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Uncertainty and Sensitivity Matrix of Parametersin Inversion of Physical BRDF Model

LiXiaowen (InstituteofRemoteSensingApplication ,CAS ,Beijing 10 0 10 1) GaoFeng (NanjingInstituteofGeographyandLimnology ,Nanjing 2 10 0 0 8)WangJindi (InstituteofRemoteSensingApplication ,CAS ,Beijing 10 0 10 1) ZhuQijiang (BeijingNor  
PhysicalBRDFmodelsareusuallyverycomplexanddifficulttoinvert Weusuallyneedtoemploya prioriknowledgeinthisorthatway ,fixsomeparametervaluesandinvertsomeothers Usuallymostofusagree thatnon -sensitiveparametersshouldbefixed Buttherehasnotbeenanyconsen -susonhowtodefinethe sensitivityofaparameterininversion LiandStrahler ,LiandWangalsosuggestedthatonlythosethemostsen sitiveandmostuncertainparametersshouldbeinvertedbyusingasubsetofobservations Buttheyfailedtospell outhowtodeterminesuch“mostsensitiveandmostuncertain” parametersandhowtofindsuchasubsetofob servations ThislackingofconsensusandquantitativerulesmakesinversionofphysicalBRDFmodelsacase -by -case“trick”oran“artbutscience” WetriedtodevelopageneralframeworkforBRDFmodelinversion Itisbasedonaccumulationofknowl edgeandaninversionstrategywhichwecalledMulti-stage ,Sample -directionDependent,Target-decisions (MSDT) Presently ,ourknowledgeinclude :1)DTM ;2 ) previousland -coverclassification ;3)seasonalchange patternoftheseland -covers ;4 )rightmodelforeverytypeoflandcovers ;5) physicallimitations (ornone) ofeachparameterineachmodel;6)abestguessofeachparametervalueandtheuncertaintyofsuchguess . OurMSDTinversionstrategyisbasedonanUncertaintyandSensitivityMatrix (USM )ofparametersat givendirections/bandsofobservations Itsdefinitionissomehowanalogoustothepartialderivativematrixused inNewtonmethodsforminimization ,buttherearethreesignificantdifferences :suchguess 1)Theuncertainty oftheinitialguessistakenintoaccount ;2 )Itislessdependentontheinitialguess ;3)Allelementshavethe sameunitandthereforequantitativelycomparable AnexampleofUSMfromLi -StrahlerGOMSmodeland ASASsamplingwillbepresented ,anditisobviousfromthematrixwhatparametershouldbeinvertedfirst , andwhatsubsetofobservationsshouldbeused AnotherexampleofUSMfromSAILmodelandhemispherical samplingisalsopresented ComparisonbetweeninversionerrorsofusingdifferentsubsetsofsamplesshowUSM couldbeahelpfulconceptinBRDFinversion
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