<title>Dynamic-stochastic method of modelling of climate of the atmosphere</title>

Abstract

ABSTRACT A dynamic-stochastic method of modeling of climatic ensembles of fields of meteorological elements is considered The results of numerical experiments on application of climatic ensembles for research of properties of an atmosphere dynamics are presented. Keywords: stochastic modeling, variational assimilation, climate For representation of a climate of an atmosphere the ensemble of possible realizations of corresponding multivariate hydrometeorological fields for the chosen interval of time and the set region is considered [1-3] { , 1,2,...} ()i [n i &, (1) where () ( ( ,), ( ,), ( ,), ) ii i i T [njkjk jk UXt TXt HXt& && & & is vector of realizations of fields of speed, temperature, geopotential etc. at spatial-temporary points (,)X j t k &of considered domain of dimension n . It is natural, that the realizations which are included in ensemble (1) are statisti cally independent, that provides the appropriate reliability of statistical estimations considered with its help. Besides one of the basic requirements for ensemble (1) is the requirement of closeness the appropriate properties of real climatic fields on some norm. With this purpose in paper for numerical construction of ensemble (1) the joint stochastic and dynamic modeling is used on the basis of association on a principle of variational assimilation of the information [1]. This approach allows to combine features of the determined numerical models of dynamics of an atmosphere and of stochastic models. The numerical hydrothermodynamics model thus serves spatial-temporary agreeing interpolator for fill and coordination of spatial- temporary realizations in some optimum sense and allows to receive those climatic characteristics, which in initial stochastic model are not inco rporated and can not be authen tically received on itself of stochastic model at all. Besides this approach allows also to receive the appropriate ensembles of statistically independent climatic realizations for the separately chosen region and short period of time. Essential feature of the given approach is that within the framework of uniform model the data of real measurements, statistical modeling and numerical model of hydrothermodynamics of an atmosphere are used. Thus the basic binding element is the variational assimilation of a information by hydrodynamical model. In ou r case the variational assimilation on all a considered time interval is used within the limits of predictability of numerical model. The essence of this approach consists in the following. On accessible statistically significant of the real climatic information given as the appropriate statistical characteristics (of distributions, norms, variance, correlations etc.), methods of statistical modeling the ensemble of realizations of climatic stochastic fields (1) with the given statistical structure is under construction [1-3]. In the given paper one of methods of statistical modeling of the hydrometeorological fields based on spectral decomposition of the appropriate correlation matrix constructed on a real data [3]. Thus, let R is a correlation matrix. Shall pr esent its spectral decomposition as RWW /