Prepared in cooperation with the

U.S. Army Corps of Engineers, Memphis District and the

Arkansas Soil and Water Conservation Commission

DEVELOPMENT AND CALIBRATION OF A GROUNDWATER FLOW MODEL FOR THE SPARTA AQUIFER OF 

SOUTHEASTERN ARKANSAS AND NORTH-CENTRAL 

LOUISIANA AND SIMULATED RESPONSE TO 

WITHDRAWALS, 1998-2027

Water-Resources Investigations Report 03-4132

U.S. Department of the Interior

U.S. Geological Survey
Cover: Oblique view of 1997 simulated hydraulic heads of the Sparta aquifer, also shown in animations

included on the compact disk in the back of the report.
DEVELOPMENT AND CALIBRATION OF A GROUNDWATER FLOW MODEL FOR THE SPARTA AQUIFER OF 

SOUTHEASTERN ARKANSAS AND NORTH-CENTRAL 

LOUISIANA AND SIMULATED RESPONSE TO 

WITHDRAWALS, 1998-2027

By Paul W. McKee and Brian R. Clark

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 03-4132

Prepared in cooperation with the

U.S. Army Corps of Engineers, Memphis Distrcit and the

Arkansas Soil and Water Conservation Commission

Little Rock, Arkansas

2003
U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

For additional information Copies of this report can be

write to: purchased from:

District Chief U.S. Geological Survey

U.S. Geological Survey, WRD Branch of Information Services

401 Hardin Road Box 25286

Little Rock, Arkansas 72211 Denver Federal Center

Denver, Colorado 80225

The use of firm, trade, and brand names in this report is for identification purposes only and does not constitute endorsement by the U.S. Geological Survey.
Contents III

CONTENTS

Abstract ............................................................................................................................................................... 1

Introduction.......................................................................................................................................................... 2

Purpose and Scope ...................................................................................................................................... 4

Previous Studies..........................................................................................................................................4

General Description of the Previous Sparta Model.....................................................................................5

Model Area Description..............................................................................................................................5

Hydrogeology of the Sparta Aquifer....................................................................................................................5

Hydrogeologic Units and Geologic Setting ................................................................................................5

Aquifer System Description........................................................................................................................6

Sparta Aquifer Development and Associated Effects .................................................................................8

Ground-Water Flow Model ..................................................................................................................................8

Numerical Method ......................................................................................................................................9

Model Assumptions ....................................................................................................................................9

Model Development..................................................................................................................................10

Spatial Discretization ....................................................................................................................... 10

Time Discretization.......................................................................................................................... 12

Boundary Conditions ....................................................................................................................... 12

Head-Dependent Boundaries.................................................................................................. 12

General-Head Boundaries.............................................................................................. 13

Rivers ............................................................................................................................. 13

Simulation of Overlying Geologic Units....................................................................... 13

Specified Flow Boundaries ..................................................................................................... 13

No-Flow Boundaries...................................................................................................... 13

Areal Recharge in Outcrop ............................................................................................ 16

Ground-Water Withdrawal............................................................................................. 16

Hydraulic Property Zones ................................................................................................................ 20

Hydraulic Conductivity........................................................................................................... 20

Faults....................................................................................................................................... 20

Storage .................................................................................................................................... 20

Vertical Hydraulic Conductivity of Layers and Confining Bed.............................................. 20

Model Calibration Procedure ............................................................................................................................. 20

Non-Linear Least-Squares Regression Method ........................................................................................ 20

Model Parameterization ............................................................................................................................ 24

Calibration Data Set .................................................................................................................................. 24

Hydraulic-Head Observations.......................................................................................................... 24

Weights............................................................................................................................................. 24

Sensitivities ...................................................................................................................................... 28

Reasonable Parameter Ranges ......................................................................................................... 28

Model Evaluation ............................................................................................................................................... 28

Optimal Parameter Estimates.................................................................................................................... 28

Model Fit and Model Error ....................................................................................................................... 29

Statistical Analysis of Residuals...................................................................................................... 29

Weighted Hydraulic-Head Residuals............................................................................................... 31

Normality of Weighted Residuals.................................................................................................... 32
IV Contents

Simulated and Observed Hydrographs of Hydraulic Heads.............................................................37

Simulated and Observed Potentiometric Surfaces............................................................................37

Ground-Water Budget................................................................................................................................48

Simulated Aquifer Response to Three Hypothetical Future Withdrawal Rate Scenarios ..................................50

Scenario 1 - Baseline 1990-97 Withdrawal Rates .....................................................................................52

Scenario 2 - Baseline 1990-97 Withdrawal Rates with Reductions in Pine Bluff and El Dorado ............59

Scenario 3 - Increased Withdrawal Rates with Reductions in Pine Bluff and El Dorado .........................59

Model Limitations ..............................................................................................................................................66

Summary and Conclusions .................................................................................................................................66

Selected References............................................................................................................................................69

Appendix - Digital three-dimensional animations of simulated potentiometric surfaces for the three

predictive scenarios................................................................................................................................71

ILLUSTRATIONS

Figure 1. Map showing location of study and model area ................................................................................3

2. Map showing surficial geology and selected structural features of the study area............................7

3. Schematic showing hydrogeologic units within generalized cross section of the

embayment aquifer system..........................................................................................................8

4-7. Maps showing:

4. Model grid of active cells with boundary conditions and river nodes........................................11

5. Hydraulic parameter names and zonations representing rivers and vertical

 hydraulic conductivity of the Cook Mountain Formation .....................................................14

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.......................................................................................................15

7. Hydraulic parameter names and zonations representing recharge rates in the

outcrop and subcrop areas of the Sparta aquifer ....................................................................17

8. Graph showing total ground-water withdrawal from the Sparta aquifer and associated

stress periods for the model area, 1898-1997............................................................................18

9-13. Maps showing:

9. Spatial distribution for ground-water withdrawals represented in stress period 28,

1990-1997 ..............................................................................................................................19

10. Hydraulic parameter names and zonations representing horizontal hydraulic

conductivity and faults ...........................................................................................................21

11. Storage parameter names and zonations .....................................................................................22

12. Hydraulic parameter names and zonations representing vertical hydraulic

conductivity used to simulate confining beds in the Sparta aquifer .......................................23

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.............................................................................................................................27

14. Bar chart showing composite scaled sensitivities (CSS) calculated using the optimal

parameter estimates of the Sparta model calibration for CSS greater than 1.0.........................30

15. Plot showing weighted residuals and weighted simulated values ...................................................32

16. Map showing spatial distribution of weighted hydraulic-head residuals for (A) 1970,

(B) 1985, (C) 1990, and (D) 1997.............................................................................................33

17. Boxplot showing distribution of weighted hydraulic-head residuals ..............................................37

18. Chart showing histogram of residuals for entire calibration data set of 795 

observations from 1970, 1985, 1990, 1997...............................................................................37
Contents V

19. Hydrographs showing simulated and observed hydraulic heads at selected observation

wells, 1900-1997.......................................................................................................................38

20. Map showing simulated and observed potentiometric surface for the Sparta aquifer,

predevelopment.........................................................................................................................45

21. Map showing simulated and observed potentiometric surface for the Sparta aquifer,

1997...........................................................................................................................................46

22. Map showing contoured difference between 1997 simulated hydraulic heads and top

of the Sparta Sand .....................................................................................................................47

23. Graph showing simulated transient ground-water budget for the Sparta aquifer

predevelopment - 1997..............................................................................................................49

24. Graph showing simulated (A) predevelopment and (B) 1997 ground-water budget for

the Sparta aquifer from current and previous Sparta models....................................................51

25-33. Maps showing:

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] .........................................................................................................................53

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 .................................................................................................55

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 .................................................................................................57

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....................................................................................................................60

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.......................................................................................................61

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.....................................................................62

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 ..............................................................................63

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 3 ..............................................................................64

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 3.......................................65
VI Contents

TABLES

Table 1. Description of geologic units and correlation to hydrogeologic units in the

Mississippi Embayment aquifer system....................................................................................... 6

2. Model stress periods and corresponding time periods represented ................................................ 12

3. Parameter names with corresponding optimal parameter estimates and composite-scaled

sensitivities................................................................................................................................. 25

4. Parameter pairs of five largest correlation coefficients .................................................................. 29

5. Weighted residual statistics for model calibration.......................................................................... 30

6. Model residual statistics for the current and previous Sparta models ............................................ 31

7. Ground-water budget comparison between predevelopment and 1997 .......................................... 48

8. Selected volumetric budget and hydraulic-head altitude data from model cells

representing cone of depression centers for model calibration (1997) and for

predictive scenario runs (2027 and steady state)........................................................................ 50

9. Percentage of selected areas where the potentiometric surface of the Sparta aquifer is

below the top of the Sparta Sand................................................................................................ 52
Contents VII

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (° F) as follows:

° F = (1.8 × °C) + 32

Temperature in degrees Fahrenheit (° F) may be converted to degrees Celsius (°C) as follows:

°C = (° F - 32) / 1.8

In this report, vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1929 (NGVD of 

1929). Horizontal coordinate information is referenced to North American Datum of 1927 (NAD 27).

Altitude, as used in this report, refers to distance above or below NGVD of 1929.

Transmissivity: The standard unit for transmissivity is cubic foot per day per square foot times foot of aquifer thickness 

[(ft3/d)/ft]ft. In this report, the mathematically reduced form, foot squared per day (ft2/d), is used for convenience.

CONVERSION FACTORS, ABBREVIATIONS, AND VERTICAL DATUM

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 2.590 square kilometer (km2)

acre 0.4047 hectare

Volume

gallon (gal) 3.785 liter (L)

gallon (gal) 0.003785 cubic meter (m3)

Rate

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

foot per second (ft/s) 0.3048 meter per second (m/s)

foot per year (ft/yr) 0.3048 meter per year (m/yr)

gallon per minute (gal/min) 0.06308 liter per second (L/s)

million gallons per day (Mgal/d) 0.04381 cubic meter per second (m3/s)

inch per year (in/yr) 25.4 millimeter per year (mm/yr)

million cubic feet per day (Mft3/d) 7.481 million gallons per day (Mgal/d)

Hydraulic conductivity

foot per day (ft/d) 0.3048 meter per day (m/d)

Transmissivity

 foot squared per day (ft2/d) 0.09290 square meter per day (m2/d)

Hydraulic gradient

foot per mile (ft/mi) 0.1894 meter per kilometer (m/km)
Abstract 1

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 and Brian R. Clark

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.

INTRODUCTION

The Sparta aquifer is a confined aquifer of 

regional importance within the Mississippi Embayment aquifer system. It consists of varying amounts of 

unconsolidated sand, interstratified with silt and clay 

lenses within the Sparta Sand of the Claiborne Group. 

It extends through eastern and southeastern regions of 

Arkansas, northern Louisiana, and portions of Texas, 

Mississippi, and Tennessee (fig. 1). The Sparta aquifer 

of southeastern Arkansas and north-central Louisiana 

is a major source of water for municipal, industrial, and 

agricultural uses. Approximately 333 million gallons 

per day (Mgal/d) was pumped from the aquifer in 

Arkansas and Louisiana in 2000 (T.W. Holland, U.S. 

Geological Survey, oral commun., 2002). Historically, 

the Sparta aquifer has provided abundant water of high 

quality. In recent years, however, the demand for water 

in some areas has resulted in withdrawals from the 

Sparta aquifer that substantially exceed recharge to the 

aquifer. Considerable drawdown has occurred in the 

potentiometric surface, and water users and managers 

question the ability of the aquifer to supply water for 

the long term. As is typical in confined systems, large 

withdrawals have resulted in the development of large 

cones of depression that are centered beneath the Grand 

Prairie area (irrigated farm land between the Arkansas 

and White Rivers) and the cities of Pine Bluff and El 

Dorado in Arkansas, and Monroe in Louisiana (Joseph, 

1998b). Hydraulic heads (often used interchangeably 

with water-level altitude or potentiometric surface) in 

the areas of these cones have declined at rates greater 

than 1 foot per year (ft/yr) for more than a decade in 

much of southern Arkansas and northern Louisiana and 

are currently below the top of the Sparta Sand (though 

not necessarily below the tops of the producing sand 

units) in parts of Union and Columbia Counties, 

Arkansas, and in several parishes of Louisiana. The 

cones of depression centered beneath El Dorado and 

Monroe have coalesced across 60 miles (mi) to form a 

single, large, elongated depression. A smaller cone of 

depression centered beneath Magnolia, Arkansas, has 

diminished substantially after the impoundment of 

nearby Lake Columbia and installation of a surfacewater supply system in March 1993 that resulted in 

decreased withdrawals from the Sparta aquifer. Continued, heavy withdrawals in the Sparta aquifer, where 

alternative water sources are not considered or available, will result in continued expansion of the cones of 

depression as well as increased drilling and pumping 

costs, decreased aquifer yield, and reduced water quality.

To address these concerns, in 1985, the U.S. 

Geological Survey (USGS), in cooperation with the 

Arkansas Soil and Water Conservation Commission 

(ASWCC) and the Louisiana Department of Transportation and Development (DOTD), began a project to 

study the hydrogeologic characteristics of the Sparta 

aquifer and evaluate the regional effects of increased 

pumpage on hydraulic heads in the aquifer. The primary product of the project was a computer model of 

ground-water flow in the Sparta aquifer (Fitzpatrick 

and others, 1990; McWreath and others, 1991) calibrated and verified using 1970 and 1985 observation 

data, respectively, hereafter, referred to as the “previous Sparta model.” In 1991, this model was updated 

and verified (Kilpatrick, 1992) through 1989 by the 

USGS in cooperation with the ASWCC and selected 

scenarios of future ground-water withdrawals in
Introduction 3

Figure 1. Location of study and model area.

Active Model

Area Boundary

Hodge

Ruston

Monroe

Camden

Belzoni

Bastrop

Magnolia

Magnolia

Cleveland

El Dorado

Springhill

Pine

Bluff

West

Monroe

Mississippi

Red

Saline

Cache

Arkansas

Mississippi

Mississippi

Bayou

White

Dorcheat

River

Ouachita

Bodcau

Creek

River

River

River

River

River

River

River

Stuttgart

Grand

Prairie

94° 93° 92° 91° 90° 89° 88° 87°

30°

31°

32°

33°

34°

35°

36°

37°

0 60 120 Miles

0 60 120 Kilometers

Mississippi Embayment Boundary

Sparta Aquifer Boundary

(Modified from Arthur and Taylor, 1990)

Southern extent of aquifer with

water having dissolved-solids

concentrations less than 10,000

milligrams per liter

Arkansas

Mississippi

Alabama

Tennessee

Missouri

Texas Louisiana Oklahoma

Kentucky
4 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

Union County, Arkansas, were simulated. In 1997, the 

USGS, in cooperation with the ASWCC and DOTD, 

again updated and reverified the same model with 

pumping stresses through 1997, and five potential 

pumping scenarios were evaluated (Hays and others, 

1998). In 2000-2002, the USGS worked cooperatively 

with both the Memphis District of the Corps of Engineers (MCOE) and the ASWCC to modify and recalibrate the previous Sparta model for the purpose of 

evaluating potential pumping scenarios and optimizing 

withdrawal rates to determine sustainable yield for the 

Sparta aquifer. 

Purpose and Scope

The purpose of this report is to document the 

modification, reconstruction, and recalibration of the 

previous Sparta model to improve the ability of the 

model to simulate aquifer behavior, and describe the 

results of model simulations of hypothetical future 

water withdrawals. The model will be used as a management tool to simulate future hydraulic heads given 

various projected water-use demands. In addition, the 

model will be used in future cooperative studies to 

develop a conjunctive-use optimization model for 

determining sustainable yield for the Sparta aquifer. 

Modifications to the previous Sparta model 

include rediscretizing the model grid, extending the 

model area northward, revising the surfaces representing the top and bottom of the Sparta Sand, and changing to the most recent version of MODFLOW, from 

MODFLOWARC to MODFLOW-2000. Reconstruction of the Sparta model includes changing representation of model layers and various boundaries. The 

calibration methodology and procedure are discussed 

along with results from three hypothetical withdrawal 

rate scenarios. 

Previous Studies

The previous Sparta model, constructed by Fitzpatrick and others (1990) and McWreath and others 

(1991) to simulate hydraulic heads from 1889-1985, 

was calibrated and verified using 1970 and 1985 

hydraulic-head observations and applied to the period 

1985-2005. The model code used was the modular 

finite-difference ground-water flow model (MODFLOW 88) developed by McDonald and Harbaugh 

(1988). MODFLOW simulates flow in three dimensions using a block-centered, finite-difference 

approach to the solution of the partial-differential equation for flow. These Sparta model reports define the initial goals of the model and describe model testing and 

simulation results for the pumping scenarios posed. 

Detailed discussion of the history of Sparta aquifer 

water use, study area hydrogeologic setting, and a 

description of the aquifer system also are included in 

the two reports and are not repeated in detail here.

Original development of the previous Sparta 

model was based on information available on the 

hydrogeology of the region provided through the U.S. 

Geological Survey’s Gulf Coast Regional Aquifer System Analysis (RASA). The Gulf Coast RASA included 

a large-scale hydrogeologic analysis of the region that 

includes the Sparta aquifer. Hydrogeologic framework 

characterization and initial parameter estimates for 

construction of the previous Sparta model largely were 

based upon Gulf Coast RASA results (Williamson and 

others, 1990; Arthur and Taylor, 1990; 1998). Additional data were obtained from reports by Broom and 

others (1984), Hosman (1982), Payne (1968), Trudeau 

and Buono (1985), and Petersen and others (1985). 

