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WORLD METEOROLOGICAL ORGANIZATIONTECHNICAL NOTE No. 91METHODS IN USEFOR THE REDUCTIONOF ATMOSPHERIC PRESSUREIWMO· No. 226.TP. 120ISecretariat of the World Meteorological Organization • Geneva • Switzerland

SUMMARYThe information received from 107 Members shows that one may now generally distinguish betweenthree main 'categories of pressure reduction methods:(a)(b)(c)Method based on a formula of Laplace in which the geometric altitude of the station elevationis entered and a correction for humidity is, in most cases, neglected;Method recommended in Technical Note No. 61, in which geopotential units are used and acorrection for humidity is, in most cases, taken into account;Other methods which are a mixed variation of the first two or are based on an approximativeformula designed for special cases.In the present Technical Note, countries are listed under one of these categories, according to themethod used. The formula of Laplace and the recommended hypsometric equation are described in somedetail in the relevant chapters, enabling a ready comparison between these two methods.RESUMEJl ressort des renseignements obtenus de 107 Membres que, d'une maniere generale, on peut maintenantclasser les methodes de reduction de la pression en trois categories principales:a) la methode, basee sur u~e formule de Laplace, dans laquelle on fait intervenir l'altitude geometriquedu niveau de la station, mais oD. l'on omet, dans la plupart des cas, le facteur de correction del'humidite;b) la methode, recommandee par la Note technique N° 61, dans laquelle on utilise les unites degeopotentiel et oD. l'on tient compte, dans la plupart des cas, du facteur de correction de l'humidite;c) d'autres methodes qui sont une combinaison des deux precedentes ou qui sont basees sur uneformule approximative mise au point pour des cas speciaux.Dans la presente Note technique, les pays sont classes dans l'une de ces categories selon la method\qu'ils appliquent. La formule de Laplace et l'equation hypsometrique recommandee sont exposees en detaildans les chapitres correspondants, ce qui permet de compareI' facilement ces deux methodes.VII

PE310MEliIH(I)OpMa~~HI, rrOJIy'IeHHaH OT 107 lIJIeHOB, rrOKa3bIBaeT, 'ITO B HaCTOHlI\ee BpeMH Boo61I\e MOiKHOBMAeJIHTb TpH OCHOBHMX KaTeropHH MeTOAOB rrpHBeAeHHH AaBJIeHHH:a) MeTOA, OCHOBbIBaIOII\HMCH Ha epopMyJIe JIarrJIaca, B KOTOpyIO BXOAHT reOMeTpH'IeCKaH BMCOTaCTaH~HH, H B 60JIbIlIHHCTBe CJIy'IaeB He y'IIITbIBaeTCH rrorrpaBKa Ha BJIaiKHOCTb,b) MeToA, peKoMeHAoBaHHbIM B TeXHH'IeCKOM 3arrIICKe ;AA 61, B KOTOpOM IICrrOJIb3YIOTCH reorrOTeH­~IIaJIbHble eAHHH~bI, II B 60JIbIlIIIHCTBe CJIy'IaeB y'IIITbIBaeTCH rrorrpaBKa Ha BJIaiKHOCTb,c) ApyrHe MeTOAM, KOTOpbIe rrpeACTaBJIHIOT C060M CMeCb rrepBbIX ABYX IIJIII OCHOBbIBaIOTCH HarrpH6JIIIiKeHHOM epopMYJIe, rrpeAHa3HaQeHHOM AJIH Crre~IIaJIbHMX CJIy'IaeB.B HaCTOHlI\eM TeXHH'IeCKOM 3arrHCKe CTpaHbI rrepe'IIICJIHIOTCH rrOA OAHOM H3 3TIIX KaTeropIIit B COOT­BeTCTBIIII C rrpHMeHHeMMM MeTOAOM. B COOTBeTCTBYIOII\IIX rJIaBaX AaeTCH AOBOJIbHO rroAPo6Hoe orrIIcaHHeepOPMYJIM JIarrJIaca H peKOMeHAOBaHHoro rIIrrCOMeTpII'IeCKOrO ypaBHeHIIH, 'ITO AaeT B03MOiKHOCTb rrpo­BeCTII JIerKOe cpaBHeHHe MeiKAY 3TIIMII AByMH MeTOAaMII.RESUMENDe la informaci6n recibida de 107 Miembros, se puede deducir que, en general, los metodos de reducci6nde la presi6n pueden actualmente clasificarse en tres categorias principales:a) metodo fundado en una f6rmula de Laplace, en la que se tiene en cuenta la altitud geometricade la elevaci6n de la estaci6n y se omite, en la mayoria de los casos, el factor de correcci6n de lahumedad;b) metodo recomendado en la Nota Tecnica N° 61, en el que se utilizan las unidades de geopotencialy se tiene en cuenta, en la mayoria de los casos, el factor de correcci6n de la humedad;c) otros metodos basados en una combinaci6n de los dos citados precedentemente 0 fundados en unaf6rmula aproximativa elaborada para casos especiales.En esta Nota Tecnica, los paises estan clasificados, segun el metodo que utilicen, en una de las trescategorias anteriores. En los capitulos correspondientes, se exponen detalladamente la formula de Laplacey la ecuaci6n hipsometrica recomendada, 10 que permite la Hcir comparaci6n de ambos metodos.VIII

CountryMethodusedPage11CountryMethodused111Ireland A 8 Romania AIsrael A 7 Rwanda C 1Italy A 5 Saudi Arabia B, C 1Jamaica A 8 Senegal B 1Japan C 13 Sierra Leone AJordan B 12 Singapore AKenya A 5 Somalia AKorea (Republic of) A 5 South Africa C 1Kuwait A 8 Southern Rhodesia C 1)Laos A 5 Spain ALebanon A 5 Sudan ALibya B 12 Surinam CLuxembourg C 15 Sweden B 1)Madagascar B 12 Switzerland AMali B 12 Syria BMauritius A 8 Tanzania AMorocco A 5 Thailand Aetherlands B 12 Togo B 1etherlands Antilles C 16 Trinidad and Tobago Aew Caledonia C 14 Tunisia ANew Zealand A 8 Turkey C 1Iger B 12 Uganda AIgena A 8 U.S.S.R. AJorway B 12 U.A.R. A lPakistan A 9 U.K. A (Peru C 17 U.S.A. B 1.Philippines C 17 Upper Volta B 1Poland A 7 Uruguay A lPortugal B 12 Viet-Nam APortuguese East Africa A 5 Yugoslavia BIi1lPortuguese "Vest Africa A 5 Zambia C V

