Analysis of Techniques 

Used to Measure Evaporation 

From Salton Sea, California

By G. H. HUGHES

STUDIES OF EVAPORATION

GEOLOGICAL SURVEY PROFESSIONAL PAPER 272-H

Comparison of results obtained by energy-budget, 

mass-transfer, and water-budget methods 

and examination of possible sources of error

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1967
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

William T. Pecora, Director

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

Washington, D.C. 20402 - Price 30 cents (paper cover)
CONTENTS

Page

Abstract.__________________________ 151

Introduction.___________________________ 151

Energy-budget method___ _____ ___ _____ _ 152

Incoming radiation (Q,+ Q0)-________-_ 154

Reflected radiation (Q-+Q0f.)_________ 155

Radiatiou emitted (Q&») by Salton Sea__________ 156

Change in energy storage (Q&) __ ____ _ _____ 157

Net energy advected (Q ,) into Salton Sea___ __ 158

Sensible-heat transfer between air and water (Qk)__ 159

Transfer of heat through the bottom of Salton Sea._ 161

Mass-transfer method_______________________________ 162

Application to periods other than the calibration

period——__ ——— __ — ________________ 163

Water-budget method____________________ 164

Surface inflow.____________________ 164

Subsurface inflow_____________________ 165

Water-budget methed — Continued

Rainfall on the water surface_____________-_______

Water level. _______ — _ ——————————— 

Change in volume_______-_-__---_-_---------__-

Correction for thermal expansion_________________

Comparison of evaporation determined by the three 

methods-... __ ___ _. ——— __._. —————————

Comparison of evaporation from Salton Sea with class A 

pan evaporation____________________________-_-___

Comparison of evaporation data for Salton Sea and Lake

Energy-budget data_ 

Mass-transfer data__ 

Conclusions ____________

References.. ____-_-_

Page

165

165

166

166

166

170

171

171

173

175

175

ILLUSTRATIONS

[All figures except fig. 48 are graphs]

Page 

FIGTTBE 48. Map of Salton Sea area_____________________________________-____--_------------ 154

49. Monthly radiation at Sandy Beach, Calif., and at Yuma Proving Ground, Ariz__ _______. — _____----_ 155

50. Monthly temperature and vapor pressure of air at Sandy Beach, Calif., and at Yuma, Ariz______— __ — - 156

51. Relation between water-surface temperatures of Salton Sea as recorded at two buoys and as measured during

thermal surveys.-___-_______________________________________-____-------_---_-_------------- 157

52. Selected temperature profiles_______________________________._________--_-_ — .____- 158

53. Relation between the average of water temperatures measured periodically at New and Alamo Rivers and

average air temperature recorded continuously at Sandy Beach____.______-_-____-_-_----_---_--- 159

54. Air temperature at Sandy Beach and temperatures of water at the surface and bottom of Salton Sea———_ 160

55. Monthly vapor pressures of air at Sandy Beach and of saturated air at the temperature of the surface of

Salton Sea_________________.____________________..__.___-.__-_______-_-_----_---- 161

56. Average wind speeds as measured at two buoys__________________-_-___---___---- — — _.__-__ 163

57. Relation between evaporation by the mass-transfer method based on vapor pressure of air at Sandy Beach

and Yuma.________________________________________________________----__-----_-_----_------ 164

58. Water level of Salton Sea______________________________-__.____..-_-____._-_-_ 166

59. Relations of area and volume to water level____-__--___---_-_-_---_-_-_--------------------------- 166

60. Evaporation by three methods.._______________________________________-_-_____-__------------ 168

61-63. Relation between evaporation by—

61. Energy- and water-budget methods____._____________________---------------_---------- 168

62. Energy-budget method and mass-transfer product, u(e0 —ea)—--------------------------------- 169

63. Water-budget method and mass-transfer product, ufa—e^—--------------------------------- 169

64. Differences between evaporation by the energy-budget method and the average of evaporation by the masstransfer and water-budget methods_______________-___-____---_--------__________--_--------- 169

65. Relation between long-wave atmospheric radiation as measured and that computed by Koberg's method-._ 170

66. Seasonal differences between measured and computed long-wave atmospheric radiation._________--_------ 171

67. Relation between redetermined energy-budget evaporation and average of water-budget and mass-transfer

evaporation. ___________________________.______________.________________-___---_-_----------- 171

68. Correlations between changes in energy storage in Salton Sea and coefficients for a class A pan.___________ 172

69. Relation of mass-transfer coefficient, N, to surface area of water body______-_-_--_----__---------_--- 174
IV CONTENTS

TABLES

Page 

TABLE 1. Average values, by periods, of terms of the energy-budget equation for Salton Sea, in calories per square centimeter

per day-_________________________________________________________________-___-_-__-------------- 153

2. Yearly surface inflow to Salton Sea, 1961-62__.______________________-__-_____-_-_---______-___--_--- 164

3. Yearly surface inflow to Salton Sea from tributary streams with continuous streamflow records, 1961-62.------- 165

4. Recorded monthly rainfall at Salton Sea___________________________-___-____-___---------------------- 165

5. Evaporation from Salton Sea computed by energy-budget, water-budget, and mass-transfer methods, and evaporation from a class A pan at Sandy Beach___________________-_______-_____---_-_------------------- 167

6. Yearly values of terms of the energy-budget equation, for Lake Mead and Salton Sea_____________.______----- 172

7. Average yearly water-surface temperature and air temperature (8-meter level) for Lake Mead and Salton Sea_-_- 172

8. Average yearly values of parameters used in mass-transfer equation, for Lake Mead (Boulder Basin) and Salton

Sea.. _.__.__-_.--___,____._.-_____-__.._____________-___-____._.__--__-_--_----------------- 172

9. Mass-transfer coefficient, N, corresponding to the vapor pressure of air at different locations, for Eoulder Basin

and Salton Sea.-_.....-.___._____._._____._.___._.______._-.__.___.--_-__-__--_-_---------------- 175
STUDIES OF EVAPORATION

ANALYSIS OF TECHNIQUES USED TO MEASURE EVAPORATION FROM SALTON

SEA, CALIFORNIA

By G. H. HUGHES

ABSTRACT

During 1961-62 the evaporation from Salton Sea, Calif., was 

determined by three different methods. Determinations for 

1- and 2-year periods by the practically independent watered energy-budget methods differ by less than 5 percent. The

•>verage evaporation determined by these two methods es- 

"ablishes an empirical coefficient for the simplified mass-' 

transfer equation, which is a basis for a third independent 

determination of the distribution of the yearly evaporation

•>mong the months or shorter periods. Comparison of the three 

ieterminations for periods of 10-29 days indicates a marked

•<easonal bias in the energy-budget evaporation, computed values

• eing as much as 60 percent lower than water-budget evaporation 

luring the winter and as much as 25 percent higher during the 

^ummer. Determinations by the water-budget and mass-trans- 

"•3- methods differ by smaller amounts that vary in a nearly raniom, rather than seasonal, pattern.

The principal cause of the seasonal bias in evaporation determined by the energy-budget method apparently is inadequate 

Tieasurement of the total incoming radiation by the flat-plate

•adiometer. The seasonal interchange of heat between water 

and the underlying sediments, which has been disregarded in 

^his and most previous applications of the energy-budget method, 

^ a less important but significant factor in shallow-water bodies 

"uch as Salton Sea.

INTRODUCTION

Investigation of the hydrologic regimen of the Salton 

3ea by the U.S. Geological Survey in 1961-62 (Hely 

and others, 1966) included the determination of evaporation by the energy-budget, water-budget, and masstransfer methods. The energy-budget and the waterbudget methods provide basically independent measurements of evaporation. Because conditions at Salton 

Sea were in many ways favorable for application of 

both these methods, it was expected that results of the 

two would agree generally within 10 percent. Yearly 

evaporation rates by the two methods did agree 

exceptionally well, but rates for periods of 10-29 days 

commonly differed by much more than 10 percent. 

Furthermore, these differences tended to vary seasonally. Application of the mass-transfer method 

indicated that the seasonal distribution of yearly

evaporation shown by the water-budget method was 

more nearly correct than that shown by the energybudget method.

Prior to the studies at Salton Sea, the application 

of energy-budget and mass-transfer theory to the field 

measurement of evaporation had been investigated 

by the Geological Survey (1954) and other Federal 

agencies at Lake Hefner, Okla., and at Lake Mead, 

Ariz.-Nev. (Harbeck and others, 1958). From the 

study at Lake Hefner, Anderson (1954, p. 117) concluded that for periods greater than 7 days accuracy 

approaching 5 percent was attainable by use of the 

energy-budget method, provided that all terms of the 

budget were carefully evaluated. This suggested 

accuracy applies to evaporation rates corresponfling 

to the warmer rather than the cooler months of the 

year. It may be presumed, further, that for a determination of such accuracy, overall conditions should be 

reasonably favorable.

The instruments used at Salton Sea were equivalent 

to those used at Lake Hefner and at Lake Mead. 

Procedures perfected during those studies were closely 

followed. The yield of usable data by the instruments 

was at least as good for Salton Sea as for either o* the 

other two studies; consequently, the appearance of 

seasonal bias in the energy-budget results for Salton 

Sea caused considerable concern.

This report reviews the fundamental equations used 

in each of the three methods of determining evaporation from Salton Sea. Data for Salton Sea and 

nearby places are examined to determine the cau^e of 

the seasonal bias in the energy-budget results. The 

adequacy of the data for each method is considered 

with regard to the relative importance of indivMual 

terms in which particular data were used. Much of 

the discussion centers around the energy-budget 

method because the error resulting from the use of this 

method is the chief concern of the report.

151
152 STUDIES OF EVAPORATION

The investigations covered by this report were under 

the general supervision of C. C. McDonald, project 

hydrologist, and the water-budget study was conducted 

by Alien G. Hely. Basic data required for the waterbudget study were obtained under the direction of 

Walter Hofmann, district engineer, Menlo Park, Calif., 

or were furnished by the Imperial Irrigation District, 

(R. F. Carter, general manager) and Coachella Valley 

County Water District (Lowell Weeks, general manager). Other records, materials, and assistance were 

supplied by the Imperial Irrigation District.

Water-level recorders at Imperial Salt Farm and 

Desert Beach (North Shore Yacht Club) were installed 

by Coachella Valley County Water District. The 

North Shore Yacht Club granted permission to use 

its marina for a recording gage site.

The Sandia Corporation of Albuquerque, N. Mex., 

granted the use of its facilities at Salton Sea Base 

(Sandy Beach) and provided additional services, including the installation of two buoys in the sea. Personnel 

of the U.S. Navy stationed at Salton Sea Base participated by removing the buoys at the end of the study.

ENERGY-BUDGET METHOD

The energy-budget method of determining evaporation from a water body has been described elsewhere 

(Anderson, 1954), and only a review of the fundamental 

relations is given here. The method is based on the 

principle of conservation of energy. As applied to a 

water body, this principle requires that the net influx 

of energy be balanced by an increase of energy stored 

in the water. The energy budget for a water body may 

be expressed as follows:

Qs- Qr+ Qa~

in which,

= Q*, (1)

Q,= solar radiation incident to the water surface,

Qr= reflected solar radiation,

Qa= incoming long-wave radiation from the atmosphere,

Qar= reflected long-wave radiation, 

Q6,= long-wave radiation emitted by the body of

water, 

Q0=net energy advected into the body of water

other than that contained in evaporated

water,

Qe= energy used by evaporation, 

Qw= energy advected by the evaporated water, 

Qft= energy conducted from the body of water to

the air as sensible heat, and 

Q*= increase in energy stored in the body of water.

Terms representing amounts of energy derived from 

or used by chemical and biological processes, transformation of kinetic energy to heat, or conduction of 

heat through the bed of the water body are not included 

in equation 1. These terms generally have been considered negligible. For shallow-water bodies, however, heat conduction through the be<? may be significant at certain times of the year. Ir a later section 

of the report the effect of such a possibility is considered 

for Salton Sea.

