### Abstract

We propose to use a decomposition of large-scale incremental four

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.

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 |
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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

Gratton, S., Rincon-Camacho, M., Simon, E., & Toint, P. (2015). Observations Thinning In Data Assimilation Computations.

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