To date most groundwater management studies have determined control policies that do not change over time. Given the natural dynamics of groundwater flow and contaminant transport, one might expect a time-varying control policy to be more cost-effective. A number of recent studies have used techniques of optimal control to identify optimal, time-varying groundwater management strategies. Optimal control methods [see Bryson and Ho, 1975] exploit the sequential time structure of the dynamic groundwater hydraulic and groundwater quality management models. They provide a systematic procedure for determining the sequence of decisions (e.g. pumping rates) that maximize the design effectiveness.
The studies of Georgakakos and Vlatsa [1991], Lee and Kitanidis [1991] and Andricevic [1993] described above use control theory to identify optimal time-varying groundwater management strategies. The focus of those studies is management design in the presence of simulation model uncertainty. A number of other studies have focused on the economic trade-offs between dynamic and static groundwater management policies. Chang et al. [1992] use differential dynamic programming to demonstrate the benefits of time-varying groundwater pumping policies. Their comparison is based on a hypothetical problem for which the goal is to determine the least-cost pumping policy that reduces groundwater concentrations to acceptable levels. For their examples, they show that static pumping policies will cost 45-75% more than policies that allow pumping rates to vary through time. By allowing for time-varying pumping, the management model can essentially `track' the contaminant plume, turning wells on and off and varying pumping rates as needed.
The study of Chang et al. [1992] demonstrates the potential advantages of dynamic groundwater management, but their approach requires pumping decisions to be made at each time step of the simulation model. Culver and Shoemaker [1992] extend this work to allow for management periods that are greater than the simulation time steps. They explore the trade-offs between the length of the management period (which relates to the computational effort required to solve the optimization problem) and the cost of groundwater remediation. It is shown that the introduction of management periods could result in significant reductions in computational effort, yet still retain the important time variations in pumping. In a related paper, Culver and Shoemaker [1993] present a quasi-Newton differential dynamic programing approach that can further reduce the computational effort associated with the dynamic management problem.