Ensemble Kalman filter with precision localization

We propose a novel localization strategy for the ensemble Kalman filter procedure based on sparse precision matrices, which we denote precision localization. We assume the latent state vector to come from a Gaussian Markov random field and use the iterative proportional scaling algorithm to estimate the associated sparse precision matrix. Precision localization is compared against a standard covariance localization technique in two simulation studies; one with a Gauss-linear model and one based on the Lorenz 96 model. We evaluate the results by their prediction accuracy and to what degree the generated ensembles give a realistic representation of the exact filtering distributions. In the Gauss-linear example we also compare our results with the Kalman filter solution. Here we see that both precision and covariance localization produce reasonably good results in terms of prediction accuracy, but that precision localization provides the best representation of the correlation structure in the filtering distribution. For the Lorenz model we cannot compare with the Kalman filter solution, but precision localization seems to provide the most accurate predictions and the most realistic uncertainty representation.