Comparison of Evaporation 

Computation Methods, 

Pretty Lake, Lagrange County, 

Northeastern Indiana

GEOLOGICAL SURVEY PROFESSIONAL PAPER 686-A
Comparison of Evaporation 

Computation Methods, 

Pretty Lake, Lagrange County, 

Northeastern Indiana

By JOHN F. FICKE

HYDROLOGIC AND BIOLOGICAL STUDIES OF 

PRETTY LAKE, INDIANA

GEOLOGICAL SURVEY PROFESSIONAL PAPER 686-A

Studies using Jive common computation methods 

found the mass-transfer method best suited for 

year-round measurement of evaporation rates

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1972
UNITED STATES DEPARTMENT OF THE INTERIOR 

ROGERS C. B. MORTON, Secretary

GEOLOGICAL SURVEY 

V. E. McKelvey, Director

Library of Congress catalog-card No: 78-179296

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

Washington, D.C. 20402 - Price 70 cents (paper cover)

Stock Number 2401-1144
CONTENTS

Page

Symbols. __________________________________________ V

Abstract_ ________________________________________ Al

Introduction. ______________________________________ 1

Acknowledgments___ __________________________ 2

Description of Pretty Lake_________________________ 2

Temperature patterns.__________________________ 5

Instrumentation and its operation ____________________ 5

Instrumentation for water budget_______________ 5

Instrumentation for energy budget._______________ 7

Thermal surveys__________________________ 9

Instrumentation for measuring mass-transfer parameters-,..............,,. ____________________ 9

Evaporation pans_____________________________ 9

Energy-budget studies__.__________________________ 9

Instrument records.___________________________ 10

Changes in energy storage.______________________ 14

Interrelation of Q e, Qh, and Q w and the Bowen ratio. _ 14

Results of energy-budget studies________________ 15

Sediment heating effects.____________________ 15

Mass-transfer studies______________________________ 18

Instrument records____________________________ 19

Mass-transfer coefficient from energy-budget

calibration. __________________________________ 19

Computation of evaporation by mass transfer. _____ 22

	Page 

Water-budget studies______________________________ A23

Instrument records_______________-__---_--_--_ 23

Balancing the water budget (seepage correction) _ _ _ _ 24

Evaporation from the water budget.___-______--__ 28

Evaporation-pan studies.__________-______----------_ 29

Kendallville station data____________ ___________ 29

Computed pan and lake evaporation-_____________ 32

Advection and energy-storage effects._____________ 32

Wintertime evaporation and energy budget _______ 33

Observed winter conditions_____________________ 34

Application of open-water evaporation methods to

winter conditions___ ____________________ 35

Limited pan season__ _ ______________----_---- 35

Water-budget application_________._--_----__ 35

Mass-transfer method_____________-___-_-- 36

Winter energy budget_____ _ ____________----_---_- 36

Comparison of results__ _ ________________--_-------_ 38

Results summarized.__________________-_--_----- 38

Characteristics of results from individual methods. _ 38

Conclusions._ _________________-_---------_--------- 46

References.___________________-_------------------- 47

Index---____-----_--------_-- ------------------ 49

ILLUSTRATIONS

Page

FIGURE 1.

2.

3. 

4-9.

Map of Pretty Lake study site. _ _____________________-__-----_----------------------------------- A3

Map of bottom configuration of Pretty Lake_____________________----_-------_---------------------

Graph of temperature patterns.___________________-____-______-----------------------------------

Photographs:

4. Stream-gaging station on Pretty Lake inlet-_________-_----_---------------------------------

5. Lake-stage control weir and recording gage on outlet channel-________-____--------------------

6. Nonrecording rain gage at edge of Pretty Lake__________________----_-----------------------

7. Lake-stage gage located at public access area____________-_----------------------------------

8. Temperature- and radiation-measuring equipment--______-_____------------------------------

9. Instrument raft,____________________________--_____-_------_-----------------------------

10. Time graphs of solar radiation (Q.)_______________________-___------------------------------------

11. Graphs showing relation of long-wave radiation (Q~) as measured by flat-plate radiometers and as computed 

by the Koberg method._____________________________________--------------------------------

12-14. Time graphs:

12. Long-wave radiation (Qa )_____._________________________---_------------------------------

13. Air and water-surface temperature records. _ _____________-_--_-----------------------------

14. Vapor-pressure records.______________________-______----__-------------------------------

in

5

6

6

7

7

9

10

11

12
IV CONTENTS

19.

20.

21.

22.

23. 

24-26.

27.

28.

29.

30.

31.

Page 

Graphs showing yearly temperature and heat-storage pattern of Pretty Lake sediment-__. ____--._______ A17

18

20

21

22

24

FIGURE 15.

16. Graph showing estimated annual cycle of average heat storage in sediment_________________________

17. Time graphs of wind speeds__________________________________________________________________

18. Graph showing relation of mass-transfer product to evaporation measured by the energy-budget method 

Graph of mass-transfer coefficients determined by different methods _______-____--_-_-____!.--__-__-.

Pretty Lake inlet hydrographs.___________________-____-____-___----_--___--_----__---_----_..

Pretty Lake outflow hydrographs._______._________________-___-__---_-__--_---

Pretty Lake stage hydrographs....__._.___..._______________________-_____---_

Graphs of daily precipitation measured at Pretty Lake___________________________

Graphs showing:

24. Relation of corrected stage change to the mass-transfer product.---________

25. Relation of corrected stage change to the mass-transfer product by subperiods _

26. Seepage during 1964 and 1965 open-water periods. ___-___-_______-._____--

Graph showing diurnal fluctuation of air and ice-surface temperatures.- - _____________

Time graphs of wintertime vapor pressure _________-______-_---_-----_---_-------

Graphs showing wintertime relation of the mass-transfer product and the water budget. 

Hydrographs of evaporation rates computed by different methods. __________________

Bar-graph comparison of summarized evaporation results __________________________

25

26

26

27

29

30

36

37

38

42

44

TABLES

TABLE 1. Periods of use for flat-plate radiometers at Pretty Lake----------------------------------------------

2. Summary of data from flat-plate radiometers.________________-_____--_--___------------------------

3. Summary of energy-budget terms and evaporation computation for open-water periods, l963-65-_____.-_-

4. Estimated energy conducted as sensible heat (Q A), according to equation 7 and assuming JV=0.0060_ _____

5. Summary of mass-transfer terms for open-water periods, 1963-65_______-___-_____---_--_-------------

6. Summary of water-budget terms for Pretty Lake open-water periods, 1963-65______________-_---_-__---

7. Corrections for seepage applied to. water budget, and water-budget evaporation.---_________-_-_-___----

8. Daily evaporation from U.S. Weather Bureau class-A pan at Kendallville, IncL____---_----------------

9. Daily evaporation from U.S. Weather Bureau class-A pan at Culver Experiment Farm, Ind_____-__-___--

10. Lake evaporation based upon data from Kendallville or Culver pan and average annual coefficient of 0.76, 

computed by Pretty Lake energy-budget periods__________________---_--------------------------

11. Computed pan and lake evaporation by use of U.S. Weather Bureau method with Pretty Lake station data__

12. Advection and storage corrections for pan-based evaporation data__________________---.--------------

13. Computed wintertime pan and lake evaporation for open-water periods that were not included in table 11- 

.TABLE 14. Wintertime water-budget terms_________________________-_________-------_------------------------

15. Summary of wintertime mass-transfer terms for Pretty Lake, with evaporation computed by equation 14_.

16. Estimated terms for wintertime energy budget. ____________________--__-__-_-----------------------

17. Summary of data requirements for different evaporation computation methods____________-_-----------

18. Pretty Lake evaporation as computed by different methods for open-water periods, 1963-65 ___-_-_-_:-

19. Pretty Lake evaporation as computed by different methods for wintertime periods, 1963-65 ___________

20. Summary of Pretty Lake evaporation, as computed by different methods, for similar periods during 1963-65_ _

21. Annual and May-October evaporation from Pretty Lake---------------------------------------------

Page

A10

11

16

17

22

28

29

31

31

32

33

34

35

35

36

39

39

39

41

41

46
SYMBOLS

A Surface area.

c Specific heat of water.

E Evaporation.

EEB Evaporation computed by the energy-budget method.

EMT Evaporation computed by the mass-transfer method.

EWB Evaporation computed by the water-budget method.

ea Vapor pressure of the air.

e,Q Saturation vapor pressure at the temperature of the water

	surface.

G Net underground seepage.

I Surface inflow.

I v Precipitation falling on lake.

L Latent heat of vaporization of water.

N Mass transfer coefficient.

n Number of days in an evaporation-computation period.

O Surface outflow.

Pa Atmospheric pressure.

pm Period of the temperature stress on the lake sediment.

Q a Incoming long-wave radiation.

Qar Reflected .long-wave radiation.

Qbs Long-wave radiation from the water.

Q e Energy used for evaporation.

Qh Energy conducted from the water as sensible heat.

Qm Total heat flow per unit area into the sediment during

	an annual cycle. 

Q r Reflected solar radiation.

AEL

be 

AH

AS 

AT 

7 

P

Incoming solar radiation.

Net energy advected into the lake.

Energy advected by evaporating water.

Increase in stored energy.

Bowen ratio.

Thermal conductivity of the sediment.

Dry-bulb air temperature.

Arbitrary base temperature (0°C) used in energy

computations.

Temperature of evaporated water. 

Amplitude of temperature stress on sediments. 

Temperature of the water surface.

Windspeed at some height z above the water surface. 

Part of additional energy from advection or storage

that is used in evaporation. 

Thermal diffusivity of the sediment. 

Effect on lake evaporation caused by advected or stored

energy.

Vapor pressure difference equal to (eo ea). 

(E G) fall in stage, corrected for inflow, outflow, and

precipitation. 

Net increase of storage. 

Temperature difference equal to (T0 Ta). 

Constant in the formula used to compute Bowen ratio. 

Density of water.

HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

COMPARISON OF EVAPORATION COMPUTATION METHODS,

PRETTY LAKE, LAGRANGE COUNTY,

NORTHEASTERN INDIANA

By JOHN F. FICKE

ABSTRACT

Evaporation from Pretty Lake has been computed for a 2%- 

year period between 1963 and 1965 by the use of an energy 

budget, mass-transfer parameters, a water budget, a class-A 

pan, and a computed pan evaporation technique. The seasonal 

totals for the different methods are within 8 percent of their 

mean and are within 11 percent of the rate of 79 centimeters 

(31 inches) per year determined from published maps that are 

based on evaporation-pan data. Period-by-period differences 

among the methods are larger than the annual differences, but 

there is a general agreement among the evaporation hydrographs 

produced by the different computation methods.

The energy budget was an excellent means of computing 

unbiased evaporation data for periods of a month or longer from 

June through September. It is not reliable in the springtime, 

when Bowen ratios are large and when the large changes in 

stored energy may be hard to measure accurately owing to errors 

in the capacity table. The need for sophisticated equipment, 

frequent temperature surveys, and complex computations makes 

the energy budget the most expensive of the several methods 

used. Effective use was made of the Koberg method in estimating 

long-wave radiation when accurate instrument records were not 

available. Effects of sediment heating and cooling were computed 

to have influenced evaporation as much as 0.03 cm day" 1 

(centimeters per day) just after the autumnal overturn. The 

change is significant during the fall, when the evaporation for 

Pretty Lake is low, and would be more significant in a shallow 

lake, where the heat storage by the sediment would be large in 

proportion to the storage by the water.

The corrected fall in stage computed by the water-budget 

method agreed well with the evaporation rates computed by 

other methods during the dryer seasons. Decreased rates of fall 

in stage during the wet seasons indicated net inflow seepage that 

was estimated to be equivalent to a stage change of more than 

0.2 cm day" 1 at some times.

Evaporation data based upon class-A pan records and computed 

pan evaporation were too large early in the season and too small 

late in the season. The differences were caused by energy storage, 

which affected the lake evaporation as energy was stored in the 

spring and released late in the season. Energy-storage effects can 

be corrected, but the corrections require some of the same expensive data that were used in the energy budget.

The mass-transfer system proved to be an effective low-cost 

means of computing evaporation, a means that is well suited

to low evaporation rates. The mass-transfer coefficient was determined to be 0.00560 cm hr day- 1 mile" 1 mb" 1 (centimeter per 

day per millibar per mile/hour), the relative standard error of the 

energy-budget calibration being about 6 percent. Springtime and 

autumn evaporation rates computed by the mass-transfer method 

were slightly higher than rates computed by other methods, and 

summer rates from mass-transfer computations were slightly lower 

than rates computed by other methods. Anemometer stalling is 

believed to have caused unreliable mass-transfer evaporation 

data during two periods having very low wind velocities.

Assuming that Pretty Lake is typical of the many small 

natural lakes in its region, it is concluded that in most cases 

the evaporation information needed for hydrologic studies can 

be provided with satisfactory accuracy by a combination of the 

mass-transfer method and one or two other methods, without 

the expense of a complex energy-budget study.

The different methods, although poor, agree that evaporation 

when there is ice cover is generally small (less than 0.1 cm day" 1 ), 

but the evaporation rates during the few days just before freezeup 

or just after ice breakup are significant.

INTRODUCTION

This comparison of evaporation computation methods 

is part of a multiphased project studying the thermal 

and biological characteristics of Pretty Lake. Other 

reports in this series will describe studies of palynology, 

thermal stratification and vertical circulation, and 

phytoplankton populations and biological productivity.

The purposes of the Pretty Lake evaporation studies 

were to evaluate the several common methods for computing lake evaporation and to determine their accuracy 

and general applicability in the central region of the 

United States. Earlier studies of evaporation have been 

conducted mainly in the more arid West, and the 

techniques developed in the western studies have not 

been fully tested in the more humid climates. Energybudget, mass-transfer, water-budget, and evaporationpan techniques have been used to compute evaporation 

from Pretty Lake. Results and methods have been

Al
A2 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

evaluated for accuracy and for ease and economy of 

use.

Pretty Lake was a good site for extended evaluation 

of the evaporation-computation techniques developed 

in the West. It is located in a region of more abundant 

rainfall; this region in the past has had only slight 

concern for evaporation loss, but it is now beginning to 

feel effects of water shortage as demand exceeds supply. 

Furthermore, the hydrology of the Pretty Lake basin 

makes it possible to determine evaporation more precisely than would be possible in most other settings. 

Small quantities of surface inflow and outflow, which 

can be measured accurately, provide the criteria-for 

computing a good water budget. The precision of the 

water budget is supplemented by a condition of small 

subsurface inflow and outflow. The small surface and 

subsurface inflow and outflow reduce the magnitude of 

the advected-energy term, which must be considered 

in an energy budget or in the application of standardpan data. The nearly circular shape of Pretty Lake 

provides the best conditions one would expect to find 

for measuring the temperature and wind parameters 

that are part of mass-transfer or energy-budget computations of evaporation.

ACKNOWLEDGMENTS

Studies of evaporation computation for Pretty Lake 

were operated as a project of the U.S. Geological 

Survey, Water Resources Division. Harvey Rutstein 

provided valuable help in the field measurements and 

computation of data. Additional assistance was provided 

by Robert G. Lipscomb and Phillip Reed. Technical 

advice and manuscript review were by G. Earl Harbeck, 

Jr., Rolland W. Carter, Malcolm D. Hale, W. S. 

Eisenlohr, and Gordon E. Koberg. Instrumentation 

advice and calibration were provided by C. R. Daum.

The Indiana Department of Natural Resources generously permitted the project to operate its instrumentation and field laboratory on the public access area 

it maintains on Pretty Lake. The Indiana University 

Department of Zoology permitted use of its solarradiation data.

Special acknowledgment is due the people who reside 

near Pretty Lake. They have given the use of their 

property, and their assistance in many instances provided an extremely valuable service.

The Indiana Institute of Technology, Fort Wayne, 

Ind., has generously provided the project with office 

space, access to its library, and advice from its faculty. 

Sincere thanks are given to the college.

DESCRIPTION OF PRETTY LAKE

Pretty Lake is a small natural lake of glacial origin 

located near the southeast corner of Lagrange County,

Ind. (lat 41°34.5' N., long 85°15' W.) (fig. 1). It has 

a water surface covering 184 acres (74.5 hectares) 

and a maximum depth of about 82 feet (25 meters) 

near its center (fig. 2). Owing to large shallow areas 

around the perimeters, the average depth is 25.6 feet 

(7.8 m), about one-third of the maximum. A sharpcrested steel weir on the outlet is designed to maintain 

the lake at an elevation of 965.5 feet (294.29 m) above 

mean sea level. When the lake stage is below the weir 

crest, there is no outflow. As the water surface rises 

above the control elevation, outflow varies according 

to the head on the weir. The weir is designed to open 

during the winter in order to lower the water surface, 

thereby protecting waterfront property from ice 

damage. Owing to the dry summers of 1963 and 1964, 

it was not necessary to lower the lake surface these 

years. Therefore, stage fluctuations during' these 

studies were not affected by intentional spilling of 

water from the lake.

At the water's edge, concrete seawalls or filled lawn 

waterfronts adjoin the lake in most places. These 

create a shoreline that is nearly vertical over the range 

of stage of the lake. As a result, the limited change of 

lake stage has no significant effect upon the lake's area.

At three places along the south and west edges of 

Pretty Lake, channels have been dredged to create a 

longer shoreline. These channels are designated by 

thermal survey stations T21, T22, and T23 in figure 2. 

Some of the dredging has been done recently enough 

that it does not show in the map from which figure 1 was 

made.

The small inlet that enters at the north edge of the 

lake drains an area of 1.96 square miles (508 hectares), 

most of which is wooded or marshlike. Relief is small, 

elevation within the basin ranging from 965 feet 

(294 m) above mean sea level at the gage to 1,050 feet 

(320 m) at the extreme north end of the drainage basin. Consequently, even the hardest rains do not produce great flow volumes. On the other hand, the inlet 

does sustain a low flow much of the time.

Overland flow into Pretty Lake can be expected 

during very hard rains. Volumes are generally small 

owing to the small basin size, the good grass cover on 

most of the surrounding land, and the numerous 

depressions which trap small quantities of water.

Pretty Lake generally freezes over during December 

or early Januarj*. Depending upon the severity of the 

season, ice will attain a thickness of as great as 2 feet 

(0.6 m). In early March the ice begins to weaken or honeycomb. Rain-and warm weather will open zones along the 

edge. Removal of the main part of the ice cover generally 

takes place within a day or two. A strong wind on a 

warm day will break and crush the ice, melting some and 

piling large mounds of crushed ice on the downwind
85°16'30'

COMPARISON OF EVAPORATION COMPUTATION METHODS

16' 15'30" 15' 14'30'

A3

85°14'

o°^.;&/

P«faji=^l II

// rT-Va^V >kJ > /\-

^rym^m^^ ^4^5^^?^

^%^^pl

1^ nonrecording rain gage, and 

*«V,/ lake-stage recorder

'> .( i i-, .nstrume^t Pretty 

}' raft Lake

Base from U.S. Geological Survey;

1:24,000, Wolcottville

and Stroh, 1959 1000, , , 0 1000 2000 FEET

SCALE 1:24000

500

I i

0

i ' i

500 METERS

CONTOUR INTERVAL 10 FEET 

DATUM IS MEAN SEA LEVEL

FIGURE 1. Pretty Lake study site.
85° 15' R. 11 E STROH 2.7 Ml.

Prepared in cooperation with the 

Indiana Department of Conservation

X BM 969

Lake level monument and reference mark 

elevation 968.82 feet M.S.L. Depth curves in 5-foot intervals referenced 

to-average normal water level.

t

<D

Lake-gaging station

+T22

Thermal survey station 

and number

Hydrographic survey of June, 1956. Aerial photograph by Department of Agriculture 

dated August 1, 1951. Volume, 1,537 million gallons or 4,717 acre-feet. 

Surface area, 184 acres. Daily water-level records available in the district office of the U.S. Geological Survey from August 18, 1949 to November 30, 1952. __-._. SEC. I6J SEC. 15 .'"" ~

85°15' R. 11 E.

FIGURE 2. Bottom configuration of Pretty Lake.

BIG LONG LAKE: 0.2 MI.
COMPARISON OF EVAPORATION COMPUTATION METHODS A5

15 20, ""25 5 10, iv/ 15'"25 C 20 5 iw !5' 

MARCH APRIL MAY

5 10 15 2°25 5 10 152°25 5 10 15 2°25 5 10 152°25 5 10 15 20 25

JUNE JULY AUGUST SEPTEMBER OCTOBER NOVEMBER DECEMBER 

FIGURE 3. Temperature structure during 1964 open-water period.

side of the lake and generally inflicting damage on 

docks, seawalls, and other waterfront improvements.

TEMPERATURE PATTERNS

The water of Pretty Lake is sufficiently deep to 

undergo thermal stratification during the summer. 

Stratification begins in late April as the water at the 

lake surface begins to warm above the temperature 

of maximum density. Maximum stratification is 

reached in midsummer, after which the surface begins 

to cool and the stratification is erased (Ficke, 1965) 

in late November. The seasonal pattern for 1964 is 

described by the temperature lines in figure 3. A form 

of stratification also takes place during the winter, 

when the surface is cooled to below the temperature 

of maximum density, 4°C. There is considerable 

warming of the lake during the winter, during which 

stratification is retained more by density differences 

caused by variations in chemical concentration than 

by temperature differences. During this period the 

ice cover protects the water from the wind actions 

which would otherwise erase stratification dependent 

upon such small differences in density.

INSTRUMENTATION AND ITS OPERATION

Pretty Lake was instrumented for evaporation 

measurement by the water-budget method, the energybudget method, the mass-transfer method, and the pan 

method. In some instances, records from certain measuring instruments were useful in the computations made 

by more than one method.

INSTRUMENTATION FOR WATER BUDGET

The study of a lake's water budget requires the best 

possible measurements of water flowing into and out of 

the lake. The largest source of inflow to Pretty Lake is 

precipitation falling directly upon the lake's surface. 

Additional water enters from the inlet channel, from 

direct overland flow to the lake, and, as will be shown

later, from underground seepage. Outflow may occur as 

direct surface flow through the outlet channel or as seepage. The water budget, like any other budget system, 

also requires a measurement of change in the storage 

term in order that it can be balanced.

Inlet station. The station for the measurement of 

inlet flow is about 300 feet (92 m) upstream from the 

point where the inlet enters the lake along its north 

shore (fig. 1). A reference point was established at the 

site, and the first regular discharge measurement was 

made on March 29, 1963. A staff gage was installed on 

May 3, 1963. A water-stage recorder was installed (fig. 

4), and daily streamflow records were begun on June 

26, 1963.

FIGURE 4. Stream-gaging station on Pretty Lake inlet. A steel 

V-notch weir and recording gage are shown. The continuoustype recorder shown was preceded by a weekly recorder.
A6 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

Initially the channel served as control for the stagedischarge relation at the station. A wooden weir was 

installed on September 6, 1963, in order that the stagedischarge relation might be better defined. The temporary wooden weir was replaced with a steel weir 

having a notch capacity of 0.5 cubic foot (0.014 cu m) 

per second. It was set in the channel on April 17, 1964, 

and washed out during the spring of 1965. Consequently, 

the steel weir plate was reset in concrete on June 2, 1965.

Rating of the streamflow station was by currentmeter or volumetric measurements and by use of the 

theoretical rating for the V-notch weirs. Water temperatures were read at the time of discharge measurements, at the time of the weekly recorder inspections, 

and at various intermediate inspections.

Outlet station. A control structure on the Pretty 

Lake outlet was built in 1951 by the Indiana Department of Conservation. The State of Indiana and the 

U.S. Geological Survey have used this site and other 

sites for the collection of lake-stage data at various times 

since the lake level was stabilized.

The control structure is located 140 feet (43 m) 

downstream from the point where the channel forms at 

the northeast corner of the lake (fig. 5). During the 

term of the project, the control was a sharp-crested weir 

with its crest at an elevation of 965.47 feet (294.28 m) 

above mean sea level. Weir width is 4.0 feet (1.22 m). 

Miscellaneous measurements at the station were begun 

March 29, 1963. A continuous record of discharge was 

begun with the installation of a water-stage recorder 

on June 26, 1963. The stage-discharge relation at the 

station was established by current-meter and voluFIGURE 5. Lake-stage control weir and recording gage on Pretty 

Lake outlet channel.

metric measurement. Water temperatures at the outlet 

were measured during weekly inspections of the gage.

Precipitation gage. Two recording rain gages were 

located within the Pretty Lake study area (fig. 1). One, 

about a mile northwest of the lake, was intended to 

measure rainfall within the inlet drainage basin. The 

other, a few hundred feet south of the lake, is considered 

to be a good indicator of precipitation actually falling 

on the lake. Resolution of the record on the weekly 

charts generally was within 0.02 inch (0.05 cm). 

Neither of the gages was equipped with a windshield. 

They were unmodified for winter operation and consequently provided a poor record of snowfall.

A simple nonrecording precipitation gage was 

mounted at the water's edge along the west side of the 

lake (fig. 6). This was a bucket and funnel 8 inches 

(20 cm) in diameter fitted with a measuring cylinder. 

It usually was inspected at weekly intervals, at about 

the same time as the inspection of the recording gages. 

The catch was measured to the nearest 0.01 inch (0.03 

cm).

Lake-stage recorder. A weekly water-stage recorder 

to measure changes in the lake's contents was situated 

in a boat-slip setback along the west side of the lake 

(figs. 1, 7). From January 1963 to November 5, 1963, it 

operated at a 1 :5 vertical chart scale, with resolution 

to the nearest 0.01 foot (0.3 cm). Thereafter it operated 

on a 1 : 1 vertical scale; the gage-height was readable to

FIGURE 6. Simple nonrecording rain gage at edge of Pretty Lake. 

