Hierarchical Bayesian Model Averaging for Chance Constrained Remediation Designs

Groundwater remediation designs are heavily relying on simulation models which are subjected to various sources of uncertainty in their predictions. To develop a robust remediation design, it is crucial to understand the effect of uncertainty sources. In this research, we introduce a hierarchical Bayesian model averaging (HBMA) framework to segregate and prioritize sources of uncertainty in a multi-layer frame, where each layer targets a source of uncertainty. The HBMA framework provides an insight to uncertainty priorities and propagation. In addition, HBMA allows evaluating model weights in different hierarchy levels and assessing the relative importance of models in each level. To account for uncertainty, we employ a chance constrained (CC) programming for stochastic remediation design. Chance constrained programming was implemented traditionally to account for parameter uncertainty. Recently, many studies suggested that model structure uncertainty is not negligible compared to parameter uncertainty. Using chance constrained programming along with HBMA can provide a rigorous tool for groundwater remediation designs under uncertainty. In this research, the HBMA-CC was applied to a remediation design in a synthetic aquifer. The design was to develop a scavenger well approach to mitigate saltwater intrusion toward production wells. HBMA was employed to assess uncertainties from model structure, parameter estimation and kriging interpolation. An improved harmony search optimization method was used to find the optimal location of the scavenger well. We evaluated prediction variances of chloride concentration at the production wells through the HBMA framework. The results showed that choosing the single best model may lead to a significant error in evaluating prediction variances for two reasons. First, considering the single best model, variances that stem from uncertainty in the model structure will be ignored. Second, considering the best model with non-dominant model weight may underestimate or overestimate prediction variances by ignoring other plausible propositions. Chance constraints allow developing a remediation design with a desirable reliability. However, considering the single best model, the calculated reliability will be different from the desirable reliability. We calculated the reliability of the design for the models at different levels of HBMA. The results showed that by moving toward the top layers of HBMA, the calculated reliability converges to the chosen reliability. We employed the chance constrained optimization along with the HBMA framework to find the optimal location and pumpage for the scavenger well. The results showed that using models at different levels in the HBMA framework, the optimal location of the scavenger well remained the same, but the optimal extraction rate was altered. Thus, we concluded that the optimal pumping rate was sensitive to the prediction variance. Also, the prediction variance was changed by using different extraction rate. Using very high extraction rate will cause prediction variances of chloride concentration at the production wells to approach zero regardless of which HBMA models used.