Adaptive Observations And Multilevel Optimization In Data Assimilation

Serge Gratton, Monserrat Rincon-Camacho, Ph Toint

Research output: Working paper

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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
Place of PublicationNamur
PublisherNamur center for complex systems
Number of pages18
Publication statusPublished - 2013


  • multilevel optimization
  • adaptive algorithms
  • data assimilation


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