science for a changing world

Prepared in cooperation with the

ARKANSAS SOIL AND WATER CONSERVATION COMMISSION

SUSTAINABLE-YIELD ESTIMATION FOR THE SPARTA 

AQUIFER IN UNION COUNTY, ARKANSAS

Water-Resources Investigations Report 99-4274

Jim,,,

U.S. Department of the Interior 

U.S. Geological Survey
U.S. Department of the Interior 

U.S. Geological Survey

SUSTAINABLE-YIELD ESTIMATION FOR THE SPARTA 

AQUIFER IN UNION COUNTY, ARKANSAS

By Phillip D. Hays ____

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 99-4274

Prepared in cooperation with the

ARKANSAS SOIL AND WATER CONSERVATION COMMISSION

Little Rock, Arkansas 

2000
U.S. DEPARTMENT OF THE INTERIOR 

BRUCE BABBITT, Secretary

U.S. GEOLOGICAL SURVEY 

Charles G. Groat, Director

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. Government

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
CONTENTS

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

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

Study Area Description............................................................................................................................................. 4

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

Ground-Water Flow Model Description.................................................................................................................... 5

Approach...............................................................................................................................................................^ 5

Sustainable- and Stabilization-Yield Simulation Results.................................................................................................... 7

Sustainable-Yield Simulation Results ....................................................................................................................... 8

Stabilization-Yield Results...................................................................................................................................... 13

Doubled-Pumpage Rate Simulation Results...................................................................................................................... 15

Summary and Conclusions................................................................................................................................................ 15

References......................................................................................................................................................................... 17

ILLUSTRATIONS

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

2. Diagrammatic section of the Sparta aquifer in the Union County area................................................................ 7

3. Graph showing observed and predicted trend for pumpage from the Sparta aquifer in Union County, Arkansas, 

1985-2027; sustainable-yield trend shows how pumpage must change to achieve Sustainable yield.................. 9

4. Map showing simulated steady state potentiometric surface of the Sparta aquifer with Union County 

pumpage decreased to 28 percent of 1997 rates (simulation la)........................................................................ 10

5. Map showing simulated transient potentiometric surface of the Sparta aquifer in 2027 with all pumpage 

increasing at the 1985-1997 rates ........................................................................................................................11

6. Volumetric budget components (entire model) for sustainable-yield scenarios................................................. 12

7. Map showing simulated steady state potentiometric surface of the Sparta aquifer with Union County 

pumpage decreased to 91 percent of 1997 rates (simulation 3a)........................................................................ 14

8. Volumetric budget components (entire model) for stabilization-yield scenarios............................................... 16

TABLES

Table 1. Union County sustainable-yield, stabilization-yield, and doubled-pumpage scenarios ..................................... 5

2. Reported and projected pumping estimates for Union County and the model area outside of Union County... 8

3. Sustainable-yield results for the top of the Sparta Sand water-level target for current rate of increase and 

double current rate of increase pumpage conditions .......................................................................................... 9

4. Stabilization-yield results for the top of the El Dorado sand water-level target for current rate of increase 

and double current rate of increase pumpage conditions.................................................................................. 13

Contents iii
SUSTAINABLE-YIELD ESTIMATION FOR THE 

SPARTA AQUIFER IN UNION COUNTY, ARKANSAS

By Phllljp D. Hays

ABSTRACT

Options for utilizing alternative sources of water 

to alleviate overdraft from the Sparta aquifer and 

ensure that the aquifer can continue to provide abundant water of excellent quality for the future are being 

evaluated by water managers in Union County. Sustainable yield is a critical element in identifying and 

designing viable water supply alternatives. With sustainable yield defined and a knowledge of total water 

demand in an area, any unmet demand can be calculated. The ground-water flow model of the Sparta aquifer was used to estimate sustainable yield using an 

iterative approach.

The Sparta aquifer is a confined aquifer of 

regional importance that comprises a sequence of 

unconsolidated sand units that are contained within the 

Sparta Sand. Currently, the rate of withdrawal in some 

areas greatly exceeds the rate of recharge to the aquifer 

and considerable water-level declines have occurred. 

Ground-water flow model results indicate that the aquifer cannot continue to meet growing water-use 

demands indefinitely and that water levels will drop 

below the top of the primary producing sand unit in 

Union County (locally termed the El Dorado sand) by 

2008 if current water-use trends continue. Declines of 

that magnitude will initiate dewatering of the El 

Dorado sand.

The sustainable yield of the aquifer was calculated by targeting a specified minimum acceptable 

water level within Union County and varying Union 

County pumpage within the model to achieve the target 

water level. Selection of the minimum target water 

level for sustainable-yield estimation was an important 

criterion for the modeling effort. In keeping with the 

State Critical Ground-Water Area designation criteria 

and the desire of water managers in Union County to 

improve aquifer conditions and bring the area out of the

Critical Ground-Water Area designation, the approximate altitude of the top of the Sparta Sand in central 

Union County was used as the minimum water level 

target for estimation of sustainable yield in the county. 

A specific category of sustainable yield stabilization 

yield, reflecting the amount of water that the aquifer 

can provide while maintaining current water levels 

also was determined and provides information for 

short-term management. The top of the primary producing sand unit (the El Dorado sand) was used as the 

minimum water-level target for estimating stabilization 

yield in the county because current minimum water 

levels in central Union County are near the top of the El 

Dorado sand.

