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| Titel |
Adjoints and low-rank covariance representation |
| VerfasserIn |
M. K. Tippett, S. E. Cohn |
| 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 ; 8, no. 6 ; Nr. 8, no. 6, S.331-340 |
| Datensatznummer |
250005879
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| Publikation (Nr.) |
 copernicus.org/npg-8-331-2001.pdf |
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| Zusammenfassung |
| Quantitative
measures of the uncertainty of Earth system estimates can be as important
as the estimates themselves. Direct calculation of second moments of
estimation errors, as described by the covariance matrix, is impractical
when the number of degrees of freedom of the system state is large and the
sources of uncertainty are not completely known. Theoretical analysis of
covariance equations can help guide the formulation of low-rank covariance
approximations, such as those used in ensemble and reduced-state
approaches for prediction and data assimilation. We use the singular value
decomposition and recently developed positive map techniques to
analyze a family of covariance equations that includes stochastically
forced linear systems. We obtain covariance estimates given imperfect
knowledge of the sources of uncertainty and we obtain necessary conditions
for low-rank approximations to be appropriate. The results are illustrated
in a stochastically forced system with time-invariant linear dynamics. |
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