A Comparison of Methc ds 

of Estimating Potential 

Evapotranspiration Frc m 

Climatological Data in 

Arid and Subhumid 

Environments

By R. W. GRUFF and T. H. THOMPSON

CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED SPATES

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1H9-M

Prepared in cooperation with 

'he California Department 

/ W^ater Resources

NITED 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 15 cents (paper cover)
CONTENTS

Page

Abstract__ _ _____________________________________________________ Ml

Introduction._____________________________________________________ 2

Purpose and scope_-_--_-_--_---__--_--_____-___--_____________ 2

Acknowledgments- -_----_-__-___-__--__-___--__-__-___________ 4

Other investigations-__________________________________________ 4

The study region_________________________________________________ 5

Methods used in this study to estimate potential evapotranspiration_____ 7

Thornthwaite method__________________________________________ 7

Weather Bureau method_______________________________________ 11

Lowry-Johnson method________________________________________ 14

Hamon method.______________________________________________ 14

Blaney-Criddle method_______________________________________ 15

Lane method_______________________________________________ 16

Analysis of estimated potential evapotranspiration_____________________ 18

Adjusted pan evaporation______________________________________ 19

Empirical methods __-_-_-___--___-_-__--_--___-____________-_ 19

Results of the analysis-___--_---__------_--_-____--_--___-_____-___ 22

Summary and conclusions__________________________________________ 26

References cited___________________________________________________ 27

ILLUSTRATIONS

Page 

FIGURE 1. Location of climatological sites used in this study.__________ M3

2. Nomograph for solution of Thornthwaite's general equation,

er=1.6(10T/7)«___ _-___ - _ _-- __ _ _- 8

3. Nomographs for solution of equation 2 for daily lake evaporation______-__--__--_---_--__-_______-_-_-_---___-__-_ 12

4. Graphical solution of equation 3 for consumptive use versus

effective heat_______________________________________ 14

TABLES

Page 

TABLE 1. Climatological data for the test sites_____________________ M6

2. Monthly heat index ____________________________________ 9

3. Mean possible duration of sunlight, in units of 30 days of 12

hours each-__________________________________________ 10

4. Density of saturated water vapor-____--_--.---_---_--__-__ 15

5. Daytime hour percentages for each month of the year for lat

24° to 50° N______________________________________ 17
IV CONTENTS

Page

TABLE 6. Average potential evapotranspiration estimated by pan evaporation and by the six empirical methods, for the entire year_ M20 

7. Average potential evapotranspiration estimated by prn evaporation and by the six empirical methods, for the growing 

season,______________________________________________ 21

8-10. Summary of differences between potential evapotranspiration 

estimated by the six empirical methods and adjusted pan 

evaporation.

8. Arid environment______________________________ 24

9. Modified arid environment______________________ 24

10. Subhumid environment-________________________ 25
CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

A COMPARISON OF METHODS OF ESTIMATING POTENTIAL EVAPOTRANSPIRATION FROM GLIMATOLOGICAL 

DATA IN ARID AND SUBHUMID ENVIRONMENTS

By E. W. CRTJPF and T. H. THOMPSON

ABSTKACT

This study compared potential evapotranspiration, computed from climatological data by each of six empirical methods, with pan evaporation adjusted 

to equivalent lake evaporation by regional coefficients. The six methods tested 

were the Thornthwaite, U.S. Weather Bureau (a modification of the Penman 

method), Lowry-Johnson, Blaney-Criddle, Lane, and Harnon methods.

The test was limited to 25 sites in the arid and subhurnid parts of Arizona, 

California, and Nevada, where pan evaporation and concurrent clirnatological 

data were available. However, some of the sites lacked complete climatological 

data for the application of all six methods. Average values of adjusted pan 

evaporation and computed potential evapotranspiration were compared for two 

periods the calendar year and the 6-month period from May 1 through 

October 31.

The 25 sites sampled a wide range of climatic conditions. Ten sites (group 1) 

were in a highly arid environment and four (group 2) were in an arid environment that was modified by extensive irrigation. The remaining 11 sites (group 

3) were in a subhumid environment.

Only the Weather Bureau method gave estimates of potential evapotransiiration that closely agreed with the adjusted pan evaporation at all sites where 

the method was used. However, lack of climatological data restricted the use 

of the Weather Bureau method to seven sites. Results obtained by use of the 

Thornthwaite, Lowry-Johnson, and Hamon methods were consistently low. 

Results obtained by use of the Lane method agreed with adjusted pan evaporation at the group 1 sites but were consistently high at the group 2 and 3 sites.

During the analysis it became apparent that adjusted pan evaporation in 

an arid environment (group 1 sites) was a spurious standard for evaluating 

the reliability of the methods that were tested. Group 1 data were accordingly 

not considered when making conclusions as to which of the six methods tested 

was best.

The results of this study for group 2 and 3 data indicated that the BlaneyCriddle method, which uses climatological data that can be readily obtained 

or deduced, was the most practical of the six methods for estimating potential 

evapotranspiration. At all 15 sites in the two environments, potential evapoMl
M2 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

transpiration computed by the Blaney-Criddle method checked the adjusted 

pan evaporation within ±22 percent. This percentage range is generally considered to be the range of reliability for estimating lake eviporation from 

evaporation pans.

INTRODUCTION

A study of the hydrologic balance for an area generally includes an 

analysis of the total water loss due to evaporation and transpiration 

from all surfaces of the area. This total of evaporation and transpiration is referred to as evapotranspiration or consumptive use. 

Potential evapotranspiration was defined by Langbein and Iseri (1960, 

p. 15) as the evapotranspiration that will occur if at no time there is 

a deficiency of water in the soil for use of vegetation.

The determination of potential evapotranspiration is of interest to 

agriculturists and hydrologists. A knowledge of the potential evapotranspiration is needed to determine irrigation requirements. In any 

given climatological regime potential evapotranspiration is affected by 

the type of soil and vegetative cover, but there is considerable agreement among hydrologists that lake evaporation may be used as a good 

average estimate of potential evapotranspiration.

The relation of evapotranspiration to climatic factors, geographic 

location, and vegetative cover has been studied by many hydrologists 

and has led to the development of various methods for estimating 

potential evapotranspiration. Most of the methods are based on empirical formulas. These formulas contain one or more climatological 

factors such as temperature, solar radiation, dewpoint, and windspeed, 

and they generally include empirically developed coefficients based on 

comparisons with actual evapotranspiration measured under conditions of ample water supply. The most commonly used methods for 

estimating potential evapotranspiration from climatological data are 

the Thornthwaite, U.S. Weather Bureau (a modification of the Penman method), Lowry-Johnson, Blaney-Criddle, Lane, and Hamon 

methods. These six methods were compared in this study.

