An efficient implementation of the ensemble Kalman filter based on iterative Sherman Morrison formula

This paper proposes an efficient implementation of the ensemble Kalman filter (EnKF) for the solution of large-scale data assimilation problems. The implementation exploits the special structure of the covariance matrix and solves the analysis step by iteratively applying the Sherman Morrison formula. The iterative implementation leads to savings in both memory and run time. The number of operations for the iterative method is O (n²_ens · n_obs), while for the standard implementation the cost is O (n³_obs) The new implementation of the EnKF is tested using the Lorenz 96 model and shows a better performance than EnKF with the direct computation of the inverse.