MANUAL ON STREAM GAUGING - E-Library - WMO

More documents

Recommendations

Info

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<strong>ON</strong>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
Page 1: QualityManagementFrameworkMANUAL ON
Page 4 and 5: WMO-No. 1044© World Meteorological
Page 6 and 7: ivmanual on stream gauging1.13.2 Fr
Page 8 and 9: vimanual on stream gauging6.5.4 Par
Page 11: PREFACEWith the adoption by the WMO
Page 16 and 17: xivMANUAL ON STREAM GAUGINGкото
Page 18 and 19: xviMANUAL ON STREAM GAUGINGse prese
Page 20 and 21: xviiiMANUAL ON STREAM GAUGINGfreque
Page 23 and 24: Chapter 1Discharge ratings using si
Page 25 and 26: Chapter 1. Discharge ratings using
Page 27: Chapter 1. Discharge ratings using
Page 63: Chapter 1. Discharge ratings using
Page 66 and 67: II.2-2manual on stream gaugingcurre
Page 68 and 69: II.2-4manual on stream gaugingtabul
Page 70 and 71: II.2-6manual on stream gaugingDelta
Page 72 and 73: II.2-8manual on stream gaugingVELOC
Page 74 and 75: II.2-10manual on stream gaugingMEAN
Page 76 and 77: II.2-12manual on stream gaugingMorl
Page 78 and 79:
II.3-2manual on stream gaugingafter
Page 80 and 81:
II.3-4manual on stream gaugingsteep
Page 82 and 83:
II.3-6manual on stream gaugingGAUGE
Page 84 and 85:
II.3-8manual on stream gauging1.0DI
Page 86 and 87:
II.3-10manual on stream gauging1.00
Page 88 and 89:
II.3-12manual on stream gauging(ii)
Page 90 and 91:
II.3-14manual on stream gaugingBy c
Page 92 and 93:
II.3-16manual on stream gauging1413
Page 94 and 95:
Page 96 and 97:
II.3-20manual on stream gauginga se
Page 98 and 99:
II.4-2manual on stream gauging4.2 T
Page 100 and 101:
II.4-4manual on stream gaugingTable
Page 102 and 103:
II.4-6manual on stream gaugingCOLUM
Page 104 and 105:
II.4-8manual on stream gaugingDISCH
Page 106 and 107:
II.4-10manual on stream gaugingScha
Page 108 and 109:
II.5-2manual on stream gauging(iv)
Page 110 and 111:
II.5-4manual on stream gaugingCrest
Page 112 and 113:
Page 114 and 115:
II.5-8manual on stream gauging(cont
Page 116 and 117:
II.5-10manual on stream gaugingh 1=
Page 118 and 119:
II.5-12manual on stream gaugingdeve
Page 120 and 121:
II.5-14manual on stream gaugingupst
Page 122 and 123:
II.5-16manual on stream gaugingthat
Page 124 and 125:
II.5-18manual on stream gauging(b)
Page 126 and 127:
II.5-20manual on stream gaugingComp
Page 128 and 129:
II.5-22manual on stream gaugingflow
Page 130 and 131:
II.5-24manual on stream gaugingPres
Page 132 and 133:
II.5-26manual on stream gaugingin o
Page 134 and 135:
II.5-28manual on stream gaugingCond
Page 136 and 137:
II.5-30manual on stream gaugingdisc
Page 138 and 139:
II.5-32manual on stream gauging(ii)
Page 140 and 141:
II.5-34manual on stream gaugingmaxi
Page 143 and 144:
Chapter 6Analysis and COMPUTATION O
Page 145 and 146:
Chapter 6. Analysis and COMPUTATION
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
Page 193 and 194:
Page 195:
show all

MANUAL ON STREAM GAUGING - E-Library - WMO

Create successful ePaper yourself

Delete template?

Save as template?