Chaotic attractors of atmospheric models

Abstract

- In this paper we consider the theoretical results obtained for atmospheric models with chaotic dynamics. To define the notion of ‘climate’ for the real climate system we introduce the concept of ‘ideal climate model’. Starting from this concept we formulate problems that should be studied for the specific climate (or atmospheric) model under consideration. Further we give the analysis of the theoretical results for some widely used atmospheric models (barotropic, two-layer quasigeostrophic, a system of ‘primitive’ equations).

In fact, most of the atmospheric and climate models are the results of some approximations to original systems (which are, in general, systems of partial differential equations). The problems of closeness for characteristics of original and approximating models are studied in the corresponding section of the paper.

The central problem of the modern climate theory is the problem of the climate sensitivity to small perturbations of system parameters. In our paper we give the analysis of possible approaches to the solution of this problem. In particular, we consider the applicability of the fluctuation-dissipation theorem for the prediction of the system response to small perturbations of the external forcing. The results of numerical experiments with barotropic and two-layer quasigeostrophic atmospheric models, which were obtained along this line, are also presented.