METHODS USED BY METEOROLOGICAL SERVICES FOR REDUCING PRESSURETO MEAN SEA·LEVELIntroductionAt its extraordinary meeting in Paris, March 1951, the Conference of Directors of the InternationalMeteorological Organization (IMO, the predecessor of WMO) decided to cancel all existing IMOresolutions concerning the reduction of pressure to mean sea-level, except Resolution 144 (CD Washington,1947). Part of this resolution requested:"Meteorological Services to publish a description of the method of reduction in use, and thatthe method of reduction be indicated on all published maps and/or tables containing pressures reducedto a fixed level or values of the geopotential (height) of a standard isobaric surface above the station."From numerous letters received by the Secretariat, it appeared necessary to obtain a more completeknowledge of the methods of pressure reduction used by various Meteorological Services and to makethese methods known to all th~se interested. The information would also contribute to the study of thestandardization of methods of reduction being undertaken by Cl 10. In a circular letter of 13 August 1952,the Secretary-General therefore drew the attention of all Meteorological Services to this question, askingthem to supply the Secretariat as soon as possible with a statement of the methods used for reducingatmospheric pressure at meteorological stations. The replies received to the circular letter supplemented byadditional information are summarized in Part 1 of WMO Technical ote No. 7 (1954).At its second session ( ew Delhi, 1958), the Commission for Synoptic Meteorology established aworking group on pressure reduction methods. The group was requested to select certain methods ofpressure reduction which, after appropriate trials, might be recommended for use in various regions ofthe world. The final report of the group was published as WMO Technical Note No. 61 (1964). The mainpart of this Jote was devoted to the consideration of different methods of pressure reduction to mean sealeveland other levels, both below and above the station level. Recommendations were suggested thereinfor the practical use of pressure reduction methods in various cases.At its fourth session (Wiesbaden, 1966) the Commission for Synoptic Meteorology examined thereplies received from Members to an inquiry asking for comments on WMO Technical Note No. 61. TheCommission considered that the replies did not represent a clear consensus in favour of a uniform methodof reduction of pressure to mean sea-level, and therefore concluded that a standard method for reducingpressure was not yet acceptable for adoption on a world-wide basis. However, the Commission recommendedthat Members make further studies of pressure reduction methods which would facilitate introduction ofa world-wide standard method that would meet requirements of synoptic meteorology including numericalweather prediction. It furthermore requested the Secretary-General to obtain from Members completemathematical descriptions of pressure reduction method now being applied and to advise Members ofthis information in a suitable publication.In a circular letter of 30 May 1967, the Secretary-General asked Members to supply the Secretariatwith the information requested by the CSM. The present publication summarizes the replies in the sameform as ha previously been used in Part 1 of WMO Technical ote o. 7.A list of the most common symbols used in the text is given in the annex and other symbols areexplained where they appear in the text.

CHAPTER IMETEOROLOGICAL SERVICES USING THE "INTERNATIONAL?' FORMULA1.1 The "international" formulaThe "international" formula is the one which appears In the International Meteorological Tables,Paris, 1890.1.1.1 THE FORMULA OF LAPLACEThe basic formula given in the Tables is that of Laplace, viz:(1 ) ( Zp) po- cos rp r psZp = K (1 + aBm) 1 k 2 1 + - log-orZp =K (1 + aBm) (1 + E) (1 + Zp) log I!!:.r ps(1)where:ZpKaBmkrprpopsEgeometric altitude corresponding to the station elevationhypsometric constantcoefficient of expansion of airmean temperature of air column0.00259latitude of stationmean terrestrial radiuspressure at mean sea-levelpres ure at tation levelk cos 2 rpT . . p_o __ Bo (1 + 5_ Zp)akmg account of the approximatIOn ps Bs 4 rwhere: B o = height of mercury column (barometric height) at mean sea-levelB s = height of mercury column (barometric height) at station levelthe above equation (1) may with sufficient approximation be written:whereZp = K (1 + b + aOm) (1 + E) (1 + ~p) log ~:5Kb = 4" r log e = 0.00157(2)If correction is made for humidity, formulae (1) and (2) become respectivelZp = K (1 + aOm) (1 + E) (1 1 p) (1 + ~p) log ;:(3)and(1 ) ( Zp) B oZp = K (1 + b + aOm) (1 + E) 1 _ P 1 + r log B8(4)

4CHAPTER 0 rEwherefJ = 0.378 !!-c and17Bs + B o17 = 2Inserting the constants, equations (3) and (4) become, in metric units:Zp = 18400 (1 '+ 0.00367 Bm) (1 + 0.00259 cos 2q;) ( 1 ) (1 + 637~~04) log po. 1- 0.378 ~~ ps17and Zp = 18400 (1.00157 + 0.00367 Bm) (1 + 0.00259 cos 2q;) 1 ) ( 1 + 6371104 Zp) log 13 B o(1- 0.378 ~c s17and, in English units:Z~ = 60368.6 [1 + 0.002039 (B:n -32)J (1 + 0.00259 cos 2q;) ( t ) (1 + Z~ ) log po (7)1 _ 0.378 ~ 20902950 . . psandZ; = 60368.6 [1.00157 + 0.002039 (0:'-:- 32)] (1 +0.00259 cos 2'i') (1~01378~) (1 + 209~~950) log ~: (8)(5)(6)1.1. 2 ANGOT'S TABLESThe method of pressure reduction indicated by Angot (Annales du Bureau Central 1\1eteorologique,1878) has been the basis of the second type of table for pressure reduction given in the International M eteorologicalTables, Paris, 1890. A discussion of these tables is given in "\VMO Technical Note No. 7, page 18.eglecting the term BmZp , the metric formulae (6) and (5) above may be rewritten respectively:Zp = (18429 + 67.53 Bm + 0.003 Zp) (1 1 fJ) (1 + E) log ~: (9)or Zp = (18400 + 67.53 Bm + 0.003 Zp) (1 1 fJ) (1 + E) log ~: (10)PuttingZp , Zpm = 18429 + 67.53 Bm + 0.003 Zp and m = 18400 + 67.53 Bm + 0.003 Zpand neglecting the humidity and latitude correcting factors, the formulaem =B olog Bs(11 a)and m' = log popswill respectively give approximate values of Bo and po.From m = log !!...:: and m' = log poB spswe obtainor, by placingandAB = Bo- B s = Bs(10 m -1) and Ap = po - ps = ps (10 m ' -1)10 m - 1 = M and 10 m ' - 1 = M'AB =Ap =MxBsM'Xps(11. b)(12 a)(12 b)

4CHAPTERONEwhere/3 = 0.378 ~c and17Bs + B o17 = 2Inserting the constants, equations (3) and (4) become, in metric units:Zp = 18400 (1 '+ 0.00367 Bm) (1 + 0.00259 cos 2rp) ( 1 ) (1 + 63"'~~04) log po1 - 0.378 ~~ I ps17and Zp = 18400 (1.00157 + 0.00367 Bm) (1 + 0.00259 cos 2rp) ( 1 ) (1 + 637~~04) log ~o (6)and, in English units:1-0.378~c'7z; ~ 60368.6 [1 + 0.002039 (e~ -32)] (1 + 0.00259 '" 2.) (1 _ 0 1 378 ~) (1 + 209g~950) log ;: (7)andz; ~ 60368.6 [1.00157 + O. 002039 (e~~ 32)] (1 + 0.00259 00' 2.) (1-01378~) (1 + 209g~950) log ~: (8)s(5)1.1. 2 ANGOT'S TABLESThe method of pressure reduction indicated by Angot (Annales du Bureau Central l11eteorologique,1878) has been the basis of the second type of table for pressure reduction given in the I ntemational M eteorologicalTables, Paris, 1890. A discussion of these tables is given in WMO Technical Note No. 7, page 18.Neglecting the term BmZ p , the metric formulae (6) and (5) above may be rewritten respectively:Zp = (18429 + 67.53 Bm + 0.003 Zp) (1 1 /3) (1 + E) log ~:(9)orZp = (18400 + 67.53 Bm + 0.003 Zp) (1 1 /3) (1 + E) log ~:(10)PuttingZp , Zpm = 18429 + 67.53 Bm + 0.003 Zp and m = 18400 + 67.53 Bm + 0.003 Zpand neglecting the humidity and latitude correcting factors, the formulaem =B oB slog-(11 a)andm' =log popswill respectively give approximate values of B o and po.(Hb)Fromwe obtainor, by placingandm = log 1!...::. and m' = log poB spsLlB = B o- Bs = B s(10 m -1) and Llp = po - ps = ps (10 m ' -1)10 m - 1 = M and 10 m ' - 1 = M'LlB =Llp =MxB sM'Xps(12 a)(12 b)

