Prepared in cooperation with the

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

Arkansas Soil and Water Conservation Commission

RECALIBRATION OF A GROUND-WATER FLOW MODEL 

OF THE MISSISSIPPI RIVER VALLEY ALLUVIAL 

AQUIFER IN SOUTHEASTERN ARKANSAS, 1918-1998, 

WITH SIMULATIONS OF HYDRAULIC HEADS CAUSED BY 

PROJECTED GROUND-WATER WITHDRAWALS 

THROUGH 2049

Water-Resources Investigations Report 03-4232

U.S. Department of the Interior

U.S. Geological Survey
Cover: Oblique view of scenario 3 showing 2009 simulated heads of the alluvial aquifer with the 50 percent 

saturated thickness shown as a transparent grid, also shown in animations included on the compact disk in 

the back of the report.
RECALIBRATION OF A GROUND-WATER FLOW MODEL 

OF THE MISSISSIPPI RIVER VALLEY ALLUVIAL 

AQUIFER IN SOUTHEASTERN ARKANSAS, 1918-1998, 

WITH SIMULATIONS OF HYDRAULIC HEADS CAUSED BY 

PROJECTED GROUND-WATER WITHDRAWALS 

THROUGH 2049

By Gregory P. Stanton and Brian R. Clark

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 03-4232

Prepared in cooperation with the

U.S. Army Corps of Engineers, Vicksburg District 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........................................................................................................................................................ 1

Purpose and Scope .................................................................................................................................... 2

Model Area ...................................................................................................................................... 2

Previous Studies............................................................................................................................... 2

Previous Model ................................................................................................................................ 4

Hydrogeologic Setting of the Mississippi River Valley Alluvial Aquifer.......................................................... 4

Description of the Ground-Water Flow Model .................................................................................................. 6

Simplifying Assumptions........................................................................................................................10

Model Specifications...............................................................................................................................10

Initial Conditions ...........................................................................................................................10

Boundary Conditions .....................................................................................................................10

Surface-Water Parameters.....................................................................................................12

Recharge ...............................................................................................................................14

Discretization .................................................................................................................................14

Spatial Discretization............................................................................................................14

Temporal Discretization........................................................................................................14

Pumping Stress - Water Use...........................................................................................................14

Stress Periods 1-7 (1918-1988).............................................................................................14

Stress Periods 8-10 (1989-March 31, 1998) .........................................................................19

Hydraulic Properties ......................................................................................................................19

Hydraulic Conductivity.........................................................................................................19

Storage ..................................................................................................................................19

Model Calibration Procedure ...........................................................................................................................19

Non-Linear Least-Squares Regression Method ......................................................................................19

Calibration Strategy ................................................................................................................................21

Calibration Data Set ................................................................................................................................21

Scaled Sensitivities..................................................................................................................................21

Calibration Results and Model Evaluation.......................................................................................................21

Water Budget...........................................................................................................................................22

Hydraulic-Head Residuals ......................................................................................................................22

Error Analysis .........................................................................................................................................26

Potentiometric Surfaces ..........................................................................................................................26

Simulated and Observed Hydrographs....................................................................................................28

Simulations of Projected Ground-Water Withdrawals .....................................................................................28

Scenario 1................................................................................................................................................31

Scenario 2................................................................................................................................................35

Scenario 3................................................................................................................................................35

Model Limitations............................................................................................................................................41

Summary ..........................................................................................................................................................46

References........................................................................................................................................................47
IV Contents

ILLUSTRATIONS

Figure 1. Map showing active model area...................................................................................................... 3

2. Hydrogeologic sections across the model area............................................................................... 5

3-8. Maps showing:

3. Ground-water levels in the alluvial aquifer in spring 1998 in the model area ........................... 7

4. Difference between model top of the alluvial aquifer and 1998 hydraulic heads ...................... 8

5. Active model grid and boundary conditions............................................................................... 9

6. Simulated predevelopment potentiometric surface of the alluvial aquifer used as

initial hydraulic-head conditions .......................................................................................... 11

7. River cell groupings based on riverbed conductance and geometry......................................... 13

8. Areal recharge zones in the model............................................................................................ 15

9. Timeline showing model time, stress periods, and pumpage descriptions ................................... 16

10. Three-dimensional chart of pumpage by county in stress periods 1-10 ....................................... 18

11. Map showing zones with uniform values of hydraulic conductivity, specific storage, and

specific yield............................................................................................................................ 20

12. Graph showing average change in hydraulic head by doubling a parameter ............................... 22

13. Chart showing ground-water model budget by stress period ....................................................... 23

14. Map showing residuals—difference between simulated hydraulic heads and 1992

observed water levels............................................................................................................... 24

15. Map showing residuals—difference between simulated hydraulic heads and 1998

observed water levels............................................................................................................... 25

16. Histogram showing frequency of residuals (plus or minus 2.5 feet of the value shown)

for 1992 and 1998 observations............................................................................................... 26

17. Map showing potentiometric map and simulated hydraulic heads for 1998................................ 27

18. Hydrographs showing observed and simulated water levels at selected locations

in the model area ..................................................................................................................... 29

19. Chart showing rates of pumpage for the three scenarios by stress period.................................... 31

20. Graphs showing comparison of model area that the simulated hyraulic heads fall below

predefined levels for each scenario.......................................................................................... 32

21-27. Maps showing:

21. Simulated hydraulic heads in feet above 50 percent saturated thickness

where greater than zero and total saturated thicknesses where heads are below 50

percent using 1997 pumpage extended unchanged until 2049, scenario 1 ........................ 33

22. Simulated hydraulic heads for the year 2049, scenario 1....................................................... 36

23. Simulated hydraulic heads in feet above 50 percent saturated thickness

where greater than zero and total saturated thicknesses where heads are below

50 percent using estimated trends in pumpage based on 1997 water-use data

extended to 2049, scenario 2 .............................................................................................. 37

24. Simulated hydraulic heads for the year 2049, scenario 2....................................................... 39

25. Model area and area to be served by proposed diversion plan ............................................... 40

26. Simulated hydraulic heads in feet above 50 percent saturated thickness 50 percent using

where greater than zero and total saturated thicknesses where heads are below

estimated trends in pumpage based on 1997 water-use data and reduced by 10 percent 

in selected zones, scenario 3............................................................................................... 43

27. Simulated hydraulic heads for the year 2049, scenario 3 ....................................................... 45
Contents V

TABLES

Table 1. Surface-water bodies simulated in the model and corresponding river codes and riverbed

conductances .................................................................................................................................12

2. Total pumpage rates simulated in stress periods 1-10........................................................................17

3. Cumulative volumes of inflow and outflow in the model at the end of stress period 10...................22

4. Summary of the model residual statistics ..........................................................................................26

5. Total pumpage rates simulated in predictive scenario model runs, stress periods 11-15 ..................28

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)

Rate

cubic foot (ft3) 0.02832 cubic meter (m3)

cubic foot per day (ft3/d) 0.02932 cubic meter per day (m3/d)

billion gallons per day (Mgal/d) 43.81 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)
Abstract 1

RECALIBRATION OF A GROUND-WATER FLOW MODEL OF THE 

MISSISSIPPI RIVER VALLEY ALLUVIAL AQUIFER IN 

SOUTHEASTERN ARKANSAS, 1918-1998, WITH SIMULATIONS OF 

HYDRAULIC HEADS CAUSED BY PROJECTED GROUND-WATER 

WITHDRAWALS THROUGH 2049

By Gregory P. Stanton and Brian R. Clark

ABSTRACT

The Mississippi River Valley alluvial aquifer, 

encompassing parts of Arkansas, Kentucky, Louisiana, 

Mississippi, Missouri, and Tennessee supplies an average of 5 billion gallons of water per day. However, 

withdrawals from the aquifer in recent years have 

caused considerable drawdown in the hydraulic heads 

in southeastern Arkansas and other areas. The effects of 

current ground-water withdrawals and potential future 

withdrawals on water availability are major concerns of 

water managers and users as well as the general public. 

A full understanding of the behavior of the aquifer 

under various water-use scenarios is critical for the 

development of viable water-management and alternative source plans. To address these concerns, the U.S. 

Geological Survey, in cooperation with the U.S. Army 

Corps of Engineers, Vicksburg District, and the Arkansas Soil and Water Conservation Commission developed and calibrated a ground-water flow model for the 

Mississippi River valley alluvial aquifer in southeastern Arkansas to simulate hydraulic heads caused by 

projected ground-water withdrawals.

A previously published ground-water flow 

model for the alluvial aquifer in southeastern Arkansas 

was updated and recalibrated to reflect more current 

pumping stresses with additional stress periods added 

to bring the model forward from 1982 to 1998. The 

updated model was developed and calibrated with 

MODFLOW-2000 finite difference numerical modeling and parameter estimation software. The model was 

calibrated using hydraulic-head data collected during 

1972 and 1982 and hydraulic-head measurements 

made during spring (February to April) of 1992 and 

1998. The residuals for 1992 and 1998 have a mean 

absolute value of 4.74 and 5.45 feet, respectively, and 

a root mean square error of 5.9 and 6.72 feet, respectively.

The effects of projected ground-water withdrawals were simulated through 2049 in three predictive 

scenarios by adding five additional stress periods of 10 

years each. In the three scenarios, pumpage was 

defined by either continuing 1997 pumpage into the 

future (scenario 1) or by continuing water-use trends 

into the future (scenario 2), and increasing water-use 

trends with a 10 percent reduction in pumpage in 

selected areas (scenario 3). Scenario 1 indicates a cone 

of depression centered in Desha County and extensive 

dewatering with areas of simulated hydraulic heads 

dropping below 50 percent saturated thickness. Scenario 2 indicates a larger area of simulated hydraulic 

heads dropping below 50 percent saturated thickness 

and additional dewatering with model cells going dry 

and smaller cones of depression appearing in Ashley 

and Chicot Counties. Scenario 3 indicates overall 

reduction in depth and extent of the cones of depression 

of those in scenario 2, and the number of dry cells are 

only about two-thirds that of dry cells in scenario 2.

