DIGITAL SIMULATION OF GROUND-WATER FLOW IN

THE HIGH PLAINS AQUIFER IN PARTS OF COLORADO,

KANSAS, NEBRASKA, NEW MEXICO, OKLAHOMA,

SOUTH DAKOTA, TEXAS, AND WYOMING

WYOMING

u_.

COLORADO

NEW MEXICO

Lj -\ « __ s 

U.S. GEOLOGICAL SURVEY PROFESSIONAL PAPER 1400-D
Digital Simulation of Ground-Water 

Flow in the High Plains Aquifer 

in Parts of Colorado, Kansas, 

Nebraska, New Mexico, Oklahoma, 

South Dakota, Texas, and Wyoming

By RICHARD R. LUCKEY, EDWIN D. GUTENTAG, FREDERICK J. HEIMES, 

and JOHN B. WEEKS

REGIONAL AQUIFER-SYSTEM ANALYSIS

U.S. GEOLOGICAL SURVEY PROFESSIONAL PAPER 1400-D

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1986
DEPARTMENT OF THE INTERIOR 

DONALD PAUL HODEL, Secretary

U.S. GEOLOGICAL SURVEY 

Dallas L. Peck, Director

Library of Congress Cataloging in Publication Data

Digital simulation of ground-water flow in the High Plains aquifer in parts of Colorado, Kansas, Nebraska, 

New Mexico, Oklahoma, South Dakota, Texas, and Wyoming.

(Geological Survey professional paper ; 1400-D) 

Bibliography: p.

Supt. of Docs, no.: 119.16:1400-D

1. Aquifers High Plains (U.S.) Data processing. 2. Aquifers High Plains (U.S.) Mathematical models. I. Luckey, Richard R. II. Series.

QB1199.3.H53D54 1986 551.49'0978 84-600400

For sale by the Branch of Distribution

Books and Open-File Reports Section

U.S. Geological Survey

Federal Center

Box 25425 

Denver, CO 80225
FOREWORD

The Regional Aquifer-System Analysis (RASA) Program was started in 1978 

after a Congressional mandate to develop quantitative appraisals of the major 

ground-water systems of the''United States. The RASA Program represents 

a systematic effort to study a number of the Nation's most important aquifer 

systems, which in aggregate underlie much of the country and which represent 

an important component of the Nation's total water supply. In general, the 

boundaries of these studies are identified by the hydrologic extent of each 

system and accordingly transcend the political subdivisions to which investigations have often arbitrarily been limited in the past. The broad objective for 

each study is to assemble geologic, hydrologic, and geochemical information, 

to analyze and develop an understanding of the system, and to develop predictive capabilities that will contribute to the effective management of the system. 

The use of computer simulation is an important element of the RASA studies, 

both to develop an understanding of the natural, undisturbed, hydrologic system, and of any changes brought about by human activities, as well as to 

provide a means of predicting the regional effects of future pumping or other 

stresses.

The final interpretive results of the RASA Program are presented in a series 

of U.S. Geological Survey Professional Papers that describe the geology, hydrology, and geochemistry of each regional aquifer system. Each study within 

the RASA Program is assigned a single Professional Paper number, and, where 

the volume of interpretive material warrants, separate topical chapters that 

consider the principal elements of the investigation may be published. The 

series of RASA interpretive reports begins with Professional Paper 1400 and, 

thereafter, will continue in numerical sequence as the interpretive products 

of subsequent studies become available.

Dallas L. Peck 

Director

PREFACE

The Regional Aquifer-System Analysis of the High Plains was conducted 

by U.S. Geological Survey personnel in each of the eight States in the High 

Plains Colorado, Kansas, Nebraska, New Mexico, Oklahoma, South Dakota, 

Texas, and Wyoming. To provide assistance, technical support, and additional 

information, contracts were awarded to the Kansas Geological Survey, New 

Mexico Natural Resources Department, Oklahoma Water Resources Board, 

and Texas Department of Natural Resources. In addition, valuable information 

was provided by many other State and local agencies throughout the High 

Plains. Their contributions are an integral part of this investigation without 

which this report would not have been possible.

The U.S. Geological Survey coordinated its investigation of the High Plains 

aquifer with a concurrent study by the Economic Development Administration 

of the U.S. Department of Commerce. The Six-State High Plains- Ogallala 

Aquifer Area Study by the Ecomomic Development Administration was authorized by Congress in 1976. The study was charged with the responsibility 

of examining the feasibility of increasing water supplies to ensure the economic 

growth and vitality of the High Plains. Together, these two studies will provide 

a comprehensive evaluation of the High Plains aquifer and the potential impacts 

of declining ground-water supplies on the region. The Economic Development 

Administration study will develop and propose alternative strategies to alleviate or mitigate those impacts and the U.S. Geological Survey has provided 

hydrologic data and models needed to evaluate the effects of those strategies 

on the ground-water resource.
CONVERSION FACTORS

The following report uses inch-pound units as the primary system of measurement. The units 

commonly were abbreviated using the notations shown below in parentheses. Inch-pound units 

can be converted to metric units by multiplying by the factors given in the following list.

Multiply inch-pound unit By To obtain metric units

inch per year (in./yr) 2.540x 101 millimeter per year

foot (ft) 3.048XKT1 meter

mile (mi) 1.609 kilometer

square foot (ft2) 9.290 xKT2 square meter

acre 4.047XKT1 hectare

square mile (mi2) 2.590 square kilometer

acre-foot (acre-ft) 1.233x10"® cubic hectometer

acre-foot per year (acre-ft/yr) 1.233 x 10"3 cubic hectometer per year

cubic foot per second (ft3/s) 2.832 x 10"2 cubic meter per second

gallon per minute (gal/min) 6.308 x 10"2 liter per second

foot per day (ft/d) 3.048 x lO"1 meter per day

National Geodetic Vertical Datum of 1929 (NGVD): A geodetic datum derived from a general 

adjustment of the first-order level nets of both the United States and Canada, formerly called 

"Mean Sea Level."
CONTENTS

Abstract .................

Introduction ...............

Purpose and scope .........

High Plains aquifer .........

High Plains aquifer flow models ....

Predevelopment-period models . . .

Development-period models .... 

Southern High Plains model calibration

Predevelopment-period calibration .

Development-period calibration . .

1

1

2

2

3

8

9

10

10

11

Central High Plains model calibration .

Predevelopment-period calibration .

Development-period calibration . . 

Northern High Plains model calibration

Predevelopment-period calibration .

Development-period calibration . . 

Sensitivity analysis ...........

Summary and conclusions ........

References cited .............

Page 

19

19

27

33

33

41

47

52

55

ILLUSTRATIONS

FIGURES 1-29. Maps showing:

1. Location of High Plains aquifer ......................................... 4

2. Division of the High Plains and grids for the models ............................ 6

3. Estimated predevelopment, long-term average recharge rates for the southern High Plains ....... 12

4. Observed and simulated predevelopment water level for the southern High Plains ............ 13

5. Simulated time required for water level in the southern High Plains to decline from land surface to predevelopment position assuming no recharge ................................. 14

6. Observed and simulated 1960 water level for the southern High Plains .................. 16

7. Observed and simulated 1980 water level for the southern High Plains .................. 17

8. Irrigated acreage in the southern High Plains during 1978 ......................... 20

9. Dryland acreage in the southern High Plains during 1978 .......................... 21

10. Generalized observed predevelopment to 1980 water-level change for the southern High Plains ..... 22

11. Simulated predevelopment to 1980 water-level change for the southern High Plains ........... 23

12. Boundary conditions for the models of the central High Plains ....................... 24

13. Hydraulic-conductivity estimates for the central High Plains ......................... 26

14. Revised hydraulic-conductivity estimates for the central High Plains .................... 27

15. Generalized soil types of the central High Plains ............................... 28

16. Estimated predevelopment, long-term average recharge rates for the central High Plains ........ 29

17. Observed and simulated predevelopment water level for the central High Plains ............. 30

18. Generalized, observed predevelopment to 1980 water-level change for the central High Plains ..... 32

19. Simulated predevelopment to 1980 water-level change with net withdrawal equal to 100 percent of irrigation

requirement for the central High Plains ................................... 34

20. Simulated predevelopment to 1980 water-level change with net withdrawal equal to 130 percent of irrigation

requirement for the central High Plains ................................... 35

21. Boundary conditions for the models of the northern High Plains ...................... 36

22. Generalized soil types of the northern High Plains .............................. 37

23. Estimated predevelopment, long-term average recharge rates for the northern High Plains using the hydraulic-conductivity estimates ............................................ 38

24. Observed and simulated predevelopment water level for the northern High Plains using the hydraulic-conductivity estimates ................................................. 39

25. Estimated predevelopment, long-term average recharge rates for the northern High Plains using the revised

hydraulic-conductivity estimates ........................................ 42

26. Observed and simulated predevelopment water level for the northern High Plains using the revised hydraulicconductivity estimates .............................................. 43

27. Generalized, observed predevelopment to 1980 water-level change for the northern High Plains .... 44

28. Composite 1960-80 recharge for the development-period model of the northern High Plains ....... 46

29. Simulated predevelopment to 1980 water-level change for the northern High Plains ........... 47

VII
VIII CONTENTS

Page

FIGURES 30-35. Graphs showing:

30. Predevelopment-period-model sensitivity analysis for the southern High Plains .............. 48

31. Predevelopment-period-model sensitivity analysis for the central High Plains ............... 49

32. Results of changing the calibration riteria for the predevelopment-period model of the southern High Plains . 50

33. Results of simultaneously changing recharge and hydraulic conductivity in the predevelopment-period model

of the southern High Plains ......................................... 50

34. Development-period-model sensitivity analysis for the southern High Plains ................ 50

35. Development-period-model sensitivity analysis for the northern High Plains ................ 51

TABLES

Page

TABLE 1. Water budget for 1940-60 development-period calibration of the southern High Plains flow model ............ 15

2. Water budget for 1960-80 development-period calibration of the southern High Plains flow model ............ 15

3. Summary of simulated outflow from the central High Plains using the predevelopment-period model .......... 25

4. Pumpage in the central High Plains, 1950 to 1980, by State ................................. 31

5. Comparison of observed and simulated water-level declines, 1950 to 1980, for the central High Plains ......... 33

6. Comparison of estimated and simulated base flow of the major river systems in the northern High Plains ...... 40

7. Pumpage in the northern High Plains, 1960 to 1980, by State ................................ 41

8. Summary of calibration of High Plains models ......................................... 53
DIGITAL SIMULATION OF GROUND-WATER FLOW IN THE

HIGH PLAINS AQUIFER IN PARTS OF COLORADO, KANSAS,

NEBRASKA, NEW MEXICO, OKLAHOMA, SOUTH DAKOTA,

TEXAS, AND WYOMING

By RICHARD R. LUCKEY, EDWIN D. GUTENTAG, FREDERICK J. HEIMES, and JOHN B. WEEKS

ABSTRACT

The flow system in the High Plains aquifer was simulated using 

a digital, finite-difference technique to solve the ground-water flow 

equation. The High Plains was divided into three parts the southern 

High Plains, central High Plains, and northern High Plains with 

each part simulated separately. A regular network of nodes spaced 

10 miles apart in both the north-south and east-west directions was 

used. Predevelopment and development periods were simulated for 

each area of the High Plains. In the predevelopment simulations, 

hydraulic conductivity and recharge from precipitation were adjusted 

to best fit the simulated water levels with the observed water levels. 

In the development-period calibrations, which were from 20 to 40 

years, return flow from pumpage and additional stresses caused by 

human activities were varied to obtain the best correspondence between observed and simulated water levels or water-level changes.

For the southern High Plains, the estimated predevelopment recharge ranged from 0.086 to 1.03 inches per year. The mean difference between the observed and simulated water levels was +0.22 

foot with a standard deviation of 41.6 feet. The estimated predevelopment recharge in the central High Plains ranged from 0.056 to 0.84 

inch per year. The mean difference between observed and simulated 

water levels was -0.28 foot, with a standard deviation of 38.5 feet. 

The estimated predevelopment recharge in the northern High Plains 

ranged from 0.075 to 1.52 inches per year. The mean difference between the observed and simulated water levels was +0.30 foot with 

a standard deviation of 55.2 feet.

Two development periods, 1940-60 and 1960-80, were used for calibration of the southern High Plains model. For each period the best 

correspondence between observed and simulated water levels was 

achieved when return flow was adjusted such that net withdrawal 

(total pumpage minus return flow) equaled 90 percent of the estimated irrigation requirement. During the 1960-80 period, an additional 2 inches of recharge were simulated on all irrigated land. The 

mean difference between observed and simulated water levels for 

the first simulation period (1940-60) was -0.22 foot, and the mean 

difference for the second simulation period (1960-80) was +0.28 foot. 

The simulated change in storage for the period 1940-60 was 19 percent less than the observed change in storage for the same period, 

whereas the simulated change in storage for the period 1960-80 was 

2 percent more than the observed change in storage. The simulated 

change in storage for the entire development period (1940-80) was 

7 percent less than the observed change in storage. The historical 

change in storage was estimated on the basis of water-level change 

in the area times the estimated specific yield of the aquifer.

Only one development period, 1950-80, was simulated for the central High Plains. The model was calibrated using water-level change 

instead of water level because the water level had not changed as 

much as it had in the southern High Plains. The best correspondence 

between observed and simulated water-level change was obtained 

when irrigation return flow was adjusted such that net withdrawal 

equaled 100 percent of the estimated irrigation requirement. On a 

volumetric basis, the simulated change was 9 percent less than the 

observed change; on an areal basis, the simulated change was 6 percent more than the observed change. The simulated change in storage 

of 54.9 million acre-feet compared favorably to the observed change 

in storage of 50.3 million acre-feet.

One development period, 1960-80, was simulated for the northern 

High Plains. The best correspondence between observed and simulated water-level change was achieved when net withdrawal equaled 

100 percent of the estimated irrigation requirement. For the northern 

High Plains, other significant stresses occurred because of human 

activities. These additional stresses contributed 47.0 million acre-feet 

of water to the aquifer during the development period. This, coupled 

with ground-water irrigation return flow of 37.5 million acre-feet, 

in large part counterbalanced the 105.0 million acre-feet of water 

pumped between 1960 and 1980 in the northern High Plains. The 

simulated net decrease in storage was 15 million acre-feet and the 

observed decrease in storage was 6 million acre-feet. The 9 million 

acre-feet difference between observed and simulated decrease in storage was less than 9 percent of the volume pumped.

INTRODUCTION

The U.S. Geological Survey began a study of the 

High Plains regional aquifer in 1978 (Weeks, 1978) as 

part of the Survey's program of Regional AquiferSystem Analysis (RASA) (Bennett, 1979). Major objectives of the High Plains study were to: (1) Provide 

hydrologic information needed to evaluate the effects 

of continued ground-water development; (2) design and 

develop computer models to simulate the aquifer system; and (3) predict aquifer response to changes in 

ground-water deveolopment.
REGIONAL AQUIFER-SYSTEM ANALYSIS

The High Plains aquifer underlies about 174,000 mi2 

of the central United States east of the Rocky Mountains in the southern part of the Great Plains. Parts 

of Colorado, Kansas, Nebraska, New Mexico, Oklahoma, South Dakota, Texas, and Wyoming are underlain by the High Plains aquifer (fig. 1). The High Plains 

aquifer is the shallowest and most abundant source of 

ground water in the region and the irrigated agricultural economy of the High Plains has depended on the 

aquifer for its growth and prosperity.

More than 20 percent of the irrigated land in the 

United States overlies the High Plains aquifer from 

which about 30 percent of the ground water used in 

the United States during 1980 was pumped. Throughout most of the High Plains, the rate of ground-water 

withdrawal greatly exceeds the rate of natural replenishment resulting in water-level declines in places. 

Consequently, many irrigators have experienced increased pumping costs and decreased well yields and 

are concerned about the future of irrigated farming on 

the High Plains.

PURPOSE AND SCOPE

The general purpose of the High Plains RASA was 

to provide the hydrologic information and analytical 

capability needed for effective management of the 

ground-water resource of the High Plains. This report 

describes the design and calibration of digital models 

of the High Plains aquifer. The models were constructed on the bases of the geologic and hydrologic 

conditions described by Gutentag and others (1984). 

Historical data on irrigation demand (Heimes and 

Luckey, 1982), water levels, and water-level changes 

(Luckey and others, 1981) were used to test or calibrate the models. The models provide water managers 

with a tool for evaluation of water-management alternatives.

HIGH PLAINS AQUIFER

The High Plains aquifer consists mainly of hydraulically connected geologic units of late Tertiary and 

Quaternary age. Late Tertiary units include part of the 

Brule Formation, the Arikaree Group (or Formation), 

and the Ogallala Formation. Quaternary deposits included in the aquifer consist of alluvial, dune-sand, and 

valley-fill deposits.

The Ogallala Formation, which underlies 134,000 mi2, 

is the principal geologic unit in the High Plains aquifer. 

The Ogallala Formation consists of a heterogeneous sequence of clay, silt, sand, and gravel deposited by 

streams that flowed eastward from the ancestral Rocky 

Mountains. Within the Ogallala, zones cemented with

calcium carbonate are resistant to weathering and form 

escarpments that typically mark the boundary of the 

High Plains.

The formations comprising the High Plains aquifer 

were deposited on an erosional surface that ranges in 

age from Permian to Tertiary. Faulting and salt dissolution also have affected the underlying surface that 

controls the thickness of the High Plains aquifer. In 

Wyoming, faults have displaced the underlying surface 

vertically as much as 1,000 ft, and, in South Dakota, 

a fault has caused about 500 ft of vertical displacement. 

