Multilevel Monte Carlo methods for ensemble variational data assimilation
<p>Ensemble variational data assimilation relies on ensembles of forecasts to estimate the background error covariance matrix <span class="inline-formula"><strong>B</strong></span>. The ensemble can be provided by an ensemble of data assimilations (EDA), which...
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2025-06-01
|
| Series: | Nonlinear Processes in Geophysics |
| Online Access: | https://npg.copernicus.org/articles/32/167/2025/npg-32-167-2025.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850167187412615168 |
|---|---|
| author | M. Destouches M. Destouches M. Destouches P. Mycek P. Mycek S. Gürol S. Gürol A. T. Weaver A. T. Weaver S. Gratton E. Simon |
| author_facet | M. Destouches M. Destouches M. Destouches P. Mycek P. Mycek S. Gürol S. Gürol A. T. Weaver A. T. Weaver S. Gratton E. Simon |
| author_sort | M. Destouches |
| collection | DOAJ |
| description | <p>Ensemble variational data assimilation relies on ensembles of forecasts to estimate the background error covariance matrix <span class="inline-formula"><strong>B</strong></span>. The ensemble can be provided by an ensemble of data assimilations (EDA), which runs independent perturbed data assimilation and forecast steps. The accuracy of the ensemble estimator of <span class="inline-formula"><strong>B</strong></span> is strongly limited by the small ensemble size that is needed to keep the EDA computationally affordable. Here we investigate the potential of the multilevel Monte Carlo (MLMC) method, a type of multifidelity Monte Carlo method, to improve the accuracy of the standard Monte Carlo estimator of <span class="inline-formula"><strong>B</strong></span> while keeping the computational cost of ensemble generation comparable. MLMC exploits the availability of a range of discretization grids, thus shifting part of the computational work from the original assimilation grid to coarser ones. MLMC differs from the mere averaging of statistical estimators, as it ensures that no bias from the coarse-resolution grids is introduced in the estimation. The implications for ensemble variational data assimilation systems based on EDAs are discussed. Numerical experiments with a quasi-geostrophic model demonstrate the potential of the approach, as MLMC yields more accurate background error covariances and reduced analysis error. The challenges involved in cycling a multilevel variational data assimilation system are identified and discussed.</p> |
| format | Article |
| id | doaj-art-c31a88a8595446ae97a3ad75d92cd2a9 |
| institution | OA Journals |
| issn | 1023-5809 1607-7946 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Nonlinear Processes in Geophysics |
| spelling | doaj-art-c31a88a8595446ae97a3ad75d92cd2a92025-08-20T02:21:14ZengCopernicus PublicationsNonlinear Processes in Geophysics1023-58091607-79462025-06-013216718710.5194/npg-32-167-2025Multilevel Monte Carlo methods for ensemble variational data assimilationM. Destouches0M. Destouches1M. Destouches2P. Mycek3P. Mycek4S. Gürol5S. Gürol6A. T. Weaver7A. T. Weaver8S. Gratton9E. Simon10CERFACS, Toulouse, FranceCECI, Université de Toulouse, CERFACS/CNRS/IRD, Toulouse, FranceMet Office, Exeter, United KingdomCERFACS, Toulouse, FranceCECI, Université de Toulouse, CERFACS/CNRS/IRD, Toulouse, FranceCERFACS, Toulouse, FranceCECI, Université de Toulouse, CERFACS/CNRS/IRD, Toulouse, FranceCERFACS, Toulouse, FranceCECI, Université de Toulouse, CERFACS/CNRS/IRD, Toulouse, FranceINPT-IRIT, Toulouse, FranceINPT-IRIT, Toulouse, France<p>Ensemble variational data assimilation relies on ensembles of forecasts to estimate the background error covariance matrix <span class="inline-formula"><strong>B</strong></span>. The ensemble can be provided by an ensemble of data assimilations (EDA), which runs independent perturbed data assimilation and forecast steps. The accuracy of the ensemble estimator of <span class="inline-formula"><strong>B</strong></span> is strongly limited by the small ensemble size that is needed to keep the EDA computationally affordable. Here we investigate the potential of the multilevel Monte Carlo (MLMC) method, a type of multifidelity Monte Carlo method, to improve the accuracy of the standard Monte Carlo estimator of <span class="inline-formula"><strong>B</strong></span> while keeping the computational cost of ensemble generation comparable. MLMC exploits the availability of a range of discretization grids, thus shifting part of the computational work from the original assimilation grid to coarser ones. MLMC differs from the mere averaging of statistical estimators, as it ensures that no bias from the coarse-resolution grids is introduced in the estimation. The implications for ensemble variational data assimilation systems based on EDAs are discussed. Numerical experiments with a quasi-geostrophic model demonstrate the potential of the approach, as MLMC yields more accurate background error covariances and reduced analysis error. The challenges involved in cycling a multilevel variational data assimilation system are identified and discussed.</p>https://npg.copernicus.org/articles/32/167/2025/npg-32-167-2025.pdf |
| spellingShingle | M. Destouches M. Destouches M. Destouches P. Mycek P. Mycek S. Gürol S. Gürol A. T. Weaver A. T. Weaver S. Gratton E. Simon Multilevel Monte Carlo methods for ensemble variational data assimilation Nonlinear Processes in Geophysics |
| title | Multilevel Monte Carlo methods for ensemble variational data assimilation |
| title_full | Multilevel Monte Carlo methods for ensemble variational data assimilation |
| title_fullStr | Multilevel Monte Carlo methods for ensemble variational data assimilation |
| title_full_unstemmed | Multilevel Monte Carlo methods for ensemble variational data assimilation |
| title_short | Multilevel Monte Carlo methods for ensemble variational data assimilation |
| title_sort | multilevel monte carlo methods for ensemble variational data assimilation |
| url | https://npg.copernicus.org/articles/32/167/2025/npg-32-167-2025.pdf |
| work_keys_str_mv | AT mdestouches multilevelmontecarlomethodsforensemblevariationaldataassimilation AT mdestouches multilevelmontecarlomethodsforensemblevariationaldataassimilation AT mdestouches multilevelmontecarlomethodsforensemblevariationaldataassimilation AT pmycek multilevelmontecarlomethodsforensemblevariationaldataassimilation AT pmycek multilevelmontecarlomethodsforensemblevariationaldataassimilation AT sgurol multilevelmontecarlomethodsforensemblevariationaldataassimilation AT sgurol multilevelmontecarlomethodsforensemblevariationaldataassimilation AT atweaver multilevelmontecarlomethodsforensemblevariationaldataassimilation AT atweaver multilevelmontecarlomethodsforensemblevariationaldataassimilation AT sgratton multilevelmontecarlomethodsforensemblevariationaldataassimilation AT esimon multilevelmontecarlomethodsforensemblevariationaldataassimilation |