On the convergence of a non-linear ensemble Kalman smoother

El Houcine Bergou; Serge Gratton; Jan Mandel

doi:10.1016/j.apnum.2018.11.008

On the convergence of a non-linear ensemble Kalman smoother

El Houcine Bergou, Serge Gratton, Jan Mandel

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Ensemble methods, such as the ensemble Kalman filter (EnKF), the local ensemble transform Kalman filter (LETKF), and the ensemble Kalman smoother (EnKS) are widely used in sequential data assimilation, where state vectors are of huge dimension. Little is known, however, about the asymptotic behavior of ensemble methods. In this paper, we prove convergence in L of ensemble Kalman smoother to the Kalman smoother in the large-ensemble limit, as well as the convergence of EnKS-4DVAR, which is a Levenberg–Marquardt-like algorithm with EnKS as the linear solver, to the classical Levenberg–Marquardt algorithm in which the linearized problem is solved exactly.

Original language	English (US)
Pages (from-to)	151-168
Number of pages	18
Journal	Applied Numerical Mathematics
Volume	137
DOIs	https://doi.org/10.1016/j.apnum.2018.11.008
State	Published - Nov 29 2018

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Partially supported by the U.S. National Science Foundation under the grant DMS-1216481, the Czech Science Foundation under the grant 13-34856S and the Fondation STAE project ADTAO.

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10.1016/j.apnum.2018.11.008

https://repository.kaust.edu.sa/bitstream/10754/630346/1/EnKS_convergence.pdf

Cite this

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title = "On the convergence of a non-linear ensemble Kalman smoother",

abstract = "Ensemble methods, such as the ensemble Kalman filter (EnKF), the local ensemble transform Kalman filter (LETKF), and the ensemble Kalman smoother (EnKS) are widely used in sequential data assimilation, where state vectors are of huge dimension. Little is known, however, about the asymptotic behavior of ensemble methods. In this paper, we prove convergence in L of ensemble Kalman smoother to the Kalman smoother in the large-ensemble limit, as well as the convergence of EnKS-4DVAR, which is a Levenberg–Marquardt-like algorithm with EnKS as the linear solver, to the classical Levenberg–Marquardt algorithm in which the linearized problem is solved exactly.",

author = "Bergou, {El Houcine} and Serge Gratton and Jan Mandel",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: Partially supported by the U.S. National Science Foundation under the grant DMS-1216481, the Czech Science Foundation under the grant 13-34856S and the Fondation STAE project ADTAO.",

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doi = "10.1016/j.apnum.2018.11.008",

language = "English (US)",

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AU - Bergou, El Houcine

AU - Gratton, Serge

AU - Mandel, Jan

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: Partially supported by the U.S. National Science Foundation under the grant DMS-1216481, the Czech Science Foundation under the grant 13-34856S and the Fondation STAE project ADTAO.

PY - 2018/11/29

Y1 - 2018/11/29

N2 - Ensemble methods, such as the ensemble Kalman filter (EnKF), the local ensemble transform Kalman filter (LETKF), and the ensemble Kalman smoother (EnKS) are widely used in sequential data assimilation, where state vectors are of huge dimension. Little is known, however, about the asymptotic behavior of ensemble methods. In this paper, we prove convergence in L of ensemble Kalman smoother to the Kalman smoother in the large-ensemble limit, as well as the convergence of EnKS-4DVAR, which is a Levenberg–Marquardt-like algorithm with EnKS as the linear solver, to the classical Levenberg–Marquardt algorithm in which the linearized problem is solved exactly.

AB - Ensemble methods, such as the ensemble Kalman filter (EnKF), the local ensemble transform Kalman filter (LETKF), and the ensemble Kalman smoother (EnKS) are widely used in sequential data assimilation, where state vectors are of huge dimension. Little is known, however, about the asymptotic behavior of ensemble methods. In this paper, we prove convergence in L of ensemble Kalman smoother to the Kalman smoother in the large-ensemble limit, as well as the convergence of EnKS-4DVAR, which is a Levenberg–Marquardt-like algorithm with EnKS as the linear solver, to the classical Levenberg–Marquardt algorithm in which the linearized problem is solved exactly.

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UR - https://www.sciencedirect.com/science/article/pii/S0168927418302575

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VL - 137

SP - 151

EP - 168

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

On the convergence of a non-linear ensemble Kalman smoother

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