Observations Thinning In Data Assimilation Computations

Serge Gratton, Monserrat Rincon-Camacho, Ehouarn Simon, Ph Toint

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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.
Original languageEnglish
Pages (from-to)31-51
JournalEURO Journal on Computational Optimization
Publication statusPublished - 2015


  • multilevel optimization
  • adaptive algorithms
  • data assimilation


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