United States 

Geological 

Survey 

Water-Supply 

Paper 

Influence of Evaporation, Ground 

Water, and Uncertainty in the 

Hydrologic Budget of Lake 

Lucerne, a Seepage Lake in 

Polk County, Florida

Prepared in cooperation 

with the Southwest Florida 

Water Management 

District

2439
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Influence of Evaporation, Ground Water, and 

Uncertainty in the Hydrologic Budget of 

Lake Lucerne, a Seepage Lake in 

Polk County, Florida

By T.M. LEE and AMY SWANCAR

Prepared in cooperation with the

Southwest Florida 

Water Management District

U.S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER 2439
U.S. DEPARTMENT OF THE INTERIOR

BRUCE BABBITT, Secretary

U.S. GEOLOGICAL SURVEY

Gordon P. Eaton, Director

Any use of trade, product, or firm names in this publication is for

descriptive purposes only and does not imply endorsement by the

U.S. Government.

Printed in the Eastern Region, Reston, Va.

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1997

For sale by the

U.S. Geological Survey, Information Services

Box 25286, Federal Center

Denver, CO 80225

Library of Congress Cataloging in Publication Data

Lee, T.M. (Terrie Mackin)

Influence of evaporation, ground water, and uncertainty in the hydrologic budget 

of Lake Lucerne, a seepage lake in Polk County, Florida / by T.M. Lee and Amy 

Swancar.

p. cm. —(U.S. Geological Survey water-supply paper ; 2439)

“Prepared in cooperation with the Southwest Florida Water Management District.”

Includes bibliographical references.

Supt. of Docs. no: I 19.13:W2439

1. Hydrologic cycle—Florida—Lucerne, Lake (Polk County)

I. Swancar, Amy. II. Southwest Florida Water Management District. III. Title.

IV. Series.

GB848.L44 1996 551.48'09759'67—dc20 94-40179

CIP
Contents III

CONTENTS

Abstract.................................................................................................................................................................................. 1

Introduction ........................................................................................................................................................................... 2

Purpose and Scope....................................................................................................................................................... 2

Previous Investigations................................................................................................................................................ 3

Acknowledgments ....................................................................................................................................................... 4

Description of Study Area ..................................................................................................................................................... 4

Physical Setting ........................................................................................................................................................... 4

Climate......................................................................................................................................................................... 4

Hydrogeologic Setting................................................................................................................................................. 6

Geologic Framework ......................................................................................................................................... 7

Ground-Water Flow Patterns ............................................................................................................................. 9

Hydrologic-Budget Approach ..................................................................................................................................... 13

Evaporation............................................................................................................................................................................ 15

Energy-Budget Method ............................................................................................................................................... 15

Theory and Equations........................................................................................................................................ 15

Energy-Budget Evaporation Rates .................................................................................................................... 17

Comparison of Thermal Survey Period and Daily Evaporation Estimates ....................................................... 18

Energy-Budget Error Analysis .......................................................................................................................... 19

Sensitivity Analysis ........................................................................................................................................... 20

Mass-Transfer Method................................................................................................................................................. 20

Theory and Equations........................................................................................................................................ 22

Mass-Transfer Coefficient ................................................................................................................................. 22

Comparison of Mass-Transfer and Energy-Budget Evaporation Rates............................................................. 22

Stability.............................................................................................................................................................. 23

Mass-Transfer Evaporation Rates...................................................................................................................... 23

Mass-Transfer Error Analysis............................................................................................................................ 23

Pan-Evaporation Method............................................................................................................................................. 24

Theory and Equations........................................................................................................................................ 25

Free Water-Surface Evaporation Rates.............................................................................................................. 25

Pan Coefficients................................................................................................................................................. 26

Evaporation Summary ................................................................................................................................................. 27

Ground Water......................................................................................................................................................................... 28

Numerical Simulation of Ground-Water and Lake Interactions.................................................................................. 28

Modeling Approach........................................................................................................................................... 28

Effect of Intermediate Confining Unit Below the Lake .................................................................................... 31

Effect of Anisotropy in the Surficial Aquifer.................................................................................................... 35

Effect of Lake Sediments................................................................................................................................... 35

Limitations of Two-Dimensional Model ........................................................................................................... 40

Summary of Modeling Results.......................................................................................................................... 40

Quantification of Ground-Water Fluxes ...................................................................................................................... 41

Ground-Water Inflow......................................................................................................................................... 41

Flow-Net Assumptions ............................................................................................................................ 41

Ground-Water Inflow Rates..................................................................................................................... 43

Errors in Ground-Water Inflow Rates...................................................................................................... 44

Lake Leakage..................................................................................................................................................... 44

Flow-Net Assumptions ............................................................................................................................ 45

Estimation of Sublake Vertical Hydraulic Conductivity ......................................................................... 45

Leakage Rates.......................................................................................................................................... 47

Errors in Lake Leakage Rates.................................................................................................................. 48

Summary of Ground-Water Fluxes.................................................................................................................... 48
IV Contents

Influence of Evaporation, Ground Water, and Uncertainty in the Hydrologic Budget......................................................... 49

Hydrologic-Budget Results......................................................................................................................................... 49

Evaluation of Budget Error ......................................................................................................................................... 51

Revised Estimates of Ground-Water Inflow and Leakage.......................................................................................... 52

Summary and Conclusions.................................................................................................................................................... 53

References............................................................................................................................................................................. 55

Appendix A. Energy-Budget Components and Evaporation Calculations for Each Thermal Survey Period ..................... 58

Appendix B. Conversion Tables for Calculation of Free Water-Surface Evaporation Rates............................................... 60

FIGURES

1, 2. Maps showing:

1. Location of Lake Lucerne and physiographic divisions in Polk County ................................................... 5

2. Lakes in the vicinity of the study area ........................................................................................................ 6

3, 4. Graphs showing:

3. Monthly rainfall at Lake Lucerne for the 1986 water year and the long-term average 

monthly rainfall at the National Oceanic and Atmospheric Administration climate station at 

Lake Alfred, 1951–80 ................................................................................................................................. 7

4. Daily mean stage of Lake Lucerne and weekly stage of Terrie Pond for the 1986 water year................... 7

5. Hydrogeologic section of the study area ............................................................................................................... 8

6–9. Maps showing:

6. Locations of wells whose logs were used to construct the hydrogeologic section ..................................... 9

7. Bathymetric and seismic-reflection contours and cross section of Lake Lucerne ...................................... 10

 8. Data-collection sites in the Lake Lucerne study area.................................................................................. 11

 9. Configuration of the water table in the Lake Lucerne area based on the minimum and the maximum

recorded water levels during the 1986 water year ...................................................................................... 11

10–12. Sections showing:

10. Vertical distribution of head during high water-level conditions, October 17, 1985 .................................. 12

11. Vertical distribution of head during low water-level conditions, May 20, 1986......................................... 13

12. Vertical distribution of head showing downward head gradient conditions, August 6, 1985..................... 14

13–23. Graphs showing:

13. Water levels in well 2PN-130 from April 1984 through September 1986 and the estimated trend in 

water levels for nonpumping conditions ..................................................................................................... 15

14. Daily average energy-budget evaporation at Lake Lucerne by thermal survey period for the 

1986 water year ........................................................................................................................................... 17

15. Daily energy-budget evaporation at Lake Lucerne for 321 days of the 1986 water year ........................... 18

16. Daily average temperature difference and vapor pressure difference between the

surface of Lake Lucerne and 2 meters above the lake surface for the 1986 water year ............................. 18

17. Daily average Bowen ratios and average Bowen ratios by thermal survey period for the 

1986 water year ........................................................................................................................................... 19

18. Sensitivity of energy-budget evaporation to errors in incident shortwave radiation, reflected

shortwave radiation, reflected and emitted longwave radiation, incident longwave radiation, 

Bowen ratio, and water-surface temperature............................................................................................... 21

19. Relation between energy-budget evaporation and the mass-transfer product by thermal 

survey period............................................................................................................................................... 22

20. Relation between the mass-transfer coefficient and the stability parameter by thermal 

survey period............................................................................................................................................... 23

21. Mass-transfer evaporation rates corrected for atmospheric stability by thermal survey period for the 

1986 water year ........................................................................................................................................... 24

22. Differences between energy-budget evaporation and mass-transfer evaporation (uncorrected), 

and mass-transfer evaporation corrected for atmospheric stability by thermal survey period for 

the 1986 water year ..................................................................................................................................... 24

23. Monthly free water-surface evaporation calculated from the evaporation pans at Lake Lucerne 

and at the Lake Alfred National Oceanic and Atmospheric Administration site, and from the 

corrected energy-budget evaporation for the 1986 water year.................................................................... 26
Contents V

24. Schematic layout of model grid for numerical ground-water simulation and enlarged model area around 

Lake Lucerne showing approximate locations of wells at sites 1PN and 2PN ..................................................... 30

25–30. Diagrams of simulated vertical head distribution for:

25. High water-level conditions with a continuous confining unit beneath Lake Lucerne and 

a breached confining unit beneath Lake Lucerne ....................................................................................... 32

26. High water-level conditions showing general pattern of ground-water flow in the basin .......................... 33

27. Low water-level conditions with a continuous confining unit beneath Lake Lucerne and 

a breached confining unit beneath Lake Lucerne ....................................................................................... 34

28. High water-level conditions with anisotropy equal to 10, 100, and 1,000.................................................. 36

29. High water-level conditions with vertical hydraulic conductivity of the sediment, Kvsed, 

equal to 0.005, 0.002, and 0.0002 foot per day........................................................................................... 38

 30. Low water-level conditions with vertical hydraulic conductivity of the sediment, Kvsed, 

equal to 0.005, 0.002, and 0.0002 foot per day........................................................................................... 39

31. Flow-net diagrams for the 1986 water year annual average, for May 20, 1986, and for June 24, 1986, 

water-table configurations ..................................................................................................................................... 43

32. Graph showing monthly and total annual ground-water inflow to Lake Lucerne for the 1986 water year .......... 44

33. Schematic of conceptual model of the leakage from Lake Lucerne...................................................................... 46

34–41. Graphs showing:

34. Predicted monthly mean, minimum, and maximum daily values of the head in well 1PN-155 

for the 1986 water year ............................................................................................................................... 47

35. Predicted monthly mean, minimum, and maximum daily values of the downward head difference 

between Lake Lucerne and well 1PN-155 for the 1986 water year............................................................ 47

36. Monthly and total annual leakage from Lake Lucerne for the 1986 water year ......................................... 47

37. Monthly and total annual leakage from Lake Lucerne under hypothetical, nonpumping conditions 

for the 1986 water year ............................................................................................................................... 47

38. Monthly and total annual net ground-water flow to Lake Lucerne for the 1986 water year ...................... 48

39. Monthly values of hydrologic-budget components of Lake Lucerne for the 1986 water year: 

precipitation, evaporation, change in storage, leakage, and ground-water inflow...................................... 50

40. Relation between the residual net ground-water flow and the calculated net ground-water flow 

to Lake Lucerne by month for the 1986 water year .................................................................................... 52

41. Monthly calculated, residual, and revised net ground-water flow to Lake Lucerne for the 

1986 water year ........................................................................................................................................... 52

A1, A2. Graphs showing:

A1. Total stored heat and daily average change in stored heat in Lake Lucerne by thermal survey 

period for the 1986 water year .................................................................................................................... 59

A2. Total stored heat and daily change in stored heat in Lake Lucerne for the 1986 water year...................... 59

TABLES

1. Monthly energy-budget evaporation rates and errors, October 1985 through September 1986 ............................ 20

2. Monthly and annual pan coefficients for Lake Lucerne for the 1986 water year................................................... 27

3. Predicted ground-water inflow and leakage rates and areas for three modeled values of anisotropy 

at high water-level conditions................................................................................................................................. 37

4. Predicted ground-water inflow and leakage rates for three Kvsed values under high and low water-level

conditions and heads for the midlake well ............................................................................................................. 40

5. Monthly residual net ground-water flow to Lake Lucerne and the associated error.............................................. 52

A1. Summary of energy-budget components and evaporation calculations for each thermal survey period ............... 58

A2. Annual average values, weighted average errors, and relative errors for energy-budget components 

and evaporation, October 1985 to September 1986................................................................................................ 59

B1. Conversion table for calculating monthly total free water-surface evaporation from monthly 

total pan evaporation at Lake Lucerne.................................................................................................................... 60

B2. Conversion table for calculating monthly total free water-surface evaporation from monthly 

total pan evaporation at Lake Alfred National Oceanic and Atmospheric Administration site ............................. 60

B3. Conversion table for calculating monthly free water-surface evaporation from monthly 

energy-budget evaporation ..................................................................................................................................... 61
VI Contents

CONVERSION FACTORS, VERTICAL DATUM, AND ADDITIONAL ABBREVIATIONS

Temperature conversions for degrees Fahrenheit (°F) and degrees Celsius (°C) follow:

°C = 5/9 x (°F - 32)

°F=1.8 °C + 32

Sea level: In this report, “sea level” refers to the National Geodetic Vertical Datum of 1929 (NGVD of 1929)--a geodetic

datum derived from a general adjustment of the first-order level nets of both the United States and Canada, formerly called

Sea Level Datum of 1929.

Additional units used in report:

cm centimeter

cm/d centimeter per day

 m meter

NOTE: Inch-pound units were selected for use in this report. An exception to the use of inch-pound units, however, is

made in the presentation of data collected for the energy-budget and mass-transfer evaporation methods. The metric unit

of langley (calories per square centimeter) is conventionally used to describe the energy terms in an energy-budget

analysis (Anderson, 1954; Sturrock, 1985). Temperatures used in the computation of energy terms are in the compatible

metric unit of degrees Celsius. The dual units that are conventionally used to describe the components of the mass-transfer evaporation method (Harbeck, 1964; Sturrock, 1985) also are used in this report.

Multiply By To obtain

inch (in.) 2.54 centimeter

inch per day (in/d) 2.54 centimeter per day

inch per year (in/yr) 2.54 centimeter per year

foot (ft) 0.3048 meter

foot per day (ft/d) 0.3048 meter per day

mile (mi) 1.609 kilometer

square foot (ft2) 0.09290 square meter 

square mile (mi2

) 2.590 square kilometer

cubic foot per day (ft3/d) 0.02832 cubic meter per day

cubic foot per day per foot [(ft3/d)/ft] 1.0000 cubic meter per day per meter

million gallons (Mgal) 3,785 cubic meter

calorie per square centimeter per day [(cal/cm2

)/d] 3.69 British thermal unit per square foot per day

calorie per gram (cal/g) 1.80 British thermal unit per pound mass

calorie per gram per degree Celsius [(cal/g)/°C] 1.00 British thermal unit per pound mass per 

degree Fahrenheit

gram per cubic centimeter (g/cm3) 0.00112 pound mass per cubic inch

millibar (mb) 0.0145 pound-force per square inch
Abstract 1

Influence of Evaporation, Ground Water, and 

Uncertainty in the Hydrologic Budget of Lake Lucerne,

a Seepage Lake in Polk County, Florida

By T.M. Lee and Amy Swancar

Abstract

Evaporation losses and the interaction of 

ground water with Lake Lucerne were studied to 

determine the influence of these two processes on 

the hydrologic budget of a seepage lake. Lake 

Lucerne is representative of the numerous 

seepage lakes of sinkhole origin in the karst 

terrain of central Florida. Because of permeable 

surficial deposits, ground-water inflow is the only 

significant contribution from the surrounding 

watershed. The lake recharges the underlying 

Upper Floridan aquifer and, as a result, is 

susceptible to increased leakage induced by 

pumping from this aquifer. Ground-water fluxes 

determined in the study were analyzed to define 

the proportion of the total lake leakage induced by 

pumping from the Upper Floridan aquifer. A 

hydrologic budget is analyzed for the 1-year 

period from October 1985 to September 1986.

Ground-water inflow and leakage are 

significant components of the hydrologic budget. 

Changes in the quantity of either of these fluxes 

can substantially alter lake stage. Ground-water 

inflow contributed from 20 to 37 percent of the 

total annual inflow to the lake. Leakage from the 

lake accounted for 18 to 23 percent of the total 

annual outflow. Water withdrawals from the 

Upper Floridan aquifer increased annual lake 

leakage by 22 percent over nonpumping 

conditions. Most of the increase (92 percent) in 

leakage occurred during April, May, and June 

1986, when local citrus irrigation was highest. 

For the study year, ground-water inflow and 

leakage volumes were calculated by flow-net 

analysis to be equal to 10.5 and 12.6 inches, 

respectively, of water depth above (or below) the 

lake surface. These estimates were revised 

upward on the basis of an analysis of the error in 

the hydrologic-budget equation. Revised groundwater inflow exceeded annual leakage from the 

lake. Ground-water inflow rates were increased 

by 120 percent to 23.6 inches, and leakage was 

increased by 40 percent to 17.5 inches. 

Differences between the two estimates probably 

reflect the uncertainty in the hydraulic 

conductivity estimates of the porous media 

around the lake and the unaccounted effect of 

transient ground-water inflow.

The geometry of the sinkhole complex 

beneath Lake Lucerne and pumping in the Upper 

Floridan aquifer are primary controls on groundwater interactions with the lake and, in particular, 

lake leakage. A numerical ground-water model 

was used to test the effects of these two factors on 

ground-water interactions with the lake. Results 

indicate that the intermediate confining unit 

below Lake Lucerne has been breached and 

replaced by materials about two orders of 

magnitude more conductive. Anisotropy in the 

surficial aquifer is approximately 100 and 

controls the depth of the ground-water flow 

intercepted by the lake. Lake sediments having 

low permeability may control the distribution of 

leakage through the lakebed but did not 

appreciably reduce total leakage rates in these 

simulations.
2 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

Evaporation loss was the major outflow 

component of the hydrologic budget. Annual lake 

evaporation determined by the energy-budget 

method was 57.9 inches, about 8 inches greater 

than long-term estimates for the region. The 

greater rate was attributed to drier than normal 

conditions: rainfall totaled 40.9 inches during the 

study year, about 10 inches less than the 

long-term average. Similar annual evaporation 

rates were determined by the energy-budget 

method, the simpler mass-transfer method, and by 

corrected pan evaporation from an onsite pan; 

however, the probable errors associated with these 

other two methods were greater than for the 

energy budget. Weekly energy-budget 

evaporation rates ranged from 0.04 inch per day 

in early January 1986 to 0.26 inch per day in early 

May 1986. The largest monthly energy-budget 

evaporation rates occurred in April and May 

1986, 7.16 and 7.12 inches per month, 

respectively. Monthly evaporation estimated 

from corrected pan evaporation generally was 

within 10 percent of the energy-budget estimate 

but differed by as much as 35 percent. Daily 

energy-budget evaporation also was computed for 

321 days during the year.

INTRODUCTION

In Florida, the more than 7,700 warm-water 

lakes form a lake district that is unique to the southern 

United States. Comparably large lake districts are 

found only within the formerly glaciated northern 

States from Minnesota to Maine (Brenner and others, 

1990). Many lakes in Florida are under enormous 

developmental pressures as the population of the State 

rapidly increases. Lakefront property is highly 

desirable as homesites, as the density of lakefront 

development can often attest. Lake basins also are 

favored sites for cultivation of citrus because lakes 

tend to moderate winter temperatures and provide 

accessible irrigation water. Increased development 

within lake basins and increased demand for 

freshwater for irrigation, industrial, and municipal 

supplies can adversely affect the water quality of and 

water-level fluctuations in many lakes in Florida.

