Efficient Implementation of the Ensemble Kalman Filter

We present several methods for the efficient implementation of the Ensemble Kalman Filter (EnKF) of Evensen. It is shown that the EnKF can be implemented without access to the observation matrix, and only an observation function is needed; this greatly simplifies software design. New implementations of the EnKF formulas are proposed, with linear computational complexity in the number of data points. These implementations are possible when the data covariance matrix is easy to decompose, such as a diagonal or a banded matrix, or given in a factored form as sample covariance. Unlike previous methods, our method for the former case uses Choleski decomposition on a small matrix from the Sherman-Morrison-Woodbury formula instead of SVD on a large matrix, and our method in the latter case does not impose any constraints on data randomization. One version of the EnKF formulas was implemented in a distributed parallel environment, using SCALAPACK and MPI.