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### 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 |
---|---|

Pages (from-to) | 31-51 |

Journal | EURO Journal on Computational Optimization |

Volume | 3 |

Publication status | Published - 2015 |

### Keywords

- multilevel optimization
- adaptive algorithms
- data assimilation

## Fingerprint Dive into the research topics of 'Observations Thinning In Data Assimilation Computations'. Together they form a unique fingerprint.

## Projects

- 2 Active

## Recent developments in optimization methods for data assimilation in oceanography

SARTENAER, A., LALOYAUX, P., TOINT, P., Tshimanga Ilunga, J. & Gürol, S.

1/09/07 → …

Project: PHD

## Activities

## A primal-dual approach of weak-constrained variational data assimilation: (Iterate) History matters

Philippe Toint (Speaker)

13 Oct 2017

Activity: Talk or presentation types › Invited talk

## Institut National Polytechnique de Toulouse

Philippe Toint (Visiting researcher)

2017 → 2019

Activity: Visiting an external institution types › Research/Teaching in a external institution

## Parallelizing Weak Constraint 4DVAR?

Philippe Toint (Speaker)

5 Oct 2016

Activity: Talk or presentation types › Invited talk

## 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.