Outline of Methods 

for Estimating 

Ground-Water Supplies

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 638-C

Outline of Methods 

for Estimating 

Ground-Water Supplies

By OSCAR EDWARD MEINZER

CONTRIBUTIONS TO THE HYDROLOGY OF THE 

UNITED STATES, 1931

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 638-C

Reprint, 1959

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1932
UNITED STATES DEPARTMENT OF THE INTERIOR 

FRED A. SEATON, Secretary

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director

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

Washington 25 D.C. - Price 20 cents (paper cover)
CONTENTS

Page 

Introduction __________-_-_-_----_-_-------------_-__---_---_.._--- 99

Rock formations as reservoirs______-__------_------_-_-___-_-_-__-- 99

General conditions.___-_--_------_------_-_--__--------_--_--- 99

Methods for estimating intake from surface streams___-__-_._.__-. 100 

Methods for estimating intake directly from rains and melting snow. . 102 

Methods for estimating discharge by overflow____________________ 105

Methods for estimating discharge by evaporation from soil and 

transpiration from plants.___._______--____--___--_-_-_-_----- 107

Storage methods in general..________________-__-__--_-__---__-_ 110

Specific yield in relation to storage methods._____________________ 113

Methods for estimating discharge from daily fluctuations of the 

water table_-_.__.._.__________.._-__.__-__--_----_--._--_ 116

Method based on ground-water rating curve.--.------------------ 119

Safe yield as compared with natural intake and discharge...--_.-__ 119 

Storage methods applied where use has become large.____-_-_.__._ 122

Leakage methods________.__._..._.-..-.--.-._-_----_-__--_--_ 124

Rock formations as conduits__._______-___-__-_--_-__--_---_------ 126

General conditions.______________-----____-------------------- 126

Methods based on field tests of velocity________________________ 126

Methods based on laboratory determinations of permeability _______ 131

Method based on permeability determined from discharge and drawdown of wells_____________________________________________ 134

Method based on area of influence of wells __ ___-_--___-_-_----__- 136

Method based on movements of water levels in relation to rates of 

withdrawal _______....__._..__-__.___-_-___-_-___-_-___-_. 138

Evaluation of extraneous influences on the water levels. --_-._--_--__-_- 140

Present status and outlook ___ __. .___ ___ 142

in

OUTLINE OF METHODS FOR ESTIMATING GROUND-WATER

SUPPLIES 1

By OSCAR EDWARD MEINZER

INTRODUCTION

The most urgent problems in ground-water hydrology at present 

are those relating to the rate at which the rock formations will supply 

water to wells in specified areas not during a day, a month, or a 

year but perennially. The permeable rock formations may be regarded 

as underground reservoirs or as underground conduits. Some waterbearing formations function chiefly as reservoirs, others chiefly as 

conduits, but all of them have some of the properties of both. In 

attempting to solve the quantitative problems above mentioned these 

two functions of rock formations must be recognized and differentiated. Quantitative methods based on the reservoir conception are 

applicable chiefly, though not exclusively, to formations or parts of 

formations that have water tables; methods based on the conduit 

conception are applicable most largely to artesian formations, in 

which the water moves laterally considerable distances from the 

intake to the discharge area.

ROCK FORMATIONS AS RESERVOIRS 

GENERAL CONDITIONS

The natural reservoirs formed by rock formations generally have 

very great capacity compared with that of ordinary artificial surface reservoirs, just as most other natural features are of huge size in 

contrast to the works of man. However, if the water derived from 

them is taken chiefly out of storage without being replaced the supply will eventually fail.

The " safe yield " of an underground reservoir, or the practicable 

rate of withdrawing water from it perennially for human use, may 

be estimated by methods that are comparable to those used in estimating the safe yield of a surface reservoir, although different in

1 The substance of this paper was presented Dec. 29, 1928, at a meeting of the Society 

of Economic Geologists in New York City, and mimeographed copies of the paper 

in abbreviated form had been sent to the members prior to the meeting. The paper has 

been revised and enlarged for the present publication.
100 CONTRIBUTIONS TO HYDROLOGY OF UNITED STATES, 1931

technique. It is necessary to measure the rate of inflow (intake 

methods) or the rate of discharge (discharge methods), or else these 

rates must be estimated by determining changes in storage (watertable or storage methods).2 In many areas the most effective method 

of studying the ground-water supply is the inventory method, in 

which all available methods are used to make periodic inventories 

of the entire water supply of the area, from its entrance into the 

area as precipitation, stream flow, or underground percolation to 

its exit as evaporation, transpiration, run-off, or underground 

leakage.

The work of Charles H. Lee 3 in Owens Valley, Calif., in 1908 to 

1911, is of outstanding importance in the history of quantitative 

methods in ground-water work, because he devised an entire system 

of quantitative methods and applied them in orderly fashion to 

obtain an average value for each element of intake into and discharge out of the underground reservoir. The term "inventory 

method " is more accurately applied, however, to investigations in 

which a detailed accounting of the several elements of intake, storage, and discharge is attempted for each of successive months, years, 

or other units of time during the entire period of observations. 

Thus, in the investigation in the Pomperaug Basin, Conn.,4 an attempt was made to organize the available data in a monthly inventory of the water supply during a period of three years.

METHODS FOB ESTIMATING INTAKE FROM SURFACE STREAMS

The principal intake method consists of establishing gaging stations on influent streams and determining the quantities of water 

lost between successive stations. The quantity of water that reaches 

the water table consists of this loss minus the loss by evaporation 

and transpiration either directly from the stream or from soil moisture supplied by the stream. The method has been used in many 

ground-water investigations in the present century, notably in California, Arizona, New Mexico, Nevada, Utah, Colorado, and Idaho. 

The earliest measurements of seepage losses from streams and 

canals were made chiefly to ascertain the losses of surface water 

for example, the investigation by Grunsky,5 in 1882, of losses from

2 Meinzer, O. B., Quantitative methods of estimating ground-water supplies: Geol. Soc. 

America Bull., vol. 31, pp. 329-338, 1920.

3 Lee, C. H., An intensive study of the water resources of a part of Owens Valley, 

Calif.: U. S. Geol. Survey Water-Supply Paper 294, 1912; The determination of safe 

yield of underground reservoirs of the closed-basin type: Am. Soc. Civil Bng. Trans., 

vol. 78, pp. 148-251, 1915.

* Meinzer, O. E., and Stearns, N. D., A study of ground water in the Pomperaug Basin, 

Conn., with special reference to intake and discharge: U. S. Geol. Survey Water-Supply 

Paper 597, pp. 73-146, 1928.

5 Grunsky, C. B., Irrigation near Presno, Calif.: U. S. Geol. Survey Water-Supply Paper 

18, pp. 71-79, 1898.
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 101

irrigation canals in the vicinity of Fresno, Calif. Later, however, 

in several investigations, seepage losses have been determined chiefly 

for the purpose of estimating the amount of ground-water recharge. 

Notable among the early ground-water investigations in which the 

seepage method was used are those of Clapp 6 and Mendenhall 7 in 

southern California, Smith in' Arizona,8 and Lee in Owens Valley. 

One of the most intensive studies of this method was made by 

Bailey 9 in his work on ground-water recharge in the Niles cone, 

California, by seepage from Alameda Creek. Bailey undertook not 

only to determine the recharge by years or other long periods, but 

also to determine the daily recharge, which required accurate data 

on changes in channel storage with changes in gage heights. He 

also investigated the relation of rate of recharge to the temperature 

of the water and to the duration of high stages of the river. Ult.i-i 

mately he developed curves to show the relation of rate of seepage 

to rate of stream flow and produced an empirical formula by which 

the recharge in any day can be computed from the records of stream 

flow and temperature. Intensive use of the seepage method has 

recently been made by Conkling 10 in the drainage basin of the San 

Gabriel River, and by Post" in the drainage basin of the Santa Ana 

River, both in California.

The seepage method gives the most reliable results for streams 

with relatively constant flow and heavy losses in proportion to the 

total flow. It is generally not applicable in times of flood, when 

the measurements of flow are relatively inaccurate and the percentage of loss is small. It is not applicable or only difficultly applicable to perennial streams in which the loss is small in comparison 

to the total flow, because with such streams small percentage errors 

in the measurements of the flow may produce large percentage errors 

in the computed seepage losses.

The seepage method is not very applicable for determining recharge from intermittent and ephemeral streams and is wholly inapplicable for determining recharge directly from rain or melting

 Clapp, W. B., in Hoyt, J. C., Report of progress of stream measurements for the 

calendar year 1903, pt. 4, Interior Basin, Pacific, and Hudson Bay drainage: U. S. Geol. 

Survey Water-Supply .Paper 100, pp. 339-356, 1904.

7 Mendenhall, W. C., The hydrology of San Bernardino Valley, Calif.: U. S. Geol. 

Survey Water-Supply Paper 142, pp. 50, 51, 1905; Ground waters and irrigation enterprises in the foothill belt, southern California: U. S. Geol. Survey Water-Supply Paper 

219, pp. 28, 29, 1908.

8 Smith, G. E. P., Ground-water supply and Irrigation in the Rillito Valley: Arizona 

Univ. Agr. Exper. Sta. Bull. 64, pp. 118, 119, Tucson, 1910.

 Bailey, Paul, Engineering investigation of percolation from Alameda Creek and groundwater studies on Niles cone: California State Water Comm. Third Bienn. Kept., pp. 95- 

131, 1921.

"Conkling, Harold, San Gabriel investigation: California Dept. Pub. Works Div. 

Water Rights Bull. 5, pp. 52-72, 1927.

11 Post, W. S., Santa Ana investigation, flood control and conservation: California 

Dept. Pub. Works Div. Eng. and Irr. Bull. 19, pp. 165-179, 1929.
snow. In humid regions almost no streams except the ephemeral 

ones are influent, and therefore this method obviously has little 

application. The method as applied to ephemeral streams presents 

two difficulties the storm run-off is too flashy to be measured accurately, and a considerable part of the surface water lost by seepage 

may be held by molecular attraction in the soil and subsoil and 

therefore may not reach the water table but may ultimately be 

returned to the atmosphere.

Studies have recently been made by White 12 of recharge from 

the flow of the Mimbres River, an intermittent stream in New Mexico, 

which generally flows about 20 to 36 hours after a torrential 

summer rain. The flow from some of the rainstorms was all lost 

within the stretch of the river that crosses the intake area, and the 

loss could be determined by measuring the flow at the upper end 

of this stretch. In the heaviest storms, however, the flow persisted 

beyond the' intake area, and measurements were made at convenient 

intervals within this stretch to determine the approximate loss. 

Borings were made in the bed of the river before and after the 

storms, and the moisture content of samples obtained from these 

borings was determined in order to ascertain how much of the 

seepage water was held by the sand of the river bed.

METHODS FOR ESTIMATING INTAKE DIRECTLY FROM BAIN AND

MELTING SNOW

Many attempts have been made to measure directly the percolation from the surface to the water table. Mariotte, in the seventeenth 

century, observed the percolation of rain water into the cellar of 

the Paris Observatory. Measurements of percolation have been 

made with lysimeters, or vessels to catch the downward percolating 

water, by several European ia and American 14 investigators, and 

some very long records have beei^ obtained in England. The first 

tests mentioned by Veatch were made by Dalton in Manchester, 

England, from 1796 to 1798, and by Maurice in Geneva, Switzerland, 

in 1796 and 1797. The longest record, that of Dickinson and Evans, 

in Hempel Hempstead, in England, extended over at least 49 years, 

from 1835 to 1884, and the records of Lawes and Gilbert and those 

of Greaves extended over 32 and 22 years, respectively. Many of

u White, W. N., Preliminary report on the ground-water supply of Mimbres Valley, 

N. Mex.: U. S. Geol. Survey Water-Supply Paper 637, pp. 77-80, 1931. (Released in 

manuscript form in 1929.)

18 Veatch, A. C., Fluctuations of the water level in wells: U. S. Geol. Survey WaterSupply Paper 155, pp. 32-34, 44-49, 1906. This paper summarizes the work that had 

been done with lysimeters in England and on the continent of Europe.

u Bark, D. H., Duty of water investigations, experiments, and results: Idaho State 

Engineer Ninth Bienn. Rept. (1911-12), pp. 302-309; Experiments on the economical use 

of irrigation water in Idaho: U. S. Dept. Agr. Bull. 339, pp. 37-39, 1916. Other American experiments could be cited.
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 103

the lysimeter tests have been made with disturbed materials and 

under other artificial conditions, which may have produced results 

very different from those that would be found under natural conditions. Moreover, even if tests are made under natural conditions, 

the fundamental difficulty will still be encountered that downward 

percolation is irregularly distributed, and it is difficult or impossible 

to find a place for the test that is even approximately representative 

of average conditions. An extensive area may have little or no 

recharge, but at a few places water may be pouring into the zone 

of saturation in large volumes.

Tests recently made by H. F. Blaney and C. A. Taylor 15 near 

Ontario, Calif., indicate that water percolating downward through 

unsaturated material tends to follow the surface of the constituent 

grains and hence to move around any vessel that is placed underground to catch it. If the material extends downward into the 

vessel, the percolating water will accumulate in the capillary openings of the material in the vessel and can be detected by laboratory 

determination of the increase in moisture content of that material. 

However, unless the material lies within the vessel to a height exceeding the capillary range, no free gravity water may appear in the 

vessel even though recharge is occurring.

The earliest attempts to determine the rate of ground-water 

recharge were doubtless based on measurements of the quantities of 

water that fall as rain or snow. This was the method of Mariotte,16 

who attempted a quantitative study of the water supply of the 

drainage basin of the Seine Kiver by making crude measurements 

of the water that fell as rain on the basin and of the water discharged by the river. By means of these measurements he disproved 

the ancient assumption that the rainfall is inadequate in amount 

to supply the water discharged by the springs. In the years that 

have elapsed since Mariotte's work the most common method of 

estimating ground-water recharge has probably been to determine 

approximately the quantity of water that annually falls as rain or 

snow on a given area and apply to this quantity the percentage that 

is assumed to reach the zone of saturation. This method is of little 

value, however, except to give an idea of the maximum possibilities, 

unless there is a reliable basis for the percentage that is assumed. 

Commonly the assumed percentage and therefore also the computed 

recharge are much too large.

15 Unpublished data. Since this paper was sent to press the following paper describing 

these methods has been published: Taylor, G. H., Investigations relating to the absorption of precipitation and its penetration to the zone of saturation: Am. Geophysical 

Union Trans. 12th meeting, pp. 206-211, 1931.

