be specified for the lowerequation, and an upper limit should be specified forthe upper equation. The same rules and guidelinesapply to these limits as stated previously for singleequation limits.6.7.3 Graphical entryGraphical input of rating curves is presently themost automated and preferred method of enteringa rating curve to the electronic processing system.Historically, rating curves have been drawnmanually and descriptor points read from the plot.The electronic processing system should provide amethod whereby the hydrographer canautomatically plot selected discharge measurementsand other rating curve information on the computermonitor, and then fit a rating curve to the plottedpoints directly on the monitor. The fitting processwill be done by specifying a series of descriptorpoints, either directly on the computer monitor orin a table displayed on the monitor. After thehydrographer is satisfied with the accuracy andsmoothness of the rating curve, the electronicprocessing system should automatically transformthe plotted rating curve into a rating table.6.8 Rating tablesThe rating table is primarily for the purpose ofdisplaying values of the dependent variable for thecomplete range of the independent variable. Ratingtables should be generated with the electronicprocessing system for all rating curves. The tablesare populated by interpolating values of thedependent variable for the complete range of theindependent variable, at intervals equal to thestated precision of the independent variable orother user-defined interval. For instance, if theindependent variable is gauge height, and its statedprecision is hundredths of a foot, then values of thedischarge would be computed for every hundredthof a foot for the range of gauge height defined bythe limits of the rating.6.8.1 Interpolation methodsThe method used to interpolate between ratinginput points should be based on the method usedto develop the rating. Rating curves defined aslinear scale ratings should be interpolated betweeninput points using simple linear interpolation.Rating curves defined as logarithmic scale ratingsshould be interpolated between log-transformedinput points using linear interpolation. Theapplicable scale offset must be subtracted from allinput values of the independent variable beforemaking the logarithmic transformations. If therating is defined with two or three scale offsets,then each offset should be applied within the rangedefined by the respective breakpoints.It is very important that the interpolation processuse the same offset(s) that are used for thedevelopment of the rating curve plot so that theresulting rating table precisely duplicates the plottedcurve. If the rating is plotted on the electronicprocessing system monitor, the rating curveautomatically is converted to a rating table, and theoffset will automatically be the same for both theplotted curve and the resulting table. If the ratingcurve is entered as a table of descriptor points, thenthe interpolation method must use the scale offset(s)entered with the descriptor points. The hydrographeris responsible for insuring that the offsets areidentical.Note that the subtraction of the scale offset fromthe independent variable is made only for thepurpose of transformation and interpolation. Thesubtraction should not alter the original values ofthe independent variable that are displayed in therating table or plotted on rating curve plots.The dependent variable (discharge) for many ratingcurves has a minimum value of zero, which cannotbe transformed to a logarithm. A simple linearinterpolation between the zero point and the nextlarger input value of the dependent variable shouldbe used for logarithmic ratings beginning with zero.To avoid appreciable distortion of the low end ofthe rating it is recommended that the input valueof the dependent variable that follows the zeroinput value be equal to or less than 0.1. Theelectronic processing system should issue a warning

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-23message to the hydrographer if 0.1 is exceeded andprovide an opportunity to make changes.The independent variable (gauge height) cansometimes be zero or negative at the low end of arating curve. This value is permissible only whensubtraction of the scale offset from the independentvariable results in a positive number.Rating curves defined by one or more equationsalso should be transformed into rating tables. Thisis a simple method of computing the dependentvariable for the entire range of each equation, asdefined by the breakpoints and input limits.6.8.2 Rating table smoothness analysisOne method of analyzing the smoothness of arating curve and/or rating table can be done bystudying the differences between successive valuesof the dependent variable. To make this task easyfor the hydrographer, the rating table should displaythe computed differences (traditionally referred toas first differences) of the dependent variablebetween every tenth value of the independentvariable displayed in the rating table. For instance,if gauge height is incremented every 0.01 ft in therating table, then the difference between dischargescorresponding to gauge heights at 0.1 ft intervalsshould be computed and displayed. For metricrating tables the differences should be displayed forevery 0.01 m.6.8.3 Other rating table informationThe rating table should include descriptiveinformation that identifies the gauging station,type of rating, period of use and other items thatare unique for that rating. An example of anexpanded rating table (English units) for alogarithmic stage-discharge rating curve is shownin Figure II.6.2. This sample rating table illustratesthe header information and a typical arrangementof table information.6.9 Rating curve plotsThe electronic processing system should plot therating curves on the computer monitor withinteraction by the hydrographer to manipulate, drawand define ratings electronically. The requirementsfor monitor plots are essentially the same as for paperplots as described in Chapter 1, Volume II of thisManual. These monitor plots should be a highlyflexible part of the electronic processing system andFigure II.6.2. Example of expanded rating table,in English unitsalso should provide the capability to produce a paperplot of the same rating, if required. The electronicprocessing system should develop and print theentire plotting form for a paper plot. It should printthe grid as well as the rating curve and other ratingcurve information.6.9.1 Linear scale plotsAn arithmetically divided, linear, plotting scale isthe simplest type of rating curve plot. Linear scaleplots are convenient to use and easy to read. Zerovalues can be plotted on the arithmetic scale,whereas these values cannot be plotted onlogarithmic scales. For this reason linear scale plotsfrequently are used for analyzing the low end ofstage-discharge ratings. However, for detailedhydraulic analysis linear scale plots have little or noadvantage over logarithmic scale plots. A stagedischargerelation plotted to a linear scale is almostalways a curved line, concave downward, whichcan be difficult to shape correctly if only a fewdischarge measurements are available. Logarithmicscale plots, on the other hand, have a number ofanalytical advantages as described in Chapter 1,Volume II of the Manual.Linear scale plots are excellent for displaying arating curve. Usually, a rating curve is first drawn

II.6-24manual on stream gaugingon a logarithmic scale plot for shaping and analysisand then transferred to a linear scale plot for display.The electronic processing system should make thisprocess simple and easy.Linear scale subdivisions should be established tocover the complete range of the independent anddependent variables, or a selected range. If onlypart of the rating is to be plotted, the hydrographershould specify the range of either the independentvariable or the dependent variable for the desiredplot. The electronic processing system should makean initial determination of scales, subdivided inuniform increments that are easy to read andinterpolate. The scales also should be chosen sothat the plotted rating curve is neither very steepnor very flat. Usually, the curve should be a slopebetween 30 and 50 degrees. The hydrographershould be able to change the scales easily andquickly so that various plots can be viewed. Theelectronic processing system should replot allmeasurements and rating curve information eachtime a scale change is made.If the range of the variables is large, it may benecessary to break the plotting scale and plot therating curve in two or more segments to providescales that are easily read with the necessaryprecision. This method may result in separate curvesfor low water, medium water and high water.Although two or three separate curves are plotted,they should be plotted within the same plottingform, if possible. The electronic processing systemshould arrange the individual plots on the form sothat they are separate and distinct, properly scaledand not overlapping. Optionally, the separatecurves could be plotted on separate forms.6.9.2 Logarithmic scale plotsMany rating curves can be analyzed best by plottingthe rating on logarithmic scale plots. Hydrauliccharacteristics that are evident in logarithmic plotsrelate to the type of control, the stream crosssection, cross-section shape changes and shiftingcontrol patterns as described by Rantz and others(1982), by Kennedy (1984) and in Chapter I,Volume II of this Manual.Logarithmic scale selection procedureThe electronic processing system should plot ratingcurves and rating curve information to logarithmicscales, by default, if the rating is defined as alogarithmic rating. Ratings defined as linear ratings,or equation ratings, may be plotted to logarithmicscales at the hydrographers option. The initial plotshould cover the full range of the rating or a selectedrange if defined. A normal logarithmic scale (nooffset) always should be used for the abscissa, ordependent variable. However, the ordinate scaleshould be adjusted, by default, by an amount equalto the offset defined for the primary rating beingplotted. If multiple offsets are defined for the rating,and the hydrographer chooses to plot a continuousrating for the complete range of all segments thenthe electronic processing system should default tothe offset corresponding to the lowest segment ofthe rating to make the initial plot. If this is a plotfor a new rating, where no other rating is to beplotted, then the electronic processing systemshould define the ordinate scale as a normal logscale (no offset), or use an offset selected by thehydrographer. Although default scale selectionsand offsets are prescribed, the hydrographer shouldbe allowed to over-ride the defaults and providehis/her own selections.Generally, it is advised that full log cycles be usedfor logarithmic scale plots. However, thehydrographer should have the option to set lowerand/or upper limits so that only partial log cyclesare used at each end of the scales. The setting ofscales should be highly flexible and easily changedso the hydrographer can plot and position therating to the best advantage.The linear measurement of a log cycle, horizontallyand vertically, must be equal. Unless thisrequirement is met it is impossible to hydraulicallyanalyze the resulting plot of the rating.Scale offsetsMany rating curves, especially stage-dischargerating curves, are analyzed and drawn on logarithmicscale plots, using a scale offset for the ordinate orgauge-height scale, as described in Chapter 1,Volume II of this Manual. The electronic processingsystem should allow up to three scale offsets foreach rating curve. This procedure conforms tomany stage-discharge rating curves where threemajor segments are present: (a) the extreme lowwater segment that usually is controlled by a sectioncontrol; (b) the within bank segment that can beeither a section control or channel control and(c) the overbank segment that usually is channelcontrol. Short transition curves that join majorrating segments usually are curved lines that willnot plot as a straight line, regardless of the scaleoffset.Scale offsets must be limited to values that are lessthan the lowest value of the independent variable

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-25for the rating curve, or segment of a curve, beingdefined. Otherwise, the mathematics would producezero or negative results, for which logarithmscannot be determined. The electronic processingsystem should not accept scale offsets that are equalto or greater than the lowest value of the independentvariable for the range in which the offset applies.Negative scale offsets are acceptable. A negativeoffset for the low segment of a stage-dischargerelation would indicate that the gauge height ofzero flow is negative. Although such a conditionusually is not advised, this condition can result atsome gauging stations.6.9.3 Rating curve shapingStage-discharge rating curves usually are shaped byfitting a curve or straight line to a series of plotteddischarge measurements. For paper plots, this fittingis easily performed by hand with straight edges andplastic curves. For electronic processing systemmonitor plots, a method(s) should be providedwhereby the hydrographer similarly can fit asmooth curve or straight line to points plotted onthe electronic processing system monitor. Thisshould be a highly interactive process between theelectronic processing system and thehydrographer.Certain aids should be made available for electronicprocessing system plots to ensure that stagedischargeratings are hydraulically correct. One is toplot a theoretical rating based on the controlproperties and the governing hydraulic equations.The computations and plotting of theoreticalratings should be performed with the electronicprocessing system, but will require interaction withthe hydrographer. Methods of computing theoreticalratings will be described in a subsequent section.The theoretical ratings are used primarily fordefining the rating shape, and not necessarily forlocating the rating position. The hydrographermust use such ratings with caution, and shouldmake discharge measurements to verify theseratings whenever possible.Another aid when working with logarithmic scaleratings for stage-discharge stations is to measure theslope of straight line rating segments for comparisonto theoretical slopes that correspond to variouscontrol conditions. Rating slope computationsshould be done automatically with the electronicprocessing system on command. The hydrographerfirst should designate the end points of the segmentof rating where the slope is to measured. Theelectronic processing system should check to be surethe selected rating curve segment is reasonably closeto a straight-line segment. This checking can be doneby computing percentage differences of dischargebetween the actual rating and the straight linedefined by the selected end points, at intermediatepoints along the rating segment. If any differenceexceeds ±1 per cent (default value), the ratingsegment should be considered curvilinear and theslope should not be computed. The electronicprocessing system should issue a statement to thehydrographer to this effect and simultaneouslyprovide an opportunity for the hydrographer toselect a different percentage to use for checking thedifferences, or to select a different rating segment tocheck. On the other hand, if the rating segment isfound to be a straight line (within the default, orselected, percentage difference), then the slopeshould be computed and displayed. When displayinga computed slope, the electronic processing systemalso should include the statement section control forslopes greater than 2.0 and channel control for slopesless than 2.0.The slope of a logarithmic rating is computed as thehorizontal distance divided by the vertical distance.These are measured as linear distances on logarithmicplotting scales. They should not be measured interms of the independent and dependent variables,but rather in terms of the logarithms of thesevariables. For a straight-line segment, two points[(Q 1, G 1) and (Q 2, G 2)] on the segment can be used tocompute the slope using:c =loglog Q− logQ( G − e) − log( G − e)2211(6.4)where c = the rating curve slope and e = the scaleoffset for the independent variable, G.6.9.4 Computer development of ratingcurvesRating curve analysis and development aredescribed in detail in previous chapters ofVolumes I and II. All rating curves, simple andcomplex, traditionally have been developed byhand plotting of measurements and manuallydrawing curves of best fit. Complex ratings, suchas slope ratings and ratings, have been developedthrough a combination of hand calculations andplotting methods. All of these methods are timeconsumingand tedious. The computerdevelopment methods that can assist thehydrographer in rating curve shaping anddefinition are given in the following sections.

