Studies of 

Evaporation

GEOLOGICAL SURVEY PROFESSIONAL PAPER 272

This volume was published 

as separate chapters A—H
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

William T. Pecora, Director
CONTENTS

[Letters designate the separately published chapters]

Page 

(A) The effect of salinity on evaporation, by G. Earl Harbeck, Jr__________-______--_--------------_------.-_------- 1

I'B) The effect of the addition of heat from a powerplant on the thermal structure and evaporation of Lake Colorado City,

Texas, by G. Earl Harbeck, Jr., G. E. Koberg, and G. H. Hughes_________________ —— _ —— _________ 7

fC) Review of literature on evaporation suppression, by George B. Magin, Jr., and Lois E. Randall___ _____-._---_-____ 53

I'D) Evaporation from the 17 Western States, by J. Stuart Meyers._______________-_--___-_-__-____-_-------_--_-_ 71

|'E) A practical field technique for measuring reservoir evaporation utilizing mass-transfer theory, by G. Earl Harbeck, Jr__ 101 

T) Methods to compute long-wave radiation from the atmosphere and reflected solar radiation from a water surface, by

Gordon E. Koberg._____._.__________________________________________ — ______ 107

'G) Evaporation study in a humid region, Lake Michie, North Carolina, by J. F. Turner, Jr______________---_-_-_-__-- 137

(H) Analysis of techniques used to measure evaporation from Salton Sea, California, by G. H. Hughes._____-__--___-__- 151

The Effect of 

Salinity on 

Evaporation

By G. EARL HARBECK, JR.

STUDIES OF EVAPORATION

GEOLOGICAL SURVEY PROFESSIONAL PAPER 272-A

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1955
UNITED STATES DEPARTMENT OF THE INTERIOR 

Douglas McKay, Secretary

GEOLOGICAL SURVEY 

W. E. Wrather, Director

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

Washington 25, D. C. - Price 15 cents (paper cover)
PREFACE

This report on the effect of salinity on evaporation was prepared in the Water Resources Division of the Geological Survey 

under the administrative supervision of R. W. Davenport, Chief, 

Technical Coordination Branch, and the technical guidance of 

W. B. Langbein.

The advice and assistance of W. W. Hastings, Quality of Water 

Branch, who also furnished the results of the chemical analyses, 

is greatly appreciated.

This report is part of the applied research investigations of evaporation jointly sponsored hy the U. S. Bureau of Reclamation, the 

U. S. Weather Bureau, and the U. S. Geological Survey.

in

CONTENTS

Page

Abstract-_-___----_-_-__-_--_-_-________-__--__-_-____________________-___-______-___-_-_--_-__-____-__-_-__-_ 1

"ntroduction__________________________________________________________________________________________________ 1

Effect of salinity on saturation vapor pressure..___________________________________________________________________ 1

Effect of salinity on evaporation.________________________________________________________________________________ 3

Comparison with data obtained by Adams____----__-_____________________-_-_____-_____--_____-_--____-___-______ 5

'^'elected biblioprraohy________________________________________________________________________________________ . 6

ILLUSTRATIONS

1. Relation between salinity and reduction in saturation vapor pressure at 15° C________--_-_-__ _______________ 2

2. The variation of evaporation ratio and temperature rise with evaporation rate and salinity____ ._______--____.._ 5

TABLE

TABLE 1. Equivalents per million, and percentage equivalents per million of various constituents in natural waters as indicated 

by selected analyses.___'__________.___________.________________________._____________________________

STUDIES OF EVAPORATION

THE EFFECT OF SALINITY ON EVAPORATION

By G. EARL HARBBCK, JR.

ABSTRACT

The effect of salinity is to reduce evaporation but at the same 

time to increase the energy returned to the atmosphere by other 

physical processes, so that under equilibrium conditions a saline 

solution reaches a temperature higher than that of pure water. 

