AI 中文总结
该研究针对集合卡尔曼滤波（EnKF）在高维场景下的虚假相关性问题，通过PDE模型实验验证了通用场景下定位方法的必要性，并对比了高维EnKF实现的计算效率。
AI 中文摘要
集合卡尔曼滤波（EnKF）形式的数据同化常被用于结合大规模基于物理的模型与关注量的真实观测数据。然而，当将EnKF应用于具有高维状态空间的数值天气预报（NWP）模型时，已知其会受到虚假相关性的不利影响。为缓解虚假相关性的影响，NWP领域文献中已提出多种定位方法。遗憾的是，这些方法在具有大空间网格尺寸的通用偏微分方程（PDE）正向模型场景中的有效性与必要性尚未得到充分理解。我们在一个示例PDE模型上开展了数值数据同化实验，以证明在NWP之外的场景中虚假相关性的存在及定位方法的必要性。此外，我们比较了多种EnKF实现方式在高维场景下的计算效率，这类场景具备理论复杂度边界但实证成本尚不明确。
英文摘要
Data assimilation in the form of the ensemble Kalman filter (EnKF) is commonly used to combine large-scale physics-based models and real-world observations of a quantity of interest. However, the EnKF is known to be adversely affected by spurious correlations when applied to Numerical Weather Prediction (NWP) models with high-dimensional state spaces. To mitigate the effect of spurious correlations, various localization methods have been proposed in the NWP literature. Unfortunately, the efficacy of and need for these methods in the setting of general PDE-based forward models with large spatial mesh sizes is not well-understood. We conducted a numerical data assimilation experiment on an example PDE model to demonstrate the presence of spurious correlations and need for localization methods outside of the context of NWP. In addition, we compared the computational efficiency of various EnKF implementations in high-dimensional settings for which theoretical complexity bounds are available but empirical costs are unclear.
