A 4D-EnKF Method via a Modified Cholesky Decomposition and Line Search Optimization for Non-Linear Data Assimilation
This paper introduces an efficient approach for implementing the Four-Dimensional Variational Ensemble Kalman Filter (4D-EnKF) for non-linear data assimilation, leveraging a modified Cholesky decomposition (4D-EnKF-MC). In this method, control spaces at observation times are represented by full-rank...
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MDPI AG
2024-11-01
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| Online Access: | https://www.mdpi.com/2073-4433/15/12/1412 |
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| author | Elías D. Nino-Ruiz Jairo Diaz-Rodriguez |
| author_facet | Elías D. Nino-Ruiz Jairo Diaz-Rodriguez |
| author_sort | Elías D. Nino-Ruiz |
| collection | DOAJ |
| description | This paper introduces an efficient approach for implementing the Four-Dimensional Variational Ensemble Kalman Filter (4D-EnKF) for non-linear data assimilation, leveraging a modified Cholesky decomposition (4D-EnKF-MC). In this method, control spaces at observation times are represented by full-rank square root approximations of background error covariance matrices, derived using the modified Cholesky decomposition. To ensure global convergence, we integrate line-search optimization into the filter formulation. The performance of the 4D-EnKF-MC is evaluated through experimental tests using the Lorenz 96 model, and its accuracy is compared to that of a 4D-Var extension of the Maximum-Likelihood Ensemble Filter (4D-MLEF). Through Root Mean Square Error (RMSE) analysis, we demonstrate that the proposed method outperforms the 4D-MLEF across a range of ensemble sizes and observational network configurations, providing a robust and scalable solution for non-linear data assimilation in complex systems. |
| format | Article |
| id | doaj-art-eced804aa1f1434a9d2e350780c7d29d |
| institution | DOAJ |
| issn | 2073-4433 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Atmosphere |
| spelling | doaj-art-eced804aa1f1434a9d2e350780c7d29d2025-08-20T02:53:18ZengMDPI AGAtmosphere2073-44332024-11-011512141210.3390/atmos15121412A 4D-EnKF Method via a Modified Cholesky Decomposition and Line Search Optimization for Non-Linear Data AssimilationElías D. Nino-Ruiz0Jairo Diaz-Rodriguez1Applied Math and Computer Science Lab, Universidad del Norte, Barranquilla 080001, ColombiaDepartment of Mathematics and Statistics, York University, Toronto, ON M3J1P3, CanadaThis paper introduces an efficient approach for implementing the Four-Dimensional Variational Ensemble Kalman Filter (4D-EnKF) for non-linear data assimilation, leveraging a modified Cholesky decomposition (4D-EnKF-MC). In this method, control spaces at observation times are represented by full-rank square root approximations of background error covariance matrices, derived using the modified Cholesky decomposition. To ensure global convergence, we integrate line-search optimization into the filter formulation. The performance of the 4D-EnKF-MC is evaluated through experimental tests using the Lorenz 96 model, and its accuracy is compared to that of a 4D-Var extension of the Maximum-Likelihood Ensemble Filter (4D-MLEF). Through Root Mean Square Error (RMSE) analysis, we demonstrate that the proposed method outperforms the 4D-MLEF across a range of ensemble sizes and observational network configurations, providing a robust and scalable solution for non-linear data assimilation in complex systems.https://www.mdpi.com/2073-4433/15/12/1412adjoint-free4D-Varline searchMLEFEnKF |
| spellingShingle | Elías D. Nino-Ruiz Jairo Diaz-Rodriguez A 4D-EnKF Method via a Modified Cholesky Decomposition and Line Search Optimization for Non-Linear Data Assimilation Atmosphere adjoint-free 4D-Var line search MLEF EnKF |
| title | A 4D-EnKF Method via a Modified Cholesky Decomposition and Line Search Optimization for Non-Linear Data Assimilation |
| title_full | A 4D-EnKF Method via a Modified Cholesky Decomposition and Line Search Optimization for Non-Linear Data Assimilation |
| title_fullStr | A 4D-EnKF Method via a Modified Cholesky Decomposition and Line Search Optimization for Non-Linear Data Assimilation |
| title_full_unstemmed | A 4D-EnKF Method via a Modified Cholesky Decomposition and Line Search Optimization for Non-Linear Data Assimilation |
| title_short | A 4D-EnKF Method via a Modified Cholesky Decomposition and Line Search Optimization for Non-Linear Data Assimilation |
| title_sort | 4d enkf method via a modified cholesky decomposition and line search optimization for non linear data assimilation |
| topic | adjoint-free 4D-Var line search MLEF EnKF |
| url | https://www.mdpi.com/2073-4433/15/12/1412 |
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