Model results show that withdrawals from the 

Sparta aquifer in Union County must be reduced to 28 

percent of 1997 values to achieve sustainable yield and 

maintain water levels at the top of the Sparta Sand if 

future pumpage outside of Union County is assumed to 

increase at the rate observed from 1985-1997. Results 

of the simulation define a very large current unmet 

demand and represent a substantial reduction in the 

county's current dependence upon the aquifer. If future 

pumpage outside of Union County is assumed to 

increase at double the rate observed from 1985-1997, 

withdrawals from the Sparta aquifer in Union County 

must be reduced to 25 percent of 1997 values to 

achieve sustainable yield. Withdrawals from the Sparta 

aquifer in Union County must be reduced to about 88 

to 91 percent (depending on pumpage growth outside 

of the county) of 1997 values to stabilize water levels 

at the top of the El Dorado sand. This result shows that 

1997 rate of withdrawal in the county is considerably 

greater than the rate needed to halt the rapid decline in 

water levels.

Abstract 1
INTRODUCTION

The Sparta aquifer is a confined aquifer of 

regional importance that comprises a sequence of 

unconsolidated sand units that are contained within the 

Sparta Sand. In the Union County area, the informal 

terms "Green sand" and "El Dorado sand" are applied 

to the upper and lower major sand units within the 

Sparta aquifer, respectively. For the sake of clarity, it 

should be noted that the term "Sparta aquifer" is 

applied to a sequence of hydraulically connected sands 

that are often separated by silts and clays and is not an 

equivalent term with "Sparta Sand" the formal name 

for the geologic formation. This distinction is important because by Arkansas law, Critical Ground-Water 

Area (CGWA) designation criteria are based on the top 

of the geologic formation rather than the top of the 

aquifer. Thus, in areas where clays and silts in the 

Sparta Sand (the geologic formation) occur above productive sands, the top of the Sparta aquifer will not 

coincide with the top of the Sparta Sand. In this report, 

the term "Sparta Sand" will always refer to the geologic formation (comprising sands, silts, and clays), 

and the term "Sparta aquifer" will refer to the sequence 

of productive, hydraulically connected sands that constitute a part of the geologic formation.

The Sparta aquifer extends across much of eastern and southeastern Arkansas and into adjoining states 

(fig. 1) and is a principle water resource for municipal, 

industrial, and agricultural uses. In Arkansas, water use 

from the aquifer has doubled since 1975 (Holland, 

1999). Currently, the rate of withdrawal in some areas 

greatly exceeds the rate of recharge to the aquifer. 

Large cones of depression are centered beneath the 

Grand Prairie area and the cities of Pine Bluff and El 

Dorado in Arkansas areas included in CGWAs designated by the Arkansas Soil and Water Conservation 

Commission (ASWCC). Water levels in the aquifer 

have declined at rates averaging greater than 1 foot per 

year (ft/yr) for more than a decade in areas of southern 

Arkansas and northern Louisiana (an average decline 

greater than 4.5 ft/yr in El Dorado since 1943) (Baker 

and others, 1948; R.L. Joseph, U.S. Geological Survey, 

written commun., 1999), and are now below the top of 

the Sparta Sand in parts of Union County, Arkansas 

(Joseph, 1998). Results from the regional-scale, digital 

ground-water flow model for the Sparta aquifer (Hays 

and others, 1998; Hays and Fugitt, 1999) indicate that 

the aquifer cannot continue to meet growing water-use 

demands indefinitely and that water levels will drop 

below the top of the primary producing sand unit in

Union County (locally termed the El Dorado sand) by 

2008 if current water-use trends continue. As water levels decline below the top of the El Dorado sand, the 

sand will begin to dewater, resulting in increased drilling and pumping costs, loss of yield, and decreased 

water quality.

Sustainable yield (sometimes termed "safe 

yield") is the volumetric rate of water that an aquifer 

can provide while maintaining desirable aquifer conditions (primarily water levels and water quality) such 

that the aquifer remains a viable resource for long-term 

use. An aquifer managed under sustainable-yield conditions is a self-renewing resource.

No accurate estimate of Sustainable yield for the 

Sparta aquifer in Union County, Arkansas, has previously been determined. Options for utilizing alternative 

sources of water to alleviate overdraft (removal of 

water at a rate greater than can be sustained indefinitely) from the Sparta aquifer and ensure that the aquifer can continue to provide abundant water of excellent 

quality for the future are being evaluated by water managers in Union County. Sustainable yield is a critical 

element in identifying and designing viable water supply alternatives. With Sustainable yield defined (and a 

clear understanding of the criteria under which that 

yield is Sustainable) and a knowledge of total water 

demand in an area, any unmet demand water that 

must be supplied from alternative sources can be calculated by taking the difference between "total 

demand" and "sustainable yield." The ground-water 

flow model of the Sparta aquifer offers a tool capable 

of determining sustainable yield using an iterative 

approach (Fitzpatrick and others, 1990; McWreath and 

others, 1991;Kilpatrick, 1992; Hays and others, 1998).

The U.S. Geological Survey (USGS) in cooperation with the ASWCC, conducted a study within the 

framework of the ongoing Sparta aquifer modeling 

project (a long-term effort maintaining and using the 

Sparta model to provide information needed for management of the aquifer) to determine and document 

sustainable yield and to provide aquifer-yield information needed to determine unmet demand for the Sparta 

aquifer in Union County. Study results will provide 

water managers in Arkansas with information needed 

to develop water-management strategies. The study is 

consistent with the USGS mission in Arkansas in that 

the understanding of the Sparta aquifer in southeastern 

Arkansas has been enhanced and scientific information 

on the aquifer has been provided to assist water mangers.

2 Sustainable-Yield Estimation for the Sparta Aquifer in Union County, Arkansas
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STUDY AREA (UNION COUNTY)

Physiographic boundaries from Fenneman, 1938 

0 2.0 40 MILES

0 20 40 KILOMETERS

Figure 1. Location of study and model areas.

Introduction 3
The purpose of this report is to present an estimation of sustainable yield for Union County. This report 

details results of the study specific to Union County 

sustainable-yield estimation and provides minimal 

description of the ground-water Sparta flow model, 

which was previously developed and applied (Fitzpatrick and others, 1990; Hays and others, 1998).

