The legal doctrines of reasonable use and correlative rights are the recognized standards for resolving legal conflicts between interfering agricultural ground‐water users in Arkansas. Assuring that an adequate saturated thickness exists for all interfering users throughout the ground‐water withdrawal season provides water users with a degree of protection from both a successful litigious charge of “unreasonable use” and a mandated curtailment of ground‐water withdrawal in a droughty season. The feasibility of maintaining a “target” saturated thickness and water‐table elevation by implementing a district‐wide sustained ground‐water withdrawal strategy has been previously demonstrated. Several models have been reported which create the spatially distributed sustained‐yield withdrawal strategies that will maintain those target levels. The development of satisfactory strategies requires knowledge of the minimum acceptable springtime saturated thickness for critical parts of the management district. This information can be gained through the iterative use of a dynamic ground‐water simulation model. In the iterative procedure, initial (springtime) saturated thickness is assumed. The change in saturated thickness resulting from withdrawals during the irrigation season is compared with an acceptability criterion. The assumed springtime saturated thickness is varied until the criterion is satisfied. The result is the minimum springtime saturated thickness needed for ground‐water users in a particular cell to achieve: (1) a measure of year‐round protection from successful litigation charging unreasonable use, and (2) some assurance that they will not need to curtail or limit ground‐water withdrawals during a droughty season. This procedure was applied to a 3‐mile by 3‐mile (5‐km by 5‐km) cell in the Arkansas Grand Prairie, an important rice‐ and soybean‐producing area. The results indicate that a minimum of 13 feet (4 m) of saturated thickness are desirable for the center of the cell to provide for a droughty season.
A method for determining a spatially distributed set of ground‐water withdrawals that maintains a regionally “optimized” potentiometric surface is presented. A goal‐programing approach, in its quadratic form, is used to minimize the sum of squares of differences between the optimized surface and a “target” potentiometric surface. Constraints on withdrawals and recharge, imposed through a two‐dimensional ground‐water flow equation, and bounds on drawdowns assure that the withdrawal strategy developed is realistic and physically feasible. Application is demonstrated using data from the Grand Prairie region of Arkansas.
S ustained-yield groundwater management strategies can be designed to closely maintain preassigned 'target' levels. Quadratic and linear goal-programming objective functions are used in two distinct models which minimize the sum of differences between 'target' and regionally optimized sets of groundwater levels. Constraints and bounds imposed on extractions, recharge and heads in each model assure that developed strategies are physically feasible and sustainable. The linear model is computationally more time-efficient, but numerical difficulties due to equality constraints are encountered when it is applied to large groundwater systems_ The quadratic model requires less computer storage and is applied to the Grand Prairie of Arkansas as an example.
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