PUEPOSE AND SCOPE

The purpose of this study was to compare the potential evapotranspiration computed by each of the six methods with eva Deration from 

a lake surface, as deduced from pan-evaporation data The observed 

pan evaporation was adjusted to equivalent lake evaporation by the use 

of widely accepted regional coefficients. In general, the methods of 

computing potential evapotranspiration had been developed and tested 

in humid regions. Their applicability in arid and subhumid regions 

had not been adequately tested; thus, this study was confined to the 

arid and subhumid parts of Southwestern United States. Twenty-five 

test sites in Arizona, California, and Nevada were used (fig. 1).
EXPLANATION

Climatological si

"HI*" 119*

FIGUBK 1. Location of cliinatological sites used 
M4 CONTRIBUTIONS TO THE HYDROLOGY OF THE U! TITED STATES

The control for this study was the monthly pan-evaporation data collected by the U.S. Weather Bureau and other Federal, State, and local 

agencies. The requirement for inclusion of a site in the study was the 

availability of pan-evaporation data and concurrent climatological 

data at or near the pan site. Generally, the latest 10-year period of 

climatological and pan evaporation data were used at eaclx site. Monthly 

values of adjusted pan evaporation (presumed lake evaporation) and 

potential evapotranspiration computed by each of the six methods were 

obtained for each year. From these monthly figures, average totals 

were computed for the calendar year and for the 6-mcnth period of 

May 1 to October 31. This period is often referred to as the growing 

season in other parts of the United States and will be so designated in 

this report. Most of the annual evapotranspiration occurs during this 

growing season, and in the Southwestern United States this period is 

generally one of acute soil-moisture deficiency. By contrast, precipitation from November through April is sufficient to partly meet the 

demands of evapotranspiration in much of the region. At each site the 

average values of computed potential evapotranspiration for both the 

year and the growing season were compared with the average values 

of adjusted pan evaporation. Estimates of potential evapotranspiration for shorter periods of time would not be reliable.

ACKNOWLEDGMENTS

This study was made under the terms of a cooperative agreement 

between the U.S. Geological Survey and the California Department 

of Water Resources. The report was prepared by the Water Resources 

Division of the Geological Survey under the general supervision of 

Walter Hofmann, district chief for California. Technical supervision 

and guidance was given by S. E. Rantz, research hydrologist, U.S. 

Geological Survey, Menlo Park, Calif., who offered valuable suggestions and criticism throughout the study.

OTHER INVESTIGATIONS

An agriculturist or hydrologist interested in the potential evapotranspiration for an area generally must estimate values from, 

climatological data by an empirically derived method. Many methods 

are available, and the investigator must determine the one most suitable for his area. Thus, investigations have been made in various parts 

of the world comparing some of the available method? of estimating 

potential evapotranspiration.
METHODS OF ESTIMATING POTENTIAL EVAPOTRANSPIRATION M5

Stephens and Stewart (1963), using data for southern Florida, presented a comparison of correlation coefficients for measured pan evaporation versus computed monthly pan evaporation and for evapotranspiration measured by a lysimeter versus computed potential 

evapotranspiration. The methods of estimating potential evapo^ranspiration from climatological data used in their study were the Thornthwaite, Hamon, Blaney-Criddle, Penman, fractional evaporation 

equivalent, and U.S. Weather Bureau. Modifications of the Penman, 

Blaney-Criddle, and fractional evaporation equivalent methods were 

also used in their comparison study that was based on a 6-year period 

of record. Of the methods compared, the Weather Bureau method had 

the highest correlation, and the Thornthwaite method had the lowest. 

Damagnez, Riou, DeVillele, and El Ammami (1963) compared the 

Thornthwaite, Blaney-Criddle, Turc, and Penman methods of estimating potential evapotranspiration from climatological data with 

evapotranspiration measured by nonweighing lysimeters. Their study 

used data from five sites in Tunisia. The climate at the five sites ranged 

from Mediterranean to hot desert, similar to the climate in this study. 

For the Tunisia areas, they found that only the Penman and Turc 

methods gave acceptable estimates of potential evapotranspiration.

Nixon, MacGillivray, and Lawless (1963) presented comparisons 

of the Blaney-Criddle and the Thornthwaite methods of estimating 

evapotranspiration from alfalfa with measured soil-moisture depletion. They used three California sites of differing climate coastal 

f ogbelt, coastal valley, and interior valley locations. All three sites were 

near lat 35° N". to eliminate the effect of latitude on the results. The 

study showed that neither method gave close estimates in these areas, 

but that the Blaney-Criddle method gave slightly closer estimates than 

the Thornthwaite method.

THE STUDY REGION

In this study 25 sites were used in arid and subhumid regions 5 

in Arizona, 17 in California, and 3 in Nevada. The sites are listed in 

table 1, and their locations are shown in figure 1. Of these 25 sites, 23 

were used for an entire year; pan evaporation is not measured at two 

of the sites during the whiter.

Altitudes at the sites range from 200 feet below to 4,400 feet above 

mean sea level. Climatic conditions at the sites range from a desert 

environment with low annual precipitation and high summer tempera -

268-007 67-
M6 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

ture to a Mediterranean environment with moderate yef.r-round temperatures, low summer precipitation, and high winter precipitation. 

Mean air temperatures for the growing season, May through October, 

range from 62° to 92° F. Mean annual precipitation ranges from 2 to 

20 inches, but at all sites the average precipitation for the growing season is 6 inches or less. The climatalogical data for each test site are 

summarized in table 1.

TABLE 1. Climatological data for the test sites

Site

Altitude 

above or 

below ( ) 

mean sea 

level 

(feet)

Mean precipitation 

(inches)

Annual May to 

Oct.

Mean temperature (°F)

May to 

Oct.

Aug.

Mean 

annual 

windspeed 

(miles 

per day)

Group 1. Arid environment

Death Valley, Calif -----

Haiwee, Calif.... ___ . __ ..

Hayfleld, Calif .._. 

Tinemaha, Calif.. -_-_-

2,600 

700 

-200 

3.100 

3,800 

1,400 

300 

2,200 

4,300 

3,900

7 

2 

2 

4 

6 

3 

6 

6 

4 

6

1 

1 

1 

1 

1 

1 

1 

2 

1 

1

75 

86 

92 

71 

72 

82 

77 

81 

74 

70

81 

03 

99

78 

79 

90 

83

87 

80

77

74 

109 

73 

260 

208 

77 

67 

67 

43 

224

Group 2. Modified arid environment

Indio, Calif-...--. __ . __ . 0 

1,100 

2,400 

200

3

7 

10 

3

1 

3 

6 

1

85 

83 

80 

83

PI

88 

83 

92

32 

13 

29 

21

Group 3. Subhumid environment

Stockton, Calif... -----

3,000 

4,400 

0 

700 

4.000 

100 

1,000 

0 

0 

1,500 

0

20 

9 

10 

16 

5 

13 

11 

16 

19 

13 

13

3

4 

1 

2 

2 

1 

1 

2 

2 

2 

1

69 

67 

65 

72 

65 

65 

71 

71 

62 

70 

71

75 

74 

68 

73 

70 

72 

75 

76 

63 

77 

75

26 

82 

83

37 

30 

49 

64 

66 

29 

40

On the basis of climatic characteristics, the test sites have been 

placed in three categories to facilitate later discussion. (See table 1.) 

Group 1 sites are in a highly arid environment of high temperatures, 

low precipitation, high windspeeds, and low humidity. Group 2 sites 

also have high temperatures and low precipitation, but windspeeds are 

low. Most important, however, is that the four test sites in group 2 are 

in an environment whose aridity has been modified locally by extensive irrigation and whose humidity is high relative to that at the sites 

in Group 1.
METHODS OF ESTIMATING POTENTIAL EVAPOTRANSPIRATION M7

Group 3 sites include several whose proximity to the Pacific Ocean 

gives them a Mediterranean climate. All sites in this group have relatively low temperatures, high precipitation, and moderate windsr»eeds 

and humidity.

METHODS USED IN THIS STUDY TO ESTIMATF 

POTENTIAL EVAPOTRANSPIRATION

Six methods Thornthwaite, Weather Bureau, Lowry-Johnson, 

Hamon, Blaney-Criddle, and Lane were used in this study. The data 

required for use of these methods at each site were latitude; type of 

vegetative cover; and the climatological parameters of daily maximum 

temperature, mean monthly temperature, mean monthly solar radiation, mean monthly dewpoint, and mean monthly windspeed.