Additional faulting and collapse are associated with salt 

dissolution. Permian salt deposits being dissolved by 

circulating ground water mainly occur south of the Arkansas River. Water from the units underlying the 

High Plains aquifer affects the quality of water in the 

aquifer and streams draining the High Plains in Kansas, Oklahoma, and Texas.

Water levels in the High Plains aquifer range from 

just below land surface to nearly 400 ft below land surface. The saturated thickness ranges from nearly zero 

to about 1,000 ft. Hydraulic conductivity (a measure 

of the aquifer's ability to transmit water) and specific 

yield (a measure of the aquifer's ability to store water) 

(Lohman, 1972, p. 6) of the aquifer depend on sediments that vary widely both areally and vertically. Hydraulic conductivity ranges from about 25 to 300 ft/d 

and averages 60 ft/d. Specific yield ranges from about 

10 to 30 percent and averages 15 percent.

Ground water in the High Plains aquifer generally 

flows from west to east, at an average rate of about 

1 ft/d. At this rate, a particle of water would take at 

least several thousand years to move from the western 

edge of the aquifer to the eastern edge of the aquifer. 

The ground water discharges naturally to streams and 

springs, and directly to the atmosphere by evapotranspiration where the water table is near land surface. 

Precipitation is the principal source of recharge to the 

High Plains aquifer. Estimated recharge rates range 

from 0.024 in./yr in part of Texas to 6 in./yr in part 

of Kansas (Gutentag and others, 1984, table 7). Typically, recharge estimates are greatest for areas with 

sandy soils. Refinement of these recharge estimates is 

one of the results of the model simulations.

During 1980, the High Plains aquifer contained about 

3.25 billion acre-ft of drainable water. This is equivalent 

to about 80 percent of the volume of water, contained 

in Lake Michigan. About 66 percent of the water in 

storage is in Nebraska, about 12 percent is in Texas, 

and about 10 percent is in Kansas. Colorado, Oklahoma, 

South Dakota, and Wyoming each have less than 4 percent of the water in storage. New Mexico, with about 

1.5 percent, has the least volume of water in storage 

in the High Plains aquifer.
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER

The quality of water in the High Plains aquifer generally is suitable for irrigation but, in many places, the 

water does not meet U.S. Environmental Protection 

Agency (1976, 1977) limits for some constituents for 

drinking water. Excessive concentrations of dissolved 

solids, fluoride, chloride, and sulfate occur in parts of 

the aquifer in all eight States (Krothe and others, 

1982).

About 95 percent of all water pumped from the High 

Plains aquifer is used for irrigation. During 1980, more 

than 170,000 wells pumped an estimated 18 million 

acre-ft of water from the High Plains aquifer to irrigate 

13 million acres (Heimes and Luckey, 1983, p. 34).

Large water-level declines have occurred in some 

areas of the aquifer. Water levels have declined more 

than 100 ft from predevelopment to 1980 in parts of 

Kansas, New Mexico, Oklahoma, and Texas in areas 

totaling 2,500 mi2 (Luckey and others, 1981). Water 

levels have declined more than 50 ft in areas totaling 

12,000 mi2 and more than 10 ft in areas totaling 50,000 

mi2.

The volume of water in storage in the aquifer has 

decreased about 166 million acre-ft since ground-water 

development began (Gutentag and others, 1984, table 

11). Most of the depletion has occurred in Kansas and 

Texas; about 114 million acre-ft have been depleted in 

Texas and 29 million acre-ft have been depleted in Kansas.

Water-level declines increase pumping lift, decrease 

well yields, and limit development of the ground-water 

resource. Well yields of more than 750 gal/min generally can be obtained throughout large areas of the High 

Plains. However, only wells yielding less than 250 gal/ 

min can be constructed where the saturated thickness 

is thin near the edge of the aquifer or where waterlevel declines have greatly decreased the saturated 

thickness.

HIGH PLAINS AQUIFER FLOW MODELS

The High Plains is divided into three parts, as shown 

in figure 2. The southern High Plains is the part of 

the High Plains in Texas and New Mexico south or 

west of Amarillo, Tex. The central High Plains is the 

area north or east of Amarillo and south of approximately 39° latitude. The northern High Plains is the 

area north of approximately 39° latitude.

A narrow isthmus, approximately 12 mi wide, joins 

the southern and central High Plains in the vicinity of 

Amarillo, Tex. The isthmus joining the central and 

northern High Plains is about 32 mi wide and follows 

a bedrock high and a thin saturated section of the

aquifer. Probably little exchange of water occurs between the northern and central High Plains or between 

the central and southern High Plains. Because of the 

narrow isthmuses joining the separate parts, constructing separate ground-water flow models for each part 

of the High Plains should not create significant errors.

The history of ground-water development in the High 

Plains was divided into two periods: the period prior 

to large-scale development of irrigation (predevelopment period) and the period of development of irrigation (development period). The development period was 

further subdivided as needed.

Four general categories of information are needed for 

model input: (1) Aquifer geometry; (2) boundary conditions; (3) aquifer parameters; and (4) aquifer stresses. 

In addition to these four categories, the developmentperiod models require an initial water-table configuration. This was generated by the predevelopment-period 

models.

Aquifer geometry defines vertical and areal extent 

of the aquifer. This requires the configuration of the 

base and the areal extent of the aquifer. The position 

of the water table, which is simulated by the model, 

defines the upper limit of the aquifer.

Boundary conditions of the model define the conditions at the limit of the aquifer. The limit of the aquifer 

could be the bottom of the aquifer where exchange of 

water with another aquifer may take place, the lateral 

edge of the aquifer where water may enter or leave 

the system, or the top of the aquifer where the aquifer 

may interact with streams or lakes. Boundary conditions at the lateral edge of the aquifer generally are 

specified as a constant water level, a constant slope 

of the water table, or no flow across the boundary. In 

the High Plains models, the boundary at the bottom 

of the aquifer was modeled as a no flow boundary. At 

some nodes where the aquifer was in hydraulic connection with streams, boundary conditions were specified 

at the top of the aquifer.

Undoubtedly, some exchange of water takes place 

between the High Plains aquifer and other aquifers, 

particularly the aquifers in the Lower Cretaceous and 

the Triassic and Jurassic units. Estimates were made 

of the quantities and direction of this exchange and 

were tested by the model. The simulations indicated 

that the model was insensitive to this exchange because 

the volume estimated was small. Hence, the interaction 

between the High Plains aquifer and the underlying 

aquifers was assumed to be negligible, and the base 

of the High Plains aquifer was simulated as an impermeable boundary.

Aquifer parameters hydraulic conductivity and specific yield describe the physical properties of the
REGIONAL AQUIFER-SYSTEM ANALYSIS

^^M?^:
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER

'I
REGIONAL AQUIFER-SYSTEM ANALYSIS

43°

40°

38°

CANADIAN s

NEW MEXICO

AQUIFER 

BOUNDARY EXPLANATION

----- BOUNDARY BETWEEN AREAS OF

THE HIGH PLAINS 

EH MODEL NODE 

{~\ COMMON NODES BETWEEN MODELS

FIGURE 2. Division of the High Plains and grids for the models.
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER

aquifer. Before irrigation development, the aquifer was 

in a state of equilibrium with no significant change in 

storage taking place. Therefore, the parameter specific 

yield was not needed for the predevelopment-period 

model. However, both parameters were needed for the 

development-period model.

Aquifer stress is defined as any addition or withdrawal of water from the aquifer that is not accounted 

for in the boundary conditions. In the predevelopment 

period, the aquifer system was in a state of dynamic 

equilibrium with recharge from precipitation equal to 

discharge to streams and across the eastern study 

boundary. Hence, the predevelopment-period model requires a description of the predevelopment recharge. 

However, as the aquifer was being developed, additional recharge occurred because of irrigation infiltration and canal and reservoir leakage and the rate of 

recharge from precipitation on dryland agriculture 

land.

The ground-water flow model calculates water levels, 

base flow to rivers, flow across the study boundaries, 

and change of water in storage. The simulated results 

were compared with historical data. Statistics were 

used to analyze the difference between the simulated 

and observed water levels and water-level changes. 

These statistics include the mean, standard deviation, 

and extremes of the water-level differences.

The flow of ground water in a heterogeneous and 

anisotropic unconfined aquifer may be expressed by the 

following partial differential equation (Trescott, 1975, 

p. 3):

dh

y, z

A, t) ... (1)

where

x, y, and z 

yy, and Kzz

b

h

S

t

W

are space coordinates,

are hydraulic conductivities in the

x, y, and z directions,

is saturated thickness,

is water level,

is specific yield,

is time coordinate, and

is stress (source-sink) term.

To solve equation 1, which is a function of aquifer parameters and stresses, boundary conditions and initial 

conditions need to be specified. Boundary conditions include either the water level or the flow at the boundary. Initial conditions include the water level throughout the area at the beginning of the simulation period. 

Equation 1 describes the flow of ground water in

three dimensions; that is, in both the vertical and horizontal directions. On a local scale, particularly near recharge or discharge areas, both horizontal and vertical 

components of ground-water flow occur in the High 

Plains aquifer. However, on a regional scale, the horizontal-flow components are so much larger than the 

vertical-flow components that the vertical-flow components may be neglected without inducing significant errors. Hence, the regional flow of ground water in the 

High Plains aquifer was modeled as two-dimensional 

flow.

Gutentag and Weeks (1981) analyzed several 

thousand lithologic logs from wells in the High Plains 

aquifer to develop a statistical relationship between 

aquifer parameters and saturated thickness. They concluded that no consistent pattern of sediment distribution occurs on a regional scale (e.g., no regional basal 

gravel) and, hence, that vertically averaged aquifer parameters may be used as a single value representing 

the physical property of the aquifer material. Using 

vertically averaged parameters and assuming two-dimensional ground-water flow, equation 1 can be rewritten as:

Two basic techiques finite-element and finite-difference usually are used to approximate equation 2. In 

this study the finite-difference technique was used. To 

approximate the flow equation by the finite-difference 

technique, the derivatives in equation 2 are replaced 

with finite-difference approximations (Trescott and 

others, 1976, p. 2) as shown below.

.j+i.fe-fet,j,fc)l 

 JP/i I °i,} L

-11i > 

JJ

 +&uWWit (3)

where 

Az, Ay, and At represent the grid spacing in the 

space and time coordinates, 

i, j, and k represent the 1th row, /h column, and 

fcth time, and other symbols are the 

same as for equation 1.
REGIONAL AQUIFER-SYSTEM ANALYSIS

Equation 3 is written for each node in the discretized 

network and all of the finite-difference equations are 

solved simultaneously by computer using either a 

strongly implicit or a direct solution numerical technique. The numerical technique is used to solve equation 3 for water levels at each node through an iterative 

process which compares water levels simulated at the 

present iteration with those simulated at the previous 

iteration. If the absolute water-level differences between the two adjacent iterations reaches a value less 

than the predescribed value (the closure error), then 

the iteration process stops and a solution of equation 

3 is obtained. The computer program used was virtually 

the one described by Trescott and others (1976) and 

modified by Larson (1978). A few minor modifications 

were made.

One modification allows more control over the iteration parameters which are used to accelerate the solution technique. This control was necessary for the High 

Plains models because of the coarse grid and the rapid 

change in aquifer parameters and thickness between 

the adjacent nodes. The additional control over the iteration parameters sometimes allowed the High Plains 

simulation program to reach a solution when the original Trescott and Larson simulation program would fail 

to reach a solution. The range that transmissivity (the 

product of hydraulic conductivity and saturated thickness) can vary between iterations (solutions of equation 

3) also was limited in the High Plains simulation program. This change was necessary for the same reason 

that more control was given over the iteration parameters.

Constant-gradient boundary conditions (constant 

slope of the water table) for a water-table aquifer were 

added to the simulation program. At each iteration the 

flow at each constant-gradient node was recalculated 

and added explicitly into the equation.

A number of other changes altered the way the data 

were entered into the program and the way the results 

were summarized by the program. An alternative 

method of entering the pumpage data was necessary 

because of the extremely large number of wells in the 

High Plains. The pumpage was defined either on a wellby-well basis or as a matrix. A more detailed summary 

of boundary conditions was given by the simulation program, including the simulated flow into and out of each 

boundary node. This supplemented the mass-balance or 

water-budget information calculated by the original 

Trescott and Larson program. A routine was added to 

calculate statistics for the simulated water-level 

changes or for the difference between the observed and 

the simulated water levels. This statistical information 

was used to evaluate the results of each simulation.

The simulation program allows a variable rectangular 

grid in both the x and y directions. However, for the 

High Plains models, a uniform regular network of nodes 

was used (fig. 2). The nodes in each of the models were 

10 mi apart in both north-south and east-west directions. The southern High Plains models had 26 rows 

and 20 columns and 303 active nodes. The central High 

Plains models had 32 rows and 37 columns and 513 active nodes. One common node existed between the 

southern and central High Plains models. The water 

level of this node was fixed in the central High Plains 

models to be identical to that simulated in the southern 

High Plains models. The northern High Plains models 

had 35 rows and 51 columns and 943 active nodes. Five 

nodes were common between the central and northern 

models. The water levels at these five common nodes 

were fixed in the northern High Plains models to be 

identical to those simulated in the central High Plains 

models.

PREDEVELOPMENT-PERIOD MODELS

Prior to extensive agricultural development on the 

High Plains, the ground-water system was in a state 

of dynamic equilibrium with long-term recharge balanced by discharge along the eastern boundary and in 

the river valleys that intercepted the water table. The 

rate and location of recharge and discharge were to be 

determined during the calibration of the predevelopment-period models. Gutentag and others (1984, table 

7) compiled various estimates of recharge for the High 

Plains and the values ranged from a minimum of 0.024 

in./yr to a maximum of 6.0 in./yr. The broad range and 

dissimilarity of the estimated recharge rate indicated 

that recharge was virtually an unknown quantity 

throughout much of the High Plains. One of the objectives of the predevelopment-period model calibration 

was to refine the estimates of the recharge rate.

The predevelopment-period models calculate a predevelopment water-table configuration by integrating 

data for the altitude of the base of the aquifer, hydraulic conductivity, and predevelopment recharge rate. 

The altitude and geology of the base of the aquifer were 

obtained from Weeks and Gutentag (1981) and the altitude of the base was not altered during calibration. 

The geology was used as a guide to places where the 

High Plains aquifer might exchange water with underlying aquifers.

The initial estimates of hydraulic conductivity were 

obtained from a map that was used to prepare the map 

presented by Gutentag and others (1984, fig. 10). The 

hydraulic conductivity was one of the two model inputs
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 9

that was altered during the predevelopment-period calibration. The location and extent of these modifications 

are described in the model-calibration sections.

The predevelopment recharge rates were estimated 

during the calibration. The method used to distribute 

recharge varied by area and also is discussed in later 

sections.

The calculated predevelopment water-table configuration was compared to a map of the predevelopment 

water table that was constructed using early waterlevel measurements from hundreds of wells. The accuracy of the map varied considerably from area to area 

depending on the density and distribution of waterlevel data, but the map was a good representation of 

the predevelopment water table except in areas where 

the saturated thickness was thin and data were sparse. 

The comparison of observed and simulated water tables 

was part of the calibration process for the predevelopment-period models. The predevelopment-period models also calculated the discharge across the eastern 

boundary of the High Plains aquifer and the base flow 

to streams that drain the aquifer. The models were 

calibrated in part by matching the calculated discharge 

with the observed or estimated discharge from the 

aquifer.

DEVELOPMENT-PERIOD MODELS

The development period in the High Plains began 

when substantial ground-water development occurred. 

The development period began in the 1940's in the 

southern High Plains, in the 1950's in the central High 

Plains, and in the 1960's or later in much of the northern High Plains. Models of the development period required all of the information from the predevelopmentperiod models plus data on specific yield of the aquifer 

and additional stress imposed on the aquifer since development began. All of the data, as refined during the 

predevelopment-period model calibration, were used in 

the development-period models.

The specific yield of the aquifer was obtained from 

a map presented in Gutentag and others (1984, fig. 11). 

This map was constructed by analyzing numerous 

lithologic logs, and the specific yield was not altered 

during the development-period calibration.

Additional stress on the aquifer during the development period consisted of pumpage, return flow to the 

aquifer from irrigation, and additional recharge caused 

by human activities. Pumpage was the largest stress 

on the aquifer, but return flow and additional recharge 

also were significant in some areas.

Pumpage was calculated using the method outlined 

by Heimes and Luckey (1982). Irrigated acreage and 

composite crop demand are given in that report for

cells of dimension 10 minutes of latitude by 10 minutes 

of longitude (10-minute cells) at 5-year intervals for 

1949 to 1978. The product of irrigated acreage and composite crop demand yields an irrigation requirement. 

