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RemoteSensingofEnvironment

journalhomepage:/locate/rse

Review

Satellite-derivedlandsurfacetemperature:Currentstatusandperspectives

Zhao-LiangLia,b, ,Bo-HuiTanga,HuaWua,HuazhongRenc,GuangjianYanc,ZhengmingWand,IsabelF.Trigoe,f,JoséA.Sobrinog

StateKeyLaboratoryofResourcesandEnvironmentalInformationSystem,InstituteofGeographicSciencesandNaturalResourcesResearch,Beijing100101,ChinaLSIIT,UdS,CNRS,BoulevardSebastienBrant,BP10413,67412Illkirch,Francec

StateKeyLaboratoryofRemoteSensingSciences,SchoolofGeography,BeijingNormalUniversity,Beijing100875,Chinad

ERI,UniversityofCalifornia,SantaBarbara,CA93106,USAe

InstitutoPortuguêsdoMaredaAtmosfera,Lisbon,Portugalf

InstitutoDomLuiz,UniversityofLisbon,Portugalg

ImageProcessingLaboratory,UniversityofValencia,Valencia46071,Spain

articleinfoabstract

Landsurfacetemperature(LST)isoneofthekeyparametersinthephysicsoflandsurfaceprocessesfromlocalthroughglobalscales.TheimportanceofLSTisbeingincreasinglyrecognizedandthereisastronginterestinde-velopingmethodologiestomeasureLSTfromspace.However,retrievingLSTisstillachallengingtasksincetheLSTretrievalproblemisill-posed.ThispaperreviewsthecurrentstatusofselectedremotesensingalgorithmsforestimatingLSTfromthermalinfrared(TIR)data.AbrieftheoreticalbackgroundofthesubjectispresentedalongwithasurveyofthealgorithmsemployedforobtainingLSTfromspace-basedTIRmeasurements.ThediscussionfocusesonTIRdataacquiredfrompolar-orbitingsatellitesbecauseoftheirwidespreaduse,globalapplicabilityandhigherspatialresolutioncomparedtogeostationarysatellites.Thetheoreticalframeworkandmethodolo-giesusedtoderivetheLSTfromthedataarereviewedfollowedbythemethodologiesforvalidatingsatellite-derivedLST.Directionsforfutureresearchtoimprovetheaccuracyofsatellite-derivedLSTarethensuggested.

Articlehistory:

Received24May2012

Receivedinrevisedform19October2012Accepted11December2012AvailableonlinexxxxKeywords:

LandsurfacetemperatureLandsurfaceemissivityRetrieval

Thermalinfrared

Contents1.2.

Introduction.........................................Basictheoreticalbackground.................................2.1.Radiativetransferequation...............................2.2.Dif cultiesandproblemsintheretrievalofLSTfromspacemeasurements........EstimationofLSTfromspace.................................3.1.LSTretrievalwithknownLSEs.............................

3.1.1.Single-channelmethod............................3.1.2.Multi-channelmethod............................3.1.3.Multi-anglemethod..............................

3.2.LSTretrievalwithunknownLSEs............................

3.2.1.Stepwiseretrievalmethods..........................3.2.2.SimultaneousLSTandLSEretrievalmethodswithknownatmosphericinformation3.2.3.SimultaneousretrievalofLST,LSEs,andatmosphericpro les..........

parisonandanalysisofdifferentmethods......................ValidationofsatellitederivedLST...............................4.1.Temperature-basedmethod(T-based).........................4.2.Radiance-basedmethod(R-based)...........................4.3.Crossvalidationmethod................................

...........................................................................................................................................................................................................................................................................................................................................................................................................151516171818181921222223262629292930

Correspondingauthorat:LSIIT,UdS,CNRS,BoulevardSebastienBrant,BP10413,67412Illkirch,France.Tel.:+33368854516.E-mailaddress:lizl@(Z.-L.

/10.1016/j.rse.2012.12.008

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

Futuredevelopmentandperspectives.................................................5.1.MethodologytosimultaneouslyderiveLST,LSE,andatmosphericpro les(atmosphericquantities)fromhyperspectralTIRdata...5.2.MethodologytosimultaneouslyderiveLSTandLSEfromthenewgenerationofgeostationarysatelliteswithmultispectraland

multi-temporaldata.......................................................5.3.Re nementofLSTretrievalalgorithmswiththeconsiderationofaerosolandcirruseffects.....................5.4.Retrievalofcomponenttemperaturesinheterogeneouspixels..................................5.5.MethodologyforretrievingLSTfrompassivemicrowavedataandforcombiningLSTsretrievedfromTIRandpassivemicrowavedata5.6.MethodologyforangularnormalizationofLST.........................................5.7.Methodologyfortemporal(time)normalizationofLST.....................................5.8.ConcernsonthenewlydevelopedHyperspectralInfraredImager................................5.9.Physicalmeaningofsatellite-derivedLSTanditsapplications..................................5.10.Validationofsatellite-derivedLST...............................................Acknowledgments............................................................References................................................................

..........................

30303131313132323233333333

1.Introduction

Asthedirectdrivingforceintheexchangeoflong-waveradiationandturbulentheat uxesatthesurface–atmosphereinterface,landsur-facetemperature(LST)isoneofthemostimportantparametersinthephysicalprocessesofsurfaceenergyandwaterbalanceatlocalthroughglobalscales(Andersonetal.,2008;Brunsell&Gillies,2003;Karnielietal.,2010;Kustas&Anderson,2009;Zhangetal.,2008).KnowledgeoftheLSTprovidesinformationonthetemporalandspatialvariationsofthesurfaceequilibriumstateandisoffundamentalimportanceinmanyapplications(Kerretal.,2000).Assuch,theLSTiswidelyusedinavarietyof eldsincludingevapotranspiration,climatechange,hy-drologicalcycle,vegetationmonitoring,urbanclimateandenviron-mentalstudies,amongothers(Arn eld,2003;Bastiaanssenetal.,1998;Hansenetal.,2010;Kalmaetal.,2008;Kogan,2001;Su,2002;Voogt&Oke,2003;Weng,2009;Wengetal.,2004)andhasbeenrecog-nizedasoneofthehigh-priorityparametersoftheInternationalGeosphereandBiosphereProgram(IGBP)(Townshendetal.,1994).Duetothestrongheterogeneityoflandsurfacecharacteristicssuchasvegetation,topography,andsoil(Liuetal.,2006;Neteler,2010),LSTchangesrapidlyinspaceaswellasintime(Prataetal.,1995;Vauclinetal.,1982)andanadequatecharacterizationofLSTdistributionanditstemporalevolution,therefore,requiresmeasurementswithdetailedspatialandtemporalsampling.Giventhecomplexityofsurfacetemper-atureoverland,groundmeasurementscannotpracticallyprovidevaluesoverwideareas.Withthedevelopmentofremotesensingfromspace,satellitedataoffertheonlypossibilityformeasuringLSTovertheentireglobewithsuf cientlyhightemporalresolutionandwithcompletespatiallyaveragedratherthanpointvalues.

Satellite-basedthermalinfrared(TIR)dataisdirectlylinkedtotheLSTthroughtheradiativetransferequation.TheretrievaloftheLSTfromremotelysensedTIRdatahasattractedmuchattention,anditshis-torydatesbacktothe1970s(McMillin,1975).TobetterunderstandtheEarthsystemattheregionalscaleandtogettheevapotranspirationwithanaccuracybetterthan10%,LSTmustberetrievedatanaccuracyof1Korbetter(Kustas&Norman,1996;Moran&Jackson,1991;Wan&Dozier,1996).However,directestimationofLSTfromtheradiationemittedintheTIRspectralregionisdif culttoperformwiththataccuracy,sincetheradiancesmeasuredbytheradiometersonboardsat-ellitesdependnotonlyonsurfaceparameters(temperatureandemis-sivity)butalsoonatmosphericeffects(Li&Becker,1993;Ottlé&Stoll,1993;Prataetal.,1995).Therefore,besidesradiometriccalibrationandcloudscreening,thedeterminationofLSTsfromspace-basedTIRmeasurementsrequiresbothemissivityandatmosphericcorrections(Li&Becker,1993;Vidal,1991).Manystudieshavebeencarriedout,anddifferentapproacheshavebeenproposedtoderiveLSTsfromsatel-liteTIRdata,usingavarietyofmethodstodealwiththeemissivityandatmosphericeffects(Becker&Li,1990b;Gillespieetal.,1998;Hooketal.,1992;Jiménez-Muñoz&Sobrino,2003;Kealy&Hook,

1993;Kerretal.,1992;PozoVazquezetal.,1997;Price,1983,1984;Qinetal.,2001;Susskindetal.,1984;Tonooka,2001;Wan&Dozier,1996;Wan&Li,1997).Consequently,therehavebeenquitealargenumberofpublicationsonLSTretrievalalgorithmsandmethods.ItisimportanttopresentanoverviewofthestateoftheartinLSTretrievalalgorithmsandtodirectfutureresearchintoimprovingtheaccuracyofsatellite-derivedLST.AlthoughtherehavebeenearlierreviewsonLSTretrievalfromspace,presentedbyPrataetal.(1995)andDashetal.(2002),sincethentherehavebeenseveralnewdevelopmentsinLSTre-trievalalgorithmsandthisreviewisintendedtosupplementthosere-viewswithlatestapproaches.TheobjectiveofthispaperistoreviewtheprogressinestimationofLSTfromTIRdataprimarilytakenusingsensorsonboardpolar-orbitsatelliteswhichhavebeenacquiringdatasincethemid-eightiesandtosuggestdirectionsforfutureresearchonthesubject.Section2providesthetheoreticalbasisforretrievingtheLSTfromsatelliteTIRdataandbrie ydiscussessomemajordif cultiesinLSTretrievalfromspacemeasurements,including:(i)thecouplingoftheLST,thelandsurfaceemissivity(LSE)andtheatmosphere;(ii)thephysicalmeaningofsatellite-derivedLST;and(iii)validationproblemsrelatedtosatellite-derivedLST.Section3presentsanoverviewofavarietyofmethodsandalgorithmsforestimatingtheLST.Foreachmethodoralgorithm,themaintheoreticalbasisandassumptionsin-volvedinthedevelopmentofthemodelwillbeoutlined,andthemethod'sadvantages,drawbacksandpotentialwillbehighlighted.Section4reviewsmethodsofvalidatingsatellite-derivedLST.Finally,Section5suggestsfuturedevelopmentsandprovidesperspectivesonretrievingLSTfromremotelysenseddata.2.Basictheoreticalbackground

Allobjectswithtemperaturesgreaterthanabsolutezeroemitradia-tion,andtheamountofradiationfromablackbodyinthermalequilib-riumatwavelengthλandtemperatureTisdescribedbyPlanck'slaw:BλðTÞ¼

C1;Cexp 1ð1Þ

λ5

whereBλ(T)isthespectralradiance(Wm 2μm 1sr 1)ofablack

bodyattemperatureT(K)andwavelengthλ(μm);C1andC2arephysicalconstants(C1=1.191×108Wμm4sr 1m 2,C2=1.439×104μm·K).Becausemostnaturalobjectsarenon-blackbodies,theemissivityε,whichisde nedastheratiobetweentheradianceofanobjectandthatofablackbodyatthesametemperature,mustbetakenintoaccount.Thespectralradianceofanon-blackbodyisgivenbythespectralemis-sivitymultipliedbyPlanck'slawasshowninEq.(1).Obviously,iftheatmosphereexertsnoin uenceonthemeasuredradiance,LST(i.e.T)canberetrievedbymakingtemperatureasthesubjectofEq.(1)oncetheemittedradianceandemissivityareknown.Thewavelengthλmax

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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

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

Rati↑ðθ;φÞ| {z }

Atmosphericemissionterm

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.

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

Forconvenienceandmathematicalshorthand,theradiancesIiandRimeasuredattheTOAandatgroundlevelaregenerallyexpressedintermsofthebrightnesstemperatureswheretheemissivityis xedat1.0.TheTOAandgroundlevelbrightnesstemperaturesTiandTgiarede nedrespectivelybyBiðTiÞ¼IandB

iTgi¼Ri

ð5Þ

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

Xi¼

∫λ21giðλÞXλdλ∫gðλÞdλ;ð6Þ

λ2

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 cantlyreducesthecorrelationoftheRTEsetsandgreatlyimprovestheaccuracyoftheestimatedLST(Lietal.,2013).Additionally,MIRchannelsarelesssensitiv-itytothewatervaporintheatmospherecomparedwithTIRchannels,andtheLSTretrievalfromtheMIRisonlyhalfassensi-tivetoerrorsinemissivityasthatfromtheTIR(Mushkinetal.,2005).Therefore,LSTretrievalwiththeMIRinsteadoftheTIRsoundsmoreappropriate.However,solareffectsaredif culttoeliminateintheMIRduringthedaytimebecausetheseparationofsolarirradiationfromthetotalenergymeasuredintheMIRre-quiresnotonlytheaccurateatmosphericinformationbutalsotheknowledgeofthebidirectionalre ectivityofthesurface.Thisinformationistypicallyunknownandaffectedbyseveralfactors(Adamsetal.,1989;Mushkinetal.,2005),resultingin

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

largeuncertaintiesthatcanleadtoanevenlargererrorontheLSTretrievedfromMIRmeasurements.Therefore,whilethein-troductionoftheMIRchannelsmaybene ttheretrievaloftheLSTincertaincases,itcanalsointroduceevenlargeruncer-taintiesinothers.

(6)HowtophysicallyinterprettheresultsoftheLSTmeasurement

remainsacrucialquestion.AsnotedbyPrataetal.(1995),thedef-initionofthesurfacetemperaturemaydependstronglyonthetypeofapplicationandthemethodofmeasurement.BecausethesurfacetemperatureTsinEq.(4)isde nedusingtheradianceemittedbyasurface,thistemperatureiscalledtheradiometrictemperature(ortheskintemperature)thatcorrespondstothera-diationemittedfromdepthslessthanthepenetrationdepthofagivenwavelength(Becker&Li,1995;Norman&Becker,1995).ThepenetrationdepthisusuallywithinafewmillimetersintheTIRregion(Wan,1999).Thisradiometrictemperaturephysicallydiffersfromotherde nitionoftemperatures,suchasthethermo-dynamictemperaturede nedforamediuminthermalequilibri-umandmeasuredbyathermometer.Forhomogeneousandisothermalsurfaces,theradiometricandthermodynamictemper-aturesarereportedtobeequivalent.Asthethermodynamictem-peratureisactuallyhardtomeasureinreality,evenforwater,theradiometrictemperatureisoftentheonlypracticalmeasureforthehomogeneousandisothermalsurface.However,mostsurfacesarenotinequilibriumandforheterogeneousandnon-isothermalsurfaces,thesetwotemperaturesaredifferent.Consideringthatthespatialresolutionofthecurrentonboardsys-temsvariesapproximatelyfrom10 2to10km2,theremaybeseveralsurfacetypeswithdifferenttemperaturesandemissivitieswithinonepixel,whichcomplicatesthephysicalunderstandingoftheLSTvaluesretrievedfromspaceandtherelationofthera-diometrictemperatureatlargescalestoothertemperaturesusedindifferentapplications.Todate,noconsensushasbeenreachedonthede nitionoftheLSTforheterogeneousandnon-isothermalsurfaces,butthede nitionbyBeckerandLi(1995),whichdependsonthedistributionsoftheLSTandtheLSEwithinapixel,ismeasurablefromspaceandisthusrecommendedforLSTretrievalfromspace.

