An Efficient Parallel Implementation of the Ensemble Kalman Filter Based on Shrinkage Covariance Matrix Estimation
An Efficient Parallel Implementation of the Ensemble Kalman Filter Based on Shrinkage Covariance Matrix Estimation
复制标题
基于收缩协方差矩阵估计的集成卡尔曼滤波器的高效并行实现
DOI：
10.1109/hipcw.2015.17
复制
发表时间：
2015
影响因子：
2.2
通讯作者：
Adrian Sandu
中科院分区：
文献类型：
--
作者：
Elías D. Nino;Adrian Sandu
提出了一种基于收缩协方差矩阵估计的集合卡尔曼滤波器（EnKF）的并行实现方法. EnKF是一种用于高度非线性模型参数和状态估计的序贯蒙特卡罗方法。在基于集成的方法的上下文中，背景误差相关性通过模型实现的集成来估计。在实践中，由于在一个单一的模型传播所涉及的计算工作量，模型的尺寸（模型组件的数量）是几倍大于合奏的大小。这种约束会导致背景误差估计中的虚假相关性（空间中遥远模型分量之间的相关性）。通常，利用定位方法以减少虚假相关的影响。例如，模型组件的相关性基于它们的物理距离的某个函数而降低。一些EnKF实现是以这样的方式制定的，定位方法隐含地涉及观测的同化。在这种情况下，最好的集合卡尔曼滤波器实现之一是局部集合变换卡尔曼滤波器（LETKF）。在LETKF中，每个模型分量被大小为r的局部框包围，然后，包含在局部域内的信息（即，观察到的成分）用于执行同化。然而，对于稀疏观测网络，r可以变得足够大，相对于合奏大小，因此，本地分析校正可能会受到虚假相关的影响。提出了一种基于Rao-Blackwell Ledoit和Wolf（RBLW）估计的背景误差协方差矩阵的集合卡尔曼滤波器实现方法。这个估计量已被证明是更好的条件比真实的（背景）误差协方差矩阵。此外，在我们的公式中不需要RBLW估计量的显式计算。考虑到背景误差协方差矩阵的典型阶数O（10 e8），这意味着在存储器方面的巨大节省。此外，所提出的EnKF实现可以高效地并行执行：每个模型分量被局部框包围，基于RBLW估计器估计局部背景误差协方差矩阵，然后，局部地使用集合卡尔曼滤波方程来计算局部分析修正。在局部同化之后，每个模式分量被映射回全模式域，从该全模式域获得全局分析解。在业务数据同化，EnKF的实现是有吸引力的，由于其潜在的并行化。利用大气环流模式SPEEDY进行实验。所提出的方法是在FORTRAN和MPI编码是用于本地同化的观测。预报的变量是纬向风和纬向风分量、温度和比湿。对于每个模型变量，考虑具有T-63分辨率（192 x 96网格点）的8个层，其提供总数为589，824个模型分量。整体尺寸为94。所使用的处理器数量为96、256、512、768、1024和1536。结果表明，RBLW估计器的使用可以减轻稀疏观测网络下伪相关的影响，而且对于不同数量的处理器，所提出的EnKF实现的计算工作量与不进行协方差估计的LETKF相当。在精度方面，所提出的实现比LETKF制定在均方根误差意义上更好。
This paper develops a parallel implementation of the ensemble Kalman filter (EnKF) based on shrinkage covariancematrix estimation. The EnKF is a sequential Monte Carlo method for parameter and state estimation of highly nonlinearmodels. In the context of ensemble based methods, background error correlations are estimated via anensemble of model realizations. In practice, the model dimension (number of model components) is several timeslarger than the ensemble size owing to the computational effort involved in one single model propagation. Thisconstraint yields to spurious correlations (correlation between distant model components in space) in the backgrounderror estimations. Commonly, localization methods are utilized in order to reduce the impact of spuriouscorrelations. For instance, correlations of model components are reduced based on some function of their physicaldistances. Some EnKF implementations are formulated in such manner that, localization methods are implicitlyinvolved in the assimilation of observations. In this context, one of the best ensemble Kalman filter implementationsis the local ensemble transform Kalman filter (LETKF). In the LETKF, each model component is surrounded by alocal box of size r and then, the information contained within the local domain (i.e., observed components) is used toperform the assimilation. However, for sparse observational networks, r can become sufficiently large with respectto the ensemble size and therefore, the local analysis corrections can be impacted by spurious correlations. Wepropose an ensemble Kalman filter implementation in which the background error covariance matrix is estimated viathe Rao-Blackwell Ledoit and Wolf (RBLW) estimator. This estimator has proven to be better conditioned than thetrue (background) error covariance matrix. In addition, the explicit computation of the RBLW estimator is notrequired in our formulation. This implies enormous savings in terms of memory considering the typical order ofbackground error covariance matrices O(10e8) Furthermore, the proposed EnKF implementation can be efficientlyperformed in parallel: each model component is surrounded by a local box, a local background error covariancematrix is estimated based on the RBLW estimator and then, the ensemble Kalman filter equations are locally used inorder to compute the local analysis corrections. After the local assimilation, each model component is mapped backonto the full model domain from where the global analysis solution is obtained. In operational data assimilation, EnKF implementations are attractive owing to their potential for parallelization. Experiments are performed making use of the Atmospheric General Circulation Model SPEEDY. The proposed method is coded in FORTRAN and MPI is used for the local assimilation of observations. The predicted variables are the zonal and meridional wind components, the temperature and the specific humidity. For each model variable, 8 layers with the T-63 resolution (192 x 96 grid points) are considered which provide a total number of 589,824 model components. The ensemble size is 94. The number of processors utilized are 96, 256, 512, 768, 1024 and 1536. The results reveal that, the use of the RBLW estimator can mitigate the impact of spurious correlations under sparse observational networks and even more, for different number of processors, the computational effort of the proposed EnKF implementation is comparable to that of the LETKF where no covariance estimation is performed. In terms of accuracy, the proposed implementation performs better than the LETKF formulation in the Root Mean Square Error sense.