Observations Thinning In Data Assimilation Computations

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

Research output: Contribution to journalArticle

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Abstract

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
Volume3
Publication statusPublished - 2015

Fingerprint

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

Keywords

  • multilevel optimization
  • adaptive algorithms
  • data assimilation

Cite this

Gratton, Serge ; Rincon-Camacho, Monserrat ; Simon, Ehouarn ; Toint, Ph. / Observations Thinning In Data Assimilation Computations. In: EURO Journal on Computational Optimization. 2015 ; Vol. 3. pp. 31-51.
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Observations Thinning In Data Assimilation Computations. / Gratton, Serge; Rincon-Camacho, Monserrat; Simon, Ehouarn; Toint, Ph.

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

Research output: Contribution to journalArticle

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.

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KW - adaptive algorithms

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EP - 51

JO - EURO Journal on Computational Optimization

JF - EURO Journal on Computational Optimization

SN - 2192-4406

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