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Abstract
We propose to use a decomposition of largescale incremental four
dimensional (4DVar) 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 lowcardinality 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 4DVar 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 1Dwave equation and on the Lorenz96 system, the latter one being of special interest because of its similarity with Numerical Weather Prediction (NWP) systems.
dimensional (4DVar) 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 lowcardinality 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 4DVar 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 1Dwave equation and on the Lorenz96 system, the latter one being of special interest because of its similarity with Numerical Weather Prediction (NWP) systems.
Original language  English 

Pages (fromto)  3151 
Journal  EURO Journal on Computational Optimization 
Volume  3 
Publication status  Published  2015 
Keywords
 multilevel optimization
 adaptive algorithms
 data assimilation
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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 primaldual approach of weakconstrained variational data assimilation: (Iterate) History matters
Philippe Toint (Speaker)
13 Oct 2017Activity: Talk or presentation types › Invited talk

Institut National Polytechnique de Toulouse
Philippe Toint (Visiting researcher)
2017 → 2019Activity: Visiting an external institution types › Research/Teaching in a external institution

Parallelizing Weak Constraint 4DVAR?
Philippe Toint (Speaker)
5 Oct 2016Activity: Talk or presentation types › Invited talk