A reduced and limited memory preconditioned approach for the 4D-Var data assimilation problem

Serge Gratton, Patrick Laloyaux, Annick Sartenaer, Jean Tshimanga Ilunga

Research output: Contribution to journalArticle

Abstract

We recall a theoretical analysis of the equivalence between the Kalman filter and the four-dimensional variational (4D-Var) approach to solve data-assimilation problems. This result is then extended to cover the comparison of the singular evolutive extended Kalman (SEEK) filter with a reduced variant of the 4D-Var algorithm. We next concentrate on the solution of the 4D-Var, which is usually computed with a (truncated) Gauss-Newton algorithm using a preconditioned conjugate-gradient-like (CG) method. Motivated by the equivalence of the above-mentioned algorithms, we explore techniques used in the SEEK filter and based on empirical orthogonal functions (EOFs) as an attempt to accelerate the Gauss-Newton method further. This leads to the development of an appropriate starting point for the CG method, together with that of a powerful limited-memory preconditioner (LMP), as shown by preliminary numerical experiments performed on a shallow-water model.
Original languageEnglish
Pages (from-to)452-466
Number of pages15
JournalQuarterly Journal of the Royal Meteorological Society
Issue number137
Publication statusPublished - 2011

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data assimilation
Kalman filter
shallow water
filter
method
empirical orthogonal function analysis
analysis
comparison

Keywords

  • empirical orthogonal functions
  • SEEK filter

Cite this

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title = "A reduced and limited memory preconditioned approach for the 4D-Var data assimilation problem",
abstract = "We recall a theoretical analysis of the equivalence between the Kalman filter and the four-dimensional variational (4D-Var) approach to solve data-assimilation problems. This result is then extended to cover the comparison of the singular evolutive extended Kalman (SEEK) filter with a reduced variant of the 4D-Var algorithm. We next concentrate on the solution of the 4D-Var, which is usually computed with a (truncated) Gauss-Newton algorithm using a preconditioned conjugate-gradient-like (CG) method. Motivated by the equivalence of the above-mentioned algorithms, we explore techniques used in the SEEK filter and based on empirical orthogonal functions (EOFs) as an attempt to accelerate the Gauss-Newton method further. This leads to the development of an appropriate starting point for the CG method, together with that of a powerful limited-memory preconditioner (LMP), as shown by preliminary numerical experiments performed on a shallow-water model.",
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TY - JOUR

T1 - A reduced and limited memory preconditioned approach for the 4D-Var data assimilation problem

AU - Gratton, Serge

AU - Laloyaux, Patrick

AU - Sartenaer, Annick

AU - Tshimanga Ilunga, Jean

PY - 2011

Y1 - 2011

N2 - We recall a theoretical analysis of the equivalence between the Kalman filter and the four-dimensional variational (4D-Var) approach to solve data-assimilation problems. This result is then extended to cover the comparison of the singular evolutive extended Kalman (SEEK) filter with a reduced variant of the 4D-Var algorithm. We next concentrate on the solution of the 4D-Var, which is usually computed with a (truncated) Gauss-Newton algorithm using a preconditioned conjugate-gradient-like (CG) method. Motivated by the equivalence of the above-mentioned algorithms, we explore techniques used in the SEEK filter and based on empirical orthogonal functions (EOFs) as an attempt to accelerate the Gauss-Newton method further. This leads to the development of an appropriate starting point for the CG method, together with that of a powerful limited-memory preconditioner (LMP), as shown by preliminary numerical experiments performed on a shallow-water model.

AB - We recall a theoretical analysis of the equivalence between the Kalman filter and the four-dimensional variational (4D-Var) approach to solve data-assimilation problems. This result is then extended to cover the comparison of the singular evolutive extended Kalman (SEEK) filter with a reduced variant of the 4D-Var algorithm. We next concentrate on the solution of the 4D-Var, which is usually computed with a (truncated) Gauss-Newton algorithm using a preconditioned conjugate-gradient-like (CG) method. Motivated by the equivalence of the above-mentioned algorithms, we explore techniques used in the SEEK filter and based on empirical orthogonal functions (EOFs) as an attempt to accelerate the Gauss-Newton method further. This leads to the development of an appropriate starting point for the CG method, together with that of a powerful limited-memory preconditioner (LMP), as shown by preliminary numerical experiments performed on a shallow-water model.

KW - empirical orthogonal functions

KW - SEEK filter

M3 - Article

SP - 452

EP - 466

JO - Quarterly Journal of the Royal Meteorological Society

JF - Quarterly Journal of the Royal Meteorological Society

SN - 0035-9009

IS - 137

ER -