局地化方法在集合转换卡尔曼滤波同化的适用性研究

An Applicability Study of Covariance Localization Method in ETKF Data Assimilation

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,ETKF)同化的适用性,本文在理论上分析了CL方法应用于ETKF同化存在的困难,发展了一种适用于ETKF同化的对集合扰动进行舒尔积运算的近似CL方法,并结合Lorenz-96模型对近似CL方法的适用性及其对同化结果的影响进行了分析。研究结果表明:CL方法不仅能消除背景误差协方差矩阵中的伪相关,还能增加背景误差协方差矩阵的秩,但CL方法并不能直接用于ETKF同化;近似CL方法可应用于ETKF同化中,但近似舒尔积破坏了ETKF同化系统的动态平衡,导致同化结果误差较大;与CL方法相反,局地化分析(Local Analysis,LA)方法可直接应用于ETKF同化,并能较好地消除ETKF同化的背景误差协方差矩阵的伪相关,获得较优的同化结果。

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 ETK_F 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 cova- fiance matrix, but the update equations of the ETKF only contain the ensemble perturbation matrix, excluding the background error covariance matrix. Moreover, the dimensiot^s 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 covari- ante localization method can be applied in the ETKF, but the approximate Schur product disrupts the dynamic balances of ETKF as- similation 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 assimila- tion 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.