II.6-26manual on stream gaugingStage-discharge ratingsStage-discharge ratings are graphical relationsbetween stream stage and discharge. These ratingscan be developed within the electronic processingsystem using various plotting and curve drawingfunctions. However, the hydrographer should usecare in ensuring that the ratings are hydraulicallycorrect. The electronic processing system can beused in providing computations that aid in thecorrect hydraulic shaping of the rating curves.Three such methods, section control, channelcontrol and step backwater, are useful for thispurpose.Section control methodsRating segments that are controlled by a specificcross section of the stream, such as a sand bar, rockoutcropping, manmade weir or other stream feature,can be approximated by flow computations basedon a surveyed cross section of the control and theweir equation. The input of cross-section data andthe computation of cross-section properties shouldbe a part of the electronic processing system asdescribed in previous sections of this Manual.Flow computations can be made for the sectioncontrol by using the cross-section properties, acoefficient of discharge, C and the weir equation.For purposes of defining the theoretical rating shapethe method defined here is simplified and some ofthe more detailed intricacies of weir computationsare not accounted for in the method.The general form for the weir equation to be usedfor section control computations is as follows:1.5Q = CLh(6.5)where Q = discharge, in cubic metres per second;C = the discharge coefficient; L = the top width, inmetres, of the water surface at the control sectionand for the gauge height of interest and h = thehead, in metres (difference between the gaugeheight and lowest point of the control section).The discharge coefficient, C, used in the weirequation may be input directly by the hydrographerat the time the cross-section data are entered. Avalue of C should be required for the lower limit ofgauge height for the computations, and for theupper limit of computations. Optionally, C valuesmay be specified for intermediate gauge heights.The electronic processing system should use linearinterpolation, based on gauge height, forintermediate values of C.For control sections where C is not known, thehydrographer may choose to obtain estimates ofthe C values computed from discharge measurementdata. The electronic processing system should allowthe hydrographer to designate specific dischargemeasurements for which a C value would becomputed, based on the gauge height and dischargeof the measurement, the cross section and the weirequation. The computation of C would be based onthe weir equation.The electronic processing system should display thecomputed values of C in tabular format for each ofthe discharge measurements. The hydrographer canuse this information to choose values of C to inputas described above. The electronic processing systemshould allow the hydrographer the option to plotgauge height and C and draw a smooth curve ofrelation. This curve could be used for defining C forthe range of theoretical rating curve computations.The range of theoretical computations for a givencross section should be specified by defining thelower and upper limit gauge height. Intermediatecomputations should be spaced at 0.1 intervals ofgauge height. The theoretical rating curve shouldbe plotted on the rating curve plot and clearlyidentified as theoretical.Channel control methodsRating curve segments that are controlled bychannel conditions such as cross-section area,channel slope, channel shape and roughness of thebed and banks can be defined by theoreticalcomputations using the Manning or Chezy equationand a typical cross section near the gauge. Suchcomputations can define the correct hydraulicshape of the rating but not necessarily the correctposition of the rating. Computations of this typehave been historically referred to as the conveyanceslopemethod as described by Rantz and others(1982). It is described also in previous chapters ofthis Manual so the details of these computationswill not be repeated here.The energy slope, S, as used in the Manning andChezy equations, can be estimated from varioussources such as topographic maps and high-watermarks. It also can be computed from the Manningor Chezy equations, the surveyed cross section anddischarge measurements. The electronic processingsystem should allow the hydrographer to designatespecific discharge measurements for which slope, S,is computed. These computed values of S should bedisplayed in tabular format, from which thehydrographer can choose values to input at the

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-27lower and upper limits of the conveyance-slopecomputations. The electronic processing systemshould use linear interpolation to determineintermediate values of slope.The electronic processing system should provide anoption for the hydrographer to plot the computedvalues of slope and gauge height so that a curve ofrelation can be drawn. This curve then would beused to determine values of S for the conveyanceslopecomputations.The range of theoretical computations for a givencross section using the conveyance-slope methodshould be specified by defining the lower and upperlimit gauge height. Intermediate computationsshould be spaced at selected intervals of gaugeheight. The theoretical rating curve should beplotted on the rating curve plot and clearly identifiedas theoretical.Step backwater methodStep backwater is a water-surface profile computationmethod that requires a minimum of two crosssections, but generally four or more cross sectionsare required to produce accurate results. The detailsof the method are described by Shearman (1990)and were described in Chapter 1, Volume II of thisManual. It is an excellent method to define theshape, and position of the rating curve, andsometimes is used instead of discharge measurementswhen they are difficult to obtain. Cross-section dataand other information necessary for step backwatercomputation are entered in the step backwaterprogram.The step backwater method computes water-surfaceelevations at each cross section in the stream reachdownstream from the gauge. The computationdepends on a given discharge in the reach and onan assumed water-surface elevation at thedownstream end of the reach. Two or moredownstream elevations are used to verify that theresults at the gauge will define a unique stagedischargerelation. The electronic processing systemshould provide an option to plot the profiles ofwater-surface elevations for the various startingelevations for each selected discharge. This type ofplot is referred to as a convergence plot that is usefulin evaluating the accuracy of the step backwaterresults.The electronic processing system should have adirect link to the step backwater software so thatresults can be transferred easily to the rating analysisfor a gauging station. Generally, a series of dischargesis selected and for each discharge in the series thestep backwater method will compute a gauge heightat each cross section used in the computations. Theparameters to be transferred are the discharges andthe corresponding computed gauge heights for thecross section at the gauge. Each transferred pair(gauge height at the gauge and correspondingdischarge) should be plotted on the rating curveand identified as a step backwater computation.The step backwater program also computes thewater-surface elevation for critical depth of flow foreach discharge at each cross section. Thehydrographer should have the option to select across section and plot the critical water-surfaceelevation computed for that section and thecorresponding discharge on the rating plot. This isan additional method to define the shape of a ratingwhere section control is in effect.Slope ratingsSlope ratings are used for stations with channelcontrols where variable stream slope downstreamfrom the base gauge affects the position of thestage-discharge relation. Variable stream slopeusually is caused by a downstream condition, suchas a reservoir, tributary stream or overbank storage.In reality, the term slope rating is a misnomer,because these ratings do not use actual streamslope as a rating parameter. Instead, an index ofstream slope is used, which usually is the watersurfacefall measured between the base gauge andan auxiliary gauge downstream from the basegauge. For some slope stations, the auxiliary gaugemay be located upstream from the base gauge, buta better index of stream slope can be obtained ifthe auxiliary gauge is located downstream fromthe base gauge.The rating method for slope stations involves acomplex relation of three separate rating curves:(a) stage-discharge, (b) stage-fall and (c) fall ratiodischargeratio. These ratings are described inChapter 2 of this Volume and detailed descriptionsof slope ratings can be found in Kennedy (1984)and Rantz and others (1982). Slope ratings usuallyare classified into three specific types: (a) unit fallratings, (b) constant fall ratings and (c) limitingfall ratings. Although these different fall ratingsare sometimes treated separately in the literature,they can be treated as one rating for computationalpurposes. This treatment is accomplished bydefining the stage-fall rating to fit the specific fallrating type. For instance, if a unit fall rating isdesired, then the fall rating is defined so that fallequals 1 ft for all gauge heights. If a constant fall

II.6-28manual on stream gaugingrating is desired, for a fall other than unity, thenthe fall rating is defined so that the desired constantfall is computed for all gauge heights. Finally, if alimiting fall rating is desired, then the stage-fallrating is defined so that a variable fall is computed,which is dependent on gauge height.The development of slope ratings must be definedempirically, using discharge measurements,simultaneous measurements of fall and a trial-anderrormethod to position and shape the individualrating curves. This procedure traditionally has beendone by hand plotting and hand computingmethods, which is a slow and tedious process. Theelectronic processing system should provide aninteractive process, whereby the hydrographermakes the decisions regarding the curve positionsand shape and the system makes the routinecomputations and plots.Velocity-index ratingsVelocity-index ratings, like slope ratings, can beused for gauging stations where variable backwaterprecludes the use of a stage-discharge rating. Forvelocity-index stations, some method of recordinga point or line velocity is required. This recordingnormally is accomplished with separateelectromagnetic or acoustic gauges. Instrumentationand rating development procedures for this purposehave been described in several chapters of Volumes Iand II of this Manual.A stage-discharge rating is not used at gaugingstations where velocity-index ratings are used.Instead, ratings are developed for velocity-indexversus mean stream velocity and gauge heightversus cross-section area. For some streams, gaugeheight may also be significant independentvariable in the velocity-index rating. When this isthe case, multiple regression analysis can be usedto develop a velocity-index rating. Each of theseratings is developed for a standard cross sectionof the stream. Details for developing velocityindexratings are given in Chapter 2 of thisVolume. The electronic processing system shouldprovide an interactive process that allows thehydrographer to fit and test the ratings sothat the best combination of ratings can beattained.The methods described in Chapter 2, Volume II ofthis Manual for velocity-index ratings usually referto a single channel rating situation. However,these methods can be used where the stream issubdivided into two or more subsections, eitherhorizontally or vertically. In such cases eachsubsection has its own set of ratings and iscomputed separately. The total discharge is thesum of the subsection discharges.Rate-of-change-in-stage ratingsRate-of-change-in-stage ratings sometimes are usedat gauging stations where changing discharge causesa variable stream slope. These ratings are used forstations with a condition frequently referred to asloop ratings. One of four methods: Jones, Boyer,Lewis or Wiggin’s, usually is used to determine therating at a station with this condition. Thesemethods are described in Chapter 2 of this Manual.Empirical, trial-and-error methods are used todevelop these ratings and require a number ofdischarge measurements. Like other complexratings, these ratings traditionally have been doneusing hand computations and hand-plottingmethods. The electronic processing system shouldprovide an interactive method so the hydrographercan quickly and easily develop a rate-of-change instage rating. The hydrographer should be allowedto fit and test trial ratings until the best combinationis attained.6.10 Discharge measurement shiftadjustmentsDischarge measurements are used primarily tocheck rating curves to insure that currently usedrating curves are still valid. The electronic processingsystem should automatically compute the shiftinformation for each discharge measurement. Theshift information should, by default, be computedon the basis of the rating curve applicable for thetime and date of the discharge measurement;however, the hydrographer should be allowed tospecify a different rating curve for which the shiftinformation is computed. If, at a later date, a newrating curve is prepared, then the shift informationshould be automatically updated for allmeasurements that fall within the period of timethat the new rating is applicable. Shift informationshould be displayed as part of the output for eachdischarge measurement.The following sections describe the methods ofcomputing shift information for individualdischarge measurements made at stage-dischargestations, slope stations, rate-of-change in stagestations and stations. Shifts are not computed orused for structure stations and BRANCH modelstations. Definition of shift curves, use of partialor average shifts and other aspects of shiftapplication are described in a later section of thisManual.

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-296.10.1 Shifts for stage-discharge ratingsThe shift information that should be computed fordischarge measurements applicable to stagedischargerating curves is as follows:(a) Rating shift, S r– This shift is the numericaldifference between the gauge height, G r, whichcorresponds with the rating curve discharge forthe measurement, and the gauge height, G m,of the discharge measurement. The resultingalgebraic sign should be observed. The equationis:S = G − G(6.6)rrm(b) Measurement percent difference, D – This isthe percent difference between the measureddischarge, Q m, and the rating curve discharge,Q r, that corresponds to the gauge height of thedischarge measurement. This represents thedifference between the measured dischargeand rating discharge if no shift is applied. Theequation is:D =100( Q m− Q r ) /Q (6.7)r(c) Shifts for the gauge height of zero flow, S 0– Ifthe gauge height of zero flow, G 0, is determinedeither when a regular discharge measurementis made, or independently during a visit to thegauging station, then it is possible to compute ashift for that gauge height if the rating curve isdefined down to zero flow. This information canbe very useful as an aid in defining the low endof a shift curve. The equation for computing theshift for the gauge height of zero flow is similarto equation 5.6 for computing the rating shift,and is:S = G(6.8)−0 rG 0Because the discharge corresponding to G 0is bydefinition zero, it is not possible to compute ameasurement percent difference.6.10.2 Shifts for slope ratingsSlope ratings usually are referred to as complexratings because they involve two sites for measuringgauge height (a base and auxiliary gauge) and threeindividual ratings of different parameters. Therequired ratings are (a) a stage-discharge rating,(b) a stage-fall rating and (c) a fall ratio-dischargeratio rating. The following paragraphs describe howshift information is computed for individualdischarge measurements at stations with sloperatings.The stage-discharge rating is the only rating of thethree slope station ratings that is allowed to beshifted, and shift information is referenced to thisrating. If either the fall rating or the ratio ratingchanges then new ratings should be prepared. Italso should be noted that slope ratings only mayapply to certain ranges of stage and in some casesonly when the fall is less than a specified amount.For slope ratings, the measured discharge, Q m, isconsidered the true discharge. The adjusteddischarge, Q adj, is an adjustment of the measureddischarge that is computed by using the observedstages at the base gauge and the auxiliary gauge, theobserved fall, which is the difference between thetwo observed stages, and the defined rating curves.This adjusted discharge is used for comparison tothe rating discharge, Q r, to determine shiftinformation. If no shift is present, then Q adjand Q rwill be equal. The method for computing Q adjandshift information is as follows:(a) Adjusted discharge, Q adj– First, compute themeasured fall, F m, as the difference betweenthe observed mean gauge height for themeasurement at the base gauge, G b, and theauxiliary gauge, G a. The equation is:F = G − G(6.9)mbaSecond, if the auxiliary gauge is upstream fromthe base gauge, reverse the order of G band G ain equation 6.9;Third, determine the rating fall, F r, thatcorresponds to the base gauge height, G b, fromthe stage-fall rating;Fourth, compute the fall ratio, R f, of themeasured fall to the rating fall. The equationis:Rf= FmFr(6.10)Fifth, determine the discharge ratio, R q,corresponding to R ffrom the ratio rating;Finally, compute the adjusted discharge, Q adj,based on the measured discharge, Q m, and thedischarge ratio, R q. The equation is:Q = Q R(6.11)adjmq(b) Stage-discharge rating shift, S r– Determine thegauge height, G r, corresponding to the adjusteddischarge, Q adj, from the stage-discharge rating.Compute the shift, S r, based on the observedgauge height, G b, for the base gauge and therating gauge height, G r. The equation is:S = G − G(6.12)rrb(c) Measurement percent difference, D – Thepercent difference, D, between the adjusteddischarge, Q adj, and the rating discharge, Q r,also should be computed. This percentagerepresents the error of the adjusted dischargefrom the rating discharge if no shift is applied.

