TY  - JOUR
A1  - Hastermann, Gottfried
A1  - Reinhardt, Maria
A1  - Klein, Rupert
A1  - Reich, Sebastian
T1  - Balanced data assimilation for highly oscillatory mechanical systems
JF  - Communications in applied mathematics and computational science : CAMCoS
N2  - 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 standard ensemble Kalman filter are discussed and demonstrated numerically for balanced motions of two prototypical Hamiltonian reference systems.
KW  - data assimilation
KW  - ensemble Kalman filter
KW  - balanced dynamics
KW  - highly
KW  - oscillatory systems
KW  - Hamiltonian dynamics
KW  - geophysics
Y1  - 2021
U6  - https://doi.org/10.2140/camcos.2021.16.119
SN  - 1559-3940
SN  - 2157-5452
VL  - 16
IS  - 1
SP  - 119
EP  - 154
PB  - Mathematical Sciences Publishers
CY  - Berkeley
ER  -