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| Titel |
Improved variational methods in statistical data assimilation |
| VerfasserIn |
J. Ye, N. Kadakia, P. J. Rozdeba, H. D. I. Abarbanel, J. C. Quinn |
| 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 ; 22, no. 2 ; Nr. 22, no. 2 (2015-04-07), S.205-213 |
| Datensatznummer |
250120975
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| Publikation (Nr.) |
 copernicus.org/npg-22-205-2015.pdf |
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| Zusammenfassung |
| Data assimilation transfers information from an observed system to a physically based model system with state
variables x(t). The observations are typically noisy, the model has errors, and the initial state
x(t0) is uncertain: the data assimilation is statistical. One can ask about expected values of
functions ⟨G(X)⟩ on the path X = {x(t0), ..., x(tm)} of the model state through the
observation window tn = {t0, ..., tm}. The conditional (on the measurements) probability distribution
P(X) = exp[−A0(X)] determines these expected values.
Variational methods using saddle points of the "action" A0(X), known as
4DVar (Talagrand and Courtier, 1987; Evensen, 2009), are utilized for estimating
⟨G(X)⟩. In a path integral
formulation of statistical data assimilation, we consider
variational approximations in a realization of the action
where measurement errors and model errors are Gaussian. We (a) discuss an
annealing method for locating the path X0 giving a consistent
minimum of the action A0(X0), (b) consider the explicit
role of the number of measurements at each tn in
determining A0(X0), and (c) identify a parameter regime for the
scale of model errors, which allows X0 to give a precise estimate
of ⟨G(X0)⟩ with computable, small higher-order corrections. |
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