DEVELOPMENT AND CALIBRATION OF A GROUND-WATER FLOW MODEL FOR THE SPARTA AQUIFER OF SOUTHEASTERN ARKANSAS AND NORTH-CENTRAL LOUISIANA AND SIMULATED RESPONSE TO WITHDRAWALS, 1998-2027

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

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Abstract

The Sparta aquifer, which consists of the Sparta Sand, in southeastern Arkansas and north-central Louisiana is a major water resource and provides water for municipal, industrial, and agricultural uses. In recent years, the demand in some areas has resulted in withdrawals from the Sparta aquifer that substantially exceed replenishment of the aquifer. Considerable drawdown has occurred in the potentiometric surface forming regional cones of depression as water is removed from storage by withdrawals. These cones of depression are centered beneath the Grand Prairie area and the cities of Pine Bluff and El Dorado in Arkansas, and Monroe in Louisiana. The rate of decline for hydraulic heads in the aquifer has been greater than 1 foot per year for more than a decade in much of southern Arkansas and northern Louisiana where hydraulic heads are now below the top of the Sparta Sand. Continued hydraulic-head declines have caused water users and managers alike to question the ability of the aquifer to supply water for the long term. Concern over protecting the Sparta aquifer as a sustainable resource has resulted in a continued, cooperative effort by the Arkansas Soil and Water Conservation Commission, U.S. Army Corps of Engineers, and the U.S. Geological Survey to develop, maintain, and utilize numerical ground-water flow models to manage and further analyze the ground-water system. The work presented in this report describes the development and calibration of a ground-water flow model representing the Sparta aquifer to simulate observed hydraulic heads, documents major differences in the current Sparta model compared to the previous Sparta model calibrated in the mid-1980's, and presents the results of three hypothetical future withdrawal scenarios.

The current Sparta model-a regional scale, three-dimensional numerical ground-water flow model-was constructed and calibrated using available hydrogeologic, hydraulic, and water-use data from 1898 to 1997. Significant changes from the previous model include grid rediscretization of the aquifer, extension of the active model area northward beyond the Cane River Formation facies change, and representation of model boundaries. The current model was calibrated with the aid of parameter estimation, a nonlinear regression technique, combined with trial and error parameter adjustment using a total of 795 observations from 316 wells over 4 different years-1970, 1985, 1990, and 1997. The calibration data set provides broad spatial and temporal coverage of aquifer conditions. Analysis of the residual statistics, spatial distribution of residuals, simulated compared to observed hydrographs, and simulated compared to observed potentiometric surfaces were used to analyze the ability of the calibrated model to simulate aquifer conditions within acceptable error. The calibrated model has a root mean square error of 18 feet for all observations, an improvement of more than 12 feet from the previous model.

The current Sparta model was used to predict the effects of three hypothetical withdrawal scenarios on hydraulic heads over the period 1998-2027 with one of those extended indefinitely until equilibrium conditions were attained, or steady state. In scenario 1a, withdrawals representing the time period from 1990 to 1997 was held constant for 30 years from 1998 to 2027. Hydraulic heads in the middle of the cone of depression centered on El Dorado decreased by 10 feet from the 1997 simulation to 222 feet below NGVD of 1929 in 2027. Hydraulic heads in the Pine Bluff cone of depression showed a greater decline from 61 feet below NGVD of 1929 to 78 feet below NGVD of 1929 in the center of the cone. With these same withdrawals extended to steady state (scenario 1b), hydraulic heads in the Pine Bluff cone of depression center declined an 2 Development and Calibration of a Ground-Water Flow Model for the Sparta Aquifer of Southeastern Arkansas and North-Central Louisiana and Simulated Response to Withdrawals, 1998-2027 additional 26 feet to 104 feet below NGVD of 1929, while the hydraulic-head decline in the El Dorado cone of depression center was only an additional 7 feet.

In scenario 2, withdrawals were extended as in scenario 1a while reducing withdrawals in industrial areas in Pine Bluff and El Dorado, Arkansas. Selected pumpage was removed to simulate effects of industry changing to alternate sources of water. Removal of selected withdrawal points in both the Pine Bluff and El Dorado areas results in shallower, less expansive cones of depression compared to scenario 1a. In the cone of depression centers, hydraulic heads recovered more than 120 and 165 feet, respectively, in the Pine Bluff and El Dorado areas. With this recovery, the area of Union County where hydraulic heads are below the top of the Sparta Sand decreased from 51.9 percent in 1997 to 7.3 percent by 2027.

In scenario 3, withdrawals gradually were increased 25 percent over 30 years while withdrawals were reduced in industrial areas of Jefferson and Union Counties. The results are similar to scenario 2, however, magnitudes of recovery are less because of continued increases in withdrawals elsewhere in the aquifer. In the cone of depression centers for Pine Bluff and El Dorado, hydraulic heads recovered more than 100 and 124 feet, respectively. Even though substantial hydraulic-head recovery occurred in both scenarios 2 and 3, hydraulic heads continued to decline in the Grand Prairie area and in much of north-central Louisiana as withdrawals increased through 2027.

