### Abstract

Language | English |
---|---|

Pages | 2159-2178 |

Number of pages | 20 |

Journal | Journal of Computational Physics |

Volume | 229 |

Issue number | 6 |

DOIs | |

Publication status | Published - 20 Mar 2010 |

### Fingerprint

### Keywords

- variational data assimilation
- parameter estimation
- optimal solution error covariances
- hessian
- preconditioning
- mathematics

### Cite this

*Journal of Computational Physics*,

*229*(6), 2159-2178. https://doi.org/10.1016/j.jcp.2009.11.028

}

*Journal of Computational Physics*, vol. 229, no. 6, pp. 2159-2178. https://doi.org/10.1016/j.jcp.2009.11.028

**On optimal solution error covariances in variational data assimilation problems.** / Gejadze, I.Y.; Le Dimet, F.X.; Shutyaev, V.; (Funder), Scottish Founding Council via GRPE.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On optimal solution error covariances in variational data assimilation problems

AU - Gejadze, I.Y.

AU - Le Dimet, F.X.

AU - Shutyaev, V.

AU - (Funder), Scottish Founding Council via GRPE

PY - 2010/3/20

Y1 - 2010/3/20

N2 - The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find unknown parameters such as distributed model coefficients or boundary conditions. The equation for the optimal solution error is derived through the errors of the input data (background and observation errors), and the optimal solution error covariance operator through the input data error covariance operators, respectively. The quasi-Newton BFGS algorithm is adapted to construct the covariance matrix of the optimal solution error using the inverse Hessian of an auxiliary data assimilation problem based on the tangent linear model constraints. Preconditioning is applied to reduce the number of iterations required by the BFGS algorithm to build a quasi-Newton approximation of the inverse Hessian. Numerical examples are presented for the one-dimensional convection-diffusion model.

AB - The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find unknown parameters such as distributed model coefficients or boundary conditions. The equation for the optimal solution error is derived through the errors of the input data (background and observation errors), and the optimal solution error covariance operator through the input data error covariance operators, respectively. The quasi-Newton BFGS algorithm is adapted to construct the covariance matrix of the optimal solution error using the inverse Hessian of an auxiliary data assimilation problem based on the tangent linear model constraints. Preconditioning is applied to reduce the number of iterations required by the BFGS algorithm to build a quasi-Newton approximation of the inverse Hessian. Numerical examples are presented for the one-dimensional convection-diffusion model.

KW - variational data assimilation

KW - parameter estimation

KW - optimal solution error covariances

KW - hessian

KW - preconditioning

KW - mathematics

U2 - 10.1016/j.jcp.2009.11.028

DO - 10.1016/j.jcp.2009.11.028

M3 - Article

VL - 229

SP - 2159

EP - 2178

JO - Journal of Computational Physics

T2 - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 6

ER -