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| Titel |
Handling non-Gaussianity of state and observations in Ensemble Kalman Filters with refined Gaussian anamorphosis |
| VerfasserIn |
Gernot Geppert, Alexander Loew, Felix Ament |
| Konferenz |
EGU General Assembly 2013
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 15 (2013) |
| Datensatznummer |
250082757
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| Zusammenfassung |
| Sequential data assimilation schemes based on the Ensemble Kalman Filter are
optimal in the sense of yielding the best linear unbiased estimate (BLUE) and the
maximum a posteriori estimate (MAP) only if the involved error distributions are
Gaussian. Nevertheless non-Gaussian error distributions are commonly encountered in
geoscience.
Gaussian anamorphosis is one method to cope with non-Gaussianity in ensemble filters. It
transforms the variables involved such that the distributions of the resulting variables are
Gaussian and usually involves a back transformation after the filter has been applied.
If only state variables are transformed, the inverse of the anamorphosis function
applied to the posterior ensemble is sufficient as a back transformation and if only
observations are transformed a back transformation might not be needed at all. If,
however, state variables and observations are transformed, the posterior ensemble
has to be corrected to yield the correct distribution of the original state variables.
Otherwise a systematic error dependent on the derivative of the anamorphosis function is
introduced.
We demonstrate this effect with illustrative examples based on distributions on the
bounded interval [0, 1] and a simplified case of assimilating albedo observations into a land
surface model. In both cases direct observations are used and both, state variables and
observations, are transformed to have Gaussian distributions on [--, -]. The posterior
ensembles are compared to the result of a Bayesian update of the bounded distributions for
the toy examples and to a synthetically generated truth for the albedo example. |
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