Estimation of Small Failure Probability in High‐Dimensional Groundwater Contaminant Transport Modeling Using Subset Simulation Coupled With Preconditioned Crank‐Nicolson MCMC

Abstract The accurate prediction of groundwater contamination is challenging due to uncertainties arising from the inherent heterogeneity of aquifers, inadequate site characterization, and limitations in conceptual mathematical models. These factors can result in an underestimation of contaminant concentrations. For effective contaminant prevention and control, it is important to estimate the probability of exceeding the allowed threshold for contaminant concentrations, known as the failure probability of groundwater contamination. Computing small failure probabilities using classical Monte Carlo simulation (MCS) requires computing a large number of samplers to converge to a stationary target value, which is time‐consuming. To address this, in this paper, we develop a novel approach for calculating small failure probabilities, known as subset simulation (SS) coupled with preconditioned Crank‐Nicolson Markov chain Monte Carlo (pCN‐SS), which combines subset simulation with preconditioned Crank‐Nicolson Markov chain Monte Carlo (pCN‐MCMC) to promote computational efficiency. We have tested the performance of the proposed algorithm in both a mathematical example and a numerical case study of groundwater contamination. The results demonstrate that pCN‐SS provides improved accuracy and efficiency for evaluating small failure probabilities for high‐dimensional groundwater contamination, specifically for hydraulic conductivity as a source of uncertainty. Compared to classical MCS and traditional SS, pCN‐SS requires fewer model evaluations but produces stable and accurate results.