Guaranteeing the convergence of the saddle formulation for weakly constrained 4D-Var data assimilation

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Abstract

This paper discusses convergence issues for the saddle variational formulation of the weakly constrained 4D-Var method in data assimilation, a method whose main interests are its parallelizable nature and its limited use of the inverse of the correlation matrices. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationally coherent variants of the algorithm are then proposed which largely retain the desirable features of the original proposal, and the circumstances in which these variants may be preferable to other approaches is briefly discussed.

Original languageEnglish
Pages (from-to)2592-2602
Number of pages11
JournalQuarterly Journal of the Royal Meteorological Society
Volume144
Issue number717
DOIs
Publication statusPublished - 1 Oct 2018

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data assimilation
erratic
matrix
method

Keywords

  • data assimilation
  • parallel computing
  • saddle formulation
  • variational methods
  • weakly constrained 4D-Var

Cite this

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title = "Guaranteeing the convergence of the saddle formulation for weakly constrained 4D-Var data assimilation",
abstract = "This paper discusses convergence issues for the saddle variational formulation of the weakly constrained 4D-Var method in data assimilation, a method whose main interests are its parallelizable nature and its limited use of the inverse of the correlation matrices. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationally coherent variants of the algorithm are then proposed which largely retain the desirable features of the original proposal, and the circumstances in which these variants may be preferable to other approaches is briefly discussed.",
keywords = "data assimilation, parallel computing, saddle formulation, variational methods, weakly constrained 4D-Var",
author = "Serge Gratton and Selime G{\"u}rol and Ehouarn Simon and Toint, {Philippe L.}",
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T1 - Guaranteeing the convergence of the saddle formulation for weakly constrained 4D-Var data assimilation

AU - Gratton, Serge

AU - Gürol, Selime

AU - Simon, Ehouarn

AU - Toint, Philippe L.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - This paper discusses convergence issues for the saddle variational formulation of the weakly constrained 4D-Var method in data assimilation, a method whose main interests are its parallelizable nature and its limited use of the inverse of the correlation matrices. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationally coherent variants of the algorithm are then proposed which largely retain the desirable features of the original proposal, and the circumstances in which these variants may be preferable to other approaches is briefly discussed.

AB - This paper discusses convergence issues for the saddle variational formulation of the weakly constrained 4D-Var method in data assimilation, a method whose main interests are its parallelizable nature and its limited use of the inverse of the correlation matrices. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationally coherent variants of the algorithm are then proposed which largely retain the desirable features of the original proposal, and the circumstances in which these variants may be preferable to other approaches is briefly discussed.

KW - data assimilation

KW - parallel computing

KW - saddle formulation

KW - variational methods

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