II.6-30manual on stream gaugingThe equation is:( QadjQr) QrD = 100 − /(6.13)Fifth, compute the adjustment factor, F adj, usingthe following equation:6.10.3 Shifts for rate-of-change-in-stageratingsFadj⎛ 1 ⎞⎛dG ⎞= 1 +⎜⎟⎜⎟(6.16)⎝USc⎠⎝dt ⎠Rate-of-change-in-stage ratings are complex ratingsapply to streams where rapid changes in stage affectthe stage-discharge rating. The most commonlyused rating of this type is the Boyer method whichis described herein. The Boyer method includes astage-discharge rating and a rating of stage versusthe factor, 1/US c. The term 1/US cis a measure offlood-wave velocity, U, and the constant dischargestream slope, S c. This term usually is definedempirically from the discharge measurements. Thegreatest effect of changing stage occurs on streamshaving relatively mild slopes and rapid changes indischarges. Frequently, this effect will happen whenthe flow regime of a stream has been changedartificially, such as below a dam when releases aremade quickly or in urban areas where basindevelopment causes rapid increases in flow rates fora stream that was previously sluggish.Shift information for Boyer ratings should becomputed only for the stage-discharge rating. Therating of stage versus 1/US cshould not be shifted. Ifthis rating changes a new rating should be prepared.The shift and percent difference should be based onthe rating discharge, Q r, and the adjusted discharge,Q adj.The method for computing the adjusted dischargeand the shift information for Boyer ratings is asfollows:(a) Adjusted discharge, Q adj– First, computethe change in stage, dG, for the dischargemeasurement as the difference between theending gauge height, G e, and the starting gaugeheight, G s. For rising stages the difference ispositive and for falling stages the difference isnegative. The equation is:dG = G e− G s(6.14)Second, compute the elapsed time, dt, forthe discharge measurement as the differencebetween the ending time, t eand the startingtime, t s. The equation is:dt = t e− t s(6.15)Third, compute the rate-of-change in stage, dG/dt, for the discharge measurement;Fourth, determine the factor, 1/US c, for the meangauge height of the discharge measurement,from the stage-1/US crating;Finally, compute the adjusted discharge, Q adj,as:Q = Q F(6.17)adjmadjThe adjusted discharge, Q adj, represents thedischarge that would be computed from thetwo ratings and the observed gauge height ifno shift is applied;(b) Rating shift, S r– Determine the rating gaugeheight, G r, corresponding to the adjusteddischarge, Q adj, from the stage-discharge rating.Compute the shift, S r, as the difference betweenthe rating gauge height, G r, and the measuredgauge height, G m, as:S = G r− G (6.18)m(c) Measurement percent difference, D – Determinethe rating discharge, Q r, from the stage-dischargerating using the measured mean gauge height,G m. Compute the percent difference, D, betweenthe adjusted discharged, Q adj, and the ratingdischarge, Q r, as:( QadjQr) QrD = 100 − /(6.19)This percent difference represents the errorbetween the Boyer adjusted discharge and therating discharge if no shift adjustment is applied.6.10.4 Shifts for stationsRatings at gauging stations with velocity index aspart of the rating system are considered complexratings and in some cases can be extremely complexif two or more velocity meters or index velocitymeasurement points along a line/plane are in use.Stream channels may be subdivided either verticallyor horizontally, with each subdivision having aspecific set of ratings, or in some cases the individualmeters may be averaged for use with one set ofratings. Also, for some stations dischargemeasurements may be made so that only the totaldischarge is computed, with no accurate method ofsubdividing the measured discharge into the variousrating components. Because of this variability it isnot possible to describe all of the ways that ratingshifts are computed. The electronic processingsystem should provide an interactive mode thatallows the hydrographer to define the shifts and theshifting method.

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-31Shift information for a basic rating is described inthe following paragraphs. A basic rating includes asingle rating of stage and cross-section area, a singlerating of velocity-index and mean velocity and insome cases an optional rating of stage and a velocitycorrection factor. The rating discharge, Q r, iscomputed by multiplying the cross-section area, A r,from the area rating, times the mean velocity, V r,from the velocity rating, and times the velocitycorrection factor, K r, from the stage-factor rating. Ifthe velocity correction factor is not used it is set toa default value of 1.00. The basic equation fordischarge is:Q = A V K(6.20)rrrrShifts are allowed only for computation of V rfromthe velocity rating. The stage-area and stage-factorratings should not be adjusted through the use ofshifts. If either the stage-area or the stage-factorratings change, then new ratings should beprepared.It also should be noted that a standard cross sectionmust be used for the ratings and for computingshifts. That is, a specific cross section in the streamchannel should be designated as the rating section.This cross section may be the same section as usedfor making discharge measurements or it may be adifferent section. All computations should berelated to and based on the standard cross section.For instance, the mean stream velocity, as used forrating purposes, should be computed by dividingthe measured discharge by the cross-section areadetermined from the stage-area rating of thestandard cross section. This mean stream velocity isthe velocity that should be used to check or definethe velocity rating and the one to be used forplotting purposes on the velocity rating for thosesites where a stage-factor rating is not used. If astage-factor rating is used then this velocity shouldbe adjusted by dividing it by the applicable factorbefore using it to check or define the velocityrating.The order of computations for shift determinationsis important because two, and in some cases three,ratings are involved. The following step-by-stepprocedure should be used:(a) Standard cross-section area, A r– Determinethe cross-sectional area, A r, of the standardcross section from the stage-area rating, usingthe mean gauge height, G m, of the dischargemeasurement;(b) Velocity correction factor, K r– Determine thevelocity correction factor, K r, from the ratingof stage and velocity correction factor, usingthe mean gauge height, G m, of the dischargemeasurement. If this rating is not used, then setthe velocity correction factor to a default valueof 1.00;(c) Adjusted mean stream velocity, V m– Computethe mean stream velocity, adjusted for thevelocity correction factor, for the standard crosssection using:QmVm= (6.21)ArKrwhere Q mis the measured discharge, and theother variables are as previously defined;(d) Rating velocity-index, V ir– Determine the ratingvelocity-index from the rating of velocity-indexand mean stream velocity, by entering therating with the adjusted mean stream velocity,V m, as computed in equation 6.21;(e) Velocity-index shift, S v– Compute thevelocity-index shift as the difference betweenthe rating velocity-index, V ir, and the meanmeasured velocity-index, V im, for the dischargemeasurement. The shift, S v, is defined by:S = V −V(6.22)virimS vshould retain the resulting algebraic sign(+ or –) for application purposes. When thecomputed shift is applied to the measuredvelocity-index, V im, it will yield a correctedvelocity-index to use for entry to the velocityrating when determining the rating meanvelocity, V r;(f) Measurement percent difference, D – The measurementpercent difference is the percentageof error between the measured discharge, Q m,and the unshifted discharge, Q r. To computethe unshifted rating discharge, Q r, use equation6.20 as described in previous paragraphs. Themeasurement percent difference is computedas:D =100 Q − Q Q(6.23)(m r) r6.11 Application of shiftadjustmentsShifts are gauge-height adjustments used to accountfor temporary changes to rating curves withouthaving to re-define the rating curve. The methodsfor computing shift information for the varioustypes of discharge measurements are described inthe previous section, Discharge measurement shiftadjustments. For surface-water computations, shiftadjustments are added to unit values of the inputparameter to yield temporary unit values that areapplied to the rating curve for computation of the

II.6-32manual on stream gaugingoutput dependent variable. The algebraic sign ofthe shift must be maintained correctly. Whenmeasurements plot above a rating curve, that is,when the actual gauge height for a given dischargeis higher than indicated by the rating curve, thesign of the shift is negative. When measurementsplot below a rating curve the sign of the shift ispositive. Also, it is important to note that a shift isa temporary correction, used only for computationalpurposes. It does not permanently alter the inputunit value.Although most shifts will apply to stage-dischargeratings they also may be defined and applied to thevelocity-index versus mean velocity rating forvelocity-index stations. Shifts should not be allowedfor any other types of rating curves except stagedischargeratings and velocity-index and meanvelocity ratings. Because shifts are predominantlyused for stage-discharge ratings, the shift discussionsin this section will relate to that type of rating.Much of the following discussion regardingapplication of shifts is based on Kennedy (1983).Shifts usually are applied only when dischargemeasurements deviate from a rating curve by morethan a specified percentage. The specified percentagefrequently is based on the accuracy of dischargemeasurements that can be made at the gaugingstation. For instance, if discharge measurementscan be made with 5 per cent or better accuracy thenshifts will be used only when measurements deviatemore than 5 per cent from the rating. Otherwise, ifmore than two or three consecutive dischargemeasurements consistently plot on one side of therating a shift curve may be used for thesemeasurements even though they are within thespecified shift percentage.The shift adjustments that apply during the periodsbetween discharge measurements must beinterpolated by an appropriate method before theunit and daily discharge records can be computed.The method used will depend on the hydrographer’sjudgment considering the nature of the shifting,the frequency of measurements and the type ofchannel and control.Small shifts that change gradually may be distributedsatisfactorily by inspection using mentalinterpolation. Larger shifts, whose variations areadequately defined by discharge measurements,warrant a more rigorous analysis with some form ofgraphic shift-adjustment-variation diagram. Theaccuracy of discharge records computed from arating with large and erratic shifts depends to agreat extent on the frequency of dischargemeasurements, and particularly unstable streamsmay need weekly or even daily measurements todefine the day-to-day shift-adjustment variation.6.11.1 Shift-adjustment variationdiagramsA shift-adjustment variation diagram (sometimescalled a V-diagram), a graph of the relation betweenshift adjustment and either time or stage, iscommonly used to interpolate shift adjustmentsbetween measurement-defined values. The V-diagram shifts can be graduated with time, stageor time and stage simultaneously either manuallyor as part of an electronic processing system.When a low-water control is scoured or filled oraffected by backwater from leaves, debris oraqueous growth, the corresponding rating shift isgreatest at low water and normally tapers to zeroat some higher stage. This is called a stage-variableshift. If the channel is alluvial and its bed is raisedand lowered by sediment being picked up ordeposited, the shift variation with stage may benegligible compared to its variation with time,and the shifts are called time variable. Moststreams have shifts that must be graduated withstage while the stage graduation is changing withtime.Time-variable-shift distribution can be mademanually or by an electronic processing systemusing interpolation between discharge measurementdefinedshifts. The hydrographer may introducearbitrary data points based on judgment andknowledge of stream conditions.Stage-variable-shift distribution can be made byusing V-diagrams similar to those in Figure II.6.3.Each diagram involves a base-rating curve (thenumbered rating in effect at the time) a shift-ratingcurve (a rating curve drawn to fit the measurementsthat define the shift, usually only on the ratingwork-curve sheet) and the V-diagram (the gaugeheightdifferences between the base curve and shiftcurve, plotted against stage). The shift curve shouldnormally be drawn first with the same considerationgiven to its shape as would be given to a numberedrating. The V-diagram is best defined by drawing itscorresponding shift curve first. The V-diagrams ofthe type in Figure II.6.3(a), for relatively small shifts,may be defined directly from measurement-definedshifts without drawing a shift curve. This process isnot recommended with other V-diagram types orfor large shifts where it could lead to grosslymisshapen equivalent ratings and dubious dischargerecords.