(7)ValidationofLSTretrievedfromspacebornemeasurementsat

thescaleofthesensor'spixelsisalsochallenging.Validationisproblematicduetothedif cultyofconductinginsituLSTmea-surements,andinobtainingrepresentativeLSTdataatthescaleofasinglepixel.Generally,temperaturesoverthelandsurfacesvarystronglyinspaceandtime(Prataetal.,1995),anditisnotunusualfortheLSTtovarybymorethan10Koverjustafewcentimetersofdistanceorbymorethan1Kinlessthanaminuteovercertaincovertypes.Appropriatelyscalingthesatellite-derivedLSTstothosemeasuredatgroundlevel,especiallyatlargescaleisalsodif cult.ThestrongspatialheterogeneityandtemporalvariationoftheLSTlimitsground-basedvalidationtoseveralrelativelyhomogeneouslandsurfaces,suchaslakes,de-serts,anddenselyvegetatedlandusingdirectcomparisonsofinsitutemperaturemeasurementswithtemperaturesretrievedfromthesatellitedata(e.g.Hooketal.,2005,2003,2007).Acom-plementaryapproachistousesiteswhicharehomogenousintermsofemissivityusingtheradiancebasedvalidationapproach(Hulleyetal.,2009).Sanddunescanbeoneexampleofthistypeofsiteswhicharereferredtoaspseudo-invariantsites(Hulleyetal.,2009).Furthermore,howtoperformarepresentativemea-surementoftheLSTofacomplexheterogeneoussurfaceisalsoacriticalquestion.Scalingmethodsshouldbedevelopedtorelatethemeasurementsatdifferentscalesandhelpvalidatethere-trievedLST(Liuetal.,2006;Wu&Li,2009).Besidesthedif cultiesmentionedaboveintheretrievalofLSTfromspace,theaccuracyoftheLSTdataalsodependsontheperformanceof

thecloudmaskusedtoisolateclearskydataandonthequalityoftheTIRdata,i.e.,thestabilityofthespectralresponsefunctiongi(λ),theSNRandtheaccuracyoftheradiometriccalibration.3.EstimationofLSTfromspace

Overthepastseveraldecades,LSTestimationfromsatelliteTIRmea-surementshassigni cantlyimproved.Manyalgorithmshavebeenpro-posedtotreatthecharacteristicsofvarioussensorsonboarddifferentsatellitesandutilizingdifferentassumptionsandapproximationsfortheRTEandLSEs.Thesealgorithmscanberoughlygroupedintothreecategories:single-channelmethods,multi-channelmethods,andmulti-anglemethods,providedthattheLSEsareknownapriori.IftheLSEsarenotknown,thenthealgorithmscanbecategorizedintothreetypes:stepwiseretrievalmethod,simultaneousretrievalofLSEsandLSTwithknownatmosphericinformation,andsimultaneousretrievalwithunknownatmosphericinformation.3.1.LSTretrievalwithknownLSEs

3.1.1.Single-channelmethod

ThesingleTIRchannelmethod,alsocalledthemodelemissivitymethod(Hooketal.,1992),usestheradiancemeasuredbythesatellitesensorinasinglechannel,chosenwithinanatmosphericwindow,andcorrectstheradianceforresidualatmosphericattenuationandemissionusingatmospherictransmittance/radiancecodethatrequiresinputdataontheatmosphericpro les.LSTisthenretrievedfromtheradiancemeasuredinthischannelbyinvertingtheRTEgiveninEqs.(3)and(4),providedthattheLSEiswellknownorestimatedinadvance(Chédinetal.,1985;Hooketal.,1992;Lietal.,2004a;Mushkinetal.,2005;Ottlé&Vidal-Madjar,1992;Price,1983;Susskindetal.,1984).Accuratedeter-minationoftheLSTusingthismethodrequireshigh-qualityatmospher-ictransmittance/radiancecodetoestimatetheatmosphericquantitiesinvolvedinEqs.(3)and(4),goodknowledgeofthechannelLSE,anac-curateatmosphericpro le,andacorrectconsiderationofthetopo-graphiceffects(Sobrinoetal.,2004b).

Generally,theaccuracyofatmospherictransmittance/radiancecodeisprimarilylimitedbytheradiativetransfermodel(RTM)usedinthecodeandbytheuncertaintiesinatmosphericmolecularabsorptionco-ef cientsandaerosolabsorption/scatteringcoef cients(Wan,1999).ThemostpopularatmosphericRTMs,suchastheseriesofMODTRAN(Berketal.,2003)and4A/OP(Chaumatetal.,2009),havebeenwidelyusedtoperformatmosphericcorrectionsand/ortosimulatesatelliteTIRdata.AfewstudieshaveshownthattheaccuracyofthedifferentRTMsrangesfrom0.5%to2%withinknownatmosphericwindows,suchas3.4–4.1μmand8–13μm,leadingtouncertaintiesintheretrievedLSTof0.4Kto1.5K(Wan,1999).Itisworthnotingthattheincompletecharacterizationsofatmosphericpro lesusedincompensationforat-mosphericabsorptionandpathradianceconstituteaseriousproblemeveniftheRTMitselfiscompletelyerror-free(Gillespieetal.,2011).Studieshavealsodemonstratedthatanerrorof1%intheLSEcangiverisetoanerrorintheLSTrangingfrom0.3Kforahotandhumidatmo-sphereto0.7Kforacoldanddryatmosphere(Dashetal.,2002).Asthesinglechannelisusuallychosenaround10μmwheretheLSEformostlandsurfacescanbeknownwithinafewpercent,theuncertaintyinLSEmayleadtoanerrorof1Kto2KinLSTifthesingle-channelmeth-odisused.However,iftheLSEisknownatawavelengthwithintheTIRatmosphericwindow,thenanyerrorwillbesolelyduetoincorrectre-movaloftheatmosphericcontribution.Atmosphericpro lesaregener-allyobtainedeitherfromground-basedatmosphericradiosoundings,fromsatelliteverticalsoundersorfrommeteorologicalforecastingmodels.Duetothehighspatialandtemporalvariabilityoftheatmo-sphericwatervapor,theuseofground-basedradiosoundingsfarfromtheareaofinterestand/orfarfromthetimeofsatelliteoverpassmayre-sultinlargeerrorsintheLST(Cooper&Asrar,1989).Ontopofthese,radiosoundingsreportedmeasurementerrorsareoftheorderof0.5K

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fortemperatureand10%forwatervapor(Maetal.,1999),andtheyaremostlyassociatedtotwotypesofuncertainties:1)theactualsoundinglocationandplacewheretheballoonissetfreemaybeseveralkilome-tersapart(upto60km);2)theatmosphericstatuswillchangewhentheballoonriseswhichmeanstheatmosphericpro lesatdifferentheightsaremeasuredatdifferenttimes.ThoseuncertaintiesabouttheatmospherewillfurtherpropagateintotheretrievedLST.Finally,asradiosoundingsarenotcurrentlyavailablewithsuf cientspatialdensi-tyorincoincidencewiththetimeofthesatelliteoverpass,theycanbeonlyusedoccasionallyforvalidationpurposesatsomespecialsites(Colletal.,2005).Incontrast,atmosphericpro lesderivedfromsatellitever-ticalsounderscan,intheory,beusedtoretrievetheLSTfromconcur-rentTIRdataintheatmosphericwindowusingthesingle-channelmethod.Unfortunately,theaccuracyoftheretrievedatmosphericpro- lesnearthesurfaceisinsuf cientforthesingle-channelmethod(Chédinetal.,1985;Ottlé&Stoll,1993;Susskindetal.,1984),andlargeerrorsintheLSTretrievalcanresult.Today,thepro lesprovidedasforecasts,analysisorreanalysisbynumericalweatherpredictioncen-ters,suchastheNationalCentersforEnvironmentalPrediction(NCEP)andtheEuropeanCentreforMedium-RangeWeatherForecasts(ECMWF),constituteapracticalalternativetotheuseofradiosoundings.Colletal.(2012a)andJiménez-Muñozetal.(2010)reportedeitherat-mosphericpro leproductsorreanalysismayyieldreasonableresultstomeettherequiredaccuracyformanycases.Furthermore,Freitasetal.(2010)quanti edtheimpactofECMWFforecasterrorsofatmospher-ichumidityonLSTretrievals,showingthatitisgenerallylessthan0.5K.Nevertheless,theatmosphericpro lesareoftenprovidedatspatialcoarserthanthatofthesatelliteanditisthereforenecessarytointerpo-latetheatmosphericquantitiesintermsoftheviewingzenithangle,theterrainaltitude,spaceandtime(Jiangetal.,2006;Schroedteretal.,2003;Tang&Li,2008).

Toreducethedependenceonradiosoundingdata,severalsingle-channelalgorithmshavebeenproposedwithinthepastdecadetoesti-matetheLSTfromsatellitedataassumingthattheLSEisknown.Qinetal.(2001)proposedamethodtoestimatetheLSTspeci callyfromLandsat-5(ThematicMapperchannel6,TM6)datausingonlythenear-surfaceairtemperatureandwatervaporcontentinsteadofatmo-sphericpro lesusingempiricallinearrelationshipsbetweentheatmo-spherictransmittanceandthewatervaporcontentandbetweenthemeanatmospherictemperatureandthenear-surfaceairtemperature.Jiménez-MuñozandSobrino(2003)andJiménez-Muñozetal.(2009)developedageneralizedsingle-channelalgorithmforretrievingtheLSTfromanyTIRchannelwithaFWHM(fullwidthathalfmaximum)of~1μm,providedthattheLSEandthetotalatmosphericwatervaporcon-tentareknown.Thisgeneralizedsingle-channelalgorithmrequirestheminimuminputdataandcanbeappliedtodifferentthermalsensorsusingthesameequationandcoef cient.Cristóbaletal.(2009)foundthattheinclusionofnear-surfaceairtemperaturetogetherwithwatervaporcontentinthesingle-channelmethodimprovesLSTretrievalespe-ciallyunderintermediateandhighatmosphericwatervaporcontentconditions.Sobrinoetal.(2004b),SobrinoandJiménez-Muñoz(2005)andJiménez-MuñozandSobrino(2010)analyzedandcomparedtheaforementionedalgorithmsandpointedoutthatallofthesingle-channelalgorithmsthatuseempiricalrelationshipsprovidepoorresultsathighatmosphericwatervaporcontentsbecausetherelation-shipsincludedinthealgorithmsbecomeunstableathighwatervaporconcentrations.

Itshouldbekeptinmindthatthesingle-channelmethodsinvolveasimpleinversionoftheRTE,providedthattheLSEandtheatmo-sphericpro lesareknowninadvance.ThesemethodscanprovidetheoreticallyaccurateLSTretrieval,butLSEisrarelyknownwiththenecessaryaccuracy.

3.1.2.Multi-channelmethod

AshighlightedinSection3.1.1,theuseofthesingle-channelmethodrequiresthatLSEisknowna-prioriforeachpixelaswellas

anaccurateRTMandaccurateknowledgeoftheatmosphericpro lesoverthestudyareaatthesatelliteoverpass.Theserequirementsaredif cultorevenimpossibletosatisfyinmostpracticalsituations.ToobtaintheLSTfromsatelliteTIRdatawithsuf cientaccuracyonaglobalorregionalscale,othermethodsmustbedeveloped.Analter-nateapproachusedovertheoceansutilizesthedifferentialatmo-sphericabsorptioninthetwoadjacentchannelscenteredat11and12μmintheso-calledsplit-windowalgorithm(SW) rstproposedbyMcMillin(1975)whichdoesnotrequireanyinformationabouttheatmosphericpro lesatthetimeoftheacquisition.Sincethen,avarietyofSWtechniqueshavebeendevelopedandmodi edtosuc-cessfullyretrievetheseasurfacetemperature(SST)(Bartonetal.,1989;Deschamps&Phulpin,1980;França&Carvalho,2004;Llewellyn-Jonesetal.,1984;McClainetal.,1985;Niclòsetal.,2007;Sobrinoetal.,1993).

EncouragedbythesuccessoftheSWmethodforestimatingtheSSTfromspacemeasurements,manyeffortshavebeenmadesincethelate1980stoextendtheSWmethodtoretrievetheLST.Withmodi cationstotreatthespatio-temporalandspectralvariationsoftheLSE,thelargedifferencebetweentheLSTandtheairtemperature,thetotalcolumnwatervapor(WV)intheatmosphere,andtheviewingzenithangle(VZA),avarietyofSWalgorithmsforLSTretrievalhavebeenproposed.ThesealgorithmsassumethattheLSEsinbothSWchannelsareknownapriori(Atitar&Sobrino,2009;Becker,1987;Becker&Li,1990b;Colletal.,1994;Prata,1994a,b;Price,1984;Sobrinoetal.,1991,1994,1996;Tangetal.,2008;Ulivierietal.,1994;Wan&Dozier,1996).BelowisabroadoverviewofthedifferentSWalgorithmsfoundintheliterature.3.1.2.1.Linearsplit-windowalgorithm.AlinearSWalgorithmcanbedevelopedutilizingthedifferentialabsorptionintwoadjacentTIRchannelsi,jinthe10–12.5μmlinearizingtheRTEwithrespecttothetemperatureorwavelength.ThisalgorithmexpressestheLSTasasimplelinearcombinationofthetwobrightnesstemperaturesTiandTjmeasuredinthetwoTIRchannels(McMillin,1975).Atypicallinearsplit-windowalgorithmcanbewrittenasLST¼aT

0þa1iþa2Ti Tj;

ð7Þ

whereak(k=0,1,and2)arecoef cientsthatdependprimarilyonthespectralresponsefunctionofthetwochannelsgi(λ)andgj(λ),thetwochannelemissivitiesεiandεj,theWV,andtheVZA.Thus:a ;ε

k¼fkgi;gj;εij;WV;VZA:

ð8Þ

ItshouldbepointedoutthattheaccuracyofthisLSTretrievalmethodisdependentonthecorrectchoiceofthecoef cientsak,whicharepre-determinedeitherbyregressingthesimulatedsatellitedatawithasetofatmospheresandsurfaceparametersorempiricallybycomparingthesatellitedataagainstinsituLSTmeasurements.Itisextremelydif culttoobtainarepresentativeinsituLSTatsatellitepixelscale(afewkm2)thatisalsosynchronizedwiththesatellite'smeasurementsoverawiderangeofsurfacetypesandatmosphericconditions.Therefore,thesimulationofTOAbrightnesstemperatures,usinganRTMsuchasMODTRAN(Berketal.,2003),representsthemostef cientwaytogeneratethedatathatallowspre-determiningrobustestimatesofthecoef cientsakbycomparingsimulatedsatel-litedataagainstthepresetLSTusedinthesimulation.

Overthepastseveraldecades,manylinearSWalgorithmshavebeendevelopedintheliterature,allofwhichhavesimilarformsbutdifferentparameterizationsofthecoef cientsak.Thesecoef cientsareparameterizedeitheraslinearornon-linearfunctionsofvariouscombinationsoftheLSEs,theWV,andtheVZA.

(1)Parameterizationofthecoef cientsakwithconsiderationofLSEs.

Variousparameterizationsofthecoef cientsakintheSWasfunctionsoftheLSEshavebeendeveloped,andallaresomewhat

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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

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.

