标题： 关于信息传播和在集合卡尔曼滤波中使用局部化的问题 显示英文标题

标题： On the propagation of information and the use of localization in ensemble Kalman filtering

摘要： 几种局部化的集合卡尔曼滤波版本已被提出。 尽管应用这些方案的测试已证明它们非常有前景，但目前对局部化的基本原理和限制仍缺乏全面的理解。 本文的目标之一是对此问题做出贡献。 第二个目标是阐明混沌波动力学在信息传播中的作用及其对预报的影响。 为了实现这些目标，这里主要使用的工具是对洛伦兹于2005年引入的一个玩具大气模型进行数值实验的分析和解释。 展示了该模型中波包的传播。 发现当使用集合卡尔曼滤波方案时，在每个预报周期中通过对背景集合成员求平均得到的空间相关函数是短程的，这与通过对模型自由演化状态求平均得到的更长范围的相关函数形成强烈对比。 研究了在一个区域进行的观测对其他区域预报的影响。 比较了带有局部化和不带局部化的分析中的误差协方差矩阵。 从这项研究中提取并总结了局部化过程和信息传播的主要特征。 显示英文摘要

摘要： Several localized versions of the ensemble Kalman filter have been proposed. Although tests applying such schemes have proven them to be extremely promising, a full basic understanding of the rationale and limitations of localization is currently lacking. It is one of the goals of this paper to contribute toward addressing this issue. The second goal is to elucidate the role played by chaotic wave dynamics in the propagation of information and the resulting impact on forecasts. To accomplish these goals, the principal tool used here will be analysis and interpretation of numerical experiments on a toy atmospheric model introduced by Lorenz in 2005. Propagation of the wave packets of this model is shown. It is found that, when an ensemble Kalman filter scheme is employed, the spatial correlation function obtained at each forecast cycle by averaging over the background ensemble members is short ranged, and this is in strong contrast to the much longer range correlation function obtained by averaging over states from free evolution of the model. Propagation of the effects of observations made in one region on forecasts in other regions is studied. The error covariance matrices from the analyses with localization and without localization are compared. From this study, major characteristics of the localization process and information propagation are extracted and summarized.