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-33The use of a stage-varied-shift adjustment isequivalent to drawing a new numbered rating curveand may be preferable for temporary rating changes.The principal use for stage-shift diagrams is onestep in the process used for varying shifts with bothstage and time as explained in subsequentparagraphs of this section.Figure II.6.3 illustrates typical stage-shift V-diagramsand the relations between their corresponding baserating curves and shift curves. The V-diagrams formanual application are usually curved and shiftsare determined by direct readings from the curve.The V-diagram must be approximated by two ormore straight lines for application by an electronicprocessing system. Selected coordinates that definethe V-diagram are entered to the electronicprocessing system and applied by interpolationbetween the entered points.Shift adjustments varied by time onlyThe simplest way to vary shift adjustments betweendischarge measurements is by time interpolation.Time-varied shifts are usually used for periods whenstage does not change very much, and the shiftingcontrol is affected by a gradual change due to scouror fill. For example, such a condition might becaused by gradual accumulation of falling leaves ona section control. Time interpolation of shifts issometimes more convenient when computingdischarge records by hand methods. For automaticdata processing, time interpolation of shifts can beaccomplished through the use of two or moreconstant (vertical) shift-variation diagrams withlinear interpolation between successive diagrams.Shift adjustments varied by stage onlyThe use of a stage-varied-shift adjustment isequivalent to drawing a new numbered rating curveand may be preferable for temporary rating changes.The shift-variation diagrams shown in Figure II.6.3are typical stage-only diagrams, as described in aprevious section. They are applied over a period oftime by manually or automatically determining theshift for each stage value for which discharge iscomputed during the specified time period. Stageonlyshift-variation diagrams are an integral part ofthe more typical situation, where shift applicationis varied by both stage and time, as described in thefollowing section.Shift adjustments varied by time and stageTwo or more shift curves can be used incombination to apply shifts to unit values so thatthe shifts are varied either by time only, or bothstage and time. Varying the shift in this way isaccomplished by defining a shift curve andassigning it a starting date and time, but noending date and time. A second shift curve isdefined with a subsequent starting date and time.If the two shift curves are defined so that eachone has a different constant shift (not varied withstage), then the electronic processing system willinterpolate between these two shifts based ontime only. This procedure commonly is referredto as time interpolation of shifts as describedpreviously. If two consecutive shift curves areentered so that one or both of them have shiftsthat vary by stage, then the electronic processingsystem will interpolate shifts based on both stageand time for all unit values between the twoassigned shift curves.Shift curves should be defined and numbered as ameans of describing and tracking specific shiftingcharacteristics at specific points in time. Each shiftcurve usually is based on one or more dischargemeasurement and other field observations thatdefine a change in the position of the rating curve,and this change usually is considered a temporarychange. To estimate shifts at other times,intermediate to the defined shift curves, a linearinterpolationprocedure is used.Individual shifts, and not entire shift curves,should be interpolated. That is, only those shiftsneeded to adjust unit values should be determinedby interpolation, and not those outside the rangeof recorded unit values. Likewise, the interpolationprocess should be continuous in time, so that ashift interpolation is performed for each unit valueto which shifts are to be applied.The interpolation procedure is described in thefollowing step-by-step example:(a) Two shift curves, numbered 001 and 002 forexample, are defined graphically for use at datesand times, t 1and t 2, respectively;(b) An interpolated shift, S n, is required for unitvalue, G n, at an intermediate date and time, t n;(c) The electronic processing system computesthe shifts, S 1and S 2, corresponding to the unitvalue, G n, from each of the shift curves, 001and 002, respectively;(d) The electronic processing system performs anun-weighted, linear time interpolation of shiftsS 1at time t 1, and S 2at time t 2, to obtain theshift, S n, at time t n;(e) The same interpolation procedure is used toestimate shifts for all other unit values resultingbetween times, t 1and t 2.

II.6-34manual on stream gaugingSTAGE-SHIFT-VARIATI**ON** DIAGRAMRATING CURVES(a)(ADP)(**MANUAL**)UpperGage ht.GageheightShiftadjustement3.0 – 0.1030.25Shift CurveBaseGage ht.LowerGage ht.2.5 – 0.251.9 – 0.25Gage Height20.25Base Curve– 0.5 0 – 0.5 0Shift Adjustement (ft)10 10 20 30 40 50 60 70 80Discharge (ft 3 /s)(b)Shift Curve(c)Shift CurveGage HeightBase CurveGage HeightBase Curve0Shift (ft)Discharge (ft 3 /s)– 0.5 0Shift (ft)Discharge (ft 3 /s)(d)Shift Curve(e)Base CurveGage HeightBase CurveGage HeightShift Curve– 0.5 0Shift (ft)Discharge (ft 3 /s)0 +Shift (ft)Discharge (ft 3 /s)Figure II.6.3. Effect of various stage-shift-variation diagram shapes on shift-curve shapeAll computed and interpolated shifts should berounded to the same number of significant figuresas used for the gauge height or other unit value towhich the shift is to be applied. Rounding shouldbe performed before any application process.6.11.2 Unit value graphical comparison ofshiftsShifts that are applied to a time series of unit valuesshould be displayed with the electronic processing

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-35system in a graphical plot. The graphicalcomparison should show a time-series plot of theunit values of gauge height (or other independentvariable) and a superimposed plot of the unitvalues of shifts. Scales for the two plots should beused so that each plot is easily discernible andreadable. The hydrographer should have theoption to change either or both of the scales. Anexample plot is shown in Figure II.6.4.6.12 Primary computationsStageShift+0–TimePrimary computations are the functions thatconvert input data, such as gauge height, velocityindex and other auxiliary data into time series ofunit values, daily values, monthly values andannual values of discharge, mean velocity, reservoircontents and other output parameters. In the pastprimary computations were generally performed byhand. Today, almost exclusively, primarycomputations are performed by automated dataprocessing systems. Therefore, the subsequentdiscussions of primary computations are describedin terms of automated data processing methods.The primary computation process is dependent onthe type of gauging station and, except for stageonlystations, always will require the use of at leastone rating curve. To carry out the conversionprocess previously developed data and informationwill be required, such as time series of inputvariables, correction diagrams, shift curves andrating tables. The conversion should be carried outwith minimal interaction from the hydrographerand should produce files of information that can beused to produce tables and graphs that commonlyare referred to as primary output.6.12.1 Unit value computationsUnit value files of uncorrected input parameters,such as gauge height and velocity index, are enteredto the electronic processing system as described inprevious sections of this chapter. Also, specificinformation such as parameter correction diagrams,shift curves and rating curves are entered asdescribed previously. The primary computationsshould produce additional unit values files ofspecific output parameters, dependent on thestation type. These unit values and their associatedtime tags are saved for the purpose of computingdaily mean values, various statistics and forarchiving. The unit values files that should becomputed for each type of station are described inthe following sections.Figure II.6.4. Example plot of unit values ofstage and shiftsStage-only stationsStage-only stations are those stations where unitand daily mean values of gauge height and associatedstatistics are required. For this type of stationonly the unit values files of gauge-height data andthe gauge- height correction information areneeded. Primary computations should create thefollowing unit values files. Unless otherwise noted,each unit value file should be saved for further useand for archiving:(a) Gauge-height corrections – The electronicprocessing system should evaluate and computethe gauge- height correction that corresponds toeach input value of gauge height. Gauge-heightcorrections include instrument errors, gaugedatum errors and gauge datum conversions (forexample, conversion to a mean sea level datum).The computations should use each correctionand correction diagram as defined by thehydrographer. The corrections and correctiondiagrams should be interpolated by time andstage, as required. If two or more correctionsor correction diagrams apply to the same timeperiod, the gauge-height correction should bedetermined from each one independently foreach time step, and summed to produce thecumulative correction for each time step. Allgauge-height corrections should be rounded tostandard gauge-height precision before usingthem in further calculations. The resulting timeseries of cumulative gauge-height correctionvalues should be saved as a working file, andfor later archiving;(b) Corrected gauge heights – A unit values file ofcorrected gauge heights should be computed byadding the cumulative gauge-height correction(see above) to the input unit values of gaugeheight for each time step. This file of corrected

II.6-36manual on stream gauginggauge heights is considered the final, and mostaccurate, gauge-height record for the gaugingstation. The file also should be saved for furthercomputations and archiving.Stage-discharge stationsStage-discharge stations are those stations whereunit and daily values of discharge are computedbased on unit values of gauge height and a stagedischargerating curve. This station is the mostcommon type of gauging station and requires unitvalues files of gauge height and information defininggauge-height corrections and shift adjustments.Unless otherwise noted each unit value file shouldbe saved for further use and archiving:(a) Gauge-height corrections – A file of unit valuesof cumulative gauge-height corrections shouldbe computed and saved for each unit valueof gauge height, as described for stage-onlystations in the preceding section;(b) Corrected gauge Heights – A file of unit valuesof corrected gauge heights should be computedand saved, as described for stage-only stationsin the preceding section;(c) Shift adjustments – Unit values of shifts shouldbe computed for each unit value of correctedgauge height. These shifts should be based onthe shift curves defined by the hydrographer andfor the applicable time period. Interpolation ofshifts by time and stage should be performedwith the electronic processing system accordingto the methods described in previous sections.All unit values of shifts should be rounded tostandard gauge-height precision before usingthem in further computations. The computedunit value shifts for each gauge height and timestep should be saved in a unit values file forfurther use and for archiving;(d) Discharge – Unit values of discharge shouldbe computed by temporarily adding the shiftadjustment to the corrected gauge height foreach time step. The corrected and shifted gaugeheight then should be used to determine thecorresponding discharge from the applicablerating curve. The shift-adjusted gauge height is aworking value only and should not permanentlyalter the gauge height. It is not required thatthe shift-adjusted gauge heights be saved. Thecomputed unit values of discharge, however,should be saved for later use, and archiving.For the low end of the rating, and if the rating isdefined to zero discharge, all shift-adjusted gaugeheights that are lower than the gauge height of zeroflow will be assigned a unit value discharge of zero.If the rating is not defined to zero flow, and a shiftadjusted gauge height is below the lowest gaugeheight of the rating, a flag should be set indicatingthe rating was exceeded on the low end. Ratingextrapolations can be made by the hydrographer ata later point in the processing.Velocity index stationsVelocity index stations are those stations whereunit values of discharge are computed on the basisof unit values of gauge height, cross-section area,an velocity-index, mean stream velocity and avelocity adjustment factor (optional). At least tworating curves are required: (a) a stage-area ratingand (b) an index velocity versus mean streamvelocity rating, or an index velocity and stage versusmean stream velocity in the case of a multipleparameter rating based on velocity and stage. Athird rating sometimes is used relating stage to avelocity adjustment factor. Information defininggauge-height corrections, velocity-index correctionsand index- velocity shift adjustments also arerequired.Two unit value input files are used for velocity indexstations: (a) an input file of unit values of gaugeheight and (b) an input file of unit values of velocityindex.For various reasons these files may not havecorresponding and simultaneous time steps whichis required for the unit value computations ofdischarge. If the time steps for the two files do notcorrespond the electronic processing system shouldautomatically interpolate each file to provideestimated unit values corresponding to all recordedtimes of both files. That is, the gauge-height fileshould be interpolated so that an estimated gaugeheight is available for all time steps of the velocityindexfile, and conversely, the velocity-index fileshould be interpolated so that a velocity-index isavailable for all time steps of the gauge-height file.Therefore, this method doubles the size of each ofthe input unit values files. The electronic processingsystem should flag, save and archive all estimatedunit values, together with the recorded unit values.Unit value files should be computed with the electronicprocessing system for the followingparameters. Unless otherwise noted, each unit valuefile should be saved for further use, and forarchiving:(a) Gauge-height correction – A file of unit valuesof cumulative gauge-height corrections shouldbe computed and saved for each unit value ofgauge height (including estimated values) asdescribed previously for stage-only stations;(b) Corrected gauge heights – A file of unit valuesof corrected gauge heights should be computed

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-37by adding the gauge-height corrections to thecorresponding unit values of gauge heights;(c) Velocity adjustment factor – If a rating of gaugeheight versus velocity adjustment factor is usedfor the gauging station a velocity adjustmentfactor should be computed from that rating foreach unit value of corrected gauge height. Shiftadjustments are not applied to gauge height foruse with the velocity adjustment factor rating.If a velocity factor rating is not used for thestation, then the velocity adjustment factorof 1.00 is used for all gauge heights. Velocityadjustment factors should be rounded to twodecimal places for application purposes;(d) Cross-section area – The cross-sectional areashould be computed for each unit value ofgauge height using the stage-area rating;(e) Velocity-index correction – Correction valuesshould be computed for each input value ofvelocity-index (including estimated values),based on the velocity-index correction valuediagrams, and the methods of interpolationas previously described. All velocity-indexcorrection values should be rounded to standardvelocity precision;(f) Corrected velocity-index – Each input value ofvelocity-index should be corrected by addingthe velocity-index correction value to thecorresponding value of the input velocityindex;(g) Velocity-index shifts – Shifts for each valueof the corrected velocity-index should becomputed based on the velocity shift curves. Allvelocity shifts should be rounded to standardvelocity precision before applying to furthercomputations;(h) Mean rating velocity – The mean rating velocityshould be computed for each shift adjustedvalue of the corrected velocity-index by usingthe rating of velocity-index versus meanvelocity;(i) Mean stream velocity – The mean streamvelocity should be computed for each time stepby multiplying the mean rating velocity timesthe velocity adjustment factor;(j) Discharge – The unit values of discharge shouldbe computed by multiplying each unit valueof cross-sectional area times the correspondingvalue of mean stream velocity.For some velocity index stations, two or morehorizontal subsections may be present, each ofwhich has its own set of unit values. For thesestations unit values files are computed for eachsubsection as described above. Unit values of thetotal discharge for the stream for each time step iscomputed as a summation of the correspondingunit values of the subsection discharges. If timesteps for the subsections do not correspond,interpolation of unit values will be required.For streams where two or more velocity-indexmeters are positioned to measure velocity atdifferent vertical positions a velocity averagingprocedure should be used to compute an averagevelocity-index for the stream. Various averagingprocedures can be used depending on the gaugeconfiguration and the number of velocity-indexgauges. The electronic processing system shouldprovide for hydrographer-defined equations tocompute average velocity-index. The ratings forsuch a station are based on the average velocityindex.All other aspects of computing unit values ofdischarge for the stream are the same as describedabove.Slope stationsSlope stations are those stations where discharge iscomputed on the basis of a stage-discharge relationthat is adjusted for variable water-surface slope.Water-surface slope cannot be measured directly sothe water-surface fall between the base gauge andan auxiliary gauge is used as an indicator of slope.The two gauges must be set to the same datum todetermine fall between the gauges. The auxiliarygauge preferably is located downstream from thebase gauge at a distance that provides a measurablefall but does not introduce hydraulically appreciablechannel changes or tributary inflow. For some sitesthe auxiliary gauge may be located upstream, butthis is not advised because the water-surface slopein the upstream reach is not as representative ofbackwater conditions as it is in the downstreamreach.Computation of discharge at a slope station requiresunit values of gauge height at the base gauge andthe auxiliary gauge. Three ratings are required:(a) stage-discharge, (b) stage-fall and (c) fall ratioversus discharge ratio. Information defining gaugeheightcorrections for the base gauge and theauxiliary gauge, and shift adjustments for the basegauge are required.Timing accuracy of unit-value data is very importantat each gauge because water-surface fallcomputations require that time synchronous stagedata be available for the base gauge and the auxiliarygauge. Even with the best timers and time-correctionmethods it is not always possible to obtain this kindof accuracy, and stage data will sometimes berecorded and/or time corrected to different timesteps for the two gauges. For such situations, the

