局地化方法在集合转换卡尔曼滤波同化的适用性研究

为了探索协方差局地化（Covariance Localization,CL）方法在集合转换卡尔曼滤波（Ensemble Transform Kalman Filter,

An Applicability Study of Covariance Localization Method in ETKF Data Assimilation

To explore the applicability of the covariance localization method in the Ensemble Transform Kalman Filter (ETKF) scheme, we firstly analyze some difficulties of the covariance localization method applied to the ETKF scheme in theory. In order to solve the current problem, then we develop an approximate covariance localization method for ETKF, which is accomplished through the Schur product on ensemble perturbations, and finally we test the suitability and the effect of the approximate covariance localization method in ETKF by combining the Lorenz - 96 model. This model is often used to do performance evaluation in data assimilation. The results show that the covariance localization method cannot be directly applied to ETKF assimilation, although it can eliminate some spurious correlations in the background error covariance matrix and increase the rank of the background error covariance matrix. Because the effective object of Schur product in the covariance localization method is the background error covariance matrix, but the update equations of the ETKF only contain the ensemble perturbation matrix, excluding the background error covariance matrix. Moreover, the dimensions between the correlation coefficient matrix and the ensemble perturbation matrix are different, so an approximate covariance localization method is developed. By the experiment, it shows that the approximate covariance localization method can be applied in the ETKF, but the approximate Schur product disrupts the dynamic balances of ETKF assimilation system ,which leads to bad assimilation results. The local analysis method is widely used to solve the localization problem in data assimilation systems, so we try to apply it into the ETKF scheme. The results show that the local analysis method can be directly applied to ETKF, it can remove the spurious correlations in background error covariance matrix and obtain better assimilation results. This paper is a theoretical innovation and experimental exploration, it helps the related researchers to do further studies on the localization in the data assimilation.