Abstract
The possibility for approximate basic statistical characteristics of atmospheric models using periodic trajectories (closed solutions of equations of dynamics) is considered. The possibility of this approximation is based on ideas of the theory of dynamical systems which states that, in some important particular cases (e.g., for hyperbolic systems), the periodic trajectories define the invariant system measure related to a notion of the system climate. It is shown that this approximation also is possible in the case of the atmospheric models under consideration. Moreover, the principal modes of circulation variability are implemented as clusters of periodic orbits oriented along the leading eigenvectors of dynamical operators of models linearized with respect to their mean states. The analysis of observational data shows that probably the same conclusion could also be made for the real atmospheric circulation.
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