None of the methods required all the above parameters, but each 

method used one or a different combination of two or more of the parameters. In this section of the report, each of the six methods for estimating potential evapotranspiration from climatological data is briefly 

described.

THOBNTHWAITE METHOD

The method of estimating potential evapotranspiration from climatological data developed by Thornthwaite (1948, p. 89-94) was derived 

from the water budget for natural watersheds and from controlled 

experiments in the humid Northeastern United States. He derived 

the following general equation for estimating potential evapotranspiration :

er=1.6(lor//)° (1) 

where

eT unadjusted potential evapotranspiration, in centimeters, for

a 30-day month ;

r^mean monthly air temperature, in degrees centigrade; 

7=heat index; and 

°=cubic function of /.

To estimate potential evapotranspiration by this method, mean 

monthly temperature at the site and the latitude of the site must be 

known. Three steps are involved in the computation, and they are 

simplified by the use of a nomograph and tables. The first step is to 

compute the heat index, /. Thornthwaite (1948, p. 92) gives a table of 

monthly heat-index values corresponding to monthly mean temperature. Summation of the 12 monthly values gives the heat index, /. (See 

table 2). The next step is to determine the unadjusted monthly values 

of potential evapotranspiration from the nomograph given by Thorn-
MS CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

thwaite (1948, p. 94). This nomograph is a solution of equation 1. (See 

fig. 2.) Finally, these monthly values of unadjusted potential evapotranspiration are adjusted for possible hours of sunligK, in units of 

30 days of 12 hours each. Thornthwaite (1948, p. 93) gires a table for 

possible hours of sunlight corresponding to latitude. (See table 3.)

30

25 

20

15

10

4

3

2

1

|

E

I

-

^

-

\ scale

o 120

o 90

o 80

o 70

o 60

^r

^s

\

X

X

X

1

Poi

^X

ito

x

fee

X

m\

X

er

X

ge

X

n<

'

e.

Temperature ( D 1)

26.5

27.0

27.5

2*0

2*5

23.0

23.5

310

315

31.0

31.5

3?.0

3?.5

33.0

33.5

34.0

34.5

35.0

35.5

36.0

36.5

37.0

37.5

J8.0

Potential

evapotranspi ration

(cm)

13.50

13.95

14.37

14.78

15.17

15.54

15.89

16.21

16.52

16.80

17.07

17.31

17.53

17.72

17.90

18.05

18.18

18.29

18.37

18.43

18.47

18.49

18.50

18.50

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 10.0 15.0 

POTENTIAL EVAPOTRANSPIRATION, IN CENTIMETERS

20.0

FIGURE 2. Nomograph for solution of Thornthwaite's general equation 

e c=rl.6 (10r//)o. From Thornthwaite (1948, p. 94)
METHODS OF ESTIMATING POTENTIAL EVAPOTRANSPIRATION M9

TABLE 2. Monthly heat index 

[From Thornthwaite (1948, p. 92)]

Temperature (°C)

0 . ......

I -

2...... ........ .....

3.. ......... .....

4......-..-.-.---...

6~. .. -----------

1.. .................

8. .. ... --

9- . -- .

10-... .

11 .

12 

13 

14-....-..--.- .-.

15...- .

16. 

17 

18. 

20 

21 

22 

23 .

24 

25....- ..- ..-

26-.- ---------

27 -

28

29....-------..-.-.

30 

31 

32 

33 

34 

35---....-.........

36 

37.-.- -

38 

39 

40-.-..- .......

0.0

0.09

.25

.46

.71

1.00

1.32

1.66

2.04

2.44

2.86

3.30

3.76

4.25

4.75

5.28

6.38

6.95

7.55

8.16

8.78

9.42

10.08

10.75

11.44

12.13

12.85

13.58

14.32

15.07

15.84

16.62

17.41

18. 22

19.03

19. 86

20.70

21. 56

23.30

0.1

0.10

.27

.48

.74

1.03

1.35

1.70

2.08

2.48

2.90

3.34

3.81

4.30

4.81

5.33

6.44

7.01

7.61

8.22

8.85

9.49

10.15

10.82

11.50

12.21

12.92

13.65

14.39

15.15

15.02

16.70

17.49

18.30

19.11

20.79

21.65 

22.51

0.2

0.01

.12

.29

.51

.77

1.06

1.39

1.74

2.12

2.52

2.94

3.39

3.80

4.35

4.86

5.38

K CW

6.49

7.07

8.28

8.91

9.55

10.21

10.89

11.57

12.28

12.99

13.72

14.47

15.22

15.99

16.78

17.57

18.38

19.20

20.03

20.87

21.73 

22 59

0.3

0.01

.13

.31

.53

.80

1.09

1.42

1.77

2.15

2.56

2.99

3.44

3.91

4.40

4.91

5.44

6.55

7.13

7.73

8.34

8.97

9.62

10.28

10.95

11.64

12.35

13.07

13.80

14. 54

15.30

16.07

16.85

17. 65

19.38

20.96

21.81

99 fiR

0.4

0.02

.15

.33

.56

.82

1.12

1.45

1.81

2.19

2.60

3.03

3.48

3.96

4.45

4.96

5.49

6 04

6.61

7.19

8.41

9.04

10. 35

11.02

11.71

12.42

13.14

13.87

14.62

15.38

16.15

16.63

17.73

18.54

19.36

20.20

21.04

21.90

0.5

0.03

.16

.35

.58

.85

1.16

1.49

1.85

2.23

2.64

3.08

3.53

4.00

4.50

5.01

5.55

6.10

6.66

7.25

9.10

9.75

10.41

11.09

12.49

13.21

13.94

14.69

15.45

16.23

17. 01

17.81

19.45

20.28

21.13

21.99 

22.86

0.6

0.04

.18

.37

.88

1.19

1.52

2.27

2.69

3.12

4.05

4.55

5.07

5.60

6.15

6.72

7.31

7 91

8.53

9.17

9.82

10.48

11.16

11.85

12.56

13.28

14.02

14.77

17.09

17.89

19.53

21.21

22.07

0.7

0.05

.20

.39

.63

.91

1.22

1.56

1.92

2.31

2.73

3.16

3.62

4.10

4.60

5.12

5.65

6 91

6.78

7.37

7 Q7

8.59

9.23

9.88

10.55

11.23

11.92

13.36

14.09

14.84

15.61

17.17

17.97

18.79

19.61

21.30

22.16 OQ n^j

0.8

0.06

.21

.42

.66

.94

1.25

1.59

1.96

2.35

2.77

3.21

3.67

4.15

4.65

5.17

5.71

6.26

6.84

7.43

8.66

9.29

9.95

10.62

11.30

11.99

12.70

13.43

14.17

14.92

15.68

17.25

18.05

18.87

19.69

20.53

21.38

22.25

0.9

0.07

.23

.44

.6ft

.97

1.29

1.63

2.00

2.39

2.81

3.72

4.20

4.70

6

QO

6.90

8 1 n

8 79

9.36

10.68

H Q7

13.50

14.24

14.99

17.33

18.13

19. 78

21.47

22.33 

23.21
M10 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES 

TABLE 3. Mean possible duration of sunlight, in units of 30 days of 12 hours each

[From Thornth-waite (1948, p. 93)]

Latitude (degrees) Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

North latitude

0 . __ __ ... .....

5 . 

10 - 

20 

25 

26 

VT

98

29 

30 --------

31 

32 

33 

34

35 

36 

37.. . ............ .......

38 

39 

40 

42... ... .. .......... ..

43 

44 

45 ........... .......... .

46 

48 

49 ...... 