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.OneoftheadvantagesoftheGSWalgorithmthatshouldbehighlightedhereisthatLSTretrievalislesssensitivetotheuncertaintiesintheLSEsandtheatmosphericconditions.Consequently,severalSWfor-mulassimilartotheGSWalgorithmhaverecentlybeendevelopedtoestimateLSTsfromdifferentsatelliteinstruments,suchastheSpinningEnhancedVisibleandInfraredImager(SEVIRI)andFengYunMeteorologicalsatellite(FY-2C)instruments(Atitar&Sobrino,2009;Jiang&Li,2008b;Tangetal.,2008).However,theerrorsintheGSWretrievedLSTsmaybelargerinbaresoilsitesincaseswhereLSTsarelargerthanTabymorethan16K(Wan&Li,2008).Asetofnewco-ef cientsdevelopedforbaresoillandsbasedonRTsimulationdatainamuchwideLSTrangehasbeenusedinthenewversionofthe

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GSWalgorithmpreparedforthereprocessingandforwardprocessingofthecollection-6orversion-6MODISLSTproductinthenearfuture.3.1.2.2.Non-linearsplit-windowalgorithm.Becauseoftheerrorsintro-ducedbylinearizingoftheRTEandalsobysomeapproximationsusedinthedevelopmentofSWalgorithms,e.g.,approximatingthetransmittanceasalinearfunctionoftheWV,thelinearSWalgorithmdescribedbyEq.(7)resultsinlargeerrorsinLSTretrievalunderwetandhotatmosphericconditions.ToimprovetheaccuracyofLSTre-trieval,non-linearSWalgorithmshavebeendeveloped:LST¼c 2

0þc1T1þc2Ti Tjþc3Ti Tj;

ð12Þ

whereck(k=0–3)arecoef cientspre-determinedbyregressingEq.(12)onsimulatedsatellitedatawithasetofatmospheresandsurfaceparameters,similartotheakinEq.(7).

Manysimilarformsofnon-linearSWalgorithmshavebeendevel-opedintheliteratureinrecentdecades(Atitar&Sobrino,2009;Coll&Caselles,1997;François&Ottlé,1996;Sobrino&Raissouni,2000;Sobrinoetal.,1994).SimilartothelinearSWalgorithms,someofthesenon-linearSWalgorithmsincorporatetheLSEsintothecoef -cientsck,someuseboththeLSEandtheWV,andsomealsoincorpo-ratetheVZA.

(1)WithconsiderationofLSEs

ToaccountfortheeffectoftheLSEsonLSTretrieval,Sobrinoetal.(1994),CollandCaselles(1997)proposedanon-linearSWalgorithmwithaformsimilartoEq.(12)withc0formulatedasalinearfunctionofεandΔε:

c0¼D0þD1ð1 εÞþD2Δε;

ð13Þ

wherethecoef cientsDk(k=0–2)areconstantsthatareinde-pendentoftheatmosphere.SunandPinker(2003)alsopro-posedanon-linearSWalgorithminwhichtheLSEsareimplicitlyconsideredbymakingeachparameterckinEq.(12)dependentonthelandsurfacetype.(2)WithconsiderationofLSEsandWV

Tofurtherimprovetheaccuracyofandreducethein uenceofwetatmosphericconditionsonLSTretrieval,SobrinoandRaissouni(2000)andSobrinoetal.(2004a)developedanon-linearSWalgorithmtoretrievetheLSTfromthegloballand1-kmAdvancedVeryHighResolutionRadiometer(AVHRR)datawithanestimat-ederrorof1.3KcomparedwithasetofthreehundredLSTsmea-suredinsituintworegionsofAustralia(Prata,1994b).TheyparameterizedDk(k=1,2)inc0(Eq.(13))aslinearfunctionsofWV,i.e.,

Dk¼E0;kþE1;kWV

ðk¼1;2Þ;

ð14Þ

inwhichthecoef cientsEaresensor-dependentconstants.(3)WithconsiderationofLSEs,WV,andVZA

ToimprovetheaccuracyofLSTretrievalfromTIRdatameasuredatlargerVZA,theVZAhastobeconsideredwhendevelopingtheLSTretrievalalgorithm.SobrinoandRomaguera(2004)andAtitarandSobrino(2009)proposedaphysics-basednon-linearSWalgorithmforSEVIRIdataintwoTIRchannels.Theysetc1=1andparameterizedthecoef cientsck(k=2,3)inEq.(12)andEinEq.(14)aslinearfunctionsofthesquareofthesecantoftheVZA.IthasbeenshownthatthistypeofSWiscapableofobtainingLSTvalueswitharootmeansquarederror(RMSE)of1.3KusingSEVIRIdataatVZAslowerthan50°.3.1.2.3.Linearornon-linearmulti-channelalgorithms.WhentherearethreeormoreTIRchannelsavailable,theLSTcanberetrievedfromalinearornon-linearcombinationoftheTOAbrightnesstemperatures

inthosechannelsusingmethodssimilartotheSWalgorithmsdescribedabove(Sun&Pinker,2003,2005,2007).Forinstance,SunandPinker(2003)developedathree-channellinearalgorithmtoretrievenight-timeLSTsfromtheGeostationaryOperationalEnvironmentalSatellite(GOES)data,assumingthattheLSEsinthesethreechannelscanbees-timatedfromthelandsurfacetypes.Theyproposedtousethecharac-teristicsoftheMIRchanneli1at3.9μmtoimprovetheatmosphericcorrectionatnight,andthecoef cientsinthethree-channellinearequationexplicitlyincludethechannelLSEs,butneglecttheWVandtheVZA:

LST¼dd1 εi1 ε!0þd1þ2

Tdj

iþd3þ4Tj iþd1 ε

5þd6

Ti1;ð15Þ

wherethecoef cientsdk(k=0–6)areconstants,parisonwithsomepublishedSWalgorithms(Becker&Li,1990b;Wan&Dozier,1996)demonstratedthatthepro-posedthree-channelalgorithmobtainedthebestLSTvalues,withanRMSElessthan1K(Sun&Pinker,2003).Furthermore,SunandPinker(2007)alsoproposedafour-channelnon-linearalgorithmtore-trievetheLSTfromSEVIRIdata,withthecoef cientsdependingonlandsurfacetypestoaccountforLSEeffects.ForLSTretrievalatnight-time,Eq.(16)isused

LST¼e 2

0þe1Tiþe2Ti Tjþþe3ðTi1 Ti2Þþe4Ti Tj

þe5ðsecVZA 1Þ;

ð16Þ

wherethesubscripti2representstheTIRchannelat8.7μmandtheco-ef cientsek(k=0–5)aredependentonthelandsurfacetype.Toac-countforthesolarradiationre ectedbytheEarth'ssurfaceintheMIRchanneli1duringthedaytime,asolarcorrectiontermd6Ti1cosθswasaddedtoEq.(16)(Sun&Pinker,2007)orasolarcorrectionmustbeperformedtotheTi1usingthemethodproposedbyAdamsetal.(1989)andMushkinetal.(2005).Whenevaluatedagainstgroundob-servations,theresultsshowedthattheLSTsretrievedusingthefour-channelalgorithmweremoreaccuratethanthoseobtainedusingtheGSWalgorithm.

However,itshouldbenotedthatMIRdatameasuredattheTOAduringthedaytimeconsistsofacombinationofre ectedsolarradi-anceandemittedradiancefromboththesurfaceandtheatmosphere,andtheerrorcausedbythesolarcorrectiontermcanaffecttheaccu-racyofLSTretrievalespeciallyinaridandsemi-aridregionswithhighre ectanceintheMIR.Inaddition,introducingonemorechannelcomeswiththeexpenseofincreasedmeasurementerrors.Theerrorsrelatedtoinstrumentalnoiseandotheruncertainties,suchasinsur-faceemissivityofthe8.7μmchannelinaridregions,alsoin uencethe nalLSTretrievalaccuracy.Therangeofemissivityvaluesandre-spectiveuncertaintyfornaturalorman-madesurfacesissigni cantlyhigherforMIRand8.7μmchannelsthanforthemostcommonlyusedSWchannels(Trigoetal.,2008b),furtherlimitingthewidespreaduseofthosechannelsforoperationalpurposes.

3.1.3.Multi-anglemethod

SimilartotherationaleofSWmethod,themulti-anglemethodisbasedondifferentialatmosphericabsorptionduetothedifferentpath-lengthswhenthesameobjectisobservedinagivenchannelfromdifferentviewingangles(Chédinetal.,1982;Lietal.,2001;Prata,1993,1994a,b;Sobrinoetal.,1996,2004c).

Thismethodwasprimarilydevelopedbasedonthe rstsensortooperateinbiangular-mode,theAlongTrackScanningRadiometer(ATSR)onboardthe rstEuropeanRemoteSensingSatellite(ERS-1).ATSRcanachieveadual-angleobservationofthesameregionoftheEarth'ssurfacewithinabout2min.Oneviewingangleisthenadir

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withazenithalanglefrom0°to21.6°,andtheotheristheforwardviewwithazenithalanglefrom52°to55°.AssumingthattheLSTandSSTareindependentontheVZAandthattheatmosphereishorizontallyuni-formandstableovertheobservationtime,Prata(1993,1994a)derivedadual-anglemethodtoretrievetheSSTandtheLSTfromATSRdata.Sobrinoetal.(1996)laterproposedanimproveddual-anglealgorithmthatincorporatestheemissivityεnatnadirandtheemissivityεfatfor-wardview:

LST¼T

nþp1Tn Tfþp2þp3ð1 εnÞþp4εn εf;

ð17Þ

wherepk(k=1–4)arecoef cientsrelatedtotheatmospherictransmit-tancesandmeanairequivalenttemperaturesinthenadirandforwardviews;TnandTfarethebrightnesstemperaturesmeasuredinthenadirandforwardviews,respectively.ThisalgorithmincludesonlyemissivitydependenceandhasnoexplicitWVdependence.Anon-lineardual-anglealgorithmhasbeendevelopedbySobrinoetal.(2004c)toreducethein uenceofatmosphericWVontheLSTretrieval:LST¼Tnþq

1Tn Tfþq2Tn Tf

þðq3þq4WVÞð1 εnÞ

þðq5þq6WVÞΔεþq0;

ð18Þ

whereqk(k=0–6)ingsimulatedTIRdata,SobrinoandJiménez-Muñoz(2005)comparedtheLSTsretrievedusingthedual-anglealgorithmgiveninEq.(18)andthenon-linearSWalgorithmincorporatingLSEs,WV,andVZAdescribedin3.1.2.2.Theresultsshowedthatthedual-anglealgorithmissuperiortotheSWalgorithmprovidedthatthespectralandangularvariationsoftheLSEsarewellknown.

However,itshouldbenotedthatalthoughthemulti-angle(dual-angle)algorithmprovidesbetterresultsthantheSWalgorithm,thedual-anglealgorithmhasseveralpracticaldif cultieswhenappliedtosatellitedata(Sobrino&Jiménez-Muñoz,2005).Acriticalphenome-noninthemulti-anglemethodistheangulardependenceoftheemis-sivity,astheangularbehaviorofnaturalsurfacessuchassoilsandrocksisnotwellknownatthescalesofsatellite'sspatialresolution(Sobrino&Cuenca,1999).TheangulardependenceoftheLSTisalsoanissue.Inadditiontotherequirementthattheatmosphereisfreeofcloudsandhorizontallyuniform,themulti-angularmeasurementsmusthavesigni cantdifferenceinslantpath-lengths.Otherwise,themeasurementswillbehighlycorrelated,andthealgorithmwillbeun-stableandextremelysensitivetomeasurementnoise(Prata,1993,1994a).Furthermore,“thesame”objectobservedatdifferentviewinganglescancoverdifferentsensorareas(intermsofpixels).Eventhoughthesamepixelsizemaybeobtained,anobjectobservedatdifferentobservationanglesmayalsoappeartotallydifferentbecauseofthethree-dimensionalstructureoftheobject.Finally,mis-registrationofpixelsunderdifferentviewinganglescanresultindrasticerrorsintheLSTretrievalresults.Consequently,multi-anglemethodscanonlybeappliedtohomogeneousareas(forexample,thesurfaceoftheseaordenselyvegetatedforest)inidealatmosphericconditionsbutnottoheterogeneousareas.

3.2.LSTretrievalwithunknownLSEs

AllofthemethodsmentionedaboveestimatetheLSTbyassumingthattheLSEisknown.Inpractice,theheterogeneityofthesurfaceandtheangularandspectralvariationoftheLSE(Lietal.,2013)makeitchallengingtoexactlydeterminetheLSEatthesatellitepixelscaleinadvance.Theemissivityofland,unlikethatofoceans,candiffersigni cantlyfromunityandcanvarywithvegetation,sur-facemoisture,roughness,andviewingangle(Salisbury&D'Aria,1992).Therefore,theLSEsmeasuredinthelaboratorycannotbearbi-trarilyusedatthepixelscale.Generally,anuncertaintyof1%inthe

LSEwillresultinabout0.5KerrorsintheLSTundernormalcondi-tions.Toensurethetargetof1KaccuracyinLSTretrieval,methodstoestimatetheLSEfromspacemustalsobedeveloped.Todate,thereareatleastthreedistinctmethodstoestimatetheLSTfromspacewhentheLSEisnotknown.The rstisastepwiseretrievalmethodthatdeterminestheLSEandtheLSTseparately.TheLSEises-timated rst,andthentheLSTisretrieved.Thesecondisasimulta-neousretrievalmethodthattreatsboththeLSTandtheLSEasunknownsandresolvesbothofthemfromtheatmosphericallycorrectedradiancesorwithapproximatedatmosphericpro les.Thethirdisafurtherdevelopmentofthesimultaneousretrievalmethodthatsimultaneouslyretrievestheatmosphericpro les(oratmo-sphericquantitiesintheRTE)withtheLSTandLSE.

3.2.1.Stepwiseretrievalmethods

ThistypeofmethodretrievestheLSTusingtwoconsecutivesteps.First,theLSEis(semi-)empiricallydeterminedfromvisible/near-infrared(VNIR)measurementsorphysicallyestimatedfrompairsofatmosphericallycorrectedMIRandTIRradiancesatgroundlevel.Then,theLSTisestimatedusinganyofthesingle,multi-channel(SW)ormulti-angle(dual-angle)retrievalmethodsde-scribedinSection3.1.Representativestepwisemethodsincludetheclassi cation-basedemissivitymethod(Peres&DaCamara,2005;Snyderetal.,1998;Sun&Pinker,2003),thenormalizeddifferencevegetationindex(NDVI)-basedemissivitymethod(Sobrino&Raissouni,2000;Valor&Caselles,1996;VandeGriend&Owe,1993),andthetemperature-independentspectral-indicesmethod(Becker&Li,1990a;Li&Becker,1993;Lietal.,2000).AsidefromthepreviouslydiscussedadvantagesanddisadvantagesoftheLSTre-trievalmethodswithknownLSEs,stepwiseretrievalmethodspresentspeci ccharacteristicsthatwillbebrie ypresentedinthefollowingsections.

3.2.1.1.Classi cation-basedemissivitymethod(CBEM).Thismethodas-sumesthatsimilarlyclassi edlandcoversexhibitedverysimilarLSEs.TheLSEcanbeassignedfromlook-uptablesbasedonconventionallandcoverclassi cationinformation.Snyderetal.(1998)reportedthattheLSEvaluesof70%oflandcovercanbeestimatedwithinsuf cientaccuracy(about0.01)usingthismethodbyconsideringseasonalanddynamicstatechanges,thusmeetingthegoalof1Kac-curacyofLSTretrieval,intheory.

