Electrical-Analog Analysis 

of Ground-Water Depletion 

in Central Arizona

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1860
Electrical Analog Analysis 

of Ground-Water Depletion 

in Central Arizona

By T. W. ANDERSON

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1860

An electrical model of the hydrologic system 

indicates probable water-table conditions 

in 1974 and 1984

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1968
UNITED STATES DEPARTMENT OF THE INTEPIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

William T. Pecora, Director

Library of Congess catalog-card No. GS 68-235

For sale by the Superintendent of Documents, U.S. Government PriTtmg Office 

Washington, D.C. 20402
CONTENTS

Page

Abstract _______________________-_ _ 1

Introduction _________ -_ 2

Purpose and scope of investigation ________ 3

Physical and geologic setting ___________ , 4

Hydrologic system __________________________ - 5

Predevelopment conditions _______________-- _ 5

Postdevelopment conditions _____________________ - 7

Aquifer characteristics ___________________ _ - 9

Electrical system _________ . ___________ - 10

Model construction _________________________ _ 12

Generalizations and limitations ____________ _ 14

Original model design __________________________ _ 16

Final model design _____________________________ 17

Future ground-water conditions - ____________________ 18

Summary and conclusions ___________________________ 20

References cited ___________________________________ 21

ILLUSTRATIONS

[Plates are in pocket]

PLATES 1-4. Maps showing 

1. Altitude of the water table and water-level 

declines in central Arizona.

2. Transmissibility and pumpage in central Arizor a.

3. Depth to water, spring 1964, in central Arizona.

4. Predicted depths to water in central Arizona. 

FIGURE 1. Map showing area of report and Arizona's water

provinces ____-_-____________________________

2. Graph showing annual water use, 1923-64 __________

3. Photographs of the electrical-analog model __________

4. Graph showing method of generalizing pumpage

data for model input ____________________________

Page

2

7

12

15 

ill
ELECTRICAL-ANALOG ANALYSIS OF GROUND-WATER 

DEPLETION IN CENTRAL ARIZONA

BY T. W. ANDERSON

Abstract

The Salt River Valley and the lower Santa Cruz River basin are the 

two largest agricultural areas in Arizona. The extensive use of ground 

water for irrigation has resulted in the need for a thorough appraisal of 

the present and future ground-water resources. The ground-water reservoir provides 80 percent (3.2 million acre-feet) of the total annual water 

supply. The amount of water pumped greatly exceeds the rate at which 

the ground-water supply is being replenished and has resulted in waterlevel declines of as much as 20 feet per year in some places. The depletion problem is of economic importance because ground water will become 

more expensive as pumping lifts increase and well yields decrease.

The use of electrical-analog modeling techniques has made it possible 

to predict future ground-water levels under conditions of continued withdrawal in excess of the rate of replenishment. The electrical system is a 

representation of the hydrologic system: resistors and capacitors represent transmissibility and storage coefficients. The analogy between the 

two systems is accepted when the data obtained from the model closely 

match the field data in this instance, measured water-level change since 

1923. The prediction of future water-table conditions is accomplished by a 

simple extension of the pumping trends to determine the resultant effect 

on the regional water levels.

The results of this study indicate the probable depths to water in central 

Arizona in 1974 and 1984 if the aquifer characteristics are accurately 

modeled and if withdrawal of ground water continues at the same rate 

and under the same areal distribution as existed between 1958 and 1964. 

The greatest depths to water in 1984 will be more than 700 feet near 

Stanfield and more than 650 feet in Peer Valley and northeast of Gilbert. 

South of Eloy and northwest of Litchfield Park, a static water level of more 

than 550 feet is predicted. The total water-level decline in the 20-year 

period 1964-84 at the deepest points of the major cones of depression 

will range from 150 to 300 feet, and the average decline in the entire central Arizona area will be about 100 feet.
2 ANALYSIS, GROUND-WATER DEPLETION, CENTRAL ARIZONA

INTRODUCTION

The extensive use of ground water for irrigation in central 

Arizona (fig. 1) has resulted in the need for appraisals of the 

present and future ground-water resources. The central Arizona 

area consists of 3,500 square miles in western Final and eastern 

Maricopa Counties, of which about 1,250 square miles (800,000 

acres) is under cultivation. The largest irrigated areas in the 

State are the Salt River Valley and the lower Santa Cruz River 

basin. The agricultural economy is dependent on a reliable source 

of irrigation water.

114 C

112 110°

36"

110

FIGURE 1. Area of report (shaded) and Arizona's water provinces.
INTRODUCTION o

Ground water from more than 4,000 irrigation wells provides 

80 percent of the total water used in central Arizona (White 

and others, 1964, p. 8); this ground water amounts to 3.2 million acre-feet per year, which is greatly in excess of the rate 

at which water is being recharged to the ground-water reservoir. The overdraft from the ground-water reservoir is causing 

the water levels to decline as much as 20 feet per year in some 

places. The ground-water supply may never be exhausted, but if 

the present rates of decline continue, pumping lifts may become 

so great that further use of ground water for agricultural purposes could be uneconomical.

