GEOLOGICAL SURVEY CIRCULAR 110

March 1951

PROGRESS REPORT

HYDROLOGY OF STOCK-WATER

RESERVOIRS IN ARIZONA

By

W. B. Langbein, C. H. Hains, and R. C. Culler

Prepared in cooperation with the Division of Land Utilization, 

Office of the Secretary of the Interior
UNITED STATES DEPARTMENT OF THE INTERIOR 

Oscar L. Chapman, Secretary

GEOLOGICAL SURVEY 

W. E. Wrather, Director

Washington, D. C.

Free on application to the Geological Survey, Washington 26, D. C.
PREFACE

Many agencies and individuals have aided 

materially in the stock-pond investigations. 

Most of the gaging installations are located 

on Indian reservations or in grazing districts 

where official employees have helped locate 

suitable reservoirs for study, sometimes providing tools and labor, and often arranging 

for the gathering of gage readings. Among those 

who have been especially helpful are W. H. 

Berry, regional conservation!st, and Bernard 

Hodgin, engineer, Bureau of Indian Affairs, 

Phoenix, Ariz.; Paul Buss, forest supervisor, 

and Keith Douglass, conservationist, San Oarlos Indian Reservation; J. J. Schwarz, engineer, 

and William Pair, conservationist, Navajo 

Indian Reservation; Ward Kindred, conservationist, Port Apache Indian Reservation; V. D.

Smith, forester, Hualpai Indian Reservation; 

and Clarence Kinkor, conservationist, Papago 

Indian Reservation. The services of these men 

are greatly appreciated.

The field work was carried out in the Water 

Resources Division of the Geological Survey as 

part of the Soil and Moisture Conservation 

program of the Department of the Interior, 

under the supervision of H. V. Peterson, staff 

geologist, by C. H. Hains, hydraulic engineer, 

until 1949, and thereafter by R. C. Culler, 

hydraulic engineer. This report was prepared 

by W. B. Langbein, hydraulic engineer. G..B. 

Smith, hydraulic engineer, assisted in the observations at Juniper Lake on August 5-6, 

1950.
PROGRESS REPORT

HYDROLOGY OF STOCK-WATER RESERVOIRS IN ARIZONA

By 

W. B. Langbein, C. H. Hains, and R. C. Culler

CONTENTS

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

Determination of runoff and water losses

Black Hills Tank. .....................

Postoffice Tank. ......................

Annual runoff ...........................

Seasonal distribution of recharge.....

Page 

1 

3

5

6

n 

11

Reservoir water losses.........

Performance....................

Principles of reservoir design. 

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

Page

 13

 16 

. 17

 18

ILLUSTRATIONS

Page 

Figure 1, Map of Arizona showing location of stock-water reservoirs Investigated............ 3

C. Hydrograph of water surface at Black Hills Tank near Cave Creek, Ariz............. 4

3. Area and capacity curves, Black Hills Tank near Cave Creek, Ariz................... 5

4. Area and capacity curves, Postoffice Tank near Whiter!ver, Ariz................... 6

5. Hydrograph of water surface at Postoffice Tank near Whiter!ver, Ariz., and monthly

precipitation for average of Whiter!ver and McNary, Ariz........................ 7

6. Seasonal variation in water loss, Postoffice Tank, Ariz........................... 8.

7. Evaporation and seepage from Postoffice Tank, Ariz................................ 9

8. Relation of monthly recharge to precipitation, Postoffice Tank, Ariz.............. H

9. Monthly distribution of recharge.................................................. 11

10. Diurnal variation in rate of recession in water level............................. 14

11. Variation in rate of recession with u3 /4 (ew - ea )................................ 15

12. Relation of performance to runoff, water area, water loss, and frequency of

recharge......................................................................... 17

TABLES

Page 

Table 1. Dry periods, Postoffice Tank........................................................ 8

2. Computations of recharge and runoff, Postoffice Tank near Whiteriver, Ariz.......... 10

3. Summary of data for reservoir gaging stations....................................... 12

4. Observations at Juniper Tank........................................................ 16

INTRODUCTION

The many thousands of stock-water reservoirs 

throughout the Western Range provide a large 

part of the watering facilities for the Nationb 

livestock industry. The individual stockwatering pond represents a small investment 

but the aggregate of all ponds is an investment of many million dollars.

Harvesting of the forage crop by stock on 

the Wes'tern Range depends oh the accessibility 

of water. In general, cattle do not graze more 

than 3 miles from water'. Where the water 

supplies are far apart, forage close to water 

Is so intensively cropped that destructive

erosion is induced,' whereas valuable forage at 

a distance remains unharvested. Uniform and 

efficient utilization of the forage requires 

a large number of water supplies only short 

distances apart. 1 For this reason, many thousands of reservoirs have been built. A recent 

survey in the 9,000-square-mile basin of the 

Cheyenne River in Wyoming shows that there are 

nearly 10,000 reservoirs, or about one per 

square mile. Although this density of reservoirs may not apply throughout the Intermontane 

Plateau, it is nevertheless indicative of a 

high state of development in some areas. Considering the construction under way and proposals for even greater construction, it is 

evident that the performance of stock-water
reservoirs is a matter of great economic concern.

>

The availability of a dependable supply of 

stock water at the proper time or times during 

the grazing seasons is of extreme importance 

to the range-livestock industry. In humid 

areas, rivers, creeks, natural ponds, or lakes 

provide dependable waters and providing stock 

water is no problem. At the other end of the 

scale are the many arid ranges that do not 

contain any "live" waters. Between these two 

extremes there are still other ranges where 

seasonal water may be available or where water 

must be artificially provided. The arid or 

semiarid range areas present a unique problem 

in range management to livestock operators. 

Under these circumstances and conditions many 

and varied approaches to the solution of the 

water problem on such areas have been made.

Advantage is taken of the fact that water is 

a "key" resource on the arid range, providing 

or withholding water for livestock permits 

better management of range and the livestock^ 

For example, such use of water as a control 

in many instances limits the necessity for 

construction and maintenance of costly fencing 

projects. Water control, in lieu of fencing* 

is being used more and more to provide protection for areas that have been reseeded or are 

in other ways being rehabilitated under the 

departmental soil and moisture conservation 

program. Water control also permits range managers to provide for short-time water on lambling grounds, around loading stations adjacent 

to railroad shipping points, or at shearing 

pens, in holding pastures or roundup grounds.

For the best operating practices, yearlong 

water is not always desirable in the management of range and stock on western range areas. 

Some ranges, because of the character of the 

forage, are usable to advantage only in the 

spring; others only in the fall; whereas still 

others could be used for longer periods, and 

in some sections of the West many ranges are 

used the year long.

Attempts of stockmen and range managers to 

meet the problems that are frequently complicated during wet years or seasons of drought, 

have produced a varied pattern of stock-water 

developments and stock-water use. Lack of hydroiogic and geologic data pertaining to watersupply possibilities has heretofore resulted 

in many unwise or impractical developments or 

attempts to provide water. Unfortunately some 

of these attempts that failed brought about 

considerable damage to the range or to values 

downstream. Better land and livestock management requires that Improved practices be instituted. The Division of Land Utilization 

for the past several years has been sponsoring 

studies of the problems involved for the purpose of providing sound geologic and hydrologio 1 

data to the land management agencies to enable 

 ^them to manage the range lands more effectively and at a reasonable cost.