An irrigation efficiency factor (crop demand divided by 

application) for these years is all that was needed to 

estimate total pumpage from irrigation requirement for 

each 10-minute cell. Numerous estimates of the irrigation efficiency factor are available. Most estimates 

range from about 40 percent to 80 percent of application with efficiency improving with time. The following 

irrigation efficiency factors were used to generate pumpage estimates for the indicated years for the High 

Plains:

Year

Southern 

High Plains

Central 

High Plains

Northern 

High Plains

1949

1954

1959

1964

1969

1974

1978

55 percent 

55 percent 

55 percent 

60 percent 

65 percent 

70 percent 

70 percent

45 percent 

45 percent 

45 percent 

60 percent 

60 percent 

70 percent 

70 percent

45 percent 

60 percent 

60 percent 

70 percent 

70 percent

Total pumpage for the 7 years in the above table 

was used to calculate an average pumpage for a 5-year 

period for each 10-minute cell for 1940-SO. For 1940-50, 

a backward projection was made based on the rate of 

increase of irrigation in the major areas irrigated between 1940 and 1950. For 1950-SO, an interpolation between years was used. The 5-year average pumpage 

for each period was calculated as follows:

1940-44: 0.18 x (1949 pumpage)

1945-49: 0.7 x (1949 pumpage)

1950-54: 0.4 x (1949 pumpage) + 0.6 x (1954 pumpage)

1955-59: 0.4x(1954 pumpage) + 0.6x(1959 pumpage)

1960-64: 0.4x(1959 pumpage)+ 0.6x(1964 pumpage)

1965-69: 0.4x(1964 pumpage) + 0.6x(1969 pumpage)

1970-74: 0.4 x (1969 pumpage) + 0.6 x (1974 pumpage)

1975-79: 0.5 x (1974 pumpage) + 0.5 x (1978 pumpage)

Return flow to the aquifer from irrigation was the 

principal unknown variable during the developmentperiod simulations. Return flow was assumed to be a 

function of the difference between total pumpage and 

irrigation requirement. The manner in which return 

flow was varied is discussed in the model calibration 

sections. A change in recharge due to human activities 

was the other component that was varied during the 

development-period calibrations.
10 REGIONAL AQUIFER-SYSTEM ANALYSIS

SOUTHERN HIGH PLAINS MODEL 

CALIBRATION

The southern High Plains consists of about 29,000 

mi2 in New Mexico and Texas. The area includes most 

of the High Plains south of the Canadian River. This 

was the first area of the High Plains that was extensively developed for irrigation, with some development 

beginning in the late 1930's. A predevelopment period 

and two development period calibrations were done for 

the southern High Plains flow models. The predevelopment-period model was calibrated by matching observed and simulated predevelopment water levels and 

the development-period model was calibrated by matching observed and simulated water levels for 1960 and 

1980. Parts of the southern High Plains have been modeled by Knowles and others (1982) and McAda (1984).

PREDEVELOPMENT-PERIOD CALIBRATION

In the predevelopment-period model, hydraulic conductivity and recharge from precipitation were adjusted. Estimates of recharge for the High Plains of 

Texas and New Mexico range from a minimum of 0.024 

in./yr to a maximum of 1.0 in./yr (Gutentag and others, 

1984, table 7). White and others (1940) estimated the 

ground-water discharge along 75 mi of the eastern 

boundary to be about 160 gal/min per mi and the discharge by evapotranspiration from shallow water-table 

areas to be about one-half that rate. Therefore, the 

total discharge was estimated to be 240 gal/min per mi.

The discharge along the eastern boundary was simulated by specifying constant heads along the boundary; 

the flow across the boundary was then simulated by 

the model. Discharge to streams and from shallow 

water-table areas was not specified explicity because 

many of these areas are close to the eastern boundary 

and were included in the boundary nodes. Other boundaries were specified as no-flow boundaries.

A hydraulic-conductivity map was constructed prior 

to model calibration. The minimum contour value was 

15 ft/d and the maximum contour value was 300 ft/d. 

Mean values for each model node were determined from 

the map and the values ranged from 10 to 280 ft/d.

The discharge across the eastern boundary was estimated using Darcy's law on the bases of the predevelopment water-table and hydraulic conductivity 

maps. Darcy's law indicated an outflow of about 250 

ft3/s for the entire 370 mi of the eastern boundary or 

an average of 300 gal/min per mi. This is equivalent 

to a long-term average recharge throughout the entire 

area of 0.11 in./yr.

A simulation with the above hydraulic conductivity 

map and the mean recharge of 0.11 in./yr resulted in

simulated water levels significantly lower than observed water levels in the northern part of the southern High Plains and somewhat higher than the observed water levels in the southern part. A decrease 

of hydraulic conductivity and recharge by 50 percent 

resulted in a similar pattern. Using a constant hydraulic conductivity for all nodes of 40 ft/d, which was the 

mean value, somewhat decreases the differences between the observed and simulated water-levels but the 

simulated water levels still were not satisfactory.

Most of the large differences between the observed 

and simulated water levels occurred in the areas with 

large estimates of hydraulic conductivity. A series of 

simulations in which the largest estimates of hydraulic 

conductivity were decreased indicated that the difference between the observed and the simulated water 

levels were minimized when all hydraulic conductivity 

estimates of more than 50 ft/d were decreased using 

the following formula:

(160-50) 

(300-50)

(4)

where

KI is initial hydraulic conductivity, and 

Kf is final hydraulic conductivity to be used in 

the model.

Equation 4 effectively decreased a hydraulic-conductivity estimate of 300 ft/d to 160 ft/d while leaving a hydraulic-conductivity estimate of 50 ft/d or less unchanged. A number of well logs in areas with large 

estimates of hydraulic conductivity were reevaluated 

and the decrease in hydraulic-conductivity estimates 

appeared reasonable. With this decrease, the hydraulic 

conductivity for the model nodes ranged from 10 to 150 

ft/d.

The revised hydraulic-conductivity distribution corresponds to that presented by Gutentag and others (1984, 

fig. 10). The simulated discharge along the eastern 

boundary using the revised hydraulic-conductivity estimates was 210 ft3/s or 250 gal/min per mi. This is similar to White and others' (1940, p. 10-11) estimate of 

about 240 gal/min per mi for discharge from shallow 

water-table areas plus discharge along the boundary for 

a 75-mi length.

A discharge rate of 210 ft3/s means that the longterm average recharge for the entire 29,000 mi2 area 

would be approximately 0.095 in./yr. Because no information was available on the distribution of recharge, 

possible recharge distributions were tested by the 

model. Assigning every node the average recharge rate 

resulted in an unsatisfactory correspondence between
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 11

observed and simulated predevelopment water levels. 

An assumed recharge distribution based on soil type 

also resulted in an unsatisfactory result. Several simulations that varied recharge according to variations in 

precipitation and potential evapotranspiration indicated 

that the recharge rate in the northern part of the 

southern High Plains had to be more than three times 

the rate in the southern part and the recharge rate 

does not vary from west to east, so neither mean annual precipitation nor evapotranspiration probably was 

the controlling factor for recharge.

Finch and Wright (1970) described the Running 

Water Draw-White River lineaments in the northern 

part of the southern High Plains as a zone of structural 

weakness and possible faulting that might be an appropriate site for recharge through the caliche caprock. 

This zone was at and south of Running Water Draw 

and the White River. Simulating greater recharge rates 

in this area, as shown in figure 3, resulted in the best 

correspondence between observed and simulated predevelopment water levels. The total recharge for this 

simulation was 270 ft3/s or an average of about 0.13 

in./yr which was greater than the 0.095 in./yr described 

previously. This average recharge rate of 0.13 in./yr 

and the recharge distribution shown in figure 3 were 

used for the final simulations. The statistical values of 

the final simulation results are: (1) The mean difference 

between the simulated and observed water levels at 

the 303 nodes was +0.22 ft; (2) the standard deviation 

was 41.6 ft; (3) the mean of the absolute values of the 

differences was 31.9 ft; and (4) the extreme values of 

the differences were -113 ft and +99 ft.

The observed and simulated predevelopment water 

tables are shown in figure 4. In general, a satisfactory 

correspondence exists between the observed and simulated water levels but certain differences are notable. 

In the southeast and east-central part of the area, the 

simulated water level is generally above the observed 

water level. This indicates that either the predevelopment recharge was even less than 0.086 in./yr or some 

discharge was not accounted for. The latter is a more 

likely explanation. In the southwest part of the area 

and in the extreme northern part, the simulated water 

level generally is below the observed water level. This 

indicates that either the predevelopment recharge was 

greater than the rate estimated or that the hydraulic 

conductivity actually is less than estimated. No physical 

evidence indicates that either the recharge estimate 

should be increased or the hydraulic conductivity estimate should be decreased; therefore, no further adjustment was made.

A second, totally different, approach to simulating 

the predevelopment water levels was tested. This approach was based on the premise that, due to a cooler 

or wetter climate and greater recharge, the water table 

was probably at or near the land surface at various 

times in the geologic past and, during warmer and 

dryer episodes, the aquifer received no recharge and 

the water table slowly declined as the aquifer drained. 

The most recent lengthly period of more effective precipitation in the southern High Plains, called the Lubbock subpluvial (Wendorf, 1970), occurred about 10,000 

years ago and at that time the water table could have 

been near land surface. A 10,000-year simulation with 

the initial position of the water-table at land surface, 

no recharge, uniform specific yield of 0.15, and constant 

water levels along the eastern boundary (set equal to 

predevelopment water levels) indicated that the aquifer 

would be virtually drained in a few thousand years. 

The approximate time that the water table would take 

to decline from land surface to the predevelopment position if the area received no recharge is shown in figure 

5. This analysis indicated that the above premise of no 

recent recharge is untenable and that significant recharge has occurred, at least at irregular intervals, during the recent past.

DEVELOPMENT-PERIOD CALIBRATION

The development period of the southern High Plains 

was divided into two periods: 1940-60 and 1960-80. By 

1940, only relatively small areas of the aquifer had been 

significantly disturbed. The development-period models 

were calibrated by matching observed and simulated 

water levels for 1960 and 1980.

Additional stresses on the aquifer since 1940 consisted of pumpage, return flow to the aquifer from irrigation infiltration, and additional recharge from precipitation due to change of soil characteristics by cultivation that did not occur during the predevelopment 

period. Pumpage was the largest additional stress on 

the system, but return flow and additional recharge 

also were significant. Pumpage for irrigation was more 

than 97 percent of the pumpage for all uses, so pumpage for other uses was neglected in the southern High 

Plains model.

The following estimates of total pumpage for irrigation were made:

1940-44: 

1945-49: 

1950-54: 

1955-59: 

1960-64: 

1965-69: 

1970-74: 

1975-79:

0.5 million acre-ft/yr 

2.1 million acre-ft/yr 

4.6 million acre-ft/yr 

6.3 million acre-ft/yr 

7.0 million acre-ft/yr 

6.7 million acre-ft/yr 

6.4 million acre-ft/yr 

6.2 million acre-ft/yr
12

104°

REGIONAL AQUIFER-SYSTEM ANALYSIS

103° 102° ior

EXPLANATION

RECHARGE, IN INCHES PER YEAR

0.086

0.86

1.03

FIGURE 3. Estimated predevelopment, long-term average recharge rates for the southern High Plains.
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 13

EXPLANATION

WATER LEVEL CONTOUR Contour 

interval 200 feet. National Geodetic 

Vertical Datum of 1929

 -3000- Observed

 3000 Simulated

FIGURE 4. Observed and simulated predevelopment water level for the southern High Plains.
14 REGIONAL AQUIFER-SYSTEM ANALYSIS

101 C

EXPLANATION

.950 LOCATION AND TIME OF DECLINE IN YEARS

FIGURE 5. Simulated time required for water level in the southern High Plains to decline from land surface to predevelopment position assuming no recharge.

About 200 million acre-ft of water have been pumped 

from the aquifer since 1940. These estimates are 15-20 

percent more than those reported by the Texas Department of Water Resources (1981). The above estimates

probably are greater because of the implicit assumption 

that the irrigators try to get maximum yields from 

their crops. In water-short areas such as the southern 

High Plains, irrigators may apply only a fraction of the
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 15

TABLE 1. Water budget for 1940-60 development-period calibration of the southern High Plains

flow model

[units are in millions of acre-feet]

Budget item

Net withdrawal equal Net withdrawal equal Net withdrawal equal

to 73 percent of to 90 percent of to 100 percent of

irrigation requirement irrigation requirement irrigation requirement

Outflows:

Total pumpage..... 

Boundary outflow.

Total

70.34

2.46

72.80

70.20

2.40

69.92

2.37

72.60 72.29

Inflows:

Total.......................................

42.20

3.19

45.39

-27.41

35.10

3.19

38.29

-34.31

31.47

3.19

34.66

-37.63

irrigation requirements and accept less than maximum 

yield (P. L. Rettman, U.S. Geological Survey, oral 

commun., 1982).

Several simulations for 1940-60 were made with the 

return flow to the aquifer from irrigation being the 

component that was changed between simulations. 

Total pumpage changed slightly between simulations 

because pumpage was curtailed at one node near the 

boundary at different times as the node became virtually unsaturated. Major components of the water 

budget for three simulations are summarized in 

table 1.

The minimum mean residual between observed and 

simulated water levels for 1960 was obtained for a return flow of 50 percent of the applied irrigation water 

or net withdrawal (total pumpage minus return flow) 

equal to approximately 90 percent of the irrigation requirement. The mean difference between the observed 

and simulated water levels was -0.22 ft with a standard deviation of 27.2 ft. The simulated decrease in 

storage of 34.3 million acre-ft was 19 percent less than 

the observed change in storage of 42.2 million acre-ft. 

The observed and simulated water levels for 1960 are 

shown in figure 6. The simulated water-level contours 

follow the observed water-level contours fairly closely 

with the simulated water-level contours usually being 

smoother.

For 1960-80, total ground-water pumpage in the 

southern High Plains was nearly twice as large as during the previous 20 years. For this period, the return 

flow to the aquifer from irrigation was again the principal component that was changed between simulations.

Total pumpage changed slightly between simulations 

because pumping was curtailed at some nodes which 

became virtually unsaturated. Major water-budget 

components for two simulations are summarized in 

table 2.

The minimum mean residual between observed and 

simulated water levels was again obtained for net withdrawal equal to 90 percent of the irrigation requirement. However, because a better irrigation efficiency 

was assumed for this period, the return flow to the

TABLE 2. Water budget for 1960-80 development-period calibration 

of the southern High Plains flow model

[units are in millions of acre-feet]

Budget item

Net withdrawal equal Net withdrawal equal

to 90 percent of to 110 percent of

irrigation requirement irrigation requirement

Outflows:

Total pumpage..... 

Boundary outflow.

Total...............

Inflows:

Return flow from irrigation 

Recharge from precipitation on agricultural land.. 

Recharge from precipitation on rangeland and 

along streams..............

Total..........................

Change in storage:

139.35

1.71

141.06

58.55

23.34

3.19

85.08

-55.98

137.42

1.58

139.00

40.03

23.06

3.19

66.28

-72.72
16

104'

REGIONAL AQUIFER-SYSTEM ANALYSIS

103° 102°

EXPLANATION

WATER LEVEL CONTOUR - Contour 

interval 200 feet. National Geodetic 

Vertical Datum of 1929

 4000 Observed

 4000 Simulated

FIGURE 6. Observed and simulated 1960 water level for the southern High Plains.
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER

104° 103° 102° 101°

17

EXPLANATION

WATER LEVEL CONTOUR - Contour 

interval 200 feet. National Geodetic 

Vertical Datum of 1929

 4000 Observed

 4000 Simulated

FIGURE 7. Observed and simulated 1980 water level for the southern High Plains.
18 REGIONAL AQUIFER-SYSTEM ANALYSIS

aquifer was a smaller percentage of total pumpage than 

during 1940-60. The simulated return flow ranged from 

46 percent of total pumpage during the early part of 

the period to 37 percent during the later part. The 

mean difference between observed and simulated water 

levels in 1980 shown in figure 7 was +0.28 ft with a 

standard deviation of 25.8 ft. The simulated change in 

storage of 56.0 million acre-ft was 2 percent larger than 

the observed change in storage of 54.9 million acre-ft. 

Most of the major differences between observed and 

simulated water levels occur away from the major 

pumping centers except for one area in the vicinity of 

Double Mountain Fork in Texas (the 3,000-ft contour 

in figure 7). In this area, the simulated 1980 water level 

is considerably below the observed water level. This 

probably is due to overestimating the total pumpage 

in water-short areas. This area is one of the most 

water-short areas of the High Plains.

In the 1960-80 simulations, additional recharge to the 

aquifer was added on all cropland. Cropland includes 

both irrigated land (fig. 8) and dryland (fig. 9). Mapped 

irrigated and dryland acreage were available only for 

1978 (G. P. Thelin and F. J. Heimes, U.S. Geological 

Survey, written commun., 1984). These two maps were 

used under the assumption that the total cropland had 

not significantly changed since 1960 even though irrigated land has been converted to dryland and dryland 

to irrigated land. In various simulations, additional recharge ranging from 0 to 3.5 in./yr was applied uniformly to all cropland. The simulated water levels were 

compared to the observed water levels, particularly in 

the areas that were predominantly dryland. The simulated water levels most closely matched the observed 

water levels when the additional recharge was 2 in./yr. 

This recharge represents an addition of water to the 

aquifer of about 1 million acre-ft per year over the 19 

million acres of the southern High Plains or about 0.6 

in./yr if it were evenly distributed throughout the modeled area.

Tommy Knowles, Texas Department of Water Resources (oral commun., 1982), noted that in 1970 play as 

were full of water and water was standing in fields in 

a broad area of the southern High Plains, and between 

1970 and 1980, water levels rose 0.5 to 1.0 ft per year 

in this area. Based on Knowles' observations, an alternate way to simulate the additional recharge would be 

to double the recharge rate and only apply it to the 

last one-half of the simulation period (1970-80). This 

procedure would have produced almost identical results 

to the procedure that was used. The additional recharge was necessary and appropriate for the 1960-80

simulation; however, it would not be appropriate to include it when using the model to make future evaluations because the additional recharge probably was the 

result of an unusual circumstance that occurs only infrequently.