PURPOSE AND SCOPE OF INVESTIGATION

The purpose of the investigation was to analyze the groundwater data by means of an electrical-analog model and to determine the probable future effects of continued ground-wr.ter withdrawal in central Arizona. A model was constructed by using 

the known hydrologic characteristics of the water-bearing rocks 

and the pumping history through 1964. The model electronically 

duplicated the changes that occurred in the aquifer system from 

1923 to 1964 and enabled the prediction of ground-water levels 

for 1974 and 1984 based on the same pumping rate and areal 

distribution that existed in 1964.

The model averaged hydrologic cause-and-effect conditions in 

the upper 1,000 to 1,200 feet of alluvial material. Although alluvial material deeper than 1,200 feet contains ground vater and 

is tapped by wells, the existing data were insufficient for quantitative evaluation and were not included in the model. Data used 

in the construction of the model included measurements of surface-water flow, ground-water pumpage, water levels, ard specific 

capacities of wells and also included estimates of the storage 

capacity of the alluvial material.

The model defined the entire hydrologic system by reconstructing the entire history of ground-water development in the basin. 

It was necessary to analyze the aquifer characteristics in order 

to establish numerical values for the transmissibility ard storage 

coefficients of the system. These data were then converted to a 

conceptual design of the system in the form of an analog model, 

which, after its similitude to the actual system was proved, 

could be used as a hydrologic tool to predict future water-level 

conditions; future uses of the model may include aralyses of 

well-field management problems or the effects of artificial recharge on the regional water levels.
4 ANALYSIS, GROUND-WATER DEPLETION, CENTRAL ARIZONA

PHYSICAL AND GEOLOGIC SETTING

The central Arizona area is in the north part of the arid to 

semiarid Basin and Range Lowlands province of Arizona. Rainfall 

averages about 8 inches per year and, except for unusual floods, 

most of the streambeds are dry. In the area is th^ junction of 

three major rivers the Salt, Gila, and Santa Cruz, The rivers 

drain large areas and flow southwestward to the Colorado River. 

The Salt River and its tributary, the Verde River, drain the less 

arid Central Highlands province, which is north of the central 

Arizona area. The Gila and Santa Cruz Rivers drain southeastern 

Arizona, which is mainly in the Basin and Range Lowlands province. The Salt and Gila Rivers rarely carry surface flow, either 

because of dams or because of the lack of precipitation. The 

Santa Cruz River, although unchecked by dams, also rarely carries surface flow.

Central Arizona is characterized by low mountains surrounded 

by very broad flat-lying valleys or basins. The mountains, which 

are composed mainly of impermeable crystalline rocks with 

minor amounts of sedimentary rocks, form physical boundaries 

to surface-water drainage and hydrologic boundaries to groundwater flow. The valleys are underlain by thousands of feet of 

unconsolidated to consolidated alluvial deposits, which range in 

size from gravel to clay (Hardt and others, 1964; Hardt and Cattany, 1965; Kam and others, 1966). The alluvium is an aquifer 

and stores large quantities of water that may be removed by wells. 

Hardt, Cattany, and Kister (1964, p. 6) divided the alluvium into 

an upper sand and gravel unit 0 to 600 feet thick, a middle silt 

and clay unit 0 to 2,000 feet thick, and a lower sand and gravel 

unit 0 to 500 feet thick. In most of central Arizona, the water 

table is in the highly permeable upper sand and gravel unit, and 

most of the water is produced from this unit. The middle silt 

and clay unit is less permeable and yields less water to wells; 

however, the unit does not extend over the entire area. The lower 

sand and gravel unit is more permeable than the medial silt and 

clay unit but is not as productive as the upper sand and gravel 

unit (Hardt and others, 1964, fig. 4).

The information used in this report is mainly from wells that 

tap the uppermost 1,000 to 1,200 feet of alluvium, and the results dominantly reflect or can be used to interpret ground-water 

conditions only in the upper sand and gravel and part of the silt 

and clay units.
ANALYSIS, GROUND-WATER DEPLETION, CENTRAL ARIZONA 5

HYDROLOGIC SYSTEM

In central Arizona, the major part of the hydrologic system 

consists of ground water, which is stored in the very thick and 

permeable alluvium of the broad basin. In 1923, ground water 

flowed slowly northwest and toward the Salt River ard was replenished through recharge from runoff from the three major 

river basins. The ground-water storage and flow systerr has since 

been changed owing to the effects of pumping.

The amount of water that enters the ground-water reservoir 

annually is very small. The water enters the reservoir by seepage from stream channels during surface flow, seepage from 

canals and irrigated land, and underflow from adjacent groundwater basins. When the rate of pumping in an area exceeds the 

rate of replenishment, some water must be taken from storage, 

and the result is a decline of the regional water table. Since the 

early 1920's, pumping has exceeded replenishment in central 

Arizona. Beginning in the early 1940's, pumping was greatly accelerated and within a few years reached a rate many times 

greater than the rate of recharge. Water levels have declined in 

the entire area, and the rate of decline in some places is as much 

as 20 feet per year.

