Prepared in cooperation with the

Arkansas Soil and Water Conservation Commission and the

U.S. Army Corps of Engineers, Memphis District

RECALIBRATION OF A GROUND-WATER FLOW 

MODEL OF THE MISSISSIPPI RIVER VALLEY 

ALLUVIAL AQUIFER OF NORTHEASTERN ARKANSAS, 

1918-1998, WITH SIMULATIONS OF WATER LEVELS 

CAUSED BY PROJECTED GROUND-WATER 

WITHDRAWALS THROUGH 2049

Water-Resources Investigations Report 03-4109

U.S. Department of the Interior

U.S. Geological Survey
Front Cover: Photograph of rice fields and well by Paul W. McKee, U.S. Geological Survey.
RECALIBRATION OF A GROUND-WATER FLOW 

MODEL OF THE MISSISSIPPI RIVER VALLEY 

ALLUVIAL AQUIFER OF NORTHEASTERN ARKANSAS, 

1918-1998, WITH SIMULATIONS OF WATER LEVELS 

CAUSED BY PROJECTED GROUND-WATER 

WITHDRAWALS THROUGH 2049

By T.B. Reed

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 03-4109

Prepared in cooperation with the

Arkansas Soil and Water Conservation Commission

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

Little Rock, Arkansas

2003
U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

For additional information Copies of this report can be

write to: purchased from:

District Chief U.S. Geological Survey

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

401 Hardin Road Box 25286

Little Rock, Arkansas 72211 Denver Federal Center

Denver, Colorado 80225

The use of firm, trade, and brand names in this report is for identification purposes only and does 

not constitute endorsement by the U.S. Geological Survey.
Contents iii

CONTENTS

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

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

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

Study Area Description.............................................................................................................................3

Previous Studies........................................................................................................................................3

Previous Model .........................................................................................................................................3

Hydrologic Setting ............................................................................................................................................. 6

Sources and Sinks of Water.......................................................................................................................7

Upper Boundary—Areal Recharge..................................................................................................7

Lower Boundary—Hydrologic Interchange Between Underlying Aquifers ...................................7

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

Flow From the North...................................................................................................................... 13

Lateral Flow from the West from Older Sediments....................................................................... 13

Hydraulic Properties ............................................................................................................................... 13

Hydraulic Conductivity.................................................................................................................. 13

Storage ........................................................................................................................................... 14

Water Use................................................................................................................................................ 14

Model Development and Calibration ...............................................................................................................14

Simplifying Assumptions........................................................................................................................ 14

Finite-Difference Grid............................................................................................................................. 15

Initial Water-Level Altitudes................................................................................................................... 15

Stress Period Discretization .................................................................................................................... 15

Flux Boundaries ...................................................................................................................................... 18

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

Recharge.................................................................................................................................................. 21

Water Use................................................................................................................................................ 21

Storage .................................................................................................................................................... 22

Model Calibration Procedure .................................................................................................................. 22

Calibration Results and Model Evaluation.......................................................................................................25

Simulations of Water Levels Caused by Projected Ground-Water Withdrawals .............................................42

Summary ..........................................................................................................................................................52

Selected References .........................................................................................................................................53

CD-ROM with Digital Animations of Scenario Simulations and a PDF File of the Printed

Report .............................................................................................................................. In back pocket
iv Contents

ILLUSTRATIONS

Figure 1. Map showing location of study and modeled area.......................................................................... 4

2. Map showing finite-difference grid of model cells......................................................................... 5

3. Hydrogeologic section through the alluvial aquifer and underlying units...................................... 6

4-13. Maps showing:

4. Water-level altitudes in the alluvial aquifer in spring 1998 ....................................................... 8

5. Areas of confined and unconfined conditions within the alluvial aquifer in 1998.................... 9

6. Thickness of the alluvial aquifer.............................................................................................. 10

7. Thickness of the clay cap overlying the alluvial aquifer ........................................................ 11

8. Difference between the alluvial aquifer water levels in 1998 and the underlying

Sparta aquifer water levels in 1999...................................................................................... 12

9. Initial water-level altitudes assigned to model cells in both layers.......................................... 16

10. Simulated initial water-level altitudes in the lower layer produced by steadystate stress period 1 at the beginning of the transient simulations....................................... 17

11. Parameter zones used to calibrate the hydraulic properties and recharge ............................... 20

12. Distributions of pumpage used for 1994-1998 (stress period 11) ........................................... 23

13. Observation wells used in the calibration process................................................................... 24

14. Graph showing the average change in water level from a doubling of the parameter................ 26

15. Volumetric budget component rates for 1968-1972 and 1994-March 1998 (stress

periods 5 and 11) .................................................................................................................... 27

16. Graph showing selected volumetric budget component rates for the model

by stress period ....................................................................................................................... 28

17. Selected hydrographs of observed and simulated water levels showing water levels

used for calibration ................................................................................................................. 29

18-21. Maps showing water-level residuals for observation wells:

18. At the end of 1972 (stress period 5)....................................................................................... 30

19. At the end of 1982 (stress period 7)....................................................................................... 31

20. On March 31, 1992 (stress period 9) ..................................................................................... 32

21. On March 31, 1998 (stress period 11) ................................................................................... 33

22-25. Histograms showing difference between observed and simulated water levels from:

22. 1968 to 1972 (stress period 5)................................................................................................ 35

23. 1978 to 1982 (stress period 7)................................................................................................ 35

24. 1989 to March 1992 (stress period 9) .................................................................................... 36

25. 1994 to March 1998 (stress period 11) .................................................................................. 36

26-37. Maps showing:

26. Simulated water-level altitudes for March 31, 1998 (stress period 11) ................................. 37

27. Simulated river, specified head, and general head boundary fluxes for

model cells from 1994 to March 1998 (stress period 11) ................................................. 39

28. Simulated recharge fluxes for 1918 to 1972 (stress periods 1- 6) ......................................... 40

29. Simulated recharge fluxes for 1994 to March 1998 (stress period 11).................................. 41

30. Selected zones used for pumping changes in model projection simulations......................... 43

31. Simulated water levels at the end of 2049 (stress period 16) with 1997 pumpage

extended unchanged (scenario 1)...................................................................................... 44

32. Simulated water levels at the end of 2049 (stress period 16) with 1997 pumpage

extended by county trends (scenario 2)............................................................................. 45

33. Simulated water levels at the end of 2049 (stress period 16) with pumpage reduced

to 90 percent of county trends in selected zones (scenario 3)........................................... 46
Contents v

34. Simulated saturated thickness at the end of each stress period where the aquifer

is less than or equal to half saturated, and saturated thickness in excess of

50 percent of the aquifer thickness where the aquifer is more than half saturated, 

using 1997 pumpage extended unchanged.........................................................................47

35. Areas of extreme water-level declines produced by model projection scenarios ...................48

36. Simulated saturated thickness at the end of each stress period where the

aquifer is less than or equal to half saturated, and saturated thickness in excess of 

50 percent of the aquifer thickness where the aquifer is more than half saturated,

using 1997 pumpage extended by county trends ...............................................................49

37. Simulated saturated thickness at the end of each stress period where the

aquifer is less than or equal to half saturated, and saturated thickness in excess of 

50 percent of the aquifer thickness where the aquifer is more than half saturated,

using 1997 pumpage extended by county trends but reduced to 90 percent

in selected zones................................................................................................................51

TABLES

Table 1. Stress periods and water use simulated............................................................................................18

2. Values of hydrologic parameters derived from the calibration process...........................................25

3. Statistics for residuals for water-level observations.........................................................................34

4. Actual total pumpage for projection simulations.............................................................................42
vi Contents

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 1983 (NAD 83).

CONVERSION FACTORS, ABBREVIATIONS, AND VERTICAL DATUM

Multiply By To obtain

inch (in.) 25.4 millimeter (mm)

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

foot (ft) 0.3048 meter (m)

foot per mile (ft/mi) 0.3048 meter per kilometer (m/km)

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

mile (mi) 1.609 kilometer (km)

square mile (mi2) 2.590 square kilometer (km2)

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

cubic foot per day (ft3/d) 0.02832 cubic meter per day (m3/d)

billion gallons per day (Bgal/d) 0.04381 cubic meter per second (m3/s)
Abstract 1

RECALIBRATION OF A GROUND-WATER FLOW MODEL OF 

THE MISSISSIPPI RIVER VALLEY ALLUVIAL AQUIFER OF 

NORTHEASTERN ARKANSAS, 1918-1998, WITH 

SIMULATIONS OF WATER LEVELS CAUSED BY PROJECTED 

GROUND-WATER WITHDRAWALS THROUGH 2049

By T.B. Reed

ABSTRACT

 A digital model of the Mississippi River Valley 

alluvial aquifer in eastern Arkansas was used to simulate ground-water flow for the period from 1918 to 

2049. The model results were used to evaluate effects 

on water levels caused by demand for ground water 

from the alluvial aquifer, which has increased steadily 

for the last 40 years. The model results showed that 

water currently (1998) is being withdrawn from the 

aquifer at rates greater than what can be sustained for 

the long term. The saturated thickness of the alluvial 

aquifer has been reduced in some areas resulting in dry 

wells, degraded water quality, decreased water availability, increased pumping costs, and lower well yields. 

 The model simulated the aquifer from a line just 

north of the Arkansas-Missouri border to south of the 

Arkansas River and on the east from the Mississippi 

River westward to the less permeable geologic units of 

Paleozoic age. The model consists of 2 layers, a grid of 

184 rows by 156 columns, and comprises 14,118 active 

cells each measuring 1 mile on a side. It simulates time 

periods from 1918 to 1998 along with further time periods to 2049 testing different pumping scenarios. Model 

flux boundary conditions were specified for rivers, general head boundaries along parts of the western side of 

the model and parts of Crowleys Ridge, and a specified 

head boundary across the aquifer further north in Missouri. 

Model calibration was conducted for observed 

water levels for the years 1972, 1982, 1992, and 1998. 

The average absolute residual was 4.69 feet and the 

root-mean square error was 6.04 feet for the hydraulic 

head observations for 1998. 

Hydraulic-conductivity values obtained during 

the calibration process were 230 feet per day for the 

upper layer and ranged from 230 to 730 feet per day for 

the lower layer with the maximum mean for the combined aquifer of 480 feet per day. Specific yield values 

were 0.30 throughout the model and specific storage 

values were 0.000001 inverse-feet throughout the 

model. Areally specified recharge rates ranged from 0 

to about 30 inches and total recharge increased from 

1972 to 1998 by a factor of about four.

Water levels caused by projected ground-water 

withdrawals were simulated using the calibrated 

model. Simulations represented a period of 50 years 

into the future in three scenarios with either unchanged 

pumpage, pumpage increased by historic trends, or 

pumpage increased by historic trends except in two 

areas of the Grand Prairie. If pumping remains at 1997 

rates, this produces extreme water-level declines (areas 

where model cells have gone dry or where the water 

level in the aquifer is equal to or less than the original 

saturated thickness, assuming confined conditions in 

the aquifer everywhere in the formation in predevelopment times) in the aquifer in two areas of the aquifer 

(one in the Grand Prairie area between the Arkansas 

and White Rivers and the other west of Crowleys Ridge 

along the Cache River) with about 400 square miles 

going dry. Increasing the pumping rates to that which 

would be projected using historic data led to increased 

extreme water-level declines in both areas with about 

1,300 square miles going dry. Declines in both scenarios generally occurred most rapidly between 2009 and 

2019. Reducing the pumping rates to 90 percent of that 

used for projected historic rates in areas between the 

Arkansas and White Rivers relating to two diversion 

projects of the U.S. Army Corps of Engineers and other 

agencies did little to decrease the extreme water-level 

declines. However, these pumpage reductions are small 

(amounting to about 16 percent of the reductions that 
2 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

could result from implementation of these diversion 

projects). 

INTRODUCTION

The Mississippi River Valley alluvial aquifer 

(hereinafter referred to as the alluvial aquifer), located 

in eastern Arkansas, and parts of Missouri, Kentucky, 

Tennessee, Mississippi, and Louisiana, also locally 

called the Delta, encompasses an area of about 32,000 

mi2

 and supplies an average of 4.4 Bgal/d of water 

(1994 data). Historically, the aquifer has been an 

important water resource driving agriculture, business, 

and community growth in eastern Arkansas by providing abundant water of high quality. However, in recent 

years demand has outstripped recharge of the aquifer, 

and water users and water-use planners are questioning 

the ability of the aquifer to meet increasing water 

demands in the long term. Withdrawals from the aquifer have caused considerable declines in aquifer water 

levels. The effects of current (1998) 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 watermanagement and alternative source plans. 