Generally,theCBEMisthesimplestmethodintermsofprocess-ing,anditcanprovideaccurateLSEsforLSTretrievalaslongasthelandsurfacesareaccuratelyclassi edandeachclasshaswell-knownLSEs(Gillespieetal.,1996).Evenfordataatcoarseresolu-tions,suchasgeostationarysatellitedata,theCBEMcanbeapplicableusingalinearmixingmodel(Peres&DaCamara,2005;Sun&Pinker,2003;Trigoetal.,2008b).However,theLSEwillbelessaccuratebe-causeitisdif culttoestimatetheweightsofeachcomponent(endmember)withinacoarsepixel.

OncetheLSEisobtained,theLSTcanbeestimateddirectlyfromthemethodsdescribedinSection3.1.TheLSTretrievalaccuracyisde-terminedprimarilybytheaccuracyoftheLSEs.AsdescribedbySnyderetal.(1998),theaccuracyofCBEMcandegradeduetouncer-taintiesinthesoilmoisture,theannualbiophysicalcycleofvegeta-tion,andtheappearanceofsnowandice.Inaddition,classi cationsbasedonVNIRdataaregenerallynotwellcorrelatedtotheLSEintheTIRchannel.Forexample,estimatingtheLSEusingtheCBEMforgeologicsubstratesisuncertainbecausetheVNIRre ectivitiesusedtoclassifythelandsurfacesrespondmainlytoOH-andFe-oxidesinthelandsurface,whiletheLSEintheTIRchannelsaremainlyrespon-sivetotheSi-Obond(Gillespieetal.,1996).Furthermore,discontinu-itiesintheclassi cationwillcauseinappropriatediscontinuitiesintheLSEmap,whichcanappearseamedorcontoured(Gillespieetal.,1996).Finally,theCBEMismostsuitableforspectralregionswithlowspectralcontrastLSEs,forexamplearound11μmand

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12μmformostterritorialsurfaces.Otherwise,alargeretrievalerrormaybecausedbyvariationsintheemissivity.Alloftheseuncer-taintiesmaypreventanaccurateestimationoftheLSEfromCBEM,thusdegradingtheaccuracyofLSTretrieval.

3.2.1.2.NDVI-basedemissivitymethod(NBEM).ThismethodisbasedonastatisticalrelationshipbetweentheNDVIderivedfromtheVNIRbandsandtheLSEintheTIRchannels.VandeGriendandOwe(1993) rstfoundaveryhighcorrelationbetweentheLSEintheTIRchannelscovering8–14μmandthelogarithmicNDVI.Subse-quently,ValorandCaselles(1996)appliedthismethodtoestimatetheeffectiveLSEofaroughrow-distributedsystem.StartingfromthemethodproposedbyValorandCaselles(1996),SobrinoandRaissouni(2000)reducedthecomplexityandformulatedanopera-tionalNDVIthresholdmethodtoderivetheLSEfromspace.Thismethodassumesthat:1)thesurfaceisonlycomposedofsoilandveg-etation;2)theemissivityofthebaresoilcanbelinearlyrepresentedbythesurfacere ectivityintheredchannel;3)theLSEchangeslin-earlywithrespecttothefractionofvegetationinapixel.Therefore,theLSEofTIRchannelicanbeestimatedusingthreelinearfunctionscorrespondingtoconditionsinwhichapixeliscomposedoffullveg-etation,offullsoilorofmixedsoil/vegetationcontent.

Becauseofitssimplicity,thismethodhasalreadybeenappliedtovarioussensorswithaccesstoVNIRdata(Momeni&Saradjian,2007;Sobrino&Raissouni,2000;Sobrinoetal.,2002,2004b,2008,2003).SimilartotheCBEM,anaccurateatmosphericcorrectionisun-necessary.However,theNDVIthresholdsthatindicatebaresoilandfullvegetationcover,thevegetationfraction,anycavityeffects,andtheLSEsforbaresoilandfullvegetationmustbeknowninadvance.SinceNDVIisusedasaproxyforthefractionofvegetatedsurfacewithinthepixel,itcanbereplacedbymoreaccurateestimatesofthisvariable(e.g.,Trigoetal.,2008b).Nevertheless,oneofthedrawbacksofthismethodisthelackofcontinuityintheLSEvaluesofregionstransitioningfromsoil-typetovegetation-type,becausetheLSEsinthoseregionsarecalculatedusingdifferentformulae(Sobrinoetal.,2008).Usingnumericalanalysis,Sobrinoetal.(2008)foundthatthismethodcanonlyprovideacceptableresultsinthe10–12μminterval,becausetheNDVI-LSErelationshipforbaresoilsamplesdoesnotprovidesatisfactoryresultsbeyondthesespectralintervals.Inaddition,thisrelationshipmayholdforsoilandvegetationmixingareas,butsurfaceslikewater,ice,snowandrocksmustbetreatedseparately(Sobrinoetal.,2008).Becauseitrequiresaprioriknowledgeoftheemissivitiesofsoilandvegetation(Sobrino&Raissouni,2000),thedeterminationofthesoilemissivitymaybetheprimarysourceoferrorinthismethod(Jiménez-Muñozetal.,2006).

3.2.1.3.Day/nighttemperature-independentspectral-indices(TISI)basedmethod.BeckerandLi(1990a),andLiandBecker(1990) rstproposedaTISI-basedmethodtoperformspectralanalysisintheTIRregion.Subsequently,assumingthattheTISIij(iistheMIRchan-nelandjistheTIRchannel)inthedaytimewithoutthecontributionofsolarilluminationisthesameastheTISIijinthenight-time,LiandBecker(1993)andLietal.(2000)furtherdevelopedaday/nightTISI-basedmethodto rstextractthebidirectionalre ectivityinMIRchannelibyeliminatingtheemittedradianceduringthedayinthischannelbycomparingtheTISIijinthedaytimeandthenighttime.Oncethebidirectionalre ectivityinanMIRchannelisretrieved,thedirectionalemissivityinthatMIRchannelcanbeestimatedtobecomplementarytothehemispheric-directionalre ectivity,whichcanbeestimatedfromabidirectionalre ectivitydataseriesusingeitheranangularformfactor(Lietal.,2000),asemi-empiricalphe-nomenologicalmodel(Petitcolinetal.,2002)orakernel-drivenbidi-rectionalre ectivitymodel(Jacobetal.,2004;Jiang&Li,2008a;Lucht&Roujean,2000;Roujeanetal.,1992;Wanneretal.,1995).Finally,basedontheconceptoftheTISI,theLSEsintheTIRchannelscanbe

obtainedfromthetwo-channelTISIandtheemissivityintheMIRchannel(Jiangetal.,2006;Lietal.,2000).OncetheLSEsareknown,theLSTcanberetrievedusingthemethodsdescribedinSection3.1.

Becausethesingle-channelmethodissensitivetouncertaintiesintheatmosphericcorrections,themulti-channel(SW)LSTretrievalmethodsarerecommendediftheLSEsareestimatedusingtheday/nightTISImethod.LiandBecker(1993)indicatedthattheuseofanapproximate(standard)atmosphereinsteadofanactualatmosphereleadsto3%orsmallererrorsintheLSEand0.5KintheLSTusingtheSWalgorithms.

Becauseofitsphysicalbasis,theday/nightTISIbasedmethoddoesnotrequireanyaprioriinformationaboutthesurfaceandcanbeap-pliedtoanysurface,eventhosewithstrongspectraldynamics.General-ly,thetime-invariantLSEassumptionappearstobereasonableinmostsituations.TheLSEswillremainunchangedoverseveraldaysunlessrainand/orsnowoccur.Itisworthnotingthatnighttimedewformationmayaffecttheassumption,especiallyforlow-emissivitysurfacesindryareas(Snyderetal.,1998).Althoughthefrequencyofdewoccurrenceisnotsohighinmostsemi-aridandaridregions,itisworthtotrycheckingtherelativehumidityvalueinthelowboundarylayertoavoidheavydeweventsbecomingaseriousproblem(Wan,1999).Therefore,thismethodissuperiortothe(semi-)empiricalstepwisere-trievalmethodsabove,especiallyonbareandgeologicsubstratesthatexhibitcontrastemissivities.

However,severalrequirementsmaylimittheusageofthisalgo-rithminLSTretrievalfromspace.Firstofall,approximateatmospher-iccorrectionsandconcurrenceofbothMIRandTIRdataarerequired(Sobrino&Raissouni,2000).Then,accurateimageco-registrationmustbeperformed(Dashetal.,2005).Additionally,thesurfacesmustbeobservedundersimilarobservationconditions,e.g.,viewingangle,duringbothdayandnight(Dashetal.,2005).

3.2.2.SimultaneousLSTandLSEretrievalmethodswithknownatmosphericinformation

BecausetheaccuracyoftheretrievedLSTisprimarilydependentontheaccuracyoftheLSE,simultaneousdeterminationoftheLSEandtheLSThasbeenproposedtoimprovetheretrievalaccuracy.Manysimulta-neousLSTandLSEretrievalmethodswithgivenknownatmosphericin-formationhavebeendevelopedsincethe1990s.Thesemethodscanberoughlygroupedintotwocategories:themulti-temporalandmulti(hyper)-spectralretrievalmethods.Themulti-temporalretrievalmethodsprimarilymakeuseofmeasurementsatdifferenttimestoretrievetheLSTandtheLSEundertheassumptionthattheLSEistime-invariant.Therepresentativesofthesemethodsarethetwo-temperaturemethod(Watson,1992)andthephysics-basedday/nightoperationalmethod(Wan&Li,1997).Themulti(hyper)-spectralretrievalmethodsrelyontheintrinsicspectralbehavioroftheLSEratherthantemporalinformation.Therepresentativesofthemulti(hyper)-spectralincludethegraybodyemissivitymethod(Barducci&Pippi,1996),thetemperatureemissivityseparation(TES)method(Gillespieetal.,1996,1998),theiterativespectrallysmoothtempera-tureemissivityseparationmethod(Borel,2008),andthelinearemissiv-ityconstraintmethod(Wangetal.,2011).Basedonsomereasonableassumptionsorconstraints,thesemethodscanretrievetheLSTandLSEfromtheatmosphericallycorrectedradiancesatthegroundleveleitherbyreducingthenumberofunknownsorbyincreasingthenum-berofequations.

3.2.2.1.Two-temperaturemethod(TTM).TheideaunderlyingtheTTMisthereductionofunknownsthroughmultipleobservations.ProvidedthataccurateatmosphericcorrectionsintheTIRchannelshavebeenperformedandthattheLSEsaretime-invariant,thereare2NmeasurementswithN+2unknowns(NchannelLSEsandtwoLSTs)ifthelandsurfaceisobservedbyNchannelsattwodifferenttimes.TheNLSEsandthetwoLSTscanthereforebesimultaneouslydeterminedfromthe2NequationsifN≥2(Watson,1992).Note

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thattheassumptionofthetime-invariantLSEsimplicitlyrequiresthesurfacetobehomogenousandhaverelativelystablesoilmoisture.The rstrestrictionistoalleviatetheLSEvariationcausedbypixelsizesandbyviewingangles,whilethesecondistoavoidtheLSEchangeswithsoilmoisture,suchastheoccurrenceofprecipitationanddew.

TheprimaryadvantageoftheTTMisthatitmakesnoassumptionaboutthespectralshapeoftheLSEs,onlythattheyaretime-invariant.Thismethodhasasimpleandstraightforwardformulation;however,theretrievalaccuracyisnotalwaysguaranteedbecausethe2Nequa-tionsarehighlycorrelatedandtheirsolutionsmaythusbeunstableandverysensitivetoinstrumentnoiseanderrorsintheatmosphericcorrections(Casellesetal.,1997;Gillespieetal.,1996;Watson,1992).Becauseaccurateatmosphericcorrectionsaredif culttoperformwithoutsimultaneousatmosphericpro lemeasurements,theuseofapproximatepro lescouldleadtolargeuncertaintiesintheLSTandLSEretrievals.PeresandDaCamara(2004)foundthatincreasingthenumberofobservationsand/orthetemperaturedifferenceimprovedtheretrievalaccuracy,butthisimprovementislimitedbythehighcorrelationbetweenTIRmeasurements.

Inadditiontotheproblemsmentionedabove,thismethodrequiresaccurategeometricregistrationofimagesacquiredattwodifferenttimes(Gillespieetal.,1996;Watson,1992).Similartotheday/nightTISIbasedmethod,theimpactofmis-registrationontheLSTandLSEer-rorsissmallforhomogeneousareasbutlargeforheterogeneousareas(Wan,1999).AchangeinthesatelliteVZAcausesachangeintheLSE,consequentlyviolatingtheassumptionoftime-invariantLSEsandde-creasingtheaccuracyoftheTTM(Lietal.,2013).

3.2.2.2.Physics-basedday/nightoperationalmethod(D/N).Inspiredbytheday/nightTISIbasedmethodandTTMmethod,WanandLi(1997)furtherdevelopedaphysics-basedD/Nmethodtosimulta-neouslyretrieveLSTandLSEsfromacombineduseoftheday/nightpairsofMIRandTIRdata.ThismethodassumesthattheLSEsdonotsigni cantlychangefromdaytonightandthattheangularformfactorhasverysmallvariations(b2%)intheMIRwavelengthrangeofinteresttoreducethenumberofunknownsandmaketheretrievalmorestable.Toreducetheeffectoftheresidualerrorofatmosphericcorrectionsontheretrieval,twovariables,theairtemperatureatthesurfacelevel(Ta)andtheatmosphericWV,areintroducedtomodifytheinitialatmosphericpro lesintheretrieval.Withtwomeasure-ments(dayandnight)inNchannels,thenumbersofunknownsareN+7(NchannelLSEs,2LSTs,2Ta,2WV,and1angularformfactorintheMIRchannels).Thus,tomaketheequationsdeterministic,Nmustbeequaltoorgreaterthanseven.

Generally,thephysicalD/paredwiththeTTMandTISImentionedpreviously,thisD/Nmethodishighlightedbyseveralfacets:

(1)ThecontributionofsolarirradiationtotheradianceoftheMIR

channelsindaytimesigni cantlydecreasesthecorrelationsamongtheequationsandmakesthesolutionmorestableandac-curate.UnliketheTISImethodthat rstobtainsthebi-directionalre ectivityofthepixelandthencalculatesLSEandLSTseparate-ly,theD/NmethodretrievessimultaneouslyLSTandLSEandavoidsthepropagationoferrorfromstepwiseretrieval.Inaddi-tion,theD/NmethodscanaccuratelydetermineLSTsandLSEseventhoughtheLSTsareequalatthetwotimes(dayandnighttimes);whiletheTTMwithonlyTIRmeasurementsrequiresig-ni cantdifferenceinthetemperatures.

(2)TheaccuracyoftheretrievedLSTsandLSEsisstronglyimproved

byintroducingtwovariables(TaandWV)toaccountfortheun-certaintiesintheinitialatmosphericpro les.Asaresult,theac-curacyoftheatmosphericcorrectionisnotrequiredtobeashighasthatofTISIandTTM.

