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Selected Papers in the Hydrologic Sciences, 1988-1992, Water Supply Paper 2340


S. Subitzky


U.S. Geological Survey

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Rigorous models for maximizing sustainable groundwater withdrawals may require more computer memory for their constraint set than is available. In some situations, alternative constraint formulations yield similar or identical answers resulting in great saving in computer memory requirements. In order to evaluate the efficiency of using alternative constraints1 maximum ground-water withdrawal pumping strategies were computed by three digital models for a hypothetical area for a five-decade period. Model A maximized steady ground-water withdrawal. Model B maximized unsteady ground-water mining. Model C maximized unsteady ground-water mining subject to a constraint that final pumping be sustainable after the end of the 50-year period. Change in pumping with time was forced to be monotonic (variably increasing or decreasing but not oscillating) in time. The models were tested by assuming constant transmissivity and by using a range of recharge constraints for four scenarios with stressed and unstressed initial potentiometric surfaces and with constant and changing upper limits on pumping. In situations where upper limits on pumping changed with time, Model A was run repetitively, by using monotonicity constraints. In -those situations, optimality of solution is not assured in all cells. Models A and C computed pumping strategies sustainable after the end of the 50-year period. Model C was the most detailed in that it allowed pumping to vary in time and recharge constraints were based both on unsteady-state flow at 50 years and on steady flow after that time. Model A considered only steady pumping and recharge constraints. Pumping strategies from Model B were not necessarily sustainable because it considered only recharge constraints at 50 years. Results indicate that, when recharge through the study area periphery is unconstrained, all models compute identical pumping. For an initially undeveloped aquifer, or for a developed aquifer if steady pumping is assumed, Model A computes strategies very similar to those computed with Model C and requires only 28 percent of the computer memory and 38 percent of the execution time. For an initially overdeveloped aquifer, Model B computes identical pumping strategies to those computed with Model C and requires 73 percent of the computer memory and 78 percent of the computation time. For that situation, Model A is more conservative and computes less pumping than Model C if pumping in Model C is permitted to vary. Although Model A may compute lower pumping rates during the first 50 years, the sustainable pumping rate thereafter may be greater for Model A than for Model C.