General data assimilation scheme based on diffusion-type process approximation for linear or non-linear models

A data assimilation method based on a special type of stochastic process approximation is considered and applied. Unlike the standard Kalman-filter theory, this method does not require model linearity and can be rigorously proved for arbitrary non-linear model under some reasonable conditions. In practice, it can be coupled with an ocean circulation model used as a black-box. The idea of the method is to use the diffusion process and, hence, the corresponding Fokker-Planck equation as an evolution law for the covariance function of the model error. In order to avoid the complex numerical computations that appear in the numerical solution of Fokker-Planck equations, further simplifications can be done. In particular, the perturbation theory allows simplifying the form of FokkerPlanck equation and reducing the scheme to ordinary differential equations.