Observations Thinning In Data Assimilation Computations

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

Résultats de recherche: Contribution à un journal/une revueArticle

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
Pages31-51
journalEURO Journal on Computational Optimization
Volume3
étatPublié - 2015

Empreinte digitale

Data Assimilation
Thinning
data assimilation
thinning
decomposition
Decomposition
wave equation
Wave equations
Numerical Weather Prediction
Linear systems
Decompose
Conjugate Gradient Algorithm
Lorenz System
A Posteriori Error Estimates
Computational Techniques
weather
Error Estimates
Wave equation
Cardinality
prediction

mots-clés

    Citer ceci

    Gratton, S., Rincon-Camacho, M., Simon, E., & Toint, P. (2015). Observations Thinning In Data Assimilation Computations.
    Gratton, Serge ; Rincon-Camacho, Monserrat ; Simon, Ehouarn ; Toint, Ph. / Observations Thinning In Data Assimilation Computations. Dans: EURO Journal on Computational Optimization. 2015 ; Vol 3. p. 31-51
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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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    Observations Thinning In Data Assimilation Computations. / Gratton, Serge; Rincon-Camacho, Monserrat; Simon, Ehouarn; Toint, Ph.

    Dans: EURO Journal on Computational Optimization, Vol 3, 2015, p. 31-51.

    Résultats de recherche: Contribution à un journal/une revueArticle

    TY - JOUR

    T1 - Observations Thinning In Data Assimilation Computations

    AU - Gratton,Serge

    AU - Rincon-Camacho,Monserrat

    AU - Simon,Ehouarn

    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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