19 Mariotte, Edme, Traites du mouTements des eaux et des autres corps fluides, 1686.

497117 O-59-2
104 CONTRIBUTIONS TO HYDROLOGY OP UNITED STATES, 1931

Attempts have been made to compute the recharge in an intake 

area by deducting the run-off and the evaporation (including transpiration) from the precipitation, but the results have generally 

been unreliable, especially because of uncertainty as to the amount 

of evaporation and transpiration. The method is inapplicable 

where the recharge is relatively so small that a moderate percentage 

error in precipitation, run-off, or evaporation may produce a large 

percentage error in the computed recharge. It apparently gave useful results as applied by McCombs 1T and Kunesh 18 in estimating the 

ground-water supply of the island of Oahu, where fairly accurate 

data are available as to precipitation and run-off and where the 

intake facilities are so good that a large proportion of the precipitation seeps into the rocks and percolates to the water table. The 

weakest element in the Oahu computations was the estimate of 

evaporation, for which reliable data were not available. To overcome this weakness, tests of soil evaporation and transpiration are 

now being made.

Recently a detailed study has been made with this method by 

Blaney 19 in certain intake areas in southern California. From the 

quantity of water produced by each rain during the winter rainy 

season were deducted the carefully estimated quantities of run-off 

produced by the rain and of soil evaporation and transpiration during the subsequent period of fair weather. Borings and tests of 

soil moisture proved that the remaining water was stored in the soil 

to satisfy the deficiency of soil moisture in the root zone. After 

this deficiency had been completely supplied and the soil moisture 

had been brought up to the specific retention, or quantity of water 

that the soil can hold by molecular attraction against the pull of 

gravity, any remaining surplus was assumed to percolate downward 

beyond the reach of plant roots and ultimately to reach the water 

table. If an impermeable bed intervened between the root zone 

and the water table, the downward percolating water would necessarily form a body of perched ground water above the impermeable bed.

The method of following the movements of water in the soil by 

making periodic borings with soil augers and determining the 

moisture content of soil samples obtained from different depths has 

been extensively used in connection with agricultural investigations 

and less frequently to determine the ground-water recharge. Re17 McCombs, John, Methods of estimating safe yield of Honolulu artesian area: Honolulu Sewer and Water Comm. Kept., 1927, pp. 55-61.

M Kunesh, J. F., Surface, spring, and tunnel water investigations : Honolulu Sewer and 

Water Comm. Kept., 1929, pp. 85-92.

"Blaney, H. F., Disposal of rainfall, in Post, W. S., op. cit. (Santa Ana investigation), 

pp. 152-157.
METHODS FOE ESTIMATING GROUND-WATER SUPPLIES 105

cently, however, earnest attempts have been made to use this method 

in ground-water investigations in California by Sonderegger,20 by 

Blaney and C. A. Taylor, and by Stearns, Eobinson, and G. H. 

Taylor.21 In the latest work by G. H. Taylor the moisture equivalent, or amount of moisture retained by the soil in a centrifuge, 

was taken as a rough measure of the specific retention in computing 

deficiencies in the belt of soil moisture, or " root zone."

METHODS FOE, ESTIMATING DISCHARGE BY OVERFLOW

An underground reservoir, like a surface reservoir, may lose water 

by overflow, evaporation, diversion, and underground leakage. The 

overflow of an underground reservoir may appear in definite springs 

or in general seepage that contributes to the flow of the surface 

streams. If it appears in a few large and definite springs the 

ground-water discharge can be determined by measuring the flow of 

these springs. If the springs are relatively constant it may be 

sufficient to make occasional measurements with current meter, weir, 

or other device; if they are relatively variable it may be necessary 

to establish gaging stations in order to obtain records of daily or 

continuous rate of flow. An excellent example of an extensive 

survey made largely by the first method is that by Crandall 22 and 

others of the very large and relatively constant springs that issue 

from the lava rocks into the Snake Kiver, in Idaho. Examples of 

the second method are afforded by gaging stations, some of them 

with automatic water-stage recorders, maintained by the United 

States Geological Survey on several of the springs of first magnitude in Missouri and Texas that issue from limestone and have great 

fluctuations.23

If the overflow of the underground reservoir appears in many 

small, widely scattered springs or in general seepage its quantity 

may be estimated by establishing gaging stations on the effluent 

streams to measure the total run-off and then differentiating between 

the two components of the total the direct run-off and the groundwater run-off. This differentiation can best be made by studying

80 Sonderegger, A. L., Water supply from rainfall on valley floors: Am. Soc. Civil Bng. 

Proc., vol. 55, pp. 1144-1150, 1929. Since this paper was sent to press the following 

paper relating to this subject has been published: Blaney, H. F., Taylor, C. A., and 

Young, A. A., Rainfall penetration and consumptive use of water In Santa Ana River 

valley and coastal plain: California Div. Water Resources Bull. 33, 1931.

a Stearns, H. T., Robinson, T. W., and Taylor, G. H., Geology and water resources of 

the Mokelumne area, California: U. S. Geol. Survey Water-Supply Paper 619, pp. 174, 

175, 1930; also more recent report released in manuscript form (on file in public library, 

Lodi, Calif.).

23 Crandall, Lynn, The springs of Snake River Canyon: Idaho Irr. Bng. and Agr. 

Societies Joint Conf., 1918 and 1919, Proc., pp. 146-150. See also Meinzer, 0. E., Large 

springs in the United States: U. S. Geol. Survey Water-Supply Paper 557, pp. 42-47, 1927.

23 Meinzer, O. E., op. cit. pp. 17-41.
106 CONTRIBUTIONS TO HYDEOLOGY OF UNITED STATES, 1931

small representative drainage basins rather than by gaging the 

trunk stream of a large drainage basin, because the large basin is 

likely to have more frequent rainfall in some parts of its area and a 

longer and less definite period for complete delivery of the direct 

run-off.

In a study by the United States Geological Survey of the drainage 

basin of the Pomperaug River, in Connecticut, which has an area 

of 89 square miles, a gaging station was established near the mouth 

of the river. It was determined, from considerations of channel 

storage, velocity of the water, and rate of movement of flood crests, 

that the direct run-off is nearly all delivered from the basin within 

a week of the time the water falls as rain, and that therefore the 

stream flow a week or more after the latest rain is virtually all 

derived from ground water. A hydrograph was constructed of the 

total run-off for the years covered by the investigation, 1913 to 1916, 

and a hydrograph of the ground-water run-off was then made which 

coincided with that for total run-off in the periods of prolonged fair 

weather and was interpolated between these periods. The groundwater run-off was computed from this hydrograph.24 This general 

method was earlier used in the flood-control investigation of the 

drainage basin of the Miami River, in Ohio, by Houk,25 who prepared a hydrograph of the ground-water run-off of the Mad River 

for the period 1915 to 1919 by connecting the low points of the 

hydrograph for total run-off.

The method can be improved by obtaining gage-height records at 

enough points in the drainage system to permit an estimate of the 

channel storage of the system on each day. The daily ground-water 

run-off can then be computed as soon after a rain as the storm water 

has reached the streams. For any day with a falling stage after the 

storm water has reached the streams, the ground-water run-off will 

be the total run-off minus the decrease in channel storage. The 

decrease in channel storage can be estimated by maintaining gages 

at several points on the trunk stream and on selected tributaries and 

making surveys of the stream system showing the approximate 

water areas of different parts of the system at different gage heights. 

Calculations show that in a drainage basin which is not larger than 

the Pomperaug the total quantity of water stored in the stream system at any time is rather small compared with the rate of discharge, 

and hence that errors in the measurement of decrease in storage will 

introduce relatively small errors in the estimates of ground-water 

run-off. The proposed method would have the advantage that the

2* Meinzer, O. E., and Stearns, N. D., A study of ground water in the Pomperaug Basin, 

Conn., with special reference to intake and discharge: U. S. Geol. Survey Water-Supply 

Paper 597, pp. 107-116, pi. 19, 1929.

25 Houk, I. E., Rainfall and run-off in Miami Valley, State of Ohio: Miami Conservancy 

Dist. Tech. Repts., pt. 8, 1921.
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 107

record would cover a much larger part of each period between rains 

and that the entire process would be one of observation and measurement with less of the arbitrary .feature of the present method. It 

would not be necessary to make current-meter measurements to develop rating curves at the subsidiary stations, as only change in 

storage, indicated by change in gage height, would be involved.

METHODS FOB ESTIMATING DISCHARGE BY EVAPORATION FROM 

SOIL AND TRANSPIRATION FROM PLANTS

Where the water table is near the surface the underground reservoir loses water by evaporation from the soil and by transpiration from plants. In some arid regions all or nearly all the ground 

water is disposed of in this way, and little or no water remains to be 

discharged through springs and seeps. In humid regions, however, 

the ground-water recharge is greater, and more soil moisture is 

supplied directly by the rains and melting snow, with the result 

that evaporation from the soil and transpiration from plants make 

less heavy demands on the ground water. For these reasons in humid regions there is generally an excess of ground-water discharge 

over the consumption by soil evaporation and transpiration, and this 

excess feeds the streams and maintains their flow during dry seasons.

Tests of the rate of discharge of ground water by capillary rise 

from the zone of saturation and subsequent evaporation from the 

soil were made by Slichter 26 in 1905, Lee 27 in 1910 and 1911, 

Sleight 28 in 1916, and other investigators more recently. In the 

Escalante Valley investigation, by White,29 records were obtained 

of evaporation from columns of undisturbed soil for comparison 

with evaporation from similar columns of soil that was dug up and 

artificially packed into tanks. The rate depends on the evaporativity 

of the atmosphere, the depth to the water table, and the texture of the 

soil, which controls both the height and the rate of capillary rise. 

The standard method of estimating the quantity of ground water lost 

by soil evaporation is to map the discharge area with reference to 

specified depths to the water table for different seasons, and to determine by means of tank experiments the rate of discharge for each 

range of depth. The problem is likely to be complicated by diversity 

in the texture of the soil, which may require a soil map of the discharge area and tank experiments for soils of different types.

28 Slichter, C. S., The underflow in Arkansas Valley in western Kansas: U. S. Geol. 

Survey Water-Supply Paper 153, pp. 43, 44, 1906.

27 Lee, C. H., An intensive study of the water resources of a part of Owens Valley, 

Calif.: U. S. Geol. Survey Water-Supply Paper 294, pp. 57, 119, pi. 15, 1912.

28 Sleight, R. B., Evaporation from the surfaces of water and river-bed materials: 

.Tour. Agr. Research, vol. 10, pp. 209-261, 1917.

29 White, W. N., A method of estimating ground-water supplies based on discharge of 

plants and evaporation from soil; results of investigations in Escalante Valley, Utah 

(released in manuscript form in 1930),
108 CONTRIBUTIONS TO HYDEOLOGY OF UNITED STATES, 1931

Not much work has yet been done to establish the relations of 

the rate of soil evaporation to the factors that determine the rate. 

In most tank experiments data are obtained as to the atmospheric 

conditions and the depth to the water table, which give some basis 

for generalizations as to the variations of soil evaporation with 

variations in these factors. Generally records are also obtained of 

the rate of evaporation from a free water surface, so that the data 

as to soil evaporation can be expressed in terms of evaporation 

opportunity, or ratio of soil evaporation to evaporation from a free 

water surface. In the experiments by Sleight mechanical analyses 

were made of five soils used in the evaporation tests, and these analyses gave a basis for determining the evaporation opportunity for 

different sizes of grain with each of several depths to the water 

table. It is desirable that in future tank experiments tests be made 

of the mechanical composition, porosity, permeability, and capillary 

range of the soils used.

The rate at which soil discharge occurs may be controlled either 

by the rate at which the water can be lifted by capillarity to the 

level at which it is evaporated or by the rate at which it can be 

evaporated. The rate at which water is lifted through the soil from 

the water table to the point at which it is evaporated depends chiefly 

on the permeability of the soil, the height the water is lifted, and 

the capillary head or difference between the potential and actual 

capillary lift. In other words, the law of capillary rise is essentially Darcy's law of flow, in which the energy is furnished by 

capillary attraction instead of by hydrostatic head. Therefore, if 

the water table is very near the surface and the soil is very permeable the rate of discharge is determined by the possible rate 

of evaporation; but if the water table is at greater depth and the 

soil is less permeable the limiting factor may be the possible rate 

of capillary rise. Further investigation of the processes involved 

in soil discharge and of the controllng laws should help to make 

the field methods more applicable and exact.

As a rule, vegetal discharge, which is effected by transpiration, is 

greater than soil discharge and occurs over wider areas, because the 

roots of certain plants lift water much higher than it is lifted by the 

capillary interstices of the soil. In arid regions nearly all the vegetal discharge of ground water is accomplished by plants of a few 

dominant and well-recognized species.30 To determine the quantity 

of ground water discharged by the ground-water plants in any particular area it is necessary to make a map of the area showing, so 

far as may be practicable, the distribution, density, and growth of

""Meinzer, O. E., Plants as indicators of ground water: U. S. Geol. Survey WaterSupply Paper 577, p. 1, 1927.
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 109

the principal species, and ,to determine the rate at which they discharge water. Holes should also be dug to investigate the root 

habits of different species of plants and to determine to what depths 

their roots extend to reach the capillary fringe and feed on water 

from the zone of saturation.

Maps showing areas of ground-water discharge and the distribution of dominant species of ground-water plants have been made for 

several1 western valleys investigated by the Geological Survey for 

example, the Independence district of Owens Valley, Calif.,81 Sulphur Springs Valley, Ariz.,82 Big Smoky Valley, Nev.,88 Steptoe 

Valley, Nev.,84 and parts of Escalante Valley, Utah.85 Information 

that will be helpful in the construction of such maps is given in 

several of the United States Geological Survey water-supply papers.86

The rate of vegetal discharge has generally been determined by 

means of tanks in which the different species are grown with measured 

quantities of water and in some investigations with different depths 

to the water table. In Lee's investigations in Owens Valley the discharge of salt-grass areas was investigated by means of tank experiments in which natural conditions were reproduced as nearly as 

practicable. Since the work by Lee was done tank experiments have 

been made in connection with several ground-water investigations. 

In the recent investigation by White in the Escalante Valley records 

of discharge were obtained from soil tanks in which water tables 

were maintained and salt grass, alfalfa, and greasewood were grown. 