INTRODUCTION

Since the early 1900’s, southeastern Arkansas 

has produced agricultural crops (rice, soybeans, and 

cotton) that are highly dependent on ground water for 

irrigation. More recently, fish farming and other types 

of aquaculture are becoming major users of ground 

water. The most areally extensive and abundant source 

of water for irrigation in the Mississippi Embayment is 

the Mississippi River Valley alluvial aquifer. The Mississippi River Valley Alluvial aquifer, herein will be 

referred to as the alluvial aquifer. Overlying the alluvial 

aquifer in most of the study area is the Mississippi 

River Valley confining unit (Gonthier and Mahon, 

1993), herein referred to as the overlying confining 

unit.
2 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

The alluvial aquifer, located in eastern Arkansas, 

and parts of Kentucky, Louisiana, Mississippi, Missouri, and Tennessee, supplies an average of 5 billion 

gallons of water per day (Grubb, 1998). Historically, 

the aquifer has been an important water resource for 

agriculture, business, and community growth in eastern 

Arkansas by providing abundant water of high quality. 

However, in recent years, demand has exceeded 

recharge to the aquifer, and water users and water managers are concerned about the ability of the aquifer to 

meet increasing long-term water demands. Withdrawals from the aquifer have caused considerable drawdown in the potentiometric surface. The effects of 

current ground-water withdrawals and potential future 

withdrawals on water availability are major concerns of 

water managers and users as well as the general public. 

A full understanding of the behavior of the aquifer 

under various water-use scenarios is critical to development of viable water-management and alternative 

source plans. To address these concerns, the U.S. Geological Survey, in cooperation with the U.S. Army 

Corps of Engineers, Vicksburg District (USACE) and 

the Arkansas Soil and Water Conservation Commission (ASWCC) has developed and calibrated a groundwater flow model for the alluvial aquifer in southeastern Arkansas that is used to simulate hydraulic heads 

(often used interchangeably with water-level altitude or 

potentiometric surface) and flow in response to various 

projected ground-water withdrawal scenarios.

Purpose and Scope

This report describes the flow model and calibration, and results of simulations of hydraulic heads 

caused by projected ground-water withdrawals for the 

alluvial aquifer in southeastern Arkansas. The model 

described in this report is an updated and recalibrated 

version of the Mahon and Poynter (1993) “south 

model” with updated pumpage and recalibrated 

hydraulic values. This report briefly describes the 

hydrogeology of the model area, specifically in relation 

to application of model boundary conditions and 

hydraulic parameters. The model was calibrated using 

hydraulic heads from 1918 to 1998, and various scenarios of projected ground-water withdrawals were simulated for 1998-2049.

This report is limited to the digital modeling of 

ground-water flow in the alluvial aquifer and the effects 

of pumping within the alluvial aquifer. The conjunctive-use optimization modeling using this flow model 

is published in a separate report (Czarnecki and others, 

2003).

Model Area

The model area includes all or parts of six counties in Arkansas south of the Arkansas River (Ashley, 

Chicot, Desha, Drew, Jefferson, and Lincoln) and parts 

of three parishes in northeastern Louisiana (East Carroll, West Carroll, and Morehouse) (fig. 1). The flow 

model of the alluvial aquifer north of the Arkansas 

River is described in a separate report (Reed, 2003).

Previous Studies

The unconsolidated sediments of the Mississippi 

alluvial plain have been described in several publications. One of the earliest reports describing subsurface 

geology and ground-water resources in southern 

Arkansas and northern Louisiana was written by 

Veatch (1906). Fisk (1944) reported on extensive geologic investigations along the Mississippi River Valley 

made by the USACE between 1941 and 1944. This 

compilation consists of text accompanied by more than 

110 illustrations describing the alluvial sediments. 

Krizinsky and Wire (1964) expanded on the hydrogeologic work of Fisk with a comprehensive study of the 

ground-water conditions. Cushing and others (1964) 

and Boswell and others (1968) provided an overview of 

the alluvial aquifer in their discussions of Quaternaryage aquifers on the Mississippi Embayment. Boswell 

and others (1968) first referred to the water-yielding 

sediments underlying the alluvial plain as the Mississippi River Valley Alluvial aquifer.

Several reports have been published documenting the results of model simulations of the flow system 

within and across boundaries of the alluvial aquifer. A 

two-dimensional planar model of the alluvial aquiferstream system in southern Arkansas was published by 

Reed and Broom (1979). This model simulated streamaquifer interaction and streamflow with the finite-difference equation (Pinder and Bredehoeft, 1968) and 

was the first digital model of the alluvial aquifer south 

of the Arkansas River. Regional model investigations 

were conducted by Ackerman (1989a, 1990) under the 

framework of the USGS Gulf Coast Regional AquiferSystem Analysis; these reports describe the model 

development and results and show the characteristics of 

the flow system on a regional basis. Predictive sim-
Introduction 3

Figure 1. Active model area.

River

Monticello Ridge

Bayou Macon

Boeuf

River

Big Bayou

Drew

Ashley

Desha

Chicot

Lincoln

Bradley

Jefferson

Arkansas

Union

Union

Morehouse

Bolivar

Washington

Phillips

West Carroll East Carroll

Issaquena

Active Model

Area Boundary

92° 91°

33°

34°

0 10 20 Miles 5

0 10 5 20 Kilometers

Arkansas

Louisiana

Mississippi

Arkansas

River

Mississippi

River

Saline River

Ouachita

Bayou Bartholomew

Louisiana

Arkansas

Mississippi

Base from U.S. Geological Survey digital data, 1:100,000
4 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

ulations presented by Ackerman (1989a, 1998) were 

based on hypothetical increases in pumping. 

Previous Model

Substantial hydraulic-head declines in the alluvial aquifer in the 1980’s (Ackerman, 1989b; Westerfield and Poynter, 1994) prompted the need to better 

understand the flow system in the aquifer which, in 

turn, led to the development of digital ground-water 

flow models of the alluvial aquifer. The previously 

published model of the alluvial aquifer used in this 

report was authored by Mahon and Poynter (1993). 

Mahon and Poynter (1993) described the development, 

calibration, and results of two separate models for eastern Arkansas: one for the area north of the Arkansas 

River and one for the area south of the Arkansas River 

(herein referred to as the north model and the south 

model, respectively). The north and south models utilized the MODFLOW finite difference numerical-modeling software (McDonald and Harbaugh, 1988). The 

models were calibrated using hydraulic-head data from 

1972 and 1982. Model grids had a cell size of 1 square 

mile. Recharge to the aquifer was simulated using 

head-dependent surface infiltration through the overlying confining unit and seepage through riverbeds. The 

active cells of the south model encompassed the area in 

Arkansas south of the Arkansas River, west of the Mississippi River, east of the Monticello Ridge, the Saline 

River, and the Ouachita River, and south into northern 

Louisiana for about 10 miles (fig. 1).

HYDROGEOLOGIC SETTING OF THE

MISSISSIPPI RIVER VALLEY ALLUVIAL 

AQUIFER

The alluvial aquifer is the uppermost aquifer system in eastern Arkansas and is part of a much larger 

sedimentary system known as the Mississippi Embayment (Cushing and others, 1964). The Mississippi 

Embayment plunges southward from Illinois to the 

Gulf of Mexico in a fan shaped trough, and covers 

about 160,000 square miles in parts of Alabama, 

Arkansas, Illinois, Kentucky, Louisiana, Mississippi, 

Missouri, and Tennessee (Cushing and others, 1964; 

Williamson and others, 1990). The ages of the embayment sediments range from Jurassic to Quaternary, but 

only units of Cretaceous age and younger are exposed 

in Arkansas. The central axis of the Mississippi 

Embayment nearly parallels the Mississippi River, and 

the embayment surface drainage in Arkansas is ultimately to the Mississippi River (Mahon and Poynter, 

1993).

The Mississippi Alluvial Plain is a broad, flat 

plain that lies within the Coastal Plain physiographic 

province (Fenneman, 1938) and is part of the Mississippi Embayment. The alluvial plain encompasses an 

area of about 32,000 square miles, with more than 54 

percent occurring in eastern Arkansas. The alluvial 

plain in Arkansas is bounded on the west by sediments 

of Paleozoic age with very low hydraulic conductivity 

and by sediments of Tertiary age of the Mississippi 

Embayment that have a distinctly lower hydraulic conductivity than sediments composing the alluvial aquifer 

(Ackerman, 1990; Mahon and Poynter, 1993).

Deposition of sediment from the Mississippi and 

Arkansas Rivers during Pleistocene and Holocene time 

(herein referred to as Mississippi River alluvium) has 

produced a sequence of sands, silts, and clays that constitute the alluvial aquifer in eastern Arkansas. From a 

regional perspective, this collection of sediment can be 

divided into two units. The lower unit, which contains 

the alluvial aquifer, is composed of coarse sand and 

gravels that grade upward to fine sand. The upper unit 

consisting of fine sand, silt, and clay confines the alluvial aquifer over most of the area. The alluvial aquifer 

and overlying confining unit, along with its flow system, has been defined and investigated previously (fig. 

2) (Broom and Lyford, 1981; Broom and Reed, 1973; 

Ackerman, 1989a, 1989b, 1990; Mahon and Ludwig, 

1990; Mahon and Poynter, 1993). The overlying confining unit ranges in thickness from 0 to 60 feet within 

the model area (Gonthier and Mahon, 1993). The sands 

and gravels that underlie the overlying confining unit 

and comprise the alluvial aquifer range from about 50 

to about 100 feet thick.

The geology of most of the model area typically 

is characterized by clay and sand beds of the Mississippi River alluvium of Pleistocene and Holocene time 

overlying the silt and clay sequence of the Jackson 

Group of Tertiary age (Ackerman, 1989a). Channel fill, 

point bar, and backswamp deposits, associated with 

present or former channels of the major rivers, locally 

can produce abrupt differences in lithology of alluvial 

deposits, that result in spatial variations in the hydraulic 

properties of both the aquifer and confining unit within 

small distances (fig. 2). Alluvial deposits are dominated by the complex heterogeneity of small, discontinuous clay, silt, sand, and gravel beds dispersed 
Introduction 5

Figure 2. Hydrogeologic sections across the model area.