II.6-38manual on stream gaugingstage data for the base gauge should be interpolatedso that estimated stage values are available for eachcorresponding stage value at the auxiliary gauge.Likewise, the stage data at the auxiliary gaugeshould be interpolated so that estimated stagevalues are available for each corresponding stagevalue at the base gauge. This procedure effectivelydoubles the number of stage values at each gauge,half of which are measured values and half areestimated values. The electronic processing systemshould flag, save and archive all estimated unitvalues, together with the recorded unit values.Computations of discharge using the slope methodare subject to constraints that should be checkedand applied for each unit value computation. Theseconstraints are:(a) Slope ratings should not be used if the measuredfall values are negative. In these cases, dischargesshould not be computed and the electronicprocessing system should issue a warning thatnegative fall values have been encountered;(b) Slope affected ratings may apply throughoutthe range in stage measured at a station or theymay apply only for a specific range in stage.The hydrographer should designate the lowerand upper limits of the slope rating by enteringa minimum gauge height and a maximumgauge height, below and above which theslope rating procedures should not be used.Discharge should be computed directly fromthe stage-discharge rating for gauge heightsthat are outside these limits;(c) Slope ratings may, in some situations, havemaximum fall constraints. That is, for measuredfall values exceeding a designated amount, orfor measured fall exceeding the fall from thestage-fall rating, no slope adjustments shouldbe applied. The hydrographer should entera maximum fall so that when measured fallsexceed this value, slope adjustments will notbe made. Likewise, the hydrographer shoulddesignate that when measured fall exceeds therating fall slope adjusted computations willnot be made. For both of these situations, unitvalues of discharge should be computed bydirect application of the stage-discharge rating;(d) For some slope stations, constraints 2 and 3both may apply, and should be checked.Unit value files should be computed with theelectronic processing system for the followingparameters, subject to the above constraints. Unlessotherwise noted, each unit value file should besaved for further use and archiving:(a) Gauge-height corrections, base gauge – A fileof unit values of cumulative gauge-heightcorrections for the base gauge should becomputed and saved for each correspondingunit value of gauge height (including estimatedvalues), as described previously for stage-onlystations;(b) Corrected gauge heights, base gauge – A file ofunit values of corrected gauge heights for thebase gauge should be computed by adding thegauge-height corrections for the base gaugeto the corresponding unit values of gaugeheights;(c) Gauge-height corrections, auxiliary gauge – Afile of unit values of cumulative gauge-heightcorrections for the auxiliary gauge should becomputed and saved for each correspondingunit value of gauge height (including estimatedvalues), as described previously for stage-onlystations;(d) Corrected gauge heights, auxiliary gauge – A fileof unit values of corrected gauge heights for theauxiliary gauge should be computed by addingthe gauge-height corrections for the auxiliarygauge to the corresponding unit values of gaugeheights;(e) Measured water surface fall – A file of unitvalues of measured water-surface fall shouldbe computed by subtracting each unit value ofgauge height at the auxiliary gauge from thecorresponding gauge height at the base gauge.If the auxiliary gauge is located upstream fromthe base gauge, fall should be computed bysubtracting the base gauge height from theauxiliary gauge height;(f) Shift adjustments – For slope stations shiftadjustments are used only for the stage-dischargerating for the base gauge. A unit values file ofshift adjustments should be computed for eachbase gauge height, including estimated values,by using the defined shift curves and thetime/stage interpolation procedures describedpreviously. If shift curves are not applicable forspecific time periods, shifts should default tozero for that time period;(g) Rating discharge – Unit values of ratingdischarge are computed for each unit value ofshift adjusted gauge height for the base gauge,using the stage-discharge rating for the basegauge. The rating discharge is an unadjusteddischarge value, and does not represent thetrue discharge of the stream;(h) Rating fall – Unit values of rating fall arecomputed for each unit value of gauge height(not shift adjusted) for the base gauge, usingthe stage-fall rating for the base gauge;(i) Fall ratio – Unit values of fall ratio are computedby dividing the measured water-surface fall bythe rating fall;

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-39(j) Discharge ratio – Unit values of the dischargeratio are computed using the rating curve of fallratio versus discharge ratio;(k) Discharge – Unit values of discharge arecomputed by multiplying the rating dischargetimes the discharge ratio. The resulting dischargerepresents the true discharge of the stream.Rate-of-change-in-stage stationsRate-of-change-in-stage stations are those stationswhere discharge is computed on the basis of a stagedischargerelation that is adjusted for variable ratesof change in stage. Computation of discharge, asbased on the Boyer Method, requires unit values ofgauge height. Two ratings are required: (a) a stagedischargerating and (b) a stage versus 1/US crating.Information defining gauge-height corrections andshift adjustments also are required.Computation of discharge using the Boyer Methodis subject to constraints that should be checked andapplied for each unit value computation. Theseconstraints are:(a) Rate-of-change-in-stage ratings apply onlyto high discharges where channel controlconditions are effective. The hydrographershould specify a minimum gauge height anda maximum gauge height, below and abovewhich the rate-of-change-in-stage computationsshould not be applied. Discharge should becomputed directly from the stage-dischargerelation when the stage is outside these limits;(b) Rate-of-change-in-stage computations arefrequently not made when the Boyeradjustment factor results in only a smallchange of the rating discharge. The electronicprocessing system should use default values of0.96 to 1.04 as the range of Boyer adjustmentfactors for which adjustments would not bemade. The hydrographer should be allowed tochange these values, if necessary (for example,to achieve smoothness of the computed unitvalues of discharge).Unit value files should be computed with theelectronic processing system for the parameterslisted below, subject to the above constraints. Unlessotherwise noted, each unit value file should besaved for further use and archiving:(a) Gauge-height corrections – A file of unit valuesof cumulative gauge-height corrections shouldbe computed and saved for each correspondingunit value of gauge height, as describedpreviously for stage-only stations;(b) Corrected gauge heights – A file of unit valuesof corrected gauge heights should be computedby adding the gauge-height corrections to thecorresponding unit values of gauge heights;(c) Rate of change in stage – A rate-of-change instage (dG/dt) should be computed for each unitvalue of corrected gauge height that is withinthe range of gauge heights defined by theminimum and maximum constraint. First, thedifference in stage is computed by subtractingthe previous unit value of corrected gaugeheight from the next unit value of the correctedgauge height. This difference in gauge heightis converted to the rate-of-change in stage, infeet (or mm) per hour, by dividing it by thetime difference of the previous and next unitvalues. This method of computation providesan average rate-of-change-in-stage for the timeperiod extending one time interval before andone time interval after the current unit valueof gauge height. The algebraic sign of thecomputed rate-of-change-in-stage should beretained as computed. A positive sign indicatesa rising stage, and a negative sign indicates afalling stage;(d) Shift adjustment – For rate-of-change-in-stagestations, shift adjustments are used only forthe stage- discharge rating. A unit values file ofshift adjustments should be computed for eachcorrected gauge height by using the definedshift curves and the time and stage interpolationprocedures described previously. If shift curvesare not applicable for specific time periods, shiftsshould default to zero for that time period;(e) Rating discharge – Unit values of rating dischargeare computed for each unit value of shift adjustedgauge height using the stage-discharge rating.The rating discharge is an unadjusted dischargevalue, and does not represent the true dischargeof the stream for periods when rate-of-changeadjustments are applicable;(f) Boyer factor, 1/US c– The Boyer Factor shouldbe computed for each corrected gauge height(not shift adjusted) that is within the range ofgauge heights defined by the minimum andmaximum constraint, by application of thestage versus 1/US crating;(g) Discharge adjustment factor – Unit valuesof the discharge adjustment factor, F adj, arecomputed based on the Boyer Factor and therate-of-change-in-stage, by using the followingequation. Discharge adjustment factors shouldbe computed only for gauge heights that arewithin the range of gauge heights defined bythe minimum and maximum constraint as:Fadj=⎛ 1 ⎞⎛dG ⎞1 +⎜⎟⎜⎟(6.24)⎝USc⎠⎝dt ⎠

II.6-40manual on stream gauging(h) Discharge – Unit values of discharge arecomputed by multiplying the rating dischargetimes the discharge adjustment factor. All unitvalues of discharge that are based on adjustmentfactors from 0.96 to 1.04, by default, shouldnot be used unless overridden or otherwisespecified by the hydrographer. Instead, therating discharges based on the shift adjustedgauge heights should be used directly.Reservoir stationsReservoir stations are those stations where unit anddaily values of reservoir elevation and reservoircontents are required. If only reservoir elevation isrequired, no rating is needed. However, if reservoircontents are required, then a rating of reservoirelevation versus contents is needed. Input requiresunit values of elevation and information definingelevation corrections. Generally, for reservoirstations, the term elevation is used rather thangauge height because the elevation above a NationalGeodetic Vertical Datum (NGVD), such as mean sealevel is used for many reservoir gauges. However,gauge heights are allowed and used at manyreservoir stations. Unit values files should becomputed with the electronic processing system forthe parameters listed below. Unless otherwise noted,each unit value file should be saved for further useand archiving:(a) Elevation correction – A file of unit values ofcumulative elevation corrections should becomputed and saved for each correspondingunit value of elevation, as previously describedfor stage-only stations;(b) Corrected elevations – A file of unit valuesof corrected elevations should be computedby adding the elevation corrections to thecorresponding unit values of elevations;(c) Reservoir contents – A file of unit values ofreservoir contents should be computed byapplication of the corrected elevations to theelevation versus contents rating.required. Information defining gauge height orelevation corrections also is required. Each unitvalue file should be saved for further use andarchiving:(a) Gauge-height or elevation correction – A fileof unit values of cumulative gauge height orelevation corrections should be computed andsaved for each corresponding unit value of gaugeheight or elevation as described previously forstage-only stations. This correction value isseparate from the datum-conversion value usedto convert gauge height to NGVD;(b) Corrected gauge height or elevation – A fileof unit values of corrected gauge heights orelevations should be computed by adding thegauge-height or elevation corrections to theunit values of gauge heights or elevations.Hydraulic structure stationsHydraulic structure stations are those stations whereunit and daily values of discharge are computedusing special ratings and equations for spillways,gates, turbines, pumps, siphons and other controlledconveyances. A special software program, such asthe program developed by Sanders and Feaster(2004) is available for this purpose. The basic theoryand concepts are described by Collins (1977). Inputdata may include unit values of headwater gaugeheights, tailwater gauge heights, individual gateopenings for each gated conveyance, turbinepressures and lockage and other variables as requiredfor a specific site. Hydraulic structure gaugingstations are extremely complex and may have manysub-units (individual gates, turbines and others) forwhich unit values of discharge are computed. Unitvalues of total discharge are computed as asummation of the individual subunits. Because ofthe complexity and variability of hydraulic structuregauges, a listing of unit values files will not be givenhere. However, the electronic processing systemshould save all unit values files for further use andarchiving.Tide stationsTide stations are those stations located in estuariesand along tidal affected rivers and streams toprovide the daily information on diurnal and/orsemi-diurnal variations of surface-water levels inthose areas. Tide stations may be set to an arbitrarydatum or to an elevation based on a NGVD, such asmean sea level. When an arbitrary datum is used,unit values of elevation are determined by adding aconstant datum conversion to the unit values ofgauge height. No other conversions to otherparameters are required, therefore, no ratings areBRANCH model stationsA BRANCH model gauging station utilizes acalibrated digital computer model for simulatingthe unsteady flow in a channel reach which isusually affected by variable backwater. The modelcalibration requires basic field data, principallycross-section definition at a number of locations inthe gauged reach, roughness coefficients, calibrationdischarge measurements and gauge-height data atthe upstream and downstream end of the gaugedreach. Details of calibration and computation aregiven by Schaffrannek and others (1981). Primary

