Evaporation Study in a 

Humid Region, Lake Michie 

North Carolina

By J. F. TURNER, JR.

STUDIES OF EVAPORATION

GEOLOGICAL SURVEY PROFESSIONAL PAPER 272-G

Prepared in cooperation with 

the city of Durham, N.C.

An evaluation of evaporation

using mass-transfer and water-budget techniques

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1966
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 20 cents (paper cover)
CONTENTS

/ bstract. ___________-_____-_-_____----___----___---

Introduction _____________________________ — _______

Description of Lake Michie______________________

Instrumentation of the study _ __________________

Development of the calibration. ______________________

Methods and analyses_______-___-__-_____-______

Computations. _________________________________

Hydrographic data: .adjusted change in stage,

Outflow and inflow______________________

Errors in hydrographic data _ ___________

Meteorological data: the mass-transfer product, 

u(e0 —ea) _____-_-_-.__ ———— __ ——— — ___

Page 

137 

137 

137 

139 

139 

139 

142

142

143

143

144

Development of the calibration—Continued 

Computations—Continued

Saturation vapor pressure.___. 

Wind speed-_________________

Air vapor pressure.___________

Errors in meteorological data._. 

The calibration curve.________________

Plotting and limitations of periods.. 

Characteristics of the calibration....

Application of the calibration._____________

Summary. _______________________________

Selected references._____________--___---_-

Page

144

145

145

145

146

146

147

148

149

150

ILLUSTRATIONS

F'GURE 37. Map of Lake Michie._____________________-___________-___________-_--_-------_

38. Photograph of raft station at Lake Michie_________________.__-______-___--------_.

39. Photograph of anemometer and wind and water-surface temperature recorder. __________

40. Diagram showing determination of adjusted change in stage, AH^______________---_-

41. Graph showing ungaged inflow plotted against Dial Creek discharge_________________

42. Graph showing stage-area relation.______________________________________________

43. Diagram showing daily computation of the mass-transfer product, u(e<> — e0)-______ -.._

44. Graph showing calibration curve_____________________--___-___-__--_--_------_-

45. Graph showing deviations from the calibration curve plotted against Dial Creek discharge.

46. Histogram showing Lake Michie monthly evaporation and precipitation._____________

47. Graph showing approximate monthly average of evaporation plus seepage.___________

138

139

140

142

143

144

145

146

148

149

149

TABLES

I'ABLE 1. Hydrographic and meteorological instruments,______-_____-__-______-_____----__

2. Examples of computation of adjusted change in stage, AHA, for calibration points_

3. Errors in adjusted change in stage resulting from normal errors in streamflow records.

4. Calibration data___________________________________________________________

5. Monthly evaporation_______________________________________________________

Page

141

142

144

147

148

SYMBOLS

S Net ground-water seepage rate.

AH Average change in lake stage.

AHA Average change in lake stage, adjusted for inflow, outflow (including pumpage), and rainfall.

A£ Error in water-surface temperature.

E Evaporation from water surface.

ea Actual air vapor pressure corresponding to the product of relative humidity, /, and saturation vapor 

	pressure, es.

in
IV CONTENTS

e0 Saturation vapor pressure corresponding to water-surface temperature, T0.

es Saturation vapor pressure corresponding to dry-bulb temperature, Ta.

f Relative humidity.

7 Inflow.

N Slope of the calibration curve; the mass-transfer coefficient.

O Outflow.

(O—I) Outflow minus inflow.

QD Dial Creek discharge.

R Rainfall.

Ta Dry-bulb temperature.

TQ Temperature of lake water surface.

u Wind speed.
STUDIES OF EVAPORATION

EVAPORATION STUDY IN A HUMID REGION, LAKE MICHIE, NORTH CAROLINA

BY J. F. TURNER, JR.

ABSTRACT

The mass-transfer and water-budget techniques of calibrating 

s reservoir for evaporation were evaluated through a study of 

Lake Michie, N.C. The techniques appear adequate for estimation of lake evaporation and net seepage in humid regions 

vhere lake storage is affected by streamflow and ground-water 

seepage, under conditions no more adverse than those affecting 

Lake Michie.

The analysis of 25 months of mass-transfer and water-budget 

d'fta collected at Lake Michie indicates pronounced seasonal 

variation in both evaporation and seepage.

INTRODUCTION

In past years, water losses by evaporation in humid 

regions have been given only limited consideration 

because abundant water resources made concern unr^cessary. The growing industry and population of 

t^e Eastern United States are now making such great 

demands on water resources that studies are needed to 

evaluate evaporation losses from reservoirs.

The Lake Michie investigation is of special significance because of the scarcity of lake evaporation 

studies in humid regions where lake storage is apprerably influenced by inflow and outflow. Streamflow 

b<is commonly been negligible or completely absent as 

a, factor in evaporation studies in arid and semiarid 

regions. The present investigation is also useful in 

t at it suggests some basic design elements for future 

evaporation studies in humid areas.