EXPLANATION

MISSISSIPPI RIVER VALLEY CONFINING UNIT

MISSISSIPPI RIVER VALLEY ALLUVIAL AQUIFER

DEPOSITS OF TERTIARY AGE AND OLDER

TRACE OF HYDROGEOLOGIC SECTION--Points

on the trace are location of wells used for control

WELL USED FOR CONTROL

A A’ B - B' Chicot County Desha County

VERTICAL SCALE GREATLY EXAGGERATED MODIFIED FROM GONTHIER AND MAHON, 1993

200

150

100

50

NGVD of 1929

250

200

150

100

50

NGVD of 1929

FEET

250

SOUTH NORTH

B B’

NGVD of 1929

FEET

100

50

150

Ashley County

Chicot County

A - A'

VERTICAL SCALE

GREATLY EXAGGERATED

MODIFIED FROM GONTHIER AND

MAHON, 1993

NGVD of 1929

100

50

150

WEST EAST

0 25 50 MILES

0 25 50 KILOMETERS

B

B’

A

Lincoln A’

Arkansas

Desha

Drew

Ashley

Chicot

Arkansas

Mississippi
6 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

laterally and vertically, which represent local features 

of the aquifer and flow system. Laterally to the west, 

the contact between alluvial deposits and older strata is 

masked by terrace deposits (Ackerman, 1989a), which 

form a slight topographic high, locally referred to as the 

Monticello Ridge. During Tertiary time, the last marine 

inundation of the Mississippi Embayment occurred 

depositing the clays and silts of the Jackson Group. The 

Jackson Group underlies the Mississippi River alluvium in most of the model area forming an effective 

underlying hydraulic confining unit (Cushing and others, 1964). 

The complexity of the geology within the alluvium is paralleled by that of the ground-water system. 

Although ground-water flow is made more complex by 

the heterogeneities in the aquifer and overlying confining unit, the flow system can be generalized and conceptualized as water moving laterally in a single zone 

or layer. This simplistic conceptualization of flow is 

compatible with conditions observed in the field 

(Mahon and Poynter, 1993).

The hydrologic conditions of the alluvial aquifer 

in the model area are the result of both regional and 

local flow systems in the alluvial sediments. Regionally, ground-water levels have been measured and 

mapped for several years (Ackerman, 1989b; Plafcan 

and Edds, 1986; Plafcan and Fugitt, 1987; Westerfield, 

1990; Westerfield and Poynter, 1994; Stanton and others, 1998; Joseph, 1999; Schrader, 2001). These measurements indicate that ground water in the alluvial 

aquifer in southeastern Arkansas currently flows southward with local flow toward the areas of depressed 

hydraulic heads. A depressed hydraulic-head trough 

presently (2000) exists as a north-south feature 

between the Arkansas and Mississippi Rivers and 

Bayou Bartholomew on potentiometric maps (fig. 3) 

(Stanton and others, 1998; Joseph, 1999; Schrader, 

2001). This trough induces local flow toward the axis 

of the trough, but regionally, a southeast flow direction 

is dominant.

Throughout most of the model area, the overlying silts, clay, and fine-grained sands of the overlying 

confining unit impede areal recharge (Krinitzsky and 

Wire, 1964) into the alluvial aquifer. Recharge to the 

top of the alluvial aquifer has been estimated by previous model studies. The most recent previous model by 

Mahon and Poynter (1993) estimated a recharge rate of 

1.4 inches/year. A model by Broom and Lyford (1981) 

estimated between 0.4 and 2.0 inches/year of recharge 

to the alluvial aquifer through the overlying confining 

unit. Results of simulation analysis by Ackerman 

(1989a) indicated an average recharge rate through the 

overlying confining unit to be 0.8 inches/year. 

Hydraulic heads in the aquifer have decreased 

with the increase in pumpage from the aquifer. Portions 

of the aquifer that had been under confined conditions 

now are under unconfined conditions. The aquifer is 

presently unconfined in most of the eastern part of the 

model area (fig. 4). The aquifer is confined in most of 

the western part of the model area.

The alluvial aquifer is hydraulically connected to 

major rivers and lakes resulting in considerable volumes of water being contributed to or taken from these 

surface-water bodies. Prior to the development of the 

alluvial aquifer, most major rivers and lakes in eastern 

Arkansas received part of their water from ground 

water. This ground-water derived component of flow 

constituted a significant part of total flow in major rivers (Ackerman, 1989a). Increased pumping from wells 

induces greater rates of recharge from rivers to the 

aquifer (Ackerman, 1989a; Czarnecki and others, 

2002). Most rivers now lose water to the aquifer 

(recharge), and minimum observed flows in the rivers 

have decreased (Elton Porter, U.S. Geological Survey, 

written commun., 2002). 

DESCRIPTION OF THE GROUND-WATER 

FLOW MODEL

The USGS finite-difference, three-dimensional, 

ground-water flow model MODFLOW-2000 (Harbaugh and others, 2000) was used to develop and calibrate the ground-water flow model for the alluvial 

aquifer. The calibrated model was used to simulate 

ground-water flow in the aquifer and to evaluate the 

range of plausible values for hydraulic characteristics 

(hydraulic conductivity, specific storage, storativity, 

and recharge). MODFLOW-2000 was used to solve 

finite difference, ground-water flow equation approximations for spatial distributions of hydraulic head over 

time with certain simplifying assumptions. The preconditional-conjugate-gradient (PCG) solver option was 

used within MODFLOW-2000 to solve the finite-difference equation.

A map of the alluvial aquifer in southeastern 

Arkansas was overlain by a rectangular, one square 

mile grid that discretized the aquifer into cells (fig. 5). 

Spatial and vertical variations in hydraulic characteristics and the aquifer framework are represented by discrete values in model cells. The model grid consists of
Description of the Ground-Water Flow Model 7

Figure 3. Ground-water levels in the alluvial aquifer in spring 1998 in the model area.

Boeuf R ver i

Big Bayou

80

90

140

100

130

160

120

110

170

180

190

100

Drew

Ashley

Desha

Chicot

Arkansas

Jefferson

Bradley

Lincoln

Cleveland

Union

Union

Morehouse

Bolivar

Washington

Phillips

West Carroll Issaquena

East Carroll

Mississippi

150

100

Bayou Macon

90

Ouachita River

Saline River

Arkansas River

M ssissippi i

River

Arkansas

Louisiana

92° 91°

33°

34°

Active Model

Area Boundary

Modified from Joseph, (1999) 0 10 20 Miles 5

0 10 20 Kilometers 5

EXPLANATION

POTENTIOMETRIC CONTOUR--

Shows altitude at which water level

would have stood in tightly cased

wells. Dashed where approximately

located. Contour interval 10 feet.

Datum is National Geodetic Vertical

Datum of 1929

OBSERVATION WELL COMPLETED

IN ALLUVIAL AQUIFER

20
8 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

Figure 4. Difference between model top of the alluvial aquifer and 1998 hydraulic heads.

Drew

Ashley

Desha

Chicot

Bradley

Lincoln

Arkansas

Jefferson

Cleveland

Union

Union

Morehouse

Bolivar

Washington

West Carroll

PhillipsIssaquena

East Carroll

Arkansas

Mississippi

Louisiana

92° 91°

33°

34°

0 10 20 5 Miles

0 10 20 5 Kilometers

EXPLANATION

Alluvial aquifer top

elevation minus 1998

hydraulic heads, in feet.

Datum is National

Geodetic Vertical Datum

of 1929

-49 to -40

-39 to -20

-19 to 0

1 to 20

21 to 40

41 to 60

61 to 80

Base from U.S. Geological Survey digital data, 1:100,000
Description of the Ground-Water Flow Model 9

Figure 5. Active model grid and boundary conditions.

Bayou Bartholomew

Arkansas River

Mississippi

River

Drew

Ashley

Desha

Chicot

Bradley

Lincoln

Arkansas

Jefferson

Cleveland

Union

Union

Morehouse

Bolivar

Washington

West Carroll

Phillips

East Carroll Issaquena

Arkansas

Mississippi

Louisiana

Crooked Bayou

92° 91°

33°

34°

EXPLANATION

Active cell

River cell

Drain cell

0 10 20 5 Miles

0 10 20 5 Kilometers

No-Flow

Boundary

Saline River

Ouachita River

Big Bayou

Boeuf River

Bayou Macon

Lake

Chicot

Base from U.S. Geological Survey digital data, 1:100,000
10 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

a single layer of variable thickness, with 102 rows and 

75 columns, which represents only the alluvial aquifer.

Simplifying Assumptions

By necessity, a ground-water flow model is a 

simplification of the actual system. Several simplifying 

assumptions were made in the construction of the 

model: 1) a single layer is adequate to represent the 

alluvial aquifer; 2) flow is horizontal; 3) each cell is 

homogeneous and isotropic with respect to aquifer 

properties; 4) a finite grid is adequate for defining the 

vertical and lateral changes in aquifer properties; 5) 

recharge through streambeds is a function of river stage 

which is fixed in time; and 6) areal recharge is invariant 

in time and uniform over large areas. Mahon and Poynter (1993) describe wells close to one another in the 

alluvial aquifer and open to both the upper and lower 

zones in the aquifer as having negligible hydraulichead differences. Thus, vertical flow as compared to 

lateral flow within the alluvial aquifer likely is small 

and using a single layer to represent the alluvial aquifer 

in the model is reasonable. Hydraulic-head altitude 

data indicate that pumping has drawn down hydraulic 

heads below the overlying confining bed throughout 

much of the alluvial aquifer. Streams supply recharge 

to the aquifer and receive discharge from the aquifer. 

Other potential recharge to the aquifer occurs as infiltration from the surface and as upward flow from the 

underlying Jackson confining unit, and these two 

recharge sources are simulated as a combined inflow 

term by the recharge package. 

Model Specifications

Initial Conditions

Initial conditions for the model simulations are 

hydraulic heads estimated to have existed before 

ground-water development began in the early 1900’s. 

The earliest potentiometric maps for the alluvial aquifer are for the Grand Prairie Region, north of the study 

area (Engler and others, 1945). Very little hydraulichead data exist before the beginning of ground-water 

development, and no predevelopment potentiometric 

maps are available. Results from previously developed 

flow models (Ackerman, 1989a; Broom and Lyford, 

1981) include hydraulic heads that represent conditions 

prior to pumping in the alluvial aquifer (fig. 6). These 

hydraulic heads were used as initial conditions for simulations of the Mahon and Poynter (1993) south model 

and were used as initial heads in the model described in 

this report. Ackerman (1989a) indicated that predevelopment of recharge to the alluvial aquifer was from 

underlying aquifers and from the overlying confining 

unit. Nearly all regional discharge was to rivers (Ackerman, 1989a).