Optimum management of lakes in Florida 

requires an improved understanding of the influence 

of lakes on the hydrologic system. Hydrologic 

budgets that describe the sources and losses of water 

to lakes are essential to many lake-management 

decisions, for example, to adopt the best management 

practices and to evaluate lake-restoration projects. 

However, many available hydrologic budgets lack the 

necessary accuracy to define cause and effect clearly 

when lake levels begin to change.

Uncertainties about evaporation and groundwater fluxes from seepage lakes are major obstacles in 

the determination of accurate hydrologic budgets. 

Approximately two-thirds of all lakes in Florida are 

seepage lakes that lack channelized surface-water 

inflows or outflows. Overland runoff is minimal 

because of the high infiltration rate of the sandy soils 

near these lakes. The principal sources of water to 

these lakes are rainfall, which can be measured easily, 

and ground-water inflow. Principal water losses are 

by evaporation and leakage of lake water to the 

underlying aquifer. The lack of adequate information 

on these hydrologic-budget components makes it 

difficult to distinguish the effects of evaporation, lake 

leakage, and ground-water withdrawals on lake-level 

declines.

In 1983 the U.S. Geological Survey, in 

cooperation with the Southwest Florida Water 

Management District, began a detailed 5-year study of 

the hydrologic budget of Lake Lucerne in Polk 

County, Fla. The study focused on determining the 

influence of evaporation and ground water in the 

overall hydrologic budget and also evaluated the 

uncertainty in each budget component. The study also 

examined the influence of the geology underlying the 

lake and water withdrawals from the Upper Floridan 

aquifer on the ground-water interactions with Lake 

Lucerne.

Purpose and Scope

This report describes the evaporative losses and 

ground-water fluxes to Lake Lucerne and the 

influence of these processes on the hydrologic budget 

of the lake for the period October 1, 1985, to 

September 30, 1986. Also described are the effects of 

ground-water pumping near the lake on ground-water 

fluxes to Lake Lucerne. The ability to define the 

importance of evaporative losses and ground-water 

fluxes on the hydrologic budget of the lake is limited 

by the accuracy of each component. Therefore, the 

uncertainty in each budget component is estimated, 
Introduction 3

and its influence on the interpretation of individual 

budget components is evaluated. The magnitude and 

seasonality of uncertainty in the final hydrologic 

budget are examined to provide insight into potentially 

unaccounted fluxes.

Precipitation and lake-stage components of the 

hydrologic budget were measured directly on a daily 

basis. Evaporation and ground-water fluxes were 

computed indirectly from climatologic and hydrologic 

variables. In this report, estimates of lake evaporation 

are computed by the energy-budget method and the 

simpler mass-transfer method. Evaporation estimates 

also are compared and contrasted with each other and 

with those determined by the National Oceanographic 

and Atmospheric Administration (NOAA) panevaporation method. A steady-state numerical 

ground-water model was used to evaluate qualitatively 

the influence of geology and pumping from the Upper 

Floridan aquifer on ground-water interactions with the 

lake. Ground-water fluxes to and from the lake were 

estimated by flow-net analysis of head data measured 

in 36 wells. The uncertainty in each budget 

component was either computed or estimated from 

values reported in the literature.

Previous Investigations

Numerous investigations of hydrologic budgets 

for lakes in Florida have concentrated on 

understanding the ground-water component of the 

hydrologic budget of the lake; few, however, have 

attempted to quantify accurately the evaporation 

component. Previous budget studies that focused on 

ground-water fluxes generally are based on one of 

three approaches. The most common approach treats 

net ground-water flow (the difference between 

ground-water inflow and leakage) as the sole unknown 

term in the hydrologic-budget equation (Clark and 

others, 1963; Hughes, 1974; Lichtler and others, 1976; 

Baker and others, 1988; Deevey, 1988). In a variation 

on this approach, ground-water inflow is estimated by 

Darcy’s law, leaving leakage to be derived as the 

residual term (Henderson, 1983; Henderson and 

others, 1985). When ground-water flow is calculated 

as a residual of the budget equation, it includes the 

measurement errors in all other budget terms and, 

thus, may be inaccurate (Winter, 1981b).

Less frequently, seepage-measuring devices 

modeled after Lee (1977) have been used to measure 

directly the flux of water through lakebeds. (The 

general term “seepage” can describe flow either into 

or out of a lake.) Point measurements of seepage have 

been used to estimate ground-water inflow to Lake 

Conway and Lake Apopka (Fellows and Brezonik, 

1980) and Lake Washington (Conner and Belanger, 

1981). Leakage (negative seepage) was observed only 

by Conner and Belanger (1981) but was not 

quantified. In both studies, ground-water inflow was 

presented as a fraction of the total inflow to the 

hydrologic budget of each lake. Finally, trend analysis 

has been used to establish indirectly a relation between 

lake stage and such hydrologic variables as local 

ground-water levels and ground-water pumping rates 

(Geraghty and Miller, Inc., 1980; Henderson and 

Lopez, 1989).

In each of these studies, evaporation was 

computed from NOAA pan-evaporation data 

(Farnsworth and others, 1982). Because evaporationpan measurements overestimate lake evaporation, pancorrection factors are available to estimate the annual 

average evaporation in Florida (Farnsworth and 

others, 1982). In previous studies, evaporation 

estimates have been made for periods as short as 

7 days (Lichtler and others, 1976) or 1 month 

(Hughes, 1974; Hammett and others, 1981; Deevey, 

1988) to as long as 1 year (Clark and others, 1963). 

The validity of lake evaporation estimates derived 

from pan evaporation for periods less than 1 year is 

highly questionable (Winter, 1981b). However, few 

alternative estimates of short-term lake evaporation 

exist for Florida. 

Of the two common, theoretically based 

techniques for computing lake evaporation losses, the 

energy-budget method and the mass-transfer method, 

only the mass-transfer method has been used in 

previous investigations in Florida. Pride and others 

(1966) used a mass-transfer method to determine 

monthly evaporation losses from Lake Helene in 

central Florida. The accuracy of the evaporation 

estimates in their study, however, cannot be 

determined, as the assumptions used in the method, 

instrumentation, and data were not reported. Bartholic 

and others (1978) determined evaporation from 

Orange Lake in north-central Florida over one 24-hour 

period by using a third method—the eddy-correlation 

technique.

 The most common means of estimating shortterm evaporation in Florida lakes is monthly pan 

evaporation corrected by factors developed by Kohler 

(1954) from the work of Langbein (1951). Langbein 
4 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

(1951) determined the monthly evaporative loss from 

Lake Okeechobee in southern Florida by computing it 

as the residual term to the hydrologic-budget equation 

for the lake. However, Langbein made no analysis of 

the potential importance of measurement errors on this 

residual term. Kohler (1954) subsequently related 

these losses to a NOAA evaporation pan at Belle 

Glade, Fla., and developed pan-correction factors for 

Lake Okeechobee. These monthly pan-correction 

factors, or coefficients, are commonly used to estimate 

lake evaporation outside of southern Florida, although 

the error due to regional differences in climate is rarely 

considered. In an exception to this rule, Deevey 

(1988) “normalized” these monthly pan coefficients 

for use in central and northern Florida by an 

adjustment based on the long-term average pan 

evaporation in each region.

None of the studies systematically considered 

the measurement errors in each budget term in relation 

to the overall hydrologic budget. Discussion is usually 

restricted to the importance of measurement errors on 

the residual term, most often of errors in evaporation 

on net ground-water flow (Hughes, 1974; Henderson, 

1983).

Acknowledgments

The authors gratefully acknowledge the 

landowners around Lake Lucerne who allowed access 

to the lake and gave permission for construction of 

observation wells on their property. These landowners 

are Orange-Co of Florida, Inc., Chester and Mabel 

Standfield, Wallace Blackburn, and Lamond 

Whittaker. The authors are particularly grateful to 

Andrew and Lois Kinsey for providing the site for the 

land-climate station and for their cooperation over the 

course of the study. Lois Kinsey also provided 

invaluable assistance as the operator of the landclimate station.

DESCRIPTION OF STUDY AREA

Physical Setting

Lake Lucerne is about 4 miles (mi) northeast of 

the city of Winter Haven in northern Polk County 

within the Central Highlands physiographic region of 

west-central Florida. It lies on the Winter Haven 

Ridge, one of three ridges that trend northwest to 

southeast through Polk County (fig. 1) (White, 1970). 

Lake Lucerne is typical of the many small, nearly 

circular lakes of sinkhole origin that characterize this 

region. It has a surface area of approximately 44 

acres, a maximum depth of about 22 feet (ft), and an 

average depth of about 15 ft.

The surrounding drainage basin (fig. 2) is small, 

0.26 square mile (mi2

), has no streams, and consists of 

the lake and a small wetland pond, herein named 

“Terrie Pond,” upgradient from the lake. Lake 

Lucerne is at an altitude of about 125 ft above sea 

level, and the highest point in the surrounding basin is 

about 180 ft above sea level. The lake is several feet 

higher than four larger lakes that surround it (fig. 2). 

Except along the lake margin, soils within the basin 

generally consist of a washed silica sand. As a result, 

the lake receives minimal surface runoff; precipitation 

and ground-water inflow are the major sources of 

water to the lake. Thus, the watershed relevant to the 

lake is underground. Homesites surround the lake, and 

most of the land in the basin is used for citrus 

agriculture.

Climate

The climate of the study area is humid and 

subtropical. High temperatures and frequent afternoon 

thundershowers from convective storms characterize 

the wet summer period from June through September. 

October through May is generally drier, except for a 

shorter winter wet season from December through 

February as a result of frontal storms. Seventy-one 

years of climatic data for the area are available from 

the Lake Alfred Agricultural Research and Education 

Center, a NOAA climate-reporting station 2 mi 

northwest of Lake Lucerne (fig. 2). Long-term rainfall 

at the Lake Alfred station averages 50.83 inches per 

year (in/yr) for the period 1951 to 1980. The average 

annual air temperature is 71.6 degrees Fahrenheit (°F), 

and monthly averages range from 59.6 °F in December 

to 81.9 °F in August (National Oceanic and 

Atmospheric Administration, 1986).

The monthly rainfall at Lake Lucerne during 

data collection for this study followed the expected 

seasonal pattern (fig. 3). However, rainfall was well 

below normal for May, July, and September 1986. As 

a result, the total rainfall for the study year (40.88 in.) 

was substantially less than the long-term average 

(50.83 in/yr), and the stage in Lake Lucerne and Terrie 

Pond declined steeply (fig. 4).
Description of Study Area 5

Figure 1. Location of Lake Lucerne and physiographic divisions in Polk County (modified from Lee and others, 1991).

28°20′ Eva

82° 81°20′ 81°40′

28°

27°40′

Polk City

Haines

City

Mulberry

Bartow

Frostproof

Winter

Haven

Fort

Bradley Meade

Junction

Lakeland

(1)

(2)

(3)

0 5 10 KILOMETERS

0 5 10 MILES

Lake

Lucerne

30°

88° 86° 84° 82° 80°

28°

26°

Polk

County

FLORIDA

EXPLANATION

RIDGES

WINTER HAVEN KARST

CENTRAL HIGHLANDS

BOUNDARY

All boundary lines are

dashed where approximate

(1) Lakeland Ridge

(2) Winter Haven Ridge

(3) Lake Wales Ridge
6 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

Hydrogeologic Setting

The hydrogeologic setting of Lake Lucerne has 

a significant effect on ground-water interaction with 

the lake. The geometry and vertical hydraulic 

conductivity of the confining unit beneath Lake 

Lucerne, for example, are critical hydrogeologic 

controls on lake leakage.

The hydrogeologic setting of Lake Lucerne has 

been described in detail by Lee and others (1991) but 

is discussed briefly here as background to later 

sections on the ground-water component of the 

hydrologic budget. A hydrogeologic section through 

the basin depicts the geology underlying and 

surrounding the lake and describes the hydrogeologic 

units (fig. 5). The locations of the wells whose 

Figure 2. Lakes in the vicinity of the study area (modified from Lee and others, 1991).

lithologic logs were used to construct this section are 

shown in figure 6.

The three hydrogeologic units of interest at 

Lake Lucerne are, from bottom to top, the Upper 

Floridan aquifer, the intermediate confining unit, and 

the surficial aquifer (fig. 5). Because the groundwater flow patterns that influence the lake occur 

mostly in the shallowest deposits around the lake, the 

description of the Upper Floridan aquifer here is 

limited to its two uppermost units, the limestone Ocala 

Group and the carbonate part (Arcadia Formation) of 

the overlying Hawthorn Group (fig. 5). The Upper 

Floridan aquifer constitutes the upper 300 to 400 ft of 

the Floridan aquifer system in the study area (Miller, 

1986). This limestone aquifer is highly transmissive 

but is confined above by the intermediate confining 

unit, a thin sequence of clastic material approximately 
Description of Study Area 7

15 ft thick within the Peace River Formation of the 

Hawthorn Group (Lee and others, 1991) (fig. 5). The 

low permeability of this intermediate confining unit 

slows recharge from the surficial aquifer to the Upper 

Floridan aquifer. The surficial aquifer consists of the 

surficial deposits of undifferentiated sand and clay 

overlying the intermediate confining unit. These 

deposits range in thickness from 50 to 100 ft in the 

study area and consist of alternating lenses of fine to 

coarse sand, clay, and clayey sand. The clay content 

generally increases with depth.

Geologic Framework

The geologic framework beneath Lake Lucerne 

was interpreted from a marine seismic-reflection 

survey and indicates the sinkhole origin of the lake 

basin. The survey was used to map the depth to the 

contact between the undifferentiated surficial deposits 

and the clay-rich Hawthorn Group beneath the lake. 

Variations in the altitude of this contact indicated 

subsidence and discontinuity of the clay layer beneath 

the lake as a result of sinkhole development (fig. 7) 

(Lee and others, 1991). Features indicated by the 

configuration of this surficial deposit–clay contact are 

voids, vertical pipes, and pinnacles. The steep-sided 

walls of the pipe structures probably represent the 

boundary between the limestone and the subsided 

overburden. Pinnacles and raised areas between the 

pipe features probably represent residual limestone 

that can retain overlying caps of the Hawthorn Group 

clays (fig. 7).

The solution features below Lake Lucerne are 

characteristic of the cover-subsidence-type sinkholes 

described by Sinclair and others (1985). This is the 

most prevalent type of sinkhole in the region of westcentral Florida that includes Lake Lucerne. In the 

formation of cover-subsidence-type sinkholes, a cavity 

is dissolved in the limestone, whereas a relatively 

thick overburden is suspended above the cavity by a 

thin clay confining unit. The confining unit collapses 

before the horizontal dimension of the cavity becomes 

large, and the unconsolidated sand and clay of the 

surficial deposits stream down into the cavity. As 

dissolution of the limestone continues, accelerated by 

the vertical movement of water, surficial deposits 

gradually channel into the vertical solution feature in a 

process referred to as “piping” (Sinclair and others, 

1985).

The collapse of surficial deposits of 

unconsolidated sand and clay into solution cavities in 

the underlying limestone is considered to be the origin 

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

0

2

4

6

8

10

12

MONTHLY RAINFALL, IN INCHES

LAKE LUCERNE LAKE ALFRED LONG-TERM

AVERAGE (1951-80)

1985 1986

MONTHLY RAINFALL, IN CENTIMETERS

1986 WATER YEAR

30

25

20

15

10

5

0

Figure 3. Monthly rainfall at Lake Lucerne for the 1986 

water year and the long-term average monthly rainfall at the 

National Oceanic and Atmospheric Administration climate 

station at Lake Alfred, 1951–80.

131

130

129

128

1985 1986

127

126

125

124

Terrie Pond

Lake Lucerne

WEEKLY STAGE, 

IN FEET ABOVE SEA LEVEL

DAILY MEAN STAGE, 

IN FEET ABOVE SEA LEVEL

1985 1986 

38.6

38.4

38.2

38.0

37.8

39.8

39.6

39.4

39.2

39.0

WEEKLY STAGE,

IN METERS ABOVE SEA LEVEL

DAILY MEAN STAGE,

IN METERS ABOVE SEA LEVEL

1986 WATER YEAR

A.

B.

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

Figure 4. (A) Daily mean stage of Lake Lucerne and 

(B) weekly stage of Terrie Pond for the 1986 water year 

(modified from Lee and others, 1991).
8 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

of the numerous small, circular lake basins in 

Florida (White, 1958). If the material infilling these 

cavities is of sufficiently low permeability, the 

resultant topographic depression will hold water. 

Large, irregularly shaped lakes can form when 

several sinkholes develop in close enough 

Figure 5. Hydrogeologic section of the study area (modified from Lee and others, 1991).

proximity to merge (Beck and others, 1984). The 

similarity between the bathymetric contours of the 

lake bottom and those of the solution features in the 

underlying limestone supports the conclusion that 

the Lake Lucerne basin developed as a sinkhole 

complex (fig. 7).
Description of Study Area 9

Ground-Water Flow Patterns

Ground-water flow patterns around Lake 

Lucerne were determined from contour maps of the 

water table in the surrounding surficial aquifer and 

from the vertical head distribution near the lake. The 

altitude of the water table and vertical head 

distribution around Lake Lucerne were measured in a 

network of 36 observation wells. Head also was 

measured in the surficial aquifer beneath the center of 

the lake. A well at the center of the lake was finished 

8 ft below the lake bottom in clayey sand (fig. 8). Lee 

and others (1991) present a thorough discussion of the 

ground-water monitoring network and wellconstruction characteristics.

Figure 6. Locations of wells whose logs were used to construct the hydrogeologic section (modified from Lee 

and others, 1991).

Ground-water flow patterns, determined from 

the configuration of the water table, indicate that the 

surficial aquifer around the lake is not part of a larger 

regional flow system. Instead, the lake and the 

surrounding surficial aquifer usually are isolated in a 

“closed” ground-water basin coincident with the 

topographic drainage basin. A ground-water divide in 

the aquifer generally coincided with the topographic 

drainage divide for the basin, and the water table 

around Lake Lucerne generally conforms to 

topographic contours. As a result, ground water in the 

surficial aquifer generally flowed in a centripetal 

pattern toward the lake. The configurations of the 

water table around Lake Lucerne for the dry (May 

1986) and wet (October 1985) seasonal conditions for 
10 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

the 1986 water year are shown in figure 9. The month 

of highest water-table altitude (October 1985) lagged 

behind the highest rainfall months of June and August 

1985. The altitude of the water table in the 

surrounding basin never exceeded the lake stage by 

more than about 8 ft (fig. 9). The topography of the 

basin is shown in figure 6.

Figure 7. (A) Bathymetric and (B) seismic-reflection contours and (C) cross section of Lake Lucerne (modified from Lee and 

others, 1991).

The surficial aquifer is approximately 45 to 55 ft 

thick around Lake Lucerne; however, the entire 

thickness of the aquifer does not contribute inflow to 

the lake. As lateral flow converges at the lake, it 

divides into upward and downward flowing 

components. The upward flow component contributes 

ground-water inflow to the lake. The downward 
Description of Study Area 11

component flows beneath the lake and recharges the 

Upper Floridan aquifer through the breaches in the 

confining unit beneath the lake (Lee and others, 1991). 

