Résumé
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.
| langue originale | Anglais |
|---|---|
| Lieu de publication | Namur |
| Éditeur | Namur center for complex systems |
| Nombre de pages | 18 |
| Volume | NTR-06-2013 |
| état | Publié - 2013 |
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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 travail › Article de travail
TY - UNPB
T1 - Adaptive Observations And Multilevel Optimization In Data Assimilation
AU - Gratton, Serge
AU - Rincon-Camacho, Monserrat
AU - Toint, Ph
PY - 2013
Y1 - 2013
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 - Working paper
VL - NTR-06-2013
BT - Adaptive Observations And Multilevel Optimization In Data Assimilation
PB - Namur center for complex systems
CY - Namur
ER -