Abstract: In recent year, widely attentions have been paid to ensemble-based data assimilation methods and application researches have been carried out to test in the operational data assimilation systems in order to replace the variational data assimilation systems. Ensemble Kalman Filter（EnKF） methods depend highly on the sizes of the ensemble. If ensemble numbers are too small, they will bring the related issues such as under sampling, covariance underestimation, filter divergence and distanced spurious correlations. Local technology can effectively solve the related problems in the small ensembles circumstances. On the basis of the Lorenz-96 model, this paper studies the differences of data assimilation with or without localization and discusses the advantages of local analysis under the condition of small ensemble. It develops a method based on Power Spectral Density（PSD） to judge the effect of ensemble data assimilation. The results show that with a finite ensemble of numbers, Kalman gain values and PSD can be used to evaluate the assimilation effect combined with the local technology.

Key words: data assimilation, lorenz-96 model, Ensemble Kalman Filter（EnKF）, covariance localization, local analysis

摘要： 基于集合的数据同化方法近年来得到广泛的重视和研究，已经逐步实验在业务大气数据同化系统中来替代变分类方法。集合Kalman滤波方法高度依赖于集合的大小，集合数过小会带来欠采样，协方差低估，滤波发散和远距离的虚假相关等问题。局地化技术可以有效改善小集合带来的相关问题。在Lorenz-96模型的基础上，研究有无局地化的效果差异，探讨小集合条件下的局地化技术的优劣性；提出一种基于功率谱密度（PSD）判断集合数据同化效果的办法。实验证明：在有限集合数下，采用Kalman增益值和PSD可以评价同化效果，结合局地化技术，可以获得效率更高的同化算法。

关键词: 数据同化, Lorenz-96模型, 集合Kalman滤波, 协方差局地化, 局地化分析