The method of evaluation used in this study requires 

t e establishment and application of a calibration 

c'lrve (a curve relating observed evaporation rates to a 

c imbination of several meteorological variables). The 

r mss-transfer water-budget techniques as described by 

Harbeck (1962) was chosen for the Lake Michie study 

frimarily because the method is simple to apply, 

requires inexpensive instrumentation, and allows a 

seepage estimate to be made. The relative merits of 

t ns technique and another frequently used method for 

c o.termining evaporation are discussed later in the 

report.

The Lake Michie study is a continuing project, 

rnanced through a cooperative program of the city of

Durham, N.C., and the U.S. Geological Survey to 

evaluate the water resources of the upper Neuse River 

basin.

DESCRIPTION OF LAKE MICHIE

Location and physical features.—Lake Michie is the 

municipal water supply for the city of Durham and the 

State Sanitorium at Camp Butner, N.C. Electric 

power is occasionally generated and supplements the 

power required to pump water. The dam, completed 

in April 1926, is a reinforced concrete gravity-type 

structure situated about 5)4 miles above the mouth of 

the Flat River and about 13 miles northeast of Durhr.m. 

(See fig. 37.)

The sparsely populated Lake Michie region is 

generally wooded and hilly, with some open land that is 

used for small grain, pasture, and row crops. The lake 

is narrow, irregular, and meandering, and the shorel:ne 

is nearly covered by trees and small brush. Lake 

Michie has an average surface area of about 480 acres; 

its volume ranges from about 11,200 to 14,500 acre-feet. 

The average flow through the lake is about 170 cfs 

(cubic feet per second).

The drainage at the dam is 170 square miles, of which 

155 square miles of the inflow area is continuously 

gaged, 8 square miles is gaged periodically, anc1 7 

square miles is totally ungaged. (Drainage areas are 

only approximate.) Thus, about 9 percent of the total 

drainage is not continuously gaged.

Climatology.—Long-term averages of climatological 

and hydrologic data pertinent to the evaporation study 

are listed in the following table:

Annual precipitation (inches)___________--_------- 44.5

Temperature (°F)—__------------------------ 60

Wind speed (mph) and direction.----------------- 7.7 (SYr.)

Percent of possible sunshine..________-___-__----- 60

Relative humidity (percent):

1 a.m__----------------------------------- 81

7 a.m._______----_------------------------ 83

1 p.m______-_----------------------------- 53

7 p.m_______-__--------------------------- 68

Average runoff (cfs per sq mi) ——— ___-____-__---- 1.0

137

EVAPORATION STUDY IN A HUMID REGION, LAKE MICHIE, NORTH CAROLINA 139

FIGURE 38.—Lake Michie raft station.

Except for runoff, the listed values were observed by 

the U.S. Weather Bureau at Raleigh and RaleighDurham Airport.

INSTRUMENTATION OF THE STUDY

The location of the hydrographic and meteorological 

equipment used in this study is shown on the map of 

Lake Michie and surrounding area (fig. 37). The 

instruments are listed in table 1, along with an indication of their location and the types of data collected in 

the past. The raft station is shown in figure 38, and 

the anemometer and wind and water-surface temperature recorder are shown in figure 39.

As indicated in table 1, lake-stage records have been 

collected at the dam since about 1927. These records 

and the rainfall data used in the study were collected 

by employees of the city of Durham. Rainfall data

are furnished to the Geological Survey monthly. The 

hourly distribution for the rainfall data is provided by 

the tipping bucket attachment to the water-level 

recorder at the dam.

DEVELOPMENT OF THE CALIBRATION 

METHODS AND ANALYSES

The calibration for Lake Michie was developed by 

relating observed changes in lake stage (adjusted for 

inflow, outflow, and rainfall) to a combination of 

several meteorological variables observed at Lake 

Michie and at the Raleigh-Durham Airport.

This technique basically requires a simultaneous 

solution of the mass-transfer equation as suggested by 

Harbeck (1962; with a water-budget equation (Linsley
140 STUDIES OF EVAPORATION

FIGURE 39.—Anemometer and wind and water-surface temperature recorder.
EVAPORATION STUDY IN A HUMID REGION, LAKE MICHIE, NORTH CAROLINA 141

TABLE 1.—Hydrographic and meteorological instruments

Instrument

recording).

Do.-———-.

Hygrothermograph

Do.-— — — —

Psychrometer 

(hourly).

gage.

eter. 

Water-stage recorder. _

Water-stage recorder 

(digital). 

Do. — — — ———

Location

basin) . On lake (near

dam).

Weather station. —

Dam __ —___.__ — .do..— — —

Raleigh-Durham 

Airport.

——do.-——.—

Flat River (below 

dam).

Dial Creek (above 

lake). 

Flat River (above

lake).

Data collected

Rainfall————.

— .do..— ———

——do.. ———— .

temperature. 

Air temperature 

and relative 

humidity.

— ..do.— — —— — -do.— — —

Dry-bulb temperature and relative humidity.

Durham and 

Camp Butner. 

Rainfall—————

Outflow (drainage 

area, 170 sq mi) .

Inflow (drainage 

area, 4.71 sq mi).

area, 150 sq mi) .

