In this paper, we propose a dynamic localization method for ensemble-based data assimilation via a modified Cholesky decomposition. The method exploits the information brought by ensemble members to estimate optimal radius lengths of model components. This estimation process is performed by using Bayes’ Theorem; our prior beliefs and likelihood functions are modeled via Gamma distributions: in priors, hyper-parameters are fixed based on our prior knowledge of error dynamics while to build likelihood functions, model parameters are fitted with empirical statistics from background ensembles at assimilation steps. Once the optimal radius lengths are estimated, a modified Cholesky decomposition is employed to estimate precision covariances of background error distributions. The assimilation process is then performed similarly to that of the EnKF based on a modified Cholesky decomposition (EnKF-MC). Experimental tests are performed by using the Lorenz-96 model. To compare our results, we employ an EnKF-MC implementation with different structures of background error correlations. In terms of ${\ell }_2$-norm of errors, the proposed filter implementation can outperform the EnKF-MC method for fixed radius lengths across all model components, and even more, different hyper-parameters can be tried in our filter formulation without degrading its convergence.

在本文中，我们提出了一种通过改进的Cholesky分解对基于集合的数据同化的动态定位方法。该方法利用集合成员带来的信息来估计模型组件的最佳半径长度。该估计过程是使用贝叶斯定理执行的；我们的先验信念和似然函数是通过Gamma分布建模的：在先验中，超参数是基于我们对误差动态的先验知识而固定的，而要建立似然函数，模型参数将在同化步骤中由来自背景合奏的经验统计量进行拟合。一旦估计了最佳半径长度，便会使用改进的Cholesky分解来估计背景误差分布的精确协方差。然后，基于改进的Cholesky分解（EnKF-MC），类似于EnKF进行同化过程。通过使用Lorenz-96模型进行实验测试。为了比较我们的结果，我们采用了具有不同背景误差相关结构的EnKF-MC实现。按照${\ell }_2$避免错误，对于所有模型组件中固定半径的长度，建议的滤波器实现都可以胜过EnKF-MC方法，甚至可以在我们的滤波器公式中尝试使用不同的超参数而不会降低其收敛性。