基于sailh模型的參數(shù)化模型及其應(yīng)用

基于sailh模型的參數(shù)化模型及其應(yīng)用

1非織造工藝參數(shù)laincipalitorpoelinglai（leaf區(qū)指數(shù)）是將拉米區(qū)域或從側(cè)面區(qū)域中拉米區(qū)域的特征之一（chen，1992）。拉米是一個緩慢的區(qū)域，有一個簡單的區(qū)域，沒有時間，有一個接一個的結(jié)構(gòu)。它是一個不同于微電機的過程，微電機是一個緩慢的過程。體積學(xué)、離體和微電機的特征是可以概括的。它可以被視為微電機進(jìn)程中的一個步驟，微電機可以被視為一個步驟中的一個步驟，微電機可以被視為一個步驟中的一個步驟。Atpresent,thequantitativeLAIretrievalmethodsusingremotesensingaremainlyclassifiedastheempiricalstatisticalmodelbasedmethodandthephysicalmodelinversionbasedmethod.TheempiricalstatisticalmodelsusethevegetationindexasthevariableandretrieveLAIbyestablishingthestatisticalrelationshipbetweenVIsandLAI(Fang&Zhang,2003).ThismethoddominatestheLAIretrievalduetoitssimpleexpressionandlessparameters.Otherwisethismethodislackofphysicalmeaning,andthedevelopedrelationshipsbetweentheVIsandLAIaredependentonthespecifictimeandspecificregion.Asaresult,itishardtoexpanditsuseintemporalandspatialdimensions.Onthecontrary,thephysicalmodelsaremorerealisticandapplicable.Alltheparametersofthemodelshavephysicalmeanings.Therearesomeshortcomingsinphysicalmodels,includingtoomuchparameterswhichareintroducedintothemodelsinordertodescribetheearth’ssurfacefeaturesaccuratelyasmuchaspossible,andtheirexpressionarealsoverycomplicated.Althoughthemulti-spectralandmulti-angleremotesensingtechnologyprovidesmoreobservationalinformation,theremotesensingretrievalstillfacestheill-posedproblem,andthephysicalmodelretrievalistooslowtomeetawiderangeofapplicationrequirements.Therefore,itisimportanttofindaparameterizedmodelwithcertainphysicalmeaningandsimpleformatthesametimeforthegenerationoflargeareaLAIproducts.Inthispaper,weproposesaparameterizedmodelbasedontheSAILHmodel,andthenwecomparetheretrievalaccuracy,efficiencyandstabilitybetweentheparameterizedmodelandtheSAILHmodelwithsimulateddataandground-basedmeasurementswhicharetakenintheHeiheriverbasin.2標(biāo)準(zhǔn)4.3.3回亞國里亞國里亞國里亞國里羅胺政府分類性別與同人民群眾sigsifeci能夠sofracienra能,sofracienra能,sofracienra能,sofracienra能,soinratiinra能,sofunsiinra能,soinratiin,etizact.sigCanopyreflectancemodelscanbedividedintothreekindsofmodelinaccordancewithwhetheritisestablishedaccordingtothetheoreticalanalysis,thatistheempiricalmodels,semi-empiricalmodelsandphysicalmodels(Zhao,2007),whilethephysicalmodelscanbedividedintoradiativetransfermodels,geometricopticsmodels,andcomputersimulationmodels.SAILHmodelisonekindoftheradiativetransfermodels.Thebasisoftheradiativetransfermodelsistheradiativetransferequation,whichisanintegral-differentialequation.Intheory,theequationissolvableiftheboundaryconditionsaredetermined.Sofar,thereisnorigorousanalyticalsolutiontotheradiationtransferequationbutonlyavarietyofapproximatesolutions(Xu,2006).ThecommonlyusedsolutionistheK-MequationproposedbyKubelkaandMunk.TheincidentlightisdividedintofourpartsintheSAILmodel(ScatteringbyArbitrarilyInclinedLeaves)(Verhoef,1984)basedontheK-Mequation,thataretheupwardanddownwardradiationfluxdensityaswellastheupwardanddownwardparallelradiationirradiation.Bysolvingnineintermediatevariables(includingtheextinctioncoefficient(ks)ofthedirectradiationfluxdensity,attenuationcoefficient(att),back-scatteringcoefficient(sig),forwardandbackwardscatteringcoefficientofthedirectradiation(sf,sb),conversioncoefficientsfromupward,downwardradiationfluxdensityandupwardparallelradiationtotheobservedradiance(uf,ub,ω),theextinctioncoefficientoftheradiationfluxdensityontheobserveddirection(ko)),thecanopyreflectancecanbegot.SoSAILmodelisafour-streamlineardifferentialequationwithninecoefficients.Itsinputparametersincludethreestructuralparametersandfourspectralparameters,wherethethreestructuralparametersaretheleafareaindexandthetwoparameterswhichareusedtodescribetheleafinclinedangles.Thefourspectralparametersaretheratioofskylight,leafreflectance,leaftransmittanceandsoilreflectance.AstheSAILmodelcannotsimulatethehot-spoteffectwell,Kuuskaddedthehot-spoteffecttotheSAILmodelanddevelopedtheSAILHmodel(Kuusk,1991).Hotspoteffectiscausedbythesinglescatteringoftheilluminatedcanopy.Therefore,Kuuskestablishedtherelevantprobabilitymodelbetweenthedirectionofobservationandthedirectionoftheincidentlighttoconsiderthecanopyhot-spoteffectbasedontheSAILmodel.InSAILHmodel,thecontributionofthesinglescatteringofthewholecanopyisdecomposedintomulti-layersingle-scatteringcontributionandsummedtogetherasthecontributionofthewholecanopy.Inthecalculationofthesinglescatteringcontributionofeachlayer,abi-directionaltransmissiondensityfunctionisused.Thebi-directionaltransmissiondensityfunctioncalculationneedstointroduceanewparameter—thehot-spoteffectfactor.ThenthereareeightinputparametersinSAILHmodel(SeeTable1,themeaningsoftheseparameterscanbefoundintheappendix).3sailhmoligactrafteribution、非織造業(yè)的slain建模Inpracticalapplications,remotesensingisthemosteffectivetechniquewhichisabletogetlarge-scaleandtimeseriesLAIofdifferentsurfacetypes.AlargenumberofstudieshaveshownthatusingremotesensingtechnologycanextractregionalandglobalLAIrapidlyandperiodically,andcanprovidespatialandtemporaldistributionofLAI(Huietal.,2003).AlthoughSAILHmodelisawidelyacceptedmodeltodescribethedirectionalreflectanceofcontinuousvegetationcanopy,itspracticalityislimitedduetoitscomplicatedcalculationandlowretrievalefficiency.Soinordertoimprovetheretrievalefficiencyandkeeptheaccuracy,itisnecessarytomakesomereasonablesimplificationstothemodel.WeproposedaparameterizedmodelbasedonSAILHmodelinthispaper,andevaluatedtheretrievalaccuracy,efficiencyandstabilityoftheparameterizedmodelbasedonthesimulateddataandground-basedmeasureddata.Thisworkaimedatthefollowingtwosteps:(1)SimplifyingthecalculationofthenineintermediatevariablesoftheSAILHmodel.(2)Simplifyingthecalculationthecontributionofthesinglescatteringoftheilluminatedcanopy.3.1規(guī)訓(xùn)4.4—Simplificationofthecalculationofthenineinter-mediatevariablesoftheSAILHModelThemainreasonofthelowretrievalefficiencyofSAILHmodelisthatwhencalculatingthecanopyreflectance,theleafinclinedanglesofcontinuouscanopyaredividedinto13anglesandthenineintermediatevariablesareexpressedasthefunctionsoftheseleafinclinedangles,thentheresultiscalculatedbysummingthese13termsiteratively.IfwecansimplifythecalculationsofthesenineintermediatevariablesandkeeptherestcalculationsinSAILHmodel,wemayimprovetheefficiencygreatly.ThroughanalyzingandcomparingthecalculationofthenineintermediatevariablesinSAILHmodel,wehavethesimplifiedcalculationsshowninTable2,where,LAIistheleafareaindex,Inthecalculationofnineintermediatevariables,themoscomplexoneisω,whichindicatesthatiftheilluminationdirectionandtheobserveddirectionintersectatthesamesideoftheleaf,theleafreflectanceshouldbeusedtorepresentthereflectionoftheleaftothelight,otherwisetheleaftransmittanceshouldbeusedtorepresenttheweakenoftheleaftothelight.Inthissense,ωrepresentsasimilarconceptwiththescatteringphasefunction,butthedifferenceisthatitcontainsLAI,sointhecalculationlater,weusethescatteringphasefunctiontoapproximatethecalculationofThetwo-parameterellipticdistributionisusedtodescribetheleafinclinedangledistributioninSAILHmodel.Inordertomakeabetterapproximationtothescatteringphasefunctionofthisdistribution,wechoosethescatteringphasefunctionofsphericaldistributiontoreplaceit.Wecangetabetterapproxi-mationusingthisscatteringphasefunctioninsteadof3.2出適數(shù)字號和出口品種Supposedthatthecontinuousvegetationcanopyiscomposedbyaseriesofhorizontalanduniformlayers,thenthecontributionofsinglescatteringoftheilluminatedcanopycPwhereΓ(ΩInEq.(3),PwherePs_Listhehotspotfactorparameter,thecalculationofΔis:TotestthecorrectnessoftheEq.(4),wecomparedtheresultcalculatedbyitwiththeresultoftheSAILHmodel(Fig.2).PThen,thecontributionofthesinglescatteringoftheilluminatedcanopycanbecalculatedasfollows:Sofar,thecalculationsofthenineintermediatevariablesandthecontributionofsinglescatteringoftheilluminatedcanopyhavebeensimplified,andtheothercalculationskeepthesameasSAILHmodel.WedesigneagroupofexperimentstocompareandevaluatetheforwardBRDFsimulatedabilityoftheparameterizedmodelWesetthesunzenithangleat35°andthesolarazimuthangleat0°,theobservationzenithanglesarechangesfrom0°to85°withanincrementof5°,andtheobservationazimuthanglesarefrom0°to355°withthesameintervalchangesof5°,sothereareatotalof1296observationcombinationsintheupwardhemisphere.ThevaluesoftheinputstructuralparametersareshowninTable3.Wedesigntheparametersforthefollowingthreeconsiderations:(1)GroupⅠ:theellipticaleccentricityissetat0.001,inwhichcasetheleafinclinedangledistributionneartoasphericalleafangledistribution,theforwardBRDFsimulationabilityoftheparameterizedmodelisevaluatedwhenLAI=2andLAI=4,respectively;(2)GroupⅡ:theellipticaleccentricityissetat0.9,andtheaverageleafinclinedangleissetatdifferentvalues,whenθTheRMSEsandthecorrelationcoefficientsoftheforwardsimulatedBRDFoftheentireupwardhemispherebetweentheparameterizedmodelandSAILHmodelareusedastheevaluatecriterion.TheresultsareshowninTable4.Throughanalysiswecanseethat,intheentireupwardhemisphere,theRMSEsoftheforwardsimulatedBRDFbetweentheparameterizedmodelandSAILHmodelcanbemaintainedbelow0.01intheredband,andbelow0.04inthenear-infraredband;whetherinredornear-infraredband,thecorrelationcoefficientsoftheparameterizedmodelandSAILHmodelhasreachedmorethan96%.4通過mehateritydmortgage,grounge/sailhmortrace-acculacemortracemortrace-solega-acculacemorymeasulace.ThereisahighpositivecorrelationbetweentheBRDFsimulationsbetweentheparameterizedmodelandSAILHmodel,sotheSAILHmodelcanberepresentedbytheparameterizedmodeltosomedegree.Thenweevaluatedtheretrievaaccuracy,efficiencyandstabilityofthesetwomodelsusingsimulateddataandground-basedmeasureddata.4.1prior-to保護(hù)的alga:si農(nóng)村天監(jiān),非價值的自然價值Thegenerationofsimulateddataisasfollows:supposingagrouporseveralgroupsofinputparameters,givingtheappropriatepriorknowledge,takingtheSAILHforwardsimulatedvaluesastheobservedtruevalues,andthenretrievingparametersusingtheparameterizedmodelwithPowelloptimizationalgorithm.Forthepurposeofcomparison,wealsoretrievedtheLAIvaluesusedtheSAILHmodelwiththesamepriorknowledgeatthesametime.Weadded10%Gaussiannoisetotheobservedvaluesduringretrieval.4.1.1retefteriecevi接法laiWeusetheabsoluteerrorsbetweentheretrievedLAIvaluesandtheinputLAIvaluesinforwardsimulationastheevaluationcriterionoftheretrievalaccuracy.Fig.3showstherelationshipbetweentheinputLAIvaluesandtheretrievedLAIvalues,inwhichtheXaxisisfortheinputLAIvalues,andtheYaxisfortheretrievedLAIvalues.Fig.4indicatestherelationshipoftheretrievalabsoluteerrors’changeswiththeinputLAIchanges.FromFig.3andFig.4wecanconcludethat:thereisnogreatdegreelossoftheretrievalaccuracyfortheparameterizedmodelcomparedwithSAILHmodel;fromtheabsoluteerrorterms,themaximumretrievalerrorsis0.180and0.122inredandnear-infraredbandsrespectivelyforSAILHmodel,whilethemaximumretrievalerrorswas0.179and0.197inredandnear-infraredbandsrespectivelyfortheparameterizedmodel.4.1.2價格retexThemethodweusetoevaluatetheretrievalefficiencyoftheparameterizedmodelisasfollows:using6observationsofdifferentanglesineachretrievals,settingdifferentretrievaltimesof50times,100times,200timesand500timesrespectively,andthencomputingtherunningtime.Eachtestisrepeatedforfivetimes,andthentaketheaveragedrunningtimeastheevaluationcriterionoftheretrievalefficiency.TheresultsareshowninFig.5.WhatwecanseefromFig.5isthat,inthetermsofretrievalefficiency,theretrievalefficiencyissignificantlyimprovedby10timesoftheparameterizedmodelcomparedwithSAILHmodel.4.1.3relacketin-sitching,sig/sailityForthestabilityevaluationofthemodel,weusethefollowingmethods:intheretrieval,wecomparedtheretrievalaccuracyofLAIbyincreasingthenoiseinthesimulateddata(choosetherelativeerrorastheevaluationcriterion).TheresultsareshowninFig.6.WecanseefromFig.6that,theretrievalerrorisbiggerasthenoiseincreases,andthestabilityoftheparameterizedmodelissuperiortoSAILHmodelwhetherintheredbandorthenear-infraredband.4.2index,measunen,lai,lai,lai,lai,lai,lai,lai,lai,lai,lai,lai,lai,lai,lai,lai,lai,lai,lai,lai,lai:3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.4.