饱和蒸汽压计算方法.docx

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.