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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-11-01
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| Series: | Atmosphere |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-4433/15/12/1412 |
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| Summary: | 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. |
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| ISSN: | 2073-4433 |