Application of the fokker-planck equation to data assimilation into hydrodynamical models

Abstract

A numerical ocean model with an original data assimilation technique is considered. The data-assimilation approach is based on the well-known Kalman filter theory, but the method of computation of the covariation matrix is new. This method uses a diffusion stochastic representation of the error (difference between the model and observative values), and then the Fokker-Planck equation is solved for determination of the joint distribution of errors in each of two different space points. Compared to the ordinary Kalman-filter technique, which requires n2 operations, where n is the number of grid points, this method requires only m2 operations, where m is the number of observations. Also, the method does not requiere linearity of the model. This method is considered in conjunction with a thermodynamic ocean model based on the primitive equations. Some model experiments have been carried out. The stability of this technique is examined, and possible applications to other models is also discussed.