温度反演经典文章(5)

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

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solar-relateditems(paths③,⑥and⑦inFig.1)inEqs.(3)and(4)canbeneglectedwithoutlossofaccuracy.

Forconvenienceandmathematicalshorthand,theradiancesIiandRimeasuredattheTOAandatgroundlevelaregenerallyexpressedintermsofthebrightnesstemperatureswheretheemissivityis xedat1.0.TheTOAandgroundlevelbrightnesstemperaturesTiandTgiarede nedrespectivelybyBiðTiÞ¼IandB

i

iTgi¼Ri

ð5Þ

Itisworthnotingthatallvariables/parametersinEqs.(3)–(5),ex-ceptfortheangles(θ,φ,θsandφs),arechannel-effectivevalues.Mostsatellitesensorsmeasuretheoutgoingradiationwitha nitespectral-bandwidth,andthechannel-effectivequantitiesofinterestarethereforeaweightedaverageexpressedby:λ

Xi¼

∫λ21giðλÞXλdλ∫gðλÞdλ;ð6Þ

λ2

1i

wheregi(λ)isthespectralresponsefunctioninchanneli;λ1andλ2arethelowerandupperboundariesofthewavelengthinchanneli;andXstandsforB(T),I,R,Rat↑,Rsl↑,Rat↓,Rsl↓,E,ε,τ,orρb.

Eqs.(3)and(4)areactuallyapproximationstothetheoreticalRTEinwhichmonochromaticquantitiesarereplacedwithchannel-effectivevalues,buttheseapproximationsorsimpli cationsrequireseveralimportantpreconditions:

Theintegralofaproductisassumedtobeequaltotheproductoftheintegrals.Thisassumptionistrueonlyifthevariablesarecon-stantwithintheintegrationlimits,whichisrarelythecase.Fortu-nately,thebandwidthofthechannelisgenerallynarrow,andthevariousspectralquantitiesXλinvolvedinEq.(6)shouldnotfeaturerapidvariations.Therefore,theuseoftheweightedaveragesde- nedbyEq.(6)inEqs.(3)and(4)isagoodapproximationtotheRTEwithmonochromaticquantities.

EitherthesurfaceisassumedtobeLambertianorthedownwardat-mosphericandsolardiffuseradiationareassumedtobeisotropicinthecalculationofthedownwardradiationsre ectedbythesurface(paths⑤and⑥inFig.1).Inpractice,theseconditionsareneverful lled.However,becausethesurface-re ecteddownwardatmo-sphericthermalradiationtermismuchsmallerthanthesurfacethermalemission,andthesurface-re ecteddiffusesolarradiationtermismuchsmallerthanthesurface-re ecteddirectsolarterm,thissimpli cationofEqs.(3)and(4)isreasonableanddoesnotin-troducesigni canterrors.

2.2.Dif cultiesandproblemsintheretrievalofLSTfromspacemeasurements

AsseenfromEqs.(3)and(4),estimatingtheLSTfromtheradi-ancemeasuredattheTOArequirescorrectionsforbothatmosphericandemissivityeffects.Applyingthesecorrectionsisnotasimpletask,andsomekeydif cultiesandproblemsinvolvedintheretrievaloftheLSTmustbeovercomeandresolved.Thesekeydif cultiesandproblemsarethefollowing:

(1)TheretrievaloftheLSTfromspaceismathematically

underdeterminedandunsolvable(Hooketal.,1992;Kealy&Hook,1993).TheRTEdescribedinEqs.(3)and(4)showsthat,iftheradianceismeasuredinNchannels,therewillalwaysbeN+1unknowns,correspondingtoNemissivitiesineachchannelandanunknownLSTforNequations,evenifquantitiesotherthantheemissivitiesandLSTareknownapriori.Suchanill-posedproblemmakesthesolutionoftheRTEsetsunderdeterminedatgroundleveleveniftheatmosphericquantitiesinvolvedinEqs.(3)and(4)areaccuratelyestimated.TomakeLST

deterministic,oneormoreoftheLSEsmustbeknown,ortheLSTandLSEshavetobesimultaneouslysolvedwiththeaidofsomeassumptionsorconstraintsontheLSEs(Dashetal.,2002;Gillespieetal.,1996;Hooketal.,1992;Kealy&Hook,1993).(2)

MeasurementsintheTIRregionarehighlycorrelated,implyingthatinstrumentalnoiseanderrorsintheatmosphericcorrectionsexertstrongin uencesontheaccuracyoftheLSTretrieval.ThiscorrelationrepresentsaproblemeveniftheLSTismadesolvableeitherbyreducingthenumberofunknownsorbyincreasingthenumberofequationsthroughreasonableassumptionsorcon-straintsontheLSEs(Gillespieetal.,1996;Lietal.,2013).ThesehighlycorrelatedmeasurementsmakeLSTretrievalunsta-bleandhavehamperedthemethodologicaldevelopmentofLSTretrieval.

(3)

Itisdif culttodecoupletheLST,theLSEs,andthedownwardat-mosphericradianceinthemeasuredradiances.AsseenfromEq.(4),thedownwardatmosphericradianceandthesurfaceemittedradiancearecoupledtogetherthroughLSEs.

Thenon-unityLSEofanaturalsurfacereducesthesurface-emittedradiancewhileincreasingthere ectionofthedown-wardatmosphericradiancebacktotheatmosphere,whichcom-pensatespartlyforthereductioninthesurface-emittedradiance.Thisprocesscanreduceorincreasethetotalsurface-leavingradi-ancedependingontheatmosphericandsurfaceconditions.Thiscouplingofthere ecteddownwellingandsurface-emittedradi-ationcanbeusedtoretrieveLSTwiththeonline/of inemethodbutrequireshighspatialresolutiondata.HoweverinpassivelyobservedmultispectralTIRdata,itisimpossibletoseparate,onaphysicalbasis,thecontributionsoftheLSTfromthecontribu-tionsoftheLSEsandtheatmosphereintheobservedradiance.Forthisreason,determiningLSTfromspacerequiresnotonlytheatmosphericcorrectionsbutalsotheknowledgeoftheLSEsandviceversa.

(4)

Theatmosphericcorrectionsaredif culttoimplement.Thepres-enceoftheatmospherebetweenthesurfaceandthesensorsaf-fectstheradiancesmeasuredbyaradiometerattheTOA.Theseradiancesresultprimarilyfromemission/re ectionatthesurfacemodulatedbytheeffectsoftheattenuation,andemissionoftheatmosphere.Theatmosphericcorrectionsthusconsistofcorrectingtheradiancemeasuredbythesensorsfortheeffectsofatmosphericattenuation,emissionandemission-re ection.Correctingfortheatmosphericeffectsrequiresaccurateknowl-edgeoftheverticalpro lesofatmosphericwatervaporandtem-peraturebothofwhicharehighlyvariable(Perry&Moran,1994).(5)

Duringthedaytime,there ectedsolarradiationisdif culttore-moveintheMIRmeasurements.Asmentionedearlier,thehighlycorrelatedTIRmeasurementsmakeLSTretrievalunstableevenifthesolutionoftheRTEsetsbecomesdeterministicthroughsomeassumptionsandconstraintsontheLSEs.IntheMIRsincethedi-rectsolarirradiationre ectedbythesurfaceisonthesameorderofmagnitudeastheradiancedirectlyemittedbythesurface,ifthesurfacealbedoisabout0.1,theintroductionoftheMIRchan-nelsinLSTretrievalsigni …… 此处隐藏：4416字，全部文档内容请下载后查看。喜欢就下载吧 ……