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Variable-storage Quasi-Newton Operators as Inverse Forecast/Analysis Error Covariance Matrices in Variational Data Assimilation

Fabrice Veersé 1
1 IDOPT - System identification and optimization in physics and environment
Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : UMR5527
Abstract : Two approximations of the Hessian matrix as limited-memory operators are built from the limited-memory BFGS inverse Hessian approximation provided by the minimization code, in view of the specification of the inverse analysis/forecast error covariance matrix in variational data assimilation. Some numerical experiments and theoretical considerations lead to reject the limited-memory DFP Hessian approximation and to retain the BFGS one for the applications foreseen. Conditioning issues are explored and a preconditioning strategy via a change of control variable is proposed, based on a suitable Cholesky factorization of the limited-memory inverse Hessian matrix. This factorization is implemented as the composition of linear operators. The memory requirements and the number of floating-point operations required by the method are given and confirmed by numerical experiments. The method is found to have a strong potential for variational data assimilation systems using high resolution ocean or atmosphere general circulation models.
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https://hal.inria.fr/inria-00072984
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 11:31:03 AM
Last modification on : Wednesday, November 4, 2020 - 2:45:19 PM
Long-term archiving on: : Sunday, April 4, 2010 - 9:34:54 PM

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  • HAL Id : inria-00072984, version 1

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Fabrice Veersé. Variable-storage Quasi-Newton Operators as Inverse Forecast/Analysis Error Covariance Matrices in Variational Data Assimilation. RR-3685, INRIA. 1999. ⟨inria-00072984⟩

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