These reports present information on the distribution of 

hydrogeologic characteristics and ground-water conditions, and provide additional hydrogeologic information for the Sparta aquifer including boundaries, faults, 

transmissivity, storage coefficients, specific yield, 

recharge, and hydraulic heads.

Kilpatrick (1992) updated pumping data in the 

model for 1985-1989 and performed a verification. The 

model was used to predict the effects of six hypothetical pumping scenarios (1990-2019) on hydraulic heads 

in the area of El Dorado, Arkansas.

Hays and others (1998) converted the model to 

run in MODFLOWARC, a version of MODFLOW that 

allows interface with a geographical information system (Orzol and McGrath, 1992). The model conversion 

was successfully validated to ensure that functionality 

and output were unchanged from originally reported 

results. Hays and others (1998) then updated pumping 

data in the model for 1990-1997 and performed a reverification. This model was used to predict the effects of 

five hypothetical pumping scenarios (1998-2027) on 

hydraulic heads in southeastern Arkansas and northcentral Louisiana. 

Although not used directly in the calibration of 

the current Sparta model described in this report, the 

1999 (Joseph, 2000) and 2001 (Schrader, 2003) potentiometric maps of the Sparta aquifer and additional 
Hydrogeology of the Sparta Aquifer 5

hydrogeologic information by Brantly and others 

(2002) were useful in analyzing model results for withdrawal scenarios after the 1997 calibration.

General Description of the Previous 

Sparta Model

The previous Sparta model consists of two layers 

discretized on a variably spaced grid of 113 rows and 

95 columns, which represents a 267-mile by 218-mile 

area. Active model cells constitute 8,996 of 10,735 grid 

cells. Cell dimensions range from 1 mile by 1 mile to 

10 miles by 23 miles. Hydraulic heads are simulated 

only in layer 2, which represents the Sparta aquifer. 

Layer 1, which represents the overlying Mississippi 

River Valley alluvial and Cockfield aquifers, is modeled as a constant-head layer; heads remain unchanged 

throughout the simulation and are a constant source of 

water to the simulation. Flow from layer 1 to layer 2, 

through the Cook Mountain confining unit, is controlled by the vertical hydraulic conductance assigned 

to layer 1. Because the Sparta aquifer is underlain by 

the relatively impervious Cane River confining unit, 

the base of layer 2 is modeled as a no-flow boundary. 

Lateral boundary conditions are a combination of noflow and specified-head boundaries. The specifiedhead boundaries are at the north, east, and south boundaries of the model; specified heads change at designated intervals throughout the simulation period to 

account for long-term Sparta aquifer hydraulic-head 

declines since predevelopment. Hydraulic conductivities used for computation of transmissivity of the 

Sparta aquifer ranged from 1 to 35 feet per day (ft/d). 

Vertical hydraulic conductivities used for computation 

of conductances of the Cook Mountain confining unit 

ranged from 9x10-6 to 3x10-4 ft/d. The calibrated storage coefficient for the Sparta aquifer was 1x10-4 (Kilpatrick, 1992). More comprehensive discussions of 

model construction and calibration are included in the 

Fitzpatrick and others (1990) and McWreath and others 

(1991). The period for model simulation is from 1898 

(predevelopment) to 1997. During initial model construction and calibration, the period 1898 to 1985 was 

divided into 4 simulation periods (intervals for adjusting specified heads) and 25 stress periods (intervals for 

changing ground-water withdrawals). Kilpatrick 

(1992) represented the period 1986-1989 with an additional simulation period and stress period. Hays and 

others (1998) represented the period 1990-1997 by 1 

additional simulation period and stress period for a 

total of 6 simulation and 27 stress periods.

Model Area Description

The model area includes southern and east-central Arkansas, northern Louisiana, and northwestern 

Mississippi (fig. 1). This area lies within the Mississippi Alluvial Plain and West Gulf Coastal Plain sections of the Coastal Plain physiographic province 

(Fenneman, 1938). Land-surface altitudes range from 

more than 500 ft along the western boundary and outcrop recharge zones to less than 100 ft along the Mississippi River. The principal rivers draining the study 

area are the Mississippi, Arkansas, Saline, Ouachita, 

and Red Rivers, Bayou Dorcheat, and Bodcau Creek. 

Mean annual precipitation is approximately 50 inches 

(Freiwald, 1985). Water withdrawn from the Sparta 

aquifer in the study area is used for municipal supply, 

agriculture, aquaculture, and manufacturing of forest 

products, chemicals, and other industrial products. 

HYDROGEOLOGY OF THE SPARTA

AQUIFER

Detailed description of the hydrogeology of the 

Sparta aquifer is discussed in numerous reports including Payne (1968), Hosman and others (1968), Petersen 

and others (1985), and Fitzpatrick (1990). Therefore, 

the following is only a brief summary of the hydrogeology of the Sparta aquifer.

Hydrogeologic Units and Geologic Setting

The Sparta aquifer is an aquifer of regional 

importance within the Mississippi Embayment aquifer 

system, and comprises a sequence of unconsolidated 

sand, silt, and clay units within the Sparta Sand of Claiborne Group. The Mississippi Embayment (fig. 1) is a 

structural basin with an axis trending northward 

roughly following the Mississippi River (Petersen and 

others, 1985). The Sparta Sand extends through eastern 

and southeastern regions of Arkansas, northern Louisiana, western Mississippi, and portions of Texas and 

Tennessee (fig. 2). The western extent in Arkansas parallels the “Fall Line” separating the embayment from 

the mountainous highlands. Surface materials in a large 

part of the area are Quaternary-age alluvial and terrace 
6 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

deposits. The Sparta Sand, ranging in total thickness 

from 100-1,000 feet, is stratigraphically positioned 

between the overlying Cook Mountain Formation and 

underlying Cane River Formation, both Tertiary-age 

units of the Claiborne Group (table 1). These units generally dip and thicken from the east and west outcrop 

areas toward the axis of the embayment where they are 

deeply buried in the subsurface (fig. 3). The Cook 

Mountain and Cane River Formations are predominantly clay units with thickness ranges of 100-150 ft 

and 300-800 ft, respectively. North of 35 degrees latitude, the Sparta Sand becomes part of the Memphis 

Sand as the Cane River Formation undergoes a facies 

change from marine clays to sand (Hosman and others, 

1968).

Aquifer System Description

The Sparta aquifer outcrops and is unconfined on 

both the west and east sides of the Mississippi Embayment, and then becomes confined as it dips toward the 

axis of the embayment and southward toward the Gulf 

of Mexico. It is confined above by the Cook Mountain 

confining unit and below by the Cane River confining 

unit (fig. 3). Sand within the aquifer generally ranges in 

thickness from 200 to 600 ft. Sources of flow to the 

Sparta aquifer are direct recharge from precipitation on 

the outcrop, recharge from rivers in the outcrop, downward flow from the alluvial aquifer where the Sparta 

subcrops (intersects the overlying alluvium), and leakage from confining units where the vertical hydraulic 

gradient is towards the Sparta Sand. Discharge from the 

Sparta aquifer occurs by withdrawal from wells and by 

natural discharge. Natural discharge is primarily leakage through the overlying and underlying confining 

beds to adjacent units with lower hydraulic heads and 

to rivers in the outcrop. Ground-water flow in the 

Sparta aquifer generally coincides with structural dip 

and is from the outcrop areas to the axis of the embayment and southward toward the gulf coast (fig. 3). This 

flow pattern dominated the regional movement of water 

in the Sparta aquifer prior to aquifer development 

(Reed, 1972). However, continued, large withdrawals 

caused cones of depression in the potentiometric surface since development that have altered the natural 

flow paths toward the centers of these depressions. An 

additional factor affecting ground-water flow is the 

presence of faults in southwest Arkansas. Individual 

faults are not well defined, so a fault zone is identified 

on figure 2.

Table 1. Description of geologic units and correlation to hydrogeologic units in the Mississippi Embayment aquifer system 

(modified from Petersen and others, 1985)

Group Geologic Unit

Maximum

thickness

(feet) Lithology

Hydrogeologic

unit

Alluvium and terrace deposits 200

Base - gravel

Surface - sand, silt, clay

Mississippi River Valley

alluvial aquifer

Jackson Undifferentiated 300 Clay; some fine sand

Vicksburg-Jackson

confining unit

Claiborne

Cockfield Formation <300 Lignitic sand, carbonaceous clay Cockfield aquifer

Cook Mountain Formation 150

Carbonaceous clay, some lignitic 

sand

Cook Mountain

confining unit

 Memphis Sand

Sparta Sand 1,000 Sand; some clay interbeds

Sparta Greensand aquifer

aquifer Middle confining unit

 El Dorado aquifer

Memphis aquifer

Cane River Formation 800 Clay, sand Cane River confining

unit

Carrizo Sand 400 Fine to medium sand Carrizo aquifer

Wilcox Undifferentiated 1,100 Interbedded sand and clay, lignitic Wilcox Group aquifers
Hydrogeology of the Sparta Aquifer 7

Figure 2. Surficial geology and selected structural features of the study area.

Fall Line

FAULT

ZONE

Qal

Tc

Tm

Tw

Ts

Tm

Tcl

Tj/Tv

Tc

Tcm

Tcr

Ts

Ts

Tcr

Tc

Ts

Tc

Qal Tj/Tv

Tj/Tv

Tw

Tcr

Tj/Tv

Ts

Tmi

Tcl

Tcm

Tw Tcm

Tcl

Tcr

Qlg

Qlg

Tcm

Tw

Tc

Tw

Tms

Tcz

Tmi

Tw

Tmi

Qlg

Tcz

Tcz

Tw

Tw

Ts

Tw

Tw

Tw

Tcr

Arkansas

Louisiana

Mississippi

Monroe Uplift

Sabine Uplift

Tennessee

Texas

94° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

Geology modified from Hosman (1988)

93°

EXPLANATION

Geology

Ts Sparta Sand

Tcm Cook Mountain Formation

Tj/Tv Vicksburg Group and Jackson Group

Tc Cockfield Formation

Tw Wilcox Group

Tcz Carrizo Sand

Tmi Midway Group

Tcr Cane River Formation

Qal Alluvial, Terrace deposits

Tcl Claiborne Group Undifferentiated

Tms Memphis Sand

Qlg Loess, silt, sand, gravel deposits

Tm Undifferentiated
8 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

Figure 3. Hydrogeologic units within generalized cross section of the Mississippi Embayment aquifer system.

WEST EAST

MISSISSIPPI RIVER VALLEY

ALLUVIAL AQUIFER

GROUND-WATER

FLOW

DIRECTION

GROUND-WATER

FLOW

DIRECTION

Qt

OUTCROP

AREA

OUTCROP

AREA

QUATERNARY TERRACE DEPOSITS

VICKSBURG - JACKSON CONFINING UNIT

COCKFIELD AQUIFER

SPARTA AQUIFER

WILCOX GROUP AQUIFERS

CARRIZO AQUIFER

CANE

RIVER CONFINING

UNIT

COOK MOUNTAIN CONFINING UNIT

NOT TO SCALE Geology modified from Arthur and Taylor (1990)

Sparta Aquifer Development and 

Associated Effects

Rates of flow into and discharge from the Sparta 

aquifer are controlled by hydraulic gradients, which are 

affected by ground-water withdrawal from the aquifer. 

The term “predevelopment” used in this report indicates aquifer conditions before 1898 or before the aquifer was stressed by appreciable ground-water 

withdrawal. The term “post-development” in this report 

indicates aquifer conditions after development of the 

aquifer began.

The earliest known withdrawals from the Sparta 

aquifer in the study area began in 1898 for industrial 

use in Pine Bluff, Arkansas. About 1920 substantial 

withdrawals totaling an estimated 10 million gallons 

per day (Mgal/d) or 1.3 million cubic feet per day 

(Mft3/d) began in the aquifer for rice irrigation in the 

Grand Prairie area. Since that time, the aquifer has been 

used heavily for industrial and municipal supply, providing water of excellent quality. Ground-water withdrawal from wells altered the predevelopment 

potentiometric-surface gradients and changed the naturally occurring flowpaths in the aquifer system. Continued ground-water withdrawal through time has caused 

the potentiometric surface to decline in the aquifer 

(Joseph, 1998b; Schrader, 2003). Wells completed in 

the Sparta aquifer generally produce 100-500 gallons 

per minute (gal/min), with less common rates up to 

1,200 gal/min. Withdrawals from the aquifer in Arkansas and Louisiana totaled 355 Mgal/d or 47.5 Mft3/d in 

1995 (Joseph, 1998b) and decreased to 333 Mgal/d or 

44.6 Mft3/d in 2000 (Terry Holland, U.S. Geological 

Survey, written commun., 2002). The principal areas of 

ground-water withdrawal in the study area are in El 

Dorado and Pine Bluff, Arkansas, the Grand Prairie 

area, Monroe and West Monroe, Louisiana, and Cleveland, Mississippi. 

GROUND-WATER FLOW MODEL

The transient, three-dimensional, numerical 

model of ground-water flow in the Sparta aquifer 

described in this report is a modified and reconstructed 

version of the previous flow model described in Fitzpatrick and others (1990), McWreath and others 

(1991), Kilpatrick (1992), and Hays and others (1998). 
Ground-Water Flow Model 9

Although the last verification of the previous Sparta 

model indicated that it was simulating conditions in the 

aquifer within acceptable error for study goals at that 

time, analysis of reverification results identified specific areas where recalibration could improve the ability of the model to simulate behavior in areas with steep 

hydraulic gradients and increasing withdrawals (Hays 

and others, 1998). Because the Sparta model is being 

maintained as a tool to improve understanding of the 

aquifer and help with management issues, it was necessary to develop, construct, and calibrate the current 

Sparta model. Modifications from the previous Sparta 

model incorporated more hydrologic and geophysical 

data since the 1985 calibration and were designed to 

meet the current needs of Federal, State, and local 

water managers and planners. Modifications to the previous Sparta flow model include rediscretizing the 

model grid, extending the model area northward, revising the surfaces representing the top and bottom of the 

Sparta Sand, and changing the model to MODFLOW2000, the most recent version of the model code from 

the USGS. Reconstruction of the previous Sparta 

model included changing representation of model layers and various boundaries. The reconstructed model, 

referred hereafter as the current model, was calibrated 

using both trial and error and parameter-estimation 

techniques to simulate hydraulic heads from predevelopment (1898) to 1997. 

Numerical Method

Transient, three-dimensional ground-water flow 

in a confined, anisotropic, heterogeneous aquifer is 

described by the following partial differential equation 

where the partial derivatives represent hydraulic conductivity in three dimensions:

(1)

where x, y are cartesian coordinates in the horizontal 

direction (L);

z is cartesian coordinate in the vertical direction (L);

Kxx, Kyy, Kzz is hydraulic conductivity in the 

x, y, and z directions (LT-1);

h is hydraulic head (L);

W is volumetric flux per unit volume (T-1);

Ss is specific storage (L-1); and 

t is time.

For this report, the modular three-dimensional 

(3D) finite-difference code, USGS MODFLOW-2000 

(Harbaugh and others, 2000), was used to approximate 

the differential equation, and the preconditioned conjugate gradient solver (Hill, 1990) was used for the 

numerical solution technique. The aquifer is subdivided into a set of discrete blocks in space and time. 

The blocks represent cells of porous material within 

which the hydraulic properties are the same. Each cell 

then has a finite-difference equation describing the 

flow through it. These equations can be solved for 

either steady state to simulate equilibrium conditions, 

or transient to simulate changes in stresses over fixed 

periods of time. The model simulates 100 years of system response to stress by dividing the model into stress 

periods with each stress period representing a period of 

time for which ground-water withdrawal rates (water 

use) are relatively unchanged. MODFLOW-2000 provides a parameter estimation feature (Hill and others, 

2000) that uses a nonlinear least-squares regression 

method to aid in estimating hydrologic properties and 

to further evaluate the model. The aquifer is subdivided 

into a set of discrete blocks in space and time. The 

blocks represent cells of porous material within which 

the hydraulic properties are the same. Each cell then 

has a finite-difference equation describing the flow 

through it. 

Model Assumptions

A model is a simplification of a process or a system. The objective of the current model is to maintain 

a balance between simplicity and adequate representation of the complex aquifer system. Simplifications and 

assumptions used in the development of this flow 

model include: (1) two layers are adequate to represent 

the Sparta aquifer; (2) hydraulic properties are homogeneous within a model cell of the finite-difference 

grid; (3) the system is horizontally isotropic; (4) pumpage in a model cell may represent multiple wells, but is 

simulated as a single withdrawal from the cell center; 

(5) pumpage throughout a stress period is constant and 

represents an average pumping rate throughout that 

time period; and (6) recharge from precipitation is constant throughout the entire model simulation. 

∂

∂x

----- Kxx

∂h

∂x

-----     ∂

∂y

----- Kyy

∂h

∂y

-----     ∂

∂z

----- Kzz

∂h

∂z

-----   + +   – W Ss

∂h

∂t = -----
10 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

Model Development

The following is a description of how the physical system was represented and integrated into the current numerical model. In addition, major differences 

from the previous Sparta model are discussed, however, 

the interested reader should refer to Fitzpatrick and others (1990) for complete details of the previous Sparta 

model to better understand differences between these 

models.

Spatial Discretization

The current model area is discretized into a 

finite-difference grid of 267 rows by 218 columns of 

uniform 1-square mile (mi2) cells covering 58, 206 mi2. 