Because of the many variables, of which some are interrelated, 

it is impossible to define a simple relationship between salinity 

and the decrease in evaporation. The theory presented in this 

report is general, and for any given rate of evaporation from 

pure water, the effect of salinity on evaporation and the 

attendant temperature rise can be determined on the basis of 

measurements of air and water temperatures, humidity, and 

atmospheric pressure.

INTRODUCTION

It has long been known that evaporation from a free 

water surface is reduced by salinity. Several investigators have presented the results of experimental 

determinations of the reduction in evaporation with 

increasing salinity. Lee (1927) compared the evaporation from distilled water with evaporation from Owens 

Lake brine of varying specific gravities, and presented 

a chart showing that up to a certain limit the ratio of 

evaporation of brine to that of distilled water decreased 

about 1 percent for a change in specific gravity of 0.01. 

Young (1947) presented the results of experiments 

using varying concentrations of sodium chloride, and 

his findings did not differ greatly from those of Lee.

The effect of dissolved solids is, of course, to reduce 

the saturation vapor pressure of the solution. In 

almost all of the equations based on the theory of 

mass-transfer or turbulent transport of energy and in 

nearly all empirical evaporation equations, evaporation 

is directly proportional to the vapor-pressure difference. 

Among these are the equations proposed by Sverdrup 

(1937) and Sutton (1949), which were among those 

tested during the Lake Hefiier studies (U. S. Geol. 

Survey, 1952, p. 54-61). Although there is still 

diversity of opinion concerning wind laws, atmospheric 

stability, and certain other aspects of the mass-transfer 

theory, there seems to be general agreement that with 

other variables held constant, evaporation is directly 

proportional to the difference between the vapor

pressure of the air in contact with the water (usually 

taken as the saturation vapor pressure of air at the 

temperature of the water surface) and the vapor 

pressure of the air at some height.

EFFECT OF SALINITY ON SATURATION VAPOR 

PRESSURE

Unfortunately, experimental data on the effect of 

various salts on saturation vapor pressure, in varying 

concentrations and at different temperatures are incomplete. Sverdrup, Johnson, and Fleming (1942) presented rather complete data for sea water (salinity 

35,000 ppm) 1 at temperatures from —2° C to 32° C. 

For other concentrations the International Crtical 

Tables (National Kesearch Council, 1928) provided 

data for solutions of other salts. (See fig. 1.) Within 

the range of temperatures experienced in natural waters, 

the percent reduction in saturation vapor pressure is 

affected only slightly by temperature. A temperature 

of 15° C was therefore arbitrarily chosen as the standard temperature at which to compare the effects of the 

different salts. Data for sodium chloride, magnesium 

chloride, and potassium chloride cover a fairly wide 

range of concentrations as shown by the light solid 

lines of figure 1. Data for sodium sulfate and sodium 

carbonate cover a limited range of concentrations. 

Extrapolations in the direction of decreasing salinity 

were made by auxiliary plotting on arithmetic coordinates. The other salts commonly found in natural 

waters, calcium bicarbonate, calcium sulfate, and 

magnesium bicarbonate, are only slightly soluWe so 

that it is not surprising that data are lacking on their 

effect on reduction in saturation vapor pressure. Data 

on the effect of magnesium sulfate are available only 

at temperatures of 50° C and above.

In order to define a curve for average natural waters 

(see fig. 1), approximate percentages of various salts

i Salinity as the term is used by oceanographers is the total amount of solid riaterial 

in grams contained in one kilogram of sea water, or in parts per thousand. Published 

analyses of natural inland waters show dissolved solids in parts per million, v^hich is 

the unit of measure used throughout this discussion.
STUDIES OF EVAPORATION

100,000

CO

Q

_i

o

CO

Q 

LU 

>

O 

CO

CO

Q

10,000

1,000

.001

Great Salt Lake

Salton Sea 

Sea water

EXPLANATION

Based on data from International Critical Tabhs 

Extrapolated 

Average natural water 

Computed for hypothetical combinations of sa'*s

in selected natural waters

Decrease in saturation vapor pressure owing to salinity _

Saturation vapor pressure of pure water 

FIGURE 1.—Eelation between salinity and reduction in saturation vaper pressure at 15°

in hypothetical combination were computed for certain 

selected natural waters, based on the data given in 

table 1. These percentages were used as weighting 

factors in computing the reduction in saturation vapor 

pressure for the various samples of natural water. 