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-41computations require unit values of gauge height atthe upstream and downstream ends of the reach, asgiven below. Information defining gauge-heightcorrections for the upstream and downstreamgauges is required:(a) Gauge-height corrections, upstream gauge – A file ofunit values of cumulative gauge-height correctionsfor the upstream gauge should be computed andsaved for each corresponding unit value of gaugeheight (including estimated values), as describedpreviously for stage-only stations;(b) Corrected gauge heights, upstream gauge – Afile of unit values of corrected gauge heightsfor the upstream gauge should be computedby adding the gauge-height corrections forthe upstream gauge to the corresponding unitvalues of gauge heights;(c) Gauge-height corrections, downstream gauge –A file of unit values of cumulative gauge-heightcorrections for the downstream gauge shouldbe computed and saved for each correspondingunit value of gauge height (including estimatedvalues);(d) Corrected gauge heights, downstream gauge – Afile of unit values of corrected gauge heights forthe downstream gauge should be computedby adding the gauge-height corrections for thedownstream gauge to the corresponding unitvalues of gauge heights.BRANCH model gauges have a unique characteristic,in that the parameters of gauge height, mean streamvelocity and discharge are computed for each crosssectionlocation, as well as at the upstream anddownstream gauge locations. For this reason, unitvalues of each of these parameters, for each crosssection, can be saved for future use and archiving.The electronic processing system should allow thehydrographer to designate which output parameters,and for which cross sections and gauge sites, shouldbe saved for future use and archiving.6.12.2 Daily value computationsVarious kinds of daily values are computed for eachstation type, and are based on the unit values filesdescribed in the previous sections. Daily values for thevarious parameters consist of mean values, minimuminstantaneous values, maximum instantaneous valuesand instantaneous values at selected times. Dailyvalues for a gauging station usually are computed forthe local time zone designation, for the location ofthe gauging station. This computation includes theuse of daylight savings time wherever applicable.However, the electronic processing system shouldallow computation of daily values ⎛ forq0+anyq1⎞other time ⎛ q1+⎜ ⎟ t1− t0+ ⎜zone, as selected by the hydrographer. ⎝ 2 ⎠ ⎝ 2Q =The electronic processing system should allow thehydrographer to compute daily values for temporaryuse and study, without requiring that they be savedand archived. Such files of daily values could beused for review and comparisons before finalizationof the records.Daily mean valuesDaily mean values, frequently referred to as dailyvalues, consist of a time-weighted arithmetic meanof selected parameters, and are computed from thefiles of unit values. Daily mean values may becomputed for the following parameters:(a) Gauge height;(b) Discharge;(c) Cross-section area (velocity-index stations);(d) Velocity-index;(e) Mean stream velocity;(f) Fall (slope stations);(g) Elevation (reservoir and tide stations);(h) Contents (reservoir stations).A file of all computed daily mean values should besaved for future use and archiving.The time-weighted arithmetic method of computingdaily mean values is referred to as the trapezoidalmethod. The trapezoidal method is a mathematicalintegration of the unit value hydrograph andprovides an accurate computation of the meanparameter value. With a large number ofinstantaneous values for each day, the trapezoidalmethod closely approximates actual integration.The trapezoidal method assumes that all unit valuesare instantaneous values, and that each unit valuehas a specific, designated time of occurrence. Thetime interval between unit values may be constantor variable. The file of unit values used for thecomputation of the daily mean value by thetrapezoidal method must include a unit value at themidnight time for each day. If actual values are notrecorded for the midnight time, a unit value shouldbe interpolated based on the recorded unit valueson either side of the midnight time. Theseinterpolated midnight values should be flagged asinterpolated, and should be retained in the unitvalues file for future use and archiving. The equationfor the trapezoidal method is:q ⎞⎟ 2⎠t − t⎛ q0+ q1⎞⎜ ⎟⎝ 2 ⎠Q =2( n−1)( ) ( t − t ) ⋅ ⋅⋅ + ⎜n01⎛ q1+ q2⎞( n−1) n( t − t ) + ( t − t ) ⋅ ⋅⋅ + ⎜ ⎟(t1⎛ q + qn⎞⎟⎝ 2 ⎠0⎜⎝( t − t )n( n−1)2⎟ 2⎠t − tn01⎛ q + q ⎞⎝ 2 ⎠(6.25)n−

II.6-42manual on stream gaugingwhere Q = daily mean parameter value (in the aboveequation; Q represents discharge; however, thesame equation can be used for any other parameter,such as gauge height, velocity and others); q 0= theparameter unit value at the midnight time at thebeginning of the day; q 1, q 2....., q (n – 1)= consecutiveunit values of the parameter during the day; q n=the parameter unit value at the midnight time atthe end of the day; t 0= midnight time at thebeginning of the day, or zero time; t 1, t 2......, t (n – 1)=consecutive times corresponding to the parameterunit values during the day and t n= midnight timeat the end of the day, or 24.00 hour time. Note thatall times must be expressed in hours and decimalparts of an hour.Daily values will not be computed for days whentime gaps exceed a value specified as the abortinterval. The abort interval, by default, is 2 hours;however, the hydrographer should be allowed tochange this interval to any other value less than24 hours.Daily minimum and maximum valuesThe minimum and maximum values for some ofthe parameters are required for each day. Thesevalues are determined from the unit value files forthe various parameters and the selection processshould consider all recorded and interpolated unitvalues for each day, including the midnight valuesat the beginning and end of each day. For someparameters corresponding values of other parametersalso should be determined.Daily values at selected timesSome stations require additional daily values atselected times for some parameters. For instance,reservoir stations sometimes require daily elevationand contents at specific times, such as 0800, 1200or 2400. If unit values are not available at thespecified times, interpolated values should be used.The hydrographer should be able to specify, for allstation types, the parameter and time for whichselected daily values are required.Daily values for tidal stationsTidal stations require the determination of thegauge heights or elevations of tidal peaks andtroughs for diurnal and semi-diurnal variations ofthe water-surface level. The unit values file of thecorrected gauge height or elevation data areexamined sequentially to determine the two hightides and the two low tides for each day for semidiurnalfluctuations. The procedure for computingdaily values for tidal stations also recognizes diurnaland mixed fluctuations when they occur. Thefollowing discussion is excerpted from Hutchinsonand others (1977):“In order to find true tidal peaks and troughswhich occur once or twice in relation to the lunarday rather than the solar day, the record is NOTbroken up into groups of observations in a calendarday before processing. Instead, the wholerecord is scanned continuously for successivepeaks and troughs within periods of given lengthfollowing the time of the previous extreme. Aftereach extreme is found, the calendar day in whichit occurred and time is determined. Thiscompletely eliminates any confusion with inclusionor exclusion of extremes occurring just beforeor just after midnight.The method of finding successive tidal peaksand troughs is to look for an opposite extremein a selected time period (normally 10 1/2hours) following each recognized peak ortrough. That is, when a tidal peak is found (andits date and time are stored) a search is made forthe lowest stage in the selected time periodfollowing the time of the previous tidal peak.Then having found the time of this tidal trough,a search is made for the highest stage in theselected time period following the time of theprevious tidal trough. Comparison of two peaksfound within a calendar day and two troughsfound within the same calendar day are used toassign each as a HIGH-HIGH, a LOW-HIGH, aHIGH-LOW, or a LOW-LOW for the day.Although the normal tide on most of the UnitedStates coastline is semi-diurnal, at a few placesthe tides are diurnal or are mixed semi-diurnal.This program tries to give meaningful results ina situation by the following logic. Starting eachsearch for a peak or trough, a normal, semi-diurnaltidal cycle is assumed and the length of theselected time period for the search is set at about10-1/2 hours (0.44 day). This length of the searchperiod was picked so as to be long enough toinclude the normal time of occurrence of thenext peak or trough for a semi-diurnal tide(which should occur about 6-1/2 hours after thepreceding trough or peak) and short enough toavoid confusion with the advance side of thenext following tidal wave if the two tidal wavesare of greatly different magnitude. (If a 12-hoursearch period were used, confusion could occursuch as when the second tidal wave of the day isso much higher than the first that the water level12 hours after the previous tidal trough is rapidlyrising and already higher than it was at the timeof the first real peak which occurred about 6-1/2hours after the previous tidal trough).

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-43In order to be able to produce meaningful resultsfor sites where the tide is actually diurnal or is amixture of semi-diurnal and diurnal, an additionaltest is made after each search for the nextapparent extreme. If the next extreme is foundto occur in the last hour of the 10-1/2 hour searchperiod, it is assumed that this extreme is not atrue tidal peak or trough in a semi-diurnal cyclebut is instead falling toward a trough or risingtoward a peak in a diurnal tidal cycle. Then inorder to find the real tidal peak or trough in thislonger cycle, that particular search period isextended by another 12 hours and the new resultsused as the next peak or trough. However, afterfinding the next tidal peak or trough, the followingsearch is again made for an initial period of10-1/2 hours so that a change back from a diurnaltide to a semi-diurnal tide is not missed.”The daily values of HIGH-HIGH, LOW-HIGH,HIGH-LOW, and LOW-LOW determined in theabove procedure should be saved for further use,and for archiving. In addition, the cumulativeelevation correction values corresponding to eachof the peak and trough elevations should be savedand archived.There are special considerations for computations ofmean daily discharge for tidally affected sites. Ruhland Simpson (2005) discuss these considerations forseveral stations where the index-velocity methodwas used to compute discharges at tidally affectedgages. Calculating daily discharge in a tidallyinfluenced environment cannot be accomplishedsimply by averaging all of the values collected duringthat 24-hour period. Simple averaging causes cyclicalvariations, or aliasing, in the data that are spuriousand are a function of the averaging scheme, not thedata. Therefore, a low-pass filter is used to removefrequencies that have periods less than 30 hours. Themost energetic variations removed in this process arethe astronomical tides (typically with periods at oraround 12 and 24 hours); however, other variations(meteorological, hydrologic, or operational) thathave periods less than 30 hours also are removed.These considerations are discussed in more detailin Chapter 2 of this Volume and will not berepeated here.6.12.3 Summary of primary computationsPrimary computations include the determinationof unit values and daily values for numerousparameters. It is important and necessary tosummarize these results in tables that can be usedfor review, analysis and publication. Standardformatted tables include unit values, primarycomputations and daily value tables. The electronicprocessing system should allow for the design ofother summary tables, as needed, and as specifiedby the hydrographer.Unit values tablesThe electronic processing system should provide aflexible array of unit values tables to allow for theanalysis and review of individual parameters, orselected groups of parameters. For instance, a unitvalues table may show only the final, correctedvalues of gauge height for a selected period of time;or the unit values table may show the final gaugeheightvalues and the corresponding dischargevalues. The hydrographer should select the inputparameters needed in a unit values table. The unitvalues should be displayed in chronological orderand generally grouped by day, month and year. Thehydrographer also should specify selected timeintervals for a unit values table. For instance, anhourly table may be selected, even though 15-minuteunit values are available or, even-hour unit valuesmay be selected that require interpolation of unitvalues that are not recorded on the even-hour.Primary computations tablesPrimary computations involve the application ofvarious instructions to derive the final dischargerecord (or other parameter such as reservoircontents, tide, and others) for a gauging station.These instructions include gauge-height corrections,shifts and rating curves. The computations shouldbe displayed in a table that shows input data andcomputed information so that they can be easilyreviewed. Each gauging station type, such as stagedischarge,slope, velocity-index and others, willhave primary output formats specifically designedfor the station type. A listing of items, by stationtype, recommended for inclusion in a primarycomputation form is shown in Table II.6.1.Arrangement of the information is not critical.Daily values tablesA daily values table is a listing of the daily values foreach day of the year for selected parameters at agauging station. Generally, daily values are the dailymean discharges for a gauging station, but otherparameters such as stage, elevation, reservoir contentsor other statistics such as daily maximum, dailyminimum and daily unit value at a specific time maycompose a daily values table. The hydrographershould specify time periods in the daily values tableand include multiple parameters in one table. Inaddition, the daily values table should show monthly

II.6-44manual on stream gaugingTable II.6.1. Items recommended for inclusion in primary output tables for various gauging station typesItemStation Type1 2 3 4 5 6 7 8 9HEADER INFORMATI**ON**Station ID number X X X X X X X X XStation name X X X X X X X X XWater year information X X X X X X X X XDate of primary processing X X X X X X X X XName of responsible hydrographer X X X X X X X X XList of ratings used X X X X XUnit value recording interval X X X X X X X X XStation type (i.e., processing method) X X X X X X X X XDatum adjustment (if applicable) X X X X X X X X XTABULAR INFORMATI**ON**Date X X X X X X X X XHourly gauge heights for base gauge X X X X XMaximum daily gauge height X X X X X X XTime of maximum gauge height X X X X X X XShift corresponding to maximum gaugeheightX X XGauge height correction correspondingto max. ghtX X X X X X XMinimum daily gauge height X X X X X X XTime of minimum gauge height X X X X X X XShift corresponding to minimum gaugeheightX X XGauge height correction correspondingto min. ghtX X X X X X XMean daily gauge height X X X X X X XMaximum daily discharge X X X X X XTime of maximum discharge X X X X X XMinimum daily discharge X X X X X XTime of minimum discharge X X X X X XMean daily discharge X X X X X XHourly discharges X X X XMaximum daily index velocityXTime of maximum index velocityXShift corresponding to max. indexvelocityXIndex velocity correction for max. indexvelocityXMinimum daily index velocityXTime of minimum index velocityXShift corresponding to min. index velocityXIndex velocity correction for min. indexvelocityXMean daily index velocityXMaximum daily cross section areaXTime of maximum cross section areaXMinimum daily cross section areaXTime of minimum cross section areaXGauging station type:1 - Stage only; 2 - Stage-discharge; 3 - Velocity index; 4 - Slope; 5 - Rate-of-change in stage; 6 - Reservoir.

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-45Table II.6.1 (continued)ItemMean daily cross section areaMaximum daily stream velocityTime of maximum stream velocityMinimum daily stream velocityTime of minimum stream velocityMean daily stream velocityMaximum daily reservoir contentsTime of maximum reservoir contentsMinimum daily reservoir contentsTime of minimum reservoir contentsMean daily reservoir contentsReservoir gauge height at specified timeGauge height correction at specified timeReservoir contents at specified timeHigh-high daily gauge height w/o datum adj.High-high gauge height w/datum adj.Time of high-highGauge height correction for high-highLow-high daily gauge height w/o datum adj.Low-high gauge height w/datum adj.Gauge height correction for low-highHigh-low daily gauge height w/o datum adj.High-low gauge height w/datum adj.Time of high-lowGauge height correction of high-lowLow-low daily gauge height w/o datum adj.Low-low gauge height w/datum adj.Time of low-lowGauge height correction for low-lowMean daily tide gauge height w/o datum adj.Mean daily tide gauge height w/datum adj.Maximum daily gauge height at auxiliarygaugeTime of max. daily ghtGht correction corresponding to max. aux ghtMinimum daily gauge height at auxiliarygaugeTime of min. daily ghtMean daily ght at auxiliary gaugeMaximum daily fallTime of max. daily fallMinimum daily fallTime of min. daily fallMaximum rate of change in stageTime of max. rate of change in stageMaximum adjustment factorTime of max adjustment factorMinimum adjustment factorTime of min. adjustment factorStation Type1 2 3 4 5 6 7 8 9XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXGauging station type:1 - Stage only; 2 - Stage-discharge; 3 - Velocity index; 4 - Slope; 5 - Rate-of-change in stage; 6 - Reservoir.