PREDEVELOPMENT CONDITIONS

Prior to 1923, the hydrologic system in central Arizona was 

considered to be about in equilibrium; that is, inflow was equal 

to outflow. The first development of ground water be^an about 

1900 (Lee, 1905). In the Eloy and Maricopa-Stanfield areas in the 

lower Santa Cruz basin, ground-water development was necessary to irrigate the land because of the lack of surface water. 

Development in these areas was sparse, and the amourt of water 

pumped annually was small and did not increase marVedly until 

the early 1940's. West of Phoenix along the Salt Rivev, most of 

the pumping from wells was done to drain land that had become 

waterlogged owing to the application of surface water.

Surface water has been diverted for irrigation alorg the Salt 

and Gila Rivers since the time of the prehistoric Indians. The 

surface-water diversion and distribution systems in use in 1923 

had been constructed in the late 1800's (Skibitzke and others, 

1961). The surface-water resources available for cMstribution 

during the equilibrium period (1923) were much the same as 

they are today.

295-462 0-68-2
6 ANALYSIS, GROUND-WATER DEPLETION, CENTRAL ARIZONA

In 1923 the configuration of the ground-water surface generally conformed to that of the land surface, and the direction of 

flow was at right angles to the contour lines (pi. 1). A general 

view of the ground-water system during the equilibrium period 

would show that water entered the ground-water reservoir by 

infiltration of surface-water flow, seepage from canals and irrigated land, and underflow from adjacent ground-water basins. 

Outflow from the system resulted from pumping, surface runoff 

where ground water discharged to streams, evaporation from 

open water surfaces and shallow ground water, anc1 plant transpiration.

The direction of ground-water flow in the lower Santa Cruz 

basin during the undisturbed conditions was, in general, from 

southeast to northwest. Inflow to the basin occurred along its 

periphery as underflow or infiltration from surface flow in the 

many desert washes entering the valley. Inflow from canal seepage was limited to the Florence-Coolidge-Cas'a Grande area, 

the only area in Final County that had a surface-water distribution system. Outflow from the system occurred as pumpage or 

underflow. The underflow out of the lower Santa Cruz basin into 

the adjacent Salt River Valley occurred near the confluence of 

the Salt and Gila Rivers southwest of Phoenix. There is no absolute division between these two ground-water systems, which 

are hydraulically connected along the course of the Gila River 

from the Santan Mountains to the Sierra Estrella. The division 

of central Arizona into two units is for simplicity cf discussion 

and does not mean that the units represent separate entities in 

the ground-water system.

In the Salt River Valley, ground-water flow was generally from 

east to west. Inflow occurred along the periphery of the valley 

and as infiltration in streambeds during surface flow. Groundwater inflow in this part of the area also resulted from canal 

and irrigation seepage, as indicated by the fact that part of the 

land was becoming waterlogged prior to and during the equilibrium period (1923) selected as the base period for this study. 

The area where true equilibrium conditions did not exist because 

of this waterlogging was relatively small and is considered negligible in its effect on the entire system. The waterlogged area 

was along the Salt River above its confluence with the Gila and 

extended downstream along the Gila for several miles. In 1923 

the Gila River was a gaining stream in this area and represented 

one of the methods of outflow from the ground-w^ter system
HYDROLOGIC SYSTEM 7

(Thomas and others, 1963, p. 46). The shallow water-table area 

also represented a source of discharge from the system through 

direct evaporation from the shallow water table and through 

plant transpiration.

POSTDEVELOPMENT CONDITIONS

Since 1923 the ground-water system has been developed extensively in central Arizona. The surface-water resources were 

already being fully utilized and continue to provide an important 

source of irrigation water for a part of the area. Except for 

floodwater, all the flow in the Gila-Salt Rivers system is diverted for irrigation. The increasing water requirements of an 

expanding agricultural economy have been met by the groundwater supply (fig. 2). The withdrawal of ground water to meet 

the increasing needs of agriculture caused the rapidly declining 

water levels.

From spring 1923 to spring 1964, the water levels declined as 

much as 360 feet in central Arizona (pi. 1). In the lower Santa 

Cruz basin the water-level declines ranged from 0 near Casa 

Grande to as much as 340 feet in the large cone of depression 

near Stanfield (pi. 1). A similar cone exists around Eloy; here

5.0 

FIGURE 2. Annual water use, 1923-64.
8 ANALYSIS, GROUND-WATER DEPLETION, CENTRAL ARIZONA

the maximum water-level decline was only 200 feet, but it extends over a much larger area. In the Salt River Valley there 

are three large cones of depression northeast of Gilbert, in Deer 

Valley northwest of Phoenix, and northwest of Litchfield Park. 

The largest is northeast of Gilbert where the maximum decline 

was 360 feet. The water level in Deer Valley declined as much 

as 300 feet, and northwest of Litchfield Park the maximum 

decline was about 250 feet. The average decline for the entire 

central Arizona area is about 140 feet.

