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dc.contributor.authorSondergaard, Thomas
dc.contributor.authorLermusiaux, Pierre F. J.
dc.date.accessioned2013-05-16T20:23:13Z
dc.date.available2013-05-16T20:23:13Z
dc.date.issued2012
dc.identifier.issn0027-0644
dc.identifier.issn1520-0493
dc.identifier.urihttp://hdl.handle.net/1721.1/78912
dc.description.abstractThis work introduces and derives an efficient, data-driven assimilation scheme, focused on a time-dependent stochastic subspace, that respects nonlinear dynamics and captures non-Gaussian statistics as it occurs. The motivation is to obtain a filter that is applicable to realistic geophysical applications but that also rigorously utilizes the governing dynamical equations with information theory and learning theory for efficient Bayesian data assimilation. Building on the foundations of classical filters, the underlying theory and algorithmic implementation of the new filter are developed and derived. The stochastic Dynamically Orthogonal (DO) field equations and their adaptive stochastic subspace are employed to predict prior probabilities for the full dynamical state, effectively approximating the Fokker-Planck equation. At assimilation times, the DO realizations are fit to semiparametric Gaussian mixture models (GMMs) using the Expectation-Maximization algorithm and the Bayesian Information Criterion. Bayes’ Law is then efficiently carried out analytically within the evolving stochastic subspace. The resulting GMM-DO filter is illustrated in a very simple example. Variations of the GMM-DO filter are also provided along with comparisons with related schemes.en_US
dc.description.sponsorshipUnited States. Office of Naval Research (Grant N00014-08-1-1097)en_US
dc.description.sponsorshipUnited States. Office of Naval Research (Grant 00014-09-1-0676)en_US
dc.description.sponsorshipUnited States. Office of Naval Research (Grant N00014-08-1-0586)en_US
dc.language.isoen_US
dc.publisherAmerican Meteorological Societyen_US
dc.relation.isversionofhttp://dx.doi.org/10.1175/MWR-D-11-00295.1en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alike 3.0en_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/en_US
dc.sourceMIT web domainen_US
dc.titleData Assimilation with Gaussian Mixture Models using the Dynamically Orthogonal Field Equations. Part I. Theory and Schemeen_US
dc.typeArticleen_US
dc.identifier.citationSondergaard, Thomas, and Pierre F. J. Lermusiaux. “Data Assimilation with Gaussian Mixture Models Using the Dynamically Orthogonal Field Equations. Part I: Theory and Scheme.” Monthly Weather Review (2012): 121011101334009.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mechanical Engineeringen_US
dc.contributor.mitauthorSondergaard, Thomas
dc.contributor.mitauthorLermusiaux, Pierre F. J.
dc.relation.journalMonthly Weather Reviewen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsSondergaard, Thomas; Lermusiaux, Pierre F. J.en
dc.identifier.orcidhttps://orcid.org/0000-0002-1869-3883
mit.licenseOPEN_ACCESS_POLICYen_US


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