Study Area Description

The study focuses on Union County in central 

southern Arkansas. The county comprises approximately 1,055 square miles (mi ) in total area and has a 

population of approximately 47,000 (1990 estimate) 

(fig. 1). The study area lies almost entirely within the 

West Gulf Coastal Plain section of the Coastal Plain 

Physiographic Province (Fenneman, 1938). In Union 

County, land-surface altitudes range from about 80 feet 

(ft) above sea level 1 along the Ouachita River to more 

than 300 ft in the southwestern part of the county; 

topography is predominated by low-relief rolling hills 

and lowland areas. Surficial geology is predominated 

by the unconsolidated clastic sediments of the Tertiary 

Claiborne Group with more minor exposures of Quaternary Alluvium deposits proximal to local streams. 

Geological structure in the area is characterized by 

abundant normal and growth faults with the occurrence 

of fault-associated folding; otherwise strata in the area 

are relatively flat lying. The principal surface-water 

drainages in Union County are the Ouachita River, 

Smackover Creek, Three Creeks Bayou, Little Cornie 

Bayou, Lapile Creek and Bayou Loutre. The major surface-water bodies present in the county are Lakes 

Felsenthal and Calion; a total of 17 mi2 of land area is 

inundated in the county. Mean annual precipitation is 

approximately 50 inches (Freiwald, 1985). Land use in 

the area predominantly comprises agriculture, silviculture, forest, wetland, urban, commercial, and industrial 

uses; land-use activities have a strong affect on water 

resource use patterns.

Water use from the Sparta aquifer in the study 

area reflects predominant land uses; ground water is 

intensively used for municipal supply, agriculture, and 

manufacturing of forest products, chemicals, and other 

industrial products. For data reported to ASWCC in

1997, approximately 50 facilities in the county reported 

water use totaling about 2.2 million cubic feet per day 

(ft3/d). Based on quality control work and responses 

tendered by major water uses (Hays and others, 1998), 

this figure was increased to 2.8 million ft3/d for application in the model. Of the reported total, 56 percent is 

used for public supply, 2 percent is used for singledwelling domiciles, 40 percent is used for industry, and 

2 percent is used for agriculture.

Previous Studies

In 1985, the USGS, in cooperation with the 

ASWCC and the Louisiana Department of Transportation and Development (LaDOTD), began a study of the 

hydrogeologic characteristics of the Sparta aquifer and 

the regional effects of increased pumpage on water levels in the aquifer. The primary product of the study was 

a digital model of ground-water flow in the Sparta 

aquifer (Fitzpatrick and others, 1990; Me Wreath and 

others, 1991), referred to here as the "Sparta model." 

Model construction, calibration , and first application 

are fully described in Fitzpatrick and others (1990) and 

Me Wreath and others (1991). These 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, model area hydrogeologic setting, and a 

description of the aquifer also are included in the two 

reports and are not repeated here. In 1991, the model 

was verified (Kilpatrick, 1992) by the USGS in cooperation with the ASWCC; selected scenarios of future 

ground-water withdrawals in Union County, Arkansas, 

were simulated. The model was reverified with updated 

pumpage and potentiometric data in 1997, and various 

pumping scenarios were simulated (Hays and others, 

1998).

^n this report, sea level refers to National Geodetic Vertical 

Datum of 1929 a geodetic datum derived from a general adjustment of the first-order level nets of the United States and Canada, 

formerly called Sea Level Datum of 1929.

4 Sustainable-Yield Estimation for the Sparta Aquifer in Union County, Arkansas
Ground-Water Flow Model Description APPROACH

The computer code used by Fitzpatrick and others (1990) and Me Wreath and others (1991) for development of the Sparta model was the modular finitedifference ground-water flow model (MODFLOW) 

developed by McDonald and Harbaugh (1988). MODFLOW simulates flow in three dimensions using a 

block-centered, finite-difference equation approach to 

the solution of the partial-differential equation for flow. 

Details of model development, construction, and calibration are presented in Fitzpatrick and others (1990) 

and Me Wreath and others (1991). Details on pumpage 

data updating, assimilation and input, model reverification and error analysis are given in Kilpatrick (1992) 

and Hays and others (1998). For this study, as for the 

modeling work described in Hays and others (1998), 

the Sparta model was converted to run in 

MODFLOWARC, a MODFLOW pre- and post-processor that allows interface with a geographical information system (Orzol and McGrath, 1992). The model 

was re-run after conversion (Hays and others, 1998) to 

ensure that functionality and output were unchanged 

from originally reported results.

For the current sustainable-yield modeling, 

described in this report, no basic model parameters, or 

calibration parameters, were changed, and no changes 

in input that would violate model assumptions were 

applied. Study objectives were achieved by varying of 

well pumpage stress in a discrete area.

The sustainable yield of the aquifer was calculated by targeting a specified minimum acceptable 

water level within Union County and varying Union 

County pumpage within the model to achieve the target 

water level. A specific category of sustainable yield 

stabilization yield, reflecting the amount of water that 

the aquifer can provide while maintaining current 

water levels also was determined using the same 

approach. In this report, the term "sustainable yield" 

will refer to the yield that can be sustained without 

water levels declining below the top of the Sparta Sand, 

and "stabilization yield" will refer to the yield that can 

be sustained without having water levels decline below 

their current position (just above the top of the El 

Dorado sand). Sustainable and stabilization yields were 

estimated for each of two pumping conditions outside 

of the county: One with simulated future pumpage outside of Union County accelerating at the rate of 

increase observed from 1985-1997 (table 1), and a second with future pumpage outside of Union County 

accelerating at twice the rate of increase observed from 

1985-1997 (table 1).

To provide information on aquifer conditions if 

the rate of pumpage from the Sparta aquifer accelerates 

within Union County, a simulation was conducted representing a scenario in which the current (1985-1997) 

rate of increase in pumpage in the county was doubled 

(table 1). This scenario represents the potential for a 

large increase in community and industrial growth and 

tests the viability of relying exclusively upon the Sparta 

aquifer to supply water needs associated with such 

growth.