The grid is aligned roughly with the Fall Line with the 

y-coordinate axis at an azimuth of approximately 

N.45°E. In the previous Sparta model developed by 

Fitzpatrick and others (1990), the grid was variably 

spaced ranging in rectangular size from 10 by 23 mi to 

1 mi2 with identical grid orientation. The uniform grid 

spacing of 1 mi2

 in the current model improves numerical accuracy in areas where hydraulic gradients are 

large and continue to steepen or where new cones of 

depression have formed since the previous Sparta 

model was developed in 1985.The active model area 

covers 38,220 mi2

 with 38,220 active model cells representing the Sparta aquifer (fig. 4). The active model 

area was extended northward from the north boundary 

of the previous Sparta model. This extension goes 

northward beyond the facies change where the Sparta 

Sand, Cane River Formation, and Carrizo Sand become 

the single hydrogeologic unit of the Memphis aquifer. 

The extension of the active model area northward was 

necessary to adequately cover additional counties of 

Arkansas where aquifer withdrawals are causing substantial hydraulic-head declines. Northward beyond the 

facies change of the Cane River Formation, properties 

and geometry of the Memphis aquifer are used in the 

model. Clays of the Wilcox Group are assumed to provide adequate confining conditions to justify the bottom of the model as a no-flow boundary in that area. 

The Sparta Sand thickness varies spatially. The 

current model is a two-layer representation of the upper 

and lower water-bearing zones in the Sparta aquifer 

separated by a quasi-3D confining bed representing a 

semiconfining unit of clay that exists, but is not well 

defined, in southern Arkansas and north-central Louisiana (Baker and others, 1948; Broom and others, 1984). 

This differs from the previous two-layer Sparta model 

in which only one layer, the lower one, was used to simulate hydraulic heads in the Sparta aquifer and the overlying layer represented the Cockfield aquifer as a 

constant-head boundary. These layers in the previous 

Sparta model were separated with a quasi-3D confining 

unit to simulate vertical flow through the clay confining 

unit of the Cook Mountain Formation. The influence of 

overlying aquifers on the Sparta aquifer are represented 

in the current model by a head-dependent boundary 

discussed in a later section.

Surfaces representing the Sparta Sand top and 

total thickness were modified from the previous Sparta 

model. The altitude of top of the Sparta Sand (layer 1) 

is based on a composite map created by digitizing separate, but similar maps of the top of the Sparta Sand and 

selectively combining them. Petersen and others (1985) 

cover Arkansas, and Brantley and others (2002) cover 

Louisiana in detail. Pugh and others (2000) provide 

additional detail in selected areas of Arkansas. The 

Gulf Coast RASA publication series provided regional 

coverage to substitute any missing information from 

the more detailed maps to cover the model area (Grubb, 

1998; Hosman, 1996; Hosman and Weiss, 1991). The 

composite map provided a detailed representation of 

the top of the Sparta Sand based on all available information for use in the current model.

The Sparta Sand comprises layers of sand interbedded with clay lenses and discrete clay units. Based 

on data from the Gulf Coastal RASA study (A.K. Williamson, U.S. Geological Survey, written commun., 

2001; Hosman and Weiss, 1991) and geophysical logs 

from Union County and surrounding areas, the thickness of the Sparta aquifer was calculated by summing 

the thickness of the discrete sand beds. From the total 

sand thickness, 60 percent was assigned to the lower 

water-bearing zone (layer 2) and the remaining 40 percent was assigned to the upper water-bearing zone 

(layer 1). The remaining thickness of the total formation is assumed to be clay and is represented in the 

model as a quasi-3D confining bed. Therefore, the 

thickness associated with the quasi-3D confining bed is 

the total formation thickness based on data from the 

Gulf Coastal RASA study minus the total sand thickness. The continuous confining unit averaged approximately 100 ft thick. The extension of this confining unit 

outside the Union County area also is variable, either 

representing an assumed discrete clay unit of defined 

thickness or a combination of interbedded clay lenses 

which combine to effectively restrict vertical flow. The

bottom of the Sparta Sand was computed as the top of

the Sparta Sand minus the total formation thickness.
Ground-Water Flow Model 11

Figure 4. Model grid of active cells with boundary conditions and river nodes.

ARKANSAS

LOUISIANA

MISSISSIPPI

Winn

Lee

Union

White

Rapides

Union

Hinds

Drew

Yazoo

Clark

Caddo

Ashley

Desha

Rankin

Bolivar

Copiah

Saline

Bossier

Lonoke

Pulaski

Arkansas

Grant

Holmes

Chicot

Grant

Miller

Panola

Cross

Dallas

Prairie

Phillips

Bienville

Tensas

Tate

Madison

Jefferson

Poinsett

Nevada

Avoyelles

Columbia

Ouachita

La Salle

Bradley

Warren

Adams

Monroe

Jackson

Lincoln

Lincoln

Carroll

Claiborne

LeFlore

Calhoun

Franklin

Tunica

Webster

Ouachita

Morehouse

Jackson

Catahoula

Concordia

Hempstead

Coahoma

Franklin

Simpson

Craighead

Sunflower

Richland

De Soto

Washington

Lincoln

Woodruff St. Francis

Caldwell

Clevleand

Hot Spring

Crittenden

Lafayette

Sharkey

Tallahatchie

Jefferson

Clairborne

Quitman

Issaquena

Red River

Grenada

Humphreys

West

Carroll

East

Carroll

Madison

TENNESSEE

TEXAS

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

ghb_7

ghb_6

ghb_5

ghb_4

ghb_3

ghb_2

ghb_1

EXPLANATION

General-head boundary

River cells

Facies change transition zone

of which the southern edge was

the approximate northern extent

of the previous Sparta model

(Fitzpatrick, 1990)

General head boundary and

associated parameter name

Model grid

Inactive model area

No flow boundary

ghb_6
12 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

Time Discretization

Ground-water flow in the Sparta aquifer in the 

current model is simulated from 1898 through 1997. 

Steady-state conditions are simulated prior to 1898 and 

represent predevelopment aquifer conditions. This was 

done to obtain a head distribution that would not vary 

with time and would be in equilibrium with model 

boundary conditions. MODFLOW 2000 allows the 

user to define steady-state and transient stress periods 

in the same simulation. Therefore, stress period 1 in the 

model represents steady-state conditions of predevelopment. The transient simulation from 1898 to 1997 is 

divided into 27 stress periods for a total of 28 stress 

periods in the model (table 2). Stress period lengths 

were selected on the basis of intervals of relatively constant ground-water withdrawals; pumping stresses in 

the model are constant for the duration of a stress 

period. The length of each stress period ranges from 1 

to 20 years. Because withdrawal amounts generally are 

reported as annual totals, the minimum stress period is 

1 year and pumpage rates are averaged over the entire 

year. With this temporal discretization, seasonal 

effects, such as irrigation wells, are not simulated. 

However, because the Sparta aquifer is predominantly 

used for industry and public supply, error because of 

seasonal fluctuations in water use is minimal. In addition, the objective is to simulate effects of stress over 

long periods of time; therefore, seasonal variations are 

not examined in this model. 

Boundary Conditions

Model boundaries determine the locations and 

quantities of simulated flow into and out of the model; 

therefore, the selection of appropriate boundaries for 

the model is a major concern in any modeling effort. 

The selection of model boundaries for the aquifers in 

the current model is based on a conceptual interpretation of the flow system developed using information 

reported by Payne (1968), Hosman and others (1968), 

Petersen and others (1985), and that of the previous 

Sparta model (Fitzpatrick and others, 1990). Boundaries require the definition of model input variables, 

also called parameters. 

Head-Dependent Boundaries

Head-dependent boundaries represent a potentially infinite supply of water, whereby rate of flow 

from or to the boundary is affected by changes in 

hydraulic head within the aquifer and the resultant 

hydraulic gradient. Appropriate uses of this boundary 

type to represent hydrologic conditions include rivers, 

lakes, and adjacent geologic units. Flows into and out 

of the aquifer can change over time with changes in 

aquifer hydraulic head because of system stresses, such 

as ground-water withdrawals.

Table 2. Model stress periods and corresponding time 

periods represented

Stress

period

Start of

year

End of

year

Total

years

1 Steady state with no pumping

2 1898 1899 2

3 1900 1919 20

4 1920 1924 5

5 1925 1929 5

6 1930 1930 1

7 1931 1934 4

8 1935 1937 3

9 1938 1942 5

10 1943 1943 1

11 1944 1947 4

12 1948 1949 2

13 1950 1951 2

14 1952 1954 3

15 1955 1956 2

16 1957 1957 1

17 1958 1962 5

18 1963 1964 2

19 1965 1967 3

20 1968 1969 2

21 1970 1970 1

22 1971 1972 2

23 1973 1977 5

24 1978 1980 3

25 1981 1982 2

26 1983 1985 3

27 1986 1989 4

28 1990 1997 8
Ground-Water Flow Model 13

General-Head Boundaries

Head-dependent boundaries used to represent 

lateral inflows to and outflows from the Sparta aquifer 

are represented in the current model using the MODFLOW general-head boundary package. The conductance term of the general-head boundary was the 

parameter considered for inclusion in the set of parameters to be adjusted during the parameter estimation 

process. These boundaries are shown in figure 4.

The general-head boundaries in the model on the 

north and south do not represent natural boundaries 

based on structural features; however, they are artificially placed far enough from primary areas of concern 

and interest that boundary effects are minimal. The 

southern boundary in Louisiana is beyond the radius of 

influence of any significant pumping center and thus 

boundary effects are minimal. The southern boundary 

in Mississippi and the northern boundary in Arkansas, 

while not totally beyond the radius of influence of 

pumping outside the boundary, are located such that the 

effects on hydraulic heads in major areas of interest of 

the model in southeastern Arkansas and north-central 

Louisiana are negligible. General-head boundaries in 

the current model differ from the previous Sparta 

model, which used constant-head boundaries varied 

over defined simulation periods to represent lateral 

flows into and out of the aquifer system. 

Rivers

Head-dependent flow representing rivers is simulated using the river package of MODFLOW-2000 

(Harbaugh and others, 2000). In the river package, flow 

between a stream and the underlying cell of the groundwater flow model is a function of the altitude or stage 

of the stream; the simulated hydraulic head in the cell; 

the length (L) and width (W) of the stream in the cell; 

and the altitude, vertical hydraulic conductivity (K), 

and thickness (M) of the streambed. For rivers simulated in this model, the streambed conductance (KLW/

M) was the parameter considered for inclusion in the 

set of parameters to be adjusted during the parameterestimation process. 

Stream segments from 15 rivers and streams in 

Arkansas and Louisiana were simulated in the model in 

the Sparta outcrop area (fig. 5). The simulated streams 

include the Bayou Deview, Cache River, White River, 

Cypress Bayou, Arkansas River, Saline River, Ouachita 

River, Smackover Creek, Bodcau Creek, Caney Creek, 

Bayou Dorcheat, Black Lake Bayou, Saline Bayou, and 

Dugdemona River. Streams were initially selected 

based on mean annual flows greater than 1,000 cubic 

feet per second (ft3

/s) then smaller streams were 

included to better define the ground-water/surfacewater interaction in the outcrop area. Streamflows and 

equivalent stream stages (fig. 6) were prorated 

upstream and downstream using mean annual flow data 

for the period of record from nearby USGS streamflow 

gaging stations located within the reaches being modeled based on discharge/drainage area relations (Elton 

Porter, U.S. Geological Survey, written commun., 

2001). 

Simulation of Overlying Geologic Units

Leakage from overlying geologic units was simulated in the current 2-layer model using the MODFLOW-2000 river package described previously. The 

specified stage represents water levels of the Cockfield 

aquifer (fig. 6). Where the Cockfield aquifer is absent, 

the stage represents hydraulic heads in Quaternary-age 

aquifers or in the Cook Mountain Formation where 

they are hydraulically connected to the Cockfield aquifer. The length and width of the “streambed” are the 

cell dimensions. The altitude of the “streambed” represents the top of the Sparta Sand and the “streambed 

thickness” represents the Cook Mountain Formation 

thickness. Using this boundary condition, the vertical 

hydraulic conductivity of the “streambed,” which represents the vertical hydraulic conductivity of the Cook 

Mountain Formation (fig. 5), is the parameter considered for inclusion in the set of parameters to be adjusted 

during the parameter-estimation process. 

Construction and explanation of the contoured 

potentiometric surface of the overlying aquifers (Cockfield and Quaternary-age aquifers) are discussed in 

detail in Fitzpatrick and others (1990). These were 

modified to provide additional input data in the 

extended area north of the Cane River Formation facies 

change. Changes in hydraulic head in the Cockfield 

aquifer through time relative to those in the Sparta 

aquifer were small and resulted in negligible effects on 

system response in the Sparta aquifer (Ackerman, 

1987; Brantley and Seanor, 1996; Joseph, 1998a; 

Trudeau and Buono, 1985).

Specified Flow Boundaries

No-Flow Boundaries

The Cane River confining unit, which underlies 

the Sparta aquifer, is considered relatively impervious 

(Petersen and others, 1985) and is represented in the 
14 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

Figure 5. Hydraulic parameter names and zonations representing rivers and vertical hydraulic conductivity of the Cook 

Mountain Formation.

Red

River

White River

0.000031 ft/d

Saline

River

Cache

River

Caney

Creek

Bodcau

Creek

Ouachita

River

Arkansas

River

0.00931 ft/d

Smackover

Creek

Dugdemona

River

Saline

Bayou

Bayou Deview

Arkansas

Louisiana

Bayou

Dorcheat

Cypress Bayou

Texas

Black Lake

Bayou

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model Area

Boundary

Simulated rivers and streams

Rivers and streams with

corresponding parameter

name

EXPLANATION

Vertical hydraulic conductivity

specified in river package

representing the presence

or absence of the Cook

Mountain Formation with

corresponding parameter name

Presence (0.000031 ft/d)

Absence (0.00931 ft/d)

(ck_riv)

(absent_ck)

Tennessee

Mississippi
Ground-Water Flow Model 15

Figure 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.

Arkansas

Louisiana

Tennessee

Mississippi

Texas

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

EXPLANATION

40 to 50

50 to 75

75 to 100

100 to 125

125 to 150

150 to 175

175 to 200

200 to 225

225 to 250

250 to 275

275 to 300

300 to 325

Stage specified in river

package, in feet above

NGVD of 1929
16 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

model as a no-flow boundary throughout the entire 

study area at the bottom of layer 2 (Fitzpatrick and others, 1990). In the active model area extended northward 

beyond the Cane River Formation facies change, clays 

of the Wilcox Group are assumed to provide sufficient 

confining conditions to justify a no-flow boundary at 

the bottom of layer 2. The western and southwestern 

updip limits of the Sparta outcrop are simulated as noflow boundaries. This corresponds to the Fall Line and 

Sabine uplift, respectively. The Fall Line and the Mississippi River, where aligned with the model boundary, 

represent no-flow boundaries because vertical flow is 

assumed along these boundaries.

Areal Recharge in Outcrop

An average of about 50 inches per year (in/yr) 

(Freiwald, 1985) of precipitation falls on the aquifer 

outcrop area. Only a small fraction of the precipitation 

enters the confined ground-water-flow system as 

recharge. To account for this recharge, remaining outcrop area not covered by rivers and streams was represented as a specified-flux boundary. The outcrop area 

was initially subdivided into zones distinguishing subcrop and outcrop areas, each representing a specific 

rate of recharge. These zones were subsequently further divided during the calibration process to improve 

model fit (fig. 7). The recharge rate of each zone is the 

parameter to be adjusted during the parameter-estimation process.

Ground-Water Withdrawal

The model simulates 100 years of system 

response to stress by dividing the model into stress 

periods with each stress period representing a period of 

time for which ground-water withdrawal rates (water 

use) are relatively unchanged. Stress periods with associated ground-water withdrawal rates are shown in figure 8. The spatial distribution of model cells 

representing ground-water withdrawal for stress period 

28 (1990-1997) is shown in figure 9. All ground-water 

withdrawals are taken from layer 2 because the majority of wells are completed and screened in the lower, 

more productive zone of the aquifer.

The water-use data and stress periods used in the 

current model are the same as compiled for the previous Sparta model (Fitzpatrick and others, 1990) 

through 1985. The northern extension of the model area 

required water-use data to be compiled and analyzed in 

nine Arkansas counties (or parts of) including Crittenden, Cross, Lee, Lonoke, Monroe, Poinsett, Prairie, 

St. Francis, and Woodruff Counties north of the Cane 

River Formation facies change (approximately 35 ° latitude) (fig. 4). Water use for these counties prior to 

1965 was compiled (Terry Holland, U.S. Geological 

Survey, written commun. 2001) using similar methods 

and procedures described in Fitzpatrick and others 

(1990). From 1965 through 1985, a database of groundwater withdrawals reported every 5 years was used to 

estimate county totals for corresponding stress periods. 

The county water-use totals were distributed equally 

between pumping wells known to exist during that time 

period. This method assumes that monitored wells represent a similar distribution of wells used for water supply and was preferred to the other alternative of 

dividing the pumpage equally over all cells. Withdrawal amounts used in the previous Sparta model 

through 1985 (through stress period 26) were adapted 

to the current model grid by distributing the same 

pumpage over an equivalent area in cases where the 

previous and current model cells were not the same. For 

the period 1986 to 1997 (stress periods 27 and 28), 

water-use data were recompiled for the entire model 

from withdrawal and well location information available from Arkansas, Louisiana, and Mississippi wateruse data bases for 1985, 1989, 1990, 1995, 1996, and 

1997 (Terry Holland, U.S. Geological Survey, written 

commun., 2001; Sargent, 2000; David Burt, U.S. Geological Survey, written commun., 2001). The withdrawal amounts used in the current model are slightly 

different from those in the models of Fitzpatrick and 

others (1990), Kilpatrick (1992), and Hays and others 

(1998) because pumpage data were adjusted based on 

improved water-use compilation and estimation procedures. This adjustment is supported by the need for 

withdrawal rates within any one stress period to adequately represent the entire stress period and not just 

one specific year. Adjusted rates were compared to 

data published for 1990 and 1995 as part of the 5-year 

national water-use compilation to assure that the rates 

were within acceptable ranges (Terry Holland, 

U.S.Geological Survey, oral commun., 2002). Differences in the amount of withdrawals reported and published in a specific year and the amount of withdrawals 

used in a corresponding model stress period could be 

caused by several factors including: (1) withdrawals in 

a stress period represent multiple years compared to 

reported water use for an individual year; (2) exclusion 

of water-use data for wells with unknown completion 

zones; and (4) exclusion of some gross livestock and 

irrigation estimates. 
Ground-Water Flow Model 17

Figure 7. Hydraulic parameter names and zonations representing recharge rates in the outcrop and subcrop areas of the 

Sparta aquifer.