TABLE OF CONTENTS

• Abstract
• Introduction
  • Purpose and Scope
  • Previous Studies
  • General Description of the Previous Sparta Model
  • Model Area Description
• Hydrogeology of the Sparta Aquifer
  • Hydrogeologic Units and Geologic Setting
  • Aquifer System Description
  • Sparta Aquifer Development and Associated Effects
• Ground-Water Flow Model
  • Numerical Method
  • Model Assumptions
  • Model Development
    • Spatial Discretization
    • Time Discretization
    • Boundary Conditions
      • Head-Dependent Boundaries
        • General-Head Boundaries
        • Rivers
        • Simulation of Overlying Geologic Units
      • Specified Flow Boundaries
        • No-Flow Boundaries
        • Areal Recharge in Outcrop
        • Ground-Water Withdrawal
    • Hydraulic Property Zones
      • Hydraulic Conductivity
      • Faults
      • Storage
      • Vertical Hydraulic Conductivity of Layers and Confining Bed
• Model Calibration Procedure
  • Non-Linear Least-Squares Regression Method
  • Model Parameterization
  • Calibration Data Set
    • Hydraulic-Head Observations
    • Weights
    • Sensitivities
    • Reasonable Parameter Ranges
• Model Evaluation
  • Optimal Parameter Estimates
  • Model Fit and Model Error
    • Statistical Analysis of Residuals
    • Weighted Hydraulic-Head Residuals
    • Normality of Weighted Residuals
    • Simulated and Observed Hydrographs of Hydraulic Heads
    • Simulated and Observed Potentiometric Surfaces
  • Ground-Water Budget
• Simulated Aquifer Response to Three Hypothetical Future Withdrawal Rate Scenarios
  • Scenario 1 - Baseline 1990-97 Withdrawal Rates
  • Scenario 2 - Baseline 1990-97 Withdrawal Rates with Reductions in Pine Bluff and El Dorado
  • Scenario 3 - Increased Withdrawal Rates with Reductions in Pine Bluff and El Dorado
• Model Limitations
• Summary and Conclusions
• Selected References
• Appendix - Digital three-dimensional animations of simulated potentiometric surfaces for the three predictive scenarios

1. Map showing location of study and model area
2. Map showing surficial geology and selected structural features of the study area
3. Schematic showing hydrogeologic units within generalized cross section of the embayment aquifer system
4. Model grid of active cells with boundary conditions and river nodes
5. Hydraulic parameter names and zonations representing rivers and vertical hydraulic conductivity of the Cook Mountain Formation
6. River package stage values representing mean annual water levels in rivers in the Sparta outcrop/subcrop and a combined potentiometric surface of aquifers overlying the Sparta Sand
7. Hydraulic parameter names and zonations representing recharge rates in the outcrop and subcrop areas of the Sparta aquifer
8. Graph showing total ground-water withdrawal from the Sparta aquifer and associated stress periods for the model area, 1898-1997.
9. Spatial distribution for ground-water withdrawals represented in stress period 28, 1990-1997
10. Hydraulic parameter names and zonations representing horizontal hydraulic conductivity and faults
11. Storage parameter names and zonations
12. Hydraulic parameter names and zonations representing vertical hydraulic conductivity used to simulate confining beds in the Sparta aquifer
13. Locations of 316 wells for which hydraulic-head measurements for 1970, 1985, 1990, and 1997 are included in the calibration data set with hydrographs from 14 wells labeled A-N
14. Bar chart showing composite scaled sensitivities (CSS) calculated using the optimal parameter estimates of the Sparta model calibration for CSS greater than 1
15. Plot showing weighted residuals and weighted simulated values
16. Map showing spatial distribution of weighted hydraulic-head residuals for (A) 1970, (B) 1985, (C) 1990, and (D) 1997
17. Boxplot showing distribution of weighted hydraulic-head residuals.
18. Chart showing histogram of residuals for entire calibration data set of 795 observations from 1970, 1985, 1990, 1997.
19. Hydrographs showing simulated and observed hydraulic heads at selected observation wells, 1900-1997
20. Map showing simulated and observed potentiometric surface for the Sparta aquifer, predevelopment
21. Map showing simulated and observed potentiometric surface for the Sparta aquifer,
22. Map showing contoured difference between 1997 simulated hydraulic heads and top of the Sparta Sand
23. Graph showing simulated transient ground-water budget for the Sparta aquifer predevelopment - 1997
24. Graph showing simulated (A) predevelopment and (B) 1997 ground-water budget for the Sparta aquifer from current and previous Sparta models.
25. Simulated potentiometric surface (layer 2) for the Sparta aquifer using baseline 1990-1997 withdrawal rates through (A) 2027 [scenario 1a] and to (B) steady state [scenario 1b].
26. Map showing contoured change in simulated hydraulic heads for the Sparta aquifer from 1997 to (A) 2027 [scenario 1a] and (B) steady state [scenario 1b] using baseline 1990-1997 withdrawal rates.
27. Map showing contoured difference from (A) 2027 [scenario 1a] and (B) steady-state [scenario 1b] simulated hydraulic heads to the top of the Sparta Sand using baseline 1990-1997 withdrawal rates.
28. Map showing simulated potentiometric surface for the Sparta aquifer using baseline 1990-1997 withdrawal rates with reductions in Pine Bluff and El Dorado through 2027, scenario 2
29. Map showing change in simulated hydraulic head between 1997 and 2027 using baseline 1990-1997 withdrawal rates with reductions in Pine Bluff and El Dorado through 2027, scenario 2
30. Map showing difference between 2027 simulated hydraulic heads and top of the Sparta Sand using baseline 1990-1997 withdrawal rates with reductions in Pine Bluff and El Dorado through 2027, scenario 2
31. Map showing simulated hydraulic-head surface for the Sparta aquifer using baseline 1990-1997 withdrawal rates increased by 25 percent with reductions in Pine Bluff and El Dorado through 2027, scenario 3
32. Map showing changes in hydraulic head between 1997 and 2027 using baseline 1990-1997 withdrawal rates increased by 25 percent with reductions in Pine Bluff and El Dorado through 2027, scenario
33. Map showing difference between 2027 simulated hydraulic heads and top of the Sparta Sand using baseline 1990-1997 withdrawal rates increased by 25 percent with reductions in Pine Bluff and El Dorado through 2027, scenario 365

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