Simultaneous identification of groundwater contaminant sources and simulation of model parameters based on an improved single-component adaptive Metropolis algorithm

Abstract

The Bayesian approach is attractive because it can consider various uncertainties in the inverse process. Although the Bayesian algorithm has strong random ergodicity, it still lacks the ability to perform local optimization. Therefore, an improved single-component adaptive Metropolis (SCAM) algorithm based on Bayesian theory was developed to solve this problem and it was applied to the simultaneous identification of groundwater contaminant sources and simulation model parameters. The nondeterministic simulation model parameters have been introduced into the prior distribution as random variables. However, this will increase the number of random variables in the inverse problem, besides making the solution difficult. To alleviate this difficulty, the SCAM algorithm was applied to groundwater contaminant source identification. The acceptance probability formula was adjusted to enhance the local optimization ability of the SCAM algorithm. This improves the searching efficiency of the algorithm in the second stage, without losing the ergodicity in the first stage. In the inverse process, the simulation model is used multiple times to evaluate the likelihood function. To reduce the computational burden, the likelihood function is calculated by the surrogate model of the simulation model instead of by the simulation model itself, which greatly accelerates the process of Bayesian inversion. The effectiveness of this approach has been demonstrated by a hypothetical case study. Finally, the results of previous and improved algorithms have been compared. The results indicate that the improved SCAM algorithm can identify groundwater contaminant sources and simulation model parameters, simultaneously, with high accuracy and efficiency.