At each of the nested well sites, the highest head most 

often occurred in the well at the 20-ft depth (see wells 

1PN-20 and 2PN-20 in figs. 10 and 11, respectively), 

and head decreased in the wells above and below this 

depth. Thus, as an approximation, it can be considered 

that upward flow in the surficial aquifer above this 

depth generally contributed ground-water inflow to 

the lake, whereas downward flow below this depth did 

not (figs. 10 and 11).

Occasionally, downward head gradients 

occurred at all depths in the surficial aquifer, as 

indicated by measurements in the nested wells. The 

downward head gradients reflected downward flow 

and minimal lateral inflow to the lake (fig. 12). This 

downward flow pattern was short lived and usually 

resulted from rapid recharge to the surficial aquifer 

during the early part of the summer wet season. 

Downward head gradients also occurred at sites 1PN 

and 3PN during a dry period between January and 

March 1985 when rainfall was below normal, when 

water levels in the surficial aquifer were declining 

rapidly, and when a substantial drawdown of the water 

levels in the Upper Floridan aquifer was occurring 

(Lee and others, 1991).

Leakage through deeper regions of the lakebed 

flows downward toward the Upper Floridan aquifer. 

Leakage is indicated by the downward head difference 

between the lake and the midlake well (figs. 10 and 

11). This vertical head distribution and the fact that 

radial flow in the surficial aquifer converges at Lake 

Lucerne indicate that the sinkhole complex beneath 

the lake is the preferential path for recharge to the 

Upper Floridan aquifer. Focused recharge below the 

lake supports the interpretation (based on the 

seismic-reflection survey) that the confining unit 

below the lake has been replaced by more permeable 

sands and clays and that the Upper Floridan aquifer is 

less confined below the lake than elsewhere in the 

surrounding basin.

Figure 8. Data-collection sites in the Lake Lucerne study 

area (modified from Lee and others, 1991).

Figure 9. Configuration of the water table in the Lake 

Lucerne area based on (A) the minimum and (B) the 

maximum recorded water levels during the 1986 water year 

(modified from Lee and others, 1991).
12 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

Further evidence of substantial recharge to the 

Upper Floridan aquifer beneath Lake Lucerne is 

indicated by the head measurements in the midlake 

well, which were always substantially lower than 

heads measured at the same altitude in the three nested 

well locations. This head difference increased when 

the head in the Floridan aquifer was drawn down by 

pumping, as is the case in figure 11. Correlation 

analysis also indicated that head in the midlake well 

was more highly correlated to the head in the Upper 

Floridan aquifer than any other wells in the surficial 

aquifer near the lake (Lee and others, 1991).

Generally, the head distribution around the lake 

changed less in response to climate than it did to 

pumping from the Upper Floridan aquifer. Although 

the water table generally responded slowly to rainfall, 

the head in the Upper Floridan aquifer underwent large 

seasonal drawdowns as a result of pumping from 

citrus irrigation wells in and around the basin (Lee and 

others, 1991). Drawdown in the Upper Floridan 

Figure 10. Vertical distribution of head during high water-level conditions, October 17, 1985 (modified 

from Lee and others, 1991).

aquifer approximately doubled the downward head 

gradient beneath the lake in May 1986, compared with 

October 1985, increasing the potential for lake leakage 

as well as recharge from the surficial aquifer to the 

Upper Floridan aquifer (figs. 10 and 11). The 

hydrograph for well 2PN-130 shows the rapid waterlevel declines caused by pumping (fig. 13). As a 

result, during the 1986 water year, downward head 

differences between the lake and the Upper Floridan 

aquifer were at a minimum during the late summer and 

fall (minimum monthly average value of 5.05 ft, 

September 1986). Maximum downward head 

differences occurred in the dry spring months from 

March to early June of 1986, when irrigation pumping 

was at a maximum (maximum monthly average value 

of 12.50 ft, May 1986). The approximate seasonal 

variation of the head in the Upper Floridan aquifer 

without the local effects of pumping was estimated by 

connecting the highest points in the hydrograph into a 

smooth curve (fig. 13).
Description of Study Area 13

Hydrologic-Budget Approach

The hydrologic-budget approach provides the 

basis for determining the relative importance of 

evaporation and ground-water fluxes to Lake Lucerne. 

In this section the hydrologic-budget approach is 

discussed, along with the approach for estimating error 

in computed budget components, such as evaporation 

and ground water. Error estimates are an important 

part of any hydrologic-budget equation because they 

indicate how well individual hydrologic fluxes are 

understood and measured. They also provide a 

measure of reliability or accuracy of the hydrologic 

budget as a predictive tool.

Because Lake Lucerne is a seepage lake and 

receives negligible overland flow, the hydrologicbudget equation can be stated simply:

Figure 11. Vertical distribution of head during low water-level conditions, May 20, 1986 (modified from 

Lee and others, 1991).

(1)

where

∆S is the change in lake storage or volume for the 

period of interest,

P is direct precipitation to the lake,

 E is evaporation from the lake surface,

GI is ground-water inflow to the lake,

GO is leakage outflow from the lake, and

ei is the standard deviation or confidence limits 

around each measured term i.

This standard deviation is considered to be the 

uncertainty or error in each term i. The unit of volume 

for each term is the equivalent depth, in feet, over the 

lake surface.

Measured terms (for example, P) have an 

associated error depending on the method of 

∆S eS P eP – E e

E GI eGI ± – GO eGO ± = ± ± + ±
14 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

measurement. Budget terms that are calculated from 

more than one measured variable accumulate the 

errors in the measured terms. If a term is derived as 

the sum or difference of other measured terms, error is 

the sum of the variances in the measured terms 

(Ramette, 1981; Winter, 1981b; LaBaugh, 1985). For 

example, if a residual term R is calculated as

(2)

in which A, B, and C are measured quantities with 

associated errors eA , eB, and eC, respectively, eR is 

calculated as

(3)

and the error in R is independent of the measured 

values of A, B, and C.

Figure 12. Vertical distribution of head showing downward head gradient conditions, August 6, 1985 

(modified from Lee and others, 1991).

R eR ± A eA ± B eB C eC = + ± + ±

eR eA

2

eB

2

eC

2 = + +

The standard deviation around each 

measurement was not determined as a part of this 

study. Instead, the percentage error ascribed in the 

literature to various methods was used to define the 

confidence limits around measured values. Equation 3 

becomes

(4)

where %ei

 is the percentage error (expressed 

fractionally) attributed to the average measurement of 

component i for a given method. Winter (1981b) used 

this approach to compare the errors in net groundwater flow terms derived as residual terms to the 

hydrologic-budget equation.

Alternately, if a term is calculated by the 

multiplication or division of other measured terms, as 

in

eR %eA ( ) •A 2 %eB ( ) •B 2 %eC ( ) •C 2 = + +
Evaporation 15

R ± eR = (A ± eA) [(B ± eB)/(C ± eC)] (5)

then

(6)

It is important to note that these calculated 

errors represent the maximum probable error in the 

computed term. This approach is based on the 

assumption that the measurement of each hydrologicbudget component is independent of other components 

and that no intercorrelations or covariances exist 

between measurement errors (Winter, 1981b; LaBaugh 

and Winter, 1984).

EVAPORATION

Numerous lakes and intense solar radiation 

make lake evaporation an important hydrologic 

process in Florida. The occurrence of a large, natural 

lake district at a subtropical latitude is an unusual 

geographic feature that Florida shares only with the 

country of China. Because of its low latitude, Florida 

has the highest annual evaporation of any State east of 

the Mississippi River (Farnsworth and others, 1982). 

It also is the warmest State in the Nation and has the 

smallest seasonal range in air temperatures (about 

30 °F) around warm annual mean temperatures. The 

annual mean air temperature ranges from the upper 

60’s in north Florida to the middle 70’s in southern 

Florida, excluding the Florida Keys, which average 

nearly 78 °F (Heath and Conover, 1981). Water 

temperatures are correspondingly warm. Lakes in 

Florida never freeze, and because they tend to be 

shallow, most are well mixed and do not thermally 

stratify for long periods (Brenner and others, 1990).

In this section, lake evaporation is computed by 

three different methods, the energy-budget method, 

mass-transfer method, and pan-evaporation method. 

These three techniques vary considerably in their 

complexity and reported accuracy. The energy-budget 

method is the most accurate of the three methods, but 

it also is the most complicated. It provides the 

evaporation estimate used in the hydrologic budget. 

The mass-transfer method also is presented and 

compared with the energy-budget method as a simpler 

but less accurate alternative. Finally, pan evaporation, 

the most widely used index of lake evaporation, is 

compared with the two theoretically based evaporation 

methods. The possible error in each method is also 

discussed.

Energy-Budget Method

An energy budget accounts for all fluxes of 

energy into and out of a system, such as a lake. The 

energy budget is considered to be the most accurate 

method for measuring evaporation from lakes for 

periods of a week or longer (Winter, 1981b). It also 

is a complex method that is costly and manpower 

intensive; therefore, the method is used 

infrequently.

Theory and Equations

When the energy-budget method is applied to a 

system, the energy used for evaporation is calculated 

as the residual energy after all other energy fluxes are 

summed. The volume of water evaporated is 

calculated by dividing the residual energy used for 

evaporation by the latent heat of evaporation and the 

density of water. The general form of the energybudget equation is

Qs – Qr + Qa – Qa r – Qb s + Qv – Qw – Qh – Qe = Qx (7)

where

Qs is incident shortwave solar radiation,

Qr is reflected shortwave solar radiation,

Qa is incident longwave radiation from the 

atmosphere,

Figure 13. Water levels in well 2PN-130 from April 1984 

through September 1986 and the estimated trend in water 

levels for nonpumping conditions.

125

120

115

110

1984 1985 1986

ALTITUDE OF WATER LEVEL, 

IN FEET ABOVE SEA LEVEL

UPPER

FLORIDAN

AQUIFER

A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S

ESTIMATED TREND FOR

NONPUMPING CONDITIONS

WELL 2PN-130 38

37

36

35

34

ALTITUDE OF WATER LEVEL,

IN METERS ABOVE SEA LEVEL

%eR %eA ( )2 %eB ( )2 %eC ( )2 = + +
16 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

Qar is reflected longwave radiation,

Qbs is longwave radiation emitted by the lake,

Qv is net energy advected by streamflow, ground 

water, and precipitation,

Qw is energy advected by evaporating water,

Qh is energy conducted and convected from the 

lake to the atmosphere as sensible heat,

Qe is energy used for evaporation, and

Qx is change in stored energy.

The energy flux units used in this study are 

metric units of calories per square centimeter per day. 

Metric units are conventionally used in studies of 

energy-budget and mass-transfer evaporation. 

Therefore, fundamental equations are presented in 

metric units and metric units are used for calculation 

purposes in this study (see app. A and B). Final 

evaporation results in this section, however, are 

presented in inch-pound units to be consistent with the 

inch-pound units used in the remainder of the report.

The terms Qs, Qr

, Qa, Qar, Qbs, Qv , and Qx were 

all measured directly. Three other types of energy 

flux—conduction of heat through the lake bottom, 

heating due to chemical and biological processes, and 

the conversion of kinetic energy to heat energy—are 

assumed to be negligible (Anderson, 1954). The 

instrumentation used to measure energy fluxes and the 

resulting energy values are discussed in detail by Lee 

and others (1991). Briefly, three radiometers were 

used to measure incident and reflected shortwave 

radiation (Qs and Qr) and incident longwave radiation 

(Qa). One longwave radiometer, positioned facing 

downward toward the lake surface, was used to 

measure the sum of reflected (Qar) and backscattered 

(Qbs) longwave radiation from the lake. 

Advected heat (Qv) enters lakes from rainfall, 

surface-water, and ground-water inflow, and it leaves 

through surface-water and ground-water outflow. Qv

may be a difficult component to measure accurately in 

a lake or reservoir with large surface-water inflow and 

outflow, and the error in this measurement can be a 

limiting factor to successful application of the energybudget method. Rainfall is assumed to be the only 

source of advected heat to Lake Lucerne. Advected 

heat from ground water is assumed to be negligible for 

this study. Advected heat energy from rainfall is 

calculated from the daily rainfall amount and the 

average wet-bulb temperature.

The change in stored energy (Qx) is an 

important component of the energy budget because the 

large specific heat capacity of water allows even a 

small lake to store and exchange large amounts of heat 

energy. Stored heat was computed from weekly 

thermal surveys of the lake. Each thermal survey 

consisted of vertical temperature measurements at 1-ft 

intervals taken at six sites on the lake. The time 

interval between successive thermal surveys is the 

thermal survey period. In addition, a string of 

thermocouples on a midlake raft measured the water 

temperature at 1-ft depth intervals. The thermocouple 

string provided a continuous record of lake 

temperatures from which daily heat content values 

were calculated. A strong correlation (R = 0.99) 

between the average thermal survey temperatures and 

the temperatures measured by the thermocouples at 

each depth supported the use of thermocouple data to 

compute total heat content of the lake on a daily and 

weekly basis.

 In previous energy-budget studies the thermal 

survey period between manual thermal surveys 

defined the shortest time period for which evaporation 

could be calculated, often 7-day periods or longer. In 

this study, because of the high correlation of the 

thermocouple measurements with the thermal survey 

data, it was possible to calculate stored heat and 

evaporation on a daily basis for 321 days. During 

periods when daily thermocouple readings were 

missing, only weekly evaporation computations were 

made. The total stored heat and daily average change 

in stored heat for each thermal survey period and daily 

total stored heat and change in stored heat from the 

thermocouple string measurements are shown in 

figures A1 and A2 of appendix A.

Three components of the energy budget—the 

energy advected by evaporating water (Qw), the 

energy conducted to the atmosphere as sensible heat 

(Qh), and the energy used for evaporation (Qe)—were 

not measured directly but were calculated by using the 

following relations.

Energy advected by evaporating water can be 

computed as

Qw = cρEEB (T0 – Tb ) (8)

where

c is specific heat of water [1 calorie per gram 

per degree Celsius (cal/g/°C)];
Evaporation 17

ρ is density of evaporating water [1 gram per 

cubic centimeter (g/cm3)];

EEB is volume of evaporating water by the energybudget method, in cubic centimeters per 

square centimeter per day;

T0 is water-surface temperature, in degrees Celsius; and

Tb is reference base temperature (0 °C).

The energy used for evaporation (Qe) also can 

be expressed as

Qe = ρEEBL (9)

where

L is latent heat of vaporization, in calories per 

gram.

Qh and Qe are combined by using a theoretical 

relation derived by Bowen (1926). The Bowen ratio 

(BR) is the ratio of sensible heat (Qh ) to the heat 

energy used for evaporation (Qe):

BR = Qh/Qe (10)

As neither Qh nor Qe can be measured directly, the 

Bowen ratio has been widely used in evaporation 

studies. The ratio can be calculated as

BR = 0.00061P(T0 – Ta)/(e0 – ea) (11)

where

P is barometric pressure, in millibars;

T0 is water-surface temperature, in degrees 

Celsius;

Ta is air temperature at 2 m above the lake, in 

degrees Celsius;

e0 is saturation vapor pressure at the water-surface temperature, in millibars; and

ea is vapor pressure at 2 m above the lake, in 

millibars.

By placing the three components that were not 

measured directly (Qw, Qh, and Qe) on one side of 

equation 7, substituting relations 9, 10, and 11, and 

solving for EEB, the final energy-budget equation used 

in this study is produced:

(12)

The results of the energy-budget calculation by 

thermal survey periods are summarized in appendix A. 

Thermal survey periods range from 5 to 9 days in 

length; 72 percent are 7 days in length.

Energy-Budget Evaporation Rates

The energy-budget evaporation rates calculated 

for each thermal survey period, and for 321 days when 

daily measurements of stored heat were available, are 

shown in figures 14 and 15. The total evaporation for 

the 52-week period of record from October 1, 1985, to 

September 30, 1986 (1986 water year), was 57.87 in. 

The highest daily average rate of evaporation 

calculated by thermal survey period was 0.264 inches 

per day (in/d) between April 29 and May 5, 1986, and 

also between May 27 and June 2, 1986; a total of 1.85 

in. for each week. The lowest rate was 0.040 in/d 

between December 31, 1985, and January 6, 1986; a 

total of 0.28 in. for the week.

Annual lake evaporation derived by the energybudget method was 8 to 10 in. greater than the estimated 

long-term average evaporation at Lake Lucerne. 

Annual “shallow” lake evaporation published by 

NOAA, based on pan-evaporation data, ranged from 48 

to 50 in/yr for the period 1946 to 1955 (Kohler and 

others, 1955). The average for the period 1956 through 

1970 was 48 in/yr (Farnsworth and others, 1982). 

Increased solar radiation during the drought that 

coincided with the study period is probably responsible 

for the increase in evaporation rates.

EEB

Qs Qr Qa Qar Qbs Qv Qx – + + – + –

L( ) 1 + BR T0 + = ------------------------------------------------------------------------------------------

Figure 14. Daily average energy-budget evaporation at Lake 

Lucerne by thermal survey period for the 1986 water year.

0.6

0.4

0.2

0 OCT NOV DEC JAN FEB MAR APR MAY JUNEJULY AUG SEPT

1985 1986

0.30

0.25

0.20

0.15

0.10

0.05

0

DAILY AVERAGE ENERGY-BUDGET 

 EVAPORATION, IN INCHES PER DAY

DAILY AVERAGE ENERGY-BUDGET

EVAPORATION, IN CENTIMETERS PER DAY

1986 WATER YEAR
18 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

Comparison of Thermal Survey Period and Daily 

Evaporation Estimates

Daily evaporation estimates closely agreed with 

the results by thermal survey period (figs. 14 and 15). 

To compare the evaporation estimates computed for 

different time periods, daily evaporation rates were 

averaged to compute an equivalent evaporation estimate 

by thermal survey period. All the components in the 

energy budget, except for stored heat and the Bowen 

ratio, were calculated by averaging daily estimates over 

each thermal survey period. The correlation between 

evaporation rates computed by these two different 

approaches was very good (0.94), the standard error of 

estimate being 0.02 in/d.

The largest differences between daily and 

thermal survey estimates occurred during periods of 

low evaporation in the winter. For periods when the 

evaporation rate was less than 0.138 in/d, average 

differences, expressed as the relative percent 

difference between daily and thermal survey 

calculations, were 25 percent. When the evaporation 

rate was greater than 0.138 in/d, the average relative 

percent difference was 5 percent.

Use of the Bowen ratio in developing equation 

12 has been recognized as a source of uncertainty in 

the energy-budget method (Anderson, 1954). When 

evaporation rates are high, the Bowen ratio functions 

as a small correction factor. When evaporation is low, 

the Bowen ratio can cause instability in the energybudget equation, which results in unrealistic 

evaporation estimates. Instability in the equation 

occurs when the temperature gradient (T0 – Ta) is 

negative (when the average lake-surface temperature 

JUNE JULY

1.0

0.5

0

-0.5

1985 1986

 OCT NOV DEC JAN FEB MAR APR MAY AUG SEPT

DAILY ENERGY-BUDGET EVAPORATION,

IN INCHES PER DAY

DAILY ENERGY-BUDGET EVAPORATION,

IN CENTIMETERS PER DAY

0.3

0.2

0.1

0

-0.1

-0.2

0.4

1986 WATER YEAR

Figure 15. Daily energy-budget evaporation at Lake 

Lucerne for 321 days of the 1986 water year.

is lower than the average air temperature) or when the 

vapor pressure gradient (e0 – ea) approaches zero. 

