饱和蒸汽压计算方法.docx
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饱和蒸汽压计算方法.docx
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饱和蒸汽压计算方法
Thereisalargenumberofsaturationvaporpressureequationsusedtocalculatethepressureofwatervaporoverasurfaceofliquidwaterorice.Thisisabriefoverviewofthemostimportantequationsused.Severalusefulreviewsoftheexistingvaporpressurecurvesarelistedinthereferences.PleasenotetheupdateddiscussionoftheWMOformulation.
1)VaporPressureoverliquidwaterbelow0°C
GoffGratchequation
(SmithsonianTables,1984,afterGoffandGratch,1946):
Log10pw= -7.90298(373.16/T-1) [1]
+5.02808Log10(373.16/T)
-1.381610-7(1011.344(1-T/373.16) -1)
+8.132810-3(10-3.49149(373.16/T-1) -1)
+Log10(1013.246)
withTin[K]andpwin[hPa]
WMO
(Goff,1957):
Log10pw= 10.79574(1-273.16/T) [2]
-5.02800Log10(T/273.16)
+1.5047510-4(1-10(-8.2969*(T/273.16-1)))
+0.4287310-3(10(+4.76955*(1-273.16/T))-1)
+0.78614
withTin[K]andpwin[hPa]
(Note:
WMObaseditsrecommendationonapaperbyGoff(1957),whichisshownhere.TherecommendationpublishedbyWMO(1988)hasseveraltypographicalerrorsandcannotbeused.Acorrigendum(WMO,2000)showstheterm+0.4287310-3(10(-4.76955*(1-273.16/T))-1)inthefourthlinecomparedtotheoriginalpublicationbyGoff(1957).Notethedifferentsignoftheexponent.Theearlier1984editionshowsthecorrectformula.)
HylandandWexler
(HylandandWexler,1983):
Logpw= -0.58002206104/T [3]
+0.13914993101
-0.4864023910-1T
+0.4176476810-4T2
-0.1445209310-7T3
+0.65459673101Log(T)
withTin[K]andpwin[Pa]
Buck
(BuckResearchManual(1996);updatedequationfromBuck,A.L.,Newequationsforcomputingvaporpressureandenhancementfactor,J.Appl.Meteorol.,20,1527-1532,1981)
pw=6.1121 e(18.678-t/234.5)t/(257.14+t) [1996] [4]
pw=6.1121e17.502t/(240.97+t) [1981] [5]
withtin[°C]andpwin[hPa]
Sonntag
(Sonntag,1994)
Logpw= -6096.9385/T [6]
+16.635794
-2.71119310-2*T
+1.67395210-5*T2
+2.433502*Log(T)
withTin[K]andpwin[hPa]
MagnusTeten
(Murray,1967)
Log10pw=7.5t/(t+237.3)+0.7858 [7]
withtin[°C]andpwin[hPa]
Bolton
(Bolton,1980)
pw=6.112e17.67*t/(t+243.5) [8]
withtin[°C]andpwin[hPa]
Atlowtemperaturesmostofthesearebasedontheoreticalstudiesandonlyasmallnumberarebasedonactualmeasurementsofthevaporpressure.TheGoffGratchequation[1]forthevaporpressureoverliquidwatercoversaregionof-50°Cto102°C[Gibbins1990].Thisworkisgenerallyconsideredthereferenceequationbutotherequationsareinuseinthemeteorologicalcommunity[ElliottandGaffen,1993].Thereisaverylimitednumberofmeasurementsofthevaporpressureofwateroversupercooledliquidwaterattemperaturesbelow°C.Detwiler[1983]claimssomeindirectevidencetosupporttheextrapolationoftheGoff-Gratchequationdowntotemperaturesof-60°C.However,thiscurrentlyremainsanopenissue.
TheHylandandWexlerformulationisusedbyVaisalaandisverysimilartotheformulabySonntag(6).TheMagnusTetenformulation[7]iswidelyusedinMeteorologyandappealsforitssimplicity.
Thecomparisonfortheliquidsaturationvaporpressureequations[2]-[8]withtheGoff-Gratchequation[1]infigure1,showsthatuncertaintiesatlowtemperaturesbecomeincreasinglylargeandreachthemeasurementuncertaintyclaimedbysomeRHsensors.At-60°Cthedeviationsrangefrom-6%to+3%andat-70°Cthedeviationsrangefrom-9%to+6%.ForRHvaluesreportedinthelowandmidtropospheretheinfluenceofthesaturationvaporpressureformulausedissmallandonlysignificantforclimatologicalstudies[ElliottandGaffen1993].
TheWMOrecommendedformulaisaderivativeoftheGoff-Gratchequation,originallypublishedbyGoff(1957).ThedifferencesbetweenGoff(1957)andGoff-Gratch(1946)arelessthan1%overtheentiretemperaturerange.TheformulationpublishedbyWMO(1988)cannotbeusedduetoseveraltypographicalerrors.ThecorrectedformulationWMO(2000)stilldiffersinthesignofoneexponentcomparedtoGoff(1957).ThisincorrectformulationisincloseragreementwiththeHylandandWexlerformulation;however,itistobeassumedthatGoff(1957)wastoberecommended.