Period

1926-. 1

1946-61.1 2

September 1961- 

December 1962.

August 196 1-.3

August 1961-.

1927-1961 (about). 1944-.1 

1927-.1

August 1927-September 1959; 

August 1961-. 

October 1925-.

July 1925-.

1 Data collected by other agencies.

2 Fragmentary.

» Except for winter months 1962, 1963, 1964.

and others, 1958, p. 93). Harbeck's equation relates 

evaporation to several meteorological factors,

E=Nu(e0 —ea}, (1)

where

E= evaporation, in feet;

JV= proportionality constant (mass-transfer co- 

• efficient);

ii=wind speed, in miles per hour;

e0 — saturation vapor pressure, in millibars, corresponding to temperature at the air-water 

boundary;

e a= actual vapor pressure of the air, in millibars.

According to mass-transfer theory, this equation 

describes the physical process by which water evaporates from a free surface. The difference ea —ea 

reflects the absorptive capacity of air moving across 

the water surface, and the wind speed, u, represents 

the rate of transport for the absorbed water vapor.

The water-budget equation (simplified for computational convenience) is of the form

&HA =E+6 (2) 

where

AHA =average change in water-surface elevation 

adjusted for inflow, outflow (including 

diversions), and rainfall, in feet; 

E= evaporation, in feet; 

5=net ground-water seepage, in feet.

Equation 2 was derived from the more complex waterbudget equation, in which evaporation and other lake 

losses are positive:

E-AH+(0-r)-R+8=0 (3) 

where

Aff = average change in water-surface elevf .tidn,

in feet;

(0—1} = total outflow minus inflow, in cubic feet 

per second, but converted to an equivalent depth in feet over lake surface; 

#=rainfall, in feet.

The following substitution is made to simplify computations:

(4)

and equation 3 reduces to equation 2. 

The simultaneous solution of equations 1 and 2 gives,

0 -e&) +8 (5)

the equation by which the parameters 8 and N were 

evaluated to define the Lake Michie mass-transfer and 

water-budget calibration.

Equations similar in form to equation 5 have been 

successfully used to develop calibrations for several 

lakes and small stock ponds in the western United 

States, where surface water flow was small or nonexistent, and therefore water budgets were determined with 

relative ease.

The mass-transfer concept is old, and consequently 

there are many mass-transfer equations predating the 

one used in this study. Equation 1 was originally suggested in the Lake Hefner and Lake Mead studies; 

it is very similar to many of the older mass-transfer 

equations, which show evaporation to be proportioral to 

wind speed and to saturation vapor pressure minus air 

vapor pressure. Usually, these equations include 

various complex factors to adjust for minor variations; 

some include constants of proportionality to impose 

dimensional exactness; others are mathematically 

derived (Harbeck and others, 1958, p. 29-35). Equation 1 was primarily designed for practical application. 

(See Harbeck, 1962.)

Recent evaporation studies indicate that Harbeck's 

equation is adequate to define lake evaporation whereas 

other mass-transfer equations are not, because complex 

structure makes a practical numerical evaluation impossible. The basic advantages of equation 5 are 

simplicity in application and practicality of field 

instrumentation.

Lakes and reservoirs that have large inflows, outflows, 

and seepage rates usually produce large errors in waterbudget computation; consequently, it may be impossible
142 STUDIES OF EVAPORATION

to develop a calibration using hydrographic data. 

Because of this inadequacy or for other reasons, a 

measure of evaporation by energy-budget techniques 

may be substituted for the water budget to develop a 

mass-transfer coefficient, N. However, this use of 

the energy-budget method is expensive and also restrictive in that it eliminates seepage (5) from equation 

5. This may or may not be a desirable feature in a 

particular situation.

COMPUTATIONS

HYDROGRAPHIC DATA: ADJUSTED CHANGE IN STAGE,

AffA

The change in lake stage, AH, is the average difference between midnight readings (for a calibration period 

of the two stage gages. This average change in stage, 

when adjusted for inflow, outflow, and rainfall, is the 

water-budget estimate of evaporation and seepage and 

is denoted by &HA . The computational procedure is 

shown schematically in figure 40 and is demonstrated by 

two examples in table 2. At the beginning of the study, 

computations such as those in table 2 were made for 

each day, and trial plotting points were obtained by

AH

Average change in lake 

stage (feet)

Inflow (cubic feet per 

second)

Outflow including pumpage (cubic feet per 

second)

Total precipitation 

observed at dam 

(feet)

AHA =AH-fO-/j + R 

Equivalent water-budget 

evaporation plus net 

seepage (feet)

FIGURE 40.—Determination of adjusted change in stage, A/fA .

averaging selected groups of days. After final selection 

of plotting points full periods were recomputed as 

shown, thus eliminating computational errors. The 

plotting points finally selected are summarized in table 

4. The calibration is shown in figure 44 and is discussed 

later in this report.

TABLE 2.—Examples of computation of adjusted change in stage, AHA, for calibration points

Date_-__. -__-_-_-_--.___.._____ ..............

Lake stage, in feet: 

At bridge... _ .....

Net change __

AH...._____ ........... ,.