Plots of the daily vapor pressure and temperature 

gradients in figure 16 show that these conditions 

occurred during the winter months from November to 

March.

The effect of small or inverted temperature and 

vapor pressure gradients on the Bowen ratio can be 

seen in the plot of daily Bowen ratios (fig. 17). The 

validity of this ratio is questionable if it is less than 

–1.0 or greater than 1. When this occurs, normally 

acceptable errors in daily measurements of 

temperature and vapor pressure result in unrealistic 

evaporation estimates. One example of the effect of a 

Bowen ratio outside this range on the energy budget 

occurred on January 10, 1986, when the Bowen ratio 

was –1.32. The use of this value in the energy budget 

resulted in a highly unlikely negative evaporation 

(condensation) rate of –0.461 in/d. 

Figure 16. (A) Daily average temperature difference and 

(B) vapor pressure difference between the surface of Lake 

Lucerne and 2 meters above the lake surface for the 1986 

water year.

10

5

0

-5

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1985 1986

15

10

5

0

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1985 1986

A .

B.

25

20

15

10

 5

 0

-5

0.20

0.15

0.10

0.05

0

0.25

-10

DAILY AVERAGE TEMPERATURE

DIFFERENCE, IN DEGREES FAHRENHEIT

DAILY AVERAGE TEMPERATURE

DIFFERENCE, IN DEGREES CELSIUS

DAILY AVERAGE VAPOR PRESSURE

DIFFERENCE, IN POUNDS PER SQUARE INCH

DAILY AVERAGE VAPOR PRESSURE

DIFFERENCE, IN MILLIBARS

1986 WATER YEAR
Evaporation 19

At Lake Lucerne, Bowen ratios outside of the 

range –1.0 to +1.0 occurred on 21 days, a total of 5.8 

percent of the record. All but one of these occurrences 

were between November and March. When 

evaporation was calculated over longer time periods, 

such as the thermal survey periods, the averaging of 

daily values generally resulted in Bowen ratios within 

the acceptable range (fig. 17). On a thermal survey 

basis, there was only one small negative Bowen ratio, 

and there were no negative values for evaporation.

Energy-Budget Error Analysis

Error associated with energy-budget 

evaporation rates is primarily a function of instrument 

precision and the adequacy of data estimation methods 

for periods of missing record. Instrument errors were 

determined from either instrument specifications of 

the manufacturer or from field or office calibrations. 

Errors in data estimates were quantified as the 

standard errors of the linear regression relations used 

to estimate values for periods of missing record. 

These standard errors were always greater than 

instrument errors alone because of the imperfect linear 

relation between variables. The instrumentation used 

for this study and the data estimation methods are 

described by Lee and others (1991).

The weighted average error for a measured 

component is calculated for a given time interval as 

follows:

Weighted average error = (13)

where

ei is type i error, in measured units;

ni is number of days of type i error; and

nT is total number of days.

After a weighted average error was calculated 

for each energy-budget component, the errors were 

combined to produce an error in computed 

evaporation. The algebraic manipulation of each 

component in equation 12 determined the way the 

errors were combined (Ramette, 1981).

The weighted average error of each energybudget component was calculated for the 1-yr study 

period. The greatest relative error occurred in the Qx

term (60.7 percent). Lake-water temperature 

measurements were accurate to ±0.1 °C, resulting in 

an error of less than 0.5 percent in the total stored heat 

for the lake. However, this error can be large in 

comparison with the change in stored heat (Qx ) 

between thermal surveys. The Bowen ratio also is 

subject to large errors because it too is a function of 

the difference between absolute measurements of 

temperature and vapor pressure (eq. 10). Relative 

errors for the remaining components of the energy 

budget generally were less than 5 percent (see app. A).

 The error in the total evaporation for the study 

period is 16.4 percent. Without estimated data, the 

error would be 13.6 percent, and if all the data were 

estimated, the error could be as great as 24.9 percent. 

Evaporation errors also were calculated by month 

(table 1). In general, errors were greatest relative to 

evaporation when evaporation rates were least, which 

was during the winter months from November to 

March. This primarily reflects the large relative error 

associated with making measurements of the smaller

Figure 17. (A) Daily average Bowen ratios and (B) average 

Bowen ratios by thermal survey period for the 1986 water 

year.

4

3

2

1

0

-1

-2

0.8

0.6

0.4

0.2

0

-0.2

A.

B.

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1985 1986

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1985 1986

DIMENSIONLESS

1986 WATER YEAR

BOWEN RATIO,

DIMENSIONLESS

BOWEN RATIO,

Σ eini ( )

nT

-----------------
20 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

energy components that contribute to evaporation 

during these months. Large relative errors also 

occurred when the errors contained in data estimates 

were much greater than measurement errors.

Sensitivity Analysis

To determine which errors have the greatest 

effect on energy-budget evaporation, a simple 

sensitivity analysis was performed using the thermal 

survey period data. The results of this analysis 

indicate which components require the most attention 

during data collection for seepage lakes in Florida.

Each component of the energy budget was 

varied from 50 percent less to 50 percent more than 

the original value, and the evaporation for each 

thermal survey period was then recalculated. The 

results are shown in figure 18 as change in calculated 

evaporation expressed as a percentage of the original 

evaporation.

Terms in the numerator of equation 12 cause a 

linear increase in the evaporation error, but the slopes 

vary considerably, depending upon the magnitude of 

the component and its sign (fig. 18). A change in the 

sum of reflected and emitted longwave radiation, 

which is the largest term in the numerator, causes the 

largest change in the computed evaporation. A 

10-percent error in this term causes a 35-percent error 

in computed evaporation. Errors in incident 

shortwave and longwave radiation also are important 

and produce 20- and 30-percent errors in the rate of 

evaporation, respectively (fig. 18).

Terms that appear in the denominator of 

equation 12 have a nonlinear relation with computed 

evaporation. Of these, water-surface temperature is 

most important because it appears in three places in 

the denominator: in the Bowen ratio, in the 

calculation of the latent heat of vaporization, and as a 

constant. Underestimating the water-surface 

temperature increases the error of the calculated 

evaporation more than does overestimation (fig. 18).

Other components of the energy budget have 

less effect on the error in evaporation at Lake Lucerne. 

Large errors in smaller components, such as reflected 

shortwave radiation, advected heat, and stored heat, 

have little effect. The energy budget is only 

moderately sensitive to the value of the Bowen ratio; a 

10-percent error in the Bowen ratio produces a 2-

percent error in the calculated evaporation. Changes 

in barometric pressure, which was measured at Lake 

Lucerne (Lee and others, 1991), had an insignificant 

effect on the calculation of energy-budget evaporation. 

Barometric pressure varied less than 2 percent of the 

mean [1,021 millibars (mb)] for the period of record. 

An average barometric pressure could have been used 

without adding to the error in the method.

The priorities for measurement accuracy 

suggested by this analysis should apply to energybudget calculations for other seepage lakes in central 

Florida. However, other terms can be of greater 

importance for lakes in different settings. For 

example, changes in stored heat will be greater for 

lakes in temperate climates, and advected heat can be a 

major source of error for lakes with surface-water 

inflows and outflows.

Mass-Transfer Method

The mass-transfer method relates evaporation to 

the processes affecting the removal of water vapor 

from the boundary layer above the air-water interface 

at the surface of the lake. As the wind speed over the 

water surface increases, water vapor is removed from 

the system more rapidly. This causes the vapor 

pressure gradient above the lake to increase, thereby 

increasing evaporation. Thus, evaporation can be 

directly related to both wind speed and vapor pressure 

gradient.

Table 1. Monthly energy-budget evaporation rates and 

errors, October 1985 through September 1986

Year and 

month

Monthly

evaporation

(inches)

Relative

error

(percent) 

1985:

October 4.70 27.1

November 3.49 27.6

December 2.65 22.8

1986:

January 2.29 27.1

February 2.56 20.0

March 4.32 15.6

April 7.16 16.2

May 7.12 19.1

June 5.63 12.8

July 6.04 13.4

August 6.08 13.5

September 5.83 15.7
Evaporation 21

50

40

30

20

10

-10

-20

-30

-40

-50

-50-40-30-20-10

1020304050

50

40

30

20

10

-10

-20

-30

-40

-50

-50-40-30-20-10

10203040

.50

.

50

40

30

20

10

-10

-20

-30

-40

-50

-50-40-30-20-10

1020304050

50

40

30

20

10

-10

-20

-30

-40

-50

-50-40-30-20-10

1020304050

50

40

30

20

10

-10

-20

-30

-40

-50

-50-40-30-20-10

1020304050

. .

. .

50

40

30

20

10

-10

-20

-30

-40

-50

-50-40-30-20-10

1020304050

INCIDENT SHORTWAVE

RADIATION (Qs)

PERCENT CHANGE

IN Qs

PERCENT CHANGE

IN EVAPORATION

REFLECTED

AND EMITTED

LONGWAVE 

RADIATION

(Qar + Qbs)

PERCENT CHANGE

IN Qar + Qbs

BOWEN RATIO

 (BR)

PERCENT CHANGE

PERCENT CHANGE

REFLECTED SHORTWAVE

RADIATION (Qr)

PERCENT CHANGE

IN EVAPORATION

PERCENT CHANGE 

IN Qr

INCIDENT LONGWAVE

RADIATION (Qa)

PERCENT CHANGE 

IN Qa

WATER-SURFACE 

TEMPERATURE

(T0)

PERCENT CHANGE

IN EVAPORATION

PERCENT CHANGE

IN T0 IN BR

IN EVAPORATION 

A. B.

C. D.

E. F.

PERCENT CHANGE

IN EVAPORATION

PERCENT CHANGE

IN EVAPORATION

Figure 18. Sensitivity of energy-budget evaporation to errors in (A) incident shortwave radiation, 

(B) reflected shortwave radiation, (C) reflected and emitted longwave radiation, (D) incident longwave 

radiation, (E) Bowen ratio, and (F) water-surface temperature.
22 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

Theory and Equations

The mass-transfer method was developed 

during studies of Lake Hefner (Marciano and Harbeck, 

1954) and Lake Mead (Harbeck and others, 1958). 

Reports from these two studies contain theoretical 

discussions of the boundary layer structure and derive 

the following general equation for mass transfer: 

EMT = Nu2(e0 – ea) (14)

where

EMT is evaporation by the mass-transfer method, 

in centimeters per day;

N is mass-transfer coefficient;

u2 is daily average wind speed at 2 meters (m) 

above the lake, in miles per hour;

e0 is saturation vapor pressure at the water-surface temperature, in millibars; and

ea is vapor pressure of the air at 2 m above the 

lake surface, in millibars.

The two vapor pressure measurements also are used 

for the energy-budget method, so wind speed at 2 m 

(6.6 ft) above the lake surface was the only additional 

measurement needed to calculate evaporation by the 

mass-transfer method.

Mass-Transfer Coefficient

A number of methods have been used to 

determine N, the mass-transfer coefficient. For studies 

where an energy budget also has been done, the best 

estimate of N is a calibration between the masstransfer method and the energy-budget method. 

Energy-budget evaporation is regressed against the 

mass-transfer product (the product of the wind speed 

at 2 m (6.6 ft) and the vapor pressure gradient) 

averaged for a given period, and N is estimated as the 

slope of the best-fit line through the data.

A plot of the relation of energy-budget 

evaporation to the mass-transfer product for the 52 

thermal survey periods is shown in figure 19. Three 

methods were used to estimate the slope of the line of 

relation fitted to the data in figure 19. A linear 

regression through the origin produced a slope (N) of 

0.0112 and the standard error of estimating energybudget evaporation with the regression is 0.04 in/d 

(0.10 cm/d). A ratio of the mean energy-budget 

evaporation to the mean mass-transfer product for the 

entire 52 weeks was 0.0114. The mean of the ratios of 

energy-budget evaporation to the mass-transfer 

product by thermal survey period was 0.0115. 

Because there was a less than 3-percent difference 

between these three estimates, the mean (0.0114) was 

selected as the final value for N.

Comparison of Mass-Transfer and Energy-Budget 

Evaporation Rates

Pronounced seasonal differences exist between 

evaporation calculated by the energy-budget and 

mass-transfer methods. Mass-transfer evaporation was 

greater than the energy-budget evaporation in the 

winter and less in the summer. Seasonal differences 

between the two methods also have been found in other 

energy- budget and mass-transfer studies (Harbeck and 

others, 1958; Ficke, 1972). These differences have 

been attributed to errors in the energy-budget method, 

the mass-transfer method, or both.

At Lake Mead the seasonal difference between 

the energy-budget and mass-transfer methods was 

attributed to the influence of seasonal changes in 

atmospheric stability on evaporation estimated by the 

mass-transfer method (Harbeck and others, 1958). 

The empirically based form of the mass-transfer 

equation used for this study and for the Lake Mead 

study (eq. 14) is based on the assumption that 

atmospheric stability and N, the mass-transfer 

coefficient, are relatively constant. Before an equation 

of this type is used, however, each set of mass-transfer 

data should be tested to ensure that this assumption is 

valid.

Figure 19. Relation between energy-budget evaporation 

and the mass-transfer product by thermal survey period.

WINTER—

 

(OCT. 8, 1985 - MAR. 31,1986)

SUMMER— (APR.1, 1986 - SEPT. 30,1986)

 Y (cm/d) = 0.0112X

STANDARD ERROR = 0.10 cm/d

0.6

0.4

0.2

0

10 20 30 40 50 60 70

MASS-TRANSFER PRODUCT, MILLIBAR MILES PER HOUR 

0.30

0.25

0.20

0.15

0.10

0.05

0

ENERGY-BUDGET EVAPORATION,

IN INCHES PER DAY

EQUATION OF LINE—

ENERGY-BUDGET EVAPORATION,

IN CENTIMETERS PER DAY
Evaporation 23

Stability

A stability parameter, SMT, which is proportional 

to the Richardson number, can be defined as follows 

(Harbeck and others, 1958):

SMT = ( Th – T0)/(uh)2 (15)

where

Th is temperature at height h, in degrees Celsius;

T0 is temperature of the lake surface, in degrees 

Celsius; and

uh is wind speed at height h, in miles per hour.

The stability parameter is a measure of buoyant forces 

(represented by the temperature gradient) relative to 

the turbulent forces (represented by the wind speed) 

acting on an airmass. When buoyant forces dominate, 

SMT is high and the mass-transfer equation 

underestimates evaporation. When turbulent forces 

dominate, SMT is low and the mass-transfer equation 

tends to overestimate evaporation (Rosenberg and 

others, 1983).

Changes in atmospheric stability at Lake 

Lucerne explained some of the difference between 

evaporation computed using the energy-budget and 

mass-transfer methods. Components of the energybudget and mass-transfer methods were checked for 

correlation with the difference between the two 

methods. The difference was correlated with the 

stability parameter and the water-surface temperature 

for data by thermal survey periods. The atmospheric 

stability parameter (SMT) increases in the summer, 

when wind speeds and vapor pressure gradients are 

small and temperatures are high, and decreases in the 

winter. For the Lake Lucerne data, the stability 

parameter also was correlated with N (see Harbeck 

and others, 1958). An alternative mass-transfer 

equation was developed by adding a correction factor 

based on the relation between N and the stability 

parameter to the original mass-transfer equation:

EMT = u2(e0 – ea )[–0.0337(SMT) + 0.0074] (16)

where

EMT is mass-transfer evaporation, in centimeters 

per day;

u2 is wind speed at 2 m (6.6 ft) above the lake, in 

miles per hour;

e0 is saturation vapor pressure at the water-surface temperature, in millibars;

ea is vapor pressure at 2 m (6.6 ft) above the 

lake, in millibars; and

SMT is stability parameter

In this equation, N was determined by a linear 

regression against SMT with a slope equal to –0.0337 

and y-intercept equal to 0.0074 (fig. 20). N is no 

longer a constant but is dependent on stability.

Mass-Transfer Evaporation Rates

The mass-transfer evaporation rates, corrected 

for atmospheric stability for each thermal survey 

period, are shown in figure 21. The total evaporation 

for the 52-week period of record from October 1, 

1985, to September 30, 1986 (1986 water year), was 

57.39 in. The largest daily average rate of evaporation 

calculated by thermal survey period was 0.265 in/d 

between April 22 and 29, 1986; a total of 1.86 in. The 

smallest rate was 0.047 in/d between December 31, 

1985, and January 6, 1986; a total of 0.33 in. 

Mass-Transfer Error Analysis

The maximum probable error in the uncorrected 

mass-transfer estimate of evaporation for the 1-yr 

period of record was 31 percent when the value of 

0.0114 was used for N. The large error in this method 

is due to the large standard error in determining N

from the linear regression of the mass-transfer product 

with the energy budget (25 percent) and errors in the 

measurement of vapor pressure gradients (18 percent).

0.025

0.020

0.015

0.010

0.005

-0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0 0.05

EQUATION OF LINE

N = -0.0337SMT + 0.0074

STABILITY PARAMETER (SMT)

MASS-TRANSFER COEFFICIENT (

N) Figure 20. Relation between the mass-transfer coefficient 

(N) and the stability parameter (SMT) by thermal survey 

period.
24 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

Incorporating the effects of atmospheric 

stability reduced the error in the mass-transfer method 

by 10 percent. The differences between the energybudget evaporation and both the corrected and 

uncorrected mass-transfer evaporation by thermal 

survey period are shown in figure 22. Improvement in 

the relation after correction for atmospheric stability is 

illustrated by the increased balance, or symmetry, of 

errors throughout the year; however, some seasonal 

discrepancy is still evident even after stability is 

accounted for in the mass-transfer equation. These 

results emphasize the need to test each new set of 

mass-transfer data for the effects of atmospheric 

stability. In addition to testing each set of masstransfer data for the effects of atmospheric stability, 

future studies also should consider measuring wind 

speed and vapor pressure at heights other than 2 m (6.6 

ft), because stability is height dependent.

Other causes of the differences between the two 

methods are unclear but are probably related to 

random errors in measurement in both the energybudget and mass-transfer methods. Unaccounted 

energy fluxes, such as heat exchange between the 

water in Lake Lucerne and the lake sediments, may 

have contributed slightly to the deviation between the 

two methods.

By failing to account for heat flux through the 

bottom of the lake, the energy-budget estimate of 

evaporation might be lower than actual evaporation in 

the winter. Bottom sediments can be a source of heat 

energy to the lake during winter that is not accounted 

for in the budget. The opposite would be true in the 

summer, when the lake is relatively warm in 

Figure 21. Mass-transfer evaporation rates corrected for 

atmospheric stability by thermal survey period for the 1986 

water year.

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1985 1986

0.30

0.25

0.20

0.15

0.10

0.05

0

0.6

0.4

0.2

0

1986 WATER YEAR

CORRECTED MASS-TRANSFER

EVAPORATION, IN INCHES PER DAY

CORRECTED MASS-TRANSFER

EVAPORATION, IN CENTIMETERS PER DAY

comparison with ground water and bottom sediments. 

