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

Serge Gratton, Selime Gürol, Ehouarn Simon, Philippe L. Toint

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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
Issue number717
Publication statusPublished - 1 Oct 2018



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

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