A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering
The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent covariance information, and are affected by sampling errors in operational settings where the number of model realizations is much smaller than the model state dimension. To alleviate the effects of these errors EnKF relie...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Stockholm University Press
2023-04-01
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| Series: | Tellus: Series A, Dynamic Meteorology and Oceanography |
| Subjects: | |
| Online Access: | https://account.a.tellusjournals.se/index.php/su-j-tadmo/article/view/214 |
| _version_ | 1797824081099227136 |
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| author | Andrey A. Popov Adrian Sandu Elias D. Nino-Ruiz Geir Evensen |
| author_facet | Andrey A. Popov Adrian Sandu Elias D. Nino-Ruiz Geir Evensen |
| author_sort | Andrey A. Popov |
| collection | DOAJ |
| description | The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent covariance information, and are affected by sampling errors in operational settings where the number of model realizations is much smaller than the model state dimension. To alleviate the effects of these errors EnKF relies on model-specific heuristics such as covariance localization, which takes advantage of the spatial locality of correlations among the model variables. This work proposes an approach to alleviate sampling errors that utilizes a locally averaged-in-time dynamics of the model, described in terms of a climatological covariance of the dynamical system. We use this covariance as the target matrix in covariance shrinkage methods, and develop a stochastic covariance shrinkage approach where synthetic ensemble members are drawn to enrich both the ensemble subspace and the ensemble transformation. We additionally provide for a way in which this methodology can be localized similar to the state-of-the-art LETKF method, and that for a certain model setup, our methodology significantly outperforms it. |
| first_indexed | 2024-03-13T10:33:41Z |
| format | Article |
| id | doaj.art-0dd65713dacd49bca8eeb0fb8996e374 |
| institution | Directory Open Access Journal |
| issn | 1600-0870 |
| language | English |
| last_indexed | 2024-03-13T10:33:41Z |
| publishDate | 2023-04-01 |
| publisher | Stockholm University Press |
| record_format | Article |
| series | Tellus: Series A, Dynamic Meteorology and Oceanography |
| spelling | doaj.art-0dd65713dacd49bca8eeb0fb8996e3742023-05-18T07:04:37ZengStockholm University PressTellus: Series A, Dynamic Meteorology and Oceanography1600-08702023-04-01751159–171159–17110.16993/tellusa.214747A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman FilteringAndrey A. Popov0https://orcid.org/0000-0002-7726-6224Adrian Sandu1https://orcid.org/0000-0002-5380-0103Elias D. Nino-Ruiz2https://orcid.org/0000-0001-7784-8163Geir Evensen3https://orcid.org/0000-0002-2458-6152Computational Science Laboratory, Department of Computer Science, Virginia TechComputational Science Laboratory, Department of Computer Science, Virginia TechApplied Math and Computer Science Lab, Universidad del NorteNorwegian Research Center (NORCE) and Nansen Environmental and Remote Sensing Center (NERSC)The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent covariance information, and are affected by sampling errors in operational settings where the number of model realizations is much smaller than the model state dimension. To alleviate the effects of these errors EnKF relies on model-specific heuristics such as covariance localization, which takes advantage of the spatial locality of correlations among the model variables. This work proposes an approach to alleviate sampling errors that utilizes a locally averaged-in-time dynamics of the model, described in terms of a climatological covariance of the dynamical system. We use this covariance as the target matrix in covariance shrinkage methods, and develop a stochastic covariance shrinkage approach where synthetic ensemble members are drawn to enrich both the ensemble subspace and the ensemble transformation. We additionally provide for a way in which this methodology can be localized similar to the state-of-the-art LETKF method, and that for a certain model setup, our methodology significantly outperforms it.https://account.a.tellusjournals.se/index.php/su-j-tadmo/article/view/214ensemble kalman filtercovariance shrinkagedata assimilationsynthetic ensemblelocalization |
| spellingShingle | Andrey A. Popov Adrian Sandu Elias D. Nino-Ruiz Geir Evensen A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering Tellus: Series A, Dynamic Meteorology and Oceanography ensemble kalman filter covariance shrinkage data assimilation synthetic ensemble localization |
| title | A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering |
| title_full | A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering |
| title_fullStr | A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering |
| title_full_unstemmed | A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering |
| title_short | A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering |
| title_sort | stochastic covariance shrinkage approach in ensemble transform kalman filtering |
| topic | ensemble kalman filter covariance shrinkage data assimilation synthetic ensemble localization |
| url | https://account.a.tellusjournals.se/index.php/su-j-tadmo/article/view/214 |
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