THE"INTERNATIONAL" FORMULA5Similar formulae can be deduced from formulae (7) and (8) above, using English units.1.2 Versions of formula in which metric units are usedFrance. The following formula is used:10 po = Zpg ps 18429 + 67.53 em + 0.003 Zpwhere Bm is the mean temperature of the "air column" in QC,ZpBm = t s + 400and the vertical temperature gradient is taken as 0.5°C/l00 m.Correction for humidity is neglected. Correction for latitude is carried out separately.Pressure is reduced to mean sea-level only at stations whose altitude is less than 600 metres.Alternatively, the formula of Dedebant is used, in the form:JpZp . psJp = 7991 + 29.271 t s - 0.414 ZpIII which: t s all' temperature at the station, in degrees Celsiuscorrection to be applied to the pressure ps in order to obtain the pressure at meansea-level poThese two methods are stated to give equal results in practice, differences in po being res'tricted toabout one-tenth of a millibar.The "international" formula is used as in France by Algeria, Cambodia, Ethiopia (for stations whosealtitude is less than 500 metres), French Polynesia, French Territory of the Afars and the Issa, Laos, Lebanon,Morocco, Portuguese East Africa, Sudan, Thailand, Tunisia and Viet-Nam. In French Territory of theAfars and the Issa the vertical temperature gradient is taken as 0.65°C/l00 m.Italy and Somalia.Both as France, but em is calculated from3Zpem = t + s 1000indicating that the vertical temperature gradient is taken as 0.6°C/l00 m.Kenya, Tanzania and Uganda. As France, but taking em = t s • At stations situated more than600 metres above mean sea-level, the height of the 850-mb surface is computed.Portuguese West Africa. Formula (5) above is used, omitting the humidity correction.temperature of the "air column" is found byem =t + to2The vertical temperature gradient is taken as 0.65°C/l00 m.,The meanKorea. Formula (11 b) is used, taking the vertical temperature gradient as 0.5°C/l00 m and substitutingZpem = t s + 400Union of Soviet Socialist Republics. Three methods depending upon the station elevation are used forpressure reduction.

6 CHAPTER ONEA. For stations at an elevation of 100 metres or less a simplified barometric height formula is used:where: h station elevation in metrestemperature at the station15982 (1 + at) + hpo = ps 15982 (1 + at) - ha coefficient of expansion of air (a = 0.00367)For practical purposes the formula is used in the form:Jp po - ps [ 2 ]h = h = ps .15982 (1 + at)-hThe right-hand side of the formula is tabulated, with arguments ps and t and taking h =thus gives approximate pressure increments per metre elevation.1. The tableB. For stations at an elevation between 100 and 500 metres a reduced Laplace formula is used:I po Zpog ps = 18400 (1 + a(}m)C. For stations at an elevation greater than 500 metres the full Laplace formula is used (see formula (1)).However, for stations at an elevation of 300 metres or more the following equation is preferred:g Zppo = ps e - R (}vmIn which:and Zp IS(}vmcomputed frommean virtual temperature of the fictitious air column between sea-level and stationlevelZp = (g

6 CHAPTER ONEA. For stations at an elevation of 100 metres or less a simplified barometric height formula is used:where: h station elevation in metresID which:8 vmtemperature at the station15982 (1 + at) + hpo = ps 15982 (1 + at) - ha coefficient of expansion of air (a = 0.00367)For practical purposes the formula is used in the form:L1 p po - ps [ 2 ]T= h =ps .15982 (1+at)-hThe right-hand side of the formula is tabulated, with arguments ps and t and taking h =thus gives approximate pressure increments per metre elevation.1. The tableB. For stations at an elevation between 100 and 500 metres a reduced Laplace formula is used:1 po Zpog ps = 18400 (1 + a8m)C. For stations at an elevation greater than 500 metres the full Laplace formula is used (see formula (1)).However, for stations at an elevation of 300 metres or more the following equation is preferred:and Zp ISwhere:andwhere:andin which:computed fromgZppo= pse---R8vmmean virtual temperature of the fictitious air column between sea-level and stationlevelZp = ( g'l' - 0.0003086"2H)980Hacceleration of gravity in cm sec- 2 for latitude qJ at sea-levelelevation of the station, in metres.The vertical virtual temperature gradient T is computed fromyaTvTqvertical temperature gradientT=y+aL1factor indicating the vertical humidity gradient, calculated once only on the basisof mean annual vertical distribution of specific humidity estimated from daily radiosondedataL1 = T v - T = T (1 + 0.6059 q) - T = 0.6059 Tqvirtual temperatureobserved temperature, ID Of(specific humidityThus, the mean virtual temperature is determined byTH8vm = T + L1 + 2

THE " INTERNATIONAL"FORMULA 7Further particulars of these methods are given in (1) Instructions for the Hydrometservice Offices,No. 5, Gidrometeoizdat, Leningrad, 1951; (2) .Use of barometric formulae for pressure reduction to mean sealevel, Gidrometeoizdat, 1949; and (3) Instructions for the Hydrometservice Offices, No. 15, Gidrometeoizdat,Leningrad, 1954.Byelorussian S.S.R. uses the same formulae as given above for U.S.S.R.China. the international formula is used, neglecting the factors for latitude and gravity variationswith height, and also humidity correction.with1 po Zpog ps = 18400 (1 + a Bm)The same formula as given above for China is used by Israel (also for stations with an elevationexceeding 500 m) and, with the following variations of application, by Romania, Foland and Switzerland.Romania takes the coefficient of expansion of air as a = 0.00366 and the vertical temperature gradientas 0.5°Cj100 m. The mean temperature of the "air column" is found byFor t s the screen temperature is used.Bm=to+t s2Foland takes a = 273- 1 and the vertical temperature gradient as 0.5°Cj100 m. The mean temperatureof the "air column" is found byThe same formula and constants are used to determine the height of the 850-mb surface level fromthe pressure and temperature as read at mountain stations, substituting for po the value of 850 mb and forZp the thickness, in metres, of the layer between the pressure levels ps and 850 mb.Switzerland. The same formula as given above for China is used, but Switzerland applies it differently.The monthly mean value for the pressure difference between the pressure at station level and at MSL iscalculated. For reducing the pressure to MSL, this mean monthly value is added to the pressure at thestation.whereThis mean monthly value LIp is calculated by the formula:()mvZptmv + a 2Fom1og-=F smZp]((1 + aBmv)withandandtmvF omF sroNote:](mean virtual temperature at the station (mean monthly temperature based onhourly means, corrected according to mean vapour pressure)is the mean monthly pressure at sea-levelis the mean monthly pressure at the stationa is taken as 0.5°Cj100 m18458

8 CHAPTER ONESwiss international stations have used provisionally from May 1952 the following formula:whereBmvZpt + a 2andlog po =psZpK (1 + aBmv)a0.65°C/'100 metresGravity corrections are ignored.Chile also uscs thc international formula.Democratic Republic of Congo (see also page 12).log po =psThe following formula is used:Zp18428 + 74.38 (tm+ 0.00265 Zp)t m is the mean temperature of the station (screen temperature, 0C). This formula results from means madfrom radiosondes. It takes account implicitly of the virtual temperature tv, which is given by the followinempirical formula, the result itself of numerous statistics:Burundi. As Democratic Republic of Congo.tv = - 28.03 + 1.1029 tUnited Arab Republic. Formula (11) is used, but Bm is taken as equal to t.Spain uses the Intemational111eteorological Tables, Paris, 1890.Uruguay. As Spain, and taking the vertical temperature gradient equal to 0.65°C/l00 m and thwater vapour pressure equal to 11 mm mercury.1. 3 Versions of formula in which English units are usedwhere(a)(b)(c)United Kingdom. Angot's tables (paragraph 1.1.2 above) are used, based onIn this methodM = 10 ID -lZ' pm = 56525 + 123.1 B:n, + 0.003 Z~The variation of gravity with height is neglected;The air temperature at station level (t') is taken as the effective temperature of the "column of air'between the station and mean sea-level (B:n, = t');The effect of water vapour on the density of the "column: of air" is neglected.This method is also used by Australia, Barbados, Hong Kong, Ireland, Kuwait, Mauritius, Nigeriand Singapore.Guyana, Jamaica, Sierra Leone, Trinidad and Tobago and British Caribbean Territories. As the Unite'Kingdom, except that the temperature of the thermometer attached to the barometer is used instea'of the screen temperature. Most of the barometers are near sea-level and in well-ventilated buildings.New Zealand. As the United Kingdom, except that the temperature of the thermometer attache'to the barometer is used instead of the screen temperature where the barometer is less than 50 feet abovmean sea-level.