Arkansas

Louisiana

Tennessee

Mississippi

Texas

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model Area

Boundary

0.11

0.39

1.1

0.88 0.39

0.39

0.71

0.45

0.39

0.77

rch_2 (0.39)

rch_3 (0.88)

rch_4 (0.11)

rch_5 (0.45)

rch_6 (1.10)

rch_7 (0.71)

rch_8 (0.77)

EXPLANATION

Recharge parameter

names and values in

inches per year
18 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

Figure 8. Total ground-water withdrawal from the Sparta aquifer and associated stress periods for the model area, 1898-1997.

05

101520253035

1895 1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 197

YEAR

2 3

4 5

6

7 8

9

10 11

12 13

14 15

16

18

17

19

20

2122

2

5 MODEL STRESS PERIOD

(Stress period 1 is a steadystate simulation before aquiferdevelopment.)

AVERAGE WITHDRAWAL, IN MILLION CUBIC FEET PER DAY
Ground-Water Flow Model 19

Figure 9. Spatial distribution for ground-water withdrawals represented in stress period 28, 1990-1997.

Arkansas

Louisiana

Tennessee

Mississippi

Texas

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the

Sparta Aquifer Outcrop-Subcrop

Active Model Area

Boundary

EXPLANATION

Model cell representing

ground-water withdrawals
20 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

Hydraulic Property Zones

Hydraulic properties of the Sparta aquifer vary 

spatially in the model. These properties include 

hydraulic conductivity, storage, and vertical leakance. 

In addition, there are areas that have been faulted and 

the properties associated with faults were specified. 

Hydraulic Conductivity

Horizontal hydraulic-conductivity parameter 

values and zones initially were assigned and defined 

from all available hydraulic data throughout the model 

area. Identical hydraulic-conductivity parameter zones 

are used for layers 1 and 2. Three hydraulic-conductivity parameter zones were defined (fig. 10) in each layer 

(six total). The initial values were adjusted during the 

calibration process. A single zone for vertical hydraulic 

conductivity was assigned in each layer and was 

defined by one parameter. The hydraulic conductivities 

of these zones are parameters considered for inclusion 

in the set to be adjusted during the parameter-estimation process.

Faults

The existence of faults in and around Columbia 

and Union Counties are supported by previous studies 

(Hosman, 1988; Tait and others, 1953; Baker and others, 1948; Broom and others, 1984), geophysical logs, 

and analysis of historical hydraulic heads and potentiometric maps (Joseph, 1998b, 2000; Schrader, 2003). 

The previous Sparta model documented the need to 

improve simulation of heads in these two counties 

where faults are known to exist, but not well defined 

(Hays and others, 1998). Faults were simulated in the 

current model using the Horizontal Flow Barrier (HFB) 

package that allows a reduction in horizontal hydraulic 

conductivity between adjacent cells to represent faults. 

Six faults were represented in the model, each with a 

separate parameter considered for inclusion in the set to 

be adjusted during the parameter-estimation process 

(fig. 10). For simplication, the width of the horizontal 

flow barrier is assumed to be 1.0 ft. The vertical 

hydraulic conductivity of cells containing faults is 

unaffected by the presence of the fault in the model.

Storage

Two specific-storage parameter zones and values 

for each layer were adjusted during calibration (fig. 

11). Zones representing specific storage were the same 

for both layer 1 and 2 and were defined based on all 

available hydraulic data in the model area and known 

storage values of similar materials. One parameter for 

each layer (two total) represents specific yield where 

the aquifer is unconfined. These two parameters were 

fixed during the parameter-estimation process.

Vertical Hydraulic Conductivity of Layers and

Confining Bed

Six parameter zones and values representing vertical hydraulic conductivity of the quasi-3D confining 

bed between layers 1 and 2 were adjusted based on limited analysis of geophysical logs and parameter estimation. Zonation of the quasi-3D confining bed is shown 

in figure 12. Only one parameter represents the vertical 

hydraulic conductivity of both layers and was adjusted 

during the parameter-estimation process. The initial 

value was based on one-tenth of the horizontal hydraulic conductivity.

MODEL CALIBRATION PROCEDURE

Calibration is the process of adjusting the model 

input variables, also called parameters, to produce the 

best match between simulated and observed aquifer 

heads. During calibration, parameters representing 

aquifer hydraulic properties were adjusted both manually and using automatic parameter-estimation techniques to match observed hydraulic heads from observation wells. MODFLOW-2000 provides a parameterestimation feature (Hill and others, 2000) that uses a 

nonlinear least-squares regression method to aid in 

estimating hydrologic properties and to further evaluate 

the model. The parameters estimated in the calibration 

process represent the hydrologic properties distributed 

as constant values over broad parameter zones or over 

extended linear features such as rivers and, therefore, 

are not intended to represent specific values of field 

tests at individual points within that zone. 

Non-Linear Least-Squares Regression 

Method

Non-linear least-squares regression is an automated parameter-estimation technique that is more efficient and objective compared to trial-and-error 

calibration because parameter values are adjusted automatically to obtain the best possible fit between simulated and observed values. The numerical difference 

between observed minus simulated values is 
Model Calibration Procedure 21

Figure 10. Hydraulic parameter names and zonations representing horizontal hydraulic conductivity and faults.

Arkansas

Louisiana

2.50

14.0

16.1

17.2

Tennessee

Mississippi

Texas

40.5

47.9

40.5

47.9

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model Area

Boundary

EXPLANATION

Layer 1 (40.5)

hk2_2 Layer 2 (47.9)

hk1_2

Layer 1 (2.50)

hk2_1

hk1_1

Layer 2 (17.2)

Layer 1 (14.0)

hk2_3

hk1_3

Layer 2 (16.1)

Horizontal hydraulic conductivity

parameter name (hk[zone #]_[layer #])

and value, in feet per day

mod_mck2 (layer 2)

mrdata_1

mrdata_2

th_fault

union_fault

Horizontal flow barrier fault parameter

name and value, in feet squared per

day (values are for both layers unless

otherwise noted)

1 mod_mck1 (layer 1)

1 x 10-4

1 x 10+5

1

5 x 10-6

5 x 10-3
22 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

Figure 11. Storage parameter names and zonations.

Arkansas

Louisiana

Tennessee

Mississippi

Texas

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model Area

Boundary

EXPLANATION

Specific yield, dimensionless

Layers 1 and 2 (0.2)

Specific storage parameter name

(ss[zone #]_[layer #]) and value,

in feet -1

Layer 1 (1.00 X 10 )

ss2_1 Layer 2 (3.54 X 10 )

ss1_1 -6

-6

Layer 1 (1.50 X 10 )

ss2_2 Layer 2 (1.00 X 10 )

ss1_2 -4

-5

Entire

Model

Area

3.54 x 10-6

1.00 x 10-6

1.00 x 10-5

1.50 x 10-4
Model Calibration Procedure 23

Figure 12. Hydraulic parameter names and zonations representing vertical hydraulic conductivity used to simulate confining 

beds in the Sparta aquifer.

Arkansas

Louisiana

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

Texas

Tennessee

Mississippi

1.0

1.0 x 10-6

5.4 x 10-6

2.2 x 10-4

1.0

1.0 x 10-4

EXPLANATION

Vertical hydraulic

conductivity parameter

name (vkcb[zone #]) and

value of the confining

bed, in feet per day

vkcb1 (1.0)

vkcb2 (1.0 X 10 )

vkcb3 (5.4 X 10 )

vkcb4 (2.2 X 10 )

vkcb5 (1.0)

vkcb6 (1.0 X 10 )

-6

-6

-4

-4
24 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

called a residual. In the regression method, parameter 

values are estimated by minimizing the squared 

weighted residuals, called the objective function. The 

model is constructed to maintain parameter values 

within reason and plausibility. This method is 

explained with great detail in Cooley and Naff (1990); 

Hill (1992, 1994, and 1998); and Hill and others 

(2000). 

Model Parameterization

In the model, grid cells assumed to have similar 

hydrologic properties are grouped together as a parameter zone and assigned a value that can be adjusted during the calibration process. The current Sparta model 

used a total of 56 hydraulic parameters (table 3). These 

parameters include horizontal hydraulic conductivity 

(hk), specific storage (ss), specific yield (sy), horizontal flow barriers, vertical hydraulic conductivity of 

Cook Mountain confining unit, riverbed conductance, 

vertical hydraulic conductivity of quasi-3D confining 

bed (vkcb), recharge (rch), and general-head boundary 

conductance (ghb). Many parameters are represented 

with the abbreviated name followed by the corresponding layer, when appropriate, and zone number. Thus 

hydraulic conductivity in layer 1, zone 1 is represented 

using hk1_1 and so on. Riverbed conductance parameters were named based on the corresponding river 

name. The value of ck_riv represents vertical hydraulic 

conductivity and is multiplied by length and width of 

each model cell, and divided by the thickness of the 

overlying Cook Mountain confining unit for input to 

the model. Horizontal flow barriers were named based 

on reference or spatial location. This is done for a number of aquifer properties, which will be discussed in 

detail in later sections of this report. For each boundary 

condition or hydraulic property, an associated parameter was considered for inclusion in the set of parameters 

to be estimated by the regression method during the 

calibration process, and an initial value for the parameter was assigned. Because the success of parameter 

estimation can be affected by the values of initial 

parameters, the values in the previous Sparta model and 

hydraulic-test data collected since that model was 

developed were used to assign initial parameter and 

model-input values. For parameters included in the 

estimated set, optimal parameter values were computed 

by the regression method. 

Calibration Data Set

Hydraulic-Head Observations

A total of 795 hydraulic-head observations 

(water-level measurements) from 316 individual observation wells in Arkansas and Louisiana representing 

four time periods of 1970, 1985, 1990, and 1997 was 

used in the calibration data set (fig. 13). These observation periods were selected for two reasons: (1) they 

were used in potentiometric map reports for the Sparta 

aquifer (Edds and Fitzpatrick, 1986; Fitzpatrick and 

others, 1990; Joseph, 1998a; Kilpatrick, 1992); and (2) 

these observation years correspond to those used in the 

calibration and subsequent verifications of the previous 

Sparta model. The previous Sparta model was calibrated only to hydraulic-head observations in 1970 and 

verified with observations from each of the other 3 

years. The 316 observation wells were selected from 

the wells used to generate the 1997 potentiometric map 

of the Sparta aquifer by Joseph (1998b). All hydraulic 

heads measured in the spring for any or all of the four 

time periods were used in the calibration. Spring measurements are least likely to be affected by localized 

drawdown caused by summertime pumping. All wells 

from which observations were used are assumed to be 

screened in the lower, higher producing section of the 

Sparta aquifer and assigned to model layer 2. These 

data provide broad spatial and temporal coverage of 

aquifer conditions. 

Weights

The purpose of weighting the model calibration 

data is to reduce the influence of hydraulic-head observations that are less accurate and to increase the influence of observations that are more accurate. Weights on 

observation data account for measurement error associated with the method of determining land surface, 

affects of recent pumpage, unknown screened intervals 

of wells, presence of faults, and other factors. In theory, 

weights on the observations used in the regression procedure can be calculated from estimates of the variance 

or standard deviation of measurement error (Hill, 

1998). The weights are calculated by dividing 1 by the 

variance of the measurement errors for the observation. 

To estimate these variances, the measurement errors 

can be assumed to have a normal distribution, and a 95-

percent confidence interval for the measurement can be 

constructed. The 95-percent confidence interval spans 

a range equal to the measurement +/-1.96 times the 
Model Calibration Procedure 25

Table 3. Parameter names with corresponding optimal parameter estimates and composite-scaled

sensitivities

[Numbers in parameter names indicate layer and zone as described in the parameter description. Composite scaled sensitivities as defined by Hill (1998). ft/

d, foot per day; hk, horizontal hydraulic conductivity; ft2

/d, foot squared per day; in/yr, inch per year; NA, not applicable; vk, vertical hydraulic conductivity]

Parameter

name

Parameter

description

(units)

Reasonable

parameter

values

Optimal

parameter

estimate

Compositescaled

sensitivity

hk1_1 Horizontal hydraulic

conductivity of

layer and zone (ft/d)

10-200a

0.1-600b

2.5 2.7

hk1_2 40.5 7.8

hk1_3 14 1.5

hk2_1 17.2 35.6

hk2_2 47.9 31.0

hk2_3 16.1 32.3

ss2_1 Specific storage of

layer and zone (ft-1)

1x10-7-1x10-6a

<1x10-4c

3.54x10-6 7.0

ss2_2 1.0x10-6 3.0

ss1_1 1.0x10-6 0.3

ss1_2 1.5x10-4 11.5

sy_1 Specific yield of layer

(dimensionless)

0.01-0.30b 0.2 2.1

sy_2 0.2 0

ghb_3 General head boundary

conductance of zone

(ft2/d)

NAd 1 1.5x10-3

ghb_1 1 3.6x10-4

ghb_2 1 3.3x10-4

ghb_4 1 1.0x10-2

ghb_5 1 2.2x10-3

ghb_6 1 4.9x10-3

ghb_7 1 5.6x10-3

ck_riv Vertical hydraulic

conductivity of Cook

Mountain confining 

unit (ft/d)

9x10-6-3x10-4 3.1x10-5 10.6

absent_ck 9.3x10-3 0.3

Arkansas River Riverbed conductance

of rivers and streams

in outcrop (ft2/d)

100,000d,e 115,000 3.2x10-2

Bayou Deview 0 2.8x10-10

Black Lake Bayou 500 0.1

Bodcau Creek 2,494 1.0

Cache River 86,200 2.0x10-2

Caney Creek 0 3.6x10-11

Cypress Bayou 10,000 5.8x10-3

Bayou Dorcheat 40,900 7.3x10-2
26 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

Dugdemona River 10,000 1.7x10-2

Ouachita River 575,000 1.5x10-2

Red River 305,000 7.0x10-3

Saline River 538,000 7.8x10-3

Saline Bayou 300 1.2

White River 137,000 9.6x10-3

Smackover Creek 200 0.7

all-vk Vertical hydraulic

conductivity of

both layers (ft/d)

hk divided by 10f 1.62 6.4x10-2

vkcb6 Vertical hydraulic

conductivity of

quasi-3D confining

bed zone (ft/d)

NAd,g 1.0x10-4 2.2

vkcb5 1 4.3x10-3

vkcb4 2.2x10-4 5.6

vkcb3 5.4x10-6 4.0

vkcb2 1.0x10-6 1.0

vkcb1 1 6.9x10-2

mrdata_1 Horizontal flow within 

a fault zone (ft/d)

NAd,h 1.0x105 2.6x10-8

mrdata_2 1 2.6x10-3

mod_mck1 1 4.2x10-5

mod_mck2 1.0x10-4 5.4

th_fault 5.0x10-6 0.2

union_fault 5.0x10-3 8.9x10-2

rch_2 Recharge of zone

(in/yr)

0-4e 0.39 4.4

rch_3 0.88 10.4

rch_4 0.11 2.2

rch_5 0.45 4.6

rch_6 1.10 3.5

rch_7 0.71 12.6

rch_8 0.77 6.7

a

 Multi-well hydraulic tests (Payne, 1968; Hosman and others, 1968). b

 Comparable hydrologic units (Fetter, 1994). c

 Common values (Freeze and Cherry, 1979). d No data available to estimate reasonable range.

e

 Previous Sparta model (Fitzpatrick and others, 1990).

f

 Assumed vk one-tenth of hk in stratified depositional environment. g Delineation of zones based on geophysical logs around Union County and hydrologic judgement elsewhere. h

 Barrier locations based on mapped faults (Hosman, 1988) and hydrologic judgement.

Table 3. Parameter names with corresponding optimal parameter estimates and composite-scaled

sensitivities--Continued

[Numbers in parameter names indicate layer and zone as described in the parameter description. Composite scaled sensitivities as defined by Hill (1998). ft/

d, foot per day; hk, horizontal hydraulic conductivity; ft2/d, foot squared per day; in/yr, inch per year; NA, not applicable; vk, vertical hydraulic conductivity]

Parameter

name

Parameter

description

(units)

Reasonable

parameter

values

Optimal

parameter

estimate

Compositescaled

sensitivity
Model Calibration Procedure 27

Figure 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.

K L

J I

N

M

E

H

F

G

D C

B

A

Arkansas

Louisiana

Tennessee

Mississippi

Texas

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model Area

Boundary

EXPLANATION

Observation well with

hydrograph (Fig. 19)

Observation wells

A
28 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

standard deviation (square root of the variance). Examples and detailed calculations of weights are given by 

Hill (1998). 

For this report, a variance of 1.0025 ft2 was used 

for all but 28 observations with a calculated weight of 

0.998 (practically 1.0). Based on a 95-percent confidence interval, these measurements are assumed to be 

within approximately +/- 2 ft. The other 28 observations were weighted using estimated variances of 5 ft2 

and 10 ft2 because of measurement uncertainty for reasons described above. These two variances result in 

calculated weights of 0.20 and 0.10 and 95-percent 

confidence intervals of approximately +/- 4.4 and 6.2 

ft, respectively. These 28 observations were from only 

13 of 316 observation wells used in the model calibration. 

