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An approach to quantifying the efficiency of a Bayesian filter

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dc.contributor.authorNearing, Grey S.
dc.contributor.authorGupta, Hoshin V.
dc.contributor.authorCrow, Wade T.
dc.contributor.authorGong, Wei
dc.contributor.otherUniversity of Arizona
dc.contributor.otherUnited States Department of Agriculture (USDA)
dc.contributor.otherBeijing Normal University
dc.contributor.otherUniversity of Alabama Tuscaloosa
dc.date.accessioned2018-10-11T21:57:28Z
dc.date.available2018-10-11T21:57:28Z
dc.date.issued2013-04-26
dc.description.abstractData assimilation is the Bayesian conditioning of uncertain model simulations on observations to reduce uncertainty about model states. In practice, it is common to make simplifying assumptions about the prior and posterior state distributions, and to employ approximations of the likelihood function, which can reduce the efficiency of the filter. We propose metrics that quantify how much of the uncertainty in a Bayesian posterior state distribution is due to (i) the observation operator, (ii) observation error, and (iii) approximations of Bayes' Law. Our approach uses discrete Shannon entropy to quantify uncertainty, and we define the utility of an observation (for reducing uncertainty about a model state) as the ratio of the mutual information between the state and observation to the entropy of the state prior. These metrics make it possible to analyze the efficiency of a proposed observation system and data assimilation strategy, and provide a way to examine the propagation of information through the dynamic system model. We demonstrate the procedure on the problem of estimating profile soil moisture from observations at the surface (top 5 cm). The results show that when synthetic observations of 5 cm soil moisture are assimilated into a three-layer model of soil hydrology, the ensemble Kalman filter does not use all of the information available in observations.en_US
dc.format.mimetypeapplication/pdf
dc.identifier.citationNearing, G., Gupta, H., Crow, W., Gong, W. (2013): An approach to quantifying the efficiency of a Bayesian filter. Water Resources Research, 49. DOI: 10.1002/wrcr.20177
dc.identifier.doi10.1002/wrcr.20177
dc.identifier.orcidhttps://orcid.org/0000-0001-7031-6770
dc.identifier.orcidhttps://orcid.org/0000-0001-9855-2839
dc.identifier.orcidhttps://orcid.org/0000-0001-9855-2839
dc.identifier.orcidhttps://orcid.org/0000-0003-3622-7090
dc.identifier.orcidhttps://orcid.org/0000-0002-8217-261X
dc.identifier.urihttp://ir.ua.edu/handle/123456789/4009
dc.languageEnglish
dc.language.isoen_US
dc.publisherAmerican Geophysical Union
dc.subjectdata assimilation
dc.subjectinformation theory
dc.subjectLAND DATA ASSIMILATION
dc.subjectSOIL-MOISTURE
dc.subjectSEQUENTIAL ASSIMILATION
dc.subjectMODEL
dc.subjectTEMPERATURE
dc.subjectENTROPY
dc.subjectPROFILE
dc.subjectEnvironmental Sciences
dc.subjectLimnology
dc.subjectWater Resources
dc.subjectEnvironmental Sciences & Ecology
dc.subjectMarine & Freshwater Biology
dc.titleAn approach to quantifying the efficiency of a Bayesian filteren_US
dc.typetext
dc.typeArticle

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