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| Titel |
The diffuse ensemble filter |
| VerfasserIn |
X. Yang, T. DelSole |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 16, no. 4 ; Nr. 16, no. 4 (2009-07-16), S.475-486 |
| Datensatznummer |
250013228
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| Publikation (Nr.) |
 copernicus.org/npg-16-475-2009.pdf |
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| Zusammenfassung |
| A new class of ensemble filters, called the Diffuse Ensemble Filter (DEnF),
is proposed in this paper. The DEnF assumes that the forecast errors
orthogonal to the first guess ensemble are uncorrelated with the latter
ensemble and have infinite variance. The assumption of infinite variance
corresponds to the limit of "complete lack of knowledge" and differs
dramatically from the implicit assumption made in most other ensemble
filters, which is that the forecast errors orthogonal to the first guess
ensemble have vanishing errors. The DEnF is independent of the detailed
covariances assumed in the space orthogonal to the ensemble space, and
reduces to conventional ensemble square root filters when the number of
ensembles exceeds the model dimension. The DEnF is well defined only in data
rich regimes and involves the inversion of relatively large matrices,
although this barrier might be circumvented by variational methods. Two
algorithms for solving the DEnF, namely the Diffuse Ensemble Kalman Filter
(DEnKF) and the Diffuse Ensemble Transform Kalman Filter (DETKF), are
proposed and found to give comparable results. These filters generally
converge to the traditional EnKF and ETKF, respectively, when the ensemble
size exceeds the model dimension. Numerical experiments demonstrate that the
DEnF eliminates filter collapse, which occurs in ensemble Kalman filters for
small ensemble sizes. Also, the use of the DEnF to initialize a conventional
square root filter dramatically accelerates the spin-up time for convergence.
However, in a perfect model scenario, the DEnF produces larger errors than
ensemble square root filters that have covariance localization and inflation.
For imperfect forecast models, the DEnF produces smaller errors than the
ensemble square root filter with inflation. These experiments suggest that
the DEnF has some advantages relative to the ensemble square root filters in
the regime of small ensemble size, imperfect model, and copious observations. |
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