Sensitivities

The sensitivity of hydraulic heads with respect to 

various model parameters was calculated using the sensitivity-equation method (Hill and others, 2000). Composite scaled sensitivities (CSS) were calculated for 

each parameter (table 3). CSS values aid in determining 

if there is adequate information in the calibration data 

to estimate a particular parameter. CSS values less than 

about 0.01 times the largest CSS indicate that the 

regression may not be able to estimate the parameter 

(Hill, 1998). In many initial calibration attempts, estimations of various parameters were adjusted toward 

physically unreasonable values. In these cases, the 

parameter value was fixed at a reasonable value based 

on published studies in the area or literature review of 

similar hydrogeologic units. As the calibration 

improved, so did the ability of the parameter-estimation 

process to adjust parameters to reasonable values. 

Therefore, parameters that were initially fixed were 

allowed to be estimated by the parameter-estimation 

process later in the calibration. 

Reasonable Parameter Ranges

The parameter-estimation process does not allow 

for upper and lower bounds on estimates to be specified; thus, it is possible for model-computed parameter 

estimates to lie outside of expected or reasonable 

ranges. A check for reasonableness of the optimal 

parameter estimates is an important step in the analysis 

of regression results. 

Reasonable ranges of values for most of the 

parameters included in the set to be estimated by the 

regression procedure were determined (table 3). These 

ranges were determined from existing hydrologic 

information, including previous studies and model 

results, hydraulic tests, and material properties of similar aquifers and confining units. It was not possible to 

identify plausible ranges of flux values for each general-head boundary and horizontal-flow barrier prior to 

parameter estimation. 

MODEL EVALUATION

Optimal Parameter Estimates

The final optimal parameter estimates of the 

model are considered reasonable estimates for the type 

of material and conditions found in the Sparta aquifer. 

Horizontal hydraulic conductivity values of 2.5 to 47.9 

ft/d occur within the expected range of hydraulic conductivities for silty to clean sand (Freeze and Cherry, 

1979). The smallest value of hydraulic conductivity 

occurs in the upper layer (table 3). This may be the 

result of fining upward in the stratigraphic sequence 

(Payne, 1968; Hosman and others, 1968). In any case, 

overall values for hydraulic conductivity are within the 

same order of magnitude and represent average values 

for large areas in the aquifer. Horizontal hydraulic conductivities of horizontal flow barriers, representing 

faults, range from 5 x 10-6 to 1.0 ft/d. In one case, the 

fault (mod_mck1 and 2) is thought to be a growth fault. 

Therefore, it may exist only in the lower portion of the 

Sparta aquifer. To simulate this, the fault was given a 

hydraulic conductivity of 1 x 10-4 ft/d in the lower layer 

(mod_mck2), and 1 ft/d in the upper layer (mod_mck1) 

(fig. 10). Another fault, mrdata_1 was found to be 

insensitive to the calibration data set because of the 

position of the fault near the western model boundary. 

Therefore, the value of mrdata_1 was set to 1 x 105

ft2/d to simulate a lesser effect on the ground-water system. Specific yield values throughout the model were 

fixed at 0.2. Specific storage values range from 1 x

10-6 to 1.5 x 10-4 per foot (fig.10). Riverbed conductances for Bayou Deview and Caney Creek effectively 

were removed from the calibration by setting the riverbed conductance to 0 after determining their minor 

impact on calibration. The next smallest value of riverbed conductance is in a portion of Smackover Creek, 

which reflects the size and depth of the small stream. 

The largest value of riverbed conductance is in the Ouachita River, probably because of the large size of the 
Model Evaluation 29

river. Riverbed conductance typically varied by river 

size, however field measurements of streambed properties do not exist to estimate riverbed conductance for 

comparison. The vertical hydraulic-conductivity value 

used in the calculation of riverbed conductance for 

parameter ck_riv, which represents leakance through 

overlying units, ranged from 9.3 x 10-3 to 3.1 x 10-5

ft/d. The larger value of parameter absent_ck is associated with an area overlying the Sparta aquifer where the 

Cook Mountain confining unit does not exist (Hosman 

and Weiss, 1991) and represents impeded flow through 

overlying hydrogeologic units (fig. 5). Recharge from 

infiltration of precipitation ranges from 0.11 to 1.10

in/yr. Although these rates are less than 2 percent of the 

average precipitation, the total recharge rate for the outcrop is greater than that used in the previous Sparta 

model. Recharge rates from precipitation in the Sparta 

outcrop have not been quantified by field measurements. Table 3 lists all parameter names.

Parameter correlations for each calibration were 

computed using the approximate covariance matrix for 

the parameters, which is calculated as part of the nonlinear-regression method (Hill and others, 2000). If a 

pair of parameters has a correlation coefficient near 1.0 

or -1.0, independent estimation of the two parameters is 

not possible given the calibration data set used in the 

regression. In the calibration, five parameter pairs have 

correlations greater than 0.85 (table 4).

Typically, correlations greater than 0.95 suggest problems with parameter non-uniqueness (Hill, 1998) and 

that there was not enough observation data to independently estimate the model parameters. In these cases, 

the model may only be estimating the ratio or sum of 

the highly correlated parameters. Bayou Deview: rch_4 

and Black Lake Bayou: rch_8 have the largest absolute 

correlations of any parameter pair at -0.96 and 0.97, 

respectively. The other parameter correlations are not 

large enough to be problematic. Therefore, the river 

parameters in each of the two parameter pairs were set 

at fixed values while the other parameters were allowed 

to adjust during calibration.

The CSS calculated using initial parameter values provided an indication of which model parameters 

to estimate in the nonlinear-regression procedure and 

which to set to fixed values. However, the CSS values 

are dependent on the parameter values because the sensitivities are a nonlinear function of the model parameters. The CSS values calculated using the optimal 

parameter estimates for the calibrated model also are 

listed in table 3. Less than half of the defined parameters (23 of 56) have CSS values greater than 1.0 (fig. 

14). The three hydraulic conductivity zones of the 

lower layer have a CSS more than double any other 

parameters. The next highest parameters with a CSS 

over 10 are rch_7, ss1_2, ck_riv, and rch_3. Parameters 

with very low CSS values (less than 1.0) were fixed 

instead of adjusted because of their minimal effect on 

the calibration.

Model Fit and Model Error

Statistical Analysis of Residuals

Analysis of residual statistics, such as maximum, 

minimum, and root mean square error (RMSE), provides a measure of model fit and expected model performance as a management tool. RMSE is a statistical 

representation of variance, and, as such, smaller values 

of RMSE indicate better model calibration. RMSE is 

determined using the equation:

(2)

where ho is observed hydraulic head, 

hs is simulated hydraulic head, and

n is number of observations.

Table 4. Parameter pairs of five largest correlation 

coefficients

[Correlation dimensionless]

Parameter paira

(see table 3 for explanation)

a

 See table 3 for explanation.

Correlation coefficient

Bayou Deview : rch_4 -0.96

Black Lake : rch_8 0.97

ghb_5 : ghb_6 -0.88

Cache River : vkcb5 -0.89

Saline Bayou : rch_8 0.89

RMSE Σ ho hs ( ) – 2 [ ] ⁄ n

1 2 ⁄ =
30 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

Figure 14. Composite scaled sensitivities (CSS) calculated using the optimal parameter estimates of the Sparta model 

calibration for CSS greater than 1.0.

0

5

10

15

20

25

30

35

40

hk1_1

hk1_2

hk1_3

hk2_1

hk2_2

hk2_3

ss2_1

ss2_2

ss1_2

sy_1

ck_riv

Saline Bayou

vkcb6

vkcb4

vkcb3

mod_mck2

rch_2

rch_3

rch_4

rch_5

rch_6rch_7

rch_8

Hydraulic Conductivity

Parameters

Specific Storage

Parameters

Riverbed Conductance

Parameters

Vertical

Hydraulic

Conductivity

Parameters

Horizontal Flow Barrier Parameter

Recharge

Parameters

PARAMETER NAME

COMPOSITE SCALED SENSITIVITY

RMSE’s for the current model range from 16.0 to 

18.9 ft for individual time periods, varying only slightly 

throughout time with no apparent trend (table 5).

This indicates the ability of the model to simulate 

observed hydraulic heads under different sets of pumping stress and strengthens prediction confidence for 

future pumping stress scenarios. The RMSE for all 795 

observations is 18.0 ft over a range in observed hydraulic-head altitudes from -224 to 306 ft. For only 1997 

observations, the RMSE is 18.9 ft compared to 31.3 ft 

for the previous Sparta model reverification (Hays and 

others, 1998) using 316 and 283 observation wells, 

respectively. Additional comparisons of residual statistics for all years between the models are shown in table 

6.

Standard error of the regression is a similar statistic that corrects the degrees of freedom for the number of parameters being estimated. The “n” in equation 

2 is replaced by “n-p” where p is the number of parameters estimated. The standard error is 18.7 ft for all 

observations.

The mean or average of residuals is a simple 

measure of skewness from zero and indicates model 

bias depending on the magnitude and direction of the 

mean away from zero. The more closely the mean is to 

zero and more evenly divided between positive and 

negative residuals, the less model bias. A negative mean 

indicates the model tends to overpredict (simulated 

hydraulic heads greater than observed), and a positive 

mean indicates underprediction (simulated hydraulic 

heads less than observed). Out of 795 observations, 393 

residuals were greater than or equal to zero (underprediction) and 402 residuals were less than zero (overprediction) resulting in a mean weighted residual of +0.4 ft 

Table 5. Weighted residual statistics for model calibration

Year

Number

of wells

Mean

(feet)

Minimum

(feet)

Maximum

(feet)

Mean

absolute

(feet)

Root

mean

square

error

(feet)

1970 119 -2.7 -39.0 52.0 13.9 17.5

1985 197 0.6 -41.3 53.3 12.3 16.0

1990 163 -0.3 -54.9 47.4 14.3 18.9

1997 316 1.7 -56.5 48.4 14.5 18.9

All 795 0.4 -56.5 53.3 13.8 18.0
Model Evaluation 31

Table 6. Model residual statistics for the current and previous Sparta models

Statistic 1970a

a

Results from Fitzpatrick and others (1990).

1970b 1985a 1985c 1985b 1990d 1990b 1997e 1997c 1997b

b

Results for current model; wells used to generate 1997 Sparta potentiometric surface map (Joseph, 1998b) having data available for 

1970, 1985, 1990, 1997. c

Results from Hays and others (1998); wells within the model area having data available for both 1985 and 1997, generating a common 

key well set for the two simulations. d Results from Kilpatrick (1992).

e

 Results from Hays and others (1998); all well data available within the model area for 1997.

Number of wells 192 119 233 197 197 113 163 283 197 316

Mean (feet) 1.8 -2.7 5.8 -12.1 0.6 18.3 -0.3 -2.3 -0.8 1.7

Minimum absolute (feet) 0.3 0.4 0.0 0.1 0.1 0.5 0.3 0.3 0.1 0.0

Maximum absolute (feet) 70.6 52.0 78.2 148.1 53.3 68.4 54.9 143.0 143.3 56.5

Standard deviation (feet) 13.5 17.3 14.2 30.7 16.0 15.4 18.9 31.2 31.8 18.9

Variance (feet squared) 180.8 300.0 202.3 815.0 255.1 236.6 355.7 974.6 1014.8 355.5

Root mean square error (feet) 21.2 17.5 22.3 32.9 16.0 24.0 18.9 31.3 31.7 18.9

(table 5). The minimum and maximum weighted residuals were closely balanced at -56.5 and +53.3 ft, 

respectively. In addition, the mean for individual years 

shows no appreciable trend in increasing value from 

zero in either direction. This residual balance both in 

magnitude and direction and through time without 

trend is another desirable characteristic of model calibration that gives confidence to use of the model as a 

management tool.

Weighted Hydraulic-Head Residuals

Graphical analyses of the weighted residuals 

facilitate assessment of model bias or error and of 

model fit to the calibration data. These analyses include 

plots of the weighted residuals and weighted simulated 

values and of the spatial and temporal distribution of 

the weighted hydraulic-head residuals.

The plot of weighted residuals and weighted 

simulated equivalents for an unbiased model ideally 

should show a random distribution of the weighted 

residuals above and below zero for all weighted simulated equivalents. In this case, the model fit is generally 

similar over the entire range of available hydraulic head 

values, and the calibration has, in general, the desired 

random distribution of weighted residuals (fig. 15). 

Additional assessments of model error are 

accomplished through analysis of the spatial and temporal distribution of weighted residuals (fig. 16) for 

years 1970, 1985, 1990, and 1997. Residuals representing 1997 observation data provided the best guide during model calibration because (1) improved water-use 

data for later years, (2) highest number and uniform 

distribution of wells, and (3) the last observation time 

before prediction scenarios begin. Negative residuals, 

shown in blue, indicate simulated hydraulic heads that 

are higher than observed, while positive residuals, 

shown in red, indicate simulated hydraulic heads that 

are lower than observed. Different ranges in residuals 

are represented by a variety of geometric symbols for 

visual analysis of model bias. 

Ideally, negative and positive weighted residuals 

should be small and randomly distributed in space. 

Clustering of residuals with similar magnitudes and 

signs is indicative of model bias. Overall, residuals (fig. 

16) appear to be well distributed in both magnitude and 

sign (+/-). Some clustering of residuals occurs in the 

Grand Prairie area with a trend through time from negative to positive residuals, which may be the result of 

inaccurate water-use data. Inaccurate assessment of 

water use in the Grand Prairie area may occur because 

of wells incorrectly reported as being completed in the 

alluvial aquifer that are actually completed in the 

Sparta aquifer, or wells with screened intervals in both 

the alluvial and Sparta aquifers. In many cases, insufficient reporting of well completion data makes it difficult to determine (1) in which aquifer the well is 

screened or (2) whether it is screened in both aquifers. 

Another possible cause of model bias occurs in 

Columbia and Union Counties where geologic studies 

suggest considerably more heterogeneity in geologic 
32 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

Figure 15. Weighted residuals and weighted simulated values.

-72

-54

-36

-18

0

18

36

54

72

-200 -150 -100 -50 0 50 100 150 200 250 300

WEIGHTED SIMULATED EQUIVALENT, IN FEET

WEIGHTED RESIDUAL, IN FEET

conditions and faulting than is presently mapped and 

represented by the simple zonations and flow boundaries in the current model. In addition, model bias 

through time may be caused by (1) the temporal averaging of ground-water withdrawals to obtain the mean 

annual pumpage used in each stress period, and (2) the 

spatial averaging of pumpage from several wells 

located in a single model cell. 

The weighted residuals ideally should show no 

temporal trends and be balanced around zero. All of the 

weighted residuals (fig. 17) are less than 56.5 ft in absolute value. Increasing trends with time may occur 

because of some wells having hydraulic-head measurements only at later times in the simulation. For each 

year, the number of positive residuals is approximately 

equal to negative residuals, and there appears to be a 

slight trend through time from underprediction to overprediction as indicated (fig. 17). 

Normality of Weighted Residuals

Normality of weighted residuals is a prerequisite 

for a valid regression. If the model accurately represents the system, the weighted residuals are expected to 

be random, independent, and normally distributed 

(Hill, 1998). The normality and independence of the 

weighted residuals can be assessed through use of (1) 

the correlation coefficient R2N between the ordered 

weighted residuals and order statistics from the normal 

probability distribution function (Hill and others, 2000) 

and (2) a histogram of the weighted residuals. The 

weighted residuals are thought to be independent and 

normally distributed if the computed value of R2N for 

a calibration is higher than the tabulated critical value. 

The critical value of R2N is 0.987 for a set of 200 observations (maximum number of observations for which a 

value has been tabulated). This value will be even larger 

for the 795 observations used in the current model calibration because the critical value increases with the 

number of observations. The value of R2N for the 

model calibration is 0.993, which is larger than the critical value, indicating that the weighted residuals are 

independent and normally distributed. This is additionally supported by a histogram (fig. 18) of all 795 

weighted residuals showing normal distribution (typical bell curve) about zero. 
Model Evaluation 33

Figure 16. Spatial distribution of weighted hydraulic-head residuals for (A) 1970, (B) 1985, (C) 1990, and (D) 1997.

Arkansas

Louisiana

Tennessee

Mississippi

Texas

A

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

Grand

Prairie

Union

Columbia

EXPLANATION

Hydraulic head residual,

in feet (observed minus

simulated)

-56 to -50

-50 to -40

-40 to -30

-30 to -20

-20 to -10

-10 to 0

0 to 10

10 to 20

20 to 30

30 to 40

40 to 50

50 to 60
34 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

Figure 16. Spatial distribution of weighted hydraulic-head residuals for (A) 1970, (B) 1985, (C) 1990, and (D) 

1997—Continued.

Columbia Arkansas

Louisiana

Tennessee

Mississippi

Grand Prairie

Union

Texas

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

B EXPLANATION

Hydraulic head residual,

in feet (observed minus

simulated)

-56 to -50

-50 to -40

-40 to -30

-30 to -20

-20 to -10

-10 to 0

0 to 10

10 to 20

20 to 30

30 to 40

40 to 50

50 to 60
Model Evaluation 35

Figure 16. Spatial distribution of weighted hydraulic-head residuals for (A) 1970, (B) 1985, (C) 1990, and (D) 

1997—Continued.

Arkansas

Louisiana

Tennessee

Mississippi

Grand Prairie

Union

Columbia

Texas

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

C EXPLANATION

Hydraulic head residual,

in feet (observed minus

simulated)

-56 to -50

-50 to -40

-40 to -30

-30 to -20

-20 to -10

-10 to 0

0 to 10

10 to 20

20 to 30

30 to 40

40 to 50

50 to 60
36 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

Figure 16. Spatial distribution of weighted hydraulic-head residuals for (A) 1970, (B) 1985, (C) 1990, and (D) 

1997—Continued.