Photograph shows cattails that grow along parts of the shoreline and lily-pad complex with associated submerged rooted 

aquatic plants that cover less than an acre along the west 

shore.
COMPARISON OF EVAPORATION COMPUTATION METHODS A7

FIGURE 7. Lake-: gage located at public access area on 

Pretty Lake.

the nearest 0.001 foot (0.03 cm). At the 1:1 ratio the 

recorder trace at times showed considerable surge and 

at times registered low as a result of westerly winds and 

the gage's location in a setback along the west shore. 

Resulting difficulty in setting the instrument necessitated constant application of corrections to the recorded 

lake levels.

The 1:1 vertical scale of the lake-stage recorder made 

the record useful as a measure of the amount of precipitation falling directly on the lake. During periods of 

extended precipitation and significantly large inflow or 

outflow, it was necessary to correct the stage change for 

the inflow and outflow effect in order to get a measurement of precipitation. For instance, on this 184-acre 

(74.5-hectare) lake, each cubic foot per second inflow, 

or inflow-outflow difference, would result in a stage 

change of 0.005 inch (0.127 mm) per hour. The record 

of lake stage also provided a measurement of the 

quantity of direct overland flow to the lake during and 

immediately after storms. Significant differences 

between the quantities of precipitation caught by the 

rain gages and shown on the stage recorder were attributed to overland flow. At times the overland flow 

could be computed from recorded rates of rainfall and 

changes of lake stage. An obvious increase of stage that 

continued for several hours after the rain gages showed 

that rain had stopped and that was unaccounted for by 

inlet flow was attributed to direct overland flow into 

the lake.

Temperature-volume correction. The instrument 

that measures changes of lake stage not only records the 

effect of changes of lake contents but also registers the 

effect of changes in lake volume resulting from thermal 

expansion and contraction of the water. Measurements 

of heat storage made as part of the energy-budget

studies provided the data necessary to correct lake-stage 

changes for the effects of thermal expansion over periods 

between thermal surveys; such effects sometimes 

amounted to more than 0.02 foot (0.6 cm).

INSTRUMENTATION FOR ENERGY BUDGET

Measurement for a lake's energy budget requires 

a quantitative determination of all the forms of energy 

entering or leaving the lake as well as a determination 

of the change in storage of energy within the lake. 

Specifically, these deteiminations are the direct measurement of incoming radiation, advected energy, 

and heat storage..Other terms are estimated as functions 

of temperatures of the air and water, vapor pressures, 

and other measured phenomena.

Psychrometric measurements. A continuous record 

of wet- and dry-bulb temperatures for the computation 

of vapor pressure was provided by a recording psychrometer located along the west side of the lake (fig. 1). 

The device consisted of two thermocouples, one wet 

and one dry, and a water reservoir mounted beneath a 

radiation shield (fig. 8) (Anderson and others, 1950). 

Situated on the side of the lake from which the prevailing winds generally blow, the instrument provides 

measurements of vapor pressure and air temperature 

largely unaffected by passage of the air over the lake.

The instrument was serviced at weekly intervals, at 

which time temperatures were measured with a mercury-in-glass sling psychrometer. Generally the reading

FIGURE 8. Temperature- and radiation-measuring equipment 

located at the west side of Pretty Lake.
A8 HYDEOLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

of the sling psychrometer agreed with the readings 

of the recording psychrometer within 34° C. The 

output of the copper-constantan thermocouples, calibrated to 25° C per millivolt, were referenced and 

recorded by a recording potentiometer.

Pyrheliometer. A 10-junction Eppley pyrheliometer was used to measure solar radiation. It was mounted 

on the west side of the lake near the other recording 

instruments and was connected to the same recording potentiometer that was used with the recording 

psychrometer. The glass bulb covering the black-andwhite thermopile was cleaned during weekly inspections. No operating difficulty was experienced during 

the entire study period. A voltage divider was used to 

reduce the manufacturer's calibration to a convenient 

factor of 1 millivolt equal to 1 cal cm~2 mkr 1 (calorie 

per square centimeter per minute).

Flat-plate radiometer. A Beckman-Whitley flatplate radiometer was used to measure total radiation. 

The sensing part of this instrument consists of a black 

upper plate and a reflective lower plate.

A motor-driven ventilator fan provided uniform 

airflow past the upper and lower surfaces. The amount 

of long-wave radiation was computed by subtracting 

solar radiation from the total radiation as measured 

by the flat plate. The complexity of the measuring 

unit provides several potential sources of error, including unlevel mounting, weathering of the plate finish, 

poor ventilation, and the condensation of water on 

the sensing surface. The flat-plate radiometer and 

pyrheliometer are shown in figure 8.

Different flat-plate radiometers were used in each of 

the three different seasons of Pretty Lake study. Each 

instrument was calibrated before installation and was 

fitted with a voltage divider designed to reduce the 

thermopile outputs to a common calibration that most 

suitably fit the range of the recording potentiometer. 

After the reduction of the 1963 data, it became obvious 

that the measured values of long-wave radiation were 

not correct and that instrumental error might be the 

source. Subsequent testing found that instrumental error 

was present in both the 1963 and 1964 data. Additional 

calibration produced enough data to make correction 

of the 1964 data possible, but such a correction could 

not be made to the 1963 data.

Recording potentiometer. The psychrometer, pyrheliometer, and flat-plate radiometer were all connected 

to the same multipoint recorder. This recorder had 

eight channels and a range from 1.0 to 2.0 millivolts. 

It recorded one signal each 30 seconds or went through 

its eight-channel cycle once each 4 minutes.

A five-channel integrator device was attached to the 

recorder to simplify the computation of psychrometric 

and radiation data. The mechanical device was connected to the moving stylus of the multipoint recorder 

by a cable assembly. As the stylus moved to balance 

the potentiometer circuit on each signal input, it rotated 

a simple revolution counter, so that the degree of rotation 

of the counter was proportional to the size of the signal 

recorded from one of the sensing instruments. The-total 

revolution of one of the counters over several cycles was 

proportional to the integral of one of the measured 

signals. Therefore, the average of one of the variables, 

dry-bulb temperature for instance, could be computed 

simply from any two simultaneous readings of the 

integrator totalizing dials.

During the period of operation of the Pretty Lake 

study, the integrator totalizing dials were read every 

time the field site was visited by project personnel. The 

intervals between consecutive inspections ranged from 

less than a day to as great as 7 days. Except for simple 

infrequent failure of such minor parts as cable, springs, 

or switches, the recorder and its integrator operated 

very well.

Advectate-heat measurement. Heat is advected to 

the lake directly by the inflow, outflow, and rainfall. 

Temperatures of the water in the inflow and outflow 

channels were measured as a part of recorder inspections. 

For the outflow channel, however, it is possible that 

the water may have been warmed or cooled in its flow 

through the channel, especially at low velocities. 

Because of this possibility, the temperature of the water 

surface of the lake was a better measurement of the 

outflow temperature than was the temperature 

measured at the streamflow station.

The wet-bulb temperature recorded at the psychrometric station at the time of rainfall was considered to 

be a satisfactory measurement of the temperature of 

the precipitation.

Lake-surface temperature. Temperature of the 

water at the lake's surface was recorded by a thermograph mounted on the raft anchored near the lake center 

(figs. 1, 2, and 9). This instrument's sensing unit was 

mounted beneath the raft 1 or 2 cm (0.2 to 0.4 inch) below the water surface. Calibration of the thermogiaph 

was checked with a mercury-in-glass thermometer at the 

times of the weekly chart change. The recorded values 

were adjusted to within 0.3°C of the true temperature.

Data from the periodic temperature surveys show 

that at times the temperature over the surface of the 

lake varied over a range of more than 2° C, from place 

to place. When there was wind, the warm, less dense 

water piled up on the downwind side, while the cold 

water stayed on the upwind side. Under these conditions the temperature at the center of the lake was 

always nearly the same as the mean of the survey 

points. On calm days, there was greater warming in 

the shallow areas, and the temperature measured at
COMPARISON OF EVAPORATION COMPUTATION METHODS A9

FIGURE 9. Instrument raft anchored in Pretty Lake. Pontoon 

floats are 20 feet long.

the raft station was sometimes 0.5°C less than the 

mean. However, the evaporation rate also was low on 

these calm days, and the error in the evaporation 

computation caused by use of the thermograph data 

is believed to be minimal.

THERMAL SURVEYS

Thermal surveys to measure heat storage of Pretty 

Lake were conducted at intervals ranging from 7 to 56 

days. Normal procedure was to measure at each of the 

24 points shown in figure 2 (Tl through T23, and raft). 

At each survey point the temperature profile was 

measured at 2.5-foot (0.76 in) intervals. In those 

instances where the lake was ice covered, the measurements were more closely spaced in the zone near the 

ice, where temperature changes more rapidly with 

depth. Readings were made using a thermistor thermometer which incorporated an out-of-balance bridge 

circuit. Temperatures were read to the nearest 0.1 °C. 

Instrument calibration was maintained by frequent comparison with a precision mercury-in-glass thermometer.

A complete survey of the lake generally could be 

completed in 2 or 3 hours. Points of survey were located 

by sextant angles; six prominent shore points were 

used as targets. In early surveys, buoys submerged about 

2 feet (0.6 m) below the water surface were located 

and used to confirm the sextant technique. As familiarity 

with the sextant increased, use of the buoys was 

abandoned. Sextant-located positions were generally 

within 20 or 30 feet (6 or 9 m) of the true location of 

the measuring points.

INSTRUMENTATION FOR MEASURING MASS-TRANSFER 

PARAMETERS

Computation of evaporation by the mass-transfer 

method requires a determination of the vapor pressure 

of the air, the saturation vapor pressure corresponding 

to the temperature of the water surface, and the wind

speed at the lake center. The instrumentation for 

measuring temperatures upon which the computation 

of vapor pressure is based was described with the 

instrumentation used in the energy-budget studies.

Wind measurements. Wind movement was recorded 

by a three-cup totalizing anemometer mounted on 

the raft anchored at lake center (fig. 2). The anemometer was constructed to give an electrical signal for 

every 10 miles (16.1 km) of wind movement. Neither 

of the two types of recorders used to record these 

signals operated successfully over any extended length 

of time. As a result of recorder malfunction, much of 

the wind record has been discredited, and this report 

is based largely upon wind records computed from the 

totalizer-dial readings that were made at the times of 

instrument inspection.

The totalizing anemometers used are simple instruments which proved to be quite reliable. Occasional 

icing of the anemometer cups caused by spray, sleet, 

or freezing rain resulted in small losses of record. In 

addition, the dial counters failed twice.

During springtime periods when the instrument raft 

was removed from the lake for short periods following 

ice breakup, the anemometers were operated on the 

bank on the access area.

At the beginning of the Pretty Lake study, the anemometer was installed with its cups 1.73 meters (5.64 

ft) above the water surface. A second anemometer was 

later installed at the 2.00-meter (6.56-ft) level. Simultaneous readings of the two instruments were made in 

order to correlate the data from the two different levels.

EVAPORATION PANS

Pan-evaporation data used in the study of Pretty 

Lake are from the pan operated by the U.S. Weather 

Bureau in Kendallville, Ind., a site about 9 miles (14 

kilometers) south of Pretty Lake. This installation is 

shown in an earlier report of Indiana lakes (Perry and 

Corbett, 1956, p. 51). The station normally is operated 

for the 7-month summer period April through October. 

Figures of daily pan evaporation are listed in the U.S. 

Weather Bureau's monthly publication, "Climatological 

Data," for Indiana. Copies of the original observer's 

notes were made available for the Pretty Lake study. 

At times it was necessary to supplement with records 

from other pan stations operated by the Weather

Bureau.

ENERGY-BUDGET STUDIES

Estimation of evaporation by budgeting energy terms 

is a practice that dates back about 50 years. An excellent 

review and explanation of the method is presented in 

the reports describing studies on Lake Mead (Anderson 

and others, 1950 p. 38-49) and Lake Hefner (Anderson,
A10

1952). The budget, as used in the study of Pretty Lake, 

is written to equate the net sum of energy into and out 

of the lake to changes in stored energy, as

,-Q.-Qit-Q1l> =Qfl (1)

where Qs =^incoming solar radiation,

Qr reflected solar radiation,

Qa=incoming long-wave radiation, 

Qar= reflected long-wave radiation, 

Qts= long-wave radiation from the water,

Qt>=net energy advected into the lake,

Qe= energy used for evaporation,

Qh= energy conducted from the water as sensible 

heat,

$«, energy advected by evaporating water, and

Qx= increase in stored energy.

INSTRUMENT RECORDS

Solar radiation. Data from the Eppley pyrheliometer were complete, except for short periods when 

record was lost owing to power failure or malfunction 

of the recorder or integrator. Much of the record lost 

was estimated from the record of a bimetallic pyrheliometer. The bimetallic instrument, which was mounted 

on the raft at the center of the lake, was owned by 

Indiana University and was maintained at Pretty Lake 

as part of a biological study conducted by the university. 

Other short periods of missing pyrheliometer data were 

filled in by estimates based upon tabulated values of 

clear-sky radiation and records of hours of sunshine at 

the U.S. Weather Bureau station at Fort Wayne.

Figure 10 is a time graph of solar-radiation (Qs) values

recorded at Pretty Lake during 1963, 1964, and 1965. 

The many short lines of varying length represent the 

average values computed for the periods between integrator readings.

Reflected solar radiation (Qr) was estimated as a part 

of the mean Qs for the energy-budget periods according 

to the graph developed by Koberg (1964, fig. 36).

Long-wave radiation. Three different flat-plate radir 

ometers were used in the study of Pretty Lake. The 

durations of their periods of use are listed in table 1. 

As processing of the 1963 data was completed in mid1964, it became obvious that the results were unreasonable and that the measured values of long-wave radiation seemed to be too large. Consequently, the 

instrument change in October of 1964 was preceded by 

careful calibration checks throughout the range of 

instrument 263. Then instruments 245 and 263 were 

operated side by side for 16 days. Finally, when instrument 245 was removed, it was subjected to extensive 

laboratory calibration.

The laboratory studies of flat-plate radiometer 245 

showed that the radiometer errors were caused by 

electrical potentials being generated by thermocouple 

action within a voltage divider that had been installed

TABLE 1. Periods of use for flat-plate radiometers at Pretty Lake

Instrument serial No. From To

500______----------_------~- Apr. 5,1963 Nov. 21, 1963

245____________-____-__------ Nov. 22, 1963 Oct. 14,1964

263________________--____---- Sept. 28, 1964 Sept. 22, 1965

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JANUARY FEBRUARY MARCH APRIL MAY JUNE JULY AUGUST SEPTEMBER OCTOBER NOVEMBER DECEMBER

FIGURE 10. Solar radiation (Qa) striking Pretty Lake. Lengths of lines represent duration of periods between integrator readings.
COMPARISON OF EVAPORATION COMPUTATION METHODS All

in the radiometer. The field and laboratory studies 

found that the sizes of these errors were largely functions of wind conditions. An effective correction procedure was devised, and the corrections were applied 

to the 1964 records from flat-plate radiometer 245.

When instrument 500 was removed, the calibration 

problem had not yet been discovered, so that the 

sensing element was refinished without first making 

calibration. It was reasoned, but later proved erroneous, 

that it might be possible to apply the corrections 

developed for instrument 245 to the records obtained 

from instrument 500.

Figure 11 is a plot of the measured long-wave radiation from the records of the three radiometers against 

values of long-wave radiation estimated by the Koberg 

(1964) method. Short arrows indicate the values

900

850

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750

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C 60°

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EXPLANATION

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X Period 42 (FP 245)

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O Period 57 (FP 245 & 263)

+ Period 58-60 and 66-69 (FP 263)

450 500 550 600 650 700 750 800 

COMPUTED Qa , IN CALORIES PER SQUARE CENTIMETER PER DAY

FIGURE 11. Relation of long-wave radiation (Q a) as measured 

by flat-plate (FP) radiometers and as computed by the 

Koberg method. Arrows point to places where uncorrected 

data would have plotted.

before corrections of the data from flat-plate radiometers 500 and 245. As indicated by the pattern of 

the plot in figure 11 and by the summary of averages 

in table 2, it appears that the data from flat-plate 

radiometer 263 and the corrected data from flat-plate 

radiometer 245 agree quite well with the long-wave 

radiation values computed by the Koberg method. 

On the other hand, the correction developed for flatplate radiometer 245 did not seem to work well in 

correcting data for 1963 from flat-plate radiometer 

500. Measured values differ from the computed values 

by 7 percent or more in 47 percent of the periods. 

This wide scatter of the individual periods and the 

average difference of 5.6 percent supported the conclusion that the correction of the 1963 data was not 

good enough. Consequently, values of Qa used in the 

energy-budget computations for 1963 were those computed by the Koberg method. A computed value of 

Qa also was used for period 42 because the large deviation from the rest of the data cannot be explained.

The values of long-wave radiation used in the energybudget computation are graphed in figure 12. The pattern of figure 12 illustrates how well the seasonal patterns of long-wave radiation agree with each other from 

year to year.

Reflected long-wave radiation, QaT, was estimated to 

be 3.0 percent of the measured or computed incoming 

radiation, Qa.

Air temperature and vapor pressure. Long-wave 

radiation from the water surface (Qbs) was determined, 

as a function of the average surface temperature over 

the computation period, from the record of the raftmounted thermograph. The Stefan-Boltzman law was 

used, with an emissivity of 0.97 (Anderson, 1952, p. 97). 

Figure 13 is a time plot of the daily mean temperatures 

recorded at the center of Pretty Lake. The figure has 

scales to enable the reader to estimate values of Qhs.

Records of wet-bulb and dry-bulb temperatures were 

computed largely from the integrator records of the 

recorder connected to the psychrometer described 

earlier. Except for minor difficulties caused by integrator failure or by broken thermocouple leads, the records 

were quite complete. It was difficult to evaluate the

TABLE 2. Summary of data from flat-plate radiometers

Instrument

serial No.

500

245_ -.-_

Energybudget

periods

included

21-35

43-56

58-60,

66-69

Number

of days

199. 0

185. 2

198. 8

Average 

measured

Qa

(cal cm-2

day-i)

i 722

1 708

659

Average 

computed

Qa (cal cm-2 day-2 )

684

698

674

Difference, 

measured

from computed

(percent)

+ 5. 6

+ 1. 4

-1. 3

1 Corrected.

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A12 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

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MARCH APRIL MAY JUNE JULY AUGUST SEPTEMBER OCTOBER NOVEMBER DEC

FIGURE 12. Long-wave radiation (Q0) measured at Pretty Lake for open-water energy-budget periods (identified by numbers).

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JANUARY FEBRUARY MARCH APRIL MAY JUNE JULY AUGUST SEPTEMBER OCTOBER NOVEMBER DECEMBER

FIGURE 13. Air and water-surface temperature records for Pretty Lake. Air temperatures are shown by lines representing duration of periods between integrator readings. Values of Q b$ . correspond to water-surface temperature (jP 0).
COMPARISON OF EVAPORATION COMPUTATION METHODS A13

effect of freezing upon the wet-bulb temperature record. 

Consequently, most vapor-pressure records for periods 

when air temperature was below freezing or when equipment failed were estimated from published dewpoint 

temperatures by the U.S. Weather Bureau at Fort 

Wayne.

As indicated by the temperature and vapor-pressure 

records in figure 14, values of air vapor pressure (ea) 

often were computed from temperatures averaged over 

several days. Errors could be expected to result from 

this type of computation because the relationship 

between temperature and vapor pressure is not linear. 

On the other hand, the errors are small and the cost of 

additional accuracy afforded by more frequent integrator readings or hand reduction of the recorder chart 

could not be justified. If future studies of this type are 

to attain greater accuracy by use of more frequent 

data readings, the results will have to be achieved by 

the use of automatic recording that can be machine 

processed.

In checking the data computations, values of ea 

were computed from even longer term average temperatures than were used in the original data computations. 

The method produced results that checked the original 

computations generally within 0.3 millibar. Errors 

caused by the shorter term averaging probably are 

even less, owing to the smaller temperature ranges 

over the shorter periods.

Values of saturation vapor pressure at the temperature of the water surface (e0) were selected from tables 

of the saturation vapor pressure of water, as functions 

of daily mean temperatures computed from records of 

the thermograph on the raft in the center of the lake. 

The few days of record loss immediately following each 

spring ice breakup was filled in by interpolating between 

thermistor-thermometer readings made every 3 or 4 

days. Records of e0 are shown in figure 14.

Advected energy. Volume and temperature records 

for rainfall, inflow, and outflow were used to compute 

advected energy (Qv). Computations were made using 

the base temperature of 0° C and considering heat 

inflow as positive. Temperature-volume products were 

computed for the rainfall from each storm and for inflow 

and outflow over periods of a week or less. Summations

JANUARY FEBRUARY MARCH APRIL MAY JUNE JULY

25 5 15 25 5 15 25 

AUGUST SEPTEMBER OCTOBER NOVEMBER DECEMBER

FIGURE 14. Pretty Lake vapor-pressure records. Values of ea are shown by lines representing duration of periods between integrator readings.
A14 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

of temperature-volume products over a computation 

period were divided by length of the period, surface 

area of the lake, and a units-conversion factor to yield 

values of Qt, in calories per square centimeter per day. 

These values generally were positive and small. The 

volumes of inflow and outflow were small, and often 

their effects tended to negate each other. Sizable Qv 

values resulted from heavy summer rains. The maximum of 24 cal cm~ 2 day" 1 for any one energy-budget 

period occurred during a short period in July 1963, 

when 3.5 inches (8.9 cm) of precipitation fell during a 

7-day period.

CHANGES IN ENERGY STORAGE

Temperature-survey data were used to compute 

the mean temperature in each of the 2.5-foot (0.76-m) 

horizontal layers sampled. All readings were weighted 

equally except those made in the dredged setbacks 

(T21, T22, and T23), which were weighted at one-third 

of the value of measurements in the main lake body. 

The energy in each layer, measured above a base of 

0° C, was computed as the product of temperature 

and volume of the layer. Finally, average storage in 

calories per square centimeter was computed as the 

sum of the individual layers divided by the surface 

area of the lake. Changes in the stored energy between 

any two surveys, divided by the length of the period, 

yielded the term Qx in calories per square centimeter 

per day.

Volumes used in the computation of energy storage 

were computed from a capacity table developed from 

the data of the survey made to construct the map in 

figure 2. Volumes between the 5-foot (1.52-m) depth 

contours were computed using the average-end-area 

formula. The average-end-area formula is generally 

known to yield results that are too large in cases where 

there is a considerable difference between the areas of 

the two ends of the solid whose volume is being computed. In addition, it is believed that errors in the Pretty 

Lake capacity table may result from uneven shape 

within the shallow area that lies above the 5-foot 

(1.52-m) depth-contour line.

Computation of evaporation would not be affected 

by errors in the capacity table during those periods 

when there is little or no change in heat storage. The 

greatest error could be expected during periods of rapid 

heating in the spring.

It is obvious that reliable values of Qx can be computed only between two accurate measurements of 

energy storage. Consequently, solutions of the energybudget formula are limited to those periods between 

major temperature surveys. Solutions of the energybudget formula for short periods by use of data from a

single vertical were not attempted. Unlike the vaporpressure and Qhs terms, the energy-storage computation 

cannot tolerate even a 0.2°C error in average lake 

temperature. Such an error would result in an error of 

155 cal cm~2 (calories per square centimeter) in energystorage computation. The effect would be magnified to 

unacceptable proportion if the data were to be used over 

short periods of 2 or 3 days.

INTERRELATION OF Qe, Q h , AND Qw AND THE BOWEN RATIO

The three remaining terms of the energy-budget 

equation, Qe , Qh , and Qw, have been defined as functions 

of the evaporation rate (EEB). Energy used in evaporation is simply defined as

/"\ __ 777 J~ (*}}

where p is density and L is latent heat of vaporization. 

Using metric units within the water temperature range 

found in Pretty Lake, density is considered to be unity. 

Latent heat is determined, as a function of temperature, 

from a physics handbook. The energy advected by the 

evaporating water is expressed as

pcE-EB (Te (3)

where c is specific heat, Te is temperature of the evaporated water, and Tb is a base temperature. In this 

case, c is taken to be unity, Te is presumed to be equal 

to the surface temperature of the lake (T0), and T* is 

assumed to be 0°C, the same as the base used for computation of Qv . Conducted sensible heat was estimated 

as a function of Qe by use of the Bowen ratio (Bowen, 

1926), R, as

Qn=RQe (4) 

The Bowen ratio is computed by the formula

R=~; \- ,->/->/-/ \5)

Here 7 is a coefficient equal to about 0.61 in the units 

used, and Pa is atmospheric pressure in millibars. In 

the study of Pretty Lake, the values of temperature 

and vapor pressure used to compute the Bowen ratio 

were those determined by the instrumentation described 

earlier. Koberg (1958, p. 23) has determined that the 

overland data are sufficiently accurate for estimating 

the Bowen ratio for the lake. Ratios used in the evaporation computation were computed from equation 5 

by use of average temperatures and vapor pressures 

for the energy-budget computation periods. Diurnal or 

other short-term changes of the type described by Webb 

(1960) were not believed to be significant in the climate 

that prevails in the Pretty Lake region. However, the
COMPARISON OF EVAPORATION COMPUTATION METHODS A15

observed conditions were similar to those that Anderson 

(1952, p. 106-109) has cited in his extensive discussion 

of the eccentricities of the Bowen ratio. With a few 

exceptions, the ratio varies from 0.1 to +0.4. During 

57 percent of the open-water periods, the ratio was 

between 0 and 0.2. High Bowen ratios occurred most 

frequently in the fall, when evaporation rates decreased 

and the cool autumn air caused a higher proportion of 

the energy transfer to take place as sensible heat. 

Negative ratios occasionally occurred in the spring 

under stable atmospheric conditions within the boundary layer.