Energy used in the evaporation process and the 

sensible-heat exchange between air and a water surface 

are difficult to measure directly but tHir sum may be 

determined by the energy-budget equation as follows:

.- Qr+ Qa- Qar- ,~ &= Q.+ Qn+ Q«, (2)

The terms on the left side of eqration 2 can be 

measured or can be computed by known theoretical and 

empirical relations. The net energy represented by 

these terms can be distributed among the terms on the 

right according to the following relations:

Qe=PEL, Qh=RQe, and Q.=PcE(2V-2Il), 

where

p= density of evaporated water, 

E= volume of evaporated water, 

L=latent heat of vaporization, 

JB=the Bowen ratio,

c= specific heat of water, 

Te=temperature at which evaporation takes place,

and 

Tb= arbitrary base temperature.

If these relations are substituted in equation 2 and 

Eis isolated, the following equation results:

.- Qr+ Qq~ Qar- - Q

P(L(l+R)+c(Te -T»)] (3)

Equation 3 is applicable to any period for which all 

terms are evaluated. If quantities are expressed in 

terms of unit area and unit time, Eis equivalent to the 

depth (volume per unit area) of water evaporated per 

unit time.

The water-surface temperature generally is used for 

Te. The base temperature, Tb) may be selected arbitrarily provided the same value is used to evaluate Q, 

and Q*. Generally 0°C is used for convenience. The 

methods of determining other terms o* equation 3 are 

described in sections that follow. Table 1 lists average 

values for each term of the energy-budget for Salton 

Sea (eq. 1).
TECHNIQUES USED TO MEASURE EVAPORATION, SALTON SEA, CALIFORNIA

TABLE 1.—Average values, by periods, of terms of the energy-budget equation for Salton Sea 

[Values in calories per square centimeter per day except as Indicated]

153

Period

1961-62 

,1'an. 9 to 23 __ .._._ — __ _ _____ __ __

,"in. 24 to Feb. 6.. _ .. __ .__ _ . __ . ....

:^eb. 6 to 21 ______ - ___ -. _ .--- ___ .

"eb. 21 to Mar. 8 ___ . __ . ________ ...

: tar. 8 to 20., ______ . ____ ... _ ..._.

"tar. 20 to Apr. 4 _ _.__. ______ ..........

Apr. 4 to 17— _-_-__--_---_----___---_____

Apr. 17 to May !_-._ ————— _--_ — __ _____

'lay 1 to 15 __ -. ———— ._...___.--.. _ ...

" Tay 15 to June 12____ — __ ——— ——— __ ...

~une 12 to 26 ____ — _ .._..__. _.._._._.

'une 26 to July 10.___ __ _. _____ .... __

'uly 10 to 24 __ ... _____ ....._.__.___ ...

July 24 to Aug. 8. _____________ . __

*ug. 8 to 21 _ ___- ---. .._ _. --_.

\ug. 21 to Sept. 11..- ______________ .

"'ept. 11 to 22.. ___ _--_-_. ____ -_-.._-_.

"'ept. 22 to Oct. 2 __ --...-..---_.-.---__...

Oct. 2 to 31_. ____ . ____ --- — -.--_.._-.

Oct. 31 to Nov. 14 ____ ._.-. _ _______ _ .

"Tov. 14 to 28----------_-------_.---. ......

xTov. 28 to Dec. ll_.__-_--------_-----_.__._

Oec. 11 to Jan. 2. __________________________

Total __ _ _

Average. -___----_____________-______

1968-68 

Tan. 2 to 15. ___ -... ___ ..._ _ ..._ __ _

Tan. 15 to 29. _ _______ __ -_-__. ______

Tan. 29 to Feb. 12.... _____________ .

"eb. 12 to Mar. 2 _____ . ___________

Mar. 2 to 19.. __________ .. ________

Mar. 19 to Apr. 2 ___ _ _____________________

Apr. 2 to 16_._ ._._..._ _____ ___ ______

Apr. 16 to 30 _______________ . _._._.__

Apr. 30 to May 17 _ ... ___ . __ . _ ....._

May 17 to June 4 ____ ____ __ ..-._____.__

Tune 4 to 18 __ ______________________ _.__

-Tune 18 to July 2_ ___ . _ ________________

July 2 to 16 _______ . _ ...... _ . _ ...

July 16 to 30 _____ _ _ ...---... _ . _ ...

July 30 to Aug. 13.. __________ . ________

Aug. 13 to 27-__. _____ _ _ . ____ _ __

Aug. 27 to Sept. 10... _ .... __ . _ .......

Sept. 10 to 24. _____________ . _ .

Sept. 24 to Oct. 7 _ ________________ _ . __

Oct. 7 to 22..-. _ . ____ ... __ . ___ ...

Oct. 22 to Nov. 5 __ _ ___ ........... ...

Nov. 5 to 20.. . _____ ____ __._.

Nov. 20 to Dec. 3 __ ... ...

Dec. 3 to 17 ___ . ____ .... ___ . _

Dec. 17 to Jan. 8-____-__ ._ _

Total Jan. 2, 1962, to Jan. 8, 1963___.__

Total Jan. 9, 1961, to Jan. 8, 1963. ___.

Average Jan. 2, 1962, to Jan. 8, 1963.. __

Average Jan. 9, 1961, to Jan. 8, 1963__._

Number 

of days

14

13.5

151 *»

19

15

13

14

14

28

14

14

14

15

13

21

11

10

29

14

14

13

22

357.5

13

14

14

18

17

14

14

14

17

18

14

14

14

14

14

14

14

14

13

15

14

15

13

14

22

371

728.5

0.

Onn

Q1 O

403

AM

AQK

KOQ

R<)A

664 fi^fi

fiQ4

673

665

607

610

540

573

528

505

403

341

289

267

242

495

294

275

312

389

456

514

571

583

624

657

674

665

659 KQ-I

612

538

536

483

442

400

340

303

271

257

222

464

479

Or

Ofl

on

35

on

DO

4fl

AK

46

41

44

42

43

38

40

37

41

38

38

33

32

29

28

25

37

31

27

29

33

35

38

°.Q

40

41

42

42

42

42

38

41

37

38

35

33

32

30

30

28

28

24

35

36

0.

enc

fil t

621

603

fi91

678

7flK

673

686

770

925

898

0^4

970

952

853

839

764

705

641

611

595

585

731

563

591

640

598

617

667

772

758

739

764

807

875

904

953

904

939

867

895

794

731

711

648

633

599

580

736

734

Qor

18

10

1Q

18

10

9n

91

Ofl

21

23

28

27

9Q

29

29

26

25

23

21

19

18

18

18

22

17

18

19

18

18

20

23

23

22

23

24

26

27

29

27

28

26

27

24

22

21

19

19

18

17

22

22

Qt,

769

778

7QQ

7Qt\

817

822

844

852

860

883

964

965

990

987

982

963

938

923

884

822

795

780

765

868

767

754

776

777

777

804

853

869

877

864

893

941

946

970

967

982

972

959

946

902

889

869

823

814

791

868

868

0.

6

6

7

8

10

11

12

12

12

12

16

15

15

16

16

18

15

17

11

8

6

6

4

11

3

6

6

6

7

10

15

13

13

12

13

16

15

17

17

18

17

20

19

13

11

9

7

7

6

12

11

0.

45

72

1AR

180

167

269

337

404

421

450

379

509

444

518

450

540

483

272

328

252

131

112

51

308

104

72

36

177

185

201

256

431

471

419

497

383

529

428

510

403

465

364

419

289

133

223

75

37

59

283

295

0*

-6

-5

-10

-9

-8

-27

-28

-16

-26

-28

-39

-31

-12

-20

-21

-14

5

2

-4

10 -1

8

-12

-1

1

_ 7

11

_ i

-19

-38

-29

-15

-25

-34

-43

-43

-29

-38

-29

-12

-18

22

14 -3

20

10

3

8

-11

-12

0.

1

2

4

5

5

8

12

15

16

18

20

27

25

29

25

28

24

13

13

8

4

3

1

13

3

2

1

4

5

6

9

17

19

16

21

19

27

23

27

22

25

19

21

13

6

9

2

1

2

12

13

Q*

43

3940

45

88

86

110

28

21

86

220

38

62

13

6

-140

-131

22 -162

-139

-81

-72

-37

1

-61

-2

104 -27

61

141

216

3

-39

94

51

188

50

102 -1

52 -94

12 -210

-128

-14

-210

-46

-38

-93

3

2
164 STUDIES OF EVAPORATION

INCOMING RADIATION (QB +Qa)

The total incoming radiation—solar radiation (Qs) plus 

long-wave atmospheric radiation (Qa)—supplies nearly 

all of the energy involved in the energy-budget equation; hence, accurate determination of incoming radiation is critical. Solar and atmospheric radiation 

generally are derived as individual components so that 

reflected solar radiation (QT) and reflected atmospheric 

radiation (Qa) may be computed rather than actually 

measured over the water surface.

Radiation was measured at Sandy Beach on the 

shore of the Salton Sea (fig. 48). Total incoming

\Coachella

115°30'

101234 MILES

FIGURE 48.—Map of Salton Sea area, showing principal tributaries and sites where 

data were collected.

radiation was measured by a flat-plate radiometer; 

solar radiation, by an Eppley pyrheliometer. The 

output of each instrument was recorded alternately, 

in sequence at 3-minute intervals, by a MinneapolisHoney well recording potentiometer. Hourly values 

of total incoming radiation and of solar radiation were 

determined from the recorded data. Atmospheric

radiation was computed as the dif erence between 

these measured values.

The assumptions that incoming radiation at Sandy 

Beach equalled the average rate for Salton Sea and 

that intermittently recorded intensities were representative of those during the intervening periods 

should be valid for periods lasting several days.

The recording instrument performed satisfactorily 

except during one period of about a month when the 

chart-drive mechanism failed intermittently. Periods 

of no record due to power failures, cimmonly during 

thunderstorms, seldom involved more than a few hours. 

Records of radiation were complete for 96 percent of 

the total study period.

For the short periods of no record, both solar radiation and atmospheric radiation were estimated from 

trends for the preceding and following periods. For 

the longer periods of no record, solar radiation was 

estimated from measurements by the U.S. Army 

Meteorological Team at Yuma Proving, Ground (formerly Yuma Test Station), near Yvma Ariz. Also, 

for the longer periods of no record, atmospheric radiation was estimated from an empirical relationship 

formulated by Koberg (1964) involving solar radiation, 

air temperature, and the vapor pressure of air. Atmospheric radiation could have been estimated from 

measurements of total incoming radiation at Yuma 

Proving Ground made by the U.S. Army Meteorological Team using a flat-plate radiometer identical 

with that used at Sandy Beach; however, the correlation of radiation data for the two stations was not as 

consistent for total incoming radiation as it was for 

solar radiation. As the temperature and vapor 

pressure of air at Sandy Beach often were recorded 

during periods when radiation data were lacking, use 

of Koberg's method probably provided the most 

reliable estimates of atmospheric rriiation.

Measurements of total incoming radiation at Sandy 

Beach and at Yuma Proving Ground should be equally 

reliable as identical instruments were used. Comparison of measurements for the two stations may 

suggest the probable reliability of surt.h measurements 

in general. The two stations are about 100 miles 

apart, but similarly exposed and thry are commonly 

affected by the same air-mass systems. Some differences in solar radiaton might occur because of the 

local variation of absorption properties of the lower 

atmosphere. It was expected, however, that total 

incoming radiation would be about the same at each 

location.

Measured total incoming radiation was greater at 

Sandy Beach than at Yuma Proving Ground during 

most of 1961, but the two were about equal during most 

of 1962. Throughout both years, however, solar
TECHNIQUES USED TO MEASURE EVAPOEATION, SAI/TON SEA, CALIFORNIA 155

radiation at Sandy Beach was substantially less than 

that at Yuma Proving Ground (see fig. 49). At 

Sandy Beach total incoming radiation was neither 

significantly greater nor significantly less in 1961 

than in 1962, but solar radiation was generally less in 

1962. In contrast, at Yuma Proving Ground total 

incoming radiation was consistently less in 1961 than 

in 1962, whereas solar radiation was about the same in 

both years. The monthly average temperature and 

vapor pressure at the two places suggests that total 

incoming radiation should be about the same (fig. 50). 

Also, solar radiation at each of two U.S. Weather 

Bureau stations—Las Vegas, Nev., and Phoenix, 

Ariz.—was about the same for both years.

As measured in 1961-62, monthly total incoming 

radiation at Sandy Beach and at Yuma Proving Ground 

differed by as much as 12 percent and, in 12 of the 24 

months, differed by as much as 3 percent or more. 