Flow in the small drainage courses on graz* 

ing lands is infrequent and erratic. In order 

to provide carryover between storms, the tendency has been for the stockmen to make their 

reservoirs large, thus creating great surface 

areas and thereby increasing losses of water 

by evaporation and seepage. It seems significant thajj the amount of water consumed by 

stock from the ordinary reservoir is only a

small fraction of the total flow in the washes; 

most of the water is lost by evaporation or 

disappears by seepage.

An'important problem in water conservation 

is to minimize waste by permitting the surplus 

waters to flow downstream for the benefit of 

other users and for useful "native vegetation. 

The solution of this problem depends largely 

on adequate data on runoff and sedimentation 

in the "dry" washes in the semiarid and arid 

parts of the country. Hydrologlc information 

in the desert areas is needed not only for designing stock-water reservoirs but for determining source areas of flow in the major 

streams and of ground-water recharge. The flow 

in the dry-washes is too erratic and the 

channels are too unstable to Justify operation 

of stream-gaging and sediment stations. Gageheight records on dry washes can be obtained 

by "kickoff recorders" (triggered by a flow 

of water), but dependable discharge ratings 

are difficult to define on these ephemeral 

streams. Obtaining discharge measurements and 

sediment samples on washes of this kind would 

require_the full-time residence of a hydrographer,'entailing costs too high to warrant 

the work except perhaps on an intensive experimental scale.

In 1944 and 1945, in connection with reservoir performance studies, gages were installed 

on several stock-water reservoirs. The initial 

purpose was to learn when the reservoirs contained usable water, the rate of loss, and 

the frequency and amount of replenishment the 

chief factors that determine the success or 

failure of a reservoir. Later it was found 

that the records of water level could also be 

interpreted in terms of the runoff into the 

reservoir. A group of reservoirs in Arizona, 

where they are commonly called "tanks" by 

stockmen, was selected for these initial 

studies (see fig. 1). Enameled gage plates 

graduated to 0.02 foot were installed on posts 

in the banks of the reservoirs. As most of 

these reservoirs are at locations remote from 

ranch houses or routes of frequent travel, the 

best that could be done was to obtain weekly 

readings. Nevertheless, readings were uncertain, and gaps of several weeks are numerous 

in the records. These gaps, although vexing, 

were not critical because for many months the 

reservoirs were slowly receding and it" was not 

difficult to piece out the record. Spilling 

was more troublesome, except for those reservoirs with sufficient capacity for overflow 

to be infrequent-. Experience in Arizona indicates that reservoirs with a capacity of 10 

acre-feet or more per square mj.le of drainage 

area are best suited to stock-reservoir studies. 

Reservoirs of this size are also sufficiently 

large to trap all the sediment carried by the 

inflow.

It was found that records of this kind could 

yield considerable information in comparison 

with their cost. 'From the record of fluctuations of water levels, data on runoff, seepage, 

and evaporation can be obtained. Repeated capacity surveys provide information on volumes 

of sediment carried by the floods in the dry 

'washes.

It is believed that the stock-reservoir 

studies begun in Arizona will help relieve the 

shortage in hydrologic data for the' arid country. The studies have since been expanded to 

include a few basins in Wyoming, Colorado,, and
Beautiful Valley*

. Thornton Tank 

 Blue. Mountain Tank

Clay,

Tank 

Plain* 

Tank

Black Hills Tank

tMesquite Tank

Tufastone« «JuniperTank ) I 

Tank

Davas Tank 

Lonestar Tank*

Kennedy Tank !

 Alhambne Tank

Figure 1. Map of Arizona showing location of stock-water reservoirs investigated.

Utah. It is planned, at tiiese new sites, to 

study sedimentation and erosion as well as 

runoff. This report, however, will be confined 

to performance at the original Arizona installations; but when longer periods of record are 

available, later reports will include the additional sites. This investigation was directed 

mainly toward evaluation of reservoir performance; problems of design or construction of 

dams were not included, nor were any studies

made of flood discharges or spillway design.

DETERMINATION OP RUNOFF AND WATER LOSSES

The common type of dry wash in the arid 

country carries flows only as a result of the 

more intensive summer storms. The stream rise 

is rapid, sometimes as a wave front advancing 

downstream. The peak is sharp; the stream
20

16 G ige readings.

12

*. *

to 

at 

O

Water mark 14.24 ft

-r Water mark 9.36 ft

Water mark 10.15 ft

Dry

Dry

Dry

1946 1947 1948

Water year 

Figure 2. Hydrograph of water surface at Black Hills Tank near Cave Creek, A
recedes quickly} and the channel may be dry 

again within a few hours.

When this flow Is Impounded by a stock-water 

reservoir, there Is a rapid rise In stage until the Inflow ceases. The duration of Inflow 

Is so short that seepage and evaporation 

losses from the reservoir-may be assumed to be 

negligible during the period. Hence the total 

volume of flow may be closely determined by 

the Increment In volume In the reservoir. After 

Inflow ends, the stage In the reservoir begins 

to decline, rapidly at first and then more 

slowly as the seepage rate becomes less. If 

Inflow does not recur for some time, the reservoir may go.dry.

Records of water levels were obtained for 18 

reservoirs In Arizona. The method of analysis 

Is Illustrated In this report by two examples; 

the first Is typical of performance In the 

arid country and the second of the more humid 

mountainous country.

Black Hills Tank

Black Hills- Tank near Cave Creek, Maricopa 

County, Arlz., Is typical of a reservoir In 

the desert. The climate at this reservoir Is 

similar to that of the valleys of the lower 

Olla Basin and west-central Arizona. Annual 

rainfall averages about 8 Inches and annual 

temperature 70®p. A study of rainfall records 

obtained at Camelback, Arlz., 17 miles southwest of the reservoir, shows that rainstorms 

In excess of 0.5 Inch per day average only 3 

for a year.

The reservoir Is formed by an earthflll dam, 

28 feet high across a dry wash approximately 

2| miles long, and has a total capacity of 

about 65 acre-feet. The reservoir Intercepts 

the runoff from an area of 1.56 square miles 

that is drained by a network of small washes 

6 inches to 2 feet deep draining to the southeast on a slope of about 2 percent. The granitic rock that underlies the basin is capped 

by a thin mantle of coarse residual soil. Vegetation is of the mountain-brush type, consisting mainly of snakeweed, yucca, creosote bush, 

cactus, and small paloverde trees. Mesquite 

grows along the main drainage channels. The 

altitude (determined by aneroid barometer) 

ranges from 2,600 feet at the reservoir to 

3,200 feet at the head of the basin.

The hydrograph of water levels in the reservoir, as constructed from gage readings and 

high-water marks, is shown on figure 2. Only 

one period of inflow occurred in each year of 

record. Because of the infrequency of rainstorms of sufficient volume and intensity to 

produce runoff, and particularly because of 

the perviousness of its bottom, the reservoir 

is dry more than half the year. The volumes of 

runoff associated with each rise in the reservoir, which occurred in August in every year 

listed, are as follows:

The 4-year average runoff is 13.5 acre-feet-- 

8.5 acre-feet per square mile or 0.16 inch.

