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Adaptive Observations And Multilevel Optimization In Data Assimilation

Serge Gratton(serge.gratton***at***enseeiht.f)
Monserrat Rincon-Camacho(monserratrc***at***cerfacs.fr)
Philippe L. Toint(philippe.toint***at***unamur.be)

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.

Keywords: multilvel optimization, adaptive algorithms, data assimilation

Category 1: Applications -- Science and Engineering (Optimization of Systems modeled by PDEs )

Category 2: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Citation: NAXYS report NTR-05-2013, Namur Center for Complex Systems, University of Namur, Namur, Belgium

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Entry Submitted: 05/21/2013
Entry Accepted: 05/21/2013
Entry Last Modified: 05/21/2013

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