If such differences indicate errors in measurement, they

are large enough to affect seriously the accuracy of 

evaporation computed by the energy-budget method. 

Specifically, an error of only 1 percent in the measurement of total incoming radiation would result in an 

error of about 4-10 percent in computed evapc ration, 

depending on the season considered.

REFLECTED RADIATION (Qr+Qar)

Incident radiation is reflected by a water surface 

according to the angle of incidence and the reflective 

properties of the water. Short-wave radiation from 

the sun that reaches the earth's surface is partly diffuse 

but largely directional. Long-wave radiation from the 

atmosphere, on the other hand, is entirely diffuse. 

Consequently, the proportion of long-wave atmospheric radiation that is reflected by the water surface is 

constant, but the proportion of solar radiation that is 

reflected varies according to the hour of the day and 

the season of the year.

2000

EXPLANATION

Sandy Beach (Lat 33° 121) 

Yuma Proving Ground (Lat 32°50')

FIGUHE 49.—Monthly radiation at Sandy Beach, Calif., and at Yuma Proving Ground, Arlz., 1961-62.
156 STUDIES OF EVAPORATION

FIGURE 50.—Monthly temperature and vapor pressure of air at Sandy Beach, Oalif., and at Yuma, Arlz. (U.S. Weather Bureau station, about 18 miles

southwest of Yuma Proving Oround), 1961-62.

Reflected solar radiation was computed by applying 

hourly reflectivity coefficients to corresponding values 

of incident solar radiation. Coefficients were derived 

from an empirical relation between reflectivity and the 

sun's altitude (Anderson, 1954). As clear-sky conditions were predominant, especially during periods of 

highest evaporation, clear-sky reflectivities were applied 

in all computations. Any error in reflected solar 

radiation caused by disregarding cloud cover would be 

small (Koberg, 1964, fig. 36), probably less than 5 

percent for any budget period. Reflected solar radiation was equal to about 6 percent of the incident solar 

radiation during the summer and about 10 percent 

during the winter.

Reflected long-wave atmospheric radiation was computed as the product of values of incoming atmospheric 

radiation and a reflectivity coefficient of 0.030. This 

coefficient was shown by J. T. Gier and R. V. Dunkle 

(in U.S. Geological Survey, 1954, p. 96-98) to be

applicable to ocean water (and, consequently, to the 

Salton Sea) as well as to fresh water.

RADIATION EMITTED (Qb8) BY F ALTON SEA

Long-wave radiation emitted by Salton Sea depends 

on the temperature and emissivity of the water at the 

surface and was computed in accordance with the 

Stefan-Boltzman law using an emissivity of 0.970 as 

determined by J. T. Gier and R. V. Dunkle (in U.S. 

Geological Survey, 1954, p. 96-98).

Temperature of the water surface was recorded continuously at two buoys anchored at the positions shown 

in fig. 48. The recorded temperature? were verified by 

readings of a mercury thermometer when the recorder 

charts were changed. These readings generally agreed 

within 0.5°C. The recorder was adjusted when the 

discrepancy exceeded this value. Instrument failure at 

the north buoy, resulted in loss of record for one period 

of about a month. Losses of record f~om other causes
TECHNIQUES USED TO MEASURE EVAPORATION, SALTON SEA, CALIFORNIA 157

were infrequent and usually were for periods of only a 

few days. The record of water-surface temperature for 

the entire study was 91 percent complete for the north 

buoy and 97 percent complete for the south buoy.

The average of the water-surface temperatures at the 

two buoys was assumed to represent the entire water 

surface. The record for one buoy was used for both 

when data for the other buoy were missing. W hen data 

for both buoys were missing, the water-surface temperature was estimated from trends of the preceding and 

following periods.

The term <2&« w&s the largest single term of the 

energy-budget equation; among the several budget 

periods it was from 2- to 20-fold greater than the energy 

used for evaporation (see table 1). Consequently, a 

relatively small error in the term Qbs has an appreciable 

affect on the accuracy of the computed evaporation. 

For example, the deviation in long-wave radiation from 

the Salton Sea corresponding to a 1°C change in average 

yearly water-surface temperature is equivalent to about 

4 percent of the energy used for evaporation. Thus, 

the extent to which the average of water-surface 

temperatures at the two buoys represented the mean 

temperature for the entire surface of the Salton Sea is 

critical.

The daily water-surface temperatures at the two buoys 

commonly differed but seldom by more than 1° C; 

the temperature differences tended to balance over a 

period of several days. The diurnal variation of the 

water-surface temperature usually was greater at the 

south buoy but seldom exceeded 5° C at either buoy. 

The range of water-surface temperatures observed 

during individual thermal surveys (described in the 

following section) was about the same as the daily 

range recorded at the buoys. The average range for 

all surveys was 3.3° C; the maximum range was 5.8° C.

Figure 51 shows that for corresponding periods the 

difference between water-surface temperatures recorded 

at the two buoys and those observed during thermal 

surveys seldom exceeded 1° C and never exceeded 2° C. 

The data indicate that during periods of relative cahn, 

when thermal surveys could be made, the water-surface 

temperatures recorded at the two buoys represented 

the mean temperature of the entire surface of Salton 

Sea within 1° or 2° C. Representation probably was 

as good or better at other times because the water 

frequently was well mixed by high winds. Accordingly, it is presumed that error in the emitted longwave radiation, Qbs, generally does not exceed 2 percent.

CHANGE IN ENERGY STORAGE (Q#)

The thermal energy content of Salton Sea was based 

mainly on the temperature readings made during 

thermal surveys at intervals of 10-29 days. These

20 30 

TEMPERATURE RECORDED AT TWO BUOYS, IN °C

40

FIGURE 51.—Relation between water-surface temperatures of Salton Sea &•* recorded 

at two buoys and as measured during thermal surveys.

readings were taken at specific depths at 35 stations 

that were spaced to provide representative sampling.

The temperature readings were obtained by a Whitney underwater thermometer having a small thermistor 

for a sensing element. Accuracy was verified at the 

end of the study period by means of simultaneous 

temperature readings obtained in a common medium 

by both the Whitney thermometer and a precisiongrade mercury thermometer. Differences between 

readings averaged 0.2° C and ranged from 0° to 0.3° C 

over the operating temperature range of 11-37° C. 

Similar, but less comprehensive, temperature checks 

made in the field during the study period provided 

assurance that the calibration of the Whitney thermometer did not change. This consistency war more 

important than the absolute accuracy of the calibration because the change in energy storage 

rather than the total storage was required.

Energy storage was computed for successive 2-footthick layers of water from the surface to a denth of 

10 feet and for successive 4-foot-thick layers below 

that depth. Temperatures observed at midlaye^ were 

averaged to obtain a mean temperature of water 

in each layer, except for the top layer in which temperatures observed at the surface and at 1- and 2-foot 

depths were averaged. The energy content of the 

layer, relative to a base temperature of 0° C, was the 

product of the volume of water and its mear temperature, density, and specific heat. The difference 

between successive determinations of energy content
158 STUDIES OF EVAPORATION

was divided by the product of the average surface 

area of the Salton Sea for the period and the number 

of days in the period to obtain the change in energy 

storage (Q#) in the units used for the energy-budget 

computations.

The time required to make the thermal surveys 

varied with the condition of the power boat and the 

roughness of the water surface but averaged about 8 

hours per survey. All except the first two of the 49 

thermal surveys made during the study period were 

completed in one day, and all were begun between 

9 and 11 a.m.

The water temperature varied considerably more 

with depth than with area during any individual 

thermal survey. The average variation with depth 

for all surveys was 6.0° C; the maximum variation 

was 12.8° C.

Figure 52 shows typical variations of temperature 

with depth. In all but a few of the several thermal 

surveys made, most of the temperature variation 

occurred in the uppermost 10 feet of water. If the 

trend of the water temperature below a depth of 10 

feet is projected upward, the surface temperature so 

indicated ordinarily is a close approximation of the 

predawn water-surface temperature at the two buoys 

on the day of the thermal survey. This observation 

suggests that most of the thermal stratification that 

might have existed the preceding day was dispersed 

during the night and that much of the observed stratification was created after sunrise on the day of the 

thermal survey. During sustained periods of calm, 

however, stratification extended to greater depths and 

undoubtedly persisted through the night.

Changes in volume of Salton Sea during periods 

between thermal surveys were small relative to the

12 14 16 18 20 22 24 26 | 28 30 32 34 

TEMPERATURE, IN ° C \

FIGURE 52.—Selected temperature profiles of Salton Sea illustrating seasonal 

changes of water temperature, 1961.

total volume; therefore, the energy content of the sea 

varied mainly with the temperature of the water. 

As there are no pronounced irregularities in the configuration of the sea to retard mixing by wind- or 

thermal-induced currents, temperature readings taken 

at each sampling station should represent a relatively 

large part, of the sea. Consequently, the changes in 

energy storage that are dependent on the definition of 

the thermal structure of the sea are believed to be 

accurately determined. Changes in energy storage 

were small relative to the energy used by evaporation 

except during a few periods hi the sprng and autumn 

when the temperature was changing rapidly and in 

the winter when evaporation rates wer?, low.

NET ENERGY ADVECTED INTO SALTON SEA

As there was neither surface-water nor ground-water 

outflow from Salton Sea, the advected energy term, 

Qv, consisted only of heat added by inflowing water. 

Inflow to the sea consisted of drainage from irrigated 

lands, runoff from nonirrigated lands, rainfall on the 

water surface, and ground-water seepage. Methods 

of measuring or estimating each of these inflow components are described in the section on water budget. 

Although the volume of inflow was substantial, the 

advected energy per unit area was relatively small 

because the surface area was large.

In principle, the temperature as well as the volume 

of each inflow component is needed to determine the 

advected-energy term. Actually, however, a mean 

temperature representing inflow from o^ly the principal 

sources was used for the total inflow, even though the 

temperature of inflow from other sources may have 

differed by several degrees. The mean temperature 

selected was that of the New and Alamo Kivers, which 

together contributed more than 80 penent of the total 

inflow. The resulting error in computed evaporation 

is negligible because the advected-energy term is 

relatively insignificant in the overall energy budget for 

the sea.

Temperature of the water in each river was measured 

once weekly during the first 8 months of the study and 

twice weekly thereafter, generally during daylight 

hours. For a complete year, the average of all these 

temperature measurements probably would be close to 

the average for all inflow because seasonal temperature 

fluctuations were adequately sampled. However, the 

average temperature for the relative!^ short energybudget periods could not be reliably determined with 

only one or two measurements a vr^ek because of 

diurnal and other short-term temperature fluctuations. 

Consequently, a parameter that was measured continuously and that correlated well with the water
TECHNIQUES USED TO MEASURE EVAPORATION, SALTON SEA, CALIFORNIA 159

temperatures was sought as the basis of more reliable 

temperatures for the budget periods.

The average of water temperatures obtained periodically during energy-budget periods were found to 

correlate reasonably well with the average air temperature recorded at Sandy Beach during the same periods 

(fig. 53). The apparent linear relation between the 

two temperatures is approximated by the equation:

r.=1.5+0.832fB, (4)

where Tw and Ta are the temperatures of water and air, 

respectively, in degrees centigrade.

Hence, the temperatures applied to the total volume 

of inflow to compute advected energy were estimated 

from the air temperatures at Sandy Beach according 

to equation 4. The specific heat and density values 

for pure water were applied in these computations, and 

they were considered to be constant.

20 30 

WATER TEMPERATURE, IN ° C

40

FIGUEE 53.—Relation between the average of water temperatures measured periodically at New and Alamo Rivers and the average air temperature recorded continuously at Sandy Beach, for energy-budget periods.

SENSIBLE-HEAT TRANSFER BETWEEN AIR AND 

WATER (Qj)

The solution of the energy-budget equation depends 

on a determination of the ratio of the sensible-heat exchange between air and water to the energy used by 

evaporation from the water surface. Bowen's (1926) 

expression of this ratio, shown by the Lake Hefner 

studies to be satisfactory for use in evaporation computations, is as follows:

/T_T\ T>

(5)

in which

TO=temperature of the water surface, in der*rees

centigrade,

Ta=temperature of the air, in degrees centigrade, 

P=atmospheric pressure, in millibars, 

e0=vapor pressure of saturated air at the temperature

of the water surface, in millibars, and 

ea=vapor pressure of the air, in millibars.