Table 1. Union County sustainable-yield, stabilization-yield, and doubled-pumpage scenarios 

Sustainable yield

(1) Pumpage outside of Union County increasing at 1985-1997 rate

(2) Pumpage outside of Union County increasing at double the 1985-1997 rate 

Stabilization yield

(3) Pumpage outside of Union County increasing at 1985-1997 rate

(4) Pumpage outside of Union County increasing at double the 1985-1997 rate 

Doubled pumpage

(5) Current (1985-1997) rate of increase of pumpage in Union County is doubled

Approach 5
Sustainable yield and stabilization yield refer to 

the rate at which water may be pumped out of the aquifer while maintaining the target water level, whether 

that level be the top of the Sparta Sand (for Sustainable 

yield) or the top of the El Dorado sand (for stabilization 

yield). Under steady-state conditions, there is no contribution from aquifer storage to water removed by 

pumping, and the amount of water moving into the 

aquifer is equal to the amount being removed. Under 

transient conditions, a time period in which to achieve 

the target water level is selected (30 years in this case), 

and pumpage is varied to achieve the target at the end 

of the simulation; water contributed from storage helps 

to meet the target water level under the given pumping 

conditions if the time period selected is less than that 

required to achieve steady-state conditions.

Selection of the minimum target water level for 

sustainable-yield estimation was an important criterion 

for the modeling effort. Arkansas law has established 

that an area served by a confined aquifer be designated 

as a CGWA if 1) water levels have dropped below the 

top of the geologic formation containing the aquifer or 

2) water levels are dropping more than 1 ft/yr. The 

Sparta aquifer in Union, Columbia, Ouachita, Calhoun, 

and Bradley Counties meets CGWA designation criteria, and these counties were designated as the State's 

first CGWA in 1996. The CGWA law was developed 

by the State using available hydrologic data and applying hydrologic principles; when water levels drop 

below the top of a confined aquifer, the aquifer 

becomes unconfined in that area and dewatering 

ensues. In addition, as water levels drop below the top 

of the aquifer, offset of lithostatic pressure by hydraulic 

pressure head reaches a minimum and buoyant support 

of the aquifer by water is lost. These conditions result 

in compaction of the aquifer matrix and can damage the 

aquifer by decreasing hydraulic conductivity. Therefore, maintaining water levels above the top of a confined aquifer protects the integrity of the aquifer for 

long-term use. The top of the uppermost producing 

sands defining the Sparta aquifer does not necessarily 

coincide with the top of the Sparta Sand (the gross geologic formation); the top of the uppermost producing 

sand may be interpreted as the top of the aquifer. Vertical position and areal extent of producing sands within 

the Sparta Sand vary considerably across the region. 

By defining the top of the Sparta Sand as a minimum 

water-level criterion for CGWA designation, regulators 

have avoided adapting the law from one area of the 

State to another to address facies changes and extent of

individual sand units and provide protection for more 

minor sand units that may be above primary producing 

sands (fig. 2).

In keeping with the State CGWA designation criteria and the desire of water managers in Union County 

to improve aquifer conditions and bring the area out of 

the CGWA designation, the approximate altitude of the 

top of the Sparta Sand in central Union County (50 ft 

below sea level) was used as the minimum water level 

target for estimation of sustainable yield in the county. 

The top of the primary producing sand unit (the El 

Dorado sand, with an approximate altitude of about 

300 ft below sea level in central Union County) was 

used as the minimum water-level target for estimating 

stabilization yield in the county; this estimation was 

conducted to provide information for short-term management. Minimum water levels in the county are very 

near the top of this unit at this time, and as such this 

yield is termed the stabilization yield, representing the 

amount of water that the aquifer can provide while 

maintaining current water levels.

Sustainable and stabilization yields of the aquifer were calculated by targeting the specified minimum 

desired water level within Union County and varying 

simulated pumpage within Union County to achieve 

that water level. The final solution was calculated iteratively; pumpage was input for each of a series of 

model runs, a resultant minimum water level was determined, and if the resultant was not the target water 

level, Union County pumpage was adjusted in a succeeding run to move closer to the target water level. 

Changes to pumpage in Union County for each iteration were applied as uniform percentage increases or 

decreases in pumping cells across the county. For 

example, in a solution whereby 28 percent of current 

pumpage in the county was used and the resulting 

model-derived water levels were equal to the target 

water level, then 28 percent of current pumpage is the 

aquifer yield estimated to result in the target water 

level. Basically, pumpage needed to be decreased to 

achieve the target level.

Steady-state and transient (achieving the target 

water level at 30 years) solutions were generated for 

sustainable and stabilization yields under both pumping conditions. The steady-state solutions calculate 

flows and water levels resulting from applied pumping

6 Sustainable-Yield Estimation for the Sparta Aquifer in Union County, Arkansas
NORTHWEST SOUTHEAST

NOT TO SCALE 

DATUM IS SEA LEVEL

CITY OF 

ELDORADO

LAND 

.SURFACE 

FEET

BOTTOM OF 

SPARTA SAND 

-550 FEET

Figure 2. Diagrammatic section of the Sparta aquifer in the Union County area.

stress without any input into the system from storage 

and provide the most definitive estimation of sustainable yield. The transient solutions are valuable for 

characterizing contribution from storage through time 

and showing the amount of time in which the aquifer 

will respond to decreased pumping stress. Thus, two 

separate solutions were generated for each pumping 

condition outside of Union County. More than 600 

model runs were conducted in the iterative approach to 

achieve the target water levels for the steady-state and 

transient solutions for the sustainable- and stabilization-yield pumping scenarios. The iterations were continued at 1 percent adjustment increments for each 

scenario until the percentage value that resulted in a 

minimum water level closest to the target was obtained. 