Boundary Conditions

The model includes several rivers that exchange 

water with the ground-water system, and also is adjacent to areas that conceptually distribute little or no 

flow to or from the aquifer. The boundary conditions 

represented in the model reflect these conditions (fig. 

5). The northern and eastern boundaries of the model 

are river cells representing the Arkansas River and Mississippi River, which function as large potential sources 

of inflow and outflow to and from the aquifer. The 

southern boundary of the model is about 10 miles south 

of the Arkansas border and is comprised of drain cells 

representing water flowing south in the alluvial aquifer 

into northern Louisiana. The western boundary is simulated with a no-flow boundary coinciding with a surface-water divide and the line of outcrop of sediments 

of Tertiary age. The exception to this no-flow condition 

is in western Ashley County where the western model 

boundary is river cells representing the Saline and Ouachita Rivers. 

The flow from the apparent confining unit below 

the aquifer (Jackson Group), is assumed to be negligible and the base of the alluvial aquifer is simulated as a 

no-flow boundary. Data related to the movement of 

ground water between the alluvial aquifer and the 

deeper underlying units during predevelopment time 

are sparse. Because outcrop areas of the units are topographically higher than the alluvium, it is presumed 

that flow was upward from these underlying older 

rocks to the alluvium. However, hydraulic heads in the 

underlying aquifers recently have declined, and 

hydraulic-head measurements indicate that in some of 

the model area, hydraulic heads in the alluvium are 

now higher than those in the underlying rocks indicating that if flow does exist, it is downward to the underlying units (Grubb, 1998).
Description of the Ground-Water Flow Model 11

Figure 6. Simulated predevelopment potentiometric surface of the alluvial aquifer used as initial hydraulic-head conditions.

Boeuf R ver i

Big Bayou

Drew

Ashley

Desha

Chicot

Arkansas

Jefferson

Bradley

Lincoln

Cleveland

Union

Union

Morehouse

Bolivar Washington

Phillips

West Carroll Issaquena

East Carroll

Arkansas

Louisiana

Mississippi

Bayou Macon

Ouachita River

Saline River

92° 91°

33°

34°

0 10 20 5 Miles

Active Model

Area Boundary

20

EXPLANATION

POTENTIOMETRIC CONTOUR -

Shows altitude of simulated

predevelopment potentiometric

surface. Contour interval 10

feet. Datum is National Geodetic

Vertical Datum of 1929.

Modified from Mahon and Poynter, 1993

0 10 20 5 Kilometers

190

180

170

160

150

140

130

120

110

100

90

80

Bayou Bartholomew

Arkansas River

Mississippi

River

Grand Prairie
12 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

Surface-Water Parameters

Rivers, streams, and lakes contribute water to or 

drain water from the ground-water system based on the 

gradient between the surface-water body and the 

ground-water system and the hydraulic characteristics 

of the separating materials. Many rivers flow across the 

alluvial plain and exchange water with the alluvial 

aquifer (fig. 3). Rivers act as both sources of recharge 

and areas of discharge at different times of the year and 

at different locations along their reaches (Ackerman, 

1989a). Rivers such as the Mississippi and the Arkansas are assumed to be in good hydraulic connection 

with the aquifer because they are deeply incised into 

the aquifer. The hydraulic head in the aquifer adjacent 

to the river is nearly identical to the river stage (Ackerman, 1989a; 1990; Mahon and Ludwig, 1990). The 

Saline and Ouachita Rivers and Bayou Bartholomew 

are not as well connected hydraulically with the aquifer, and hydrographs for wells near these rivers reflect 

attenuated changes in river stage. Field observations, 

hydraulic-head measurements, and model simulations 

indicate that other smaller streams such as the Boeuf 

River and Big Bayou in the alluvial plain generally 

have less hydraulic connection with the aquifer than the 

larger rivers (Ackerman, 1990).

The river package in the model allows simulation 

of a surface-water body separated from the groundwater system by a layer of lower permeability material. 

River-stage elevation was calculated using the mean 

annual stage data obtained from USGS stream gages. 

Stage elevations for river cells were prorated between 

gaging stations to create a realistic gradient. Stage elevation is constant through the model simulation time 

for all river cells. The river package is used only to simulate actual surface-water bodies.

Ten rivers and one lake are simulated in the 

model to be hydraulically connected with the alluvial 

aquifer (fig. 7). The rivers and the lake and the number 

of river cells, and riverbed conductances used during 

the simulations are listed in table 1.

Table 1. Surface-water bodies simulated in the model and corresponding river codes and riverbed conductances

Surface-water body Number of cells River code

Riverbed

conductance

(feet squared

per day) Parameter names

Arkansas River 76 3 2.51× 106 ark_miss

Bayou Bartholomew 139 2 1.51 × 106 bart_saline

Big Bayou 26 5 5.0 × 103 boeuf_big

Boeuf River 25 5 5.0 × 103 boeuf_big

Lake Chicot 31 4 2.03 × 106 lk_chicot

Crooked Bayou 14 5 5.0 × 103 boeuf_big

Bayou Macon 30 5 5.0 × 103 boeuf_big

Mississippi River 93 3 2.51 × 106 ark_miss

Ouachita River 18 1 1.32 × 106 ouachita

Saline River 15 2 1.51 × 106 bart_saline

White River 3 3 2.51 × 106 ark_miss
Description of the Ground-Water Flow Model 13

Figure 7. River cell groupings based on riverbed conductance and geometry.

Drew

Ashley

Desha

Chicot

Bradley

Lincoln

Arkansas

Jefferson

Cleveland

Union

Union

Morehouse

Bolivar

Washington

West Carroll

Phillips

Issaquena East Carroll

Arkansas

Mississippi

Louisiana

92° 91°

33°

34°

EXPLANATION

River codes and

names (table 1)

1 Ouachita

2 bart_salin

3 ark_miss

4 lk_chicot

5 boeuf_big

Non-river cells

0 10 20 5 Miles

0 10 20 5 Kilometers

Base from U.S. Geological Survey digital data, 1:100,000
14 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

Riverbed conductance was calculated assuming 

conditions of stage and dimensions of the river channels in the model and estimates of thickness and 

hydraulic conductivity of the riverbed using the equation:

(1)

where C is riverbed conductance, in feet squared per 

day;

K is hydraulic conductivity of the riverbed 

material, in feet per day;

L is length of the reach, in feet;.

W is width of the river, in feet; and

M is thickness of the riverbed, in feet.

Rivers (or segments of rivers) were assigned one of five 

riverbed conductance values. These values ranged from 

5.0 × 103 feet squared per day to 2.51 × 106 feet 

squared per day (fig. 7 and table 1). A portion of the 

Ouachita River is represented by river code 1. Bayou 

Bartholomew and a portion of the Saline River are represented by river code 2. The Arkansas, Mississippi and 

White Rivers are represented by river code 3, Lake Chicot is represented by river code 4, and the Boeuf River, 

Crooked Bayou, Bayou Macon and Big Bayou are represented by river code 5 (fig. 7 and table 1).

Recharge

The overlying confining unit limits recharge 

entering the alluvial aquifer from the surface. Previous 

models have estimated areal recharge to be 0.4 to 2.0 

inches in eastern Arkansas. However, these values have 

not been corroborated by field studies. The alluvial 

aquifer is reported as obtaining most of its recharge 

from surface-water bodies (Ackerman, 19891; Mahon 

and Poynter, 1993).

Areal recharge zones for the model were based 

on five zones of surficial geology (Haley, 1993) and 

soil type (Schwarz and Alexander, 1995) (fig. 8). Variations in soil type and soil permeability have the potential to affect recharge to the underlying alluvial aquifer, 

thus parameter zones based on soil type and geology 

were used to vary the estimates of recharge within reasonable limits. 

Discretization

Spatial Discretization

The model is spatially discretized by dividing the 

model area into a grid of 1 square- mile cells (fig. 5). 

The grid is identical to the grid used in the south model 

(Mahon and Poynter, 1993). The total model grid is 102 

cells by 75 cells, with the active area encompassing 

3,819 cells. 

Temporal Discretization

The model was initially discretized into 10 stress 

periods each with 10 time steps, which reflect the seven 

stress periods of the south model (Mahon and Poynter, 

1993), and 3 additional stress periods that bring the 

model forward in time to 1998 (fig. 9). One 11-year 

stress period and four 10-year stress periods were later 

added for predictive scenarios (years 1998 through 

2049) to create a total of 15 stress periods for the scenario model. 

Pumping Stress - Water Use

Pumpage in eastern Arkansas varies annually, 

but generally has increased since the early 1900’s. The 

pumping stress for the model is distributed areally and 

temporally to simulate reported water use. The source 

of the pumping stress distribution and amounts for 

stress periods 1-7 (1918-1988) is the south model 

(Mahon and Poynter, 1993). The source of the pumping 

stress distribution and amounts for stress periods 8-10 

(1989-1998) is the site-specific water-use information 

in the USGS and ASWCC Water-Use Database (T.W. 

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

2000). The database contains site-specific water-use 

rates as reported by farmers, municipalities, and industrial users. 

Stress Periods 1-7 (1918-1988)

Simulated pumpage for stress periods 1-7 (1918-

1988) was transferred from the south model (Mahon 

and Poynter, 1993). Computation of pumpage distributions was based on estimates of ground-water use for 

six, 5-year time periods beginning in 1960 (Stephens 

and Halberg, 1961; Halberg and Stephens, 1966; Halberg, 1972 and 1977; Holland and Ludwig, 1981; Holland, 1987). Pumpage distribution for stress periods 1-

7 was determined by Mahon and Poynter (1993) (table 

2, fig. 10). Pumpage for the period of time prior to 1960 

was estimated based on results of previous models in 

eastern Arkansas (Mahon and Ludwig, 1990). 

C KLW M = ⁄
Description of the Ground-Water Flow Model 15

Figure 8. Areal recharge zones in the model.