Values of e0 for Salton Sea were obtained from standard vapor pressure tables for a sodium chloride solution 

approximately equal in concentration to the water of 

Salton Sea (Harbeck, 1955). The values of T0 were 

the same as those used to compute long-wave radiation 

emitted by the water surface (p. 156). Daily values of 

Ta and ea were determined for air at Sandy Beach from 

dry- and wet-bulb temperatures measurecj. about 6 

meters above land surface (about 8 m above the surface of the Salton Sea). The Bowen ratio was computed for each energy-budget period by using average 

values of temperature and vapor pressure and the 

standard atmospheric pressure corresponding tc the 

altitude of the Salton Sea.

Dry- and wet-bulb temperatures were obtained by 

means of thermocouple psychrometers similar to those 

used at Lake Mead and Lake Hefner, except that small 

suction fans were added to assure sufficient air movement past the wick-covered wet-bulb thermocouple 

during calm periods. Amplified thermocouple outputs 

were recorded by a recording milliammeter. An ice 

bath, replenished twice weekly, provided a constant 

reference temperature of 0° C for the thermocouple 

outputs. Twice-weekly servicing also maintained sufficient distilled water in the wet-bulb reservoirs and 

kept the wet-bulb wicks free of dust.

Comparison of recorded air temperatures with readings by a conventional mercury thermometer revealed 

that the values indicated by the recording milliammeter were substantially in error—the error increasing 

nonlinearly with temperature. The temperature-error 

relation was reasonably consistent, however, and satisfactory corrections based on this relation were made 

until April 18, 1961, when the recording of dry- and 

wet-bulb temperatures was switched to the Honeywell 

recorder to eliminate the need for such correctionr.

The recorded dry- and wet-bulb temperatures were 

verified twice weekly by means of a small portable 

psychrometer aspirated by an electrically powered 

suction fan. These verification readings comironly 

agreed with corresponding values from the Honeywell 

recorder within 0.5°C. The records of dry- and wetbulb temperatures were complete for 96 percent o* the 

total study period.
160 STUDIES OF EVAPORATION

The precision required in determining the ratio of 

sensible-heat transfer to the energy used by the evaporation depends to a large extent on the magnitude of 

the ratio. When the ratio is small relative to unity, 

an error in its determination results in a much smaller 

error (percentagewise) in the computed evaporation, 

as noted by Anderson (1954, p. 106). Hence, whether 

or not all of the assumptions underlying Bowen's 

expression for this ratio are entirely correct matters 

little so long as the ratio remains small.

Because the temperature of the Salton Sea responded 

rather quickly to seasonal changes in air temperature, 

the temperature difference between the air and the 

water surface ordinarily was small, commonly less than 

2°C (fig. 54). Because of the warm climate, the vapor 

pressure of saturated air at the temperature of the 

water surface was large in relation to the vapor pressure 

of the ambient air during the entire year (fig. 55). As 

a consequence of these two relationships, the Bowen 

ratio tended to be small throughout the study period. 

Mean values ranged from —0.10 to+0.10 for 80 percent 

of the energy-budget periods; the extremes among all 

periods were —0.15 and +0.20. Daily values were 

larger, as would be expected, but ordinarily they were 

between —0.3 and +0.3; most of the exceptions 

occurred during the winter. If the measured parameters used to derive these values tr^ly represented 

conditions at Salton Sea, any error in the computed 

evaporation that might be attributed to the use of 

Bowen's ratio presumably would not be appreciable.

In the preceding discussion of long-wave radiation 

emitted by Salton Sea, it has been inferred that the 

water-surface temperatures at the two buoys adequately 

represented the temperature of the total water surface, 

T0 ; hence, values of e0 also may be assumed to be 

representative. However, before the sr.me assumption 

may be made regarding Ta and ea, the temperature and 

humidity of air at Sandy Beach must be considered. 

Koberg (1958) showed that the energy budget for Lake 

Mead was little affected when values representing the 

temperature and humidity of air at different places were 

used in the Bowen ratio. Data appliec1 were those for 

the barge anchored near the center of Boulder Basin 

(2- and 8-meter levels) and for the Las Vegas Airport. 

Temperature and humidity at Las Vegr»s Airport were 

considered to represent unmodified* air in the vicinity 

of Lake Mead, after appropriate adjustment was made 

for difference in altitude. Air at the bar^e was modified 

to a different degree at each level, but its representativeness did not vary with wind direction.

At Sandy Beach, however, air may or may not be 

modified by the Salton Sea, depending on the directio n

Air 

Water surface

JFMAMJJASONDJFMAMJ JASOND

FIGURE 54.—Monthly mean air temperature at Sandy Beach, monthly mean water-surface temperature of Salton Sea, and mean temperatrre of water at

the bottom of the sea during thermal surveys.
TECHNIQUES USED TO MEASURE EVAPORATION, SALTON SEA, CALIFORNIA 161

FIGURE 55.—Monthly average vapor pressures of air at Sandy Beach («„) 

and of saturated air at the temperature of the surface of Salton Sea (eo),

of the wind. Although wind direction and velocity 

varied appreciably during periods lasting several days, 

the pattern of such variations differed seasonally. 

Hence, energy-budget evaporation rates based on 

measurements of the air at Sandy Beach might be 

expected to be biased seasonally.

Because the environments are similar and the two 

places are relatively close to each other, the temperature 

and humidity of air at Yuma, Ariz., may be assumed to 

represent unmodified air at Salton Sea. Thus, the 

degree of possible bias due to using data for Sandy 

Beach in energy-budget computations for the sea can 

be evaluated by substituting, in equation 5, values of 

Ta and ea derived from data published by the U.S. 

Weather Bureau for Yuma. With Bowen ratios so 

revised, the evaporation rates computed for the 48 

energy-budget periods differed from those in table 1 by 

an average of only 2 percent. The difference was 

greater than 2 percent in 11 of the periods, but it did

not exceed 6 percent in any period. Seasonal bias of 

the differences was not evident. Thus, for periods 

lasting several days, the seasonal variation in the 

influence of the sea on the average temperature and 

humidity of air at Sandy Beach presumably wae not 

great enough to be reflected as seasonal bias ir the 

energy-budget evaporation rates.

TRANSFER OF HEAT THROUGH THE BOTTOM OF 

SALTON SEA

The transfer of heat through the bottom of the 

water body has been considered to be negligee in 

other studies of evaporation and was not included in 

computations of evaporation from Salton Sea. However, comparisons of evaporation from the sea computed 

by different methods suggest a seasonal bias in some 

of the data. As heat transfer through the bed could 

contribute to such bias, the probable rates of heat 

transfer (heat flux) were investigated.

The amount of energy conducted through the bed 

owing to the ordinary geothennal gradient of the 

earth's crust would be negligibly small in energybudget determinations of evaporation. On the other 

hand, for periods lasting several days, heat flux through 

the bed due to the seasonal variation in water temperature may be significant in the energy budget of a water 

body, even though net flux for a year is negligit^e.

Heat flux through the bed may be assumed to vary 

with the deviation of the bottom water temper Hure 

from its mean value and with the thermal conductivity 

and heat-storage capacity of the bed materials in vhich 

changes of heat storage take place. Fluctuations of 

bottom water temperature would tend to dirrinish 

with increasing depth of the water body; ordinarily, 

the fluctuation is small for water bodies 100 tV.t or 

more deep. Shallow water bodies, however, msy be 

mixed almost completely by wind- or thermal-induced 

currents and, as a result, the range of temperature 

variation at the bottom may approach that of the 

monthly mean air temperature at the surface.

The seasonal variation of water temperature at the 

bottom of Salton Sea is shown in figure 54. As the 

graph of bottom water temperature is approximated 

by a sine curve having an amplitude of about 8° C 

and a period of one year, simple heat-flow theory as 

described by Pearce and Gold (1959), may be applied 

to estimate the heat flux through the bed of the sea.

Where periodic heating at the surface of a semiinfinite homogeneous medium is sinusoidal, the heatflux distribution is defined by the following equation:

sn (6)
162 STUDIES OF EVAPORATION

in which

2=heat flux at distance x at time t, in cal cm"2 

sec"1 , 

fcG, a=^Pk'

Ce=volumetric heat capacity, in cal cm"3 °C~1 , 

k=thermal conductivity, in cal cm"1 sec"1 °C~1 , 

P=period of the temperature variation, in seconds,

w=-p-> in radians sec"1,

Ts=amplitude of the temperature variation at the

surface, in degrees centigrade, and 

<£=phase angle of the temperature variation at 

the surface, depending on choice of zero 

time, in radians.

For the condition of maximum heat flux at the surface 

(«=0), equation 6 simplifies to

(7)

As deduced from heat-flow theory and the known 

fluctuation of the bottom temperature of Salton Sea 

(fig. 54), maximum heat flux from the water into the 

bed of the sea occurred about the first of July and the 

maximum flux from the bed into the water occurred 

about mid-December. Each date is about 45 days 

before the bottom water of the sea reached its maximum 

or minimum temperature, respectively. Similarly, 

there was no heat flux at the bed near mid-April and 

mid-September.

Values of k and (70 for the bottom material of Salton 

Sea are not available from direct measurements; 

however, values for ocean floor sediments and sandysilt or clay soil having a high water content should 

be applicable. Pearce and Gold (1959, p. 1296) computed values of 0.00235 cal cm"1 sec"1 °C"1 and 0.77 

cal cm~3 °C~X for k and (70, respectively, from measurement of temperature and heat flux in a "Leda Clay" 

soil of relatively high water content. These values 

agree closely "with corresponding values for "wet 

marshy soil" by Geiger (1959, p. 28) and values of 

k alone given for ocean floor sediments by several 

investigators (Gerard and others, 1962, p. 785-802; 

Von Herzen and Uyeda, 1963, p. 4226; Uyeda and 

others, 1962, p. 1186). A maximum of 13 cal cm"2 

day"1 was computed for heat flux at the bottom of 

Salton Sea by substituting, in equation 7, values given 

by Pearce and Gold for k and Cv and a value of 8° C 

for T..

Including a heat-flux term having such a maximum 

value in the energy budget of Salton Sea would have 

decreased computed evaporation (table 1) for the

period mid-June to mid-July by an average of almost 

3 percent and would have increased that for December 

by almost 20 percent. Accordingly, the precision of 

energy-budget evaporation rates for shallow water 

bodies can be improved for weekly or rronthly periods 

by including a term for heat flux at the bed.

MASS-TRANSFER METHOD

Evaporation from a water surface can be treated as 

the turbulent transport of water vapor in the overlying 

boundary layer in accordance with mass-transfer theory. 

A simplified empirical equation that retains the fundamental principles of this concept was formulated by 

Marciano and Harbeck (1954) in the Lake Hefner 

studies. An equation of the same type was used in the 

Salton Sea study, as follows:

where

E=Nu(e0 -ea), (8)

E=T&te of evaporation, in inches p^r day,

N=&n empirical coefficient,

u=average wind speed, in miles per hour,

e0=average vapor pressure of saturated air at the 

temperature of the water surface, in millibars, and

ea=average vapor pressure of the sir, in millibars.

Equation 8 relates evaporation to measured parameters that reflect the movement of air over a water 

surface and the capacity of the air to te.ke up moisture 

from the water surface. The coefficient, N, represents 

the combined effect of all other factors that may influence evaporation. At present, an accurate determination of N for a specific water .body depends on independent measurement of the evaporation. However, 

experience suggests that future studies employing 

standardized measuring techniques mf.y lead to empirical relations from which an approximate coefficient 

can be determined without resort to other measurements of evaporation.

The coefficient, N, for Salton Sea was determined to 

be 0.00156 from the average results of the energy- and 

water-budget determinations for the 2-year study 

divided by the average value of the product, u(e0—ea), 

for the same period. The coefficient thus derived 

applies with certainty only to Salton Sef, and only when 

base data are obtained at points essentially the same 

as those used during the study.

