Climate model attractors: chaos, quasi-regularity and sensitivity to small perturbations of external forcing

In this paper we discuss some theoretical results obtained for climate models (theorems for the existence of global attractors and inertial manifolds, estimates of attractor dimension and Lyapunov exponents, symmetry property of Lyapunov spectrum). We define the conditions for “quasiregular behaviour” of a climate system. Under these conditions, the system behaviour is subject to the Kraichnan fluctuation-dissipation relation. This fact allows us to solve the problem of determining a system’s sensitivity to small perturbations to an external forcing. The applicability of the above approach to the analysis of the climate system sensitivity is verified numerically with the example of the two-layer quasigeostrophic atmospheric model.