All minimum water levels were within 2 ft of the target 

water level.

SUSTAINABLE- AND STABILIZATIONYIELD SIMULATION RESULTS

Sustainable-yield simulations were run for 

steady-state and transient conditions using two scenarios (table 1). Steady-state solutions were derived to 

provide the best long-term estimation of sustainable 

yield; the steady-state solution is important because 

that solution provides the Union County pumpage estimate (presented as a percentage of 1997 pumpage in 

this report) that would maintain water levels at the top 

of the Sparta Sand indefinitely and enable the county to 

address the CGWA criteria. Transient solutions were 

derived to provide information on the response of the 

aquifer over time; the transient solution provides the 

county pumpage estimate that would achieve water 

levels at the top of the Sparta Sand after 30 years, but 

not necessarily for an indefinite period of time. Under 

scenario 1, pumpage from the Sparta aquifer outside of 

Union County was increased at the 1985-1997 rate of

Sustainable- and Stabilization-Yield Simulation Results
increase for 1998-2027 in the transient simulation and 

was set at the projected 2027 maximum in the steadystate simulation (table 2). The trends derived from 

1985-1997 data were determined separately for each 

individual county and applied on a county-by-county 

basis to the 1998-2027 simulation period. Under scenario 2, pumpage from the Sparta aquifer outside of 

Union County was increased at double the 1985-1997 

rate of increase for 1998-2027 in the transient simulation and was set at the projected 2027 double-rate maximum in the steady-state simulation.

Table 2. Reported and projected pumping estimates for 

Union County and the model area outside of Union County 

[ftVd, cubic foot per day]

Union County Outside Union County

2.8 million frVd 30.3 million ft3/d 

3.7 million frVd 49.1 million tf/d

1997

2027 

(projected)

2027 4.8 million ft3/d 100.1 million 

(projected rate x 2)

Stabilization yield simulations also were run for 

both steady-state and transient conditions using two 

scenarios (table 1, scenarios 3 and 4). Just as for the 

sustainable-yield target, the steady-state and transient 

solutions provide long-term and 30-year results, 

respectively, for the stabilization target. Under scenario 

3, pumpage from the Sparta aquifer outside of Union 

County was increased at the 1985-1997 rate of increase 

for 1998-2027 in the transient simulation and was set at 

the projected 2027 maximum in the steady-state simulation (table 2). Under scenario 4, pumpage from the 

Sparta aquifer outside of Union County was increased 

at double the 1985-1997 rate of increase for 1998-2027 

in the transient simulation and was set at the projected 

2027 double-rate maximum in the steady state simulation.

Sustainable-Yield Simulation Results

For simulation la, a steady state simulation in 

which future pumpage outside of Union County is 

assumed to increase at the rate observed from 1985- 

1997, withdrawals from the Sparta aquifer in Union 

County must be reduced to 28 percent of 1997 values 

(table 3) to achieve sustainable yield and maintain 

water levels at the top of the Sparta Sand (50 ft below 

sea level). Pumpage in this simulation was assigned as

the rate attained after 30 years of assumed increases. 

Results of simulation la define a very large current 

unmet demand and represent a substantial reduction in 

the county's current dependence upon the aquifer (fig. 

3). Unmet demand refers to the amount of water that is 

required for various uses that cannot be provided by the 

aquifer on an indefinite basis. A comparison of the simulated potentiometric surface generated from results of 

simulation la (fig. 4) with the potentiometric surface 

simulated for a scenario completed for a previous study 

(Hays and others, 1998) in which all pumpage (including Union County) continues to increase at the 1985- 

1997 rate for 30 years (fig. 5) underscores the magnitude of the unmet demand and the effect on the aquifer. 

To achieve sustainable yield, the unmet demand 

defined by the model simulation and any future 

increases in demand resulting from growth in the 

county would require measures such as reducing water 

use through conservation and the use of alternative 

sources. Water levels in central Union County (near El 

Dorado) could be expected to rebound to near the top 

of the Sparta Sand quite rapidly with reduction of 

pumpage. Because the Sparta aquifer is confined in 

Union County, changes in stress are communicated 

rapidly across the aquifer, and water levels will respond 

quickly.

Whereas the result of simulation la provides the 

appropriate sustainable yield for long-term management of the aquifer (28 percent of 1997 pumpage rates), 

a transient solution simulation Ib set up to achieve 

a specific target water level at a specific point in time 

provides information on the volumetric flows to and 

from the aquifer through time. This information facilitates improved understanding of aquifer behavior and 

temporal response. We expect that the resultant in a 

transient solution would be greater than that for the 

steady-state solution for a given scenario in which all 

other factors remain constant, because water can still 

be removed from storage in the transient solution. 

Thus, the allowable pumpage for the transient solution 

would be greater than the sustainable yield pumpage 

for steady-state solution although achieving the same 

water-level target.

To evaluate aquifer response, transient simulation (simulation Ib) results, in which pumpage outside 

of Union County was increased over six 5-year stress 

periods, indicate that pumpage from the aquifer in

8 Sustainable-Yield Estimation for the Sparta Aquifer in Union County, Arkansas
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_ \ TREND

1 1 1 1

1980 1990 2000 2010 2020 2030

Figure 3. Observed and predicted trend for pumpage from the Sparta aquifer in Union County, Arkansas, 1985-2027; 

sustainable-yield trend shows how pumpage must change to achieve sustainable yield.

Union County should be reduced to 32 percent of current values (table 3) to maintain water levels at the top 

of the Sparta Sand and show that most of the targeted 

rebound occurs within 5 years of decreasing withdrawals. The simulation potentiometric surface (after 30 

years) is similar to that shown in figure 4 for simulation 

la. Volumetric budget components are shown in figure 

6; simulated inflows to and outflows from the aquifer pumpage removed by wells, net recharge added 

by precipitation, water moving from and to rivers, 

water moving from and into the overlying Cockfield 

aquifer, boundary flow, and changes in water stored in 

the aquifer are depicted.