Simulated discharge across the eastern boundary decreased significantly during this calibration period. The 

simulated boundary outflow was 270 ft3/s during the 

predevelopment simulation, decreased to an average of 

165 ft3/s by 1960, and decreased further to an average 

of 118 ft3/s by 1980 as a result of development. If flow 

along the boundary were uniform, the simulated outflow decreased from about 340 gal/min per mi prior to 

development to about 150 gal/min per mi by 1980. Both 

boundary outflow and the decrease in this flow were 

greatest in the northern one-half of the modeled area.

The generalized predevelopment to 1980 water-level 

change is shown in figure 10 and the simulated waterlevel change for the same period is shown in figure 11. 

The observed change map was not available prior to 

model calibration and, hence, was not used in calibration. Even though the change maps were not used in 

calibration, they are shown here to make this section 

comparable with later sections. In the northern one-half 

of the southern High Plains the two maps are similar 

but in the southern one-half significant differences exist 

between the two maps. The differences between the 

water-level change maps could have been reduced if the 

additional recharge simulated between 1960 and 1980 

would have been increased in the southern one-half of 

the area. However, if this were done, the difference 

between the observed and simulated 1980 water levels 

would have been increased.

For the development-period simulations, only the difference between total pumpage and return flow from 

irrigation is needed because the two items were subtracted from each other in the stress term of the flow 

equation (equation 1). In the 1940-80 calibrations, total 

pumpage was estimated as 210 million acre-ft and return flow from pumpage was estimated as 94 million 

acre-ft. The difference is a net withdrawal of 116 million acre-ft. Although the calibrations indicated that net 

withdrawal must be close to 116 million acre-ft for the 

40 years, quite possibly, total pumpage and return flow 

were both considerably less. The relationship between 

total pumpage and return flow becomes more important 

when using the models to evaluate future development. 

Decreasing total pumpage in the future may not decrease the net withdrawal significantly but may only 

decrease the return flow to the aquifer.
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 19

CENTRAL HIGH PLAINS MODEL 

CALIBRATION

The central High Plains consists of about 48,500 mi2 

in Colorado, Kansas, New Mexico, Oklahoma, and 

Texas. This area is mostly between the Canadian River 

in Texas and the Smoky Hill River in Kansas. The 

aquifer in the central High Plains was developed for 

irrigation later than in the southern High Plains with 

some development beginning by the 1950's. Two model 

calibrations were made one simulating the system 

prior to irrigation development and the other simulating the system after irrigation development. The predevelopment-period calibration consisted of matching 

observed and simulated water levels and the development-period calibration consisted of matching observed 

and simulated water-level changes. Parts of the central 

High Plains have been modeled by Lindner-Lunsford 

and Borman (1984), Dunlap and others (1984), Cobb and 

others (1983), Havens and Christensen (1983), Knowles 

and others (1982), Morton (1980), Dunlap and others 

(1980), and Kapple and others (1977). In 1984, model 

studies were being conducted by the U.S. Geological 

Survey in western Kansas.

PREDEVELOPMENT-PERIOD CALIBRATION

For the predevelopment-period calibration, hydraulic 

conductivity and recharge from precipitation were adjusted. Estimates of recharge for the central High 

Plains range from a minimum of 0.05 in./yr to a 

maximum of 6.0 in./yr (Gutentag and others, 1984, 

table 7). These estimates were adjusted during model 

calibration. Prior to development, the aquifer was in 

a state of equilibrium and, therefore, the amount of 

recharge was in balance with the discharge along the 

eastern boundary and along numerous river valleys. 

The nodes along the eastern boundary were treated as 

constant-head nodes and the nodes along the principal 

river valleys were treated as river nodes to simulate 

the interaction of the streams with the aquifer (fig. 12). 

The primary difference between the constant-head 

nodes and the river nodes is that the simulated hydraulic head in the aquifer can change at the river nodes. 

The head in the aquifer at the river nodes controls the 

simulated exchange of water between the aquifer and 

the river. The hydraulic conductivity of the river bed 

was assumed to be the same as that of the aquifer and, 

hence, did not limit the rate of leakage. The simulated 

head in the aquifer cannot change at a constant head

node and it is the gradient to the constant-head node 

that controls the flow of water from the aquifer at the 

node.

The initial estimates of hydraulic conductivity for the 

central High Plains (Gutentag and others, 1984, fig. 10) 

ranged from about 10 to 300 ft/d. Average values determined for each node ranged from 12 to 209 ft/d with 

a mean of 61 ft/d. During simulation, it was necessary 

to significantly decrease many of the hydraulic conductivity estimates to achieve the best match of the observed and simulated water levels. Hydraulic conductivities adopted from Gutentag and others (1984, fig. 

10) are shown in figure 13 and the modified hydraulicconductivity estimates as a result of model calibrations 

are shown in figure 14. The modified hydraulic-conductivity estimates range from 12 to 189 ft/d with a mean 

of 50 ft/d.

The areas where the hydraulic-conductivity estimates 

were modified correspond to the areas where the base 

of aquifer surface has been significantly altered by salt 

dissolution and sinkhole formation in the underlying 

Permian rocks. Sinkholes and other collapse structures 

are found in a broad area from northern Texas to central Kansas (Gutentag and others, 1984, p. 17). They 

were formed prior to, during, and after the deposition 

of the High Plains aquifer. The broad area where saturated thickness is more than 200 feet between the 

Smoky Hill and Canadian Rivers (Weeks and Gutentag, 

1981) probably is a result of coalescing collapse features. Well yields in this area are consistent with the 

hydraulic conductivities indicated by Gutentag and 

others (1984). However, the regional flow simulated by 

models indicates significantly less hydraulic conductivity in this area.

A similar discrepancy between regional and local 

aquifer parameters was noted by Emmett and others 

(1978, p. 31) in a dolomite aquifer in Missouri. In a 

heterogeneous aquifer, the hydraulic parameters are 

scale dependent. On a small scale, local values are the 

important factor in the parameter value. However, on 

a large scale, the parameter value is a harmonic average of local extremes. Salt dissolution and sinkhole formation in the central High Plains cause extreme local 

variation in hydraulic conductivity because of disturbed 

and chaotic bedding combined with extreme changes in 

lateral lithologies. These extreme local variations 

exaggerate the scale dependence of the hydraulic conductivity.

Identical model results could have been obtained, 

using the hydraulic conductivity estimates without revision and changing the saturated thickness, by redefin-
20

104'

REGIONAL AQUIFER-SYSTEM ANALYSIS 

103° 102°

EXPLANATION

DENSITY OF IRRIGATED ACREAGE, IN PERCENT

OtolO 

10 to 25

25 to 50 

More than 50

FIGURE 8. Irrigated acreage in the southern High Plains during 1978.
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER

104° 103° 102° 101°

21

32° F=--

EXPLANATION

DENSITY OF DRYLAND ACREAGE, IN PERCENT

OtolO 

10 to 25

25 to 50 

More than 50

FIGURE 9. Dryland acreage in the southern High Plains during 1978.
22

104'

REGIONAL AQUIFER-SYSTEM ANALYSIS

103° 102°

32° --

EXPLANATION

WATER-LEVEL CHANGE, IN FEET

Rise more than 10

+10 to-10 

-10 to-25

-25 to -50

-50 to-100

Decline more than 100

FIGURE 10. Generalized observed predevelopment to 1980 water-level change for the southern High Plains.
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER

104° 103° 102° 101°

23

EXPLANATION

WATER-LEVEL CHANGE. IN FEET

Rise more than 10 ' ' -25 to -50 

+10 to-10 I -50 to-100 

-10 to-25 Decline more than 100

FIGURE 11. Simulated predevelopment to 1980 water-level change for the southern High Plains.
24

104°

39° 

103°

REGIONAL AQUIFER-SYSTEM ANALYSIS

102° 101° 100° 97°

38'

EXPLANATION

CONSTANT-HEAD NODE 

RIVER NODE

FIGURE 12. Boundary conditions for the models of the central High Plains.

ing the location of the base of the aquifer. Although 

the map by Weeks and Gutentag (1981) is a good representation of the physical base of the Tertiary sediments, the effective base of the flow system might be 

significantly above the base of the sediments in the 

broad area of coalesced collapse features. Preliminary 

calculations tend to discount this effect, but further 

study is necessary to answer these questions.

Recharge from precipitation was the other parameter 

that was adjusted during the predevelopment-period 

calibration. Different recharge distributions were 

evaluated and the best correspondence between the observed and simulated water levels occurred when the 

recharge distribution was related to soil type. This is 

different from that found for the southern High Plains. 

Generalized soils for the central High Plains are shown
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 25

TABLE 3. Summary of simulated outflow from the central High 

Plains predevelopment-period model

[Streams located on Figure 12]

Outflow element 

(rivers include tributaries)

Canadian River...........................

Wolf Creek ................................

Beaver River .............................

South Fork Ninnescah.................

Boundary outflow, south of

Boundary outflow, between 

Canadian and Arkansas River... 

Boundary outflow, north of the 

Arkansas River .......................

Total ...................................

Outflow, in cubic 

feet per second

67

23

78

106

27

81

38

41

4

18

27 

33

543

in figure 15. Sandy soils are expected to be more conducive to recharge for two reasons: (1) Sandy soils are 

more permeable and (2) they have smaller water-holding capacity. These factors allow precipitation to more 

readily percolate below the root zone and ultimately 

become recharge to the aquifer. Topography also can 

be a major factor in the distribution of recharge. Recharge is much more likely to occur in dune areas with 

a poorly developed drainage pattern than in areas with 

a well-developed drainage pattern.

The recharge distribution that resulted in the predevelopment calibration for the central High Plains is 

shown in figure 16. The sand-dune areas have the 

maximum recharge rate with a long-term average of 

0.84 in./yr or 15 times greater than the minimum value. 

The small zone of sand in the southwest part of the 

area has an estimated recharge rate of 0.39 in./yr. The 

large zone of sandy loams in the northeastern part of 

the area was assigned a recharge rate of 0.28 in./yr. 

The smaller areas of sand-loam soils were lumped with 

the silt-loam and the clay-loam soils because the simulations did not indicate that these areas received significantly more recharge. The clay and sandy loams in the 

extreme southern part of the model were assigned recharge rates of 0.11 in./yr. The minimum value, 0.056 

in./yr, occurred over the remainder of the clay-, silt-, 

and sandy-loam soils. The overall mean long-term predevelopment recharge rate for the central High Plains 

was estimated to be 0.14 in./yr. This recharge rate is 

close to the mean predevelopment recharge rate estimated for the southern High Plains (0.13 in./yr).

The total predevelopment recharge from precipitation to this area was estimated to be 522 ft3/s. Another 

21 ft3/s flowed into the central High Plains from the 

southern and northern High Plains. The rivers that 

originate to the west of the High Plains, particularly 

the Cimarron River, probably contribute some recharge to the aquifer. However, this component of recharge was difficult to detect because of the coarse grid 

used in this model; this recharge was included as part 

of the recharge from precipitation assumed in the sanddune areas.

The total inflow of 543 ft3/s was balanced by an 

equivalent quantity of outflow. This outflow consisted 

of discharge to rivers and seepage across the boundaries of the aquifer. A summary of the outflow is given

in table 3.

The long-term ground-water contribution to rivers is 

difficult to evaluate, but estimates are available for 

some rivers. Fader and Stullken (1978, p. 11) estimated 

base flow to the North and South Fork Ninnescah 

River as 38 and 94 ft3/s; the model simulated 38 and 

41 ft3/s, respectively. Gutentag and others (1981, p. 43) 

measured the base flow of the Cimarron River as about 

60 ft3/s at the Kansas-Oklahoma State line. The flow 

computed by the model at the same place was 80 ft3/s. 

Winter flow records for 189&-1908 for the Arkansas 

River indicate a ground-water contribution to the river 

between Garden City and Hutchinson, Kans., of about 

80 ft3/s. The model simulated 71 ft3/s for the same 

reach. Winter flow records for 1938-50 for the Canadian River between Armarillo and Canadian, Texas, indicate a ground-water contribution of about 45 ft3/s; the 

model simulated 56 ft3/s. Flow records for the same 

period indicate that the Beaver River and Wolf Creek 

each received about 30 ft3/s from the High Plains 

aquifer. The model indicated a gain of 78 ft3/s for the 

Beaver River and 23 ft3/s for Wolf Creek.

The simulated seepage across the eastern boundary 

was very small, averaging less than 0.2 ft3/s per mi. 

This was somewhat less than the estimated flow across 

the eastern boundary of the southern High Plains, but 

it is probably reasonable.

The observed and simulated predevelopment water 

levels were quite similar throughout most of the central 

High Plains (fig. 17). The mean difference between the 

observed and simulated water levels at 513 nodes was 

-0.28 ft with a standard deviation of 38.5 ft. At 98 

percent of the nodes, the simulated water level was 

within 100 ft of the observed water level. Most of the 

major discrepancies were in areas of sparse water-level 

data. The major difference was in Texas on the north 

side of the Canadian River. To properly simulate the 

observed water levels in this area, recharge would have 

to be increased considerably, but analysis gave no indi-
26 REGIONAL AQUIFER-SYSTEM ANALYSIS

EXPLANATION

HYDRAULIC CONDUCTIVITY, 

IN FEET PER DAY

I

Less than 25 

25 to 50 

50 to 100 

100 to 200 

200 to 300

FIGURE 13. Hydraulic-conductivity estimates for the central High Plains adapted from Gutentag and others (1984).

cation that this area should receive more recharge than 

other areas of similar soil type. Therefore, no more recharge was added to the model in this area. A smaller 

area of discrepancy was south of the Canadian River

where the model indicated that too much recharge was 

being simulated. Other minor differences were throughout the area, but in general the correspondence between the observed and simulated water levels is good.
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 27

104° 103° 102° 101

38° l

EXPLANATION

HYDRAULIC CONDUCTIVITY, 

IN FEET PER DAY

Less than 25 

25 to 50 

50 to 100 B 100 to 200

FIGURE 14. Revised hydraulic-conductivity estimates for the central High Plains.

DEVELOPMENT-PERIOD CALIBRATION

Two development calibration periods were used in 

the southern High Plains because of the long history

of development. However, the central High Plains has 

a shorter history of development and, hence, only one 

development period, 1950-80, was simulated. By 1950, 

only relatively small areas had been significantly dis-
28

104'

REGIONAL AQUIFER-SYSTEM ANALYSIS

102° 101° 100°

35°; 

EXPLANATION

SOIL TEXTURES

Sand

Sandy loam 

Silt loam 

Clay loam 

Caliche

FIGURE 15. Generalized soil types of the central High Plains.

turbed from predevelopment conditions, and the simulated predevelopment water levels were used as the 

initial water levels for the development-period simulation.

Throughout a substantial part of the central and 

northern High Plains, the water levels have changed 

much less than 50 ft since development began so to 

comparing water-level contours was difficult. The mod-
104°

DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER

99° 98 C

29

103° 102° 101

EXPLANATION

RECHARGE, IN INCHES 

PER YEAR

97°

FIGURE 16. Estimated predevelopment, long-term average recharge rates for the central High Plains.

els, therefore, were calibrated by adjusting the input 

data to obtain a reasonable match between observed 

and simulated water-level changes. Areas and volumes 

of water-level change were compared.

Pumpage for the central High Plains was divided into 

three categories: (1) Pumpage for irrigation; (2) pumpage for municipal and industrial use; and (3) pumpage 

for stock and domestic use. The last category was insig-
30

104°

39°!--

103°

REGIONAL AQUIFER-SYSTEM ANALYSIS

102° 101° 100° 97°

EXPLANATION

WATER LEVEL CONTOUR - Contour interval

200 feet. National Geodetic Vertical Datum of 1929

- - 2OOO Observed

 20OO Simulated

FIGURE 17. Observed and simulated predevelopment water level for the central High Plains.

nificant compared to the other two categories and was 

ignored. Municipal and industrial pumpage, which was 

only a few percent of the total pumpage, was estimated 

from data from various State agencies and from published population figures. The pumpage estimates for 

the central High Plains are given in table 4 which indicates that approximately 94 million acre-ft of water had

been pumped from the aquifer in the central High 

Plains from 1950 to 1980. This is about one-half the 

total pumped from the southern High Plains.

A generalized observed water-level change map (fig. 

18) was constructed from the water-level change map 

presented by Luckey and others (1981) by estimating 

the average change at each 100 mi2 node, and then con-
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 

TABLE 4. Pumpage in the central High Plains, 1950 to 1980, by State

Pumpage, in thousands of acre-feet per year

31

State

Total

Municipal and 

industrial

Irrigation

1950-64 1966-79 1950-54 1955-59 1960-64 1965-69 1970-74

89.4 178.8 637

1975-79

Colorado ...........

Kansas..............

New Mexico......

Texas ...............

0.4

.. 62

11

.. 16

0.8

124

21

33

6

447

5

43

136

19

279

8

113

459

40

1,363

11

195

847

60

1,812

35

422

1,352

79

2,418

46

537

1,517

92

3,127

43

572

1,571

1,578 2,456 3,681 4,597 5,405

touring these estimated changes. The water-level 

change map of Luckey and others (1981) was reinterpreted and modified in northern Texas near and north 

of the Canadian River. Water-level changes for each 

simulation were contoured and the resulting map was 

compared with the generalized, observed change map.

Return flow to the aquifer from irrigation was adjusted among simulations. Because return flow was assumed to reach the aquifer within the 5-year pumping 

period, changing return flow was exactly equivalent to 

changing net withdrawal (total pumpage minus return 

flow). Return flow was assumed to be a function of the 

difference between total pumpage and irrigation requirement. Simulated water-level changes when return 

flow was equal to 100 percent of this difference (net 

withdrawal equal to irrigation requirement) are shown 

in figure 19. For this simulation, the return flow ranged 

from 55 percent of total pumpage early in the development period to 30 percent later and averaged 43 percent. This return flow appears large, but, as in the 

southern High Plains development-period model, only 

the difference between total pumpage and return flow 

was important and both may be considerably overestimated whereas the difference remains correct. The extent of the area of significant water-level declines 

(greater than 10 ft) was similar between the observed 

and simulated water-level change maps but the area 

of decreases in excess of 50 ft was much larger on the 

observed change map.

In a second simulation, net withdrawal was assumed 

to be 130 percent of irrigation requirement. For this 

case, return flow ranged from 42 percent of total pumpage early in the development period to 9 percent later 

and averaged 17 percent. The water-level change for 

this simulation is shown in figure 20. Although no simulated water-level decline exceeds 100 ft, one node (100 

mi2) had an average decline of 96 ft. The area where

simulated water-level declines exceed 50 ft is much 

larger in this simulation than in the previous simulation.

A summary of the results of these two simulations 

is given in table 5. Data in the table indicate both the 

area! extent of the declines and the volume of aquifer 

material dewatered. The total volume of aquifer material dewatered was chosen as a comparison factor 

rather than volume of water removed because the measurement of the volume of aquifer dewatered does not 

require knowledge of the specific yield of the aquifer.

For the areas where the observed water-level declines exceed 50 ft, the second simulation (net withdrawal equals 130 percent of irrigation requirement) 

fits the observed water-level declines better, but, overall, the first simulation (net withdrawal equals 100 percent of irrigation requirement) provides a better result. 

On a volumetric basis, the water-level declines for the 

first simulation were 9 percent less than the observed 

water-level declines. On an areal basis, the water-level 

declines for the first simulation were 6 percent greater 

than the observed declines. For the first simulation, 

the simulated change in storage was 54.9 million acreft; the observed change in storage was 50.3 million 

acre-ft.

The differences between the observed and simulated 

water-level change maps are believed to be primarily 

due to errors in the distribution of pumpage. Pumpage 

was estimated based on data presented by Heimes and 

Luckey (1982). Although these data were presented for 

10-minute cells, the irrigated-acreage data originally 

came from county-level census data. The acreage was 

then distributed to the 10-minute cells within each 

county as described in that report. The 10-minute cells 

did not correspond to the 100-mi2 nodes used in the 

model, so the pumpage data had to be redistributed 

from the 10-minute cells to the model nodes. Both pro-
32

104° !03

REGIONAL AQUIFER-SYSTEM ANALYSIS

102° 101° 100°

EXPLANATION

WATER-LEVEL CHANGE, IN FEET

Decline less than 10

-10 to-25

-25 to -50

-50 to -100

Decline more than 100

FIGURE 18. Generalized, observed predevelopment to 1980 water-level change for the central High Plains.

cesses, allocating county data to 10-minute cells and redistributing 10-minute data to 100-mi2 model nodes, 

tend to spread the pumpage throughout a somewhat 

broader area than where it actually occurred. Additionally, the model assumes that the pumpage occurred uniformly throughout the node; this tends to spread the 

effects of pumpage even further. This spreading of the 

pumpage probably was a less serious problem in the 

southern High Plains because that area has been densely developed throughout broad areas for a long time.
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 33

TABLE 5. Comparison of observed and simulated water-level declines, 1950 to 1980, for the central

High Plains

Water-level 

decline,

Volume of aquifer material dewatered, 

in millions of acre-feet

Simulated declines

Area of water-level decline, 

in square miles

Simulated declines

in reet

More than 10......

More than 25......

More than 50......

More than 100.....

10 to 25 ..........

25 to 50..........

50 to 100.........

uoservea 

declines

339

257

124

11

82

133

113

Net withdrawal 

of 100 percent 

of irrigation

requirement

306

215

47

0

91

168

47

Net withdrawal 

of 130 percent 

of irrigation

requirement

450

298

130

0

152

168

130

UDservea 

declines

15,200

7,900

2,400

100

7,300

5,500

2,300

Net withdrawal 

of 100 percent 

of irrigation

requirement

16,100

8,000

1,000

0

8,100

7,000

1,000

Net withdrawal 

of 130 percent 

of irrigation

requirement

23,300

9,700

2,700

0

13,600

7,000

2,700

Spreading of the pumpage causes the simulated waterlevel declines to be more extensive but less severe in 

local areas.

NORTHERN HIGH PLAINS MODEL 

CALIBRATION

The northern High Plains consists of about 96,500 

mi2 of the High Plains in Colorado, Kansas, Nebraska, 

South Dakota, and Wyoming. This area generally is 

north of the Smoky Hill River. The northern High 

Plains flow model includes all of the northern High 

Plains except a small part in the northwest corner 

which was not included because the geology in this region is too complex for the scale of the model. The 

northern High Plains was the last area of the High 

Plains to be developed for irrigation, with development 

generally starting after 1960. By 1980, a large part of 

this area was still virtually undeveloped. Two separate 

calibrations were made, one simulating the system 

prior to development and the other simulating the system after development. However, because of the lack 

of development in the northern High Plains, the second 

calibration is limited. The first calibration consisted of 

matching observed and simulated predevelopment 

water levels and comparing observed and simulated 

predevelopment base flow to major rivers. The second 

calibration consisted of matching observed and simulated water-level changes.

Small areas of the northern High Plains have been 

modeled by a number of investigators. LindnerLunsford and Borman (1984) and Reddell (1967) modeled the northern High Plains in Colorado. Kapple and

others (1976) and Luckey and Hofstra (1973a and 

1973b) modeled parts of the High Plains in Colorado. 

Lappala and others (1979) modeled a substantial part 

of Nebraska, and smaller areas of Nebraska were modeled by Pettijohn and Chen (1984), Cady and Ginsberg 

(1979), Lappala (1978), Huntoon (1974), and Emery 

(1966). The High Plains in South Dakota has been modeled by Kolm and Case (1983), and the High Plains in 

Wyoming has been modeled by Grist (1975, 1977, and 

1980) and Hoxie (1977 and 1979). In 1984, model studies 

were being conducted by the U.S. Geological Survey 

in western Kansas.

PREDEVELOPMENT-PERIOD CALIBRATION

In the predevelopment-period model hydraulic conductivity and recharge from precipitation were adjusted. Estimates of recharge for the northern High 

Plains ranged from a minimum of 0.17 in./yr to a 

maximum of 5.0 in./yr (Gutentag and others, 1984, 

table 7). Ground-water recharge in the northern High 

Plains aquifer ultimately discharges along the boundaries, along river valleys, and in areas where the water 

level is close to land surface. The nodes along the 

boundary were treated as constant-head nodes and the 

nodes along the principal river valleys were treated as 

river nodes (fig. 21). The discharge to areas where the 

water level is close to land surface, such as lakes and 

wet meadows in the sandhills, was not handled directly 

in the model. Instead, this discharge was subtracted 

from total recharge for the node; hence, the modeled 

recharge at each node represents the net recharge 

(total recharge minus total discharge) for the node.
34

104° 103°

REGIONAL AQUIFER-SYSTEM ANALYSIS

102° 101° 100° 99°

39'

EXPLANATION

WATER-LEVEL CHANGE, IN FEET 

Decline less than 10

-10 to-25

-25 to -50

Decline more than 50

FIGURE 19. Simulated predevelopment to 1980 water-level change with net withdrawal equal to 100 percent of irrigation requirement

for the central High Plains.

The initial hydraulic-conductivity estimates were obtained from Gutentag and others (1984, figure 10). Average values were determined for each node; the values 

ranged from 15 to 300 ft/d with a mean of 43 ft/d.

Predevelopment discharge to major rivers was estimated from streamflow records. Discharge along the 

northern and eastern boundaries were estimated using 

Darcy's law. Estimating the long-term discharge in
104

DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER

103° 102° 101° 100° 99° 98°

35

EXPLANATION

WATER-LEVEL CHANGE, IN FEET 

Decline less than 10

y 

-10 to-25 

-25 to-50 

Decline more than 50

FIGURE 20. Simulated predevelopment to 1980 water-level change with net withdrawal equal to 130 percent of irrigation requirement

for the central High Plains.

areas where the water level is close to land surface 

is difficult; that is why only net recharge was modeled 

in these areas. 

Results obtained during calibration of the central

High Plains model indicated that recharge was related 

to soil type; the same correlation was assumed for the 

northern High Plains. Generalized soil types for the 

northern High Plains are shown in figure 22. The re-
36 REGIONAL AQUIFER-SYSTEM ANALYSIS

Aquifer boundary 

COLORADO

H

EXPLANATION

CONSTANT-HEAD NODE 

RIVER NODE

FIGURE 21. Boundary conditions for the models of the northern High Plains.

charge distribution that resulted in a good correspondence between the observed and simulated predevelopment water levels is shown in figure 23. The net recharge ranged from 0.06 in./yr in the silt loam and clay 

loam soils to 1.20 in./yr in most of the sandy soils in 

central Nebraska. The sandy soils throughout most of 

the northern High Plains are in areas of sand dunes. 

The net recharge in the western part of the sandy soil 

of Nebraska is 0.30 in./yr. This area has numerous 

lakes and marshes in the interdune area and probably 

has a much larger ground-water discharge to evapotranspiration than the rest of the areas containing 

sandy soil. These estimates of recharge, particularly for 

the sandy soil, generally are less than those reported 

by other investigators (Gutentag and others, 1984,

table 7). However, these estimates are for net recharge. The relationship between soil type and estimated net recharge for the northern High Plains is:

Soil types and location

Estimated net recharge, 

in inches per year

Clay loam and silt loam soils

Loam soils

Sandy loam soils

Sandy soils in west-central Nebraska

Sandy soils in Colorado and southwestern

Nebraska 

Sandy soils elsewhere

0.06 

.11 

.20 

.30

,84 

1.20
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 37

Aquifer boundary 

COLORAD

Fl '.vV.v.'-v".-""'-:''.-'

Loam 

Sand

EXPLANATIC

SOIL TEXTURE

N

S

V~:->::::

Silt loam 

Clay loam

Sandy loam

FIGURE 22. Generalized soil types of the northern High Plains.

The observed and simulated predevelopment water 

levels are shown in figure 24. In general, they are 

closely correlated with the calculated water-level contours somewhat smoother. The biggest difference is 

near the 3,800-ft contour north of the North Platte 

River in the area of numerous sandhill lakes. The water 

level in this area is controlled by evapotranspiration 

from lakes and marshes. The model cannot adequately 

simulate the complex hydrology of this area because 

of the large node spacing. Smaller node spacing is 

needed to better simulate dunes, interdune areas, and

the relationship between depth to water and evapotranspiration rate. Such a model is beyond the scope 

of the present study.

The mean difference between the observed and simulated predevelopment water level at 943 nodes was 

+ 0.94 ft with a standard deviation of 55 ft. At 93 percent of the nodes, the simulated water-level altitude 

is within 100 ft of the observed altitude.

Throughout much of the northern High Plains, the 

position of the water table largely is controlled by river 

systems, particularly in central Nebraska where sev-
38 REGIONAL AQUIFER-SYSTEM ANALYSIS

106

Aquifer boundary

^

COLORADO

EXPLANATION

RECHARGE, IN INCHES 

PER YEAR

0.06

0.11

0.20 I

0.30

0.84

1.2

FIGURE 23. Estimated predevelopment, long-term average recharge rates for the northern High Plains using the hydraulic-conductivity

estimates adapted from Gutentag and others (1984).

eral major rivers drain the aquifer. In areas near major 

rivers, the model generally produces a water level configuration similar to that of observed predevelopment 

water levels because the river nodes control the model. 

The effect of the rivers on the water level in the aquifer 

far outweighs all other effects. Hence, to properly compare the observed and simulated water levels, more 

weight needs to be given to the areas away from the 

rivers.

Comparing the estimated and simulated base flow of 

the rivers is another way of measuring how well the 

model simulates the system. The base flow of a river 

represents the ground-water contribution to the river. 

Base flow is not a constant but varies from season to

season and year to year. Base flow generally is highest 

during the winter months when evapotranspiration is 

minimal and lowest during the summer. Because 

evapotranspiration near rivers was not handled directly 

in the model, the winter period was used to compare 

base flows. The estimates of the base flow (table 6) 

are a combination of published estimates (Newport, 

1959, p. 299; Sniegocki, 1959, p. 16-31,42; Bentall and 

Shaffer 1979, p. 98-121) and an examination of the 

November-February streamflow records. The estimated base flow includes only that part of the river 

within the northern High Plains. The estimates of the 

base flow are more accurate for the rivers that drain 

the sandhills because the flow of these rivers is much
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 39

106"

EXPLANATION

WATER LEVEL CONTOUR - Contour 

interval 200 feet. National Geodetic 

Vertical Datum of 1929

- - 6000 Observed

 6000 Simulated

FIGURE 24. Observed and simulated predevelopment water level for the northern High Plains using the hydraulic-conductivity estimates

adapted from Gutentag and others (1984).

more consistent. The estimate of the base flow of the 

Platte River system probably is the least accurate because this river is extensively regulated.

A comparison of the estimated and simulated base 

flows show that the simulated base flow is less than 

the estimated base flow for all river systems except 

the Republican for this simulation (column 3 of table 

6). The smaller simulated base flow probably is because 

some of the base flow is contributed from local and intermediate aquifer systems which are excluded in 

large-scale regional models such as the northern High 

Plains model.

The hydraulic conductivity, aquifer thickness, and 

hydraulic gradient control the rate of movement of 

water through the aquifer. For a given water-table configuration, greater hydraulic conductivity causes greater flow through the system and implies greater recharge and discharge rates. Gutentag and others (1984, 

fig. 10) indicate that the hydraulic conductivity of the 

northern High Plains is relatively small, particularly in 

the sandhills north of the Platte River. A major part 

of the recharge and the base flow to the rivers comes 

from the sandhills of Nebraska; therefore, the value assumed for the hydraulic conductivity in the sandhills 

is critical to the comparison of estimated and simulated 

base flows. The aquifer material in this region is principally fine sands and silts with little hydraulic conductivity. Determining an average hydraulic conductivity for 

these fine-grained sediments is subject to considerable 

interpretation. For example, Gutentag and others
40 REGIONAL AQUIFER-SYSTEM ANALYSIS

TABLE 6. Comparison of estimated and simulated base flow of the 

major river systems in the northern High Plains

Base flow, in cubic feet per second

River sytem

Simulated by model

Niobrara ........

Elkhorn .........

Loup .............

Platte............

Blue..............

Republican .....

Total .......

Estimated

1,000

600

1,850

1,250

260

300

5,260

Initial 

hydraulic 

conductivity 

and recharge

600

250

740

560

60

340

2,550

Increased 

hydraulic 

conductivity 

and recharge1

780

320

930

670

80

430

3,210

Increased 

recharge in 

sandhills2

1,090

460

1,570

920

80

410

4,350

'Recharge was 27 percent more than that used during the initial simulation. 

2Recharge in the sandhills was 2 in./yr; recharge outside of the sandhills was 20 percent 

more than in the initial simulation.

(1984, table 5) estimated the hydraulic conductivity of 

both silty sand and fine sand from drillers' logs to be 

50 ft/d while Lappala (1978, table 6) estimated the hydraulic conductivity of the same sediments from 

geologist-interpreted logs as 13 and 40 ft/d, respectively. The hydraulic-conductivity map of the Nebraska 

part of the High Plains was adapted from the map presented by Gutentag and others (1984, fig. 10). They 

constructed their map on the basis of 2,685 geologist-interpreted logs and the table presented in Lappala 

(1978, table 6). The hydraulic-conductivity map outside 

of Nebraska was constructed during this study using 

mainly drillers' logs and the table presented by Gutentag and others (1984, table 5).

Records from 117 test holes in northwestern 

Nebraska were analyzed and a mean hydraulic conductivity at each site was computed using both of the tables referenced above. The mean hydraulic conductivity 

from the 117 test holes computed using Gutentag and 

others (1984) averaged 40 percent more than that using 

Lappala (1978). The hydraulic conductivity also was 

computed at 40 points in the Platte River basin from 

the saturated thickness and transmissivity maps in 

Lappala and others (1979). These values, which were 

distributed throughout much of Nebraska, averaged 30 

percent more than the corresponding points on the hydraulic-conductivity map in Gutentag and others (1984, 

fig. 10). Although it was not possible to know which 

estimate for hydraulic conductivity is closest to the true 

value, the map used to obtain the hydraulic conductivities for the model consistently presents smaller estimates than other investigations using comparable 

geologist-interpreted logs. Larger hydraulic conductivities in the sandhills would result in larger computed 

base flow, but the estimates would have to be approximately doubled to make the simulated base flow correspond to the estimated base flow.

As a result of the above analysis, a simulation was 

made in which all of the hydraulic conductivities in 

Nebraska were increased by 33 percent. The pattern 

for recharge was the same as in the previous simulation 

but the individual values were increased because of the 

increased hydraulic conductivity throughout a large 

part of the model. The best correspondence between 

observed and simulated water levels occurred when all 

recharge values were increased 27 percent compared 

to the previously shown values (fig. 23). Recharge in 

this simulation ranged from 0.076 in./yr on the silt-loam 

and clay-loam soils to 1.52 in./yr in the sandhills in 

Nebraska as shown in figure 25.