50 

1.04 

1.02 

1.00 

.97 

.95

.93 

.92 

.92 

.91 

.91

.90 

.90 

.89 

.88 

.88

.87 

.87 

.86 

.85 

.85

.84 

.83 

.82 

.81 

.81

.80 

.79 

.77 

.76 

.75 

.74

0.94 

.93 

.91 

.91 

.90

.89 

.88 

.88 

.88 

.87

.87 

.87 

.86 

.86 

.85

.85 

.85 

.84 

.84 

.84

.83 

.83 

.83 

.82 

.82

.81 

.81 

.80 

.80 

.79 

.78

1.04 

1.03 

1.03 

1.03 

1.03

1.03 

1.03 

1.03 

1.03 

1.03

1.03 

1.03 

1.03 

1.03 

1.03

1.03 

1.03 

1.03 

1.03 

1.03

1.03 

1.03 

1.03 

1.02 

1.02

1.02 

1.02 

1.02 

1.02 

1.02 

1.02

1.01 

1.02 

1.03 

1.04 

1.05

1.06 

1.06 

1.07 

1.07 

1.07

1.08 

1.08 

1.08 

1.09 

1.09

1.09 

1.10 

1.10 

1.10 

1.11

1.11 

1.11 

1.12 

1.12 

1.J3

1.13 

1.13 

1.14 

1.14 

1.14 

1.15

1.04 

1.06 

1.08 

1.11 

1.13

1.15 

1.15 

1.16 

1.16 

1.17

1.18 

1.18 

1.19 

1.19 

1.20

1.21 

1.21 

1.22 

1.23 

1.23

1.24 

1.25 

1.26 

1.26 

1.27

1.28 

1.29 

1.30 

1.31 

1.32 

1.33

1.01 

1.03 

1.06 

1.08 

1.11

1.14 

1.15 

1.15 

1.16 

1.16

1.17 

1.18 

1.19 

1.20 

1.20

1.21 

1.22 

1.23 

1.24 

1.24

1.25 

1.26 

1.27 

1.28 

1.29

1.29 

1.31 

1.32 

1.33 

1.34 

1.36

1.04 

1.06 

1.08 

1.12 

1.14

1.17 

1.17 

1.18 

1.18 

1.19

1.20 

1.20 

1.21 

1.22 

1.22

1.23

1.24 

1.25 

1.25 

1.26

1.27 

1.27 

1.28 

1.29 

1.30

1.31 

1.32 

1.33 

1.34 

1.35 

1.37

1.04 

1.05 

1.07 

1.08 

1.11

1.12 

1.12 

1.13 

1.13 

1.13

1.14 

1.14 

1.15 

1.15 

1.16

1.16 

1.16 

1.17 

1.17 

1.18

1.18 

1.19 

1.19 

1.20 

1.20

1.21 

1.22 

1.22 

1.23 

1.24 

1.25

1.01 

1.01 

1.02 

1.02 

1.02

1.02 

1.02 

1.02 

1.02 

1.03

1.03 

1.03 

1.03 

1.03 

1.03

1.03 

1.03 

1.03 

1.04 

1.04

1.04 

1.04 

1.04 

1.04 

1.04

1.04 

1.04 

1.04 

1.05 

1.05 

1.06

1.04 

1.03 

1.02 

1.01 

1.00

.99 

.99 

.99 

.98 

.98

.98 

.98 

.98 

.97 

.97

.97 

.97 

.97 

.96 

.96

.96 

.96 

.95 

.95 

.95

.94 

.94 

.93 

.93 

.93 

.92

1.01 

.99 

.98 

.95 

.93

.91 

.91 

.90 

.90 

.90

.89 

.89 

.88 

.88 

.87

.86 

.86 

.85 

.84 

.84

.83 

.82 

.82 

.81 

.80

.79 

.79 

.78

.77 

.76 

.76

1.04 

1.02 

.99 

.97 

.94

.91 

.91 

.90 

.90 

.89

.88 

.88 

.87 

.86 

.86

.85 

.84 

.83 

.83 

.82

.81 

.80 

.79

.77 

.76

.75 

.74 

.73 

.72 

.71 

.70

South latitude

5- ............. ... ..

10........ ................ .

15 . 

20-........-. ........

25 

30 ....... ....... 

35... .. ... .

40....... ..............

42... ... ............ .......

44. ...... .............. .

46 

48........ .................

50.... .....................

1.06 

1.08 

1.12

1.14 

1.17

1.20 

1.23 

1.27 

1.28 

1.30

1.32 

1.34 

1.37

.95 

.97 

.98

1.00 

1.01

1.03 

1.04 

1.06 

1.07 

1.08

1.10 

1.11 

1.12

1.04 

1.05 

1.05 

1.05 

1.05

1.06 

1.06 

1.07 

1.07 

1.07

1.07 

1.08 

1.08

1.00 

.99

.98 

.97 

.96

.95 

.94 

.93 

.92 

.92

.91

.90 

.89

1.02 

1.01 

.98 

.96 

.94

.92 

.89 

.86 

.85 

.83

.82 

.80

.77

.99 

.96 

.94 

.91 

.88

.85 

.82 

.78 

.76 

.74

.72 

.70 

.67

1.02 

1.00 

.97 

.95 

.93

.90 

.87 

.84 

.82 

.81

.79 

.76 

.74

1.03 

1.01 

1.00 

.99 

.98

.96 

.94 

.92 

.92 

.91

.90

.89 

.88

1.00 

1.00 

1.00 

1.00 

1.00

1.00 

1.00 

1.00 

1.00 

.99

.99 

.99 

.99

1.05 

1.06 

1.07 

1.08 

1.10

1.12 

1.13 

1.15 

1.16 

1.17

1.17 

1.18 

1.19

1.03

1.05 

1.07 

1.09 

1.11

1.14 

1.17 

1.20 

1.22 

1.23

1.25 

1.27 

1.29

1.06 

1.10 

1.12 

1.15 

1.18

1.21 

1.25 

1.29 

1.31 

1.33

1.35 

1.37 

1.41
METHODS OF ESTIMATING POTENTIAL EVAPOTRANSPIRATION Mil 

WEATHER BUREAU METHOD

The Weather Bureau method was developed by Kohler, Nordenson, 

and Fox (1955). It is a modification of the method developed by 

Penman (1948) and was derived by applying the Penman approach 

to a composite record of a number of weather stations in the United 

States and to the Lake Hefner studies by Kohler (1954). Estimation 

of lake evaporation, which, as previously stated, is assumed to 

approximate potential evapotranspiration, is determined from the 

equation:

EL=0.7Q[(Qnd+Ea7)][(8+y)], (2) 

where

EL=average daily lake evaporation, in inches; 

Qn=uet radiant energy, in inches per day; 

5 slope of the curve relating saturation vapor pressure to

temperature at the observed air temperature; 

Ea=evaporation given by the aerodynamic equation (Kohler 

and others, 1955, p. 2) in which water temperatures are 

assumed equal to air temperature; and

7=factor defined by the equation for Bowen's (1926) dimensionless ratio.

To simplify the computation, Kohler, Nordenson, and Fox (1955, 

p. 15) have presented nomographs (fig. 3) for the solution of equation 2.

The nomograph solution assumes a value of y=0.0105. Data needed 

to use these nomographs for estimating mean daily lake evaporation are 

mean daily or monthly values of air temperature, dewpoint temperature, wind movement, and solar radiation. If daily values of the climatic parameters are used, monthly lake evaporation is obtained by 

adding the values of daily lake evaporation for each day of the month. 