Arkansas

Louisiana

Texas

Tenneessee

Mississippi

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

D

Grand Prairie

Union

Columbia

EXPLANATION

Hydraulic head residual,

in feet (observed minus

simulated)

-56 to -50

-50 to -40

-40 to -30

-30 to -20

-20 to -10

-10 to 0

0 to 10

10 to 20

20 to 30

30 to 40

40 to 50

50 to 60
Model Evaluation 37

Figure 17. Distribution of weighted hydraulic-head residuals.

Simulated and Observed Hydrographs of 

Hydraulic Heads

Simulated and observed hydrographs were compared for fourteen wells with long periods of record 

(fig. 19 A-N). These wells were originally selected by 

Fitzpatrick and others (1990) based on location in or 

near areas of large hydraulic-head gradients of cones of 

depressions formed from large, long-term withdrawals. 

The simulated and observed hydrographs, representative of hydraulic heads in the lower Sparta aquifer 

(layer 2) in different regions of the model area, show 

good agreement for most locations.

Simulated and Observed Potentiometric Surfaces

Potentiometric surfaces representing the lower 

Sparta aquifer (layer 2) are used to determine similarities and differences in general hydraulic head and flow 

direction between simulated and observed potentiometric surfaces. Predevelopment potentiometric surface contours (Reed, 1972) show good correlation to 

the simulated predevelopment potentiometric surface 

(steady-state model run with no pumping stresses 

applied) (fig. 20). Although sparse predevelopment 

hydraulic-head observation data limit the qualitative 

comparison in the outcrop area, the data are still useful 

to support the conceptual model of generalized predevelopment flow directions. Potentiometric-surface contours for spring 1997, overlain on simulated hydraulic 

heads, give reasonable qualitative match to cones of 

depression in Jefferson, Union, and Columbia Counties, and Ouachita Parish (fig. 21). The simulated 

hydraulic heads also approximate large gradients in 

Columbia County, thought to be influenced by faulting 

in the area (Hosman, 1988; Pugh and others, 2000) (fig. 

21).

Figure 18. Histogram of residuals for entire calibration data 

set of 795 observations from 1970, 1985, 1990, and 1997.

The simulated and observed (Joseph, 1998b) 

1997 potentiometric surface in the Sparta aquifer is 

already below the top of the Sparta Sand (fig. 22) in 

much of southwestern Arkansas and north-central Louisiana. This area includes much of Columbia and Union 

Counties and parts of Ouachita, Lonoke, Prairie, and 

Monroe Counties in Arkansas and much of Webster, 

Claiborne, Lincoln, Bienville, and Jackson Parishes, 

and parts of Ouachita, Union, and Bossier Parishes in 

Louisiana. Based on the 1997 simulated hydraulic 

heads and the top of the Sparta Sand represented in the 

model, the percent area of the aquifer with hydraulic 

heads below the top of the Sparta Sand in Arkansas and 

Louisiana was 7.9 and 19.4, respectively. In Union 

County, Arkansas, over 50 percent of the county had 

hydraulic heads below the top of the Sparta Sand; Jefferson County had no area with hydraulic heads below 

the top of the Sparta Sand.

YEAR

1970 1985 1990 1997

WEIGHTED HYDRAULIC-HEAD RESIDUALS,

IN FEET

-60

-40

-20

0

20

40

60

90th percentile

75th percentile

50th percentile

25th percentile

10th percentile

data outside10th

and 90th percentile

0

50

100

150

200

-50 -40 -30 -20 -10 0 10 20 30 40 50 60

RESIDUAL, IN FEET

NUMBER OF RESIDUALS

-60
38 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

Figure 19. Simulated and observed hydraulic heads at selected observation wells, 1900-1997. Observation well locations are 

shown in figure 13. WATER LEVEL, IN FEET ABOVE NGVD OF 1929

0

20

40

60

80

100

120

140

160

180

200

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

B

0

20

40

60

80

100

120

140

160

180

200

Simulated

Observed

A Grand Prairie Area, Arkansas

01S05W20ABB1

Grand Prairie Area, Arkansas

04S05W01BAA1
Model Evaluation 39

Figure 19. Simulated and observed hydraulic heads at selected observation wells, 1900-1997. Observation well locations are 

shown in figure 13—Continued.

0

20

40

60

80

100

120

140

160

180

200

Simulated

Observed

C

WATER LEVEL IN FEET ABOVE NGVD OF 1929

Pine Bluff, Arkansas

04S08W35BCD2

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

140

160

180

200

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

YEAR

D

Pine Bluff, Arkansas

05S09W35AAB1
40 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

Figure 19. Simulated and observed hydraulic heads at selected observation wells, 1900-1997. Observation well locations are 

shown in figure 13—Continued. WATER LEVEL IN FEET ABOVE NGVD OF 1929 -50

-30

-10

10

30

50

70

90

110

130

150

170

190

210

230

250

Simulated

Observed

Magnolia,Arkansas

17S21W11DCC2

0

20

40

60

80

100

120

140

160

180

200

220

240

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

YEAR

East of Magnolia, Arkansas

17S19W15ABD1

E

F
Model Evaluation 41

Figure 19. Simulated and observed hydraulic heads at selected observation wells, 1900-1997. Observation well locations are 

shown in figure 13—Continued.

50

70

90

110

130

150

170

190

210

230

250

WATER LEVEL IN FEET ABOVE NGVD OF 1929

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

YEAR

-200

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

140

160

180

200

Simulated

Observed

El Dorado, Arkansas

17S15W18DBB1-MONSANTO

G

H Springhill. Louisiana

WB-27
42 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

Figure 19. Simulated and observed hydraulic heads at selected observation wells, 1900-1997. Observation well locations are 

shown in figure 13—Continued. WATER LEVEL IN FEET ABOVE NGVD OF 1929 -150

-130

-110

-90

-70

-50

-30

-10

10

30

50

70

90

Simulated

Observed

Bastrop, Louisiana

MO-5

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

140

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

YEAR

Between Bastrop and Monroe, Louisiana

IN-26

I

J
Model Evaluation 43

Figure 19. Simulated and observed hydraulic heads at selected observation wells, 1900-1997. Observation well locations are 

shown in figure 13—Continued. WATER LEVEL IN FEET ABOVE NGVD OF 1929 -100

-80

-60

-40

-20

0

20

40

60

80

100

120

140

160

180

200

Simulated

Observed

Ruston, Louisiana

L-25

-220

-200

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

YEAR

Monroe, Louisiana

OU-77

K

L
44 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

Figure 19. Simulated and observed hydraulic heads at selected observation wells, 1900-1997. Observation well locations are 

shown in figure 13—Continued. WATER LEVEL IN FEET ABOVE NGVD OF 1929

0

20

40

60

80

100

120

140

Simulated

Observed

M Jackson Parish, Louisiana

0

20

40

60

80

100

120

140

160

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

YEAR

N Winnfield, Louisiana

W-16
Model Evaluation 45

Figure 20. Simulated and observed potentiometric surface for the Sparta aquifer, predevelopment.

180

140

160

120

100

200

220

240

260

280

300

160

160

180

200

180

260

200

22

240

0

240

220

140

140

200

220

Arkansas

Louisiana

Texas

Tennessee

Mississippi

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

Simulated predevelopment potentiometric

surface, in feet. Contour interval 25 feet.

Datum is NGVD of 1929

EXPLANATION

-100- POTENTIOMETRIC CONTOUR--

Shows altitude at which water level

would have stood in tightly cased wells,

predevelopment. Contour interval

20 feet. Datum is NGVD of 1929.

Contour modified from Reed (1972)

400

300

200

100

50
46 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

Figure 21. Simulated and observed potentiometric surface for the Sparta aquifer, 1997.

-100

0

100

200

200

100

200

0

300

200

100

-100

0

100

Arkansas

Louisiana

Tennessee

Mississippi

Texas

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

Simulated 1997 potentiometric surface,

in feet. Contour interval 25 feet. Datum

is NGVD of 1929

-200

-100

0

100

200

300

350

-250

-100- POTENTIOMETRIC CONTOUR--

Shows altitude at which water level

would have stood in tightly cased wells,

predevelopment. Contour interval

25 feet. Datum is NGVD of 1929.

Contours modified from Joseph (1997)

EXPLANATION
Model Evaluation 47

Figure 22. Contoured difference between 1997 simulated hydraulic heads and top of the Sparta Sand.

Arkansas

Louisiana

Tennessee

Mississippi

Texas

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model Area

Boundary

Bossier

Columbia Union

Claiborne Union

Ouachita

Jackson

Lincoln

Bienville

Webster

Ouachita

Jefferson

Lonoke

Prairie

Monroe

EXPLANATION

-291 to -200

-200 to -100

-100 to -50

-50 to 0

0 to 50

50 to 100

100 to 200

200 to 300

300 to 500

500 to 1000

1000 to 2000

2000 to 4050

1997 simulated hydraulic

heads minus top of Sparta

Sand, in feet. Datum is

NGVD of 1929
48 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

Ground-Water Budget

The ground-water flow budget from predevelopment to 1997 indicates changes in flow into (inflows) 

and out of (outflows) the Sparta aquifer (fig. 23). Negative rates indicate outflows from the ground-water 

system, and positive rates indicate inflows to the 

ground-water system. The net flow is computed by 

inflows minus outflows. Total flow through the Sparta 

aquifer in the model was about 18.9 million ft3

/d before 

development, and about 40.6 million ft3

/d in 1997 

(table 7). There are five inflows to the model: recharge, 

river leakage through streambeds, leakage through the 

Cook Mountain confining unit, aquifer storage, and 

head-dependent boundaries. There are five discharges 

or outflows: withdrawals from wells, river leakage 

through streambeds, leakage through the Cook Mountain confining unit, aquifer storage, and head-dependent boundaries. Wells remove the most water of any 

outflow component with a volumetric rate of 32.0 million ft3

/d by the end of the model simulation in 1997. 

Ground-water withdrawals from wells are offset by 

river leakage, leakage through the Cook Mountain confining unit and changes in storage in the Sparta aquifer. 

The amount of water removed from storage increases 

throughout the simulated time as withdrawals increase 

to balance the water budget. Analysis of flow indicates 

that the aquifer is behaving as conceptualized under 

increased pumping stress throughout the model area. 

Fitzpatrick and others (1990) discuss analysis of the 

ground-water budget in greater detail for the previous 

Sparta model, but much of the same observations still 

apply, only the magnitudes of the components change.

Table 7. Ground-water budget comparison between predevelopment and 1997

Predevelopment 1997

Inflow Volumetric rate

 (cubic feet per day)

Volumetric rate

 (cubic feet per day)

Component

difference

Storage 0 8,366,842 8,366,842

Leakage through Cook Mountain confining unit 1,926,614 13,180,139 11,253,525

Head-dependent boundaries 24,422 32,375 7,953

Wells 0 0 0

Recharge 16,754,894 16,754,894 0

River leakage 202,951 2,237,671 2,034,720

Total in 18,908,881 40,571,921 21,663,040

Outflow Volumetric rate

(cubic feet per day)

Volumetric rate

(cubic feet per day)

Component

difference

Storage 0 170,507 170,507

Leakage through Cook Mountain confining unit 5,397,643 643,234 -4,754,409

Head-dependent boundaries 871 249 -622

Wells 31,995,434 31,995,343

Recharge 0 0 0

River leakage 13,520,117 7,761,769 -5,758,348

Total out 18,918,631 40,571,193 21,652,562
Model Evaluation 49

Figure 23. Simulated transient ground-water budget for the Sparta aquifer, predevelopment - 1997.

-40

-30

-20

-10

0

10

20

0 5 10 15 20 25 30

STRESS PERIOD

VOLUMETRIC RATE, IN MILLION CUBIC FEET PER DAY

Flow in and out from head

dependent boundaries is

insignificant and therefore

not shown

OUTFLOW

INFLOW

Wells

Storage

River leakage

through streambeds

River leakage

through streambeds

Leakage through Cook

Mountain confining unit

Storage

Recharge Leakage through Cook

Mountain confining unit
50 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

Comparison of ground-water budgets for the current model and the previous Sparta model show similarity in total volumetric flow rates for the groundwater system with only a 7 percent decrease from the 

previous model for both predevelopment and 1997. 

Therefore, this supports the conclusion that the basic 

conceptualization of the ground-water flow system has 

remained relatively unchanged. Major differences 

appear between individual budget components (fig. 24 

A-B), primarily with flows from head-dependent 

boundaries (lateral boundaries and overlying aquifers) 

and to lesser degree flows from recharge and rivers. 

The use of general-head and river boundaries in the 

current model instead of constant-head boundaries as 

in the previous Sparta model to represent flows from 

lateral boundaries and overlying aquifers is the reason 

for this difference. With constant-head boundaries, the 

only restriction on amount of water provided to the 

aquifer is the hydraulic head difference between the 

constant head and the simulated hydraulic head in the 

cell. The other boundary types provide greater control 

on the amount of water allowed into the ground-water 

system through hydraulic conductance in the cell and 

limits on hydraulic-head gradients. Minor differences 

of flow from recharge and rivers can be explained 

within reasonable error with which these boundaries 

are known.

SIMULATED AQUIFER RESPONSE TO 

THREE HYPOTHETICAL FUTURE

WITHDRAWAL RATE SCENARIOS

The current model was used to predict the effects 

of three hypothetical future withdrawal rate scenarios 

on hydraulic heads over a 30-year period from 1998-

2027 and one scenario with withdrawals extended 

indefinitely until equilibrium conditions are attained 

(steady-state conditions). The 30-year transient simulation period was segmented into six stress periods of 5 

years each. Total withdrawals for each scenario are 

listed in table 8 with other selected volumetric budget 

information and hydraulic-head altitude data from 

model cells representative of cone of depression centers for model calibration (1997) and for predictive scenarios. Development of the scenarios was based on 

information collected from Sparta aquifer water users 

and managers in Arkansas, Louisiana, and Mississippi, 

and in collaboration with ASWCC and MCOE representatives. 

The future withdrawal rate scenarios were 

designed to address various management schemes and 

the sustainability of current withdrawal rates. Sustainability is the development and use of ground water for 

an indefinite time without causing unacceptable environmental, economic, or social consequences (Alley 

Table 8. Selected volumetric budget and hydraulic-head altitude data from model cells representing cone of depression 

centers for model calibration (1997) and for predictive scenario runs (2027 and steady state)

[Net flow is inflow minus outflow; cell 193,64 represents cell at row 193 and column 64; dry cell indicates where hydraulic head computed in model is 

below bottom of layer 2; hydraulic head as altitude in feet above National Geodetic Vertical Datum of 1929; NA, not applicable]

1997

calibration

2027

scenario 1a

Steady-state

scenario 1b

2027

scenario 2

2027

scenario 3

Pumpage (million cubic feet per day) 32.0 32.0 32.0 27.4 33.9

Net flow to rivers (million cubic feet per day) -5.5 -4.6 -2.4 -5.5 -4.6

Net flow from Cockfield aquifer (million cubic feet 

per day)

12.5 14.6 17.6 -12.7 14.5

Change in storage (million cubic feet per day) 8.2 5.2 NA 3.4 7.1

El Dorado hydraulic head (feet) (cell 193,64) -212 -222 -229 -47 -88

Pine Bluff hydraulic head (feet) (cell 114,40) -61 -78 -104 61 -41

Magnolia hydraulic head (feet) (cell 216,38) -184 -194 -220 -184 dry cell

Arkansas County hydraulic heada (feet) (cell 87,42)

a

Arkansas County hydraulic-head data are representative of the area and are not from a cone of depression.

14 -8 -44 11 -15

Monroe hydraulic head (feet) (cell 204,122) -250 -258 -264 -255 -307
Simulated Aquifer Response to Three Hypothetical Future Withdrawal Rate Scenarios 51

Figure 24. Simulated (A) predevelopment and (B) 1997 ground-water budget for the Sparta aquifer from current and previous 

Sparta models.

Predevelopment Volumetric Rates

-15

-10

-5

0

5

10

15

20

Previous model

Current model

1997 Volumetric Rates

Qs Qck Qb Qw Qr Qsw

GROUND-WATER BUDGET COMPONENT

SIMULATED FLOW, IN MILLION CUBIC FEET PER DAY

30

20

10

0

-10

-20

-30

-40

A

B

Net flow from storage

Net flow from leakage through Cook

Mountain confining unit

Net flow from head-dependent boundaries

Net flow from wells

Net flow from recharge

Net flow from river leakage

*(Net flow equal inflow minus outflow)

Qs

Qck

Qb

Qw

Qr

Qsw
52 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

and others, 1999). In Arkansas, the ASWCC has established criteria for designating a “Critical Ground-Water 

Area” based on significant ground-water declines or 

water-quality degradation. For a confined aquifer like 

the Sparta, the criteria include (1) hydraulic heads in 

wells below the top of the aquifer formation and (2) the 

rate of decline in hydraulic heads in wells is more than 

1 ft /yr over a 5-year period. This designation is used to 

promote education and public awareness for protection 

of the ground-water system. As indicated by the 1997 

simulated hydraulic heads and observations, hydraulic 

heads in the Sparta aquifer are below the top of the 

Sparta Sand in some areas. Continued pumping at 1997 

withdrawal rates causes further hydraulic-head decline 

(shown later in Scenario 1) and therefore, 1997 withdrawal rates are by definition unsustainable.