The wind speed used in equation 8 ^vas measured 2 

meters above the water surface by anemometers mounted 

on the two buoys located as shown in figure 48. The 

anemometer bearings were cleaned and oiled biweekly 

and apparently remained in good condition. The 

mechanical counter of the anemometf at the south
TECHNIQUES USED TO MEASURE EVAPORATION, SALTON SEA, CALIFORNIA 163

buoy jammed twice, resulting in loss of record for two 

periods of about 1 month each. There was no loss of 

record at the north buoy. Estimates of wind speed at 

the south buoy for periods of no record were based on 

the wind speed data for Sandy Beach.

Anemometer counters usually were read only on days 

when thermal surveys were made; therefore, the average 

wind speed at the buoys could be determined precisely 

only for the energy-budget periods previously described. 

Average values of e0 and ea , from which the vaporpressure difference was computed, also were determined 

for energy-budget periods as described in the section on 

the sensible-heat transfer (p. 159). Consequently, it 

was most convenient, as well as desirable, to compute 

evaporation by equation 8 for the same periods so 

that results for the two methods would be directly 

comparable.

APPLICATION TO PERIODS OTHER THAN THE 

CALIBRATION PERIOD

As the mean mass-transfer coefficient, N, was determined from data for the 2-year period, it should apply to 

any year-long period. For periods shorter than a year, 

however, its use would produce consistent results only 

if the parameters, as measured, represented conditions 

for Salton Sea with equal faithfulness during all periods. 

This restrictive requirement might not have been

satisfied by data for periods lasting only a few days, 

because of inadequate sampling of variable meteorologic conditions provided by the relatively small 

number of instruments used; however it may have been 

satisfied by data for periods as long as those used for 

the evaporation computations.

The average wind speed at each of the two buoys 

undoubtedly represented wind movement over a large 

part of Salton Sea. Consequently, the mean wind 

speed for the two buoys probably always represented 

the entire Salton Sea even though speeds at tbs two 

buoys at times differed appreciably (fig. 56). Similarly, the temperature measurements at the two buoys, 

from which values of e0 were derived, probably were 

representative (p. 157). The same is not necessarily 

true of values for ea, however, because the influence of 

the Salton Sea on the temperature and humidity of 

air at Sandy Beach varied with wind direction, which 

tends to vary with the season.

The discussion of the energy-budget method r.rrived 

at the conclusion that the representativeness of the 

vapor-pressure difference (eQ —ea) was about the same 

during most energy-budget periods. However, in the 

energy-budget method the vapor-pressure difference 

appeared only in the Bowen ratio, which functioned 

as a small corrective term. In the mass-transfer 

method, to the contrary, evaporation is directly proJFMAMJJASONDJ FMAMJ JASOND

FIGUEK 56.—Average wind speeds for energy-budget periods as measured at two buoys in Salton Sea, 1961-62.

231-822 O—67———2
164 STUDIES OF EVAPORATION

portional to vapor-pressure difference (eq 8). Accordingly, pronounced seasonal bias might be introduced 

through the ea term.

As a means of appraising how large such seasonal 

bias might be, values of ea for Yuma, Ariz. (fig. 50), 

were substituted in equation 8 for those observed at 

Sandy Beach. Leaving u and e0 unchanged, a new 

coefficient (A/) was computed, and the evaporation 

for energy-budget periods was redetermined accordingly. Figure 57 compares these results with those

0.4

0.3

I O

— m

•z. > - o

i\

0.2

0.1

/^Equal-value line

Dashed lines represent 

deviation of 10 percent from equal-value 

line

0.1 0.2 0.3

EVAPORATION, IN INCHES PER DAY 

(ea AT YUMA, ARIZ.)

FIGURE 57.—Relation between evaporation from Salton Sea by the mass-transfer 

method based on the vapor pressure of air at Sandy Beach and that based on the 

vapor pressure of air at Yuma, for energy-budget periods.

derived from values of ea at Sandy Beach. Slight 

seasonal bias is apparent. However, the difference 

for individual budget periods averaged less than 6 

percent and exceeded 10 percent in only eight periods.

WATER-BUDGET METHOD

As Salton Sea has no outflow except by evaporation, 

the water-budget equation can be written as follows:

where

1=inflow from all sources, 

£=evaporation, and 

A<7= increase in stored water.

(9)

Hence, evaporation can be determined by an evaluation 

of the other two terms. Successful application of this 

method depends on the relative magnitudes of the 

individual terms, as well as on the relative accuracy 

of the measured terms, because the computed evaporation term contains the residual of errors in all other 

terms. Fortunately, several condition?1 at the Salton 

Sea were favorable for a reasonably accurate determination of evaporation by the water-budget method. 

Evaporation was nearly equal to total inflow; the 

principal sources of the inflow were adequately measured; changes in volume, which were relatively small, 

were adequately determined; and rainfall occurred 

infrequently and was of small consequence.

Water enters Salton Sea from three sources: surface 

inflow from irrigation drains and natural streams, subsurface seepage, and precipitation on the water surface.

SURFACE INFLOW

Drainage from irrigated land in Imperial and Coachella Valleys was by far the largest sonrce of inflow. 

Most of the drainage from Imperial Valley entered 

Salton Sea through New and Alamo Fivers (fig. 48) 

but substantial amounts entered the sea directly 

from more than 30 minor channels. Whitewater 

River contributed more than half the surface drainage 

from Coachella Valley, 18 minor channels contributed 

the remainder. San Felipe Creek and Salt Creek, the 

principal tributaries from nonirrigated laud, contributed 

small amounts of surface inflow to Salton Sea.

The instrumentation and procedures used to measure 

or estimate surface-inflow items are described in 

another report (Hely and others, 19°xf>). Amounts 

of surface inflow shown in table 2 were taken from that 

report. Of the total amount shown, 91.5 percent was 

measured at recording gages, 6.5 percent was estimated 

from periodic measurements, and only 2 percent was 

ungaged. Table 3 shows the annual contributions of 

the principal tributaries.

TABLE 2.— Yearly surface inflow to Salton Sea, ir, acre-feet, 1961-62

Contributing area

Other __._._._._,-._.-_-__...___

TotaL-_.__-_ -------------

1961

1, 242, COO

83, £90

10, ?00

1,336,000

1962

1, 280, 000

112,700

9,850

1,403,000

For this report, computations of evaporation by the 

water-budget method are for periods defined by the 

dates of thermal surveys (p. 157), rathc-r than months, 

so that results by all three methods can be compared 

directly. The assumptions required to estimate the
TECHNIQUES USED TO MEASURE EVAPORATION, SALTON SEA, CALIFORNIA 166

TABLE 3. — Yearly surface inflow to Salton Sea from tributary 

streams with continuous streamflow records, in acre-feet, 1961-62

Stream

New River.. ______ ___._____.__.

Salt Creek__-_._.___-_-_____ __

San Felipe Creek ________________

Five minor channels _ _.-__-.____

Total.... --____ ___ ._--__

1961

675, 500 

437, 000 

53, 390 

3,470 

1, 130 

30, 350

1, 201, 000

1962

681, 300 

455, 300 

69, 590 

4,420 

374 

31, 480

1, 242, 000

9.5 percent of the surface inflow that was not continuously recorded probably were about as valid for energybudget periods as for the monthly periods used in 

making the estimates. Consequently, little reliability 

was sacrificed by the choice of periods used for the 

water-budget computations.

SUBSURFACE INFLOW

On the basis of estimates of subsurface inflow from 

Coachella Valley, made by the California Department 

of Water Resources (1964), and of preliminary estimates of subsurface inflow from other contributing 

areas, made by the U.S. Geological Survey, Hely,

Hughes, and Irelan (1966) concluded that the total 

ground-water inflow to Salton Sea was about 50,000 

acre-feet yearly. As this inflow is less than 4 percent 

of the surface inflow, a large percentage error in the 

estimate would have little effect on the computed evaporation. Subsurface inflow was assumed to occur at a 

uniform rate during the year.

RAINFALL ON THE WATER SURFACE

The average rainfall on Salton Sea was assumed to be 

equal to the average rainfall at three recording rain 

gages located on the shore at Sandy Beach, Imperial 

Salt Farm, and Devils Hole. The average of rainfall 

measured at three U.S. Weather Bureau station^ near 

the sea (Niland, Mecca, and Ocotilla Wells) was about 

the same as that of the three stations on the shon.

Table 4 shows that rainfall on the water surface was 

an insignificant item of the water budget for Salton 

Sea, amounting to only 32,700 acre-feet in 1961 and 

23,200 acre-feet in 1962. As the total rainfall for a 

month commonly occurred in a single storm period 

lasting only 1 or 2 days, only a few budget periods were 

affected by rainfall.

TABLE 4.—Recorded monthly rainfall of three gages at Salton Sea, in inches, 1961-62 

[Records furnished by Imperial Irrigation District. No rain recorded In January 1963]

Month

Jan.... _-_-_-_-_.._.-

Feb... ._._--__-.-___.

Mar_ ________________

Apr _ ___._._._._.___

May.. -.-_.__ — — ..

June. _.___-_-_--___._

July..... _._-........

Aug.. ._..-.-.-_-_._.

Sept _ . ____ . .....

Oct _______ . .....

Nov. _____-__.-_____.

Dec.... _ -_-_-_-_.__

Total..........

Sandy 

Beach

0.25

0

04

0

0

0

0

1.75

0

0

0

.65

2.69

1

Devils 

Hole

0.05

0

.06

0

0

0

0

. 15

0

0

.03

.57

.86

961

Salt 

Farm

0.26

0

0

0

0

0

0

cc

.20

0

0

.60

1.71

Average

0. 19

0

03

0

0

0

0

.85

.07

0

.01

.61

1.76

Sandy 

Beach

0.70

. 11

.05

0

0

0

0

0

.20

0

0

.61

1.67

19

Devils 

Hole

0. 05

.10

.05

0

0

0

0

0

0

.15

0

.40

.75

62

Salt Farm

0.74

.07

0

0

0

0

0

0

0

0

0

.48

1.29

Average

0.50

.09

.03

0

0

0

0

0

.07

.05

0

.50

1.24

WATER LEVEL

A record of water level and a relation between water 

level and the volume of Salton Sea were required to 

determine the change in volume during each budget 

period.

Continuous records of water level were obtained at 

three points on Salton Sea—Sandy Beach, Desert Beach, 

and Imperial Salt Farm (fig. 48). The recording gages 

at Desert Beach and Imperial Salt Farm were adjusted 

to the datum of the previously existing gage at Sandy 

Beach by reference to the water level during a period of

sustained calm. After this adjustment, the average 

daily water-level readings at the three gages usually 

were within 0.01 foot of a mean value during per'ods of 

relative calm and within 0.10 foot during windy periods. 

Instantaneous values sometimes differed appreciably, 

however, because wind-induced surface oscillations 

(seiches) were not in phase at the three places. The 

period of the seiches was about 3.2 hours and tH amplitudes commonly were less than 0.05 foot but vrere as 

large as 0.50 foot following high winds. Definition of 

the water level at the beginning and the end of energy-
166 STUDIES OF EVAPORATION

233

z < - U

234

235

JFMAMJJASONDJ FMAMJ JASOND

1961 1962 

FIGUBE 58.—Water level of Salton Sea at midmonth and at end of month, 1981-62.

budget periods was unaffected by inaccuracies due to 

winds because all energy-budget periods necessarily 

began and ended on days of relative calm.

The water level of the sea changed slowly and varied 

within a range of about 1 foot, as indicated in figure 58. 

Daily changes of the average water level usually were 

less than 0.02 foot; thus, for energy-budget periods the 

average water levels for the beginning and ending days 

were considered to be satisfactory for determining 

changes in volume of the sea.

200

AREA, IN THOUSANDS OF ACRES 

100 200 300

< 220

m 240

260

280

5 10 

VOLUME, IN MILLIONS OF ACRE-FEET

15

FIGURE 59.—Relations of area and volume to water level of Salton Sea. (From 

relations dated February 1958 and used prior to 1965.)

CHANGE IN VOLUME

Relations of area and volume to the water level of 

Salton Sea (fig. 59) applied in this report were derived 

trom U.S. Geological Survey photogrammetric maps 

for altitudes above —240 feet. For lower altitudes, 

the relations probably were based on surveys made 

prior to 1905, but the source of the data used could not 

be ascertained. However, the general reliability of the 

relations in this range was confirmed from soundings 

made in 1962 by Shawn Beihler of California Institute 

of Technology (in Hely and others, 1966).