Comparative data were obtained on tanks with undisturbed salt-grass 

sod and on tanks which were filled and planted in the ordinary way. 

The method was also introduced of obtaining the dry weight of 

vegetable matter produced in the tank experiments and determining 

the ratio of weight of water consumed to weight of dry matter produced. This ratio was then applied to data on dry matter naturally 

produced in order to compute the natural discharge of ground water. 

The method of determining vegetal discharge from daily fluctuations 

of the water table is described on pages 116-119.

In humid regions the problems of both vegetal and soil discharge 

of ground water are complicated by the soil moisture that is derived

51 Lee, C. H., An intensive study of the water resources of a part of Owens Valley, 

Calif.: U. S. Geol. Survey Water-Supply Paper 294, pi. 25, 1912.

^Meinzer, O. E., and Kelton, F. C., Geology and water resources of Sulphur Spring 

Valley, Ariz.: U. S. Geol. Survey Water-Supply Paper 320, pis. 1, 2, 1913.

^Meinzer, O. E., Geology and water resources of Big Smoky, Clayton, and Alkali 

Spring Valleys, Nev.: U. S. Geol. Survey Water-Supply Paper 423, pi. 2, 1917.

"Clark, W. O., and Riddell, C. W., Exploratory drilling for water and use of ground 

water for irrigation in Steptoe Valley, Nev.: U. S. Geol. Survey Water-Supply Paper 

467, pi. 2, 1920.

36 White, W. N., op. cit., pi. 1 (map by W. N. White and Depue Falck).

88 See especially Water-Supply Paper 423, pp. 92-102, and Water-Supply Paper 577, 

already cited.
HO CONTRIBUTIONS TO HYDROLOGY OF UNITED STATES, 1931

directly from rain and snow. The problem of vegetal discharge is 

further complicated by the breaking down of the distinction between 

ground-water plants and plants that do not depend on ground water. 

No definite method has been developed for humid regions, but there 

are several possible lines of attack. More or less exact information 

on the extent of vegetal discharge of ground water in humid regions 

can bd obtained from observations on the depth to the water table, 

the distribution of vegetation of different types, the relation of the 

root systems to the water table and overlying capillary fringe, and 

the amount of soil moisture and changes in soil moisture at different 

depths, especially in periods of drought. E. D. Burchard, district 

engineer in the Geological Survey, found from the record of an 

automatic water-stage recorder that the flow of a small stream in 

North Carolina had considerable daily fluctuations in the very dry 

month of July, 1926. These fluctuations were apparently caused by 

differences in the rate of evaporation in different parts of the 24-hour 

period, chiefly in vegetal and soil discharge of ground water, and 

they suggest a possible method for humid regions. It is likely, however, that such a method would give less than actual quantities. In 

the Pomperaug investigation some consideration was given to a 

possible method based on a ground-water rating curve (see p. 119), 

but the method actually used was merely to compute the groundwater evaporation as the difference between ground-water recharge 

and ground-water run-off.87

STORAGE METHODS IN GENERAL

If a capacity table or curve has been developed for a surface reservoir, a gage showing the changes in its water level will indicate for 

any period the net increase or decrease in storage. When the water 

level is rising it will register the excess in rate of recharge over rate 

of discharge, and vice versa. If it is known that there is no discharge in a certain period the record of rise will show the total rate 

of recharge during that period.

Because of the frictional resistance of water-bearing materials to 

the flow of the water from the intake to the discharge area of an 

underground reservoir the water table is almost nowhere a level surface, such as the water surface of an ordinary reservoir. Therefore, when this storage method is applied to underground reservoirs 

the depths to the water level in numerous wells are measured every 

week or month, or at other more or less frequent intervals, and continuous records are generally obtained on a few representative wells 

by means of automatic water-stage recorders. Levels are usually run

»7 Meinzer, O. E., and: Stearns, N. D., A study of ground water in the Pomperaug 

Basin, Conn.: U. S. Geol. Survey Water-Supply Paper 597, pp. 138-139, 143, 1929.
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 111

to the observation wells, and a series of contour maps of the water 

table at successive dates are constructed. From these maps or from 

the base data it is possible to compute the volume of water-bearing 

material that became saturated or drained in a given period.

In order to evaluate these results in terms of water instead of 

water-bearing material it is necessary to apply a factor generally 

known as the specific yield. This factor represents the interstitial 

space that is emptied when the water table declines, expressed as a 

percentage of the total volume of material that is unwatered. The 

same factor generally represents the space that is occupied by water 

going into storage when the water table rises. If, however, the material into which the water rises has been further desiccated by soil 

evaporation or vegetal discharge the amount of recharge is greater 

for each unit of rise.

The water level in a well is sensitive to every force that acts 

upon the body of water with which the well communicates. Hence, 

in most wells the water level fluctuates almost constantly, often in 

a complicated manner. The curve produced by an automatic waterstage recorder over a well gives an accurate record of the resultant 

of the forces that act upon the ground water. A well that extends 

only slightly below the water table generally records faithfully 

both recharge and discharge, but great care must be taken in applying this method to use only wells in which the water level is a continuation of the water table and not the upper surface of a column 

of water that is supported by artesian pressure in the water-bearing 

formation and that therefore fluctuates as a result of atmospheric 

or other changes in pressure. Even in a true water-table well 

there may be fluctuations produced by changes in temperature 

which affect capillarity, by confinement of air in the interstices of 

the overlying zone of aeration by rain or frozen ground, or by other 

causes that have nothing to do with recharge or discharge.

In summer, when the vegetation makes heavy demands on the 

soil moisture, most rainstorms do not contribute at all to the supply 

of ground water and hence do not affect the water levels in wells. 

But in unusually heavy and prolonged storms or series of storms 

water may penetrate to the water table and the water levels may 

rise, or at least their rate of decline may be diminished.88 Likewise recharge from stream flow or irrigation produces a rise in the 

water levels.89

In most regions of the United States recharge of the underground 

reservoirs occurs chiefly in the winter or in late autumn-or early 

spring, when there is not much evaporation from the soil and little

88 Meinzer, O. B., and Stearns, N. D., op. cit, pi. 19.

89 Smith, G. E. P., Ground-water supply and Irrigation in the Rillito Valley: Arizona 

Univ. Agr. Bxper, Sta. Bull. 64, pp. 176-186, 1910.

497117O-59-3
112 CONTRIBUTIONS TO HYDROLOGY OF UNITED STATES, 1931

or no transpiration from plants to consume the water that falls as 

rain or is produced by the melting of snow. Hence in most regions 

the water table is usually at its lowest stage in the autumn and at 

its highest stage in the spring. In very cold regions, however, the 

ground is likely to be frozen continuously during a long period in 

the winter, and the lowest stage may occur just before the ground 

thaws out in the spring. In arid regions such as New Mexico, in 

which the principal rainy season occurs in the summer, the annual 

recharge may be relatively small, but there may be a rise in the 

water table either in the summer or in the winter. In regions 

such as California, in which the rainy season is in the winter, 

nearly all the recharge may occur during this season of relatively 

small discharge. In such regions the increase in storage from the 

lowest stage in autumn to the highest stage in spring may represent 

approximately the annual recharge. In irrigated districts recharge 

may, of course, occur during the irrigation season.

The report by Smith *° on the Rillito Valley, Ariz., includes a map 

on which are shown two sets of 5-foot contours of the water table 

one set for the position of the water table on November 1, 1906, at 

the end of a dry season, and the other for its position on February 1, 

1907, after the beginning of the spring flood season. It also contains 

a cross section of the valley on which are shown the profiles of the 

water table on successive dates in 1906 and 1907. From the rise in 

the water table shown in these illustrations and an assumed effective 

porosity, or specific yield, rough calculations were made of the 

recharge from the Rillito River in the flood season and of the probable supply of ground water annually available for irrigation. This 

method was applied more definitely and in more detail by Clark 41 

in the Santa Clara Valley, Calif., from 1912 to 1920, and by Lee 42 

in San Diego County, Calif., in 1914 and 1915. In both of these 

investigations numerous measurements were made of water levels in 

wells, data were obtained for estimating the specific yield, maps 

were prepared showing the contours of the water table at different 

dates, and computations were made of the seasonal increase in storage represented by the rise in the water table. More recently the 

same method has been used in making computations of net semiannual additions of water to or removals of water from the under40 Smith, G. E. P., Ground-water supply and irrigation in the Rillito Valley: Arizona 

Univ. Agr. Exper. Sta. Bull. 64, pp. 194, 195, figs. 55, 56, 1910.

41 Clark, W. O., Ground-water resources of the Niles cone and adjacent areas, Calif. : 

U. S. Geol. Survey Water-Supply Paper 345, pp. 149-162, pi. 10, 1915; Ground water for 

irrigation in the Morgan Hill area, Calif.: U. S. Geol. Survey Water-Supply Paper 400, 

pp. 66-68, 76-105, pis. 6, 7, 1917; Ground water in Santa Clara Valley, Calif.: U. S. 

Geol. Survey Water-Supply Paper 519, pp. 58-75, 129-183, pis. 10-19, 1924.

42 Mils, A. J., and Lee, C. H., Geology and ground waters of the western part of San 

Diego County, Calif.: U. S. Geol. Survey Water-Supply Paper 446, pp. 121-155, pis. 

20-25, 1919.
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 113

ground reservoir of the Mokelumne Kiver area in California.43 For 

this purpose monthly or semiannual measurements were made of the 

water levels in about 500 observation wells. On account of uncertainties as to the specific yield and as to pressure effects in observation wells there may be large percentage errors in the computed 

recharge in all these investigations, and in the present stage of 

development of this method it is impossible even to state what may 

be the limits of error.

SPECIFIC YIELD IN RELATION TO STORAGE METHODS

Perhaps the greatest difficulty in the application of quantitative 

methods lies in the variability in the texture and hence in the 

hydrologic properties of the water-bearing materials. The hydrologic properties vary greatly, even with apparently slight differences 

in texture. Hence the ordinary geologic descriptions are quite 

inadequate for hydrologic purposes, and quantitative descriptions 

based on laboratory determinations have become essential. However, the hard rocks that yield their water largely from joints or 

crevices are not amenable to laboratory tests, and the incoherent 

materials are difficult to handle without disturbing and repacking, 

which may considerably change theft texture and hydrologic 

properties.

The two hydrologic properties of greatest significance are specific 

yield and permeability. Mechanical analyses and determinations of 

porosity and moisture equivalent are useful chiefly as indirect means 

of determining these two essential hydrologic properties. Any 

quantitative method that does not involve either of these properties 

has a great advantage in avoiding the complications that result 

from the heterogeneity of the water-bearing materials. Most storage methods involve the perplexing problem of specific yield.

Seven more or less distinct methods have been used to determine 

specific yield, but none of them have been thoroughly developed. 

These methods 44 are as follows: (1) Saturating samples in the 

laboratory and allowing them to drain; (2) saturating in the field 

a considerable body of material situated above the water table and 

above the capillary fringe and allowing it to drain downward 

naturally; (3) collecting samples immediately above the capillary 

fringe after the water table has gone down an appreciable distance, 

as it commonly does in summer and autumn;/(4) ascertaining the

48 Stearns, H. T., Robinson, T. W., and Taylor, G. H., Geology and water resources of 

the MokeUrame area, California: U. S. Geol. Survey Water-Supply Paper 619, pp. 112-172, 

185-188, 292-398, pis. 6-8, 13, 1930; also later report released in manuscript form (on 

file in public library, Lodi, Calif.).

"Meinzer, O. E., The occurrence of ground water in the United States, with a discussion of principles: D. S. Geol. Survey Water-Supply Paper 489, pp. 67-76, 1923.
114 CONTRIBUTIONS TO HYDROLOGY OF UNITED STATES, 1931

volume of sediments drained by heavy pumping, a record being kept 

of the quantity of water that is pumped; (5) ascertaining the volume 

of sediments saturated by a measured amount of seepage from one or 

more streams; (6) making indirect determinations in the laboratory 

with small samples by the application of centrifugal force; and (7) 

making mechanical analyses and determinations of porosity and 

estimating therefrom the specific retention and the specific yield.

The laboratory saturation and drainage method consists of draining high columns of saturated materials by gravity and determining 

both the volume of material drained and the volume of water 

yielded. The volume of water yielded can be measured directly or 

can be computed from the porosity and the moisture content after 

draining. The columns must be high enough to avoid the vitiating 

effects of the capillary fringe, and care must be taken to prevent 

loss by evaporation. As molecular forces vary with the temperature 

of the water, the tests must be made at a uniform temperature, or 

corrections for temperature must be applied. As drainage continues 

for a long time at a diminishing rate, the specific yield should be 

determined for specified periods of draining. If the material is fine, 

appreciable drainage may occur during a period of several weeks.

This method was used by Hazen 45 and by King.46 In both sets of 

experiments the yield of successive segments of the different columns 

of water-bearing materials was determined by deducting the moisture 

content after drainage from the porosity, but in the King experiments 

the volume of water drained from each column was also measured at 

appropriate intervals of time.47

Much careful work has been done on this method by White 4S in 

1925-1927, and by Taylor 49 since 1927. In White's work the following procedure was followed: A pit was dug and in the bottom a heavy 

metal cylinder, 36 or 42 inches high and 18 inches in diameter, was 

driven vertically into the water-bearing material within a few inches 

of the water table. The earth around the cylinder was then removed, 

and a metal plate was shoved under the cylinder and soldered to 

it, thus confining the column of undisturbed material in a water-tight 

vessel. Small wells were then sunk in the material in the cylinder,

46 Hazen, Alien, Experiments upon the purification of sewage and water at the Lawrence experiment station: Massachusetts Board of Health Twenty-third Ann. Kept, 

pp. 428-434, 1892.

48 King, P. H., Principles and conditions of the movements of ground water: U. S. 

Geol. Survey Nineteenth Ann. Kept., pt. 2, pp. 86-91, 1899.

47 Meinzer, O. E., The occurrence of ground water in the United States, with a discussion of principles: U. S. Geol. Survey Water-Supply Paper 489, pp. 53-57, 1923. This 

paper gives a concise presentation and discussion of the Hazen and King experiments.

43 White, W. N., Note in regard to investigation in the Escalante Desert, Utah: U. S. 

Geol. Survey Water-Resources Bulletin, March 10, 1927 (mimeographed reprint).