(3)TheD/Nmethoddoesnotrequire12-hourintervalmeasure-ments(dayandnight).Aslongasthesurfaceemissivitydoesnotchangesigni cantly,daytimeandnight-timedatacollectedoverseveraldaysarealsoappropriate.However,similartotheothermulti-temporalmethods,theD/Nmethodstillsuffersfromthecriticalproblemsofgeometrymis-registrationandvariationsintheVZA.Wan(1999)aggregatedtheMODISpixelstoincreasethescalefrom1kmto5kmor6kminordertoovercomethemis-registrationproblems.Meanwhile,16VZAsubrangesareusedtoensurequalityofdayandnightVZAsubranges(Wan&Li,2010).Asetofnewre nements(Wan,2008)wereimplementedtorejecttheworstsolutionsandforbetterLSTre-trievalseveninlessidealconditionssuchasundertheeffectsofnear-bycloudsandheavyaerosols,differentsurfaceemissivityvaluesintheMIRand8.75μmchannelsduringthedayandnightduetoeventsofrain,snowandnighttimedew(giventherelativelyhighemissivityvaluesinbands31and32lessaffectedbytheseeventseveninaridregions).TheimprovementsincludethecombineduseofTerraandAquaMODISdata,settinglargerweightsonthedaytimedata,fullyin-corporatingtheviewing-angledependentGSWmethodintotheD/NalgorithmasaclosecomponentandrelatedconstraintsonLSTdiffer-ences,usingthevariablesofemissivitiesinbands31and32,WVandTaintheiterationsofsolutionoftheD/Nalgorithmandeffectivelyin-creasingtheweightsonthehighestqualitydataofbands31and32.MoredetailsontheMODISD/Nmethodcanbefoundintheliterature(Wan,2008;Wan&Li,1997,2010).

3.2.2.3.Graybodyemissivitymethod(GBE).ThismethodassumesthattheLSEhasa atspectrum,i.e.,theLSEisindependentofthewave-length,forwavelengthslargerthan10μmtoreducethenumberofunknownsandstabilizetheretrievalalgorithm(Barducci&Pippi,1996).

ThemainadvantageoftheGBEisthatnoadditionalassumptionabouttheshapeoftheemissivityspectrumisrequired,excepttheas-sumptionthatitis atinsomewavelengthinterval.Intheory,theLSTandLSEscanbesimultaneouslyretrievedaslongasatleasttwochan-nelshavethesameLSE(notnecessarilythegraybody)inthewave-lengthintervalofinterest.However,thelimitationsofthemethodareevident.TheapplicationoftheGBEmethodtospace-basedmea-surementsrequiresaccurateatmosphericcorrectionsintheTIRchan-nelsandatleasttwochannelswiththesameLSE.SimilartotheTTM,thismethodisverysensitivetoinstrumentnoiseanderrorsintheat-mosphericcorrectionsbecausetheTIRmeasurementsarehighlycor-related.Moreover,requiringspectrally atLSEsoftenhamperstheuseoftheGBEinmultispectralTIRdataunlessatleasttwochannelswiththesameLSEcanbeidenti ed.ThisproblemcanbemoreorlessovercomewithhyperspectralTIRdata,becauseitiseasierto ndatleasttwochannelswiththesameLSEinhyperspectraldatathaninmultispectraldata,andhundredsoreventhousandsofchan-nelscanfurtherimprovetheretrievalaccuracy.Therefore,theGBEmethodisthoughttobemoreapplicabletohyperspectralTIRdata.3.2.2.4.Temperatureemissivityseparationmethod(TES).Thismethodwas rstdevelopedbyGillespieetal.(1996)toseparatetheLSTandtheLSEusingatmosphericallycorrectedAdvancedSpaceborneThermalEmissionandRe ectionRadiometer(ASTER)TIRdata.Thismethodreliesonanempiricalrelationshipbetweenthespectralcontrastandtheminimumemissivitytoincreasethenumberofequa-tions(equivalenttoreducingthenumberofunknowns)sothattheundeterminedretrievalproblembecomesdeterministic.TheTESmethodcomprisesthreematuremodules:thenormalizationemissiv-itymethod(NEM)(Gillespie,1995),thespectralratio(SR),andthemaximum–minimumapparentemissivitydifferencemethod(MMD)(Matsunaga,1994).

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TheNEMmoduleis rstusedtoestimatetheinitialLSTandthenormalizedemissivitiesfromtheatmosphericallycorrectedradiancesatgroundlevel(Gillespieetal.,1996).Subsequently,theSRmoduleisemployedtocalculatetheratioofthenormalizedemissivitiestotheiraverage.AlthoughtheSRmodulecannotdirectlyobtaintheactualLSE,ithasbeendemonstratedtodescribetheshapeoftheemissivityspectrumwellevenifthesurfacetemperatureisroughlyestimatedbytheNEMmodule.Finally,onthebasisoftheresultsoftheSRmod-ule,theMMDmoduleisutilizedto ndthespectralcontrast(i.e.,theMMD)inNchannels,thentoestimatetheminimumLSEusingtheempiricalrelationshipbetweentheminimumLSE(LSEmin)inNchan-nelsandtheMMD.OnceLSEminisestimated,theLSEsintheotherchannelscanbestraightforwardlyderivedfromtheSR,andthentheLSTcanbere nedandestimated(Gillespieetal.,1998).

ThemainadvantageoftheTESisthatitcombinesattractivefea-turesofthreeprecursorsandusesanempiricalrelationshipbetweentherangeofemissivitiesandtheminimumemissivityintheNchan-nelstoretrievetheLSTandLSEs.Consequently,itcanbeappliedtoanykindofnaturalsurfacewithoutconsideringspectralvariationsintheemissivity,especiallyforsurfaceswithhighspectralcontrastemissivitiessuchasrocksandsoils(Gillespieetal.,1998;Sobrinoetal.,2008).Numericalsimulationandsome eldvalidationshavedem-onstratedthattheTEScanretrievetheLSTtowithinabout±1.5KandtheLSEstowithinabout±0.015whentheatmosphericeffectsareaccuratelycorrected(Gillespieetal.,1996,1998;Sawabeetal.,2003).Besides,HulleyandHook(2011)recentlyre nedtherelation-shipbetweenLSEminandMMDtomakeTESalgorithmavailableforMODIS'sthreeTIRchannels(29,31and32).

However,somereportshaveindicatedthattheTESmethodexhibitedsigni canterrorsintheLSTandLSEsofsurfaceswithlowspectralcontrastemissivity(e.g.,water,snow,vegetation)andunderhotandwetatmosphericconditions(Colletal.,2007;Gillespieetal.,1996,2011;Hulley&Hook,2009b,2011;Sawabeetal.,2003).Saboletal.(2009)pointedoutthatthelowemissivitycontrastandhighemis-sivitycontrasthavebeentreateddifferentlyinoriginalversionofTES.Consequently,theretrievedLSEsaretoolowandtheLSTistoohighintheoriginalversionforthematerials(suchassoils,vegetationandwater/snow)thatareplottedabovetheregressionlineinthescatterplotofLSEminandMMD.Thatiswhysomestudieshavereportedthatin-accurateatmosphericcorrectionsmayproduceLSTerrorsof2–4Kforbaresoil(Dashetal.,2002).Forwarmandwetatmosphericconditions,thecauseofsigni canterrorsisdifferent.Theuncertaintiesintheatmo-sphericcorrectionswillresultinalargeapparentemissivitycontrast.Thiseffectismoreseriousovergraybodysurfaces(Hulley&Hook,2011).Tominimizeatmosphericcorrectionerrors,Gillespieetal.(2011)improvedtheTESmethodbyusingawatervaporscaling(WVS)approachproposedbyTonooka(2005).

Asshownbynumericalsimulations,theuncertaintiesontheLSTandLSEretrievalsincreasewhenthenumberofchannelsisreduced,makingtheTESmethodinapplicabletomostoperationalsensors(Sobrinoetal.,2008).Moreover,sensorcalibrationerrorsandnoiseintheTIRchannelsalsocauseuncertaintiesintheretrievedLSTandLSEs(Gillespieetal.,2011;Jiménez-Muñozetal.,2006;Sobrinoetal.,2008).Inaddition,TESscaleslow-andhigh-contrastsurfacesdif-ferently,whichleadstostepdiscontinuitiesattheedgesofgraybodyunitssuchaswater,forests,andcrops(Sobrinoetal.,2007).Toover-cometheseproblems,Saboletal.(2009)recentlyreplacedthepowerrelationshipofLSEminandMMDintheoriginalTESmethodwithalinearexpression,andappliedthenewrelationshipavailableforallmaterialstoalleviatesuchdiscontinuities.Thisrevisionwasreportedtoreduceslightlytheaccuracyforbothrocksurfacesandgraybodiesbutcanimprovetheprecisionfornear-graybodysurfaces.

3.2.2.5.Iterativespectrallysmoothtemperatureemissivityseparationmethod(ISSTES).HyperspectralTIRdataprovidesmuchmoredetailedspectralinformationabouttheatmosphereandlandsurface.Borel

(1997,1998,2008)reportedthatatypicalemissivityspectrumisrathersmoothcomparedwiththespectralfeaturesintroducedbytheatmosphere.AccordingtotheRTEgiveninEq.(4),iftheLSTisnotaccuratelyestimated,thecorrespondingLSEspectrumwillexhib-ittheatmosphericspectralfeatures,i.e.,therewillbesawteethcausedbytheatmosphericabsorptionlinesontheestimatedLSEspectrum.ThebestestimatesoftheLSTandLSEshouldbeobtainedwhenthespectralsmoothnessoftheretrievedLSEismaximized.Basedonthisproperty,theiterativespectrallysmoothtemperatureemissivityseparationmethod(ISSTES)hasbeendevelopedtoiterativelyre-trievetheLSTandLSEsfromhyperspectralTIRdata.Varioussmooth-nesscriteriaincludingthe rstandsecondderivativehavebeenproposed(Borel,2008;Chengetal.,2010;Kananietal.,2007;OuYangetal.,2010),thoughtheyallleadtothesamestatisticalper-formanceregardlessofthedetailsofthesmoothnessfunction.

IngramandMuse(2001)analyzedthemethod'ssensitivitytosmoothnessassumptionsandmeasurementnoiseandfoundthattheretrievalaccuracycausedbytheassumptionsisnegligiblefortyp-icalmaterialsbutisdependentontheSNR,i.e.,highaccuracycanbeobtainedwithhighSNR.Similartomostmethodspresentedabove,theatmosphericcorrectionneedstobeaccuratelyperformed,anditsimpactontheretrievalresultsisthegreatestamongallin uences.Theretrievalaccuracyisalsosensitivetoshiftsinthecentralwave-lengthsandbandwidthsoftheTIRchannels(Borel,2008).Inaddition,Wangetal.(2011)reportedthattheoccurrenceofsingularpointsmayleadtodif cultiesin ndinganacceptablesolutionwhentheLSTisclosetotheeffectivetemperatureofthedownwardatmospher-icradiance.

3.2.2.6.Linearemissivityconstrainttemperatureemissivityseparationmethod(LECTES).InspiredbytheGBEinitiallyproposedbyBarducciandPippi(1996),Wangetal.(2011)proposedanewTESmethodtore-trievesimultaneouslybothLSTandLSEsfromatmosphericallycorrectedhyperspectralTIRdata.Thismethodassumesthattheemis-sivityspectrumcanbedividedintoMsegmentsandthattheemissivityineachsegmentvarieslinearlywiththewavelength.Thus,theemissiv-ityspectrumcanbereconstructedusingapiecewiselinearfunctionwithgainsaakandoffsetsbbk(k=1,…,M),andtheLSTandLSEscanbesimultaneouslyobtainedprovidedthatthenumberofequationsN(correspondingtotheNchannelmeasurements)isequaltoorgreaterthanthenumberofunknowns(2M+1correspondingto1LST,Maak,andMbbk).TherequirementofN≥2M+1iseasilyful lledforhyperspectralTIRdatabecauseahugenumberofnarrowchannelsareavailableinahyperspectralTIRsensor.

Wangetal.(2011)carriedoutaseriesofsensitivityanalysesandconcludedthattheerrorsintroducedbytheassumptionoflinearemissivitycanbeneglectedifthesegmentlengthiswellchosen.Asegmentlengthofabout10cm paredwithISSTES,thismethodproduceslessfrequentsingularpointsandismoreresistanttobothwhitenoiseanduncertaintyinthedownwardatmosphericradiance.Becauseatmosphericspectralfeaturesaremoresigni cantunderwetandwarmatmosphericconditions,theLECTESmethodperformsbetterinwetandwarmatmospheresthanindryandcoldatmospheres.SimilartotheISSTES,thismethodisonlysuitableforhyperspectralTIRdataandrequiresaccurateatmo-sphericcorrections.However,becausethenumberofunknownscanbegreatlyreducedwithapiecewiselinearfunction,thismethodex-hibitsgreatpotentialasatechniqueforsimultaneouslyretrievingtheLST,theLSE,andatmosphericpro les,aswillbedescribedin3.2.3.2and5.1.Recently,Pauletal.(2012)developedamethodologyforthesimultaneousretrievalofLSTandemissivityspectrafromtheInfraredAtmosphericSoundingInterferometer(IASI)hyperspectraldata.Inthiscase,theLSTandLSEretrievalmakeuseofa rstguessforlandemissivity,whichisestimatedfromsixMODISchannelsin-terpolatedtotheIASIhyperspectralrangeusinganon-linearstatisti-cal(neuralnetwork)scheme.

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3.2.3.SimultaneousretrievalofLST,LSEs,andatmosphericpro les

AlthoughthesimultaneousLSTandLSEretrievalmethodsreviewedabovecanaccuratelyobtaintheLSTandLSEsiftheatmo-sphericcorrectionsareperformedproperly,accurateatmosphericpro lesareusuallyunavailablesynchronouslywithTIRmeasure-ments,andthustheaccuracyoftheretrievedLSTandLSEscanbede-graded.AnidealsolutionistosimultaneouslyretrievetheLST,LSEs,andatmosphericparameters(e.g.,atmosphericpro les)(Maetal.,2002).BecausethenarrowbandwidthofferedbyhyperspectralTIRsensorswiththousandsofchannelscanimprovetheverticalresolu-tionandallowatmosphericpro lesandsurfaceparameters(LSTandLSEs)tobeobtainedmoreaccurately(Chahineetal.,2001),severalmethodshavebeenproposedtoretrievesimultaneouslythesurfaceandatmosphericparameters.Therepresentativesofthesemethodsarethearti cialneuralnetwork(ANN)method(Wangetal.,2010)andthetwo-stepphysicalretrievalmethod(Maetal.,2002,2000).

3.2.3.1.Arti cialneuralnetwork(ANN)method.BecauseanANNcanrobustlyperformhighlycomplex,non-linear,parallelcomputations,ANNshavebecomeincreasinglyutilizedbytheremotesensingcom-munity(Mas&Flores,2008).ANNsresemblethebrainintwoas-pects:theyacquireknowledgethroughalearningprocess,andstoretheacquiredknowledgeusinginterneuronconnectionstrengths(Mas&Flores,2008).Therefore,ANNsrepresentmassivelyparalleldistributedprocessorsthatcanacquireexperientialknowledgeandmakethatknowledgeavailableforuse.

