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By Paul W. McKee, Brian R. Clark, and John B. Czarnecki

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Conjunctive-use optimization modeling was done to assist water managers and planners by estimating the maximum amount of ground water that hypothetically could be withdrawn from wells within the Sparta aquifer indefinitely without violating hydraulic-head or stream-discharge constraints. The Sparta aquifer is largely a confined aquifer of regional importance that comprises a sequence of unconsolidated sand units that are contained within the Sparta Sand. In 2000, more than 35.4 million cubic feet per day (Mft3/d) of water were withdrawn from the aquifer by more than 900 wells, primarily for industry, municipal supply, and crop irrigation in Arkansas. Continued, heavy withdrawals from the aquifer have caused several large cones of depression, lowering hydraulic heads below the top of the Sparta Sand in parts of Union and Columbia Counties and several areas in north-central Louisiana. Problems related to overdraft in the Sparta aquifer can result in increased drilling and pumping costs, reduced well yields, and degraded water quality in areas of large drawdown.

A finite-difference ground-water flow model was developed for the Sparta aquifer using MODFLOW, primarily in eastern and southeastern Arkansas and north-central Louisiana. Observed aquifer conditions in 1997 supported by numerical simulations of ground-water flow show that continued pumping at withdrawal rates representative of 1990 - 1997 rates cannot be sustained indefinitely without causing hydraulic heads to drop substantially below the top of the Sparta Sand in southern Arkansas and north-central Louisiana. Areas of ground-water levels below the top of the Sparta Sand have been designated as Critical Ground-Water Areas by the State of Arkansas. A steady-state conjunctive-use optimization model was developed to simulate optimized surface-water and ground-water withdrawals while maintaining hydraulic-head and streamflow constraints, thus determining the "sustainable yield" for the aquifer.

Initial attempts to estimate sustainable yield using simulated 1997 hydraulic heads as initial heads in Scenario 1 and 100 percent of the baseline 1990-1997 withdrawal rate as the lower specified limit in Scenario 2 led to infeasible results. Sustainable yield was estimated successfully for scenario 3 with three variations on the upper limit of withdrawal rates. Additionally, ground-water withdrawals in Union County were fixed at 35.6 percent of the baseline 1990-1997 withdrawal rate in Scenario 3. These fixed withdrawals are recognized by the Arkansas Soil and Water Conservation Commission to be sustainable as determined in a previous study. The optimized solutions maintained hydraulic heads at or above the top of the Sparta Sand (except in the outcrop areas where unconfined conditions occur) and streamflow within the outcrop areas was maintained at or above minimum levels. Scenario 3 used limits of 100, 150, and 200 percent of baseline 1990-1997 withdrawal rates for the upper specified limit on 1,119 withdrawal decision variables (managed wells) resulting in estimated sustainable yields ranging from 11.6 to 13.2 Mft3/d in Arkansas and 0.3 to 0.5 Mft3/d in Louisiana. Assuming the total 2 Conjunctive-Use Optimization Model and Sustainable-Yield Estimation for the Sparta Aquifer of Southeastern Arkansas and North-Central Louisiana water demand is equal to the baseline 1990-1997 withdrawal rates, the sustainable yields estimated from the three scenarios only provide 52 to 59 percent of the total ground-water demand for Arkansas; the remainder is defined as unmet demand that could be obtained from large, sustainable surface-water withdrawals.


  1. Map showing extent of Sparta aquifer and location of model area with Arkansas Soil and Water Conservation Commission Critical Ground-Water Areas shaded
  2. Flow chart of optimization modeling process
  3. Map showing control point locations for Sparta aquifer hydraulic-head and streamflow constraints
  4. Map showing baseline 1990-1997 ground-water withdrawal rates used in conjunctive- use optimization model
  5. Map showing difference between Sparta aquifer 1997 simulated heads and top of the Sparta Sand
  6. Map showing ratio of optimal ground-water withdrawal to baseline 1990-1997 withdrawals (in percent) for (A) scenario 3A, (B) scenario 3B, and (C) scenario 3C including locations where hydraulic-head constraints are reached.
  7. Graph showing scenario results of estimated sustainable yield as a function of the maximum allowable ground-water withdrawal
  8. Map showing difference between steady-state simulated hydraulic heads and the top of the Sparta Sand for (A) scenario 3a, (B) scenario 3b, and (C) scenario 3c using optimized withdrawals in the Sparta aquifer flow model for verification.
  1. Characteristics of the Sparta aquifer ground-water flow model
  2. Flow and optimized surface-water withdrawals for major rivers within the Sparta aquiferoutcrop area specified within the conjunctive-use optimization model for all three scenarios (3A-3C)
  3. Summary of optimization scenarios and associated constraints including sustainable yield estimates and total 1997 withdrawals for Arkansas and Louisiana
  4. Estimated sustainable yield and unmet demand by county and parish for each scenario in Arkansas and Louisiana

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