The results of capacity surveys are shown 

on figure 3. The original capacity in 1945 

below a stage of 19 feet was 30 acre-feet. A 

resurvey in June 1949, when the reservoir was 

dry, showed a capacity of 26.5 acre-feet, indicating a 4-year deposition of 3.5 acre-feet, 

most of which was located below a stage of 10 

feet. The original low point was at a gage 

height of zero, but in June 1949 the bottom 

was at a gage height of 2.4 feet. The year-toyear rise in the bottom is shown by the hydrograph on figure 2. About half of the sediment accumulated was produced by a small debris wave'that accompanied the runoff of 

August 1948. A field examination shortly thereafter showed that this wave deposited 2-foot 

mud clods, 6-inch rocks, and whole mesquite 

trees in a fan at the entrance to the tank; 

but only fine sediments reached the bottom of 

the reservoir.

The record shows, therefore, that in addition to. the average annual water runoff of 

13.5 acre-feet, there was sediment amounting 

to 0.9 acre-foot per year (0.55 acre-foot per 

square mile per year), or 6 percent by volume 

of the runoff.

19

10' 15 20 25 30 

Capacity, in acre-feet

Figure 3.-- Area and capacity curves. 

Black Hills Tank near Cave Qreelc, Aria.

Date

1945

1946

1947

1948

Runoff in 

acre-feet

7

14

7

26
Postoffice Tank

A quite different analysis must be made of 

the records on reservoirs that contain perennial or more nearly perennial water. In general, the fluctuation In water level of a reservoir Is given by the equation:

AH - R/A+ P - E - S - U/A

in which AH represents change in water level 

In feet; R Is runoff In acre-feet; A Is the 

water-surface area In acres; P is precipitation on the pond surface In feet; E Is evaporation In feet; S Is seepage In feet; and 

the term U/A represents the effect of use by 

livestock, expressed also In feet. The sum of 

the inflow terms R/A+ P is called recharge, 

and the sum of the terms E+S Is called water 

loss. The observed data are AH, P, and A; 

the problem Is to determine the values of R, 

E, and S. For most reservoirs utilization of 

the water by stock is relatively small, amounting to 0.3 acre-foot or less per year.

Postoffice Tank near Whiterlver, Ariz., on 

the Port Apache Indian Reservation, is an example of a perennial reservoir. This reservoir 

has a capacity of 3.5 acre-feet (see fig. 4)

Impounded by an earth dam about 11 feet high. 

The reservoir Intercepts the runoff from a 

drainage area of 0.29 square mile on the 

Mogollon Rim. The drainage course lies in a 

canyon that runs parallel and adjacent to Postoffice Canyon and Is separated from that canyon, as well as from the drainage area on the 

south, by ridges with side slopes of 25 percent. The altitude at the dam is 5,725 feet 

above mean sea level (by aneroid barometer) 

and the drainage basin heads on a mountain 

peak 500 feet higher. The sandstone that underlies the basin Is mantled by a fairly thick 

sandy soil containing boulders and cobbles. 

The fill In the canyon bottom is fairly thick 

and consists of sandy loam. The basin lies in 

a dense pine forest with much litter. Very 

little evidence of recent erosion is noted, 

except for minor washing of the main channel 

near the reservoir.

The hydrograph of water levels in this reservoir, based on weekly readings on a staff 

gage, Is shown on figure 5. It may be observed 

that the hydrograph consists, in the main, of 

abrupt rises in stage caused by runoff followed 

by slow depletions due to evaporation and 

seepage. However, recharge is frequent and 

the water supply is perennial. There are

100

Flow Line

Note:- Capacity curve below 91.0 feet is approximate.

Capacity, in acre-feet 

2

0.1 0.2 0.3 0.4 0.5 

Area, in acres

0.6 0.7 0.8 0.9

Figure 4.-- Area and capacity curves, Postoffice Tank near Whiteriver, Ariz.
feet in height, Gage 

2 * 

O h^ 

 

U

If 

11

Is

J1 3. 

* N 

 VUr.l

i

Sept.

Mar.

Sept,

Mar,

Sept.

Mar.

Sept.

co 

 o

precipitation, Average 

inches in 
1.2

1.0

0.8

0.6

0.4

0.2

Jan.

Feb.

Mar.

Apr.

May

June

July .

Aug.

Sept.

Oct.

Nov.

Dec.

Water loss

feet

0.26

.31

.42

.60

.82

.98

.98

.89

.74

.54

.35

.26

7.13

Seepage

feet

0.10

.12

.14

.16

.18

.20

.20

.18

.16

.14

.12

.10

1.80

Evaporation

feet

0.16

.19

.28

.44

.64

.78

.78

.71

.58

.40

.23

.16

5.33

FMAMJJASOND 

Figure 6.--Seasonal variation in water loss, Postoffice Tank, Ariz.

periods when the water level in the reservoir 

rises slowly or is quite stable (as in January 

1946 when it was indicative of slow contribution from snowmelt)-

The analysis is begun by first considering 

those dry periods in which it is obvious that 

no runoff occurred. The quantity P - AH in 

such periods is equal to the water losses 

i.e., seepage and evaporation (see table 1).

Figure 6 presents a hydrograph showing the 

seasonal variations in the water loss. The 

graph shows that water losses range from a

high of 1 foot per month in midsummer to a low 

in winter of about 0.25 foot per month. The 

major cause of the seasonal variation in water 

loss is evaporation. Except for the effects of 

changes in viscosity due to changes~in water 

temperature, seepage should be fairly uniform 

during the year in reservoirs with perennial 

water.

Figure 7 shows a graphic study of the water 

losses during dry periods taken from table 1 

plotted against evaporation as measured in a 

class-A pan at Sierra Ancha (55 miles west), 

the nearest place where such observations are

Table 1. Dry periods, Postoffice Tank 

[T = trace.]

Period

Sept. 8-Oct. 2, 1945

Nov. 1945

Apr. 1946

May 1946

June 1946

Oct. 8-22, 1946

Nov. 1946

Jan. 1947

Jan. 30-Feb. 25, 1947

Apr. 1947

Sept. 2-16, 1947

Dec. 2-24, 1947

May 15- June 9, 1948

Mean gage

height

(feet)

94.3

93.7

92.8

92.1

91.2

96.3

96.6

96.3

96.0

95.7

, 93.75

93.6

95.5

Change

in water

level

(ft per 

month)

-0.74

- .47

- .50

- .90

- .98

- .52

- .24

- .26

- .28

- .56

- .73

. - .24

- .90

Precipitation

(feet)

0

0

.10

T

T

T

.08

.01

.02

T

0

0

.01

Water losses

(ft per 

month)

0*74

.47

.60

.90

.98

.52

.32

.27

.30

.56

.73

.24

.91

.Pan evaporation

at

Sierra Ancha

(ft per 

month)

0.65

.30

.60

.76.

.94

.48

.22

.16

.22

.57

.70

.18

.85
9

made. The points are fairly consistent and 

define a straight line that shows a water loss 

of 0.1 foot per month when pan evaporation is 

zero. This value very likely represents a minimal rate of seepage from Postoffice Tank during the winter season. To the extent that the 

rate of seepage would vary with the water viscosity, the maximal rate of seepage, in midsummer, should be about 1.8 times the minimal 

rate. Figures 6 and 7 show this suggested segregation of the water losses into evaporation 

and seepage. The total annual evaporation is 

shown as about 5.3 feet, 85 percent of that 

from the evaporation pan at Sierra Ancha.

