Localization Methods for a Multivariate Ensemble Kalman Filter

• Activity Number: 279
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Korean International Statistical Society
• Author(s): Soojin Roh*+ and Mikyoung Jun and Istvan Szunyogh and Marc G. Genton
• Companies: Texas A&M and Texas A&M and Texas A&M and King Abdullah University of Science and Technology
• Keywords: Kalman filter ; Multivariate localization ; Ensembles

Abstract

In the ensemble Kalman filter (EnKF) algorithms, small ensemble sizes cause sampling variability and the underestimation of the background error covariance terms. The localization of the background-error covariance has long been used to counter this behavior, and has proven to be efficient in reducing the sampling errors. In the case of multiple state variables, the localization filters should be carefully applied in order to guarantee the positive-definiteness of the background-error covariance matrix. However, rigorous localization methods for the EnKF frameworks with multiple state variables are rarely considered in the literature. This paper introduces several ways to localize the background-error cross-covariance terms in the EnKF schemes, to ensure that the background-error covariance matrix is positive-definite. The effectiveness of the proposed methods is tested with the help of a bivariate Lorenz model.