### Abstract

Original language | English |
---|---|

Pages (from-to) | 1847-1874 |

Number of pages | 28 |

Journal | SIAM Journal on Scientific Computing |

Volume | 30 |

Issue number | 4 |

Early online date | 2 May 2008 |

DOIs | |

Publication status | Published - Jun 2008 |

### Fingerprint

### Keywords

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

### Cite this

*SIAM Journal on Scientific Computing*,

*30*(4), 1847-1874. https://doi.org/10.1137/07068744X

}

*SIAM Journal on Scientific Computing*, vol. 30, no. 4, pp. 1847-1874. https://doi.org/10.1137/07068744X

**On analysis error covariances in variational data assimilation.** / Gejadze, I.Y.; Le-Dimet, F.; Shutyaev, V.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On analysis error covariances in variational data assimilation

AU - Gejadze, I.Y.

AU - Le-Dimet, F.

AU - Shutyaev, V.

PY - 2008/6

Y1 - 2008/6

N2 - 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.

AB - 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.

KW - data assimilation

KW - optimal control

KW - analysis error

KW - hessian

KW - covariance operator

U2 - 10.1137/07068744X

DO - 10.1137/07068744X

M3 - Article

VL - 30

SP - 1847

EP - 1874

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

SN - 1064-8275

IS - 4

ER -