8 CHAPTER ONESwiss international stations have used provisionally from May 1952 the following formula:whereBmvZt + a 2 Pandlog po =psZpK (1 + aBmv)a 0.65°C/100 metresGravity corrections are ignored.Chile also uses the international formula.Democratic Republic of Congo (see also page 12).The following formula is used:10)' po =g psZp18428 + 74.38 (tm + 0.00265 Zp)t m is the mean temperature of the station (screen temperature, 0C). This formula results from means madefrom radiosondes. It takes account implicitly of the virtual temperature tv, which is given by the followingempirical formula, the result itself of numerous statistics:Burundi. As Democratic Republic of Congo.t v = - 28.03 + 1.1029 tUnited Arab Republic. Formula (11) is used, but Bm is taken as equal to t.Spain uses the International Meteorological Tables, Paris, 1890.Uruguay. As Spain, and taking the vertical temperature gradient equal to 0.65°C/100 m and thewater vapour pressure equal to 11 mm mercury.I. 3 Versions of formula in which English units are usedwhere(a)(b)(c)United Kingdom. Angot's tables (paragraph 1.1. 2 above) are used, based onIn this methodM = 10 ffi -1Z' pm = 56525 + 123.1 e:n + 0.003 Z~The variation of gravity with height is neglected;The air temperature at station level (t') is taken as the effective temperature of the "column of air"between the station and mean sea-level (B:n = t');The effect of water vapour on the density of the "column of air" is neglected.This method is also used by Australia, Barbados, Hong Kong, Ireland, Kuwait, Mauritius, Nigeriaand Singapore.Guyana, Jamaica, Sierra Leone, Trinidad and Tobago and British Caribbean Territories. As the UnitedKingdom, except that the temperature of the thermometer attached to the barometer is used insteadof the screen temperature. Most of the barometers are near sea-level and in well-ventilated buildings.New Zealand. As the United Kingdom, except that the temperature of the thermometer attachedto the barometer is used instead of the screen temperature where the barometer is less than 50 feet abovemean sea-level.

THE "INTER ATIONAL" FORMULA 9Iraq. As the United Kingdom for stations whose altitude does not exceed 1000 ft.1000 ft, the following formula is used:z~ = CTm (log po - log ps)where C = 221.1 and T m is the mean absolute temperature of the "air column".For stations aboveIndia. .The full formula (8) with the omission only of the factor (1 + 209~~950) is used, but Indiawrites the formula in logarithms.In this method, corrections for humidity and latitude are included.'+ 'e:n is found by the formula e:n = y or a vertical gradient of 1°F/300 ft is assumed.The tables in use by India have been revised so as to be applicable to Kew Pattern barometers graduatedin millibars and absolute degrees. Recently, the tables have been recomputed in metric units.This method is also applied by Burma and by Pakistan (using English units).

CHAPTER IIMETEOROLOGICAL SERVICES USING THE RECOMMENDED FORM·OF HYPSOMETRIC EQUATION2.1 Recommended form of hypsometric equationThe form of the hypsometric equation specially designed for reduction of pressure to sea-level andrecommended for practical use in WMO Technical Note o. 7 (page 20) and WMO Technical Jote o. 61(page 22) is:where:pspoTsHpKaesChlog po = K Hp (14)psstation pressure, In mbpressure reduced to sea-level, III mbstation temperature argument, in oK( Ts + a:p + es Ch)station elevation, in geopotential metreshypsometric constantassumed lapse rate in the fictitious air column extending from sea-level to the levelof the station elevation, in °C/gpmvapour pressure argument at the station, in mba function of Hp (expressed in °C /mb)If the atmosphere is regarded as a perfect gas, K = 0.0148275 °K/gpm. In calculating K, the gas constantI for dry air was taken to be R = 2.8704 X 10 6 erg gm- 1 oK-1.Equation (14) is predicated upon a constant lapse rate. The function Ch is based on the assumptionthat the vertical distribution of aqueous vapour pressure in the fictitious atmosphere varies with altitudein accordance with Hann's well-known equation:Zee: = 10 - 6300where: e aqueous vapour pressure at altitude Z in metresaqueous vapour pressure at sea-level(See Hann-Siiring, Lehrbuch der Meteorologie, 4th ed., 1926.)Function Ch also involves some assumptions to the effect that the pressure and temperature distributionsare in accord with the standard atmosphere, merely for the purpose of permitting a unique determinationof the function. These assumptions have nothing to do with what is assumed regarding thelapse rate (a) in the fictitious air column to which equation (14) applies.Table 1 yields the values of Ch as a function of Hp, for intervals of 100 gpm.(15)

CHAPTER 11METEOROLOGICAL SERVICES USING THE RECOMMENDED FORM 'OF HYPSOMETRIC EQUATION2.1 Recommended form of hypsometric equationThe form of the hypsometric equation specially designed for reduction of pressure to sea-level andrecommended for practical use in WMO Technical Note IO• 7 (page 20) and WMO Technical Note No. 61(page 22) is:log po = K Hp (14)ps(Ts + a ~p + es Cb)where:pspoT sHpKastation pressure, III mbpressure reduced to sea-level, III mbstation temperature argument, in oKstation elevation, in geopotential metreshypsometric constantassumed lapse rate in the fictitious air column extending from sea-level to the levelof the station elevation, in °C/gpmvapour pressure argument at the station, in mba function of Hp (expressed in oC/mb)If the atmosphere is regarded as a perfect gas, K = 0.0148275 0K/gpm. In calculating K, the gas constant'fordry air was taken to be R = 2.8704 X 10 6 erg gm- 1 oK-I.Equation (14) is predicated upon a constant lapse rate. The function Cb is based on the assumptionthat the vertical distribution of aqueous vapour pressure in the fictitious atmosphere varies with altitudein accordance with Hann's well-known equation:where:eaqueous vapour pressure at altitude Z in metresaqueous vapour pressure at sea-levele(See Hann-Silring, Lehrbuch der Meteorologie, 4th ed., 1926.)Function Cb also involves some assumptions to the effect that the pressure and temperature distributionsare in accord with the standard atmosphere, merely for the purpose of permitting a unique determinationof the function. These assumptions have nothing to do with what is assumed regarding thelapse rate (a) in the fictitious air column to which equation (14) applies.Zea = 10 - 6300Table 1 yields the values of Ch as a function of Hp, for intervals of 100 gpm.(15)

