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Chaotic dynamics and the role of covariance inflation for reduced rank Kalman filters with model error

Grudzien, C., Carrassi, A. and Bocquet, M. (2018) Chaotic dynamics and the role of covariance inflation for reduced rank Kalman filters with model error. Nonlinear Processes in Geophysics, 25 (3). pp. 633-648. ISSN 1023-5809

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To link to this item DOI: 10.5194/npg-25-633-2018

Abstract/Summary

The ensemble Kalman filter and its variants have shown to be robust for data assimilation in high dimensional geophysical models, with localization, using ensembles of extremely small size relative to the model dimension. However, a reduced rank representation of the estimated covariance leaves a large dimensional complementary subspace unfiltered. Utilizing the dynamical properties of the filtration for the backward Lyapunov vectors, this paper explores a previously unexplained mechanism, providing a novel theoretical interpretation for the role of covariance inflation in ensemble-based Kalman filters. Our derivation of the forecast error evolution describes the dynamic upwelling of the unfiltered error from outside of the span of the anomalies into the filtered subspace. Analytical results for linear systems explicitly describe the mechanism for the upwelling, and the associated recursive Riccati equation for the forecast error, while nonlinear approximations are explored numerically.

Item Type:Article
Refereed:Yes
Divisions:No Reading authors. Back catalogue items
Faculty of Science > School of Mathematical, Physical and Computational Sciences > National Centre for Earth Observation (NCEO)
Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:90557
Publisher:European Geosciences Union

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