Lake-sediment heat flux could contribute to the 

difference between the methods, but this heat flux is 

small in relation to the total difference between 

methods (less than 10 percent for differences greater 

than 0.0079 in/d), so it cannot be the sole explanation 

for seasonal trends in residual errors.

Pan-Evaporation Method

National Weather Service (NWS) class A panevaporation data are widely used to estimate 

evaporation and evapotranspiration in the United 

States. Class A pan evaporation was measured at 

Lake Lucerne throughout this study to compare with 

UNCORRECTED

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1985 1986

0.2

0.1

0

-0.1

-0.2

EVAPORATION DIFFERENCE, 

IN CENTIMETERS PER DAY

CORRECTED FOR ATMOSPHERIC STABILITY 

0.10

0.05

0

-0.05

EVAPORATION DIFFERENCE,

IN INCHES PER DAY 0.10

0.05

0

EVAPORATION DIFFERENCE,

-0.05

IN INCHES PER DAY

0.3

0.2

0.1

0

-0.1

-0.2

EVAPORATION DIFFERENCE, 

IN CENTIMETERS PER DAY

A.

B.

1986 WATER YEAR

0.15

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

1985 1986

- 0.10

-0.10

Figure 22. Differences between energy-budget 

evaporation and (A) mass-transfer evaporation 

(uncorrected), and (B) mass-transfer evaporation corrected 

for atmospheric stability by thermal survey period for the 

1986 water year.
Evaporation 25

the theoretically based energy-budget and masstransfer measures of evaporation. The depth of water 

evaporated, minimum and maximum water 

temperature, and total wind across the pan were 

recorded daily by an observer. Pan-evaporation data 

also are available from a NOAA station about 2 mi 

northwest of Lake Lucerne at the Lake Alfred 

Agricultural Research and Education Center (National 

Oceanic and Atmospheric Administration, 1986) 

(fig. 2).

Theory and Equations

Pan-evaporation data from the Lake Lucerne 

and the Lake Alfred pans were analyzed and adjusted 

to “free water-surface evaporation” (the maximum 

potential evaporation from a water body) on a monthly 

basis by using methods originally developed by 

Kohler and others (1955). A summary of more recent 

applications of these methods, and national long-term 

pan-evaporation data, can be found in the report by 

Farnsworth and others (1982).

Free water-surface evaporation is computed by 

using these methods to correct for the different heat 

storage capabilities of the water in the pan and in the 

lake. Lakes may differ greatly from evaporation pans 

and from other lakes in their ability to store heat. As a 

result, evaporation rates for lakes of different volumes 

can differ even under similar climatic conditions. 

Before pan evaporation can be directly compared with 

lake evaporation, differences in heat storage and 

advection from the two systems must be accounted for. 

When these effects are removed, a new term, free 

water-surface evaporation, describes the theoretical 

evaporation rate from a shallow water body that does 

not store significant amounts of heat.

A pan coefficient can be used to predict free 

water-surface evaporation from pan evaporation. The 

coefficient is calculated as the ratio of free watersurface evaporation to observed pan evaporation:

Pan coefficient = 

(17)

Free water-surface evaporation, which also is 

used to estimate evapotranspiration, can be calculated 

from pan-evaporation measurements by using an 

equation from Kohler and others (1955):

free water-surface evaporation (inches)

pan evaporation inches ( ) ---------------------------------------------------------------------------------------------------------

(18)

where

FWSp is free water-surface evaporation from a pan, in 

inches;

Ep is pan evaporation, in inches;

P is barometric pressure, in inches of mercury;

αp is ratio of advected energy used in evaporation to the total energy advected from the 

pan;

Up is wind travel over the pan, in miles per day;

T0 is average pan water temperature, in degrees 

Fahrenheit; and

Ta is average air temperature, in degrees Fahrenheit.

This equation is based on the assumption that any 

energy advected into the lake is balanced by a change 

in energy storage and that the pan exposure is 

representative of the lake. Measurements are required 

for pan evaporation, average wind speed over the pan, 

average pan water temperature, and average air 

temperature. Barometric pressure at Lake Lucerne 

was assumed to be constant at 30.21 in. of mercury. 

The ratio αp can be taken from a plot of αp in relation 

to water-surface temperature and wind speed (Kohler 

and others, 1955, fig. 5).

For comparison, the energy-budget evaporation 

rates can be converted to free water-surface 

evaporation from a lake (FWSl

) by using a correction 

factor from Ficke (1972):

(19)

The terms Qx , Qw, and Qv are defined in equation 7. 

The value of αl

, the ratio of advected energy used in 

evaporation to the total energy advected from the 

lake, is taken from a plot of αl

 in relation to water 

temperature and wind speed at 2 m (6.6 ft) above the 

lake surface (Harbeck, 1964, fig. 2).

Free Water-Surface Evaporation Rates

Monthly free water-surface evaporation 

calculated from the pan-evaporation data (FWSp) for 

Lake Lucerne and Lake Alfred is shown in figure 23. 

FWS

p 0.70[Ep

0.00051Pα

p

0.37 0.0041U

p = + ( ) +

T0 Ta ( ) – 0.88]

∆E αl Qx Qw Qv = ( ) + – /ρ( ) L

FWSl EEB = + ∆E
26 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

FWSp at Lake Lucerne ranged from 0.078 in/d in 

December 1985 to 0.208 in/d in May 1986 and totaled 

54.54 in/yr. FWSp at Lake Alfred ranged from 0.094 

in/d in January 1986 to 0.247 in/d in May 1986 and 

totaled 60.64 in/yr. The pan evaporation is always 

greater at Lake Alfred than at Lake Lucerne; as a 

result, the FWSp is consistently greater. Although the 

Lake Alfred pan is only about 2 mi away, it is not 

representative of climatic conditions at Lake Lucerne.

Free water-surface evaporation calculated from 

energy-budget evaporation at Lake Lucerne (FWSl

) is 

also shown in figure 23. FWSl

 ranged from 0.055 in/d 

in December 1985 to 0.249 in/d in April 1986 and 

totaled 58.61 in/yr. Conversion tables for calculating 

all monthly free water-surface evaporation rates are 

given in appendix B.

Theoretically, the FWSp and FWSl

 for Lake 

Lucerne should be nearly equivalent. Although FWSp

and FWSl agree to within 7 percent on an annual basis, 

they are dissimilar on a monthly basis. The FWSp

differs from FWSl by up to 68 percent, and 5 months 

had deviations greater than 20 percent. Surprisingly, 

FWSp is a more accurate predictor of actual lake 

evaporation on a monthly basis than it is of FWSl

. The 

FWSp from Lake Lucerne underestimated actual lake 

evaporation calculated by the energy budget by 

6 percent on an annual basis. The monthly deviation 

from the energy-budget evaporation ranged from 

−20 percent in September 1986 to +35 percent in 

February 1986. Errors were less than 10 percent for 

all but 3 months. 

In general, FWSp overestimates energy-budget 

evaporation during the winter months (December 

through March) and underestimates it in spring (April 

and May) (fig. 23). During the winter months 

(December and January), when the lake rapidly loses 

stored heat, lake evaporation is higher than FWSp

because more energy is available to evaporate water 

than there would be in a free water surface where no 

energy is stored. In the spring the opposite is true, and 

energy that goes into stored heat in a lake is not 

available for evaporation, as it would be in a free water 

surface. These effects could be expected to be even 

greater in more temperate climates.

Pan Coefficients

The best estimate of the pan coefficient for a 

given lake should be the ratio of the free water-surface 

evaporation derived from the corrected energy-budget 

evaporation to the observed pan evaporation 

(FWSl

/Ep) because energy-budget evaporation is 

assumed to have the highest accuracy. Because local 

energy-budget evaporation rates are seldom available, 

the pan coefficient is usually calculated as the ratio of 

the free water-surface evaporation derived from the 

pan data to the observed pan evaporation (FWSp/Ep ) 

(Farnsworth and others, 1982).

The pan coefficients calculated for this study are 

listed in table 2. Maps of annual pan coefficients for 

the continental United States, based on panevaporation data from 1956 to 1970, are presented by 

Farnsworth and others (1982). The pan coefficient for 

Lake Lucerne interpolated from this map is just over 

0.74. Monthly pan coefficients for Lake Okeechobee, 

Fla., which were calculated from a water budget by 

Langbein (1951) for the years 1940–46, also are listed. 

A ratio of the energy-budget evaporation to pan 

evaporation (EEB /Ep ) also was computed for 

comparison with pan coefficients.

On an annual basis, the pan coefficients 

calculated by the various methods were similar. The 

average pan coefficient calculated for the 1986 water 

year using the Lake Lucerne pan data or the data from 

Lake Alfred was 0.73. These results agreed well with 

the long-term annual average coefficient of 0.74 of 

Farnsworth and others (1982). The pan coefficient 

derived from the corrected energy-budget evaporation 

was higher, the average for the year being 0.75. The 

mean coefficient for Lake Okeechobee was 0.81, but 

unlike the Lake Alfred data, the results were not 

directly comparable with the Lake Lucerne results 

because they did not cover the same time period.

Figure 23. Monthly free water-surface evaporation (FWSp) 

calculated from the evaporation pans at Lake Lucerne and at 

the Lake Alfred National Oceanic and Atmospheric 

Administration site, and from the corrected energy-budget 

evaporation (FWSl

) for the 1986 water year. (Energy-budget 

evaporation rates (EEB) are shown for comparison).

0.30

0.25

0.20

0.15

0.10

0.05

0

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

FWS l

FWS P

FWSp

1985 1986

LAKE ALFRED )

LAKE LUCERNE )

(

(

E EB

0.6

0.4

0.2

0

1986 WATER YEAR

FREE WATER-SURFACE EVAPORATION,

IN CENTIMETERS PER DAY

FREE WATER-SURFACE EVAPORATION,

IN INCHES PER DAY
Evaporation 27

Larger differences appeared among pan 

coefficients when they were calculated on a monthly 

basis. The range of the Lake Lucerne pan coefficient 

was from 0.70 to 0.77. This was slightly larger than 

the range of the pan coefficient at Lake Alfred, 0.71 to 

0.75. Both the Lake Lucerne and Lake Alfred pan 

coefficients varied less from month to month in 

comparison with the ratios derived from corrected 

(0.42 to 0.96) or uncorrected (0.50 to 0.92) energybudget evaporation.

Theoretically, pan coefficients calculate free 

water-surface evaporation rather than lake evaporation 

because heat storage is not accounted for. 

Nevertheless, the results of this study indicate that 

pan-evaporation data corrected to free water-surface 

evaporation were similar to actual lake evaporation at 

Lake Lucerne and might be a reasonable predictor for 

periods of at least a month. Annual FWSp was about 

6 percent less than the annual energy-budget 

evaporation at Lake Lucerne during the 1986 water 

year. Errors in estimates of lake evaporation based on 

FWSp data on a monthly basis were generally less than 

10 percent but were as large as 35 percent. Larger 

errors occurred during periods of high or low rates of 

evaporation or periods of rapid change in lake 

temperature.

Table 2. Monthly and annual pan coefficients for Lake 

Lucerne for the 1986 water year

[FWSl, free water-surface evaporation from lake; FWSp, free water-surface 

evaporation from pan; Ep, pan evaporation; EEB, energy-budget evaporation]

Year and

month FWSp /Ep 

FWSp/Ep 

(Lake 

Alfred)

FWSl /Ep EEB/Ep

Langbein

(1951)

1940–46

1985:

October 0.74 0.73 0.77 0.79 0.76

November .72 .72 .68 .72 .71

December .70 .72 .42 .69 .83

1986:

January .70 .71 .67 .64 .77

February .77 .74 .57 .50 .69

March .72 .74 .79 .71 .73

April .74 .74 .96 .92 .84

May .72 .73 .92 .86 .82

June .76 .74 .76 .73 .85

July .75 .74 .76 .75 .91

August .76 .75 .76 .75 .91

September .75 .75 .95 .95 .85

Annual 

mean

.73 .73 .75 .75 .81

Evaporation Summary

The energy-budget method was used to obtain 

the most accurate available measurement of 

evaporation at Lake Lucerne. The total energy-budget 

evaporation calculated on a thermal survey basis for 

52 weeks from October 1, 1985, to September 30, 

1986, was 57.87 in. This was greater than the longterm average evaporation for the area but probably 

was a result of drier than average conditions during the 

study year. The largest evaporation rate was 

0.264 in/d between April 29 and May 5, 1986. The 

smallest was 0.040 in/d between December 31, 1985, 

and January 6, 1986 (fig. 14 and app. A). The error for 

the energy-budget method for the 52-week period of 

record was 16.4 percent.

Daily energy-budget evaporation rates were 

computed by using daily changes in stored heat and 

were averaged and compared with the thermal survey 

evaporation rates. These two estimates generally 

agreed closely except for periods of low evaporation, 

when unrealistic values for the Bowen ratio were a 

limiting factor in the use of daily values. When data 

were averaged over weekly thermal survey periods, 

these effects were minimized.

The total mass-transfer evaporation with a 

correction for atmospheric stability for the 1986 water 

year was 57.39 in. The largest evaporation rate was 

0.265 in/d between April 22 and April 28, 1986. The 

smallest was 0.047 in/d between December 31, 1985, 

and January 6, 1986 (fig. 21).

The error in the uncorrected mass-transfer 

estimate of evaporation for the 1-yr study period was 

31 percent when a value of 0.0114 was used for N. 

The large error in this method is a result of the large 

errors in determining N from the linear regression with 

the energy budget (25 percent) and the vapor pressure 

gradient (18 percent).

Pronounced seasonal differences existed 

between the energy-budget and the mass-transfer 

methods, the mass-transfer evaporation being greater 

than the energy-budget evaporation in the winter and 

less in the summer. At Lake Lucerne, changes in 

atmospheric stability explained part of the difference 

between evaporation computed by using the energybudget and mass-transfer methods. By incorporating 

the effects of atmospheric stability, the error in the 

mass-transfer method was reduced to 21 percent. 

FWSp at Lake Lucerne totaled 54.53 in. for the 

1986 water year and ranged from 0.078 in/d in 

December 1985 to 0.208 in/d in May 1986. FWSp at 
28 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

the Lake Alfred NOAA station totaled 60.65 in. and 

ranged from 0.094 in/d in January 1986 to 0.247 in/d 

in May 1986. FWSl

 from Lake Lucerne totaled 58.59 

in. and ranged from 0.055 in/d in December 1985 to 

0.249 in/d in April 1986. The FWSp at Lake Lucerne 

underestimated actual lake evaporation calculated 

from the energy-budget method by 6 percent on an 

annual basis, and the monthly deviation from the 

energy-budget evaporation ranged from −20 percent in 

September 1986 to +35 percent in February 1986. 

Deviations were less than 10 percent for all but 3 

months. The FWSp deviated from FWSl

 by up to 

68 percent on a monthly basis, an annual deviation 

being 7 percent. Five months had deviations greater 

than 20 percent.

On an annual basis, the pan coefficients 

calculated by the various methods were similar. The 

average pan coefficient calculated for the 1986 water 

year using the Lake Lucerne pan data or the data from 

Lake Alfred was 0.73. These results agreed well with 

the long-term annual average coefficient of 0.74 of 

Farnsworth and others (1982). The pan coefficient 

derived from the corrected energy-budget evaporation 

was higher, an average for the year being 0.75. 

Differences of as much as 68 percent appeared among 

pan coefficients when they were calculated on a 

monthly basis.

Within the study period, pan-evaporation data, 

corrected to free water-surface evaporation, were 

reasonable predictors of monthly lake evaporation 

measured by the energy-budget method. The largest 

discrepancies between pan evaporation and energybudget evaporation occurred during periods of high or 

low rates of evaporation or periods of rapid change in 

lake temperature.

GROUND WATER

Understanding lake and ground-water 

interaction is critical to understanding the hydrologic 

budget of seepage lakes such as Lake Lucerne. In this 

section the analysis of the ground-water fluxes to Lake 

Lucerne is undertaken in two parts. The first, a 

qualitative analysis based on numerical modeling, 

improves the conceptual and physical understanding 

of ground-water interactions with the lake and defines 

the physical constraints needed to quantify groundwater fluxes. In the second part, ground-water fluxes 

are quantified using flow-net analysis, and the 

potential errors in these estimates are discussed.

Numerical Simulation of Ground-Water and 

Lake Interactions

Ground-water flow simulations that are 

described in this section were used to refine the 

interpretation of the hydrogeologic setting of Lake 

Lucerne. This interpretation was based largely on 

point observations of the geology and head 

distribution around the lake and, consequently, could 

not completely describe the small-scale flow patterns 

that control ground-water exchange with the lake, 

particularly in the large sublake region. In this region, 

geophysical data provided indirect evidence of the 

geometry of the sinkhole complex beneath the lake, 

and the heads in the midlake well provided physical 

evidence of probable flow patterns. Simulation results 

indicated the possible distribution of ground-water 

inflow to and leakage from Lake Lucerne under high 

and low water-level conditions by interpolating heads 

in the areas between the field observations. Modeling 

results also provided insight into the factors 

controlling ground-water interactions with Lake 

Lucerne as well as other sinkhole-type lakes.

Modeling Approach

Three simulated cases were used to test the 

influence of the geologic framework of the lake on the 

ground-water and lake interactions. In the first case, 

cover-subsidence-type sinkholes were simulated in the 

sublake region. The geometry of the sinkholes was 

based upon the seismic survey. In the second and third 

cases, ground-water flow simulations were used to test 

the degree of anisotropy in the surficial aquifer and the 

possible influence of low-permeability lake sediments 

on lake and ground-water interactions, respectively. 

For each of these cases, simulations also were made to 

test the possible influence of the head in the Upper 

Floridan aquifer on ground-water and lake 

interactions. A low-head condition in the Upper 

Floridan aquifer, representative of drawdown due to 

pumping, was simulated for steady-state conditions 

and compared with results for higher head conditions. 

The two conditions were used to demonstrate the 

potential range of influence of the head in the Upper 

Floridan aquifer on ground-water interactions with 

Lake Lucerne.

Ground-water flow at Lake Lucerne was 

simulated using a steady-state, finite-difference, 

ground-water model (McDonald and Harbaugh, 1984). 

Two-dimensional ground-water flow was simulated 
Ground Water 29

along a cross section through the lake basin using a 

single model layer of unit width. To minimize the 

flow that occurs through the plane of the cross section, 

the model cross section was aligned along stream lines 

that enter the lake. This transect is shown on figure 9. 

The finite-difference grid for the ground-water basin 

along this transect had varied spacing and is shown in 

figure 24. The model was used to simulate flow 

patterns only within the surficial aquifer and the 

intermediate confining unit.

The hydrogeologic framework represented in 

the model incorporates the sublake geology 

interpreted from the seismic-reflection survey and the 

local geology shown in the hydrogeologic section 

(fig. 5). Adjacent to the lake, the surficial deposits 

overlie the intermediate confining unit. Beneath the 

lake, however, the surficial deposits make irregular 

contact with the intermediate confining unit or, where 

this unit is absent, with the Upper Floridan aquifer. In 

keeping with field observations, organic lake 

sediments are modeled only in the deepest regions of 

the lake bottom.