Each scenario description includes figures to 

illustrate (1) simulated hydraulic heads for 2027 or 

steady-state, (2) change in simulated hydraulic heads 

from 1997 to 2027 (or to steady-state), and (3) the difference between simulated hydraulic heads for 2027 

and the top of the Sparta Sand. Three-dimensional animations of simulated hydraulic heads from each of the 

three scenarios are included on the enclosed compact 

disk in the appendix. An explanation of software used 

and a description of each animated scenario is included 

in the appendix. 

Scenario 1- Baseline 1990-1997 

Withdrawal Rates

A model simulation using constant withdrawal 

rates from 1990-1997 was conducted for the period 

1998-2027 (scenario 1a), and then extended to steady 

state (scenario 1b). The potentiometric surfaces for 

2027 and steady state from this scenario are presented 

in figures 25a and 25b. This scenario provides a baseline for comparison of other simulations in which 

future withdrawals may increase or decrease. Results 

of the steady-state baseline scenario (fig. 25b) indicate 

a substantial number of dry cells (simulated hydraulic 

head in a cell drops below the cell bottom) in northern 

Lonoke County and a few in south Nevada County, all 

within the Sparta outcrop/subcrop area. In general, dry 

cells result from withdrawal rates exceeding available 

water. Dry cells in the Grand Prairie area could indicate 

that, based on model assumptions and results, recent 

increased withdrawals from the Sparta aquifer for irrigation cannot be indefinitely continued. In addition, the 

cone of depression in the Grand Prairie area expands 

from 2027 to steady state toward the northwest (fig. 

25b) as a result of continued withdrawal from the 

Sparta aquifer for agricultural crop irrigation in lieu of 

dwindling alluvial aquifer supplies (Joseph, 1998b; 

T.P. Schrader, U.S. Geological Survey, written commun., 2003).

Results of this scenario indicate that simulated 

hydraulic heads continue to decline (fig. 26a and 26b) 

and drop below the top of the Sparta Sand (fig. 27a and 

27b). Dry cells affect simulated hydraulic heads by 

eliminating withdrawals and acting as barriers to flow. 

As a result, hydraulic head rises occur upgradient of 

dry cell areas where recharge boundary conditions exist 

(fig. 26b). Through 2027, hydraulic heads continue to 

decline in the center of cones of depression in areas of 

El Dorado, Pine Bluff, Magnolia, and Arkansas 

County, and in areas of Monroe, Louisiana (table 8). 

Cones of depression continue to deepen and expand, 

increasing the areas where hydraulic heads have 

dropped below the top of the Sparta Sand in Arkansas 

from 7.9 percent in 1997 to 9.6 percent in 2027, a 20.5 

percent increase (table 9). For steady-state conditions, 

this area increases to 12.0 percent, a 50.6 percent 

increase from 1997.

Table 9. Percentage of selected areas where the potentiometric surface of the Sparta aquifer is below the top of the Sparta 

Sand

Percent of model area below top of Sparta Sand

Selected area 1997 Scenario 1aa

a

Scenario 1a - Baseline 1990-1997 withdrawal rates extended 30 years through 2027.

Scenario 1bb

bScenario 1b - Baseline 1990-1997 withdrawal rates extended indefinitely until equilibrium conditions are 

attained (steady-state). 

Scenario 2c

c

Scenario 2 - Baseline 1990-1997 withdrawal rates with reductions in Pine Bluff and El Dorado through 

2027.

Scenario 3d

d

Scenario 3 - Increased withdrawal rates with reductions in Pine Bluff and El Dorado through 2027.

Arkansas 7.9 9.6 12.0 5.8 6.9

Louisiana 19.4 20.5 22.4 17.6 20.7

Union County 51.9 55.5 57.4 7.3 16.6
Simulated Aquifer Response to Three Hypothetical Future Withdrawal Rate Scenarios 53

Figure 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].

Arkansas

Louisiana

Texas

Tennessee

Mississippi

Grand Prairie

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

Simulated 2027 potentiometric A

surface for scenario 1a, in feet.

Contour interval 25 feet. Datum

is NGVD of 1929

-275

-200

-100

0

100

200

300

350

EXPLANATION
54 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

Figure 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]—Continued.

Arkansas

Louisiana

Texas

Tennessee

Mississippi

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

Simulated steady-state B

potentiometric surface for

scenario 1b, in feet. Contour

interval 25 feet. Datum is

NGVD of 1929

Dry

-275

-200

-100

0

100

200

300

350

EXPLANATION

Union

Lonoke

Nevada

Grand Prairie
Simulated Aquifer Response to Three Hypothetical Future Withdrawal Rate Scenarios 55

Figure 26. 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.

Arkansas

Louisiana

Texas

Tennessee

Mississippi

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

Simulated change in hydraulic A

head from 1997-2027, scenario

1a, change in feet

-30 to -20

-20 to -10

-10 to -5

-5 to 0

0 to 5

EXPLANATION

Magnolia El Dorado

Monroe

Pine

Bluff Arkansas
56 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

Figure 26. 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—Continued.

Arkansas

Louisiana

Texas

Tennessee

Mississippi

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

B

Magnolia El Dorado

Monroe

Pine

Bluff

Simulated change in hydraulic

head from 1997-steady-state,

scenario 1b, change in feet

Dry

-100 to -50

-50 to -30

-30 to -20

-20 to -10

-10 to -5

-5 to 0

0 to 5

5 to 10

10 to 20

20 to 30

EXPLANATION

Arkansas
Simulated Aquifer Response to Three Hypothetical Future Withdrawal Rate Scenarios 57

Figure 27. 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.

Arkansas

Louisiana

Texas

Tennessee

Mississippi

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

A

Magnolia El Dorado

Arkansas

Monroe

Pine

Bluff

Scenario 1a simulated

hydraulic heads minus top

of Sparta Sand, in feet

-300 to -200

-200 to -100

-100 to -50

-50 to 0

0 to 50

50 to 100

100 to 200

200 to 300

300 to 500

500 to 1,000

1,000 to 2,000

2,000 to 4,000

EXPLANATION
58 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

Figure 27. 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—Continued.

Arkansas

Louisiana

Texas

Tennessee

Mississippi

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

B

Magnolia

El Dorado

Arkansas

Monroe

Pine

Bluff

Scenario 1b simulated

hydraulic heads minus top

of Sparta Sand, in feet

Dry

-400 to -200

-200 to -100

-100 to -50

-50 to 0

0 to 50

50 to 100

100 to 200

200 to 300

300 to 500

500 to 1,000

1,000 to 2,000

2,000 to 4,000

EXPLANATION
Simulated Aquifer Response to Three Hypothetical Future Withdrawal Rate Scenarios 59

Scenario 2 - Baseline 1990-1997 

Withdrawal Rates with Reductions in Pine 

Bluff and El Dorado

Scenario 2 presents a model simulation that was 

conducted to determine the effects of continued baseline 1990-97 withdrawal rates throughout most of the 

model area while reducing the withdrawal in the industrial areas in Pine Bluff and El Dorado. Selected industrial withdrawals in the Pine Bluff and El Dorado cones 

of depression were removed to simulate effects of 

industry changing to alternate sources of water (water 

reuse, surface-water diversions). These withdrawals 

represent the three largest industrial users of water 

from the Sparta aquifer in El Dorado and single largest 

industrial user in Pine Bluff.

The results of scenario 2 indicate that the 

removal of selected industrial withdrawals in the Pine 

Bluff area results in a shallower and less expansive 

cone of depression (fig. 28) relative to the baseline scenario (fig. 25A). In the center of the cone, hydraulic 

heads rise more than 120 ft by 2027 (fig. 29). Removal 

of selected industrial withdrawals in the El Dorado area 

also results in a shallower and less expansive cone of 

depression (fig 28) relative to the baseline scenario (fig 

25A). In the center of the cone, hydraulic heads recover 

more than 165 feet by 2027 (fig. 29). Hydraulic heads 

recover above the top of the Sparta Sand by 2027 over 

most of Union County (fig. 30). The area of Union 

County where hydraulic heads are below the top of the 

Sparta Sand decreases from 51.9 percent in 1997 to 7.3 

percent in 2027 (table 9). 

The effects of withdrawal removal in Pine Bluff 

and El Dorado on areas outside of Jefferson and Union 

Counties appear to be minimal because of the great distance between these cities and the hydrogeologic properties of the flow system. Although substantial 

hydraulic-head recovery occurs in these counties, the 

change map (fig.29) indicates continued hydraulichead decline in the Grand Prairie area as withdrawal 

rates remain at the 1990 to 1997 rate. A maximum 

decline of about 30 ft occurs in central Lonoke County. 

Hydraulic-head recovery occurs in much of north-central Louisiana, with a maximum decline of less than 10 

ft in Ouachita Parish.

Scenario 3 - Increased Withdrawal Rates 

with Reductions in Pine Bluff and El 

Dorado

A model simulation was conducted to determine 

the effects of increased pumpage throughout most of 

the model area with removal of selected industrial withdrawals in Pine Bluff and El Dorado for the period 

1998-2027. This scenario provides information on 

aquifer conditions in the region if the water withdrawal 

rates continue to increase while conservation initiatives 

in Pine Bluff and El Dorado support a reduction in 

industrial use as in scenario 2. The baseline 1990-97 

withdrawal rate was linearly increased by 25 percent 

over the 30-year period from 1998 to 2027. The simulation period was segmented into six stress periods of 5 

years each. Withdrawal rates at each well were multiplied by an appropriate percentage for each stress 

period that totals a 25 percent increase over 30 years. 

The results of scenario 3 show that throughout 

most of the model area the predicted hydraulic heads 

for this scenario (fig. 31) are higher than levels predicted for the baseline scenario (fig. 25a) and that substantial recovery results in the cones of depression 

located in the Pine Bluff and El Dorado areas. Similar 

to scenario 2, the removal of selected withdrawals in 

the Pine Bluff and El Dorado areas results in shallower, 

less expansive cones of depression (fig. 31) relative to 

the baseline scenario (fig. 25a); however, recovery is 

less because of continued increases in pumping elsewhere in the aquifer. Hydraulic heads recover more 

than 100 ft by 2027 in Pine Bluff and more than 124 ft 

by 2027 in El Dorado (fig. 32). Hydraulic heads also 

recover above the top of the Sparta Sand, as in Scenario 

2, by 2027 over most of Union County (fig. 33). However, the percentage area of Union County where 

hydraulic heads are below the top of the Sparta Sand is 

greater compared to Scenario 2 (16.6 percent compared 

to 7.3 percent in 2027) (table 9). 

Even though substantial hydraulic-head recovery 

occurs in this scenario, the change map (fig. 32) indicates continued hydraulic-head decline not only in the 

Grand Prairie area, as in Scenario 2, but also noticeably 

in much of north-central Louisiana because withdrawals increase through 2027 in areas outside Pine Bluff 

and El Dorado. The maximum decline in Scenario 3 

increases to 36 ft in central Lonoke County. North-central Louisiana hydraulic-head declines are substantially 

more compared to Scenario 2 with a maximum decline 

of 56 ft in Ouachita Parish.
60 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

Figure 28. 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.

Arkansas

Louisiana

Texas

Tennessee

Mississippi

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

El Dorado

Pine

Bluff

-275

-200

-100

0

100

200

300

350

EXPLANATION

Simulated 2027 potentiometric

surface for scenario 2, in feet.

Contour interval 25 feet. Datum

is NGVD of 1929
Simulated Aquifer Response to Three Hypothetical Future Withdrawal Rate Scenarios 61

Figure 29. 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.

El Dorado

Pine

Bluff

Arkansas

Louisiana

Texas

Tennessee

Mississippi

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

Simulated change in hydraulic

head from 1997-2027, scenario

2, change in feet

-27 to -30

-30 to -20

-20 to -10

-10 to -5

-5 to 0

0 to 5

5 to 10

10 to 20

20 to 30

30 to 50

50 to 100

100 to 170

EXPLANATION
62 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

Figure 30. 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.

Arkansas

Louisiana

Texas

Tennessee

Mississippi

El Dorado

Pine

Bluff

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

Scenario 2 simulated hydraulic

heads minus top of Sparta Sand,

in feet

-300 to -200

-200 to -100

-100 to -50

-50 to 0

0 to 50

50 to 100

100 to 200

200 to 300

300 to 500

500 to 1,000

1,000 to 2,000

2,000 to 4,050

EXPLANATION

Union
Simulated Aquifer Response to Three Hypothetical Future Withdrawal Rate Scenarios 63

Figure 31. Simulated potentiometric 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.

Arkansas

Louisiana

Texas

Tennessee

Mississippi

El Dorado

Pine

Bluff

Ouachita

Union

Grand Prairie

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

Dry

-200

-300

-100

0

100

200

300

350

EXPLANATION

Simulated 2027 potentiometric

surface for scenario 3, in feet.

Contour interval 25 feet. Datum

is NGVD of 1929
64 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

Figure 32. 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 3.

El Dorado

Pine

Bluff

Arkansas

Louisiana

Texas

Tennessee

Mississippi

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

Grand Prairie

Union

Ouachita

Simulated change in hydraulic

head from 1997-2027, scenario

3, change in feet

Dry

-70 to -50

-50 to -30

-30 to -20

-20 to -10

-10 to -5

-5 to 0

0 to 5

5 to 10

10 to 20

20 to 30

30 to 50

50 to 100

100 to 170

EXPLANATION
Simulated Aquifer Response to Three Hypothetical Future Withdrawal Rate Scenarios 65

Figure 33. 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 3.

El Dorado

Pine

Bluff

Arkansas

Louisiana

Texas

Tennessee

Mississippi

94° 93° 92° 91° 90°

31°

32°

33°

34°

35°

0 40 80 Miles

0 40 80 Kilometers

Eastern Extent of the Sparta

Aquifer Outcrop-Subcrop

Active Model

Area Boundary

Grand Prairie

Union

Ouachita

Scenario 3 simulated

hydraulic heads minus

top of Sparta Sand, in feet

Dry

-400 to -200

-200 to -100

-100 to -50

-50 to 0

0 to 50

50 to 100

100 to 200

200 to 300

300 to 500

500 to 1,000

1,000 to 2,000

2,000 to 4,050

EXPLANATION
66 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

MODEL LIMITATIONS

An understanding of model limitations is essential to effectively use flow model results. The accuracy 

of ground-water models is limited by simplification of 

complexities within the flow system, by space and time 

discretization effects, and by assumptions made in the 

formulation of the governing flow equations. Model 

accuracy is limited by cell size, number of layers, 

boundary conditions, accuracy and availability of data 

on hydraulic properties, accuracy of calibration, accuracy of pumpage estimates, historical data for calibration and verification, and parameter sensitivity. Model 

accuracy also is limited by the availability of data and 

by the interpolations and extrapolations that are inherent in using data in a model. Although a model might 

be calibrated, the calibration parameter values are not 

necessarily unique in yielding acceptable distributions 

of hydraulic head.

Surface discretization of the study area into a 

rectangular grid of square cells and vertical discretization of the Sparta aquifer requires an averaging of 

hydraulic properties. The model developed in this 

report is suitable for analyzing regional ground-water 

flow and simulating hydraulic heads resulting from 

local and regional stresses of ground-water withdrawal 

within a scale of 1 mi2. Local variations and distributions of pumping stress within a 1 mi2

 area are not well 

represented in this model. Also, hydraulic heads simulated by the model represent the hydraulic head at the 

cell center of the 1 mile square grid, not at the pumping 

well.

Some of the water that enters the ground-water 

flow system travels only a short distance before being 

discharged locally into streams and other drains. The 

digital model does not simulate all the localized flow 

because of the 1-mi discretization. The model simulations represent the intermediate- and regional-scale 

flow system. Because of the minimum stress period 

length of 1 year, seasonal changes in hydraulic-head 

measurements were not simulated. Average withdrawal 

rates are used in the model, and simulated hydraulic 

heads could be higher or lower than actual hydraulic 

heads measured during different seasons.

As the validation period of the model increases, 

the greater is the probability of generating more reliable model results. Maintaining the model by incorporating continued hydraulic-head observations and 

hydraulic-test data increases the length of the validation period and enhances the model’s capability to generate realistic projection results.

Hydraulic properties in the model do not vary 

with time. However, substantial desaturation of the 

aquifer can result in reduction in storage and hydraulic 

conductivity due to compaction of sediments. Analysis 

of such processes is possible (Galloway and others, 

2000; Kasmarek and Strom, 2002) but was not done for 

this model.

SUMMARY AND CONCLUSIONS

Concern over long-term declining hydraulic 

heads in the Sparta aquifer has resulted in a continued, 

cooperative effort by the Arkansas Soil and Water Conservation Commission, the U.S. Army Corps of Engineers, and the U.S. Geological Survey to develop, 

maintain, and use numerical ground-water flow models 

to manage and further analyze the ground-water system. The Sparta aquifer 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 recharge to the aquifer. Hydraulichead declines have caused water users and managers to 

question the ability of the aquifer to supply water for 

the long term. Large cones of depression are centered 

beneath the Grand Prairie area and the cities of Pine 

Bluff and El Dorado in Arkansas, and the city of Monroe in Louisiana. Hydraulic heads in the aquifer have 

declined at rates greater than 1 ft/yr for more than a 

decade in much of southern Arkansas and northern 

Louisiana and are now below the top of the Sparta Sand 

in parts of Columbia and Union Counties, Arkansas 

and in much of north-central Louisiana (Joseph, 1998b, 

T.P. Schrader, U.S. Geological Survey, written commun., 2003). Problems related to overdraft in the Sparta 

could result in increased drilling and pumping costs, 

decreased aquifer yield, and reduced water quality in 

areas of large drawdown. 

