Optimization Design of Groundwater Pollution Monitoring Scheme and Inverse Identification of Pollution Source Parameters Using Bayes’ Theorem

Abstract

In the process of identifying groundwater pollution sources, in order to solve the problem that the monitoring data of monitoring wells was insufficient or the correlation between monitoring data and model parameters was weak, a monitoring well optimization method based on Bayesian formula and information entropy was proposed. Two-dimensional phreatic groundwater solute transport model was built and solved by using GMS software. To reduce the computational load of calling the numerical model repeatedly in the optimization design of the monitoring schemes and the identification process of the pollution sources, the Kriging method was used to establish the surrogate model of the numerical model. Under the condition of single well monitoring and determined monitoring frequency, with the target of optimization of monitoring position number D and monitoring time interval ∆t, both the single-objective monitoring scheme with the minimum information entropy of the model parameter posterior distribution and the multi-objective monitoring scheme with the minimum information entropy and the shortest monitoring time were optimized respectively. According to the above-optimized monitoring schemes, the delayed rejection adaptive Metropolis algorithm was used to identify the pollution source parameters. The case study results showed that under the condition of pre-set single well monitoring with monitoring frequency of 10 times, the single-objective optimized monitoring scheme was D = 37 and Δt = 20 days. Under this monitoring scheme, the mean errors of inversion pollution source parameters α = (XS, YS, T1, T2, QS) were 0.09%, 0.4%, 4.72%, 2.43%, and 9.29%, respectively. The multi-objective optimized monitoring scheme was D = 37 and Δt = 2 days. Under this monitoring scheme, the mean errors of the inversion parameters α = (XS, YS, T1, T2, QS) were 12.76%, 3.77%, 5.13%, 1.36%, and 7.68%, respectively. Compared with the monitoring scheme based on the single-objective optimization, although the inversion mean error of the five parameters based on the multi-objective optimized monitoring scheme increased by 2.75%, the monitoring time significantly reduced from 180 to 18 days.