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

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

Résultats de recherche: Contribution à un journal/une revueArticle

Résumé

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.
langue originaleAnglais
Pages (de - à)452-466
Nombre de pages15
journalQuarterly Journal of the Royal Meteorological Society
Numéro de publication137
étatPublié - 2011

Empreinte digitale

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

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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.",
    keywords = "empirical orthogonal functions, SEEK filter",
    author = "Serge Gratton and Patrick Laloyaux and Annick Sartenaer and {Tshimanga Ilunga}, Jean",
    year = "2011",
    language = "English",
    pages = "452--466",
    journal = "Quarterly Journal of the Royal Meteorological Society",
    issn = "0035-9009",
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    A reduced and limited memory preconditioned approach for the 4D-Var data assimilation problem. / Gratton, Serge; Laloyaux, Patrick; Sartenaer, Annick; Tshimanga Ilunga, Jean.

    Dans: Quarterly Journal of the Royal Meteorological Society, Numéro 137, 2011, p. 452-466.

    Résultats de recherche: Contribution à un journal/une revueArticle

    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 -