Adaptive Observations And Multilevel Optimization In Data Assimilation

Serge Gratton, Monserrat Rincon-Camacho, Ph Toint

Résultats de recherche: Papier de travailArticle de travail

Résumé

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.
langueAnglais
Lieu de publicationNamur
EditeurNamur center for complex systems
Nombre de pages18
VolumeNTR-06-2013
étatPublié - 2013

Empreinte digitale

data assimilation
decomposition
wave equation
weather
prediction
method

mots-clés

    Citer ceci

    Gratton, S., Rincon-Camacho, M., & Toint, P. (2013). Adaptive Observations And Multilevel Optimization In Data Assimilation. Namur: Namur center for complex systems.
    Gratton, Serge ; Rincon-Camacho, Monserrat ; Toint, Ph. / Adaptive Observations And Multilevel Optimization In Data Assimilation. Namur : Namur center for complex systems, 2013.
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    abstract = "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.",
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    Gratton, S, Rincon-Camacho, M & Toint, P 2013 'Adaptive Observations And Multilevel Optimization In Data Assimilation' Namur center for complex systems, Namur.

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

    Namur : Namur center for complex systems, 2013.

    Résultats de recherche: Papier de travailArticle de travail

    TY - UNPB

    T1 - Adaptive Observations And Multilevel Optimization In Data Assimilation

    AU - Gratton,Serge

    AU - Rincon-Camacho,Monserrat

    AU - Toint,Ph

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    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

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    BT - Adaptive Observations And Multilevel Optimization In Data Assimilation

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    Gratton S, Rincon-Camacho M, Toint P. Adaptive Observations And Multilevel Optimization In Data Assimilation. Namur: Namur center for complex systems. 2013.