Optimal Empirical Prognostic Models of Climate Dynamics
Abstract:In this report the empirical methodology for prediction of climate dynamics is suggested. We construct the dynamical models of data patterns connected with climate indices, from observed spatially distributed time series. The models are based on artificial neural network (ANN) parameterization and have a form of discrete stochastic evolution operator mapping some sequence of systems state on the next one . Different approaches to reconstruction of empirical basis (phase variables) for system's phase space representation, which is appropriate for forecasting the climate index of interest, are discussed in the report; for this purpose both linear and non-linear data expansions are considered. The most important point of the methodology is finding the optimal structural parameters of the model such as dimension of variable vector, i.e. number of principal components used for modeling, the time lag used for prediction, and number of neurons in ANN determining the quality of approximation. Actually, we need to solve the model selection problem, i.e. we want to obtain a model of optimal complexity in relation to analyzed time series. We use MDL approach  for this purpose: the model providing best data compression is chosen. The method is applied to space-distributed time-series of sea surface temperature and sea level pressure taken from IRI datasets : the ability of proposed models to predict different climate indices (incl. Multivariate ENSO index, Pacific Decadal Oscillation index, North-Atlantic Oscillation index) is investigated.
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