Base from U.S. Geological Survey digital data, 1:100,000

Drew

Ashley

Desha

Chicot

Bradley

Lincoln

Arkansas

Jefferson

Cleveland

Union

Union

Morehouse

Bolivar

Washington

West Carroll

Phillips

Issaquena East Carroll

Arkansas

Mississippi

Louisiana

92° 91°

33°

34°

EXPLANATION

Areal recharge,

in inches per year

0.83

1.5

2

2.5

0 10 20 5 Miles

0 10 20 5 Kilometers
16 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

Figure 9. Model time, stress periods, and pumpage descriptions.

Jan. 1, 1918

Jan. 1, 1958

Jan. 1, 1963

Jan. 1, 1968

Jan. 1, 1973

Jan. 1, 1978

Jan. 1, 1983

Jan. 1, 1988

Jan. 1, 1989

Mar. 31, 1992

Jan. 1, 1994

Mar311998

S.P. 1 14,610 days

S.P. 2 1,826 days

S.P. 3 1,826 days

S.P. 4 1,826 days 1972 obs. (old calibration)

S.P. 5 1,826 days

S.P. 6 1,826 days 1982 obs. (old calibration)

(end of Mahon and Poynter,

1993)Continue S.P. 7

Pumpage

1991 Reported

Pumpage

0

14610

16436.2

18262.4

20088.6

21914.8

23741

25567.2

25933

27117

27759

29307

MODEL TIME (days)

MODEL TIME DISCRETIZATION

EXPLANATION

1997 Reported

Pumpage

CALIBRATION TIME

obs., HYDRAULIC HEAD OBSERVATION

END OF PREVIOUS MODEL E

S.P., STRESS PERIOD

S.P. 7 2,192 days

S.P. 8 1,184 days

S.P. 9 642 days

S.P. 10 1,548 days
Description of the Ground-Water Flow Model 17

Table 2. Total pumpage rates simulated in stress periods 1-10[Units are in cubic feet per day; negative designates outflow from the model]

State County or parish Stress period 1 (1918-1957) Stress period 2 (1958-1962) Stress period 3 (1963-1967) Stress period 4 (1968-1972) Stress period 5 (1973-1977) Stress period 6 (1978-1982) Stress Period 7 (1983-1988) Stress Period 8 (1989-3/31/1992

Arkansas Ashley -5,880,694 -5,162,436 -2,976,426 -4,480,370 -6,691,450 -13,615,510 -9,713,190 -9,099,961 

Chicot -1,215,002 -1,881,027 -1,744,270 -3,499,854 -6,538,087 -10,043,610 -10,752,910 -16,844,487 Desha -1,920,746 -2,977,729 -5,436,854 -9,903,450 -13,734,731 -17,770,490 -15,513,720 -19,955,596 Drew -483,472 -749,614 -1,072,044 -2,697,840 -1,348,066 -5,209,340 -4,856,160 -4,355,999 Jefferson -649,076 -1,003,899 -1,173,600 -1,466,340 -2,992,290 -3,929,100 -2,672,750 -4,035,457 Lincoln -1,538,143 -2,345,496 -3,417,860 -8,737,530 -10,653,590 -11,304,540 -10,939,470 -12,794,742 

Louisiana East Carroll -128,251 -198,802 -202,168 -348,323 -350,552 -1,015,569 -881,604 -542,272 

Morehouse -1,142,604 -1,771,485 -2,176,285 -2,631,851 -5,565,665 -3,290,439 -2,884,800 -1,430,115 West Carroll -28,543 -44,278 -136,369 -216,108 -309,140 -407,793 -498,508 -277,988 Total -12,986,531 -16,134,766 -18,335,876 -33,981,666 -48,183,571 -66,586,391 -58,713,112 -69,336,617 
18 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

Figure 10. Pumpage by county in stress periods 1-10.

Stress Period 1 (1918-1957)

Str

Stress

ess Period 2 (1958-1962)

Period 3 (1963-1967)

Stress Period 4 (1968-1972)

Stress Period 5 (1973-1977)

Stress Period 6 (1978-1982)

Stress Period 7 (1983-1988)

Str

Stress Period 10 (199

Stress Period 9 (4/1/1992-1993)

ess Period 8 (1989-3/31/1992)

4-3/31/1998)

West Carroll

East Carroll

Morehouse

Drew

Jefferson

Chicot

Ashley

Lincoln

Desha

0

5

10

15

20

25

MODEL PUMPAGE, IN MILLIONS OF CUBIC

FEET PER DAY

COUNTY OR PARISH
Description of the Ground-Water Flow Model 19

Stress Periods 8-10 (1989-March 31, 1998)

Simulated pumpage distribution for stress periods 8-10 (1989-1998) was derived from the reported 

pumpage for 1991 and 1997 (table 2 and fig. 10). The 

water-use data were verified by reported crop-type 

water-use amounts before being used in the model. 

Reported pumpage for 1991 was used for stress periods 

8 and 9, encompassing 1989 through 1993 and reported 

pumpage for 1997 was used for stress period 10, 

encompassing 1994 through March 31, 1998. 

Hydraulic Properties

The model was divided into five parameter zones 

(fig. 11) based on the surficial geology map of Arkansas (Haley, 1993) and the state soil geographic 

(STATSGO) (Schwarz and Alexander, 1995) database 

utilizing a similar geologic/soil type zonation developed for recharge into the aquifer. These surficial geologic and soil units were considered to adequately 

represent the spatial variability of hydraulic properties 

from which to assign or estimate hydraulic conductivity and other hydrogeologic properties. 

Hydraulic Conductivity

Horizontal hydraulic conductivity values for 

model cells were estimated using the parameter-estimation process of MODFLOW-2000 (Hill and others, 

2000; discussed in the Model Calibration section). The 

south model (Mahon and Poynter, 1993) used a value 

of 275 feet per day for hydraulic conductivity of the 

alluvial aquifer in Arkansas. Arthur (2001) used a value 

of 425 feet per day for hydraulic conductivity in the calibration of a model of the alluvial aquifer east of the 

Mississippi River in Mississippi. Values of hydraulic 

conductivity used in the current model range from 250 

to 450 feet per day and are discussed in detail in the 

Model Calibration Procedure section. 

Storage

Specific storage and specific yield parameter

values for model cells were estimated using the parameter-estimation process of MODFLOW-2000. The 

parameter zones were based on the same zonation as 

used with horizontal hydraulic conductivity (fig. 11). 

The south model (Mahon and Poynter, 1993) used values of 2.50 × 10-4 to 3.76 × 10-3 per foot for specific 

storage and 0.28 for specific yield. Arthur (2001) used 

values of 1.60 × 10-3 per foot for specific storage and 

0.32 for specific yield in calibration of a model of the 

alluvial aquifer east of the Mississippi River in Mississippi. These values were used as a guide for a range of 

plausible values during the calibration process for this 

model. Values of specific storage used in the current 

model range from 3x10-5 to 9x10-4 and are discussed in 

detail in the Model Calibration Procedure section. 

MODEL CALIBRATION PROCEDURE

Calibration is the process of adjusting the model 

parameters to produce the best match between simulated and observed hydraulic heads. During calibration, 

parameters representing aquifer hydraulic properties 

were adjusted both manually and using automatic 

parameter-estimation techniques to match observed 

hydraulic heads. 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 parameters estimated in the parameterestimation process represent the hydrologic properties 

distributed as constant values over large areas and, 

therefore, are not intended to represent specific values 

of field tests at individual points within the model area. 

Non-Linear Least-Squares Regression 

Method

Non-linear least-squares regression is more efficient and objective compared to trial-and-error calibration because parameter values are adjusted 

automatically to obtain the best possible fit between 

observed and simulated values. The numerical difference between simulated minus observed values is 

called a residual. In the regression procedure, parameter values are estimated by minimizing the squared 

weighted residuals thus reducing residuals throughout 

the model, 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).
20 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

Figure 11. Zones with uniform values of hydraulic conductivity, specific storage, and specific yield.

Drew

Ashley

Desha

Bradley Chicot

Lincoln

Arkansas

Jefferson

Cleveland

Union

Union

Morehouse

Bolivar

Washington

West Carroll

Phillips

Issaquena

East Carroll

Arkansas

Mississippi

Louisiana

1

2

4

3

5

92° 91°

33°

34°

0 10 20 5 Miles

0 10 20 5 Kilometers

EXPLANTATION

Specific

yield

0.27

0.27

0.30

0.30

0.30

Specific

storage, in

feet-1

0.00003

0.00003

0.0009

0.0003

0.0001

Hydraulic

conductivity,

in feet per day

400

300

400

450

250

Hydraulic property values and

zone numbers.

1

2

3

4

5

Base from U.S. Geological Survey digital data, 1:100,000
Calibration Results and Model Evaluation 21

Calibration Strategy

In the model, grid cells assumed to have similar 

hydrologic properties are grouped together as a parameter zone and assigned a constant value that is adjusted 

during the calibration process. The model used 5 

hydraulic properties and 5 different zones for a total of 

25 parameters. These properties include horizontal 

hydraulic conductivity (hk), specific storage (ss), specific yield (sy), riverbed conductance, and recharge 

(rch). Many parameters are represented with the abbreviated name followed by the corresponding zone number. Thus, hydraulic conductivity in zone 1 is 

represented using hk_1 and so on. Each parameter was 

considered for estimation by the nonlinear-regression 

procedure. In the initial calibration process, estimations 

of various parameters were adjusted toward physically 

unreasonable values. In these cases, the parameter values were fixed at a reasonable value based on published 

studies in the area or literature review of similar hydrogeologic units.

Calibration Data Set

The calibration data set consisted of 1972, 1982, 

1992, and 1998 hydraulic-head observations (Mahon 

and Poynter, 1993, Ackerman, 1989b; Edds, 1982; 

Westerfield and Poynter, 1994; and Joseph, 1999). All 

published hydraulic-head observations (531) measured 

during the simulation period were used in the calibration process as head observations, but nine of these 

observations were omitted during the simulation 

because they were near the edge of the model boundary. The hydraulic head could not be interpolated 

between an inactive cell and the center of the active cell 

where the observation existed. Almost half of these 

omitted observations occurred in 1972.