RECOMMENDED FORM OF HYPSOMETRIC EQUATION 11Table 1Hp Cb Hp Cbgpm oCJmb gpm oCJmb0 0.107lo 600 0.1218100 0.1097 700 0.12lo4200 0.1120 800 0.1270300 0.1H4 900 0.1298loOO 0.1168 1000 0.1325I500 0.1192The most general expression of the hypsometric equation is:log po = J( HpPB Tmvwhere: Tmv integral mean virtual temperature of the aIr column, In OK.A precise definition of T mv in oK is given byfpoT mv = 1 Td pIn (~:) (1- 0.378~) Pwhere: T aIr temperature (in OK) at pressure pand e aqueous vapour pressure at pressure pUnits of e and p must be consistent.pB(16)(17)It follows that equation (14) is a special case of equation (16). To summarize, equation (14) is anexcellent approximation of the latter, based on two principle assumptions, namely that the lapse rate (a)is a constant, and that the vertical distribution of aqueous vapour pressure is in accord with equation (15).A special advantage in using either equation (14) or (16) is that there is no need to take account oflatitude or gravity parameters once the value of the station elevation Hp has been expressed in geopotentialunits. Therefore, in order to make use of those equations, it is necessary to have a method ofcalculating Hp in terms of geopotential metres (gpm) (see WMO Technical Note No. 7, page 22).It is suggested as the basis for a recommended practice that TB be defined by the equation:(18)where:TFair temperature at the station at the time of observation, in oKair temperature at the station observed 12 hours previous to T, in oKa function, in OK, of parameters found to give TB the desired propertiesIn simple cases as at fairly low plains stations it will be found advantageous to take F = O. A discussionof methods to determine the function F is given in WMO Technical Note No. 61, paragraph 3.4.

12 CHAPTER TWO2 . 2 Meteorological Services using the recommended formulaThe following Meteorological Services use formulae (14), (15) and (18), taking a = 0.0065°Cjgpm,F = 0 and for es the annual mean water vapour pressure: Afghanistan, Cameroon, Canada (using forhumidity correction the Smithsonian Tables, 5th edition, Table 54), Central African Republic, Republicof Congo, Dahomey, Ecuador, Gabon, Iceland (for two stations at an elevation more than 150 m, see alsopage 16), Libya (neglecting the humidity correction and substituting T s = T for stations at an elevationless than 150 m), Madagascar, Mali, Netherlands (in principle), Niger, IVorway, Saudi Arabia (see alsopage 13), Senegal, Syria (with es = 0.23 T s + 5.60, based on 5 years' statistical series for Damascus andother stations), Togo, Upper Volta and YugoslafJia (for stations at an elevation less than 700 m and neglectingthe humidity correction).The United States of America takes also into account the function F. Full particulars of this methodare given in the Manual of Barometry (WBA N), Volume I, first edition, Washington, D.C. (1963), chapter7, Appendices 7.1 and 7.2, and chapter 14, tables.Sweden, Brazil, El SalfJador, the Dominican Republic also use the function F.The Democratic Republic of Congo has indicated its intention to use, as from 1968, formulae (14)and (15).The Federal Republic of Germany substitutes T s = T and takes for es a mean water vapour pressureat the temperature T, which was computed on the basis of a long eries of observations.Jordan takes F = 0 for stations at an elevation less than 500 m and uses the following table fordetermining F for stations at higher elevation.TOOOC10°20°F -1.5°C -3.0° --4.5° -5.5° -6.0°For stations which are situated below mean sea-level (some as much as -400 gpm) it was found thatthe terms a :p and e s Ch practically cancel each other. The reduction formula for these stations is thereforelog po ------:- K Hpps Ts.Portugal substitutes T s = T and uses Table 48 A of the Smithsonian Meteorological Tables (6threvised edition) for correction for humidity.Finland uses a simplified formula in which the vertical temperature gradient in the fictitious aIrcolumn between sea-level and barometer level is assumed to be zero and the effect of humidity is beingdisregarded.'po =ps + bps30°40°where:b - e gHp -1- RTT being the air temperature at the station.In Finland, where the elevation of all stations is relatively small, the effect of these simplificationshas been found to be smaller than 0.1 mb.

12 CHAPTER TWO2.2 Meteorological Services using the recommended formulaThe following Meteorological Services use formulae (14), (15) and (18), taking a = 0.0065°Cjgpm,F = 0 and for es the annual mean water vapour pressure: Afghanistan, Cameroon, Canada (using forhumidity correction the Smithsonian Tables, 5th edition, Table 54), Central African Republic, Republicof Congo, Dahomey, Ecuador, Gabon, Iceland (for two stations at an elevation more than 150 m, see alsopage 16), Libya (neglecting the humidity correction and substituting T s = T for stations at an elevationless than 150 m), Madagascar, Mali, Netherlands (in principle), Niger, Norway, Saudi Arabia (see alsopage 13), Senegal, Syria (with es = 0.23 T s + 5.60, based on 5 years' statistical series for Damascus andother stations), Togo, Upper Volta and Yugoslavia (for stations at an elevation les~ than 700 m and neglectingthe humidity correction).The United States of America takes also into account the function F. Full particulars of this methodare given in the Manual of Barometry (WBAN), Volume I, first edition, Washington, D.C. (1963), chapter7, Appendices 7.1 and 7.2, and chapter 14, tables.Sweden, Brazil, El Salvador, the Dominican Republic also use the function F.The Democratic Republic of Congo has indicated its intention to use, as from 1968, formulae (14)and (15).The Federal Republic of Germany substitutes T s = T and takes for e s a mean water vapour pressureat the temperature T, which was computed on the basis of a long series of observations.Jordan takes F = 0 for stations at an elevation less than 500 ill and uses the following table fordetermining F for stations at higher elevation.TOooC10°20°30°40°Fwhere:-1.5°C-3.0°-4.5°-5.5°-6.0°For stations which are situated below mean sea-level (some as much as -400 gpm) it was found thatthe terms a ~p and e s Ch practically cancel each other. The reduction formula for these stations is thereforelog po ---,--ps.Portugal substitutes T s = T and uses Table 48 A of the Smithsonian Meteorological Tables (6threvised edition) for correction for humidity.Finland uses a simplified formula in which the vertical temperature gradient in the fictitious all'column between sea-level and barometer level is assumed to be zero and the effect of humidity is beingdisregarded.'T being the air temperature at the station.J( HpTspo = ps + bpsb = e gH p -1RTIn Finland, where the elevation of all stations is relatively small, the effect of these simplificationshas been found to be smaller than 0.1 mb.

CHAPTER IIIMETEOROLOGICAL SERVICES USING OTHER METHODS3.1 Reduction of pressure at Iow coastal stationsAt low coastal stations where the deviation of the temperature from the normal is relatively small,it is most practical, and ufficiently accurate, to reduce pressure to sea-level by applying an appropriateadditive constant correction to the station pressure. suitable formula is:where:HpT avC = additive reduction constant = 34.68 T Hp *avstation elevation, in gpmmean annual normal value of virtual temperature at the station, in oKThe constant 34.68 in equation (13) is based on the assumption that the mean annual normal valueof P is equal to 1015.9 mb.This formula should only be used for stations of such low elevation that if the absolute extremevalues of virtual temperature are substituted for Tv in the formula, the deviation of the result from thereduction constant should not exceed 0.2 mb. (See Recommendation 13 (CIMO-I).)C =Hp0.03414 p - T av(13)where:pT avbarometric pressure (mb)virtual temperature (OK)0.03414 = 9.800~X 10 4andRgas constant for dry aIr2.8704x 10 6 erg g-l 01(-1Formula (13) is used by Surinam, Saudi Arabia (coa tal stations only), France (French Departmentof Reunion) - except the mountain station "Plaine des Cafres", where pressure i not reduced to ealevel-andSouth Africa ( tations at an elevation of 500 gpm and lower; see also page 19).3.2 Formulae in which geometric units are usedJapan. The following formula is used:LIp = po- ps =[ ~ ] RT mve-1 ps* This formula, which is ba ed on the following more exact expression for small values of Hp, was adopted by theWMO Executive Committee at its fourth session.

