A probabilistic collocation based iterative Kalman filter for landfill data assimilation

Accurate forecast of landfill gas (LFG) transport has remained as an active research area, due to the safety and environmental concerns, as well as the green energy potential. The iterative ensemble Kalman filter (IEnKF) has been used to characterize the heterogeneous permeability field of landfills. As a Monte Carlo-based method, IEnKF requires a sufficiently large ensemble size to guarantee its accuracy, which may result in a huge computational cost, especially for large-scale problems. In this study, an efficient probabilistic collocation based iterative Kalman filter (PCIKF) is developed. The polynomial chaos expansion (PCE) is employed to represent and propagate the uncertainties, and an iterative form of Kalman filter is used to assimilate the measurements. To further reduce the computational cost, only the zeroth and first-order ANOVA (analysis of variance) components are kept in the PCE approximation. As demonstrated by two numerical case studies, PCIKF shows significant superiority over IEnKF in terms of accuracy and efficiency. The developed method has the potential to reliably predict and develop best management practices for landfill gas production.