The annual withdrawal of ground water from the Salt River 

Valley and the lower Santa Cruz River basin increased from about 

450,000 acre-feet in 1923 to 3,700,000 acre-feet in 1953 (fig. 2). 

In 1964 the annual withdrawal of ground water was about 3,200,- 

000 acre-feet, of which about 2,200,000 acre-feet was from the 

Salt River Valley and 1,000,000 acre-feet was from the lower 

Santa Cruz basin. The total volume of water pumped in central 

Arizona from 1923 through 1964 was 80 million acre-feet.

The large withdrawal from the ground-water reservoir has 

changed the regional flow pattern from a relatively uniform undisturbed state to a series of individual systems, each one located 

at a relative center of pumping (pi. 1). In places, the gradient 

was reversed after ground-water development, and the water now 

moves in the opposite direction. A general regional flow pattern 

no longer exists, and the flow is directed radially toward the 

center of the large cones of depression.

Increased pumping from the ground-water reservoir has resulted in less natural discharge. The Gila River no longer flows 

as it once did in the reach downstream from its confluence with 

the Salt. Because the regional water table has declined in this 

reach, the amount of water lost to evapotranspiration is less than 

when the area was waterlogged. It also is possible that some small 

change h?.s occurred in the amount of underflow entering the 

system between 1923 and 1964; however, the change is small 

enough to be considered negligible.

All the factors that affect the ground-water system must be 

considered in an analog-model study, and all changes in stress on 

the system that have occurred since the assumed steady-state 

time (1923) must be included in the model. The stresses that 

existed during steady-state time were not included in the model 

because they were not causing depletion of the ground-water supply. Increased pumping that resulted in water-level declines and 

other major changes in the regional flow system, such as reduced
HYDROLOGIC SYSTEM 9

evapotranspiration and changes in recharge, are simulated in 

the model.

AQUIFER CHARACTERISTICS

The aquifer system can be denned in terms of two parameters 

 the coefficient of transmissibility and the coefficient of storage. 

The coefficient of transmissibility has been defined ty Ferris, 

Knowles, Brown, and Stallman (1962, p. 72-73) as the rate of 

flow of water, in gallons per day, through a vertical st~ip of the 

aquifer 1 foot wide extending the full saturated height of the 

aquifer under a hydraulic gradient of 100 percent. A map of the 

regional transmissibility pattern must be prepared before it is 

possible to utilize the analog techniques. The map provides the 

basis for the construction of an electrical-resistor network analogous to the aquifer system. The ideal means of developing a 

quantitative pattern of regional transmissibility is provided by 

aquifer tests; however, this means was not used in this study 

because sufficient aquifer-test data were not available. The only 

data available in sufficient quantity that were a function of 

aquifer characteristics were values of specific capacity. Specific 

capacity is the yield of a well, in gallons per minute, divided by 

the pumping drawdown in the well, in feet. Discharge and drawdown data have been collected in central Arizona by personnel 

of the U.S. Geological Survey, irrigation districts, r.nd pump 

companies for many years.

The method of converting specific-capacity data to values of 

transmissibility is based on the work of Thomasson, Olmsted, 

and LeRoux (1960), who computed a coefficient of proportionality ranging from 1,460 to 1,990 for similar alluvial deposits in 

Solano County, Calif. This method was applied to several sites of 

known transmissibility in the Salt River Valley, and the average 

coefficient of proportionality was computed to be about 2,000. 

The specific-capacity data used are dependent on the construction 

and performance characteristics of the wells and on the aquifer 

characteristics. In order to use the same relating coefficient for 

the entire area, the assumption was made that the entrance losses 

were fairly consistent throughout the area.

Using the empirical relation between specific capacity and 

transmissibility, an approximate areal pattern of transmissibility ranging from 10,000 to 200,000 gallons per day per foot was 

determined for central Arizona (pi. 2). Plate 2 is a general representation of the areal pattern of transmissibility for only the
10 ANALYSIS, GROUND-WATER DEPLETION, CENTRAL ARIZONA

upper 1,000 to 1,200 feet of alluvial material, as the wells from 

which specific-capacity data were obtained penetrated less than 

1,200 feet. The accuracy of the map is limited by the inherent 

restrictions of the method used to determine the transmissibility. 

The storage coefficient of an aquifer has been defired by Ferris, 

Knowles, Brown, and Stallman (1962, p. 74) as the volume of 

water it releases from or takes into storage per unit surface area 

of the aquifer per unit change in the component of head normal 

to that surface. Storage coefficients have been computed for large 

areas in central Arizona based on the ratio of a known volume 

of pumpage to a known volume of sediments dewatered by that 

amount of pumpage. The average coefficients of storage for these 

areas range from 15 to 20 percent. These calculations provided 

the basis for the storage-coefficient values used in the electricalanalog model. A storage coefficient of 19 percent was used, except where further refinement based on known subsurface characteristics was possible.