The boundary conditions that define the 

modeled ground-water flow system occur within the 

surficial aquifer and in the Upper Floridan aquifer, just 

below the intermediate confining unit. Because of the 

large transmissivity of the Upper Floridan aquifer, 

recharge from the surficial aquifer could be assumed 

to have little effect on the head in this aquifer. 

Consequently, the Upper Floridan aquifer is simulated 

along the base of the modeled flow system as a 

specified-head boundary. Because the lateral model 

boundaries were coincident with the ground-water and 

topographic drainage divides, these were specified as 

no-flow boundaries. The top of the flow system, 

which consists of the water table, Lake Lucerne, and 

Terrie Pond, also was modeled as a specified-head 

boundary condition.

Franke and others (1984) discussed the effects 

of using two constant-head boundaries (a particular 

case of the specified-head boundary) and two no-flow 

boundaries when modeling head distributions and 

flow rates within a confined, two-dimensional flow 

system. They showed that modeled head distributions 

are insensitive to the chosen values of hydraulic 

conductivity used (although sensitive to the contrast in 

hydraulic conductivity between units) but that 

modeled flows do increase proportionately to this 

value. For this reason, head distributions modeled at 

Lake Lucerne are presumed to be influenced only by 

the relative magnitude of the hydraulic conductivity 

and the anisotropy in different geologic units. 

Fortunately, the contrast of hydraulic conductivity 

between units is often more accurately represented in 

models than is the actual value of each unit. The 

quantity of flow entering the system from the 

specified-head boundary along the water table depends 

only upon the specified head imposed at the lower 

model boundary and the distribution of hydraulic 

conductivities within the model.

The hydraulic characteristics of the surficial 

aquifer and intermediate confining unit were defined 

as follows. The horizontal hydraulic conductivity (Kh) 

was estimated to be 8 feet per day (ft/d) in the upper 

part of the surficial aquifer and 2 ft/d in the lower part 

of the surficial aquifer. The vertical hydraulic 

conductivity (Kv ) in the intermediate confining unit 

was estimated to be 0.0001 ft/d (Lee and others, 1991). 

The Kv of the lake sediments was varied between 

0.0002 and 0.005 ft/d. Anisotropy in the surficial 

aquifer, or the ratio of Kh to Kv , was set initially to 

100 and changed in subsequent simulations to 10 and 

1,000. The model could accommodate only one value 

of anisotropy for the entire model cross section. 

Therefore, Kh within the intermediate confining unit 

was selected to produce the desired Kv value of 

0.0001 ft/d when divided by the anisotropy.

Munter and Anderson (1981) defended this 

simplification in flow systems similar to Lake 

Lucerne. Their simulations showed that Kh in 

formations through which the flow is predominantly 

vertical makes negligible difference in the rate of 

ground-water flux to the lake. Instead, they found that 

vertical seepage was sensitive to Kv (the quotient of 

Kh and anisotropy). This same assumption was used 

to model the Kv in the lake sediments, as flow through 

both the confining unit and the lake sediments was 

predominantly vertical.

Two seasonal extremes in the heads in the 

surrounding aquifers were simulated by imposing 

different specified-head conditions along the upper 

and lower model boundaries. High water-level 

conditions were modeled for both the surficial and the 

Upper Floridan aquifers using head conditions 

observed on October 17, 1985 (figs. 9B and 10). The 

head in the Upper Floridan aquifer in well 1PN-155 

was 120.23 ft above sea level, and the downward head 

difference between the lake and this aquifer was 

5.73 ft. The high water-level condition generally is 

representative of the basin between August and 
30 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

COLUMNS 1 2 3 4 5 6 7 8 9 11 12 43 44 46 47

ROWS

3

10

20

30

40

48

SEA

LEVEL

10

20

30

40

50

60

70

80

90

100

110

120

130

CONSTANT HEAD BOUNDARY

ALTITUDE, IN FEET ABOVE SEA LEVEL

INTERMEDIATE CONFINING UNIT

CONSTANT HEAD BOUNDARY

UPPER FLORIDAN AQUIFER

LAKE LUCERNE

11 15 44

COLUMNS

SEA

LEVEL

130

120

110

100

90

80

70

60

50

40

30

20

10

ROWS

5

10

20

30

40

48

2PN-20

2PN-35

2PN-50

1PN-7

1PN-20

1PN-35

1PN-50

0 200 FEET

LAKE LUCERNE

2PN-9

TERRIE POND

0 50 METERS

A.

UPPER

LOWER

B.

0 600 FEET

0 100 METERS

10 45

SEDIMENT

140

20 25 30 35 40

EXPLANATION

1PN-7 OBSERVATION WELL—Approximate location of the shallow well sites at 1PN and 2PN and the Midlake well

VERTICAL SCALE GREATLY EXAGGERATED

VERTICAL SCALE GREATLY EXAGGERATED

ALTITUDE, IN FEET ABOVE SEA LEVEL

SURFICIAL AQUIFER

SURFICIAL AQUIFER

NO-FLOW BOUNDARY

NO-FLOW BOUNDARY

MIDLAKE

Figure 24. Layout of model grid for (A) numerical ground-water simulation and (B) enlarged model area 

around Lake Lucerne showing approximate locations of wells at sites 1PN and 2PN.
Ground Water 31

February. During these months of the 1986 water 

year, heads in the Upper Floridan aquifer were high 

and ranged from 118 to 121 ft above sea level.

The low water-level condition was simulated 

using head conditions observed in the surficial and 

Upper Floridan aquifers on May 20, 1986. The watertable configuration for this date is shown in figures 9A

and 11. The head in the Upper Floridan aquifer was 

112.93 ft above sea level, and the downward head 

difference between the lake and Upper Floridan 

aquifer was 11.85 ft. This low water-level condition 

was characteristic of the driest months of the year: 

April, May, and early June. Heads were below 115 ft 

above sea level for 60 days (16 percent) of the 1986 

water year due to irrigation pumping. These days 

occurred continuously during April, May, and June of 

1986, with a minimum head of 109.96 ft above sea 

level occurring on May 30.

Comparisons between observed and modeled 

head distributions were used to evaluate the realism of 

the hydrogeologic setting simulated by the model. 

Model simulations that compared well with observed 

heads were used to improve parameter estimates used 

in the flow-net analyses. These parameters were depth 

of the ground-water inflow component and area of 

leakage through the lake bottom.

Although neither water-level condition was, in 

fact, steady state, the high water-level simulation most 

closely approximated steady state, as this condition 

persisted for nearly 7 months of the year. Therefore, 

simulated heads should resemble heads observed in 

the field. In contrast, extremely low heads in the 

Upper Floridan aquifer existed for a period of 

approximately 2 months during the 1986 water year 

and were preceded and followed by weeks in which 

the head in the Upper Floridan aquifer was higher, but 

fluctuating. For this reason, steady-state results might 

overpredict the effects of the low water-level 

conditions.

Effect of Intermediate Confining Unit Below the 

Lake

The geometry of the intermediate confining unit 

beneath Lake Lucerne is one of the most important 

geologic factors controlling the lake and ground-water 

interaction. Figure 25 compares the results of 

simulations with a continuous confining unit beneath 

the lake and with the confining unit geometry inferred 

from the seismic-reflection survey. Both simulations 

are for the seasonally high water-level condition. 

Model parameters for the two simulations are identical 

except that, in the simulation shown in figure 25B, the 

lower surficial deposits (Kh = 2 ft/d) replace the 

confining unit in areas below the lake and extend 

downward into the Upper Floridan aquifer. Lake 

sediments are omitted in these simulations.

Because the general pattern of ground-water 

flow in the basin at high water-level conditions was 

similar for all simulations (fig. 26), figures hereafter 

show only the enlarged area of interest shown in 

figure 25. As seen in figure 26, ground water in the 

surficial aquifer moves laterally from the flow 

boundary at the basin drainage divides toward the 

lake, as well as downward. Due to vertical head 

gradients, recharge occurring farthest from the lake 

probably leaks across the confining unit before 

reaching the lake. Closer to the lake, flow in the upper 

part of the surficial aquifer can be intercepted by the 

lake, while the remainder bypasses the lake and flows 

downward toward the Upper Floridan aquifer.

With a continuous confining unit beneath the 

lake, the model predicts upward flow at all depths 

within the surficial aquifer adjacent to the lake 

(fig. 25A). The extensive upward flow around the lake 

results in only minimal leakage through a small 

percentage (17 percent) of the lake bottom (expressed 

as a percentage of the lakebed length along the cross 

section). Leakage is not predicted to occur at the 

location of the midlake well (fig. 25A). Instead, a 

large downward head difference occurs across the 

intermediate confining unit below the lake.

Alternately, the simulation shown in figure 25B

indicates that horizontal flow near the lake diverges 

into upward and downward flow. A flow divide 

occurs at both sides of the lake at a depth of about 16 ft 

below the lake level or between the depths of the 20- 

and 35-ft-deep wells at sites 1PN and 2PN. The area 

of the lake bottom that receives ground-water inflow 

has decreased significantly, and leakage occurs from 

approximately 74 percent of the lake bottom. The 

model more closely predicts the heads observed in the 

lower part of the surficial aquifer and also closely 

predicts the head observed in the midlake well (125.63 

and 125.70 ft above sea level, predicted and observed, 

respectively).

The contrasts between simulations, with and 

without a continuous confining unit, increase for the 

low water-level condition. With the confining unit 

intact, the model predicts weak, upward head 

gradients in the surficial aquifer adjacent to the lake 
32 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

Figure 25. Simulated vertical head distribution for high water-level conditions with (A) a continuous confining 

unit beneath Lake Lucerne and (B) a breached confining unit beneath Lake Lucerne.

128.5

125.96 127.5

126

125.5

125

123

121

128

127 126

B.

200 FEET

VERTICAL SCALE GREATLY EXAGGERATED

125.96

127

126.5 126

125

123

121

126 126.5

127.5

128.5

128

A.

SEA

LEVEL

130

120

110

100

90

80

70

60

50

40

30

20

10

ALTITUDE, IN FEET ABOVE SEA LEVEL

30

SEA

LEVEL

130

120

110

100

90

80

70

60

50

40

20

10

ALTITUDE, IN FEET ABOVE SEA LEVEL

LAKE LUCERNE

LAKE LUCERNE

127.5 127 

127 

126.5

127.5

126.5

VERTICAL SCALE GREATLY EXAGGERATED

EXPLANATION

HEAD CONTOUR—Model simulated head contour, in feet. Contour interval varies.

 

 Datum is sea level 

DIRECTION OF GROUND-WATER FLOW

OBSERVATION WELL—Approximate location of the shallow wells identified in Figure 24B

125

CONFINING UNIT

INTERMEDIATE

UPPER FLORIDAN AQUIFER

SURFICIAL

AQUIFER

SURFICIAL

AQUIFER

CONFINING UNIT

INTERMEDIATE

UPPER FLORIDAN AQUIFER

0 200 FEET

0 50 METERS
33

(fig. 27A). However, the predicted area of leakage 

increases to nearly half of the lake bottom 

(47 percent). Leakage occurs at the midlake well, but 

the predicted head in the midlake well is nearly 1 ft 

higher than the observed head (124.77 and 123.88 ft 

above sea level, predicted and observed, respectively) 

(figs. 27A and 11). 

With breaches in the confining unit, the 

predicted head for the midlake well (124.10 ft above 

sea level) approaches the observed head (123.88 ft 

above sea level) but is still higher (fig. 27B). The 

similarity between predicted and observed heads 

indicates that the head distribution below the lake 

could approach steady state within the duration of the 

low water-level conditions. The predicted pattern of 

flow adjacent to the lake also more closely resembles 

the observed conditions (fig. 27B). Leakage 

Figure 26. Simulated vertical head distribution for high water-level conditions showing general pattern of 

ground-water flow in the basin.

SEA

LEVEL

10

20

30

40

50

60

70

80

90

100

110

120

130

ALTITUDE, IN FEET ABOVE SEA LEVEL

VERTICAL SCALE GREATLY EXAGGERATED

TERRIE POND

135

130.60

125.96

SURFICIAL AQUIFER

INTERMEDIATE CONFINING UNIT

134 133 132 131 130 129

128

127

126 125

124

123

122

121

126 127

128

129

130

131

0 600 FEET

0 100 METERS

UPPER FLORIDAN AQUIFER

LAKE LUCERNE

EXPLANATION

HEAD CONTOUR—Model simulated head contour, in feet. Contour interval varies.

 

 Datum is sea level 

DIRECTION OF GROUND-WATER FLOW

125

SEDIMENT

140

dominates the predicted ground-water interactions 

with Lake Lucerne at extreme low water-level 

conditions and is predicted to occur through nearly 

88 percent of the lake bottom. Ground-water inflow 

occurs only to a depth of 6 to 8 ft below the lake 

surface.

The pattern of leakage from Lake Lucerne is 

strongly dependent on the geometry of the breaches in 

the confining unit. For example, the presence of even 

small areas of confining unit between sinkholes 

redirects flow lines and significantly reduces the 

leakage that occurs from the nodes in the overlying 

lakebed (fig. 27B). Thus, differences in confining unit 

geometries below the numerous lakes of sinkhole 

origin along the Central Highlands Ridge should result 

in significantly different quantities of leakage under 

low head conditions in the Upper Floridan aquifer.
34 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

124.5

123

121

119

117 

125

B.

0 200 FEET

0 50 METERS

113

126 125.5

125

125

125.5

123

A.

121

119

117 

121

119

115

113 113

124.78

130

120

110

SEA

LEVEL

100

90

80

70

60

50

40

30

20

10

VERTICAL SCALE GREATLY EXAGGERATED

ALTITUDE, IN FEET ABOVE SEA LEVEL

SEA

LEVEL

130

120

110

100

90

80

70

60

50

40

30

20

10

ALTITUDE, IN FEET ABOVE SEA LEVEL

125.5

125

LAKE LUCERNE

LAKE LUCERNE

124.78

EXPLANATION

HEAD CONTOUR—Model simulated head contour, in feet. Contour interval varies.

 

 Datum is sea level 

DIRECTION OF GROUND-WATER FLOW

OBSERVATION WELL—Approximate location of the shallow wells identified in Figure 24B

125

INTERMEDIATE CONFINING UNIT

UPPER FLORIDAN AQUIFER

123

115 117 

SURFICIAL AQUIFER

SURFICIAL AQUIFER

INTERMEDIATE

CONFINING UNIT

UPPER FLORIDAN AQUIFER

115

125.5

Figure 27. Simulated vertical head distribution for low water-level conditions with (A) a continuous confining 

unit beneath Lake Lucerne and (B) a breached confining unit beneath Lake Lucerne.
35

Effect of Anisotropy in the Surficial Aquifer

The anisotropy of the surficial aquifer has a 

major effect on the amount of ground-water inflow 

intercepted by the lakebed and on the rate of lake 

leakage. Reliable estimates of anisotropy determined 

from field investigations, however, are rare, and none 

exists for the surficial aquifer around Lake Lucerne. 

As a result, anisotropy is often estimated during the 

process of calibrating a model to reproduce observed 

head distributions. Anisotropy values reported in both 

field and modeling investigations generally range 

from 10 to 1,000 (Winter, 1976).

Simulation results for three values of 

anisotropy at Lake Lucerne are shown in figure 28 

for the high water-level condition. The predicted 

areas of ground-water inflow and leakage across the 

lakebed and the rates of inflow and leakage for the 

three values of anisotropy considered are 

summarized in table 3.

Increasing anisotropy in the surficial aquifer 

causes a more pronounced divergence between 

upward flow into the lake and downward flow 

toward the Upper Floridan aquifer. When 

anisotropy is 10, little vertical variation in head 

occurs in the surficial aquifer near the lake, and the 

flow divides that were observed at sites 1PN and 

2PN were not reproduced (fig. 28A). When 

anisotropy is increased to either 100 or 1,000, 

distinct flow divides occur near the lake (figs. 28B

and 28C). When anisotropy is increased from 100 to 

1,000, the upward flow component is distributed 

farther beneath the lake (fig. 28C). Thus, increasing 

anisotropy increases the area of the lakebed that 

receives ground-water inflow and decreases both the 

area and the rate of leakage. 

The area of the lakebed that receives inflow 

increases with increasing anisotropy, however, there 

is little change in the magnitude of predicted inflows 

(table 3). This result follows from the fact that 

variations in model anisotropy do not affect the Kh

value in the surficial aquifer. As the majority of the 

ground-water inflow occurs along horizontal flow 

lines near the lakeshore, anisotropy has little effect 

on the magnitude of ground-water inflow.

Increasing anisotropy has a dual effect on 

leakage. It decreases both the area of the lakebed that 

leaks and the rate of leakage by decreasing Kv . 

Greater anisotropy also increases the vertical head 

drop in the surficial aquifer below the flow divide. As 

a result, when anisotropy is 1,000, heads predicted for 

the lower part of the surficial aquifer (wells 1PN-50 

and 2PN-50) are much lower than observed. Whereas 

changes in anisotropy did not significantly alter the 

predicted head in the midlake well, increasing 

anisotropy from 10 to 1,000 reduced total leakage 

rates by three orders of magnitude from 19.4 to 

0.06 cubic feet per day per foot [(ft3

/d)/ft] (table 3).

Simulation results for the three anisotropy 

values suggest that anisotropy on the order of 100 is 

appropriate for the surficial aquifer surrounding Lake 

Lucerne. An anisotropy of 10 does not simulate the 

vertical flow divide in the surficial aquifer. The higher 

value of 1,000 results in too much vertical head loss 

and an unlikely low leakage rate. Anisotropy equal to 

100 most closely approximates the vertical head 

distribution near the lake and, therefore, is considered 

most representative of the surficial aquifer around 

Lake Lucerne.

This value also agrees closely with the 

anisotropy reported for surficial sand deposits in 

northwest Hillsborough County, approximately 50 mi 

west of Lake Lucerne (Sinclair, 1974). For a 

noncohesive, “clean, well-sorted, fine to very fine 

quartz sand” with a combined silt and clay content 

ranging from 0.9 to 4.7 percent, the respective 

anisotropies ranged from 1 to 37. (Anisotropy was 

computed from reported vertical and horizontal 

coefficients of permeability.) At Lake Lucerne, grain 

sizes were determined in split-spoon samples collected 

at 5-ft intervals at a test hole at site 1PN. The 

combined silt and clay content in the surficial deposits 

ranged from 4.5 to 24.8 percent by weight. The higher 

percentages of silt and clay in the surficial deposits at 

Lake Lucerne support anisotropy values on the order 

of 37 or greater.

Effect of Lake Sediments

Lake sediments could play a major role in 

regulating the ground-water interaction with sinkholetype lakes, yet few data exist to describe sediment 

hydraulic characteristics. Frequently, sediment Kh

values are assumed to be several orders of magnitude 

less than the Kh value in the surrounding aquifer 

(Winter, 1976; Munter and Anderson, 1981). Such 

low permeabilities below lakes in recharge settings 

could act as an important confining unit to impede 

vertical leakage from the lake. Lake sediments 

preferentially accumulate in the deepest regions of the 

lakebed. At Lake Lucerne, depressions in the 

bathymetry overlie sinkhole features in the underlying 

limestone. Therefore, sediments could inhibit lake 

leakage that would otherwise be facilitated by 

breaches in the underlying confining unit.
36 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

Figure 28. Simulated vertical head distribution for high water-level conditions with anisotropy equal to (A) 10, (B) 

100, and (C) 1,000.