Equations 1, 2, 3, and 4 can be combined to form an 

equation to compute the energy-budget evaporation 

rate for any period between thermal surveys. This 

equation has the form

(6)

When the energy terms are in units of calories per square 

centimeter per day and latent heat and temperature 

are in gram-calorie-centimeter-degree Celsius units, 

evaporation rates will be in grams per square centimeter 

per day or centimeters per day.

When the Bowen ratio is large and negative, the 

denominator in equation 6 is small, and small differences 

or errors in the numerator can cause large differences 

in the estimated Qh . There is even the possibility that 

the equation may become indeterminate. When large 

negative Bowen ratios occur, the possible error may be 

avoided by use of an alternate method of estimating Qfl. 

Use is made of the mass-transfer equation for estimating 

evaporation in the form

where N is a coefficient and u2 is wind speed measured 

2 meters (6.56 ft) above the water surface. From equations 4, 5 and 11 it is possible to estimate conducted 

energy as

(7) l,000(e0 -<O

which may be substituted into the energy-budget 

equation to give

i,ooo(£+r0)

(8)

RESULTS OF ENERGY-BUDGET STUDIES

Computations of evaporation by the energy-budget 

method for 1963, 1964, and 1965 open-water periods are

listed in table 3. All periods except 43 and 44 were 

solved for £"EB according to equation 6. Values of Qe , 

Qh , and Qw were then computed using equations 2, 3 

and 4. Owing to errors in rounding to whole numbers the 

sum of the 10 energy terms is not always exactly zero.

Periods 43 and 44 had Bowen ratios that were near 

enough to 1 to make the term L(l+R) + T0 very 

small. Such small values created an unacceptable condition. For instance, in period 43 the six terms in the 

numerator of equation 6 total zero. Consequently, 

evaporation computed for this period would be zero. 

However, with L(l-\-R}-\-T^ equal to 35, the computed 

evaporation is very sensitive to small changes in the 

numerator. An energy subtotal of 15 cal cm~2 day" 1 in 

the numerator would have raised the computed evaporation from 0 to 0.43 cm day" 1 .

Table 3 lists values of £"EB for periods 43 and 44 

that were computed according to equation 8. The Qh 

term was estimated from equation 7 by use of the terms 

listed in table 4. The values of Qe and Qw listed in table 3 

for periods 43 and 44 were computed from equations 2 

and 3 in the same manner as for the other periods.

Evaporation rates and amounts computed by the 

energy-budget method are shown graphically and further summarized in figures 30 and 31 and in tables 20 

and 21 in a later section of this report.

In the evaporation studies on Lake Mead, Koberg 

(1958, p. 29) estimated errors in evaporation caused 

by errors in the different terms of the energy-budget 

equation. Volume, inflow, and outflow differences 

would make the values of such estimates for Pretty 

Lake slightly different; however, as in Lake Mead, 

the principal sources of error in evaporation are errors 

in the Qh term caused by errors in the Bowen ratio, 

and errors in the Qx term caused by errors in the 

thermal surveys and in the capacity table. Unfortunately, large errors in the Bowen ratio occur most 

often in the spring at the time changes in stored 

energy are the greatest. Consequently, a larger error 

is to be expected in the computed evaporation values 

early in the spring than for those from later in the 

season. For example, table 3 shows low evaporation 

rates that are highly variable during April and May. 

It is possible that much of the scatter in the data 

result from errors in the Qh and Qx terms. Values of Qx 

obviously are more accurate for longer computation 

periods than they are for shorter periods.

SEDIMENT HEATING EFFECTS

The computations here described have followed the 

form, of most previous evaporation studies that used 

the energy-balance approach. Heat-storage terms have 

included only the water content of the lake, and heatexchange terms have included only the factors at the
A16 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

TABLE 3. Summary of energy-budget terms and evaporation computation for open-water periods, 1963-65

[Q values given in calories per square centimeter per day]

Period

No.

18

19

20

21

22

23

24

25____-_-.

27

28

29

30

31

32

33

34

35

36

Record

season.

42. _

44

45__ _

47__

49

50

51

52

53_______.

55

56

57

58

59

60

Record

season.

66

67

68

69. _ __

Record

season.

Length 

(days)

._ 7.0

8. 0

._ 10. 9

._ 10. 0

._ 21. 0

._ 5.4

.- 13. 1

._ 13.0

._ 7.6

7 4

7. 0

._ 13. 9

.. 14. 1

27 5

-_ 13. 1

-_ 17. 9

.- 14. 0

._ 14.0

17 1

242. 0

. _ 14. 9

._ 7.0

7 1

ft Q

._ 11. 1

._ 14.0

q 9

._ 25. 1

._ 16.0

.- 12.9

._ 18.0

14 0

14 0

12 0

17 2

. - 17. 8

12 8

n o

12 0

254. 6

_ 56. 1

_ 30.0

_ 43.0

- 33. 0

162. 1

Dates

1963

Apr. 5-12 _ _ __

12-20 __ ______

20-May !._____

May 1-11. ________

fi-IQ

19- July 2______

July 2-10______,____

17-24_ _ ______

24- Aug. 7____-_

Aug. 7-21__________

21-Sept. 18____

Sept. 18-Oct. !_-____

Oct. l-19--_----_ _

19-Nov. 2______

Nov. 2-16-________

16-Dec. 3______

Apr. 5-Dec. 3___ _

1964

Mar. 20- Apr. 4_

Apr. 4-ll_________

18-25

9^ TV/To v ft

May 6-20_________

9ft 3ft,

30-June 24____

June 24- July 10 _ __

July 10-23___.______

23-Aug. 10 _

Aug. 10-24_________

24-Sept. 7_____

Sept. 7-19__________

19-Oct. 6_____

Oct. 6-24___________

24-Nov. 6____.

Nov. 6-18__________

i o Qn

Mar. 20-Nov. 30 _._

1965

Apr. 13- June 8 _

June 8- July 8_______

July 8- Aug. 20____-_

Aug. 20-Sept. 22____

Apr. 13-Sept. 22 __.

Qs

4.OK

396

419

512

557

KC9

663

648

507

557

513

449

qqK

331

314

199

164

188

qKq

4.4.3

464

31 3

4.9Q

478

cqc

496

ZAR

383

376

31Q

98ft

970.

184

1 AK

500

628

cq9

qnR

Q'

00

on

97

01

35

36

36

39

39

34

36

qK

3?,

3ft

9K

i a

16i a

98

39

39

26

01

00

o />

qc

qo

Oft

98

33

98

9ft

24

94.

18

i ft

O A

38

qc

qn

Qa

522

606

Kq9

663

ftqK

7K.7

716

736

729

77K

7C7

7ft3

ftQI

661

ftKQ

cqo

cq9

4Q7

en,7

619

ccc

cno

7ft3

79Q

7Q9

8ft4-

O 1 ft

791

704

ft en

c.4.4.

cqi

ci9

ft OO

79ft

Tnc

ft O A

Q.

16

18

18

9ft

19

93

91

99

99

99

93

93

91

9ft

9O

19

17

16

15

1 z>

10

17i a

91

20

99

24

24

94.

99

99

21

9ft

16

17i a

i ^

1Q

99

91

91

QbJ

7ftQ

798

747

779

afti

071

079

908

908

884.

oqo

910

aaft

863

832

81 1

7Q5

7fta

662

*7f\a

790

770

809

84-Q

860

Qlft

906

090

863

871

ocq

81 3

766

745 740

7ft9

*? Oft

867

OOft

occ

Q.

-1

9

-4

-1

1

6

7

0

0

94.

q

1 9

0

1

2

0

1

1

9

4

0

9

4

0

4

c

0

19

4

1

0

1

1

1

0

q

Q

Qr

1 £.4.

CO

93ft

341

i ft

99

89

57

116

Q

-76

-30

-95

-27

-134

-184

-111

379

19Q

9ft7

1 3ft

0

67

4.9

64

4.3

-71

1 90

_ i OA

26

_ 4.9

331

19ft

48

33

33

Q.

72

9K

Kfl

1 £.

202

45

346

286

4.3K.

233

233

265

227

161

167

124

109

101

60

97

31

111

181

97ft

94.8

983

938

qcc

227

240

9ft3

1 87

106

41

29

i ^n

158

339

933

1 7^

Q*

21

_ q

17

-1

50

2

32

32

35

29

25

45

58

37

38

16

28

47

30

K«

31

-165

K

-1

1

31

36

29

44

42

28

36

47

43

2

4

124

10

37

3ft

31

Q,.

1

0

1

0

6

14

13

19

10

10

12

9

6

6

4

3

1

1

0

1

0

0

5

10

9

1 3

11

17

q

9

8

6

1

1

4

13

10

7

ratio 

R

0. 298

-. 113

. 336

-. 039

. 249

. 041

094

. Ill

.080

. 125

. 105

. 171

. 256

. 228

. 231

. 129

. 254

.461

. 579

- 1. 296

1Q3

-. 122

. 008

. 163

. 125

. 127

. 122

. 124

. 185

. 118

. 180

. 249

. 404

. 041

. 130

.828

. 065

. 110

. 128

. 176

Evaporation

Centi- Centimeters meters 

per day per period

0. 121

. 043

.084

. 026

. 344

. 078

.593

. 492

. 748

. 399

. 401

. 455

. 390

. 275

. 285

.211

. 186

. 172

. 102

.286

. 163

1 . 052

1 . 187

-. 043

.013

. 309

.471

.424

.487

.409

. 611

. 389

.412

.347

.320

. 181

.070

.050

. 253

. 300

. 269

. 569

. 399

.300

. 365

0. 85

. 34

.92

. 26

7. 22

. 42

7.73

6. 38

5.71

2. 93

2.82

6. 32

5. 50

7. 57

3. 74

3. 78

2. 60

2.41

1. 74

69. 24

2.43

i . 36

il. 33

-.30

. 14

4. 34

4. 64

10. 66

7.78

5. 27

11. 02

5.45

5. 77

4. 17

5.49

3. 23

.90

. 59

3.03

76.30

15.09

17.04

17. 16

9. 91

59. 20

1 Periods 43 and 44 computed using alternate energy budget.
COMPARISON OF EVAPORATION COMPUTATION METHODS A17

TABLE 4. Estimated energy conducted as sensible heat (Qh), 

according to equation 7 and assuming N = 0.0060

Period

U2- - .

Qhmile hr~^

______ ___ _ ° c

7 73

-1. 9

-31

U OQ

-6. 5

-165

surface, plus inflow and outflow. Energy advected 

through the bottom sediments or stored by the sediments has been ignored.

Compared with the effects of radiation, the flow of 

geothermal heat through the lake bottom is believed 

to be negligibly small (Anderson and others, 1950, 

p. 42). The radiation heating of bottom material has 

been shown to be significant in the case of a mudflat 

that is alternately exposed and flooded (Ayres, 1965). 

However, in the case of shallow waters of a lake of 

constant area, the sediments are creating much the 

same effect as would a deep-water column. Radiant 

energy is absorbed by the bottom in the shallow water 

and then is conducted back to the water. On a unitarea basis the effect of radiant heating of the shallowwater sediments probably can be ignored, except on a 

diurnal basis.

The sediment below the lake bottom influences the 

energy system by absorbing heat from the water 

during warm seasons and releasing it as the Jake cools. 

Generally it has been believed that the role the sediment played in the heat budget was small, and obviously 

the annual net change is zero. Heat storage in the 

sediment is difficult to measure, and its short-term 

effects have not been believed to be important enough 

to warrant investigation. A limited amount of sedimenttemperature data is available from the studies on 

Pretty Lake, so that the effect of sediment heating 

upon evaporation can be discussed on a rough basis.

A probe containing thermocouples at 1-foot (0.30-m) 

intervals to a depth of 17.5 feet (5.33 m) below the lake 

bottom was placed in Pretty Lake 82 feet (25 m) 

below the instrument raft in late 1963. Temperatures 

sensed by the thermocouples were recorded on the 

instrument raft. Equipment-operation problems caused 

loss of records from some of the sensors at different 

times, but enough data were collected to construct the 

temperature lines in figure 15. The lower part of the 

figure is a graph of heat storage within the 17.5-foot 

(5.33-m) layer, assuming heat capacity of the sediment 

to be 1.00 cal cm"3 °C~1 (calorie per cubic centimeter 

per degree Celsius).

One of the very few reported previous studies of the 

heat budget of lake sediment was made on Lake 

Mendota, Wis., in the years 1916-21 (Birge and others, 

1928). Birge and Juday used a probe which had an 

electrical-resistance thermometer in its point and which 

was driven into the lake bottom. Over 200 profiles of 

sediment temperatures were made at four selected 

stations beneath water ranging in depth from 8 to 

23.5 meters (26 to 77ft).

The Lake Mendota study showed that the upper 5 

meters (16.4 ft) of sediment had a total annual budget 

involving the exchange of about 3,000 cal cm~2 beneath 

8 meters (26 ft) of water, 2,200 cal cm"2 beneath 12 

meters (39 ft) of water, and 1,100 cal cm"2 beneath 

18 and 23.5 meters (59 and 77 ft) of water. The annual 

heat budget for the entire lake was computed to involve 

the average exchange of about 2,000 cal cm"2 with the 

sediment. In each of the data-collection sites, the top 

meter of sediment accounted for about 50 percent of 

the annual budget, and the second meter accounted 

for about 25 percent.

Data from the two deepest Lake Mendota stations 

are similar to the Pretty Lake data represented in

5 10 15 20 25 5 10 15 20 25 5 10 15 20 25 5 10 15 20 25 5 10 15 20 25 5 10 15 20 25 5 10 15 20 25 5 10 15 20 25 5 10 15 20 25 5 10 15 20 25 5 10 15 20 25 

FEBRUARY MARCH APRIL MAY JUNE JULY AUGUST SEPTEMBER OCTOBER NOVEMBER DECEMBER

1964

< 10 15 20 2 

JANUARY

1965

FIGURK 15. Yearly temperature and heat-storage pattern in the upper 17.5 feet (5.33 m) of sediment below 82 feet (25 m) of 

water near the center of Pretty Lake. Heat storage is computed above a base of 0°C, assuming heat capacity to be 1.00 

calorie per cubic centimeter per degree Celsius.
A18 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

figure 15. Lake Mendota has about the same maximum 

.depth as Pretty Lake, and its average depth is only 

about 4 meters (13 ft) greater, but Lake Mendota's 

area is about 50 times greater than that of Pretty Lake. 

Therefore, the greater wind fetch at Lake Mendota 

causes it to stratify later and to have a deeper thermocline than is found in Pretty Lake. The result is a 

greater range of hypolimnetic temperature and a 

higher mean annual temperature in the hypolimnion, 

which in turn causes higher mean sediment temperature and a greater total annual heat budget of the sediment. The annual heat budget of about 800 cal cmT2 

for Pretty Lake deep-water sediment differs from the 

Lake Mendota budget in direct proportion to differences in the range of hypolimnetic temperature.

A simple expression for total heat transfer through a 

plane subjected to a sinusoidal temperature stress of 

amplitude Tm and period p m is given by the equation

_ /2pm

i S1 m\l r, 

V 7TP

(9)

where Qm is heat flow per unit area, s is thermal conductivity, and 0 is thermal diffusivity (Ingersoll and others, 

1954, p. 50). It is recognized that the thermal stress on 

the Pretty Lake bottom is not truly sinusoidal, but it 

is possible, without going through the complex Fourier 

analysis used by March (Birge and others, 1928), 

to determine from the data and equation 9 that the 

thermal diffusivity of Pretty Lake is about the same as 

the value of 0.00325 cm2 sec" 1 (square centimeters 

per second) computed for Lake Mendota.

Values of Qm for different depths in Pretty Lake 

were computed by use of Tm values from the thermalsurvey data. The Qm values were then weighted according to the size of the bottom area they represented in 

order to compute the mean annual heat budget for the 

lake, which was found to be about 2,000 cal cm"2 . 

Judging from the similarity of figure 15 and several 

similar plots of Lake Mendota data, the annual change 

in heat storage in Pretty Lake sediments can be represented by a curve similar to the one in figure 15, but 

having an amplitude about 2 3/2 times as great (fig. 16). 

The slope of figure 16 represents the rate at which abJAN FEE MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC

FIGURE 16 Estimated annual cycle of average heat storage 

in the upper 5 meters (16.4 ft) of Pretty Lake sediment.

sorption of heat energy into the lake sediment is influencing the lake's energy budget as it is used to 

compute evaporation. During May, June, and July, it 

is estimated that the net energy available for evaporation is about 17 cal cm"2 day"1 less than the quantities 

shown in table 3. In late November, when the lake is . 

cooling rapidly, the bottom sediments are releasing 

more than 30 cal cm"2 day" 1 .

Corrections for the sediment heat storage in the 

energy-budget evaporation terms were estimated from 

figure 16. During the early summer warmup the heat 

entering the sediment is equivalent to a reduction in 

computed evaporation of about 0.025 cm day"1 . Generally this reduction is about a 5-percent correction. The 

cooling corrections in the fall periods increased the 

computed evaporation about 0.03 cm day"1 , which is 

more than 50 percent for a period like number 59.

Sediment-heating corrections made for Pretty Lake 

are not considered to be accurate enough for use in the 

subsequent sections of this report, such as in the calibration of mass transfer. Sediment temperatures from 

two shallower stations are needed for a reasonably 

accurate computation of the budget. The assumed heat 

capacity of 1 cal gram"1 °C"1 (calorie per gram ^per 

degree Celsius) which was used in these computations 

and in the Lake Mendota computations probably is 

too large. However, the sediment-heating factor is 

sometimes significant, and undoubtedly it will receive 

further consideration in other evaporation studies that 

utilize the energy-budget technique.

MASS-TRANSFER STUDIES

The mass-transfer method of evaporation computation is widely used. Bibliographies prepared by the 

U.S. Geological Survey (Robinson and Johnson, 1961) 

and Utah State University (Christiansen and Lauritzen, 

1963) make numerous references to the use of the 

method within the United States. Papers by Budyko 

(1948) and by Braslavskii and Vikulina (1954) present 

lengthy bibliographies that are indicative of the use 

of the method within the Soviet Union. For an excellent 

description of the theory and a discussion of the development of the method, the reader is referred to the reports 

of the Lake Mead study (Anderson and others, 1950) 

and of the Lake Hefner study (Marciano and Harbeck, 

1952) and to the thesis of Al-Barrak (1964) that 

summarizes many of the present forms of the masstransfer method as it is used to estimate evaporation 

and evapotranspiration.

Equations for estimating evaporation by the masstransfer method take the form

E^=-f(u,}(en-en), (10)
COMPARISON OF EVAPORATION COMPUTATION METHODS A19

where

uz=windspeed at some height z above the water

surface, 

e0= saturation vapor pressure calculated from the

temperature of the water surface, and 

e a=vapor pressure of the air.

Various forms of the equation use different multiplier 

constants and different functions of wind speed based 

upon area, season, lake size, temperature and other 

factors.

The study of Pretty Lake assumed the mass-transfer 

relationship to be in the form developed in the Lake 

Hefner study (Marciano and Harbeck, 1952) as

EM T=Nu2(eo e^, (11)

which is the same equation used with equations 4 and 

5 to estimate Qh in the previous section. Here, N is a 

constant for a specific lake, and w2 is the average wind 

speed measured 2 meters (6.56 ft) above the water 

surface. Harbeck, realizing that the mass-transfer coefficient, N, summarizes many variables such as wind 

and vapor profiles and wave heights, has made an 

empirical relationship1 A7"=0.00859/.Aao5 between the 

constant and the surface area, A, of the body of water 

to which it applies (Harbeck, 1962, fig. 31). The constant N can be only roughly related to lake size, for it 

also is affected by local peculiarities, topography, and 

point of wind measurement. One purpose of the Pretty 

Lake study was to determine the mass-transfer, coefficient and to compare the Pretty Lake coefficient 

with those of other lakes or with a coefficient of 0.00661 

predicted by Harbeck's surface-area method.

INSTRUMENT RECORDS

Vapor pressure. The mass-transfer study made use 

of the same vapor-pressure data that were used in the 

energy-budget study for estimating the Bowen ratio. 

Figure 14 includes the values of e0 and ee , and the difference e=e0 ea is represented linearly by the separation of the two plots on the figure.

The difference between average values of e0 and e a 

over the energy-budget periods were used in the calibration of N and in the computation of evaporation. 

Values of (e0 ea) for the energy-budget periods are 

listed in table 5.

Wind record. Records from the anemometer dial 

readings were supplemented by the recorder-chart 

records when it was necessary to interpolate between 

dial readings for special study purposes. An approximate correction was applied to the springtime bankmeasured values to make them more nearly equivalent 

to the rest of the records.

1 This form assumes that equation 11 will have Eyn in centimeters per day, «2 in 

miles per hour, and ea and ea in millibars. Surface area A is in acres.

Anemometer height correction. Records from the

1.73-meter (5.68 ft) anemometers were adjusted to 

make them equivalent to the windspeed at 2.0 meters 

(6.56 ft) (u2 ). The correction factor to be applied to 

the 1.73-meter (5.68 ft) records was determined by 

comparing the average windspeed between consecutive 

dial readings for the two anemometers.

Four sets of data that seemed to be affected by 

anemometer icing or stalling were disregarded, and the 

remaining 85 pairs of data were equally weighted to 

define a regression line

0=1.032 1/.J .73+ 0.118, (12)

which had a standard error of 0.275 miles per hour 

(0.123 m per second). Upon testing the significance of 

the slope and intercept, it was found that the slope of 

1.032 was significantly different from unity but that the 

intercept of the ordinate was not significantly different 

from zero. Restricting the regression line to make 

it pass through the origin, a line was constructed by 

least squares that defined the relation

162.0= 1-046^1.73

All iij.73 data were corrected to 2-meter (6.56-ft) data 

by multiplying them by the constant 1.046. Figure 17 

is a time plot of values of u2 .0 computed between dial 

readings of the anemometers. Average values of u2 .o over 

the energy-budget periods are tabulated in table 5.

MASS-TRANSFER COEFFICIENT FROM ENERGY-BUDGET 

CALIBRATION

Assuming that evaporation can be computed as the 

product of the three terms in equation 11, the constant 

N for a particular lake can be defined as the slope of a 

straight line of calibration relating the product u(e0 e& ) 

to some independent measure of evaporation. It is 

common practice to use energy-budget data as the independent measure. Figure 18 is a plot of the products 

of u and (e0 e& ) values listed in table 5 against the 

evaporation values computed from the energy-budget 

studies. Figure ISA shows rates of evaporation and 

figure 18B shows total amounts of evaporation during 

the computation periods. A symbol n represents the 

number of days in a computation period.

If N, as expressed in equation 11, is a constant, a 

straight line fitted to figure 18 must pass through the 

origin. There is a physical basis to support such an 

assumption. At the time when wind is calm or when 

there is no driving force of the vapor pressure difference 

(e 0 ea= 0), turbulent exchange of vapor between the 

lake surface and the air is negligibly small. Likewise, 

the vapor exchange by simple molecular diffusion also 

would be small enough to be negligible.
A20 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

12

10

8

6

4

2 

0

16

- 14

o 

= 12

£ 10

GO

=; 8

z 6

s 4

UJ

S5 2

i o

16

14

12

10

6

4

2

0

.

1963

-

.

- 1964

. _

-

-

-

.

-

- 1965

'

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-

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5 10 15 20 25 

JANUARY

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5 10 15 2025 

FEBRUARY

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1 4..J..J-J5 10 15 20 25 

NOVEMBER

_

. ___ "

-

__~

_

-

-

-

-

i I I I I ...

5 10 15 20 25 

DECEMBER

FIGURE 17. Wind speeds. Length of lines represent duration of periods between integrator readings.

Several techniques were used in the attempt to 

determine the proper fit of a relation line to figure 18. 

Lines were fitted to the rate plot (fig. 18-4) by standard 

least-squares technique and by using weighting factors 

for each period proportional to the period lengths. 

Weighting factors are a way of accounting for the 

greater accuracy of the longer energy-budget periods. 

Lines also were fitted to figure 185 for what is, in effect, 

a double-weighted regression. The results showed very 

little difference between the weighted and unweighted 

lines fitted to figure 18.4. but gave the weighted lines 

fitted to figure 185 flatter slopes and intercepts nearer 

to the origin.

Limitations of regression analysis must be remembered in interpreting the fitting of the regression lines, 

which assumes that the dependent variable is normally 

distributed about the true regression line and has 

constant variance throughout the range of the independent variable.

Tests of the lines fitted to figure 18 do not unanimously support the assumption of an origin intercept, 

but it is believed that the springtime errors in the 

short periods have biased greatly the data points 

near the origin of figure ISA

Several techniques exist to determine the slopes of 

straight lines that are fitted to figure 18 and that will 

satisfy equation 11. A simple ratio technique would 

define a line passing through the origin and through 

the means of the two variables on figure ISA The 

ratio also can be weighted to account for varying 

lengths of the computation periods to define a line 

that would have the same slope as would a simple ratio 

computed for figure 185. Values of N computed for 

each period can be averaged, or they can be weighted 

according to period length or amount of evaporation. 

Regression techniques also may be used to fit unweighted, weighted, and double-weighted lines passing 

through the origin with slopes that will minimize the 

squares of the deviations of the dependent variable.

Figure 19 represents the slopes of straight lines 

passing through the origin and fitted by different 

methods. The 95-percent confidence limits computed 

for the regression fits give some idea of the expected 

error. The ratio techniques give greater consideration 

to the short low-rate values, whereas the doubleweighted regression is influenced most by the longer 

periods of 1965 and by the high-rate periods. Even 

the ratio-estimated slopes lie within the confidence
COMPARISON OF EVAPORATION COMPUTATION METHODS A21

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MASS-TRANSFER PRODUCT (nuAe), IN DAYS TIMES MILES PER HOUR TIMES MILLIBARS

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FIGURE 18. Relation of the mass-transfer product to evaporation measured by the energy-budget method. A (upper), 

Using evaporation rates. B (lower), Using amounts of evaporation per period. Dashed lines are at a slope of 0.00560.
A22 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

1963

1964 Unweighted ratio 1965

3 years

1963 

1964 Weighted ratio 1965 

3 years

1963 

Regression 1964 

through origin 1965 

3 years

1963 

Weighted regression 1964

through origin 1965 

3 years

Double weighted 1963 

regression through 1Q&5 

origin 3 years

EEB i Qfi^ Average of uAe {954 

values computed for 1965 

each period 3 yea rs

Average of uE «"e J|g 

values, weighted by ! QCK 

amount of evaporation 3 years

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MASS-TRANSFER COEFFICIENT(N)

FIGURE 19. Mass-transfer coefficients determined by different 

methods. Lines drawn through some symbols represent 

95-percent confidence limits.

intervals of the slopes of the unweighted and weighted 

regressions through the origin.

