Reconstruction and prediction of the state of the near-Earth space environment is important for anomaly analysis, development of empirical models, and understanding of physical processes. Accurate reanalysis or predictions that account for uncertainties in the associated model and the observations, can be obtained by means of data assimilation. The ensemble Kalman filter (EnKF) is one of the most promising filtering tools for nonlinear and high dimensional systems in the context of terrestrial weather prediction. In this study, we adapt traditional ensemble-based filtering methods to perform data assimilation in the radiation belts. By performing a fraternal twin experiment, we assess the convergence of the EnKF to the standard Kalman filter (KF). Furthermore, with the split-operator technique, we develop two new three-dimensional EnKF approaches for electron phase space density that account for radial and local processes, and allow for reconstruction of the full 3D radiation belt space. The capabilities and properties of the proposed filter approximations are verified using Van Allen Probe and GOES data. Additionally, we validate the two 3D split-operator Ensemble Kalman filters against the 3D split-operator KF. We show how the use of the split-operator technique allows us to include more physical processes in our simulations and is a computationally efficient data assimilation tool that delivers an accurate approximation of the optimal KF solution, and is suitable for real-time forecasting. Future applications of the EnKF to direct assimilation of fluxes and nonlinear estimation of electron lifetimes are discussed.

中文翻译：

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用VERB-3D编码用标准和集成卡尔曼滤波器重建外电子辐射带的动力学

近地空间环境状态的重建和预测对于异常分析、经验模型的开发和物理过程的理解非常重要。可以通过数据同化获得准确的再分析或预测，以解释相关模型和观测中的不确定性。集成卡尔曼滤波器 (EnKF) 是陆地天气预报背景下非线性和高维系统最有前途的滤波工具之一。在这项研究中，我们采用传统的基于集合的滤波方法在辐射带中进行数据同化。通过执行异卵双胞胎实验，我们评估了 EnKF 与标准卡尔曼滤波器 (KF) 的收敛性。此外，使用拆分运算符技术，我们开发了两种新的三维 EnKF 方法，用于解释径向和局部过程的电子相空间密度，并允许重建完整的 3D 辐射带空间。使用 Van Allen Probe 和 GOES 数据验证了所提出的滤波器近似值的能力和属性。此外，我们针对 3D 拆分运算符 KF 验证了两个 3D 拆分运算符 Ensemble Kalman 滤波器。我们展示了拆分算子技术的使用如何允许我们在模拟中包含更多物理过程，并且是一种计算效率高的数据同化工具，可提供最佳 KF 解决方案的准确近似值，并且适用于实时预测。讨论了 EnKF 在通量的直接同化和电子寿命的非线性估计方面的未来应用。