The Mississippi River Valley alluvial aquifer is a water-bearing assemblage of gravels and sands that underlies about 32,000 square miles of Missouri, Kentucky, Tennessee, Mississippi, Louisiana, and Arkansas. Because of the heavy demands placed on the aquifer, several large cones of depression over 100 feet deep have formed in the potentiometric surface, resulting in lower well yields and degraded water quality in some areas. A ground-water flow model of the alluvial aquifer was previously developed for an area covering 14,104 square miles, extending northeast from the Arkansas River into the northeast corner of Arkansas and parts of southeastern Missouri. The flow model showed that continued ground-water withdrawals at rates commensurate with those of 1997 could not be sustained indefinitely without causing water levels to decline below half the original saturated thickness of the aquifer.

To develop estimates of withdrawal rates that could be sustained in compliance with the constraints of critical ground-water area designation, conjunctive-use optimization modeling was applied to the flow model of the alluvial aquifer in northeastern Arkansas. Ground-water withdrawal rates form the basis for estimates of sustainable yield from the alluvial aquifer and from rivers specified within the alluvial aquifer model. A management problem was formulated as one of maximizing the sustainable yield from all ground-water and surface-water withdrawal cells within limits imposed by plausible withdrawal rates, and within specified constraints involving hydraulic head and streamflow. Steady-state flow conditions were selected because the maximized withdrawals are intended to represent sustainable yield of the system (a rate that can be maintained indefinitely).

Within the optimization model, 11 rivers are specified. Surface-water diversion rates that occurred in 2000 were subtracted from specified overland flow at the appropriate river cells. Included in these diversions were the planned diversions of 63,339,248 ft3/d for the Bayou Meto project area and 55,078,367 ft3/d for the Grand Prairie project area, which factor in an additional 30 and 40 percent transmission loss, respectively. Streamflow constraints were specified at all 1,165 river cells based on average 7-day minimum flows for 10 years. Sustainable yield for all rivers ranged from 0 (Current, Little Red, and Bayou Meto Rivers) to almost 5 billion cubic feet per day for the Arkansas River. Total sustainable yield from all rivers combined was 12.8 billion cubic feet per day, which represents a substantial source for supplementing ground water to meet the total water demand.

Sustainable-yield estimates are affected by the allowable upper limit on withdrawals from wells specified in the optimization model. Ground-water withdrawal rates were allowed to vary as much as 200 percent of the withdrawal rate in 1997. As the overall upper limit on withdrawals is increased, the sustainable yield generally increases. Tests with the optimization model show that without limits on pumping, wells adjacent to sources of water would have optimized withdrawal rates that were orders of magnitude larger than rates corresponding to those of 1997. The sustainable yield from ground water for the entire study area while setting the maximum upper limit as the amount withdrawn in 1997 is 360 million cubic feet per day, which is only about 57 percent of the amount withdrawn in 1997 (635.6 million cubic feet per day). Optimal sustainable yields from within the Bayou Meto irrigation project area and within the Grand Prairie irrigation project area are 18.1 and 9.1 million cubic feet per day, respectively, assuming a maximum allowable withdrawal rate equal to 1997 rates. These values of sustainable yield represent 35 and 30 percent respectively of the amount pumped from these project areas in 1997.

Unmet demand (defined as the difference between the optimized withdrawal rate or sustainable yield, and the anticipated demand) was calculated using different demand rates based on multiples of the 1997 withdrawal rate. Assuming that demand is the 1997 withdrawal rate, and that sustainable-yield estimates are those obtained using upper limits of withdrawal rates of 100-, 150-, and 200-percent of 1997 withdrawal rates, then the resulting unmet demand for the entire model area is 275.5, 190.9, and 110 million cubic feet per day, respectively. Whereas, if the demand is specified as 100-, 150-, and 200-percent of the 1997 withdrawal rate, and the sustainable-yield estimates remain the same, then the resulting unmet demand for the entire model area is 275.5, 508.8, and 745.8 million cubic feet per day, respectively. These unmet demands for ground water could be obtained from large sustainable surface-water withdrawals.