Estimating model error covariances in nonlinear state-space models using Kalman smoothing and the expectation-maximisation algorithm

Handle URI:
http://hdl.handle.net/10754/623262
Title:
Estimating model error covariances in nonlinear state-space models using Kalman smoothing and the expectation-maximisation algorithm
Authors:
Dreano, D.; Tandeo, P.; Pulido, M.; Ait-El-Fquih, Boujemaa; Chonavel, T.; Hoteit, Ibrahim ( 0000-0002-3751-4393 )
Abstract:
Specification and tuning of errors from dynamical models are important issues in data assimilation. In this work, we propose an iterative expectation-maximisation (EM) algorithm to estimate the model error covariances using classical extended and ensemble versions of the Kalman smoother. We show that, for additive model errors, the estimate of the error covariance converges. We also investigate other forms of model error, such as parametric or multiplicative errors. We show that additive Gaussian model error is able to compensate for non additive sources of error in the algorithms we propose. We also demonstrate the limitations of the extended version of the algorithm and recommend the use of the more robust and flexible ensemble version. This article is a proof of concept of the methodology with the Lorenz-63 attractor. We developed an open-source Python library to enable future users to apply the algorithm to their own nonlinear dynamical models.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Dreano D, Tandeo P, Pulido M, Ait-El-Fquih B, Chonavel T, et al. (2017) Estimating model error covariances in nonlinear state-space models using Kalman smoothing and the expectation-maximisation algorithm. Quarterly Journal of the Royal Meteorological Society. Available: http://dx.doi.org/10.1002/qj.3048.
Publisher:
Wiley-Blackwell
Journal:
Quarterly Journal of the Royal Meteorological Society
Issue Date:
5-Apr-2017
DOI:
10.1002/qj.3048
Type:
Article
ISSN:
0035-9009
Sponsors:
We are thankful to the two reviewers whose constructive comments helped significantly improve this work.
Additional Links:
http://onlinelibrary.wiley.com/doi/10.1002/qj.3048/abstract
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorDreano, D.en
dc.contributor.authorTandeo, P.en
dc.contributor.authorPulido, M.en
dc.contributor.authorAit-El-Fquih, Boujemaaen
dc.contributor.authorChonavel, T.en
dc.contributor.authorHoteit, Ibrahimen
dc.date.accessioned2017-04-20T08:08:16Z-
dc.date.available2017-04-20T08:08:16Z-
dc.date.issued2017-04-05en
dc.identifier.citationDreano D, Tandeo P, Pulido M, Ait-El-Fquih B, Chonavel T, et al. (2017) Estimating model error covariances in nonlinear state-space models using Kalman smoothing and the expectation-maximisation algorithm. Quarterly Journal of the Royal Meteorological Society. Available: http://dx.doi.org/10.1002/qj.3048.en
dc.identifier.issn0035-9009en
dc.identifier.doi10.1002/qj.3048en
dc.identifier.urihttp://hdl.handle.net/10754/623262-
dc.description.abstractSpecification and tuning of errors from dynamical models are important issues in data assimilation. In this work, we propose an iterative expectation-maximisation (EM) algorithm to estimate the model error covariances using classical extended and ensemble versions of the Kalman smoother. We show that, for additive model errors, the estimate of the error covariance converges. We also investigate other forms of model error, such as parametric or multiplicative errors. We show that additive Gaussian model error is able to compensate for non additive sources of error in the algorithms we propose. We also demonstrate the limitations of the extended version of the algorithm and recommend the use of the more robust and flexible ensemble version. This article is a proof of concept of the methodology with the Lorenz-63 attractor. We developed an open-source Python library to enable future users to apply the algorithm to their own nonlinear dynamical models.en
dc.description.sponsorshipWe are thankful to the two reviewers whose constructive comments helped significantly improve this work.en
dc.publisherWiley-Blackwellen
dc.relation.urlhttp://onlinelibrary.wiley.com/doi/10.1002/qj.3048/abstracten
dc.rightsThis is the peer reviewed version of the following article: Estimating model error covariances in nonlinear state-space models using Kalman smoothing and the expectation-maximisation algorithm, which has been published in final form at http://doi.org/10.1002/qj.3048. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.en
dc.subjectexpectation-maximisationen
dc.subjectEnKFen
dc.subjectEnKSen
dc.subjectextended Kalman filteren
dc.subjectmodel erroren
dc.subjectstate-space modelsen
dc.titleEstimating model error covariances in nonlinear state-space models using Kalman smoothing and the expectation-maximisation algorithmen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalQuarterly Journal of the Royal Meteorological Societyen
dc.eprint.versionPost-printen
dc.contributor.institutionLab-STICC- PÔle CID, Telecom Bretagne; Brest Franceen
dc.contributor.institutionDepartment of Physics; Universidad Nacional del Nordeste; Corrientes Argentinaen
kaust.authorDreano, D.en
kaust.authorAit-El-Fquih, Boujemaaen
kaust.authorHoteit, Ibrahimen
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