128.5 127.5

126

126.5 125.5

125

123 

121

127 

126.5

126

127.5

B. anisotropy = 100

127 

126.5

126

125.5

125

123 

121

126 126.5

127 

127.5

128.5

A. anisotropy = 10

125.96

SEA

LEVEL

130

120

110

100

90

80

70

60

50

40

30

20

ALTITUDE, IN FEET ABOVE SEA LEVEL

10

30

SEA

LEVEL

130

120

110

100

90

80

70

60

50

40

20

ALTITUDE, IN FEET ABOVE SEA LEVEL

10

127.5

127.5

128

ALTITUDE, IN FEET ABOVE SEA LEVEL

SEA

LEVEL

130

120

110

100

90

80

70

60

50

40

30

20

10

0 200 FEET

0 50 METERS

126 126.5 127 

126 126.5

125.5 127 

125

123

121

C. anisotropy = 1,000

128

127.5

128 127 

LAKE LUCERNE

LAKE LUCERNE

LAKE LUCERNE

125.96

125.96

EXPLANATION

HEAD CONTOUR —Model simulated head contour, in feet. Contour interval varies.

 Datum is sea level 

DIRECTION OF GROUND-WATER FLOW

OBSERVATION WELL—Approximate location of the shallow wells identified in Figure 24B

125

SURFICIAL

AQUIFER

VERTICAL SCALE GREATLY EXAGGERATED

CONFINING UNIT

INTERMEDIATE SURFICIAL

AQUIFER

UPPER FLORIDAN AQUIFER

CONFINING UNIT

INTERMEDIATE

CONFINING UNIT

INTERMEDIATE

SURFICIAL

AQUIFER

UPPER FLORIDAN AQUIFER

UPPER FLORIDAN AQUIFER
37

To explore the potential influence of lake 

sediments on ground-water interactions at Lake Lucerne, 

three simulations were performed with equal to 25, 

10, and 1 percent of the Kh of the lower part of the 

surficial aquifer. Using an anisotropy of 100, the 

resulting values ranged from 0.005 to 0.0002 ft/d. 

The spatial distribution of lake sediments used in the 

simulations is shown in figure 29. Sediments were 

modeled only in the deeper regions of the lake, and no 

sediments were modeled at the location of the midlake 

well. Sediment thickness in Lake Lucerne is unknown; 

however, a maximum sediment thickness of 6 ft was 

assumed. All other model parameters were kept as 

previously stated, with anisotropy equal to 100. The 

modeling results also reflect the assumptions that the 

lake-water surface is a constant-head boundary and that 

steady-state conditions exist. 

The simulation results for the three values are 

shown in figure 29 for the high water-level conditions 

and in figure 30 for the low water-level conditions. 

Predicted ground-water inflow and leakage rates are 

summarized in table 4, along with the predicted heads at 

the midlake well.

The inclusion of lake sediments in this steady-state 

model had a negligible effect on the vertical head 

distribution in the surficial aquifer adjacent to the lake, or 

on the magnitude of ground-water inflow to the lake 

(table 4). Lake sediments also made a negligible 

difference in the area of the lakebed experiencing inflow 

relative to leakage. For example, the change from no 

sediments to sediments with the lowest increased 

the area of leakage from 1,100 ft (expressed as a length 

along the model cross section) to 1,150 ft. Because the 

area of inflow was nearly constant and because sediments 

Table 3. Predicted ground-water inflow and leakage rates 

and areas for three modeled values of anisotropy at high 

water-level conditions

Parameter Anisotropy

10 100 1,000

Percent inflow1

1 Percentage of the cross-section projection of lakebed (length 

1,475 ft) experiencing either ground-water inflow or leakage.

12 26 53

Percent leakage1 88 74 47

Depth of inflow (feet) 8–10 8–12 16

Inflow rate (cubic feet per day 

per foot)

2.76 2.20 1.70

Leakage rate (cubic feet per day 

per foot)

19.4 1.80 .06

hsed

vsed

vsed

vsed

were modeled only along the deeper parts of the lakebed, 

inflow rates at the shallower depths were not significantly 

altered by the presence of sediments at either high or low 

water-level conditions (table 4).

Decreasing increased the downward head 

gradient across the sediments. Vertical head gradients 

also increased across the lakebed in areas where 

sediments were absent (figs. 29 and 30). For example, 

the head predicted in the midlake well declined 

slightly from 125.49 to 125.28 ft above sea level when 

 was decreased from 0.005 to 0.0002 ft/d. The 

increased downward head gradient across the lakebed 

where sediments are absent increases leakage in these 

areas and decreases it in the areas with sediments.

The increased leakage through “bare” areas of 

the deeper lakebed is apparent in the leakage rates 

summarized in table 4. Reducing from 0.002 to 

0.0002 ft/d only decreased the predicted leakage from 

1.53 to 1.15 ft3/d under the high water-level conditions 

and from 3.74 to 3.03 ft3/d under the low water-level 

conditions (table 4). Reducing from 0.005 to 

0.0002 ft/d under high water-level conditions 

increased leakage through nodes without lake 

sediments from 40 to 84 percent of the total. Because 

of this effect, none of the simulations significantly 

reduced the total leakage rate over simulations in 

which sediments were absent (table 3).

The effect of the sediments in these simulations 

in which lake stage is held constant is to decrease the 

leakage through the deeper areas of the lakebed where 

sediments are present and to increase it in areas where 

the sediments are either thin or absent. This effect can 

be seen in the shape of the potentiometric contours 

beneath the lake. These contours are convex below 

sediments and concave around the midlake well, where 

sediments are absent. The concave potentiometric 

lines indicate a recharge mound at the lakebed. This 

recharge mound becomes more pronounced as the 

 is reduced and as water levels go from high to 

low conditions. Flow lines exiting the lakebed where 

the sediments are absent eventually converge farther 

below the lakebed and move toward the openings in 

the confining unit (fig. 30C). For a system with 

predominantly vertical flow, some estimate of the true 

 could be determined by comparing predicted and 

observed vertical head gradients across a sediment 

lens. This comparison, however, would require 

several midlake wells to be finished in the surficial 

aquifer below the sediment lens. The midlake well at 

Lake Lucerne was in an area with a thin sediment 

hsed

hsed

hsed

vsed

vsed

vsed
38 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

Figure 29. Simulated vertical head distribution for high water-level conditions with vertical hydraulic 

conductivity of the sediment, Kvsed, equal to (A) 0.005, (B) 0.002, and (C) 0.0002 foot per day.

128.5

128 

127.5

127 

126.5

126

121

123

125 125.5

126 126.5

127 

127.5

Kvsed = 0.002 ft/d

60

SEA

LEVEL

130

120

110

100

90

80

70

50

40

30

20

10

128.5

128

127 

127.5

126.5

126

ALTITUDE, IN FEET ABOVE SEA LEVEL

121

125 125.5

126 126.5

127.5

127 

Kvsed = 0.0002 ft/d

125.96

LAKE LUCERNE

128.5

128

127.5

126.5

126

121

123

125 125.5 126 126.5127 

127.5

Kvsed = 0.005 ft/d

127 

VERTICAL SCALE GREATLY EXAGGERATED

125.96

LAKE LUCERNE

125.96

LAKE LUCERNE

EXPLANATION

HEAD CONTOUR—Model simulated head contour, in feet. Contour interval varies. Datum is sea level 

DIRECTION OF GROUND-WATER FLOW

OBSERVATION WELL—Approximate location of the shallow wells identified in Figure 24B

125

SURFICIAL

AQUIFER

SEDIMENT

UPPER FLORIDAN AQUIFER

CONFINING UNIT

INTERMEDIATE

B. 

A.

C. 

60

SEA

LEVEL

130

120

110

100

90

80

70

50

40

30

20

ALTITUDE, IN FEET ABOVE SEA LEVEL

10

60

SEA

LEVEL

130

120

110

100

90

80

70

50

40

30

20

10

ALTITUDE, IN FEET ABOVE SEA LEVEL

0 200 FEET

0 50 METERS

SURFICIAL

AQUIFER

SURFICIAL

AQUIFER

UPPER FLORIDAN AQUIFER

CONFINING UNIT

INTERMEDIATE

UPPER FLORIDAN AQUIFER

CONFINING UNIT

INTERMEDIATE

123
39

Figure 30. Simulated vertical head distribution for low water-level conditions with vertical hydraulic 

conductivity of the sediment, Kvsed, equal to (A) 0.005, (B) 0.002, and (C) 0.0002 foot per day.

125.5

124.5 125

123 121

119

117 

115

113

124.5 125 125.5

Kvsed = 0.005 ft/d

125.5

ALTITUDE, IN FEET ABOVE SEA LEVEL

SEA

130

120

110

100

90

80

70

60

50

40

30

20

10

LEVEL ALTITUDE, IN FEET ABOVE SEA LEVEL

SEA

130

120

110

100

90

80

70

60

50

40

30

20

10

LEVEL ALTITUDE, IN FEET ABOVE SEA LEVEL

SEA

130

120

110

100

90

80

70

60

50

40

30

20

10

LEVEL

125

115

117 

119 121

123

125

Kvsed = 0.0002 ft/d

113

124.5

125.5

125.5

125

125.5

119

117 

121

123

124.5

125

115

113

Kvsed = 0.002 ft/d

124.78

LAKE LUCERNE

124.78

LAKE LUCERNE

124.78

LAKE LUCERNE

EXPLANATION

HEAD CONTOUR—Model simulated head contour, in feet. Contour interval varies. Datum is sea level DIRECTION OF GROUND-WATER FLOW

OBSERVATION WELL—Approximate location of the shallow wells at sites identified in Figure 24B

125

VERTICAL SCALE GREATLY EXAGGERATED

SURFICIAL

AQUIFER

SEDIMENT

0 200 FEET

0 50 METERS

A.

B.

C.

SURFICIAL

AQUIFER

UPPER FLORIDAN AQUIFER

UPPER FLORIDAN AQUIFER

UPPER FLORIDAN AQUIFER

SURFICIAL

AQUIFER

CONFINING UNIT

INTERMEDIATE

CONFINING UNIT

INTERMEDIATE

CONFINING UNIT

INTERMEDIATE
40 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

layer and, as such, was not a sensitive indicator of the 

potential at Lake Lucerne. Despite this fact, 

heads predicted in the midlake well did respond 

slightly to changes in and were closest to the 

observed head for both high and low head conditions 

when was the highest (0.005 ft/d).

Limitations of Two-Dimensional Model

Modeling ground-water flow patterns along a 

cross section through Lake Lucerne provided a simple 

and useful tool for testing the influence of the 

hydrogeologic setting on ground-water interactions 

with the lake. Regardless of the hydrogeologic 

framework or hydraulic properties used, however, 

two-dimensional model simulations of ground-water 

flow did not duplicate the extent and magnitude of the 

upward head gradients that were consistently observed 

in the nested observation wells near Lake Lucerne at 

sites 1PN and 2PN.

This discrepancy is most likely due to the 

limitations of using a two-dimensional model instead 

of a three-dimensional model to simulate groundwater flow around the lake. Winter (1978) compares 

ground-water flow patterns simulated around a 

hypothetical circular lake using a two-dimensional and 

a three-dimensional, steady-state model. For a given 

hypothetical lake setting, upward head gradients near 

the margin of the lake were larger and distributed 

farther beneath the lake for a cross-section projection 

taken from the three-dimensional simulation than for 

the same cross-section projection simulated with a 

two-dimensional model. Also, if “outseepage” or 

leakage was predicted in the two-dimensional 

analysis, much less or no outseepage was predicted in 

the three-dimensional simulation. For lakes that 

showed outseepage in both two-dimensional and 

three-dimensional results, the area of the outseepage 

was reduced in the three-dimensional results over the 

two-dimensional results.

These conclusions are partly intuitive if the 

primary assumption of a two-dimensional model is 

considered, namely, symmetry along the y-axis. When 

applied to a nearly circular lake such as Lake Lucerne, 

or the hypothetical lake modeled by Winter (1978), a 

two-dimensional, cross-section model lacks the 

capability to simulate the radial pattern of flow lines 

that converge inward toward the center of the lake. 

Therefore, the reinforcing effect of this crowding, or 

convergence, of flow lines along the perimeter of the 

lakebed is not accounted for in the head distribution 

predicted by the two-dimensional model. The result is 

an underprediction of the magnitude of the lateral and 

upward head gradients that cause ground-water inflow 

to Lake Lucerne.

 The cross-section model also might 

underpredict the vertical hydraulic conductivity below 

the lake. By using the same parameters as the twodimensional model, a three-dimensional model would 

tend to decrease both the predicted downward head 

gradient below the lake and the area of leakage. Thus, 

the vertical hydraulic conductivity below Lake 

Lucerne would probably have to be increased in the 

three-dimensional model in order to reproduce 

observed heads in the midlake well.

Summary of Modeling Results

Numerical modeling results generally support 

the initial interpretation of the hydrogeologic setting 

of Lake Lucerne. Although the model is used 

primarily as a qualitative tool, it simulates with 

reasonable accuracy the head distribution around Lake 

Lucerne at high and low water-level conditions, 

especially if the differences between the two- and 

three-dimensional approach, just mentioned, are taken 

into account. The model confirms the presence of 

Table 4. Predicted ground-water inflow and leakage rates 

for three Kvsed values under high and low water-level 

conditions and heads for the midlake well

[Kvsed, vertical hydraulic conductivity of lake sediments]

Parameter Kvsed, (in feet per day)

0.005 0.002 0.0002 

High water level:

Ground-water inflow1

1 Computed by multiplying discharge rate by the fraction of the total 

lakebed area represented by the model cross section, in cubic feet per day 

per foot.

2.15 2.13 2.08

Leakage1 1.53 1.37 1.15

Percent leakage 

through nodes 

with sediments

60 44 16

Low water level:

Ground-water inflow1 .67 .65 .62

Leakage1 3.74 3.42 3.03

Percent leakage 

through nodes with 

sediments

53 38 13

Midlake-well heads:

High water level2

2 Observed midlake-well head equals 125.70 for high and 123.88 for 

low water-level conditions.

125.49 125.40 125.28

Low water level2 123.79 123.60 123.35

vsed

vsed

vsed
41

breaches in the confining unit below the lake. These 

breaches are required to reproduce the flow divide in 

the surficial aquifer near the lake and to simulate 

heads observed in the midlake well.

The simulated flow divide in the surficial 

aquifer indicates the area of the lakebed that receives 

lateral ground-water inflow and the area that loses 

water by vertical leakage. The shape of this flow 

divide is most accurately simulated when anisotropy 

in the surficial aquifer is on the order of 100. With this 

anisotropy value, the depth (or thickness) of groundwater inflow is about 18 ft for the high water-level 

condition and about 10 ft for the low water-level 

condition.

At the high water-level condition, leakage 

occurs from areas of the lakebed that are below an 

altitude of 114 ft above sea level. At low water-level 

conditions, the area of leakage increases to the area 

below about 118 ft above sea level. These levels 

correspond to the areas below the 14-ft and 10-ft 

contours on the bathymetric map, respectively (fig. 7). 

The predicted upward head gradients associated with 

the flow divide in the two-dimensional simulations 

were never as large as the observed gradients. This 

effect is most likely the result of representing threedimensional flow in two dimensions.

Lake sediments, even of low hydraulic 

conductivity, did not significantly inhibit the simulated 

leakage loss from Lake Lucerne. Though no definitive 

conclusions can be drawn about the value of for 

Lake Lucerne, the influence of lake sediments appears 

to depend on their distribution in the lakebed. If 

sediment-filled depressions in the lakebed are 

separated by elevated areas that are bare or thinly 

covered, then substantial leakage can occur from these 

elevated areas. This result indicates that leakage 

might be greater from sinkhole-type lakes with an 

irregular morphometry formed by multiple, 

discontinuous “pools” than from lakes with a more 

regular shape in which sediments are uniformly thick. 

Alternately, if lake sediments are not significantly less 

conductive than the adjacent aquifer, then leakage 

might be somewhat evenly distributed across the 

lakebed.

Results from the ground-water flow model 

provide information helpful for calculating groundwater fluxes to Lake Lucerne using less complex 

analytical methods. Ground-water inflow can be 

computed by an areal flow-net analysis if the inflow is 

predominantly along horizontal flow lines and the 

depth of inflow is known. Leakage, as a steady, onedimensional flow phenomenon, can be computed 

using Darcy’s law. These methods were selected for 

ground-water flux calculations at Lake Lucerne 

because they are relatively simple, they rely on the 

actual head distribution observed in the field, and they 

can be applied to any specific time period for which 

observations are available.

Modeling results support the use of these 

methods in several ways. First, they support the 

conclusion that ground-water inflow to Lake Lucerne 

follows predominantly horizontal flow lines and, 

therefore, can be calculated by an areal flow-net 

analysis. Despite the complex sublake geology, the 

model indicates that lake leakage is primarily vertical 

and, thus, can be calculated by a one-dimensional flow 

equation. These simplifications provide the basis for 

the calculations of ground-water fluxes in the 

following section. Other model results are used to 

support assumptions about the depth of the groundwater inflow component and the area of leakage.

Quantification of Ground-Water Fluxes

Ground-Water Inflow

An areal flow-net analysis was used to estimate 

the ground-water inflow to Lake Lucerne. A flow-net 

analysis is a graphical solution technique to the 

LaPlace equation describing steady, two-dimensional, 

ground-water flow in a homogeneous, isotropic 

aquifer. A thorough discussion of the approach was 

given by Davis and De Wiest (1966, p. 189–198).

Flow-Net Assumptions

The use of an areal flow-net analysis is 

appropriate under a set of limiting conditions or 

assumptions, namely, that (1) ground-water flow is 

two dimensional; (2) hydraulic head, or its derivative 

normal to the flow region boundary, is known along 

the entire flow system boundary; (3) ground-water 

flow is steady, that is, no changes in ground-water 

storage occur with time; (4) Darcy’s law is valid for 

the flow region (Reynolds number, Re

<

= 1); and (5) 

the effective depth of the horizontal flow component is 

known.

If the above conditions are met, the LaPlace 

equation can then be solved graphically, and groundwater discharge can be computed using a form of 

Darcy’s law:

vsed
42 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

Q = mKh HD/n (20)

where

Q is total discharge of the considered flow 

region, in cubic feet per second;

m is the number of stream tubes within a flow 

region;

Kh is the horizontal hydraulic conductivity in the 

surficial aquifer, in feet per day;

H is the total head drop across the considered 

flow region, in feet;

D is the effective depth of the horizontal flow 

intercepted by the lake, in feet; and

n is the number of equipotential drops along the 

considered flow region.

If 1-ft contour intervals are used to describe the 

water-table altitude, then H is equal to n, and the 

equation reduces to

Q = mKhD (21)

The horizontal flow component contributing 

inflow to the lake is assumed to be bounded above and 

below by no-flow boundaries. In reality, near the 

margin of the lake, near-vertical flow lines converge 

and terminate along a seepage face in the water table 

adjacent to the lake, as well as along the lakebed. In 

this analysis, however, vertical flow near the lake is 

ignored. All of the water that flows horizontally 

toward the lake at some distance away from the lake 

margin is assumed to discharge ultimately into the 

lake. This analysis ignores potential losses of ground 

water due to evapotranspiration in the water table near 

the edge of the lake.