Scaled Sensitivities

MODFLOW-2000 calculates sensitivities for 

values of hydraulic head throughout the model using 

the sensitivity-equation method (Yeh, 1986). These 

sensitivities then are used to calculate 1 percent scaled 

sensitivities. One percent scaled sensitivities are the 

change in hydraulic head at each observation point that 

would occur with a 1 percent change in the parameter 

and are helpful in determining which parameter will 

invoke the most change in hydraulic head. The 1 percent scaled sensitivities are multiplied by 100, which 

results in a 100 percent increase, to approximate the 

change in hydraulic head by doubling the value of a 

parameter. The least sensitive parameter is Ouachita, 

likely due to the distance from this parameter to observations. The average hydraulic-head change value for 

two parameters, hk_2 and boeuf_big, are negative (fig. 

12). Negative values indicate the average hydraulic 

head would decline if the values of hk_2 and boeuf_big 

were doubled. This decline would be negligible 

because of the small negative values of average hydraulic-head change. Consequently, this indicates that the 

model is not as sensitive to changes in hk_2 and 

boeuf_big as it may be with other parameters. However, a doubling in the value of hk_3, rch_1, rch_2, or 

rch_4 could result in approximate hydraulic-head 

changes greater than 1 foot, with the most sensitive 

parameter rch_4 inducing hydraulic-head changes up 

to 3.2 feet. These parameters tend to be more sensitive 

because of their spatial location with respect to large 

numbers of observations.

CALIBRATION RESULTS AND MODEL 

EVALUATION

A calibrated model results in reasonable aquifer 

property values and a reasonable fit to observed field 

measurements. Values of aquifer properties in the 

model fall within ranges found in aquifer tests in the 

alluvial aquifer and similar aquifer materials. Hydraulic conductivity values of 250 to 450 feet per day were 

simulated and fall within the range of hydraulic conductivities for silty to clean sand (Freeze and Cherry, 

1979). The lowest value (250 feet per day) of hydraulic 

conductivity occurs near Bayou Bartholomew in zone 

5 (fig. 11). This may be the result of model reaction to 

differences in riverbed conductance, or the introduction 

of silt and clay into the aquifer by leakage from the 

bayou. Overall values for hydraulic conductivity are 

within the same order of magnitude and represent average values for large areas in the aquifer. Values for specific yield in the model range from 0.27 to 0.30. 

Specific storage values range from 3.0 × 10-5 to 9.0 ×

10-4 per foot. The riverbed conductances range from 5 

× 103 to 2.51 × 106. Areal recharge ranged from 0.83 

to 2.5 inches per year with the highest recharge applied 

to the northern portion of the model area between the 

Arkansas River and Bayou Bartholomew.
22 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

Figure 12. Average change in hydraulic head by doubling a parameter.

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

hk_1hk_2hk_3hk_4hk_5

ss_1ss_2ss_3ss_4ss_5

sy_1sy_2sy_3sy_4sy_5

rch_1rch_2rch_3rch_4rch_5

Ouachita

bart_salin

ark_miss

lk_chicot

boeuf_big

PARAMETER NAME

AVERAGE CHANGE, IN FEET

Parameter Names

hk - hydraulic conductivity, 1 through 5 are zone numbers

ss - specific storage

sy - specific yield

rch - areal recharge

Ouachita through boeuf_big

represent riverbed conductance parameters (table 1)

Drain elevation and conductance also were 

adjusted to represent flow southward into Louisiana. 

The drain elevation was set at an arbitrary altitude of -

10 feet and was given a conductance value of 1,900 feet 

squared per day to allow the “best fit” of simulated 

heads based on comparison with published potentiometric-surface maps.

Water Budget

Examination of the ground-water model water 

budget indicates cells where ground-water flow enters 

or leaves in the active model area. Negative volumes 

indicate water removed from the model (outflow), and 

positive volumes indicate water introduced to the 

model (inflow) (fig. 13). There are three basic inflows 

to the model: release of water from aquifer storage, 

areal recharge, and riverbed leakage; and four withdrawals or outflows: aquifer storage, riverbed leakage, 

drains, and wells. Wells remove the most water with a 

total volume of 8.94x1011 cubic feet by the end of the 

simulation (table 3). Water removed by pumpage is offset by river leakage and water released from storage 

into the model. 

Hydraulic-Head Residuals

Residuals can indicate how well a ground-water 

flow model represents actual ground-water conditions 

in the aquifer. Residuals for the MODFLOW-2000 

model software are calculated by subtracting the simulated hydraulic head from the observed hydraulic head. 

Negative residuals, colored in blue on figures 14 and 

15, indicate simulated hydraulic heads that are higher 

than observed. Positive residuals, colored in red 

Table 3. Cumulative volumes of inflow and outflow in the 

model at the end of stress period 10

[Units are in cubic feet]

Inflow Outflow

Storage 1.68 × 1011 5.48 × 1010

Wells 0 8.94 × 1011

Drains 0 2.63 × 1011

River leakage 4.38 × 1011 5.17 × 1011

Recharge 1.12 × 1012 0

Totals 1.73 × 1012 1.73 × 1012
Calibration Results and Model Evaluation 23

Figure 13. Ground-water model budget by stress period.

-80

-60

-40

-20

0

20

40

60

1 2 3 4 5 6 7 8 9 10

STRESS PERIOD

VOLUMETRIC RATE, IN MILLION CUBIC FEET PER DAY

OUTFLOW

INFLOW

Recharge

Storage

River leakage

Wells

Drains

Storage

River leakage
24 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

Figure 14. Residuals—difference between simulated hydraulic heads and 1992 observed hydraulic heads.

Drew

Ashley

Desha

Chicot

Arkansas

Jefferson

Bradley

Lincoln

CLEVELAND

Union

Union

Morehouse

Bolivar

Washington

Phillips

Issaquena West Carroll East Carroll

Arkansas

Louisiana

Mississippi

92° 91°

33°

34°

0 10 20 5 Miles

EXPLANATION

1992 hydraulic head

residual (observed

minus simulated), in feet

-14 to -10

-9 to -3

-2 to 0

1 to 3

4 to 10

11 to 15

0 10 20 5 Kilometers

Active Model

Boundary

Base from U.S. Geological Survey digital data, 1:100,000
Calibration Results and Model Evaluation 25

Figure 15. Residuals—difference between simulated hydraulic heads and 1998 observed hydraulic heads.

Drew

Ashley

Desha

Chicot

Arkansas

Jefferson

Bradley

Lincoln

Union

Union

Morehouse

Bolivar

Washington

Phillips

West Carroll Issaquena East Carroll

Arkansas

Louisiana

Mississippi

92° 91°

33°

34°

0 10 20 5 Miles

EXPLANATION

1998 hydraulic head

residual (observed

minus simulated), in feet

-14 to -10

-9 to -3

-2 to 0

1 to 3

4 to 10

11 to 15

16 to 20

0 10 20 5 Kilometers

Active Model

Boundary

Base from U.S. Geological Survey digital data, 1:100,000
26 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

on figures 14 and 15, indicate simulated hydraulic 

heads that are lower than observed. Residuals calculated for 1992 and 1998 spring measurements primarily 

were used to guide model calibration because of better 

constrained site-specific water-use data collected during this period of time (figs. 14 and 15). The histograms 

for 1992 and 1998 residuals in the model show a slight 

positive bias partially resulting from model error in 

stressed areas of higher withdrawals (fig. 16). However, the overall fit of simulated heads were considered 

reasonable in the current calibration.

Figure 16. Frequency of residuals (plus or minus 2.5 feet of 

the value shown) for 1992 and 1998 observations.

Error Analysis

Statistics on hydraulic-head residuals, such as 

mean, minimum, maximum, root mean squared error 

(RMSE), and mean of absolute values aid in evaluation 

of model calibration. The RMSE for the four observation periods ranged from 5.90 to 6.72 indicating relatively good and consistent fit to observed values of 

hydraulic head (table 4).

.

The sign of the mean value can indicate skewed residuals depending on the magnitude of the mean away 

from zero. A more negative mean value indicates that 

the model tends to simulate hydraulic heads too high, 

and a more positive mean indicates a tendency to simulate hydraulic heads too low. The mean residual for 

the model in 1992 and 1998 is 1.61 and 0.66 feet, 

respectively. The mean absolute value is calculated as 

the mean for the absolute value of all residuals for a 

given year. The residuals for 1992 and 1998 have a 

mean absolute value of 4.74 and 5.45 feet, respectively, 

and an RMSE of 5.9 and 6.72 feet, respectively. The 

most negative residual value in the model is -19.62 feet 

(north-central Ashley County) and the most positive 

residual is 21.87 feet (on the Louisiana/Arkansas State 

line in Ashley County and Morehouse Parish). Both the 

minimum and maximum residuals occurred in 1972.

Potentiometric Surfaces

Potentiometric-surface maps are used to determine similarities and differences in general hydraulic 

head and flow direction between simulated and 

observed potentiometric surfaces. Potentiometric-surface contours for spring 1998 (Joseph, 1999) overlain 

on simulated hydraulic heads show similar results with 

ground-water flow southward into Louisiana, westward to the Ouachita River, and flow from the Arkansas 

River into the aquifer (fig. 17).

0

5

10

15

20

25

30

35

-25 -20 -15 -10 -5 0 5 10 15 20 25

RESIDUAL, IN FEET

NUMBER OF RESIDUALS

0

5

10

15

20

25

30

35

1998

1992

Table 4. Summary of the model residual statistics

Year Mean Minimum Maximum

Root

mean

squared

error

Mean

 absolute

1972 -2.56 -19.62 21.87 6.69 5.15

1982 -1.02 -12.25 12.74 6.49 5.03

1992 1.61 -12.58 14.89 5.90 4.74

1998 0.66 -13.43 19.98 6.72 5.45

All -0.98 -19.62 21.87 6.51 5.11
Calibration Results and Model Evaluation 27

Figure 17. Potentiometric map and simulated hydraulic heads for 1998.

