Mathematical foundation, application, and comparison of general data assimilation method based on diffusion approximation with other data assimilation schemes

Data assimilation methods commonly used in numerical ocean and atmospheric circulation models for weather and climate prediction produce approximations of state variables in terms of stochastic processes. This approximation consists of random sequences of Markov chains, which converge to a diffusion-type process. The conditions for this convergence are investigated. The optimization problem associated with the search of the best possible approximation of the state variable and the results of a numerical experiment are discussed. It is shown that the data assimilation method can be used in practical applications in meteorology and oceanography. Several applications of the methods as an example of the modern operational data processing system with the ocean circulation model HYCOM and data from ARGO drifters are performed and the results as well as comparisons with other assimilation schemes are presented.