Visual inspection of figure 18, especially of the rate 

plot, may give reason to suspect the validity of an 

assumed straight-line function. A curved line, logarithmic, parabolic, or second degree, might seem to be 

better, especially if it is restricted to pass through the 

origin. However, in consideration of the origin of the 

data and the errors contained in the low-rate energybudget computation, a curved line is not believed to 

be a better representation of the mass-transfer function 

than is the straight line. Further discussion of this 

problem is in a later section of this report.

Considering the various coefficients computed by 

different methods, the relation

#MT =0.00560 (14)

was selected to compute mass-transfer evaporation.2 

The mass-transfer coefficient in equation 14 is 15 percent 

less than the coefficient of 0.00661 preducted by 

Harbeck's (1962, fig. 31 )method.

2 The constant N, here expressed as 0.00560 with E in centimeters per day and MJ.O 

in miles per hour, would be 0.0125 with E in centimeters per day and ut.o in meters 

per second, and would be 0.00220 with E in inches per day and M2.o in miles per hour. 

Vapor pressure is in millibars.

COMPUTATION OF EVAPORATION BY MASS TRANSFER

Evaporation rates and quantities were computed for 

the energy-budget periods by use of equation 14. Table 

5 lists the terms of the computation. Evaporation rates 

and amounts computed by the mass-transfer method 

are shown graphically and further summarized in. 

figures 30 and 31 and in tables 20 and 21 in a later 

section of this report.

Accuracy of the mass-transfer data is difficult to 

estimate because there is no absolutely accurate 

control. Often the judgment of the investigator provides the most tangible estimate of accuracy.

The regression analyses of the calibration data 

indicated standard errors about the line fitted to 

figure l&A of about 0.08 cm day" 1 . The estimated 

confidence interval at the origin spread 0.04 cm day"1

TABLE 5. Summary of mass-transfer terms for open-water periods,

1963-65

Period

No.

Length 

(days) Dates

M2.0

miles 

per 

hour

eo ea 

(mb)

Evaporation

Centi- Centimeters per meters per 

day period

7.0

8.0

10.9

10.0

21.0

5.4

13.1

13.0

7.6

7.4

7.0

13.9

14.1

27.5

13.1

17.9

14.0

14.0

17.1

Apr. 5-12....._.

12-20......

20-May 1.. 

May 1-11........

11-June 1.. 

June 1-6 _....

6-19........

19-July2_. 

July 2-10........

10-17-----..

17-24...--..

24-Aug. 7.. 

Aug. 7-21.......

Sept. 18... 

Sept. 18-Oct. 1.. 

Oct. 1-19......_

19-Nov. 2.. 

Nov. 2-16..-.-..

16-Dec. 3..

6.92

8.70

7.15

7.80

6.23

3.57

5.79

2.65

5.43

5.93

5.72

5.77

5.04

4.85

5.26

4.41

5.13

7.54

8.29

5.0

4.0

6.6

6.1

8.9

8.7

14.0

17.3

21.7

13.4

11.4

13.6

13.8

12.6

11.9

10.2

8.7

5.7

3.5

0.193

.196

.265

.267

.310

.174

.454

.256

.660

.445

.365

.440

.390

.342

.351

.252

.250

.241

.162

1.36

1.57

2.89

2.67

6.51

.95

5.92

3.33

5.04

3.27

2.57

6.10

5.49

9.42

4.60

4.51

3.49

3.38

2.77

Record 

season.

242. 0 Apr. 5-Dec. 3. .313

14.9

7.0

7.1

6.9

11.1

14.0

9.9

25.1

16.0

12.9

18.0

14.0

14.0

12.0

17.2

17.8

12.8

11.9

12.0

1964

Mar. 20-Apr. 4..

Apr. 4-11.------

11-18---.-- 

18-25-.-.-- 

25-May 6- -

May 6-20-.------

20-30---.-. 

30-June 24.

June 24-July 10-

July 10-23.-.-...

23-Aug. 10. 

Aug. 10-24_.____

24-Sept. 7- 

Sept. 7-19.......

19-Oct. 6- 

Oct. 6-24........

24-Nov. 6.. 

Nov. 6-18-------

18-30-.----

6.68

7.73

11.89

8.41

7.14

8.50

6.87

6.01

4.36

4.44

3.89

5.30

5.16

4.82

6.77

5.10

4.05

6.65

8.76

3.1

I.2 

3.0 

3.4 

4.4 

7.6 

14.3

II.5 

17.4 

13.2 

19.3 

13.7 

12.7 

13.3 

9.3 

8.8 

5.3 

5.1 

6.1

.116

.052

.200

.160

.176

.362

.550

.387

.425

.328

.421

.407

.367

.359

.353

.253

.120

.192

.300

1.73

.36

1.42

1.10

1.94

5.08

5.42

9.73

6.79

4.23

7.58

5.69

5.14

4.31

6.05

4.50

1.54

2.28

3.58

Record 

season.

254.6 Mar. 20-Nov. 30. .308 78.47

69-

56.1

30.0

43.0

33.0

1965

Apr. 13-June 8-... 

June 8-July 8- - - - 

July8-Aug. 20-.- 

Aug.20-Sept.22..

7.53

6.10

5.39

5.99

7.2

13.0

12.8

9.8

.304

.444

.386

.329

17.03

13.29

16.62

10.85

Record 

season.

162.1 Apr. 13-Sept. 22. .357 57.79
COMPARISON OF EVAPORATION COMPUTATION METHODS A23

on either side of the regression line. Relative standard 

error of the slope of the regression line through the 

origin is about 6 percent.

Standard error about the line fitted to figure 185 

was 1.37 cm (0.54 inch) per period, and the confidence 

interval at the origin spread 0.70 cm (0.28 inch) on 

either side of the line. The slope of the regression line 

fitted through the origin of figure 185 had a standard 

error of 7 percent.

All of these statistics were computed under the 

assumption that all the error in the calibration fit 

was contained in the energy-budget control. They are 

reasonable estimates of the validity of the calibration, 

but they give little specific information regarding the 

individual errors in the two different methods.

Consideration of the errors in the individual vaporpressure and wind terms tells a little about the accuracy 

of the mass-transfer method. Comparison of the two 

anemometers indicates that average windspeed is 

being measured with an accuracy of about 2 percent. 

The difference (e0 ea) is believed to be within about 

0.3 millibar at lower temperatures and within about 

0.8 millibar at the highest lake temperatures. Percentage 

error varies from a minimum at the higher evaporation 

rate to a large number when Ae is small. However, 

low vapor-pressure difference often was a result of a 

calm damp day, so that evaporation rate estimates 

for these days contain only small absolute errors.

The errors in the mass-transfer computations for 

the days with low evaporation rates generally are 

smaller than the errors in the energy-budget evaporation for similar days.

WATER-BUDGET STUDIES

The water-budget technique for measuring evaporation from a lake makes use of common hydrographic 

techniques of measuring stage, precipitation, and 

streamflow. The formula for computation simply 

equates the total inflow to the sum of the total outflow 

and change of storage, or

I+IP+G=EWB+0+AS (15) 

where

1= surf ace inflow,

Ip= precipitation falling on lake,

6?=net underground seepage, considered positive

for inflow, 

EWB = evaporation, 

0= surf ace outflow, and

A$=net change of storage, considered positive 

for increase.

In order to compute evaporation, it is necessary 

directly to measure or somehow to determine all the

other factors. The ground-water seepage term cannot 

be directly measured, so that in preliminary computations it is combined with evaporation as (E G), a 

difference designated as AH". Equation 15 then may be 

rewritten as

=E- G=1+IP -0-AS (16)

where it is seen that the AH term may be described as 

the fall in stage, corrected for inflow, outflow, and precipitation, if all other terms are reduced to change per 

unit area of water surface. Further analysis of the water 

budget requires an additional means of defining evaporation or seepage in order to understand completely 

all the terms of the water budget.

INSTRUMENT RECORDS

The records of inflow, outflow, and precipitation used 

in the water-budget studies were the same records used 

in the computation of the advected-energy term of the 

energy-budget studies.

The small volume of water moving into, and out of 

Pretty Lake reduced the requirement of accuracy in the 

computation of the data for the Qv term of the energy 

budget. In the water budget, it is necessary that the 

errors of the measurements be reduced to a minimum 

to maintain accuracy.

Surface inflow and outflow. Records of streamflow 

into and out of the lake were computed by standard 

Geological Survey methods (Corbett and others, 1943). 

Gage-height records of the water-stage recorders were 

applied to ratings defined by current-meter or volumetric measurements. Figures 20 and 21 illustrate the 

magnitude and variability of the flow.

Daily streamflows for the inlet station have been 

published by the U.S. Geological Survey in the series 

"Surface Water Records of Indiana." These records 

have been rated as poor, meaning that daily discharges 

generally are more than 15 percent in error. This estimate of large error is due to the very low flow, which 

normally is computed to the nearest 0.01 cfs (cubic foot 

per second); a change or error in stage reading of 0.01 

toot can result in a 20-percent change or error in the 

daily discharge. Over several days the errors of the daily 

measurements would tend to compensate one another, 

and errors in the volumes of inflow used in the waterbudget computations would be more in the order of 5 

percent instead of greater than 15 percent.

The outlet station, which also is weir controlled, has 

the same problems of rating sensitivity at low flows as 

has the inlet station. Whereas the inlet station used a 

V-notch weir, the outlet had a wider weir and most 

probably had about twice as much error in the computed 

outflow values.
A24 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

5l0 15 20 2 5 510152025 510152025 5 10l520 2 5 

JANUARY FEBRUARY MARCH APRIL MAY

5 10 15 2(l25 5 1 0l5 20 25 

JUNE JULY AUGUST SEPTEMBER OCTOBER NOVEMBER DECEMBER

FIGURE 20. Discharge of Pretty Lake inlet.

Lake stage. Figure 22 illustrates on a small scale the 

variations in the stage of Pretty Lake. The pattern 

shows a rise with each rain followed by a slow fall in 

stage caused by outflow and evaporation. The instrumentation section of this report describes the limitations 

of the two recorders used to measure stage. Although 

the recorder operating at 1:1 ratio was readable to the 

nearest 0.001 foot (0.03 cm) the accuracy of such a 

float-operated instrument probably is not within the 

limits of readability. Conservative estimates of the 

error in the change-of-storage term indicate that the 

value over one computation period was within 0.02 

foot (0.6 cm) during the 1963 season and was within 

0.01 foot (0.3 cm) during 1964 and 1965.

Precipitation. The values used in the precipitation 

terms of the Pretty Lake water budget were selected 

from the records of the two recording rain gages, the 

nonrecording gage, and the stage gage (fig. 23). It was 

not unusual for differences among the gages to be more 

than 15 percent. The differences resulted from areal 

differences in the precipitation and from catch errors of 

the unshielded gages. Unless the chart indicated poor 

operation of the recorder, the lake stage gage generally 

was considered to be the most reliable measurer of the 

average precipitation falling directly upon the lake.

The topography around the lake is flat enough to

prevent large amounts of ungaged surface runoff from 

running into the lake. A good deal of the water falling 

along the shoreline soaked directly into the grasscovered fields and lawns or was caught by the many 

small closed basins. Runoff which did reach the lake 

was measured by the stage recorder and was treated in 

computation the same as was precipitation. In a few 

cases, it was possible to separate overland ungaged 

flow into the lake after the rain had ceased to fall. 

Such instances were the result of rainfall of 1.5 

inches (3.8 cm) or more.

BALANCING THE WATERBUDGET (SEEPAGE CORRECTION)

The values of individual terms of the water budget 

for the three years of study are presented in table 6. 

The table is arranged to solve for AH in centimeters 

per day for the same periods that were used in the 

energy-budget computations and in the mass-transfer 

calibration.

Values of evaporation computed by the water-budget 

method (£"WB) would be expected to plot with the same 

kind of mass-transfer calibration as did the energybudget values used in figure 18, if it is assumed that the 

water budget was accurate. A certain amount of information also can be gotten from a plot of the corrected 

fall in stage, AH, against the mass-transfer product,
COMPARISON OF EVAPORATION COMPUTATION METHODS A25

10 15 20 25 5 10 15 20 

JANUARY FEBRUARY MARCH APRIL

:10 15 20,

MAY

10 1E 20, e C 10, 5 20 5 

JULY

5 1U 15^25 

JUNE

10 15 20 25 

AUGUST

10 15 20 ; 

SEPTEMBER OCTOBER

10 15 2 °; 

NOVEMBER DECEMBER

FIGUBE 21. Pretty Lake outflow.

uAe (Langbein and others, 1951). Such a plot for the 

three years of study is shown in figure 24, which shows 

both rate and amount-per-period scales. The line shown 

in figure 24 is drawn with the slope defined in the masstransfer calibration (eq 14). If the seepage, G, were zero 

or negligibly small, a line fitted to the points in figure 24 

would be nearly identical to the line shown and definitely 

would pass through the origin.

Most of the data points on the figure agree well with 

the relation line shown. The fit is as good as the fit 

of the energy-budget data. However, a group of data 

points (Nos. 42-48, 66, and 69) seem to define a separate 

line approximately parallel to the relation line shown 

but intersecting the ordinate axis somewhere below the 

origin. Rather than being a part of the total set of data, 

these points seem to be part of a separate population. 

Undoubtedly they describe periods when the fall in 

stage, A H, is influenced by seepage as well as by evaporation. This conclusion is further supported by the

coincidence of the periods represented by these points 

with the times of moderate, heavy, or frequent rainfall. 

The vertical distance between the point position and 

the line is the measure of the rate or amount of seepage 

during the period represented by the point.

The differences of the deviations of the several points 

indicate that the seepage rate is variable between and 

within the periods. A better analysis of variability is 

provided by breaking the data periods into subperiods 

representing fewer days. The mass-transfer and waterbudget data are easily arranged for such analyses.

Figure 25 is a plot of the subperiod data for periods 42 

through 48 in 1964 and for all the periods in 1965. It is 

estimated that the error for each subperiod may be 0.2 

cm (0.08 inch), which is 0.03 to 0.2 cm day' 1 for the 1- to 

7-day-long subperiods. The seepage estimates based 

upon the deviations of the subperiod points from the line 

are plotted as a function of time in the seepage plot of
A26 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

UJ

966.0

965.8

965.6

965.4

965.2

965.0

964.8

964.6 

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1965

0"

i i i i _i I i i i

294.4

294.3

294.2

294.1

294.3

294.2

294.1

294.0

294.4

294.3

294.2

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10 20

5 15 25 10 20 10 20 10 20 10 20 10 20 10 20 . 10 20 10 20 10 20 10 20 10 20

5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25

JANUARY FEBRUARY MARCH APRIL MAY JUNE JULY AUGUST SEPTEMBER OCTOBER NOVEMBER DECEMBER

FIGURE 22. Pretty Lake stage, 1963-65.

o.u

2.5

2.0

1.5

.1.0

0.5 

0

3.0

2.5

20

1.5

1.0

0.5

0

3.0

25

2.0

1

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-

-

-

-

i i i i

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1

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5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 

JANUARY FEBRUARY MARCH APRIL MAY JUNE JULY AUGUST SEPTEMBER

5 15 25 5 15 25 5 15 25 

OCTOBER NOVEMBER DECEMBER

FIGURE 23. Daily precipitation measured at Pretty Lake.
COMPARISON OF EVAPORATION COMPUTATION METHODS A27

- 0.20

- 0.30

- 0.25

- 0.15

- 0.10

- 0.05

20 40 60 80 100 

MASS-TRANSFER PRODUCT (uAe), IN MILES PER HOUR TIMES MILLIBARS

- -0.05

120

66.'+-

EXPLANATION 

O 1963 

X 1964 

+ 1965

Q 

O

c tr

O 11 l 

Q_

cr

UJ

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4 co

LJ

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3 z

s

<,

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<

500 1000 1500 2000 2500 

MASS-TRANSFER PRODUCT (nuAe), IN DAYS TIMES MILES PER HOUR TIMES MILLIBARS

3000

FIGURE 24. Relation of corrected stage change to the mass-transfer product by energy-budget periods. The line 

shown has the slope determined by the calibration plot of figure 18.
A28 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA 

TABLE 6. Summary of water-budget terms for Pretty Lake open-water periods, 1968-65

No.

26

27

28

29

30

31

32

33

34

35

36

Record 

season.

42__ _ __

44 ______

45_ __ ____

47

48

49

50

51 _____

53

54

55

56

57

58

59

60

Record

season.

67

68

69

Record 

season.

Length 

(days)

7. 6

7.4

7.0

13. 9

14. 1

27. 5

13. 1

17. 9

14. 0

14. 0

_ 17. 1

153. 6

14. 9

7. 0

7. 1

6 9

11. 1

14. 0

9. 9

25. 1

16. 0

12. 9

_ 18.0

14. 0

14. 0

12. 0

17. 2

_ 17.8

12. 8

_ 11.9

12. 0

254. 6

56. 1

30. 0

43. 0

33. 0

162. 1

Period

July

Aug.

Sept. 

Oct.

Nov.

July

Mar. 

Apr.

May

June 

July

Aug. 

Sept. 

Oct. 

Nov.

Mar.

Apr. 

June 

July

Aug.

Apr.

Dates

1968

10-17

17-24

24- Aug. 7______

21-Sept. 18_____

18-Oct. 1__ _ __

1-19

19-Nov. 2______

16-Dec. 3 ____

2-Dec. 3 ______

1964 

20- Apr. 4 ___

11-18

18-25

25-May 6__ _ _

6-20 __________

30- June 24_____

24- July 10_ _ _ _ _

23- Aug. 10_____

24-Sept. 7______

7-19

19-Oct. 6 _______

24-Nov. 6____._

18-30

20-Nov. 30_____

1965 

13- June 8__---_

8-July 8_______

8- Aug. 20_-____

20-Sept. 22_____

13-Sept. 22_____

Precipitation

runoff (cm)

0

8. 66

Q 07

9. 12

afi

1. 42

1 fia

00

1 aa

2.79

i a Q9

1. 70

qo

3 A K.

3

OQ

3.23

1.47

9.60

3 afi

9 a9

90

7.52

Q4-

2.87

1 ao

afi

QQ

afi

1 90

1 17. 70

4. 7a

18. 59

i 16. 64

Inlet inflow 

(cm)

0. 07 

. 10 

. 12 

. 53 

. 22 

. 17 

. 03 

0 

. 05 

. 04 

. 07

1 72 

47 

34 

1 02 

1 34 

73 

11 

27 

03 

01 

0 

0 

0 

0 

0 

0 

0 

0 

0

10. 94 

. 43 

. 88 

2. 91

Outflow

(cm)

0 

0 

0. 13 

.59 

. 55 

0 

0 

0 

0 

0 

0

0 

. 34 

.77 

1. 66 

4.41 

3. 12 

.27 

. 10 

. 01 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0

29. 79 

. 49 

0 

3. 32

Storage Them 

change expans 

(cm) (cm

-5. 

6.

4. 

-5. 

-7. 

-3. 

-3. 

_ 2

11. 

2.

-l!

-2'. 

 1. 

-10. 

2. 

-3. 

-2. 

-4. 

_ 4.

-6.

-8. 

3.

8.

49 0 

40 - 

91 

27 - 

49 

92 - 

66 - 

96 - 

13 - 

91 - 

15 -

13 0 

65 

15 

14 

21 

62 

44 0 

94 

96 

68 

49 

16 - 

93 

47 

45 - 

11 - 

85 

61 

37 -

89 

72 

47 

87

ial AH

ion 

Centimeters Centimeters 

per period per day

12 5. 

15 2. 

15 2. 

03 4. 

18 5. 

12 9. 

18 5. 

06 4. 

24 3. 

24 2. 

09 2.

__._ 48.

03 -'. 

12 -. 

06 -. 

24 

24 2. 

4. 

27 9. 

12 6. 

15 4. 

12 10. 

12 5. 

03 4. 

15 5. 

30 5. 

24 4. 

03 1. 

03 1. 

21 2.

____ 69.

64 6. 

25 13. 

25 16.

20 7.

___. 43.

68 0 

21 

30 

76 

84 

39 

19 

18 

82 

26 

62

25 ______

49 - 

79 - 

08 - 

27 - 

61 

70 

75 

10 

96 

66 

57 

24 

90 

19 

95 

73 

87 

44 

06

10 ______

38 

69 

25 

16

48 _-_-__

743 

301 

327 

343 

414 

341 

396 

233 

273 

161 

154

033 

113 

OH 

039 

055 

192 

482 

362 

436 

362 

586 

374 

350 

432 

347 

265 

146 

121 

172

114

457 

. 378 

. 217

1 Includes obvious overland runoff.

figure 26, which also illustrates the time duration of the 

numbered periods and letter-designated subperiods.

A line (long dashes) appears in figure 26 as an estimate 

of the changing rate of seepage as defined by the 

periods and subperiods. A rapidly fluctuating line also 

is shown as an estimate of the manner in which the 

seepage rate probably fluctuates with each rain and 

with dry periods of several days. The many depressions 

in the flat sandy land around the lake are responsible 

for rapid and frequent changes in the ground-water 

gradient which controls the rate of seepage into Pretty 

Lake. Although the rapidly fluctuating curves lack 

absolute accuracy and bases in data, they are a reasonable estimate of the real phenomenon.

EVAPORATION FROM THE WATER BUDGET

The water budget is a poor means of evaporation 

estimation unless the seepage rate is determined independently, is known to be constant, or is known to be 

zero. As it was used on Pretty Lake, the water budget 

is more of an estimator of seepage than an estimator of 

evaporation because evaporation already has been 

estimated by other methods. A line might have been 

fitted to figure 24 that satisfied the data and intercepted 

the ordinate in such a way as to define a high N and a 

constant seepage of about 0.2 cm day"1 . The scatter 

about the line would not have been much greater than 

the scatter about the mass-transfer calibration based
COMPARISON OF EVAPORATION COMPUTATION METHODS A29

0.6

0 ' 5 

0.4

0.3

0.2

~ 

0.1

°

_fl 1 U.I

-0.2

0 47D

0 46A 44C 

'45A 0 0 42B

46B 0o 0 45B

43B 

-I i i i

0 44B

43C

0.20

0.15

0.10

0.05

-0.05

-5 0 10 20 30 40 50 60 70 80 90 100 

MASS-TRANSFER PRODUCT (uAe), IN MILES PER HOUR TIMES MILLIBARS

T

-5 0 10 20 30 40 50 60 70 80 90 100 

MASS-TRANSFER PRODUCT (uAe), IN MILES PER HOUR TIMES MILLIBARS

FIGURE 25. Relation of corrected stage change to the masstransfer product by subperiods during 1964 and 1965. The 

lines shown have the slope determined by the calibration plot 

of figure 18.

upon the energy-budget data. The seasonal bias found 

in the water-budget term, A#, must be removed in order 

to properly calibrate the mass-transfer equation. Although the energy-budget data contain larger errors 

in each period than do the water-budget data, it can be 

assumed that the errors are more random and that bias 

is not so likely to result.

It is common practice to use lake-stage data to 

determine an N value from a regression line fitted to a 

plot similar to figures 24 and 25. Use of this method 

often produces an N value considerably larger than 

would have been estimated by Harbeck's (1962, fig. 

31) method. It is possible that many lakes could be 

affected by high inflow-seepage rates during periods of 

low evaporation, much the same as was Pretty Lake.

The method of determining seepage rate dictates 

that total evaporation computed by the water budget 

will agree closely with the evaporation measured by 

mass-transfer or energy-budget methods. Table 7 lists 

the seepage estimates by energy-budget periods and 

gives the computed values of -E"WB . Evaporation rates 

and amounts computed by the water-budget method

are shown graphically and are further summarized in 

figures 30 and 31 and in tables 20 and 21 in a later 

section of this report.

EVAPORATION-PAN STUDIES

It has long been a practice to attempt to estimate 

lake evaporation from records of evaporation measured 

in a small pan. One standard pan used within the 

United States is the class-A pan. The pan is metal, 4 

feet (1.22 m) in diameter and 1 foot (0.30 m) deep, 

and is set on wood planks above the ground. The 

weaknesses in its performance in duplicating lake 

evaporation are well known. The principal criticisms 

concern distortions of the temperatures and wind 

regime, considerable increase in the values of evaporation, and instability of reduction coefficients. Nevertheless, the class-A pan has been the basis for records for 

a long time, and its advantages of simple installation, 

easy service, and moderate cost undoubtedly will 

encourage its use for a long time in the future.

Excellent discussions of research and interpretative 

work that have been done to improve the effectiveness 

of pan records are contained in U.S. Weather Bureau 

(USWB) Research Paper 38 (Kohler and others, 1955), 

USWB Technical Paper 37 (Kohler and others, 1959), 

and the Geological Survey reports on the Lake Hefner 

(Kohler, 1952) and Lake Mead (Kohler and others, 

1958) studies.

KENDALLVILLE STATION DATA

Pan studies were not a principal part of the Pretty 

Lake project, but some insight can be gained from the 

consideration of records from a nearby evaporation 

pan. The U.S. Weather Bureau maintains a class-A 

pan in Kendallville, Ind., at a site about 9 miles (14

TABLE 7. Corrections for seepage applied to water budget, and 

water-budget evaporation

26-36_______ ----- _

42__ _________________

43__ 

44_______-_-__--_-_-_

45__ 

46 - - _ -

47__- 

48__._ 

49-60.__- -

66__ --- _ 

67..--.--- ---

68__ - - 

69__ 

i Use AH, table 6.