The observed and simulated predevelopment water 

levels for this simulation are shown in figure 26. As 

in the previous simulation, the two correspond reasonably well. The mean difference between water levels at 

943 nodes was +0.30 ft with a standard deviation of 

55.2 ft. At 92 percent of the nodes, the simulated water 

level is within 100 ft of the observed water level. The 

difference between the water level in this simulation 

and the water level in the previous simulation is not 

large. The principal difference between the two simulations was in the base flow of the major river systems 

(column 4 of table 6). The simulated base flow was significantly larger than in the previous simulation for all 

river systems. For this simulation, the total simulated 

base flow was slightly more than 60 percent of the estimated base flow. The simulated base flow in the Loup 

and Elkhorn Rivers was still about one-half the estimated base flow even though it was significantly larger 

than in the previous simulation. The base flow in these 

rivers is well known and the model might be expected 

to simulate a higher base flow for these rivers.

Because the major river systems, particularly the 

Loup, Elkhorn, and Niobrara, are associated with the 

sandhills, a simulation with a larger recharge rate in 

the sandhills attempted to more accurately simulate the 

base flows. In this simulation, 2.0 in./yr recharge was 

assumed for the sandhills north of the Platte River and 

the rest of the recharge was 20 percent more than that 

shown in figure 23. The correspondence between the 

observed and simulated predevelopment water levels 

for this simulation is not nearly as good as the previous 

simulations. The mean difference between the observed
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 41

and simulated water levels is +10.6 ft with a standard 

deviation of 56 ft. However, the simulated base flows 

(column 5 of table 6) were much closer to the estimated 

base flows. The total simulated base flow was about 

86 percent of the total estimated base flow. The simulated base flows in the Elkhorn and Loup systems were 

somewhat less than the estimated flow, and the simulated base flow in the Niobrara system was somewhat 

more than the estimated base flow. Although this simulation was rejected because of the large differences between the observed and simulated water levels, it does 

indicate that the net recharge from precipitation that 

reaches the river systems from the sandhills probably 

exceeds 2.0 in./yr.

The last two simulations indicate that either: (1) The 

hydraulic-conductivity estimates for Nebraska need to 

be increased even more; or (2) the model does not 

adequately calculate the base flow to the rivers. The 

hydraulic conductivity, as altered, appears to represent 

the best currently available knowledge and needs to 

remain unchanged. In contrast, this model is a regional 

model that was not designed to calculate base flow to 

rivers and it does not accurately represent the flow system in the vicinity of rivers. The small calculated base 

flow probably is a result of the scale of the model.

Winter (1976) investigated the interaction of lakes 

and ground water. He divides the ground-water flow 

system into a local flow system, an intermediate flow 

system, and a regional flow system. In the local flow 

system, recharge travels through the aquifer to be discharged into the adjacent lake; in the intermediate flow 

system, recharge travels to a nearby lake. If these results are applicable to the northern High Plains, the 

base flow simulated in the model is only the regional 

component of the base flow. The estimated base flow 

contains the local and intermediate flow-system components as well as the regional component. The relative 

magnitudes of each of these components are unknown. 

Hence, drawing conclusions about the difference between the estimated base flow and the base flow simulated by the model is difficult, except that the simulated regional base flow should be less than the total 

estimated base flow. The degree of the difference between the simulated and estimated base flows is dependent on the scale of the model.

The simulation, in which (1) the hydraulic conductivity in Nebraska was increased by one-third compared 

to the previously estimated values, and (2) the recharge 

ranged from 0.076 to 1.52 in./yr, was selected as the 

simulation that best represents the regional aquifer 

system. This simulation was used as the basis for the 

development-period calibration.

TABLE 7. Pumpage in the northern High Plains, 1960 to 1980, by

State

Irrigation pumpage, in thousands of acre-feet per year

State

1960-64 1965-69 1970-74 1975-79

Colorado .........

Kansas............

Nebraska ........

South Dakota.. 

Wyoming.........

195

182

2,988

1

43

Total 3,409

409

322

3,437

4

60

4,232

637

470

4,589

9

75

5,780

905

577

6,091

18

96

7,687

DEVELOPMENT-PERIOD CALIBRATION

The northern High Plains has the shortest history 

of development of the three areas of the High Plains. 

Even by 1960, most of the northern High Plains had 

undergone little development for irrigation and the predevelopment water levels were virtually undisturbed. 

Hence, only one development period, 1960 to 1980, was 

simulated. Because of this relatively short period, the 

development-period calibration of the northern High 

Plains is less definitive than the development-period 

calibration of the other two areas.

Several additional stresses have been imposed on the 

aquifer in the northern High Plains since 1960. Pumpage for irrigation and return flow from irrigation were 

still the dominant new stresses on this part of the 

aquifer. However, additional recharge from various 

sources also was a very significant new stress on the 

aquifer in the northern High Plains.

In the northern High Plains, pumpage for irrigation 

was the only significant pumpage and pumpage for 

municipal, industrial, stock, and domestic use were ignored in the simulation. The pumpage estimates for 

1960-80 for the northern High Plains are given in table 

7. The data in the table indicate that approximately 

105 million acre-ft of water were pumped from the 

aquifer in the northern High Plains between 1960 and 

1980. This was somewhat more than that pumped in 

the central High Plains and about one-half that pumped 

in the southern High Plains.

A generalized water-level change map (fig. 27) was 

constructed from the map presented by Luckey and 

others (1981) by estimating the average water-level 

change for each node (100 mi2) and contouring the 

changes. Water-level changes for each simulation were 

contoured and compared with the generalized observed 

water-level change map.
42 REGIONAL AQUIFER-SYSTEM ANALYSIS

I 

42°\-

SOUTH N-fo DAKOTA

Aquifer boundary 

COLORADO

40'

EXPLANATION

RECHARGE, IN INCHES 

PER YEAR

0.076

0.14

0.25 I

0.38

1.07

1.52

FIGURE 25. Estimated predevelopment, long-term average recharge rates for the northern High Plains using the revised hydraulicconductivity estimates.

The return flow to the aquifer from irrigation was 

one of the two components of the model that was adjusted during calibration. Because return flow was assumed to reach the aquifer within the 5-year pumping 

period, changing return flow was exactly equivalent to 

changing net withdrawal. The return flow was assumed 

to be a function of the difference between total pumpage and irrigation requirement. The simulated waterlevel changes most nearly matched the observed waterlevel changes when return flow was equal to 100 percent of the difference between total pumpage and irrigation requirement. In this simulation, the return flow 

ranged from 46 percent of total pumpage early in the 

period to 30 percent later in the period and averaged 

36 percent.

Additional recharge from various sources was the 

other component of the model that was adjusted during 

calibration. The recharge from precipitation determined 

during the predevelopment-period calibration was assumed to have continued during the development 

period. For the 20 years simulated, recharge from precipitation was 46.9 million acre-ft for the northern High 

Plains.

Recharge to the aquifer in the northern High Plains 

has been significantly increased by human activities. 

The most dramatic effects of increased recharge occur 

in central Nebraska on the south side of the Platte 

River. Leakage from canals and reservoirs and return 

flow from surface-water irrigation have caused water 

levels to rise as much as 90 ft (Johnson and Pederson,
DIGITAL SIMULATION OF GROUND WATER FLOW OF THE HIGH PLAINS AQUIFER 43

106 105° 104° 103

WYOMING |

EXPLANATION

WATER LEVEL CONTOUR Contour 

interval 200 feet. National Geodetic 

Vertical Datum of 1929

 4OOO Observed

 40OO Simulated

FIGURE 26. Observed and simulated predevelopment water level for the northern High Plains using the revised hydraulic-conductivity

estimates.

1982, p. 22). Canal and reservoir leakage for this area 

was estimated from canal diversion and delivery records to be 5.0 million acre-ft for 1960-80. Additional 

canal and reservoir leakage along the Loup River was 

estimated by the same procedure to be 1.2 million acreft for the same period. Return flow from surface-water 

irrigation, principally along the Platte River, was estimated to be 3 in./yr throughout the irrigated land for 

a total of 3.2 million acre-ft for the 20 years.

Cultivation practices associated with dryland farming 

can increase recharge from precipitation compared to 

the rate of recharge on rangeland (Ogilbee, 1962, p. 

25). For the northern High Plains, additional recharge 

due to cultivation was estimated to be 0.5 in./yr 

throughout the dryland area. Water-level changes due 

to this additional recharge have been small, so this

value cannot be accurately estimated. The total estimated increased recharge throughout the dryland area 

for 1960-80 was 9.7 million acre-ft.

Additional recharge was needed east of 100° longitude to successfully simulate the observed water-level 

changes. The additional recharge was added only on 

the irrigated land at a rate of 2.5 in./yr north of 41° 

latitude and 5.0 in./yr south of 41° latitude. The total 

for the 20 years was 28.0 million acre-ft. Several factors 

that could account for the recharge increase were investigated: (1) Decrease in runoff to streams due to cultivation; (2) decrease in base flow to streams due to 

ground-water withdrawal; (3) decrease in downward 

leakage to underlying aquifers; (4) reduction of evapotranspiration due to lower water levels; (5) increase in 

recharge from precipitation due to conversion of natural
44 REGIONAL AQUIFER-SYSTEM ANALYSIS

Aquifer boundary

«

COLORADO

41-

EXPLANATION

WATER-LEVEL CHANGE, IN FEET

Rise more than 25 -10 to-25

+10 to +25 ^^^^H Decline more than 25

+10 to-10

FIGURE 27. Generalized, observed predevelopment to 1980 water-level change for the northern High Plains.

grasslands to croplands; (6) increase in downward leakage from a saturated zone above the water table; (7) 

greater specific yield of the aquifer than previously estimated; (8) smaller total pumpage than estimated; and 

(9) significantly more return flow from irrigation east 

of 100° longitude. These factors were studied in the Big 

Blue and Little Blue River basins in southeastern 

Nebraska.

Streamflow records were examined to evaluate the 

first two factors. A decrease in runoff should result in 

a decrease in the high flow of streams. A decrease in 

base flow should result in a decrease in the low flow 

of streams. The estimated combined decrease in the 

high and low streamflow for 1960-80 for the Big Blue

and Little Blue River basins was 2.5-3.0 million acre-ft. 

This was equivalent to about 15 percent of the increase 

in recharge in these basins.

The third through sixth factors could contribute only 

minor quantities to the apparent increase in recharge. 

Estimates of the change in downward leakage to underlying aquifers were made using what few data were 

available. These estimates indicate that the change in 

downward leakage could at most be a small fraction 

of 1 percent of the apparent increase in recharge. Salvage of evapotranspiration in shallow-water table areas 

also could account for only an insignificant proportion 

of the water because of the very limited area with a 

shallow water table. Increased recharge from precipita-
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 45

tion resulting from the conversion of grassland to cropland must have been small or water levels would have 

risen significantly during the period of dryland farming. 

If all of the increased recharge came from this source, 

water levels would have risen about 1 ft per year during the period of dryland farming. Water-level records 

do not show such rises; therefore, the increased recharge due to grassland conversion could only be a 

small proportion of the apparent increase in recharge. 

The sixth factor, increased downward leakage from a 

saturated zone above the water table, may occur in 

some areas but the extent of these areas is much too 

small to provide a significant proportion of the apparent 

increase in recharge.

The seventh factor, greater specific yield than previously estimated, was considered. The specific yield for 

the entire High Plains was estimated in the same manner, but possibly some of the estimates should have 

been made differently in the eastern part of the High 

Plains. The specific yield of the aquifer was estimated 

from lithologic logs (Gutentag and others, 1984, p. 23). 

A value for the specific yield was assigned to each 

lithologic unit and a mean value was computed for each 

site. Although the aquifer material in the eastern part 

of the northern High Plains is younger than the aquifer 

material in most of the High Plains, this procedure 

should work regardless of the age of the aquifer material. The specific yield would have to be approximately 

doubled to about 0.35 in the Big Blue and Little Blue 

River basins to make the model simulate accurately 

without increasing recharge, and such a specific yield 

appears unrealistically large.

The eighth factor depends on the method used to estimate total pumpage and irrigation requirement. Total 

pumpage was estimated from the data presented in 

Heimes and Luckey (1982). The estimates were dependent on the crop demands computed using the modified 

Blaney-Criddle formula (U.S. Department of Agriculture, 1967). The Blaney-Criddle formula was developed 

for semiarid areas, but the eastern part of the High 

Plains has a more humid climate. Data presented by 

Heimes and Luckey (1983, tables 2 and 4) indicate that 

the ratio between measured 1980 total pumpage and 

calculated irrigation requirement for corn is about 15 

percent less for York County in eastern Nebraska than 

it is for Kit Carson County in eastern Colorado. Although no definitive conclusions can be drawn from 

such meager data, they indicate that the irrigation requirement may be somewhat overestimated in eastern 

Nebraska. This overestimate could account for part of 

the additional recharge needed to calibrate the model.

The last factor, greater return flow, also depends on 

calculated irrigation requirement. Huntoon (1974) was

able to calibrate a model of the Big Blue River basin 

by assuming return flow was 60 percent of total pumpage, but he noted that this appeared highly suspect 

(Huntoon, 1974, p. 44). Return flow throughout the rest 

of the High Plains during 1960-80 was about 40 percent 

of total pumpage based on this study; no reason exists 

to believe that return flow in the Big Blue River basin 

should be significantly different from the rest of the 

High Plains. If return flow were increased to 60 percent of total pumpage for this area, irrigation requirement would be less than 70 percent of that estimated 

using the modified Blaney-Criddle formula. However, 

greater return flow east of 100° longitude could account 

for part of the apparent increase in recharge if the 

Blaney-Criddle formula significantly overestimated 

crop demand for this area.

None of these factors individually could account for 

the 28 million acre-ft of apparent increase in recharge, 

but collectively they might account for this quantity of 

water. Undoubtedly, all nine factors could contribute 

some to the apparent increase in recharge needed to 

calibrate the model. However, additional research on 

total pumpage, crop demand, specific yield, and related 

factors is needed before this apparent increase in recharge can be fully understood.

The development-period composite recharge is shown 

in figure 28. This recharge is assumed to be the sum 

of five separate components: (1) Predevelopment-period 

calibration recharge; (2) canal and reservoir leakage; (3) 

return flow from surface-water irrigation; (4) increased 

recharge due to dryland cultivation; and (5) additional 

recharge east of 100° longitude.

The additional development-period recharge due to 

human activities (47.0 million acre-ft) and the return 

flow from ground-water irrigation (37.5 million acre-ft) 

balance most of the 105.0 million acre-ft that were 

pumped in the northern High Plains between 1960 and 

1980. Hence, the overall change in storage has been 

small, even though large water-level declines and rises 

have occurred in various areas.

The simulated water-level changes for the northern 

High Plains are shown in figure 29. Generally, a good 

correlation exists between the simulated water-level 

changes and observed water-level changes shown in figure 27. In the western part of the area, the observed 

and simulated declines match very closely. In the eastern part of the area between the Platte and Republican 

Rivers, the simulated declines are greater than the observed declines. Along the downstream reach of the 

Elkhorn River, the model simulated an area of waterlevel rise that does not exist on the observed waterlevel change map. These discrepancies in the eastern 

part of the High Plains indicate that, even with the
46 REGIONAL AQUIFER-SYSTEM ANALYSIS

103° 1D2° im° inn° 99°

Aquifer boundary

«

COLORADO

EXPLANATION

COMPOSITE RECHARGE, IN 

INCHES PER YEAR

0.0 to 0.1 

0.1 to 0.2 

0.2 to 0.4 

0.4 to 1.0

I

1.0 to 2.0 

2.0 to 4.0 

More than 4.0

FIGURE 28. Composite 1960-80 recharge for the development-period model of the northern High Plains.

recharge that was added east of 100° longitude, the 

model does not adequately simulate the hydrologic system in this area.

The simulated water-level rises in south-central 

Nebraska are of about the same order of magnitude 

as the observed water-level rises but are less extensive. This may be due to the coarseness of the grid 

of the model. The model failed to simulate water-level 

rises between the Middle Loup and North Loup Rivers. 

This probably is due to the scale of the model. The 

model in this area is completely controlled by river 

nodes so that simulated water-level rises do not occur.

The model simulated a net decrease in storage in the 

aquifer of about 15 million acre-ft of water. The observed change in storage outside of the +10 to 10 

ft change area was 6 million acre-ft. The other 9 million 

acre-ft of change probably occurred in the +10 to -10 

ft change area.

This simulation was accepted as a reasonable representation of the development-period operation of the 

aquifer in the northern High Plains. Despite the shortcomings discussed above, it is adequate for calculating 

the future state of the system.
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 47

96°

Aquifer boundary 

COLORADO

EXPLANATION

WATER-LEVEL CHANGE, IN FEET

Rise more than 25 

+10 to+25 

+10 to-10

-10 to-25

Decline more than 25

FIGURE 29. Simulated predevelopment to 1980 water-level change for the northern High Plains.

SENSITIVITY ANALYSIS

A sensitivity analysis was performed on the High 

Plains models to determine the response of the models 

to changes in model inputs. The response of the simulated water levels and base flows to changes in the 

model inputs was determined. The sensitivity analysis 

can be used to guide future data collection.

A separate sensitivity analysis was made for the predevelopment- and the development-period models for 

each of the three areas of the High Plains. The sensitivity analysis consisted of uniformly increasing or decreasing the model inputs and noting the change in 

water levels and base flow to rivers. The simulation

results were recorded either as a change in the absolute 

value of the mean residual between the observed and 

the simulated water levels or as a change in the total 

base flow to rivers. For the predevelopment-period 

models, the effects of change in recharge and hydraulic 

conductivity were investigated. For the developmentperiod models, the effects of the change in hydraulic 

conductivity, specific yield, and net withdrawal were 

investigated. Each of these items was increased or decreased uniformly; the effect of a change in distribution 

of the parameters was not investigated. In general, the 

distribution of a particular model input for the High 

Plains aquifer is well defined; so, it is not appropriate 

to check the effect of a change in distribution.
48 REGIONAL AQUIFER-SYSTEM ANALYSIS

100

75

50

25

-60 -40 -20 0 20 40 60 

CHANGE FROM CALIBRATED VALUE, IN PERCENT

FIGURE 30. Predevelopment-period-model sensitivity analysis for 

the southern High Plains.