The alluvial aquifer is the most prolific aquifer 

supplying water to the Grand Prairie area and other 

parts of the Delta of eastern Arkansas. Aquifer withdrawal rates probably are much greater than recharge; 

and furthermore, they cannot be sustained for the long 

term. Massive cones of depression in aquifer water levels have formed in numerous areas and continue to 

grow in area and depth. For example, in some areas the 

saturated thickness of the alluvial aquifer has been 

reduced to less than 20 ft from an original total estimated saturated thickness greater than 200 ft. The consequences of excessive pumping fo the aquifer are 

serious: dry wells, decreasing water quality, decreasing 

water availability, increased pumping costs, and damage to the ability of the aquifer to yield water.

 Surface water is abundant in the region at certain 

times during the year, and the conjunctive use of surface water with ground water is a key element to assuring sustainable use of the alluvial aquifer and future 

growth in the region. However, surface water is not 

readily or economically available in all areas, and surface-water withdrawals are subject to limitation by 

mandated minimum streamflows. Surface-water availability also is affected by intense pumping of regional 

aquifers. Surface- and ground-water systems in the 

region are intimately connected; great volumes of 

water are transferred between surface-water bodies and 

the alluvial aquifer. In the early 1900’s, predevelopment conditions existed and most rivers in the region 

received part of their flow from ground water, especially during dry summer months. This transfer of 

water has reversed as development of the alluvial aquifer has increased and water levels have declined. Many 

rivers now lose water to the aquifer, and minimum 

observed streamflows in unregulated streams have 

decreased, especially during the summer months. 

Ground-water gradients tend to show flow from the rivers to the aquifer during most of the year, except for the 

Mississippi River.

To address these concerns, the U.S. Geological 

Survey (USGS), in cooperation with the Arkansas Soil 

and Water Conservation Commission and the U.S. 

Army Corps of Engineers, Memphis District, conducted an investigation using a digital ground-water 

flow model.

Purpose And Scope

The purpose of this report is to evaluate the 

regional effects on water levels in the alluvial aquifer 

located north of the Arkansas River caused by projected ground-water withdrawals. An existing groundwater flow model (Mahon and Poynter, 1993), discretized at a uniform 1 mi by 1 mi cell size was recalibrated using more recently developed modeling 

software. Additional water-use and observation well 

data from succeeding years provided an opportunity to 

verify or, as proved necessary, recalibrate this model.

This report describes the hydrogeologic setting, 

model design, calibration procedures, and results of 

simulations using the calibrated model on water levels 

caused by projected ground-water withdrawals. Hypothetical pumpage for 50 years into the future (through 

2049) was computed and effects on water levels caused 

by the projected pumpage were simulated using three 

different pumpage scenarios. 

In addition to the interpretations, tables, and figures in the printed report, an accompanying compact 

disk contains a pdf file of this report as well as a set of 

digital animations of the three scenarios simulating different rates of hypothetical pumpage through 2049. 

These animations show changes in water levels result-
Introduction 3

ing from model simulations associated with each of the 

projected scenarios.

Study Area Description

The area studied and modeled includes all or 

parts of 23 counties north of the Arkansas River in 

Arkansas and all or part of 5 counties in southeastern 

Missouri (fig. 1). The modeled area included the area of 

the Mississippi River Valley alluvial aquifer north of 

the Arkansas River, west of the Mississippi River, east 

of the consolidated formations of Paleozoic age, and an 

area north of the Arkansas-Missouri border, encompassing a small part of southeastern Missouri.

Previous Studies

Many investigators have described the underlying sediments of the Mississippi Alluvial Plain. One of 

the earliest reports describing subsurface geology and 

ground-water resources in southern Arkansas and 

northern Louisiana was written by Veatch (1906).

Ground-water resources of northeastern Arkansas were 

described and a detailed inventory was provided by 

Stephenson and Crider (1916). Fisk (1944) reported 

on extensive geologic investigations along the Mississippi River Valley made by the U.S. Army Corps of 

Engineers between 1941 and 1944. This compilation 

consists of text accompanied by more than 110 illustrations describing the alluvial sediments. Counts and 

Engler (1954) reported on changes in water levels in 

the alluvial aquifer showing as early as 1938 a large 

cone of depression up to 60 ft deep in the Grand Prairie 

area covering Arkansas County (Counts and Engler, 

1954, fig. 1). Krinitzsky and Wire (1964) expanded on 

the hydrogeologic work of Fisk with a comprehensive 

look at ground-water conditions. Cushing and others 

(1964) and Boswell and others (1968) provided an 

overview of the alluvial aquifer in their discussions of 

Quaternary-age 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. Joseph 

(1999) provided a contour map of water levels for the 

aquifer for measurements made in the spring of 1998 as 

did Schrader (2001) for measurements made in the 

spring of 2000.

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

within and across boundaries of the alluvial aquifer. 

Broom and Lyford (1981) described the flow system of 

the alluvial aquifer based on the results of a model of 

the Cache and St. Francis River Basins in northeastern 

Arkansas. Peralta and others (1985) estimated future 

Quaternary-age (alluvial aquifer) ground-water availability in the Grand Prairie area by using a flow model 

coupled to an optimization routine. Regional model 

investigations were conducted by Ackerman (1989a, 

1989b, 1990) under the framework of the USGS Gulf 

Coast Regional Aquifer-System Analysis; these reports 

describe the model development and results, and show 

the characteristics of the flow system on a regional 

basis. Predictive simulations presented by Ackerman 

(1989a) were based on hypothetical increases in pumping. 

Previous Model

Substantial water-level declines in the alluvial 

aquifer prompted the need to better understand the flow 

system in the alluvial aquifer, which led to the development of digital ground-water flow models of the alluvial aquifer. Models developed previously were either 

at a scale that was too large to analyze the effects of 

projected pumpage or they were limited in their areal 

extent. The model discussed in this report is based on 

the previous model of the alluvial aquifer documented 

by Mahon and Poynter (1993). Their report included 

model 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. The model utilized the MODFLOW finite difference numerical-modeling software 

(McDonald and Harbaugh, 1988) to simulate transient 

conditions, and simulated time from 1918 to 1987 in 

seven stress periods. Model grids were based on a cell 

size of 1 mi2

 throughout the study areas. The models 

consisted of one layer with no-flow boundaries below 

that layer. Recharge was simulated as entering the aquifer from head-dependent surface infiltration through 

the overlying confining unit and through seepage 

through underlying units and riverbeds using the river 

package of MODFLOW. The active model cells of the 

Mahon and Poynter (1993) north model encompassed 

the same area as the active cells calibrated for the 

model described in this report (fig. 2). 
4 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

Figure 1. Location of study and modeled area.

Tennessee

Mississippi

Missouri

Arkansas

LEE

WHITE

CLAY

SHELBY

IZARD

LONOKE

ARKANSAS

RIPLEY

SHARP

CROSS

PANOLA

OREGON

PRAIRIE

PHILLIPS

DESHA

TATE

MISSISSIPPI

JEFFERSON

POINSETT

STONE

MONROE

GREENE

JACKSON

BUTLER

LINCOLN

TUNICA

PULASKI

DUNKLIN

CRAIGHEAD

BOLIVAR

RANDOLPH

COAHOMA

DE SOTO

CLEBURNE

ST FRANCIS

TIPTON

LAWRENCE

WOODRUFF

CRITTENDEN

PEMISCOT

INDEPENDENCE

GRANT

NEW MADRID

CLEVELAND

FAULKNER

DYER

STODDARD

LAUDERDALE

SALINE

Mississippi

River

St. Francis

River

L'Anguille

River

River

Cache

White

River

Arkansas

River

92° 90°

34°

36°

0 10 20 MILES

0 10 20 KILOMETERS

EXPLANATION

Boundary of active model

cells

Mississippi River Valley

alluvial aquifer

Crowleys Ridge

Consolidated formations of

Mesozoic and Paleozoic

age

Jackson Group

Base from U.S. Geological Survey digital data, 1:100,000 and 1:2,000,000

Digital geological data adapted from Haley and others (1976) and Bicker (1969)

A

A'

Trace of

section shown

on Figure 3

GRAND PRAIRIE

AREA

MISSISSIPPI

ALLUVIAL

PLAIN

MISSISSIPPI

ALLUVIAL

PLAIN
Introduction 5

Figure 2. Finite-difference grid of model cells.

Tennessee

Mississippi

Missouri

Arkansas

Current

River

Black

River

Cache

River

Little Red

River

White

Rive

Bayou

r

Meto

Arkansas

River

Mississippi

River

L'Anguille

River

Right

Hand

Chute

of

Little

River

St. Francis

River

92° 90°

34°

36°

0 10 20 MILES

0 10 20 KILOMETERS

EXPLANATION

Specific head boundary

cells

Other active cells

River cells

General head boundary

cells

Base from U.S. Geological Survey digital data, 1:100,000
6 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

HYDROLOGIC SETTING

The alluvial aquifer, the uppermost aquifer system in eastern Arkansas, is part of a much larger sedimentary system known as the Mississippi Embayment. 

The Mississippi embayment extends southward in a fan 

shaped geosyncline, plunging southward from southern 

Illinois to the Gulf of Mexico, and covers about 

160,000 mi2 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 crop out 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.

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 in Arkansas is 

bounded on the west by consolidated formations 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 of the alluvial aquifer (Ackerman, 

1990).

Deposition of sediment from the Mississippi and 

Arkansas Rivers during Pleistocene and Holocene time 

has produced deposits of alluvium (fig. 3) consisting of 

a sequence of sands, silts, and clays that constitute the 

alluvial aquifer and semi-confining units in eastern 

Arkansas. From a regional perspective, this collection 

of sediment can be divided into two units. The upper 

unit consisting of clay, silt, and fine sand confines the 

alluvial aquifer in places and is often referred to as the 

“clay cap.” The lower unit, which contains the alluvial 

aquifer, is composed of coarse sand and gravel that 

grades upward to fine sand. Hydraulic conductivity of 

the aquifer will thus be higher towards the bottom. It is 

this confining unit and alluvial aquifer, along with its 

flow system, that has been defined and investigated 

previously (Broom and Lyford, 1981; Ackerman, 

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

and Poynter, 1993). The alluvium is underlain by older 

water-bearing units including the Cockfield Formation 

and the Sparta Sand, and still older units known as the 

Carizzo Sand, Wilcox Group, Midway Group, and 

Nacatoch Sand (Renken, 1998). These units are shown 

in a hydrogeologic section shown in figure 3.

Figure 3. Idealized hydrogeologic section through the alluvium and underlying units. Trace of section shown in inset map on 

figure 1.

2,500 0

0

25

25

50 MILES

50 KILOMETERS

FEET

500

National Geodetic

Vertical Datum of

1929

500

1,000

1,500

2,000

VERTICAL SCALE GREATLY EXAGGERATED

COCKFIELD

FORMATION

ALLUVIUM ALLUVIUM

MOUNTAIN FORMATION

COOK

SPARTA SAND

CARIZZO SAND

WILCOX GROUP

MIDWAY GROUP

NACATOCH SAND

ROCKS

OF

PALEOZOIC

AGE

CANE RIVER

FORMATION

Adapted form Renken (1998, fig. 69)

MEMPHIS

SAND

A A'

RIPLEY FORMATION SELMA

GROUP
Hydrologic Setting 7

Both regional and local flow systems exist in the 

alluvial aquifer. Regional flow in the alluvial aquifer is 

considered to be water that has entered the deeper, 

coarse sand and gravel part of the aquifer and traveled 

for tens or hundreds of miles before discharging to 

major rivers such as the Mississippi, Arkansas, or 

White. Regionally, ground-water levels have been measured and mapped for several years(Ackerman, 1989b; 

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

Westerfield, 1990; Joseph, 1999). Ground water enters 

the modeled area laterally from the north and the west, 

flowing southward and eastward towards the Mississippi River or into cones of depression (fig. 4). Waterlevel altitudes range from nearly 300 ft in the north to 

less than 100 ft in the south over a distance of about 200 

mi.

The alluvial aquifer underlies nearly all of eastern Arkansas, with the exception of Crowleys Ridge 

(fig. 1), which trends nearly north to south and divides 

the aquifer, north of the Arkansas River, into two 

hydraulically separate flow regimes. Crowleys Ridge 

averages about 10 mi in width and is an erosional remnant of strata of Tertiary age capped, in places, by several tens of feet of loess. In southern Craighead and 

northern Poinsett Counties the ridge is narrow, and the 

hydrologic units cropping out are the most transmissive 

of those comprising the ridge. Theoretically, this area 

would be the most likely to allow the transfer of ground 

water from one side of the ridge to the other. However, 

potentiometric maps of ground-water levels (Joseph, 

1999; Schrader, 2001) indicate that there is about 20 to 

30 ft of head difference from one side of the ridge to the 

other, which indicates that the ridge is a substantial barrier to flow. There is also a difference between water 

levels in the alluvial aquifer and those in the ridge with 

water levels in the ridge generally higher.