The data in table 1 Indicate no appreciable 

effect of reservoir stage or depth of water 

on water losses. This is not to be interpreted 

as a general conclusion, although It may be 

fairly true of reservoirs with perennial water 

supply and limited range in water-level fluctuation. It may be noted that the hydrograph 

of Black Hills Tank (fig. 2) shows a substantial lessening In the rate of water loss with 

drop in stage.

The graph on figure 7 Is a basic relationship for computation of the recharge to Postoffice Tank. The sum of an observed change in 

stage and the rate of depletion as controlled 

by water losses, indicated by the graph, must 

be attributed to recharge; thus AH + L = R/A+P, 

where L equals the water losses. When water 

level remains stationary ( AH = 0), then water 

losses are balanced by recharge; when water 

level drops at a rate equal to losses, then 

recharge is zero.

The computations of recharge and runoff to 

Postoffice Tank by months are given in table 2

for the period of useful record, August 1945 

to September 1948. The items in this table are 

generally self-explanatory. The recharge to 

the tank is calculated from the formula AH +L, 

where L is total water loss as determined from 

figure 7. The terra AH is net change in water 

level as determined from the stage record. The 

recharge in feet multiplied by the mean watersurface area, corresponding to the monthly 

mean gage height (se.e fig. 4), equals recharge 

In acre-feet. The runoff into the reservoir is 

equal to the recharge minus the precipitation 

on the water surface. Figure 8, p. 11, shows 

precipitation as observed at McNary and Whiteriver (the nearest regular rain-gage stations) 

plotted against recharge to Postoffice Tank. 

It shows that the computed recharge In feet 

is always greater than the precipitation, the 

excess Increasing with precipitation. The excess, of course, represents the runoff into 

the tank from the contributory drainage area. 

The amount of runoff is highly variable. A 

satisfactory definition of a rainfall-runoff 

relationship would require better rainfall 

data.

The reservoir overflowed on Sept. 17, 1946, 

and from March 31 to April 1, 1948. The volume of spill in acre-feet has been calculated 

from the following formula, based on normal 

shapes of flood hydrographs: Q times total lag 

divided by 6. Q is peak rate of outflow in 

cubic feet per second, as calculated from the 

peak stage used in a broad-crested-weir formula applied to the spillway cross section; 

thus Q = 2.5 LH3/2 where L is length of spillway in feet, and H is maximum depth of water 

over spillway, in feet. Total lag is the sura 

of the detention time, in hours, of the sur1.2

1.0

1-

.6

^3 » * 4" 

Cti

£

.2

Nov. '45»

Nov. '46 v'

* -Feb. '47 June '47 ,,'

, Dec. '47

May '46 

Sept. '45 /. Sept. «47

June '46

I 

May - June '48

. '46- 

 Apr. «47 

 Oct. '46

.2 .4 .6 .8 1.0 1.2 

Evaporation from pan at Sierra Ancha, in feet per month

Figure 7.-- Evaporation and seepage from Postoffice Tank, Ariz.

1.4
10

2. Computations of recharge and runoff, Postoffice Tank near Whlterlver, Arlz,

[T * trace]

Date

1945

July

Aug.

Sept.

Tota

Oct.

Nov.

Dec.

1946

Jan.

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Tota

Oct.

Nov.

Dec.

1947

Jan.

Feb.

Mar.

Apr.

May )

June)

July

Aug.

Sept.

Tota

Oct.

Nov.

Dec.

1948

Jan.

Feb.

Mar.

Apr.)

May )

June)

July)

Aug.

Sept.

Sage height

end of

nerlod

(feet!

95.00

94.62

93.92

1

93.89

93.42

93.55

93.55

93.40

93.08

92.58

91.68

90.70

90.26

90.42

96.58

1 1946 watei

96.72

96.48

96.38

96.14

96.20

96.00

95.44

94.14

93.64

93.94

93.96

1 1947 watei

93.78

93.71

93.47

93.22

93.50

96.96

95.40

93.9

93.59

93 . 14

Mean gage

height

(feet)

94.8

94.3

94.1

93.7

93.4

93.6

93.5

93.3

92.8

92.1

91.2

90.3

90.5

93.3

- year

96.4

96.6

96.4

96.3

96.0

96.1

95.7

95.2

93.9

93.9

93. 9

- year

93.9

93.7

93.6

93.4

93.3

95.2

96.2

94.5

93.9

93.3

Change of

gage height

(feet)

-0.38

- .70

- .03

- .47

+ .13

.0

- .15

- .32

- .50

- .90

- .98

- .44

+ .16

+ 6.16

+ .14

- .24

- .10

- .24

+ .06

- .20

- .56

-1.30

- .50

+ .30

+ .02

- .18

- .07

- .24

- .25

+ .28

+3.46

-1.56

-1.50

- .31

- .45

Precipitation a/

(feet)

0,19

.31

.05

.21

0

.23

.16

.06

.10

.10

T

T

.23

.45

.39

.12

.08

.13

.01

.10

.01

.01

.26

.17

.53

.22

.27

.13

.04

,02

.23

.16

.01

.30

.18

.13

Water

loss

(feet)

0.83

.80

.52

.40

.28

.24

.34

.46

.70

.86

1.04

.93

.74

.68

.52

.32

.30

.26

.38

.47

.66

1.72

.99

.80

.76

155

.30

.28

.31

.30

.33

1.60

2.10

.85

.80

Mean surface area

(acres)

0.52

.47

.46

.43

..41

.43

.42

.40

.37

.34

.29

.24

.26

.40

.60

.62 '.60

.60

.58

.59

.56

.53

.44

.44

.44

Recharge

(feet)

0.45

.10

.49

0

.41

.24

.19

.14

.20

0

.06

.49

.90

6.84

.66

.08

.20

.02

.44

.27

.10

.42

.49

1.10

.78

.44

.43

.43

.41

.40

.53

.59

.48

.44

.40

.37

.23

.04

.06

.58

3.79

.04

.60

.54

.35

Total 1948 water year

(acrer 

ffiftirl

0.23

.05

.28

.23

0

.17

.10

.08

.06

.07

0

.02

.12

.23

2.74

3.82

.40

.05

.12

.01

.25

.16

.06

.22

.22

.48

.34

2.31

.16

.10

.02

.02

.23

2.01

.02

.36

.17

.14

3.23'

Runoff

(feet)

0.14

.05

.58

0

.18

.08

.13

.04

.10

0

.06

.26

.45

6.45

.54

0

.07

0

.34

.26

.09

.16

.32

.57

.56

.10

.10

0

.04

.35

3.63

.03

.30

.36

.23

<K3»

0.07

.02

.09

.13

0

.07

.03

.06

.02

.04

0

.02

.06

.12

b/2,8

3.35

.32

0

.04

0

.20

.15

.05

.09

.14

.25

.25

1.49

.04

.04

0

.02

.14

b/2.5

.02

.14

.16

.09

3.15

a Mean of Whlterlver and McNary precipitation.1 "b Includes overflow.

charge (volume above the spillway crest) In 

the reservoir and that of the drainage basin. 

The detention time of the reservoir surcharge 

Is computed from the formula 12 S/^J, where 3 

Is the maximum volume In temporary storage 

above the spillway-crest level In acre-feet, 

and Q Is peak rate of outflow In cubic feet 

per second as computed previously. Detention 

time of the drainage basin In hours Is estimated as equal to the square root of the 

drainage area In square miles.