Seepage

per day)

_____ 0

_____ . 16

_-.-_ . 18

.21

_____ .20

_____ . 15

_____ . 13

_____ .06

_____ 0

_ ___ . 19

_____ 0

_____ 0

. 11

E

Centimeters 

per day

0)

0 13

07

20

16

21

32

54

0)

30

46

38

33

NB

Centimeters 

per period

0)

1. 94

.49

1.42

1. 10

2. 32

4.49

5. 32

(0

16.83

13. 69

16. 25

10. 90
A30 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

 1 

- 1964

1 ! - j -j , | 

1 h .III ill

1 1 1 1 1 

1, . 1

-

3 z 

o

2 fe

1 1 

0 £

 " 1 1 1

1964

-

ft

1 1 I 1 1 8

i

-=t:±:z] -3==3#

'4 ^~

Period 4 

i i

2

A ~\

£

1

-AH

43 

i i

^<L

ft.

44

±

$

45 

I

1 1 1 1 1 A o ' h

*V

H K£

4 6

,

..AH o

l^

kcj 

47

 -5h 

s^-

*&

-

-

-H 0.05 _, 23

2 3 6 

<c LJ .

* S *

o 5 '

? o 0

i i

" 1965

-

I 1 1 1 1

.,., h,

i i i i i

. ..1.

 i i i ii

1. . .. 1

I 1 i i i

., , 1

1 1 1 1 1

1,1 , | I

1 1 1 1

,

-

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3 i

2 fe

1 C

o £

15 20 25 5 10 15 20 25 5 10 15 20 25 5 10 15 20 25 5 10 15 20 25 5 10 15 20 25 5 10 15 20 25 

MARCH APRIL MAY JUNE JULY AUGUST SEPTEMBER

FIGUKE 26. Seepage during 1964 and 1965 open-water periods, showing precipitation and duration of subperiods. Horizontal 

dashed lines represent measured values by periods and subperiods. Curved lines are estimates of long-term and shortterm variations in seepage.

km) south of Pretty Lake. The station is operated by a 

lay observer who makes daily readings of air temperature and precipitation the year round and who reads 

pan evaporation and wind passage over the pan daily 

during the summer months. The station would have to 

be classified as nonstandard, in the strictest sense, 

owing to trees in the vicinity, grass growing around the 

pan, and irregularities of cleaning and maintenance. 

However, the irregularities in the maintenance and 

location of this station probably are of no greater 

consequence than those found in many other stations.

Records from the Kendallville evaporation station are 

published in the Climatological Data series for Indiana. 

Those records for the 3 years of the Pretty Lake study 

are repeated in table 8.

Another Weather Bureau pan station is located at 

the Purdue University experiment station near Culver, 

Ind. This location is about 70 miles (112 km) eastsoutheast of Pretty Lake. Records for the station are 

published, and those for the period of the Pretty Lake 

study are repeated in table 9.

Both the Kendallville and Culver pan records are 

missjng several days' readings. For short periods of a day

or two, one record has been used to estimate evaporation 

at the other pan, or estimates have been made using 

computed pan evaporation techniques, which will be 

explained in the following paragraphs.

Nationwide evaporation patterns are described in 

USWB Technical Paper 37 (Kohler and others, 1959). 

The following factors for the Pretty Lake location were 

obtained from the five plates in that report:

Average annual pan evaporation is 42 inches (107

cm). 

Average annual lake evaporation is 31.5 inches

(80. cm.)

Average annual pan coefficient is 76 percent. 

Average annual May-October lake evaporation is 

82 percent of annual lake evaporation. This is 

equal to 26 inches (66 cm). 

Standard deviation of annual pan evaporation is

2.4 inches (6cm).

It is an 'easy, common practice to multiply the daily 

evaporations from a pan by a coefficient in order to 

estimate lake evaporation. For northeastern Indiana, 

such estimates might be made by multiplying pan evaporation values listed in table 8 by the 0.76 annual co-
COMPARISON OF EVAPORATION COMPUTATION METHODS A31

TABLE 8. Daily evaporation, in inches, from U.S. Weather Bureau class-A pan at Kendallville, Ind.

[Values are for the 24 hours ending at 4 p.m. on the date shown]

Day

1

2

3

4

5

6

7

8

9

10

11

1?,

13

14

15

16

17

18

19

?,0

21

22

23

74

25

26

27

28

29

30

31

Apr.

_. _ _ 0. 18

________ . 15

________ .28

____-.__ .10

__--___. . 10

________ .28

__--_-__ . 11

________ . 14

_______ . 13

_.--_-__ .15

_______ . 14

________ .17

________ .26

________ . 10

__--_-__ .20

________ .10

________ .24

________ . 13

________ .33

. 20

________ .22

________ .08

________ .08

14

________ . 14

_______ . 14

________ .24

________ .17

________ . 11

Total.. 4 4. 98

May

0.06

1Q

. 20

.20

. 13

. 16

. 23

. 34

.28

. 21

. 15

. 20

. 13

. 21

. 17

OQ

. 22

. 16

.22

. 14

. 23

. 16

. 11

. 18

. 21

0)

.51

.08

. 11

. 30

. 11

5. 69

June

0. 22

. 21

. 27

. 18

. 34

. 13

. 26

. 18

.27

. 24

. 30

. 28

. 14

. 29

. 18

.23

. 14

. 24

.27

. 18

.25

1Q

.25

. 33

.26

. 30

OC

.29

. 26

. 30

7.23

1963

July

0. 24

. 34

. 31

qn

. 30

. 32

. 35

. 18

. 33

. 34

. 31

. 34

. 17

. 17

. 32

19

.26

. 29

97

2 91

. 32

. 17

. 20

39

19

. 27

99

. 24

.26

00

. 22

8. 18

Aug.

0.20

19

2 . 15

01

. 14

1 3

. 16

91

1 Q

. 17

OK

1 9

. 13

. 12

. 17

. 22

. 16

1 *.

. 10

09

9O

. 15

. 21

. 11

9O

90

19

. 10

09

.26

. 10

5. 11

Sept.

C1 )

O OQ

. 10

1 8

. 13

1 8

. 15

09

. 16

OQ

. 22

1 9

19

. 18

. 24

OQ

1Q

. 16

. 22

. 10

0*.

. 14

. 13

. 15

. 17

on

. 16

. 16

. 14

. 14

4.66

Oct.

0. 17 .

24

90

09

. 16 .

. 21 .

OQ

1 ^

1 ^

. 16

. 14

. 15

. 17

. 11

. 12

1 3

. 16

09

.04

. 07

OQ

. 11

1 3

i q

. 11

. 15

OQ

. 15

. 11

09

. 07 .

4. 22

June

qn

. 34

97

OK

' 30

OK

i o

1 8

.26

. 17

.29

QO

. 14

1 *.

qn

QQ

oq

_>7

94.

1 8

qn

94-

July

0. 30

qi

on

C)

59

OK

. 34

3 . 15

94.

99

97

90

. 20

. 15

. 16

qn

OK

18

99

qn

1Q

1Q

. 24

97

91

93

Oft

. 30

97

qq

. 29

7.61

1964

Aug.

0. 20

.29

qo

qi

qn

98

. 30

. 31

90

1 a

. 21.

19

. 10

. 20

. 16

.26

. 28

. 14

99

. 15

i q

. 17

90

. 15

90

. 16

1 8

9O

. 16

OQ

. 22

6.65

Sept.

0. 16

99

OK

on

. 22

C1 )

. 45

3 9K.

. 21

98

. 13

1 8

. 16

. 21

. 15

. 10

. 10

.06

. 05

. 04

. 14

19

. 36

1 *.

. 10

. 10

1 3

. 12

. 10

19

4. 95

Oct.

0. 14

09

. 14

19

. 13

.06

. 07

. 08

. 03

09

. 10

.08

. 07

. 09

09

. 10

. 11

1Q

. 08

.06

. 14

. 05

.07

OQ

1 Q

. 10

. 08

. 06

nQ

. 08

. 05

2. 83

May

0. 23

. 24

. 20

19

. 18

. 30

.26

. 16

: 13

19

June

0. 29

. 10

. 21

.25

. 18

. 21

. 11

. 21

.27

. 22

. 27

1965

July Aug.

______ 0. 08

______ .22

______ .22

______ . 10

______ . 18

______ . 33

______ . 14

______ . 16

______ .08

______ . 11

______ .23

______ .25

______ .30

.__--- .27

______ .27

______ .26

______ .22

______ .13

______ . 17

______ .22

______ . 16

______ .09

______ .12

______ . 19

______ . 17

______ . 19

______ .31

0. 35 . 22

.25 .14

.20 .11

.16 .04

______ 5. 68

Sept.

0. 19

. 12

. 15

. 11

(')

. 37

. 09

.08

. 17

. 13

. 15

. 11

. 10

.09

2 . 22

2 . 11

. 04

. 12

. 20

. 12

. 16

. 06

. 12

. 16

. 10

.09

. 09

. 10

. 09

. 03

3.67

1 Included in next observation.

2 Estimated (Kohler and others, 1959, fig. 1).

3 Estimated, based on Culver record.

4 Total adjusted by Weather Bureau.

TABLE 9. Daily evaporation, in inches, from U.S. Weather Bureau class-A pan at Culver Experiment Farm, Ind.

[Values are for the 24 hours ending at 8 a.m. on the date shown]

1.-.. -__..-.

2

3.. .__._.._....__....

4 . _ _._.. .

5....._. _._..._ .

6... .._.__.._._.__.

7_. ._.___._._..______

9. _.__.___.._._._ .

10._.__... .____._._._

11. ___ _ .

12. _ _____ .

14

15. ..__.___.__.._____

17_. .._.._..___ ....

18... _._.._.._.._ .

20. ._.._.__.____.____

21_ _.___.. .

22. ._.._._._.._ . . 

23. .._______._.._____

24. _._._._ 

25. __._._.__.._ . ... 

26_ _..__..

27. _._._.--._ _.. . 

28. ._...__.._.___.._.

W~.~-~-~.~-~-~-~.'-".'.~.".~"~

31... ___..

Total..........

Apr.

0.23 

.25

.08

.27

.21

.38

19

.32 

.17

.07 

.06 

.12

.16 

.23 

.29

May

0.26

.14

.22

.21

.22

.09

.22

.31 .

.29 .

.40 .

.20 .

99

.17

.30 

.06

.21

.26

.13

.22 

.13

.15 

.16 

.04

.62 

.05 

.11 

.14 

.30 .

6.31

June

(>)

0.55

.27

.25

.27

.19

19

.10 _

.29

.24 .

.35

.31 _

.27

.21 

22

.32 

.30 

.26

.29 

.26 

.31 

.24

4 7. 77

1963

July

0.31

.32 _

.41 _

.23

.27

.21

.22

.27

.36

JO

.24

.26

.14

.26 

.24 

.16 

.32 

.20

4 8. 32

Aug.

0.13

.06

90

.21

1 K

.13

1 K

.22 1 °.

1 K

10

.02

.17

.20

10

.15 

.21

.21 

. 19 

.07 

.14 

.18

« 5. 26

Sept.

0.15

.30

08

08

.15

. .36

12

.16

.18 

.14

1 ^

10

.11

.17

.13 

.13 

.26

.01 

.23 

.23 

.14

4 4.84

Oct.

0.18 _

.27

.26

.15

.19

.23

.14

.17

.10

.16

1 0

.16

.17

09

.08

.05 

19

.13 

.08 

.16

.18 

.12 

.14 

.07 

.10

4.49

May

0.20

.16

20

OQ

.37

.27

QQ

29

.38

.11

.06

.22 

29

oo

oe

29

45

nc

.28 

.35

.38 

.34 

.34

.23 

.31 

.22 

.23 

.15 .

4 8. b8

June

0 °8

.26

on

00

00

.14

oo

.42

39

01

10

OK

.23

on

.10

°8

3.30

.22

.09

98

.45 

.29 

.27

.31 

.33

.29 

.34

8.26

July

0.28

.20

00

.16

.46

10

.14

.13

.26

on

.10

.20

97

.18 

.21

!l9

.25 

.33 

.41 

.33 

.26

7.75

1964

Aug.

0.16

.28

.32

.34

00

.20

.36

.27

90

.08

.22

.25

19

.46

.16 

.26 

.16

.19 

.23 

.23 

.19 

.29 _

4 7.48

Sept.

0.24

.18

.18

OK

OQ

.20

.24

.39

19

19

.15

.31 

.02

.09

.05

QI

.15

.38 

.10 

.08

.22 

.13 

. 14 

.13

6.00

Oct.

0.00

.25

.15

.14

.11

.08

.23

.05

.06

.05

.07

.08

.08

.14 

.07

.08

.09

.00

.47

.13

.15 

.08

.06 

.07 

.15

.14 

.03 

.04 

.07 

.07

3.46

Nov.

0.11 .

.09

.11

.09

. 10

.07

.09

.05

.04

.00

.01

.24

.31

.09

.12 

.01

.05

.06

.00

May

0.47

.40

.40

.32

.15

.08

.32

.28

.24

.28

.21

.27

.34

.27 

.15

.33

.21

.15

.29

.35

.26 

.09

.33

.20 

.17

.17 

.29 

.27 

.19 

.20 _

4 7. 94

June

0.23

.16

.09

.35

.31

.21

.17

.07

3.25

.20

.32

.22

.43

.28

.31 

.34

.22

.31

.34

.33

.38

.31 

.32

.23 

.33

.28

.31 

.34 

.41 

.17

8.22

1965

July

0.27

.28

.10

.25

.20

.26

2.17

.08

.27

.20

.26

.28

.28

.36

.16 

.33

.45

.23

.28

.27

.27

. 19 

.20

.22 

.28 

. 29

.28 

.26 

.31 

.25 

.23

7.76

Aug.

0. 10

.07

.25

.25

.11

.26

.32

.21

.18

.07

.24

.18

.27

.30

.29 _. 

.31

.54

.16

3 20

.24

.22

.15 

.13 _.

.17 

.23 

.21

.51 

.26 

.19 

.14 

.07 ..

6.83

Sept.

0.06

.23

.17

.16

.08

.31

.14

.14

.16

.19

.15

.10

.12

.19

""."28

.03

.28

.17

.11

.24

.21

.19 

.06 

.24

.06 

.11 

.09 

.16

M.75

1 Included in next observation.

2 Estimated (Kohler and others, 1959, fig. 1).

3 Estimated, based on Kendallville record.

4 Total adjusted by Weather Bureau.
A32 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

efficient. These estimates have been made for Pretty 

Lake to illustrate the way results of such computations 

differ from the results of other methods of evaporation 

computation. The estimates, averaged over Pretty Lake 

energy-budget computation periods, are listed in table 

10. They are plotted as a function of time and are further 

summarized in tables 20 and 21 and in figures 30 and 31 

in a later section of this report.

COMPUTED PAN AND LAKE EVAPORATION

As pan data have become widely used as a means of 

estimating evaporation or evapotranspiration, a demand 

has developed among data users for more widespread 

and complete data. Although pan installations are less 

costly than most other means of evaporation estimation, 

the stations still are separated by several hundred miles. 

Often a station will be out of service for part of a year, 

and at times data are of questionable accuracy. Consequently, hydrologists, agronomists, climatologists, and

TABLE 10. Lake evaporation based upon data from Kendallville 

(K) or Culver (C) pan and average annual coefficient of 0.76, 

computed by Pretty Lake energy-budget periods

Period

No. Length 

(days)

Dates

Pan

data 

used

Pan evaporation Lake evaporation

Centi- Centimeters meters

per per

period day

Centi- Centimeters meters

per per

period day

18........

19........

20........

21........

22.........

23........

24........

25........

26...... .

27........

28...... .

29........

30........

31........

32........

33........

34........

1963 

7.0 Apr. 5-12........

8.0 12-20.......

10.9 20-Mayl... 

10.0 May 1-11.........

11-June 1... 

June 1-6......... 6 19

19-July" 2"-".\ 

July 2-10.. . . .

10-17 . . . 

17-24 ......

24-Aug. 7... 

Aug. 7-21-__.._._ 

21-Sept. 18. 

Sept. 18-Oct. 1.. 

Oct. 1-19.. . . .

19-Nov. 2...

21.0

5.4

13.1

13.0

7.6

7.4

7.0

13.9

14.1

27.5

13.1

17.9

14.0

K 

K 

K 

. K 

K 

K 

K 

K 

K 

K 

K 

K 

K 

K 

K 

K 

K

2.64

3.84

4.09

5.21

9.52

3.12

7.67

8.76

5.94

4.67

4.50

7.42

5.61

11.23

5.00

7.01

3.71

Record 

season.

210. 9 Apr. 5-Nov. 2. 9.94

0.38 

.48 

.37 

.52 

.45 

.57 

.59 

.68 

.78 

.64 

.64 

.53 

.40 

.41

.27 

.474

2.01

2.91

3.11

3.96

7.24

2.37

5.83

6.66

4.52

3.55

3.42

5.64

4.27

8.53

3.80

5.33

2.82

0.29 

.36 

.28 

.40 

.34 

.44 

.45 

.51 

.59 

.48 

.49 

.41 

.30 

.31 

.29 

.30 

.20

75. 97 .360

9.73

7.34

47.. ..... 14.0 May6-20............ C

48 .... 9.9 20-30........... C

49.. . . 25.1 30-June24._._. C

50 ..... . 16.0 June24-July 10..... K

51........ 12.9 July 10-23........... K

52.. ... . 18.0 23-Aug. 10..... K

53........ 14.0 AUK. 10-24.-..-..... K

54-.....-. 14.0 24-Sept. 7-...- K

55....... 12.0 Sept. 7-19........... K

56.---... 17.2 19-Oct. 6--.... K

57.. ... . 17.8 Oct. 6-24 ....... ... K

58........ 12.8 24-Nov. 6...... C

59........ 11.9 Nov. 6-18........... C

195.6 May6-Nov. 18..-...------- 98.10 .501 74.54

10.67

7.09

12.37

6.55

7.59

4.88

5.69

3.73

2.95

2.62

.74 

.67 

.67 

.55 

.69 

.47 

.54 

.41 

.33 

.21 

.23 

.22

7.39

5.58

12.83

8.11

5.38

9.40

4 98

5. 77

3.71

4.32

2.84

2.24

1.99

Record 

season.

.53

.57 

.51 

.51 

.42 

.52 

.36 

.41 

.31 

.25 

.16 

.17 

.17

.381

1965 

30.0 June8-July8....... C

43.0 July 8-Aug. 20, . . C 

33. 0 Aug. 20-Sept. 22 ... K

20.90

27.15

11.84

Record 

season.

15.88

20.63

8.99

106.0 June 8-Sept. 22.

. 565 45.50

.53

.48 

.27

.429

other interested persons have tried to develop means of 

estimating evaporation from other variables, such as 

wind, humidity, and cloud cover, which are more frequently measured. The relationships generally have been 

highly empirical. In most cases they have used pan data 

as the control.

Stephens and Stewart (1963) compared nine different 

methods of estimating pan evaporation and ranked the 

Weather Bureau method described in USWB Research 

Paper 38 (Kohler and others, 1955) as the best of the 

group. Stephens (1965), discussing the work of Lane, 

emphasized the importance of pan-operating technique 

and presented additional analysis of data from several 

parts of the United States.

Computed pan evaporation and lake evaporation for 

the 3 years of Pretty Lake study have been determined 

using the Weather Bureau method (Kohler and others, 

1959, fig. 1 and 2) and are listed in table 11. They are 

shown graphically and are further summarized in figures 

30 and 31 and in tables 20 and 21 in a later section of 

this report. Ratios of the computed lake evaporation to 

the computed pan evaporation also are shown as computed pan coefficients. The estimates have been computed for the same energy-budget periods used for the 

other forms of computation. Data observed at Pretty 

Lake field instruments have been incorporated. Wind 

speeds observed at 1.73 meters (5.68 ft) above the lake 

at its center have been used to estimate wind movement 

at pan height by use of a power law having an exponent 

of 0.3.

ADVECTION AND ENERGY-STORAGE EFFECTS

In the study of Lake Mead (Kohler and others, 

1958, p. 57-59), the influence of advected and stored 

energy was shown to be an important factor contributing to the difference between pan and lake evaporation. 

Nordenson (1963) has concluded that these factors are 

the main cause of the apparently large seasonal variation 

in the pan coefficient. Whereas the varying effects of 

energy advected through the sides and bottom of a pan 

can be computed from meteorological data, the effects 

of energy advected into or out of a lake, or stored by the 

lake from season to season, must be determined from 

field measurements of water volume and temperature.

As they were defined earlier in the energy-budget 

section of this report, the advected and stored energy 

are contained in the three terms, Qv , the net advected 

energy from precipitation, inflow, and outflow; Q*, the 

energy advected by evaporating water; and Qx , the 

increase in stored energy. All these represent terms that 

act upon the lake and not upon the pan. All additional 

mergy from advection or storage will not go directly 

into evaporation. Part of it will dissipate as increased
COMPARISON OF EVAPORATION COMPUTATION METHODS A33

TABLE 11. Computed pan and lake evaporation by use of U.S. 

Weather Bureau method with Pretty Lake station data

[Method from Kohler and others (1959), figs. 1 and 2]

Computed pan Computed lake

Period evaporation evaporation Com-

 puted

Centi- Centi- Centi- Centi- pan

No. Length Dates meters meters meters meters coeffi-

(days) per per per per cient

day period day period

18----.-

19.......

20.......

21..... .

22-.... .

23.......

24..... .

25-.... .

26..... .

27.......

28.......

29.......

30.......

31.......

32.......

33.......

34.......

35--.....

36.......

7.0

8.0

10.9

10.0

21.0

5.4

13.1

13.0

7.6

7.4

7.0

13.9

14.1

27.5

13.1

17.9

Apr.

May 

June

July

Aug.

Sept. 

Oct

1963

5-12........

12-20.......

20-May 1...

I-11........

II-June 1... 

1-6.........

6-19........

19-July 2... 

2-10. ...

10-17.......

17-24.......

24-Aug. 7... 

7-21........

21-Sept. 18. 

18-Oct. 1 

1-19........

14.0

14.0

17.1

Nov.

19-Nov. 2... 

2-16........

16-Dec. 3...

0.33 

.37 

.27 

.51 

.43 

.56 

.71 

.69 

.95 

.60 

.64 

.53 

.41 

.36 

.33 

.43 

.24 

.18 

.13

2.31

2.96

2.95

5.10

9.02

3.05

9.26

8.94

7.26

4.41

4.51

7.36

5.78

9.91

4.33

7.71

3.36

2.52

2.22

0.25 

.25 

.18 

.33 

.33 

.43 

.51 

.56 

.64 

.42 

.46 

.39 

.30 

.27 

.22 

.24 

.14 

.09

1.75

2.00

1.96

3.30

6.92

2.34

6.65

7.26

4.89

3.09

3.24

5.41

4.23

7.43

2.89

4.30

1.96

1.26

1.36

0.77 

.69 

.67 

.65 

.76 

.77 

.71 

.81 

.67 

.70 

.72 

.74 

.75 

.75 

.65 

.56 

.58 

.50 

.60

Record 

season.

42.......

43.......

44.......

45.......

46.......

47......

48.......

49-.....-

50.......

51.......

52.......

53.......

242.0 Apr. 5-Dec. 3..... .426 102.96 .299 72.24 .702

1964

14.9

7.0

7.1 

6.9 

11.1

Mar. 20-Apr. 4... 

Apr. 4-11.........

11-18........

18-25.......

25-May 6 . 

14.0 May 6-20.........

9.9 20-30........

25.1 30-June24.. 

June 24-July 10.. 

July 10-23.......

23-Aug. 10. 

Aug. 10-24..-.-.

24-Sept. 7- 

Sept. 7-19.......

19-Oct. 6..

16.0

12.9

18.0

14.0

14.0

12.0

17.2

17. 8 Oct. 6-24.

12.8

11.9

12.0

24-Nov. 6.. 

Nov. 6-18.......

18-30.....

.13

.25 

.71 

.25 

.46 

.58 

.65 

.58 

,65 

.51 

.66 

.44 

.55 

.42 

.30 

.22 

.25 

.23 

.10

1.94

1.75

5.03

I.72

5.09

8.14

6.41

14.58

10.39

6.57

II.90 

6.16 

7.71 

5.05 

5.15 

3.92 

3.21 

2.73 

1.20

.11 

.22 

.44 

.17 

.29 

.41 

.46 

.42 

.47 

.39 

.47 

.30 

.38 

.28 

.20 

.17 

.17 

.14 

.06

1.64

1.54

3.12

1.17

3.21

5.76

4.54

10.56

7.51

5.02

8.47

4.20

5.32

3.37

3.43

3.03

2.18

1.66

.72

Record 

season.

254.6 Mar. 20-Nov. 30... . 427 108. 65 . 300 76. 45

.90 

.85 

.63 

.65 

.64 

.70 

.71 

.72 

.73 

.78 

.71 

.69 

.70 

.67 

.67 

.76 

.65 

.61 

.62

.704

Record 

season.

1965

56.1 Apr. 13-June8.__.

30.0 June8-July8.....

43.0 JulyS-Aug. 20....

33.0 Aug. 20-Sept. 22..

.47 

. 71 

.57

26.37

21.26

24.51

11.89

.36 

.53 

.43

.28

20.20

15.87

18.49

9.25

.76 

.75 

.76 

.79

162.1 Apr. 13-Sept. 22... .503 84.03 . 394 63.81 .759

back radiation and increased sensible heat transfer. 

