A local ensemble data assimilation algorithm for nonlinear geophysical models

For optimal estimation of quantities of interest from observational data and a model (optimal filtering problem) in the nonlinear case, a particle method based on a Bayesian approach can be used. A disadvantage of the classical particle filter is that the observations are used only to find the weight coefficients with which the sum of the particles is calculated when determining an estimate. The present article considers an approach to solving the problem of nonlinear filtering which uses a representation of the posterior distribution density of the quantity being estimated as a sum with weights of Gaussian distribution densities. It is well-known from filtration theory that if a distribution density is a sum with weights of Gaussian functions, the optimal estimate will be a sum with weights of estimates calculated by the Kalman filter formulas. The present article proposes a method for solving the problem of nonlinear filtering based on this approach. An ensemble $\pi$-algorithm proposed earlier by the author is used to implement the method. The ensemble $\pi$-algorithm in this new method is used to obtain an ensemble corresponding to the distribution density at the analysis step. This is a stochastic ensemble Kalman filter which is local as well. Therefore, it can be used in high-dimensional geophysical models.