Stochastic climate dynamics: Random attractors and time-dependent invariant measures |
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| Authors: | Mickaë l D. Chekroun,Eric SimonnetMichael Ghil |
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| Affiliation: | a Department of Atmospheric Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095-1565, USAb Environmental Research and Teaching Institute (CERES-ERTI), École Normale Supérieure, 75231 Paris Cedex 05, Francec Institut Non Linéaire de Nice (INLN)-UNSA, UMR 6618 CNRS, 1361, route des Lucioles 06560 Valbonne, Franced Geosciences Department and Laboratoire de Météorologie Dynamique (CNRS and IPSL), École Normale Supérieure, 75231 Paris Cedex 05, France |
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| Abstract: | This article attempts a unification of the two approaches that have dominated theoretical climate dynamics since its inception in the 1960s: the nonlinear deterministic and the linear stochastic one. This unification, via the theory of random dynamical systems (RDS), allows one to consider the detailed geometric structure of the random attractors associated with nonlinear, stochastically perturbed systems. We report on high-resolution numerical studies of two idealized models of fundamental interest for climate dynamics. The first of the two is a stochastically forced version of the classical Lorenz model. The second one is a low-dimensional, nonlinear stochastic model of the El Niño-Southern Oscillation (ENSO). These studies provide a good approximation of the two models’ global random attractors, as well as of the time-dependent invariant measures supported by these attractors; the latter are shown to have an intuitive physical interpretation as random versions of Sinaï-Ruelle-Bowen (SRB) measures. |
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| Keywords: | Climate dynamics Dissipative dynamical systems Intermittency Pullback and random attractor Sample invariant measure SRB measure |
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