Balanced data assimilation for highly oscillatory mechanical systems
- Data assimilation algorithms are used to estimate the states of a dynamical system using partial and noisy observations. The ensemble Kalman filter has become a popular data assimilation scheme due to its simplicity and robustness for a wide range of application areas. Nevertheless, this filter also has limitations due to its inherent assumptions of Gaussianity and linearity, which can manifest themselves in the form of dynamically inconsistent state estimates. This issue is investigated here for balanced, slowly evolving solutions to highly oscillatory Hamiltonian systems which are prototypical for applications in numerical weather prediction. It is demonstrated that the standard ensemble Kalman filter can lead to state estimates that do not satisfy the pertinent balance relations and ultimately lead to filter divergence. Two remedies are proposed, one in terms of blended asymptotically consistent time-stepping schemes, and one in terms of minimization-based postprocessing methods. The effects of these modifications to the standardData assimilation algorithms are used to estimate the states of a dynamical system using partial and noisy observations. The ensemble Kalman filter has become a popular data assimilation scheme due to its simplicity and robustness for a wide range of application areas. Nevertheless, this filter also has limitations due to its inherent assumptions of Gaussianity and linearity, which can manifest themselves in the form of dynamically inconsistent state estimates. This issue is investigated here for balanced, slowly evolving solutions to highly oscillatory Hamiltonian systems which are prototypical for applications in numerical weather prediction. It is demonstrated that the standard ensemble Kalman filter can lead to state estimates that do not satisfy the pertinent balance relations and ultimately lead to filter divergence. Two remedies are proposed, one in terms of blended asymptotically consistent time-stepping schemes, and one in terms of minimization-based postprocessing methods. The effects of these modifications to the standard ensemble Kalman filter are discussed and demonstrated numerically for balanced motions of two prototypical Hamiltonian reference systems.…
Author details: | Gottfried HastermannORCiD, Maria ReinhardtORCiDGND, Rupert Klein, Sebastian ReichORCiDGND |
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DOI: | https://doi.org/10.2140/camcos.2021.16.119 |
ISSN: | 1559-3940 |
ISSN: | 2157-5452 |
Title of parent work (English): | Communications in applied mathematics and computational science : CAMCoS |
Publisher: | Mathematical Sciences Publishers |
Place of publishing: | Berkeley |
Publication type: | Article |
Language: | English |
Date of first publication: | 2021/06/22 |
Publication year: | 2021 |
Release date: | 2023/10/12 |
Tag: | Hamiltonian dynamics; balanced dynamics; data assimilation; ensemble Kalman filter; geophysics; highly; oscillatory systems |
Volume: | 16 |
Issue: | 1 |
Number of pages: | 39 |
First page: | 119 |
Last Page: | 154 |
Funding institution: | Deutsche Forschungsgemeinschaft (DFG)German Research Foundation (DFG) [CRC 1114, 235221301] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |