Stochastic climate dynamics: Random attractors and time-dependent invariant measures

M.D. Chekroun (1, 2) , E. Simonnet (3) , Michael Ghil (2, 4, 1)

1 CERES-ERTI - Centre d'Enseignement et de Recherche sur l'Environnement et la Societé / Environmental Research and Teaching Institute
2 IGPP - Institute of Geophysics and Planetary Physics [Los Angeles]
3 INLN - Institut Non Linéaire de Nice Sophia-Antipolis
4 LMD - Laboratoire de Météorologie Dynamique (UMR 8539)

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 NioSouthern 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 SinaRuelleBowen (SRB) measures. © 2011 Elsevier B.V. All rights reserved.

Domaines: Climatologie; Géophysique [physics.geo-ph]

M.D. Chekroun, E. Simonnet, Michael Ghil. Stochastic climate dynamics: Random attractors and time-dependent invariant measures. Physica D: Nonlinear Phenomena, 2011, 240 (21), pp.1685-1700. ⟨10.1016/j.physd.2011.06.005⟩. ⟨hal-01120519⟩