Ever since its inception, the ensemble Kalman filter (EnKF) has elicited many heuristic approaches that sought to improve it. One such method is covariance localization, which alleviates spurious correlations due to finite ensemble sizes by using relevant spatial correlation information. Adaptive localization techniques account for how correlations change in time and space, in order to obtain improved covariance estimates. This work develops a Bayesian approach to adaptive Schur-product localization for the deterministic ensemble Kalman filter (DEnKF) and extends it to support multiple radii of influence. We test the proposed adaptive localization using the toy Lorenz'96 problem and a more realistic 1.5-layer quasi-geostrophic model. Results with the toy problem show that the multivariate approach informs us that strongly observed variables can tolerate larger localization radii. The univariate approach leads to markedly improved filter performance for the realistic geophysical model, with a reduction in error by as much as 33 %.

中文翻译：

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基于贝叶斯方法的基于集合的数据同化中具有时间依赖扩展的多元自适应定位

自成立以来，集成卡尔曼滤波器（EnKF）引发了许多启发式方法，试图对其进行改进。一种这样的方法是协方差局部化，其通过使用相关的空间相关性信息来减轻由于有限整体大小而引起的虚假相关性。自适应定位技术说明了相关性如何随时间和空间变化，以便获得改进的协方差估计。这项工作为确定性集合卡尔曼滤波器（DEnKF）开发了一种针对自适应Schur积定位的贝叶斯方法，并将其扩展为支持多个影响半径。我们使用玩具Lorenz'96问题和更现实的1.5层拟地转模型测试了建议的自适应定位。玩具问题的结果表明，多元方法告诉我们，强烈观察到的变量可以忍受较大的定位半径。对于实际的地球物理模型，单变量方法可显着改善过滤器性能，并减少多达33％的误差。