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.
ThestudybyFukut