Adaptive Observations And Multilevel Optimization In Data Assimilation

Serge Gratton, Monserrat Rincon-Camacho, Ph Toint

Research output: Working paper

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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
Place of PublicationNamur
PublisherNamur center for complex systems
Number of pages18
VolumeNTR-06-2013
Publication statusPublished - 2013

Fingerprint

data assimilation
decomposition
wave equation
weather
prediction
method

Keywords

  • multilevel optimization
  • adaptive algorithms
  • data assimilation

Cite this

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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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.

Research output: Working paper

TY - UNPB

T1 - Adaptive Observations And Multilevel Optimization In Data Assimilation

AU - Gratton, Serge

AU - Rincon-Camacho, Monserrat

AU - Toint, Ph

PY - 2013

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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.

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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.