ThemainadvantagesofANNmethodsoverconventionalretrievalmethodsaretheirabilitytolearncomplexpatterns,generalizationtonoisyenvironments,andincorporationofbothknowledgeandphys-icalconstraints(Mas&Flores,2008).BecauseofANNs'powerfulnon-linearretrievalabilities,anumberofattemptshavebeenmadetodevelopneuralnetworkstoretrieveboththesurfaceandatmo-sphericbiophysicalvariableswithoutexactknowledgeofthecom-plexphysicsmechanisms.Forexample,Maoetal.(2008)usedanANNtoestimatetheLSTandLSE,whileAiresetal.(2002b)andBlackwell(2005)usedanANNtoretrieveatmosphericpro les.Tore-ducetheeffectofcouplingbetweenthesurfaceandatmosphereontheretrievalaccuracy,Airesetal.(2002a)proposedusinganANNtoretrieveboththeatmosphericandsurfacetemperatures,andWangetal.(2010)attemptedtoestablishaneuralnetworktosimul-taneouslyretrievetheLST,LSE,andatmosphericpro lesfromhyperspectralTIRdata.ThepreliminaryresultsdemonstratedthatANNscanbeusedtosimultaneouslyretrievetheLST,LSEsandatmo-sphericpro lesfromhyperspectralTIRdatawithacceptableaccuracyforsomeapplications.RMSEsofLSTandtemperaturepro lesintroposphereareabout1.6Kand2K,respectively;RMSEofWVisaround0.3g/cm2.RMSEofLSEislessthan0.01inthespectralinter-valfrom10μmto14μm(Wangetal.2013).

However,becauseANNsperformlikeblackboxesandcanproducecorrespondingoutputsfromanygiveninputs,theretrievalprocesscannotbewellcontrolled,anditisdif culttointerprettheweightsassignedtoeachinputandimprovetheoutputduetothecomplexnatureofthenetwork.Inaddition,theimplementationofanANNde-pendslargelyonitsarchitectureandthetrainingdata(Mas&Flores,2008).Itisdif culttodeterminethearchitecturesandlearningschemesforanANN,whicharedirectlyrelatedtoitsabilitytolearnandgeneralize.Althoughoneortwohiddenlayersarerecognizedtobeenoughformostproblems(Airesetal.,2002b;Mas&Flores,2008;Sontag,1992),anumberofexperimentsarestillrequiredtode-terminewhatarchitecture-relatedparameterswillimprovetheaccu-racy,suchasthenumberofinputandhiddennodes,theinitialweightrange,theactivationfunctions,thelearningrateandmomentum,andthestoppingcriterion.Untilnow,noANNarchitectureisuniver-sallyacceptedforaparticularproblem.Thecharacteristicsofthetrainingdata,suchasthesizeandtherepresentativeness,arealsoof

considerableimportance.Theuseoftoofeworunrepresentativetrainingsampleswillresultinanetworkthatcannotaccuratelyre-trievetheoutputs,whiletheuseoftoomanytrainingsamplesre-quiresmoretimeforlearning.Becausephysicalunderstandingisnotrequired,ANNmethodsmayberegardedasempiricalmethods.However,theirresultscanbeusedtoprovideinitialguessesforfur-therimprovementsinthephysicalretrievalmethods(Motteleretal.,1995).MoredetailedinformationabouttheapplicationofANNscanbefoundintheworkofMasandFlores(2008).

3.2.3.2.Two-stepphysicalretrievalmethod(TSRM).Becausethemea-suredradianceattheTOAisafunctionofthesurfaceandatmosphericparameters,thesurfaceandatmosphericvariablescantheoreticallybeobtainedbyselectingappropriatechannelsevenfrommultispec-traldata.Maetal.(2000)madeaninitialattemptatsimultaneouslyretrievingtheLSTandatmosphericpro lesbyassumingthattheLSEisinvariantwithintheMIRchannelsandalsoinvariantwithintheTIRchannelsandbyignoringthesolarcontributioninMIRchan-nels.However,theseroughassumptionsmayleadtodegradedaccu-raciesinthetroposphere.Alongthislineofreasoning,Maetal.(2002)furtherconsideredthesolarcontributionandproposedanex-tendedtwo-stepphysicalretrievalmethodthatsimultaneouslyex-tractstheLST,theLSE,andtheatmosphericpro lesfromMODISdata.

ThemainideaunderlyingtheTSRMinheritsthatofatmosphericpro leretrieval.The rststepistotangent-linearizetheatmosphericRTEwithrespecttotheatmospherictemperature-humiditypro les,theLST,andtheLSEs.Giveninitialguessesforthoseatmosphericandsurfacevariables,asetofequationsbasedonthetangent-linearizedRTEcanbederivedusingtheremotelysensedmeasurements(Lietal.,1994;Maetal.,1999;Smith,1972).Atthesametime,theprinciple-component-analysis(PCA)techniqueandtheTikhonovregularizationmethodareemployedtoreducethenumberofunknownsandstabilizetheill-posedproblem(Maetal.,2000;Smith&Woolf,1976),whichmakesthesolutionoftheseequationsstableanddeterministic.AccordingtothestatisticalanalysisintheworkofMaetal.(2000,2002),only vetemperatureandthreewatervaporeigenvectorscanexplainalloftheinformationof40atmospherictemperatureandwatervaporlevels,respectively.Inthesecondstep,theNewtonianiter-ationalgorithmisutilizedwiththeregularizedsolutionastheinitialguesstoobtainthe nalmaximumlikelihoodsolutionoftheatmo-spherictemperature-humiditypro les,LST,andLSEs.

Thereareatleastthreeassumptionsinvolvedinthismethod:(1)theRTEcanbetangent-linearizedaroundaninitialguess;(2)acon-stantangularformfactorisusedforthesolarbeamintheMIRregiontosimplifytheRTE;(3)thePCAcanbeusedtoreducethenumberofunknownswithoutsigni cantlossofaccuracy.Theseassumptionsensuretheexistenceofstableandaccuratesolutionswithoutaprioriatmosphericcorrections,asopposedtootherconventionalmethods.However,Maetal.(2002)foundthatthesolutionsarehighlydepen-dentontheinitialguess.Therefore,onepossibleimprovementtothistypeofmethodistoimprovetheinitialguess.Aspointedoutearlier,theresultsofanANNcanbeusedastheinitialguessesinthephysicalretrievalmethod.Itisworthnotingthatthephysicalnatureofthealgorithmrequiresanadequatenumberofchannelsineachspeci cwindow,anditscomplexnaturemayleadtoalowcomputationalef ciency.Thesetwopropertiesmaketheuseofthismethoddif culttoapply.

parisonandanalysisofdifferentmethods

ThereisnouniversalmethodcapableofalwaysaccuratelyretrievingLSTsfromallsatelliteTIRdatabecausetheLSTretrievalmethodsreviewedabovewereproposedforuseunderdifferentconditionswithdifferentassumptions.Itismeaninglesstoperformacomparisonofthesealgorithmswithoutconsideringthoseassumptions.Therefore,itisgenerallydif culttodecidewhichalgorithmissuperiortoothers.

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TheoptimalmethodtoretrievetheLSTfromspaceinpracticecanbese-lectedbyconsideringthecharacteristicsofthesensor,theavailabilityofemissivitydataandatmosphericinformation,thecomplexityofthemethod,andotherconsiderations.

BecausetheSWalgorithmsaresimple,effectiveandgenerallysuitableformostsensors,manycomparativestudiesevaluatingtheperformanceofthesemethodshavebeencarriedout.Vazquezetal.(1997)foundthatmostSWalgorithmsarestatisticallyindistinguish-able.Kerretal.(2000)performedanalgorithmcomparisonandcon-cludedthattheselectionofthebestLSTalgorithmmaydependonaprioriknowledgeofthewatervaporcontentandtheLSE.SòriaandSobrino(2007)reportedthattheRMSEofretrievedLSTinSWalgo-rithmsgenerallydecreasesasmoreinputsparametersareexplicitlyincluded.Howevermoreinputsparameterswillintroducemoreun-certaintiesanddecreasetheaccuracyoftheLSTretrieval.Yuetal.(2008)haveevaluatedninepublishedSWalgorithmstodeterminewhicharemostcapableofgeneratingaconsistentLSTclimatedatarecordacrosssatellitesensorsandplatforms.TheresultsshowedthattheSWalgorithmsthatdependonboththemeanandthediffer-enceofchannelemissivitiesarethemostaccurateandstableoverawiderangeofconditionsiftheemissivitiesareaccuratelyknown.However,Yuetal.(2009)reportedthattheuseofboththemeanandthedifferenceofchannelemissivitiesmaybetoosensitivetotheemissivityuncertaintyandshouldnotbeusedinoperationalpractice.Asacompromise,theSWalgorithmsthatonlyusethemeanemissivitiesarerecommendedbyYuetal.(2009).

BecausealloftheassumptionsandrestrictionsinvolvedintheLSTretrievalmethods,suchastherequirednumberofTIRchannelsandtheknowledgeregardingemissivitiesoratmosphericquantities,can-notbemetsimultaneously,comparisonsareseldommadeexceptforSWalgorithms.Toprovideaconciseoverview,theassumptions,ad-vantages,andlimitationsofeachofthesemethodsaresummarizedinTable1tohelpusersselecttheoptimalmethodinpractice.

4.ValidationofsatellitederivedLST

Validationisaprocessofindependentlyassessingtheuncertaintyofthedataderivedfromthesystemoutputs.Withoutvalidation,nomethods,algorithms,orparametersderivedfromremotelysenseddatacanbeusedwithcon dence.AstheretrievedLSTsfromsatelliteTIRdatainvolvecorrectionstothesatellite-observedradiancestoac-countforatmosphericeffectsandnon-unityLSEs,itisnecessarytoas-sesstheaccuracyoftheretrievaltoprovidepotentialLSTuserswithreliableinformationregardingthequalityoftheLSTproductandtoprovidefeedbacktothedevelopersofLSTretrievalalgorithmsforfu-tureimprovement.AlthoughmanyalgorithmshavebeenproposedanddevelopedoverrecentdecadestoretrievetheLSTfromsatelliteTIRdata,farfewerstudieshavebeenundertakentovalidatethesatellite-derivedLSTsduetothedif cultyofmakinggroundmeasure-mentsoftheLSTthatarerepresentativeatthesatellitepixelscaleandalsoduetothelargespatio-temporalvariationsintheLSTitself.Inrecentyears,severalstudieshavebeenperformedtovalidatetheLSTsderivedfromavarietyofsensors,fromlargelyhomogenoustargets.SensorvalidatedincludeTM/ETM+(ThermaticMapper/EnhancedThematicMapperPlus),ASTER,AVHRR,AATSR(AdvancedAlong-TrackScanningRadiometer),MODISandSEVIRIdata(Colletal.,2005,2010,2012b;Hooketal.,2005,2003,2007;Hulley&Hook,2009a;Niclòsetal.,2011;Prata,1994b;Saboletal.,2009;Sawabeetal.,2003;Sobrinoetal.,2007;Sòria&Sobrino,2007;Trigoetal.,2008a,b;Wan,2008;Wan&Li,2008;Wanetal.,2002,2004;Wang&Liang,2009).ThreemethodsaregenerallyutilizedtovalidateLSTvaluesretrievedfromspace:thetemperature-basedmethod(T-based),theradiance-basedmethod(R-based),andcross-validation.Thefollowingsectionswillintroduceeachvalidationmethod,discusstheiradvan-tagesanddisadvantages,andshowthattheyshouldberegardedas

complementarystrategiesfortheassessmentofsatellite-basedLSTproducts.

4.1.Temperature-basedmethod(T-based)

TheT-basedisaground-basedmethodthatdirectlycomparesthesatellite-derivedLSTwithinsituLSTmeasurementsatthesatelliteoverpass(Colletal.,2005;Pinkeretal.,2009;Prata,1994b;Slateretal.,1996;Wanetal.,2002).However,performingLSTmeasure-mentsinthe eldisacomplexanddif culttaskduetothedifferenceofthescalesprobedbysatellitepixels(afewkm2)and eldsensors(afewm2orcm2).Moreover,naturallandcoverandthecorrespond-ingLSTandLSEvaluesarequitevariableatthescaleofkm2.Snyderetal.(1997)pointedoutthathomogeneousand atsurfacesthatcanbeeasilyinstrumentedandcharacterized,includinginlandwater,sand,snow,andice,canserveasvalidationsites(Colletal.,2005;Guillevicetal.,2012;Sobrinoetal.,2004c;Wan,2008).Thesizeoftheareathatneedstobeviewedbythevalidationinstrumentdependsontheinter-pixelvariabilityofthesurfaceandonhowwellmeasurementsofseveral“endmembers”canbecombinedtoobtainarepresentativevalueforthesatellitepixel.Thisprocessremainschal-lengingduetothedif cultiesinherentto ndingadequatesurfacesintheimageandperformingarepresentativethermalsamplingontheground.

BecausemostoftheEarth'ssurfaceisheterogeneousatthesatel-litepixelscale,high-qualitygroundLSTvalidationdataarescarceandarelimitedtoafewhomogeneoussurfacetypessuchaslakes,siltplayas,grasslands,andagricultural eldscollectedduringdedicat-edcampaigns(Colletal.,2005,2010,2009;Wanetal.,2002,2004).Onceathermallyhomogeneousareaisidenti ed,ingthismethod,manyau-thorshaveperformedvalidationstudiesoftheLSTvaluesproducedusingdifferentsensors(Colletal.,2005,2010,2009;Peresetal.,2008;Saboletal.,2009;Wan,2008;Wanetal.,2002).

ThemainadvantageoftheT-basedmethodisthatitprovidesadi-rectevaluationoftheradiometricqualityofthesatellitesensorandtheabilityoftheLSTretrievalalgorithmtocorrectforatmosphericandemissivityeffects.However,thesuccessofT-basedvalidationsdependscruciallyontheaccuracyofthegroundLSTmeasurementsandhowwelltheyrepresenttheLSTatthesatellitepixelscale.Be-causethespatialandtemporalvariationsoftheLSTatdaytimemightbe10Kormoreoverafewmetersorovershorttimeintervalsdependingonthenatureofthesurface,thesolarirradiationlevel,andthelocalmeteorologicalconditions,T-basedvalidationactivitiesareoftenrestrictedtonighttimeandhomogeneoussurfacessuchaslakes,densegrasslands,andvegetatedregions.Moreover,evenifground-levelLSTmeasurementscanbeperformed,thereisstillaproblematicdif cultyinscalingupfromthegroundpointmeasure-mentstothepixelscaleunderthe eldofviewofthesatellitesensor,especiallyoverheterogeneoussurfaces(Wanetal.,2002).Asaresult,onlyafewsurfacetypesaresuitableforT-basedvalidationwithinanuncertaintyof±1KforthegroundmeasuredLSTatthepixelscale.Thecollectionofinsitumeasurementsisalsoademandingtaskandisoftenlimitedtoshort-term,dedicated eldcampaigns.Therefore,theT-basedmethodisnotappropriateforglobalvalidationofsatellite-derivedLSTmeasurements.

4.2.Radiance-basedmethod(R-based)

Theradiance-basedmethod(R-based)isanadvancedalternativemethodforvalidatingspace-basedLSTmeasurements(Colletal.,2012b;Wan&Li,2008).Thismethoddoesnotrelyonground-measuredLSTvaluesbutdoesrequirebothLSEspectra,whichcanbemeasuredinthe eldorestimatedfromland-covertypesorfrom

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otherauxiliarydata,andmeasuredatmosphericpro lesovertheval-idationsiteatthetimeofthesatelliteoverpass(Wan,2008;Wan&Li,2008).Thismethodusesthesatellite-derivedLSTandtheaforemen-tionedinsituatmosphericpro ingthedifferencebetweenthesimulatedTOAradianceandthemeasuredradiance,theinitialLSTwillbeadjustedandthesimulatedradiancewillbeiterativelyrecalculatedtomatchthesatellite-measuredradiance.ThedifferencebetweentheadjustedLSTandtheinitialsatellite-derivedLSTistheaccuracyoftheretrievedLST.MoredetailsabouttheR-basedmethodareprovidedbyWanandLi(2008).

