基于DEnKF的背景误差协方差局地化和协方差膨胀研究

尽管DEnKF同化不会引入观测采样误差,但小集合仍会造成背景误差协方差矩阵存在伪相关,出现滤波发散。为了减少小集合对数据同化结果的影响,结合Lorenz96模型和DEnKF同化方案分析了协方差局地化和协方差膨胀方法对背景误差协方差矩阵、增益矩阵及同化结果的影响。实验表明:协方差局地化方法能消除背景误差协方差矩阵和增益矩阵中的伪相关,增大背景误差协方差矩阵的秩,有助于滤波算法收敛到真实解;而协方差膨胀方法不能消除背景误差协方差矩阵和增益矩阵中的伪相关,只能改善在每个同化周期内背景误差协方差系统性被低估的现象;同化过程中采用合适的局地化半径和方差膨胀因子能够较好地改善同化结果的精度。

An Experimental Analysis of Background Error Covariance Localization and Covariance Inflation in DEnKF Data Assimilation

Although DEnKF assimilation scheme naturally does not introduce any observation sampling error,but small ensemble will still bring the spurious correlation into the background error covariance matrix and lead to the filter divergence.Toward reducing the side|effects of small ensemble on the data assimilation,this paper designs an experiment of Lorenz96 model with DEnKF assimilation scheme,and analyzes the impacts of the covariance localization method and the covariance inflation method on the background error covariance matrix,gain matrix and data assimilation results.The experimental results show that the covariance localization method can eliminate the spurious correlation of the background error covariance matrix and the gain matrix,and it can also increase the rank of background error covariance matrix,which is helpful for the filter converging to the real solution.However,the covariance inflation method cannot remove the spurious correlation of the background error covariance matrix and the gain matrix,and it can only improve the systematic underestimation of the background error covariance in each data assimilation cycle.It is noteworthy that an appropriate localization radius and an inflation factors are critical to improve the data assimilation analysis results.