EnKF同化的背景误差协方差矩阵局地化对比研究

A Comparative Study of Background Error Covariance Localization in EnKF Data Assimilation

在集合数据同化中,背景场误差的协方差估计特别重要。通常有限个成员的集合在估计背景误差协方差矩阵时会引入伪相关,从而造成协方差被低估、滤波发散。虽然协方差膨胀的经验性方法能一定程度缓解协方差被低估的问题,但不能消除协方差的伪相关问题。因此,结合EnKF方案探讨2种消除伪相关的局地化方法(协方差局地化方法和局地分析方法),分析这2种局地化方法对背景误差协方差矩阵、增益矩阵、集合转换矩阵以及同化结果的影响。实验结果表明:局地化方法不仅能消除背景误差协方差矩阵的伪相关,还可以增加背景误差协方差矩阵的秩;在"弱"同化强度下,2种局地化方法的增益矩阵和集合转换矩阵相等;随着同化强度的增大,增益矩阵和集合转换矩阵的差异会变大;在不同的同化强度下,2种局地化方法各具特色,相对而言,协方差局地化方法在更新集合均值和集合扰动上具有较强的鲁棒性。研究结论有助于背景场误差协方差的精细分析和估计。

In ensemble data assimilation, the estimate of background error covariance is particuarly important. In general, the use of a finite ensemble size for estimating the background error covariance matrix easily introduces spurious correlations, which leads to the underestimation of covariance and filter divergence. Covariance inflation is an empirical method of correcting the underestimation of background error covariance, but it does not help to solve the problem of long-range spurious correlations. Therefore, based on the EnKF scheme, we explored two localization methods to eliminate the spurious correlations, which were the covariance localization method and the local analysis method. We analyzed their impacts on the background error covariance matrix, gain matrix, ensemble transform matrices and data assimilation results. The experimental results have been obtained. That is, the localization method not only can remove the spurious covariance in the background error covariance matrix, but also can increase the rank of the matrix. In a ＂weak＂ assimilation, the gain matrix and ensemble transform matrices of two methods are very close, but the differences of the gain matrix and ensemble transform matrices become more evident with the increase of assimilation strength. Under the different strength of assimilation, two localization methods have their own characteristics, and relatively the covariance localization method has stronger robustness on the update of ensemble mean and ensemble anomalies. This study is very helpful for the fine analysis and estimate of the back- ground error covariance.