It is presumed that before development of the 

ground-water resource in the alluvial aquifer, flow was 

in a southward direction, with a general slope of about 

1.2 ft/mi (Counts and Engler, 1954). Discharge from 

the aquifer was most likely to major rivers such as the 

Mississippi, Arkansas, and White. Prior to development, regional flow probably was southward beneath 

the Grand Prairie and the Arkansas River into the 

southern part of the alluvial aquifer and then into Louisiana.

Water levels in the aquifer have decreased with 

the increase in pumpage from the aquifer during development. Parts of the aquifer that once were confined are 

now (1998) unconfined (fig. 5).

The alluvial aquifer thickness as presented in the 

model presented by Mahon and Poynter (1993) varies 

substantially in the study area ranging from about 15 to 

195 ft and averages about 100 ft (fig. 6). Pugh and others (1997, sheet 1) report thicknesses of 0 to 180 ft with 

an average of about 100 ft. The aquifer is thickest 

where the confining unit is thin or where depressions 

occur in the underlying Tertiary-age sediments. 

The thickness of the confining unit or clay cap 

varies within the study area and as presented in the 

Mahon and Poynter (1993) model ranges from 0 to 

nearly 200 ft in the Grand Prairie (fig. 7). Thickness 

generally is 50 ft or less and the average thickness is 

about 25 ft. Gonthier and Mahon (1993, sheet 1) 

reported the clay thickness as 0 to 140 ft.

The thickness of the clay cap effects the integrity 

of the confining unit. The interconnection of laterally 

discontinuous but moderately transmissive sediments 

within the clay also affects the confining unit integrity.

Sources and Sinks of Water

Upper Boundary—Areal Recharge

Annual precipitation within the study area averages about 49 in. annually (Freiwald, 1985), some of 

which seeps through the fine-grained material overlying the aquifer to the water table. Areal recharge to the 

aquifer is equal to precipitation minus (1) runoff into 

streams, (2) evaporation, and (3) evapotranspiration 

from plants in the soil zone. Infiltration of precipitation 

probably accounts for the largest amount of recharge to 

the aquifer. 

Lower Boundary—Hydrologic Interchange 

Between Underlying Aquifers

Data related to the movement of ground water 

between the alluvial aquifer and the underlying hydrologic units during predevelopment time are sparse. 

Because outcrop areas of the older units are topographically higher than the aquifer, it is presumed that flow 

was upward from these older strata to the aquifer. However, water levels in the underlying aquifers have 

declined over time (Joseph, 2000) indicating that water 

levels in parts of the aquifer are now greater than those 

in the underlying sediments. In the southern part of the 

alluvial aquifer, including the Grand Prairie area, the 

alluvial aquifer water levels measured in 1998 were 

often 50 ft or more higher than the water levels measured in 1999 in the underlying Sparta aquifer (fig. 8). 
8 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

Figure 4. Water-level altitudes in the alluvial aquifer in spring 1998 (modified from Joseph, 1999).

280 290

270

260

250

240

230

220

210

200

190

140

150

150 160

170

180

270

260

250 240

220

230

240

250

220

210

200

190

180

170

150

190

160

140130

170

180

160

170

180

190

80

90

100

110

120

130

130

140

150

160

100

210

190

180

170

160

150

140

130

120

110

Tennessee

Mississippi

Missouri

Arkansas

92° 90°

34°

36°

0 10 20 MILES

0 10 20 KILOMETERS

EXPLANATION

Boundary of active model cells

POTENTIOMETRIC CONTOUR--

Shows altitude at which water

level would have stood in tightly

cased wells. Contour interval 10

feet. Datum is National Geodetic

Vertical Datum of 1929

180

Base from U.S. Geological Survey digital data, 1:100,000
Hydrologic Setting 9

Figure 5. Areas of confined and unconfined conditions within the alluvial aquifer in 1998.

Tennessee

Mississippi

Missouri

Arkansas

Mississippi

River

Arkansas

River

92° 90°

34°

36°

EXPLANATION

Boundary of active model cells

Unconfined aquifer

Confined aquifer

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

0 10 20 MILES

0 10 20 KILOMETERS
10 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

Figure 6. Thickness of the alluvial aquifer.

Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

Arkansas River

92° 90°

34°

36°

EXPLANATION

Boundary of active model cells

Alluvial aquifer thickness (feet)

0- 25

25 - 50

50 - 75

75 - 100

100 - 125

125 - 150

150 - 175

175 - 200

0 10 20 MILES

0 10 20 KILOMETERS

Base from U.S. Geological Survey digital data, 1:100,000
Hydrologic Setting 11

Figure 7. Thickness of the clay cap overlying the alluvial aquifer.

Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

Arkansas River

92° 90°

34°

36°

0 10 20 MILES

0 10 20 KILOMETERS

EXPLANATION

Boundary of active model cells

Thickness of clay cap (feet)

Overlying clay cap absent

1-5

5 - 10

10 - 15

15 - 20

20 - 25

25 - 50

50 - 100

100 - 200

Base from U.S. Geological Survey digital data, 1:100,000
12 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

Figure 8. Difference between the alluvial aquifer water levels in 1998 and the underlying Sparta aquifer water levels in 1999.

Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

ArkansasRiver

92° 90°

34°

36°

EXPLANATION

Boundary of active model cells

Water-level difference (feet)

[alluvial aquifer minus Sparta aquifer]

-120 to -25

-25 to -10

-10 to 0

0 to 25

25 to 50

50 to 100

100 to 260

0 10 20 MILES

0 10 20 KILOMETERS

Base from U.S. Geological Survey digital data, 1:100,000
Hydrologic Setting 13

This indicates that flow was from the aquifer into the 

underlying hydrologic units. Changing head relations 

between the alluvial aquifer and the underlying Sparta 

aquifer could over time change flows between the two 

aquifers. If water levels decline more rapidly in the 

alluvial aquifer than in the underlying units, flows 

downward into the Sparta aquifer will decline. Conversely, if water levels decline more rapidly in the 

Sparta aquifer, flows downward will increase.

Rivers

Many rivers flow across the alluvial plain and 

exchange water with the aquifer. The flow of water 

through riverbeds is dependent on the transmissive 

properties of the riverbed and the difference between 

the head in the aquifer and the river stage. The Mississippi and the Arkansas Rivers are presumed to have a 

good hydraulic connection with the aquifer because 

they are deeply incised into the aquifer, and the water 

level in the aquifer adjacent to the river is nearly identical to the river stage (Ackerman, 1989a, 1990; Mahon 

and Ludwig, 1990). The White and St. Francis Rivers 

may not be as well connected hydraulically with the 

aquifer although some hydrographs for wells near these 

rivers closely reflect changes in river stage (Ackerman, 

1990, fig. 8). Field observations and water-level measurements indicate that other smaller streams such as 

the Cache River and L’Anguille River in the alluvial 

plain generally have less hydraulic connection with the 

aquifer (Ackerman, 1990, fig. 8). Model simulations 

and measured water-level altitudes (Joseph, 1999, plate 

1) indicate that the Mississippi River remains a gaining 

stream throughout the study area from predevelopment 

times onwards. For other rivers, the general direction of 

water movement shifts from gaining to losing from predevelopment times to 1982 (Ackerman, 1990, p. 75). 

Flow from the North

Recharge to the study area also includes the 

ground water that moves southward in the alluvial aquifer from Missouri. Because the hydrologic connection 

is continuous between the alluvial aquifer in Arkansas 

and the alluvial aquifer in Missouri, this flow from the 

north may be quantitatively important.

Lateral Flow from the West from Older Sediments

A small amount of the total recharge enters the 

aquifer from Tertiary- and Cretaceous-age sediments 

underlying the aquifer and from the consolidated formations of Paleozoic age flanking the western side of 

the study area (Ackerman, 1990). Potentiometric-surface maps (Joseph, 1999; Schrader, 2001) show flow 

eastward from the consolidated formations on the west.

Hydraulic Properties

The heterogeneity of the sediments within the 

aquifer is paralleled by that of the hydraulic properties 

of the ground-water system; that is, small stringer sand 

and silt beds are dispersed laterally and vertically, and 

represent local features of the aquifer and flow system. 

Ground-water flow related to these features may be 

hydraulically independent on a local scale. Although 

flow is made more complex by the multitude of heterogeneities in the aquifer and upper confining unit, the 

flow system can be generalized and conceptualized as 

water moving laterally in one or two zones or layers 

within the alluvial aquifer. This simplistic conceptualization of flow and hydraulic properties may be compatible with conditions observed in the field because of 

the coarse sand and gravel at the base of the aquifer that 

grades upward to fine sand.

A regional simplification of ground-water flow 

and hydraulic properties may be inappropriate when 

examined in detail at a local scale. Channel fill, point 

bar, and backswamp deposits associated with present or 

former channels of the major rivers locally can produce 

abrupt differences in lithology, resulting in spatial variations in the hydraulic properties of both the aquifer 

and confining unit within small distances. The local 

lithologic variations allow for small scale or localized 

flow systems that may have flow characteristics that 

differ somewhat from the regional flow system. Local 

flow systems may have recharge and discharge zones 

occurring within short distances, such as tens of feet to 

a few miles, from each other. Well yields in these shallow local aquifers are sufficient to provide for domestic 

sources of water but are much less than those from 

wells completed in the underlying regional system. For 

the purpose of this report in which the aquifer is considered at a regional scale, these local variations in 

lithology and flow characteristics are not considered.

Hydraulic Conductivity

Hydraulic conductivity of the alluvial aquifer 

ranges from 120 to 390 ft/d (Krinitzsky and Wire, 

1964; Ackerman, 1989a). Geophysical and drillers’ 

logs typically show an increasing particle size in the 
14 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

lower parts of the aquifer and the hydraulic conductivity is greatest in the coarse sand and gravel near the 

base of the aquifer. Because there are no laterally 

extensive confining units within the alluvial aquifer, the 

aquifer responds hydraulically as a single unit from a 

regional perspective.

Storage

Specific yield (applicable to unconfined conditions) and specific storage (applicable to confined conditions) are both required to characterize ground-water 

flow in the alluvial aquifer. Specific yield is the amount 

of water released per unit decline in hydraulic head; 

specific storage is the amount of water released from 

storage resulting from the compression of the aquifer 

matrix per unit decline in hydraulic head. Freeze and 

Cherry (1979, p. 60) present a range of 0.005 to 

0.00005 for storage coefficient (dimensionless) in confined aquifers, which relates to specific storage values 

of 0.00005 to 0.0000005 (1/foot) with an average aquifer thickness of 100 ft, and a range of 0.01 to 0.30 for 

specific yield in unconfined aquifers. Driscoll (1986, p. 

67) presents 0.10 to 0.30 as a representative range for 

specific yield for sand.

Water Use

Pumpage of water from the alluvial aquifer in 

eastern Arkansas varies annually, but has increased 

since the early years of development and is used mostly 

for irrigation. Ground-water pumpage in the study area 

ranges from an average of about 83,000,000 ft3

/d during 1918-1957 (Mahon and Ludwig, 1990) to about 

636,000,000 ft3/d in 1998 (Terry Holland, U.S. Geological Survey, written commun., 2002).

MODEL DEVELOPMENT AND

CALIBRATION

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 hydrologic characteristics. 

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 Preconditioned-Conjugate-Gradient (PCG) solver, included in MODFLOW2000, was invoked to solve the finite difference equation.

MODFLOW-2000 provides several additional 

processes (Hill and others, 2000) that were used to help 

estimate hydrologic properties and further evaluate the 

model. Cells considered to have a similar hydrologic 

properties were grouped together and assigned a common value for that property (referred to here as a 

parameter). This was done for a number of hydrologic 

properties. The sensitivity process and observation process were used together to calculate the sensitivity of 

hydraulic heads, called grid sensitivities, throughout 

the model with respect to each of these parameters 

using the accurate sensitivity-equation method. The 

observation process then uses these grid sensitivities to 

calculate sensitivities for the simulated water-level altitudes associated with the observed water-level altitudes. Thus, the sensitivity process and the observation 

process are used with observed and simulated waterlevel altitudes to evaluate the relative importance of the 

parameters to the modeling process and to calculate the 

objective function used by the parameter-estimation 

process. The parameter-estimation process uses a 

modified Gauss-Newton method to adjust values of 

user-selected input parameters in an iterative procedure 

to minimize the value of the weighted least-squares 

objective function. Thus, estimates of parameters were 

calculated to minimize difference between observed 

and simulated water-level altitudes.

The model simulated steady-state and transient 

conditions. For steady-state simulations, selected 

model parameters are constant with time during a single stress period. For transient simulations, selected 

model parameters may change with time during multiple stress periods.

Simplifying Assumptions

By definition, a model is a mathematical simplification of a process or a system. In that regard, two layers were used to represent the aquifer in the model 

described in this report to show vertical variations in 

horizontal hydraulic conductivity. Mahon and Poynter 

(1993) describe nearby wells in the alluvial aquifer 

open to both the upper and lower zones in the aquifer 

as having negligible head differences. Thus, vertical 

flow within the alluvial aquifer is likely to be low. In 
Model Development and Calibration 15

that regard, the model can be represented effectively 

with one or two layers. However, as vertical variations 

in hydraulic conductivity were believed to be important, two layers were used to represent the aquifer in 

this model. As water-level altitudes decrease due to 

pumpage, the arithmetic mean of the horizontal 

hydraulic conductivity will be higher if the lower layer 

has a higher value than the upper layer than if a single 

layer with the lower value is used.

