Optimal groundwater quality management under parameter uncertainty


  • Brian J. Wagner,

  • Steven M. Gorelick


To date optimization models for groundwater quality management give no assurance that water quality standards will be met. This is in part because they ignore errors in hydraulic heads, flows, and solute concentrations due to flow and transport model parameter uncertainty. Here we explicitly incorporate parameter estimation and estimate uncertainties into a model for the optimal design of an aquifer remediation scheme. Parameter uncertainty is incorporated into the decision-making process. The objective is to identify the best remediation strategies (well site selection and pumping-recharge rates) so that water quality standards are met at a specified reliability level. The procedure couples three methods: (1) a finite element flow and transport simulation model combined with nonlinear least squares multiple regression for simultaneous flow and transport parameter estimation; (2) first-order first- and second-moment analysis to transfer the information about the effects of parameter uncertainty to the management model; and (3) nonlinear chance-constrained stochastic optimization combined with flow and transport simulation for optimal decision making. This joint approach enables one to estimate unknown aquifer parameters, quantify the uncertainty of the parameter estimates, simulate flow and transport responses, and automatically account for parameter uncertainty in the decision-making process through the simulation management model. Results show that remediation requirements can increase dramatically due to parameter uncertainty. Risk-averse design solutions automatically provide insurance by “overdesigning” the strategy relative to the risk-neutral case. The approach is fairly general and is applicable to a variety of groundwater management problems. The influence on design solutions of the reliability level and verification of the underlying statistical assumptions of the first-order analysis are explored in a sensitivity study and 2000 Monte Carlo simulations, respectively.