For Postoffloe Tank the detention time of 

the reservoir surcharge Is estimated to be 12 

hours and that of the drainage basin 0.5 hour.

The spillage was therefore estimated to be 

0.2 acre-foot in 1946 and 0.6 acre-foot in 

1948. The annual runoff into Postoffice Tank 

was as follows:

Water year

1946

1947

1948

Acre-feet

3.35

1.49

3.15

The 3-year average runoff is 2.66 acre-feet, 

or'9.2 acre-feet per square mile. Because of 

the slow rate of sedimentation no repeat capacity survey was made.
1.0

0.8

0.6

0.4

Direct recharge

0.2 0.4 0.6 0.8 1.0 1.2

Monthly recharge in feet

PiRure 8.-- Relation of monthly recharge to precipitation, 

Postoffice Tank, Ariz

ANNUAL RUNOFF

The annual runoff at the reservoirs studied, 

as listed In columns 20 and 21 of table 3, 

ranged from 2 to 37 acre-feet per square mile, 

with a general average of about 9 acre-feet. 

The amount of runoff that a basin will produce depends on the amount and Intensity of 

precipitation, the soil, the geology, and 

other aspects of the terrain. Adequate Information Is not at hand for evaluating the 

effects of each of these factors. An estimate 

 of the runoff from a catchment area can be 

made from the range noted and by comparison 

with similarly situated drainage basins.

Ordinarily, for different drainage basins, 

one may associate the major part of the variations In mean annual runoff with variations 

In climate. The runoff values are typical of 

those that might be expected in semiarid and 

arid regions, but an examination shows that 

factors other than climatic are operative. 

For example, the climatic setting of Black 

Hills Tank is considerably more arid than 

that of Postoffice Tank, yet each reservoir 

has about the same annual runoff per unit of 

drainage area. In such cases the differences 

might be attributed to the geologic characteristics of the drainage basins. The runoff 

into Black Hills Tank appears high because 

of the large flow In 1948. The aridity at 

Black Hills Tank Is evident In the year to 

year variability of the runoff, compared with 

that into Postoffice Tank.

The high runoff into Beautiful Valley Tank 

may be due in part to low-inflltration capacity of the shale bedrock underlying its drainage basin. The low runoff into Clay Tank in 

the Hualapai Indian Reservation may be due to 

the many cracks and fissures in the limestones 

that lie at the surface over most of this 

drainage basin.

Arizona had a general drought during the 

period of these Investigations. Because of the 

drought, which seemed to be most Intense in 

the Hualapai Indian Reservation, general 

storms were infrequent, but local convectional 

storms occurred sporadically. The chance occurrence of summer storms'explains, it Is believed, most of the diversity in runoff shown 

by the records. A continuation of these ob11

servatlons should average out most of the erratic effects of the desert climate, so that 

the Influence of general climatic and terrain 

factors may be discerned.

Nevertheless, diversity In drainage basins 

as small as these is to be expected. The differences appear to be nearly as great between 

basins as between years. This diversity Indicates that more meaningful information can be 

obtained from a large number of observations 

under widely different terrain and climatic 

conditions than from a few precise records 

for long periods at a few points.

Seasonal distribution of recharge

. At reservoirs below 5,000-foot altitude, 

the records of water level show that recharge 

occurred in 2.25 months of the year on the average. The distribution of these months (fig. 

9A) shows that periods of recharge are heavily 

grouped during July to October.

At reservoirs above 5,000 feet, the frequency -of recharge averaged 3.0 months per 

year, somewhat greater than at the lower levels. 

However, as shown on figure 9B, there Is less 

seasonal contrast between winter and summer. 

The frequency of summer-recharge at these 

higher levels is not significantly less, but 

the major difference In recharge distribution 

is the added occurrence of winter rainfall 

and snowmelt.

ONDJ FMAMJ J A >S 

A-Reservoirs below 5000 teet

0.8

0.6

0.4

0.2

ONDJ FMAMJ J AS 

B-Reservoirs above 5000 feet

Figure 9.-- Monthly distribution of recharge.
Table S. Summary of data for reservoir gaging stations

Location 

Reservoir (Tank)

(1)

Ft. Apache Indian Rea.

Postern ee

Bualpal Indian Rea.

Blue Mountain

Clay

Plain

Thornton

lava Jo Indian Bea.

Beautiful Valley

Spreader 1-42

Papago Indian Bea.

AlhamDre 

lank 76-.

San Carloa T«HIITI Rea.

Hilltop

Juniper

Tufas tone

Bracing Dlst.'Ko. S

Heaquite

Yum

Gracing Dlst. Bo. 4

Da vis

Kennedy

Loneatar

Public Domain

Black Bills

Drainage basin

Area

(sq ml)

(2)

.0.29

.88

22.9

13.6

.6

.52

18.8

6.61 

1.17

10.6

2.0

15.4

10*

-

d/.81

.87

.07

1.S6

Length

dales)

(3)

2.1

.75

7.5

6.5

1.2

1.76

7

3

1.9

5

1.75

9.0

6*

-

2.5

2.6

.5

 2.5

Relief

(feet)

(4)

500

450

900

.400

300

500

900

2960 

1160

1000

650

1000

300 "-

300

1600

1500

600

Altitude

(feet)

(5)

572S

5500

5100

4800

6550

5800

7000

3900 

2900

5300

4800

2900

1300

1300

3900

4150

4270

2600

Reservoir

Capacity

fecre-ft)

(6)

3.5

5.7

96

144

15.7

32.7

Depth

(feet)

(7)

11.8

8.3

12.3

7.4

11.5

6.4

a/lDO a/22.9

16 

9.4

130

20

110

8.7

10

2.5

4.7

2.1

e/6S

23 

10.1

18.4

7.5

20.3

16.2

14.2

8.7

8.9

11.2

28.2

Area

(acres)

(8)

0.62

2.0

16.6

37.4

3.7

11.7

11.0

1.8 

3.3

18.6

6.5

11

1.3

1.26

.75

1.52

.44

e/5

v/ah 

(see p, 

16)

(9)

0.48

.34

.47

.52

.37

.44

.40

.39 

.28

.38

.41

.49

.41

.56

.38

.35

.43

.46

Spillway 

elevation

(feet)

(10)

96.8

95.0

95.0

95.0

95.0

81.2

-1.4 

84.9

95.4

94.2

29.0

98.2

89.0

91.9

83.7

86.2

28.2

Extreme water levels

Maximum

Stage Contents

(feet)

(11)

97.0

91.7

93.45

93.2

93.8

79.6

-1.0 

86.75

95.6

95.2

-

100.3

89.9

92.5

84.0

86.2

19.7

(acre-ft)

(12)

3.5

2.5

80

89

11.6

17.5

16 

9.4

130

20

-

8.7

11.2

2.5

4.7

2.1

25

Minimum

Stage contents

(feet)

(13)

90.2

86.4

82.7

87.6

63.5

74.8

-

-12.62 

74.8

78.0

90.98

-

81.8

75

63.5

75

75.0

0.0

(acre-ft)

(14)

0.7

0

0

0

0

0

-

3 

0

0.4

6.1

-

0

0

0

0

0

0

Performan

Mater loss (ft per mont

Mean 

watersurface

area

(acres)