Rainfall, R, in feet.. . .

Streamflow, in cfs: 

Inflow, 7:

Total inflow _

Outflow, 0:

Total outflow..... __ __________________ _____________

Outflow minus inflow (0—7). _____________ _____ _____

A#A =AH-(0-/)+.R:

Calibration Point 7, Nov. l-«, 1961

1 i

11.34

26.52

0

11 

.7 

.3

12.0

18.7 

11

29.7

19.0

2

0

11 

.7 

.3

12.0

20.4 

11

31.4

19.0

3

0.005

11 

.7 

.3

12.0

20.4 

11

31.4

19.0

4

0.008

12 

.8 

.3

13.1

19.3 

11

30.3

19.0

5

0

12 

.8 

.3

13.1

19.1 

11

30.1

18.9

62

10.91

26.09

0

12 

.8 

.3

13.1

20.4 

11

31.4

18.9

Total 

period

0.43

.43

.43

.013

75.3

184.3 

109

19.0

.496

-.053

-.009

Calibration Pofnt 24, Oct. 23-26, 1962

231

12.35

27.64

0

11

.6 

.2

11.8

18.4 

12

30.4

19.6

24

0

11 

.5 

.2

11.7

18.6 

12

30.6

19.6

25

0

11 

.5 

.2

11.7

24.1 

12

36.1

19.6

262

11.94

27.14

0

11

.5 

.2

11.7

21.3 

12

33.3

19.5

Total 

period

0.41

.40 

.405 

0

46.9

130.4

84

19.6 

.370

.035 

.009

1 0000 hours.

2 2400 hours.
EVAPORATION STUDY IN A HUMID REGION, LAKE MICHIE, NORTH CAROLINA 143

OUTFLOW AND INFLOW

Inflow (/) is the sum of streamflow observed at the 

gaging stations (Flat River at Bahama, N.C., and Dial 

Creek near Bahama, N.C.) and the estimated inflow 

from about 15 square miles of ungaged drainage. The 

ungaged surface inflow was estimated from a regression 

(shown in fig. 41) established by relating discharge at 

the Dial Creek gage to estimates of the ungaged inflow. 

The estimates were based on periodic observations of 

streamflow, made primarily during base-flow periods, 

at eight sites on small tributaries.

The total outflow, 0, is computed as the sum of the 

discharge observed at the outflow gage (Flat River at 

dam near Bahama) plus diversions to Durham and 

Camp Butner. The diversion is recorded daily at the 

Lake Michie dam and is furnished monthly to the 

Geological Survey by the city of Durham.

Stage-area relation.—A stage-area curve of relation is 

required for conversion of outflow minus inflow, 0—I 

(in cfs), to an equivalent depth in feet over the lake 

surface as is shown in table 2. Unfortunately, a usable 

relation was not available for the Lake Michie study; 

a stage-area relation was developed from data collected 

from a local engineering firm, the U.S. Soil Conservation Service, and the North Carolina Department of

Conservation and Development. Data from those 

sources were supplemented by surface-area estimates 

made from aerial photographs and from reservoir and 

high-flow records.

Lake areas estimated from high-flow records were 

used as a supplement because the relation was poorly 

defined at intermediate lake stages and there were 

disagreements between the various sources of information. These computed data provided the additional 

information necessary to define the relation for stages 

ranging from 322 to 350 feet above mean sea level. 

They were computed from the observed incremental 

changes in lake stage and flood volumes gaged during 

flood periods of a few hours. Areas were computed as 

the quotient of gaged volume and change in stag''1, and 

were plotted against the average lake stage observed 

during the incremental flood period. The stag>area 

curve is shown in figure 42. Although this relation is 

probably the most accurate that could be obtained 

with available data, a certain degree of error is inherent 

in the basic relation, and this error probably varies 

with stage.

ERRORS IN HYDROGRAPHIC DATA

The errors associated with the determination o^ &HA 

result from errors in AH, and 0—1. The errors in AH

DIAL CREEK DISCHARGE, CUBIC FEET SECOND IN PER 

[° J>CTiOOC O >-- 

b bbbc j>CT>bob K)!-• /•^ 

X

>-

^

*

oxxxX

X

x

X1 x

^

^^O

/

x^ O

^

^-

*^X

X

X

X

r

X

X

X

-e ——

X

X

1

-€Y0.01 0.02 0.04 0.06 0.1 0.2 0.4 0.6 0.8 1

UNGAGED INFLOW, IN CUBIC FEET PER SECOND

8 10

FIGURE 41.—Ungaged inflow plotted against Dial Creek discharge.
144 STUDIES OF EVAPORATION

354

350

346

uj 342

338

O 334

m

<

UJ

O 

<

fc 330

326

322

AREA, IN ACRES 

300 400 500 600 700

1 1 1 1 1

/

/

/

/

f

/

y

/

Cres

J

/

tof c

./

/

ami

/

12 16 20 24 28 32 

AREA, IN MILLIONS OF SQUARE FEET

FIGURE 42.—Stage-area relation.

are the result of wave action, seiche action, areal 

variation (slope in lake), and purely instrumental 

inadequacies. Most of the errors were avoided by 

rejection of certain lake-stage data for use in developing 

the calibration, as discussed later.

