Crisan D, Ghil M. Asymptotic behavior of the forecast-assimilation process with unstable dynamics.
CHAOS (WOODBURY, N.Y.) 2023;
33:023139. [PMID:
36859194 DOI:
10.1063/5.0105590]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2022] [Accepted: 01/23/2023] [Indexed: 06/18/2023]
Abstract
Extensive numerical evidence shows that the assimilation of observations has a stabilizing effect on unstable dynamics, in numerical weather prediction, and elsewhere. In this paper, we apply mathematically rigorous methods to show why this is so. Our stabilization results do not assume a full set of observations and we provide examples where it suffices to observe the model's unstable degrees of freedom.
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