Optimal groundwater quality management under parameter uncertainty

Abstract

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.

Reliable groundwater management in hydroecologically sensitive areas

“…Examples of stochastic simulation-optimization formulations for cases primarily involving aquifer remediation are the studies reported by Tung [1986], Wagner and Gorelick [1987], Gaily and Gorelick [1993], and Tiedeman and Gorelick [1993]. Stochastic optimization that includes a comprehensive sensitivity analysis has yet to be applied to groundwater resource allocation in hydroecologically sensitive regions.…”

A hydro-economic modeling framework for optimal management of groundwater nitrate pollution from agriculture

“…One of the most difficult issues in groundwater management modeling is dealing adequately with the effect of model uncertainty in optimal decision making (Wagner and Gorelick, 1987). The uncertainty stems from a wide variety of factors ranging from partial knowledge about the aquifer properties, its boundary conditions, land use practices, onground nitrogen loading, nitrogen soil dynamics, soil characteristics, depth to water table, flow and transport parameters affecting nitrate fate and transport in groundwater, to economic, regulatory and political factors.…”

“…Unlike the classic chance-constrained applications (e.g., Tung, 1986;Wagner and Gorelick 1987;McSweeny and Shortle, 1990;Wagner 1999), this formulation considers uncertainty in the response matrix coefficients and does not require a priori definition of the distribution. The "classic" chance-constrained programming (Charnes et al, 1958;Charnes and Cooper, 1963) is a stochastic programming method that enables the integration of parameter uncertainties into the optimization framework at time that permits constraint violations up to specified probability limits.…”

“…A second approach is related to the probabilistic "chance-constrained" programming, which allow the determination of optimal groundwater quality management subject to a specified system performance reliability requirement (e.g., Tung, 1986;Wagner and Gorelick 1987;McSweeny and Shortle, 1990;Sawyer and Lin 1998;Wagner 1999). This approach has also the advantage of requiring less computational effort than the multiple realization model.…”

“…The deterministic equivalent-based methods can be solved by linear or nonlinear programming methods (e.g., Charnes and Cooper, 1963;Kataoka, 1963). Nevertheless, they entail a series of drawbacks such as requiring assumptions of parameter distributions that may induce to errors (for mathematical convenience, the most widely used statistical model is the normal distribution, e.g., Tung, 1986;Wagner and Gorelick, 1987), or to be unsuitable for complex nonlinear problems where the deterministic equivalent may be difficult or even impossible to establish. Furthermore, they become cumbersome whenever reliability is defined as the probability of meeting a set of constraints simultaneously, rather than one or more (Ng and Eheart, 2008).…”