Groundwater pollution source identification using Metropolis-Hasting algorithm combined with Kalman filter algorithm

Abstract

Increasing the precision of groundwater pollution source identification (GPSI) is crucial for groundwater pollution control and risk management. Bayesian theory based on the Markov Chain Monte Carlo (MCMC) method is a useful strategy of solving the GPSI problem. However, because of the nonlinear and uncertainty characteristics of GPSI, the Metropolis-Hasting (MH) algorithm, one of the most well-known MCMC algorithms, has the disadvantage of relatively low precision and is time-consuming. To address this problem, the Kalman filter (KF) algorithm was combined with the MH algorithm and referred to as the Kalman filter Metropolis-Hasting (KF–MH) algorithm. The algorithm generates a new initial distribution that is close to the true value through a prior distribution, and the new initial distribution is used to perform subsequent iterations of the calculation. The viability and superiority of the proposed KF-MH algorithm were assessed in three hypothetical GPSI cases under different conditions. In the inversion process, a surrogate model was constructed using a temporal convolutional network (TCN) to reduce the computational pressure imposed by the numerical simulation model. The results of the TCN surrogate model in the cases illustrate the high accuracy of the TCN surrogate model in fitting the groundwater numerical model. In the three cases, the normalized errors between the identification results and the true values of the source features obtained with the KF–MH algorithm were significantly lower than those of the MH algorithm. The results indicate that the proposed KF–MH algorithm has higher inversion accuracy than the MH algorithm.