The alluvial aquifer is modeled as two layers of 

equal thickness—the upper layer (layer 1) and lower 

layer (layer 2). The aquifer is modeled in this manner 

because of differences in hydraulic conductivities. 

Flow in both layers is modeled as confined or unconfined. Water-level altitude data indicate that pumping 

has drawn down these water levels below the upper 

confining bed throughout much of the alluvial aquifer. 

All lateral model boundaries are impermeable except 

for portions of the western boundary, portions of Crowleys Ridge, and a boundary of specified heads along the 

northern border.

Other simplifying assumptions in the model 

include: (1) the system is isotropic causing hydrologic 

properties to be spatially invariant; (2) all pumpage in a 

model cell can be simulated as coming from the cell 

center; (3) the pumpage throughout a stress period is 

applied equally throughout the stress period; (4) 

recharge is invariant over large periods of time; (5) 

small scale variations of hydraulic conductivity within 

cells are negligible; (6) all pumping and observation 

wells are completed in the lower layer; and (7) the head 

difference between the upper and lower layer is negligible.

Finite-Difference Grid

A finite-difference grid was used to subdivide the 

model area into a horizontally uniform cell network of 

184 rows and 156 columns each 1 mi by 1 mi in size 

(fig. 2) as was done with the Mahon and Poynter (1993) 

model. The vertical dimensions of the cells also were 

derived from Mahon and Poynter (1993). The model 

code calculates a ground-water level at the center, or 

node, of each cell and a ground-water flux across each 

cell face based on water-level gradients between nodes. 

Of the 28,704 model cells, 14,104 are active. The 

model represents the alluvial aquifer in all or parts of 

23 counties in Arkansas and 5 counties in southeastern 

Missouri.

Spatial and vertical variations in hydrologic 

characteristics in the aquifer framework were represented by discrete values in each of the model cells. 

Model cells extend vertically into the aquifer and 

divide the aquifer into discrete volumes of aquifer 

material that are assumed to have uniform hydrologic 

characteristics. 

Initial Water-Level Altitudes

Initial water levels were specified at each model 

cell to represent conditions that probably existed before 

ground-water development began in the early 1900's 

(termed predevelopment conditions). Earliest potentiometric maps for the study area are limited to the Grand 

Prairie area (Engler and others, 1945), but even these 

water levels reflect that ground-water development had 

already begun. Consequently, a complete, accurate 

potentiometric-surface map for predevelopment conditions could not be constructed; however, previously 

developed flow models (Ackerman, 1989a; Broom and 

Lyford, 1981) have produced a distribution of water 

levels corresponding to approximate predevelopment 

conditions. It is these distributions, shown in figure 9, 

that were used as initial water-level altitude (predevelopment) conditions for the upper and lower model layers. The first stress period (stress period 1) was 

simulated so that steady-state conditions were attained. 

In this way, the hydraulic properties and boundary conditions were brought into hydrologic balance with the 

water-level altitudes used at the beginning of the transient time steps in 1918. Simulated initial water-level 

altitudes produced by the steady-state stress period 1 

are shown in figure 10.

Stress Period Discretization

The stress periods for the model are shown in 

table 1. Stress period 1 was specified as steady-state to 

bring hydraulic heads into balance with the boundary 

conditions. Additional stress periods were all specified 

as transient. Stress periods 2 through 7 are the same as 

stress periods 1 through 6 used by Mahon and Poynter 

(1993) in their model. Stress period 8 is stress period 7 

by Mahon and Poynter (1993) with the stress period 

extended through 1988 to extend the stress period 7 

pumpage of the model of Mahon and Poynter (1993). 

Stress periods 5 and 7 stop at the ends of 1972 and 

1982, respectively. Stress periods 9 and 11 are dis-
16 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

Figure 9. Initial water-level altitudes assigned to model cells in both layers.

Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

Arkansas River

92° 90°

34°

36°

EXPLANATION

Boundary of active model cells

Water-level altitude (feet above

the National Geodetic Vertical

Datum of 1929)

133 - 140

140 - 160

160 - 180

180 - 200

200 - 220

220 - 240

240 - 260

260 - 280

280 - 304

0 10 20 MILES

0 10 20 KILOMETERS

Base from U.S. Geological Survey digital data, 1:100,000
Model Development and Calibration 17

Figure 10. Simulated initial water-level altitudes in the lower layer produced by steady-state stress period 1 at the beginning of 

the transient simulations.

Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

Arkansas River

92° 90°

34°

36°

EXPLANATION

Boundary of active model cells

Water-level altitude (feet above

the National Geodetic Vertical

Datum of 1929)

134 - 160

160 - 180

180 - 200

200 - 220

220 - 240

240 - 260

260 - 280

280 - 304

0 10 20 MILES

0 10 20 KILOMETERS

Base from U.S. Geological Survey digital data, 1:100,000
18 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

cretized to end in the spring (March) of 1992 and 1998, 

respectively, to allow the simulated water levels calculated at the ends of stress periods 9 and 11 to better 

match in time the water levels of observation wells 

measured during the springs of those years. Five additional stress periods (stress periods 12 to 16) were 

added in the projection simulations of future pumpage 

scenarios after 1998. These were roughly 10 years in 

length and stop at the end of 2049. 

Flux Boundaries

Various flux-boundary conditions were specified 

in the model to represent different geohydrologic conditions in the flow system. The upper recharge boundary of the model represents the bottom of the confining 

bed or water table of the aquifer. The bottom of the 

aquifer is simulated as a no-flow boundary because 

data are insufficient to model the interaction between 

the alluvial and underlying aquifers. Flow to or from 

underlying aquifers is lumped with the areally distributed recharge. 

Because of the relatively low hydraulic conductivity of the rocks flanking the aquifer, no-flow conditions were specified on much of the western side of the 

model. The potentiometric-surface map by Joseph 

(1999) indicates flow from the west in some areas, and 

general-head boundary cells were placed at selected 

locations (fig. 2). Values of hydraulic head for these 

cells were derived from the steady-state simulation of 

stress period 1 in the model. The conductance for cells 

defining this boundary were estimated during the 

parameter-estimation process.

Table 1. Stress periods and water use simulated

Stress

period

Pumpage

(cubic feet per day)

Length

(days)

Length

(years) Beginning End

1 0 Steady-state Not applicable Not applicable Not applicable

2 82,806,688 14,610 40.00 1918 1957

3 92,879,304 1,826 5.00 1958 1962

4 127,464,032 1,826 5.00 1963 1967

5 142,161,888 1,826 5.00 1968 1972

6 249,573,216 1,826 5.00 1973 1977

7 434,081,856 1,826 5.00 1978 1982

8 391,937,728 2,192 6.00 1983 1988

9 621,882,112 1,184 3.24 1989 March 31, 1992

10 621,709,632 642 1.76 March 31, 1992 1993

11 631,324,480 1,549 4.24 1994 March 31, 1998

12 623,440,512-749,344,192 4,293 11.75 March 31, 1998 December 31, 2009

13 614,197,568-844,568,640 3,652 10.00 January 1, 2010 December 31, 2019

14 605,206,656-782,530,496 3,653 10.00 January 1, 2020 December 31, 2029

15 596,392,384-761,897,344 3,652 10.00 January 1, 2030 December 31, 2039

16 590,821,760-746,841,088 3,653 10.00 January 1, 2040 December 31, 2049
Model Development and Calibration 19

No natural geohydrologic boundary separates 

flow in the alluvial aquifer between Arkansas and 

southeastern Missouri. Accordingly, the alluvial aquifer in southeastern Missouri was included in the simulations because pumpage in that area may affect 

pumpage east of Crowleys Ridge in eastern Clay and 

Greene Counties, Arkansas. A specified-head boundary was placed in southeastern Missouri, even though 

this is not a natural boundary, because agricultural 

development of ground water in this area is minimal 

compared to that in Arkansas. This arbitrary boundary 

is about 10 mi (10 rows of cells) north of the ArkansasMissouri border west of Crowleys Ridge and extends 

eastward to the Mississippi River. The placement of 

this boundary is sufficiently far from the areas of major 

pumping in Arkansas so as not to adversely affect simulation of water levels in these areas of interest. There 

are 63 specified-head nodes within the model governing, in part, the flow of water from southeastern Missouri into Arkansas. The heads for these specified-head 

nodes represent predevelopment conditions that were 

derived by Ackerman (1989a).

Some potential for flow exists between the aquifer and sediments underlying and composing Crowleys 

Ridge. In particular, the Memphis Sand, which is the 

coalescing of the Sparta Sand, Cane River Formation, 

and Carrizo Sand starting on the west of the hydrogeologic section shown in figure 3, extending out on both 

sides of the ridge in southern Craighead, northern 

Cross, and Poinsett Counties. Hydraulic connection 

with the Memphis Sand underlying the aquifer could 

account for some flow between the hydrologic units. In 

1990, water levels in the Memphis Sand beneath western Cross and Poinsett Counties (Westerfield, 1990) 

were higher than water levels in the alluvial aquifer 

indicating possible ground-water flow from the Memphis Sand into the alluvial aquifer. For purposes of this 

report, parts of the ridge were simulated with a generalhead boundary condition in the same manner as modeled by Ackerman (1989a) and Mahon and Poynter 

(1993). The conductances for the general-head boundaries were estimated during the parameter-estimation 

process.

River cells representing the Mississippi River 

were used to allow flux along the eastern boundary of 

the model as well as cells representing the Arkansas 

River along the southern boundary of the model (fig. 

2). The hydrologic effect of these large rivers presents 

an effective hydrologic sink preventing ground-water 

flow to the east and south from the model area.

Eleven rivers were chosen to be actively simulated within the alluvial model. These rivers include the 

Arkansas River, Bayou Meto, Black River, Cache 

River, Current River, L’Anguille River, Little Red 

River, Mississippi River, Right Hand Chute of the Little 

River, St. Francis River, and the White River (fig. 2). 

Most of these rivers were classified as perennial by 

Hunrichs (1983). The river stages, which were modeled 

as constant throughout all stress periods, were derived 

from mean historic gage stages that were then interpolated to all river cells. The riverbed altitudes were set to 

zero in order to ensure underlying sediments never 

become unsaturated because these large, perennial 

streams would over time have saturated the underlying 

sediments down to the water-level altitude. The conductances for these 10 rivers were individually estimated during the parameter-estimation process and 

subsequently adjusted to better match the water-level 

altitude residuals. No attempt was made to relate these 

river conductances to stream lengths or widths within 

each model cell.

Hydraulic Conductivity

Horizontal hydraulic conductivities for model 

cells were estimated with the aid of the parameter-estimation process of MODFLOW-2000 and available 

aquifer test. The model was divided areally into 10 

parameter zones (fig. 11) based on the surficial geology 

map of Arkansas (Haley and others, 1976). These surficial geologic units were considered to adequately represent the spatial variability of hydraulic properties 

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

arbitrarily discretized into two equally thick vertical 

layers of aquifer material because of the vertical variability of horizontal hydraulic conductivity. This permitted a higher horizontal hydraulic conductivity to be 

used in the lower layer where coarser sands and gravels 

are present.

The model developed by Mahon and Poynter 

(1993) used a uniform value of 275 ft/d for hydraulic 

conductivity. Arthur (2001) specified a value of 425

ft/d for hydraulic conductivity in his calibration of a 

model of the alluvial aquifer east of the Mississippi 

River in Mississippi.
20 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

Figure 11. Parameter zones used to calibrate the hydraulic properties and recharge.

Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

ArkansasRiver

92° 90°

34°

36°

EXPLANATION

Boundary of active model cells

1

2

3

11

12

4

5

6

7

8

9

10

Hydraulic property and

recharge parameter zones

0 10 20 MILES

0 10 20 KILOMETERS

Additional recharge

zones within zone 1

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

Rovey and Cherkauer (1995) describe the scale 

dependency of hydraulic conductivity obtained from 

hydraulic testing of wells. They showed that as the 

radius of investigation increases, so does the value of 

hydraulic conductivity. The hydraulic conductivities 

used in this model with model cells 1 mi in width may 

represent values larger than those calculated from aquifer tests with test radii much smaller than 1 mi. As such, 

the plausible upper limits for hydraulic conductivity 

used in this model may be 400 to 600 ft/d.

