### Abstract

dimensional (4D-Var) data assimilation problems in order to make their

numerical solution more efficient. This decomposition is based on exploiting an adaptive hierarchy of the observations. Starting with a low-cardinality set and the solution of its corresponding optimization problem, observations are adaptively added based on a posteriori error estimates. The particular structure of the sequence of associated linear systems allows the use of a variant of the conjugate gradient algorithm which effectively exploits the fact that the number of observations is smaller than the size of the vector state in the 4D-Var model. The method proposed is justified by deriving the relevant error estimates at different levels of the hierarchy and a practical computational technique is then derived. The new algorithm is tested on a 1D-wave equation and on the Lorenz-96 system, the latter one being of special interest because of its similarity with Numerical Weather Prediction (NWP) systems.

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

Pages (from-to) | 31-51 |

Journal | EURO Journal on Computational Optimization |

Volume | 3 |

Publication status | Published - 2015 |

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### Keywords

- multilevel optimization
- adaptive algorithms
- data assimilation

### Cite this

*EURO Journal on Computational Optimization*,

*3*, 31-51.

}

*EURO Journal on Computational Optimization*, vol. 3, pp. 31-51.

**Observations Thinning In Data Assimilation Computations.** / Gratton, Serge; Rincon-Camacho, Monserrat; Simon, Ehouarn; Toint, Ph.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Observations Thinning In Data Assimilation Computations

AU - Gratton, Serge

AU - Rincon-Camacho, Monserrat

AU - Simon, Ehouarn

AU - Toint, Ph

PY - 2015

Y1 - 2015

N2 - We propose to use a decomposition of large-scale incremental fourdimensional (4D-Var) data assimilation problems in order to make theirnumerical solution more efficient. This decomposition is based on exploiting an adaptive hierarchy of the observations. Starting with a low-cardinality set and the solution of its corresponding optimization problem, observations are adaptively added based on a posteriori error estimates. The particular structure of the sequence of associated linear systems allows the use of a variant of the conjugate gradient algorithm which effectively exploits the fact that the number of observations is smaller than the size of the vector state in the 4D-Var model. The method proposed is justified by deriving the relevant error estimates at different levels of the hierarchy and a practical computational technique is then derived. The new algorithm is tested on a 1D-wave equation and on the Lorenz-96 system, the latter one being of special interest because of its similarity with Numerical Weather Prediction (NWP) systems.

AB - We propose to use a decomposition of large-scale incremental fourdimensional (4D-Var) data assimilation problems in order to make theirnumerical solution more efficient. This decomposition is based on exploiting an adaptive hierarchy of the observations. Starting with a low-cardinality set and the solution of its corresponding optimization problem, observations are adaptively added based on a posteriori error estimates. The particular structure of the sequence of associated linear systems allows the use of a variant of the conjugate gradient algorithm which effectively exploits the fact that the number of observations is smaller than the size of the vector state in the 4D-Var model. The method proposed is justified by deriving the relevant error estimates at different levels of the hierarchy and a practical computational technique is then derived. The new algorithm is tested on a 1D-wave equation and on the Lorenz-96 system, the latter one being of special interest because of its similarity with Numerical Weather Prediction (NWP) systems.

KW - multilevel optimization

KW - adaptive algorithms

KW - data assimilation

M3 - Article

VL - 3

SP - 31

EP - 51

JO - EURO Journal on Computational Optimization

JF - EURO Journal on Computational Optimization

SN - 2192-4406

ER -