On analysis error covariances in variational data assimilation

I.Y. Gejadze, F. Le-Dimet, V. Shutyaev

Research output: Contribution to journalArticle

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Abstract

The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function (analysis). The equation for the analysis error is derived through the errors of the input data (background and observation errors). This equation is used to show that in a nonlinear case the analysis error covariance operator can be approximated by the inverse Hessian of an auxiliary data assimilation problem which involves the tangent linear model constraints. The inverse Hessian is constructed by the quasi-Newton BFGS algorithm when solving the auxiliary data assimilation problem. A fully nonlinear ensemble procedure is developed to verify the accuracy of the proposed algorithm. Numerical examples are presented.
Original languageEnglish
Pages (from-to)1847-1874
Number of pages28
JournalSIAM Journal on Scientific Computing
Volume30
Issue number4
Early online date2 May 2008
DOIs
Publication statusPublished - Jun 2008

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Data Assimilation
Error Analysis
Error analysis
Covariance Operator
Mathematical operators
Quasi-Newton
Fully Nonlinear
Tangent line
Optimal Control Problem
Linear Model
Ensemble
Initial conditions
Verify
Numerical Examples
Model

Keywords

  • data assimilation
  • optimal control
  • analysis error
  • hessian
  • covariance operator

Cite this

Gejadze, I.Y. ; Le-Dimet, F. ; Shutyaev, V. / On analysis error covariances in variational data assimilation. In: SIAM Journal on Scientific Computing. 2008 ; Vol. 30, No. 4. pp. 1847-1874.
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On analysis error covariances in variational data assimilation. / Gejadze, I.Y.; Le-Dimet, F.; Shutyaev, V.

In: SIAM Journal on Scientific Computing, Vol. 30, No. 4, 06.2008, p. 1847-1874.

Research output: Contribution to journalArticle

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