Discharges are subject to errors of 5 percent or more 

in the components 0 and /; therefore, the consequent 

error in the difference 0—1 could be larger than the 

error in either individual component and could influence 

the accuracy of the calibration curve.

An analysis was made of the water-budget calibration 

data to determine the relative errors in the computed 

adjusted change in lake stage, resulting from errors 

occurring in the total surface inflow. The analysis is 

shown in table 3.

Inflow rates ranging from 3 to 40 cfs are typical of 

the periods used in determining the calibration. The 

percentages shown in the last column are computed on 

the basis of AHA =0.0056 feet per day, which is the 

average (disregarding signs) of those data shown in 

the fourth column of table 4. Gaging-station records 

used in the Lake Michie study are rated excellent or 

good (5-10 percent), and pumpage records may be 

assumed to be reliable.

The size of the errors shown in table 3 demonstrates 

the necessity of placing restrictions on flow data selected 

for computing calibration points. Tie errors vary 

inversely with the lake area, a fact which indicates the 

critical relationship between lake size and streamflow.

Outflow is an additional source of error hi computing 

calibration points. Errors in each of tl e gaging station 

records are independent; the combined effect is reduced 

to a single random error component and does not 

seriously restrict calibration computation.

TABLE 3.—Errors in adjusted change in stage resulting from normal 

errors in streamflow record?

Inflow (cfs)

46———————————————

27——————————————

17——————————————

10.5. — ————— ——— —— — —

5.5.——————— ———————— —

3.O.——— ———— ————— ————— -

1.5. ———— — — —— ———— ———

Recurrence 

interval of 

minimum 

annual flow 

(years)

1.05 

1.2 

1.5 

2 

3 

5 

10

5 percent error in inflow

cfs

2.3 

1.4

.85 

.52 

.28 

.15 

.08

feet per day

0.0095 

.0058 

.0035 

.0021 

.0012 

.0006 

.0003

Error In 

AHA 

(percent)

170 

104 

62 

37 

21 

11 

5

The total error in AH" is also due to errors in the 

stage-area relation, and in pumpage and stage records, 

and to variations in net seepage. All euch errors cause 

points on the calibration curve to scatter. To minimize this scattering, the following limiting conditions 

were used in evaluating the water-budget equation:

1. Uniform stage hydrograph: |AH|<C.20 feet per day.

2. Negligible rainfall during period.

3. Small, uniform discharge at inflow stations:

(a) Dial Creek discharge <2 cfs.

(b) Flat River discharge <40 cfs.

(exceptions: points 12 and 25, table 4).

4. Uniform outflow.

5. Accurate gaging station and pumpage records—no 

periods of estimated record were included.

Calibration points still scatter, despite these precautions; nevertheless, the average curve is well defined 

in the range where all but rare period^1 of evaporation 

occur. Thus estimates of evaporation are possible 

within acceptable limits of accuracy.

METEOROLOGICAL DATA: THE MAS^-TRANSFER 

PRODUCT, u(eo-e a)

The meteorological instruments us<»-d hi the Lake 

Michie evaporation study are listed hi table 1 and 

several are shown in figures 38 and 39. The computational procedure is diagrammed in figure 43.

SATURATION VAPOR PRESSURF

The water-surface temperature was continuously 

recorded at the Lake Michie raft station, first by a 

weekly recorder and later by a continuous recorder, 

shown in figure 39.
EVAPORATION STUDY IN A HUMID REGION, LAKE MICHIE, NORTH CAROLINA 145

Water-surface temperature 

observed at raft station

Ta ,f

Air temperature and relative humidity observed 

at Lake Michie or at 

Raleigh-Durham Airport

Wind observed at 

raft station

FIGURE 43.—Daily computation of the mass-transfer product, u(e<>—ea).

Graphical daily averages of water-surface temperature, TQ , are determined from recorder charts and 

converted to saturation vapor pressure, e0 , by means of 

standard vapor-pressure tables. During early stages 

of the study, analytical comparisons were made to find 

the most feasible computational method for determining daily average vapor pressures, since the relation of 

temperature and vapor pressure is curvilinear. These 

comparisons indicated that vapor pressures determined 

directly from daily average temperatures are sufficiently 

accurate, and determination from smaller incremental 

averages is unwarranted.

WIND SPEED

The wind movement, u, at a height of 2 meters 

above Lake Michie is recorded by a totalizing anemometer on the raft, and the data are averaged for 24-hour 

periods and tabulated in units of miles per hour. 

Some wind records used in the study were incomplete 

in minor details, and it was necessary to use estimated 

values adjusted to the total wind movement during 

a chart period.

AIR VAPOR PRESSURE

The air vapor pressure, ea, is defined as the product 

of saturation vapor pressure, eg) and relative humidity,/. 