When the total amount of dissolved solids is small, 

calcium and magnesium salts form a relatively large 

part of the total. The percentage of sodium chloride, 

however, often increases in waters with greater dissolved solids. About 87 percent of the dissolved 

solids in Great Salt Lake is sodium chloride, with 

relatively small proportions of magnesium sulfate and 

magnesium chloride. This is to be expected because 

of the much greater solubility of sodium chloride as 

compared with the calcium salts. Thus, the curve for 

natural water shown in figure 1 closely approximates 

the sodium chloride curve at high concentrations. 

However, impounded return flow from irrigated lands

in sedimentary deposits in the semiarid west is frequently high in sodium sulfate, and the chloride content 

may- be insignificant. In this instance, the curve for 

average natural waters shown in figure 1 would not be 

applicable, and the curve shown for sodium sulfate 

would be more nearly correct.

Unfortunately figure 1 cannot be ured directly for 

the computation of the reduction in evaporation owing 

to salinity. The reduction in saturation pressure shown 

in figure 1 applies to a saline solution at the same temperature as pure water (15° C in this illustration). If 

a pan of brine and a pan of pure water are similarly 

exposed, the temperature of the brine will be higher 

than that of the pure water after equilibrium has been 

reached. If the amount of incoming energy is assumed 

to be the same for both pans, the amount of outgoing 

energy must also be the same. Because the saturation 

vapor pressure of the brine (and thereby the vapor
THE EFFECT OF SALINITY ON EVAPOEATION

TABLE 1.—Equivalents per million (epm), and percentage equivalents per million of various constituents in natural waters as ind'vated

by selected analyses J

Ion

Ca_. ..._.._

Mg__ ______

Na+K_...__ 

Fe___-_____

Total. ___ 

HCO3 _--___

SO4— -- — _

Cl__--__. ._

NO3— — __

Total __..

Lake Mead, Ariz.- 

Nev. (660 ppm)

epm 

4.04 

2. 14 

3. 47 

0

9. 65

2. 06 

5.93 

1.66 

0

9. 65

Percent 

epm 

42 

22 

36 

0

100

21 

62 

17 

0

100

May wood, 111., water supply (1,060 

ppm)

epm 

4.86 

2.25 

8. 54 

.01

15. 66

5.39 

2.48 

7.79 

0

15. 66

Percent 

epm 

31 

14 

55 

0

100

34 

16 

50 

0

100

Elsinore Lake, Calif. 

(3,800 ppm)

epm 

0.65 

2.06 

53. 62 

0

56.33

18. 99 

4.29 

33. 05 

0

56. 33

Percent 

epm 

1 

4 

95 

0

100

34 

7 

59 

0

100

Pecos River near 

Qirvin, Tex. 

(11,000 ppm)

epm 

36. 8 

32.2 

113. 1

.7

182. 8

2.5 

63.7 

116. 6 

0

182.8

Percent 

epm 

20 

18 

62 

0

100

1 

35 

64 

0

100

Sea water 

(35,000 ppm)

epm 

21 

107 

476 

0

604

2

56 

546 

0

604

Percent 

epm 

3 

18 

79 

0

100

0 

9 

91 

0

100

Salton Sea, Calif. 