CORRECTION FOR THERMAL EXPANSION

The computed change in volume of the Salton Sea 

was adjusted for effects of thermal expansion of water 

by a method similar to that described in the Lake 

Hefner report (U.S. Geological Survey, 1954, p. 19). 

The average adjustment for all periods was only 4 

percent of the computed evaporation, but adjustments were as large as 13 percent durng the spring 

and autumn when temperature changes were relatively 

large. The net adjustment for a year was negligible.

COMPARISON OF EVAPORATION DETERMINED BY THE 

THREE METHODS

Table 5 gives the evaporation determined for Salton 

Sea by the energy-budget, mass-transfer, and waterbudget methods. The yearly evaporation for the 

study period averaged 72.81 inches computed by the 

energy-budget method and 70.52 inchee by the waterbudget method. The mean evaporation for the total 

study period, as determined by these two methods, 

was used to compute the mass-tranter coefficient, 

AT"; hence, a corresponding figure of mep/n yearly evaporation for the mass-transfer method would not be 

independently determined. Nevertheless, the distribution of the total evaporation among individual periods
TECHNIQUES USED TO MEASURE EVAPORATION, SALTON SEA, CALIFORNIA 167

TABLE 5.—Evaporation from Salton Sea computed by energybudget, water-budget, and mass-transfer methods, and evaporation 

from class A pan at Sandy Beach

Period

1961-6%

Jan. 24 to Feb. 6. __ . ........

Feb. 6 to 21....—— .........

Feb. 21 to Mar. 8...— .... ... . Mar. 8 to 20. _ __ . .......

Apr. 4 to 17... .———__——

May 1 to 15———————

May 15 to June 12... ____ .

June 26 to July 10. _____ ..

Aug. 21 to Sept. 11. ___ ——

Sept. 11 to 22..................

Sept. 22 to Oct. 2...... ........

Oct. 2 to 31———————

Oct. 31 to Nov. 14.—————

Nov. 14 to 28———————

Nov. 28 to Dec. 11— __ . ....

Dec. 11 to Jan. 2.— . ..........

Total————————

1962-63

Feb. 12 to Mar. 2..............

Apr. 30 to May 17 .............

July 2 to 16— ————————

July 16 to 30—————————

Aug. 13 to 27-.——————

Sept. 10 to 24.————————

Sept. 24 to Oct. 7... __ ------

Oct. 7 to 22—————————

Oct. 22 to Nov. 5—— ... - —

Nov. 20 to Dec. 3.. ----------

Dec. 3 to 17-. — — ------

Total-..-. — ------

Number 

of days 

in period

14 

13.5 

15 

15 

12 

15 

13 

14 

14 

28 

14 

14 

14 

15 

13 

21 

11 

10 

29 

14 

14 

13 

22

357.5

13 

14 

14 

18 

17 

14 

14 

14 

17 

18 

14 

14 

14 

14 

14 

14 

14 

14 

13 

15 

14 

15 

13 

14 

22

372

Evaporation (inches)

Energy 

budget

0.42 

.65 

1.47 

1.81 

1.35 

2.70 

2.95 

3.82 

3.98 

8.51 

3.60 

4.86 

4.23 

5.28 

3.99 

7.70 

3.61 

1.86 

6.40 

2.37 

1.23 

.97 

.75

74.51

.90 

.67 

.34 

2.13 

2.11 

1.89 

2.42 

4.07 

5.42 

5.09 

4.69 

3.65 

5. 04 

4.06 

4.87 

3.83 

4.43 

3.47 

3.71 

2.94 

1.25 

2.26 

.65 

.35 

.87

71.11

Water 

budget

0.67 

.88 

1.44 

1.84 

1.42 

2.34 

2.30 

3.60 

4.03 

7.20 

3.00 

3.81 

3.67 

4.36 

3.28 

7.71 

3.43 

1.85 

7.10 

3.01 

1.37 

1.36 

1.08

70.75

1.40 

.77 

.57 

2.36 

2.11 

1.50 

1.71 

3.53 

5.07 

4.57 

3.75 

3.08 

4.30 

3.44 

4.38 

3.44 

4.17 

3.26 

4.22 

3.58 

1.47 

3.09 

1.40 

.92 

2.20

70.29

Mass 

transfer

0.78 

.97 

1.62 

2.20 

1.73 

2.62 

2.60 

3.89 

4.28 

7.64 

3.16 

3.89 

3.56 

4.30 

3.33 

6.97 

3.07 

2.07 

6.79 

2.23 

1.53 

1.31 

1.17

71.71

1.22 

1.09 

.66 

2.21 

2.12 

2.03 

2.18 

3.63 

5.10 

4.52 

3.71 

3.39 

3.98 

3.23 

4.63 

3.39 

4.24 

3.44 

4.12 

3.54 

1.83 

3.16 

1.08 

.97 

2.09

71.56

Class A 

pan

4.24 

6.12 

6.04 

7.96 

8.70 

16.16 

7.61 

8.71 

7.21 

8.08 

6.58 

12.12 

4.81 

4.09 

10.44 

3.45 

2.47 

2.39 

1.85

2.05 

2.08 

1.74 

4.59 

4.65 

4.82 

6.26 

7.28 

9.85 

10.42 

8.40 

9.32 

9.56 

7.77 

9.29 

7.97 

7.31 

6.81 

5.29 

4.97 

3.50 

3.73 

1.89 

1.67 

2.59

143.81

within the study period that is provided by the masstransfer method is entirely independent of that for 

the water-budget method and is nearly independent 

of that for the energy-budget method because factors 

common to both the energy-budget and mass-transfer 

equations do not affect the computed evaporation to 

the same degree.

The agreement among evaporation rates determined 

by different methods for periods ranging in length 

from 10 to 29 days is much less satisfactory than the 

agreement among annual rates. Figure 60 indicates 

the seasonal variation in evaporation rates by the 

three methods. Appreciable spread among rates for 

occasional periods might be expected because of random 

errors in the measurements or estimates utilized in 

each method, but some of the discrepancies shown tend 

to follow a seasonal pattern.

Figure 61 shows that energy-budget evaporation 

rates generally were less than water-budget rates during 

periods of low evaporation and greater during periods 

of high evaporation. Figure 62 shows the same relative bias by a comparison of energy-budget evaporation 

rates and corresponding values of the mass-transfer 

product, u(e0—ea) , used in equation 8. In contrast, figure 

63, which plots the same mass-transfer products 

against water-budget rates, does not indicate seasonal 

bias.

As the water-budget and mass-transfer results were 

in satisfactory agreement for at least two-thirds of the 

periods involved, they were averaged to provide r. basis 

for further study of the seasonal bias that seemingly is 

inherent in the energy-budget results.

Figure 64 shows the differences between the energybudget rates and the average of the water-budget and 

mass-transfer rates, expressed as the energy required 

to evaporate an equivalent amount of water and as 

percentages. These differences, because they are so 

large, must be caused chiefly by errors in one or more 

of those energy-budget terms that consistently an relatively large, such as, solar radiation, Qs, atmospheric 

radiation, Qa, and long-wave radiation emitted Vy the 

water, Q6s.

If the differences in figure 64 were to be ascribed 

entirely to the effect of error in the water-surface temperature on the computed long-wave radiation emitted 

by the water (#&«), that error would have to be af great 

as 8°C and, disregarding sign, would have to average 

4°C. The average range of the water-surface temperatures taken during individual thermal surveys was only 

3.3°C, and correlation between these readings and the 

temperatures recorded at the two buoys was reasonably 

close (fig. 51). It is doubtful, therefore, that error in 

the average surface temperature could have exceeded 

1 or 2°C in any period.

J. T. Gier and R. V. Dunkle (in U.S. Geological Survey, 1954, p. 96-98) showed that for a range in temperature that applies to natural water bodies in the 

Southwest, the emissivity of water for long-wave radiation does not vary with temperature of the water. 

They also showed that the emissivity changes when 

the water surface is contaminated by an oil film. At 

Salton Sea, however, no such film was noted on the 

surface, and the surface of the sea did not appear 

abnormal in any way. Consequently, the apparent 

seasonal bias in the evaporation by the energy-Hidget 

method cannot reasonably be attributed to the emitted 

radiation term.

Owing to the manner in which the components of 

incoming radiation, Qa and Q,, were used in the energybudget computations, a relatively large error in measured solar radiation, Qs, has little effect on the accu-
168 STUDIES OF EVAPORATION

0.4 i———i———i———i———i———i———I I I I I

EXPLANATION

Energy-budget method

Mass-transfer method

Water-budget method

J FMAMJ JASONDJ FMAMJ JASOND

FIGURE 60.—Evaporation from Salton Sea by three methods for energy-budget periods.

racy of the computed evaporation. For insertion in 

equation 3, atmospheric radiation, Qa, was computed 

as measured total incoming radiation minus measured 

solar radiation, Qs. However, Qs appears in the same

0.4

0.3

o

h0 Q

s

hffl 0.2

0.1

0.1 0.2 0.3 0.4

ENERGY-BUDGET EVAPORATION, 

IN INCHES PER DAY

FIGURE 61.—Eelation between evaporation (for energy-budget periods) by the 

energy-budget method and evaporation by the water-budget method.

equation as a plus term, and thereby eliminates almost 

all effect of any possible error in Qs. Some slight effect 

remains, however, because any incorrect distribution of 

the total incoming radiation between Qs and Qa causes 

some error in the reflected-radiation terms, Qr and Qar. 

These terms were computed from Qs and Qa , respectively, by means of small but slightly different reflectivity coefficients (p. 156). Error in the computed 

yearly evaporation due to an error of 15 percent in 

measured solar radiation (table 1), for example, would 

amount to only 1 percent. In conclusion, therefore, 

the seasonal bias of the energy-budget results must be 

attributed largely to the measurement of total incoming 

radiation.

In regard to the importance of error in measured 

solar radiation, however, a distinction must be made 

between methods by which atmospheric radiation is 

obtained. If, by any means, atmospheric radiation 

should be determined independently of solar radiation, 

any error in solar radiation would be fully reflected in 

the computed evaporation.

Measurements of total incoming radiation by the 

flat-plate radiometer have not alwayr been reliable. 

Differences have been noted between measurements of 

total incoming radiation at Sandy Beach and at Yuma 

Proving Ground (fig. 49), but apparently these differences were not biased seasonally. Of course,
250

200

150

100

50

TECHNIQUES USED TO MEASURE EVAPORATION, SALTON SEA, CALIFORNIA

250

169

o o

oo

s Evaporation=0.00156 U ( €0 - ea

0.1 0.2 0.3

ENERGY-BUDGET EVAPORATION, 

IN INCHES PER DAY

0.4

FIGURE 62.—Relation between evaporation (for energy-budget periods) by the 

energy-budget method and corresponding values of the mass-transfer product, 

u(eo—€<.).

200

150

100

50

Evaporation =0.00156 U( €0 - e a )

0.1 0.2 0.3

WATER-BUDGET EVAPORATION, 

IN INCHES PER DAY

0.4

FIGURE 63.—Relation between evaporation (for energy-budget periods) by fie waterbudget method and corresponding values of the mass-transfer product, «(*>—««).

JFMAMJJASONDJFMAMJJASOND

FIGURE 64.—Differences between evaporation (for energy-budget periods) by the energy-budget method and the average of evaporation by the mass-transfer and waterbudget methods.

seasonal bias would not be detectable in measurements 

from identical instruments if the cause of bias were 

inherent in those instruments.

In the studies at Lake Hefner and at Lake Mead 

(Anderson, 1954; Koberg, 1958) the determination of 

atmsopheric radiation as the difference between measured total incoming radiation and measured solar 

radiation was concluded to be inaccurate. In those 

studies, therefore, estimates of atmospheric radiation 

based on nighttime measurements by the flat-plate 

radiometer were used instead, seemingly with success. 

In the energy budget for Salton Sea, however, similar
170 STUDIES OF EVAPORATION

use of nighttime measurements by the flat-plate 

radiometer resulted in winter evaporation rates that 

were unreasonably small.

