Uncertainty and Sensitivity Matrix of Parametersin Inversion of Physical BRDF Model

LiXiaowen

doi:10.11834/jrs.19970102

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Uncertainty and Sensitivity Matrix of Parametersin Inversion of Physical BRDF Model
Issue 1, Pages: 5-14(1997)
Published：1997
DOI： 10.11834/jrs.19970102
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[1]李小文,高峰,王锦地,朱启疆.遥感反演中参数的不确定性与敏感性矩阵[J].遥感学报,1997(01):5-14. DOI： 10.11834/jrs.19970102.

LiXiaowen. Uncertainty and Sensitivity Matrix of Parametersin Inversion of Physical BRDF Model[J]. Journal of Remote Sensing, 1997, (1): 5-14. DOI： 10.11834/jrs.19970102.

摘要

多角度遥感中二向性反射（BRDF）物理模型的反演

是当前国际遥感界学术研究的热点之一。反演中先验知识的表达和利用

参数敏感性的判别和处理

已提出了若干年

但只是到最近

才有了将参数的先验概率引入拟合误差平方加权

及定义参数对观测值敏感性的尝试。该文简述了这些最新进展

并首次建议了反演中参数的“不确定性与敏感性矩阵”的定义。并以作者最近的反演实例

说明这样定义的矩阵

如何直接用于反演的多阶段目标决策

Abstract

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