Estimating model‐error covariances in nonlinear state‐space models using Kalman smoothing and the expectation–maximization algorithm
Specification and tuning of errors from dynamical models are important issues in data assimilation. In this work, we propose an iterative expectation–maximization (EM) algorithm to estimate the model‐error covariances using classical extended and ensemble versions of the Kalman smoother. We show tha...
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| Vydané v: | Quarterly journal of the Royal Meteorological Society Ročník 143; číslo 705; s. 1877 - 1885 |
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| Hlavní autori: | , , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Chichester, UK
John Wiley & Sons, Ltd
01.04.2017
Wiley Subscription Services, Inc Wiley |
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| ISSN: | 0035-9009, 1477-870X |
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| Abstract | Specification and tuning of errors from dynamical models are important issues in data assimilation. In this work, we propose an iterative expectation–maximization (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.
We propose an iterative expectation–maximization algorithm to estimate the model‐error covariances using classical extended and ensemble versions of the Kalman smoother. We show convergence of the algorithm on the Lorenz‐63 model, including for non‐Gaussian model errors. We have developed an open‐source Python library to enable future users to apply the algorithm to their own nonlinear dynamical models. |
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| AbstractList | Specification and tuning of errors from dynamical models are important issues in data assimilation. In this work, we propose an iterative expectation–maximization (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. Specification and tuning of errors from dynamical models are important issues in data assimilation. In this work, we propose an iterative expectation–maximization (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. We propose an iterative expectation–maximization algorithm to estimate the model‐error covariances using classical extended and ensemble versions of the Kalman smoother. We show convergence of the algorithm on the Lorenz‐63 model, including for non‐Gaussian model errors. We have developed an open‐source Python library to enable future users to apply the algorithm to their own nonlinear dynamical models. |
| Author | Chonavel, T. Hoteit, I. Ait‐El‐Fquih, B. Dreano, D. Tandeo, P. Pulido, M. |
| Author_xml | – sequence: 1 givenname: D. surname: Dreano fullname: Dreano, D. organization: CEMSE Division, King Abdullah University of Science and Technology (KAUST) – sequence: 2 givenname: P. surname: Tandeo fullname: Tandeo, P. organization: Lab‐STICC—Pôle CID, Telecom Bretagne – sequence: 3 givenname: M. surname: Pulido fullname: Pulido, M. organization: Universidad Nacional del Nordeste – sequence: 4 givenname: B. surname: Ait‐El‐Fquih fullname: Ait‐El‐Fquih, B. organization: CEMSE Division, King Abdullah University of Science and Technology (KAUST) – sequence: 5 givenname: T. surname: Chonavel fullname: Chonavel, T. organization: Lab‐STICC—Pôle CID, Telecom Bretagne – sequence: 6 givenname: I. orcidid: 0000-0002-3751-4393 surname: Hoteit fullname: Hoteit, I. email: ibrahim.hoteit@kaust.edu.sa organization: CEMSE Division, King Abdullah University of Science and Technology (KAUST) |
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| Title | Estimating model‐error covariances in nonlinear state‐space models using Kalman smoothing and the expectation–maximization algorithm |
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