An examination of geophysical and drillers’ logs 

indicates coarser alluvial material towards the bottom 

of the aquifer (Mahon and Ludwig, 1990; Mahon and 

Poynter, 1993). With such vertical variation in horizontal hydraulic conductivity, a vertical discretization of 

the aquifer may provide a better approximation of 

hydrologic properties. Earlier simulations of this model 

indicated that temporal variation in the arithmetic mean 

of horizontal hydraulic conductivity might provide a 

partial solution to some problems in calibration, particularly with simulated head variations over time north of 

the Arkansas River. The model was, therefore, divided 

vertically into two layers of equal thickness and provided with different parameter values for horizontal 

hydraulic conductivity. These parameter values were 

calibrated so the mean between them remained within 

reasonable values for overall horizontal hydrologic 

conductivity.

Recharge

Recharge zones for the model were based on the 

same parameter zones used for horizontal hydraulic 

conductivity (fig. 11). Recharge values were then modified locally to improve model fit. Although minimally 

constrained, recharge estimates are a function of vertical hydraulic conductivity which is a function of geology. Hence, surficial geologic units are likely to 

represent a reasonable initial distribution of recharge. 

The model developed by Mahon and Poynter (1993)

simulated recharge using the MODFLOW River Package to simulate flow from the upper clay cap down into 

the aquifer. As simulated water-level altitudes in the 

aquifer declined, flows from this upper region into the 

aquifer increased by a factor of 2.3, in effect increasing 

recharge over time. Because the current model simulates recharge directly using the MODFLOW recharge 

package, it was necessary to simulate recharge differently for earlier and later stress periods in a manner that 

increases recharge over time, like the model of Mahon 

and Poynter (1993).

The recharge specified in the model represents 

the lumping of recharge due to precipitation, flow to or 

from some rivers, and ground-water flow to or from 

underlying aquifers. Fluxes from underlying aquifers 

such as the Sparta aquifer may either augment or counteract the recharge from precipitation, depending on the 

difference between the alluvial aquifer and Sparta aquifer water levels (fig. 8). Ground-water flux to and from 

underlying aquifers will depend on differences in 

water-level altitudes. Also, the surface of the aquifer is 

crossed with numerous perennial and ephemeral 

streams not accounted for directly in the model. These 

streams may saturate the aquifer material down to the 

ground water and, therefore, fluxes to and from the 

aquifer and these rivers will depend on differences in 

water-level altitudes. These different processes represented in the model recharge package may be strongly 

dependent on water-level altitudes and therefore will 

vary over time as these water-level altitudes change. 

Also, reducing water-level altitudes below the root 

zone will have the effect of reducing evapotranspiration 

and increasing recharge due to precipitation. Underestimates of water use also will have the effect of increasing apparent recharge. Thus, many different factors that 

are poorly understood and accounted for in the model 

may have the effect of increasing flows into the model 

from the recharge package over time. As such, recharge 

zones were modified locally during the calibration process to better match observed water levels. This was 

done first for recharge flows for the stress periods 1-5 

(1918-1972) and then for stress period 11 (1994-March 

1998). Recharge flows for the intervening stress periods 6-10 (1973-1993) were prorated on a cell by cell 

basis from the first recharge flows to the last.

Water Use

Water use for model cells in Arkansas was 

obtained from Mahon and Poynter (1993) for 1918 to 

1988 (stress periods 2 through 8). Pumpage for 1918 to 

1958 (stress period 2) was estimated based on results of 

previous models in eastern Arkansas (Mahon and Ludwig, 1990). Although pumpage has been documented 

as county totals, category totals, and aquifer totals in 

water-use reports, the documentation of the spatial distribution of pumpage within a county prior to 1997 is 

lacking. Computation of pumpage distributions for 

stress periods 3 through 8 was based on estimates of 
22 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

ground-water use for six, 5-year time periods beginning in 1958 (Stephens and Halberg, 1961; Halberg and 

Stephens, 1966; Halberg, 1972 and 1977; Holland and 

Ludwig, 1981; Holland, 1987). The total pumpage 

from the alluvial aquifer reported for each county was 

used to compute the distribution of pumpage within the 

county. The total pumpage simulated in each stress 

period is given for the model in table 1. 

From 1989 through March 1998 (stress periods 9 

through 11), water-use estimates were compiled for the 

model described in this report (Terry Holland, U.S. 

Geological Survey, written commun., 2002) using sitespecific water-use data augmented by estimates of total 

ground-water use. Reported pumpages for 1991 were 

used for 1989 through 1993 (stress periods 9 and 10) 

while reported pumpages for 1997, which included 

water-use data from about 33,000 wells, were used for 

1994 through March 1998 (stress period 11).

Total water use simulated by the model ranged 

from about 83,000,000 ft3

/d for 1918-1957 to about 

392,000,000 ft3

/d for 1983-1988, and about 

631,000,000 ft3

/d for 1994-1998. Figure 12 shows the 

distribution of pumpages used for 1994 to 1998 (stress 

period 11), which is the latest period of actual wateruse estimates used in the model.

The pumping rates for model cells in Missouri 

were obtained from Mahon and Poynter (1993) for the 

period 1918 through 1988 (stress periods 2 through 8). 

From 1989 through March 1998 (stress periods 9 

through 11), pumping rates were based on data 

obtained from National Water-Use Information System 

(Terry Holland, U.S. Geological Survey, written commun., 2000; http://water.usgs.gov/watuse/spread95/

moco95.txt, accessed May 17, 1997) for county totals 

for 1991 and 1997. These county totals were prorated 

over model cells by an area-weighted process. 

Storage

Specific storage and specific-yield values for 

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

zones were based on the same delineations as the horizontal hydraulic conductivity and recharge (fig. 11).

Mahon and Poynter (1993) used values of 0.25 to 

0.35 for specific yield in their model and 0.05 for storage coefficient, which relates to about 0.0005 for specific storage assuming an average aquifer thickness of 

100 ft. Arthur (2001) used values of 0.32 for specific 

yield and 0.0016 for specific storage in his calibration 

of a model of the alluvial aquifer east of the Mississippi 

River in Mississippi. These values were used as a guide 

for plausible values during the calibration process.

Model Calibration Procedure

During calibration, various aquifer parameters 

were adjusted, either with the parameter-estimation 

process or manually, so that the observation well waterlevel altitudes located throughout the modeled area 

(fig. 13) matched as closely as possible the water levels 

simulated by the model. All simulated water levels 

used in the calibration were taken from the lower layer. 

At stress period 11, in the final simulation, the maximum difference between heads in the upper and lower 

layers was less than 0.06 ft. All observation wells penetrated the lower model layer. The observed water levels were measured in the springs of 1972, 1982, 1992, 

and 1998. The residuals associated with observed and 

simulated water-level altitudes were reduced to a minimum value during the calibration process. The observation process of MODFLOW-2000 allows for the 

weighting of observed water levels to reflect assumed 

differences in importance to the calibration process. 

Because water-use data in 1991 and 1997 are believed 

to be more accurate than those of earlier years, the 

observations for 1992 and 1998 were weighted more 

heavily than those of the earlier stress periods. 

A parameter-estimation process of MODFLOW2000 was used in the first phase of the calibration process. The parameters estimated in this phase were 

recharge, hydraulic conductivity, specific storage, specific yield, and conductances for cells with riverbeds 

and general-head boundaries. Parameter values were 

applied over broad parameter zones or over extended 

linear features such as rivers.

Not all parameters were estimated together in a 

single parameter-estimation process but were estimated 

iteratively during several successive processes. Nevertheless, all these parameters could be evaluated within 

the same sensitivity process, which produces scaled 

sensitivities for each parameter allowing the importance of each parameter to the calibration process to be 

compared. Although the parameter-estimation process 

can be used to estimate hydrologic parameters over 

large areas, local variations in these parameters may be 

important. During the calibration process, these parameters may be adjusted manually to better reflect local 

hydrologic conditions. 
Model Development and Calibration 23

Figure 12. Distributions of pumpage used for 1994-1998 (stress period 11).

Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

ArkansasRiver

92° 90°

34°

36°

EXPLANATION

Boundary of active model cells

Pumpage (cubic feet per day)

0-10,000

10,000-25,000

25,000-50,000

50,000-100,000

100,000-250,000

250,000-850,000

0 10 20 MILES

0 10 20 KILOMETERS

Base from U.S. Geological Survey digital data, 1:100,000
24 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

Figure 13. Observation wells used in the calibration process.

B

Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

ArkansasRiver

A

A

F

D

I

J

G

H

E

C

92° 90°

34°

36°

EXPLANATION

Boundary of active model cells

Observation wells

Observation wells

with hydrographs

(see figure 17)

0 10 20 MILES

0 10 20 KILOMETERS

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

During the parameter-estimation process, the 

two hydrologic parameters most important to the 

model, hydraulic conductivity and specific storage, 

tended to increase to unrealistic levels in some areas. 

This may have been due to the underestimation of 

recharge in some of the earlier simulations. A decision 

was made to manually adjust the recharge parameter 

using small local zones based largely on areas with 

high residuals. Using professional judgment, recharge 

rates were modified within plausible limits in these 

zones to reduce these residuals. In these local areas, 

local multipliers were provided for the recharge parameter for the applicable zone. This was done first for 

recharge rates used for stress periods 1-5 and then for 

stress period 11 with the recharge rates for the intervening stress period prorated between these two recharge 

rates on a cell-by-cell basis.

Similarly, as river fluxes were believed to be 

locally important as sources of flow into the alluvial 

aquifer, professional judgment was used to alter riverbed conductances within plausible limits locally to 

reduce residuals. As with the recharge parameters, the 

riverbed conductance parameters were altered locally 

with multipliers to better reduce water-level altitude 

residuals.

Other hydrologic parameters of the model 

including horizontal and vertical hydraulic conductivity, specific yield, specific storage, and the conductances of the general-head boundaries were similarly 

estimated with the parameter-estimation process. The 

parameters were altered manually to better reduce 

water-level altitude residuals but without local multipliers to provide local variation as with recharge.

CALIBRATION RESULTS AND MODEL 

EVALUATION

Through a combination of the parameter-estimation process and manual alterations of hydrologic 

parameters and the application of localized multipliers 

for the recharge and river conductance parameters, the 

difference between observed and simulated water-level 

altitudes was minimized. Table 2 shows the final calibrated values for the hydrologic parameters of horizontal hydraulic conductivity and specific storage. 

Hydraulic conductivity values were much higher for 

the lower layer than for the upper layer to be consistent 

with the occurrence of coarser, more transmissive sediments in the lower layer. Hydraulic conductivity in the 

upper layer was set at 230 ft/d throughout the model. In 

zone 2, hydraulic conductivity ranged from 230 ft/d to 

730 ft/d, giving a maximum mean for the two model 

layers of 480 ft/d. 

A uniform value of 0.30 was specified throughout the model for specific yield. Vertical hydraulic conductivity was set as a uniform value of 23 ft/d for layer 

1 and 73 ft/d for layer 2, which represented values of 10 

percent of horizontal hydraulic conductivity for most of 

the modeled area. For calculations of VKCB, the vertical conductance of the quasi-three dimensional layer 

dividing the two model layers as described in Harbaugh 

and others (2000, p. 29), the harmonic mean of these 

two vertical conductivities was subsequently used. The 

need to translate this model into a form usable by 

MODFLOW-96 to be used in connection with MODMAN optimization modeling (Greenwald, 1998) 

required this approach. As field observations (Mahon 

and Poynter, 1993, p. 11) show vertical flow within the 

aquifer vertical flow between the two layers is negligible and was not regarded to be of likely hydrologic significance and was not included in the parameterization 

process. These values produce a very low vertical 

hydraulic gradient between the two layers consistent 

with field observations (Mahon and Poynter, 1993,

p. 11). 

The average change in water level over the modeled area caused by a doubling of a given parameter, 

while others remain constant, is shown in figure 14. 

This demonstrates the sensitivity of each parameter to 

Table 2. Values of hydrologic parameters derived from the 

calibration process

Zone

(fig. 12)

Hydraulic

conductivity,

upper 

layer

(feet per

day)

Hydraulic

conductivity,

lower layer

(feet per

day)

Mean of

hydraulic

conductivity

(feet per

day)

Specific

storage for

both layers

1 230 230 230 0.000001

2 230 730 480 0.000001

3 230 730 480 0.000001

4 230 730 480 0.000001

5-7 230 730 480 0.000001

8-10 230 730 480 0.000001
26 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals through 2049

Figure 14. Average change in water level from a doubling of the parameter.

