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| Titel |
Diagnostics on the cost-function in variational assimilations for meteorological models |
| VerfasserIn |
Y. Michel |
| 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 ; 21, no. 1 ; Nr. 21, no. 1 (2014-02-05), S.187-199 |
| Datensatznummer |
250120884
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| Publikation (Nr.) |
 copernicus.org/npg-21-187-2014.pdf |
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| Zusammenfassung |
Several consistency diagnostics have been proposed to evaluate variational
assimilation schemes. The "Bennett-Talagrand" criterion in particular shows
that the cost-function at the minimum should be close to half the number of
assimilated observations when statistics are correctly specified. It has been
further shown that sub-parts of the cost function also had statistical
expectations that could be expressed as traces of large matrices, and that
this could be exploited for variance tuning and hypothesis testing.
The aim of this work is to extend those results using standard theory of
quadratic forms in random variables. The first step is to express the
sub-parts of the cost function as quadratic forms in the innovation vector.
Then, it is possible to derive expressions for the statistical expectations,
variances and cross-covariances (whether the statistics are correctly
specified or not). As a consequence it is proven in particular that, in a
perfect system, the values of the background and observation parts of the
cost function at the minimum are positively correlated. These results are
illustrated in a simplified variational scheme in a one-dimensional context.
These expressions involve the computation of the trace of large matrices that
are generally unavailable in variational formulations of the assimilation
problem. It is shown that the randomization algorithm proposed in the
literature can be extended to cover these computations, yet at the price of
additional minimizations. This is shown to provide estimations of background
and observation errors that improve forecasts of the operational ARPEGE
model. |
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