Derivative-free optimization for large-scale nonlinear data assimilation problems

Research output: Contribution to journalArticle

Abstract

The computation of derivatives and the development of tangent and adjoint codes represent a challenging issue and a major human time-consuming task when solving operational data assimilation problems. The ensemble Kalman filter provides a suitable derivative-free adaptation for the sequential approach by using an ensemble-based implementation of the Kalman filter equations. This article proposes a derivative-free variant for the variational approach, based on an iterative subspace minimization (ISM) technique. At each iteration, a subspace of low dimension is built from the relevant information contained in the empirical orthogonal functions (EOFs), allowing us to define a reduced 4D-Var subproblem which is then solved using a derivative-free optimization (DFO) algorithm. Strategies to improve the quality of the selected subspaces are presented, together with two numerical illustrations. The ISM technique is first compared with a basic stochastic ensemble Kalman filter on an academic shallow-water problem. The DFO algorithm embedded in the ISM technique is then validated in the NEMO framework, using its GYRE configuration.

Original languageEnglish
JournalQuarterly Journal of the Royal Meteorological Society
DOIs
Publication statusAccepted/In press - 28 May 2013

Fingerprint

Kalman filter
data assimilation
shallow water

Keywords

  • 4D-Var
  • Derivative-free optimization
  • Empirical orthogonal functions

Cite this

@article{182132f58e044981aa7829f13d9629ba,
title = "Derivative-free optimization for large-scale nonlinear data assimilation problems",
abstract = "The computation of derivatives and the development of tangent and adjoint codes represent a challenging issue and a major human time-consuming task when solving operational data assimilation problems. The ensemble Kalman filter provides a suitable derivative-free adaptation for the sequential approach by using an ensemble-based implementation of the Kalman filter equations. This article proposes a derivative-free variant for the variational approach, based on an iterative subspace minimization (ISM) technique. At each iteration, a subspace of low dimension is built from the relevant information contained in the empirical orthogonal functions (EOFs), allowing us to define a reduced 4D-Var subproblem which is then solved using a derivative-free optimization (DFO) algorithm. Strategies to improve the quality of the selected subspaces are presented, together with two numerical illustrations. The ISM technique is first compared with a basic stochastic ensemble Kalman filter on an academic shallow-water problem. The DFO algorithm embedded in the ISM technique is then validated in the NEMO framework, using its GYRE configuration.",
keywords = "4D-Var, Derivative-free optimization, Empirical orthogonal functions",
author = "S. Gratton and P. Laloyaux and A. Sartenaer",
year = "2013",
month = "5",
day = "28",
doi = "10.1002/qj.2169",
language = "English",
journal = "Quarterly Journal of the Royal Meteorological Society",
issn = "0035-9009",
publisher = "John Wiley and Sons Ltd",

}

TY - JOUR

T1 - Derivative-free optimization for large-scale nonlinear data assimilation problems

AU - Gratton, S.

AU - Laloyaux, P.

AU - Sartenaer, A.

PY - 2013/5/28

Y1 - 2013/5/28

N2 - The computation of derivatives and the development of tangent and adjoint codes represent a challenging issue and a major human time-consuming task when solving operational data assimilation problems. The ensemble Kalman filter provides a suitable derivative-free adaptation for the sequential approach by using an ensemble-based implementation of the Kalman filter equations. This article proposes a derivative-free variant for the variational approach, based on an iterative subspace minimization (ISM) technique. At each iteration, a subspace of low dimension is built from the relevant information contained in the empirical orthogonal functions (EOFs), allowing us to define a reduced 4D-Var subproblem which is then solved using a derivative-free optimization (DFO) algorithm. Strategies to improve the quality of the selected subspaces are presented, together with two numerical illustrations. The ISM technique is first compared with a basic stochastic ensemble Kalman filter on an academic shallow-water problem. The DFO algorithm embedded in the ISM technique is then validated in the NEMO framework, using its GYRE configuration.

AB - The computation of derivatives and the development of tangent and adjoint codes represent a challenging issue and a major human time-consuming task when solving operational data assimilation problems. The ensemble Kalman filter provides a suitable derivative-free adaptation for the sequential approach by using an ensemble-based implementation of the Kalman filter equations. This article proposes a derivative-free variant for the variational approach, based on an iterative subspace minimization (ISM) technique. At each iteration, a subspace of low dimension is built from the relevant information contained in the empirical orthogonal functions (EOFs), allowing us to define a reduced 4D-Var subproblem which is then solved using a derivative-free optimization (DFO) algorithm. Strategies to improve the quality of the selected subspaces are presented, together with two numerical illustrations. The ISM technique is first compared with a basic stochastic ensemble Kalman filter on an academic shallow-water problem. The DFO algorithm embedded in the ISM technique is then validated in the NEMO framework, using its GYRE configuration.

KW - 4D-Var

KW - Derivative-free optimization

KW - Empirical orthogonal functions

UR - http://www.scopus.com/inward/record.url?scp=84878004310&partnerID=8YFLogxK

U2 - 10.1002/qj.2169

DO - 10.1002/qj.2169

M3 - Article

JO - Quarterly Journal of the Royal Meteorological Society

JF - Quarterly Journal of the Royal Meteorological Society

SN - 0035-9009

ER -