AbstractThe Square-Root Ensemble Kalman Filter (ESRF) is a variant of the Ensemble Kalman Filter used with deterministic observations that includes a matrix square-root to account for the uncertainty of the unperturbed ensemble observations. Due to the difficulties in solving this equation, a serial approach is often used where observations are assimilated sequentially one after another. As previously demonstrated, in implementations to date the serial approach for the ESRF is suboptimal when used in conjunction with covariance localization as the Schur product used in the localization does not commute with assimilation. In this work we present a new algorithm for the direct solution of the ESRF equations based on finding the eigenvalues and eigenvectors of a sparse, square, symmetric positive semi-definite matrix with dimensions of the number of observations to be assimilated. This is amenable to direct computation using dedicated, massively parallel, and mature libraries. These libraries make it relatively simple to assemble and compute the observation principal components and solve the ESRF without using the serial approach. They also provide the eigenspectrum of the forward observation covariance matrix. Our parallel direct approach neglects the near-zero eigenvalues, which regularizes the problem. Numerical results show this approach is a highly scalable parallel method.
Journal of Atmospheric and Oceanic Technology – American Meteorological Society
Published: Jul 26, 2017
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