14 CHAPTER THREEwhere T mv is the mean virtual temperature of the "air column". This temperature is taken as the sumof the mean temperature and the mean virtual increase of temperature which is obtained as a functionof the temperature alone.Taking 0.5°C/l00 m as the temperature lapse rate in the column, the mean temperature Om is easilyobtained. The specific humidity is considered a a unique function of temperature, and from the specifichumidity-temperature curve the mean virtual increase of temperature is determined by the followingformula:em =0.608 (273.2 + Om) Srnwhere Srn is the mean specific humidity corresponding to the mean temperature Om.In the following table, numerical values of em are given against Om.3530252015105o-5-10-20-30em3.33.22.82.11.41.00.70.50.40.30.10.1Iran.· The corrected barometer readings are reduced to mean sea-level according to the followingformula published by the Institute of Meteorology of the University of Chicago:T mv is defined as follows:g ZpR T mvpo= pse1 1T mv = 2 (T + T 12) + 2 . Zp . 0.0065where T 12 is the absolute air temperature at the station 12 hours previous to current observation (T).The elevation of the Iranian stations, many of which are above 1000 metres, naturally makes reductionof pressure to mean sea-level somewhat doubtful. From experience based on analysis of surface synopticcharts it seems that the formula given for T mv gives fairly satisfactory results.France.m which:t sJp(See also page 5.)The formula of Dedebant is used as an alternative method, in the form:Zp . psJp = 7991 + 29.271 t s -0.414 Zpair temperature at the station, in degrees Celsiuscorrection to be applied to the pressure ps in order to obtain the pressure at meansea-level po.lVew Caledonia. As France, usmg the formula of Dedebant.Belgium uses the formula19 ;: = R(T' + a ~P + C)where:RZp287.05 joule kg- 1 °K-lheight, in metres, of the barometer cistern

'I14 CHAPTER THREEwhere T mv is the mean virtual temperature of the "air column". This temperature is taken as the sumof the mean temperature and the mean virtual increase of temperature which is obtained as a functionof the temperature alone.Taking 0.5°C/l00 m as the temperature lapse rate in the column, the mean temperature Bm is easilyobtained. The specific humidity is considered as a unique function of temperature, and from the specifichumidity-temperature curve the mean virtual increase of temperature is determined by the followingformula:Gm =0.608 (273.2 + Bm) Smwhere Sm is the mean specific humidity corresponding to the mean temperature Bm.In the following table, numerical values of Gm are given against Bm.Bm 35 30 25 20 15 10 5 0 -5 -10 -20 -30Gm 3.3 3.2 2.8 2.1 1.4 1.0 0.7 0.5 0.4 0.3 0.1 0.1Iran.· The corrected barometer readings are reduced to mean sea-level according to the followingformula published by the Institute of Meteorology of the University of Chicago:Tmv IS defined as follows:g ZpRT mvpo= pse1 1T mv = '2 (T + T 12 ) + '2 . Zp . 0.0065where T 12 is the absolute air temperature at the station 12 hours previous to current observation (T).The elevation of the Iranian stations, many of which are above 1000 metres, naturally makes reductionof pressure to mean sea-level somewhat doubtful. From experience based on analysis of surface synopticcharts it seems that the formula given for T mv gives fairly satisfactory results.France.m which:t sLfp(See also page 5.)The formula of Dedebant is used as an alternative method, in the form:Zp . psLfp = 7991 + 29.271 t s - 0.414 Zpair temperature at the station, in degrees Celsiuscorrection to be applied to the pressure ps in order to obtain the pressure at meansea-level po.New Caledonia. As France, usmg the formula of Dedebant.Belgium uses the formula19 ~: = R ( T s + a ~p + C)where:RZp287.05 joule kg-I °K-Iheight, in metres, of the barometer cistern

SERVICES USING OTHER METHODS 15aCLuxembourg.0.6 °C/l00 mcorrection for humidity, as a function of dew point and station elevation. The correctionis obtained from the Smithsonian Meteorological Tables, 1951 edition, Table 48 A.As Belgium.Czechosloyakia.The following formula is used:In po =psg ZpR T amwhere T am is the arithmetic mean of air temperature at the top and the base of the fictitious air columnbetween mean sea-level and station level. A lapse rate of 0.5°C/l00 m is assumed.This formula is used and applied in the same way by Denmark.Austria. Three methods are used alternatively.A. Formula of Laplace (6) with the exception of minor differences in the magnitude of the coefficients.Nearly all tables for the reduction of pressure which are used in Austria are evaluated with Riihlmann'stables as published in Jelinek's Anleitung zur AusfUhrung meteorologischer Beobachtungen, Vienna,1910, 2nd part, pages 37 to 42.B. Practice has shown that the reduction tables can be evaluated with almost the same accuracy usingthe simple formula of Koppen, cited in Meteorologische Zeitschrift 17, page 84 (1882).C. Recently ihe method used in the Federal Republic of Germany has also been applied.Regardless which of the three methods is t~ken,real temperatures at the station are always used.Greece. As stations are mostly above 500 m, special tables are used, based on the Tables meteorologiquesde l'OMM, Paris, 1930 edition; "Cours de meteorologie a l'usage des observateurs de l'Office NationalMeteorologique", neuvieme partie.Boliyia uses the Smithsonian Meteorological Tables for reduction of pressure (6th edition, Table 48).Indonesia. For stations at an elevation less than 100 metres Table 52 of the Smithsonian MeteorologicalTables (ed. 1951) is used in a simplified way in so far that a constant temperature of 81°F (25°C) is usedinstead of a varying temperature argument. A preliminary analysis of this simplified method has indicateda probable error which falls a little outside the limit recommended by WMO.For stations whose elevation is more than 100 metres the altimeter setting formula is used as givenby Table 65 of the Smithsonian Meteorological Tables (ed. 1951). Almost all Indonesian stations belongingto this class are situated at aerodromes.Hungary.The method of pressure reduction is based on the formulaID which:yhvertical temperature gradientheight of the station above mean sea-level"temperature" at mean sea-level

16 CHAPTER THREEOn condition that (1) the height of the stations is under 500 m, (2) the gravitational acceleration isconstant and (3) the vertical temperature gradient is kept constant, i.e. To = T s + yh where T s is thetemperature at station level, the above formula can be reduced towhereg h s h'po-ps= --R T sh' = h (1 + 2.~04)The above conditions are within the tolerated limit of error fulfilled in the case of stations situated inHungary. The effect of the air humidity is taken into account by taking for T s the virtual temperature.Iceland.The following formula is used at stations between 40 and 150 metres above mean sea-level:g Zp 1 ( g Zp )2J11 p = ps [ R (}mv +"2 R (}mvwhere (}mv is the mean virtual temperature of the "air column" in °C and is given by(}mv =t + 0.00; Zp + 273.2 + ewhere e is the correction for humidity which varies as follows:When t + 0.00; Zp = _ 260C, e IS taken to be 0.0" "" "- - 1°C, e " " " "0.4= + 22°C, e " " " " 1.7Between these values, e is considered to increase proportionally with temperature.For stations below 40 metres above mean sea-level the second term between the square brackets isneglected.Turkey uses the formula:Bulgaria uses the reduction formula:polog ps =Zp67.4 Tpo = ps (1 - 0.000196 h)where:h is station elevation in metres.Sea-level is related to the Black Sea.Netherlands Antilles uses the formula of Babinet:h =P-p16.000 (1 + 0.004 tm ) -P­In which: h height of the barometer above sea-level, in metrest m mean temperature between station level and sea-level, In °CP pressure at sea-level, in mbp pressure at station level, in mb+p