Simulation 2a is a steady state simulation in 

which future pumpage outside of Union County is 

assumed to increase at double the rate observed from 

1985-1997. Pumpage in this simulation was assigned 

as the rate attained after 30 years of projected increases. 

Under this scenario, withdrawals from the Sparta aquifer in Union County must be reduced to 25 percent of 

1997 values (table 3) to achieve sustainable yield and 

maintain water levels at the top of the Sparta Sand (50 

ft below sea level). Again, there is a large unmet 

demand. However, only an additional 3 percent reduction in Union County pumpage as compared to the

Table 3. Sustainable-yield results for the top of the Sparta Sand water-level target for current rate of increase and double 

current rate of increase pumpage conditions

Scenario Union County pumpage 

(percent of 1997 rate)

Pumpage outside of Union County set at projected 2027 value for steady-state 

solution, and increasing at the 1985-1997 rate of increase for 1998-2027 in transient solution

Simulation la, Steady state 

Simulation Ib, Transient

Pumpage outside of Union County set at projected 2027 double-rate maximum 

value for steady-state solution, and increasing at double the 1985-1997 rate for 

1998-2027 for transient solution

Simulation 2a, Steady state 

Simulation 2b, Transient

28 percent 

32 percent

25 percent 

30 percent

Sustainable- and Stabilization-Yield Simulation Results
_93° 92°30' 91°30'

a 

m 

&

io 

I

5' c

I 

8

I

33°30' - EXPLANATION MODEL - BOUNDARY SIMULATED POTENTIOMETRIC CONTOUR Shows water level altitude in tightly cased wells. Contour interval 25 feet. Datum is sea level

32°30' - 0 10 20 30 40 50 KILOMETERS

Figure 4. Simulated steady state potentiometric surface of the Sparta aquifer with Union County pumpage decreased to 28 percent of 1997 rates (simulation 1a).
93° 92°30' 91°30'

8?

§3

er? o>Q.

$

o <E

3

33°30' - EXPLANATION MODEL BOUNDARY SIMULATED 2027 POTENTIOMETRIC CONTOUR-Shows altitude at which water level would have stood in tightly cased wells. Contour interval 25 feet. Datum is sea level

\B0UNDAR\

32°30' r

0 10 20 30 40 KILOMETERS

Figure 5. Simulated transient potentiometric surface of the Sparta aquifer in 2027 with all pumpage increasing at the 1985-1997 rates (Hays and others, 1998).
Cook Mountain 

confining unit

Lateral boundaries

and overlying

aquifer

(Specified head) 

40.7 

2.1 «<-

t

=

: 

-^

~rn *- Pumpage = 49.9 Lakes 

and Recharge

Cockfield aquifer

^

r 1 ^-

Lx -10 o JT IO.O

6.3 4l3

Sparta aquifer

Change in storage = 0

Simulation 1a, Steady state simulation, Union County pumpage at 28 percent of 1997 value.

Pumpage outside of Union County assigned as the rate attained after 30 years at 1985-

1997 rate of increase

Cook Mountain 

confining unit

Lateral boundaries 

and overlying

aquifer

(Specified head) 

37.2 

2.1 +

Simulation 1b, 30-year transient simulation, Union County pumpage at 32 percent of 1997 value. 

Pumpage outside of Union County increasing at 1985-1997 rate of increase

Recharge

Cook Mountain 

confining unit

Lateral boundaries 

and overlying

aquifer

(Specified head) 

86.8 

1.6 <

6.1 8.4

Sparta aquifer

Change in storage = 0

Simulation 2a, Steady state simulation, Union County pumpage at 25 percent of 1997 value.

Pumpage outside of Union County assigned as the rate attained after 30 years at double

the 1985-1997 rate of increase

Cook Mountain 

confining unit

Lateral boundaries 

and overlying

aquifer

(Specified head) 

69.0 

1.7 <*

i

_^^

L~in~) ^Pumpage = 100.9 Lakes 

and Recharge

r*nr»kfiAlri am lifar - JTVj

k

7.6 

Sparta aquifer

Storage loss = 23.5

"-*^_ I

4*

4.3

Simulation 2b, 30-year transient simulation. Union County pumpage at 30 percent of 1997 vaiue. 

Pumpage outside of Union County increasing at double the 1985-1997 rate of increase

Figure 6. Volumetric budget components (entire model) for sustainable-yield scenarios. 

12 Sustainabie-Yield Estimation for the Sparta Aquifer in Union County, Arkansas
1985-1997 increase rate scenario (simulation la) is 

required to offset the greater rate of pumpage in surrounding counties. This finding corroborates area 

pumpage data showing that withdrawals in Union 

County constitute a predominant portion of total pumpage in the area. The transient solution for this scenario in which water may be removed from storage in 

the aquifer shows that reducing withdrawals to 30 

percent of current values would achieve the top-ofSparta Sand water-level target.

Stabilization-Yield Results

Simulation 3a is a steady state simulation in 

which future pumpage outside of Union County is 

assumed to increase at the rate observed from 1985- 

1997; pumpage in this simulation was assigned as the 

rate attained after 30 years of projected increases. Simulation 3a shows that withdrawals from the Sparta 

aquifer in Union County must be reduced to 91 percent 

of 1997 values (table 4) to stabilize water levels at the 

top of the El Dorado sand (300 ft below sea level; fig. 