River
28 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

Simulated and Observed Hydrographs

Hydrograph comparison allows for the evaluation of simulated hydraulic heads over time at a given 

observation point. Sixteen wells with hydraulic-head 

data for each calibration period, 1972, 1982, 1992, and 

1998, were selected. All available hydraulic-head data 

were used for the 16 wells. Much of these data included 

an intense collection period in the 1960’s during the 

construction of the lock and dam system on the Arkansas River. Because the model was calibrated to spring 

(January to April) observations, only measurements 

from January to April were used in the hydrographs to 

allow for consistency with other observation data and 

to ensure having a static hydraulic head. These data 

then were used to calculate residuals for each observation. Hydrographs were constructed to compare the 

simulated hydraulic head to the observed hydraulic 

head. Eight hydrographs from various sites in the 

model area are shown to illustrate the differences and 

similarities in the simulated and observed hydraulic 

head (fig. 18). Most simulated hydrographs coincide 

with the general trend of observed data. Intense data 

collection during the lock and dam construction on the 

Arkansas River from the late 1950s to the early 1990s 

can be seen in wells F and G. The effects of lock and 

dam construction were not explicitly simulated. Erratic 

changes in the hydrographs, such as those for well A, 

during 1988 and 1990 are not simulated. These spikes 

in the hydrograph may be because of short-term, localized recharge events or conditions that cannot be simulated with the available data.

SIMULATIONS OF PROJECTED

GROUND-WATER WITHDRAWALS

To evaluate the effects on hydraulic heads caused 

by projected ground-water withdrawals, three scenarios were used to simulate a range of possible pumping 

demands. Five additional stress periods of 10 years 

each were added to the model to simulate conditions to 

2049. Pumpage used in the predictive scenarios were 

either 1997 pumpage continued into the future (scenario 1) or increased pumpage based on water-use 

trends into the future (scenario 2) or increased pumpage with reductions in a selected area (scenario 3). The 

ASWCC Critical Ground Water area designation 

includes a requirement that a 50-percent saturated formation thickness be maintained. For this reason, the 

hydraulic head that would result in 50-percent of the 

thickness of the formation being saturated is used as a 

reference hydraulic head evaluating the simulated 

hydraulic heads. The model results from the scenarios 

are presented in maps of simulated hydraulic heads for 

2049, and maps showing simulated hydraulic heads 

minus 50 percent saturated formation thickness for 

each stress period (ending in 2009, 2019, 2029, 2039, 

and 2049). Where less than 50 percent saturated formation thickness occurs, the total saturated thickness is 

shown. Animations showing simulated hydraulic heads 

changing through time are included on the enclosed 

compact disk. In the animations, the hydraulic head of 

50 percent saturated formation thickness is indicated 

by a mesh surface and the dry cells appear as voids in 

the model surface. Pumpage rates for the predictive 

scenarios are shown in table 5 and figure 19. The 

decrease in pumpage is caused by dry cells that develop 

from 2019 to 2049 (stress periods 12, 13, 14, and 15), 

thereby eliminating pumping in those cells. Figure 20 

shows the amount of model area that is simulated as 

being dry, less than 30 feet of the total saturated thickness, and less than 50 percent saturated of the formation thickness. The 30 feet of saturated thickness was 

used as a minimum thickness needed to pump a sufficient amount of water for uses such as irrigation.

Table 5. Total pumpage rates simulated in predictive 

scenario model runs, stress periods 11-15

[Units are in cubic feet per day]

Stress

period

Dates

simulated Scenario 1 Scenario 2 Scenario 3

 11 3/31/1998-2009 73,526,344 100,669,800 91,747,944

 12 2010-2019 73,526,344 117,609,744 108,789,104

 13 2020-2029 73,526,344 115,227,304 108,408,192

 14 2030-2039 73,526,344 111,180,616 105,171,352

 15 2040-2049 73,526,344 109,454,576 103,327,144
Simulations of Projected Ground-Water Withdrawals 29

Click here to open figure 18.
Simulations of Projected Ground-Water Withdrawals 31

Figure 19. Rates of pumpage for the three scenarios by stress period.

0

20

40

60

80

100

120

140

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

STRESS PERIOD

PUMPAGE RATE, IN MILLIONS OF CUBIC FEET PER DAY

Scenario 1

Scenario 2

Scenario 3

1957 1962 1967

1972

1977

1982

1988

1992 1993

1998

2009

2019 2029

2039 2049

Scenario 1

In the first scenario, 1997 pumpage was 

extended unchanged through 2049. No cells in the 

model became dry in this scenario (fig. 20), however, 

many cells (square miles) have simulated hydraulic 

heads below 30 feet and 50 percent of the saturated formation thickness. Simulated hydraulic heads drop 

below 30 feet of saturated thickness over an area 7 

square miles in 2009 to 53 square miles in 2049. The 

model area with simulated hydraulic heads below 50 

percent of the saturated formation thickness range from 

12 square miles in 2009 to 81 square miles in 2049.

In 2009, a few areas where simulated hydraulic 

heads that are below the level of 50 percent saturated 

formation thickness occur in Ashley and Desha Counties (fig. 21). The two southernmost areas in Ashley 

County approaching and falling below 50 percent saturated formation thickness that appear at the 2009 timeframe are in areas where the aquifer is thinnest. The 

simulated hydraulic heads in these two areas in Ashley 

County are below 50 percent saturated formation thickness over the entire model simulation period. Other 

areas in Ashley County that approach less than 10 feet 

above or fall below 50 percent saturated formation 

thickness are related to high-density pumping. The area 

centered in Desha County that ranges between 0 and 20 

feet above 50 percent saturated formation thickness and 

falls below 50 percent saturated formation thickness in 

two model cells is a pumpage-induced depression in 

simulated hydraulic heads. The two cells that fall below 

50 percent saturated formation thickness indicate a 

simulated total saturated formation thickness of 30 to 

40 feet. This pumpage-induced depression extends 

northwest from the center of Desha County and northeast into Lincoln County. The 2019 simulated hydraulic heads (fig. 21) indicate enlargement and deepening 

of the depressions seen in the 2009 simulated hydraulic 

heads. 
32 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

Figure 20. Comparison of model area where the simulated hydraulic heads fall below predefined levels for each scenario.

0 0 0 0 0 7 12

24

40 53

12 25

52

68 81

0

50

100

150

200

250

300

350

400

450

Scenario 1

0

10

49

79 93

15

135

254

285 301

40

203

317

371

417

0

50

100

150

200

250

300

350

400

450

Scenario 2

0 3

33

51 64

15

103

200

249 276

40

175

283

330

374

0

50

100

150

200

250

300

350

400

450

2009 2019 2029 2039 2049

YEAR

Scenario 3

MODEL AREA, IN SQUARE MILES

EXPLANATION

DRY + SATURATED THICKNESS LESS THAN 30 FEET

AND AQUIFER THICKNESS HALF DEPLETED--Number

is area of less than half saturated aquifer thickness, in

square miles

DRY + SATURATED THICKNESS LESS THAN 30 FEET--

Number is area of saturated thickness less than 30 feet, in

square miles

DRY CELLS--Number is area of dry aquifer, in square miles
Simulations of Projected Ground-Water Withdrawals 33

Click here to open figure 21.
Simulations of Projected Ground-Water Withdrawals 35

Two areas of less than 50 percent saturated thickness in northwestern Desha County and north-central 

Ashley County not seen in the 2009 and 2019 timeframe appear in 2029, 2039, and 2049. The area of 

depressed simulated hydraulic heads centered in Desha 

County shows extensive aquifer dewatering with areas 

of simulated hydraulic heads continuing to drop below 

50 percent saturated formation thickness reducing the 

total saturated formation thickness to less than 10 feet. 

Simulated hydraulic heads for 2049 shown in figure 22 

indicate the hydraulic-head altitudes range from 200 

feet above NGVD of 1929 in central Jefferson County 

to less than 70 feet above NGVD of 1929 in the center 

of the Desha County cone of depression.

Scenario 2

In scenario 2, pumpage was increased according 

to current water-use trends to simulate likely demands 

in the future. A regression was developed to determine 

a trend in the rate of increase for each county using 

water-use data from 1988 through 2000 (Holland, 

1993; Holland, 1999; T.W. Holland, U.S. Geological 

Survey, written commun., 2002). The water-use trend 

was applied to the 1997 pumpage to increase pumpage 

for successive stress periods to a maximum value of 

1.25 times the estimated 2000 pumpage for each 

county. Scenario 2 limits pumpage to 1.25 times the 

estimated 2000 pumpage rates because most of the land 

in the model area suitable for growing crops is already 

in agricultural production and little increase in agricultural acreage or changes in farm practices is anticipated. Rates of model pumpage for scenario 2 decrease 

after 2019 (stress period 12) (fig. 19). The decrease in 

pumpage is caused by dry cells that develop from 2019 

to 2049 (stress periods 12, 13, 14, and 15), thereby 

eliminating pumping in those cells (fig. 20).

The results of scenario 2 show a number of cells 

that fall below the fixed criteria of 30 feet saturated 

thickness and 50 percent saturated formation thickness. 

The model area that becomes dry during the simulation 

of scenario 2 ranges from 0 square miles in 2009 to 93 

square miles in Desha, Lincoln, and Ashley Counties. 

However, there are many cells (square miles) that have 

simulated hydraulic heads that fall below 30 feet saturated thickness and 50 percent of the saturated formation thickness (figs. 20 and 23). The model area that 

simulated hydraulic heads drop below 30 feet of saturated thickness ranges from 15 square miles in 2009 to 

301 square miles in 2049. Simulated hydraulic heads 

drop below 50 percent saturated formation thickness 

over an area of 40 square miles in 2009 to 417 square 

miles in 2049. Figure 23 shows areas of simulated 

hydraulic heads that are below 50 percent saturated formation thickness in 2009 in Ashley and Desha Counties. A similar pattern of pumpage-induced areas below 

50 percent saturated formation thickness simulated by 

scenario 1 in year 2039 (fig. 21) appears in 2009 scenario 2 (fig. 23). An additional area of less than 50 percent saturated formation thickness appears in Lincoln 

County in the 2009 simulated hydraulic head. The simulated total saturated thickness where the aquifer is less 

than or equal to half saturated in 2009 varies from 40 to 

60 feet in western Ashley County and northeastern Lincoln County to 10 to 20 feet in eastern Ashley County.

The simulated hydraulic heads (fig. 23) for scenario 2 indicate enlargement and deepening of the area 

of depressed simulated hydraulic heads and the presence of dry cells in Desha County in 2019. A total of 10 

dry cells appears in the 2019 timeframe all in Desha 

County. The pumpage-induced area of depressed simulated hydraulic heads elongates further to the southeast and to the northwest into Lincoln County from 

2019 through 2049. An area in southern Desha County 

that was previously greater than 50 percent saturated 

formation thickness drops below the 50 percent saturated formation thickness level to a total thickness of 11 

to 30 feet in 2019.