ThestudybyFukutaandGramada[2003]showsdirectmeasurementsofthevaporpressureoverliquidwaterdownto-38°C.Theirresultindicatesthatatthelowesttemperaturesthemeasuredvaporpressuremaybeasmuchas10%lowerthanthevaluegivenbytheSmithsonianTables[1],andasshowninfigure1lowerasanyothervaporpressureformulation.
Itisimportanttonotethatintheuppertroposphere,watervapormeasurementsreportedintheWMOconventionasrelativehumiditywithrespecttoliquidwaterdependcriticallyonthesaturationvaporpressureequationthatwasusedtocalculatetheRHvalue.
Figure1:
Comparisonofequations[2]-[8]withtheGoffGratchequation[1]forthesaturationpressureofwatervaporoverliquidwater.ThemeasurementsbyFukutaetal.[2003]areshownaswell.
(*)WMO(2000)isalsoshown.ThisisbasedonGoff(1957)withthedifferentsignofoneexponent,likelyduetoatypographicalerror.
2)VaporPressureoverice
GoffGratchequation
(SmithsonianTables,1984):
Log10pi= -9.09718(273.16/T-1) [9]
-3.56654Log10(273.16/T)
+0.876793(1-T/273.16)
+Log10(6.1071)
withTin[K]andpiin[hPa]
HylandandWexler
(HylandandWexler,1983.):
Logpi= -0.56745359104/T [10]
+0.63925247101
-0.9677843010-2T
+0.6221570110-6T2
+0.2074782510-8T3
-0.9484024010-12T4
+0.41635019101Log(T)
withTin[K]andpiin[Pa]
MagnusTeten
(Murray,1967)
Log10pi=9.5t/(t+265.5)+0.7858 [11]
withtin[°C]andpiin[hPa]
Buck
(BuckResearchManual(1996);updatedequationfromBuck,A.L.,Newequationsforcomputingvaporpressureandenhancementfactor,J.Appl.Meteorol.,20,1527-1532,1981)
pi=6.1115 e(23.036-t/333.7)t/(279.82+t) [1996] [12]
pi=6.1115e22.452t/(272.55+t) [1981] [13]
withtin[°C]andpiin[hPa]
MartiMauersberger
(Marti,J.andKMauersberger,Asurveyandnewmeasurementsoficevaporpressureattemperaturesbetween170and250K,GRL20,363-366,1993)
Log10pi=-2663.5/T+12.537 [14]
withTin[K]andpiin[Pa]
TheGoffGratchequation[9]forthevaporpressureovericecoveraregionof-100°Cto0°C.Itisgenerallyconsideredthereferenceequation;however,otherequationshavealsobeenwidelyused.Theequationsdiscussedherearemostlyofinterestforfrost-pointmeasurementsusingchilledmirrorhygrometers,sincetheseinstrumentsdirectlymeasurethetemperatureatwhichafrostlayerandtheoverlyingvaporareinequilibrium.Inmeteorologicalpractice,relativehumidityisgivenoverliquidwater(seesection1)andcareneedstobetakentoconsiderthisdifference.
BuckResearch,whichmanufacturesfrost-pointhygrometers,usestheBuckformulationsintheirinstruments.Theseformulationsincludeanenhancementfactor,whichcorrectsforthedifferencesbetweenpurevaporandmoistair.Thisenhancementfactorisaweakfunctionoftemperatureandpressureandcorrectsabout0.5%atsealevel.Forthecurrentdiscussionithasbeenomitted.
TheMartiMauersbergerequationistheonlyequationbasedondirectmeasurementsofthevaporpressuredowntotemperaturesof170K.
Thecomparisonofequations2-6withtheGoffGratchequation(figure2)shows,thatwiththeexceptionoftheMagnusTetenformula,thedeviationsinthetypicalmeteorologicalrangeof-100°Cto0°Carelessthan2.5%,andsmallerthantypicalinstrumentalerrorsoffrost-pointhygrometersof5-10%.
NotshownistheWMOrecommendedequationforvaporpressureoverice,sinceitisnearlyidenticalwiththeGoff-Gratchequation[9].
Figure2:
Comparisonofequations[10]-[14]withtheGoffGratchequation[9]forthesaturationpressureofwatervaporoverice.
3)References
Bolton,D.,Thecomputationofequivalentpotentialtemperature,MonthlyWeatherReview,108,1046-1053,1980.equation(10).
Buck,A.L.,Newequationsforcomputingvaporpressureandenhancementfactor,J.Appl.Meteorol.,20,1527-1532,1981.
BuckResearchManuals,1996
Detwiler,A.,ExtrapolationoftheGoff-Gratchformulaforvaporpressureoverliquidwaterattemperaturesbelow0°C,J.Appl.Meteorol.,22,503,1983.
Elliott,W.P.andD.J.Gaffen,Ontheutilityofradiosondehumidityarchivesforclimatestudies,Bull.Am.Meteorol.Soc.,72,1507-1520,1991.
Elliott,W.P.andD.J.Gaffen,Effectsofconversionalgorithmsonreportedupperairdewpointdepressions,Bull.Am.Meteorol.Soc.,74,1323-1325,1993.
Fukuta,N.andC.M.Gramada,Vaporpressuremeasurementofsupercooledwater,J.
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