Ensemble Driven Shrinkage Covariance Matrix Estimation for Sequential Data Assimilation
This paper proposes efficient and practical implementations of the ensemble Kalman filter via shrinkage covariance matrix estimation. Our methods exploit the practical properties of shrinkage covariance matrix estimators such as the Rao-Blackwell Ledoit and Wolf (RBLW), and the Oracle Approximating Shrinkage (OAS) to develop efficient ensemble Kalman filter implementations. These shrinkage-based estimators combine the information brought by the ensemble covariance and (typically) a static one: the resulting estimator is a convex combination of both matrices. As part of our formulations, we dynamically combine the OAS and the RBLW estimators by exploiting the information encapsulated in the
eigenvalues of the ensemble covariance matrix; this is, the directions along which forecast errors develop quickly. By imposing a threshold on them, we can target the directions to grow faster forecast errors. Experimental tests are performed by using the Lorenz-96 model and an Atmospheric General Circulation Model. The results reveal that the proposed methods can improve the EnKF based on the RBLW in Root-Mean-Square-Errors. Besides, the computational efforts of our formulations are similar to that of state-of-the-art filter implementations.
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