(37,000 ppm)

epm 

32 

6 

602 

0

640

35 

114 

491 

0

640

Percent 

epm 

5 

1 

94 

0

100

5 

18

77 

0

100

Great Salt Lake, 

Utah (210,000 

ppm)

epm 

18 

478 

3, 112 

0

3,608

4 

238 

3,366 

0

3,608

Percent 

epm

13 

86 

0

100

0 

7 

93 

0

100

Analyses of Elsinore Lake and Salton Sea by Department of Agriculture; others by Geological Survey.

pressure difference) is less than for water, the amount 

of energy utilized for evaporation is also less. The temperature of the brine must rise until the energy made 

available by the decrease in evaporation can be returned 

to the atmosphere by means of other physical processes. 

Evaporation from the brine will be less, although 

greater than if the two fluids were at the same temperature. It is therefore necessary to determine the 

effect of salinity and other factors on the temperature 

rise of the brine.

EFFECT OF SALINITY ON EVAPORATION

The energy budget for a body of water may be expressed as follows:

in which Qs — solar radiation incident to the water

surface

Qr= reflected solar radiation 

$a = incoming long-wave radiation from the

atmosphere

Qar=: reflected long-wave radiation 

$6s =long-wave radiation emitted by the body

of water

Qe= energy utilized by evaporation 

Qh= energy conducted from the body of water

as sensible heat

Qv=net energy advected into the body of water 

Qw = energy advected by the evaporated water 

Q#= change hi energy stored in the body of

water

Consider two identical insulated shallow pans similarly 

exposed, one containing pure water, the other containing 

brine. Each will have an energy budget, and many 

items will be the same for both pans. If the exposures

are the same, it may be assumed that the solar and 

atmospheric radiation received by both pans will bo the 

same. The amount of incoming solar radiation tha"t is 

reflected depends on sun altitude and cloud cover, 

according to Anderson (U. S. Geol. Survey, 1952, p. 87) 

and should be the same for both pans. Long-y^ave 

radiation reflected by the body of water and emitted 

by the body of water depends only on the emissivity. 

A study made by Gier and Dunkle (U. S. Geol. Survey, 

1952, p. 96-98) indicated that the emissivity of water is 

0.970 (reflectivity =1—emissivity=0.030 when source 

and water temperatures are equal), and it is independent 

of water temperature and dissolved solids. Although 

the maximum salinity of any water sample tested was 

33,420 ppm, there is no evidence to indicate that 

emissivity does not remain constant for even greater 

amounts of dissolved solids. If no water is added to 

either pan, the advected energy term is zero for both 

pans. If the pans are very shallow, it may be safely 

assumed that at least for short periods of time, the changes 

in energy storage, on a unit-area basis, are negligible. 

After equilibrium has been attained, the sum of certain items in the energy budget for the pan of pure water 

may be equated to the sum of the same items ir the 

energy budget for the pan of brine, as follows:

(2)

Throughout this discussion the symbols with primes 

refer to the pan of brine and the symbols without 

primes refer to the pan of pure water.

Combinations of various terms in equation (2) may 

be evaluated using certain familiar relations, as follows 

(units: cal cm~2 day"1 )

(3)
4 STUDIES OF EVAPORATION

in which <r=Stefan-Boltzman constant for black-body

radiation

= 1.171X10~7 cal cm-2 deg~4 day-1 

T0 —water surface temperature in degrees C

Q' e -Qe=pE'L'-pEL (4)

in which p=average density of evaporated water (=1

gm cm"3) 

E= average daily evaporation in gm cm"2

day" 1 (= cm day" 1 )

Z,=latent heat of vaporization at To in cal 

gin"1

Q'h ~Qh=R'Q' e -RQe=R'pE'L'-RpEL (5)

in which R=the Boweii ratio 2= 0- 61 P(T0 ~T^ ^

1,000 (e0 -ea )

Tu = air temperature in degrees C 

e0 =saturation vapor pressure at T0 in mb 

ea =vapor pressure of the air in mb 

P=atmospheric pressure in mb

(6)

in which c= specific heat of water (= 1 cal gm" 1 deg" 1 ) 

