Investigation of Structure of Climate Attractors by Observed Data Series
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In this chapter the theory and the results of numerical experiments on reproduction of some characteristics of attractors (there are primarily a correlation dimension and Kolmogorov entropy) from the observed data series are presented. This problem is of great importance from various point of view. First, reproducing the characteristics of attractor of the real atmosphere and assuming that the observed series of parameters of climatic system are generated by some ideal system, we have the possibility to identify from this point of view the adequacy of models in use. Second, it becomes possible to compute the predictability characteristics of quantities, for the description of which we have not even the approximate idea on the corresponding dynamical system (e.g., time and space averaged meteoparameters). The principal task here is to find the necessary length of the observed data series, as in computing the invariant measure and Lyapunov exponents for the problem with known operator. Some presently known estimates of the solution to this problem will be given below. The basis for the further discussion are the following Takkens theorems .
KeywordsLyapunov Exponent Correlation Dimension Positive Lyapunov Exponent Real Atmosphere Gauss Distribution
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