Means of estimating a, that part of additional energy 

that is used in evaporation, are derived and summarized 

graphically in USWB Research Paper 38 (Kohler and 

others, 1955, fig. 4). Another method of estimating a, 

which has been reported by Harbeck (1964), gives veiy 

similar results (Nordenson, 1965). It is simple to 

compute

= '- T^ - (17)

where &EL is the effect on lake evaporation and L is 

the latent heat of vaporization.

Table 12 summarizes the advection and energystorage influences on Pretty Lake. Energy terms are 

repeated from the summary in table 3, and heat storage 

by the sediments is not considered. To illustrate the 

small effect of advection, a summation of the 1963 and 

1964 Qv and Qw terms was made that showed that the 

two terms account for about a 1 cm (0.4 inch) decrease 

in evaporation during the year. The large negative 

total shown for 1965 is the result of an incomplete 

record for the year, whereby the energy storage at the 

end of the period of record is considerably higher than 

it was at the beginning of the season. On an annual 

basis the sum of the energy-storage term is always 

very nearly zero.

When only part of the season, is considered, the 

storage term plays an important role in the amount of 

evaporation from Pretty Lake. Energy storage makes 

it impossible to use pan data alone to measure evaporation from a deep lake on any other than a complete 

season's basis.

Evaporation rates and amounts based upon class-A 

and computed pan data and corrected for advection 

and energy storage are shown and further summarized 

in figures 30 and 31 and in tables 20 and 21 in a later 

section of this report.

Energy advected through the sides and bottom of a 

class-A pan is accounted for by the pan coefficient. 

The coefficient of 0.76 used for class-A pan data is only 

a seasonal average. Advection rates vary through the 

year, and the corrections made by class-A pan coefficients should vary in much the same manner as do the 

computed coefficients in table 11. Techniques are available for computing variable pan coefficients (Kohler 

and others, 1955, p. 16), but they require data on panwater temperature. Water temperature data were not 

available for the class-A pans that were used to compute 

Pretty Lake evaporation; therefore, only the average 

coefficient can be used.

WINTERTIME EVAPORATION AND ENERGY 

BUDGET

Evaporation from lakes and reservoirs is very slow 

during ice-covered periods. Many pan studies and 

hydrologic studies consider the wintertime evaporation 

to be zero. There are some factors about wintertime 

records, however, that merit further discussion. Obviously, evaporation from a deep lake does not stop at 

the same time a pan on the bank freezes over. Then 

too, for the completeness of hydrologic records and socalled annual averages, the wintertime accounts of 

budgeted water and energy at least should be estimated.
A34 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

OBSERVED WINTER CONDITIONS

During the period of the Pretty Lake evaporation 

study, a variety of ice conditions was observed. Prior 

to the spring breakup in March of 1963, the lake was 

covered with a heavy layer of ice, more than 2 feet 

(0.6 m) thick. Covers of ice observed during the other 

two winters of study were not nearly so heavy.

The freezeup in 1963 was rapid and produced a passable ice cover in just a few days of very cold weather. 

By contrast, the freezeup in December 1964 and 

January 1965 was a month-long seesaw between open

water and ice cover. A few cold days would cause a 

thin ice cover to form, which then would be removed 

on a warmer windy day.

Snow cover on the lake was not always the same as 

on surrounding land. The flat surface of the ice could 

cause light, windblown snow to pile up along one shore. 

At other times heavy snow would uniformly blanket the 

lake. The snow cover at times would melt and refreeze 

as ice cover. The runoff of snowmelt water from the 

surrounding land would sometimes flow out onto the ice 

cover or flow under it along the shorelines. Sublimation

TABLE 12. Advection and storage corrections for pan-based evaporation data

No.

18______________

19___________ _

20____-_.___.____

21_____ _

22____

23 _

24________- _

25----_-___._____

26___.____-__ _

27_________

28----__________

29___.___._____

30____.__________

31____

32____ _

33_________

34_______ _

35------._.

36__-____-______

Record season _ _

42____

43___

44________

45___. ________

46

47____

48____

49__

50__________

51__________ _

52____

53_________

54_ _

55_____- __

56_________

57____

58_________

59_____

60___________

Record season

66______ _

67___

68_________ -

69_________

Record season. _

Period

Length 

(days)

---. 7.

--__ 8.

____ 10.

---. 10.

..__ 21.

--__ 5.

-___ 13.

.___ 13.

--__ 7.

--__ 7.

-___ 7.

.___ 13.

-___ 14.

.___ 27.

.___ 13.

--__ 17.

14

.___ 14.

17.

. _ _ _ 242.

_ ___ 14.

____ 7.

."___ 7.

.___ 6.

.___ 11.

.___ 14.

.--_ 9.

.___ 25.

-___ 16.

12.

.___ 18.

.___ 14.

.___ 14.

.-._ 12.

.___ 17.

.___ 17.

.-._ 12.

--__ 11.

12

.___ 254.

.___ 56.

30.

43.

33,

___ 162.

0 

0 

9 

0 

0 

4 

1 

0 

6 

4 

0 

9 

1 

5 

1 

9 

0 

0 

1

0

9 

0 

1 

9 

1 

0 

9 

1 

0 

9 

0 

0 

0 

0 

2 

8 

8 

9 

0

6

1

0 

0 

0

1

Apr.

May 

June

July

Aug.

Sept, 

Oct.

Nov.

Apr.

Mar. 

Apr.

May

June

July

Aug. 

Sept, 

Oct.

Nov.

Mar.

Apr. 

June 

July 

Aug.

Apr.

Dates

1963 

5-12_________________

12-20

20-May 1__ _________

l-ll_______-____.____

l-6__________________ 6-19

19-July 2_ __________

2-10 _________ ___ __

10-17_ __ __ __ .

17-24________________

24-Aug. 7 _ ________

7-21. _ _

21-Sept. 18 ________

, 18-Oct. !____________

1-19__.______________

19-Nov. 2 _________

2-16 - __-._______.

16-Dec. 3_ ____ ___ _.

5-Dec. 3--________-_._

1964 

20-Apr. 4____________

4-ll_________________

11-18____________.___

18-25________________

25-May 6 _ _

6-20

20-30________________

30-June 24 ___ ___ __

24-July 10_-___---____.

10-23________________

23-Aug. 10_--________-

10-24________________

24-Sept. 7_______.____

. 7-19______________ _

19-Oct. 6__, ___'_______ 6 24

24-Nov. 6_ ________ __

6-18

18-30____

20-Nov. 30_ __

1965 

13-June 8____________.

8- July 8__ _ __ _.

8- Aug. 20. _

20-Sept. 22___ __ _.

13-Sept. 22___________.

Q,

- / cal \

V cm^ day J

_ j

_____ 2

-4

--_-_ -1

_____ 1

_____ 6

_____ 7

--_-_ 0

_____ 0

94.

9

_____ 12

_____ 0

_____ 1

9

0

1

_____ 1

2

_____ 4

2

_____ 0

_____ 2

-4

0

3

_____ 8

4

_____ 5

0

_____ 12

9

_____ 4

1

--_-_ 0

_____ 1

_____ 1

_____ 1

..___ 0

.-___ 3

q

q

Qw 

( Cal ")

\ cm2 day /

1 

0 

1 

0 

6 

2 

14 

13 

19 

10 

10 

12 

9 

6 

6 

4 

3 

2 

1

1 

0 

1 

0 

0 

5 

10 

9 

13 

11 

17 

9 

9 

8 

6 

2 

1 

1 

2

4 

13 

10

7

Q* i ( caM *

Vcm2day7

154 0. 42 

205 . 46 

68 .47 

236 . 52 

35 . 52 

341 . 52 

-16 .58 

99 .51 

-82 . 60 

57 .60 

116 . 61 

-8 . 62 

-76 . 57 

-30 . 55 

-95 . 53 

-27 .49 

-134 .49 

-184 .45 

-111 .43

2 . 35 

232 . 38 

379 . 45 

129 . 46 

207 . 50 

130 . 56 

-8 . 58 

67 . 58 

42 . 58 

64 . 58 

-43 . 59 

-75 .56 

8 . 56 

-71 .55 

-129 .54 

- 134 . 46 

26 . 42 

-42 . 49 

-331 .44

126 . 52

48 . 58 

33 . 58 

-33 .57

Evaporation

Centimeters 

per day

-0. 112 

-. 160 

-. 059 

-. 211 

-. 036 

-. 300 

. 009 

-. 098 

.065 

-.044 

-. 122 

. 008 

.065 

. 024 

.082 

. 019 

. Ill 

. 141 

.082

. 001 

-. 149 

-. 292 

-. 100 

-. 180 

-. 129 

. 001 

-. 067 

-. 051 

-. 069 

. 026 

. 075 

-. 014 

. 063 

. 114 

. 104 

-. 019 

.035 

. 248

-. 116

-. 058 

-. 034 

. 034

effect AE

Centimeters 

per period

-0. 78 

-1.28 

-.64 

-2. 11 

-.75 

-1. 63 

. 12 

 1. 27 

.50 

-. 32 

-.86 

. 11 

.92 

.66 

1. 08 

. 34 

1.55 

1. 98 

1. 40

-.98

. 01 

-1. 04 

-2. 07 

-. 69 

 1. 99 

-1. 81 

. 01 

-1.68 

-.81 

-. 89 

.47 

1. 05 

-.20 

.76 

1. 96 

1. 85 

-. 24 

. 42 

2. 97

-1. 92

-6.51 

-1. 74 

-1.46 

1. 12

-8. 59
COMPARISON OF EVAPORATION COMPUTATION METHODS A35

of the snow and ice and evaporation of the melt waters 

were the two forms of water loss to the atmosphere.

APPLICATION OF OPEN-WATER EVAPORATION METHODS 

TO WINTER CONDITIONS

The methods that have been described and used for 

the estimation of evaporation during open-water periods 

have limited winter use. Data previously listed estimate 

the evaporation during the periods between the first 

open-water thermal survey in the spring and the last 

open-water survey in the fall. The following sections 

are intended to fill in the remaining open-water records 

for the times just before freezing and just after breakup 

and will at least estimate conditions for times when the 

lake was ice covered.

LIMITED PAN SEASON

Evaporation pans generally freeze earlier than the 

lakes, owing to their smaller volume and greater exposure. In the spring, they generally are not set up as 

soon as the lakes break up. If they are set up early in 

the spring, their records are influenced by the few days 

of late freezing that often occur in the spring.

The Weather Bureau methods of computing pan and 

lake evaporation can be applied to the early and late 

periods as a means of estimating evaporation. Table 13 

lists the Pretty Lake evaporation estimates made to 

extend the listing in table 11 to include the entire 

open-water season. It is obvious that evaporation rates 

during these periods are small and that they are only 

small parts of the seasons' totals. Values of EL cannot 

be computed for these periods because thermal survey 

data are not available.

The pan methods used to estimate open-water 

evaporation seem to have no application in estimating

TABLE 13. Computed wintertime pan and lake evaporation for 

open-water periods that were not included in table 11

Period

No.

37a"~L 

61a."_~~

62a... 

62c... 

66b...

Length 

(days)

6.6 

14.4 

3.6 

8.6 

8.0 

3.0 

0.6

1.5 

4.0 

6.4

Mar. 

Dec. 

Mar. 

Nov 

Dec.

Apr.

Dates

, 30-Apr. 5, 1963... 

3-17,1963........

.17-20,1964....... 

. 30-Dec. 8, 1964... 

12-19,1964.......

26-27,1964.......

2,1965............

2-3,1965..........

8-11,1966.........

8-13,1966........

Computed pan 

evaporation

Centimeters 

per 

day

0.37 

.06 

.19 

.06 

.13 

.06 

.05 

.13 

.18 

.22

Centimeters 

per 

period

2.44 

.86 

.68 

.42 

1.04 

.18 

.02 

.20 

.72 

1.19

Computed lake 

evaporation

Centimeters 

per 

day

0.26 

.06 

.13 

.01 

.09 

.05 

.03 

.09 

.10 

.17

Centimeters 

per 

period

1.66

.72 

.47 

.08 

.72 

.16 

.02 

.14 

.40 

.92

Computed 

pan coefficient

0.69 

.80 

.67 

.26 

.70 

.80 

.60 

.70 

.57 

.76

the amount of evaporation and sublimation during the 

periods of ice cover.

WATER-BUDGET APPLICATION

The applications of the water-budget technique in 

computing lake evaporation are much the same during 

the winter as they are in warmer seasons, but there are 

limitations that reduce accuracy. Precipitation in the 

form of snowfall is not measured accurately by rain 

gages. Overland runoff from snowmelt is large because 

of frozen ground, and the timing is hard to judge from 

weather records. The stage record, which generally was 

excellent during the open-water periods, may suffer from 

shoreline effect on the ice sheet. Except for those 

times when streamflow is zero, inflow and outflow 

records suffer loss of accuracy caused by ice effect. 

During a wet winter, as 1964-65, inflow and outflow 

were large, meaning that a 15-percent error in flow 

measurement can greatly affect computed evaporation 

values. Undoubtedly seepage influence is significant, 

especially when a wet winter follows a wet autumn.

Table 14 shows wintertime data similar to the

TABLE 14. Wintertime water-budget terms

Period

No. Length 

(days)

37a____ 

37b__._

38___._

39___._

40_____

41a_.__ 

41b____ 

61_____

62____.

63_.___

64____.

65a____ 

65b_.__

14. 4 

13. 5 

18.0 

20. 1 

22. 0 

16. 4 

3. 6 

33. 0 

26. 2 

33.9 

23. 0 

12. 4 

5.4

Dec.

Jan. 

Feb.

Mar. 

Nov. 

Jan.

Mar. 

Apr.

Dates

3-17, 1963_. .____._..__

18-31, 1963____________

31, 1963- Jan. 18, 1964__.

18-Feb. 7, 1964_ _______

7-29, 1964_____________

29-Mar. 16, 1964_______

17-20, 1964____________

30, 1964- Jan. 2, 1965___

2-28, 1965_____________

28-Mar. 3, 1965________

3-26, 1965__ ___________

26- Apr. 7, 1965_ ________

8-13, 1965__. __________

Pr

n

__ Ice____-_ __ __

TPP

TPP

' TPP

Ice ____ _ --. _

Open

 ecipitation 

d overland 

moff (cm)

1.37 

.23 

1 1. 07 

1 3. 15 

1. 32 

4. 04 

. 43 

1 9. 80 

1 9. 70 

1 9. 80 

1 8. 56 

1 3. 00 

i 2. 49

Inlet 

inflow

(cm)

0. 03 

0 

0 

. 12 

.07 

.57 

.07 

.03 

2. 16 

3. 40 

8.23 

3. 76 

2. 27

Outflow

(cm)

0 

0 

0 

0 

0 

0 

0 

0 

0 

.56 

12. 20 

6. 52 

3. 83

Storage 

change 

(cm)

-1.04 

 1. 04 

. 15 

3. 11 

.76 

5. 55 

. 18 

7.53 

10.39 

11.34 

5. 39 

1. 40 

3. 02

AH

Centimeters 

per period

2. 

1.

2. 

1. 

1.

-1. 

-2.

44 

27 

92 

16 

63 

94 

32 

30 

47 

30 

80 

16 

09

Centimeters 

per day

0. 169 

. 094 

. 051 

. 008 

. 029 

-.057 

. 090 

. 070 

.056 

. 038 

-.035 

-. 093 

-. 386

1 Includes obvious overland runoff.

427-149 O - 72 - 2
A36 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

open-water data listed in table 6. The data are summarized by energy-budget periods. Negative values of 

AH listed for several periods indicate inflow seepage 

or incorrect estimates of ungaged overland runoff.

MASS-TRANSFER METHOD

The mass-transfer method previously was described 

as the best means of computing evaporation for periods 

having low evaporation rates. Although the relation 

given in equation 11 applies to wintertime conditions, 

the terms are neither so easily evaluated nor so accurate as those for open-water conditions.

In a discussion of wintertime evaporation problems, 

Williams (1961) points out that surface roughness is 

different under ice and snow conditions than it is for 

open water. Consequently, the TV term for Pretty Lake, 

which was given as 0.00560 in equation 14, might be 

altered significantly when the lake is covered by ice 

or snow.

It is difficult to measure ice temperature at the 

surface to determine the term e0 . At night or on a 

cold overcast day, the temperature of the ice surface 

will be the same as or a little colder than the air temperature because of evaporative cooling. On a clear 

day, radiant heating will warm the ice, but obviously 

the temperature of the ice or of the overlying thin film 

of water will not exceed 0°C. Figure 27 is a representation of diurnal changes in ice temperature under different conditions. The vapor pressure of ice does not vary 

much with temperature, so that large errors in e0 are 

not likely to result from improper estimates of ice 

temperature. However, the vapor-pressure difference, 

e0 ea , is small in winter, and small changes in either e0 

or e a cause a sizable percentage change in the difference 

and in the evaporation estimate. Figure 28 illustrates 

the air vapor pressure, ea , computed as the over-water 

equivalent to dewpoint values published for the U.S. 

Weather Bureau station at Fort Wayne. The figure also 

shows the probable range of e0 between the over-ice

TIME, OVER 3 DAYS

FIGTJEE 27. Diurnal fluctuation of air and ice-surface temperatures over a cold, cloudy day; a cold, clear day; and a warm 

day.

vapor pressure at Pretty Lake air temperatures and the 

freezing-point pressure of 6.11 millibars.

Table 15 presents wintertime mass-transfer data 

similar to those shown in table 5. Average values of 

e0 have been computed as the average of the two 

extremes of e0 illustrated in figure 28. Estimates of 

evaporation listed in table 15 assume the mass-transfer 

constant, N, to be the same as the N used for openwater conditions.

Figure 29 shows wintertime data analogous to figures 

24 and 25. Considering the many weaknesses in the data, 

there is surprising agreement of the plotted points 

with the mass-transfer relationship defined by the openwater energy budget. The deviation of the several 

points to the right of the line could be explained as 

seepage, ungaged overland runoff, or overestimation of 

e0 . It is possible also that the slope of the mass-transfer 

relation for winter might properly be different from the 

0.0056 defined for open water. Undoubtedly, the 

late-winter periods (Nos. 41, 64, and 65) are influenced 

by seepage at about the same rates as previously 

defined for their following periods, Nos. 42 and 66

(fig. 26).

WINTER ENERGY BUDGET

The energy-budget method is unlike the mass-transfer 

and the water-budget methods in that it cannot be used 

even as a gross estimator of winter evaporation. Some of 

the wintertime energy parameters can be estimated or 

measured in much the same way as can the summertime 

data. However, the reflected solar radiation, Qr, and the 

conducted energy, Qh, present difficult problems.

Table 16 has been constructed as part of an attempt 

to present a complete annual energy budget for Pretty 

Lake. Radiation data, Qs and Qa , were derived from 

the same type of pyrheliometer, flat plate-radiometer, 

and Koberg-method records that were used for the openwater records. They should be equally reliable.

TABLE 15. Summary of wintertime mass-transfer terms for Pretty 

Lake, with evaporation computed by equation 14

No. Length 

(days)

17b_- 

37a... 

37b... 

38....

39.. _. 

40-... 

41a._. 

41b... 

61....

62....

63. ... 

64...- 

65a._. 

65b--.

6.6 

14.4 

13.5 

18.0

20.1 

22.0 

16.4 

3.6 

33.0

26.2

33.9 

23.0 

12.4 

5.4

Period

Dates

Mar. 30-Apr. 5, 1963,-- 

Dec. 3-17, 1963-........

-18-31,1963........

31, 1963-Jan. 18, 

1964. 

Jan. 18-Feb. 7,1964....

Feb. 7-29, 1964-.....--. 

29-Mar. 6. 1964. ...

Mar. 17-20, 1964....... 

Nov. 30, 1964-Jan. 2, 

1965. 

Jan. 2-28, 1965.. - -

28-Mar. 3, 1965 ..

Mar. 3-26, 1965-....--.. 

26-Apr. 7,1965 .

Apr. 8-13, 1965.. -.-.-.-

Evaporation

Lake 

condition

Open.. .

Ice........

Open _ .. 

40 percent 

ice. 

79 percent 

ice.

Ice . -----

Open.....

«!.0

(mph)

11.0 

8.09 

8.10 

9.72

8.68 

6.65 

7.80 

8.69 

7.28

8.85

9.22 

8.36 

7.27 

5.91

en e a 

(mb)

-0.2 

4.7 

2.0 

1.6

.7 

1.9 -.1 

4.4 

1.93

1.25

1.57 

1.22 

.11 

-1.55

Centimeters 

per 

day

-0. 012 

.213 

.091 

.087

.034

.071 

-.004 

.214 

.078

.062

.081 

.057 

.004 

-.052

Centimeters 

per 

period

-0.08 

3.07 

1.23 

1.57

.68 

1.56 

-.06 

.76 

2.58

1.62

2.74 

1.31 

.05 -.28
COMPARISON OF EVAPORATION COMPUTATION METHODS A37

5 10 15 20 25 30 

DECEMBER 1964

10 15 20 25 30 

JANUARY 1965

5 10 15 20 25 

FEBRUARY 1965

10 15 20 25 30 

MARCH 1965

5 10 15 

APRIL 1965

FIGURE 28. Wintertime air vapor pressure and probable range of lake-surface vapor pressure for Pretty Lake.

Dorsey (1940, p. 491-494) cites reports concluding 

that infrared absorptivity and emissivity for ice and 

snow are about the same as for water. Consequently, 

for table 16, Qar has been estimated as 3 percent of Qa , 

and Q bs has been computed using the Stefan-Boltzman 

law and 0.97 emissivity. The same technique has been 

used to estimate T0 as was used to estimate e0 in the 

mass-transfer estimates for ice conditions. In the range 

of computation, a 1-degree error in estimating T0 

results in an error of about 9 cal cm~2 day"1 (calorie 

per square centimeter per day) in Q bs.

Changes in energy storage, Qx , listed in table 16 

were computed from wintertime thermal surveys. The 

latent heat of freezing entered the computations in 

that the ice was considered to be at an effective 

temperature of 79.7°C. The sediment heat storage was 

not considered in the construction of table 16.

The 0°C base temperature used in computation 

causes the advected-energy terms, Qv and Qw , listed in 

table 16 to be small. Negative values of Q v result from 

computing values of snowfall energy advection by 

multiplying water-equivalent volume by an effective 

temperature of 79.7°C, or colder.

Values of Qe listed in table 16 were computed as the 

product of the EMT values listed in table 15 and the 

latent heat of vaporization or sublimation. Latent 

heat of sublimation of ice was considered to be 679 

calories per gram, or greater.

Conducted energy has been estimated for open-water 

conditions by use of the Bowen ratio (eq 4, 5, 6, 7, and 

8). Serious doubts arise when the use of this ratio is 

considered for winter conditions, for which the thermal 

conductivity of ice is different from that of water. 

Williams (1961) reports that reliable wintertime Bowen 

ratios can be computed but warns that serious errors 

can result from the very small values of AT and Ae. 

The method used to estimate T0 values for the Pretty 

Lake ice could cause errors of several hundred percent 

in the Bowen ratio. Very little confidence should be 

placed in the Qh values listed in table 16.

Snow and ice reflect considerably larger proportions 

of the solar radiation than does a water surface. Data 

from wintertime flights over snow-covered regions in 

Wisconsin (Rung and others, 1964) list numerous 

instances when the ratio Qr/Qs (albedo) is more than 

50 percent. Field studies by Lyubomirova (1962)
A38 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

0.2

0.1

-0.1

LU -0.2

-0.3

-0.4 D 65b

164

i65a

EXPLANATION 

O

1963-64 winter

D

1964-65 winter

Shaded symbols represent 

ice-covered periods

0.05

-0.05

-0.10

- -0.15

-10 0 10 20 30

MASS-TRANSFER PRODUCT (u Ae), IN 

MILES PER HOUR TIMES MILLIBARS

40

-2 I,

41a

'65b

63

,64

( 65a

EXPLANATION 

O

1963-64 winter

a

1964-65 winter

Shaded symbols represent

ice-covered periods

1.0

0.5 Q0 -

-0.5 <

I 

O

-1.0

0 100 200 300 400 500

MASS-TRANSFER PRODUCT (nuAe), IN DAYS TIMES

MILES PER HOUR TIMES MILLIBARS

FIGURE 29. Wintertime relation of the mass-transfer product, 

uAe, and the water budget, as indicated by the corrected stage 

change, A//. The lines shown represent the open-water masstransfer relation.

related the angle of incidence to albedo and showed 

albedo ranging from 30.7 to 58.4 percent for dry ice,, 

and from 24.0 to 35.3 percent for wet ice, as the angle 

of incidence increased from 0 to 80 degrees. In an 

energy budget of a lake, about all that can be said 

about the magnitude of the QT term is that it is large 

and highly variable.

The data in table 16 are present only to illustrate 

the probable magnitude of some of the winter energy 

terms. If values of Qr were estimated based upon information in the literature, the totals of (Qs QT+

Qa-Qar-Qbs+Qv-Qx-Qe-Qn-Qw) table 16 WOUld

be large negative numbers for many periods. These 

obviously are wrong and illustrate well the probable 

error in the other terms.

COMPARISON OF RESULTS

This report has been organized to demonstrate the 

common techniques used in an evaporation study. It 

also shows the dependence of one method upon another 

and the uses of the same data by different methods 

(table 17). Energy budget data were considered to be 

the prime independent measure of evaporation and were 

used to calibrate the mass-transfer constant, N. 

Mass-transfer data, obtained by use of the energybudget-calibrated A/", were used to define seepage 

effects in the water budget.

No absolutely correct evaporation data are available 

for evaluating the results of the several computation 

methods discussed in the earlier sections of this report. 

The energy-budget and pan methods produce independent data, but the mass-transfer and water-budget 

methods each rely on some other method to get a complete answer. Evaluation of the results, therefore, consists of comparing the evaporation data computed by 

the different methods. Where differences occur among 

the various results, an attempt must be made to explain 

them and to evaluate which answers are most nearly

correct.