ELECTRICAL SYSTEM

The resistor-capacitor network is the basic element in the 

analysis of a ground-water system by electrical-analog methods. 

The network is simply a scaledown electrical version of the actual 

ground-water system and is analogous to the ground-water system in shape and aquifer characteristics. The resistors are analogous to the energy-dissipation characteristics of the rock 

matrix through which the ground water flows, and their value is 

inversely proportional to the transmissibility. Capacitors store 

electrical energy in a manner that is analogous to the storage 

of ground water in the pore spaces of the aquifer. The capacitor 

values are directly proportional to the storage coefficient of the 

aquifer.
ELECTRICAL SYSTEM 11

The stress imposed on the aquifer system by the withdrawal 

of ground water is simulated electrically by the withdrawal of 

electric current. The change in voltage that occurs on the model 

as a result of the current withdrawal is analogous to the change 

in water levels that occurs when ground water is pumped. Voltage and current in the electrical system are equivalent to the 

head and volume rate of flow in the ground-water system. The 

analogous units of the electrical and hydrologic systems are as 

follows:

Hydrologic system Electrical system

Transmissibility, in gallons per day

per foot __________ _ _ Electrical resistance, in ohms. 

Storage coefficient ______ ___ Electrical capacitance, in farads. 

Pressure or head of water, in feet__ Voltage potential, in volts. 

Time, in years __ _ Time, in microseconds. 

Volume of water, in gallons _____ Coulombs of electrical charge.

The response of the model to the simulated pumping stress is 

shown on an oscilloscope in the form of a hydrograph. Thus, 

the oscilloscope acts as a water-stage recorder, which continually 

measures the water level in an observation well. The horizontal 

scale of the hydrograph is in time units, and the vertical scale is 

in voltage. By the application of appropriate constants, voltage 

is converted to feet of water-level change. By measuring with the 

oscilloscope at different points, it is possible to prepare a contour 

map of water-level changes caused by a specific stress applied 

for any specific length of time. The maps prepared from the 

model data are compared with maps showing water-level changes 

measured in wells. If the maps are similar, it can be assumed 

that the conceptual design of the model is reasonably correct.
12 ANALYSIS, GROUND-WATER DEPLETION, CENTRAL ARIZONA

MODEL CONSTRUCTION

To construct an electrical-analog model that properly represents the real ground-water system, it is necessary to define the 

real system in terms of transmissibility, storage coefficient, 

amount of pumping, distribution of wells, and the historical 

pumping pattern. It is also necessary to make certain generalizations that tend to simplify the overall picture and the construction of the model. Robinove (1962) gives a general description 

of the required data and procedures for the construction of an 

electrical-analog model.

The electrical-analog model for central Arizona was constructed on a scale of 1 inch equals 1 mile. The scale was governed by the size limitations of the model and the accuracy of 

the available data. Resistor junctions were placed at 1-inch intervals. Because each resistor in the network represents the resistance to flow of a specific part of the aquifer, local variations in 

transmissibility can be simulated by changing the value of a 

resistor. The transmissibility this resistor represents is the averA 

FIGURE 3. Electrical-analog model. A, Front view. B, Back view.
ELECTRICAL SYSTEM 13

age value for the upper part of the aquifer to a maximum depth 

of about 1,200 feet.

A front view of the model and the required electronic apparatus are shown in figure 3A. The resistor grid is superimposed 

on the base map, and the dark areas indicate the land under cultivation. Figure 3# shows the reverse side of the model with 

the pumpage-programming board attached. The board consists 

of a half-scale map, and the pumping centers are represented by 

the black junctions. Additional resistors on the back of this 

board control the amount of current withdrawn from the analog 

system. Five time periods are used in the model 1923-37, 1937- 

42, 1942-52, 1952-58, and 1958-64. The pumpage for a given 

period was assumed to occur at a constant annual rate, and the 

break between periods was made at a time when there was a 

significant change in pumping in some part of the area. Each 

resistor simulates the average amount of ground water withdrawn annually from a 4-square-mile area for a certain time 

period. Thus, the entire pumping history for 1923-64 and the

FIGURE 3. Continued.
14 ANALYSIS, GROUND-WATER DEPLETION, CENTRAL ARIZONA

predicted pumping regimen for 1964-84 are duplicated electronically on the board.

GENERALIZATIONS AND LIMITATIONS

The model is a generalization of the real hydrologic system. 

The averaging and generalizing techniques used in the construction of the model were designed to remove some of the extreme 

complexities from the hydrologic system. These techniques by 

no means degrade the analysis but serve to keep it within the 

realm of accuracy of the basic data used to design the model 

and the electrical components used in its construction.

