温度反演经典文章(8)

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20

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

similarinformulation.ManyarebasedonthelinearizationofvarioustermsoftheRTE.Forinstance,BeckerandLi(1990b)de-velopedalocalSWalgorithmandparameterizedakasfunctionsofthemean(ε=(εi+εj)/2)anddifference(Δε=εi εj)ofthetwochannelLSEsa0¼constant;ak¼A0;kþA1 ε1;k

þAΔε

2;kðk¼1;2Þ;

ð9Þ

ε

2wherethecoef cientsAareconstantandindependentoftheat-mosphereiftheatmosphereisrelativelydry(WVb2.5g/cm2).

Someauthorshaveproposedmodifyingtheconstantcoef cienta0inEq.(7)tocorrectforemissivityeffectswhilekeepingtheothercoef cientsa1anda2independentoftheLSEsastheyareforSSTretrieval.Otherformsofa0havebeenproposed,includinga0=B0+B1(1 ε)+B2Δε(Sobrinoetal.,1994;Ulivieri&Cannizzaro,1985;Ulivierietal.,1994)ora0=B0+B1(1 ε)/ε+B2Δε/ε2(Vidal,1991),inwhichthecoef cientsBaresensor-dependentandatmosphere-independent.Ageneralformofa0canbewrittenasa0=f0(gi,gj,ε,Δε)wheref0isalinearornon-linearfunction.Someauthorshaveproposedageneralparameter-izationofakasak=fk(gi,gj,εi,εj)(Sun&Pinker,2003,2005).(2)Parameterizationofthecoef cientsakwithconsiderationofLSEs

andWV

Theatmosphere-independentcoef cientsakdescribedaboveareonlyvalidinrelativelydryatmospheres(WVb2.5g/cm2).TomaketheSWalgorithm(Eq.(7))applicabletomoregeneralat-mosphericconditions,theWVcontentintheatmospherehastobeexplicitlyincludedinthecoef cientsakasshowninEq.(8).ManyauthorshaveproposedincorporatingboththeLSEsandtheWVintothecoef cientsak,andallofthemempiricallyde-scribedthecoef cientsakaslinearcombinationsoftheLSEsandtheWV(Becker&Li,1995;Sobrinoetal.,1991,2004a,1994).FrançoisandOttlé(1996)proposedanotherparameteriza-tionofakinwhichtheakareexpressedasquadraticfunctionsoftheWVatagivenLSE,i.e.

a2

k¼C0;kþC1;kWVþC2;kWV;

ð10Þ

wherethecoef cientsCareconstantforagivenLSE.

(3)Parameterizationofthecoef cientsakwithconsiderationofLSEs,

WV,andVZA

NotethattheatmospherictransmittanceisexpectedtodecreaseatlargerVZAduetotheincreasedabsorptionpathlength.ToachievetherequiredLSTaccuracyof1Koverawiderangeofat-mosphericandsurfaceconditions,erroranalysisdemonstratesthattheVZAmustalsobeconsideredintheLSTretrievalalgo-rithm,particularlyinhotandhumidatmospheres.ManystudieshaveshownthatLSTretrievalcanbesigni cantlyimprovedatVZAlargerthan50°byintroducingthecosineoftheVZAintotheparameterizationofak(Becker&Li,1995;Minnis&Khaiyer,2000;Pinheiroetal.,2004).Forinstance,BeckerandLi(1995)furthermodi edtheirlocalSWalgorithmtoexplicitlyincorpo-ratethecosineofVZAandtheWVinthecoef cientsakasinEq.(8).ThefunctionfkinEq.(8)isanempiricallydeterminedlin-earcombinationofLSEs,WV,andcos(VZA).WanandDozier(1996)developedageneralizedsplit-window(GSW)algorithm,whichusesaformulasimilartothatproposedbyBeckerandLi(1990b),toretrieveLSTfromtheModerateResolutionImagingSpectroradiometer(MODIS)TIRchannelsi(channel31)andj(channel32).TheGSWalgorithmcanbewrittenas:

