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| Titel |
Separating fast and slow modes in coupled chaotic systems |
| VerfasserIn |
M. Peña, E. Kalnay |
| 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 ; 11, no. 3 ; Nr. 11, no. 3 (2004-07-27), S.319-327 |
| Datensatznummer |
250009237
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| Publikation (Nr.) |
 copernicus.org/npg-11-319-2004.pdf |
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| Zusammenfassung |
| We test a simple technique based on breeding to separate fast and slow
unstable modes in coupled systems with different time scales of evolution and
variable amplitudes. The technique takes advantage of the earlier saturation
of error growth rate of the fastest mode and of the lower value of the
saturation amplitude of perturbation of either the fast or the slow modes.
These properties of the coupled system allow a physically-based selection of
the rescaling time interval and the amplitude of initial perturbations in the
"breeding" of unstable modes (Toth and Kalnay, 1993, 1996, 1997; Aurell et
al., 1997; Boffetta et al., 1998) to isolate the desired mode. We perform
tests in coupled models composed of fast and slow versions of the Lorenz
(1963) model with different strengths of coupling. As examples we present
first a coupled system which we denote "weather with convection", with a
slow, large amplitude model coupled with a fast, small amplitude model,
second an "ENSO" system with a "tropical atmosphere" strongly coupled with
a "tropical ocean", and finally a triply coupled system denoted
"tropical-extratropical" in which a fast model (representing the
"extratropical atmosphere") is loosely coupled to the "ENSO" system. We
find that it is always possible to isolate the fast modes by taking the limit
of small amplitudes and short rescaling intervals, in which case, as
expected, the results are the same as the local Lyapunov growth obtained with
the linear tangent model. In contrast, slow modes cannot be isolated with
either Lyapunov or Singular vectors, since the linear tangent and adjoint
models are dominated by the fast modes. Breeding is successful in isolating
slow modes if rescaling intervals and amplitudes are chosen from physically
appropriate scales. |
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