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| Titel |
Theory of the norm-induced metric in atmospheric dynamics |
| VerfasserIn |
T.-Y. Koh, F. Wan |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1680-7316
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| Digitales Dokument |
URL |
| Erschienen |
In: Atmospheric Chemistry and Physics ; 15, no. 5 ; Nr. 15, no. 5 (2015-03-09), S.2571-2594 |
| Datensatznummer |
250119503
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| Publikation (Nr.) |
 copernicus.org/acp-15-2571-2015.pdf |
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| Zusammenfassung |
| We suggest that some metrics for quantifying distances in phase space are
based on linearized flows about unrealistic reference states and hence may
not be applicable to atmospheric flows. A new approach of defining a norm-induced
metric based on the total energy norm is proposed. The approach is
based on the rigorous mathematics of normed vector spaces and the law of
energy conservation in physics. It involves the innovative construction of
the phase space so that energy (or a certain physical invariant) takes the
form of a Euclidean norm. The metric can be applied to both linear and
nonlinear flows and for small and large separations in phase space. The new
metric is derived for models of various levels of sophistication: the 2-D
barotropic model, the shallow-water model and the 3-D dry, compressible
atmosphere in different vertical coordinates. Numerical calculations of the
new metric are illustrated with analytic dynamical systems as well as with
global reanalysis data. The differences from a commonly used metric and the
potential for application in ensemble prediction, error growth analysis and
predictability studies are discussed. |
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