The main task of the thesis research is to reveal the nature of the connection of responses of the main climatic characteristics of the regional climates of Eastern Europe with the processes that are developing in the waters of the North Atlantic. An important phase in solution of the scientific problem is the interpretation of the basic mathematical model, which is a system of nonlinear regression equations with inverse responses. The model is constructed on the basis of the probabilistic approximation method. By this method, the factors on the input to the system must be centered, normalized and orthogonal, and at the output - centered and normalized. This model is adapted for solution of various hydrometeorological and climatological tasks taking into account possible formations of input samples of significant factors.
Initially, the orthogonal components of the vectors of states of meteorological characteristics in the surface layer were considered as responses. Subsequently, due to the reverse transformation, the transition to the value of climate indicators in the regions of the European part of the Eurasian continent, which included the territory of Ukraine, was carried out.
In order to form totality of existing factors and responses of regional climates, as the initial data the data of the ERA-40 are taken. The data are given in the nodes of the regular 2.5×2.5º grid of points during the period of 1957-2002.
To detect the regions of active interactions of the atmosphere and the ocean in the North Atlantic region and the identification of areas that have a significant impact on the formation of the distinctive features of climatic conditions in the area of responses, to operating factors that reflect the characteristics of heat and water exchange in the surface layer, as well as heat, moisture content and circulating properties of air at 850 hPa and 700 hPa surfaces, methods of cluster and component analysis were applied before their inclusion in the model.
By means of component analysis, from the totality of the initial data, in each node of the grid, three main components were identified by means of an orthogonal transformation. Vectors of the principal components in the nodes of the selected area of the North Atlantic formed the initial sample for cluster analysis. The author's method of cluster analysis of the Universal Iteration Method of Data Clustering, applied to each of these samples, allowed to identify homogeneous regions with characteristic representative nodes in the fields of the main components. Similar procedures were also used when preparing sample responses.
The calculations and physical substantiation of the statistical characteristics of the zones of different energy activity of interactions of atmospherere and underlying surface in the regions of the North Atlantic and Eastern Europe were conducted, their boundaries were determined, and new zones of elevated energy activity in the atmosphere were discovered. Representative vectors of the main components in homogeneous regions compiled further initial samples for checking the efficiency of the multivariative regression model in question. Determination of the significance of the factors in the model equations was carried out by means of Fisher's criterion (the "sifting" procedure).
The preceding phase of the formation of the structure of the mathematical model of responses in different regions of the Eastern Europe on the processes of energy interaction of the atmosphere and the ocean in the North Atlantic was the assessment of its adequacy. For the comparative analysis, multiplicity correlation coefficients that characterize the adequacy of the models: the output (the coefficients of the system of equations, defined before the sifting procedure, remain unchanged, only minor factors, reviews and corresponding coefficients are eliminated from the system of equations) and modified (with recalculation of coefficients systems of equations for meaningful factors and inverse relationships), were calculated. High values of the correlation coefficients confirm that the constructed mathematical models have the necessary degree of adequacy. Numerous experiments have shown that responses to situations with different ages in different regions of Eastern Europe differ significantly in composition of operating factors and sensitivity to processes that are developing in the North Atlantic.