TheR-basedmethoddoesnotrequiregroundLSTmeasurements,anditcanthereforebeappliedtothesurfacesonwhichgroundLSTmeasurementsareunfeasibleandextendedtohomogeneousandnon-isothermalsurfaces.ThepromisingperformanceoftheR-basedmethodoffersthepossibilityofvalidatingsatellite-derivedLSTvaluesduringthedaytimeandnighttimeoverhomogeneousandnon-isothermalsurfaces.However,thestrongestlimitationsoftheR-basedmethodaretheuseofmeasuredorestimatedLSEsrepresentativeatpixelscale,howtochecktheactualatmospherereallyfreeofclouds,andhowwellthepro lesusedinsimulationsrepresenttheactualat-mosphereatthetimeofobservations(Colletal.,2012b).ThesuccessoftheR-basedmethoddependsontheaccuraciesoftheatmosphericRTM,theatmosphericpro les,andtheLSEsatpixelscale.4.3.Crossvalidationmethod

Thismethodinvolvescross-validatingtheLSTvaluesretrievedbythemethodundertestwithwelldocumentedandvalidatedLSTvaluesretrievedfromothersatellitedata(Trigoetal.,2008a).ThistechniquerepresentsanalternativemethodforLSTvalidationiftherearenoatmosphericpro lesorgroundLSTmeasurementsavail-ableoriftheT-andR-basedvalidationscannotbeconducted.

Thecross-validationmethodusesawellvalidatedLSTproductasareferenceandcomparesthesatellite-derivedLSTtobevalidatedwiththereferenced(wellvalidated)LSTderivedfromothersatellites.DuetothelargespatialandtemporalvariationsintheLST,geographiccoor-dinatematching,temporalmatching,andVZAmatchinghavetobeperformedbeforethetwosatellite-derivedLSTproductscanbecom-pared(Qianetal.,2013;Trigoetal.,2008a).ThemainadvantageofthismethodisthattheLSTcanbevalidatedwithoutanygroundmea-surements,anditcanbeusedanywhereintheworldifwellvalidatedLSTproductsareavailable.Asmentionedabove,theaccuracyofthismethodissensitivetospatialandtemporalmismatchesofthetwoLSTmeasurements.Theobservationtimeintervalbetweenthetwomeasurementsshouldbeasshortaspossible.ConsideringthattheLSEalsodependsontheviewingzenithangleandthatthepixelsofthetwosensorscoverdifferentareasandcontaindifferentlandsurfacein-formationunderdifferentviewingangles,onlypixelswiththesameornearlysameviewingzenithanglesshouldbeusedforcross-validation.5.Futuredevelopmentandperspectives

AccuratelyacquiringLSTsattheglobalscaleiscrucialtomany eldsofstudyincludingtheEarth'ssurfacewaterandenergybal-ances,materialandenergyexchangeinterrestrialecosystemsandglobalclimatechange.Variousmethodshavebeendevelopedtore-trievetheLSTfrommultispectralormulti-angularTIRdata.Becauseofthelimitedspectralinformationprovidedinmultispectraldata,allofthesemethodsrelyondifferentapproximationstotheRTEandondifferentassumptionsandconstraintstosolvetheinherentlyill-posedretrievalproblem.Thoseapproximations,assumptions,andconstraintsmightnotholdtrueundercertaincircumstances.There-fore,usersmustchoosetheoptimalapproachtoestimatetheLSTfromspacebyconsideringthesensorcharacteristics,therequired

accuracy,thecomputationaltime,theavailabilityofatmospherictemperatureandwatervaporpro les,andtheLSEs.Consideringthesigni cantprogressmadeinrecentdecadesinLSTestimationfrommultispectralTIRdata,therewillbenosigni cantfurtherprogressinLSTretrievalfrommultispectralsatellitedataiftherearenoinno-vationsintheacquisitionofremotelysenseddata.ToovercometheshortageofmultispectraldataandtoradicallyimprovetheaccuracyofLSTretrievalfromspace,itisnecessarytoexplorenewideasandbreaknewpathsinremotesensing.

Undoubtedly,hyperspectralTIRsensorswiththousandsofchannelsarebetterabletoextractatmosphericandlandsurfaceparametersthanmultispectralTIRsensors.Ahugenumberofchannelswithnarrowbandwidthscanimprovetheverticalresolutionofatmosphericsound-ings(Chahineetal.,2001)andextracttheatmosphericquantitiesusedinatmosphericcorrections.ThehyperspectralTIRdatameasuredwith-intheatmosphericwindowcanprovidemoredetailedlandsurfacein-formation,particularlytheLSEspectrumratherthanthediscreteLSEsinmultispectraldata,aswellasmorereasonableassumptionsorcon-straintsusedtoradicallyseparatetheLSTandtheLSEs.Thesereasonshavedriventhedevelopmentofquantitativeremotesensingandotherrelateddisciplines.TheexplorationofhyperspectralTIRdataforLST/LSEseparationandtheretrievalofatmosphericpro lesoratmo-sphericquantitiesinvolvedinatmosphericcorrectionswillbecomeoneofthehotspotsinquantitativeremotesensing.

ProgresscanalsobeexpectedinthedevelopmentofnewmethodsforextractingtheLSTfromacombinationofmultispectralandmulti-temporalTIRdataacquiredfromthemultispectralsensorson-boardthenewgenerationofgeostationarysatellites,suchasSEVIRI,GOESandtheFY-2series,whichcanprovidediurnalcoveragedataandcanscanthesurfaceatleasthourlywitha xedVZA.ExceptfortheTTM,day/nightTISI,andphysics-basedD/Nmethodsinwhichdatameasuredattwodifferenttimes(oneindaytimeandtheotherinnighttime)areused,allofthemethodsdevelopedtoretrievetheLSTfromspacearebasedonmultispectraldatabutdonotconsidertemporalinformation.Itisthereforeveryattractivetoutilizethemulti-temporalinformationtoderivetheLSTfrommultispectral,multi-temporalTIRdata.

Inaddition,mostofthecurrentavailableLSTmethodsretrievetheLSTinstantaneouslyfrommultispectraldataacquiredbypolar-orbitsatellitesunderclear-skyconditions.Therearenolong-termLSTprod-uctsderivedunderallweatherconditions.Consideringthecomplemen-tarityofpassivemicrowaveandTIRdata,aphysics-basedmodelforretrievingLSTsfrompassivemicrowavedataandaneffectivemodelofcombiningLSTsretrievedfromTIRandpassivemicrowavesatellitedatamustbedevelopedinthefuturetoproduceLSTswithhighspatialresolutionunderallweatherconditions.Moreover,becauseofthein-trinsicscanningpropertyofthesensorsonboardthepolar-orbitsatel-lites,LSTsretrievedatagivenlocationfromdataacquiredbythesamepolar-orbitsatelliteondifferentdaysorLSTsretrievedatdifferentloca-tionsinthesamedaycorrespondtodifferentlocalsolartimesofobser-vationanddifferentVZAs,letaloneLSTsretrievedfromdifferentpolar-orbitsatellites.AstheLSTvarieswithbothtimeandVZA,thereisnocomparabilityamongLSTsofonepixelretrievedondifferentdaysorLSTsofdifferentpixelsonthesameday,whichsigni cantlylimitstheapplicationsoftheLSTproducts.Toaddresstheseissues,ase-riesofLSTmodels,includingangularnormalizationandtemporalnor-malization,mustbedevelopedtoproducealong-term,time-andangle-normalizedconsistentLSTproductunderallweatherconditions.

FuturestudiesoughttofocusonthefollowingsubjectstoimproveLSTestimationfromspace-basedmeasurements.

5.1.MethodologytosimultaneouslyderiveLST,LSE,andatmosphericpro les(atmosphericquantities)fromhyperspectralTIRdata

AsstatedbyLietal.(2013),thecouplingofthesurface-emittedradianceandtheatmosphericabsorption,diffusionandemission

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complicatestheseparateretrievalofsurfaceparameters(LSTandLSEs)andatmosphericpro les.Thedeterminationofsurfaceparam-etersfromspacerequiresknowledgeoftheatmosphericpro lesandviceversa.ItisthereforenaturalthoughchallengingtodevelopamethodthatsimultaneouslyretrievestheLST,LSEs,andatmosphericpro les(oratmosphericquantitiesusedintheatmosphericcorrec-tions)withoutanyaprioriknowledgeaboutthesurfaceoratmo-sphere.Maetal.(2000,2002)madea rstattemptatretrievingthoseparametersfrommultispectralTIRmeasurements.WiththeappearanceofhyperspectralTIRsensors,thethousandsofnarrowbandwidthchannelsinTIRcansupplyenoughverticalresolutiontoallowextractionofatmosphericinformationandcanalsoprovidemorephysicalconstraintstoaccuratelyseparatetheLSTandtheLSEs.Althoughafewstudieshavebeenconductedinrecentyears(Lietal.,2007;Wangetal.,2013),therearestillatleasttwoaspectsthatrequireincreasedattentioninthefuture.First,rapidandaccurateRTEmodelsmustbedevelopedtomeettherequirementsofaccuracyandspeedintheretrievalprocess.Second,ANNsandphysicalretriev-almethodsshouldalsobemodi edordevelopedtoimprovethere-trievalaccuracies.Forexample,moredetailsshouldbeconsideredintheANNs,includingthearchitecturesandlearningschemes,selec-tionofrepresentativetrainingdata,andthechannelsemployed.Atthesametime,additionalconstraints,suchasthelinearemissivityconstraintproposedbyWangetal.(2011),biningANNsandphysics-basedmethodsalsorepresentsanoptioninthenearfuture,becausetheadvantagesofthesetwotechniquescancomplementeachother:ANNscanprovideini-tialguessesfortheLST,LSEs,andatmosphericpro les(oratmosphericquantities),andthenphysicalretrievalmethodscanfurtherimprovetheseinitialguesses.

5.2.MethodologytosimultaneouslyderiveLSTandLSEfromthenewgenerationofgeostationarysatelliteswithmultispectralandmulti-temporaldata

Thenewgeostationarysatellitesareprevailingoverthepolar-orbitsatellitesininvestigatingthetemporalevolutionoflandsurfaceandatmosphericinformationbecausetheyprovidehigh-frequencyobservationsat xedviewinganglesoverthesamesurfacedespitetheircoarserspatialresolutions.EffortshavefocusedonretrievingtheLSTfrommultispectraldatabutwithoutconsideringmulti-temporalinformation.ItisthereforeveryattractivetodevelopanewmethodtosimultaneouslyretrievetheLSTandLSEbytakingad-vantageofthemultispectralandmulti-temporalinformationprovid-edbythegeostationarysatellites.Withthegeostationarysatellitedata,time-andangle-consistentLSTscanbedirectlyproducedusingthesenewLSTretrievalmethodswithoutneedingtotemporallyorangularlynormalizetheLST.

5.3.Re nementofLSTretrievalalgorithmswiththeconsiderationofaerosolandcirruseffects

AtmosphericcorrectionisoneofthemostimportantissuesintheLSTretrievalalgorithms,anderrorsinatmosphericcorrectiondirectlydecreasetheaccuracyofthe nalderivedLST.BecauseofthehightransmittanceofaerosolintheTIRchannel(approximately0.95–0.98inMODISTIRchannels)(Wan,1999)undernormalclear-skyconditionsandthelackofreal-timeaerosolestimates(aerosolload-ing,sizedistributions,types,andscatteringphasefunctions),anaver-ageaerosoldistributionandaconstantaerosolloadinghavebeenusedinthedevelopmentofalloftheLSTretrievalalgorithmsreviewedinSection3.TheeffectofaerosolonLSTretrievalisrelative-lysmallcomparedwiththeeffectofwatervapor,butitcannotbeig-noredwhenaimingforhighlyaccurateLSTsforuseincertainspecial

applications,especiallyinthepresenceofheavyaerosolloadings(Jiménez-Muñoz&Sobrino,2006).ToimprovetheaccuracyofLSTre-trieval,existingLSTretrievalalgorithmsmustbere ned,ornewalgorithmsmustbedevelopedtocorrectfortheaerosoleffect,partic-ularlyinthecaseofheavyaerosolloading.

Inaddition,theeffectofcirruscloudsonLSTretrievalshouldalsobeconsidered.Cirruscloudsarealwaysconsideredtobecloudcon-taminationinmanyLSTretrievalalgorithmsandthepixelscoveredbycirruscloudsarescreenedoutindatapreprocessing.Becausether-malinfraredwavelengthscanpenetratecirruslayers,itispossibletoobtaintheLSTundercirruscoverfromTIRdata.Tothisend,newLSTretrievalalgorithmsshouldbedevelopedtocompensatefortheeffectofthecirrusclouds.

5.4.RetrievalofcomponenttemperaturesinheterogeneouspixelsInaheterogeneousandnon-isothermalpixel,theobservedradi-anceistheensembleradianceofseveralcomponents(e.g.,soilandvegetation).Thepixel-averagetemperaturedoesnotre ecttherealtemperatureofeachcomponent.Ifeachcomponentisassumedtobeisothermal,thecomponenttemperatureencapsulatesmorephys-icalmeaningthanthepixel-averagevalueandprovidesbetterparam-eterizationsoftheheat uxesattheland-atmosphereinterface.Therefore,thecomponenttemperaturesofamixedpixelaremoreimportantthantheaveragevalues.However,theretrievalofcompo-nenttemperaturesisdif cultbecausemorevariables,includingthecomponentemissivitiesandatmosphericeffects,mustbeknowninadvance.Severalauthorshaveattemptedtoretrievecomponenttem-peraturesfrommulti-angulardata(Jiaetal.,2003;Lietal.,2001;Menentietal.,2001;Shi,2011).Themethodsthattheyhavedevel-opedarefarfromsatisfyingandshouldbeimprovedinthefuture.Inaddition,furtherinvestigationsshouldfocusonminingtheauxilia-ryinformationprovidedbyspatial,temporal,andspectraldata.Be-causedifferentVZAsmaycorrespondtodifferentpixelsizes,newalgorithmsareexpectedtousehyperspectralTIRdataatagivenVZA,astheinformationregardingthecomponenttemperatureswith-inamixedpixelisincludedinthehyperspectralTIRdata.

5.5.MethodologyforretrievingLSTfrompassivemicrowavedataandforcombiningLSTsretrievedfromTIRandpassivemicrowavedataTheTIRdataprovidestheLSTwitha nespatialresolution(e.g.,severalkilometers),butitlosesef ciencywhenthelandsurfaceisfullyorpartlycoveredbyclouds.Incontrast,microwavescanpene-trateclouds,allowingforLSTretrievalinallweatherconditionsbutwithacoarserspatialresolution(uptotensofkilometers)(Airesetal.,2004).TIRandmicrowavedatacanthuscomplementeachother,andthecombinationofthetwoisapromisinglineofresearchforproducinglong-termLSTproductsinallweatherconditionswithaspatialresolutionas neasthatofTIRdata.Futurestudiesareadvisedtofocusonthefollowingsubjects.

