Adaptive multi-fidelity probabilistic collocation-based Kalman filter for subsurface flow data assimilation: numerical modeling and real-world experiment

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.