II.6-46manual on stream gaugingand annual totals, means and extremes, asappropriate.6.13 Hydrograph plotsHydrographs are useful for graphical viewing,verification, editing and comparisons of streamflowinformation, including most of the basic informationthat contributes to the primary computation ofstreamflow records. Hydrograph plots of unit valuesof discharge along with comparative plots of otherparameters such as gauge height, velocity and shifts,and supplementary data such as peak discharge, peakstage and discharge measurements, provide anexcellent means of reviewing and editing primarycomputations. Likewise, hydrograph plots of dailydischarge records can be combined with hydrographplots of other station records, precipitation recordsand temperature records for estimating missingrecords. Hydrograph plots provide a graphicalsummary of the records for visual presentation andpublication.All hydrograph plots, both unit value and dailyvalue, should be viewable on the computer monitor.In addition, the hydrographer should have theoption to plot all hydrographs on paper plots. Allscales and grid lines should be generated by theelectronic processing system. Preprinted plottingforms are not advised.6.13.1 Unit value hydrographsThe electronic processing system should allow thehydrographer to choose any of the unit values filesfor hydrograph plotting. Generally, hydrographsshowing unit values of discharge will be of mostinterest, but other unit values hydrographs, such asgauge height, elevation and reservoir contents alsomay be required. Other unit values files ofsupplementary information, such as for shifts,gauge-height corrections, auxiliary gaugeinformation and others should be superimposed onthe same plot if these additional parameter plotsare specified. Also, unit value information fromother gauging stations, precipitation stations andtemperature stations should be superimposed onthe same plot, as specified by the hydrographer.When more than one unit values file is shown on aunit values hydrograph plot, each should be clearlyidentified by a distinctive plotting symbol.Individual scales should be shown for eachparameter, labeled with the correct parameter nameand units of measurement.The abscissa scale for a unit values hydrograph plot istime, with hours being the primary unit of subdivision.Each day, month and year are shown as secondarysubdivisions. The ordinate scale should conform tothe parameter being plotted. Discharge scales shoulddefault to logarithmic but should be changeable tolinear if specified. All other scales, such as for gaugeheight, elevation, shifts, rainfall, temperature andothers, should default to linear scales. The range ofthe ordinate scale should default to one that willinclude the full range of the plotted unit values filebut should be changeable to any specified range.6.13.2 Daily value hydrographsA daily values hydrograph is one of the most commonmethods for displaying the results of streamflowcomputations for a gauging station. This hydrographusually is an annual plot showing the daily valuesfor a water year but can be for any other period oftime. Daily value hydrographs usually are plots ofdaily mean discharge for a gauging station, withcomparative hydrograph plots of daily meandischarge for one or more nearby gauging stations.For some stations, the daily values hydrograph alsomay include daily values of precipitation and/ortemperature. Daily values hydrographs also can beused to display other parameters, such as gaugeheight, elevation and reservoir contents.When more than one daily values file is shown ona daily values hydrograph plot, each should beclearly identified by a distinctive plotting symbol.Individual scales should be shown for eachparameter, labeled with the correct parameter nameand units of measurement.The abscissa for daily values hydrographs is a timescale, with days being the primary subdivision.Months and years are secondary subdivisions. Theordinate should be logarithmic for discharge plots,unless otherwise specified by the hydrographer.Other daily values parameters should be plottedusing linear scales. The range of the ordinate scalefor the primary parameter should default to onethat will include the full range of the daily valuesfor the time period being plotted.6.14 Computation of extremesFor most discharge gauging stations it is requiredthat the maximum peak stage and discharge, thesecondary peak stages and discharges and theminimum discharge be computed for each wateryear. The maximum peak stage and discharge, and

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-47the minimum discharge are referred to as the annualpeak and annual minimum. Guidelines for thesecomputations are given in the following sections.6.14.1 Annual peak stage and dischargeThe annual peak stage and discharge are defined asthe highest instantaneous (unit value) gauge heightand discharge associated with the highest floodpeak that occurred during the water year. Theannual peak stage and discharge and the associateddate and time, should be determined with theelectronic processing system. If the highest gaugeheight and discharge was at the beginning or end ofthe water year as a result of a recession from or riseto a peak that occurred in the previous or followingwater year, they should not be included as anextreme. For some gauging stations, thehydrographer may designate that the maximumdaily discharge be used rather than the maximuminstantaneous discharge.The annual instantaneous maximum gauge heightmay sometimes occur at a different time than theannual instantaneous maximum discharge. Inthese cases, the annual maximum instantaneousdischarge should be determined and the gaugeheight corresponding (at the same date and time)to this discharge. In addition, the annual maximuminstantaneous gauge height should be determinedand also the discharge corresponding (at the samedate and time) to this gauge height. Dates andtimes for both pairs of values should bedetermined.6.14.2 Secondary peak stages anddischargesSecondary peak stages and discharges are thosepeaks that are less than the annual peak stage anddischarge, but greater than a specified base discharge.Furthermore, the secondary peaks must conform toguidelines that insure their independence. That is,to provide reasonable certainty that a peak has notbeen influenced, or affected, by another peak. Theseguidelines are described by Novak (1985) and aregiven as follows:“Two peaks are considered independent if thehydrograph recedes to a well-defined troughbetween the peaks. Publish both peaks if theinstantaneous discharge of the trough is equalto or less than 75 per cent of the instantaneousdischarge of the lower peak; otherwise publishonly the higher peak.For small, highly responsive watersheds, onlythe highest peak discharge resulting from anobvious single storm event should be reportedregardless of the trough configuration ormagnitude between peaks.For periods of diurnal peaks caused by snowmelt,report only the highest peak during eachdistinct period of melting, if such periods canbe identified, even though other peaks maymeet the preceding criteria. Identification ofeach distinct period of melting is largely amatter of individual judgment, but the principleas explained in paragraph 1 above forinstantaneous discharges can be applied to dailydischarges as an identification guide.”All secondary peak stages and discharges should bedetermined with the electronic processing system.In addition, the date and time for each secondarypeak should be determined.6.14.3 Annual minimum dischargeThe annual minimum discharge is defined as thelowest instantaneous (unit value) discharge thatresults during the water year. For some gaugingstations, the hydrographer may specify that thelowest daily discharge be determined as the annualminimum discharge. In either case, the electronicprocessing system should determine the annualminimum discharge and the associated date andtime (if applicable) for the water year.6.15 Estimating missing recordsComplete records of daily discharges, and otherparameters, are necessary in order to computemonthly and annual totals and other statistics.Complete records also are needed to compute totalrunoff from a drainage basin, to calibrate runoffmodels and to compute chemical and sedimentloads. Data sometimes are missing because ofinstrument failures and other reasons, thus notpermitting the normal computation of daily records.Also, normal computation methods may not beapplicable at times such as during backwater fromice, debris or other abnormal stream conditions.Therefore, it is necessary to make estimates ofdischarge or other hydrologic parameters for theseperiods of missing record.The electronic processing system should allow thehydrographer to estimate both unit values and dailyvalues. However, estimation of missing recordsshould be kept to a minimum, and usually shouldbe limited to those parameters that will be publishedand to those parameters that may be required forthe purpose of computing a published parameter.

II.6-48manual on stream gaugingFor example, in some cases it may be reasonable toestimate unit values of gauge height for the purposeof computing daily values of discharge, providedthe gauge heights can be estimated with reasonableaccuracy. The electronic processing system shouldprovide estimating methods that commonly areaccepted but the hydrographer must be able tointeract and apply unique site specific informationand procedures in order to make the best estimateof missing records. Several estimating techniquesare described in the following sections.6.15.1 Hydrographic and climaticcomparison methodThe hydrographic and climatic comparison method,as described in Chapter 1 of this Volume, is themost common method used to estimate dischargeduring periods of missing record and ice-affectedperiods. A semi-logarithmic hydrograph of dailydischarge is plotted, encompassing the period ofmissing record, and valid records for periods priorto and after the missing record period. Other dataand information, as shown below, may besuperimposed on this plot to aid in the estimationprocedure:(a) Hydrographs of nearby stations (referencesites);(b) Hydrographs based on the direct application ofice-affected gauge heights to the rating (withoutcorrection for ice-induced backwater);(c) Daily or hourly precipitation;(d) Daily temperature, and/or daily maximum andminimum temperatures;(e) Discharge measurements;(f) Recession curves for the station beingestimated;(g) Notes and observations (for example, observedice conditions).The electronic processing system should allowvertical and horizontal repositioning of thehydrograph of the reference site (or sites) until itcorresponds as closely as possible to the availablegood record of the site to be estimated. When longperiods of missing record must be estimated, thisrepositioning process may need to be performedvarious times, each time for a different segment ofthe missing period. Values of daily mean dischargeare then estimated by using the reference site as aguide and drawing a hydrograph for the missingperiod, taking into account all of the other availabledata and information, such as the dischargemeasurements, climatic data and notes. Thisestimation process is performed by the hydrographeron the electronic processing system monitor, Afterthe estimated hydrograph segment is completedand accepted by the hydrographer, the electronicprocessing system automatically should determinethe daily values of discharge, flag the values asestimated, and insert them into the daily valuesfile.A period of missing record resulting during anunbroken recession can be estimated by connectingthe adjacent periods of good record with a straightline or a smooth recession curve on a semilogarithmicplot. This procedure is improved ifrecession curves, within the range of discharge tobe estimated, are available for the station in questionto superimpose on the plot. Recessions also mayvary by season; therefore, it is useful to categorizethe recession curves by season of the year. Thehydrographer should be able to re-position therecession curves vertically and horizontally toobtain the best fit of the recession curves. Theelectronic processing system should allow for thestorage, and later recall, of recession curve data forthis purpose.6.15.2 Discharge ratio methodThe discharge ratio method is used for estimatingdischarge during ice-affected periods and isdescribed in Chapter 1 of this Volume. The electronicprocessing system should automatically displaycomputed correction factors, K, for each dischargemeasurement on a semi-logarithmic plot, alongwith the equivalent open-water daily dischargehydrograph and the climatic data. The hydrographershould define the interpolation between computedK values, and the electronic processing systemshould then compute daily values of dischargebased on the interpolated K values and the openwater discharges. Daily values files of the openwaterdischarge and the corresponding correctionfactors, K, should be saved and archived for all iceaffectedperiods.6.15.3 Regression methodMultiple, stepwise, regression is a useful method ofrelating time series discharge data of one gaugingstation to concurrent time series discharge data of anearby reference gauge(s). Regression equations canbe developed for specific ranges of discharge, forinstance, low flows, medium flows and/or highflows. They also can be developed for seasonalperiods and for ice-affected periods. The electronicprocessing system should provide a flexible methodof developing regression equations, allowing thehydrographer to specify reference gauge records,time periods and discharge ranges. The regressionequations should include the ability to time-lag

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-49reference gauge records, and to use transformationsof discharges (for example, logarithmic). Also,developed regression equations and their associatedlimitations should be documented and archived forlater use.A useful addition to the regression method is toplot the 95 per cent confidence limits about thepredicted discharges. When the observed dischargesfall outside the confidence limits for several days ormore, there is an indication of error in the dischargerecord, such as an incorrect shift analysis. Thisassumes, of course, that there is a strong correlationbetween the base gauge and the reference gauge.A regression equation can be applied to provideestimated discharges for periods of missing record.In addition, the same regression equation shouldbe used to compute discharge values for short timeperiods adjacent to the estimated period wheredischarges are known. These adjacent periodssometimes can be used for verifying the accuracy ofthe regression results, and for adjusting theestimated discharges during the period of missingrecord to more closely fit the adjacent knownrecords.6.15.4 Water-budget methodRecords missing for a gauging station just upstreamfrom a reservoir, for the purpose of measuring inflowto the reservoir, can be estimated using the waterbudgetmethod if accurate records are available forthe outflow from the reservoir and the change incontents of the reservoir. The daily inflow to thereservoir is equal to the daily outflow plus or minusthe change in reservoir contents. In some cases, wherethe flow at the inflow station may not represent thetotal inflow to the reservoir, an adjustment may berequired. The adjustment may be simply theapplication of a drainage area ratio, or othermultiplication factor supplied by the hydrographer.The adjustment factor can also be estimated byapplying the water-budget equation during periodswhen inflow, outflow and storage records are allavailable. The water-budget method is:( Q + ΔC)Q = K(6.26)iowhere Q i= flow at inflow gauge; Q o= outflow fromreservoir; K = inflow adjustment factor and ∆C =change in contents of reservoir, computed asmidnight contents on current day minus midnightcontent on previous day.The same principle can be used to estimate missingoutflow records for gauging stations located justdownstream from a reservoir. Equation 6.26 simplyis rearranged to solve for outflow, Q o.6.15.5 Mathematical translation methodThe mathematical translation method is a set ofvarious mathematical functions that can be used totranslate streamflow records for other gaugingstations (referred to as reference gauges) intoestimates of streamflow for the gauge site wheremissing records result. Some of these functions aresimilar to the regression method described previouslybut are defined independently from regressionmethods. The selection of reference gauges to use formaking an estimate is important because thereference stations should be hydrologically relatedto the station for which estimates are made. For thisreason reference stations usually are nearby stations,have similar runoff characteristics and are sometimesstations on the same stream. The hydrographershould use considerable care and judgment inselecting stations to use with the mathematicaltranslation method. This method includes thefollowing mathematical functions:(a) Combining two streamflow records by addition,subtraction, multiplication or division;(b) Transforming a streamflow record into adifferent record using:Q = a + b Q + c(6.27)e( ) drwhere Q e= estimated discharge; Q r= discharge atreference gauge and a, b, c, and d, are constantsdefined by the hydrographer;(c) Offsetting a reference gauge record by aspecified time period. The offset record canbe mathematically combined with anotherreference record or can be transformed by anequation. Two or more reference records can beoffset with the same, or different, offsets;(d) Transformation of reference gauge records intolog10 and inverse log10. These transformationscan be made prior to performing any of theabove mathematical functions.6.15.6 Flow routing methodsVarious flow routing models can be used to route astreamflow record from a reference gauge to adownstream location on the same stream, therebyproviding an estimate of the flow at a downstreamgauge site. However, these models are used externalto the electronic processing system, and the resultsmust be imported to the streamflow data base.Generally, it is not expected that such models willbe used very often for estimating streamflow recordsbecause of the complex and intense efforts neededfor calibration and application.