48 Stearns, H. T., Robinson, T. W., and Taylor, G. H., Geology and water resources of 

the Mokelumne area, California: U. S. GeoL Survey Water-Supply Paper 619, pp. 151- 

172, 1930.
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 115

and the effects on the water levels in these wells produced by adding 

or withdrawing measured quantities of water were observed. From 

these data the specific yield was computed. This work was done in 

the autumn, when the water table was at its lowest stage; hence the 

tests were made on the material through which the water table fluctuates and which is therefore subjected to alternate draining and 

resaturation.

In the work by Taylor the general method developed by White 

was employed, but improvements were made in the technique, and 

extensive tests were made to determine the effects of changes in 

temperature and the periods required in different materials to reach 

approximate capillary equilibrium.

The method of field saturation and drainage is similar in principle 

to the laboratory method. A plot of land is selected where the water 

table and capillary fringe are at sufficient 'depth below the surface. 

The material underlying the plot is thoroughly wetted by applying 

water at the surface and is then allowed to drain, care being taken 

to avoid much evaporation. After a sufficient period of draining 

samples are taken for determination of moisture content and porosity, 

and the specific yield is computed as the difference between these two. 

This method lias been used by Israelsen eo and other students of soil 

water. If the specific yield of material below the soil that is more 

representative of the water-bearing material is desired, it is necessary to apply enough water to wet this deeper material and to obtain 

samples from it. In some situations it might be advantageous to dig 

pits to the material to be tested.

In the direct sampling method samples are obtained by boring 

into the material immediately above the capillary fringe after the 

water table has declined appreciably, and the moisture content and 

porosity of the samples are determined. This is essentially the 

method used by Lee 51 in San Diego County, Calif. The essential 

feature in this method is to take a sample where the water table has 

gone down, as it generally does during the dry summer season in 

California. For the most conclusive results the sample should be 

taken from a point which in the preceding wet season was below the 

water table and which at the time of taking the sample is far enough 

above the water table not to be seriously affected by the capillary 

fringe. Where the fluctuation of the water table is less than the 

thickness of the capillary fringe the most significant samples are those 

taken just above the fringe. As in practice this position can not be 

very definitely determined it is advisable to take samples at several

50 Israelsen, O. W., Studies in capacities of soils for irrigation water: Jour. Agr. 

Research, vol. 13, pp. 1-28, April 1, 1918.

51 Ellls, A. J., and Lee, C. H., Geology and ground waters of the western part of San 

Diego County, Calif.: U. S. Geol. Survey Water-Supply Paper 446, pp. 121-123, 1919.
116 CONTRIBUTIONS TO HYDROLOGY OF UNITED STATES, 1931

levels, as was done by Lee. In making tests of this kind it is essential 

to ascertain that the part of the deposit from which the sample is 

taken has not received any recent contribution of water from rain or 

irrigation and has not been exposed to evaporation or to absorption 

by plants, both of which consume water that is retained against gravity by molecular attraction.

The pumping method consists in observing the lowering of the 

water table and hence the volume of sediments drained by pumping a 

measured volume of water. TEe specific yield is, of course, the ratio 

of the volume of water pumped to the volume of material drained. 

Serious errors may be introduced by pumped water returning to the 

water table and by other percolation into or out of that part of the 

underground reservoir which is supplying the pumped water. This 

method was used by Clark 62 with records obtained in the Morgan 

Hill area, California, and is more or less applicable to other areas 

having water-table conditions and heavy seasonal pumpage.

The recharge method, which is the converse of the pumping method, 

consists of observations on the seepage losses from streams or canals 

and on the resultant rise of the water table, from which is computed 

the volume of material saturated. It is, of course, merely the storage method of determining recharge, with the specific yield instead 

of the quantity of water as the unknown factor.

The moisture-equivalent and mechanical-analysis methods are based 

on investigations by Briggs, Veihmeyer, and others 53 on the relations 

between the moisture equivalent or mechanical composition of the 

water-bearing materials, on one hand, and the specific retention, on 

the other hand. The specific yield is computed as the difference 

between porosity and specific retention as determined by one of these 

indirect methods. Both of these methods are valuable, at least in 

giving a general check on the results from other methods, and they 

deserve further investigation.

METHODS FOB ESTIMATING DISCHARGE FROM DAILY 

FLUCTUATIONS OF THE WATER TABLE

In most localities in which plants draw water from the zone of saturation there are daily fluctuations of the water table ranging from a 

small fraction of an inch to several inches. To obtain curves of these 

daily fluctuations the most sensitive water-stage recorders are used.

M Clark, W. 0., Ground water for irrigation in the Morgan Hill area, Calif.: U. S. 

Geol. Survey Water-Supply Paper 400, pp. 84-86, 1917.

68 Briggs, L. J., and McLane, J. W., The moisture equivalents of soils: U. S. Dept. 

Agr. Bur. Soils Bull. 45, 1907. Briggs, L. J., and Shantz, H. L., The wilting coefficient 

for different plants and its Indirect determination: U. S. Dept. Agr. Bur. Plant Industry 

Bull. 230, 1912. Briggs, L. J., Martin, 0. F., and Pearce, J. R., The centrifugal method 

of mechanical soil analysis: U. S. Dept. Agr. Bur. Soils Bull. 24, 1904. Veihmeyer, 

F. J., and Hendrickson, A. H., The moisture equivalent as a measure of the field capacity 

of soils (unpublished manuscript).
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 117

During the daytime the plants withdraw water and consequently 

lower the water table. This drawdown of the water table produces a 

head in the underlying strata, which causes continual upward percolation. Therefore at night, when there is little or no withdrawal by 

plants, the water table rises much as the water level in a well rises 

when pumping is stopped. The daily transpiration is equal to the 

upward percolation throughout the 24-hour period plus or ininus the 

comparatively small amount of water represented by the net decline 

or rise of the water table during the same period. The average rate 

of upward percolation occurs when the water table stands about midway between its lowest and highest daily stages. This occurs twice a 

day during the declining phase, some time in the afternoon, and 

during the rising phase, usually late in the night. The nocturnal 

mid-stage occurs at a time when there is little or no withdrawal from 

the zone of saturation, and hence at a time when the replenishment 

of storage that causes the rise of the water table is approximately the 

average rate of upward percolation for the 24-hour period.54 In 

order to ascertain the quantity of water withdrawn by the plants 

from the zone of saturation it is therefore necessary to determine the 

quantity of water that is required to raise the water table an inch, a 

foot, or other unit of height that is, to determine the specific yield 

of the material through which the water table fluctuates.

Daily fluctuations of the water table were observed by King 55 in 

his experiments at Madison, Wis., in 1888 and subsequent years, and 

he recognized their possible significance in recording the discharge 

of ground water through vegetation. However, he dismissed the subject as too complicated for solution without more elaborate investigation. The method was successfully applied by G. E. P. Smith, in 

1917 and subsequent years, by the use of automatic water-stage recorders on wells in tracts of cottonwood and mesquite and later also 

on wells in tracts of salt grass and alkali sacaton. To Smith, therefore, belongs the credit for the introduction of this method. He also 

developed the theory of upward percolation and showed that the daily 

vegetal discharge could be computed from the rate of rise of the 

water table at the nocturnal mid-stage if the specific yield were 

known.56

In 1925 the United States Geological Survey undertook an intensive investigation to develop this promising method and especially 

to devise means for interpreting the fluctuations in terms of quantity

64 Smith, G. E. P., The effect of transpiration of trees on the ground-water supply 

(unpublished paper given before the Geological Society of Washington, Nov. 22, 1922). 

See Washington Acad. Sci. Jour., vol. 14, p. 160, 1924.

K King, P. H., Observations and experiments on the fluctuations in the level and rate 

of movement of ground water on the Wisconsin Agricultural Experiment Station farm 

at Whitewater, Wis.: TJ. S. Weather Bur. Bull. 5, 1892.

68 Smith, G. E. P., Washington Acad. Sci. Jour., vol. 14, p. 160, 1924.
118 CONTRIBUTIONS TO HYDROLOGY OF UNITED STATES, 1931

of ground water discharged by the plants. For this purpose the 

Escalante Valley, Utah, was chosen, and W. N. White, who had 

already done considerable hydrologic work in that valley, was 

assigned to make the investigation. A preliminary statement of the 

results of the first two years of his work on this method was published in 1927,57 and a comprehensive report on the results of all 

three years of his work is nearly ready for publication.58

In the course of the Escalante Valley investigation three methods 

of determining the specific yield were devised and put into practice. 

One of these methods consisted of driving cylinders and making 

direct tests as above described (p. 114). In another method several 

soil tanks were used in which the three principal ground-water 

plants of the region alfalfa, salt grass, and greasewood were 

grown. The natural hydraulic conditions were reproduced as closely 

as possible, daily water-table curves were obtained comparable to 

those obtained in the field, and observations of the quantity of water 

fed into the tanks to replace the upward percolation were made at 

frequent intervals. Thus data were obtained for the evaluation of 

every process involved, including the interpretation of the rise and 

fall of the water table in terms of quantity -of water. In the third 

method the ratio of dry alfalfa hay produced in the tank experiment to the quantity of water consumed was determined, and this 

ratio was used to compute the water consumed by a known weight 

of alfalfa growing as a ground-water plant in a field in which a 

well was dug and a water-stage recorder was operated. Thus it 

became possible to interpret the curve of water-tajt>le fluctuations in 

terms of quantity of water and hence to compute the specific yield. 

This might be regarded as an eighth method of determining specific 

yield. Similar ratios were also determined for salt grass and greasewood, and these were applied directly to the seasonal growth of these 

species in the field to compute the quantities of water that they discharged. As these computations did not involve the fluctuations of 

the water table they served as a check on the daily fluctuation method.

The studies of the daily fluctuations of the water table in areas 

of vegetal discharge have given valuable results. However, the 

application of the method is complicated in several ways, chiefly by 

the variability in the texture of the soil and water-bearing material 

as it affects the specific yield, permeability, capillarity, and root

w White, W. N., Notes in regard to the work in the Escalante Valley, Utah, on the 

discharge method of estimating ground-water supplies: U. S. Geol. Survey Water-Resources 

Bulletin, Mar. 10, 1927, pp. 22-29. See also Washington Acad. Sci. Jour., vol. 17, 

pp. 238-240, 1927.

68 White, W. N., A method of estimating ground-water supplies based on discharge by 

plants and evaporation from soil; results of investigations in Escalante Valley, Utah 

(released in manuscript form in 1930).
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 119

distribution. The method is not applicable where the water-bearing 

formation consists of very permeable material without interstratified confining beds, because the fluctuations are too slight to be 

accurately recorded by available instruments, and, moreover, the 

mid-stage of the rising phase, as well as that of the declining phase, 

occurs while discharge is occurring. The method will probably 

have to be used to determine the approximate consumption of water 

by the principal species of ground-water plants, and these results 

will have to be applied to maps that will show in as much detail 

as practicable the area, density, and growth of each of these species.

METHOD BASED ON GROUND-WATER BATING CURVE

In the Pomperaug investigation weekly measurements were made 

of the depths to the water levels in a number of observation wells, 

and the average depth for each week was plotted against the corresponding ground-water run-off. It was, of course, found that the 

run-off for a given stage of the water table was much less in summer, when vegetal discharge and soil evaporation were active, than 

in the colder part of the year, when there was very little loss by 

these processes. A curve was drawn through or near the coordinate 

points for winter weeks, according to the empiric method used in 

making rating curves for surface streams. This gave a rating curve 

for ground-water run-off during the winter. It was hoped that the 

curve would show approximately the total ground-water discharge 

in summer and that the ground-water evaporation could be obtained 

by subtracting the ground-water run-off from the total discharge as 

shown by the curve. In fact, however, this difference seems to give 

minimum rather than actual figures for ground-water evaporation, 

because the roots of plants and the soil capillaries do not wait for 

the water to appear at the surface but pump it up from some depth.59 

Further investigation will be required to determine whether it will 

be practicable under any circumstances to use the stage of the water 

table as an index either of ground-water run-off or of total groundwater discharge.

SAFE YIELD AS COMPARED WITH NATURAL INTAKE AND

DISCHARGE

The safe yield of a water-bearing formation, or the practicable 

rate of withdrawing water from it perennially for human use, may 

be either greater or less than the rate of natural recharge or discharge as determined before heavy withdrawals are begun. It may

89 Meinzer, O. E., and Stearns, N. D., A study of ground water in the Pomperaug 

Basin, Conn., with special reference to intake and discharge: TJ. S. Geol. Survey WaterSupply Paper 597, fig. 13, 1928.

497117O-59-4
120 CONTRIBUTIONS TO HYDROLOGY OF UNITED STATES, 1931

be less because natural discharge can not be wholly prevented, even 

by heavy withdrawals through wells. On the other hand, it may be 

greater because of artificial increase of the rate of recharge.

Before any large ground-water developments are made the average rate of discharge for any long period is obviously about equal to 

the average rate of recharge. When heavy pumping from wells is 

begun the water table declines, and this results in curtailing the loss 

from the underground reservoir by spring flow, seepage, soil evaporation, vegetal discharge, and perhaps underground leakage. It is, 

however, not practicable to prevent all the natural discharge even if 

the water table is greatly lowered. Obviously the water that is at 

first pumped is largely water taken out of storage. As pumping 

progresses the water table continues to decline and the salvage from 

natural discharge increases, until, if the safe yield is not exceeded, 

the pumpage is eventually all salvage, and there is no further net 

withdrawal from storage and no further permanent lowering of the 

water table. If, however, the pumpage exceeds the safe yield, withdrawal from storage will continue and the water table will persistently decline. In all investigations of undeveloped underground 

reservoirs the factor of unsalvageable natural discharge should be 

recognized.

Surface reservoirs that are full have no capacity for additional 

storage. Underground reservoirs are also limited in their capacity, 

though not so definitely as surface reservoirs. In a long period of 

wet weather the water table may become so high and effluent seepage 

may become so general that the underground storage will not be 

increased even by heavy precipitation, and after the rains cease 

stored water will be rapidly discharged until the water table reaches a 

more normal stage. This temporary storage capacity depends 

largely on the relief of the land, as has been pointed out by George 

Otis Smith.59* If the land surface is nearly level there is little opportunity for the underlying water-bearing beds to drain, and hence 

the springs will decline or dry up completely while the underground 

reservoir remains nearly full. On the other hand, if the region is 

deeply dissected the lowland springs may continue to flow" with little 

decrease in volume throughout longp periods of drought, during 

which they are gradually draining the underground reservoir. If 

prior to a wet season the water table has been lowered either by 

the flow of springs or by pumping from wells, the available 

capacity of the underground reservoir is increased, and more of the 

surface water will go into underground storage than would otherwise 

be possible. In this respect the recharge may be increased by use.