Alternative values of the atmospheric-radiation term, 

Qa, for Salton Sea were computed independently from 

measurements of air temperature, humidity, and solar 

radiation at Sandy Beach, according to the empirical 

method of Koberg (1964). In this method, measured 

solar radiation is used to establish an index of cloud 

cover; the effect of a specific percentage of cloud cover 

diminishes with increasing air temperature. The air 

temperatures at Sandy Beach ranked with the highest 

of those included by Koberg in the formulation of his 

method; hence, the accuracy of the atmospheric radiation so computed for Sandy Beach depends only slightly 

on the accuracy of the measured solar radiation.

Figure 65 shows the relation between measured 

atmospheric radiation (total incoming radiation minus 

solar radiation) and the corresponding computed values; 

the measured atmospheric radiation is greater during 

periods of high radiation and less during periods of low 

radiation. Differences between measured and computed values (fig. 66), expressed in units of energy, 

not only are similar in magnitude to equivalent differences between evaporation rates by the energy-budget 

method and the average of those by the water-budget 

and mass-transfer methods, but they also vary in a 

similar seasonal pattern.

10

°i- 2%

~tx 6

O 

O

5 6 7 8 9 10

MEASURED RADIATION, IN HUNDREDS OF CALORIES 

PER SQUARE CENTIMETER PER DAY

FIGURE 65.—Relation between long-wave atmospheric radiation as measured 

and that computed by Koberg's method.

Evaporation from Salton Sea was redetermined by 

the energy-budget method using the values of Qa computed by the Koberg method. Figure 67 shows these 

redetermined results plotted against the average from

the water-budget and mass-transfer methods and 

suggests only a slight seasonal bias. The redetermined 

yearly evaporation differs by less than half of one 

percent from that shown in table 5.

The better agreement obtained by u?e of the computed values of atmospheric radiation suggests, but does 

not prove, that the measured values are in error. Percentagewise, the differences between measured and 

computed values (fig. 65) were small. The average 

difference for all periods was less than 4 percent; the 

maximum less than 10 percent. These differences are 

no greater than those reported by Kot 0,rg (1964) for 

similar data used in the formulation of his empirical 

method. The only evidence implying greater reliability 

of the computed values for Sandy Beach is the reduction 

of apparent seasonal bias caused by their use. On the 

other hand, the field performance of the flat-plate 

radiometer has not been always satisfactory (Koberg, 

1964, p. 108).

COMPARISON OF EVAPORATION FROM SALTON SEA 

WITH CLASS A PAN EVAPORATION

Evaporation from a U.S. Weather F'lreau class A 

pan was measured at Sandy Beach begirning February 

28, 1961, and pan evaporation for subsequent energybudget periods is included in table 5. Tve annual pan 

coefficient (ratio of evaporation from the Salton Sea 

to pan evaporation) was 0.50, based on energy- and 

water-budget evaporation results for a period of about 

a year. Pan coefficients for energy-budget periods 

varied seasonally, those based on the average of masstransfer and water-budget evaporation ranging from 

0.31 to 0.83. No adjustments were made for heat 

transfer through the sides and bottom cf the pan.

The seasonal variation of a pan coefficient may be 

attributed largely to the temperature la» in the water 

body that results from the difference in heat storage 

capacities of a pan and of a larger body of water 

(Kohler, 1954, p. 148). Hence, the pan coefficients for 

energy-budget periods should correlate v^ell with corresponding changes in energy storage in Salton Sea that 

are due only to natural heating by the snin and atmosphere. These changes are the difference between the 

measured changes in energy storage and the net of 

advected energy, &-(&-&), including that associated with the evaporated water. Similar values for 

the pan might be considered also, but they are extremely 

small in comparison to the energy used for pan evaporation and may be neglected.

A plot of the term Qt-(Q,-QJ versus class A pan 

coefficients (fig. 68) shows fair correlation when coefficients were determined from either water-budget or 

mass-transfer data but little correlation when pan 

coefficients were based on energy-budget data. This
TECHNIQUES USED TO MEASURE EVAPORATION, SALTON SEA, CALIFORNIA 171

J FMAMJJASONDJFMAMJ JASOND

FIGTJKE 66.—Seasonal differences between measured and computed long-wave atmospheric radiation.

0.4

0.3

Q CC 

DU 

CQ Q-

(Z X 

LU O

5?

0.1

0.1 0.2 0.3 0.4

AVERAGE OF WATER-BUDGET AND MASS-TRANSFER 

EVAPORATION, IN INCHES PER DAY

FIGURE 67.—Relation between redetermined energy-budget evaporation and the 

average of water-budget and mass-transfer evaporation. Qa computed by Koberg's 

method was substituted for measured values in this redetermination.

lack of correlation with energy-budget data confirms 

the apparent seasonal bias in the energy-budget results.

COMPARISON OF EVAPORATION DATA FOR SALTON 

SEA AND LAKE MEAD

Lake Mead is about 200 miles north-northeast of 

Salton Sea and about 1,500 feet higher in altitude, but 

similarity of the desert environments of the two water 

bodies suggests that evaporation rates should be similar. 

Therefore, useful information may be obtained by comparing energy-budget and mass-transfer data for Salton 

Sea with corresponding data for Lake Mead (Harbeck 

and others, 1958).

Comparisons of evaporation data for the nonconcurrent studies should be valid for complete yfirs, if 

evaporation during each study period was about average for the respective areas involved. Records of 

evaporation now available for Lake Mead (U.S. Geological Survey annual water-supply papers) irdicate 

that during the 1952-53 study period evaporation from 

Lake Mead was nearly average. Similarly, records of 

pan evaporation measured at Salton Sea during the 

years 1948-62 (Hely and others, 1966) indicate that 

during 1961-62 evaporation from Salton Sea exceeded 

the 1948-62 average by only 3 percent. Hence, 

comparisons of the nonconcurrent data should be 

meaningful.

ENERGY-BUDGET DATA

The approximate yearly evaporation by the energybudget method was 72.8 inches for Salton Sea during 

1961-62 and was 85.0 inches for Lake Mead during 

1952-53. The yearly value for each station represents 

the average for 2 complete years. However, the Lake 

Mead study covered only 18 months, so some of the 

data were used to derive values for both years. Corresponding average values of terms in the energy budget and of associated parameters for each water body 

are shown in tables 6-8; certain terms were combined 

to facilitate later comparisons. These values are 

based on data published in tables or graphs in the 

Lake Mead report. Consideration of these terms, and 

some of the factors that influence their magnitude, may 

help explain why the difference in evaporation was 

larger than expected.

Net incoming radiation from the sun and atmosphere, 

Qs— Qr+Qa— Qar, was nearly the same at the two locations. This factor suggests that evaporation rates for 

each water body should be about the same; however, 

as Salton Sea is south of Lake Mead by abort 2.5°
172 STUDIES OF EVAPORATION

CALORIES IN,

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Energy budget Water budget Mass transfer

CLASS A PAN COEFFICIENT 

FIQUEE 68.—Correlation between changes in energy storage in Salton Sea and coefficients for a class A pan at .Sandy Beach.

TABLE 6.— Yearly values of terms of the energy-budget equation 

for Lake Mead and Salton Sea

[Values in calories per square centimeter per day except as indicated; values for Lake 

Mead based on data by Harbeck, Kohler, Koberg, and others (1958, p. 28, table 7)]

Water body

Lake Mead. _ _

Difference . .

Q,-Qr+Q,-Q,,

1,150

1,155

5

P*.

846

868

22

P*

-5

-12

7

Qw

13

13

0

Q.-Q*

56

9

47

<?.

352

295

57

Evaporation

(inches)

85.0

72.8

12.2

TABLE 7.—Average yearly water-surface temperature, T0 and air 

temperature (8-meter level), T8, for Lake Mead and Salton Sea, 

in degrees centigrade

[Values for Lake Mead based on data by Harbeck, Kohler, Koberg, and others (1958): 

To derived from data for Qi,, given in table, T» from graph in fig. 4]

Water body

Salton Sea____- __

To

20.6

22. 4

T8

20.9 (Boulder Basin) _ _

23.2 (Sandy Beach) ___. -

To-Ts

-0.3

-0.8

TABLE 8.—Average yearly values of parameters used in masstransfer equation, for Lake Mead (Boulder Basin) and Salton 

Sea

[Values for Lake Mead based on data by Harbeck, Kohler, Koberg, and others (1958)' 

e« derived from temperature data for Boulder Basin barge in table 18; e a from graph 

for Las Vegas Airport in fig. 6; us from data for Boulder Basin in table 16]

Water body

Boulder Basin __

Vapor pressure, (millibars)

ea

24.8

38.3

e a

6.0 (Las Vegas).....

9.5 (Yuma) .........

ea— e a

18.8

18.8

Wind speed, 

wj, (mph)

7.5

7.6

Product,

«2(eo— e B)

137

145

latitude, slightly greater net incoming radiation might 

be expected at Salton Sea.

The long-wave radiation emitted by the water body 

Qbs, was substantially greater for Salton Sea than for 

Lake Mead. As might be expected, the difference corresponded almost exactly with the difference in watersurface temperatures for the two water b odies (table 7). 

The higher water-surface temperature for Salton Sea 

appears reasonable in view of the fact that the air 

temperatures were higher at Salton Ser, than at Lake 

Mead (table 7).

Owing to the effect of salinity on evaporation, the 

water-surface temperature of Salton Sea was 0.1°-0.2° 

C higher than, it would have been for a comparable 

fresh-water body (Harbeck, 1955). As a result of 

reservoir operation, on the other hand, the watersurface temperature of Lake Mead may have been as 

much as 0.7° C higher than it would have been for a 

comparable water body from which only the uppermost 

water was released (Harbeck and others, 1958). The 

relatively smaller temperature difference between air 

and the water surface at Lake Mead is consistent with 

these facts.

Although the yearly evaporation rate was greater 

for Lake Mead than for Salton Sea, the temperature 

at which evaporation took place was less. Consequently, the energy per unit area that was advected 

by the evaporated water, Qw, \vas the same for each 

water body.

The energy conducted from the ws.ter as sensible 

heat, Qft, varies with the temperature gradient of the 

air above the water surface and the eddy diffusivity 

of the air for heat. As the diffusivity factors for Lake 

Mead and Salton Sea probably are the same, the Qh 

terms (table 6) should be proportional to the corre-
TECHNIQUES USED TO MEASURE EVAPORATION, SALTON SEA, CALIFORNIA 173

spending differences between air and water-surface 

temperatures (table 7). The rough proportionality 

between Qh terms and the temperature differences, 

however, is partly coincidental. Air temperatures 

used in the energy-budget computations for Lake Mead 

were those for the 2-meter level at Boulder Basin barge 

rather than those for the 8-meter level; temperatures 

at the 2-meter level averaged about 0.3° C lower than 

those at the 8-meter level. There is little doubt, 

however, that the sensible-heat exchange between the 

ah* and the water was a small item in the energybudget of each water body. Net transfer of sensible 

heat was from the air to the water in each case, as 

indicated by the negative sign shown with values of 

Qn in table 6.

If, during any period, the net energy advected into a 

water body, Qv, is balanced by a change in energy 

storage, Q#, evaporation during the period is not 

affected. Therefore, comparisons involving Qv and Q# 

are most effective when the difference, Qv—Q&, is used 

rather than the separate terms.

The large value of the Qv— Q# term for Lake Mead 

(table 6) resulted chiefly from the large volume of 

water that moved through the lake each year and the 

fact that the average temperature of the outflowing 

water was less than the temperature of the inflowing 

water (Koberg, 1958). Boih inflow and outflow of 

Lake Mead averaged about 14 million acre-feet per 

year during the study period, and the weighted-average 

temperature of the inflow exceeded that of the outflow 

by about 5° C. (Koberg, 1958, figs. 3 and 16). In 

contrast, during the study period, inflow to Salton Sea 

averaged about 1.4 million acre-feet per year, with 110 

surface outflow, and the average temperature of the 

inflow was about 21° C. From these values the total 

energy advected by flowing water was 2.4 times greater 

for Lake Mead than for Salton Sea. Moreover, the 

average surface area of Salton Sea was about 1.8 times 

that of Lake Mead during the respective study periods. 

Hence, on a unit-area basis, the Qv term for Lake Mead 

was more than 4 times that for the Salton Sea.

The advected energy might have been stored temporarily but eventually had to be dissipated by conductive, radiative, or evaporative processes—just as 

energy from all other sources was dissipated.