0123456789

10

hk_11_1

hk_12_1

hk_13_1

hk_2_1

hk_3_1

hk_4_1

hk_11_2

hk_12_2

hk_13_2

hk_2_2

hk_3_2

hk_4_2

ss_1_1

ss_2_1

ss_3_1

ss_4_1

ss_1_2

ss_2_2

ss_3_2

ss_4_2

sy_1_1

sy_2_1

sy_3_1

sy_4_1

sy_1_2

sy_2_2

sy_3_2

sy_4_2

riv_ark

riv_miss

riv_sfran

riv_white

riv_bmeto

riv_cache

riv_langl

RCH_11

RCH_14

RCH_15

RCH_12

RCH_13

RCH_2

RCH_31

RCH_32

RCH_33

RCH_41

RCH_42

RCH_43

RCH_1972

RCH_1977

RCH_1982

RCH_1988

RCH_1992

RCH1993

AVERAGE CHANGE IN WATER LEVEL, IN FEET

hk_11_1...hk_4_2 Horizontal hydraulic conductivity, zone...zone 4 layer 2ss_1_1_....ss_4_2 Specific storage, zone 1 layer 1..zone 4 layer 2sy_1_1....sy_4_2 Specific yield, zone 1 layer 1..zone 4 layer 2riv_ark Arkansas River bed conductanceriv_miss Mississippi River bed conductanceriv_sfran St. Francis River bed conductanceriv_white White River bed conductanceriv_bmeto Bayou Meto bed conductanceriv_cache Cache River bed conductanceriv_langl L'Anguille River bed conductance

RCH_11...RCH_43 Recharge stress periods 11-16 for various zoRCH_1972 Recharge stress period 5RCH_1977 Recharge stress period 6RCH_1982 Recharge stress period 7RCH_1988 Recharge stress period 8RCH_1992 Recharge stress period 9RCH_1993 Recharge stress period 10CROWGHB General head boundary conductance for boun

of Crowleys Ridge

GHB_1....GHB_6 General head boundary conductance for we

boundary

EXPLANATION
Calibration Results and Model Evaluation 27

the model results. The parameters with large sensitivity, such as sy_1_1, (specific yield in zone 1, layer 1) or 

recharge represent large areas within the model. The 

recharge parameters provided the largest sensitivity for 

the model. With the exception of L’Anguille River, the 

sensitivities for river conductance were small.

Volumetric budget component rates for the 

model representing 1968 through 1972 and 1994 to 

March 1998 (stress periods 5 and 11, respectively) are 

shown in figure 15. The increase in recharge from 

stress period 5 to stress period 11 is shown. Selected 

volumetric budget component rates for the model representing all stress periods are shown in figure 16. The 

increase in pumpage in stress period 7 (1978 to 1982) 

was due to drought conditions during this period.

Hydrographs for 10 representative observation 

wells used in the calibration process, are shown on figure 17 and well location are shown on figure 13. The 

hydrographs were constructed by taking the water-level 

altitudes for the period of record for these 10 observation wells and interpolating both spatially and temporally the simulated water-level altitude for each 

observation. The four observations used for calibration 

in stress periods 5, 7, 9, and 11 are circled on each 

hydrograph. These hydrographs generally show a reasonable fit between observed and simulated water-level 

altitudes. Further analysis of these hydrographs shows 

water-level changes common to most wells probably 

are caused by changes in precipitation, but differences 

in water-level changes among wells probably are 

caused by localized changes in pumpage.

Figure 15. Volumetric budget component rates for 1968-1972 and 1994-March 1998 (stress periods 5 and 11). All numbers 

are in millions of cubic feet per day.

Rivers Recharge

Specified

Head

20.5

0.6

109.4 82.3

529.5

Change in storage in aquifer = 6.9 - 103.3

Alluvial aquifer

General

Head

Boundary

2.4

15.0

Pumpage = 631.3

1994 to March 1998 (Stress period 11)

Alluvial aquifer

Rivers Recharge

Specified

Head

22.7

0.0

96.4 36.6

141.5

Change in storage in aquifer = 0.2 - 33.8

Pumpage = 142.2

General

Head

Boundary

3.1

7.1

1968 to 1972 (Stress period 5)
28 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

Figure 16. Selected volumetric budget component rates for the model by stress period.

-800,000,000

-600,000,000

-400,000,000

-200,000,000

0

200,000,000

400,000,000

600,000,000

1 2 3 4 5 6 7 8 9 10 11

STRESS PERIODS

CUBIC FEET PER DAY

In: Storage

In: River Leakage

In: Recharge

Out: Storage

Out: Wells

Out: River Leakage

Water level residuals for observation wells representing the stress periods ending in 1972, 1982, 1992, 

and 1998 (stress periods 5, 7, 9, and 11) are shown in 

figures 18, 19, 20, and 21. Negative residuals indicate 

observed water-level altitudes were lower than those 

simulated; positive residuals indicate observed waterlevel altitudes were higher than those simulated. 

Observed water levels generally were lower than simulated water levels in periods ending in 1972, 1982, and 

1992 (stress periods 5,7, and 9), but were more random 

in distribution in the period ending in 1998 (stress 

period 11). This also is reflected in the histograms of 

residuals shown in figures 22 through 25. The simulated water levels in the Grand Prairie area during stress 

period 5 ending in 1972 were higher than observed 

water levels as shown by the negative residuals in figure 

18. This may be due to underreported pumpage for this 

area during this period or to downward fluxes into 

underlying aquifers that are larger than surficial 

recharge during this period.

Table 3 shows a series of statistical measures for 

the sets of water-level residuals. The residuals for 1994 

to March 1998 (stress period 11) have a mean for the 

absolute value of all residuals of 4.69 ft and a rootmean-square error of 6.04 ft. Histograms and statistical 

measures show minimal negative or positive bias in 

residuals for each of the four observation periods.

Figure 26 shows the simulated water-level altitudes for the stress period ending in March 1998 (stress 

period 11). These levels compare well with the contours 

of observed water-level altitudes for spring 1998 (fig. 

4). Both simulated and observed water levels show 

ground-water flow southward into cones of depression, 

flow into the Mississippi River, and flow from the 

Arkansas River into the aquifer. 
Calibration Results and Model Evaluation 29

Figure 17. Selected hydrographs of observed and simulated water levels showing water levels used for calibration. See figure 

13 for locations.

1950 1960 1970 1980 1990 2000 230

235

240

245

250

255

260

265

WATER LEVEL, IN FEET ABOVE

NGVD OF 1929

1950 1960 1970 1980 1990 2000 105

110

115

120

WATER LEVEL, IN FEET ABOVE

NGVD OF 1929 125

1950 1960 1970 1980 1990 2000 185

190

195

200

WATER LEVEL, IN FEET ABOVE

NGVD OF 1929

1950 1960 1970 1980 1990 2000

135

140

145

150

155

160

165

WATER LEVEL, IN FEET ABOVE

NGVD OF 1929

1950 1960 1970 1980 1990 2000

170

175

180

185

190

WATER LEVEL, IN FEET ABOVE

NGVD OF 1929

1950 1960 1970 1980 1990 2000 155

160

165

170

175

WATER LEVEL, IN FEET ABOVE

NGVD OF 1929

1950 1960 1970 1980 1990 2000 140

150

160

170

180

190

200

WATER LEVEL, IN FEET ABOVE

NGVD OF 1929

1950 1960 1970 1980 1990 2000 175

180

185

190

195

WATER LEVEL, IN FEET ABOVE

NGVD OF 1929

1950 1960 1970 1980 1990 2000

215

220

225

WATER LEVEL, IN FEET ABOVE

NGVD OF 1929 230

EXPLANATION

OBSERVED WATER LEVELS

SIMULATED WATER LEVELS

CALIBRATION WATER LEVELS

A. 02S04W11DBB1 B. 14N07E26DAB1

C. 17N03E02BDB1 D. 05S07W19BCC1

E. 16N11E23ADA1 F. 01S01W13CDD1

G. 10N05E15BDD1 H. 11N02E26AAB1

I. 04N05W07CDC11 J. 06N01W06BAB1

1950 1960 1970 1980 1990 2000 235

240

245

250

WATER LEVEL, IN FEET ABOVE

NGVD OF 1929
30 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

Figure 18. Water-level residuals for observation wells at the end of 1972 (stress period 5).

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Tennessee

Mississippi

MississippiRiver

Missouri

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92° 90°

34°

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0 10 20 MILES

0 10 20 KILOMETERS

EXPLANATION

Boundary of active model cells

#-24 to -20

# -20 to -15

# -15 to -10

# -10 to -5

# -5 to -2

#

-2 to 2

# 2 to 5

# 5 to 10

# 10 to 15

Water-level residual, in feet

(observed minus simulated)

Base from U.S. Geological Survey digital data, 1:100,000
Calibration Results and Model Evaluation 31

Figure 19. Water-level residuals for observation wells at the end of 1982 (stress period 7).

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Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

ArkansasRiver

-92° -90°

34°

36°

EXPLANATION

Boundary of active model cells

#-21 to -20

# -20 to -15

# -15 to -10

# -10 to -5

# -5 to -2

#

-2 to 2

# 2 to 5

# 5 to 10

# 10 to 15

! 15 to 20

$20 to 30

Water-level residual, in feet

(observed minus simulated)

0 10 20 MILES

0 10 20 KILOMETERS

Base from U.S. Geological Survey digital data, 1:100,000
32 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

Figure 20. Water-level residuals for observation wells on March 31, 1992 (stress period 9).

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$

Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

ArkansasRiver

92° 90°

34°

36°

EXPLANATION

Boundary of active model cells

#-30 to -20

# -20 to -15

# -15 to -10

# -10 to -5

# -5 to -2

#

-2 to 2

# 2 to 5

# 5 to 10

# 10 to 15

! 15 to 20

$20 to 34

Water-level residual, in feet

(observed minus simulated)

0 10 20 MILES

0 10 20 KILOMETERS

Base from U.S. Geological Survey digital data, 1:100,000
Calibration Results and Model Evaluation 33

Figure 21. Water-level residuals for observation wells on March 31, 1998 (stress period 11).

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Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

ArkansasRiver

92° 90°

34°

36°

EXPLANATION

Boundary of active model cells

Water-level residual, in feet

(observed minus simulated)

#-30 to -20

# -20 to -15

# -15 to -10

# -10 to -5

# -5 to -2

#

-2 to 2

# 2 to 5

# 5 to 10

# 10 to 15

! 15 to 20

$20 to 28

0 10 20 MILES

0 10 20 KILOMETERS

Base from U.S. Geological Survey digital data, 1:100,000
34 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals through 2049 Table 3. Statistics for residuals for water-level observations [Residuals are calculated as observed heads minus simulated heads] Mean absolut

Stress period number Date range Minimum (feet) Maximum (feet) Range (feet) Mean (feet) Median range (feet) Root- mean square error (feet) Standard error (feet) Standard deviation (feet) Residuals for all cells R

for 

rising 

Number of obser- vations Mean (feet) Numb

of obs

vatio

5 1968 to 1972 -23.77 12.74 36.51 -1.63 -2.28 5.79 0.37 5.56 223 4.69 150 7 1978 to 1982 -20.43 29.67 50.10 -0.05 -0.64 7.20 0.52 7.21 195 5.44 109 1989 to March 1992 -27.73 34.32 62.05 -0.72 -0.95 6.43 0.25 6.40 678 4.89 382 

11 1994 to March 1998 -28.74 27.95 56.69 0.55 0.60 6.04 0.25 6.00 558 4.69 254 
Calibration Results and Model Evaluation 35

0

50

100

150

200

250

-30 -25 -20-15 -10 -5 0 5 10 15 20 25 30 35

DIFFERENCE BETWEEN OBSERVED AND

SIMULATED WATER LEVELS, IN FEET

NUMBER OF OCCURRENCES

0

50

100

150

200

250

-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35

DIFFERENCE BETWEEN OBSERVED AND

SIMULATED WATER LEVELS, IN FEET

NUMBER OF OCCURRENCES

Figure 22. Difference between observed and simulated water levels from 1968 to 1972 (stress period 5).

Figure 23. Difference between observed and simulated water levels from 1978 to 1982 (stress period 7).
36 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

0

50

100

150

200

250

-30 -25 -20-15 -10 -5 0 5 10 15 20 25 30 35

DIFFERENCE BETWEEN OBSERVED AND

SIMULATED WATER LEVELS, IN FEET

NUMBER OF OCCURRENCES

0

50

100

150

200

250

-30 -25 -20-15 -10 -5 0 5 10 15 20 25 30 35

DIFFERENCE BETWEEN OBSERVED AND

SIMULATED WATER LEVELS, IN FEET

NUMBER OF OCCURRENCES

Figure 24. Difference between observed and simulated water levels from 1989 to March 1992 (stress period 9).

Figure 25. Difference between observed and simulated water levels from 1994 to March 1998 (stress period 11).
Calibration Results and Model Evaluation 37

Figure 26. Simulated water-level altitudes for March 31, 1998 (stress period 11).

Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

Arkansas River

92° 90°

34°

36°

0 10 20 MILES

0 10 20 KILOMETERS

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

Dry Cells

20 - 60

60 - 80

80 - 100

100 - 120

120 - 140

140 - 160

160 - 180

180 - 200

200 - 220

220 - 240

240 - 260

260 - 280

280 - 304

EXPLANATION

Boundary of active model cells.

