温度反演经典文章(4)

Author's personal copy

16

Z.-L.Lietal./RemoteSensingofEnvironment131(2013)14–37

ofthepeakmonochromaticradianceatagiventemperature(T)isgivenbyWien'sdisplacementlaw:Tλmax¼2897:9Kμm:

ð2Þ

withRibeingthechannelradianceobservedinchanneliatgroundlevelgivenby

Riðθ;φÞ¼εiðθ;φÞBiðTsÞþ

| {z }

Surfaceemissionterm

½1 εiðθ;φÞ Rati↓| {z }

Surfacereflecteddownwellingatmosphericemissionterm

Accordingtothisequation,thewavelengthλmaxatwhichmaxi-mumemissionoccursvariesroughlyfrom11.6μmto8.8μmiftheLSTrangesfrom250Kto330KwiththeaveragetemperatureoftheEarthbeingapproximately288K.Thewavelengthregionbe-tween8and13μmcoincideswithinaclearwindowintheatmo-spherewhichismosttransparenttoTIRradiation.Incaseswherethetemperatureofthesurfaceexceeds330K,thewavelengthpeakmovestoshorterandshorterwavelengths,forexampleforawild re(about800K),themaximumemissionisaround3.6μminthemid-infrared(MIR)region(3–5μm)whichalsocoincideswithaclearwindowintheatmosphere.2.1.Radiativetransferequation

AninfraredsensoronboardasatelliteviewingtheEarth'ingtheradiativetransferequation(RTE)andassum-ingacloud-freeatmosphereunderlocalthermodynamicequilibrium,asillustratedinFig.1,thechannelinfraredradianceIireceivedbyasensoratthetopoftheatmosphere(TOA)canbewrittenasIiðθ;φÞ¼

Riðθ;φÞτiðθ;φÞ| {z }

Surfaceoutgoingradiationtermattenuatedbytheatmosphere

þ

½1 εiðθ;φÞ Rsli↓| {z }

Surfacereflecteddownwellingatmosphericscatteringterm

þρbiðθ;φ;θs;φsÞEicosðθsÞτiðθs;φsÞ;| {z }

Surfacereflecteddownwellingsolarbeamterm

ð4Þ

inwhichθandφrepresentthezenithalandazimuthalviewingangles.Forsimplicity,thezenithalandazimuthalviewinganglesareignoredinthefollowingexpressions.τiistheeffectivetransmittanceoftheatmosphereinchanneli.Riτiistheradianceobservedatgroundlevelattenuatedbytheatmosphere(path①inFig.1).Rati↑istheupwardat-mosphericthermalradiance(path②inFig.1).Rsli↑istheupwardsolardiffusionradianceresultingfromatmosphericscatteringofthesolarra-diance(path③inFig.1).εiandTsaretheeffectivesurfaceemissivityandsurfacetemperatureinchanneli.εiBi(Ts)representstheradianceemitteddirectlybysurface(path④inFig.1).Rati↓isthedownwardatmosphericthermalradiance.Rsli↓isthedownwardsolardiffusionra-diance.(1-εi)Rati↓and(1-εi)Rsli↓representthedownwardatmosphericthermalradianceandsolardiffusionradiancere ectedbythesurface(paths⑤and⑥inFig.1).ρbiisthebi-directionalre ectivityofthesur-face,EiisthesolarirradianceattheTOA,θsandφsarethesolarzenithalandazimuthalangles.ρbiEicos(θs)τi(θs,φs)isthedirectsolarradiancere ectedbythesurface(path⑦inFig.1).BecausethecontributionofsolarradiationattheTOAisnegligibleinthe8–14μmwindowduringbothdayandnightandinthe3–5μmwindowatnight,

the

þ

Rati↑ðθ;φÞ| {z }

Atmosphericemissionterm

þ

Rsli↑ðθ;φÞ| {z }

;

Atmosphericscatteringterm

ð3Þ

Fig.1.Illustrationofradiativetransferequationininfraredregions(seethetextforthede nitionsofsymbols).Here,Iiistheradiancemeasuredbychanneliatthetopofatmo-sphere.Path①representstheradianceobservedatgroundlevelattenuatedbytheatmosphere.Paths②and③representtheupwardatmosphericthermalradianceandtheup-wardsolardiffusionradiance,respectively.Path④representstheradianceemitteddirectlybythesurface.Paths⑤and⑥representthedownwardatmosphericthermalradiance

andsolardiffusionradiancere ectedbythesurface,respectively.Path⑦representsthedirectsolarradiancere ectedbythesurface.