A Quadrature Technique for Ensemble Kalman Filtering with Efficient and Precise Covariance Localization

In ensemble data assimilation, covariance localization is critical for preventing spurious correlations between data and model variables, as well as for preventing ensemble collapse. Observations such as satellite radiance require localization to be done in model space, a computationally demanding task which involves various trade-offs between accuracy, runtime, and memory usage. This talk introduces a new algorithm for model space localization which achieves a favorable trade-off between these three factors by combining modern techniques from numerical quadrature, Krylov subspace iteration, and matrix function evaluation. This algorithm is compatible with a wide variety of spatial and spectral covariance localization schemes, is parallelizable, and is built upon linear-algebraic primitives whose accuracy is backed up by strong error analyses. We will compare the performance of our algorithm to existing covariance localization techniques such as the gain-form ensemble transform Kalman filter (GETKF). We will also discuss recent efforts to implement this algorithm in the Joint Effort for Data Assimilation Integration (JEDI) for testing with the Model for Prediction Across Scales (MPAS).