From mass transfer theory, assuming that the wind 

over both pans is the same and the possible effect of a 

change in atmospheric stability resulting from the 

small increase in water temperature in the pan of 

brine is negligible, it follows that

E e 0 -ett

in which 71= ratio of the decrease in saturation vapor 

pressure caused by salinity to the saturation vapor 

pressure of pure water. (See fig. 1.). The use of an 

average figure for water density (equations 4-6) and 

specific heat (equation 6) should be explained. Since 

the temperature rise in the brine pan is only a few 

degrees, little error is introducted by assuming that 

the density of the evaporated water (dissolved solids 

are not evaporated) is the same for the brine as for 

water. The variation of specific heat of water with 

temperature is also small and is neglected.

s Bowen (1926) suggested the use of the ratio of the energy conducted to the atmosphere as sensible heat (0*) to the energy utilized for evaporation (f.i.) as a means of 

circumventing the difficulty inherent in measuring OA directly, and presented a 

formula for computing that ratio from measurements of humidity, air and water 

temperatures, and atmospheric pressure. An instrument has been developed by 

Swinbank (1951) for measuring OA directly, but so far as is known it has not been 

used extensively in the field.

Considerable difference of opinion has arisen concerning the validity of the Bowen 

ratio. This was discussed at length by Anderson (U. S. Geol. Survej , 1952, pp. 104- 

109) , who concluded that the Bowen ratio is satisfactory for use in computing evaporation except when the vapor pressure difference is small.

Combining equations (2) to (7), we obtain 

'+CT0 ') [(l-n}e,'-ea\-(L+cT,) (e»- 

[L'(T0 '-Ta)-i(To-Ta)]

i—ea

1.136X10-7 [(T0 '+273)4 -(77o+273)4]=0 (8)

For any set of assumed values of T0 , Ta , P, and ea and

calling -—-, ^— -> and •—- constant for tH narrow range 

ell. o dl o d2 o

between TQ and TV, eq. (8) reduces to the form

(9)

in which A T= T0 ' -T0

Figure 2, which is based on equations (7), (8), and 

(9), illustrates the manner in which the temperature 

rise, AT, and the evaporation ratio, E'/E, vary with 

salinity. The relation between 11 and salinity was 

determined from figure 1. For computational purposes 

the following conditions were assumed:

T0 =15° C relative humidity =50 percent 

ru = 15°C P= 1,000mb

From figure 2 it will be noted that the evaporation 

ratio, E' IE, decreases with increasing salinity, and the 

temperature rise, AT, increases, as might be expected. 

Both the temperature rise and the evaporation ratio 

increase more rapidly with an increase in evaporation 

at high salinities than at low salinities.

With the rate of evaporation from the pan of water 

and other factors except the water temperature held 

constant as in figure 2, the evaporation ratio and the 

temperature rise vary with water surface temperature 

and salinity in much the same manner as with evaporation and salinity in figure 2.

It is of course possible to construct many graphs 

similar to figure 2 in which different factors are held 

constant. However, none would be of practical value 

because in nature those factors are seldom if ever 

constant. Thus, for any given set of conditions it is 

necessary to solve equation (8) which c<\n be reduced to 

an equation similar to (9) if the temperature rise is not 

sufficiently large to invalidate the resumption that 

the rate of change in emitted long-wave radiation, 

latent heat of vaporization, and saturation vapor 

pressure with temperature are constant over the given 

temperature range.
THE EFFECT OF SALINITY ON EVAPORATION

100,000 200,000 300,000 

SALINITY, IN PARTS PER MILLION

FIGURE 2.—The variation of evaporation ratio and temperature rise with evaporation rate and salinity.