The most important generalization probably was the modeling in two dimensions of a system that is variable in three dimensions. As previously described, the ground-water aquifer is 

made up of three units or layers of material having very different 

hydraulic characteristics. The lowering of the water table and 

the dewatering of the upper unit will result in greater pumping 

stresses being imposed on the underlying units. Because the underlying units generally yield less water, the reaction of the system to constant pumping will change with time and water-table 

decline. Two possible changes in the system will result: either 

the rate of water-table decline will increase or the amount of 

water pumped will decrease. In either instance, the assumption 

of uniform transmissibility and storage coefficients for the upper 

1,200 feet of the aquifer may be seriously in error where more 

than one unit supplies water to wells. At the present time (1964), 

there are only a few small areas where the middle clay unit is 

causing the aquifer characteristics to change with time. In the 

next 20 years, these areas will expand, but the growth will be 

small compared to the entire central Arizona area. The primary 

limitation that this factor places on the analog model is the 

length of time to which the data may be extended to predict 

future conditions.

Another generalization made in the construction of the model 

is the method of simulating pumpage. The average annual pumpage, by township, was modeled without considering any variations that occur during the year as a function of the growing 

season. The pumpage input to the model system for each township for 1923-64 is shown on plate 2. The pumpage figures were 

based on well records from irrigation districts and electric and 

gas companies for private wells. Figure 4 shows the method used
ELECTRICAL SYSTEM 15

100

90

80

70

W 60 

Q

Z

< 50

40

30

20

0- 10 hTT

Average annual rate 

of pumping

com o in o in o in Q * CMCM ro ro * ^ m m $ *

CTiCT* CTi CTi CTi CTi CTi CTi CJ> CTi

FIGURE 4. Method of generalizing pumpage data for model input for one

township.

for determining the average annual rates of pumping1 for the 

time periods used in constructing the model. For model simulation, the pumpage by township was further divided into 4-squaremile units.

The generalizations of aquifer and pumping conditions were 

necessary because of the data and time available for this study. 

Limitations are placed on the accuracy of the results by these 

generalizations; however, the model is sufficiently accurate to 

serve as a useful tool for determining how the system may react 

to a change in a particular stress. Changes in the system or 

stresses on the system may be programmed into the aralog system to determine the new reaction. Therefore, the mod^l can be 

used to predict changes in the water level for a reasonable time 

in the future under present water-use practices, or it can be used 

to predict changes that might occur under different changes that 

might be anticipated in the water-use system. One of the major 

advantages of an electrical-analog model is that it can be modified simply as additional data are obtained.
16 ANALYSIS, GROUND-WATER DEPLETION, CENTRAL ARIZONA

ORIGINAL MODEL DESIGN

After the original analog model had been designed, it was recognized that some changes might be necessary in order to make 

the conceptual design more accurately simulate the field conditions. Transmissibility, storage coefficients, and pumpage are the 

three parameters in the model system, and if these parameters 

are reasonably accurate in simulating the hydrolog; c conditions, 

the outputs of both systems should be similar.

The transmissibility values are inversely proportional to the 

resistor values, and the smaller the resistor value, the higher the 

relative transmissibility that it represents. Areas that have equal 

values of transmissibility are represented on the model by similarly shaped areas in which the resistor network is composed of 

resistors of equal value. At first, the storage coefrcient of the 

aquifer was assumed to be uniform throughout the area because 

there were no data available to prove otherwise. An assumed 

value of 19 percent was used as a reasonable first approximation 

of the probable storage coefficient based on previous determinations made in parts of the area.

The pumpage data were simulated in 4-square-mile units, and 

the amount of water pumped from a 4-square-mile E rea was simulated by a single point of withdrawal in the center of the area. 

The pumpage information was the only parameter in the model 

that could not be altered.

The simulation of the depletion environment was, from this 

point on, one of trial and error. If the model did not react to the 

applied stress in a manner similar to that of the real system, the 

cause of the discrepancy had to be determined and corrected.

The initial results indicated that about 50 percent of the 

model area was incorrectly simulated. There were three main 

areas where the water-level decline map obtained from the initial 

test of the model did not match the field data for the test intervals. The largest area was near Stanfield. The cone of depression 

indicated by the model was not as extensive nor as deep as that 

measured in the real system. The same problem occurred northeast of Gilbert where the general configuration of the potential 

distribution was similar to the field data, but the indicated declines were not as great as those measured in the field. The storage coefficient probably was wrong because the volume of 

dewatered sediments determined from the model WF* not comparable to that determined in the field.

The other problem area was near the Gila River from above 

the confluence of the Salt and the Gila downstream to the west-
ELE'CTRICAL SYSTEM 17

ern extent of the model area at Buckeye. Here, the model indicated more drawdown than that measured in the real system. 

This could have been caused by an incorrect storage coefficient; 

however, through recognition that this was the exact area where 

waterlogging had been a problem and where ground water had 

formerly been discharged by evapotranspiration and to the Gila 

River, it became apparent that some other factor had not been 

accounted for. Under equilibrium conditions, water left the aquifer in this area through seepage and evapotranspiraticn. Later, 

pumping resulted in a lowering of the water table, which, in 

turn, resulted in decreased seepage and evapotranspiration losses. 