In order to utilize fully the flow of a stream, storage is required 

to hold the excess water of high stages for. use in times of small

wa Personal communication.
METHODS FOB ESTIMATING GROUND-WATER SUPPLIES 121

flow or whenever there may be need for the water. Many of the 

underground reservoirs are so large that they have capacity to 

carry over great quantities of water not only from a wet season to 

the following dry season but also from a period of wet years to a 

period of dry years. However, to utilize these reservoirs fully it is 

necessary to pump enough water out of them to make room for all 

the inflow during the wettest seasons and during the periods of successive years of heavy precipitation. This was well illustrated by 

some of the underground reservoirs of southern California, whose 

water tables, under heavy pumping for irrigation, went down a 

little lower each summer than they had risen in the previous winter, 

until it appeared that excessive depletion must inevitably compel 

reduction in irrigation. Then came a period of wet winters when 

recharge occurred to a remarkable extent and the water levels rose 

beyond all expectations.60

The principle of increasing recharge by use was recognized by 

Smith n and Wolff 62 in early quantitative work in this country and 

has generally received due consideration in more recent investigations. In all investigations of undeveloped ground-water supplies 

the possible effect of use in increasing the yield should be recognized and so far as practicable should be evaluated. In making 

investigations where heavy pumping is already in progress, estimates based on a few years of normal or subnormal precipitation 

may be too low because they do not sufficiently take i-nto account the 

great recharge that may occur in a depleted underground reservoir 

during a season of exceptionally high precipitation.

Artificial recharge can be accomplished in some places by draining surface water into wells, spreading it over tracts underlain by 

permeable material, temporarily storing it in leaky reservoirs from 

which it may percolate to the water table, or storing it in relatively 

tight reservoirs from which it is released as fast as it can seep into 

the stream bed below the reservoir. Artificial recharge by some 

of these methods has been practiced in the United States and other 

countries. It was suggested by Hilgard 68 in 1902 for southern 

California, where it has since received considerable investigation 

and has been adopted as a conservation measure.64 Drainage

98 Ebert, F. C., Records of water levels in wells in southern California: U. S. Geol. 

Survey Water-Supply Paper 468, pis. 2, 3, 4, 1921.

« Smith, G. E. P., op. cit., p. 189.

08 Wolff, H. C., The utilization of the underflow near St. Francis, Kans.: U. S. Geol. 

Survey Water-Supply Paper 258, pp. 104-107, 1911.

68 Hilgard, E W., Subterranean water supply of the San Bernardino Valley: U. S. 

Dept. Agr. Bull. 119, pp. 133-134, 1902.

61 Lee, C. H., Subterranean storage of flood water by artificial methods in San Bernardino Valley, Calif.: California Conservation Comm. Kept, for 1912, pp. 335-400, 1913. 

Tate, C. E., Spreading water for flood control: Southern California Assoc. Members 

Am. Soc. Civil Bug. Bull., vol. 1, No. 4, pp. 76-86, Los Angeles, 1919. Post, W. S., Santa 

Ana investigation, flood control and conservation: California Dept, Public Works Div. 

Eng. and Irr. Bull. 19, pp. 165-179, 1929.
122 CONTBIBUTIONS TO HYDEOLOGY OF UNITED STATES, 1931

into wells has been practiced in many parts of the United States, 

chiefly to reclaim swampy land or to dispose of sewage and other 

wastes.65 The drainage of sewage or other wastes into wells can not 

be approved, because it may produce dangerous pollution of water 

supplies. Drainage of surface water into wells to increase the 

ground-water supply for rice irrigation in Arkansas is now under 

consideration.66 Water spreading has been practiced to a considerable extent in southern California, partly to decrease the 

effects of flood but largely to increase the supply of ground water. 

Storage in ordinary reservoirs and subsequent release has frequently 

been considered, and the unavoidable leakage of some reservoirs 

has been used to increase the ground-water supply.67 Artificial recharge by damming stream channels in the permeable lava rocks 

of the Hawaiian Islands has been considered.68 In ground-water 

investigations that involve the question of safe yield attention should 

as a matter of course be given to the possibilities of artificial recharge.

STORAGE METHODS APPLIED WHERE USE HAS BECOME LARGE

If an underground reservoir is heavily pumped a study of the 

relations of the water levels to the amount of pumpage is likely to 

give more reliable information as to the safe yield than can be obtained by any method of studying an undeveloped reservoir. If 

the water levels in the wells remain virtually stationary during a 

considerable period of pumping it may be concluded that during this 

period the rate of recharge has been about equal to the rate of discharge, including both natural discharge and withdrawals from 

wells. This principle was utilized by Mendenhall 69 in his groundwater investigations in San Bernardino Valley, Calif., early in the 

present century, where already there was heavy pumping for irrigation. He found that the records on two wells under observation for 

several years showed a net decline in water level in all years, though 

in two years of somewhat more than average precipitation the decline was only slight. He therefore concluded that in those two 

years the pumpage was virtually supplied by recharge but that in 

all other years there was a draft on storage.

« Horton, R. E., Drainage of ponds into drilled wells: U. S. Geol. Survey Water-Supply 

Paper 145, pp. 30-39, 1905. Fuller, M. L., Drainage by wells: U. S. Geol. Survey 

Water-Supply Paper 258, pp. 6-22, 1911.

M Thompson, D. G., Ground-water supplies for rice irrigation in the Grand Prairie 

region, Arkansas: U. S. Dept. Interior Press Mem. 49844, January 26, 1931.

67 Meinzer, O. E., Renick, B. C., and Bryan, Kirk, Geology of No. 3 reservoir site of the 

Carlsbad irrigation project, New Mexico, with respect to water-tightness: U. S. Geol, 

Survey Water-Supply Paper 580, pp. 21-25, 1927.

68 Stearns, H. T., and Clark, W. 0., Geology and water resources of the Kau District, 

Hawaii: U. S. Geol. Survey Water-Supply Paper 616, p. 21, 1930. The method had 

been suggested by Lincoln McCandless in Honolulu Advertiser, June 21. 1926.

68 Mendenhall, W. C., The hydrology of San Bernardino Valley, Calif.: U. S. Geol. 

Survey Water-Supply Paper 142, pp. 56-67, 1905.
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 123

Kegardless of the manner in-which the water levels fluctuate, if 

at the end of any period they return approximately to the position 

they had at the beginning of the period the record of pumpage furnishes a measure of the recharge during the same period minus the 

natural loss. In the Niles cone, in California, the water levels in 

the autumn of 1918 had returned to almost the identical levels of the 

autumn of 1913, although in the intervening period there were notable fluctuations in level as a result of wet and dry years. Bailey's 

inventory of the ground-water supply 70 covered this 5-year period 

in which there was practically no net change in storage.

Under such conditions two uncertainties remain which affect the 

practical conclusions as to safe yield first, as to how much natural 

discharge there was during the period and especially how much 

salvageable natural discharge; and, second, as to how nearly the 

recharge during the period represents the average rate of recharge 

or how much it was above or below the average. If it is known 

that during a period of such stationary or recurring conditions of 

the water table the rate of recharge has not been above the average, 

it may be concluded that pumpage has not exceeded the safe yield. 

On the other hand, the mere fact of essential equilibrium between 

recharge and discharge gives no indication of the maximum salvageable discharge that is, of the maximum pumpage that would be 

practicable. If the rate of pumping is increased, the water table 

will decline and consequently the rate of natural discharge will 

be diminished. If the safe yield has not been exceeded, this process 

of lowering the water table and decreasing the natural discharge 

will proceed until eventually the diminution in the rate of natural 

discharge will equal the increase in the rate of pumping, the aggregate of the two kinds of discharge will again be balanced by 

recharge, there will no longer be any net withdrawal from storage, 

and the water table will be approximately stabilized in its new 

position. If the safe yield has bpen exceeded and the new rate of 

pumping is greater than the maximum possible salvage, then, obviously, the pumps will continue t6 draw upon the storage and the 

water table will continue to decline indefinitely. If with a given 

rate of pumping the water table is approximately stabilized and 

the natural discharge is known to be small or to have been reduced 

nearly to the practicable limit, it may be concluded that the pumpage furnishes an approximate measure of the safe yield and that 

the ground-water supply has been fully developed but not overdeveloped.

70 Bailey, Paul, Engineering investigation of percolation from Alameda Creek and groundwater studies on Niles cone: California State Water Comm. Third Bienn. Kept, pp. 105, 

106, 1921.
124 CONTRIBUTIONS TO HYDROLOGY OF UNITED STATES, 1931

The great advantage in basing computations on a period of 

stationary water levels or on a period in which the water levels 

are about the same at the end as at the beginning of the period is 

that there is no net withdrawal from or addition to the storage, 

and consequently the specific yield of the water-bearing material is not involved. If, however, the water table declines persistently or if it is desired to make monthly or annual estimates of 

the recharge, it becomes necessary to determine the specific yield 

or at least the capacity of the underground reservoir for each foot 

of saturation within the belt through which the water table 

migrates. In regions that have distinct wet and dry seasons, such 

as California and parts of the Hawaiian Islands, the recharge 

during the dry season may be negligible in quantity. If natural 

discharge has become relatively small, the pUmpage in the dry 

season may therefore represent approximately the reduction in 

storage. If both the pumpage and the average decline of the water 

table are known, the approximate capacity of the underground 

reservoir for each foot of depth can be computed, and this figure 

can be used in computations of recharge during the wet season. 

In applying this method adequate precautions must, of course, be 

taken to get the average position of the water table for the entire 

area underlain by the underground reservoir and to distinguish 

between water levels that represent the water table and those that 

represent artesian pressure. This method was used by McCombs 71 

in the artesian basin in the vicinity of Honolulu, where there is 

continuous heavy withdrawal from wells but only a negligible 

amount of natural discharge and practically no recharge during 

the dry seasons, and where the water-bearing lava rock is so permeable that there is almost no loss of head due to friction and the 

water table in the intake area is almost exactly recorded by the 

water levels in the artesian wells.

By this method the average specific yield of the water-bearing 

material that has been drained can be determined, provided, of 

course, that the area of the water table in the underground reservoir 

is known with reasonable accuracy. This is the fourth or pumping 

method described above. However, it should be remembered that in 

the procedure followed by McCombs the specific yield is not required 

but only the storage for each foot of depth.

LEAKAGE METHODS

In some places there is good evidence of leakage from one underground reservoir into another. If the leakage occurs as underflow

71 McCombs, John, Methods of estimating safe yield of Honolulu artesian area:, Honolulu Sewer and Water Comm. Kept., 1927, pp. 61-65.
METHODS FOB ESTIMATING GROUND-WATER SUPPLIES 125

through a relatively definite underground channel it can be estimated 

by one of the conduit methods described below, as, for example, in the 

investigation made by Slichter " in 1904 of the underflow at the 

narrows of the Rio Grande near El Paso, Tex. If, however, the leakage occurs by percolation through the rocks at considerable depths it 

may be quite impracticable to estimate the quantity of water that is 

lost. An example of such a condition is afforded by the probable 

underground escape of water from Alkali Spring Valley into 

Clayton Valley, in Nevada.73

After wells have been drilled into an artesian formation much artesian water may escape into permeable beds above the confining bed 

through defective or corroded well casings. Recently a successful 

method has been developed for measuring this underground loss of 

artesian water. The principle involved is very simple. A specially 

constructed current meter is lowered into the well, where it records 

the velocity of the water at any depth desired. With the, velocity 

and the diameter of the well known, the rate of flow at any point 

can be determined. Hence a series of measurements taken at successive levels from the bottom to the top of the well will show just 

where the water enters and in what amounts, where it leaks out and 

in what amounts, and how much is delivered at the surface. For 

certain investigations it may be necessary to use apparatus for measuring the diameter of a well at any depth, but thus far no serious 

difficulties have arisen in the leakage work on account of uncertainty 

as to the diameter.

In connection with drainage investigations on the Twin Falls 

South Side project, in Idaho, from 1910 to 1914, a Price current 

meter, such as is used by the United States Geological Survey in 

stream gaging, was used by W. G. Sloan, of the Department of Agriculture, and W. B. Heroy, of the Geological Survey, to measure the 

discharge of wells and also to determine the levels at which the 

water entered the wells. Beginning in 1918, a Price meter was successfully used by the Geological Survey for making a systematic 

survey of leakage of artesian wells in Honolulu, first by R. D. 

Klise and later by John McCombs and others. In 1925 a current 

meter that is much better adapted for the well work was designed by 

Carl H. Au and was used by A. G. Fiedler, who further developed 

the method in leakage investigations in the Roswell artesian basin, 

New Mexico, and in other localities.74 A so-called " kink finder," or

ra Slichter, C. S., Observations on the ground waters of Rio Grande Valley: U. S. Geol. 

Survey Water-Supply Paper 141, pp. 9-13, 1905.

"Meinzer, O. E., Geology and water resources of Big Smoky, Clayton, and Alkali Spring 

Valleys, Nev.: U. S. Geol. Survey Water-Supply Paper 423, pp. 147-150, 1917.

74 McCombs, John, and Fiedler, A. G., Methods of exploring and repairing leaky 

artesian wells, with a preface by O. E. Meinzer: U. S. Geol. Survey Water-Supply Paper 

596, pp. 1-32, 1927. The work of Sloan and Heroy was not mentioned in this paper 

because it was not at that time known to any of the authors.
126 CONTRIBUTIONS TO HYDROLOGY OF UNITED STATES, 1931

automatic gage for determining the diameter of a well from bottom 

to top, invented by P. B. Whitney, was successfully used, in 1927, in 

a 4,700-foot well of the Kepollo Oil Co., near Boulder, Colo.75

In an investigation in the Winter Garden area, in Texas, it was 

necessary to determine whether salty water from one formation is 

entering a fresh-water formation through wells with defective casings. For this purpose an apparatus was devised which can be 

lowered into the wells and will indicate the electric conductivity and 

therefore the degree of salinity of the water at different depths.76

BOCK FORMATIONS AS CONDUITS

GENERAL CONDITIONS

Ground water travels laterally from the intake areas to the discharge areas. On account of the viscosity of the water and the 

small size of the interstices of the water-bearing material through 

which it usually percolates, there is a very appreciable resistance 

to its flow. Hence the rate of recharge is controlled not only by 

the intake facilities and the quantity of surface water that reaches 

the intake area but also by the capacity of the formation to carry 

water from the intake area to the area of natural discharge or to the 

wells where the water supply is to be recovered. If the distance 

from the intake area to the discharge area is great, as it is in some 

of the large artesian basins, the problem of safe yield relates to the 

capacity of the formation as a conduit rather than to its capacity 

as a reservoir. Quantitative methods are therefore required to 

estimate the transmission capacities of water-bearing formations.

