Dynamic-stochastic modeling and four-dimensional analysis of the meteorological fields

On the basis of the variational principle, the method of dynamic-probabilistic numerical modeling of ensembles of independent realizations of a complex of space-time stochastic fields is proposed. The ensemble of realizations satisfies the statistical structure of real fields, and the each realization of this ensemble satisfies a numerical dynamic model. For the reconstruction of the meteorological fields, on a spatial-temporal regular grid using observation data at stations, is considered. This method is based on expansion in series of required fields in finite number of natural orthogonal basis. The basis is determined on the ensemble of the spatial-temporal realizations obtained with the help of the dynamic–stochastic method with a given real statistical structure of meteorological fields. One of the methods of fast assimilation of the given observational data is proposed. The results of numerical experiments are presented.