(1)Developmentofanewphysics-basedmodelforretrievingLST

valuesfrompassivemicrowavedata.Severaltechniquestore-trievetheLSTfrompassivemicrowavedatahavebeenproposed,including(semi)empiricalstatisticalmethods,neuralnetworks,andphysicalmodels(Airesetal.,2001;Chenetal.,2011;Maoetal.,2007;McFarlandetal.,1990;Njoku&Li,1999;Weng&Grody,1998).However,thephysicalmechanismsunderlyingthoseapproachesaregenerallyunclear,andtheirassumptionsorsimpli cationsregardingtheLSEandatmosphericeffectsde-gradeboththefeasibilityandtheaccuracyofthederivedLST.Newphysics-basedmodelforLSTretrievalfrompassivemicro-wavedatashouldbedevelopedbyfocusingonbothsimplifyingtheparameterizationoftheRTManddevelopingtheemissivityrelationshipsbetweendifferentfrequenciesandpolarizations.

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AsatisfactorymodelisexpectedtoretrievetheLSTfromacom-binationofbrightnesstemperaturesmeasuredatdifferentfre-quenciesandpolarizationmodes.

(2)DevelopmentofamodeltoderivetheskinLSTfrompassivemi-crowavedata.Aswellknown,theLSTretrievedfrommicrowavedataisdifferentfromthatderivedfromTIRdata.Theformerre- ectsanaveragevalueofthesoiltemperaturefromthelandsur-facetoaparticulardepth(dependingonthefrequencyusedtoretrieveLST)underneaththesurface,whereasthelatteristheskintemperaturewithseveralmicronsofdepth.TocombinethesetwotypesofLSTandextracttheskinLST,amodelmustbedevelopedtoextracttheskinLSTfromtheLSTderivedfrompassivemicrowavedatawiththeaidofLSTsderivedfrompas-sivemicrowavedataatdifferentfrequenciesandofthethermalconductivityequationappliedtosoil.

(3)Developmentofamicrowave-TIRfusionmodel.Aneffective

modelthatfusestheLSTsretrievedfromTIRandpassivemicrowavedatamustbedevelopedinthefuturetoproducehigh-resolutionspatialLSTdatainallweatherconditions.ThekeyproblemtoberesolvedishowtorecovertheLSTatthespa-tialresolutionofTIRdatawhenamicrowavepixelisfullyorpartlycloudy.5.6.MethodologyforangularnormalizationofLST

AsreportedbyLagouardeandIrvine(2008),Lagouardeetal.(1995,2004),Chehbounietal.(2001)andLietal.(2004b),theLSTvarieswithVZA,anditsangularvariationforthree-dimensionalsurfacesresultsprimarilyfromtheangularvariationofthepixelemissivityandtherel-ativeweightsofdifferentcomponents(e.g.,vegetationandbackgroundsoil)withdifferenttemperaturesinanon-isothermalpixel.Thediffer-enceintheLSTmeasuredinnadirandoff-nadirobservationscanbeaslargeas5Kforbaresoilsandeven10Kforurbanareas.Becausemostpolar-orbitsatellites(e.g.MODIS,AVHRR)scanthelandsurfaceinthecross-trackdirectionwithdifferentVZAsvaryingfrom–65°to+65°,angle-dependentvariationsintheretrievedLSTareinevitable,makingtheLSTsofdifferentpixelsinthesameorbitincomparableandcausingerroneousresultsinapplication.ThiseffectmustalsobeconsideredforLSTsobtainedfromdifferentsensorsoratdifferenttimes.Therefore,itisverycrucialtonormalizethesatellite-derivedin-stantaneousLSTsatvariousVZAstoareferenceVZA(e.g.,atnadir).

Onemethodofperformingangularnormalizationonsatellite-derivedLSTsistosimplyattributetheangularvariationofthemea-suredeffectivetemperaturederivedfromarea-weightedemittedradiancestothedirectionalbehaviorofthepixelemissivity,aspro-posedbyLietal.(1999).However,thedirectionalemissivityde nedinthismannerisusuallynotmeasurablefromspace,andtheassump-tionthatthereisnodownwardenvironmentalthermalradiancemaycausesomeunexpectederrorsinthenormalizedresult.Anothertech-niquefornormalizingthesatellite-derivedLSTreliesonasimpli eddirectionalthermalRTMthatconsidersthecomponenttemperaturesandfractionswithinthepixel.Newmethodscanbeginbyparameter-izingthedirectionalthermalRTMwiththeminimumnumberofun-knownsbasedonthedirectionalfractionofvegetationcoverandthecomponenttemperaturesofpixels.Then,themethodshouldes-tablishrelationshipsbetweenthedirectionalradiativetemperaturesobservedfromdifferentdirections.Theoff-nadirLSTcanbenormal-izedtoareferencedirection(e.g.,atnadir)bydeterminingthefrac-tionsofvariouscomponentsandthecorrespondingcomponenttemperaturesortheirratiosfrommulti-angleormulti-channelobser-vations.Thefractionofcomponentsunderaspeci cviewinganglecanbecalculatedusingthebidirectionalre ectancedistributionfunc-tion(BRDF)modelinthevisibleandnearinfraredspectralregions.AlthoughangularvariationsintheLSThavebeendemonstratedorsimulatedatthepixelscaleintheliterature(Pinheiroetal.,2006,2004;Rasmussenetal.,2011,2010),thereisnoanypracticalway

toperformangularnormalizationofsatellite-derivedLSTsduetothecomplexityofthisnormalization.Thisissuethereforerequiresfurtherinvestigationinthefuture.Tovalidatethenormalizationmodel,angularmeasurementsofthethermalradiationatgroundlevelmustalsobeconducted.

5.7.Methodologyfortemporal(time)normalizationofLST

Itiswellknownthattheacquisitiontimes(UTC)ofallthepixelsinoneimagearenearlythesamebutthelocalsolartimesaremuchdif-ferent.Forinstances,inapolar-orbitsatelliteimagesuchasaMODISimage,thedifferenceinthelocalsolartimebetweentheeastandthewestpixelsalongthescanninglinecanbeupto1.5h,whichmeansthattheeastpixelsareexposedtosolarirradiationapproximately1.5hbeforethewestonesiftheskyisclear.Asaresult,theLSTprod-uctsderivedfromthesamesatellitecannotbecomparedifthediffer-encesinthelocalsolartimesofthepixelsaresigni cant.ThisphenomenonalsoaffectsLSTproductsacquiredbydifferentsatellitesatdifferenttimesandsigni cantlylimitstheapplicabilityofthein-stantaneousLSTproducts.Itisthereforenecessarytotemporallynor-malizethesatellite-derivedLSTstothesamelocalsolartime.Thediurnaltemperaturecycle(DTC)modelshowspromisingabilitytonormalizetheLSTtoanytimeofacloud-freeday.However,onlyDTCmodelswithsixparametershavebeendevelopedtodescribethediurnalvariationoftheLSToncloud-freedays(Göttsche&Olesen,2001;Jiangetal.,2006;Schädlichetal.,2001).Becausepolar-orbitsatellitesgenerallypassagivenlocationonlyonceortwiceperday(fourtimestotalforMODISTerraandAqua),eitheranewDTCmodelwithaminimumnumberofunknownparameters(lessthan4)oracombinationofpolar-orbitandgeostationarysatel-litesmustbedevelopedinthefuturetotemporallynormalizethepolar-orbitsatellite-derivedLSTs.Consideringthatgeostationarysat-ellitesobservethesamelocationwithhightemporalfrequency,LSTsderivedfromgeostationarysatellitedatacanbeusedtodetermineatypicalDTCmodel.AssumingthattheLSTsderivedfrompolar-orbitsatellitedataexhibitthesamediurnalpatternasthosederivedfromgeostationarydata,theonce-ortwice-dailyLSTsderivedfrompolar-orbitsatellitedatacanbeinterpolatedtoanytimeofacloud-freedayutilizingtheDTCmodeldevelopedusinggeostationarydata.However,onapartlycloudyday(nocloudcontaminationwhenthepolar-orbitsatelliteoverpasses),theseDTCmodelswillnotbeap-plicable,andalocalLSTvariationmodelshouldthereforebedevel-opedinthefuturewiththeaidoftemporalinformationprovidedbygeostationarysatellitestonormalizetheinstantaneouspolar-orbitsatellite-derivedLSTs.

5.8.ConcernsonthenewlydevelopedHyperspectralInfraredImagerTheHyperspectralInfraredImager(HyspIRI),acombinedvisible,nearinfraredandshortwaveinfrared(VSWIR)imagingspectrometerandamulti-channelTIRradiometer,isoneoftheproposedmissionsofthe“DecadalSurvey”programintheNationalResearchCouncil,U.S.Thisnewsystemisscheduledtolaunchin2013–2016anddesignedtohaveaspatialresolutionof60matnadir,andtherevisittimesattheequatorwillbe19and5daysfortheVSWIRandTIRin-struments,respectively(Robertsetal.,2012).TheobjectiveoftheHyspIRIistocontinuethespace-borneobservationontheearthinthelastdecadesandprovidesynergyanalysisbetweenVSWIRandTIRdataforthelandsurfaceparameters.Uptonow,threeinterna-tionalHyspIRIsymposiumshavebeencarriedoutbyJetPropulsionLaboratorytodiscussitspotentialapplications.Forexample,Robertsetal.(Robertsetal.,2012)investigatedsomepotentialsynergiesinurbanenvironmentusingaHyspIRI-likeairbornedatasetacquiredbytheAirborneVisible/InfraredImagingSpectrometer(AVIRIS)andtheMODIS/ASTER(MASTER)airbornesimulator,andfoundthattheatmosphericdataretrievedfromtheVSWIRdataprovidedthe

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atmosphericcorrectionsoftheTIRdata,whiletheTIRradiancecanbeusedtoimprovere ectanceretrievalsintheVSWIRespeciallywhensigni cantTIRaerosolabsorptionispresentunderhighaerosolload-ings.Moreover,thisHyspIRI-likeairbornesystemwasalsousedtodetect reregionsandretrievetheircorrespondingtemperature(Dennison&Matheson,2011;Matheson&Dennison,2012).Addi-tionally,HyspIRIisalsoprospectedtobeappliedinthe reseverityassessments,themonitoringofthevolcaniceruption,theinterpreta-tionofsnowpropertiesandtheretrievalofforestbiophysicalparam-eters,respectively(Dozieretal.,2009;Veraverbekeetal.,2012a,2012b;Zhangetal.,2012).AsfortheretrievalofLSTandLSE,HyspIRI'ssoundingchannelsinVSWIRcanprovideatmosphericdatafortheatmosphericcorrectionsoftheMIRandTIRdata,andits8spectralchannels(7between7.5and12μmand1at4μm)aresuit-ableforseveralcurrentalgorithmsintheory,suchastheTES,TISIandSWalgorithms,evenavailablefordevelopingnewretrievalLST/LSEalgorithms.Furthermore,becauseofits nerspatialresolution(60m)andrapidrevisittime(5days),theLST/LSEretrievedfromHyspIRIprovideanopportunitytovalidatetheLST/LSEproductsatcoarserresolutions,suchasMODISand(A)ATSR.Therefore,thestudyonHyspIRIwillattractmuchattentioninthefuture.5.9.Physicalmeaningofsatellite-derivedLSTanditsapplicationsTheLSTmustbephysicallyde nedwithabsolutecertainty.However,noagreementhasbeenreachedonthede nitionoftheLSTbecauseoftheunclearphysicalmeaningofthesatellite-derivedtemperature,espe-ciallyoverheterogeneousandnon-isothermalsurfaces.Thede nitionoftheLSTalsodependsonthatoftheLSEbecausetheLSTandLSEarecoupledinthetotalradiance.Therearecurrentlyseveralde nitionsoftheLSE,suchasther-emissivity(Becker&Li,1995),thee-emissivity(Norman&Becker,1995)andtheapparentemissivity(Lietal.,1999).Thesede nitionsarethesameforhomogeneoussurfacesatthermalequilibrium,butbecausenaturalsurfacesobservedfromspaceareusual-lyheterogeneous,theassumptionsofhomogeneityandthermalequilib-riumareoftenviolatedinreality,especiallyinmeasurementswithlowspatialresolution.Therefore,thedifferencesbetweenthesede nitionsareevidentinmanycases.Ther-emissivityde nitionisrecommendedforLSTandLSEretrievalfromspace-basedmeasurementsbecausether-emissivityismeasurablefromspace.

Whateverde nitionoftheLSTisused,thesatellite-derivedLST,alsoknownastheradiometrictemperatureortheskintemperature,canonlycapturethethermalradiationinformationfromaverythindepthunderneaththesurface,andthereforecannotbedirectlysubstitutedforthethermodynamicoraerodynamictemperaturesinestimatingsurface uxesorotherrelevantapplications.Instead,aconversionmustbemadebetweenthesedifferenttemperatures.However,currentstudiesseldomconsiderthesedifferencesandtreattheskintemperatureasthethermodynamicoraerodynamictemperaturewithoutanyconversion.Thissimpli cationcausesunex-pecteduncertaintiesintheirresults.Therefore,furtherattentionshouldbepaidtothisprobleminthefuturebyconsideringthephys-icalde nitionofdifferenttemperaturesandtheaccuracyrequire-mentsofrelevantapplications.5.10.Validationofsatellite-derivedLST

ThemostimportantprobleminLSTvalidationmightbetheaccu-racyandrepresentativenessoftheground-truthLSTatthesatellitepixelscale.Althoughground-basedvalidationisconsideredtobethemostreliablevalidationtechnique,measurementsoftheground-truthLSTarelimitedbythedif cultyof ndingahomoge-neousregionaslargeasthesatellitepixelsizeandbythedif cultyandassociatedcostsofsamplingoverheterogeneouslandscapes.The rstdif cultymightbesolvedbyimprovingthespatialresolutionofTIRdata,whilethesecondwillrequirethedevelopmentofanew

samplingschemeforground-levelLSTmeasurements,suchasawireless-netobservationsystemormultiple-scaleobservationmethodswithcorrespondingnewinstruments.AttemptstousetheLSTspredictedfromlanddataassimilationsystemsorclimatemodelstoindirectlyvalidatetheLSTsretrievedfromspacemustdevotemoreattentiontoimprovingtheaccuracyoftheoutputofthesemodelsanddealingwiththescalemismatchissueinbothspaceandtime.Turningtocross-validationtechniques,anappropriatescalingproceduretoremovetheeffectsofspatial,temporal,andangulareffectsontheLSTmustbedeveloped.Therefore,LSTvalidationisstillanongoingsubjectofresearch.Acknowledgments

TheauthorswouldliketothankProfessorA.R.Gillespieandotherreviewersfortheirvaluableandstimulatingcommentsthathavegreatlyimprovedthepaper.TheauthorsaregreatlyindebtedtoDr.S.J.Hookforreadingcarefullythedraftofthispaperandforgivingmanyusefulsuggestionsforimprovingitspresentation.ThisworkwassupportedbytheHi-TechResearchandDevelopmentProgramofChina(863PlanProgram)undergrantno.2012AA12A304,bytheNa-tionalNaturalScienceFoundationofChinaundergrantno.41231170and41171287,andbytheStateKeyLaboratoryofResourcesandEnvi-ronmentalInformationSystemundergrant088RA800KA.References

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