Likewise, the boundary conditions on the High Plains 

models are well defined and a sensitivity analysis on 

the effect of changing boundary conditions has not been 

made.

The results of the sensitivity analysis for recharge 

and hydraulic conductivity for the southern High Plains 

predevelopment-period model are shown in figure 30. 

Both recharge and hydraulic conductivity were changed 

by as much as 50 percent of the calibrated value. The 

effect of the change in the parameter or stress was 

measured through the change in the absolute value of 

the mean residual between observed and simulated 

water levels. The simulated water levels were about 

equally sensitive to a change in recharge or to a change 

in hydraulic conductivity. The largest absolute value of 

the mean residual in the sensitivity analysis was 78 ft 

when hydraulic conductivity was decreased 50 percent. 

This compares to the mean residual of +0.22 ft at calibration.

The sensitivity analysis for the central High Plains 

predevelopment-period model for the same two variables is shown in figure 31. Again, the simulated water 

levels were equally sensitive to changes in recharge and 

hydraulic conductivity. However, for this model, the 

largest absolute value of the mean residual was only 

about 27 ft when hydraulic conductivity was decreased 

50 percent. The central High Plains predevelopmentperiod model was less sensitive to a change in either 

recharge or hydraulic conductivity compared to the 

southern High Plains model because water levels in this 

model were partly controlled by rivers.

The sensitivity of the simulated base flow to rivers 

as related to changes in recharge and hydraulic conductivity also is shown in figure 31. The figure indicates 

that the model is more sensitive to changes in recharge 

than to changes in hydraulic conductivity. When the 

estimated hydraulic conductivity increased 50 percent, 

the simulated base flow to rivers decreased 11 percent; 

but when recharge increased 50 percent, the simulated 

base flow to rivers increased 60 percent. Increased recharge added more water to the model whereas increased hydraulic conductivity simply let some water 

that had previously been leaving the model through the 

rivers leave the model through boundary outflow.

A sensitivity analysis was done for the northern High 

Plains predevelopment-period model for changes in 

both recharge and hydraulic conductivity. The effects 

of change in recharge and change in hydraulic conductivity on both the absolute value of the mean residual 

and the base flow to rivers were very similar to the 

results for the central High Plains predevelopmentperiod model and, thus, are not presented.

Minimizing the absolute value of the mean waterlevel residual is only one possible calibration criterion. 

This criterion tends to balance the errors in the model 

but allows the possibility of compensating errors. A 

very small mean water-level residual does not necessarily imply a properly calibrated model unless the distribution of the residuals also are investigated. Two other 

calibration criteria were evaluated for the predevelopment-period model of the southern High Plains aquifer. 

Minimizing the standard deviation of the residuals between observed and simulated water levels does not 

allow for compensating errors and emphasizes the 

larger residuals. Minimizing the mean of the absolute 

values of the residuals also does not allow for compensating errors and does not emphasize the larger residuals.

The results of differing calibration criteria for the 

predevelopment period of the southern High Plains 

model are shown in figure 32. The slope of the absolute 

value of the mean residual calibration criterion is the 

steepest of the three criteria and, hence, is the best 

criterion in the sense that it is easiest to find the mini-
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 49

30

LU 20

700

500

y

CO

D 

U

Z

c/J

cc

300

100

-60 -40 -20 0 20 

CHANGE FROM CALIBRATED VALUE, IN PERCENT

40 60

FIGURE 31. Predevelopment-period-model sensitivity analysis for the central High Plains.

mum value of this criterion. The calibration criterion 

of minimizing the standard deviation of the residuals 

has the least slope. Interestingly, the minimum of each 

of the calibration criteria occurs at different places. If 

the criterion of standard deviation of the residuals were 

chosen, the average estimated recharge at calibration 

would have been about 20 percent less than it was 

using the criterion of absolute value of the mean residual.

The usual procedure in a sensitivity analysis is to 

vary one parameter at a time and evaluate the response

of the model to the change in that parameter. However, the model parameters are not all independent of 

each other and changing one parameter during calibration might necessitate changing another parameter.

The effects of simultaneously varying recharge and 

hydraulic conductivity in the southern High Plains predevelopment-period model are shown in figure 33. In 

this figure, the vertical axis shows the change in hydraulic conductivity and the horizontal axis shows the 

change in recharge. The lines in the figure are lines 

of equal mean residuals. Near the lower right corner
50 REGIONAL AQUIFER-SYSTEM ANALYSIS

70

60

t 50

LLJ 

LL.

z 

E 40

LLJ

E

O 30

20

10

Criterion of standard 

deviation of residuals

Criterion of mean of 

absolute values of residuals

riterion of absolute value 

of mean residuals

-60 -40 -20 0 20 40 

CHANGE IN RECHARGE. IN PERCENT

60

FIGURE 32. Results of changing the calibration criteria for the predevelopment-period model of the southern High Plains.

-60 -40 -20 0 20 40 

CHANGE IN RECHARGE, IN PERCENT

FIGURE 33. Results of simultaneously changing recharge and hydraulic conductivity in the predevelopment-period model of the 

southern High Plains. Lines represent equal mean residuals.

-60 -40 -20 0 20 40 60 

CHANGE FROM CALIBRATED VALUE, IN PERCENT

FIGURE 34. Development-period-model sensitivity analysis for southern High Plains.

of the figure where recharge was increased 30 percent 

and hydraulic conductivity was decreased 38 percent, 

the mean residual was 100 ft. In the upper left corner 

of the figure where hydraulic conductivity was increased 45 percent and recharge was decreased 45 percent, the mean residual was -50 ft. From the lower 

left corner to the upper right corner of the figure is 

a trough in which the mean residual is near zero. The 

existence of this trough indicates that the hydraulic 

conductivity and recharge are very interrelated, and, 

as long as these two model inputs are in balance, the 

model has a small mean residual. When these model 

inputs are out of balance with each other, the residual 

becomes large. Therefore, if the hydraulic conductivity 

is accurately known, the model can be used to accurately determine the recharge. Likewise, if the hydraulic conductivity is poorly known, then the recharge will 

be poorly determined.

The early discussions in this section could give the 

impression that these two model inputs are known 

within narrow limits, but this is based on the assumption that all of the other inputs are accurately known. 

The data in figure 33 indicate that, in the calibrated 

model, recharge and hydraulic conductivity are in balance with each other, but they are not necessarily accurately known.

The sensitivity of the development-period models to 

changes in hydraulic conductivity, specific yield, and 

net withdrawal also was evaluated. The effect of net
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 51

250

LU

£ 200

^ LU 

0

Z X

 LU

EC CO

LU LU

II

LU LU

Q Q 100 

CO I

50

25

20

10

OLL. 

CO O

52 

ui |

5 b

^ CO 

LU DC

LL. CO' 

O LU

-60 -40 -20 0 20 

CHANGE FROM CALIBRATED VALUE, IN PERCENT

40 60

FIGURE 35. Development-period-model sensitivity analysis for the northern High Plains.

withdrawal rather than total pumpage and return flow 

was studied because a change in total pumpage would 

necessitate a change in return flow because of the way 

in which return flow was simulated. The results of the 

sensitivity analysis for the southern High Plains development-period model are shown in figure 34. This 

model was extremely insensitive to changes in hydraulic conductivity; large changes in hydraulic conductivity 

caused only very small changes in the absolute value 

of the mean water-level residual. This is not surprising 

because hydraulic conductivity controls the rate of flow 

through the aquifer and the dominant factor during the 

development period is the withdrawal of water from 

the aquifer and not flow through the aquifer. The development-period model was sensitive to changes in 

both net withdrawal and specific yield. Hence, an accurate model for simulating the development history of

the High Plains aquifer requires more accurate information for net withdrawal and specific yield than for 

hydraulic conductivity.

For reasons explained previously, the central and 

northern High Plains development-period models used 

the simulated area and volume of water-level changes 

for calibration. The effect of changing net withdrawal 

and specific yield in the the northern High Plains development-period model is shown in figure 35. In this 

figure, the effect of the change in these variables on 

the volume of the aquifer dewatered and the area of 

the water-level change is shown because both were 

used during the calibration process. The volume of 

aquifer dewatered is used rather than the volume of 

water removed from storage because the measurement 

of the latter depends on the assumed specific yield 

which is one of the parameters that was varied. Under
52 REGIONAL AQUIFER-SYSTEM ANALYSIS

both criteria (volume dewatered and area of water-level 

change), the development-period model was sensitive 

to changes in both net withdrawal and specific yield 

but was slightly more sensitive to changes in net withdrawal. Near the calibration point (zero change in calibrated value), the relationship between the model variables and the calibration criteria is approximately 1:1. 

As the estimated specific yield increased significantly, 

the model became less sensitive to changes in specific 

yield. Likewise, as net withdrawal decreased significantly, the model became less sensitive to net withdrawal.

A sensitivity analysis was made for the central High 

Plains development-period model. This analysis produced results nearly identical to the results for the northern High Plains development-period model. In the analysis of the central High Plains model, the only difference was that the sensitivity to net withdrawal remained relatively constant throughout the entire range 

of change. This is because in the northern High Plains 

model, as net withdrawal decreased significantly, the 

additional recharge due to human activities began to 

dominate the model and this additional recharge was 

not present in the central High Plains model.

Although net withdrawal and specific yield were not 

varied simultaneously in the development-period model 

sensitivity analysis, indications existed during the calibration that these two model inputs are interrelated 

in the same manner that recharge and hydraulic conductivity are interrelated in the predevelopment-period 

models. Hence, if net withdrawal is accurately known, 

then the model can be used to accurately determine 

the specific yield. However, if neither is accurately 

known, then the best that the model can do is to ensure 

that net withdrawal and specific yield are in balance 

with each other.

SUMMARY AND CONCLUSIONS

The U.S. Geological Survey began a study of the 

174,000-mi2 High Plains regional aquifer in 1978. The 

High Plains is one of the major irrigated areas of the 

United States and in 1980 accounted for more than 20 

percent of the irrigated land and about 30 percent of 

the ground water pumped for irrigation in the United 

States. However, throughout much of the aquifer, the 

rate of withdrawal exceeds the rate of replenishment 

and large water-level declines have occurred in parts 

of the High Plains. One of the primary objectives of 

the study was to develop digital models of the aquifer 

system that could be used to simulate the aquifer system and evaluate future development of the water resources. This report describes the calibration of the digital models of the High Plains aquifer that were developed during the study and could be used to evaluate 

future water levels due to potential development.

The flow system in the High Plains aquifer was simulated using a digital, finite-difference technique to solve 

the ground-water flow equation. For simulation, the 

High Plains aquifer system was divided into three 

parts. The southern High Plains consists of about 

29,000 mi2 in Texas and New Mexico; the central High 

Plains consists of about 48,500 mi2 in Texas, New 

Mexico, Oklahoma, Colorado, and Kansas; and the 

northern High Plains consists of about 96,500 mi2 in 

Colorado, Kansas, Nebraska, Wyoming, and South 

Dakota. Each of the three parts of the High Plains 

aquifer system was simulated using a regular network 

of nodes spaced 10 mi apart in both the north-south 

and east-west directions. The southern High Plains 

models have 303 active nodes, the central High Plains 

models have 513 active nodes, and the northern High 

Plains models have 943 active nodes. One node is common between the southern and central High Plains 

models and five nodes are common between the central 

and northern High Plains models.

The history of the High Plains aquifer was divided 

into two periods: (1) The predevelopment period prior 

to large-scale development for irrigation and (2) the development period after the beginning of large-scale development for irrigation. Separate models were constructed and calibrated for the predevelopment and development periods with the results of the predevelopment-period calibration used as the initial conditions for 

the development-period calibration.

The objective of the predevelopment-period calibration was to simulate the system prior to human activities. The data requirements for the predevelopment-period models are simpler than the data requirements for the development-period models. Calibration 

of the predevelopment-period models increased the understanding of the hydrologic system and refined the 

estimates of hydraulic conductivity and recharge rates. 

In the predevelopment-period calibration, one aquifer 

parameter (the hydraulic conductivity) and one stress 

(recharge from precipitation) were varied to obtain the 

best correlation between the observed and simulated 

predevelopment water levels.

In the predevelopment-period model of the southern 

High Plains, the initial estimates of hydraulic conductivity were decreased in areas with large values of hydraulic conductivity. The estimated predevelopment recharge rate ranged from 0.086 to 1.03 in./yr. The
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER

TABLE 8. Summary of calibration of High Plains models

53

Area

Predevelopment-period models

Water-level residuals

Standard Nodes with

Mean deviation of residuals less

residual residuals than 100 feet

(feet) (feet) (percent)

Development-period models 

(all units in millions of acre-feet)

Change in storage

Pumpage Observed Simulated

Southern High Plains.... 

Central High Plains......

Northern High Plains....

. +0.22 

, -0.28

. +0.30

41.6 

38.5

55.2

99

98

92

210

94

107

97 

50

6

90 

55

15

largest recharge rates were assigned to the area near 

the Running Water Draw-White River lineaments. At 

calibration, the mean difference between the simulated 

and observed water levels was +0.22 ft (table 8). The 

extreme differences were -113 ft and +99 ft for 303 

nodes in the model.

In the predevelopment-period model of the central 

High Plains, the initial estimates of hydraulic conductivity were decreased in areas with thick saturated material. This decrease is postulated to be caused by disturbed and chaotic bedding in the aquifer in areas 

where the underlying bedrock has collapsed due to salt 

dissolution in Permian rocks. The overall decrease in 

the hydraulic-conductivity estimates averaged about 20 

percent. The estimated predevelopment recharge rate 

ranged from 0.056 to 0.84 in./yr. The estimates were 

distributed on the basis of soil types. Recharge rates 

were smallest for the clay-loam and silt-loam soils and 

were largest for sandy soils in the sand dunes. At calibration, the mean difference between the observed and 

simulated water levels was -0.28 ft (table 8).

The predevelopment water level in much of the 

northern High Plains was controlled by the rivers 

draining the area. Hence, the simulated water levels 

in the northern High Plains were less sensitive to the 

estimates of hydraulic conductivity and recharge from 

precipitation. Two separate simulations one using the 

initial hydraulic-conductivity estimates and one with 

the hydraulic-conductivity estimates in Nebraska increased by 33 percent of the initial values produced 

nearly identical simulated water levels. Recharge rates 

were changed during the two simulations to produce 

the best correlation between observed and simulated

water levels. However, the latter simulation produced 

a more reasonable base flow to streams, and this simulation was selected as the best representation of the 

aquifer because it was more consistent with work previously done in Nebraska.

In the northern High Plains model, the estimated 

predevelopment recharge rate ranged from 0.076 to 

1.52 in./yr and was distributed according to soil type. 

The recharge rate was smallest for the clay-loam and 

silt-loam soils and was largest for sandy soils in part 

of the sand dunes in central Nebraska. At calibration, 

the mean difference between the observed and simulated water levels was +0.30 ft and, at 92 percent of 

943 nodes in the model, the simulated water level was 

within 100 ft of the observed water level (table 8). Most 

of the errors in excess of 100 ft occurred in areas where 

data were sparse. At calibration, the simulated base 

flow averaged 61 percent of the estimated base flow, 

probably because the model can only simulate the regional component of the base flow.

The objective of the development-period calibration 

was to simulate the change in the system due to human 

activities. Calibration of the development-period models 

began with the results of the predevelopment-period 

calibration. In the development-period calibration, two 

stresses return flow from irrigation and increased recharge rates due to human activities during the development period were varied to obtain the best correlation between observed and simulated water levels 

or water-level changes.

The southern High Plains aquifer has had a long history of irrigation development dating from the 1930's. 

Because of this long history, the development-period
54 REGIONAL AQUIFER-SYSTEM ANALYSIS

calibration was divided into two periods: 1940-60 and 

1960-80. Return flow from irrigation was varied to 

achieve the best correlation between the observed and 

simulated historic water levels. In the first period 

(1940-60), the return flow was adjusted such that net 

withdrawal (total pumpage minus return flow) was 

equal to 90 percent of the estimated irrigation requirement. In the second simulation period (1960-80), the 

best correlation between observed and simulated water 

levels again occurred when net withdrawal was 90 percent of the estimated irrigation requirement.

In the 1960-80 simulation, 2 in./yr of additional recharge were added to all irrigated land. The additional 

recharge represents about 1.0 million acre-ft of water 

per year. The additional recharge from 1960 to 1980 

could be attributed to a broad area of the southern 

High Plains where the playas were full of water and 

water was standing in fields in 1970. The additional recharge could have been added at twice the rate during 

only the last one-half of the second simulation period, 

and such a simulation would produce nearly identical 

results. The mean difference between the observed and 

simulated water levels during the first simulation 

period was -0.22 ft and the simulated change in storage was 19 percent less than the observed change in 

storage. The difference between the observed and 

simulated water levels for the second period was +0.28 

ft and the simulated change in storage was 2 percent 

more than the observed change in storage. The combined simulated change in storage for the two periods 

(1940 to 1980) was 7 percent less than the observed 

change in storage (table 8).

