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arXiv · 2412.14318

Long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systems

Daniel Sanz-Alonso·Nathan Waniorek
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Abstract

Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state is high dimensional, ensemble Kalman filters are often the method of choice. This paper establishes long-time accuracy of ensemble Kalman filters. We introduce conditions on the dynamics and the observations under which the estimation error remains small in the long-time horizon. Our theory covers a wide class of partially-observed chaotic dynamical systems, which includes the Navier-Stokes equations and Lorenz models. In addition, we prove long-time accuracy of ensemble Kalman filters with surrogate dynamics, thus validating the use of machine-learned forecast models in ensemble data assimilation.

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Daniel Sanz-Alonso, Nathan Waniorek. 2024-12-18. Long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systems. https://arxiv.org/abs/2412.14318

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