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Titel |
Ensemble Kalman filtering without the intrinsic need for inflation |
VerfasserIn |
M. Bocquet |
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 ; 18, no. 5 ; Nr. 18, no. 5 (2011-10-20), S.735-750 |
Datensatznummer |
250013980
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Publikation (Nr.) |
copernicus.org/npg-18-735-2011.pdf |
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Zusammenfassung |
The main intrinsic source of error in the ensemble Kalman filter
(EnKF) is sampling error.
External sources of error, such as model error or deviations from Gaussianity, depend on the
dynamical properties of the model.
Sampling errors can lead to instability of the filter
which, as a consequence, often requires inflation and localization.
The goal of this article is to derive an ensemble Kalman filter
which is less sensitive to sampling errors.
A prior probability density function conditional on
the forecast ensemble is derived using Bayesian principles.
Even though this prior is built upon the assumption that the ensemble is
Gaussian-distributed, it is different from the Gaussian probability
density function defined by the empirical mean and the empirical
error covariance matrix of the ensemble, which is implicitly used
in traditional EnKFs. This new prior generates a new class of ensemble
Kalman filters, called finite-size ensemble Kalman filter
(EnKF-N).
One deterministic variant, the finite-size ensemble transform
Kalman filter (ETKF-N), is derived. It is tested on the Lorenz '63 and Lorenz '95 models.
In this context, ETKF-N is shown to be stable
without inflation for ensemble size greater than the model unstable subspace dimension,
at the same numerical cost as the ensemble transform Kalman filter (ETKF).
One variant of ETKF-N seems to systematically outperform the ETKF with optimally
tuned inflation.
However it is shown that ETKF-N does not account for all sampling
errors, and necessitates localization like any EnKF, whenever
the ensemble size is too small.
In order to explore the need for inflation in this small ensemble size regime,
a local version of the new class of filters is
defined (LETKF-N) and tested on the Lorenz '95 toy model. Whatever the
size of the ensemble, the filter is stable.
Its performance without inflation is slightly inferior to that of LETKF with
optimally tuned inflation for small interval between updates, and superior
to LETKF with optimally tuned inflation for large time interval
between updates. |
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