Chaotic dynamics and the role of covariance inflation for reduced rank Kalman filters with model error
<p>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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2018-09-01
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| Series: | Nonlinear Processes in Geophysics |
| Online Access: | https://www.nonlin-processes-geophys.net/25/633/2018/npg-25-633-2018.pdf |
| Summary: | <p>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.</p> |
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| ISSN: | 1023-5809 1607-7946 |