LST¼b1 εΔε

T0 þb1þb2

þbiþTj

3 ε2þb1 εT 4þb5

þbΔεiTj

6;ð11Þ

wherebk(k=0–6)areunknowncoef cientsthatneedtobe

determinedforagivenVZAandforgivensub-rangesofε,atmo-sphericWVandsurfaceairtemperature,i.e.,theairtemperatureatthesurfacelevel(Ta)(WanandDozier,1996)orLST(Tangetal.2008).UsingthesameformasEq.(7),itcanbeshownthat:a1 ε0¼b0;a1¼b1þb2

þbΔε

3ε

andab4 b1b5 b21 εb6 b32¼2þΔε

2þ2ε2:Similartotheuseofpiecewiselinearfunctionstoapproximate

nonlinearfunctions,intheoperationalalgorithm,foreachVZA,theat-mosphericWV,averagedemissivityε,andTaorLSTaredividedintoseveraltractablesub-rangestoimprovetheLSTretrievalaccuracyoverawiderangeofsurfaceandatmosphericconditions.TheWVisdi-videdintosub-rangesupto6.5g/cm2withanoverlapof0.5g/cm2.Theεisalsoseparatedintotwogroups,onevaryingfrom0.90to0.96andtheotheronevaryingfrom0.94to1.0.TheTasub-rangesaredividedby273,281,289,295,300,305,and310K.TheLSTvarieswithinTa±16KandtheLSTrangeof32Kmaybedividedintofouroverlappedsub-ranges(Wan&Dozier,1996).InsteadofdividingTaintoseveralsub-ranges,Tangetal.(2008)proposedtodivideLSTintoseveralsub-rangesthatoverlapby5K,e.g.,≤280K,275–295K,290–310K,305–325Kand≥320K.ForagivenVZAandgivensub-rangesofε,atmosphericWV,andTaorLST,thecoef cientsbk(k=0–6)aredeterminedbyminimizingEq.(11)usingradiativetransfer(RT)simu-latedTiandTjdatainrangeswideenoughtocoverthevariationsofsurfaceandatmosphericconditionsandarethensavedinasetofmulti-dimensionallookuptables(LUT).Thecoef cientsbkcanbeline-arlyinterpolatedusingthecosineoftheVZA.Accordingly,thecoef -cientsbkintheGSWalgorithmvarywiththeLSEs,theVZA,theatmosphericWVandTaorLST.Inpractice,theLSTisestimatedintwosteps.ForWanandDozier(1996)'salgorithm,theapproximateLSTis rstestimatedwithcoef cientsbkthatcovertheentireLSTrangeofTa±16KinasuitableWVsub-range,andthenamoreaccurateLSTisobtainedbythecoef cientsbkdeterminedbythedifferencebetweentheapproximateLSTandTa.ForTangetal.(2008)'salgorithm,theap-proximateLSTis rstestimatedwithcoef cientsbkthatcovertheentireLSTrangefrom240Kto330KinasuitableWVsub-range,andthenamoreaccurateLSTisdeterminedintermsofthecoef cientsbkfortheLSTsub-rangeinwhichtheapproximateLSTisfound.

Wan(1999)comparedtheviewing-angle-dependentLSTalgo-rithmtotheviewing-angle-independentalgorithmandpointedoutthatthelatterhasanLSTerrorofupto1.6Kifthereisanuncertaintyof0.01inthevalueofΔε/ε2intheGSWalgorithm.ThemajorimprovementsoftheGSWalgorithm,asdescribedbyWanetal.(2002,2004),incorporatedintheLSTretrievalinclude:(1)VZAde-pendence,(2)WVdependence,and(3)TaorLSTdependence.Valida-tionresultsshowedthatanaccuracyofLSTretrievalbetterthan1Kintherange263–322KcanbeobtainedusingtheGSWalgorithmgiveninEq.(11)forcertainlandcoversinclear-skyconditions.Oneoftheadvantag …… 此处隐藏：4145字，全部文档内容请下载后查看。喜欢就下载吧 ……