Efficient Matrix-Free Ensemble Kalman Filter Implementations: Accounting for Localization
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Abstract
This chapter discusses efficient and practical matrix-free implementations of the ensemble Kalman filter (EnKF) in order to account for localization during the assimilation of observations. In the EnKF context, an ensemble of model realizations is utilized in order to estimate the moments of its underlying error distribution. Since ensemble members come at high computational costs (owing to current operational model resolutions) ensemble sizes are constrained by the hundreds while, typically, their error distributions range in the order of millions. This induces spurious correlations in estimates of prior error correlations when these are approximated via the ensemble covariance matrix. Localization methods are commonly utilized in order to counteract this effect. EnKF implementations in this context are based on a modified Cholesky decomposition. Different flavours of Cholesky-based filters are discussed in this chapter. Furthermore, the computational effort in all formulations is linear with regard to model resolutions. Experimental tests are performed making use of the Lorenz 96 model. The results reveal that, in terms of root-mean-square-errors, all formulations perform equivalently.
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