More commonly, as in this report, monthly values of lake evaporation 

are obtained by entering the nomograph with mean monthly values of 

the climatic parameters, after which the value obtained for mean daily 

lake evaporation is multiplied by the number of days in the montK
Ml2 CONTRIBUTIONS TO THE HYDROLOGY OF THE UN7TED STATES

0.2 0.4 0.6 0.8 1.0 1.2 1.4

VAPOR PRESSURE DIFFERENCE, 

IN INCHES OF MERCURY

0.056

0.052

0.048

0.044

0.040

0.036

<

0.032

fri

0.028 C

0.024 + 'S

^

0.020

0.016

0.012

0.008

0.004

0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 

DAILY LAKE EVAPORATION, IN INCHES

FIGURE 3. Nomographs for solution of equation 2 for daily lake evaporation. 

From Kohler, Nordenson, and Fox (1955, p. 15).
o

MEAN D
M14 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

LOWBY-nJOHNSON METHOD

Lowry and Johnson (1942) noted a high correlation between consumptive use (evapotranspiration) and effective heat (accumulated 

degree-days of daily maximum temperature above 32 °F). The linear 

relation they developed is expressed by the following equation:

OT7=o.001S5 (3)

where

CU= annual consumptive use, in inches; and 

HE=effective heat, in degree-days above 32 °F.

Monthly estimates of consumptive use are determined by using a 

ratio of the monthly degree-days to the annual degree-days multiplied by the annual consumptive use. Equation 3 is expressed in 

graphical form on figure 4.

4 6 8 10 12 14 16 

EFFECTIVE HEAT, IN THOUSANDS OF DEGREE-DAYS ABOVE 32°F

18 2Q

FIGURE 4. Graphical solution of equation 3 for consumptive us? versus effective

heat.

The relation expressed in equation 3 was determined from basinwide studies of the hydrologic budget using inflow, outflow, precipitation, and change in the quantity of ground water in storage. Of 

the 20 sites in the United States used by Lowry and Johnson to 

determine consumptive use, only 2 were in arid regions.

HATVTON METHOD

Hamon (1961) formulated a simplified expression for estimating 

potential evapotranspiration. The expression is represented by the 

equation:
METHODS OF ESTIMATING POTENTIAL EVAPOTRANSPIRATION M15

ET=CD2Pt , (4) 

where

ET=average potential evapotranspiration, in inches per day; 

Z?=possible hours of sunlight, in units of 30 days of 12 hours

each;

P,=saturated water-vapor density (absolute humidity at 

saturation) at the daily mean temperature, in centigrams 

per cubic meter; and 

C coefficient chosen to give appropriate yearly valuer of

potential evapotranspiration.

Hamon empirically determined the value of C to be 0.55 from comparisons with the results of the complex Thornthwaite method and 

the Lowry-Johnson study.

The Hamon method is based on the relation between potertial 

evapotranspiration, maximum possible incoming radiant energy, and 

the moisture-holding capacity of the air at the prevailing air temperature. In equation 4 the possible hours of sunlight were used as an 

index of the maximum possible incoming radiant energy, and the 

absolute humidity at saturation is the moisture-holding capacity of 

the air. In using this method values of mean monthly temperature 

and the latitude of the site are required. The absolute humidity at 

saturation, Pt) is then determined directly from mean air temperature 

(table 4). The possible hours of sunlight, D, are determined for the 

latitude of the site (table 3).

TABLE 4. Density of saturated water vapor

Temperature

°C

-40

-30

-20

-10

0

5

10

15

20

25

o F

-40

-22

-4

14

32

41

50

59

68

77

Density (grams 

per cubic meter)

0. 12

. 4

. 89

2. 2

4.8

6. 8

9.3

12. 7

17. 1

22. 8

Temperature

°C

30

35

40

50

60

70

80

90

100

o F

86

95

104

122

140

158

176

194

212

Density (grams 

per cubic meter)

30.4

31 6

51. 1

83. 2

130. 5

19^. 4

293. 8

424. 1

59 9. 7

BLANEY-CRIDDLE METHOD

In experimental studies throughout Western United States, Blaney 

and Griddle (1950) developed a method for estimating consumptive 

use (evapotranspiration) by various crops. They found that evr.potranspiration varies with temperature, daytime hours, and available 

moisture for various crops. With ample moisture available, the
M16 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

relation between evapotranspiration and the above mentioned parameters is expressed by the equation:

where

U consumptive use, in inches, during growth of the crop;

K= empirical consumptive-use coefficient that is dependent on 

the type and location of crop ;

p=monthly percentage of total daytime hours in the year; and

jT=mean monthly temperature, in degrees Fahrenheit. 

Blaney (1956, p. 46) stated that evapotranspiration from an 

alfalfa field was approximately equal to lake evaporation. In a later 

study, Blaney and Griddle (1962, p. 49) suggested velues for K in 

equation 5 for alfalfa at a few selected locations. In written communications with the authors, Blaney suggested values for K of 

0.85 for the entire year and 1.00 for the growing season at the sites 

in groups 1 and 2 for estimating potential evapotranspiration by the 

Blaney-Criddle method. He also suggested values for K of 0.75 for 

the entire year and 0.90 for the growing season at the sites in group 

3. These values are approximately the same as those given by Blaney 

and Griddle (1962, p. 49) for alfalfa and were used in this study.

Table 5 from a report by Blaney and Griddle (1950) gives values of 

Pi the percentage of daytime hours in each month between lat 24° and 

50° N. The appropriate value of p and the mean monthly temperature, 

T, are used in equation 5 to compute monthly values of potential 

evapotranspiration.

LANE METHOD

Lane (1964), using 551 sets ot monthly data for pan evaporation, 

solar radiation, and air temperatures at various sites in the United 

States, developed the following equation to express the relation between lake evaporation, solar radiation, and temperature:

104 ^=2.67T-51.46, (6) 

tys

where

EL= average monthly lake evaporation, in inches;

Qs average monthly incoming solar radiation, in langleys per

day;

T= average monthly air temperature, in degrees Fahrenheit. 

Lane used a coefficient of 0.70 to adjust observed pan evaporation to 

the values he used for lake evaporation. A comparison of results 

obtained by equation 6 with published lake evaporation at various
H

o

o 

p

o 

o

o 

p

_ o 

o to o rfi. 60 o ib o O31 ' 02 en o 

I *

o 

p

o

o

o 

p

o 

o

h-'

o 

p

o 

o

o 

p

o 

o

h-«

o 

p

o

s^ . w, w, w OtOCnCiOOOJH-' O 

o 

p

o 

o

h-«

o 

o

h-«

o 

p

o 

o

o

cici<ipocopppjooocscs p 

o

tOOCOH-'OOOOOJOiOOOO O 

I *

o

pi pop <r> pp p ^tpoco pips p 

_ o 

CO O CD rfi-O500tOOrfi.rfi.OtO O 

o 

p

o 

o

CnOi-JCOOOOOcOOCOJOT

fa

SaOHI3I\[ GXLIVHLLS3 lVIIN3.LOd[ ^OIJLVaidSNVHXOdVA3 Lil'l 
M18 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

sites in the United States indicated to him that a coefficient of 0.92 

should be applied to his results. This reduced equation 6 to the following form for estimating lake evaporation:

#i=0.92X10-4&(2.67:r-51.46). (7)

Values of mean monthly solar radiation and mean monthly air temperature are required for use of this method.

ANALYSIS OF ESTIMATED POTENTIAL 

EVAPOTRANSPIRATION

Pan evaporation when adjusted by the proper coefficients approximates the evaporation from a shallow lake; and lake evaporation, in 

turn, is approximately equivalent to potential evapotrarspiration. Adjusted pan-evaporation data were therefore used as the standard for 

comparing and evaluating the effectiveness of each of the six methods 

of computing evapotranspiration on the basis of climr-tological data 

for both the calendar year and the growing season.