METHODS BASED ON FIELD TESTS OF VELOCITY

The rate of flow of a surface stream at a selected cross section 

is determined by measuring the velocity of the water in each unit 

of the cross section. The rate of flow through each unit is the 

product of the velocity by the area of the unit, provided the flow 

is at right angles to the cross section. The total flow of the stream 

is, then, the sum of the flows through all the units of the cross 

section.77

The same principle is applied in estimating the flow of ground 

water, but different means must be used for measuring the velocity 

and cross-section area, and a third factor, which may be called the

TO Described by Mr. Whitney in letter of May 14, 1927, to the Director, TT. S. Geological 

Survey.

n Survey of the underground waters of Texas: TJ. S. Dept. Interior Press Mem. 50678, 

Feb. 16, 1931.

77 Hoyt, 3. C., and Grover, N. C., River discharge, 4th ed., pp. 3, 4, 44-81, New York, 

John Wiley & Sons, 1927.
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 127

effective porosity, is involved. The velocity of a surface stream is 

generally measured with a current meter, but this instrument is obviously not available for measuring the velocity of ground water. 

For this purpose use has been made of salts and dyes, which are introduced into the ground water through an upstream well and later 

detected in one or more downstream wells, the velocity being computed from the observed interval of time and the measured distance 

between the wells. Common salt was first used by European hydrologists and was detected in the downstream wells by chemical tests 

for chloride in successive samples taken from these wells. Later the 

more convenient electrolytic method was devised in this country by 

Slichter.

One of the pioneers in developing methods for measuring the velocity of ground water was the German hydrologist A. Thiem,78 who 

made investigations leading to the development of ground-water 

supplies in many cities of Germany and published the results of his 

work in several papers that appeared between 1879 and 1892. He 

used common salt in his experiments because it is inexpensive, readily soluble, easily detected by the test for chloride, and not objectionable in any way. His method was to dig two test wells approximately in line with the direction of the movement of the ground 

water as determined from the slope of the water table. He then 

dosed the upper well with salt and at suitable intervals took samples 

from the lower well which he tested for their chloride content.

A notable advance in the methods of measuring the velocity of 

ground water was made in this country when the electrolytic method 

was developed by Slichter.79 His first work was done in 1901 in the 

Arkansas River Valley, near Garden City, Kans.80 In succeeding 

years he and his associates made measurements of the velocity of 

ground water by the electrolytic method on Long Island 81 and in the 

valleys of the Los Angeles,82 Hondo,83 San Gabriel,83 and Mohave 83

78 Thiem, A., Verfahren fur Messung natiirllcher Grundwasser-geschwindigkeiten: Poly. 

Notizblatt, vol. 42, p. 229, 1887. Slichter, C. S., Theoretical investigation of the motion 

of ground waters: U. S. Geol. Survey Nineteenth Ann. Kept., pt. 2, pp. 297-384 (see 

especially the bibliography, pp. 380-384), 1898; The motions of underground waters: 

U. S. Geol. Survey Water-Supply Paper 67, pp. 46-48, 1902.

TO Slichter, C. S., The motions of underground waters: U. S. Geol. Survey Water-Supply 

Paper 67, 1902; Field measurements of the rate of movement of underground waters: 

U. S. Geol. Survey Water-Supply Paper 140, 1905.

80 Slichter, C. S., The underflow in Arkansas Valley in western Kansas: U. S. Geol. 

Survey Water-Supply Paper 153, 1906.

81 Slichter, C. S., Field measurements of the rate of movement of underground waters: 

U. S. Geol. Survey Water-Supply Paper 140, pp. 65-85, 1905. Veatch, A. C., Slichter, 

C. S., Bowman, Isaiah, Crosby, W. O., and Horton, R. E., Underground water resources 

of Long Island, N. Y.: U. S. Geol. Survey Prof. Paper 44, pp. 86-115, 1906.

88 Hamlin, Homer, Underflow tests in the drainage basin of Los Angeles River: U. S. 

Geol. Survey Water-Supply Paper 112, 1905.

88 Slichter, C. S., Field measurements of the rate of movement of underground waters: 

U. S. Geol. Survey Water-Supply Paper 140, ppr. 50-64, 1905.
128 CONTRIBUTIONS TO HYDROLOGY OF UNITED STATES, 1931

Rivers, in California, the Rio Grande near El Paso, Tex.,84 the South 

Platte River, in Nebraska, 85 and the Republican River, in Kansas.86 

The method has been standardized and has been extensively used in 

ground-water work, both in the United States and in other countries.

The electrolytic method depends on the fact that the electric conductivity of water increases with its concentration of dissolved salt, 

which acts as an electrolyte. Simple electric apparatus is used with 

a battery to generate the current and an ordinary or recording ammeter to measure the current. The progress of the salt is recorded 

when the current is passed through the water from the upstream well 

to a downstream well, and its arrival in one of the downstream wells 

is indicated when the current passing from the casing of that well to 

an electrode inside of it suddenly increases. Many mechanical difficulties are involved in the installation. of the wells and the application of the electrolyte, which may introduce large errors in the results or may completely vitiate the experiments. The difficulties are 

especially serious where the velocities are small.

Dye has been used chiefly in sanitary investigations, largely to 

trace the course of rather definite underground streams, such as 

occur in limestone, and to determine whether certain water 

supplies receive contributions from polluted sources. The dye most 

commonly used is the chemical called uranin, which is the sodium 

salt of fluorescein and which has often been incorrectly called fluorescein. This is a harmless but very strong and stable dye that 

colors the water green. The dye method was described by Dole 8r 

in 1906, in a paper which also contains a historical sketch of the 

development of the method and a bibliography. Dye tests were 

made by Dr. Dionis des Carrieres in 1882, during a severe epidemic 

of typhoid fever in the city of Auxerre, in France, and since that 

tune frequent use has been made in France of various dyes to study 

the movements of ground water. In 1899 elaborate investigations 

were made by Trillat of the value of certain dyes as flow indicators 

and of the effects on them of passage through common soils. The 

fluoroscope, for detecting dyes when present in great dilution, was 

invented by Trillat and was perfected by Marboutin. Dye tests have 

frequently been made in the United States by sanitary engineers and

84 Slichter, C. SM Observations on the ground waters of Rio Grande Valley: U. SL Geol. 

Survey Water-Supply Paper 141, pp. 9-13, 1905.

»Slichter, C. S., and Wolff, H. C., The underflow of the South Platte Valley: F, S. 

Geol. Survey Water-Supply Paper 184, pp. 9-12, 1906.

86 Wolff, H. C., The utilization of the underflow near St. Francis, Kans.: U. S. Geol. 

Survey Water-Supply Paper 258, pp. 98-119, 1911.

87 Dole, R. B., Use of fluorescein in the study of underground water: U. S. GcoL Surrey 

Water-Supply Paper 160, pp. 73-85, 1906.
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 129

others, and a good example is afforded by the series of tests made by 

Stabler.88

In 1921 and subsequent years uranin dye was successfully used by 

Stiles and his assistants 89 in a a investigation to determine the extent 

to which bacteria are carried through formations of sand. This

investigation, which was ma< 

Caswell, N. C., by the United 

cooperation of the United 

minute 3-dimensional survey

of the ground water and mad \ a notable contribution in demonstrating the use of the dye methoc in fine-grained materials and in providing means for detailed study of the movement of ground water.

The use of a dye probably 

studying in detail the moveme 

easily applied in some crevi 

underground streams, but in 

dye may be very elusive, and 

more laborious and difficult t 

tion. In the Fort Caswell 

sunk in addition to some tren

chemical, or dye methods, 

degree of accuracy the cross

and the velocity of flow throu 

is accomplished by sinking tes 

the records of existing wells, 

method of underground expl 

tivity of the different rock :

limits of shallow undergroun

e at an experiment station near Fort 

States Public Health Service, with the 

states Geological Survey, involved a 

)f the direction and rate of movement

affords the most accurate method of 

nts of ground water. It may be rather 

ed rocks that have relatively definite 

porous rocks with small interstices the 

the method may be found to be much 

an would appear on casual consideraxperiment about 550 test wells were 

:hes, and the exact distribution of the

uranin was determined.

To estimate the flow of ground water, whether by electrolytic,

is necessary to ascertain with some 

.ection through which the water flows

arh each unit of the cross section. This

t wells and to some extent by studying 

It is possible that the recently devised 

oration based on the electric conducormations can be used in finding the

. conduits, but that method seems not

to be available for determining the permeability of different units 

of the cross section or the velocity of the ground water flowing 

through them.

The flow of a surface stream, in cubic feet per second, can be 

found by multiplying the average downstream component of the 

velocity of the water in feet per second by the area of the cross section of the stream in square feet. To determine the flow of ground 

water, however, a third factor, which has been called the effective

88 Stabler, Herman, Fluorescein an aid to tracing waters underground: Reclamation 

Record, vol. 12, pp. 122, 123, U. S. Reel. Service, 1921.

»Stiles, C. W., Crohurst, H. R., Thomson, G. E., and Stearns, N. D., Experimental 

bacterial and chemical pollution of wells via ground water, with a report on the geology 

and ground-water hydrology of the experimental area at Fort Caswell, N. C.: U. S. Pub. 

Health Service Hygienic Lab. Bull 147, 1927.
130 CONTRIBUTIONS TO HYDROLOGY OF UNITED STATES, 1931

porosity, must be applied. Much of the cross section is occupied 

by rock and by water that is securely attached to the rock surfaces by 

molecular attraction. The area through which the water is flowing 

is therefore less than the area of the cross section of the waterbearing material and may be only a small fraction of that area. 

In a coarse, clean gravel, which has only large interstices, the 

effective porosity may be virtually the same as the actual porosity, 

or percentage of pore space; but in a fine-grained or poorly assorted material the effect of attached water may become very great, 

and the effective porosity may be much less than the actual porosity. 

Clay may have a high porosity but may be entirely impermeable 

and hence have an effective porosity of zero. The effective porosity 

of very fine grained materials is generally not of great consequence 

in determinations of total flow, because in these materials the velocity is so slow that the computed flow, with any assumed effective 

porosity, is likely to be relatively slight or entirely negligible. The 

problem of determining effective porosity, as distinguished from 

actual porosity, is, however, important in studying the general run 

of water-bearing materials, which are neither extremely fine nor 

extremely coarse and clean.

Hitherto not much work has been done on this phase of the 

velocity methods of determining rate of flow. No distinction has 

generally been made between actual and effective pbrosity, and frequently a factor of 33% per cent has been used, apparently without 

even making a test of the porosity. It is certain that the effective 

porosity of different water-bearing materials ranges between wide 

limits and that it must be at least roughly determined if reliable 

results as to rate of flow are to be obtained. It would seem that 

each field test of velocity should be supplemented by a laboratory 

test of effective porosity, for which the laboratory apparatus 

devised by Slichter could be used.90

Velocity methods have been used chiefly on water-bearing formations lying at or near the surface. The electrolytic method has been 

used chiefly to determine the underflow of streams through alluvial 

deposits confined in rock troughs. These tests have produced data 

on the velocity of ground water through materials of certain kinds 

and under known hydraulic gradients. The data are perhaps of the 

greatest value in furnishing a general comparative basis for making 

rough estimates of velocity of ground water in other places and 

under other conditions. Their value in the specific investigations 

for which they were made has been largely in giving negative information, for they have generally shown that the rate of under80 Slichter, C. S., Field measurements of the rate of movement of underground waters: 

U. S. Geol. Survey Water-Supply Paper 140, pp. 29-49, 1905.
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 131

flow is small in comparison with the recharge that occurs all along 

the valley by downward percolation of rain or stream water. At 

the present time methods to determine the rate of flow are most 

needed in connection with water-bearing formations which lie beneath confining beds and in which the water must travel long 

distances from the intake areas to the areas of recovery. One of 

the principal difficulties in using velocity methods on such formations is the cost of sinking the deep test wells that would generally 

be required.

METHODS BASED ON LABORATORY DETERMINATIONS OF 

PERMEABILITY

About 1843 Poiseuille,91 in connection with his studies of the circulation of the blood, discovered the law of flow through capillary 

tubes namely, that the rate of flow is proportional to the hydraulic 

gradient. In 1856 Darcy,92 inspector general of the Paris waterworks, whose extensive and valuable experiments on the flow of 

water through pipes are well known, verified this law and demonstrated its application to water percolating through the capillary 

interstices of sand or other porous medium. He expressed this law

lev by means of the formula ^=~v* in which v is velocity of the water

through a column of permeable material, p the difference in head at 

the two ends of the column, h the length of the column, and k a constant that depends on the character of the material, especially on the 

size of the grains, which was to be experimentally determined.

In the 75 years since the results of Darcy's work were published 

laboratory investigations of various phases of the problem of the 

flow of liquids and gases through permeable materials have been 

made, many of them by French and German physicists and engineers.98 A critical review of the early investigations was made by 

King,9* an American physicist and hydrologist. He reviewed the 

laboratory studies on the flow of water through permeable materials 

that were made by the European investigators Hagen, Seelheim, 

Welitschkowsky, and Wollny and by the American engineer J. C. 

Trautwine; the work of Thomas Graham and O. E. Meyer, who demonstrated that the law of Poiseuille holds for gases as well as for 

liquids; and the later investigations by Fleck, Welitschkowsky, Kenk,

91 Poiseuille, J., Recherches expgrimentales sur le mouvement des liquides dans les tubes 

de tres petit diametre: Mdm. savants elrang., vol. 9, p. 433, 1846.

*Darcy, H. P. G., Les fontaines publiques de la ville de Dijon, Paris, 1856. See 

Slichter, C. S., The motions of underground waters: U. S. Geol. Survey Water-Supply 

Paper 67, pp. 18, 19, 1902.

" See bibliography in Slichter, C. S., Theoretical investigation of the motion of ground 

waters: U. S. Geol. Survey Nineteenth Ann. Rept., pt. 2, pp. 380-384, 1899.

