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RECALIBRATION OF A GROUND-WATER FLOW MODEL OF THE MISSISSIPPI RIVER VALLEY ALLUVIAL AQUIFER OF NORTHEASTERN ARKANSAS, 1918-1998, WITH SIMULATIONS OF WATER LEVELS CAUSED BY PROJECTED GROUND-WATER WITHDRAWALS THROUGH 2049

By T.B. Reed

U.S. GEOLOGICAL SURVEY
Water–Resources Investigations Report 03-4109

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Abstract

A digital model of the Mississippi River Valley alluvial aquifer in eastern Arkansas was used to simulate ground-water flow for the period from 1918 to 2049. The model results were used to evaluate effects on water levels caused by demand for ground water from the alluvial aquifer, which has increased steadily for the last 40 years. The model results showed that water currently (1998) is being withdrawn from the aquifer at rates greater than what can be sustained for the long term. The saturated thickness of the alluvial aquifer has been reduced in some areas resulting in dry wells, degraded water quality, decreased water availability, increased pumping costs, and lower well yields.

The model simulated the aquifer from a line just north of the Arkansas-Missouri border to south of the Arkansas River and on the east from the Mississippi River westward to the less permeable geologic units of Paleozoic age. The model consists of 2 layers, a grid of 184 rows by 156 columns, and comprises 14,118 active cells each measuring 1 mile on a side. It simulates time periods from 1918 to 1998 along with further time periods to 2049 testing different pumping scenarios. Model flux boundary conditions were specified for rivers, general head boundaries along parts of the western side of the model and parts of Crowleys Ridge, and a specified head boundary across the aquifer further north in Missouri.

Model calibration was conducted for observed water levels for the years 1972, 1982, 1992, and 1998. The average absolute residual was 4.69 feet and the root-mean square error was 6.04 feet for the hydraulic head observations for 1998.

Hydraulic-conductivity values obtained during the calibration process were 230 feet per day for the upper layer and ranged from 230 to 730 feet per day for the lower layer with the maximum mean for the combined aquifer of 480 feet per day. Specific yield values were 0.30 throughout the model and specific storage values were 0.000001 inverse-feet throughout the model. Areally specified recharge rates ranged from 0 to about 30 inches and total recharge increased from 1972 to 1998 by a factor of about four.

Water levels caused by projected ground-water withdrawals were simulated using the calibrated model. Simulations represented a period of 50 years into the future in three scenarios with either unchanged pumpage, pumpage increased by historic trends, or pumpage increased by historic trends except in two areas of the Grand Prairie. If pumping remains at 1997 rates, this produces extreme water-level declines (areas where model cells have gone dry or where the water level in the aquifer is equal to or less than the original saturated thickness, assuming confined conditions in the aquifer everywhere in the formation in predevelopment times) in the aquifer in two areas of the aquifer (one in the Grand Prairie area between the Arkansas and White Rivers and the other west of Crowleys Ridge along the Cache River) with about 400 square miles going dry. Increasing the pumping rates to that which would be projected using historic data led to increased extreme water-level declines in both areas with about 1,300 square miles going dry. Declines in both scenarios generally occurred most rapidly between 2009 and 2019. Reducing the pumping rates to 90 percent of that used for projected historic rates in areas between the Arkansas and White Rivers relating to two diversion projects of the U.S. Army Corps of Engineers and other agencies did little to decrease the extreme water-level declines. However, these pumpage reductions are small (amounting to about 16 percent of the reductions that could result from implementation of these diversion projects).


TABLE OF CONTENTS

Figure
  1. Map showing location of study and modeled area
  2. Map showing finite-difference grid of model cells
  3. Hydrogeologic section through the alluvial aquifer and underlying units
  4. Water-level altitudes in the alluvial aquifer in spring 1998
  5. Areas of confined and unconfined conditions within the alluvial aquifer in 1998
  6. Thickness of the alluvial aquifer
  7. Thickness of the clay cap overlying the alluvial aquifer
  8. Difference between the alluvial aquifer water levels in 1998 and the underlying Sparta aquifer water levels in 1999
  9. Initial water-level altitudes assigned to model cells in both layers
  10. Simulated initial water-level altitudes in the lower layer produced by steady-state stress period 1 at the beginning of the transient simulations
  11. Parameter zones used to calibrate the hydraulic properties and recharge
  12. Distributions of pumpage used for 1994-1998 (stress period 11)
  13. Observation wells used in the calibration process
  14. Graph showing the average change in water level from a doubling of the parameter
  15. Volumetric budget component rates for 1968-1972 and 1994-March 1998 (stress periods 5 and 11)
  16. Graph showing selected volumetric budget component rates for the model by stress period
  17. Selected hydrographs of observed and simulated water levels showing water levels used for calibration
  18. At the end of 1972 (stress period 5)
  19. At the end of 1982 (stress period 7)
  20. On March 31, 1992 (stress period 9)
  21. On March 31, 1998 (stress period 11).
  22. 1968 to 1972 (stress period 5)
  23. 1978 to 1982 (stress period 7)
  24. 1989 to March 1992 (stress period 9)
  25. 1994 to March 1998 (stress period 11)
  26. Simulated water-level altitudes for March 31, 1998 (stress period 11)
  27. Simulated river, specified head, and general head boundary fluxes for model cells from 1994 to March 1998 (stress period 11)
  28. Simulated recharge fluxes for 1918 to 1972 (stress periods 1- 6)
  29. Simulated recharge fluxes for 1994 to March 1998 (stress period 11)
  30. Selected zones used for pumping changes in model projection simulations
  31. Simulated water levels at the end of 2049 (stress period 16) with 1997 pumpage extended unchanged (scenario 1)
  32. Simulated water levels at the end of 2049 (stress period 16) with 1997 pumpage extended by county trends (scenario 2)
  33. Simulated water levels at the end of 2049 (stress period 16) with pumpage reduced to 90 percent of county trends in selected zones (scenario 3).
  34. Simulated saturated thickness at the end of each stress period where the aquifer is less than or equal to half saturated, and saturated thickness in excess of 50 percent of the aquifer thickness where the aquifer is more than half saturated, using 1997 pumpage extended unchanged
  35. Areas of extreme water-level declines produced by model projection scenarios
  36. Simulated saturated thickness at the end of each stress period where the aquifer is less than or equal to half saturated, and saturated thickness in excess of 50 percent of the aquifer thickness where the aquifer is more than half saturated, using 1997 pumpage extended by county trends
  37. Simulated saturated thickness at the end of each stress period where the aquifer is less than or equal to half saturated, and saturated thickness in excess of 50 percent of the aquifer thickness where the aquifer is more than half saturated, using 1997 pumpage extended by county trends but reduced to 90 percent in selected zones
TABLES
  1. Stress periods and water use simulated
  2. Values of hydrologic parameters derived from the calibration process
  3. Statistics for residuals for water-level observations
  4. Actual total pumpage for projection simulations



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