All six methods were used at each site except where required climatological data were lacking. The latest 10 years of available record 

was used for the comparisons. A site with less than 10 years of record 

was used only if its record was sufficiently long to give reliable results 

and its use was needed to enhance areal coverage. Where two climatological stations were in close proximity and neither had complete 

data, the data from the two sites were combined if the two sites had the 

same general climate and if an increased number of methods could be 

used by combining the data. For example, the site at Phoenix, Ariz., 

had all the required climatological data for the six-m°>thods, but no 

pan-evaporation data. At Tempe, 6 miles away, pan-evaporation data 

were available, but only part of the required climatological data was 

available. A check of the available data showed the climate at both 

sites to be approximately equivalent, and the two sets' of data were 

therefore combined and used under the site name, Phoenix.

Most of the data used in the computations monthly mean values of 

pan evaporation, air temperature, solar radiation, wind movement, and 

dewpoint and daily maximum values of air temperature (for computing degree-days) were obtained from the monthly series of U.S. 

Weather Bureau publications entitled "Climatological Data." Solar 

radiation is not measured at most of the sites used in this study. The 

mean monthly values were obtained from maps in the climatological 

data report series that show isopleths of mean monthly solar radiation. 

Pan-evaporation data for a few of the sites were obtained from reports
METHODS OF ESTIMATING POTENTIAL EVAPOTRANSPIRATION 1119

by the California Department of Public Works (1947,1948, and 1955). 

An analysis of the potential evapotranspiration estimated by each of 

the methods previously discussed is described on the pages that follow.

ADJUSTED PAN EVAPORATION

All but 4 of the 25 sites were equipped with Weather Bureau class A 

pans. Four sites Fairmont, Haiwee, Tinemaha, and Escondido, 

Calif. were equipped with Colorado-type pans. Descriptions of these 

two pans are in most standard hydrology texts (for example, Linsley 

and others, 1958, p. 99). The coefficients used to adjust observed class 

A pan evaporation to equivalent lake evaporation were obtained from a 

Weather Bureau map (Kohler and others, 1959, pi. 3) showing isopleths of the coefficients. For the 21 sites equipped with class A pans the 

coefficients ranged from 0.60 to 0.78. Coefficients for use with the Colorado pans were based on values presented in a table by Linsley and 

others (1958, p. 104). Three of the four Colorado pans were standard 

installations and a coefficient of 0.90 was used. The fourth Colorado 

pan, at Escondido, Calif., is set in concrete and a coefficient of 0.92 was 

used.

The average annual values of observed and adjusted pan evaporation are listed in table 6. Similar evaporation figures for the grovang 

season are listed in table 7. The adjusted values of pan evaporation in 

each table were used as standards to compare results of the six methods 

of estimating potential evapotranspiration from climatological data. 

The computed value is shown in the first column under each method in 

the two tables. The percentage difference between computed values and 

values of adjusted pan evaporation is shown in italic type in the second column under each method.

EMPIRICAL METHODS

Thomthwaite method. Values of potential evapotranspiration 

computed by the Thornthwaite method were less than the adjusted pan 

evaporation at all sites used in the study. The differences ranged from 

 21 to 66 percent for the entire year and from 10 to 63 percent 

for the growing season. The median differences were 39 and 33 

percent, respectively.

Weather Bureau method. Potential evapotranspiration was computed by the Weather Bureau method for only 7 of the sites because 

dewpoint data were unavailable at the other 18 sites. The differences 

ranged from 6 to +22 percent for the entire year and from 5 to 

+17 percent for the growing season. The median differences were + 6 

and 1 percent, respectively.
TABLE 6. Average potential evapotranspiration estimated by pan evaporation an

[Data are in inches except for the percentage difference (italicized) between the com

Site

Pan evaporation

Observed

Adjusted to 

equivalent 

lake 

evaporation

Potential evap

Thornthwaite

U.S. Weather 

Bureau L

Group 1. Arid environment

Fairmont, Calif.'. .............. ..................

113.0

172.7

103.8

68.0

145.5

106.4

113.5

89.7

81.4

97.0

104.0

93.4

61.2

88.8

77.6

73.7

80.7

36.6

44.8

31.8

32.8

49.0

37.0

38.6

33.1

31.0

-55

-57

-GO

-46

-45

-48

-62

73.2

Group 2. Modified arid environment

Indio, Calif.. _ . __ ............ _ .-... _ ..... 100.4

76.7

92.5

96.3

62.3

52.1

63.8

59.6

43.0

41.2

39.7

44.2

-31

-21

-38

-26

63.5

65.2

70.0

+82

+«

+17

Group 3. Subhumid environment

Chula Vista, Calif.. ._._ _....- ..-_........_.

Escondido, Calif.3 .,. ............... _ ............

Kiverside, Calif -------------------- _ - __ ...

San Francisco, Calif.. .. .... ..... _ . ______

70.8

60.0

57.9

62.6

56.7

72.2

71.7

53.8

72.8

65.5

48.8

49.5

53.3

45.1

44.2

50.5

53.1

42.0

52.4

48.5

30.0

28.2

30.0

31.3

26.9

32.1

34.6

33.2

38.0

32.5

33.1

-39

_90

-41

-40

-27

-31

-38

__ Q

-38

-3%

-39

46.7

49.7

41.3

+6

-6

-2

+6

.. 

2 No winter data. 
_L'A.ii,E '<. L'VJi'tij ; Qoi&iiifii, &'0'iftd<,<~'i''>i<i-j)i'<~'it'iO''i, tftstiwtte'i by j)'i-'i

season 

[Data are in inches except for the percentage difference (italicized) between the com

Site

Pan evaporation

Observed

Adjusted to 

equivalent 

lake 

evaporation

Potential evapo

Thornthwaite

U.S. Weather 

Bureau Lo

Group 1. Arid environment

Death Valley, Calif....... .........................

Hayfleld, Calif ....... ............... ...........

Tinemaha, Calif. '........ ..........................

104.2

124.7

50.7

99.6

81.4

79.4

68.8

66.1

74.7

70.1

60.8

59 4

51.6

59.5

on Q

34 1

36.3

26.0

41.1

30.7

29.2

26.1

-49

-45

-51

__ f}Q

-40

-32

10

_ &y

__ qry

-54

51.3 -1

Group 2. Modified arid environment

Indio, Calif. ----- ---~------~--.---.--~------ 70.1

55.2

63.4

66.3

43.5

43.6

41.1

34.3

QQ Q

32.1

35.2

-SI

-10

-m

-is

43.9

43.8

47.5

+17

0

+15

Group 3. Subhumid environment

Chula Vista, Calif-. ... .. . ......-.-.- 

Escondido, Calif. 2 _. ___. ..-_.__.... . 

San Francisco, Calif..............................

San Jactato. Calif- __ ... _ -.. ....... _ .......

Stockton, Calif.......-.- ...... . ..... ... .

47.3

53.2

41.1

40.8

44.6

38.7

46.7

53.0

40.4

52.0

51.8

32.6

36.2

30.8

37.5

32.2

30.2

32.7

31.5

37.4

25.0

24.7

23.4

21.5

26.0

on o

19.0

25.0

26.7

-as

-32

Q!

-41

-XT

-29

 HO

-40

-33

_ in

-S3

29.8

37.7

30.0

-1

-4

-5

-1

i Standard Colorado pan. 2 Colorado pan set in concret
M22 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

Lowry-Johnson method. Potential evapotranspiration was computed by the Lowry-Johnson method for 23 of the 25 sites. Maximum 

daily temperatures were not available for the period of record at two 

sites. The differences ranged from 16 to 60 percent for the entire 

year and from 8 to 60 percent for the growing season. The median 

difference was 25 percent for both periods. The value? estimated by 

the Lowry-Johnson method were lower than the adjusted pan evaporation at all sites.

