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

mots-clés

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    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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    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

    PY - 2015

    Y1 - 2015

    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

    M3 - Article

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    EP - 51

    JO - EURO Journal on Computational Optimization

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    SN - 2192-4406

    ER -