This report describes the development and calibration of a ground-water flow model representing the 

Sparta aquifer to simulate observed hydraulic heads 

and presents the results of three hypothetical future 

withdrawal scenarios. The Sparta aquifer occurs within 

the Sparta Sand consisting of interbedded sand, silts, 

and clays. The aquifer is confined above by the Cook 

Mountain confining unit and below by the Cane River 

confining unit. Generalized ground-water flow in the 

Sparta aquifer is from the outcrop areas to the axis of 

the Mississippi Embayment and to the south. Sources 
Summary and Conclusions 67

of recharge to the Sparta aquifer are precipitation and 

flow from rivers in the outcrop, and leakage from adjacent aquifers through confining layers.

A ground-water flow model of the Sparta aquifer 

was originally developed by Fitzpatrick and others 

(1990) and McWreath and others, (1991), and was subsequently validated twice by Kilpatrick (1992) and by 

Hays and others (1998). Although the last verification 

indicated that the Sparta model was simulating conditions in the aquifer within acceptable error for study 

goals at that time, analysis of reverification results 

identified specific areas where recalibration could 

improve the ability of the model to simulate behavior in 

areas with steep hydraulic gradients and increasing 

withdrawals (Hays and others, 1998). Because the 

Sparta model is being maintained as a tool to improve 

understanding of the aquifer and help with management issues, it was necessary to develop, construct, and 

calibrate a new Sparta model. Modifications from the 

previous Sparta model incorporated more hydrologic 

data since the 1985 calibration and are designed to 

meet the current needs of Federal, State, and local 

water managers and planners.

The transient, three-dimensional numerical 

model of ground-water flow simulates ground-water 

flow in the Sparta aquifer from 1898 to 1997. Although 

the conceptual model of the ground-water system has 

not changed from the previous Sparta model, the delineation and construction of hydrogeologic units in the 

flow model were revised. Currently, the numerical 

model has two layers representing upper and lower 

water-bearing zones of the Sparta aquifer separated by 

a quasi-three dimensional confining bed representing a 

clay confining unit in much of southwestern Arkansas 

and north-central Louisiana. Other substantive changes 

from the previous Sparta model include grid refinement, extension of the active model area northward 

beyond the Cane River Formation facies change, and 

representation of model boundaries, primarily lateral 

boundaries and representation of overlying aquifers. 

The current model area covers 38,220 mi2

 with a uniform grid of 1mi2

 cell size. 

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. Model 

results indicate the current calibration to be an appreciable improvement over the previous model calibration and subsequent verifications with a RMSE of 18.0 

ft for all observations and a RMSE of 18.9 ft in 1997. 

This compares with a RMSE of approximately 31 ft for 

observation data sets used in the previous Sparta 

model, an improvement of almost 39 percent.

The current model was used to predict the effects 

of three pumping scenarios on hydraulic heads over the 

period 1998-2027 with one extended indefinitely until 

equilibrium conditions were attained. The 30-year transient simulation period was segmented into six stress 

periods of 5 years each. By 1997, hydraulic heads in the 

Sparta aquifer were below the top of the Sparta Sand in 

much of southwestern Arkansas and north-central Louisiana. In Union County, Arkansas, over 50 percent of 

the county had hydraulic heads below the top of the 

Sparta Sand; Jefferson County, Arkansas, had no area 

with hydraulic heads below the top of the Sparta Sand.

In scenario 1a, withdrawals were held constant 

for 30 years at baseline 1990-97 rates. Hydraulic 

heads in El Dorado, Arkansas, decreased by 10 ft from 

the 1997 simulation to 222 ft below NGVD of 1929 in 

2027. Hydraulic-head altitudes in the Pine Bluff cone 

of depression showed a greater decline in the center of 

the cone than at El Dorado from 61 ft below NGVD of 

1929 in 1997 to 78 ft below NGVD of 1929 in 2027. 

With these withdrawals extended indefinitely (scenario 

1b), hydraulic heads in the Pine Bluff cone of depression declined another 26 feet to 104 feet below NGVD 

of 1929; however, hydraulic-head decline in the El 

Dorado cone of depression center was only an additional 7 ft compared to scenario 1a. 

In scenario 2, withdrawals were extended as in 

scenario 1a while industrial withdrawals were reduced 

in Pine Bluff and El Dorado. Selected withdrawals 

were removed to simulate effects of industry changing 

to alternate sources of water. Removal of selected withdrawals in both the Pine Bluff and El Dorado areas 

results in shallower, less expansive cones of depression 

relative to scenario 1a. In the cone of depression centers, hydraulic heads recover more than 120 and 165 ft, 

respectively, in the depression centers of these two 

areas. With this recovery, the area of Union County 

where hydraulic heads are below the top of the Sparta 

Sand decreases from 51.9 percent in 1997 to 7.3 percent by 2027. 

In scenario 3, withdrawals were gradually 

increased over 30 years by 25 percent while reducing 

withdrawals in industrial areas of Pine Bluff and El 

Dorado. The results are similar to scenario 2; however, 

recovery is less because of continued increases in withdrawals elsewhere in the aquifer. In the cone of depres-
68 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

sion centers for Pine Bluff and El Dorado, hydraulic 

heads recovered more than 100 and 124 ft, respectively. 

Even though substantial hydraulic-head recovery 

occurred in both scenarios 2 and 3, hydraulic heads 

continued to decline in the Grand Prairie area (scenario 

2 only) and in much of north-central Louisiana. 

Understanding the conceptual model of the 

ground-water system is essential to effectively use the 

model as a management tool. The numerical model is a 

simplification of a complex flow system; therefore, 

understanding the model limitations is essential in analyzing results of predictive scenarios. The Sparta model 

is a dynamic tool that needs to be maintained and 

updated as data are collected. Periodic model verification increases user confidence in the model’s ability to 

generate realistic long-term simulations. 
Selected References 69

SELECTED REFERENCES

Ackerman, D.J., 1987, Generalized potentiometric surface 

of the aquifers in the Cockfield Formation, southeastern 

Arkansas, spring 1980: U.S. Geological Survey WaterResources Investigations Report 87-4212, 1 sheet.

Alley, W.M., Reilly, T.E., and Franke, O.L., 1999, Sustainability of ground-water resources: U.S. Geological Survey Circular 1186, 78 p.

Arthur, J.K., and Taylor, R.E., 1990, Definition of geohydrologic framework and preliminary simulation of groundwater flow in the Mississippi Embayment aquifer system, Gulf Coastal Plain, United States: U.S. Geological 

Survey Water-Resources Investigations Report 86-

4364, 97 p.

——— 1998, Ground-water flow analysis of the Mississippi 

Embayment aquifer system, south-central United 

States: U.S. Geological Survey Professional Paper 

1416-I, 148 p.

Baker, R.C., Hewitt, F.A., and Billingsley, G.A., 1948, 

Ground water resources of El Dorado area, Union 

County: University of Arkansas Research Series No. 

14, 39 p.

Brantly, J.A., Seanor, R.C., and McCoy, K.L., 2002, Louisiana ground-water map no. 13: Hydrogeology and 

potentiometric surface, October 1996, of the Sparta 

aquifer in northern Louisiana: U.S. Geological Survey 

Water-Resources Investigations Report 02-4053, 3 

sheets.

Brantley, J.A., and Seanor, R.C., 1996, Louisiana groundwater map no. 9: Potentiometric surface, 1993, and 

water-level changes, 1968-93, of the Cockfield aquifer 

in northern Louisiana: U.S. Geological Survey WaterResources Investigations Report 95-4241, 2 sheets.

Broom, M.E., Kraemer, T.F., and Bush, W.V., 1984, A reconnaissance study of saltwater contamination in the El 

Dorado aquifer, Union County, Arkansas: U.S. Geological Survey Water-Resources Investigations Report 84-

4012, 47 p.

Cooley, R.L., and Naff, R.L., 1990, Regression modeling of 

ground-water flow: U.S. Geological Survey Techniques 

of Water-Resources Investigations, book 3, chap. B4, 

232 p.

Edds, Joe and Fitzpatrick, Daniel J., 1986, Maps showing 

altitude of the potentiometric surface and changes in 

water levels in the aquifer in the Sparta and Memphis 

Sands in eastern Arkansas, spring 1985: U.S. Geological Survey Water-Resources Investigations Report 86-

4084, 1 sheet.

Fenneman, N.M., 1938, Physiography of eastern United 

States: New York, McGraw-Hill Book Co., Inc., 689 p.

Fetter, C.W., 1994, Applied Hydrogeology, (3d ed.): New 

York, MacMillan College Publishing Co., Inc., 691 p.

Fitzpatrick, D.J., Kilpatrick, J.M., and McWreath, Harry, 

1990, Geohydrologic characteristics and simulated 

response to pumping stresses in the Sparta aquifer in 

east-central Arkansas: U.S. Geological Survey WaterResources Investigations Report 88- 4201, 50 p.

Freiwald, D.A., 1985, Average annual precipitation and runoff for Arkansas, 1951-80: U.S. Geological Survey 

Water-Resources Investigations Report 84-4363, 1 

sheet.

Freeze, R.A., and Cherry, J.A., 1979, Groundwater: Englewood Cliffs, New Jersey, Prentice-Hall, 604 p.

Galloway, D.L., Jones, D.R., and Ingebritsen, S.E., 2000, 

Land subsidence in the United States: U.S. Geological 

Survey Fact Sheet 087-00.

Grubb, H.F., 1998, Summary of hydrology of the Regional 

Aquifer Systems, Gulf Coastal Plain, south-central 

United States: U.S. Geological Survey Professional 

Paper 1416-A, 61 p.

Harbaugh, A.W., Banta, E.R., Hill, M.C., McDonald, M.G., 

2000, MODFLOW-2000, The U.S. Geological Survey 

Modular Ground-Water Model-User Guide to Modularization Concepts and the Ground-Water Flow Process: 

U.S. Geological Survey Open-File Report 00-92, 121p.

Hays, P.D., Lovelace, J.K., and Reed, T.B., 1998, Simulated 

response to pumping stress in the Sparta aquifer of 

southeastern Arkansas and north-central Louisiana, 

1998-2027: U.S. Geological Survey Water-Resources 

Investigations Report 98-4121, 25 p.

Hill, M.C., 1990, Preconditioned conjugate-gradient 2 

(PCG2), A computer program for solving ground-water 

flow equations: U.S. Geological Survey WaterResources Investigations Report 90-4048, 43 p.

——— 1992, A computer program (MODFLOWP) for estimating parameters of a transient, three-dimensional, 

ground-water flow model using nonlinear regression: 

U.S. Geological survey Open-File Report 91-484, 358 

p.

——— 1994, Five computer programs for testing weighted 

residuals and calculating linear confidence and prediction intervals on results from the ground-water parameter estimation computer program, MODFLOWP: U.S. 

Geological Survey Open-File Report 93-481, 81 p.

———1998, Methods and guidelines for effective model 

calibration: U.S. Geological Survey Water-Resources 

Investigations Report 98-4005, 90 p.

Hill, M.C., Banta, E.R., Harbaugh, A.W., Anderman, E.R., 

2000, MODFLOW-2000, The U.S. Geological Survey 

Modular Ground-Water Model-User Guide to the 

Observation, Sensitivity, and Parameter-Estimation 

Processes and Three Post-Processing Programs: U.S. 

Geological Survey Open-File Report 00-184, 209 p.

Hosman, R.L., 1996, Regional stratigraphy and subsurface 

geology of Cenozoic deposits, Gulf Coastal Plain, 
70 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

south-central United States: U.S. Geological Survey 

Professional Paper 1416-G, 35 p.

———1982, Outcropping Tertiary units in southern Arkansas: U.S. Geological Survey Miscellaneous Investigations Series I-1405, scale 1:250,000.

———1988, Geologic framework of the Gulf Coastal Plain: 

U.S. Geological Survey Hydrologic Investigations 

Atlas HA-695, 2 sheets, scale 1:2,500,000.

Hosman, R.L., and Weiss, J.S., 1991, Geohydrologic units of 

the Mississippi Embayment and Texas coastal uplands 

aquifer systems, south-central United States: U.S. Geological Survey Professional Paper 1416-B, 19 p.

Hosman, R.L., Long, A.T., Lambert, T.W., and others, 1968, 

Tertiary aquifers in the Mississippi Embayment, with 

discussions of quality of the water, by Jeffery, H.G.: 

U.S. Geological Survey Professional Paper 448-D, 29 

p.

Joseph, R.L., 1998a, Potentiometric surface of the Cockfield 

aquifer in southeastern Arkansas and the Wilcox aquifers in southern and northeastern Arkansas, October 

1996-July 1997: U.S. Geological Survey WaterResources Investigations Report 98-4084, 19 p.

———1998b, Potentiometric surface of the Sparta aquifer 

in eastern and south-central Arkansas and north-central 

Louisiana, and the Memphis aquifer in east-central 

Arkansas, October 1996-July 1997, 1997: U.S. Geological Survey Water-Resources Investigations Report 97-

4282, 19 p.

———2000, Status of water levels and selected water-quality conditions in the Sparta and Memphis aquifers in 

eastern and south-central Arkansas, 1999: U.S. Geological Survey Water-Resources Investigations Report 00-

4009, 34 p.

Kasmarek, M.C. and Strom, E.W., 2002, Hydrology and 

simulation of ground-water flow and land-subsidence 

in the Chicot and Evangeline aquifers, Houston area, 

Texas: U.S. Geological Survey Water-Resources Investigations Report 02-4022, 61 p.

Kilpatrick, J.M., 1992, Simulated response to future pumping in the Sparta aquifer, Union County, Arkansas: U.S. 

Geological Survey Water-Resources Investigations 

Report 91-4161, 25 p.

McDonald, M.G., and Harbaugh, A.W., 1988, A modular 

three-dimensional finite-difference ground-water flow 

model: U.S. Geological Survey Techniques of WaterResources Investigations, Book 6, Chapter A1, 586 p.

McWreath, H.C., III, Nelson, J.D., and Fitzpatrick, D.J., 

1991, Simulated response to pumping stresses in the 

Sparta aquifer, northern Louisiana and southern Arkansas: Louisiana Department of Transportation and 

Development Water Resources Technical Report No. 

51, 51 p.

Orzol, L.L., and McGrath, T.S., 1992, Modifications of the 

U.S. Geological Survey modular finite-difference, 

ground-water flow model to read and write geographic 

information system files: U.S. Geological Survey 

Open-File Report 92-50, 202 p.

Payne, J.N., 1968, Hydrologic significance of the lithofacies 

of the Sparta Sand in Arkansas, Louisiana, Mississippi, 

and Texas: U.S.Geological Survey Professional Paper 

569-A, 17 p.

Petersen, J.C., Broom, M.E., and Bush, W.V., 1985, Geohydrologic units of the Gulf Coastal Plain in Arkansas: 

U.S. Geological Survey Water-Resources Investigations Report 85-4116, 20 p.

Pugh, A.L., Westerfield, P.W., Gonthier, G.J., Poynter, D.T., 

2000, Altitude of the top of the Sparta and Memphis 

Sand in three areas of Arkansas, 1998: U.S. Geological 

Survey Water-Resources Investigations Report 98-

4002, 5 p.

Reed, J.E., 1972, Analog simulation of water-level declines 

in the Sparta Sand, Mississippi Embayment: U.S. Geological Survey Hydrologic Investigations Atlas HA434, map, scale 1:250,000.

Sargent, B.P., Water use in Louisiana, 2000: Louisiana 

Department of Transportation and Development Water 

Resources Special Report no. 15, 133 p.

Tait, D.B., Baker, R.C., and Billingsley, G.A., 1953, The 

ground-water resources of Columbia County, Arkansas, 

a reconnaissance: U.S. Geological Survey Circular 241, 

25 p.

Trudeau, D.A., and Buono, Anthony, 1985, Projected effects 

of proposed increased pumpage on water levels and 

salinity in the Sparta aquifer near West Monroe, Louisiana: Louisiana Department of Transportation and 

Development, Water Resources Technical Report no. 

39, 70 p. 

Williamson, A.K., Grubb, H.F., and Weiss, J.S., 1990, 

Ground-water flow in the Gulf Coast aquifer systems, 

south-central United States-A preliminary analysis: 

U.S. Geological Survey Water-Resources Investigations Report 89-4071, 124 p.
Appendix 71

APPENDIX - DIGITAL THREE-DIMENSIONAL ANIMATIONS OF SIMULATED

HYDRAULIC-HEAD SURFACES FOR THE 

THREE PREDICTIVE SCENARIOS

Animations illustrating each of the three hypothetical future water demand scenarios described in the 

report are included in AVI format on the enclosed compact disk. A README file also explains how to install 

and view the AVI on a PC.

The animations contained on the CD were created using Tecplot version 9.2-0-3 for MS-WINDOWS 

Copyright (c) 1988-2002 Amtec Engineering, Inc.

Hydraulic-head data for the animations were 

read from the HDS output file from MODFLOW-2000 

and reformatted using code written with the Microsoft 

Visual Basic 6.0 editor within Microsoft Access 2000 

(9.0.2720) Copyright (c) 1992-1999. 

Animations included on the CD are simulated 

hydraulic heads for the following:

sc1.avi - scenario 1a, baseline 1990-1997 withdrawal rates extended through 2027 and then to steadystate.

sc1_oblq.avi - same as scl.avi, but with an 

oblique view.

sc2.avi - scenario 2 extended through 2027, but 

reduction in withdrawals from industrial areas of Pine 

Bluff and El Dorado

sc2_oblq.avi - same as sc2.avi, but with an 

oblique view.

sc3.avi - scenario 3, 25 percent increase in baseline 1990-1997 withdrawal rates over 30 years, with 

reduction in withdrawals from industrial areas of Pine 

Bluff and El Dorado

sc3_oblq.avi - same as sc3.avi, but with an 

oblique view.