Hamon method. Potential evapotranspiration was computed for 

all sites by the Hamon method. These differences ranged from 9 to 

 65 percent for the entire year and from 4 to 65 percent for the 

growing season. The median differences were 39 and 35 percent, 

respectively. The Hamon method, like the Lowry-Johnson and Thornthwaite methods, gave estimates of potential evapotran spiration that 

were lower than the adjusted pan evaporation at all sites.

Blaney-Griddle method. Data from all sites were used for computing potential evapotranspiration by the Blaney-Criddle method. 

The differences ranged from 44 to +17 percent for the entire year 

and from 44 to +22 percent for the growing season. The median 

differences were 11 and Y percent, respectively.

Christiansen and Mehta (1965, p. 21) estimated actual pan evaporation by use of a modified Blaney-Criddle method in which K (consumptive-use coefficient) is based on mean temperature ajid windspeed rather than dependent on type and location of crop. By this 

modified method, data from several sites in this study gave results 

which were generally within ±30 percent of actual pan evaporation. 

Because this study was restricted to the estimation of potential evapotranspiration and because this modified Blaney-Cridd'e method did 

not significantly improve estimates of actual pan evaporation, a comparison of the results is not presented in this report. Also, it is somewhat difficult to find a common ground for basing the value of K on the 

type of crop as Blaney and Griddle did or on temperature and windspeed as Christiansen and Mehta did.

Lane method. Data from 22 of the 25 sites were us^d to compute 

potential evapotranspiration by the Lane method. The differences 

ranged from 33 to +58 percent for the entire year and from 33 to 

+ 54 percent for the growing season. The median differences were +15 

percent and + 8 percent, respectively.

RESULTS OF THE ANALYSIS

Tables 6 and Y present a summary of the measured and adjusted pan 

evaporation and the average values of potential evapotranspiration 

estimated by the six methods at the selected sites for the entire year
METHODS OF ESTIMATING POTENTIAL EVAPOTRANSPIRATION M23

and for the growing season. The differences, in percent, between the 

values estimated by each of the six methods and the adjusted pan 

evaporation are also shown in tables 6 and 7.

Table 8 summarizes the differences, in percent, between potential 

evapotrajispiration estimated by each of the six methods and adjusted 

pan evaporation for the sites in an arid environment. Tables 9 and 10 

are similar to table 8, except that table 9 refers to a modified prid 

environment and table 10 to a subhumid environment.

Table 8 shows that the Lane method gave satisfactory results in an 

arid environment. At eight of the nine group 1 sites, values estimated 

by the Lane method agreed within ±13 percent with the adjusted pan 

evaporation values. The Weather Bureau method was used at only one 

group 1 site, and the evapotranspiration estimated by that method 

differed from the adjusted pan evaporation by 1 percent. The four 

other methods gave much lower values of potential evapotranspiration 

than the values of adjusted pan evaporation.

Table 9 shows that the Blaney-Criddle and Weather Bureau methods 

gave satisfactory results at the sites in a modified arid environment. 

For both methods, the estimated potential evapotranspiration agreed 

within ±22 percent of the adjusted pan evaporation. More or less 

satisfactory results were obtained in this environment with the 

Hamon and Lowry-Johnson methods. The Lane method, however, gave 

estimates of potential evapotranspiration that were much higher than 

the adjusted pan evaporation, and the Thornthwaite method gave 

estimates that were much lower, particularly those for the entire year.

Table 10 shows that the Blaney-Criddle method also gave sr.tisfactory results in a subhumid environment. Results of the computations by the Blaney-Criddle method at all 11 group 3 sites were within 

±12 percent of the adjusted pan evaporation. Fair results, though 

consistently low, were obtained with the Lowry-Johnson method, and 

poor results were obtained with the Hamon, Lane, and Thornthwaite 

methods. The Hamon and Thornthwaite methods gave estimates of 

potential evapotranspiration that were much lower than the adjusted 

pan evaporation; the Lane method gave estimates that were much 

higher than the adjusted pan evaporation. The Weather Bureau 

method was used at only three group 3 sites, and, while the results 

obtained at these sites were good, they constitute too small a sample on 

which to make conclusions.

In an arid environment, an evaporation pan provides an index to 

potential evapotranspiration only for the microclimate existing at the 

pan site. Pruitt and Angus (1961) showed that evaporation from a 

Weather Bureau class A pan in a dry fallow field was about 30 percent 

greater than that from a similar pan in a grass field, 750 feet away.
M24 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

TABLE 8. Summary of differences between potential evapotrinspiration estimated ~by the six empirical methods and adjusted pan evaporation in an arid 

environment

Range of differences 

(percent)

+11 to +20.... ...........

+1 to +10.. ..............

0 .......................

-l to -10. ...............

-11 to -20...............

-21 to -30...............

-31 to -40...............

-41 to -50... ............

-51 to -60...............

-61 to -70... ............

Total..............

Number of sites with differences in indicated range

Entire year

Thornthwaite

3

4

2

9

AYeather Bureau

1

1

Lo Johnwry- son

1 

3 

3

7

g

w

2 

4 

2 

1

9

Blaney-Criddle

2 

1 

5 

1

9

ID

>5

1

1

0

3

1 

0 

1

7

Growing season

Thornthwaite

4 

3

2

1

10

Weather Bureau

1

1

Lowrv-Johnson

2 

4 

2

8

Hamon

4 

3 

2 

1

10

Blaney-Criddle

3 

3 

3 

1

10

3<s

Hi

1

3

0 

1 

2 

0 

1

8

TABLE 9. Summary of differences between potential evapotrinspiration estimated ~by the six empirical methods and adjusted pan evaporation in a modified 

arid environment

Number of sites with differences in indicated range

Range of differences 

(percent)

+61 to +70.. .............

+51 to +60........ .-..---

+41 to +50-,.. ...........

+31 to +40...............

+21 to +30...............

+11 to +20.-.-,..-.......

+1 to +10.. ........... ...

0 ................ .......

-1 to -10.. .--.-.-...... .

-11 to -20.. .......... ...

-31 to -40.. _.....-...--

Total...... .........

Entire year

Thornthwaite

2

2

4

Weather Bureau

1

1

1

3

Lo -Johnson wry 

2 

1 

1

4

Hamon

1 

2 

0 

1

4

Blaney-Criddle

0

1

4

O) 

Hi

1

1

1

1

4

Growing season

Thornthwaite

1

1

4

Weather Bureau

2

0 

1

3

Lowrv-Johnson

2 

1 

1

4

Hamon

2 

1 

1

4

Blaney-Criddle

1

1

1

1

4

ID

<s

Hi

1

1 

1 

1

4
METHODS OF ESTIMATING POTENTIAL EVAPOTRANSPIRATION M25

TABLE 10. Summary of differences between potential evapotranspiration estimated by the six empirical methods and adjusted pan evaporation in a subhumid environment

Range of differences 

(percent)

+41 to +50...............

+31 to +40-...-..-.-...

+21 to +30.. .............

+11 to +20.. ........ .....

+1 to +10... ...... .......

0...... ....................

-1 to -10... .............

-11 to -20...............

 21 to -30... ...... ..----

-31 to -40... ............

 41 to -50.. .............

Total.---...........

