### 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 |
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Place of Publication | Namur |

Publisher | Namur center for complex systems |

Number of pages | 18 |

Volume | NTR-06-2013 |

Publication status | Published - 2013 |

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### Keywords

- multilevel optimization
- adaptive algorithms
- data assimilation

### Cite this

*Adaptive Observations And Multilevel Optimization In Data Assimilation*. Namur: Namur center for complex systems.

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**Adaptive Observations And Multilevel Optimization In Data Assimilation.** / Gratton, Serge; Rincon-Camacho, Monserrat; Toint, Ph.

Research output: Working paper

TY - UNPB

T1 - Adaptive Observations And Multilevel Optimization In Data Assimilation

AU - Gratton, Serge

AU - Rincon-Camacho, Monserrat

AU - Toint, Ph

PY - 2013

Y1 - 2013

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 - Working paper

VL - NTR-06-2013

BT - Adaptive Observations And Multilevel Optimization In Data Assimilation

PB - Namur center for complex systems

CY - Namur

ER -