The central High Plains was developed for irrigation 

more recently than the southern High Plains. By the 

1950's, only relatively small areas had been significantly 

disturbed from the predevelopment condition. Only one 

development-calibration period, 1950-80, was used for 

the central High Plains model. Return flow from irrigation was varied to achieve the best correlation between 

observed and simulated water-level changes and calibration was obtained when return flow was adjusted 

such that net withdrawal equaled 100 percent of the 

irrigation requirement. On a volumetric basis, the 

simulated water-level changes were 9 percent less than 

the observed changes. On an areal basis, the simulated 

water-level changes were 6 percent more than the observed changes. The simulated change in storage was 

9 percent more than the observed change in storage.

The northern High Plains has the shortest history 

of development of the three areas of the High Plains. 

Even by 1960, most of the northern High Plains had 

undergone little development for irrigation and by 1980 

major parts of the area still were undeveloped. Only

one development-calibration period, 1960-80, was simulated for the northern High Plains aquifer. Return flow 

from irrigation was varied during the calibration process and the best correlation between observed and 

simulated water-level changes was achieved when return flow was adjusted so that net withdrawal equaled 

100 percent of the irrigation requirement. Unlike the 

other two areas of the High Plains, other stresses besides pumpage and return flow were significant in the 

development-period model of the northern High Plains 

aquifer. These stresses include: (1) Canal and reservoir 

leakage; (2) increased recharge due to dryland cultivation; (3) return flow from surface-water irrigation; and 

(4) additional recharge east of 100° longitude. These additional stresses due to human activities (47.0 million 

acre-ft) and the return flow from ground-water irrigation (37.5 million acre-ft) in large part balanced the 

105.0 million acre-ft of water pumped between 1960 and 

1980. Hence, although large stresses have occurred, the 

net overall change in storage was small. The simulated 

net decrease in storage was 15 million acre-ft and the 

observed decrease in storage was 6 million acre-ft.

A sensitivity analysis was performed on the High 

Plains models to determine how errors in model parameters affect the simulation results. The sensitivity analysis for the predevelopment-period models indicated 

that the models were about equally sensitive to changes 

in recharge or changes in hydraulic conductivity. The 

analysis further indicated that these two model inputs 

are highly interrelated and as long as the two were 

in balance, the models will have a small mean waterlevel residual. Hence, the models could be used to accurately determine the recharge rate if the hydraulic conductivity is accurately known. The development-period 

models were sensitive to changes in net withrawal and 

specific yield and insensitive to changes in hydraulic 

conductivity. Specific yield and net withdrawal also are 

highly interrelated and, one cannot be determined with 

acceptable certainty through model analyses unless the 

other is accurately known.

Although the calibrations for each of the areas of the 

High Plains were done separately, the increased understanding of the system in one area contributes to the 

understanding of the other areas. Certain similarities 

between the models of the three areas were noted. In 

the predevelopment-period calibrations, the estimated 

predevelopment recharge rate, although somewhat variable within and among areas, was uniformly small outside of the sandy soils in the sand-dune areas. In the 

development-period calibrations, the difference between total pumpage and return flow for all areas was 

close to the estimated irrigation requirement. Other 

similarities between the models exist but were not as
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 55

apparent as those already mentioned. Two such possible similarities are worth noting, although sufficient 

data were not available to pursue them further.

In the central High Plains model, the estimated hydraulic conductivity was decreased in the area where 

the bedrock was disturbed by dissolution of salts in the 

Permian age rocks. The simulated predevelopment 

water levels in the southern High Plains model were 

in error in a similar environment. If the estimated hydraulic conductivity in the extreme northern part of the 

southern High Plains had been decreased in a manner 

similar to that in the central High Plains model, the 

simulated water levels would better correlate with the 

observed water levels. The same phenomenon also 

might have occurred in the southwestern part of the 

southern High Plains.

There is a similarity between the additional recharge 

that was added to the development-period models of 

both the southern High Plains and the northern High 

Plains during 1960-80. In the southern High Plains 

model, the additional recharge was 2 in./yr throughout 

the irrigated area. In the northern High Plains model, 

the additional recharge was 5 in./yr east of 100° longitude and south of 41° latitude, and 2.5 in./yr east of 

100° longitude and north of 41° latitude. The increase 

in recharge in the southern High Plains is thought to 

be due to playas full of water and water standing in 

fields in 1970 but the source of the increase in recharge 

in the northern High Plains remains unknown. Whether 

the additional recharge required in the southern High 

Plains model was related in any way to the additional 

recharge required in the northern High Plains model 

is not known.

The results of the predevelopment-period calibrations 

for each of the three areas of the High Plains were 

used as the initial conditions for the developmentperiod calibration. Likewise, the calibrated development-period models for the southern, central, and 

northern High Plains described in this report can be 

used as the initial conditions for evaluating future 

water levels in the High Plains.

REFERENCES CITED

Bennett, G. D., 1979, The U.S. Geological Survey Regional AquiferSystem Analysis Program in relation to the drought of the 1970's 

[abs.]: American Geophysical Union Transactions, v. 60, no. 18, 

p. 250.

Bentall Ray, and Shaffer, F. B., 1979, Availability and use of water 

in Nebraska, 1975: Conservation and Survey Division, Institute 

of Agriculture and Natural Resources, University of NebraskaLincoln, Nebraska Water Survey Paper 48, 121 p.

Cady, R. E., and Ginsberg, M. H., 1979, Interpretive study and 

numerical model of the hydrogeology, Upper Big Blue Natural 

Resources District: Conservation and Survey Division, Institute 

of Agriculture and Natural Resources, University of NebraskaLincoln, 185 p.

Cobb, P. M., Colarullo, S. J., and Heidari, Manoutchehr, 1983, A 

ground water flow model for the Great Bend aquifer, south-central Kansas: Kansas Geological Survey Open-File Report 83-20, 

220 p.

Grist, M. A., 1975, Hydrologic analysis of the valley-fill aquifer, 

North Platte River valley, Goshen County, Wyoming: U.S. 

Geological Survey Water-Resources Investigations 3-75, 60 p.

 1977, Hydrologic evaluation of the Arkaree Formation near 

Lusk, Niobrara and Goshen Counties, Wyoming: U.S. Geological 

Survey Water-Resources Investigations 77-111, 23 p. 

-1980, Effect of pumpage on ground-water levels as modeled

in Laramie County, Wyoming: U.S. Geological Survey WaterResources Investigations 80-1104, 26 p.

Dunlap, L. E., Kume, Jack, and Thomas, J. G., 1980, Geohydrology 

and model analysis for water-supply management in a small area 

of west-central Kansas: U.S. Geological Survey Water-Resources 

Investigations 80-91, 59 p.

Dunlap, L. E., Lindgren, R. J., and Sauer, C. G., 1984, Geohydrology and model analysis of stream-aquifer system along the Arkansas River in Kearney and Finney Counties, southwestern 

Kansas: U.S. Geological Survey Water-Supply Paper 2253, (52 

p.).

Emery, P. A., 1966, Use of analog model to predict streamflow depletion, Big and Little Blue River basin, Nebraska: Ground Water, 

v. 4, no. 4, p. 13-19.

Emmett, L. F., Skelton, John, Luckey, R. R., Miller, D. E., 

Thompson, T. L., and Whitfield, J. W., 1978, Water resources 

and geology of the Springfield area, Missouri: Missouri Division 

of Geology and Land Survey Water Resources Report 34, 150

PFader, S. W., and Stullken, L. E., 1978, Geohydrology of the Great 

Bend Prairie, south-central Kansas: Kansas Geological Survey 

Irrigation Series 4, 19 p.

Finch, W. I., and Wright, J. C., 1970, Linear features and groundwater distribution in the Ogallala Formation of the southern 

High Plains, in Mattox, R. B., and Miller, W. D., eds., Ogallala 

Aquifer Symposium: Texas Tech University, Lubbock, 1970, International Center for Arid and Semi-arid Land Studies Special 

Report 39, p. 49-57.

Gutentag, E. D., Heimes, F. J., Krothe, N. C., Luckey, R. R., and 

Weeks, J. B., 1984, Geohydrology of the High Plains aquifer 

in parts of Colorado, Kansas, Nebraska, New Mexico, Oklahoma, 

South Dakota, Texas, and Wyoming: U.S. Geological Survey 

Professional Paper 1400-B, 63 p.

Gutentag, E. D., Lobmeyer, D. E., and Skgle, S. E., 1981, Geohydrology of southwestern Kansas: Kansas Geological Survey Irrigation Series 7, 73 p.

Gutentag, E. D., and Weeks, J. B., 1981, Evaluating vertical variability of transmissivity and specific yield for the High Plains regional aquifer system [abs.]: Geological Society of America 

Abstracts with Programs, Rocky Mountain Section, v. 13, no. 

4, p. 199.

Havens, J. S., and Christensen, S. C., 1983, Numerical simulation 

of the High Plains regional aquifer, northwestern Oklahoma: 

U.S. Geological Survey Water-Resources Investigations Report 

83-4269, 27 p.
56 REGIONAL AQUIFER-SYSTEM ANALYSIS

Heimes, F. J., and Luckey, R. R., 1982, Method for estimating historical irrigation requirements from ground water in the High 

Plains in parts of Colorado, Kansas, Nebraska, New Mexico, Oklahoma, South Dakota, Texas, and Wyoming: U.S. Geological 

Survey Water-Resources Investigations 82-40, 64 p.

 1983, Estimating 1980 ground-water pumpage for irrigation on 

the High Plains in parts of Colorado, Kansas, Nebraska, New 

Mexico, Oklahoma, South Dakota, Texas, and Wyoming: U.S. 

Geological Survey Water-Resources Investigations 83-4123, 36 

P.

Hoxie, D. T., 1977, Digital model of the Arikaree aquifer near 

Wheatland, southeastern Wyoming: U.S. Geological Survey 

Open-File Report 77-676, 54 p.

 1979, Results of transient simulations of a digital model of the 

Arikaree aquifer near Wheatland, southeastern Wyoming: U.S. 

Geological Survey Open-File Report 79-1280, 17 p.

Huntoon, P. W., 1974, Predicted water-level declines for alternative 

ground-water developments in the upper Big Blue River basin, 

Nebraska: Conservation and Survey Division, Institute of Agricultural and Natural Resources, University of Nebraska-Lincoln, Resource Report 6, 106 p.

Johnson, M. S., and Pederson, D. T., 1982, Ground-water levels in 

Nebraska 1981: Conservation and Survey Division, Institute of 

Agriculture and Natural Resource, University of Nebraska-Lincoln, Nebraska Water Survey Paper 52, 65 p.

Kapple, G. W., Luckey, R. R., and Hofstra, W. E., 1976, Digital 

ground-water model of the Ogallala aquifer in parts of 

Washington and Yuma Counties, northern High Plains of Colorado: Colorado Water Conservation Board Water-Resources 

Circular 34, 25 p.

 1977, Digital ground-water model of the Ogallala aquifer in 

parts of Cheyenne and Kiowa Counties, northern High Plains 

of Colorado: Colorado Water Conservation Board WaterResources Circular 35, 20 p.

Knowles, Tommy, Nordstrom, Phillip, and Klemt, W. B., 1982, 

Evaluating the ground-water resources of the High Plains of 

Texas: Texas Department of Water Resources Final Report 

LP-173, v. 1, 174 p.

Kolm, K. E., and Case, H. L., Ill, 1983, A two-dimensional, finitedifference model of the High Plains aquifer in southern South 

Dakota: U.S. Geological Survey Water-Resources Investigations 

Report 83-1175, 34 p.

Krothe, N. C., Oliver, J. W., and Weeks, J. B., 1982, Dissolved 

solids and sodium in water from the High Plains aquifer in parts 

of Colorado, Kansas, Nebraska, New Mexico, Oklahoma, South 

Dakota, Texas, and Wyoming: U.S. Geological Survey Hydrologic Investigations Atlas HA-658.

Lappala, E. G., 1978, Quantitative hydrogeology of the Upper Republican Natural Resources District, southwest Nebraska: U.S. 

Geological Survey Water-Resources Investigations 78-38, 200 p.

Lappala, E. G., Emery, P. A., and Otradovsky, F. J., 1979, Simulated changes in ground-water levels and streamflow resulting 

from future development (1970-2020) in the Platte River basin, 

Nebraska: U.S. Geological Survey Water-Resources Investigations 79-26, 82 p.

Larson, S. P., 1978, Direct solution algorithm for the two-dimensional 

ground-water flow model: U.S. Geological Survey Open-File Report 79-202, 25 p.

Lindner-Lunsford, J. B., and Borman, R. G., 1984, Potential well 

yields from the Ogallala aquifer in the northern High Plains of 

Colorado: U.S. Geological Survey Hydrologic Investigations 

Atlas HA-685.

Lohman, S. W., 1972, Ground-water hydraulics: U.S. Geological Survey Professional Paper 708, 70 p.

Luckey, R. R., Gutentag, E. D., and Weeks, J. B., 1981, Water-level 

and saturated-thickness changes, predevelopment to 1980, in the 

High Plains aquifer in parts of Colorado, Kansas, Nebraska, New 

Mexico, Oklahoma, South Dakota, Texas, and Wyoming: U.S. 

Geological Survey Hydrologic Investigations Atlas HA-652.

Luckey, R. R., and Hofstra, W. E., 1973a, Digital model of the hydrologic system, northern High Plains of Colorado A preliminary report: Colorado Water Conservation Board Water-Resources Circular 19, 40 p. 

 1973b, Digital model of the hydrologic system of the northern

part of the northern High Plains of Colorado: Colorado Water 

Conservation Board Water-Resources Circular 24, 22 p. 

McAda, D. P., 1984, Mathematical model of the Ogallala aquifer in 

Lea County, New Mexico: U.S. Geological Survey Water-Resources Investigations 84-4062, 84 p.

Morton, R. B., 1980, Digital-model projection of saturated thickness 

and recoverable water in the Ogallala aquifer, Texas County, 

Oklahoma: U.S. Geological Survey Open-File Report 79-565, 

34 p.

Newport, T. G., 1959, Ground-water resources of the lower Niobrara 

River and Ponca Creek basins, Nebraska and South Dakota, with 

a section on Chemical quality of the water by R. A. Krieger: 

U.S. Geological Survey Water-Supply Paper 1460-G, p. 273-^323.

Ogilbee, W., 1962, Ground-water resources of Haskell and Knox 

Counties, Texas: Texas Water Commission Bulletin 6209, 174 p.

Pettijohn, R. A., and Chen, H. H., 1984, Hydrologic analysis of the 

High Plains aquifer system in Box Butte County, Nebraska: U.S. 

Geological Survey Water-Resources Investigations Report 84- 

4046, 54 p.

Reddell, D. L., 1967, Distribution of ground-water recharge: Colorado State University, Agricultural Engineering Department 

Technical Report, 132 p.

Sniegocki, R. T., 1959, Geologic and ground-water reconnaissance of 

the Loup River drainage basin, Nebraska, with a section on 

Chemical quality of the water, by R. H. Langford: U.S. Geological Survey Water-Supply Paper 1493, 106 p.

Texas Department of Water Resources, 1981, Inventories of irrigation in Texas 1958, 1964, 1969, 1974, and 1979: Texas Department of Water Resources Report 263, 295 p.

Trescott, P. C., 1975, Documentation of finite-difference model for 

simulation of three-dimensional ground-water flow: U.S. Geological Survey Open-File Report 75-438, 108 p.

Trescott, P. C., Pinder, G. F., and Larson, S. P., 1976, Finite-difference model for aquifer simulation in two dimensions with results 

of numerical experiments: U.S. Geological Survey Techniques of 

Water Resources Investigations, Book 7, Chapter Cl, 115 p.

U.S. Department of Agriculture, 1967, Irrigation water requirements: Soil Conservation Service, Engineering Division, Technical Release 21, 88 p.

U.S. Enviromental Protection Agency, 1976, National interim primary drinking water regulations: Office of Water Supply, EPA570/9-76-003, 159 p.

 1977, National secondary drinking water regulations: Federal 

Register, v. 42, no. 62, Thursday, March 31, 1977, Part I, p. 

17143-17147.
DIGITAL SIMULATION OF GROUND-WATER FLOW OF THE HIGH PLAINS AQUIFER 57

Weeks, J. B., 1978, Plan of study for the High Plains regional 

aquifer-system analysis in parts of Colorado, Kansas, Nebraska, 

New Mexico, Oklahoma, South Dakota, Texas, and Wyoming: 

U.S. Geological Survey Water-Resources Investigations 78-70, 

28 p.

Weeks, J. B., and Gutentag, E. D., 1981, Bedrock geology, altitude 

of base, and 1980 saturated thickness of the High Plains aquifer 

in parts of Colorado, Kansas, Nebraska, New Mexico, Oklahoma, 

South Dakota, Texas, and Wyoming: U.S. Geological Survey Hydrologic Investigations Atlas HA-648.

Wendorf, Fred, 1970, The Lubbock subpluvial, in Dort, Wakefield, 

Jr., and Jones, J. K., Jr., eds., Pliestocene and recent environments of the central Great Plains: University of Kansas, Department of Geology Special Publication 3, p. 23-35.

White, W. M., Broadhurst, W. L., and Lang, J. W., 1940, Ground 

water in the High Plains in Texas: Texas State Board of Water 

Engineers, 56 p.

Winter, T. C., 1976, Numerical simulation analysis of the interaction 

of lakes and ground water: U.S. Geological Survey Professional 

Paper 1001, 45 p.

U.S. GOVERNMENT PRINTING OFFICE: 1986 773-047/46,008 REGION NO. 8