16 CHAPTER THREEOn condition that (1) the height of the stations is under 500 m, (2) the gravitational acceleration isconstant and (3) the vertical temperature gradient is kept constant, i.e. To = T s + yh where T s is thetemperature at station level, the above formula can be reduced towhereg h s h'po-ps= --R T sh' = h (1 + 2.~04)The above conditions are within the tolerated limit of error fulfilled in the case of stations situated inHungary. The effect of the air humidity is taken into account by taking for T s the virtual temperature'.Iceland. The following formula is used at stations between 40 and 150 metres above mean sea-level:[g Zp 1 ( g Zp )2JLJP = ps R B mv+"2 R B mv.where B mv is the mean virtual temperature of the "air column" in °C and is given bye - + 0.005 Zp + 273 ? +mv - t 2 .~ ewhere e is the correction for humidity which varies as follows:When t + 0.00; Zp = _ 260C, e IS taken to be 0.0" "" "- - 1°C, e " " " "0.4= + 22°C, e " " " " 1.7Between these values, e is considered to increase proportionally with temperature.For stations below 40 metres above mean sea-level the second term between the square brackets isneglected.Turkey uses the formula:Bulgaria uses the reduction formula:po Zplog ps = 67.4 Tpo = ps (1 - 0.000196 h)where:h is station elevation in metres.Sea-level is related to the Black Sea.Netherlands Antilles uses the formula of Babinet:P-ph = 16.000 (1 + 0.004 tm) -p­+pIn which: h height of the barometer above sea-level, in metrest m mean temperature between station level and sea-level, In °Cp pressure at sea-level, in mbppressure at station level, in mb

SERVICES USING OTHER METHODS3.3 Formulae in which geopotential units are usedArgentina uses the formula:po =H' ppse R'T m17where: H~ =R'Zp (go -R0.000001543 Zp)Tm1- 0.378 ~Pthe arithmetic mean of air temperature (in degrees Kelvin) at the top and the base of thefictitious air column between mean sea-level and station level. A lapse rate of0.65°C/100 m is assumed.The value for normal gravity go is taken from the Smithsonian Meteorological Tables. The ratio ofvapour pressure to atmospheric pressure is assumed constant, the values taken being the annual meansof the station..This method is also used by Peru.Philippines. The following formula is used:log po =psHp67.572 (272.5 + Bmv)The constant 272.5 is based on the observed fact that the coefficient of cubical expanSIOn of air isvery closely 0.00367 per degree Celsius, at ordinary pressures and temperatures.Hp =altitude of station in geopotential metres.3.4 Reduction to the 850-mh level in tropical regionsSouthern Rhodesia. In tropical latitudes pressure gradients are generally weak and it is necessaryto draw isobars at 1.0 mb intervals. To obtain consistency in pressure gradients, reduced pressures shouldtherefore be accurate to within a few tenths of a millibar. To this end empirical methods of obtaining meanvirtual temperatures have been devised, which yield reduced pressures of the required accuracy.Omitting all discussion of the means by which these methods were evolved and the underlying reasonsconcerned, the systems are:A. For use from 0730 GMT to 1600 GMT throughout the yearB:nv =t' + ~ a LfZ + Gm + C'where C' varies from OaF in the wet season to -4°F in the dry seasonGm IS the correction for average humidityLfZ ISathe height difference between station and standard levelIS taken as 4.5°F/1000 ftB. F9r Use from 0400 GMT to 0730 GMT during summer half-yearAs case A, except that the constant C' = average value of (maximum-dry-bulb temperatures) =-11°F

18 CHAPTER THREEC. For use from 0400 GMT to 0730 GMT during winter half-year.e:nv =t:nax + ~ aL1Z + em + C'where t:nax is the prevIOUS afternoon's maximum temperature,C' = -15°Fand a = 4.5°F/1000 ftD. For use at stations below the standard lefJel0730 GMT to 1600 GMT, during precipitation, or when much convective cloud with small dew-pointdepression0430 GMT to 0730 GMT, during precipitation, or when much convective cloud, or when strong windse:nv = t' + e + c'where c' is the correction based on assumption of dry adiabatic lapse rate to condensation level andsaturated adiabatic lapse rate aboveand eis the correction for current humidity.This category is used when applicable, in preference to A, B or C.(Note: So far, attention has been given to the problems involved in pressure reduction for daylightreductions only.)Zambia. The method of reduction currently in use is essentially the one applied in Southern Rhodesia.The main problem of pressure reduction in these regions is estimating an appropriate value for the meanvirtual temperature of the air column involved in the reduction. In favourable cases, for upward reductions,radiosonde reports can be used; but these cases are so few that they have little impact on the mamproblem and the decision has been in favour of using only the surface temperatures.The cases that arise have been grouped in three categories:(1) Normal convective day-time situation, with at least 2 oktas of cumulus, when one can assume a dryadiabatic lapse rate (D.A.L.R.) up to cloud base and a saturated adiabatic lapse rate (S.A.L.R.) athigher levels. This is not strictly accurate but, in Zambia, should give a result correct to 1 or 2 metres.(2) ormal early morning in the dry season with a marked surface inversion topped by a layer in whichthe lapse rate is almost the D.A.L.R. We would probably not be far wrong if we assumed that theD.A. layer corresponded to the previous day's maximum temperature but are faced with a difficultproblem in guessing at the thickness of the inversion layer.(3) All other cases that fall somewhere between the first two. In these cases there is little to go on as theexact relevance of the surface temperatures is indeterminate.For cases in category (1) two adjustments are made to the current dry-bulb temperature, one dependingon the dew point and the other on the dew-point depression. These two ,adjustments are not more than afew degrees each and tend to cancel each other. For cases in categories (2) and (3) the only comfortingfeature is that, on days with comparatively unimpeded insolation, there is a fairly consistent relationshipbetween the day's maximum temperature as recorded at different stations and the station. altitudes.Where possible, therefore, the maximum temperature is made the basis for estimating the mean virtualtemperature. As a result of much trial and error the following empirical scheme has been devised to coverthese cases.