Observed dry-bulb temperature, Ta, and standard 

tables of vapor pressure are used to determine es. Air 

vapor pressure, ea, is a product involving the daily 

average relative humidity and is subject to an additional error from averaging. Preliminary investigations 

to find the most feasible method of determining ea 

indicated that the product of daily averages resulted 

in values of usable accuracy, and that the added refinement of subdividing the factors Ta and / was not 

necessary.

Dry-bulb temperature and relative humidity were 

recorded at the Lake Michie weather station by a 

hygrothermograph tor the period September 1961 to 

December 1962. A statistical analysis of 475 daily 

means of air vapor pressure observed at Lake Michie 

and at Raleigh-Durham Airport (about 20 miles south

of Lake Michie) indicated that vapor pressures t,t the 

two locations are almost identical and are related by 

the equation

F=1.00J£+0.35 (6) 

where

F=Lake Michie air vapor pressure, in milTbars; 

X— Raleigh-Durham Airport air vapor pressure, 

in millibars.

The standard error of estimate is 1.20 millibars, or 

about 8.8 percent of the mean vapor pressure observed 

at Lake Michie during the period September 19"! to 

December 1962, and the correlation coefficient is 0.99. 

This similarity eliminated the need for continuing 

operation of the hygrothermograph at the Lake Michie 

weather station.

ERRORS IN METEOROLOGICAL DATA

Errors in e0 and ea resulting from instrumental or 

computational errors in the daily average of T0 and Ta 

should be kept to a minimum because errors of 2°F 

could produce errors in u(e0 —ea) up to 25 percent or 

more, depending upon the season. For example, if 

the mass-transfer product, u(e0 —ea), is subject to an 

error in e0 resulting from an error of A£ degrees in 

determining TQ)

relative error, in percent =

(e0—ea)

(7)

where

= the erroneous vapor pressure corresponding 

to T0 +At.

The following table indicates the possible relative 

errors in u(e0 — ea) resulting from an error of 2°F in 

T0 , for typical Lake Michie seasonal values (February 

and July) of T0 and Ta. Vapor pressures are in 

millibars.

T0

(July) 83°F-____.-_-___

(Feb) 42°F.__ __________

eo

38. 5

9.1

60+2° F

41.0

9.8

ea

25.2

6. 5

Relative 

error

19

28

Because errors of 2°F in the daily water-surface 

temperature cause large errors in the daily term, 

u(e0 —ea), care was taken to correct recorded temperatures to agree with accurate reference thermometers, insuring that errors are largely random and 

noncumulative and thus have a small effect on average 

values computed from 7 to 25 days of record. Such 

errors in the different plotting periods undoubtedly
146 STUDIES OF EVAPORATION

tend to compensate; but when the plotting period is 

short, as in the upper end of the calibration curve, 

which is defined by some 2-day averages, the lake 

calibration computations may be influenced. Similar 

errors in Ta and/ also produce errors in u(e0—ea).

Another source of error in evaluation of the calibration equation is the lack of homogeneity in data 

observed at the raft location during the calibration 

period. The assumption was made that data observed 

at the present raft location and true lake data are 

proportional; or more simply, that actual changes in 

the lake's environment are equivalent to changes in 

data observed at the raft. Hence, if calibration equations were developed for two different points on the 

lake (two different mass-transfer coefficients), the 

evaporation values computed from these two equations 

would be nearly equivalent—if no serious sampling 

errors were inherent in the data.

Sampling errors involve both wind and temperature 

data. Water temperature data collected during periodic thermal surveys have shown areal variations to be 

small and of minor concern. Wind movement offers 

greater possibility of error. One could hypothesize 

that a comparison of variation in the wind data observed at the raft with variations in actual wind 

conditions (if known) for the entire lake would exhibit

0.03

an extremely high degree of correlation and that slight 

differences would average out in a sufficiently long 

period. On the other hand, significant variations in 

the data, such as a seasonal bias, could occur during 

the usually short calibration period. This type of 

effect could cause large errors in tl °> mass-transfer 

coefficient, and therefore a raft locatior must be chosen 

that will assure representative data (good sampling). 

Such a location may be assumed to be an adequate 

precaution.

THE CALIBRATION CUBVE

PLOTTING AND LIMITATIONS OF PERIODS

The Lake Michie calibration cur^e is shown in 

figure 44. The plotting points, whict represent averages of &HA (ordinate) and u(e0—ea) (abscissa) for 41 

selected periods ranging in length from 2 to 25 days, 

were compiled using the limitations discussed above in 

the section titled "Errors in Hydrographic Data." 

The plotting points are shown in table 4.

During the first year of hydrographic record at 

Lake Michie (September 1961 to August 1962) few 

periods were suitable for computing points for the 

calibration curve because frequent rains made streamflow excessive, and the required accuracy in determining 

changes in lake storage could not be met. Weather

0.02

a o.oi

-o.oi

-0.02

110 120

FIGURE 44.—Calibration curve.
EVAPORATION STUDY IN A HUMID REGION, LAKE MICHIE, NORTH CAROLINA 147

conditions during the next season (summer of 1963) 

were more favorable. Deficiency of the normally 

abundant rains during the spring and early summer 

caused a drought in the Lake Michie drainage basin. 