II.6-50manual on stream gauging6.16 Monthly and annual valuecomputationsMonthly and annual values of stage, elevation,discharge, runoff, reservoir contents and tidallows and highs should be computed for eachstation as required or designated. The requiredand designated monthly and annual values willvary with station type and with specific stations.All computations of monthly values should bebased on the rounded results of daily values andall computations of annual values should bebased on rounded results of either daily ormonthly values, as indicated. Therefore,consistent agreement results amount the daily,monthly and annual values.At least two sets of annual values should becomputed for each gauging station: (a) for thecalendar year, January through December and(b) for the water year, October through September.In special cases the hydrographer may designateadditional or alternative types of years, such as theclimatic year, April through March.6.16.1 Monthly and annual valuesof stageMonthly and annual values of stage should becomputed for those stations where stage routinelyis measured for defining the gauge-heightfluctuations of a stream. For some stations, the stagemay be the primary end product, such as for a stageonlystation. In other instances the stage may bemeasured for the purpose of computing otherparameters, such as discharge.The monthly stage values that should be computedare the following:(a) Monthly mean stage – The arithmetic mean ofall daily mean stages for each month;(b) Monthly minimum daily stage – The lowestdaily mean stage for each month;(c) Monthly maximum daily stage – The highestdaily mean stage for each month.The annual stage values that should be computedare the following:(a) Annual mean stage – The arithmetic mean ofall daily mean stages for the water year andcalendar year;(b) Annual minimum daily stage – The lowest dailymean stage for the water year and calendaryear;(c) Annual maximum daily stage – The highestdaily mean stage for the water year and calendaryear.6.16.2 Monthly and annual values ofdischargeMonthly and annual values of discharge should becomputed for gauging stations where daily dischargeis routinely computed and where streamflow is theparameter of primary interest. Some of the monthlyand annual values are required, whereas others areoptional, and are computed only for specificgauging stations. The optional computationsgenerally are designated on the basis of streamflowconditions, drainage basin size, natural runoffconditions, degree of regulation and other factorsthat may affect the hydrologic value and need forthe computed parameters.The monthly discharge values that are required arethe following:(a) Monthly total discharge – Total of all dailymean discharges for each month;(b) Monthly mean discharge – The mean ofall daily mean discharges for each month,and is computed by dividing the monthlytotal discharge by the number of days in themonth;(c) Monthly minimum daily discharge – The lowestdaily mean discharge for each month;(d) Monthly maximum daily discharge – Thehighest daily mean discharge for eachmonth.The monthly discharge values that are optional areas follows:(a) Monthly runoff volume – This is the monthlytotal discharge, converted to a volume;(b) Monthly runoff depth – The monthly totaldischarge volume, converted to a depth, ininches or millimetres, that would uniformlycover the drainage basin;(c) Monthly mean unit runoff – The monthlymean flow that would emanate from 1 mi 2or 1 km 2 of drainage area, if the flow wereuniformly distributed throughout the drainagebasin.The annual discharge values that are required are asfollows:(a) Annual total discharge – The total of all dailymean discharges for the year;(b) Annual mean discharge – The mean of all dailymean discharges for the year, and is computedby dividing the annual total discharge by365 or by 366 for leap years;(c) Annual minimum daily discharge – The lowestdaily mean discharge for the year;(d) Annual maximum daily discharge – The highestdaily mean discharge for the year.

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-51The annual discharge values that are optional are asfollows:(a) Annual runoff volume – The annual total runoffvolume is computed by summing the monthlyvalues of runoff volume for the year;(b) Annual runoff depth – The annual total runoffdepth is computed by summing the monthlyvalues of runoff depth for the year;(c) Annual mean unit runoff – The annual meanunit runoff is computed by dividing the annualmean discharge by the drainage area.6.16.3 Monthly and annual values forreservoirsThe computation of monthly and annual valuesfor reservoir stations is varied and highlydependent on the type of daily values that areused for the station. Reservoir stations mayrequire daily mean elevations, daily meancontents or elevation or contents at a specifictime, The choice of daily values that are used andpublished for a reservoir station is dependent onhydrographer requirements, and consequently,the monthly values that should be computed willbe based on these.6.16.4 Monthly and annual values for tidalstationsTidal stations require the computation of variousmonthly and annual values as described below. Fortidal stations that use an arbitrary gauge-heightdatum and a datum-conversion constant to convertthe gauge heights to national datum, such as meansea level, the monthly and annual values should becomputed for both datums.The monthly tide values that may be computed areas follows:(a) Monthly mean stage and/or elevation – Themean of all daily mean stages and/or elevationsfor each month;(b) Monthly mean high tide – The mean of alldaily HIGH-HIGH tide stages and/or elevationsfor each month;(c) Monthly mean low tide – The mean of all dailyLOW-LOW tide stages and/or elevations foreach month;(d) Monthly minimum low tide – The lowest of alldaily LOW-LOW tide stages and/or elevationsfor each month;(e) Monthly maximum high tide – The highestof all daily HIGH-HIGH tide stages and/orelevations for each month.The annual tide values that may be computed are asfollows:(a) Annual mean stage and/or elevation – The meanof all daily mean stages and /or elevations forthe year;(b) Annual mean high tide – The mean of all dailyHIGH-HIGH tide stages and/or elevations forthe year;(c) Annual mean low tide – The mean of all dailyLOW-LOW tide stages and/or elevations for theyear;(d) Annual minimum low tide – The lowest of alldaily LOW-LOW tide stages and/or elevationsfor the year;(e) Annual maximum high tide – The highest of alldaily HIGH-HIGH tide stages and/or elevationsfor the year.6.17 Station analysis documentationThe station analysis documentation is a narrativedescription of the methods used to analyze thegauging station records for a water year or otherperiod of analysis. The analysis includes informationabout station equipment, performance of the gaugeand related equipment, the rating, shifting controlmethods, computation of discharge, accuracy andany other information about how the stationrecords were produced. The station analysis is oneof the most important documents produced foreach year of gauging station records because it isthe primary documentation for quality assuranceand quality control of these records.The station analysis for a gauging station usually iswritten and finalized at the end of each water year,however, parts of it may be written at any timeduring the year as information becomes available.The electronic processing system should providesome form of record processing notebook that canbe utilized as an aid in writing the station analysis.The electronic processing system automaticallyshould transfer information from the recordprocessing notebook to the appropriate paragraphsof the station analysis.The electronic processing system also shouldautomatically transfer information from other partsof the electronic processing system to the stationanalysis to assist the hydrographer. These includethe following:(a) Level and datum information from the mostrecent level summary. This information shouldinclude the date of the latest levels, and informationabout datum differences of the variousgauges at the station;

II.6-52manual on stream gauging(b) All periods (dates) of missing record, and thetotal number of days of missing record fromthe unit values files;(c) The minimum and maximum gauge heightsrecorded during the water year from the unitvalues files;(d) The number of discharge measurements madeduring the water year, and their correspondingsequence numbers, from the measurementfile. In addition, the lowest and highestmeasured gauge height and discharge from themeasurement file;(e) The comparison of measured dischargesto computed unit values of discharge fromthe measurement file and the primarycomputations;(f) Methods of estimating missing records and icerecords from the electronic processing systemdocumentation of estimating missing recordsfor the water year;(g) The listing of records used for hydrographcomparisons from the electronic processingsystem documentation of hydrographcomparisons used for the water year. This listingshould include station names, parameterscompared and periods of record compared;(h) The sequence numbers for the rating curvesand the shift curves used during the water yearfrom the rating curve file and the shift curvefile;(i) Any information relative to quality controlfrom field notes, record processing notebookand comment files that have been documentedin the electronic processing system.The transferred information, both from the recordprocessing notebook and the various other parts ofthe electronic processing system, can then be usedto write the station analysis. The station analysisshould include, at a minimum, the following itemsand paragraphs. For some gauging stations, otherparagraphs may be required in order to adequatelydescribe the computation methods. For example,for velocity-index stations there should be a velocityrecord section. See Kennedy (1983) for additionaldetails:(a) Station name;(b) Station ID;(c) Water year;(d) Equipment;(e) Gauge-height record;(f) Gauge-height and datum corrections;(g) Rating;(h) Discharge;(i) Quality assurance and control;(j) Remarks;(k) Recommendations.The name of the hydrographer who writes thestation analysis and the date of preparationautomatically should be attached to the end of thestation analysis. Also, the name of the reviewerautomatically should be attached, along with thedate of review completion.ReferencesCollins, D.L., 1977: Computation of records of streamflowat control structures. United States Geological SurveyWater-Resources Investigations Report 77-8, 57 p.Dempster, George R., Jr., 1990: National water informationsystem user’s manual. Volume 2, Chapter 3,Automated data processing system. United StatesGeological Survey Open-File Report 90-116.Hutchison, N.E., and others, 1977: WATSTORE user’sGuide. Volume 5, Chapters I-IV: United StatesGeological Survey Open-File Report 77-729-I,230 p.International Organization for Standardization, 2001:Measurement of liquid flow in open channels –Stage-fall-discharge relationships; ISO 9123, 14 pp.Kennedy, E.J., 1983: Computations of continuous recordsof streamflow. United States Geological SurveyTechniques of Water-Resources Investigation Report,Book 3, Chapter A13, 53 p.Kennedy, E.J., 1984: Discharge ratings at gaging stations.United States Geological Survey Techniques ofWater- Resources Investigation Report, Book 3,Chapter A10, 59 p.Kennedy, E.J., 1990: Levels at streamflow gaging stations.United States Geological Survey Techniques ofWater-Resources Investigation Report, Book 3,Chapter A19, 31 p.Marsh, J.J. and Stephenson, P.M., 1976: Surface waterdata processing – A guide to practice. Department ofthe Environment, Water Data Unit, Reading,United Kingdom.Oberg, K.A., Morlock, S.E., and Caldwell, W.S., 2005:Quality-Assurance Plan for Discharge MeasurementsUsing Acoustic Doppler Current Profilers. United StatesGeological Survey Scientific Investigations Report2005-5183.Novak, C.E., 1985: WRD data reports preparation guide.United States Geological Survey Open-File Report85- 480, 199 p.Rantz, S.E., and others, 1982: Measurement andcomputation of streamflow. Volumes 1 and 2,United States Geological Survey Water-Supply Paper2175, 631 p.Ruhl, C.A., and Simpson, M.R., 2005: Computation ofdischarge using the index-velocity method in tidallyaffected areas. United States Geological SurveyScientific Investigations Report 2005-5004, 31 p.

Chapter 6. Analysis and COMPUTATI**ON** OF DISCHARGE RECORDS using electronic methodsII.6-53Sanders, Curtis L., Jr., and Feaster, Toby D., 2004:Computation of flow through water-control structuresusing program DAMFLO.2. United States GeologicalSurvey Open-File Report 03-473, 99 pp.Sauer, V.B., 2002: Standards for the analysis and processingof surface-water data and information using electronicmethods. United States Geological Survey Water-Resources Investigations Report 01-4044, 92 pp.Schaffrannek, R.W., Baltzer, R.A., and Goldberg, D.E.,1981: A model for simulation of flow in singular andinterconnected channels. United States GeologicalSurvey Techniques of Water Resources InvestigationReport, Book 7, Chapter C3, 110 p.Shearman, J.O., 1990: User’s Manual for WSPRO –A computer model for water surface profilecomputations. Federal Highway AdministrationPublication No. FHWA-IP-89-027, 177 p.United States Geological Survey, 2005: User’s Manualfor the national water information system of theUnited States Geological Survey – AutomatedProcessing System (ADAPS). United StatesGeological Survey Open-file report Version 4.5,415 pp.World Meteorological Organization, 1971: MachineProcessing of Hydrometeorological data (**WMO**-No. 275),Technical Note No. 115, 79 pp.

For more information, please contact:Associated Programme on Flood Managementc/o Hydrology and Water Resources DepartmentWorld Meteorological OrganizationTel.: +41 (0) 22 730 84 79 – Fax: +41 (0) 22 730 80 43E-mail: apfm@wmo.int7 bis, avenue de la Paix – P.O. Box 2300 – CH-1211 Geneva 2 – Switzerlandwww.apfm.info