(15)

0.46

.47

4.2

10.0

.9

3.5

1.0 , 

.95

10

4.5

-

-

.83

.40

.50

.15

.95

Total

(16)

0.6

.7

-

.55

.5 '

.55

-

.75 

1.5

2.5

.65

-

1.5

1.4

1.2

1.4

5.5

4

I Mea

Seepage) eva

(17)

0.15

-

-

-

-

.05

.3

-

.25

-

-

-

-

-

-

-

(18

0.4

-

-

-

-

.5

.4

-

.4

-

-

-

-

-

-

-

a Reduced to "O» toy sedimentation.

b Additional runoff spilled.

e Probably higher since tank has sealed.

d 0.6 square mile ragulated by upstream 1 tanks, 

e Estimated.
13

RESERVOIR WATER LOSSES

Evaporation and seepage are the two chief 

causes of depletion of the water In a stockwater reservoir. Collectively they are termed 

water losses. This terra Is quite apt as applied 

to' the stock-water supply, although the water 

that seeps from a reservoir may reappear In 

part as stream flow to support stream-bank 

vegetation or In ways beneficial to downstream 

water users.

The methods of determining the rates of 

losses, as given In table Z, are explained In 

a previous section of this report. Rates of 

loss ranged from 0.5 foot to as much as 5 feet 

per month. Only four reservoirs had records 

of water level adequate for separation of 

water loss into evaporation and seepage. Evaporation rates averaged 0.4 to 0.5 foot per 

month (4.8 to 6.0 feet per year). These figures are probably representative, and seepage 

can be estimated from the difference between 

the total water loss and an evaporation rate 

of 0.45 foot per month. For most of the reservoirs studied, the rate of evaporation loss 

is the controlling factor in their performance, 

but as shown in table 3, there are several 

reservoirs for which the seepage rate greatly 

exceeds evaporation.

The rates of seepage as determined from 

analyses of the water-level records (table 3) 

are general averages. Detailed examination of 

recession hydrographs shows that seepage rates 

are variable. Some discussion has already been 

made of the effects of seasonal changes in 

water temperature upon possible changes in 

seepage rate'. One of the most marked characteristics of hydrographs is the high initial 

rate of recession Immediately after a rise in 

stage followed by a lessening in rate as the 

water level recedes. When recharge raises the 

water level in a reservoir, some water Is absorbed in bank wetting. The rate of percolation 

Is initially high while the dry soil absorbs 

water. On wetting, the clay particles of the 

soil swell and the rate of percolation diminishes. With recession of the reservoir level, 

the exposed land surface dries out, and the 

clays again shrink. The drying out represents 

a loss of the water that was absorbed in bank 

wetting. Those reservoirs that have large 

fluctuations in water level, separated by long 

periods of drying out, appear to have greater 

net seepage losses than those that have more 

stable water levels. These losses are particularly significant in reservoirs that have 

gently sloping sides. Such reservoirs are 

equally unsatisfactory because of evaporation 

losses.

The rate of seepage also varies for the 

following reasons which are related to position of water level: (1) Decreases in hydraulic head with recession in water level, and 

(2) the greater permeability of bed materials 

in the higher parts of a reservoir than of 

the thicker muds In the bottom of the reservoir.

In view of the still fragmentary nature of 

the records of water level in stock-water reservoirs, detailed investigation of variation 

in seepage losses does not appear feasible at 

this time. However, new, techniques are being 

tried for determination of rate of seepage 

and evaporation.

The problem Is to determine how much of an 

observed recession in water level during dryweather periods Is due to seepage and how much 

is due to evaporation. The principles employed 

in the separation are; (1) Evaporation varies 

in response to meteorologic controls, and (2) 

seepage is relatively uniform at a given stage 

and season. The relative proportions of evaporation and seepage are therefore variable.

In the annual cycle, loss by evaporation 

from shallow lakes reaches maximum in summer 

and minimum in winter. Figure 6 shows the seasonal variation in rate of water loss (rate 

of recession in absence of recharge) from 

Postoffice Tank. The rate of recession ranged 

from a maximum of 0.98 foot per month in June 

and July to a minimum of 0.26 foot per month 

In January. It is evident that evaporation is 

the dominant factor in this seasonal variation 

of water loss. The seasonal variation was 

used to estimate the monthly rate of seepage 

which was then deducted from the rate of recession to compute the rate of evaporation.

The diurnal cycle offers a comparable method 

for separating observed recession rates in 

seepage and evaporation. In the typical diurnal 

cycle, seepage (in or out) is uniform in rate 

but evaporation from shallow lakes is generally 

a maximum In midafternoon and a minimum sometime between midnight and sunrise. The minimum 

rate of recession approaches the rate of net 

seepage, according to a similar principle 

used by White (1932) to estimate rate of recharge from the diurnal transpiration cycle 

in ground-water level in an observation well.

A more refined technique that suggests itself is to measure the rate of recession in 

water level as precisely as possible during a 

24-hour period and to correlate the rate of 

recession against an expression that combines 

the meteorologic and water-temperature factors 

that influence evaporation. Observations for 

this purpose were made at Juniper Tank on 

June 27-28, 1949, and August 5-6, 1950.

A series of hourly observations of water 

level, water temperature, wind speed, and wetand dry-bulb temperatures were made during 

these two series. The methods used during the 

series of observations on August 5-6, 1950, 

are described below.

(1) Lake stage measured by a vernier point 

gage, reading directly to thousandths of a 

foot. A gage well was provided by a 55 gallon 

oil drum, set offshore in the northern part 

of the lake in water about 2.5 feet deep. The 

Intake was a quarter-Inch hole about 18 inches 

below water surface.

(2) Wet- and dry-bulb temperatures measured 

by standard Weather Bureau type sling psychrometer. Observations were made under the 

shade of a tractor umbrella, on the northern 

shore about 6.5 feet above water surface. 

Check observations showed no detectable difference between temperatures thus measured 

on the upwind and the downwind sides of lake.

(3) Wind speed measured by a 5-cup Priez 

anemometer, mounted about 6.5 feet above water 

surface.
14

(4) Water temperature: (a) Surface water 

measured at a point near the well, with bulb 

just under the surface and shaded from the 

sun. Check measurements of surface-water temperatures at various points in reservoir showed 

temperatures varying as much as 2° higher or 

lower from that measured at index point, (b) 

Bottom water measured by obtaining a sample 

of bottom water in a 12-ounce bottle with a 

slow air leak. Duplicate samples were taken 

to assure equilibrium between bottle and water. 

Observations were made in water 4 feet deep. 

Greatest depth is probably 5.5 feet.

The observations are given in table 4. Averages for 4-hour periods are given for the 

June 1949 series and 2-hour periods for that 

of August 1950 when more precise data were obtained.

Generalized hydrographs of rates of change 

in water level are shown on figure 10. The 

diurnal cycle is well developed in both series 

of observations, although more marked In the 

June 1949 series. The minimum rate in each 

case was reached during the hours after midnight.

The minimum rate approaches the rate of 

seepage to the extent that evaporation during 

the early morning hours was zero and might be 

taken as close approximation of the seepage 

rate, were It not that consideration must be 

given to the possibility of negative evaporation, I.e., condensation. A closer estimate 

of seepage might be calculated if allowance 

Is made for the rate of evaporation or condensation, small as the rate might be.