During the period of 2029 to 2049, areas of 

depressed simulated hydraulic heads are further deepened and enlarged and the number of dry cells 

increased in Desha, Lincoln, and Ashley Counties (fig. 

23). The area of depressed simulated hydraulic heads 

centered in Desha County deepens and 77 model cells 

go dry by 2049 compared to scenario 1 where no dry 

cells are simulated by 2049. Smaller areas of depressed 

simulated hydraulic heads that appear in Ashley and 

Chicot Counties also show increased deepening. Simulated hydraulic heads for scenario 2 ranged from 200 

feet above NGVD of 1929 in central Jefferson County 

to below 50 feet above NGVD of 1929 with dry cells 

appearing in Ashley, Desha, and Lincoln Counties (fig. 

24).

Scenario 3

For the third scenario, the pumpage was reduced 

by 10 percent from that of scenario 2 in a selected area 

(fig. 25) that represents a proposed replacement of 

ground water by surface-water diversion in that area 
36 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

Figure 22. Simulated hydraulic heads for the year 2049, scenario 1.

Drew

Ashley

Desha

Chicot

Bradley

Lincoln

Arkansas

Jefferson

Cleveland

Union

Union

Morehouse

Bolivar

Washington

West Carroll

Phillips

Issaquena East Carroll

Dallas

Arkansas

Mississippi

Louisiana

92° 91°

33°

34°

EXPLANATION

Altitude of simulated

hydraulic head for the

year 2049, in feet.

Datum is National

Geodetic Vertical Datum

of 1929

191 - 200

181 - 190

171 - 180

161 - 170

151 - 160

141 - 150

131 - 140

121 - 130

111 - 120

101 - 110

91 - 100

81 - 90

71 - 80

61 - 70

51 - 60

0 10 20 5 Miles

0 10 20 5 Kilometers

Base from U.S. Geological Survey digital data, 1:100,000
Simulations of Projected Ground-Water Withdrawals 37

Click here to open figure 23.
Simulations of Projected Ground-Water Withdrawals 39

Figure 24. Simulated hydraulic heads for the year 2049, scenario 2.

Drew

Ashley

Desha

Chicot

Bradley

Lincoln

Arkansas

Jefferson

Union

Union

Morehouse

Grant

Bolivar

Washington

West Carroll

Phillips

Issaquena

East Carroll

Arkansas

Mississippi

Louisiana

92° 91°

33°

34°

EXPLANATION

Altitude of simulated

hydraulic head for

the year 2049. Datum

is National Geodetic

Vertical Datum of 1929

191 - 200

181 - 190

171 - 180

161 - 170

151 - 160

141 - 150

131 - 140

121 - 130

111 - 120

101 - 110

91 - 100

81 - 90

71 - 80

61 - 70

51 - 60

41 - 50

Dry

0 10 20 5 Miles

0 10 20 5 Kilometers

Base from U.S. Geological Survey digital data, 1:100,000
40 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

Figure 25. Model area and area to be served by proposed diversion plan.

Drew

Ashley

Desha

Chicot

Bradley

Lincoln

Arkansas

Jefferson

Cleveland

Union

Union

Morehouse

Bolivar

Washington

West Carroll

PhillipsIssaquena

East Carroll

Arkansas

Mississippi

Louisiana

Area to be

served by

proposed

diversion plan

92° 91°

33°

34°

0 10 20 5 Miles

0 10 20 5 Kilometers

Modified from U.S Army Corps of Engineers,

written commun., 2002
Model Limitations 41

(U.S. Army Corps of Engineers, written commun., 

2002). The 10 percent reduction was applied only to the 

stress periods ending in years 2019, 2029, 2039, and 

2049. 

The result of scenario 3 shows a number of cells 

that fall below the fixed criteria of 30 feet saturated 

thickness, 50 percent of the saturated formation thickness, or become dry. Dry cells covered an area of 3 

square miles in 2019 in Desha County to 64 square 

miles in 2049 (fig. 20). Simulated hydraulic heads drop 

below 30 feet of saturated thickness over an area of 15 

square miles in 2009 to 276 square miles in 2049 and 

below 50 percent saturated formation thickness over an 

area of 40 square miles in 2009 to 374 square miles in 

2049.

Reducing pumpage by 10 percent (scenario 3) 

resulted in areas of depressed simulated hydraulic 

heads similar to those simulated in scenario 2 with 

fewer dry cells (figs. 20 and 23). By 2019, scenario 3 

simulated 3 dry cells compared with scenario 2, which 

simulated 10 dry cells (fig. 23). In the remaining three 

stress periods (2029, 2039, and 2049), scenario 3 had 

about two-thirds the number of dry cells simulated in 

scenario 2 (fig. 20). The 10 percent reduction appears 

to have delayed the development of dry cells by about 

10 years as exhibited by the similarities of hydraulic 

heads and dry cells by 2029 for scenario 2 (fig. 23) and 

by 2039 for scenario 3 (fig. 26). Overall, the areas of 

depressed simulated hydraulic heads are somewhat 

reduced in scenario 3 by the proposed ground-water 

replacement from surface water. Simulated hydraulic 

heads for scenario 3 show the hydraulic-head altitudes 

in 2049 range from 200 feet above NGVD of 1929 in 

central Jefferson County to below 50 feet above NGVD 

of 1929 with dry cells appearing in Ashley, Desha, and 

Lincoln Counties (fig. 27).

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 model area into a 

rectangular grid of square cells and vertical discretization of the alluvial 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 surface-water 

features. 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 pumpage 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 report.
42 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049
Model Limitations 43

Click here to open figure 26.
Model Limitations 45

Figure 27. Simulated hydraulic heads for the year 2049, scenario 3.

Drew

Ashley

Desha

Chicot

Bradley

Lincoln

Arkansas

Jefferson

Cleveland

Union

Union

Morehouse

Bolivar

Washington

West Carroll

Phillips

Issaquena East Carroll

Arkansas

Mississippi

Louisiana

92° 91°

33°

34°

EXPLANATION

Altitude of simulated

hydraulic head for the

year 2049. Datum is

National Geodetic

Vertical Datum of 1929

191 - 200

181 - 190

171 - 180

161 - 170

151 - 160

141 - 150

131 - 140

121 - 130

111 - 120

101 - 110

91 - 100

81 - 90

71 - 80

61 - 70

51 - 60

41 - 50

Dry

0 10 20 5 Miles

0 10 20 5 Kilometers

Base from U.S. Geological Survey digital data, 1:100,000
46 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer in Southeastern Arkansas,

1918-1998, With Simulations of Hydraulic Heads Caused by Projected Ground-Water Withdrawals Through 2049

SUMMARY

The Mississippi River Valley alluvial aquifer, 

encompassing parts of Arkansas, Kentucky, Louisiana, 

Mississippi, Missouri, and Tennessee supplies an average of 5 billion gallons of water per day. The aquifer is 

a valuable resource for agriculture, aquaculture, business, and community growth in eastern Arkansas by 

providing abundant water of high quality. However, 

withdrawals from the aquifer in recent years have 

caused considerable drawdown in the potentiometric 

surface. The effects of current ground-water withdrawals and potential future withdrawals on water availability are major concerns of water managers and users as 

well as the general public. A full understanding of the 

behavior of the aquifer under various water-use scenarios is critical to development of viable water-management and alternative source plans. To address these 

concerns, the U.S. Geological Survey, in cooperation 

with the U.S. Army Corps of Engineers, Vicksburg 

District, developed and calibrated a ground-water flow 

model, which has been used to simulate hydraulic 

heads caused by projected ground-water withdrawals.

The previously published ground-water flow 

model of the alluvial aquifer, the “south model” by 

Mahon and Poynter (1993), was updated and recalibrated to reflect present pumping stresses. The south 

model utilized the MODFLOW finite-difference 

numerical-modeling software in a transient state, and 

simulated time from 1918 to 1988 in seven stress periods. Updated water-use information was input to the 

model and additional stress periods were added to bring 

the model forward to 1998. The new model was developed and calibrated with MODFLOW-2000 finite-difference numerical-modeling and parameter-estimation 

software. The south model was calibrated to spring 

1972 and spring 1982 observations. The new model 

was calibrated to two additional observation times 

measured in the spring (January to April) of 1992 and 

1998, in addition to the previous calibration times. The 

residuals for 1992 and 1998 have a mean absolute value 

of 4.74 and 5.45 feet, respectively, and a RMSE of 5.9 

and 6.72 feet, respectively.

The effects of projected ground-water withdrawals were simulated through 2049 in three predictive 

scenarios. Five additional stress periods of 10 years 

were added to the model to facilitate predictive scenario generation. Pumpage for the three predictive scenarios was either 1997 pumpage continued into the 

future (scenario 1) or increased pumpage based on 

water-use trends into the future (scenario 2) or 

increased pumpage with reductions in a selected area 

(scenario 3). Scenario 1 resulted in an area of depressed 

simulated hydraulic heads centered in Desha County 

with simulated hydraulic heads in two cells dropping 

below 50 percent saturated thickness between 1998 and 

2009. Simulated hydraulic heads for 2029, 2039 and 

2049 indicate enlargement and deepening of the areas 

of depressed hydraulic heads with areas of simulated 

hydraulic heads continuing to drop below 50 percent 

saturated formation thickness, reducing the total saturated formation thickness to less than 10 feet. No dry 

cells were simulated in scenario 1. Scenario 2 simulated hydraulic heads over an area of 40 square miles 

below 50 percent saturated thickness by 2009 and 10 

square miles going dry between 2009 and 2019 in 

Desha County and smaller areas of depressed hydraulic 

heads appearing in Ashley and Chicot Counties. In scenario 2, there were 93 dry cells (92 square miles) simulated by 2049 in Desha, Lincoln, and Ashley 

Counties. In scenario 3, the model area that simulated 

hydraulic heads below 50 percent saturated formation 

thickness ranged from 40 square miles in 2009 to 374 

square miles by 2049. Dry cells first occur between 

2009 and 2019 covering an area of 3 square miles in 

2019 in Desha County to 64 square miles in 2049. 

Overall, the depth and extent of the areas of depressed 

hydraulic heads are reduced and the area is only about 

two-thirds of that simulated in scenario 2. 
References 47

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