Number of sites with differences in indicated range

Entire year

Thornthwaite

1 

0

1

7

1

10

Weather Bureau

1

0

2

3

Lowry-Johnson

5

5

10

§

w

3

6

1

10

Blaney-Criddle

2

1

4

3

10

1

h3

3

2

4

9

Growing season

Thornthwaite

1

4

5

1

11

Weather Bureau

3

3

Lowry-Johnson

2 

4

5

11

Hamon

3

6

2

11

Blaney-Criddle

5

0

5

1

11

I 

h3

1 

0 

5 

4

10

To attain water use equivalent to potential evapotranspiration in an 

arid environment, as at the group 1 sites, irrigation is required to 

provide an ample water supply (a condition defined as necessary for 

potential evapotranspiration). Irrigation will modify the microclimate 

by increasing the humidity of the air; therefore, to obtain a reliable 

index of the potential evapotranspiration with an evaporation pan, the 

pan must be exposed to the modified microclimate. In other words, a 

pan cannot be used at an unirrigated desert site to obtain a measure 

of the potential evapotranspiration at that site. Evaporation datr. so 

obtained provide a spurious standard for judging the reliability of 

other methods of computing potential evapotranspiration in an £,rid 

environment.

We used this standard at our group 1 sites, and it is therefore not 

surprising that the methods gave values of potential evapotranspiration that were generally lower than the adjusted pan evaporation. 

The methods that used arid-land data in their derivation were based 

on water use by irrigated crops, and these methods therefore should not 

be tested against evaporation from a pan set in an unirrigated desert 

environment. Group 1 data were therefore eliminated from consideration in determining which of the six methods was best.

Consequently, the results of this study clearly indicated that of the 

six, the Blaney-Criddle and Weather Bureau methods are the most 

effective for estimating potential evapotranspiration. At all 15 site? in 

the subhumid and modified arid environments, potential evapotran-
M26 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

spiration computed by the Blaney-Griddle method checked the adjusted 

pan evaporation within ±22 percent. Potential evap obranspiration 

computed by the Weather Bureau method also checked the adjusted 

pan evaporation within ±22 percent at the six group 2 and group 3 

sites where it was used. This percentage range is generally accepted as 

the range of reliability of the regional pan-evaporation coefficients 

used to determine lake evaporation.

Potential evapotranspiration computed by the Weather Bureau 

method agreed with adjusted pan evaporation equally veil in all three 

environments tested. This was expected as this is all the method 

attempts to do. The Blaney-Griddle method however attempts to 

predict the potential evapotranspiration that would occur under a 

condition that can only exist in the presence of an ample water 

supply. Thus, under conditions required for potential evapotranspiration to be achieved, both the Blaney-Griddle and the Weather Bureau 

methods give satisfactory results. Because of the general unavailability 

of the climatological data required for the Weather Bureau method, 

the Blaney-Criddle method was concluded to be the mo^t practical for 

use.

SUMMARY AND CONCLUSIONS

This study compared potential evapotranspiration, computed from 

climatological data by each of six empirical methods, ^ith pan evaporation adjusted to equivalent lake evaporation by coefficients. The 

comparison is based on the assumption that evaporation from a shallow 

lake approximates the potential evapotranspiration in the local area. 

The time periods used for the comparisons were the calendar year 

and the growing season, May through October. In general, the values 

compared were 10-year averages for these two periods. Tve six methods 

compared were the Thornthwaite, Weather Bureau (a modification 

of the Penman method), Lowry-Johnson, Hamon, Blaney-Criddle, 

and Lane. The region selected for the study was the arid and subhumid 

areas of Arizona, California, and Nevada.

Twenty-five sites, where pan-evaporation and concurrent climatological data were available, were used in the sfridy. Of these 

sites, 5 were in Arizona, 17 were in California, and 3 were in Nevada. 

The lack of some types of climatological data at various sites made it 

impossible to use all six methods at all sites. The 25 sites included a 

wide range of climatic conditions. Ten of the sites (group 1) were in 

a highly arid environment and four of them (group 2) were in an 

arid environment that was modified by extensive irrigation. The remaining 11 sites (group 3) were in a subhumid environment. The term 

"subhumid," as used here, refers to an environment marked by summers that are dry and cool relative to the arid environment and winters 

that have relatively high precipitation.
METHODS OF ESTIMATING POTENTIAL EVAPOTRANSPIRATION M27

For the wide range of climatic conditions in this study, only the 

Weather Bureau method gave estimates of potential evapotranspiration that closely agreed with the adjusted pan evaporation at all pites 

where the method was used. However, lack of the required climatological data restricted the use of the Weather Bureau method to se-ven 

sites. Results obtained by use of the Thornthwaite, Lowry-Johnson, 

and Hamon methods were consistently low. Results obtained by uso of 

the Lane method agreed with adjusted pan evaporation at the group 

1 sites, but were consistently high at the group 2 and 3 sites.

During the analysis it became apparent that adjusted pan evaporation in an arid environment (group 1 sites) is a spurious standard for 

judging the reliability of the methods that were tested. To attain 

water use equivalent to potential evapotranspiration in an arid environment, as at the group 1 sites, it is necessary to irrigate to provide 

an ample water supply. Irrigation will modify the microclimate by 

increasing the humidity of the air. Therefore, to obtain a reliable index 

of the potential evapotranspiration with an evaporation pan, it is 

necessary that the pan be exposed to the modified microclimate. The 

evaporation pans at the group 1 sites do not meet this criterion; tlx ose 

at the group 2 sites do. Group 1 data were accordingly eliminated from 

consideration as to which of the six methods was the best.

The results of this study indicated the Blaney-Criddle metl od, 

which uses climatological data that can be readily obtained or 

deduced, to be the most practical of the six methods for estimating 

potential evapotranspiration. At all 15 sites in the two environments, 

potential evapotranspiration computed by the Blaney-Criddle method 

checked the adjusted pan evaporation within ±22 percent. This percentage range is generally considered to be the range of reliability of 

pan-evaporation coefficients.

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Blaney, H. F., 1956, Discussion of estimating evaporation: Am. Geophys. Union 

Trans., v. 37, no. 1, p. 46-48.

Blaney, H. F., and Griddle, W. D., 1950, Determining water requirement? in 

irrigated areas from climatological and irrigation data: U.S. Dept. .Agriculture, Soil Conserv. Service, Tech. Paper 96, 48 p.

 1962, Determining consumptive use and irrigation water requirements:

U.S. Dept. Agriculture Tech. Bull. 1275, 59 p. 

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

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54-B, 98 p.
M28 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

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Kept. Proj. WR-13, 77 p.

Damagnez, J., Riou, Ch., De Villele, O., and El Ammami, S., 19"3, Estimation et 

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Hydrologie Sci. Pub. 62, p. 98-113.

Hamon, W. R., 1961, Estimating potential evapotransporation: Am. Soc. Civil 

Engineers, Hydraulics Div. Jour., v. 87, no. HY3, p. 107-120.

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

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Kohler, M. A., Nordenson, T. J., and Baker, D. R., 1959, Evaporation maps for the 

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Kohler, M. A., Nordenson, T. J., and Fox, W. E., 1955, Evaporation from pans 

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Langbein, W. B., and Iseri, K. T., 1960, General introduction and hydrologic 

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Nixon, R. R., MacGillivray, N. A., and Lawless, G. P., 1963, Evapotranspiration 

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Penman, H. L., 1948, Natural evaporation from open water, bar? soil, and grass: 

Royal Soc. [London] Proc., Ser. A, v. 193, p. 120-145.

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the first annual report on investigations of energy and mass transfers near 

the ground including influences of soil-plant atmosphere: California Univ. 

[Davis].

Stephens, J. C., and Stewart, E. H., 1963, A comparison of procedures for computing evaporation and evapotranspiration: Internat. Asso^. Sci. Hydrology 

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O