There are several formulas for combining the 

meteorological factors into an expression for 

evaporation. A review of these formulas and 

the theories upon which they are based Is 

given In a recent report by the U. S. Navy

0.003

0.002

o.ooi

6a.m. 12m.

Time of day

Figure 10. Diurnal variation in rate of recession 

in water level.

Electronics Laboratory (Anderson et al., 1950). 

We are not concerned with a formula for evaporation but rather with an expression that is 

proportional to evaporation; or more- specifically one that will reduce to zero when evaporation is zero. For this purpose, use can be 

made of the expression: E u^A (ew - ea ), 

where u is wind speed in miles per hour; ew 

is vapor pressure in Inches of mercury, corresponding to temperature of the surface water 

In the reservoir; and ea is the vapor pressure 

of the air, corresponding to the dew point.

An examination of the data in table 4 shows 

that dew points were generally stable during 

the periods of observation. Water at the surface showed significant amounts of cooling at 

night, but rates of wind movement showed the 

major diurnal change. Most of the variation 

in rate of recession in water level was associated with changes in wind speed. This association Is somewhat unfortunate because comparatively little is known about the effect 

of wind speed upon the rate of evaporation 

under differing conditions of atmospheric stability, whereas experiments generally confirm 

that, except for molecular diffusion In the 

absence of wind, evaporation is proportional 

to ew - ea . the so-called "Dalton difference." 

Rough calculation, however, Indicates that 

molecular diffusion Is of the order of 0.00005 

foot per hour, an amount too small to be considered In this analysis. Therefore, It Is 

permissible to presume that under field conditions evaporation Is zero when wind is zero, 

a condition that is satisfied by the foregoing 

expression.

The value of the exponent of the wind speed, 

3/4, as originally proposed by Mlllar (1937) 

for average atmospheric stability, is confirmed 

by these observations to the extent that a 

value of about this size yields the maximum 

correlation with the rate of recession In 

water level. Although a more general analysis 

would permit variation in the value of the exponent of wind speed In accordance with the 

degree of stability, a constant exponent Is 

considered sufficiently satisfactory for this 

study.

The values of the expression u (ew - ea ) 

are given in the final column of table 4 and 

are plotted against the observed rate of recession on figure 11. The points satisfactorily 

define two graphs of equal slope but different 

intercepts for the two series. We are concerned 

primarily with these Intercepts because they 

presumably represent the rate of recession 

when evaporation is zero. The ( rate of recession then represents seepage. 'The intercepts 

on the axis of zero evaporation are 0.00038 

foot per hour for the series of June 1949 and 

0.00064 foot per hour for the series of August 

1950. The greater seepage in the August 1950 

series is due largely to the fact that the 

water level then stood Just at the spillway, 

2.3 feet higher than in June 1949.

The water budget for 24-hour periods In tiaese 

two -series Is as follows:

Date

June 27- 

28, 1949 

Aug. 5-6, 

1950

Stage Surface 

area

Ifeert} (acres)

91.92 a. 6 

94.22 6.5

Total 

fall In 

24 hours

(feet)

0.032 

.028

Seepage

(feet)

0.009 

.015

Evaporation,. by 

difference

(feet)

O.OC3 

.013
15

CTJ 

<D 

I

0.001 0.002

Rate of recession, in feet per hour

Figure 11. Variation in rate recession with u>» (©w~ e St)«

The quantities in acre-feet can readily be 

determined, if desired, by multiplying the 

depths by the surface areas in acres on the 

respective days, as given in the table at the 

bottom of page 14.

The analysis of the seasonal variation in 

the rate of recession for Juniper Tank, by 

the methods explained in the Postoffice Tank 

illustration in this report, indicates that

the mean rate df seepage of Juniper Tank during the summer months is about 0.32 foot per 

month, or 0.01 foot per day. This value is 

within the range indicated by the above analysis of the diurnal cycle. By detailed analysis of the diurnal cycle several times during 

the year, it should be possible to define the 

influence upon seepage of stage, water temperature, and other factors.
16

Table 4.--Observations at Juniper Tank

Time

June 27, 1949:

4-8 p.m.

8-12 p.m.

June 28, 1949:

12 p.m. - 4 a.m.

4-8 a.m.

8 a.m. - 12 m.

12 m. - 4 p.m.

Average

Aug. 5, 1950:

12 m. - 2 p.m.

2-4 p.m.

4-6 p.m.

6-8 p.m.

8-10 p.m.

10 - 12 p.m.

Aug. 6, 1950:

12 p.m. - 2 a.m.

2-4 a.m.

4-6 a.m.

6-8 a.m.

8-10 a.m.

10 a.m. - 12 m.

12 m. - 2 p.m.

Average

Average rate

of recession

in water

level

(ft per hour)

Average

air tempero 4*nY»A C* UliJ O

/ Orp \

Average

dew point

(°F)

Average water

temperature

surface

(°P)

bottom

(°P)

Series of June 27-28, 1949

0.0025

.0009

.0006

.0010

.0011

.0019

.00133

.0016

.0015

.0015

.0014

.0007

.0010

.0008

.0010

.0008

.0009

.0010

.0012

.0019

.00118

83

70

56

60

77

87

30

30

32.5

33

34.5

34.8

78.5

74.0

69.4

67.5

74

79

-

-

-

-

-

-

Average

wind speed

(mph)

,,3/4 / A _ A \ u * ew ea'

(see p. 14)

9

1.5

0.5

3.8

5.8

5

4.18

,94

.41

1.32

2.41

2.69

1.99

Series of August 5-6, 1950

74.6

78.4

79.5

73.1

67.8

64.0

60.5

60.0

59.8

65.0

75.0

79.9

82.5

53.5

49.1

52.5

57.1

58

57

57

56.5

55.2

57.2

56.5

51.9

52.4

72.2

79 ~

79

77

75.1

73'. 6

72.5

71.5

70.9

70.2

73.4

79.8

83.0

-

71.2

-

-

-

-

-

-

70.0

-

-

-

70.8

8.2

4.0

4.0

3.5

0.6

1.7

1.2

2.5

1.75

2.9

2.6

3.8

5.7

1.85

1.83

1.68

1.18

.26

.54-

.38

.62

.48

.60

.75

1.70

2.73

1.12

PERFORMANCE

The results obtained at the reservoir gaging stations as summarized in table 3 are, in 

general, self-explanatory. The capacities of 

the reservoirs studied ranged from 2.1 to 144 

acre-feet. In relation to size of drainage 

area the capacities averaged about 9 acre-feet 

per square mile. Reservoirs with less capacity 

than this generally spilled one or more times 

during the period of gage readings.

Reservoir shape is indicated by the ratio 

v/ah (see column 9 of table 3), where a is 

the area in acres at spillway level (column 

8), h the depth in feet from spillway level to 

bottom of the reservoir (column 7), and v the 

total capacity in acre-feet to spillway level 

(column 6). This ratio averages about 0.4 and 

suggests a rough rule for estimating capacity 

of a reservoir capacity = 0.4 x area x depth.

Table 3 includes a summary of the maximum 

and minimum water levels and coritents during 

the period of observation, generally 1945-48. 