RESULTS SUMMARIZED

Tables 18 and 19 summarize evaporation data for 

summer and winter periods; the results are shown on 

an amount-per-period basis. Evaporation rates for each 

open-water period, as computed by different methods, 

are shown by the evaporation hydrograph (fig. 30).

Seasonal totals and averages shown in table 10 are 

hard to compare on a year-by-year basis, or even among 

methods, because the season lengths are different. 

Table 20 is presented to summarize similar results 

for all three years of study. The bar graph of figure 31 

also compares totals but is broken down to permit use 

of some of the shorter term data.

CHARACTERISTICS OF RESULTS FROM INDIVIDUAL 

METHODS

Energy budget. Evaporation rates computed by 

the energy-budget method generally are lower than rates 

computed by other methods (except uncorrected pan 

and water -budget) during the springtime and autumn 

periods. This characteristic is shown clearly by the 

hydrograph of figure 30 and by the summary bar graph 

(fig. 31) for 31 autumn days in 1963 and 47 springtime 

days in 1964. All these periods of low energy-budget
COMPARISON OF EVAPORATION COMPUTATION METHODS A39

TABLE 16. Estimated terms for wintertime energy budget 

[Q values given in calories per square centimeter per day]

Period

No. Length 

(days)

37_________ 27.9

38_________ 18.0

39_________ 20.1

40 ________ 22. 0

41 ________ 20. 0

61_________ 33.0

62_________ 26.2

63_________ 33.9

64_________ 23.0

65_______._ 17.8

Dates

Dec. 3-31, 1963 _ ____

31, 1963- Jan. 18, 1964____ .

Jan 18- Feb. 7, 1964_ ______ ____

Feb. 7-29, 1964____ ______

29-Mar. 20, 1964

Nov. 30, 1964- Jan. 2, 1965__ ____

Jan. 2-28, 1965_____ ___

28-Mar. 3, 1965

Mar. 3-26, 1965 _

26- Apr. 13, 1965_ ___

(percent)

48

100

100

100

82

40

79

100

100

70

^s

178

220

223

290

255

102

149

256

258

409

382

343

470

418

521

532

499

463

569

541

11

10

14

13

16

16

15

14

17

16

629

611

624

612

635

642

593

608

621

636

-3

-2

0

-5

-4

-8

-8

-12

0

-185

-19

76

-20

102

-89

-31

23

6

208

93

61

20

48

24

48

36

54

41

-7

110

40

-16

27

-28

44

-33

-29

-19

-33

0

0

0

0

0

0

0

0

0

0

TABLE 17. Summary of data requirements for different evaporation 

computation methods

Data required

Inflow volume ... _

Outflow volume . .

Lake stage.-..-- . . .

Precipitation.... . .

Surface temperature .............

Radiation... ..

Temperature structure .......... .

Inflow and outflow temperatures. .

Air temperature and vapor pressure

Wind..:.......

Class-A pan and rain gage ...._.

Independent measure of evaporation

®

 s

d

fi

1

aW

Xi \/

X

X

X

X2 \f

,«

I

C3 ^

"S

d

fi

<3

03 ^

X

'X

I

i

j&

o

73 03

1^

0-3

X

X

X

Ia

13

d 

t

O

§

'S'S

H a

Q«

y

X

X

y

1 Low accuracy requirement.

2 Only when Bowen ratio questionable.

evaporation occurred when the evaporation rate was 

less than about 0.35 cm day" 1 .

Energy-budget evaporation rates are higher than 

those determined by other methods during the two 

highest rate periods in 1963, during several of the highest 

rate periods (nos. 50, 51, 52, and 54) in 1964, and during 

the highest rate period in 1965. All these periods having 

high energy-budget evaporation rates are during June, 

July, and August. All have evaporation rates of more 

than 0.4 cm day ~ l .

The record-season totals in table 20 and the 160-day 

totals in table 20 show that long-term total evaporation 

computed by the energy budget is near the mean of 

evaporation amounts computed by other methods. The 

160-day totals for the energy-budget method (table 20) 

are within 3 percent of the mean, and the record-season

TABLE 18. Pretty Lake evaporation as computed by different methods for open-water periods, 1963-1965

Period

Energy

No. or season

18

19

20

21

22

23

24__ _ _ _

26

27

28

29

30

31

32

33

34

35

36

Principal

season.

Length

7.0

8. 0

10. 9

10. 0

21. 0

5. 4

13. 1

13. 0

7.6

7. 4

7. 0

13. 9

14. 1

27. 5

13. 1

17. 9

14. 0

14. 0

17 1

242. 0

May

July

Aug.

Sept.

Oct.

Apr.

Dates

1963

5-12___ __ _

12-20________

20-May 1 __ _

1-11_________

l-6__________

6-19

19- July 2_____

2-10__. _______

17-24_________

24- Aug. 7__.__

7 21

21-Sept. 18___

, 18-Oct. 1 _____

1-19

19-Nov. 2 __ _

2-16_. _______

16-Dec. 3____

5-Dec. 3 _ ___

budget

_____ 0.

_____ 7.

7.

6.

_____ 5.

_____ 2.

9

---__ 6.

---._ 5.

_____ 7.

_____ 3.

----- 3.

9

2.

1.

2 69.

85

34

09

9fi

4?,

7q

qo

71

93

8?,

3?,

50

57

74

78

60

41

74

24

Mass

transfer

1. 36

1 57

o co

2 67

6. 51

. 95

K. Q9

q qq

K 04.

3. 27

2. 57

6. 10

^ 4Q

9.42

4.60

4. 51

3. 49

3. 38

9 77

2 75. 84 .

Water

budget

C fifi

2. 21

2. 30

4. 76

5. 84

9. 39

5. 19

4. 18

3. 82

2. 26

2. 62 .

Evaporation

(cm)

Class-A

pan

2. 01

2. 91

3. 11

3. 96

7. 24

2. 37

5. 83

6. 66

4. 52

3. 55

3. 42

^ 64

4. 27

8. 53

3. 80

5. 33

2. 82

Corrected 1

class-A

pan

1. 23

1. 63

2. 47

1. 85

6. 49

. 74

5. 95

5. 39

5. 02

3. 23

2. 56

5. 75

5. 19

9. 19

4. 88

5. 67

4. 37

Computed

pan

1.75

2. 00

1. 96

3. 30

6. 92

2. 34

6. 65

7. 26

4. 89

3. 09

3. 24

5. 41

4. 23

7. 43

2. 89

4. 30

1. 96

1. 26

1. 36

2 72. 24

Corrected '

computed

pan

0. 97

. 72

1. 32

1. 19

6. 17

. 71

6. 77

5. 99

5. 39

2. 77

2. 38

5. 52

5. 15

8. 09

3. 97

4. 64

3. 51

3. 24

2. 76

2 71. 26

See footnotes at end of table.
A40 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

TABLE 18. Pretty Lake evaporation as computed by different methods for open-water periods, 1963-1965 Continued

No. or season

Water-budget

season.

Class-A pan

season.

Season

average 

(cm/day) .

42__

43_________

44_________

45___ __

46_

47__________

48____________

49___________

50_________

51___ .

52___. ______

53___ _

54___________

55________

56___ ____

57__________

58_________

59___ __ _

60___________

Principal

season.

Class-A pan

season.

Season

average 

(cm/day) .

66_. _______

67

68__

69____.____

Principal

season.

Class-A pan

season.

Season

average 

(cm/day) .

]

Length

153. 6

210. 9

14. 9

7.0

7. 1

6. 9

11. 1

14. 0

9. 9

25. 1

16. 0

12. 9

18. 0

14. 0

14. 0

12. 0

17. 2

17. 8

12. 8

11. 9

12. 0

254. 6

195. 6

56. 1

30. 0

43. 0

33. 0

162. 1

106. 0

3eriod

Dates

. 1963 Continued 

July 2-Dec. 3__

Apr. 5-Nov. 2

1964 

Mar. 20-Apr. 4

Apr. 4-11

11-18____

18-25__

25- May 6

May 6-20

20-30

30-June 24_ _

June 24-Julv 10 _

July 10-23_I__

23- Aug. 10__

Aug. 10-24

24-Sept. 7_

Sept. 7-19____

19-Oct. 6____ _

Oct. 6-24_______

24-Nov. 6___

Nov. 6-18

18-30____

Mar. 20-Nov. 30

May 6-Nov. 18

1965

July 8- Aug. 20.

Aug. 20-Sept. 22

Apr. 13-Sept. 22__

June 8-Sept. 22

Energy 

budget

45. 12

65. 09

. 286

9 43

. 36

1. 33

-. 30

. 14

A, 34

4. 64

10. 66

7 78

5. 27

11. 02

5. 45

^ 77

4. 17

r. 40

3. 23

90

. 59

Q f|Q

_ 2 76. 30

69. 31

. 300

1 c no

17. 04

17. 16

Q Q1

_ 2 59. 20

44. 11

. 365

Mass 

transfer

50. 64

69. 69

. 313

1 73

. 36

1.42

1. 10

1 Q4

c ns

5. 42

n 79

6 7Q

4 93

7 ^8

5. 69

K 14

4 31

6. 05

4. 50

1 ^4

2. 28

3 CO

2 78. 47

68. 34

. 308

1 7 03

iq on

16. 62

10. 85

2 ^7 7Q

40. 76

. 357

Water 

budget

48. 25 _

. 314

3 1 Q4

3 49

3 1. 42 _

3 1. 10 _

3 2. 32 _

3 4 40

3 ^ 39

9 10

6. 96

4. 66

10. 57

5. 24

4 90

^ 1Q

5. 95

4. 73

1 87

1. 44

2. 06 _

2 79. 75 _

70. 42

. 313

3 16. 83 _

13. 69

16. 25 3 in QO

2 57. 67 _

40. 84

. 356

Evaporation 

(cm)

Class-A 

pan

75. 97

. 360

7. 39

5. 58

12. 83

8. 11

5. 38

9. 40

4. 98

5. 77

3. 71

4. 32

2. 84

2. 24

1. 99

74. 54

. 381

15. 88

20. 63

8. 99

45. 50

. 429

Corrected ' 

class-A 

pan

71. 61

. 340

5. 58

5. 59

11. 15

7. 30

4. 49

9. 87

6.03

5. 57

4. 47

6. 28

4.69

2. 00

2.41

75.43

. 386

14. 14

19. 17

10. 11

43. 42

. 410

Computed 

pan

40. 06

69.62

. 299

1. 64

1. 54

3. 12

1. 17

3. 21

5. 76

4. 54

10. 56

7. 51

5. 02

8. 47

4. 20

5. 32

3. 37

3. 43

3. 03

2. 18

1. 66

. 72

2 76. 45

65. 05

. 300

20. 20

15. 87

18.49

9. 25

2 63. 81

43. 61

. 394

Corrected ' 

computed 

pan

47.42

65. 26

. 294

1. 65

. 50

1. 05

. 48

1. 22

3. 95

4. 55

8. 88

6. 70

4. 13

8. 94

5. 25

5. 12

4. 13

5. 39

4. 88

1. 94

2. 08

3. 69

2 74. 53

65. 94

. 293

13. 69

14. 13

17. 03

10. 37

2 55. 22

41. 53

. 341

1 Corrected for advection and energy-storage effects in the lake. Not corrected for 

advectioii effects on class-A pan.

totals (table 18) are within 6 percent of the mean in 

1963, within 2 percent in 1964, and within 4.2 percent 

in 1965. The 160-day totals (table 20) for energy-budget 

data agree with the data from other methods, which 

showed the 1964 and 1965 totals as being within about 

1 cm (0.4 inch) of each other and the 1963 totals as 

being 3 to 6 cm (1.2 to 2.4 inches) less.

2 Total used in computing season average.

3 Corrected for seepage. See tables 6 and 7.

Evaporation hydrographs (fig. 30) for 1963 and 1964 

show significant differences between years in springtime 

evaporation patterns. Rates for periods 21 and 22 are 

considerably less than rates for periods 47 and 48. The 

energy-budget data (table 3) show that May 1963 had 

less solar and long-wave radiation than did May 1964 

and that the lake warmed later in 1963 than in 1964.
COMPARISON OF EVAPORATION COMPUTATION METHODS A41

TABLE 19. Pretty Lake evaporation as computed by different 

methods for wintertime periods, 1968-65

No.

17b..__.

070

37b_-.._ _o

39 

40__-_ _

41a_____ 

4lb 

61......

62-_____

63_____- 

64__..._

65b_--_.

Length 

(days)

6.6 

14.4 

13.5 

18.0

20.1 

22.0 

16.4 

3.6 

33.0

26.2

33.9 

23.0 

12.4 

5.4

Period

Dates

Mar. 30-Apr. 5, 1963. __

Dec. 3-17, 1963___.-__. 

Dec. 18-31, 1963.-.-...

Dec. 31, 1963-Jan. 18, 

1964. 

Jan. 18-Fep. 7, 1964 

Feb. 7-29, 1964. _______

Feb. 29-Mar. 16, 1964 

Mar. 17-20, 1964____-.- 

Nov. 30, 1964-Jan. 2, 

1965 

Jan. 2-28, 1965 __...-

Jan. 28-Mar. 3, 1965. .. 

Mar. 3-26, 1965. . ___..

Mar. 26-Apr. 7, 1965 

Apr. 8-13, 1965.... ....

Evaporation, in centimeters

condition

Open _ __

Ice.. ---._.

do.......

...do ._._._ 

.__do.......

...do....-._ 

Open. 

40 percent 

ice. 

79 percent 

ice. 

Ice _______ 

.-do_.----_

...do_.-._..

Mass 

transfer

-0.08 

3.07 

1.23 

1.57

.68 

1.56 

-.06 

.76 

2.58

1.62

2.74 

1.31 

.05

-.28

Water Cornbudget puted 

AH pan

2.44 

1.27 ...

i _/ 

i _ 2.

1.

1.

i __

9^ 

,16

94 

32 

30

47 .

30 

sn

i -1. 16 

1 -2. 09

1.65 

.72

.47

2. 97

2.54

.92

1 Probably influenced by seepage.

2 Total for open-water subperiods only.

Earlier discussions of the energy-budget method 

suggested that there could be serious errors in the Qx 

terms caused by errors in the capacity table of the lake. 

Capacity-table errors would have produced results 

that either are too high in the spring and too low in the 

fall or too low in the spring and too high in the fall. 

Pretty Lake data show energy-budget evaporation rates 

that are smaller than answers from other methods in 

both the spring and fall. These data seem to rule out the 

possibility of significant errors in the capacity table. 

Corrections to the class-A and computed pan evaporation data used the same Qx values as did the energy 

budget. These results also support the conclusion that 

capacity-table errors are small.

Heat storage in the sediments also would be expected 

to produce EES values that are too high in the spring 

and early summer and too low in the fall (fig. 16). 

None of the energy-budget data for Pretty Lake have 

been corrected for sediment heating because available 

data are not considered to be accurate enough. Such 

corrections, which probably do not exceed 0.03 cm day" 1 , 

would produce better agreement among the results of 

the different methods in the fall, but they would not 

increase the EEB values to the rates found by other 

methods. In the springtime, they only would worsen 

the already poor agreement. It also is possible that 

both capacity-table errors and sediment-heating effects 

exist and tend to compensate each other.

The year-to-year consistency in the seasonal differences between EEJi rates and evaporation rates computed by other methods suggests that there are biasing 

factors in the methods. They could be in the energybudget method of computation, in the instrument 

records, in the mass-transfer theory or calibration, in 

the seepage effect, or in some other phenomenon. 

Several sources of error probably exist.

TABLE 20. Summary of Pretty Lake evaporation, as computed by 

different methods, for similar periods during 1963-65

1963 1964 1965

PeriodsDates - -

Number of days.-..--_-__________

Energy budget:

Evaporation... _________ .cm. _ Evaporation. _____cm day-1 __ Mass transfer:

Evaporation_ __ _______ .cm..

Evaporation.......cm day-'..

Water budget:

Evaporation....___.__._. cm.. 

Evaporation......cm day-1 ..

Class-A pan, uncorrected:

Evaporation.._.-___-_-._cm_- 

Evaporation______.cm day-i..

Class-A pan, corrected:

Evaporation_____--_- _cm._ 

Evaporation_....cm day-1 ,.

Computed pan, uncorrected:

Evaporation..________ ...cm-- 

Evaporation.......cm day-1 ..

Computed pan, corrected:

Evaporation_ ________ .cm. _

Evaporation___..cm day-'_.

Average of methods, uncorrected

values excluded: 

Evaporation.......____. .cm-- 

Evaporation. ...__cm day1 ..

19-31 

Apr. 12- 

Sept. 18 

158.9

54.1 

.34

55.7 

.35

44-55 

Apr. 11- 

Sept. 19 

161.0

60.3 

.37

58.4 

.36

61.3

66-69 

Apr. 13- 

Sept. 22 

162.1

59.2 

.36

57.8 

.36

57.7 

.36

62.0 

.39

55.5 

.35

58.7 

.37

52.2 

.33

54.4 

.34

62.2

54.4 

.34

58.6 

.36

63.8 

.39

55.2 

.34

57.5 

.35

During the springtime periods (Nos. 18-21, 45, 46), 

when energy-budget rates are lower than other results, 

the EEK data cannot be considered to be so accurate 

as those from other methods. In other cases such as 

periods 23 and 24, when one of two sequential periods 

is lower and the other is higher than data from other 

methods, it seems that an error in Qx values could have 

come from inaccuracies in the thermal survey. By 

majority rule, it appears that EEB data in the fall tend 

to be about 0.05 cm day" 1 too low.

Winter energy budgets are useless for computing 

evaporation because radiation reflectivity from ice is 

not know, Qx is greatly dependent upon accurate icethickness measurements, and the Bowen-ratio concept 

is questionable.

Mass transfer. Evaporation rates computed by the 

mass-transfer method were within the ranges of rates 

computed by other methods during about three-fourths 

of the computation periods (fig. 30). They tended to be 

higher than rates from other methods during April, 

May, and November and to be lower than other rates 

during June and July. The periods when mass-transfer 

rates were higher than others had evaporation rates 

of less than 0.35 cm day" 1 , and those when £"MT rates 

were lower than others had rates greater than 0.35 

cm day" 1 .

Two of the computation periods (Nos. 25 and 52) 

that had mass-transfer evaporation rates considerably lower than lates fiom other methods also had 

veiy low wind velocities (table 5). This phenomenon 

would support the hypothesis, suggested by some 

investigators, that the wind-velocity term, u, in the 

mass-transfer equation should have an. exponent of 

less than 1.0. However, more extensive examination of
A42 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

Period 17b 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37a

c/) 0.1 -

- 0.30

- 0.25

- 0.20

- 0.15

- 0.10

- 0.05

Period

41 b 42 43 44 45 46 

I I

58 59 60

< 0.6 -

0.1

0 -

0.25

- 0.20

- 0.15

- 0.10

- 0.05

-0.1

15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 

MARCH APRIL MAY JUNE JULY AUGUST SEPTEMBER OCTOBER NOVEMBER

5 15 

DEC

FIGURE 30. Evaporation rates as computed by different methods for open-water periods, 1963-65. Data points are mean rates

for periods shown along tops of hydrographs.
COMPARISON OF EVAPORATION COMPUTATION METHODS A43

Period 65b 66 67 68 69

0.6

>

Q 0.5

LU

O.

GO

£ 0.4

1 

LU

P

5 03 

0

z.

-z.

0 0.2

1-

CE 

0

CL

^ 0.1

LU

o' 

i

-

.

-

_

_

(

1

1 II II

QCC yoo

+

/

<^ /

o_r /

IT) 

O

o

'

15 25 5

f/

i^

11111

/

+ /s J//

1 A

/

O

11111 /c^

/

/ /&*=-

/ yi^>K^

//^"

j»r

/

11111 11111

N. v ^ ^* 

^^^?\

^H^- \

^^

11111 i i i i i iiiii \

EXPLANATION

-

Energy budget

Mass transfer

 D 

Water budget

""° O

^ Water budget, without

4^ seepage correction

Class A pan, corrected

O

V

Class A pan, uncorrected

 X 

Computed pan, corrected -

Computed pan, uncorrected

15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25 5 15 25

MARCH APRIL MAY JUNE JULY AUGUST SEPTEMBER OCTOBER

5 15 25

NOVEMBER

0.20 >

Q

cc

LU 

CL

GO 0.15 ^

O

Z.

z.

0.10 §

1 

cc

0

CL

0.05 2i

A

5 15

DEC

FIGURE 30. Continued

the data shown in figures 18 and 24 shows that an 

exponent does not improve the fit of the calibration 

lines. It is more likely that at very low wind velocities 

the anemometer cups tended to stall and that the true 

mean wind velocities for these periods are higher than 

the data show.

The 160-day data summaries in table 20 show totals 

of mass-transfer evaporation that are within 3 percent 

of the several-method means for each year and within 

3 percent of the energy-budget totals for each year. 

The agreement with other method totals for the entire 

record seasons (table 18) and for shorter summation 

periods are not so good as the agreement among 160-day 

totals. These great differences reflect the seasonal 

differences among the methods.

The Pretty Lake mass-transfer coefficient of 0.00560 

(eq 14) is 15 percent less than the 0.00661 predicted by 

Harbeck's lake-area relation. This 15-percent departure is reasonable, considering the scatter of the data 

used originally to derive the relationship (Harbeck, 

1962, fig. 31). It could, however, mean that some 

atypical factor affected the Pretty Lake study or that 

the relationship between N and area developed for the 

West does not hold for more humid regions.

The coefficient N will not be changed significantly if 

the discredited energy-budget periods, with EE& rates 

of less than 0.1 cm day"1 , and the periods (nos. 25 and 

52) with very low wind velocities are disregarded in the 

mass-transfer calibration (fig. 18). The scatter among 

results from different types of calibration computation 

(fig. 19) would be reduced by ignoring these data.

Similarly, if period 52 and the periods of known or 

questionable seepage are ignored in figure 24, the data

very closely support the N value of 0.00560. The fit of 

data in either figures 18 or 24 is not improved significantly by use of a fractional exponent of u in the masstransfer equation.

A seasonal variation in N is suggested by the relationship between energy-budget and mass-transfer values 

in figure 30. This variation is similar to the phenomenon 

that Hughes (1967, p. 166-171) found on the Salton 

Sea. Hughes attributed the variation to errors in the 

radiation terms of the energy budget. Pretty Lake 

energy-budget records may be affected by radiation 

errors or by problems in the Bo wen ratio. Also, the 

closer agreement of water-budget periods (those not 

affected by seepage) with the mass-transfer data seems 

to prove that the mass-transfer coefficient is correct 

and is valid for all seasons.

Mass-transfer data give the most complete winter 

record of all the methods. The method is well suited to 

get data during the freezeup and just-thawed periods. 

Evaporation rates computed for ice-covered periods 

appear to be reasonable but could have a high percentage of error. The data in table 19 and the plot in figure 

29 show differences between the winter mass-transfer 

and water-budget results, but it is not known if the 

error is in the mass-transfer coefficient, in the vapor 

pressure data, or in seepage effect on the water budget.

Water budget. Most of the water-budget evaporation rates shown in figure 30 are within 0.05 cm day"1 

of the results obtained by other methods. There are no 

noticeable patterns of variation, other than those 

mentioned in discussions of the energy-budget and masstransfer methods. Seepage corrections that have been 

applied to periods 46-48, 66, and 69 are responsible for
A44

50 

40 

30 

20 

10 

0

HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

1 88.3 days j

1 

1963 |

1

1 

1 

. 1

6 o

%

ft i

,. 122. 6 days

1 

1 

1

ro 

ro 

6

CO 

ro 

6

~l

§ 

\ 

\

^

IT)

ro 

6 1

k

1

31.1 days

'

oo ro ^-j- O) r^ cyi

15 

10 

5 

0

ou

60

50

40

30

20

10

0

50

40

30

?0

10

0

1964

-

47.0 days 195.7 days

rv.

S-2 d 2

*-^ ^^fS^^HJ^i

iF^^fl^l , , ,

1

1 ~ 3

=

1965 56.1 days 106.0 days =

I

r~S» ^^

b p&f ° s

i .riliib; , , |

= ^

= ^

= ^

E s

= ^

*it

 S

1 s ^

m ' ' i

Y/

\y.

\%

\ y

sX

\r»

i m m

J dp

1 '

1

1 1

J J

i

i 1

i

i '

i .

,- 1 EXPLANATION

_ XTIU

$2 1

y I

IT) CT1 OICM1 CO CM ^| < 

ro «* ^l^1

^ 1

fo j Energy budget _LL .

t*-^ 1 Mass transfer H

pyj j Water budget -S3. . 

[CM Class A pan Efl

o ' Corrected class A pan H M

t't) 1 Computed pan JH_

[ :.': § | i Corrected computed pan EHl _

30

25

20

15

10

5

0

15

10

b

0

MARCH APRIL MAY JUNE JULY AUGUST SEPTEMBER OCTOBER NOVEMBER DEC

FIGURE 31. Evaporation results summarized for comparison among different methods.

the very good agreement between EMr and EWB during 

these periods.

Periods 27, 28, and 29 have £Vs values that plot 

below evaporation rates computed by other methods in 

figure 30. More than 8 inches (20 cm) of precipitation 

fell during these periods, and although flow through the 

inlet was very small, it is possible that these periods 

were affected by inflow seepage. The position of the EWB 

point for period 60 in figure 30 also suggests seepage. 

Only 0.75 inch (1.9 cm) of precipitation fell during this 

period, but snowmelt or rain on frozen ground could 

have affected the records.

Tables 18 and 20 show totals of water-budget evaporation that are about 5 percent higher than other method 

averages for 1964 and nearly the same in 1965. All the 

water-budget evaporation values in figure 31 are at 

about the average of evaporation amounts computed 

by other methods.

Water-budget and mass-transfer data frequently are 

analyzed by fitting a regression line to a plot similar to 

figure 24. The intercept of the ordinate axis is considered 

to be average seepage. The use of such a technique on

Pretty Lake data would have produced an inaccurate 

(too large) N value and would not have shown the 

variable seepage phenomenon.