The foregoing comparisons indicate that the difference in the yearly evaporation rates that were 

determined for Lake Mead and Salton Sea by the 

energy-budget method may be attributed chiefly to 

two factors: (1) The energy emitted by long-wave 

radiation from Salton Sea was substantially greater 

than that for Lake Mead, and (2) the net energy advected by inflowing and outflowing water was much 

greater for Lake Mead than for Salton Sea. Minor

differences in other energy-budget terms influenced 

the difference in computed evaporation; the effect of 

these differences alone, however, was not significant.

MASS-TRANSFER DATA

The parameters of the empirical mass-transfer 

equation are comparable for different water bodies 

only when measured in the same way. According 

to Harbeck (1962), comparison should be valid if both 

the wind speed at a low altitude above the water surface 

and the water surface temperature are measured near 

the center of the water surface area and if the vapor 

pressure of air is the same as that of the approaching 

(unmodified) air.

The water-surface temperatures and the 2-meter 

level-wind speeds used in the studies at Lake Mead 

and at Salton Sea fulfill the requirements for reliable 

comparison. However, in each case the vapor pressure 

determined was that of air partly modified by passage 

over parts of the two water bodies. As the deg-ee of 

modification varied with wind direction at Salton Sea 

(Sandy Beach) but was independent of wind direction 

at Lake Mead (Boulder Basin barge), a meaningful 

comparison would not result from use of these modified 

vapor-pressures values. Consequently, vapor pressures 

corresponding to air at Las Vegas, Nev., and Yuma, 

Ariz., which may be considered about equally representative of unmodified air at Lake Mead and at 

Salton Sea, respectively, were used in this comparison. 

The product, u2 (e0—ea) given in table 8 was computed 

as the average product of monthly values of u2 and of 

(e0—ea) rather than as the product of the average 

yearly values. Effects of the seasonal variation of 

both the wind-speed and the vapor-pressure difference 

are more accurately accounted for by this method.

In the mass-transfer studies at Lake Mead (Harbeck 

and others, 1958, p. 34, 35), because alternatives were 

lacking, the wind speed for Boulder Basin was considered to represent all basins of Lake Mead. On 

the other hand, the data showed that the vapor-pressure 

difference for Boulder Basin generally was slightly 

less than for other parts of the lake, chiefly because 

the water-surface temperature usually was slightly 

less in Boulder Basin. Allowance was made for these 

differences in the Lake Mead study.

Data for Boulder Basin were used for the comparison 

in table 8 because values for all parameters could be 

conveniently obtained from the Lake Mead report only 

for that location. Hence, the product, u2 (eQ — ea) that 

applies to the entire lake would exceed by a slight 

amount the product shown in table 8 for Bculder 

Basin. Fortunately, this difference can be approximated from data that are available. The average value 

of e0 for Lake Mead exceeded the corresponding value
174 STUDIES OF EVAPORATION

for Boulder Basin by 0.8 millibars. As the humidity 

in the various basins was not appreciably different, 

the vapor-pressure difference averaged about 19.6 millibars for the entire lake compared to 18.8 millibars for 

Boulder Basin alone. As the same wind speed must 

be used in either case, the mass-transfer product for 

Lake Mead should be larger than that for Boulder 

Basin by the ratio of 19.6 to 18.8. On this basis, the 

mass-transfer product for Lake Mead was roughly equal 

to the corresponding product for Salton Sea, a fact 

which indicates that evaporation from Lake Mead and 

Salton Sea would be about the same if the same masstransfer coefficient is applicable to each body.

If the mass-transfer parameters are measured as 

described, however, the mass-transfer coefficient apparently decreases with increasing surface area (Harbeck, 1962, fig. 31). Figure 69 shows the relation 

between the coefficient and surface area, as presented 

by Harbeck, but modified to accommodate data for 

Salton Sea. Accordingly, if the mass-transfer products 

were the same, evaporation from Lake Mead would 

exceed that from Salton Sea, but not by the amount 

indicated by the energy-budget results of the respective 

studies.

The relation in figure 69 was intended to apply only 

when the vapor pressure of unmodified air was used in 

determining the mass-transfer coefficient; the coefficients shown for most lakes are based on unmodified 

air measured some distance from the respective lakes. 

In contrast, however, the vapor pressure of air used in 

determining the indicated coefficients for Boulder Basin 

and Salton Sea was for partly modified air at the 

8-meter level measured near the center of Boulder Basin 

and at Sandy Beach, respectively.

Coefficients for Boulder Basin and Salton Sea (table 

9), based on vapor pressure of unmodified air at Las 

Vegas and Yuma, respectively, are plotted as crosses 

in figure 69. A relation line drawn near these points 

would be in reasonable agreement with data for all 

water bodies except those having surface areas of only 

1 acre. Some such shift is warranted, at least in the 

upper part of the relation line, because the vapor 

pressure of air at Las Vegas and Yuma probably more 

nearly represents that of unmodified air at Boulder 

Basin and Salton Sea, respectively, than the vapor 

pressure of air as measured at the 8-meter level in 

either study.

Harbeck (1962, p. 105) concluded that the apparent 

relation between the mass-transfer coefficient and the

FIGURE 69.—Relation between mass-transfer coefficient, N, and surface area of water 

body. Values indicated for Boulder Basin and Salton Sea by circles are based on 

vapor pressures of air measured locally at the respective water bodies; values indicated by crosses for the same water bodies are based on vapor pressures of air at 

Las Vegas, Nev., and Yuma, Ariz., respectively. (Adapted from Harbeck, 1962 

fig. 31.)

1,000,000

100,000

10,000

1000

100

0.001 0.002 0.005

MASS-TRANSFER COEFFICIENT (N)

0.01
TECHNIQUES USED TO MEASURE EVAPORATION, SALTON SEA, CALIFORNIA 175

TABLE 9. — Mass-transfer coefficient, N, corresponding to the 

vapor pressure of air at different locations, for Boulder Basin 

and Salton Sea

Water body Location of instruments

Boulder Basin barge, 8-meter 

level.

Yuma, Ariz _____ _ ___ __ _ _

N

0. 00208 

. 00167

. 00156 

. 00136

water-surface area was due in part to the effect of 

surface roughness on the slope of the wind profile 

near the surface and in part to the tendency for evaporation to decrease downwind. If this relation is valid, 

the total surface area of the water body is not an 

adequate index of either of these effects unless the 

water bodies are compact and of similar shape. Thus, 

the configuration of the water bodies may account for 

much of the scatter of the data plotted in figure 69. 

Scatter may also result from errors in the basic determinations of evaporation from which the coefficients 

for the respective water bodies were derived or from 

nonhomogeneity of the meteorological data. Because of the complexity of the many variables involved, 

such a relation may never be satisfactorily defined.

This analysis of mass-transfer data for the two 

studies confirms that average evaporation from Salton 

Sea is less than that from Lake Mead. However, 

the analysis does not conclusively establish that the 

difference was a great as indicated by the energybudget data for the two studies.

CONCLUSIONS

The application of each of the methods used to 

evaluate evaporation from Salton Sea is subject to 

practical limitations. Both the energy-budget and 

water-budget methods determine evaporation as a 

residual of several measured terms. Evaporation so 

determined contains the residual of measurement errors 

in all other terms. Application of the water-budget 

method is limited to water bodies where inflow and outflow can be measured with adequate precision—the 

required degree of precision depending generally on the 

magnitude of inflow and outflow in relation to that of 

the evaporated water.

The energy-budget method can be used for water 

bodies where inflow and outflow cannot be measured 

with sufficient precision for a water-budget determination if the thermal energy content of the inflow and 

outflow is small in relation to the energy used for 

evaporation. For successful application of this method, 

however, all other important terms of the energybudget equation must be precisely evaluated.

The mass-transfer method conveniently provides the 

relative seasonal distribution of evaporation from a 

water body, but the determination of absolute amounts 

by this method requires use of the mass-transfor coefficient, which first must be defined by some independent measurement of evaporation.

Conditions at Salton Sea were relatively favorable 

for application of both the energy- and water-budget 

methods, but, for periods lasting 10-29 days, evaporation results by these two methods tended to differ 

seasonally by substantial amounts. The seasonal distribution of yearly evaporation given by the masstransfer method generally agreed better with that by 

the water-budget method; hence, it was concluded that 

the energy-budget evaporation was seasonally b; ased.

Examination of energy-budget and other data for 

Salton Sea indicated that the techniques used provided 

satisfactory measures of all terms of the energy-budget 

equation except the total incoming radiation. The 

seasonal bias of the energy-budget evaporation was 

attributed chiefly to inadequacies of the flat-plate 

radiometer which was used to measure total incoming 

radiation. Neglect of the seasonal interchange of heat 

by conduction at the bed of the sea contributed to 

the bias.

Experiences at Salton Sea, Lake Hefner, and Lake 

Mead all indicate that total incoming radiation as 

measured by the flat-plate radiometer may be appreciably in error. Research leading to increased accuracy 

in the determination of this important paramete~ will 

be required to develop the potential usefulness c* the 

energy-budget method.

REFERENCES

Anderson, E. R., 1954, Energy-budget studies, in Water-loss

investigations—Lake Hefner studies, Technical report: U.S.

Geol. Survey Prof. Paper 269, p. 71-119. 

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

by evaporation from any water surface: Phys. Rev., v. 27,

p. 779-787. 

California Department of Water Resources, 1964, Coachella

Valley investigations: Sacramento, California Dept. Water

Resources Bull. 108, 145 p. 13 pis. 

Geiger, Rudolf, 1959, The climate near the ground: Cambridge,

Mass., Harvard Univ. Press, 494 p. 

Gerard, Robert, Langseth, M. G., Jr., and Ewing, Maurice,

1962, Thermal gradient measurements in the water and

bottom sediment of the western Atlantic: Jour. Geophys.

Research, v. 67, no. 2, p. 785-803. 

Harbeck, G. E., Jr., 1955, The effect of salinity on evaporation:

U.S. Geol. Survey Prof. Paper 272-A, p. 1-6. 

———— 1962, A practical field technique for measuring reservoir

evaporation utilizing mass-transfer theory: U.S. Geol.

Survey Prof. Paper 272-E, p. 101-105. 

Harbeck, G. E., Jr., Kohler, M. A., Koberg, G. E., and others,

1958, Water-loss investigations—Lake Mead studies: U.S.

Geol. Survey Prof. Paper 298, 100 p.
176 STUDIES OF EVAPORATION

Hely, A. G., Hughes, G. H., and Irelan, Burdge, 1966, Hydrologic regimen of Salton Sea, California: U.S. Geol. Survey 

Prof. Paper 486-C.

Koberg, G. E., 1958, Energy-budget studies, in Harbeck and 

others: U.S. Geol. Survey Prof. Paper 298, p. 20-29.

———— 1964, Methods to compute long-wave radiation from the 

atmosphere and reflected solar radiation from a water surface: U.S. Geol. Survey Prof. Paper 272-F, p. 107-136.

Kohler, M. A., 1954, Lake and pan evaporation, in Water-loss 

investigations—Lake Hefner studies, technical report: U.S. 

Geol. Survey Prof. Paper 269, p. 127-148.

Marciano, J. J., and Harbeck, G. E., Jr., 1954, Mass-transfer 

studies, in Water-loss investigations—Lake Hefner studies, 

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

p. 46-70.

Pearce, D. C., and Gold, L. W., 1959, Observations of ground 

temperature and heat flow at Ottawa, Canada: Jour. 

Geophys. Research, v. 64, no. 9, p. 1293-1298.

U.S. Geological Survey, 1954, Water-loss investigations—Lake 

Hefner studies, technical report: U.S. Geol. Survey Prof. 

Paper 269, 158 p. [previously pub. as U.S. Geol. Survey 

Circ. 229 (1952) and as U.S. Navy Electronics Lab. Rept. 

327].

Uyeda, S., Horai, K., Yasui, M., and Akamats^, H., 1962, Heatflow measurements over the Japan trench: Jour. Geophys. 

Research, v. 67, no. 3, p. 1186-1188.

Von Herzen, R. P., and Uyeda, S., 1963, Heat flow through the 

eastern Pacific Ocean floor: Jour. Geophys. Research, v. 68, 

no. 14, p. 4219-4250.