Water-level altitude (feet above

the National Geodetic Vertical

Datum of 1929)
38 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

Flux values associated with river cells, specifiedhead cells, and general-head boundary cells are shown 

in figure 27. Red and yellow colors (negative values) 

indicate flows into the model cell from the aquifer; blue 

and green colors indicate flow from the model cell (into 

the aquifer). Except for the Mississippi River, the 

White River, and the Right Hand Chute of Little River, 

flow is generally from the rivers into the aquifer. Flow 

is generally eastward and southward from consolidated 

deposits to the west and southward from the aquifer in 

Missouri. The river fluxes shown in figure 27 are about 

81,800,000 ft3

/d into the aquifer and 111,000,000 ft3/d 

out of the aquifer. The Mississippi River accounts for 

about 37,600,000 ft3

/d, almost all out of the aquifer, 

and many of the other rivers account for similar 

amounts of river flux. Knowledge gained during the 

calibration process indicates that the amount of river 

flux may be less sensitive to riverbed conductance than 

to the properties of surrounding aquifer material and 

local head relations. 

Recharge rates changed both quantitatively and 

spatially from stress period 5 to stress period 11. Figure 

28 shows fluxes from recharge into the aquifer from 

1918 through 1972 (stress periods 1 to 5), and figure 29 

shows fluxes from recharge into the aquifer from 1994 

to March 1998 (stress period to 11). Figure 15 shows 

the total rate of recharge into the aquifer throughout the 

model is 141,500,000 ft3/d for 1918 to 1972 (stress 

periods 1 to 5), and 529,400,000 ft3

/d from 1994 to 

March 1998 (stress period 11). These model fluxes 

relate to areally specified recharge rates of 0.0 to 30.0 

in/yr. The recharge rates for the intervening stress periods from 1973 to 1993 (stress periods 6 to 10) were 

prorated on a cell-by-cell basis from the rates for stress 

periods 1 to 5 and the rates for stress period 11. This 

proration was initially weighted for time but later 

altered to reduce residuals. Figure 16 shows the 

increase in recharge fluxes through time with a small 

increase between stress periods 10 and 11.

While the approach of this model to simulating 

recharge was by direct application using the MODFLOW recharge package (recharge package approach), 

as explained in the Model Development and Calibration section of this report, the model of Mahon and 

Poynter (1993) simulated areal recharge by applying 

river cells throughout the model using the MODFLOW 

river package (river package approach). In both 

approaches, recharge increases with time by either 

direct application as with the recharge package 

approach or by increased head gradients resulting from 

decreased water-level altitudes in the aquifer as with 

the river package approach. Both approaches attempted 

to incorporate a number of processes relating to 

recharge to the aquifer. This included both recharge 

from precipitation at the land surface, from leakage 

from the numerous perennial and ephemeral streams 

covering the area, and from interactions with underlying aquifers caused by increased drawdown from 

pumpage. The river package approach has the advantage over the recharge package approach because 

recharge increases are simulated continuously into the 

future, while the recharge package approach does not. 

However, during the calibration process the river package approach was unable to effectively simulate the 

additional stress periods with the additional water-use 

data and observation-well data. For the recharge package approach, the rates for stress periods 5 and 11 were 

manually adjusted for the residuals of those periods and 

the rates for stress periods 7 and 9 were prorated. Nevertheless, reasonable residuals were obtained for stress 

periods 7 and 9 as well as for stress periods 5 and 11 

with the recharge package approach.

The inability of the river package approach to 

effectively account for the additional water-use data 

and observation well data reflect the complex processes 

relating to recharge. Basically, increases in recharge are 

related to drawdown through a variety of linear and 

non-linear processes whose mechanism and spatial distribution are poorly understood. Water-level gradients 

between the alluvial aquifer and underlying aquifers 

are complex and over time may involve net flows both 

into and out of the alluvial aquifer which cannot be 

accounted for effectively with the river package 

approach. Also, the hydrologic processes involved with 

recharge infiltrating downward through the overlying 

clay cap are not well understood and the river package 

approach may not always be effective in simulating 

them. In addition, other factors relating to recharge 

such as the application of large amounts of water to the 

surface during irrigation and the use of possibly inadequate water-use data may render the river package 

approach less effective.

 The recharge package approach did not provide 

for increases in recharge after stress period 11. The 

increase in the recharge rates level off between stress 

periods 10 and 11 as shown in figure 16. This at least 

provides a basis for no change in recharge after stress 

period 11, which is reasonably consistent with trends in 

the observation-well data, and provides a generally 

conservative approach with regard to aquifer simula-
Calibration Results and Model Evaluation 39

Figure 27. Simulated river, specified head, and general head boundary fluxes for model cells from 1994 to March 1998

(stress period 11).

Tennessee

Mississippi

Missouri

Arkansas

MISSISSIPPI

RIVER

ARKANSAS

RIVER

BAYOU

METO

WHITE

RIVER

CACHE

RIVER

BLACK

RIVER

L'ANGUILLE

RIVER

ST. FRANCIS

RIVER

RIGHT

HAND

CHUTE

OF

LITTLE

RIVER

LITTLE

RED

RIVER

CURRENT

RIVER

92° 90°

34°

36°

EXPLANATION

Boundary of active model cells

Boundary flux (cubic feet per day)

Negative values indicate flow into

the model cell, or from the aquifer;

positive values indicate flow from

the model cell, or into the aquifer

-2,800,000 to -500,000

-500,000 to -300,000

-300,000 to -100,000

-100,000 to -10,000

-10,000 to -1

1 to 10,000

10,000 to 100,000

100,000 to 500,000

500,000 to 1,600,000

0 10 20 MILES

0 10 20 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 of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

Figure 28. Simulated recharge fluxes for 1918 to 1972 (stress periods 1-5).

Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

ArkansasRiver

92° 90°

34°

36°

EXPLANATION

Boundary of active model cells

Recharge flux (inches per year)

0 - 0.5

0.5 - 1

1-2

2-5

5-6

6-8

8 - 10

10 - 15

15 - 20

20 - 30

0 10 20 MILES

0 10 20 KILOMETERS

Base from U.S. Geological Survey digital data, 1:100,000
Calibration Results and Model Evaluation 41

Figure 29. Simulated recharge fluxes for 1994 to March 1998 (stress period 11).

Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

ArkansasRiver

92° 90°

34°

36°

EXPLANATION

Boundary of active model cells

Recharge flux (inches per year)

0 - 0.5

0.5 - 1

1-2

2-5

5-6

6-8

8 - 10

10 - 15

15 - 20

20 - 30

0 10 20 MILES

0 10 20 KILOMETERS

Base from U.S. Geological Survey digital data, 1:100,000
42 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

tion of hypothetical projected ground-water withdrawals after stress period 11 (discussed in the next section). 

As to whether recharge is actually stable after stress 

period 11, or whether it increases or perhaps even 

decreases, this model and the data based on it cannot 

provide an entirely reliable answer. Further studies and 

models may provide a better approach to characterizing 

recharge that can better account for recharge from the 

underlying aquifers and the hydrologic processes 

involved with recharge from the land surface and 

streams.

The ground-water flow model described in this 

report is useful in evaluating the flow system in the 

alluvial aquifer. However, model results are a simulation of the system and the following model limitations 

should be considered.

The model was discretized on a 1-mile grid and 

cannot be used to evaluate hydrologic conditions for a 

smaller scale setting such as those involving a single 

pumping well. Model input parameters are applied over 

entire cells and assumptions of uniformity for heterogeneous geologic materials and climatic conditions 

may introduce inaccuracies. The steady-state simulation used for initial head conditions for the assumed 

predevelopment conditions assumes that flows into and 

out of the alluvial aquifer were equal. If this were not 

so, the change in ground-water storage (that is, if water 

levels were actually rising or falling) would be a source 

of model error.

Further, the lumping of areal recharge from multiple sources (precipitation, flow to or from some rivers, and ground-water flow to or from underlying 

aquifers) did not allow each of these compounds to be 

evaluated independently during the modeling process. 

Also, estimates of ground-water use may not be accurate and as such may introduce error.

SIMULATIONS OF WATER LEVELS 

CAUSED BY PROJECTED GROUNDWATER WITHDRAWALS

Water levels caused by projected ground-water 

withdrawals were simulated using the calibrated 

model. Simulations represented a period of 50 years 

into the future from 1998 through 2049 in three scenarios using different assumptions regarding future pumpage trends. As a visual aid, digital animations of the 

simulated scenarios are included on a compact disk in 

the back of the report. In Scenario 1, the 1997 pumpage 

rate is extended without change. For Scenario 2, wateruse data from 1965 through 1995 (Halberg and 

Stephens, 1966; Halberg, 1972, 1977; Holland and 

Ludwig, 1981; Holland, 1987, 1993, 1999) were used 

with linear regression to establish historic trends in the 

rate of increase for each county and subsequently used 

to determine the estimated pumpage for each county 

for 2000. This trend was applied to each well in a 

county in proportion to its portion of the 1997 pumpage 

of that county to supply increased pumpage for successive stress periods. This was applied to successive 

stress periods to a maximum value of 1.25 times the 

estimated pumpage for each county in 2000. In Scenario 3, pumpage is decreased to 90 percent of that 

applied in Scenario 2 for each future stress period in 

two selected areas—the Bayou Meto diversion area 

(Natural Resources Conservation Service, 2003a) and 

in the Grand Prairie diversion area (Natural Resources 

Conservation Service, 2003b) (fig. 30)— to account for 

possible supplementation of ground water for irrigation 

by withdrawals from surface-water diversion projects 

by the U.S. Army Corps of Engineers and other parties 

in those areas. Table 4 shows the actual total pumpages 

used for these simulations. As cells went dry during 

these simulations the pumpage simulated within the 

cell was set to zero. Simulated water levels (figs. 31-33) 

and saturated thicknesses (figs. 34 and 35-36) were calculated for 10-year intervals to show the effect of 

pumpage on the aquifer during each scenario.

In each scenario water levels declined resulting 

in dry areas (aquifer depletion) by 2049 (figs. 34 and 

36-37). These dry areas generally were distributed in 

the Grand Prairie area between the Arkansas River and 

White River and along the Cache River.

Table 4. Actual total pumpage for projection simulations

[Units are in cubic feet per day]

Stress

period

With 1997

 pumpage

extended

(Scenario 1)

With 1997

pumpage

extended by

county trends

(Scenario 2)

Pumpage reduced to

90 percent of pumpage

extended by county

 trends in selected zones

(Scenario 3)

11 631,324,480 631,324,480 631,324,480

12 623,440,512 749,344,192 744,711,936

13 614,197,568 835,934,976 844,568,640

14 605,206,656 779,753,792 782,530,496

15 596,392,384 759,117,632 761,897,344

16 590,821,760 744,969,536 746,841,088
Simulations of Water Levels Caused by Projected Ground-Water Withdrawals 43

Figure 30. Selected zones used for pumping changes in model projection simulations.

Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

ArkansasRiver

92° 90°

34°

36°

0 10 20 MILES

0 10 20 KILOMETERS

EXPLANATION

Boundary of active model cells

Cache River area

East of Crowleys Ridge area

Grand Prairie area

Area of reduced pumpage - Bayou

Meto diversion area

Area of reduced pumpage - Grand

Prairie diversion area

Base from U.S. Geological Survey digital data, 1:100,000
44 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

Figure 31. Simulated water levels at the end of 2049 (stress period 16) with 1997 pumpage extended unchanged (scenario 1).

Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

Arkansas River

92° 90°

34°

36°

0 10 20 MILES

0 10 20 KILOMETERS

Dry Cells

20 - 60

60 - 80

80 - 100

100 - 120

120 - 140

140 - 160

160 - 180

180 - 200

200 - 220

220 - 240

240 - 260

260 - 280

280 - 304

EXPLANATION

Boundary of active model cells.

Water-level altitude (feet above

the National Geodetic Vertical

Datum of 1929)

Base from U.S. Geological Survey digital data, 1:100,000
Simulations of Water Levels Caused by Projected Ground-Water Withdrawals 45

Figure 32. Simulated water levels at the end of 2049 (stress period 16) with 1997 pumpage extended by county trends 

(scenario 2).

Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

Arkansas River

92° 90°

34°

36°

0 10 20 MILES

0 10 20 KILOMETERS

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

Dry Cells

20 - 60

60 - 80

80 - 100

100 - 120

120 - 140

140 - 160

160 - 180

180 - 200

200 - 220

220 - 240

240 - 260

260 - 280

280 - 304

EXPLANATION

Boundary of active model cells.

Water-level altitude (feet above

the National Geodetic Vertical

Datum of 1929)
46 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

Figure 33. Simulated water levels at the end of 2049 (stress period 16) with pumpage reduced to 90 percent of county trends 

in selected zones (scenario 3).

Tennessee

Mississippi

MississippiRiver

Missouri

Arkansas

Arkansas River

92° 90°

34°

36°

Dry Cells

20 - 60

60 - 80

80 - 100

100 - 120

120 - 140

140 - 160

160 - 180

180 - 200

200 - 220

220 - 240

240 - 260

260 - 280

280 - 304

EXPLANATION

Boundary of active model cells.

