| The dynamics of a low order coupled wind-driven Ocean-Atmosphere (OA) system is
investigated with emphasis on its predictability properties. The low-order coupled
deterministic system is composed of a baroclinic atmosphere for which 12 dominant
dynamical modes are only retained (Charney and Straus, 1980) and a wind-driven,
quasi-geostrophic and reduced-gravity shallow ocean whose field is truncated to four
dominant modes able to reproduce the large scale oceanic gyres (Pierini, 2011). The two
models are coupled through mechanical forcings only.
The analysis of its dynamics reveals first that under aperiodic atmospheric forcings only
dominant single gyres (clockwise or counterclockwise) appear. This feature is expected
to be related with the specific domain choice over which the coupled system is
defined. Second the dynamical quantities characterizing the short-term predictability
(Lyapunov exponents, Lyapunov dimension, Kolmogorov-Sinaï (KS) entropy)
displays a complex dependence as a function of the key parameters of the system,
namely the coupling strength and the external thermal forcing. In particular, the
KS-entropy is increasing as a function of the coupling in most of the experiments,
implying an increase of the rate of loss of information about the localization of the
system on his attractor. Finally the dynamics of the error is explored and indicates,
in particular, a rich variety of short term behaviors of the error in the atmosphere
depending on the (relative) amplitude of the initial error affecting the ocean, from
polynomial (at2 + bt3 + ct4) up to purely exponential evolutions. These features are
explained and analyzed in the light of the recent findings on error growth (Nicolis et al,
2009).
References
Charney J G, Straus DM (1980) Form-Drag Instability, Multiple Equilibria and
Propagating Planetary Waves in Baroclinic, Orographically Forced, Planetary Wave Systems.
J Atmos Sci 37: 1157-1176.
Nicolis C, Perdigao RAP, Vannitsem S (2009) Dynamics of Prediction Errors
under the Combined Effect of Initial Condition and Model Errors. J Atmos Sci 66:
766-778.
Pierini S (2011) Low-Frequency Variability, Coherence Resonance, and Phase Selection
in a Low-Order Model of the Wind-Driven Ocean Circulation. J Phys Oceanogr 41:
1585-1604. |