7) and that the 1997 rate of withdrawal in the county is 

considerably greater than the rate needed to halt the 

rapid decline in water levels. If withdrawals from the 

aquifer continue to increase, this demand will result in 

accelerated declines. Whereas the simulation 3a

steady-state model run result provides the appropriate 

pumpage rate in the county to permanently stabilize 

water levels at the 1997 level, the transient solution 

(simulation 3b) set up to hold the 1997 water level 

through 2027 provides an additional understanding 

of aquifer behavior and temporal response. The transient solution for determining stabilization yield in 

which water may be removed from storage in the aquifer shows that reducing withdrawals to 96 percent of 

1997 values would achieve the top-of-El Dorado sand 

water-level target at the 30-year point (table 4).

Simulation 4a is a steady state simulation in 

which future pumpage outside of Union County is 

assumed to increase at double the rate observed from 

1985-1997 and was assigned in the model as the rate 

attained after 30 years of projected increases. Pumpage 

from the Sparta aquifer in Union County must be 

reduced to 88 percent of current values (table 4) to stabilize water levels at the top of the El Dorado sand (300 

ft below sea level). As compared to the 1985-1997 

increased rate simulation (3a), only an additional 3 percent reduction in Union County withdrawals is 

required to offset withdrawals in surrounding counties. 

This finding is in agreement with area water-use data 

showing that withdrawals in Union County constitute 

the major portion of total pumpage in the area. The 

transient solution for determining stabilization yield

Table 4. Stabilization-yield results for the top of the El Dorado sand water-level target for current rate of increase and double 

current rate of increase pumpage conditions

Scenario Union County pumpage 

(percent of 1997 rate)

Pumpage outside of Union County set at projected 2027 value for steady-state 

solution and increasing at the 1985-1997 rate of increase for 1998-2027 for 

transient solution

Simulation 3 a, Steady state 

Simulation 3b, Transient

Pumpage outside of Union County set at projected 2027 double-rate maximum 

value for steady-state solution and increasing at double the 1985-1997 rate for 

1998-2027 for transient solution

Simulation 4a, Steady State 

Simulation 4b, Transient

91 percent 

96 percent

88 percent 

94 percent

Sustainable- and Stabilization-Yield Simulation Results 13
91°30'

o

0>

II

oI 

I

33°30' -

EXPLANATION MODEL 

^BOUNDARY

SIMULATED POTENTIOMETRIC CONTOUR 

Shows water level altitude in tightly cased 

wells. Contour interval 25 feet. Datum is sea 

level

32°30' -

0 10 20 30 4Q 50KILOMETERS

Figure 7. Simulated steady state potentiometric surface of the Sparta aquifer with Union County pumpage decreased to 91 percent of 1997 rates (simulation 3a).
(simulation 4b) in which water may be removed from 

storage in the aquifer shows that reducing withdrawals to 94 percent of current values would achieve the 

top-of- El Dorado sand water-level target (table 4). Volumetric budget components are shown in figure 8.

DOUBLED-PUMPAGE RATE SIMULATION 

RESULTS

For the scenario in which the rate of increase for 

Union County pumpage was double the observed 

1985-1997 rate, simulation indicates that water levels 

in central Union County would drop to more than 580 

ft below sea level. Under the extreme, final conditions 

prevailing in this scenario, the numerical result is inaccurate, although informative, because hi the current 

version of the calibrated model, the model assumes 

confined conditions are always prevalent irrespective 

of drawdown. This amount of drawdown would be 

insupportable by the aquifer; practical constraints of 

aquifer yield and well yield and transition to locally 

unconfined conditions would manifest before water 

levels dropped the amount simulated.

SUMMARY AND CONCLUSIONS

The basic results of the study provide three primary conclusions: 1) Irrespective of how withdrawals 

from the Sparta aquifer change (within reasonable limits) outside of Union County, withdrawals within 

Union County must be reduced to about 25 to 28 percent of 1997 rates to cause water levels to rise to the top 

of the Sparta Sand, thereby achieving a sustainable 

yield and addressing CGWA designation criteria.

2) Withdrawals would have to be reduced to 

about 88 to 91 percent of 1997 rates to stabilize water 

levels above the top of the El Dorado sand.

3) The yield from the aquifer is not great enough 

to support a doubling of the rate of increase in pumpage 

in Union County over the long term.

The Sparta aquifer is a confined aquifer of 

regional importance that comprises a sequence of 

unconsolidated sand units that are contained within the 

Sparta Sand. The aquifer extends across much of eastern and southeastern Arkansas and into adjoining states 

and is a principle water resource for municipal, industrial, and agricultural uses. Currently, the rate of withdrawal in some areas greatly exceeds the rate of 

recharge to the aquifer. Large cones of depression are

centered beneath the Grand Prairie area and the cities 

of Pine Bluff and El Dorado in Arkansas areas 

included in CGWA designated by the Arkansas Soil 

and Water Conservation Commission (ASWCC). 

Results from the regional-scale, digital ground-water 

flow model for the Sparta aquifer indicate that the aquifer cannot continue to meet growing water-use 

demands indefinitely and that water levels will drop 

below the top of the primary producing sand unit in 

Union County (locally termed the El Dorado sand) by 

2008 if current water-use trends continue. Declines of 

that magnitude will initiate dewatering of the El 

Dorado sand.

Options for utilizing alternative sources of water 

to alleviate overdraft from the Sparta aquifer and 

ensure that the aquifer can continue to provide abundant water of excellent quality for the future are being 

evaluated by water managers in Union County. Sustainable yield is a critical element in identifying and 

designing viable water supply alternatives. With sustainable yield defined and a knowledge of total water 

demand in an area, any unmet demand can be calculated. The ground-water flow model of the Sparta aquifer was used to estimate sustainable yield using an 

iterative approach.

