The Kalman stochastic ensemble filter with transformation of perturbation ensemble

The Kalman filter algorithm is currently one of the most popular approaches to solving the data assimilation problem. The major line of the application of the Kalman filter to the data assimilation is the ensemble approach. In this paper, we propose a version of the Kalman stochastic ensemble filter. In the algorithm presented the ensemble perturbations analysis is attained by means of transforming an ensemble of forecast perturbations. The analysis step is made only for a mean value. Thus, the ensemble $\pi$-algorithm is based on the advantages of the stochastic filter and the efficiency and locality of the square root filters.
The numeral method of the ensemble $\pi$-algorithm realization is proposed, the applicability of this method has been proved. This algorithm is implemented for the problem in the three-dimensional domain. The results of the numeral experiments with the model data for estimating the efficiency of the offered numeral algorithm are presented. The comparative analysis of the root-mean-square error behavior of the ensemble $\pi$-algorithm and the Kalman ensemble filter by means of the numeral experiments with a one-dimensional Lorentz model is made.