Streams receded to annual minimum flows having 

recurrence intervals of 2-5 years; thus, the streamflow 

data needed for accurate determination of changes in 

the water budget became available. These low flows, in 

conjunction with wide variations in the meteorological 

data (especially in wind speed), provided the records 

used to define the calibration. Without this drought, 

the necessary low flows would have been rare, and 

several more seasons might have been required to 

develop the calibration.

As indicated in table 4, several 2-day averages were 

used to compute calibration points. This was necessary 

to obtain better definition of the upper portion of the 

calibration. Also, some of the high plotting points 

were necessarily dependent; that is, several periods of 

2—4 days of high evaporation occurred during longer 

periods for which points were plotted (Nos. 2 and 28, 

table 4, for example). The upper end of the curve

TABLE 4.—Calibration data

Number

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

Period

Dates

1961

15-16——— — ——— ——— — —

Oct. 5-14————— — ——— — ———

15-19— —— —— — ——— ————

22-Nov. 2———— —— —— ———

Nov. 1-6—— —— — ——————

7-11—————————— ——

13-18—— —————————....

20-22——— ———— ———— ———

24-Dec. 9— — ——— — —— — —

1962

July 8-11————————————

18-24-.- —— — - — — — — ——

26-Aug. 2.—— — — - — ----.

Aug. 12-15... — ————— — — —

18-20.-——— — — —— —————

18-25—— — ——— — — — —

28-Oct. 3— — — — — —— -

Oct. 6-30——————————

13-16—— ———————— —

23-26———— — ————— — — —

1983 

May 9-15..——— —— — — — —

12-13__————————— —

12-15-- ————— — ——— ——— —

19-30.--. _-_ ——— —— —— —

July 12-22— ——— ————— ___ ———

24-27—— ————— ————— ———

Aug. 3-20-- —— — ———— ——— ——

13-15--——— — ———— ——— —

23-Sept. 9----. __ __ _ __

Sept. 16-27.- _ ——— ———— — ————

22-24— — —— ——— — —————

Oct. 1-15——— ——— — ———— —

20-21.- —— ——— ——— — ————

1964 

June 11-14...... ——— — ———— _ -

July 3-7— —— — —— — -. ——— „

Number 

of days

11

10

10

5

19

6

5

6

3

16

5

4

7

8

4

3

12

10

8

6

25

4

4

13

7

9

4

12

11

4

18

3

18

12

3

15

2

4

5

Adjusted 

change in

stage, &HA 

(feet per 

day)

0.004

.018

.003

-.002

.001

0

-.009

.008

-.011

.001

-.005

-.003

-.001

.001

.003

0

-.003

.002

.004

0

-.002

.002

-.010

.009

-.001

.003

.006

.014

-.010

-.001

-.002

.005

.011

.001

.007

.021

.006

.012

.004

.008

Average 

u(e0— ««)

u in miles 

per hour 

« in 

millibars

37.4

110

Oo I

14 7

23.4

6.5

44.3

U K

36.7

24.1

58.7

AQ O

EO 7

42.0

36.7

19 Q

39.7

34.2

46.6

36.2

11.6

71 ft

26.3

4<i 1

U 1

78.1

34.1

47.5

34.0

52.5

72.4

39.5

46.7

94.8

34.5

70.7

51.2

53.4

should be better defined; therefore, the necessary waterbudget instruments are being kept in operation and 

additional (and possibly longer) periods of high evaporation will be plotted as they occur (for example, see 

points 40 and 41, table 4).|

CHARACTERISTICS OF THE CALIBRATION

The equation of the Lake Michie calibration shown 

in figure 44 is

&HA =(E+ 5)=0.00030 u(e0 -ea}-0.011 (8)

where)

AHA =ad justed change in lake stage (also equivalent to water-budget evaporation and net 

seepage), in feet per day; 

0.00030 ^(^0—e0 )=mass-transfer evaporation, in

feet per day; 

—0.011 =net seepage (seasonal average), in feet

| per day.)

The mass-transfer coefficient (N— 0.00030, evaporation in feet per day; or 0.0036, evaporation in inches 

per day) shows general agreement with coefficients from 

lakes and reservoirs similar to Lake Michie in size, 

when plotted on an approximate relation suggested by 

Harbeck (1962, fig. 31).|

Variation of the seepage rate with different watertable conditions was investigated to evaluate its effect 

on the lake calibration. The conclusion was th«.t the 

deviations of the plotted points on the calibration curve 

could be assumed to be partly due to the variation in 

seepage and could be isolated (approximately) by relating the total deviation to Dial Creek discharge.

The equation of the multiple relation shovrn in 

figure 45 is

(#+«) =0.00030 u(eo-ea} - (0.0087+0.0031 &>) (9) 

where evaporation is given by 0.00030 u(eQ —ea), the 

variable seepage component is — (0.0087+0.0031 QD], 

and QD is Dial Creek discharge.)

Dial Creek discharge is probably a fair indicator of 

the surrounding ground-water conditions because base 

flow is primarily a function of the ground-water conditions. However, the Dial Creek gage is at a higher 

elevation and some distance from Lake Michie, an d the 

relation between ground-water levels (as reflected by 

streamflow records) and seepage may be partly obscured 

by time lag resulting from the slow movement of ground 

water.