Under certain conditions, as for example when 

humidity is high and there is a substantial reduction of 

saturation vapor pressure owing to salinity, it is quite 

possible that condensation may occur on the pan of 

brine while evaporation takes place from the pan of 

pure water. In the course of an experiment during the 

winter, Adams (1933) noted that on one occasion 

evaporation from a pan of frozen water was considerable, 

but that no evaporation occurred from a pan of brine. 

The point at which condensation will begin can be 

determined using equation (8), the condition being 

that the quantity (1—n)eQ— ea be zero, which can most 

easily be attained at low temperature and high humidity 

and salinity.

COMPARISON WITH DATA OBTAINED BY ADAMS

Data are available for an approximate check of figure 

2. A laboratory experiment was conducted by Adams 

(1933) during the period July to October, 1932, to 

determine the ratio of evaporation from Great Salt 

Lake brine to evaporation from fresh water. Evaporation rates from pans of brine (251,000 p. p. m.) and 

fresh water were compared. Air temperature and

relative humidity were observed only in the morring. 

During the entire period the evaporation ratio was 

found to be 0.80-0.82.

In July, Adams observed that the evaporation from 

the pan of water was 9 inches (0.74 cm per day"1 ) and 

that the temperature rise was 2° C. Although the 

meteorological conditions assumed in figure 2 are not 

strictly applicable, the figure indicates that for the g;ven 

salinity and daily evaporation, the computed temperature rise is 2.2° C and the evaporation ratio is 0.79.

During September evaporation was 3 inches (0.2f cm 

day"1 ). Adams observed a temperature rise of 1.8° C. 

From figure 2 the computed temperature ris^ is l.f° G 

and the evaporation ratio 0.75. Computed temperature 

rises in July and September check the observed values 

quite closely, but the computed evaporation ratios 

(0.79 and 0.75) are somewhat less than those (0.80 to 

0.82) observed by Adams.

An examination of Weather Bureau records at Salt 

Lake City for the two months in question indicates 

that relative humidities were probably approximately 

30 percent instead of the value of 50 percent used in 

constructing figure 2. Evaporation ratios decrease as
6 STUDIES OF EVAPORATION

humidity increases, other factors being the same, and 

it is believed that the apparent differences between 

computed and observed evaporation ratios are to a large 

extent caused by the difference in humidity.

SELECTED BIBLIOGRAPHY

Adams, T. C., 1934, Evaporation from Great Salt Lake: Bull.

Am. Meteorol. Soc., v. 15, p. 35-39. 

Bowen, I. S., 1926, The ratio of heat losses by conduction and by

evaporation from any water surface: Phys. Rev., ser. 2, v.

27, p. 779-787. 

Lee, C. H., 1927, Discussion of "Evaporation on reclamation

projects" by I. E. Houk: Trans. Am. Soc. Civ. Engineers,

v. 90, p. 340-343. 

National Research Council, 1928, International Critical Tables:

New York, McGraw Hill, 1st ed., v. 3.

Sutton, O. G., 1949, The application to microneteorology of the

theory of turbulent flow over rough surfaces: Royal

Meteorol. Soc. Quart, Jour., v. 75, no. 326, p. 335-350. 

Sverdrup, H. TL, 1937, On the evaporation from the oceans:

Jour. Marine Research, v. 1, no. 1, p. 3-14. 

Sverdrup, H. U., Johnson, M. W., and Fleming, R. H., 1942,

The oceans: New York, Prentice-Hall. 

Swinbank, W. C., 1951, The measurement of vertical transfer of

heat and water vapor by eddies in the lower atmosphere:

Jour. Meteorology, v. 8, no. 3, p. 135-145. 

LL S. Geol. Survey, 1954, Water-loss investigations; Lake Hefner

studies, technical report: U. S. Geol. Survey Prof. Paper 269.

[Also published as U. S. Navy Electronics Laboratory

report 327, 1952.] 

Young, A. A., 1947, Some recent evaporation investigations:

Trans. Am. Geophys. Union, v. 28, no. 2, p. 279-284.

O