About half the reservoirs overflowed and, 

with few exceptions, every reservoir listed 

was dry at least once during the period of observation. Reservoirs are built to hold water 

between rains. The ideal reservoir contains 

usable water all year, although in cases of 

seasonal-use of the range the reservoir need 

contain water only during seasons when the 

surrounding range is grazed. As measured by 

the average number of months per year during 

which they contained water, the reservoirs 

included in this study were fairly successful. 

Only three had water for less than 6 months, 

whereas five contained water the year long.

Depth of water is well recognized as a major 

criterion in governing performance of a reservoir; but it is important not to confuse depth 

of water with depth of reservoir, as many high 

dams impound only shallow pools of impermanent 

water.

The depth of water in a reservoir, and therefore its performance, is the result of several 

factors: Volume of inflow; frequency of inflow; 

rate of loss; and depth-area relation of reservoir. A study of these factors in relation 

to the performance of the reservoirs is shown 

on figure 12. The ordinate represents the average number of months per year that the reservoirs contain water, as given in column 19 

of table 3. In the quantity R/aL, R represents 

the annual runoff in acre-feet (column 21 of 

table 3), a the mean water-surface area in 

acres (column 15), and L the mean rate of water 

loss in acre-feet per month (column 16). The 

plotted numbers on figure 12 indicate the average number of months per year in whl.ch recharge occurs (column 20). For most of the 

reservoirs studied the value of a averaged 

about 60 percent of the area at the spillway 

(column 8 of table 3) for reservoirs with 

yearlong supply, and 30 percent for others. 

The relationship shown on figure 12 can be 

approximated by the following formula: 

p = (F - 1) » R/aL. The value of F (average 

frequency of recharge) ranged from 1 to 3 

months per year, so that the carryover term 

R/aL is the major criterion as to performance. 

In humid regions, where recharge occurs more 

frequently, high performance can be achieved 

even though the quantity R/aL is low.
17

12

&en s

I 6

<u9a

(3.5

.4.0,

Plotted figures indicate 

frequency of recharge

R 

aL

12 15

Figure 12. Relation of performance to runoff, water area, 

water loss and frequency of recharge.

PRINCIPLES OP RESERVOIR DESIGN

Unlike an Irrigation reservoir, the performance of a stock-water reservoir Is dependent 

on depth of water rather than on capacity. 

The records demonstrate that there Is generally 

little need for a reservoir to have a capacity 

greater than that necessary to store the mean 

annual runoff. Providing additional capacity 

to store the water that would spill In years 

of extraordinary runoff, according to the^ evidence obtained, does not thereby provide 

water'during extended dry periods. Rates of 

loss are great at high, Infrequent stages and 

losses at such stages may be at the expense 

of downstream users without necessarily benefiting the stock-water supply. Increasing capacity is generally an uneconomical method of 

obtaining depth. For example, doubling the 

capacity In most reservoirs adds only about 

35 percent to the depth. Nor does placing reservoirs In tandem, in lieu of a single large 

reservoir, seem to help; to the contrary, It 

even Increases losses without providing water 

during dry years. Rate of losses Imposes a 

limit on the amount of carry-over water that 

can be provided.

The problem Is to get sufficient water depth 

to carry over a reasonably long dry period. 

For economic reasons, this need not be the 

longest dry period on record, but it must be 

one that is fairly representative of the dry 

periods that are likely to occur. The waterlevel records Indicate that, this dry period 

In Arizona is rarely longer than 15 months 

and is less where recharge occurs more than 

once a year. For purposes of design, the dry 

period In months may be roughly estimated from 

the formula 15 [J2/ (F + 1)J , where F is the

average frequency of recharge per year. This 

leads to the Important criterion that depth 

should be at least equal to 15 [2/(F + 1)] L, 

 where L Is average rate of water loss In feet 

per month--provided that the capacity at this 

depth does not greatly exceed annual runoff.

Consider the following as an example. Given: 

R = 15 acre-feet per year, L = 0.6 foot per 

month, and F = 2 months; required: depth for 

IS-month performance. Depth needed Is 

15 f2/(F + 1)]L = 6.0 feet. The area-capacity 

curves for this site shows a surface area of 

2\5 acres and a capacity of 6 acre-feet at a 

6-foot depth. The mean surface area exposed 

to loss may be taken as 0.6 of the area 'at the 

6-foot depth. Annual losses would therefore 

be (0.6 x 2.5 acres) x 0.6 foot per month x 12 

months = 11 acre-feet. Since there Is ample 

runoff to supply this loss, a 6-foot reservoir 

should provide 12-months water per year, on 

the average, until this depth Is depleted by 

sedimentation. Excess water will be spilled.

If runoff were only 3 acre-feet per year 

there would be some question whether a 6 acrefoot reservoir would be economical at this 

site, Inasmuch as It would be rarely filled. 

Yearlong water supply could be obtained at 

this site only through supplementation of depth 

by excavation of a charco (pit reservoir) such 

that total capacity at a depth of 6 feet does 

not excded the annual runoff, about 3 acrefeet in this example.

The design of a stock-water reservoir requires information that is not generally available in advance. The data obtained in this investigation, nevertheless, do indicate certain 

limits that might be observed in order to
18

minimize expense without detracting from performance. Some rough rules might be as follows: 

Depth not less than about 7 feet for. a capacity 

of not more than 5 to 10 acre-feet per square 

mile of drainage area. Where this depth cannot 

be obtained within the specified limit of capacity at a natural site, charco pits are necessary. Charco pits constructed by building 

the dam from materials excavated from the reservoir bottom are desirable in every case provided excavation does not extend into permeable 

materials. Enough is known (Holtan, 1950) about 

soils to show that seepage losses may be minimized by compacting the bottom materials 

prior to filling the reservoir. The best material for compaction, is a well-graded mixture 

of not more than 30 percent or even as little 

as 5 percent of clay. The bottom should be 

loosened to a depth of at least 6 inches and 

then brought to a moisture content of good 

tilth. The loosened and moistened soil should 

be compacted by heavy machinery or cattle. The 

process is about the same as might be followed 

in building a tight dam. In important jobs, 

the method can be refined and the material made 

nearly water-tight.

For practical reasons reservoirs should have 

at least 3 acre-feet capacity, which entails 

a drainage area of at least 0.6 square mile.

Exceptions might be made in regions of high 

runoff provided seepage is very low. As reservoirs on large drainage areas tend to involve 

troublesome amounts of sediment as well as 

other expensive factors, it appears inadvisable 

to impound a wash with a drainage area of more 

than 15 square miles for a stock-water supply.

REFERENCES CITED

Anderson, E. R., Anderson, L. J., and Marciano, 

J. J., 1950, A review of evaporation theory 

and development of instrumentation, interim 

report on Lake Mead water-loss investigation: 

U. S. Navy Electronics Lab. Rept. 159, San 

Diego.

Holtan, H. N., 1950, Holding water in farm 

ponds, Soil Cons. Service, U. S. Dept. Agr., 

SCS-TP-93, 10 pp.

Millar, F; G., 1937, Evaporation from free 

water surfaces: Canadian Meteorological Memoirs, vol. 1, no. 2.

White, Walter N., 1932, A method of estimating 

ground-water supplies based on discharge by 

plants and evaporation from soil: U. S. Geol. 

Survey Water-Supply Paper 659A.

lottrior Dvplloftti&i Station, ffMhl&|to&, 0. C. t*ltl