It is apparent that significant theoretical advances in groundwater management modeling have been made over the past four years. There have also been a number of reported field studies in which simulation-optimization techniques have been applied to design groundwater management strategies. This section reviews recent studies involving groundwater management models and summarizes the experience gained from these studies. The reader is also referred to the recent review by Ahlfeld and Heidari [1994].
Stochastic groundwater management techniques have recently been applied to design groundwater hydraulic and groundwater quality management strategies. Gailey and Gorelick [1993] apply a nonlinear chance-constrained groundwater management model [Tung, 1986, Wagner and Gorelick, 1987] to design reliable plume capture schemes for a landfill site near Ottawa, Canada. Solution of the chance-constrained problem proceeded in two stages. In the first stage, a two-dimensional, steady-state groundwater flow and transient contaminant transport simulation model is combined with nonlinear least squares regression to identify the best estimates of the unknown model parameters based on contaminant concentration and hydraulic head data. The second stage involves solution of the nonlinear chance-constrained optimization problem. In this stage, the model predictions are defined probabilistically (via first-order uncertainty analysis) as functions of the pumping decisions and the parameter uncertainty. The probabilistic interpretation of the model predictions recognizes the need to overdesign to ensure a high level of reliability. In this case it was determined that an overdesign of up to 27 percent was needed to achieve a reliability level of r = 0.90.
Another application of the nonlinear chance-constrained groundwater management model is the work by Tiedman and Gorelick [1993]. In this study, a hydraulic management model is developed to identify minimum-pumping strategies to contain a vinyl chloride plume at a site in southwest Michigan. Again, a two-stage procedure is used. In the first stage, a three-dimensional, transient groundwater flow model is coupled with nonlinear least squares regression to identify the unknown model parameters based on hydraulic head data. In the second stage, the nonlinear chance-constrained optimization problem is solved to identify plume containment strategies that reliably meet the hydraulic gradient constraints in the presence of model parameter uncertainty. In this case, an overdesign of approximately 40 percent was required to reach a reliability level of r = 0.90. Additionally, it was found that using a deterministic management model with a hydraulic gradient safety factor was inadequate because the safety factors needed to ensure a reliable design vary from one constraint location to another and are unknown prior to solution of the stochastic management model [see also Morgan et al., 1993].
Marryott et al. [1993] apply simulated annealing to analyze groundwater remediation strategies at a contaminated site in northern California. A two-dimensional model was developed to simulate unconfined groundwater flow and contaminant transport subject to linear equilibrium adsorption. The simulated annealing algorithm [ Dougherty and Marryott, 1991] was applied to identify optimal groundwater remediation strategies for two different management model formulations. The first model formulation seeks to select from the potential pumping configurations (6 wells, 9 discrete pumping rates) the `least-cost' pumping strategy that meets the concentration reduction goal. The cost objective includes well costs (pumping and installation) and a penalty `cost' for exceeding the concentration reduction goal. The results of this formulation suggest that the remediation strategy in use at the site would be significantly improved (in terms of total pumping) if additional off-site wells were added. The second management model is formulated to identify the `least-cost' pumping strategy that ensures plume containment. In this case, the `cost' function has a penalty term for velocity constraint violations. The optimal pumping strategy for plume containment was found to require significantly more pumping than that required for concentration reduction.
Finney et al. [1992] develop an optimization model for the control of saltwater intrusion in the Jakarta Basin, Indonesia. Their management model combines a quasi three-dimensional sharp interface model with nonlinear programming to control saltwater intrusion. The goal is to identify the pumping and recharge policy that minimizes the squared volume of saltwater intrusion. They perform a parametric analysis to evaluate the trade-offs between water demand and saltwater volume, and they show that increased water demands will lead to a significant degradation in the basin. They then demonstrate that, in comparison to historical policies, an optimized policy that redistributes pumping and introduces artificial recharge can significantly reduce the saltwater volume.
Varljen and Shafer [1993] consider the problem of optimal capture zone design. In this case, the goal is to determine pumping rates for a well field in order to minimize the risk of withdrawing contaminated water. A simulation model is used to determine five-year time-of-travel capture zones for each well as a function of the well-field pumping policy. The `contamination risk' is defined as the number of potential contaminant sources located within the capture zones of all wells in the well field. The groundwater management model evaluates the effects of pumping policy variations on capture zones and identifies the pumping strategy that meets water demands but minimizes the `contamination risk.' The management model is applied to a well field in Pekin, Illinois. The optimized well field design provides a 50% reduction in the contamination risk as compared to the current design.
Chau [1992] uses the simulation-optimization approach to design relief-well systems for the Cochran Valley aquifer in Alberta, Canada, which has been subject to excessive pressures since the filling of a reservoir that is hydraulically connected to the aquifer. A two dimensional groundwater flow model is used to simulate changes in groundwater heads with changes in reservoir level. The management model seeks to determine the locations and discharge schedules of relief wells such that the managed hydraulic heads are less than or equal to the ground surface elevation and the total water losses from the groundwater system are minimized. The general conclusion is that existing relief wells are inadequate, but it would be possible to relieve aquifer pressure with new wells. Further, it is shown that simple functions can be used to relate necessary well discharge to reservoir stage. In this way the relief wells can be operated in real time in response to changes in reservoir levels.
Danskin and Freckleton [1992] use a simulation-optimization model to address the problem of high ground water levels in the San Bernardino Valley, California. In this case, a decrease in agricultural groundwater usage along with above-average recharge has caused groundwater heads to rebound, causing a variety of groundwater-related problems. Linear programming is coupled with a transient, multi-layer groundwater flow model to determine the most efficient pumping policy to reduce hydraulic heads in the affected areas. To account for the nonlinearities associated with the evapotranspiration function, an iterative solution method is used. Danskin and Freckleton solve twenty-six alternative model formulations, evaluating the effects of variations in the hydraulic head targets, maximum time to meet drawdown targets, amount of recharge, and number and locations of managed wells. The primary conclusion was that the head constraints could not be met in a twelve month time-frame using the existing facilities. Only with a combination of existing and new wells could the drawdown targets be met under all conditions studied.
Lall and Lin [1993] and Gharbi and Peralta [1994] develop groundwater management models for Salt Lake Valley, Utah. Lall and Lin formulate their model from the perspective of a water authority seeking to meet the demands of competing water supply agencies. The objective is to minimize the annual cost of groundwater supply subject to drawdown, water rights and water quality restrictions. In this case, water quality constraints are met by controlling groundwater flow. The model is applied for a variety of groundwater demand scenarios. It is shown that a judicious allocation of pumping could meet an increasing demand while meeting the hydraulic, water quality and water rights restrictions. The model of Gharbi and Peralta also seeks to determine a plan for sustainable groundwater yield under consideration of groundwater hydraulic and quality restrictions. In this case, the management model is formulated with the dual objective of maximizing pumping and minimizing the amount by which target concentration values are exceeded, subject to constraints on pumping, drawdown, and discharges to surface water bodies. The model is applied for different scenarios to evaluate the trade-off between maximizing pumping and preventing excessive contaminant concentration levels. The results indicate that it is possible to improve water quality conditions (as compared to conditions projected under existing pumping) and at the same time increase the groundwater yield. However, it is not possible to attain all water quality goals given existing facilities and pumping restrictions.