Enhancing Robustness of Variational Data Assimilation in Chaotic Systems: An α-4DVar Framework with Rényi Entropy and α-Generalized Gaussian Distributions
Traditional 4-dimensional variational data assimilation methods have limitations due to the Gaussian distribution assumption of observation errors, and the gradient of the objective functional is vulnerable to observation noise and outliers. To address these issues, this paper proposes a non-Gaussia...
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2025-07-01
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| Series: | Entropy |
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| author | Yuchen Luo Xiaoqun Cao Kecheng Peng Mengge Zhou Yanan Guo |
| author_facet | Yuchen Luo Xiaoqun Cao Kecheng Peng Mengge Zhou Yanan Guo |
| author_sort | Yuchen Luo |
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| description | Traditional 4-dimensional variational data assimilation methods have limitations due to the Gaussian distribution assumption of observation errors, and the gradient of the objective functional is vulnerable to observation noise and outliers. To address these issues, this paper proposes a non-Gaussian nonlinear data assimilation method called α-4DVar, based on Rényi entropy and the α-generalized Gaussian distribution. By incorporating the heavy-tailed property of Rényi entropy, the objective function and its gradient suitable for non-Gaussian errors are derived, and numerical experiments are conducted using the Lorenz-63 model. Experiments are conducted with Gaussian and non-Gaussian errors as well as different initial guesses to compare the assimilation effects of traditional 4DVar and α-4DVar. The results show that α-4DVar performs as well as traditional method without observational errors. Its analysis field is closer to the truth, with RMSE rapidly dropping to a low level and remaining stable, particularly under non-Gaussian errors. Under different initial guesses, the RMSE of both the background and analysis fields decreases quickly and stabilizes. In conclusion, the α-4DVar method demonstrates significant advantages in handling non-Gaussian observational errors, robustness against noise, and adaptability to various observational conditions, thus offering a more reliable and effective solution for data assimilation. |
| format | Article |
| id | doaj-art-9cc2ad5ad3014f52b58bbbec906d5507 |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj-art-9cc2ad5ad3014f52b58bbbec906d55072025-08-20T03:58:26ZengMDPI AGEntropy1099-43002025-07-0127776310.3390/e27070763Enhancing Robustness of Variational Data Assimilation in Chaotic Systems: An α-4DVar Framework with Rényi Entropy and α-Generalized Gaussian DistributionsYuchen Luo0Xiaoqun Cao1Kecheng Peng2Mengge Zhou3Yanan Guo4College of Meteorology and Oceanology, National University of Defense Technology, Changsha 410073, ChinaCollege of Meteorology and Oceanology, National University of Defense Technology, Changsha 410073, ChinaCollege of Computer Science, National University of Defense Technology, Changsha 410073, ChinaCollege of Meteorology and Oceanology, National University of Defense Technology, Changsha 410073, ChinaCollege of Computer Science, National University of Defense Technology, Changsha 410073, ChinaTraditional 4-dimensional variational data assimilation methods have limitations due to the Gaussian distribution assumption of observation errors, and the gradient of the objective functional is vulnerable to observation noise and outliers. To address these issues, this paper proposes a non-Gaussian nonlinear data assimilation method called α-4DVar, based on Rényi entropy and the α-generalized Gaussian distribution. By incorporating the heavy-tailed property of Rényi entropy, the objective function and its gradient suitable for non-Gaussian errors are derived, and numerical experiments are conducted using the Lorenz-63 model. Experiments are conducted with Gaussian and non-Gaussian errors as well as different initial guesses to compare the assimilation effects of traditional 4DVar and α-4DVar. The results show that α-4DVar performs as well as traditional method without observational errors. Its analysis field is closer to the truth, with RMSE rapidly dropping to a low level and remaining stable, particularly under non-Gaussian errors. Under different initial guesses, the RMSE of both the background and analysis fields decreases quickly and stabilizes. In conclusion, the α-4DVar method demonstrates significant advantages in handling non-Gaussian observational errors, robustness against noise, and adaptability to various observational conditions, thus offering a more reliable and effective solution for data assimilation.https://www.mdpi.com/1099-4300/27/7/763data assimilationnon-gaussian distributionRényi entropyLorenz-63 modelrobustness |
| spellingShingle | Yuchen Luo Xiaoqun Cao Kecheng Peng Mengge Zhou Yanan Guo Enhancing Robustness of Variational Data Assimilation in Chaotic Systems: An α-4DVar Framework with Rényi Entropy and α-Generalized Gaussian Distributions Entropy data assimilation non-gaussian distribution Rényi entropy Lorenz-63 model robustness |
| title | Enhancing Robustness of Variational Data Assimilation in Chaotic Systems: An α-4DVar Framework with Rényi Entropy and α-Generalized Gaussian Distributions |
| title_full | Enhancing Robustness of Variational Data Assimilation in Chaotic Systems: An α-4DVar Framework with Rényi Entropy and α-Generalized Gaussian Distributions |
| title_fullStr | Enhancing Robustness of Variational Data Assimilation in Chaotic Systems: An α-4DVar Framework with Rényi Entropy and α-Generalized Gaussian Distributions |
| title_full_unstemmed | Enhancing Robustness of Variational Data Assimilation in Chaotic Systems: An α-4DVar Framework with Rényi Entropy and α-Generalized Gaussian Distributions |
| title_short | Enhancing Robustness of Variational Data Assimilation in Chaotic Systems: An α-4DVar Framework with Rényi Entropy and α-Generalized Gaussian Distributions |
| title_sort | enhancing robustness of variational data assimilation in chaotic systems an α 4dvar framework with renyi entropy and α generalized gaussian distributions |
| topic | data assimilation non-gaussian distribution Rényi entropy Lorenz-63 model robustness |
| url | https://www.mdpi.com/1099-4300/27/7/763 |
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