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.Theparameterizedmodelisevaluatedbyusingtheground-basedmeasuredcanopyreflectancedataandLAIdatainYingKefromthesatellite-aircraft-groundsynchronousexperimentovertheHeiheriverbasinin2008.ThereweretwomeasurementsetsinJune22andJuly1respectivelyandonlyonemeasurementsetinJuly9intheexperimentalarea.Thus,thereweretotal5groupsofmeasurementsets.WeretrievedtheeightinputparametersmeanwhileusingthesamePowelloptimizationalgorithm.Amongtheseinputparameters,theexpectationsanduncertaintiesofLAI,leafreflectance,leaftransmittanceandsoilreflectancewereobtainedbygroundmeasurements;theexpectationsoftheaverageleafinclinedangleandtheellipticaleccentricitywereretrievedfrommeasuredLADdata,andtheuncertaintiesofthesetwoparametersweresetat0.01;theexpectationsanduncertaintiesofthehot-spoteffectfactorparameterandtheratioofskylightweresetat0.1and0.01,respectively.ThesettingoftheexpectationsanduncertaintiesoftheinputparametersarelistedindetailinTable5.4.2.1respicarespifie-acpo2004和retrie-lai,wspincipalpo底回事件4.InthegroundmeasurementsexceptthattakenonJuly9inHeihefieldcampaign,therewerecanopyreflectancedataoffourplanesineachmeasurementincludingthesolarprincipalplane,theverticalprincipalplane,theparallelrowplaneandthecrossrowplanerespectively(measurementswereonlyavailableatthesolarprincipalplaneandverticalprincipalplaneonJuly9).Inourretrievaltests,firstweusethemeasureddataofeachplanetoretrieverespectively,andthenusethedataofallfourplanestogethertoretrieveLAI.Atlast,wegettheresultsasfollows:comparedwiththegroundmeasuredLAIdata,themaximumretrievalabsoluteerroris1.344ofSAILHmodel,andtheminimumabsoluteerroris0.002;themaximumretrievalabsoluteerroris0.807oftheparameterizedmodel,andtheminimumretrievalabsoluteerroris0.056.Thus,theretrievalerroroftheparameterizedmodelisinanacceptablerange.4.2.2e-terizedmortgageWealsoevaluatetheretrievalefficiencyoftheparame-terizedmodelbyusingthemeasureddata,andgetthesameconclusionthattheretrievalefficiencyisgreatlyimprovedfor8—10timesbytheparameterizedmodel.5sailhmot簡介Inthispaper,weproposesaparameterizedmodelbasedonSAILHmodel.Inthenewmodel,wesimplifythecalculationofthenineintermediatevariablesinSAILHmodel,andalsosimplifythecalculationofthesinglescatteringcontributionoftheilluminatedcanopyatthesametime,andthenkeeptherestcalculationsthesamewiththeSAILHmodel.Weevaluatestheretrievalaccuracy,efficiencyandstabilityoftheparameterizedmodelwithsimulatedandmeasureddatarespectively,andthenwegetsomeconclusionasfollows.(1)Intheentireupwardhemisphere,thereisastrongcorrelationbetweenthesimulatedBRDFbytheparameterizedmodelandtheSAILHmodel,thecorrelationcoefficientsreachedmorethan96%inbothredandnear-infraredband,andtheRMSEintheredbandcanbemaintainedbelow0.01,whileinthenear-infraredbandcanbemaintainedbelow0.04,whichindicatesthattheparameterizedmodelcanbeusedasthesubstituteofSAILHmodel.(2)Evaluationsbasedonsimulateddataandmeasureddatashowthat:fromthetermsofretrievalabsoluteerror,theretrievalaccuracyoftheparameterizedmodelisequaltoSAILHmodel;buttheretrievalefficiencyisimprovedfor8~10times,meanwhile,thestabilityoftheparameterizedmodelisbetterthanSAILHmodel.However,whenweevaluatetheretrievalaccuracyandefficiencyofthesemodelsbyusingthemeasureddata,theexpectationsanduncertaintiesofsomeinputparametersareassumedbecauseofnoexperimentaldata,whichmightaffecttheretrievalresults.