Estimating model error covariances in nonlinear state-space models using Kalman smoothing and the expectation-maximisation algorithm
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Earth Fluid Modeling and Prediction Group
Earth Science and Engineering Program
Physical Science and Engineering (PSE) Division
Online Publication Date2017-05-24
Print Publication Date2017-04
Permanent link to this recordhttp://hdl.handle.net/10754/623262
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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.
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.
SponsorsWe are thankful to the two reviewers whose constructive comments helped significantly improve this work.