Water-level altitude (feet above

the National Geodetic Vertical

Datum of 1929)

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

0 10 20 MILES

0 10 20 KILOMETERS
47

Click here to open figure 34.
Simulations of Water Levels Caused by Projected Ground-Water Withdrawals 49

Figure 35. Areas of extreme water-level declines produced by model projection scenarios.

2009 2019 2029 2039 2049

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

2,200

AREA, IN SQUARE MILES

373 317

275 264 248

400

548 601

594

614

114 169 228

285 315

SCENARIO 1: GRAND PRAIRIE AREA WITH

PUMPAGE EXTENDED UNCHANGED

YEARS

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

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

2,200

AREA, IN SQUARE MILES

2009 2019 2029 2039 2049

SCENARIO 2: GRAND PRAIRIE AREA WITH

PUMPAGE EXTENDED BY COUNTY TRENDS

YEARS

316

591

173

290

529

492

282

562

591

278

554

657

257

614

687

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

2,200

AREA, IN SQUARE MILES

2009 2019 2029 2039 2049

SCENARIO 3: GRAND PRAIRIE AREA WITH

PUMPAGE EXTENDED BY COUNTY TRENDS BUT

REDUCED TO 90 PERCENT IN SELECTED AREAS

YEARS

363

508

140

305

606

369

287

599

522

295

595

587

266

601

628

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

2,200

AREA, IN SQUARE MILES

2009 2019 2029 2039 2049

SCENARIO 1: CACHE RIVER AREA WITH

PUMPAGE EXTENDED UNCHANGED

YEARS

500

90

4

559

162

26

605

217

45

644

240

67

684

248

86

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

2,200

AREA, IN SQUARE MILES

2009 2019 2029 2039 2049

SCENARIO 2: CACHE RIVER AREA WITH

PUMPAGE EXTENDED BY COUNTY TRENDS

YEARS

731

223

32

939

430

303

833

532

504

788

616

570

798

610

630

AREA, IN SQUARE MILES

2009 2019 2029 2039 2049

0

10

20

30

40

50

60

70

80

SCENARIO 2: EAST OF CROWLEYS AREA

WITH PUMPAGE EXTENDED BY COUNTY

TRENDS

YEARS

1

0

4

0

18

1

0

51

3

0

70

4

0
50 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

Continuation of pumpage at 1997 rates through 

2049 (Scenario 1) results in simulated cones of depression between the Arkansas River and the White River 

in the Grand Prairie area and in the Cache River area 

(figs. 31 and 34). The simulated dewatering results in 

model cells covering about 300 mi2

 going dry in the 

Grand Prairie area and about 100 mi2 going dry in the 

Cache River area on the west side of Crowleys Ridge 

by 2049. Areas of extreme water-level decline include 

areas where the model cells have gone dry and areas 

where the water level in the aquifer is equal to or less 

than 50 percent of the original saturated thickness, 

assuming confined conditions everywhere in the aquifer in predevelopment times. The latter areas are hereafter referred to as “half-saturated” or “areas of halfsaturation.” Areas of extreme water-level decline have 

increased over time in the Grand Prairie area and in the 

Cache River area (figs. 34 and 35). Dry cells and areas 

of half-saturation, shown in brighter colors in figures 

33 and 36-37 increase in area most rapidly between 

2009 and 2019 (fig. 35) and the areas of dry cells and 

cells with 30 or less feet of saturated thickness extend 

westward in the Grand Prairie area and also extend 

southward from the northern part of the Cache River 

area (west sides of Poinsett and Craighead Counties). 

The rate of increase of extreme water-level declines 

decreases slightly between 2019 and 2049 (fig. 35), but 

these affected areas continue to extend westward in the 

Grand Prairie area and extend southward from the 

northern part of the Cache River area and northward 

from the southern part of the Cache River area (intersections of Monroe, Lee, and St. Francis Counties). 

The increase in dry cells is greater in the Grand Prairie 

area than in the Cache River area, while there is a 

greater increase in half-saturation in the Cache River 

area than in the Grand Prairie area (fig. 35). 

Increasing the pumping rates to that which 

would be projected using historic water-use data (Scenario 2) results in simulated cones of depression 

between the Arkansas River and the White River in the 

Grand Prairie area and in the Cache River area that are 

substantially larger than in Scenario 1 (figs. 32 and 36). 

The extreme water-level declines in the Grand Prairie 

area are very extensive with cells covering nearly 700 

mi2

 going dry by 2049; this is more than twice the number of dry cells resulting from pumpage continuing at 

the 1997 rate (Scenario 1). In the Cache River area, 

extreme water-level declines are more extensive than 

in Scenario 1, with cells covering over 600 mi2

 dewatered by 2049; this is approximately seven times the 

number of dry cells resulting from Scenario 1 (fig. 35). 

The areas of dry cells in the northern and southern parts 

of the Cache River area nearly coalesce into a single 

area of dry cells (fig. 36). An area of half-saturation 

east of Crowleys Ridge at the intersection of Crittenden, Cross, and St. Francis Counties also grows substantially to about 70 mi2

 by 2049 (fig. 36) in Scenario 

2, although no cells go dry. 

By as early as 2019, simulated conditions resulting from Scenario 2 result in more aquifer dewatering 

than conditions in 2049 resulting from Scenario 1. 

Most of the Grand Prairie area is half-saturated and 

approximately 500 mi2 of dry cells are simulated (fig. 

36). The northern and southern parts of the Cache 

River area cover approximately 300 mi2 of dry cells 

and are connected by half-saturated cells (fig. 36).

As in Scenario 1, half-saturated cells increase in 

area most rapidly between 2009 and 2019 (fig. 37). 

These rates of increases slow somewhat between 2019 

and 2049.

Pumpage in Scenario 3 is increased at the rate of 

historic trends, except in two selected areas (fig. 30) in 

the Grand Prairie area where pumpages were reduced 

to 90 percent of that used in Scenario 2 owing to surface-water diversion projects by the U.S. Army Corps 

of Engineers and other parties (Scenario 3), and simulates cones of depression between the Arkansas River 

and the White River in the Grand Prairie area and in the 

Cache River area that are substantially larger than in 

Scenario 1 (figs. 33 and 37). Water levels and half-saturation areas outside of the Grand Prairie area containing the two selected areas differ little from those in 

Scenario 2. However, water levels and areas of halfsaturation within the Grand Prairie area also are little 

different from water levels in Scenario 2 (figs. 32 and 

36). Also, areas of extreme water-level decline also 

decrease little in the Grand Prairie area compared to 

Scenario 2 (fig. 35). 

The extreme water-level declines of the Grand 

Prairie area again is very extensive with cells covering 

more than 600 mi2

 going dry by 2049 (fig. 37); this is 

approximately twice the area resulting from pumpage 

continuing at the 1997 rate (Scenario 1), but is approximately 60 mi2 less than in Scenario 2 (fig. 35). In the 

Cache River area, extreme water-level declines are 

similar to Scenario 2 and much more extensive than in 

Scenario 1, with cells covering over 600 mi2

 dry by 

2049 (figs. 35 and 37) and with the areas of dry cells in 

the northern and southern parts nearly coalescing into a 

single area of nearly continuous dry cells (fig. 37). As 
51

Click here to open figure 36.
53

Click here to open figure 37.
Summary 55

in Scenario 2 the area of half-saturation east of Crowleys Ridge at the intersection of Crittenden, Cross, and 

St. Francis Counties also grows substantially to about 

70 mi2 by 2049 (figs. 35 and 37) although no cells go 

dry. 

The relatively small differences between the 

Scenario 2 and Scenario 3 measures of water-level 

decline in 2049 indicate that a 10 percent reduction of 

pumpage from the historic rate within the Bayou Meto 

and Grand Prairie diversion areas would do little to 

improve water levels in those areas. However, these 

reductions in pumpage (which in 2049 would be about 

12 million

ft3/d) are small, about 16 percent, relative to the reductions that could result (about 76 million ft3/d; Ken 

Bright, U.S. Army Corps of Engineers, written. commun., 2003) from implementation of these diversion 

projects.

Model results from the scenarios indicate that at 

1997 pumpage rates water is being withdrawn from the 

aquifer at rates greater than can be sustained for the 

long term. 

SUMMARY

The Mississippi River Valley alluvial aquifer 

lies in a broad alluvial plain that encompasses an area 

of about 32,000 mi2 in parts of six states, more than 54 

percent occurring in eastern Arkansas. The alluvial 

aquifer in Arkansas is bounded on the west by consolidated formations of Paleozoic age that have a distinctly 

smaller hydraulic conductivity than unconsolidated 

deposits of the alluvial aquifer, and on the east by the 

Mississippi River. The alluvial sediments of eastern 

Arkansas are composed of a sequence of sands, silts, 

and clays that can be divided vertically into two units 

from a regional perspective: the upper unit consisting 

of a confining unit of clay, silt, and fine sand, and the 

lower unit containing the alluvial aquifer, which contains coarse sand and gravel. In northeastern Arkansas, 

the alluvial aquifer is divided by Crowleys Ridge into 

two hydraulically separate flow regimes. Ground water 

flows mainly from the north and the west southward 

and eastward towards the Mississippi River or into 

local cones of depression.

The alluvial aquifer is the most prolific aquifer 

supplying water to eastern Arkansas. Surface water is 

abundant in the region, and conjunctive use of surface 

water with ground water is a key element to assuring 

sustainable use of the alluvial aquifer. The effects of 

current and future ground water on water availability 

concern water managers and users; a full understanding 

of the behavior of the aquifer under various water-use 

scenarios is critical to development of viable watermanagement and alternative source plans. 

A finite-difference, three-dimensional, groundwater flow model modified from an earlier model 

(Mahon and Poynter, 1993) was used to simulate 

ground-water flow in the alluvial aquifer for the period 

1918 to 2049. The aquifer was divided vertically into 

two layers and horizontally into a grid of 184 by 156 

cells each measuring 1 mi on a side. The lateral boundaries consist of the major rivers on the east and south. 

Specified heads were applied on the north, and generalhead boundaries on portions of the west and along parts 

of Crowleys Ridge along with no flow boundaries.

Hydraulic conductivity values obtained during 

the calibration process were 230 ft/d for the upper layer 

and ranged from 230 to 730 ft/d for the lower layer with 

the maximum mean for the combined aquifer of about 

480 ft/d. Specific yield values were 0.30 throughout the 

model, and specific storage values were 0.000001 

inverse-feet throughout the model. Total recharge rates 

for 1973 to 1977 were about 141,500,000 ft3

/d, and 

from 1994 to March 1998 were about 529,500,000 ft3/

d. These total recharge rates relate areally distributed 

recharges from 0 to 30 in/yr, and total recharge 

increased from 1972 to 1998 by a factor of about four.

Residuals of simulated versus observed water 

levels had a root-mean-square error of 6.04 ft and an 

absolute mean value of 4.69 ft for the period ending in 

1998 (stress period 11) and an absolute mean value of 

less than 6 ft for three earlier stress periods. The overall 

distribution of these residuals resembled a normal distribution for all stress periods. Spatial distribution of 

residuals generally was random for stress period 11 for 

simulated water levels higher or lower than observed 

water levels. For three earlier stress periods, observed 

water levels tended to be lower than simulated water 

levels.

Water levels caused by projected ground-water 

withdrawals were simulated using the calibrated 

model. Simulations represented a period of 50 years 

into the future in three scenarios with either unchanged 

1997 pumpage, pumpage increased by historic trends, 

or pumpage increased by historic trends except in two 

areas of the Grand Prairie. All scenarios produced 

extreme water-level declines (areas where model cells 

have gone dry or where the (aquifer is half-saturated). 

Two areas of the aquifer covering a total of about 400 
56 Recalibration of a Ground-Water Flow Model of the Mississippi River Valley Alluvial Aquifer of Northeastern Arkansas, 1918-

1998, with Simulations of Water Levels Caused by Projected Ground-Water Withdrawals Through 2049

mi2 go dry if pumping remains at 1997 rates. One of 

these areas is located between the Arkansas and White 

Rivers and the other west of Crowleys Ridge along the 

Cache River. Increasing the pumping rates to that 

which would be projected using historic data led to 

increased extreme water-level declines in both areas 

with about 1,300 mi2 going dry. Water-level declines in 

both scenarios generally occurred most rapidly 

between 2009 and 2019. Reducing the pumping rates to 

90 percent of that used for projected historic rates in 

areas of the Grand Prairie relating to two diversion 

projects by the U.S. Army Corps of Engineers and 

other parties did little to decrease the extreme waterlevel declines. However, these pumpage reductions are 

small (amounting to about 16 percent of the reductions 

that could result from implementation of these diversion projects). Model results from the scenarios indicate that at 1997 pumpage rates water is being 

withdrawn from the aquifer at rates greater than can be 

sustained for the long term.

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