(3)AlthoughtheparameterizedmodelcanmakeverygoodapproximationtoSAILHmodelinsimulatingcanopy’sBRDF,andcangreatlyimprovetheefficiencyofLAIretrievalwhilemaintainingtheretrievalaccuracy,thismodelisbasedontheassumptionthattheleafinclinedangledistributionissphericaldistribution,andonlycanbeappliedtocontinuousvegetationcanopyconditions.Therefore,itsapplicabilityislimitedtosomeextent.論上講,如果確定了邊界條件,那么這個方程就是可解的。但是到目前為止,還沒有求得輻射傳輸方程的嚴(yán)格的解析解,只有各種各樣的近似解法(徐希孺,2006)。目前應(yīng)用比較廣泛的解法是Kubelka和Munk提出的K-M方程。SAIL(scatteringbyarbitrarilyinclinedleaves)(Verhoef,1984)模型是在K-M方程的基礎(chǔ)上將入射源分為向上和向下傳輸?shù)妮椛渫棵芏?以及向上和向下傳輸?shù)钠叫休椛漭椪斩?個部分,通過求解9個系數(shù)(包括直射輻射通量密度的削弱系數(shù)(ks),消光系數(shù)(att),背向散射系數(shù)(sig),直射輻射的前向、后向散射系數(shù)(sf,sb)、向上、向下傳輸?shù)妮椛渫棵芏取⑾蛏蟼鬏數(shù)钠叫休椛涞妮椪斩认蛴^測方向上傳輸?shù)妮椛淞炼鹊霓D(zhuǎn)換系數(shù)(uf,ub,ω)、觀測方向上的輻射通量密度的削弱系數(shù)(ko)進(jìn)而求得冠層的反射率,因此SAIL模型是一個4流9參數(shù)的線性微分方程組。它的輸入?yún)?shù)包括3個結(jié)構(gòu)參數(shù)和4個光譜參數(shù)。3個結(jié)構(gòu)參數(shù)分別是葉面積指數(shù)和描述葉傾角分布的2個參數(shù);4個光譜參數(shù)分別是天空光比例,葉片反射率,葉片透過率和土壤反射率。由于SAIL模型不能很好的對熱點效應(yīng)進(jìn)行模擬,因此Kuusk(1991)在SAIL模型的基礎(chǔ)上加入熱點效應(yīng)從而發(fā)展了SAILH模型。熱點效應(yīng)是由葉簇對光的一次散射造成的,因此Kuusk在SAIL模型的基礎(chǔ)上通過建立光線方向與觀測方向間間隙率的相關(guān)概率模型考慮冠層的熱點效應(yīng)。在SAILH模型中整個冠層的單次散射被分解為多層冠層的單次散射貢獻(xiàn)之和;在計算每層冠層的單次散射的貢獻(xiàn)時采用了雙向透過率密度函數(shù)計算其單次散射的貢獻(xiàn)。該雙向透過率密度函數(shù)的計算需要引入一個新的參數(shù)——熱點效應(yīng)因子,這樣SAILH模型的輸入?yún)?shù)共8個(表1)。3sailh模型的建立在實際應(yīng)用中,需要不同地表類型的大范圍、長時間的LAI,遙感技術(shù)是實現(xiàn)這一目標(biāo)的途徑。大量的研究表明,利用遙感技術(shù)可以快速、大范圍、周期性地提取區(qū)域乃至全球的LAI,并能夠提供LAI空間和時間的分布狀況(惠鳳鳴等,2003)。SAILH模型雖然是被廣泛接受的描述均勻植被冠層方向性反射率的模型,但是其計算過程復(fù)雜,反演效率不高,實用性不強。因此以在保證模型反演精度的基礎(chǔ)上提高模型的反演效率為目的,對模型進(jìn)行合理的簡化是非常必要的。本文從這個目的出發(fā),提出了一種基于SAILH模型的參數(shù)化模型,分別基于模擬數(shù)據(jù)和實測數(shù)據(jù)對該參數(shù)化模型的反演精度、反演效率和程序穩(wěn)定性進(jìn)行了評價。3.1簡化計算過程SAILH模型的反演效率很低,主要原因是SAILH模型在計算冠層反射率時將連續(xù)植被冠層的葉傾角離散為13個角度,將這9個中間變量分別表示為葉傾角的函數(shù),通過對這13個角度進(jìn)行迭代求和計算得到。如果能夠?qū)⑦@9個中間變量的計算過程簡化,其余的計算過程仍然采用SAILH模型中的計算過程,那么SAILH模型的計算效率會得到提高。通過比較SAILH模型中9個中間變量的計算過程,得到的簡化計算過程如表2。在表2中,LAI為葉面積指數(shù),在9個中間變量中,計算過程最復(fù)雜的就是ω,其表示的含義是如果光照方向和觀測方向相交于葉片的同側(cè),則用葉片的反射率表示葉片對光的反射作用如果光照方向和觀測方向相交于葉片的異側(cè),則用葉片的透過率表示葉片對光的削弱作用。從這個意義上講,ω表示的是與散射相函數(shù)類似的一個概念,不同的是它包含了LAI,因此在后面的計算中,用散射相函數(shù)近似計算SAILH中的所使用的SAILH模型中的葉傾角分布函數(shù)是用雙參數(shù)橢圓分布描述的,為了能夠?qū)υ摲植嫉娜~傾角的散射相函數(shù)進(jìn)行比較好的近似,選擇用球形分布的散射相函數(shù)代替3.2參數(shù)化模型的模擬能力評價假設(shè)連續(xù)植被冠層由一系列的水平的均勻?qū)盈B加而成,各層之間相互獨立,那么整個冠層對直射光的單次散射的貢獻(xiàn)式中,Γ(Ω式中,P式中,P其中:s_L為熱點效應(yīng)因子,Δ的計算公式如下:為了檢驗式(4)的計算結(jié)果是否正確,將其與SAILH模型的計算結(jié)果比較,如圖2。P得到了P至此,9個中間變量及光照冠層單次散射貢獻(xiàn)的計算過程已得到簡化,其余的計算過程仍然使用SAILH的計算過程。設(shè)計了一組簡單的實驗參數(shù)化模型正向模擬BRDF的能力進(jìn)行評價和比較。假設(shè)太陽天頂角為35°;太陽方位角為0°;觀測天頂角從0°—85°,以5°的角度間隔變化;觀測方位角從0°—355°,同樣以5°的角度間隔變化;這樣整個上半球空間總共有1296個觀測角度組合。結(jié)構(gòu)參數(shù)的輸入值如表3。參數(shù)的設(shè)計是出于以下3個方面的考慮:(1)第1組:將橢圓離心率ε設(shè)定為0.001,這種情況下葉傾角的分布接近于球形分布,分別比較當(dāng)LAI=2和LAI=4時參數(shù)化模型正向模擬BRDF的能力;(2)第2組:將橢圓離心率ε設(shè)定為0.9,平均葉傾角θ(3)第3組:其他參數(shù)設(shè)置同(2),比較當(dāng)LAI=4時參數(shù)化模型的正向模擬能力。對于光譜參數(shù),將紅光波段的天空光比例、葉片的反射率、葉片透過率和土壤反射率分別固定為0.1,0.1,0.12和0.1,近紅外波段的值則分別固定為0.1,0.45,0.5和0.2。對參數(shù)化模型的模擬能力進(jìn)行評價的指標(biāo)為參數(shù)化模型與SAILH模型正向模擬的整個上