94 King, p. H., Principles and conditions of the movements of ground water: U. S. Geol. 

Survey Nineteenth Ann. Rept, pt. 2, pp. 178-189, 1899.
132 CONTRIBUTIONS TO HYDROLOGY OF UNITED STATES, 1931

Ammon, and Wollny concerning the flow of gases. The whole subject of the law of flow of liquids and gases through capillary tubes 

and permeable materials was reinvestigated by King, and his results 

are given in the paper cited. During the years 1902 to 1904 laboratory experiments on the flow of water through sand and gravel were 

made under the direction of Slichter 95 with lower hydraulic gradients than had previously been used, in order to approximate natural conditions more closely. Since that time permeability experiments with both liquids and gases have been made by other American 

physicists and engineers in various fields of investigation. In 1923 

a hydrologic laboratory was established in the Geological Survey, 

and tests of permeability to water were made under hydraulic gradients as low as 5 feet to the mile.96 In this laboratory standard 

permeability tests under low gradients are now made of many waterbearing materials found in the areas that are investigated by the 

Geological Survey.

The foregoing historical review shows that Darcy's law, that the 

flow of water through a permeable material varies directly as the 

hydraulic gradient, has been thoroughly tested by experiment and has 

been demonstrated to be correct for practical purposes if it is not applied with excessive extrapolation. Hence, the flow through a formation can be computed if its permeability, the hydraulic gradient of 

the water it contains, and the area of its cross section are determined.

The hydraulic gradient can be rather satisfactorily determined by 

measuring the depth to the water level in wells properly distributed 

over the area underlain by the formation. A well should not be 

yielding water at the time it is measured or for some time prior to 

its measurement; otherwise there will be a local drawdown that 

will introduce an error. There may also be a drawdown caused by 

heavy flow or pumping from other wells in the same vicinity, and 

precautions must be taken with respect to errors that might be produced by changes in atmospheric pressure or other causes. The 

water levels are measured from definite bench marks, or reference 

points, to which levels are run. A contour map of the pressureindicating surface is then constructed. Such a map shows approximately the direction of movement of the ground water and the 

hydraulic gradient at every point, the direction in any locality being 

at right angles to the contour and the gradient being the ratio of the 

contour interval to the distance between successive contours.

The area of cross section can be estimated from well records and 

outcrops that show the thickness and extent of the formation. A

95 Slichter, C. S., Field measurements of the rate of movement of underground waters: 

U. S. Geol. Survey Water-Supply Paper 140, pp. 29-49, 1905.

98 Stearns, N. D., Laboratory tests on physical properties of water-bearing materials: 

U. S. Geol. Survey Water-Supply Paper 596, pp. 144-163, 1927.
METHODS FOE, ESTIMATING GROUND-WATER SUPPLIES 133

cross section that is pertinent for this purpose must obviously have 

the same general trend as the contours of the pressure-indicating 

surface, in order to be approximately at right angles to the direction 

of flow.

The most serious difficulty with this method and one that up to the 

present time has not been effectively overcome is that of determining 

the true average permeability of the material that constitutes the 

water-bearing formation. Laboratory methods are available to 

determine accurately the permeability of the samples that are tested, 

but the difficulty lies in obtaining representative samples. Even 

apparently slight differences in texture may make great differences 

in permeability. A rather inconspicuous admixture of colloidal clay 

to an otherwise permeable sand may cut down greatly its capacity to 

conduct water. In a sand formation a few thin strata of coarse, 

clean sand may conduct more water than all the rest of the formation. 

These permeable strata may be overlooked in the sampling, or if 

samples from them are taken it may be impossible to give them the 

proper weight in comparison with samples from other parts of the 

formation. Consolidated rocks are likely to contain joints and 

crevices which conduct much of the water and which therefore render 

laboratory methods inapplicable. On the other hand, unconsolidated 

samples can not easily be recovered and tested without disturbing 

the texture of the material and thus introducing errors of unknown 

but conceivably great amount. Moreover, samples taken at the outcrop of a formation may not be representative because of changes 

.produced by weathering, and samples obtained from wells are generally nonvolumetric and greatly disturbed and may be either washed 

or mixed with clay of foreign origin. If the conditions of drilling 

can be controlled it may be possible to obtain an undisturbed or only 

moderately disturbed sample, especially if a core barrel is used, but 

such favorable conditions are rarely obtainable. In spite of the 

difficulties, the laboratory tests are of value in giving general limits 

of permeability, and it will be highly desirable to complete the 

project, now in progress, of making a set of permeability tests of all 

the leading formations in this country that conduct water through 

their pore spaces.

Efforts have been made by Hazen, King, Slichter, and others 97 to 

compute the permeability of water-bearing material from its mechanical composition and porosity. For this purpose Hazen,98 in his

87 For a review of the work of Alien Hazen, F. H. King, and C. S. Slichter on this subject, with references, soe Stearns, N. D., op. cit., pp. 170-176.

88 Hazen, Alien, Experiments upon the purification of sewage and water at the Lawrence Experiment Station, Nov. 1, 1889, to Dec. 31, 1891 : Massachusetts Board of Health 

Twenty-third Ann. Rept., p. 431, 1892; Some physical properties of sands and gravels 

with special reference to their use in filtration: Massachusetts Board of Health Twentyfourth Ann. Rept., p. 541, 1893.
134 CONTRIBUTIONS TO HYDROLOGY OF UNITED STATES, 1931

work on filter sands in 1889 to 1893, used the term " effective size of 

grain," or size of grain that would give the actual permeability of 

a more or less heterogenous material. He found that in the materials 

with which he was dealing the effective size was best shown by the 

" 10 per cent size " that is, the size that is not exceeded by the grains 

in 10 per cent of the material by weight. These indirect methods 

of computing permeability are useful for some purposes but have 

not always given consistent results and are not in general to be 

recommended. Direct tests of permeability require no more work 

and are generally more satisfactory.

METHOD BASED ON PERMEABILITY DETERMINED FROM 

DISCHARGE AND DRAWDOWN OF WELLS

One of the most promising methods of determining permeability 

is a field method proposed by G. Thiem," son of the German hydrologist A. Thiem, based on the performance of wells that enter the 

water-bearing formation. In order to make a test by this method 

it is necessary to have one well from which water can be withdrawn, 

either by pumping or by artesian flow, at a rate that will produce 

considerable drawdown, and two or more other wells that are 

located at different distances from the discharge well and near enough 

to it to have appreciable drawdown when it is discharging. This 

method has the advantage over the laboratory methods in that it 

deals with all the water-bearing materials in the vicinity of a well, 

undisturbed and in place.

The method is very simple in principle. The water level is 

measured in each of the observation wells at a time when the discharge well has been idle long enough for the water levels to have 

reached the static level. The well is then pumped or allowed to 

discharge by artesian pressure at a uniform rate until equilibrium 

has again been virtually established and the new water levels have 

become essentially stationary. If the test is made in an area of 

artesian flow, the pressure may be measured instead of the depth 

to the water level. From the ultimate drawdown in the several 

observation wells produced by the pumping or artesian discharge 

a profile of the cone of depression can be constructed, and from 

this profile the hydraulic gradient at any distance from the discharge well can be determined. If the water-bearing formation is 

of uniform character and thickness in the vicinity of the wells and 

the thickness is known, all three factors are available for computing 

the permeability. If the water in the formation is confined under 

pressure, the cross-section area is obviously 27r/"£, in which r is the 

distance from the discharge well to the point where the hydraulic

t° Thjera, G., Hydrologische Methoden, Leipzig, 1906.
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 135

gradient is determined and t is the thickness of the formation. If 

the water is not confined but forms a water table, the effective crosssection area is 27i-rtf', in which t' is the thickness of the saturated 

part of the formation or the height of the water table above the base 

of the formation during pumping at the point where the hydraulic 

gradient is determined. In either case the coefficient of permeability as defined in Water-Supply Paper 596 is equal to i-, in

which q represents the rate of pumping or artesian discharge in 

gallons a day, a the cross-section area in square feet, and g the 

hydraulic gradient as defined on page 132. Further investigation is 

needed as to inaccuracies that may be introduced by irregularities 

in the texture, thickness, and stratigraphy of the formation, by the 

natural slope or irregularity of the pressure-indicating surface, and 

by decrease in permeability that may result from compression of 

the formation when the artesian pressure of the water is relieved. 

The permeability determined by this method is used in exactly the 

same manner as the permeability determined by any other method 

in computing the rate of flow through a formation when its crosssection area and the natural hydraulic gradient of its water are 

known.

In 1906 G. Thiem published as a dissertation for the degree of 

doctor-engineer from the Konigliche Technische Hochschule at 

Stuttgart the results of his experiments and mathematical study 

relating to his field method for determining permeability. The 

experiments were made as a part of an investigation to find an 

additional water supply for the city of Prague. Ten sets of wells 

were sunk for the purpose, each set including one well that was 

pumped and two observation wells. The observation wells were 

placed in line with the pumped well but in any direction from it 

regardless of the direction of the natural hydraulic gradient. A 

formula was developed for computing the permeability from these 

tests. This formula, slightly modified in form, is as follows:

(q loge fli-loge a) 

\~ 2*-»*(£-&)

in which P is the coefficient of permeability, q is the rate of discharge, a and a^ are the respective distances of the two observation 

wells from, the discharge well, S and Sj, are the respective drawdowns in the two observation wells, and m is the thickness of the 

water-bearing bed, if artesian conditions exist, or the average thickness of the saturated part of the bed at the two observation wells, 

if water-table conditions exist. To obtain the coefficient of permeability as defined in Water-Supply Paper 596 all these factors 

should be expressed in feet except <£, which should be expressed in 

gallons a day.
136 CONTRIBUTION'S TO HYDROLOGY OF UNITED STATES, 1931

Theoretically this method can also be used for computing specific yield, but no test has been made of its practicability for this 

purpose. For example, during a specified period in the initial stage 

of a test under water-table conditions an accurate record can be 

obtained of total pumpage and of the progressive lowering of the 

water levels in the observation wells. From the record of water 

levels and the permeability, as determined by the test, the flow 

through the selected cylindrical cross-section area during the period 

can be computed. The quantity taken from storage within the cylinder can then be computed as the total pumpage minus the inflow, 

and from the records of the water levels the volume of material in 

the cylinder that was unwatered during the period can also be 

computed. Better results can doubtless be obtained, however, if 

the specific-yield test is made during a period immediately after 

the well has been shut down, when the quantity of water taken into 

storage in the cylinder will be equal to the total inflow during the 

period and the volume of material saturated can 1>e computed from 

the rise of the water levels.

Closely akin to the specific yield, but generally of much smaller 

magnitude, is the change in storage capacity of an artesian formation with changes in the artesian pressure on account of the volume 

elasticity of the formation. Obviously the increase in storage in 

an artesian formation can be computed from progressive changes in 

artesian pressure immediately after the discharge well has been shut 

down, by the procedure that has just been outlined for computing 

specific yield under water-table conditions. Rough computations 

of this kind have been made.1

METHOD BASED ON AREA OF INFLUENCE OF WELLS

Ground water obeys the law of all fluids in that it always flows 

away from a point of high pressure toward one of lower pressure. 

In other words, it flows in the direction of the hydraulic gradient. 

In a formation that has a water table the ground water flows from 

a high area of the water table toward a low area, much as surface 

water flows down the slope of a land surface. In an artesian formation the water flows in the direction of the hydraulic gradient; 

it may flow downward or upward, as in the mains and service 

pipes of a system of waterworks. In some places the artesian water 

moves in the direction of the dip of the formation, and in other 

places it moves in a direction opposite to the dip or at some angle 

to the dip. An accurate contour map of a water table or of the 

pressure-indicating surface of a formation filled with water under 

pressure shows the direction of flow at every point.

1 Meinzer, 0. E., Compressibility and elasticity of artesian aquifers: Econ. Geology, 

vol. 23, pp. 263-291, 1928.
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 137

So long as no wells have been sunk into a formation its water 

flows from the intake area toward the area of natural discharge. 

If, however, wells are sunk and water is withdrawn through them, 

either by pumping or by artesian flow, the water table or other 

pressure-indicating surface will be depressed in the vicinity of 

the wells, and water that would normally percolate to an area of 

natural discharge will be diverted toward the wells. An accurate 

contour map showing the depression in the pressure-indicating surface caused by the operation of the wells will show the area within 

which the water is diverted toward the wells.

So long as the withdrawals are relatively light the depression will 

remain small, and water which in its natural course does not flow 

near the wells will not be diverted. As the withdrawals become 

heavier, however, the depression is enlarged and a greater proportion of the ground water is diverted toward the wells, until eventually the depression may extend across the entire width of the 

formation, and practically all of the flow may be recovered through 

the wells.

The flow of ground water through a formation can be estimated 

from a record of the pumpage or artesian flow and the extent of the 

depression as determined from water levels in wells, due allowance 

being made for the quantity of water that is taken out of storage in 

developing the depression. This method has the advantage that it 

does not require determination of the permeability and involves 

specific yield only in so far as there is a change in storage. Except 

for changes in storage it involves only the rate of pumping or artesian 

flow and the altitude of the water levels in the observation wells. 

The method should prove applicable where a considerable quantity 

of water is withdrawn and sufficient wells are available for waterlevel observations.

In applying this method attention must be given to the modified 

condition of the pressure-indicating surface on the downstream side 

of the depression produced by the operation of the wells. If no 

water is permitted to pass the wells this surface will eventually be 

lowered about to the level of the natural outlet of the ground water or 

to the level of the crest of an effective underground barrier. In 

many places this drawdown would make the cost of pumping prohibitive. In order to prevent the lowering of the water levels in 

the wells below the economic limit it may be necessary to allow a 

part perhaps a large part of the water to flow past the depression, 

so that it will maintain a certain minimum gradient to the natural 

outlet.
138 CONTRIBUTIONS TO HYDROLOGY OF UNITED STATES, 1931

METHOD BASED ON MOVEMENTS OF WATER LEVELS IN RELATION 

TO RATES OF WITHDRAWAL

When a well is pumped some water is inevitably taken out of storage from the well and from the material surrounding it. This reduces the pressure, creates a hydraulic gradient toward the well, and 

causes the ground water to flow into the well. If the water-bearing 

formation has a water table, considerable ground water may have to 

be removed from storage before a gradient will be developed that is 

steep enough to make the water flow toward the well at the same 

rate that it is pumped and to establish approximate equilibrium. If 

the formation is filled with water under pressure only a comparatively small amount of water has to be removed from storage in order 

to give the required gradient, and hence drawdown will be rapid and 

approximate equilibrium will be quickly established. The quantity 

to be removed from storage in order to reach equilibrium varies in 

proportion to the compressibility of the water-bearing formation.2

When, with a constant rate of pumping, equilibrium is established, 

water is no longer removed from storage around the well but flows 

to the well as rapidly as it is withdrawn. Even after there is approximate equilibrium and the water level in the well remains virtually stationary the water may be taken from storage in distant 

parts of the formation rather than from the increments at its intake 

area. However, unless the withdrawal exceeds the recharge minus 

the unavoidable loss, the water level in the well will approach a 

limit at a constantly decreasing rate of drawdown. In most 

ground-water developments the supply available is conditioned by 

the permissible lift. A vital question, therefore, relates to the rate 

at which water will flow to the well under the gradient that will be 

established by the drawdown involved in the permissible lift.

