A Local Ensemble Data Assimilation Algorithm for Nonlinear Geophysical Models

For optimal estimation of quantities of interest using observation data and a model (optimal filtering problem) in the nonlinear case, a particle method based on the Bayesian approach can be used. A disadvantage of the classical particle filter is that observational data are applied only for search for the weight coefficients with which the sum of the particles is calculated during determination of estimate. The present article considers solving the problem of nonlinear filtering via an approach that uses a representation of the posterior distribution density of quantity to estimate as the sum with weights of Gaussian distribution densities. It is known from the filtration theory that if the distribution density is the sum with weights of Gaussian functions, the optimal estimate will be the sum with weights of estimates calculated by the Kalman filter formulas. The present article proposes a method based on this approach for solving the problem of nonlinear filtering. The method is implemented via the ensemble 7r-algorithm proposed earlier by the author. In this new method, the ensemble 7r-algorithm is used for production of an ensemble corresponding to the distribution density at the analysis step. It is the stochastic ensemble Kalman filter, which is local and thus can be used in high-dimensional geophysical models.