Since development, the decrease in water losses can be considered as recharge to the system because that amount of water is 

no longer leaving the system as natural discharge. The natural 

discharge, if treated as recharge, could correct the discrepancy 

between the drawdown measured on the model and that determined from the field data.

FINAL MODEL DESIGN

Changes were made in the model design only when the data 

indicated that there was some basis for making the change. The 

final design included several alterations in the original design. 

The transmissibility map and pumpage distribution were not altered; only the storage coefficient was changed in the three problem areas.

Although the storage coefficient in most of the area was left 

at the original 19 percent, several small areas were assigned a 

storage coefficient of 15 percent, such as in Maricopa County east 

of Mesa along the southwest slopes of the Superstition Mountains 

and in the Deer Valley area north and slightly west of Phoenix. 

The storage coefficient was reduced in these areas because of the 

high proportion of fine-grained material in the water-bearing 

zones. A storage coefficient of 10 percent was assigned to an area 

underlain by a highly cemented gravel zone west of Casa Grande 

in Final County (Hardt and others, 1964). This area extends from 

the Sacaton Mountains on the north to the Table Top Mountains 

on the south.

The only other modification of the original system was made 

at the confluence of the Salt and Gila Rivers and downstream 

along the Gila. As previously discussed, this area had formerly 

been a zone of discharge, and it was necessary to add recharge 

at this point because the amount of water leaving the area had
18 ANALYSIS, GROUND-WATER DEPLETION, CENTRAL ARIZONA

decreased since the equilibrium period. The amount of water that 

formerly had been lost by seepage and evapotranspiration was 

now available to be discharged by wells. The model system was 

manipulated on the basis of potential distribution rather than on 

quantity of flow because of the relative ease of analysis and because it was impossible to compute exactly the quantity of discharge lost through evapotranspiration prior to ground-water 

development. The method of handling the discreparcy was based 

on a similar problem described by Robinson (1964); the method 

of solving the problem is different, but the cause and type of 

problem are similar. Once these alterations were made, it was 

possible to duplicate the historic water-level-change data.

The method of verifying the analogy between the groundwater system and the electrical system is the reproduction of 

historic data in the form of water-level declines for different tinte 

periods.When the water-level-decline data from the model match 

the field data, it is assumed that the model design is similar to 

the actual system. Therefore, the model can be used to determine the reaction of the actual system to the application of any 

specific stress. In central Arizona the duplication of historic data 

was done for three different periods, and the model proved to 

be a valid representation of the actual hydrologic system for 

1923-64. The check periods used were 1923-42, 1923-52, and 

1923-64. The close comparison of the field and model data for 

these periods is the basis for the assumption that the electricalanalog system can be used to predict future ground-water conditions.

Plate 3 shows the measured depth to water in the spring of 

1964 (White and others, 1964) and the data from the electricalanalog model for the spring of 1964. The data from the model 

have been converted from water-level decline since 1923 to depth 

to water by superimposing the 1923 depth-to-watev data on the 

model data. This was done to make the model information more 

easily comparable with the field data.

FUTURE GROUND-WATER CONDITIONS

Once the analogy between the hydrologic and electrical systems had been confirmed, predictions of future water-level declines were made on the basis of an assumed pumping regimen. 

The pumping conditions used in the prediction were based entirely on past trends. The amount and areal distribution of 

pumping were assumed to be the same as the average conditions
ELECTRICAL SYSTEM 19

of the past 6 years (1958-64) for simplicity and because no 

other information was available to show that any significant 

change will occur. The amount of water pumped probably will 

be less because the ever-increasing pumping lifts will make 

pumping increasingly expensive, and economically marginal lands 

may be withdrawn from cultivation. It is assumed that 3.2 million acre-feet of water per year for the next 20 years will be 

pumped in central Arizona and that the areal distribution will 

be as at present. This assumption will cause the predicted waterlevel declines to be greater than are actually probable. The degree to which the prediction differs from actuality will be 

dependent upon the amount and location of any changes in 

ground-water withdrawal and the degree that the geologic approximations built into the model differ from the real system.

The predicted regional water-table decline will average about 

50 feet from 1964 to 1974 (pi. 4). The water levels in the present 

areas of heavy withdrawals will continue to decline at about 

the same rate as in the past, and the depth to water in 1974 

will be more than 550 feet northeast of Gilbert and in the Deer 

Valley area and nearly 550 feet near Eloy. No significant change 

will be apparent in the general shape of the regional water table.

The predicted regional water-table decline will average 100 

feet from 1964 to 1984 (pi. 4). Water levels in the mr.jor areas 

of withdrawal will continue to decline at nearly the same rate. 

Northeast of Gilbert and in the Deer Valley area, the depth to 

water will be more than 650 feet, and south of Eloy and northwest of Litchfield Park, the depth to water will be more than 

550 feet in 1984. The total increase in the depth to water in the 

20-year period 1964-84 will range from about 10 feet along the 

Gila River west of Phoenix, where the water table is relatively 

shallow, to as much as 300 feet in the Stanfield area, where the 

water table will be more than 700 feet below the land surface. 

