### Résumé

langue originale | Anglais |
---|---|

Pages (de - à) | 452-466 |

Nombre de pages | 15 |

journal | Quarterly Journal of the Royal Meteorological Society |

Numéro de publication | 137 |

état | Publié - 2011 |

### Empreinte digitale

### Citer ceci

*Quarterly Journal of the Royal Meteorological Society*, (137), 452-466.

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*Quarterly Journal of the Royal Meteorological Society*, Numéro 137, p. 452-466.

**A reduced and limited memory preconditioned approach for the 4D-Var data assimilation problem.** / Gratton, Serge; Laloyaux, Patrick; Sartenaer, Annick; Tshimanga Ilunga, Jean.

Résultats de recherche: Contribution à un journal/une revue › Article

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 -