The water-budget method offers a good means for 

estimating wintertime evaporation. It may be the best 

of all methods because it does not contain estimated 

values such as mass-transfer coefficients, reflectivity 

ratios, or pan coefficients, but seepage estimates 

present a problem. Small amounts of precipitation 

during periods 37-40 probably did not produce inflow 

seepage, but most of the other winter periods probably 

were seepage affected. Assuming a valid mass-transfer 

technique, figure 29 shows that most of the winter 

seepage rates, although low, are a high percentage of 

the evaporation. Evapotranspiration rates are very low 

during winter periods, so that seepage rates probably 

are more easily affected by small amounts of precipitation. The data seem to show that times of winter 

seepage coincide with times of flow through the inlet.

Class-A pan. The evaporation hydrograph (fig. 30) 

and the bar graph summaries (fig. 31) show that 

accurate short-term estimates of evaporation cannot be
COMPARISON OF EVAPORATION COMPUTATION METHODS A45

made from class-A pan records without correcting for 

advection and heat storage. Evaporation estimated 

from uncorrected class-A pan records are too high in the 

spring and too low in the fall. On Pretty Lake, where 

the advected energy is small, full-season estimates of 

lake evaporation computed from class-A pan records 

would be reasonably accurate because Qx terms total 

zero over a full season. However, the pan data from the 

Kendallville and Culver pans are limited, and it is not 

possible to make full season comparisons.

Corrections applied to the class-A pan records use 

the same values of Q,, Qx , and Qw that were used in the 

energy-budget computations. They do not allow for 

advected energy to and from the pan. Although this 

effect is supposed to be considered in the pan coefficient, 

it is known to vary with time. Therefore, more error is 

expected in the pan-based evaporation data for Pretty 

Lake than in the evaporation results computed by other 

methods.

Corrected lake evaporation data from class-A pan 

records are about the same as or slightly greater than 

those computed by other methods (fig. 30). The tendency for high results from the pan-based data may 

mean that the average pan coefficient of 0.76 does not 

fully compensate for advected energy to the pan. 

Periods 33 and 34 represent some very warm autumn 

weather, when heat advection to the pan probably 

affected the pan evaporation considerably. The same 

type of effect also probably influenced the May and 

June 1964 records.

Table 20 and figure 31 show good agreement of 1963 

and 1965 totals of record-season evaporation computed 

from the corrected class-A pan compared with other 

methods. The corrected pan season total is 5 to 7 cm 

(2.0 to 2.8 inches) greater than totals from other 

methods for 1964. (See 195.7-day period in fig. 31.) 

This variation is about equal to the one standard deviation of annual pan evaporation defined in USWB 

Technical Paper 37 (Kohler and others, 1959, pi. 5).

The differences between uncorrected and corrected 

pan-based evaporation rates in figure 31 shows more 

than just the difference between two computation 

methods. Table 12 shows that the Q,-QV difference does 

not exceed 19 cal cm"2 day"1 during any period and is 

less than 10 cal cm"2 day"1 during most periods. Therefore, the difference between corrected and uncorrected 

rates is largely due to the energy storage caused by the 

slow heating and cooling of the deeper lake water. The 

difference has considerable hydrologic significance. 

Lower springtime evaporation rates shown .by the corrected data mean that during the midsummer dry 

period the level of Pretty Lake is about 10 cm (4 inches) 

higher than it would be if it were not for the effects of 

energy storage caused by deep water.

The short seasons for which published class-A pan 

records are available for the Pretty Lake area make it 

difficult to compare pan-based evaporation data with 

other results. They also would be a significant detriment 

in any attempts to estimate annual lake evaporation 

using only the pan method. None of the records include 

winter periods, and it is obvious that the class-A pan 

has no value in computing winter evaporation.

Computed pan-evaporation method. Lake evaporation rates based upon the concept of computed pan 

evaporation should not be used unless they are corrected 

for advected and stored energy. Figure 30 shows how 

the uncorrected computed pan-evaporation gives lake 

evaporation rates that are too high in the spring and 

too low in the fall. The 1963 and 1964 totals in table 16 

show that the uncorrected method gives a reasonable 

estimate of annual evaporation. This is because the net 

Qx over an entire season is nearly zero and because advected energy to and from Pretty Lake is very small.

The evaporation hydrograph (fig. 30) shows that lake 

evaporation rates computed from the computed pan 

method tend to be less than evaporation rates computed 

by other methods. For most periods, they are within 

0.05 cm day"1 of rates from other methods. In some of 

the periods during early summer 1964, the corrected 

lake evaporation rates determined from computed pan 

rates were lower than all others.

The data summary of table 20 shows that 160-day 

lake evaporation totals computed from the corrected 

computed pan method were 2 to 4 cm (0.8 to 1.6 inches) 

(4 to 7 percent) below the means of all methods and 

were the lowest of all totals each year. Totals for the 

corrected computed pan methods in table 18 and in 

figure 31 and similarly low, except those for 1963 and 

early 1963, when energy-budget totals also are very low.

Some explanation of the deviations of lake evaporation data based upon class-A pan records and computed 

pan methods can be provided by the data in tables 10 

and 11. Evaporation from a class-A pan (Kendallville 

or Culver) was 1.7 cm (0.7 inch) greater than computed 

pan evaporation during periods 18-34 in 1963, 6.2 cm 

(2.4 inches) greater during periods 47-59 in 1964, and 

2.2 cm (0.9 inch) greater during periods 67-69 in 1965. 

These follow the same pattern as does lake evaporation 

computed by the two methods (fig. 31), the class-A 

pan method giving slightly higher amounts in 1963 and 

1965 and considerably higher amounts in 1964. Computed pan coefficients shown in table 11 range from 0.50 

to 0.90, the season averages being 0.70 during the two 

longer record years and 0.76 in 1965. Variations in the 

computed coefficients are more correct than the constant 0.76 used with the class-A pan because they contain pan-advection factors. By comparison with the 

results of other methods, it appears that the true annual
A46 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

pan coefficient is somewhere between the 0.70 found by 

the computed pan and the 0.76 used with the class-A 

pan.

Wintertime lake evaporation results from the computed pan method that are summarized in table 19 

include evaporation for open-water periods only. The 

data cannot be corrected for heat storage during the 

times of breakup and freezeup because accurate thermal 

survey data cannot be obtained. They do agree well with 

the totals obtained by other methods and cannot be 

given a very good accuracy rating.

Evaporation maps. Maps in U.S. Weather Bureau 

Technical Paper 37 (Kohler and others, 1959) show an 

annual lake evaporation of 31.5 inches (80 cm) and a 

May-October evaporation of 26 inches (66 cm) for the 

Pretty Lake location. They show standard deviations 

of about 2.4 inches (6 cm) in the annual pan evaporation 

and 2.0 inches (5 cm) in the May-October pan evaporation. These are equivalent to standard deviations of 

about 2.0 inches (5 cm) in the annual lake evaporation 

and 1.6 inches (4 cm) in the May-October lake evaporation. Table 21 contains seasonal totals from the Pretty 

Lake studies for comparison with these values. Corrections for advected energy have been applied to the evaporation-map estimates of annual evaporation in table 

21, and corrections for advected and stored energy have 

been applied to the May-October values. In some cases, 

estimates have been used in extending the Pretty Lake 

data to full season or in getting May-October values.

Results shown in table 21 for the various methods of 

computation have the same types of variation as did the 

the data that were discussed in earlier paragraphs. In 

general, the mean evaporation rate computed by the 

different methods used on Pretty Lake agrees well with 

the annual and May-October evaporation determined 

from the published maps. Mass-transfer data agree 

particularly well (within 2 cm or 0.8 inch) with the map 

estimates and energy-budget totals agree very well, 

except for the 1963 annual total, which is affected by 

the very low spring and autumn values. Class-A pan

TABLE 21. Annual and May-October evaporation from Pretty

Lake

Method of computation

Total annual

evaporation

(cm)

1964

May-October

evaporation

(cm)

1963 1963 1964

Published map___________________ 79 79 64 66

Energy budget____________.______ 72 79 63 69

Mass transfer. ___________________ 79 81 64 67

Water budget_________._ ._._____. ___ 82 ______ 70

Class-Apart.___________________ 81 88 68 74

Corrected class-A pan_____________ 80 87 66 74

Computed pan_ __________________ 75 78 64 64

Corrected computed pan_________ 74 77 62 64

data tend to be higher and lake evaporation from computed pan data tend to be lower than the map estimates. 

Corrections for advected and stored energy applied to 

the pan data are small.

CONCLUSIONS

This study has computed Pretty Lake evaporation 

by use of five common methods. The following paragraphs are included to summarize and evaluate the 

methods from the standpoints of cost, ease of operation, 

and accuracy of results.

In most respects the mass-transfer method proved to 

be the best means of computing lake evaporation for 

short periods throughout the year. It is particularly 

well suited to low evaporation rates and is the only 

method that provided good springtime records. The 

method also was superior to others for measuring 

evaporation just before, during, and just after ice cover. 

The mass-transfer coefficient, N, for Pretty Lake was 

computed to be 0.00560, in the units of equation 14, by 

calibration using the energy-budget records. This 

coefficient also could have been computed from seasonal 

records of the class-A pan or computed pan evaporation or from seasonal totals determined from maps 

based upon pan data (Kohler and others, 1959) simply 

by dividing the total evaporation by the summation of 

the products n u (e0 ea) for the season. For lakes with 

large inflow and outflow, the seasonal totals would 

have to be corrected for advected energy, but these 

corrections need not be precise and often can be computed from available weather and streamflow data. A 

mass-transfer coefficient computed by this method will 

not be valid for lakes having a variable coefficient, such 

as that caused by emergent aquatic vegetation. The 

mass-transfer coefficient for Pretty Lake could not be 

computed accurately from a water-budget calibration 

because the seepage rate varies. The coefficient determined for Pretty Lake was 15 percent less than that 

predicted from lake-area relationships (Harbeck, 1962). 

Evaporation computation by the mass-transfer method 

uses simple, reliable, and relatively inexpensive instruments and techniques. With rather simple modifications, these instruments and techniques can be adapted 

to automatic data processing. Short-term mass-transfer 

evaporation data were higher than results from other 

methods for early and late seasons (April, May, and 

November) with low evaporation rates and lower than 

results of other methods during periods of high evaporation rates (June and July). The mass-transfer method 

does not provide good evaporation data during periods 

of very low wind.

The energy-budget method produces evaporation 

data that are independent of the other methods. 

Shorter computation periods provide less accurate
COMPARISON OF EVAPORATION COMPUTATION METHODS A47

results than do longer periods of a month or more. 

Energy-budget evaporation rates tend to be lower than 

the results of other methods during the spring and 

autumn low-rate seasons and higher during the summer 

high-rate season. These average out, so that the seasonal 

totals are the same as those computed by other methods, 

but the springtime and short-term data probably are 

less reliable than mass-transfer data. Many factors 

contribute errors to the energy budget; these include 

instrument records, thermal-survey data, capacity 

tables, and the Bowen ratio. Of the several methods 

used in this study, the energy budget is the most 

expensive. It requires sophisticated equipment, frequent temperature surveys, and complex computations. 

An integrator device attached to the multipoint analog 

recorder reduced the amount of time required for data 

processing, and greater automation is possible by the 

use of more complex equipment.

The water-budget method is simple and inexpensive 

to operate, but it depends upon some other measure of 

evaporation, such as mass-transfer data, in order to 

compute seepage. During the dryer seasons the waterbudget studies of Pretty Lake found a corrected fall in 

stage that agreed well with the evaporation rates computed by other methods. During wet seasons the water 

budget was affected by considerable inflow seepage. 

Because of variable seepage the water budget is not a 

satisfactory independent evaporation measurement for 

computing the mass-transfer coefficient.

Standard class-A pan records and computed pan 

evaporation provide inexpensive lake evaporation data 

because they rely mainly upon data collected at U.S. 

Weather Bureau stations, plus less expensive data at the 

lake. Pan-based evaporation hydrographs are skewed 

to the left of the hydrographs produced by other 

methods. The skew is caused by energy-storage effects, 

which may be corrected, but only if thermal-survey 

data are available. Corrected lake evaporation data 

based upon class-A and computed pan evaporation 

records agree well with other evaporation records 

through the season. With only simple advected-energy 

corrections the computed and class-A pan evaporations 

provide good measures of total yearly lake evaporation. 

Class-A pan data can provide a better measure of lake 

evaporation if pan-water temperatures are available. 

It is difficult to compute complete lake evaporation 

records from published class-A pan records because 

data sometimes are missing.

REFERENCES

Al-Barrak, Ala H., 1964, Evaporation and potential evapotranspiration in central Iraq: Logan, Utah State Univ. 

Water Research Lab. Progress Report, Project WR 13, 

203 p.

Anderson, E. R., 1952, Energy-budget studies in Water-loss 

investigations: Lake Hefner studies, technical report: 

U.S. Geol. Survey Prof. Paper 269, p. 71-119 [1954].

Anderson, E. R., Anderson, L. J., and Marciano, J. J., 1950, A 

review of evaporation theory and development of instrumentation: U.S. Navy Electronics Lab. Rept. 159, 69 p., 

U.S. Navy, San Diego, Calif.

Ayers, J. C., 1965, A late summer heat budget of Barnstable 

Harbor, Massachusetts: Limnology and Oceanography, 

supplement to v. 10, p. R9-R14.

Birge, E. A., Juday, C., and March, H. W., 1928, The temperature of the bottom deposits of Lake Mendota; a chapter in 

the heat exchanges of lakes: Wise. Acad. Sci., Arts, Letters 

Trans., v 23, p. 187-231.

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

evaporation from any water surface: Physical Review, 

v. 27, p. 779-787.

Braslavskii, A. P., and Vikulina, Z. A., 1954, Evaporation norms 

from water reservoirs, translated from Russian by Israel 

Program for Scientific Translations Ltd.: Distributed by 

Office of Tech. Serv., U.S. Dept. Commerce, OTS 63-11064, 

218 p. [1963].

Budyko, M. I., 1948, Evaporation under natural conditions, 

translated from Russian by Israel Program for Scientific 

Translations Ltd.: Distributed by Office of Tech. Serv., 

U.S. Dept. Commerce, OTS 63-11061, 130 p. [1963].

Christiansen, J. E., and Lauritzen, N. W., 1963, A bibliography 

on evaporation and evapotranspiration: Logan, Utah State 

Univ., Engineering Experiment Station, Report of Project 

U-193, 18 p.

Corbett, D. M., and others, 1943, Stream-gaging procedure, a 

manual describing methods and practices of the Geological 

Survey: U.S. Geol. Survey Water-supply Paper 888, 245 p.

Dorsey, N. Ernest, 1940, Properties of ordinary water-substance: 

New York, Reinhold Publishing Corp., 673 p.

Ficke, J. F., 1965, Seasonal erasure of thermal stratification in 

Pretty Lake, Indiana in Geological Survey research 1965: 

U.S. Geol. Survey Prof. Paper 525-C, p. C199-C202.

Harbeck, G. E., 1962, A practical field technique for measuring 

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

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

 1964, Estimating forced evaporation from cooling ponds: 

Am. Soc. Civil Engineers Proc., Power Div. Jour., v. 90, 

no. PO3, p. 1-9.

Hughes, G. H., 1967, Analysis of techniques used to measure 

evaporation from Salton Sea, California: U.S. Geol. Survey 

Prof. Paper 272-H, p. 151-176.

Ingersoll, L. R., Zobel, O. J., and Ingersoll, A. C., 1954, Heat 

conduction, with engineering, geological, and other applications: Madison, Wise., Wisconsin Univ. Press, 325 p.

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

and others, Water-loss investigations: Lake Mead studies: 

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

 1964, Methods to compute long-wave radiation from the 

atmosphere and reflected solar radiation from a water 

surface: U.S. Geol. Survey Prof. Paper 272-F, p. 107-136.

Kohler, M. A., 1952, Lake and pan evaporation in Water-loss 

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

Geol. Survey Prof. Paper 269, p. 127-148 [1954].

Kohler, M. A., Nordenson, T. J., and Fox, W. E., 1955, Evaporation from pans and lakes: U.S. Weather Bur. Research 

Paper 38, 21 p.
A48 HYDROLOGIC AND BIOLOGICAL STUDIES OF PRETTY LAKE, INDIANA

 1958, Pan and lake evaporation in Harbeck, G. E., and 

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

Geol. Survey Prof. Paper 298, p. 38-60.

1959, Evaporation maps for the United States: U.S.

Weather Bur. Tech. Paper 37, 13 p., 5 plates.

Kung, E. C., Bryson, R. A., and Lenschow, D. H., 1964, Study 

of a continental surface albedo on the basis of flight measurements and structure of the earth's surface over North 

America: Monthly Weather Review, v. 92, no. 12, p. 543- 

564.

Langbein, W. B., Hains, C. H., and Culler, R. C., 1951, Hydrology 

of stock-water reservoirs in Arizona: U.S. Geol. Survey 

Circ. 110, 18 p.

Lyubomirova, K. S., 1962, Dependence of ice albedo on incidence 

of solar rays, translated from Russian by L. G. Robbins: 

Soviet Hydrology Selected Papers, 1962, no. 2, p. 124-128.

Marciano, J. J., and Harbeck, G. E., Jr., 1952, Mass-transfer 

studies in Water-loss investigations: Lake Hefner studies, 

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

p. 46-70 [1954].

Nordenson, T. J., 1963, Appraisal of seasonal variation in pan 

coefficients: Internat. Assoc. Sci. Hydrology Pub. 62, p. 

279-286.

 1965, Discussion of Harbeck, G. E., Jr., Estimating 

forced evaporation from cooling ponds: Am. Soc. Civil 

Engineers Proc., Power Div. Jour., v. 91, no. POl, p. 109- 

112.

Perry, J. I., and Corbett, D. M., 1956, Hydrology of Indiana 

lakes: U.S. Geol. Survey Water-Supply Paper 1363, 347 p.

Robinson, T. W., and Johnson, A. I., 1961, Selected bibliography 

on evaporation and transpiration: U.S. Geol. Survey WaterSupply Paper 1539-R, 25 p.

Stephens, J. C., 1965, Discussion of Lane, R. K., Estimating 

evaporation from insolation: Am. Soc. Civil Engineers 

Proc., Hydraulics Div. Jour., v. 91, no. HY 5, p. 171-182.

Stephens, J. C., and Stewart, E. H., 1963, A comparison of 

procedures for computing evaporation and evapotranspiration: Internat. Assoc. Sci. Hydrology Pub. 62, General 

Assembly of Berkley, p. 123-133.

Webb, E. K., 1960, On estimating evaporation with fluctuating 

Bowen ratio: Jour. Geophysical Research, v. 65, p. 3415- 

3417.

Williams, G. P., 1961, Evaporation from water, snow, and icie in 

Proceedings of hydrology symposium No. 2 evaporaton : 

Ottawa, Canada Dept. Northern Affairs and National 

Resources, p. 31-52.
INDEX

Page 

Acknowledgments............................ A2

Advected energy... 8,10,13,17,23,32,33,37,45,46,47 

Air temperature....._........... 7,11,13,30,36,39

Albedo....................................... 37,38

Anemometer............................ 9,19,23,43

height correction....__............... 19

Basin description............................. 2

Bibliography. _............._............... 47

Bowen ratio...................... 14,15,37,41,43,47

Capacity table........................._ 14,41,47

Class-A evaporation pan.......... 29,31,33,44,45,47

See also Evaporation-pan method. 

C omputed evaporation, lake. ___________ 32,33,45,46

pan..................... 30,32,33,39,41,45,46,47

Corrected change in stage___._____ 23,24, 25,28,29,36

Corrections for pan evaporation........ 33,41,45,46

Culver evaporation station.__________________ 30,32

Dry-bulb temperature. See Air temperature.

Energy, advected.. 8,10,13,17,23,32,33,37,45,46,47 

Energy budget............................... 7,

9, 14, 15, 17, 18, 19, 29, 33, 36, 38, 39, 40,

41,45,46,47

Energy storage........ 7,10,14,15,32,33,37,41,45,46

Evaporation, lake, computed........... 32,33,45,46

lake, Weather Bureau estimate of......... 32,

33,35,45,46 

pan, Weather Bureau estimate of.......32,33,35

wintertime.......... 33,35,36,37,41,43,44,45,46

Evaporation-pan method.. _-_______ __-_ 9,

29,30,32,35,38,41,44,46 

See also Class-A evaporation pan. 

Evaporation patterns, nationwide.__._____. 30

Evaporation station, Culver_............... 30,32

Kendallville...--__._..._--_-_---.---.-- 9,29,32

Flat-plate radiometer____________________ 8,10,36

Gage, rain....... ..... .-----.-..----.... 6,24,35

Gaging station, inlet,_______________________ 5,23

outlet-----..---- ---_ - ------_- 6,23

Harbeck estimate of mass-transfer coefficient. _ 19,

22,29,43,46 

Heat, latent...... .. -._ 14,33,37

sensible -- _ 10,14,33

Heat budget. See Energy budget. 

Heat storage. See Energy storage. 

Heating, sediment--.....-.------- 15,17,18,33,41

[Italic page numbers indicate major references]

Page 

Ice conditions.--.--_......_...__ A2,34,35,36

Ice reflectivity-.___ 37,41

Ice temperature...--....._.--____.---_-__.... 36,37

Inflow 5,17,23,24,28,32,35,39

Inlet gaging station.._.___._._...______. 5,23

Instrument records.. .-__........... 10,19,23,47

Instrumentation_....._..._ .._ _ __ B

Integrator.... _-. _- 8,11,47

Kendallville evaporation station_......... 9,29,32

Koberg estimate, long-wave radiation __.._ 11,36

reflected radiation._.________._ ___._ 10

Lake evaporation, computed. ___ . 32,33,45,46 

Weather Bureau estimate of..... 32,33,35, 45,46

Lake Mendota sediment studies.............. 17

Lake-stage recorder _ _.. 6,7,24

Lake-surface temperature. See Water temture.

Latentheat - 14,33,37

Least-squares fit. See Regression.

Long-wave radiation ______ 8,10,11,36,37,39,40

Koberg estimate of______............... 11,36

Mass-transfer coefficient . - 19, 28,29,36,38,43,46,47

Harbeck estimate of...._.__... 19,22,29,43,46

Mass-transfer method.-..-_____..._ _-___ 9,

18,22,23,24,25,29,36,38,39,41,43,46

Mendota, Lake, sediment studies...________ 17

Outflow. . . 5,17,23,25,28,32,35,39 

Outlet gaging station____........_...___._____ 6,23

Pan coefficient - . 30,32,33,45 

Pan evaporation, computed ._ . _____ 30,

32,33,39,41,45,46,47 

corrections___.................... 33,41,45,46

Weather Bureau estimate of .... 32,33,35

Potentiometer.......-__-.___.-.__.._...__.. 8

Precipitation. _. . 7,23,24,28,32,35,39 

Precipitation gage. See Rain gages. 

Psychrometer_.__.........__.........__ 7

Pyrheliometer. 8,10,36

Radiation, long-wave__....... 8,10,11,36,37,39,40

long-wave, Koberg estimate of......._.... 11,36

reflected.----.---.--.. 10,11,36,37,38,39

Koberg estimate of--.-- -- 10

solar -. -.-. 8,10,36,37,39,40

Radiometer, flat-plate. 8,10,36

Rain gage... 6,24,35

Recorder, lake-stage..----..__............. 6,7,24

Page 

Records, instrument. ----------- AlO,19,23,47

stage..- 7,23,24,29,35,39

streamflow..- 5,13,23,25

Reflected radiation - 10,11,36,37,38,39 

Koberg estimate of. - _- 10

Reflectivity, ice.---...----..-------..----- 37,41

Regression.. - 19,20,22

Sediment heating - 15,17,18,33,41 

Sediment studies, Lake Mendota------------- 17

Seepage-- -.-- 5,23,24,25,28,29,35,36,38,43,44,47 

Sensible heat. 10,14,33

Sextant technique-..-__ 9

Snow. - 6,34,35,36,37

Solar radiation..... ............. 8,10,36,37,39,40

Stage, corrected change hi . 23,24,25,28,29,35

records-------------.---.----- 7,23,24,29,35,39

Station, evaporation, Culver___........... 30,32

evaporation, Kendallville-.-------- -- 9,29,32

gaging,inlet......------------------------ 5,23

outlet---.---..-----------------.- 6,23

streamflow-------------- -------------- 6

Store energy. See Energy storage.

Stratification, thermal.- - ----- ---- 5

Streamflow records.. 5,13,23,25

Streamflow station... --- - 6

Temperature, air. 7,11,13,30,36,39 

dry-bulb. See Air temperature. 

ice... 36,37

lake-surface. See Water temperature.

patterns of------. ------------------ 5

water....---.---_-_--._--.- 5,6,8,13,14,19,39,40

wet-bulb.---- _---.-------------- 7,11

Temperature survey___._.__----- 8,9,14,32,37,39,47

Thermal expansion.._..__.. __.. 7,28 

Thermal stratification. __ ___ - - _ 5

Vapor pressure.... .... 7,11,13,19,23,36,39

Water budget ...... __- -. - 5

Water-budget method...... 23,35,38,39,41,43,46,47

Water temperature....________ 5,6,8,13,14,19,39,40

Weather Bureau estimate, lake evaporation. _. 32,

33,35,45,46 

pan evaporation---..-.-.------ ----- 32,33,35

Weighted regression.--._--.- ---------.----- 20,22

Weir 6,23

Wet-bulb temperature...---------- --------- 7,11

Wind.-----------.-- - 9,19,23,32,36,39,41,43

Wintertime evaporation._____ 33,

35,36,37,39,41,43,44,45,46

A49

U. S. GOVERNMENT PRINTING OFFICE : 1972 O - 427-149