Guaranteeing the convergence of the saddle formulation in weakly-constrained 4D-VAR data assimilation

Serge Gratton, Selime Gürol, Ehouarn Simon, Philippe Toint

Research output: Contribution to journalArticle

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, variationaly 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.
LanguageEnglish
JournalQuarterly Journal of the Royal Meteorological Society
Publication statusAccepted/In press - 2018

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Data Assimilation
Saddle
data assimilation
Formulation
Correlation Matrix
erratic
Diverge
Monotonicity
Objective function
matrix
method

Keywords

  • weather forecasting
  • numerical algorithms
  • Convergence theory

Cite this

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abstract = "This paper discusses convergence issues for the saddle variational formulationof 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, variationaly 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.",
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AB - This paper discusses convergence issues for the saddle variational formulationof 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, variationaly 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.

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