A great deal of lateral expansion will occur in the cores of depression in areas of greatest pumping.

The depth-to-water predictions correspond to nonpumping 

water levels obtained in the spring when there is relatively little 

pumping throughout the area (pi. 4). When a well is being 

pumped, the depth to water at the well is greater than when the 

well is not being pumped by the amount of drawdown required 

to allow water to flow into the well. Therefore, the pumping lift 

will exceed the predicted water-level depths by the amount of 

drawdown in the individual wells.
20 ANALYSIS, GROUND-WATER DEPLETION, CENTRAL ARIZONA

SUMMARY AND CONCLUSIONS

The amount of ground water pumped in the certral Arizona 

area increased from 450,000 acre-feet in 1923 to 3,700,000 acrefeet in 1953. In 1964, the amount of ground water pumped decreased to 3,200,000 acre-feet. The total volume of water pumped 

from the ground-water reservoir from 1923 to 1964 was 80 million acre-feet, which constitutes a serious overdraft from the 

aquifer system. The overdraft is causing water levels to decline 

as much as 20 feet per year in places. If this trend continues, 

the cost of pumping will become more expensive and will result 

in the possible curtailment of agriculture.

An electrical-analog model was constructed to determine the 

effects of continued future withdrawal on the regional water 

levels in the area. The predicted water levels are based on the 

assumption that the model system will be valid for the next 20 

years and that the areal distribution and amount of water 

pumped will remain constant.

An electrical-analog model is an electrical system that is analogous to the ground-water system. Resistors simulate the ability 

of the sediments to transmit water, and capacitors simulate the 

storage of water within the soil pores. The electrical-analog model 

is a general representation of the ground-water system in the 

lower Santa Cruz and Salt River basins. The accuracy of the results from the model is limited by the accuracy of the field data 

and by the applicability of certain simplifying assumptions.

The electrical-analog model was used to extrapolate waterlevel conditions to 1974 and 1984. The results of the extrapolation 

to 1974 indicate that water levels will decline at about the same 

rate as in the past. No change will occur in the general shape of 

the regional water table if the amount of water pumped remains 

the same as in the last 6 years, 1958-64. Further extrapolation 

of data to 1984 shows continued declines at about the same rates 

as before, and the cones of depression will continue to expand 

laterally. The total increase in the depth to water in the 20-year 

period 1964-84 will range from about 10 feet along the Gila 

River west of Phoenix to as much as 300 feet in the £tanfield area.
ANALYSIS, GROUND-WATER DEPLETION, CENTRAL ARIZONA 21

REFERENCES CITED

Ferris, J. G., Knowles, D. B., Brown, R. H., and Stallman, R. W., 1962, 

Theory of aquifer tests: U.S. Geol. Survey Water-Supply Paper 1536- 

E, 174 p.

Hardt, W. F., and Cattany, R. E., 1965, Description and analysis of the 

geohydrologic system in western Final County, Arizona: U.S. Geol. 

Survey open-file rept., 92 p.

Hardt, W. F., Cattany, R. E., and Kister, L. R., 1964, Basic ground-water 

data for western Final County, Arizona: Arizona State Land Dept. 

Water-Resources Rept. 18, 59 p.

Kam, William, Schumann, H. H., Kister, L. R., and Arteaga, F. E., 1966, 

Basic ground-water data for western Salt River Valley, Maricopa 

County, Arizona: Arizona State Land Dept. Water-Resource? Rept. 27, 

72 p.

Lee, W. T., 1905, Underground waters of Salt River Valley, Ar'zona: U.S. 

Geol. Survey Water-Supply Paper 136, 196 p.

Robinove, C. J., 1962, Ground-water studies and analog models: U.S. Geol. 

Survey Circ. 468, 12 p.

Robinson, G. M., 1964, The evaluation of water-resources development by 

analog techniques: Internat. Assoc. Sci. Hydrology Comm. Subterranean 

Waters Pub. 64, p. 442-454.

Skibitzke, H. E., Bennett, R. R., DaCosta, J. A., Lewis, D. D., and Maddock, Thomas, Jr., 1961, Symposium on history of development of water 

supply in an arid area in Southwestern United States, Salt-River Valley, Arizona: Internat. Assoc. Sci. Hydrology Pub. 57, p. 706-742.

Thomas, H. E., and others, 1963, Effects of drought in the Colorado River 

basin: U.S. Geol. Survey Prof. Paper 372-F, 51 p.

Thomasson, H. G., Jr., Olmsted, F. H., and LeRoux, E. F., 1960, Geology, 

water resources, and usable ground-water storage capacity of part of 

Solano County, California: U.S. Geol. Survey Water-Supply Paper 

1464, 693 p.

White, N. D., Stulik, R. S., and Rauh, C. L., 1964, Effects of ground-water 

withdrawal in part of central Arizona projected to 196P: Arizona 

State Land Dept. Water-Resources Rept. 16, 25 p.

Q. S. GOVERNMENT PRINTING OFFICE: 1968 O - 295-462