This elementary principle of hydraulics controls not only the practicable capacity of ah individual well but also the quantity of water 

that can be recovered by a group of wells or by a large number of 

wells distributed throughout a wide area. The details are more complicated, but the principle is the same. If the ground-water supply 

in an area is extensively developed by drilling many wells and drawing heavily on them the water levels or artesian pressures in the wells 

will inevitably decline. This decline will occur whether the conditions are primarily of the water-table or the artesian type, and 

whether the artesian wells discharge by artesian flow or by pumping. Other things being equal, however, the decline will occur more 

rapidly under artesian conditions than under water-table conditions. 

The mere fact that there is a decline in the water levels or artesian

2 Meinzer, O. H, Compressibility and elasticity of artesian aquifers: Econ. Geology, 

vol. 23, pp. 263-291, 1928.
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 139

pressures during the period of development, when the rate of withdrawal is constantly increasing, is not an indication of overdevelopment as long as the decline is not so great as to indicate the approach 

of lifts beyond the economic limit.

If the rate of pumping becomes constant the water levels in the 

wells will not immediately become stationary, but they will decline 

at a diminishing rate. If the rate of pumping exceeds the salvageable recharge the water levels will eventually decline to the bottoms 

of the wells, and the rate of recovery will unavoidably be decreased. 

If, however, the rate of pumping does not exceed the salvageable 

recharge, the water levels will approach as a limit some level above 

the bottom of the wells, though perhaps too low for practicable 

operation. To determine the limit even approximately requires the 

lapse of sufficient time to permit the development of a curve in which 

the water levels in a key well or group of wells are plotted against 

time and which can with some confidence be projected into the future. The problem will invariably be complicated by irregularities 

in the rate and location of the pumping, adequate records of which 

can not easily be obtained, and also by fluctuations in water levels 

produced by causes other than pumping.

In most areas there are fluctuations in the rate of pumping or of 

artesian flow, as the case may be. In many areas the most pronounced fluctuations are seasonal. On the whole these fluctuations 

increase the applicability of this method. It has been shown that 

some decline in water levels must be expected even after the rate 

of pumping has become constant. Furthermore, decline may even 

continue for some time after the rate of pumping has been reduced 

without indicating a dangerous amount of ultimate drawdown. 

However, if with either constant or reduced rate of pumping the 

water levels continue to decline persistently and without marked 

slowing up, excessive ultimate drawdown is indicated, although it 

may not be possible to determine the ultimate drawdown or to 

estimate the amount of overdevelopment. In the development of 

many of the areas of artesian flow there is an early period of original 

high pressure and active drilling during which the artesian discharge increases greatly and the pressure drops rapidly. This early 

period is generally followed by a long period in which there is 

progressive but gradual decline both in discharge and in pressure. 

It appears obvious that under these conditions water is being withdrawn from storage and that equilibrium will not be established 

until the pressure or the discharge or both are still further reduced.3

3 Meinzer, O. E., and Hard, H. A., The artesian water supply of the Dakota sandstone 

in North Dakota, with special reference to the Edgeley quadrangle: U. S. Geol. Survey 

Water-Supply Paper 520, pp. 73-95, 1925. Hard, H, A., Geology and water resources of 

the Bdgeley and LaMoure quadrangles, N. Dak.: U. S. Geol. Survey Bull. 801, pp. 57- 

87, 1929.
140 CONTRIBUTIONS TO HYDROLOGY OP UNITED STATES, 1931

If the rate of pumping or of artesian discharge is radically reduced, 

as it is in the autumn in irrigation districts and in some public 

waterworks, the water levels or artesian pressures that have been 

declining are likely to reverse their direction and begin to rise. 

This means that the point of equilibrium has been reached and 

passed that, with the gradient which was established by the heavier 

withdrawal, water is flowing into the area more rapidly than it is 

being removed by the reduced rate of withdrawal. In the next 

spring or summer the rate of withdrawal may be again increased 

and another reversal of the water levels may occur. If the rate of 

withdrawal is greater than in the previous summer a new low stage 

may be established. By critical study of this game of tag between 

the water levels and the rates of withdrawal a number of points 

of equilibrium can be approximately determined, but exact determination is complicated by the lag in the movements of the water 

levels due to storage, and further study needs to be given to this 

subject to develop a systematic method of interpretation that is 

mathematically sound. These points of equilibrium are points on 

a rating curve of the inflowing stream of ground water. To the 

extent that this curve can be projected it will indicate the drawdown 

that will be caused by increased rates of withdrawal and will thus 

establish the safe yield. The rating-curve method for conduit conditions was developed by Thompson in his work in New Jersey from 

1923 to 1928 and was successfully applied by him in making estimates 

of safe yield for Atlantic City and other municipalities.4

EVALUATION OP EXTRANEOUS INFLUENCES ON THE

WATER LEVELS

The movements of the water levels in wells are not the effects of 

simple forces acting singly but rather the resultants of a complex 

of interacting forces. This complexity, of course, increases the difficulties of interpretation. For example, a study of the effects produced by different rates of pumping may be complicated through 

changes produced by variations in atmospheric pressure or by the 

ebbing and flowing of oceanic tides. The barometric or tidal effects 

must be evaluated, and corrections must then be made for them. 

These extraneous agencies are, however, not wholly a detriment, for 

if they are studied jn a time and place where other agencies are 

absent or can be eliminated, they are likely to afford valuable 

information on the ground-water conditions.

If a shallow well ends in a formation that lies at the surface and 

is freely permeable throughout, only slight barometric effects or

* Thompson, D. G., Ground-water supplies in the Atlantic City region: New Jersey 

Dept. Conservation and Development Bull. 30, pp. 35-88, 1928.
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 141

none at all are to be expected, because any change in the atmospheric pressure is transmitted almost as freely to the water table 

through the permeable material as to the water level in the well. 

In the Escalante Valley investigation, by White, water-stage recorders were used on about 70 shallow water-table wells. With few 

exceptions, the records of these wells showed no evidence of fluctuations due to changes in atmospheric pressure. The exceptions 

occurred chiefly in the early spring, when aparently the soil was 

wet enough to be impervious to air. Similarly, in a shallow observation well near Washington, D. C., barometric fluctuations, 

amounting to about 20 per cent of the full fluctuations of a water 

barometer, are apparently confined to periods when the water in the 

soil tends to reduce notably its permeability to the air. Barometric 

fluctuations have been found to be virtually absent in observation 

wells equipped with automatic recorders in different parts of the 

country where water-table conditions exist.

If a well ends in an artesian formation and this formation or 

the overlying confining beds have sufficient strength to resist deformation by slight changes in pressure at the surface, the well will act 

as a barometer. The fluctuations of its water level will have virtually 

the same range of fluctuations as would be shown by a water barometer, or 13.5 times the range in a mercury barometer. However, 

for obvious reasons, the movements of the water level in the well 

will always be in the opposite direction from those in an ordinary 

mercury barometer. In a deep well at The Dalles, Oreg., that ends 

in an artesian stratum in volcanic rocks, the water level was found 

by Piper 6 to respond practically 100 per cent to changes in atmospheric pressure as indicated by the barographic records of the 

United States Weather Bureau. The record of a deep well in the 

Koswell artesian basin, New Mexico, obtained by means of a waterstage recorder, showed that on certain days when no great disturbances were caused by pumping the fluctuations of the water 

level in the well closely followed the fluctuations of the barometer. 

In general an inch of change in the mercury barometer was represented by about a foot of fluctuation in the water level.6 In another artesian well situated near the railroad in the same basin no 

rise in the water level was recorded when trains passed. Both of 

these results indicated artesian conditions in competent formations. 

If a similar well were situated near the seashore its water level 

would not be expected to show any tidal influence.

5 Piper, A. M., Geology and ground-water resources of the Dalles region, Oregon: U. S. 

Dept. Interior Press Mem. 52343, Apr. 7, 1931.

a Fiedler, A. G., Report on investigations of the Boswell artesian basin, New Mexico, 

during the year ending June 30, 1926: New Mexico State Engineer Seventh Bienn. Bept, 

p. 37, pi. 7, 1926.
142 CONTRIBUTIONS TO HYDROLOGY OF UNITED STATES, 1931

If a well ends in an artesian formation that has volume elasticity, 

such as incoherent sand, and is confined beneath beds of soft shale 

that is impermeable but yields to even slight pressure, its water level 

will have smaller fluctuations resulting from atmospheric changes 

than that of a water barometer, and the ratio of the movements in 

the well to the corresponding movements in the barometer should 

give a measure of the resistance of the water-bearing and confining 

beds. If such a well is near the seashore its water level will fluctuate 

more or less with the tide. In the Atlantic City investigation, by 

Thompson, it was found that artesian wells near the seashore ending in Coastal Plain deposits of sand overlain by clay fluctuated 

notably with the tide but showed no marked barometric fluctuations. 

These results seem to indicate artesian conditions in incompetent 

strata. In such wells the water level might be expected to rise as 

a result of the compression produced by a passing railroad train. 

In the Mokelumne area it was found that the water level in a well 

drilled through valley fill to a stratum at some depth below the 

water table rose whenever a train passed over the railroad 117 feet 

away, but in a well drilled only to the water table at the same place 

the water level was not affected by passing trains.7

If a well ends in a formation that is effectively covered by an 

impermeable bed but is unsaturated in its upper part, thus having 

an air chamber between the water table and the overlying impermeable bed, and if the well is tightly cased to a level below the water 

table, the water level in the well will behave like that iri an artesian well in competent beds. It will fluctuate through about the 

same range as the water level in a water barometer, because, as in 

the other case, the counter pressure will remain nearly constant. 

These conditions were noted by Thompson 8 in the Grand Prairie 

region of Arkansas, where some of the wells were found to perform as perfect barometers, apparently with 100 per cent of 

barometric fluctuation. These are examples of actual conditions 

which have been encountered in quantitative ground-water investigations and which must be understood if the data on water levels 

are to be correctly interpreted.

PRESENT STATUS AND OUTLOOK

The foregoing discussion shows that there are many ways in 

which the problem of available supplies of ground water can be attacked, but it also shows that the subject is complicated and that

7 Stearns, H. TM Robinson, T. W., and Taylor, G. H., Geology and water resources of 

the Mokelumne area, California: U. S. Geol. Survey Water-Supply Paper 619, pp. 148, 149, 

1930.

8 Thompson, D. G., Ground-water supplies for rice irrigation in the Grand Prairie 

region, Arkansas: U. S. Dept. Interior Press Mem. 49844, pp. 8, 9, Jan. 26, 1931.
METHODS FOR ESTIMATING GROUND-WATER SUPPLIES 143

there are difficulties in applying any of the methods that have been 

outlined. Only those who have worked on ground-water problems 

can appreciate how numerous and baffling are these difficulties. No 

one method is applicable to all conditions. In some areas several 

more or less independent methods can be used which serve to give 

checks on the accuracy of the work. In other areas only a single 

method may be applicable, or it may be almost impossible to make 

effective use of any of the known methods.

Other methods must be used in humid than in arid regions, in 

areas of large ground-water developments than in undeveloped 

areas, and in artesian areas than in areas with water-table conditions. Arid regions are, as a rule, better adapted for quantitative 

studies than humid regions, and many of the available methods have 

been developed in arid regions. More methods are available in developed than in undeveloped areas, and the demand for quantitative 

work commonly comes after there has been enough development to 

cause considerable drawdown. A number of the methods, however, 

do not depend at all on development, and considerable successful 

quantitative work has been done in areas that were virtually undeveloped. In the past most of the quantitative work has been done in 

areas in which the conditions are dominantly of the water-table or 

reservoir type, but recently quantitative attacks have been made on 

a number of artesian basins in which the capacity of the formation 

as a conduit is important, and methods are being developed for these 

conditions.

The most formidable difficulties result from the complexity of 

the texture of the water-bearing formations, which make it hard to 

get reliable figures for their two properties of chief significance 

specific yield and permeability. Some of the most promising 

methods are those which do not involve either of these properties or 

else determine them from water levels in wells or from water levels 

and pumpage.

It is becoming evident that the chief instrument of precision in 

ground-water hydrology is the water-stage recorder installed over a 

well. The water levels in wells are sensitive to every change that 

takes place in the ground water, and they can be almost perfectly 

recorded by a high-grade automatic recorder. In the interpretation 

of such records lie possibilities of a new and fruitful phase of 

ground-water hydrology that are not now fully appreciated and 

that can be realized only as a result of much critical investigation. 

It will be necessary to understand the various agencies that influence the delicate equilibrium that exists in every body of ground 

water and also the nature of the container that holds the ground 

water and how it can be expected to respond to these agencies. It
144 CONTBIBUTIONS TO HYDROLOGY OF UNITED STATES, 1931

will be necessary to recognize clearly the basic distinctions between 

a water table and the pressure-indicating surface of an artesian formation, and between changes that represent increments to or withdrawals from storage and those that represent only variations in 

pressure.

It is also becoming evident that time is required to obtain reliable 

results in most quantitative investigations of ground water. In 

this respect ground-water work differs from most other geologic 

work. It does not deal primarily with features which are the fossilized product of events that occurred in past ages and which can 

be observed and studied at any convenient time, but it deals rather 

with forces that are now operating and producing changes which 

can be kept under observation. Past changes that were not recorded 

are gone forever; future changes can be observed only with the 

lapse of time. For this reason systematic observations should be 

made and records kept in every area in which large ground-water 

developments have been made or are contemplated, so that reliable 

data will accumulate and will be available for interpretation in the 

future.

o

U.S. GOVERNMENT PRINTING OFFICE: 1959 O 497117