The sustainable yield of the aquifer was calculated by targeting a specified minimum acceptable 

water level within Union County and varying Union 

County pumpage within the model to achieve the target 

water level. Selection of the minimum target water 

level for sustainable-yield estimation was an important 

criterion for the modeling effort. In keeping with the 

State CGWA designation criteria and the desire of 

water managers in Union County to improve aquifer 

conditions and bring the area out of the CGWA designation, the approximate altitude of the top of the Sparta 

Sand in central Union County was used as the minimum water level target for estimation of sustainable 

yield in the county. A specific category of sustainable 

yield stabilization yield, reflecting the amount of 

water that the aquifer can provide while maintaining 

current water levels also was determined and provides information for short-term management. The top 

of the primary producing sand unit (the El Dorado 

sand) was used as the minimum water-level target for 

estimating stabilization yield in the county because 

current minimum water levels in central Union County 

are near the top of the El Dorado sand. Sustainable and 

stabilization yields were estimated for each of two 

pumping conditions outside of the county.

Doubled-Pumpage Rate Simulation Results 15
Cook Mountain 

confining unit

Lateral boundaries 

and overlying

aquifer

(Specified head) 

41.7 

2.0 <4

i

-^ '

ZOP ^ Pumpage = si ./ Lakes 

and Recharge

Cockfield aquifer

i

Sperta aquifer

_ Change in storage = 0

__|_

xf m

46

Simulation 3a, Steady state simulation, Union County pumpage at 91 percent of 1997 value.

Pumpage outside of Union County assigned as the rate attained after 30 years at 1985-

1997 rate of increase

Cook Mountain 

confining unit

Lateral boundaries 

and overlying

aquifer

(Specified head) 

38.2 

2.1 <

t

^

ZOP ^.Kumpage = DI .0 ^^ 

and Recharge

(Virlrfiolri am lifer -JJVj

k7.3

Sparta aquifer

 Storage loss = 7.4

U3L-.

1

JJ 13T3

2.4

Simulation 3b, 30-year transient simulation, Union County pumpage at 96 percent of 1997 value. 

Pumpage outside of Union County increasing at 1985-1997 rate of increase

Cook Mountain 

confining unit

Lateral boundaries 

and overlying

aquifer

(Specified head) 

87.9 

1.6 «4

*

:= 

_^. s

ZIZp »> Pumpage = i oz.e Lakes 

and Recharge

k

5.8 

Sparta aquifer

 Change in storage = 0

~_l_

xf 13'3

8.8

Simulation 4a, Steady state simulation, Union County pumpage at 88 percent of 1997 value.

Pumpage outside of Union County assigned as the rate attained after 30 years at double

the 1985-1997 rate of increase

Pumpage = 102.7 Lakes 

and Recharge

_ ^^.

7.3 4.4

Sparta aquifer

 Storage loss = 23.9

Cook Mountain 

confining unit

Lateral boundaries 

and overlying

aquifer

(Specified head) ^^ 70.0-

1.6 -4

Simulation 4b, Steady state simulation, Union County pumpage at 94 percent of 1997 value. 

Pumpage outside of Union County increasing at double the 1985-1997 rate of increase

Figure 8. Volumetric budget components (entire model) for stabilization-yield scenarios.

16 Sustainable-Yield Estimation for the Sparta Aquifer in Union County, Arkansas
For the simulation in which future pumpage outside of Union County is assumed to increase at the rate 

observed from 1985-1997, withdrawals from the 

Sparta aquifer in Union County must be reduced to 28 

percent of 1997 values to achieve sustainable yield and 

maintain water levels at the top of the Sparta Sand. 

Results of the simulation define a very large current 

unmet demand and represent a substantial reduction in 

the county's current dependence upon the aquifer. To 

achieve sustainable yield, the unmet demand defined 

by the model simulation and any future increases in 

demand resulting from growth in the county would 

require measures such as reducing water use through 

conservation and the use of alternative sources.

For the simulation in which future pumpage outside of Union County is assumed to increase at double 

the rate observed from 1985-1997, withdrawals from 

the Sparta aquifer in Union County must be reduced to 

25 percent of 1997 values to achieve sustainable yield. 

Only an additional 3 percent reduction in Union 

County pumpage is required to offset the greater rate of 

pumpage in surrounding counties as compared to the 

1985-1997 increase rate scenario. This finding corroborates area pumpage data showing that withdrawals in 

Union County constitute a predominant portion of total 

pumpage in the area.

For the simulation in which future pumpage outside of Union County is assumed to increase at the rate 

observed from 1985-1997, withdrawals from the 

Sparta aquifer in Union County must be reduced to 91 

percent of 1997 values to stabilize water levels at the 

top of the El Dorado sand. This result shows that 1997 

rate of withdrawal in the county is considerably greater 

than the rate needed to halt the rapid decline in water 

levels. If withdrawals from the aquifer continue to 

increase, this demand will result in accelerated 

declines.

For the simulation in which future pumpage outside of Union County is assumed to increase at double 

the rate observed from 1985-1997, pumpage from the 

Sparta aquifer in Union County must be reduced to 88 

percent of current values to stabilize water levels at the 

top of the El Dorado sand.

REFERENCES

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

Ground-Water Resources of the El Dorado area, Union 

County, Arkansas: University of Arkansas Research 

Series No. 14, 39 p.

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

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

Fitzpatrick, D.J., Kilpatrick, J.M., and Me Wreath, 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.

Hays, P.O., and Fugitt, D.T., 1999, The Sparta aquifer in 

Arkansas' critical ground-water areas Response of 

the aquifer to supplying future water needs: U.S. Geological Survey Water-Resources Investigations Report 

99-4075, 6 p.

Hays, P.O., 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.

Holland, T.W, 1999, Water use in Arkansas, 1995: U.S. 

Geological Survey Open-File Report 99-188, 1 sheet.

Joseph, R.L., 1998, 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: U.S. 

Geological Survey Water-Resources Investigations 

Report 97-4282, 19 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 Water 

Resources Investigations, Book 6, Chapter Al, 586 p.

Me Wreath, 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.

References 17

U.S. GOVERNMENT PRINTING OFFICE: 2000-555-181/40041