Generally, in determining the calibration parameters 

mass-transfer coefficient, N, and seepage, 8, the seepage 

rate (although it is a secondary consideration to the 

water budget) must be known, nonexistent, or nearly 

constant. Where net seepage variation is significant, a 

reliable calibration may be difficult or impossible to 

develop if an adjustment for seepage cannot be made.
148 STUDIES OF EVAPORATION

0.2 0.6 0.8 1.0 1.2 1.4 1.6 1.8 

DIAL CREEK DISCHARGE. IN CUBIC FEET PER SECOND

FIGUBE 45.—Deviations from the calibration curve plotted against Dial Creek discharge.

2.0 2.2 2.4

Seepage (net) at Lake Michie is variable, as demonstrated ; hence all winter records that were characterized 

by exceedingly high and probably varying seepage rates 

were eliminated. After the best data were selected, 

points on the calibration still displayed a certain 

amount of variation. Although these residual variations contain many error components, the seepage rate 

is a significant one. It is not sufficiently large, however, 

to render calibration impossible for Lake Michie.

The relation in figure 45 was not used to estimate 

seepage but was developed to demonstrate its variability. More data would be required to develop a 

relation sufficiently well defined to allow derivation of 

reliable estimates of seepage.

Nearly complete streamflow, rainfall, and pumpage 

data are available for Lake Michie from 1927 to the 

present. Thus it was possible to make a comparison 

of the seasonal seepage rate with an approximate longterm estimate of annual ground-water seepage, using 

the expanded water-budget equation 3:

E-AH+ (0—I)—R+d=Q

where AH is virtually zero over a long period; evaporation was estimated from current short-term data. 

Annual net seepage is estimated to be about — 5% cfs 

as compared with the seasonal (May through November) estimate of —2% cfs, which corresponds to the 

negative intercept of the calibration curve. Probable 

errors are too large to permit quantitative comparisons 

between these two estimates, but the difference suggests 

that winter seepage is probably much greater than that 

during other seasons.

APPLICATION OF THE CALIBRATION

The monthly totals of Lake Michn mass-transfer 

evaporation shown in table 5 were computed using the 

equation

#=0.0036 Stt(e0 -ea) (10)

which shows monthly evaporation (in inches) as the 

product of the monthly sum, Sit(ec —ea), and the 

mass-transfer coefficient, A^= 0.0036.

TABLE 5.—Monthly evaporation, in inches

1QA1

1962.-.——-

1963

1WU

Apr.

3.68

4.44

May

5.10

4.20

A Kfl

June

5.39

4.32

4.10

July

4.85

5.14

4.52

Aug.

4.38

5.20

4.05

Sept.

4.03

3.78

5.02

4.57

Oct.

3.46

3.58

4.04

2.89

Nov.

2.65

2.73

Records of monthly evaporation ard precipitation 

are graphically shown in figure 46. Precipitation is 

the average of that observed at Lake I lichie dam and 

at Rougemont, several miles northwest of the lake. 

Rough approximations of typical monthly values of 

evaporation plus seepage (shown in fig. 47) indicate a 

net water loss for May through September of about 110 

acre-feet. Annual evaporation is estimated to be 

about 39 inches or 1,550 acre-feet.

Reliable estimates of normal montliy evaporation 

cannot be determined from data collected to date, and 

therefore a program of data collection is being carried 

on so that adequate estimates can eventually be made. 

Mass-transfer data and computed evaporation will be 

compiled in a future report.
•

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EVAPORATION AND PRECIPIT
150 STUDIES OF EVAPORATION

SELECTED REFERENCES

Harbeck, G. E., Jr., 1962, A practical field technique for measuring reservoir evaporation utilizing mass-transfer theory: 

U.S. .Geol. Survey Prof. Paper 272-E, p. 101-102, 104.

Harbeck, G. E., Jr., Golden, H. G., and Harvey, E. J., 1961, 

Effect of irrigation withdrawals on stage of Lake Washington, 

Mississippi: U.S. Geol. Survey Water-Supply Paper 1460-1, 

367-373.

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, p. 29-35, 75.

Langbein, W. B., Hains, C. H., and Culler, R. C., 1951, Hydrology of stock-water reservoirs in Arizona: U.S. Geol. Survey

Circ. 110, p. 13-15. 

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

hydrologic definitions: U.S. Geol. Survey Water-Supply

Paper 1541-A, p. 1-29. 

Linsley, R. K., Kohler, M. A., and Paulhus, J. L. H., 1958,

Hydrology for engineers: New York, McGraw-Hill Book

Co., p. 90-121. 

Robinson, T. W., and Johnson, A. L, 1961, Sebcted bibliography

on evaporation and transpiration: U.S. Geol. Survey

Water-Supply Paper 1539-R, p. R1-R25. 

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

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

Paper 269, p. 46-69, 136-151.

U. S. GOVERNMENT PRINTING OFFICE : 1966 - 209-983