The ensemble Kalman filter (EnKF) has received substantial attention in hydrologic data assimilation due to its ease of implementation. In EnKF, a large enough ensemble size is often required to ensure accuracy, which may result in considerable computational overhead, especially for large-scale problems. Motivated by recent developments in multi-fidelity simulation, we develop a novel data assimilation method that provides an alternative to EnKF, namely adaptive multi-fidelity probabilistic collocation-based Kalman filter (AMF-PCKF). The appealing feature is to approximate the system response with polynomial chaos expansion (PCE) using the adaptive multi-fidelity probabilistic collocation method, which improves the computational efficiency without sacrificing accuracy. This constitutes the forecast step of AMF-PCKF, while the analysis step is established by sequentially updating the PCE coefficients. As demonstrated by a synthetic numerical case of heat transport in unsaturated flow and a real-world two-phase flow experiment, AMF-PCKF can provide more accurate estimations than EnKF under the same amount of computation, even when the number of unknown parameters is as high as 100.

集成卡尔曼滤波器（EnKF）由于易于实现，在水文数据同化中受到了广泛关注。在EnKF中，通常需要足够大的合奏大小以确保准确性，这可能会导致相当大的计算开销，尤其是对于大规模问题。基于多保真度仿真的最新发展，我们开发了一种新的数据同化方法，该方法为EnKF提供了一种替代方法，即基于自适应多保真度概率搭配的卡尔曼滤波器（AMF-PCKF）。吸引人的特征是使用自适应多保真概率配置方法用多项式混沌扩展（PCE）近似系统响应，从而在不牺牲精度的情况下提高了计算效率。这构成了AMF-PCKF的预测步骤，同时通过顺序更新PCE系数来建立分析步骤。正如在非饱和流中的热传递的综合数值案例和现实世界中的两相流实验所证明的那样，即使在相同数量的计算量下，AMF-PCKF可以提供比EnKF更准确的估计，即使未知参数的数量为高达100。