18 CHAPTER THREEC. For use from 0400 GMT to 0730 GMT during winter half-yeare:nv =t:nax + ~ a LlZ + em + C'where t:nax is the prevIOus afternoon's maximum temperature,C' = -15°Fand a = 4.5°F/1000 ftD. For use at stations below the standard lerel0730 GMT to 1600 GMT, during precipitation, or when much convective cloud with small dew-pointdepression0430 GMT to 0730 G iT, during precipitation, or when much convective cloud, or when strong windse:nv = t' + e + c'where c' is the correction based on assumption of dry adiabatic lapse rate to condensation level andsaturated adiabatic lapse rate aboveand eis the correction for current humidity.This category is used when applicable, in preference to A, B or C.(Note: So far, attention has been given to the problems involved in pressure reduction for daylightreductions only.)Zambia. The method of reduction currently in use is essentially the one applied in Southern Rhodesia.The main problem of pressure reduction in these regions is estimating an appropriate value for the meanvirtual temperature of the air column involved in the reduction. In favourable cases, for upward reductions,radiosonde reports can be used; but these cases are so few that they have little impact on the mainproblem and the decision has been in favour of using only the surface temperatures.The cases that arise have been grouped in three categories:(1) Normal convective day-time situation, with at least 2 oktas of cumulus, when one can assume a dryadiabatic lapse rate (D.A.L.R.) up to cloud base and a saturated adiabatic lapse rate (S.A.L.R.) athigher levels. This is not strictly accurate but, in Zambia, should give a result correct to 1 or 2 metres.(2) Normal early morning in the dry season with a marked surface inversion topped by a layer in whichthe lapse rate is almost the D.A.L.R. We would probably not be far wrong if we assumed that theD.A. layer corresponded to the previous day's maximum temperature but are faced with a difficultproblem in guessing at the thickness of the inversion layer.(3) All other cases that fall somewhere between the first two. In these cases there is little to go on as theexact relevance of the surface temperatures is indeterminate.For cases in category (1) two adjustments are made to the current dry-bulb temperature, one dependingon the dew point and the other on the dew-point depression. These two adjustments are not more than afew degrees each and tend to cancel each other. For cases in categories (2) and (3) the only comfortingfeature is that, on days with comparatively unimpeded insolation, there is a fairly consistent relationshipbetween the day's maximum temperature as recorded at different stations and the station. altitudes.Where possible, therefore, the maximum temperature is made the basis for estimating the mean virtualtemperature. As a result of much trial and error the following empirical scheme has been devised to coverthese cases.

SERVICES USI G OTHER METHODS19Table of temperatures to be used for making pressure conversions for cases (2) and (3)TimesMonth0500 B0600 B1100 B0800 B 1400 B 2000B1700 BJanuary Dry +4 0 Dry Dry -6° DryFebruary Dry +4° Dry Dry -6° DryMarch Dry +4 0 Dry Dry -6° DryApril Dry +4° Dry Dry -6° Max. -12°May Max. -12 0 Max. -12° Dry -6° Max. -12 0-June Max. -12 0 Max. -12 0 Dry -6° Max. -12 0July Max. -12 0 Max. -12° Dry -6° Max. -12°August Max. -12 0 Max. -12 0 Dry -6° Max. -12 0September Dry +4 0 Dry Dry -6° Max. -12 0October Dry +4 0 Dry Dry -6 0 Max. -12 0November Dry +4 0 Dry Dry -6 0 DryDecember Dry +4 0 Dry Dry -6 0 Drywhere ERwanda.The tables currently in use have been prepared on the basis of the Laplace formula:p 8501og-­psE18428 + 74.38(ts + 0.00265 E)is the thickness, in metres, of the air layer between station level and the 850-mb level; E canbe positive or negative.South Africa (see also page 13). As the greater portion of the land mass has an elevation of over900 metres whilst the area below 500 metres consists merely of a narrow fringe around the coast, the actualsolution adopted is the construction of bi-level charts, viz. 850-mb surface contour analysis for the plateauand sea-level isobars for coastal areas. Thus, for stations at an elevation above 500 gpm, pressure is reportedat the nearest 100 gpm or 1250 gpm levels. The pressures at these levels are then reduced to the 850-mbsurface. As there is no direct method of determining the virtual temperature of the column between theselevels and the 850-mb surface for the appropriate stations, empirical methods are resorted to as the onlyalternative (see South African Weather Bureau publication Notos, Vo!. 7 (1958)).

ANNEXLIST OF SYMBOLS(Further symbols are defined in the text)aB oB sB~B~eea,eAssumed vertical temperature gradient ill the fictitious an columnHeight of mercury column (barometric height) at mean sea-level, in mmHeight of mercury column (barometric height) at station level, in mmHeight of mercury column (barometric height) at mean sea-level, in inchesHeight of mercury column (barometric height) at station level, in inchesVapour pressure at station level (at pressure p)Mean annual vapour pressure at stationMean vapour pressure for the air columnVapour pressure at sea-levelVapour pressure argument at the station, ill mbV I · d Zpapour pressure at a tltu e"2M I I · d Zpean annua vapour pressure at a tltu e"2gglAcceleration of gravityAcceleration of gravity at altitude Zpg2 Acceleration of gravity at altitude Z;gcMean value of gravity between station and sea-level at same latitude11p Station elevation in geopotential metresk = 0.00259]{ Hypsometric constantpo Pressure at mean sea-level ill mbps Pressure at station level in mbLIp Pressure correction to be appliedPc Mean pressure for the air columnPom Mean monthly pressure at sea-levelPsa Mean annual pressure at stationMean monthly pressure at stationP smP a' M I I' d ZpJean annua pressure at a btu e "2rRRItt 6t 12Mean terrestrial radiusConstant of gas equation for dry airConstant of gas equation for humid airAir temperature at station at time of observation in oCTemperature at station 6 hours previous to current observation (t), in oCTemperature at station 12 hours previous to current observation (t), in oC

ANNEXLIST OF SYMBOLS(Further symbols are defined in the text)aB oB sB~B~eecIeAssumed vertical temperature gradient in the fictitious aIr columnHeight of mercury column (barometric height) at mean sea-level, in mmHeight of mercury column (barometric height) at station level, in mmHeight of mercury column (barometric height) at mean sea-level, in inchesHeight of mercury column (barometric height) at station level, in inchesVapour pressure at station level (at pressure p)Mean annual vapour pressure at stationMean vapour pressure for the air columnVapour pressure at sea-levelVapour pressure argument at the station, III IllbVapour pressure at a1 tItu · d e 2ZpggI. d ZpMean annual vapour pressure at altItu e 2Acceleration of gravityAcceleration of gravity at altitude Zpg2 Acceleration of gravity at altitude ~pgc Mean value of gravity between station and sea-level at same latitudeHp Station elevation in geopotential metresk = 0.00259K Hypsometric constantpo Pressure at mean sea-level III mbps Pressure at station level in mbL1 p Pressure correction to be appliedPc Mean pressure for the air columnPom Mean monthly pressure at sea-levelP sa Mean annual pressure at stationMean monthly pressure at stationPsmP' M 1 1· d Zpa ean annua pressure at a tItu e ""2rRRItt at l2Mean terrestrial radiusConstant of gas equation for dry aIrConstant of gas equation for humid airAir temperature at station at time of observation in QCTemperature at station 6 hours previous to current observation (t), in QCTemperature at station 12 hours previous to current observation (t), in QC

ANNEX - LIST OF SYMBOLS 21tmtotmvt.tvt'l~TT 12TamT avTmTmvToT.BmBmvBmvnB:Ue:uvZZ' pafJprp!lean temperature at the station in °CAir temperature at mean sea-level at time of observation ill °CMean virtual temperature at the station in °CStation temperature argument in °CVirtual temperature in °CAir temperature at station at time of observation in ofAir temperature at mean sea-level at time of observation ill ofAir temperature at station at time of observation in oKAir temperature at station observed 12 hours previous to current observation (T) ill oKArithmetic mean of air temperature at top and base of air column in oKMean annual value of virtual temperature at the station in oKMean temperature of air column in oKMean virtual temperature of air column in oKAir temperature at mean sea-level at time of observation ill oKStation temperature argument in oKMean temperature of air column in °CMean virtual temperature of air column III °CNormal annual value of emv in °C~!lean temperature of air column in ofMean virtual temperature of air column ill ofGeometric altitude above mean sea-level, in metresHeight of homogeneous atmosphere, in metresGeometric altitude corresponding to the station elevation, in metres (station pressure, p., refers to thisaltitude)Geometric altitude corresponding to the station elevation, in feetCoefficient of expansion of air0.378 ::115K4 -;:- log e = 0.00157B.+ Bo2Density of the aIrLatitude of station