The flow system is bounded laterally by no-flow 

boundaries that are generally coincident with the basin 

drainage divide. In the northwestern corner of the 

basin, however, this boundary is defined by the stage 

of Terrie Pond (fig. 9).

The effective depth (D) of the ground-water 

inflow intercepted by a lake greatly influences the 

magnitude of calculated flows to lakes but is difficult 

to accurately define. Like Lake Lucerne, many lakes 

partially penetrate the surficial aquifer and intercept 

only a fraction of the total horizontal flow. The 

fraction of flow intercepted depends upon such 

hydrogeologic factors as lake and aquifer geometry 

(Winter and Pfannkuch, 1984), the distribution of 

anisotropy and hydraulic conductivity in the groundwater basin (Winter, 1976), and the configuration of 

the water table (Munter and Anderson, 1981; Winter, 

1981a, 1983).

At Lake Lucerne, D is estimated to be the 

saturated thickness of the surficial aquifer above the 

vertical flow divides at sites 1PN, 2PN, and 3PN. The 

monthly average depth for these three sites ranged 

from 6 to 26 ft and was determined from plots of the 

cross-section head distribution around the lake. When 

head gradients were downward at all depths in the 

surficial aquifer, D was estimated to be 6 ft. The 

annual average value of D calculated by this method 

was equal to 16 ft.

By using this annual average value of D, the 

steady-state inflow to Lake Lucerne was calculated for 

the period between October 1985 and September 

1986. The average annual water-table configuration 

used for this analysis was the mean of the 12 monthly 

average water levels for this period (fig. 31A). 

Because seasonal rises and declines in the water table 

around Lake Lucerne are nearly equal (thus, the 

annual average change in aquifer storage is 

approximately zero), this average is a good 

approximation of steady-state conditions in the 

ground-water basin. A single representative value of 

horizontal hydraulic conductivity (Kh) of 8 ft/d was 

used in all of the flow-net calculations.

Flow nets also were used to calculate monthly 

average rates of ground-water inflow to Lake Lucerne. 

This analysis assumes no substantial change in aquifer 

storage and steady flow conditions for each month. 

Steady-state conditions are closely approximated in 

most months, as the monthly change in water-table 

altitude is often small in relation to the saturated 

thickness of the aquifer. In addition, the time required to 

establish steady flow rates in the porous surficial 

deposits is expected to be significantly less than a 

month.

The most significant departure from steady-state 

conditions occurred during June 1986, when a 

transient recharge mound was detected in the water 

table near the lake. A similar recharge mound was 

detected in the water table during the summer of 1985 

for the 3-week period July 25 to August 13, 1985 (Lee 

and others, 1991). A comparison of the flow nets for 

June 1986 and the preceding month of May shows that 

the number of stream tubes increases dramatically in 

June as a result of the steep head gradients associated 

with the recharge mounds (fig. 31B and 31C). The 

depth of the inflow component, however, is much 

smaller for June, as the transient recharge mounds 

caused a downward head gradient to occur between all 

depths in the nested observation wells.
43

To compute the ground-water inflow during 

June by flow-net analysis, four assumptions were 

made: (1) a water-table mound coincided with the 

contour of the lake in the area of site 2PN (fig. 31C), 

(2) a flow divide existed in the center of this mound 

with a head value equal to the head measured in well 

2PN-9, (3) the mound persisted unchanged for the 

month of June, and (4) D was equal to 6 ft. The results 

of calculations for June indicate that transient recharge 

mounds can contribute large quantities of groundwater inflow (fig. 32).

Figure 31. Flow-net diagrams (A) for the 1986 water year annual average, (B) for May 20, 1986, and (C) for 

June 24, 1986, water-table configurations.

Ground-Water Inflow Rates

The average inflow rate for the 1986 water year 

from the flow-net analysis was 3,900 ft3

/d, or an 

equivalent annual rise of 0.88 ft (10.5 in.) of depth over 

the area of the lake (fig. 32). The highest monthly 

ground-water inflow to Lake Lucerne occurred during 

October and November 1985. These months had the 

highest water-table configuration but lagged behind the 

highest rainfall months of July and August 1985. 

Ground-water inflow decreased steadily after October to 

an annual minimum in March (fig. 32).
44 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

Ground-water inflow to Lake Lucerne increased 

slightly between March and May, even though the 

water table surrounding the lake declined steadily. 

Inflow increased slightly during these months because 

the lake stage declined faster than the surrounding 

water table, which increased the water-table gradient 

toward the lake (fig. 32). Transient recharge mounds 

caused a twofold increase in ground-water inflow in 

June compared with May (fig. 32). The absence of a 

steady increase in the inflow rate between July and 

September 1986 probably resulted from the 

abnormally low precipitation during these months and 

the timelag between rainfall and recharge to the 

surficial aquifer. As a result, inflow in September 

1986 is less than half that in the previous October.

Errors in Ground-Water Inflow Rates

Errors in the estimates of the steady-state 

ground-water inflow to Lake Lucerne resulted from 

uncertainties in the value of hydraulic conductivity 

(Kh), hydraulic gradients, and effective depth (D). 

Errors also were introduced due to departures from 

steady-state flow conditions. Transient recharge 

mounds represent one such unsteady contribution of 

ground-water inflow. Similar recharge mounds were 

not observed later in the summer, regardless of the 

magnitude of later rainfall events. This could indicate 

less recharge to the water table and the potential for 

overland flow from the area immediately concentric to 

the lake during prolonged or high-intensity storms. 

Alternately, recharge to the water table could be 

followed by a rapid pulse of transient ground-water 

inflow. For example, Lichtler and others (1976) 

described transient ground-water inflows in their study 

of Lake Johio in central Florida. The unsteady inflow 

contribution that they estimated from a 75-ft-wide 

strip around the lake, however, was insignificant 

compared with total ground-water inflow.

The total error in the ground-water inflow can 

be computed using equation 6. Estimates of the 

uncertainty in each of the inflow variables are made in 

order to quantify the possible error in the inflow 

values. The error in the inflow is dominated by the 

large uncertainty in Kh . The standard error of 

estimate for hydraulic conductivities can be expected 

to be 100 percent of the estimated value or even higher 

(Winter, 1981b). Assumed errors of 25 percent for the 

effective depth and hydraulic gradient (number of 

stream tubes) estimates contribute only moderately to 

the total error. By use of equation 6, the error in the 

estimate of annual average ground-water inflow is 

computed to be 106 percent:

This error indicates annual ground-water inflow could 

potentially range from a negligible amount to as much 

as 21.4 in.

Lake Leakage

Unlike ground-water inflow, estimates of 

leakage from Lake Lucerne cannot reasonably be 

determined independently of other hydrologic-budget 

components. This limitation results from the lack of 

hydrogeologic information in the sublake region. An 

independent leakage calculation would require a 

description of the geometry and the hydraulic 

characteristics of the sublake region, as well as a 

complete description of the head distribution in the 

sublake region. Although marine seismic-reflection 

data have allowed the distribution of geologic 

materials in the sublake region to be inferred, the 

hydraulic characteristics of these materials, including 

lake sediments, remain unknown.

For this analysis, the leakage from Lake 

Lucerne for a 3-week period was derived from the 

residual of the hydrologic-budget equation. This 

estimate of leakage was then used in conjunction with 

available hydrogeologic data and Darcy’s law to 

calculate a single, spatially integrated value of 

vertical hydraulic conductivity below the lake ( ). 

Figure 32. Monthly and total annual ground-water inflow to 

Lake Lucerne for the 1986 water year.

0

0.5

1.0

1.5

2.0

2.5

2

1.4

1.1

0.8

0.5 0.4 0.5 0.6

1.2

0.6 0.5

0.9

GROUND-WATER INFLOW,

TOTAL ANNUAL GROUND-WATER INFLOW = 10.5 INCHES

IN INCHES PER MONTH

6

4

2

0

GROUND-WATER INFLOW,

IN CENTIMETERS PER MONTH

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT 

1985 1986

1986 WATER YEAR

eQ ( ) 1.00 2 ( ) 0.25 2+ +( ) 0.25

2

=

eQ = 106 percent

vsub
45

With this value of , annual and monthly estimates 

of leakage were computed by using Darcy’s law.

This same general approach has been applied in 

other studies in Florida (Hughes, 1974; Henderson, 

1983; Henderson and others, 1985). These studies, 

however, gave little regard to the importance of errors 

in individual budget components on the residual term. 

Much of this error comes from short-term estimates of 

lake evaporation derived from pan-evaporation data. 

The leakage rate derived in this analysis is 

significantly improved over that of previous analyses 

by the availability of more accurate short-term 

estimates of lake evaporation and also by 

consideration of the errors in the hydrologic budget. 

In addition, physical information for the flow system 

at Lake Lucerne provided by field observations and 

numerical modeling provides the basis for 

conceptualizing the vertical flow system and for 

defining the area of leakage outflow.

Flow-Net Assumptions

A simplified flow net was used to calculate the 

vertical leakage beneath the lake. The flow system 

was represented as a vertical column, or cylinder. The 

top of the cylinder was roughly coincident with the 

lakebed, and the bottom was coincident with the depth 

of well 1PN-155 in the Upper Floridan aquifer, giving 

the cylinder a height of 128 ft (fig. 33). The area of 

the top and bottom of the cylinder is the projected area 

of the lakebed through which vertical leakage occurs 

(fig. 33). The vertical flow rate through this cylinder 

can be computed from a simplified, one-dimensional 

flow analysis using the following form of Darcy’s law:

(22)

where

QGO is the leakage rate through the lakebed, in 

cubic feet per day;

Kv

sub is a spatially averaged value of vertical 

hydraulic conductivity in the sublake area, 

in feet per day;

dh/dz is the vertical head gradient between the 

lakebed and the open interval to well 1PN155; and

Aproj is the projected area of outflow of the lakebed, in square feet.

As an approximation, leakage is assumed to 

occur through the lakebed below the 12-ft depth 

contour (a projected area of 917,000 ft2), or an area 

equal to 56 percent of the average area of the lake 

surface. This area also is the mean of the leakage 

areas predicted by the model for the high and low 

water-level conditions.

The average vertical head gradients below the 

lake (dh/dz) were computed on an annual and monthly 

basis, as well as for the 3-week period when leakage 

was estimated by using daily lake stage and the 

predicted daily head in well 1PN-155 (figs. 34 and 

35). Daily average heads in well 1PN-155 were 

predicted from a linear regression between periodic 

head measurements in well 1PN-155 and continuously 

recorded heads in the Lake Alfred deep well near Lake 

Alfred (fig. 2) for the 1986 water year (U.S. 

Geological Survey, 1986) (R = 0.99, standard error 

(Se) = 0.33 ft). The high correlation between heads at 

the two locations indicates that irrigation pumping 

around Lake Lucerne not only controlled heads in the 

Lake Lucerne wells (Lee and others, 1991), but also 

largely controlled heads in the Lake Alfred well. 

Drawdowns in the Lake Alfred well also were 

considerably smaller than those in well 1PN-155, 

consistent with moving away from the center of 

pumping.

Estimation of Sublake Vertical Hydraulic Conductivity

To determine , leakage was calculated by 

solving the hydrologic-budget equation for the 

3 weeks from April 15 to May 5, l986 (thermal survey 

periods 30, 31, and 32 in the energy-budget 

evaporation analysis). During this time, no rain fell, 

ground-water inflow to the lake was near minimum, 

and the downward head gradient beneath the lake was 

at its maximum.

In the absence of precipitation, the residual term 

of the hydrologic-budget equation is equal to leakage 

plus or minus the cumulative error of estimating the 

lake evaporation, ground-water inflow, and change in 

lake storage (eq. 1). Therefore, a confidence interval 

was computed for leakage by adding and subtracting 

the cumulative error from leakage. The energy-budget 

evaporation estimate for the 3-week period (0.442 ft) 

was assumed to have error equal to the mean monthly 

error for April and May (17.6 percent) (table 1). 

Ground-water inflow during this period (0.032 ft) is 

estimated to have an error equal to 106 percent, and 

change in lake storage (0.51 ft) is estimated to have an 

error of 5 percent (Winter, 1981b).

vsub

QGO Kvsub( ) dh/dz Aproj =

vsub
46 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

Although the maximum probable error is large, 

it does not entirely explain the residual term, and 

leakage is indicated. Possible leakage losses for the 3-

week period fall in the confidence interval from 0.19 ft 

(2.3 in.) to 0.01 ft (0.12 in.). values, calculated 

by substituting these estimates of leakage into 

equation 22, fall in a range from 0.17 to 0.01 ft/d, or 

0.09±0.08 ft/d. These estimates of are supported 

by the modeling results in the previous section. Those 

results could indicate that collapse features below the 

lake are infilled with sands and clays of the surficial 

Figure 33. Conceptual model of the leakage from Lake Lucerne.

Kvsub

vsub

aquifer, which had a Kh ranging from 8 ft/d in the 

upper part of the surficial aquifer to 2 ft/d in the lower 

part. Modeling results also could indicate that 

anisotropy in these deposits was on the order of 100, 

or that model is approximately 0.08 to 0.02 ft/d, 

within the 0.17 to 0.01 ft/d interval estimated in this 

analysis by using Darcy’s law. These estimates 

range from two to three orders of magnitude larger 

than the confining unit Kv modeled in the region 

around the lake.

vsub

vsub
47

Leakage Rates

Monthly average leakage rates from Lake 

Lucerne were calculated using = 0.09 ft/d as a 

representative intermediate value. Leakage area was 

held constant for all months, allowing leakage to vary 

only as a function of the vertical head gradient. Thus, 

monthly leakage rates (fig. 36) are proportional to 

monthly variations in dh/dz (fig. 35). Monthly leakage 

rates were largest in May (1.82 in.) and smallest in 

September (0.76 in.) (fig. 36). Total annual leakage 

from the lake, based on the average monthly rates, was 

12.6 in.

To estimate the effect of ground-water pumping 

on leakage, a minimum monthly average head of 

119 ft above sea level was set in the Upper Floridan 

aquifer to simulate nonpumping conditions, and 

leakage rates were recomputed. This criterion is fairly 

liberal, as daily heads in a given month can fluctuate 

significantly around this value (fig. 34). This altitude 

was chosen because it is slightly below the 

predevelopment potentiometric surface described at 

Lake Lucerne by Johnston and others (1980). The 

apparent trend in the potentiometric surface shown in 

figure 13 generally is above this altitude.

Under hypothetical nonpumping conditions, 

annual leakage from Lake Lucerne is 10.3 in., or 

nearly equal to ground-water inflow (fig. 37). The 

estimated leakage induced by pumping is 2.3 in/yr, or 

Figure 34. Predicted monthly mean, minimum, and 

maximum daily values of the head in well 1PN-155 for the 

1986 water year.

110

112

114

116

118

120

122

MINIMUM MEAN MAXIMUM

108

36.5

35.5

34.5

33.5

PREDICTED HEAD IN WELL 1PN-155, 

IN METERS ABOVE SEA LEVEL

PREDICTED HEAD IN WELL 1PN-155,

IN FEET ABOVE SEA LEVEL

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT 

1985 1986

1986 WATER YEAR

Figure 35. Predicted monthly mean, minimum, and 

maximum daily values of the downward head difference 

between Lake Lucerne and well 1PN-155 for the 1986 water 

year.

0

2

4

6

8

10

12

14

16

MINIMUM MEAN MAXIMUM

PREDICTED DOWNWARD HEAD

DIFFERENCE, IN FEET

4

3

2

1

0

PREDICTED DOWNWARD HEAD

DIFFERENCE, IN METERS

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT 

1985 1986

1986 WATER YEAR

Kvsub

Figure 36. Monthly and total annual leakage from Lake 

Lucerne for the 1986 water year.

0

0.5

1.0

1.5

2.0

0.8

0.9 0.9 0.9 0.9

1

1.6

1.8

1.3

1

0.8

0.7

LEAKAGE, IN INCHES PER MONTH

TOTAL ANNUAL LEAKAGE = 12.6 INCHES

4

2

0

LEAKAGE, IN 

CENTIMETERS PER MONTH

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT 

1985 1986

1986 WATER YEAR

Figure 37. Monthly and total annual leakage from Lake 

Lucerne under hypothetical, nonpumping conditions for the 

1986 water year.

0

0.5

1.0

1.5

2.0

0.8

0.9 0.9 0.9 0.9

1.0 1.0

0.8 0.8 0.8 0.8

0.7

LEAKAGE, IN INCHES PER MONTH

TOTAL ANNUAL LEAKAGE = 10.3 INCHES

4

2

0

LEAKAGE, IN CENTIMETERS PER MONTH 

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT 

1985 1986

1986 WATER YEAR
48 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

2.25 million gallons (Mgal). Although this amount 

can seem small if considered over the entire year, 

nearly all of this additional leakage (92 percent) 

occurred during the 3 months of April, May, and June.

With pumping, leakage exceeded ground-water 

inflow to Lake Lucerne during the 1986 water year by 

2.1 in. (fig. 38). Net ground-water flow to Lake 

Lucerne, defined as ground-water inflow minus 

leakage, was positive October through December. Net 

flow then became negative, indicating net outflow, as 

ground-water inflow declined and leakage increased 

and reached a minimum value of −1.22 in. in May 1986. 

Net flow returned to a positive value by September, 

probably as a result of deficit rainfall during June 

through September.

Net ground-water flow steadily decreased 

between March and May despite a small increase in 

ground-water inflow during these months (fig. 38). 

The increase in ground-water inflow resulted from an 

increase in the water-table gradient toward the lake 

due to the rapidly declining lake stage. During this 

period, the lake stage declined faster than the 

surrounding water table for two reasons. The most 

significant of these was the increase in lake 

evaporation. Lake evaporation nearly doubled from 

about 0.08 to 0.12 in/d in March to about 0.24 to 

0.28 in/d by early May (fig. 14). The second factor, 

induced leakage, compounded this loss. For the same 

period, leakage nearly doubled from 1.00 in. per 

month in March to 1.8 in. per month in May. The 

increase in ground-water inflow as a result of the 

declining lake stage was too small, however, to keep 

pace with these losses, and the net flow continued to 

decline (fig. 38).

Errors in Lake Leakage Rates

Errors in leakage estimates result from the 

errors in estimating (0.09±0.08 ft/d, or 

89 percent) and from errors in holding the projected 

area of outflow constant between months. Modeling 

results indicate that the projected area of outflow can 

vary significantly between high and low water-level 

conditions. The varying depth of the ground-water 

inflow component (D) also suggests a reciprocal 

change in the area of outflow. The error in Aproj was 

estimated to be 50 percent. The resulting error in the 

leakage terms, from equation 6, was estimated to be 

102 percent. These errors imply a potential range of 

annual leakage from a negligible amount to a 

maximum of 25.6 in.

Summary of Ground-Water Fluxes

Ground-water fluxes to Lake Lucerne were 

computed for a year that had significantly less rainfall 

(40.88 in.) than the local long-term average 

(50.83 in.). Thus, ground-water inflow to Lake 

Lucerne was possibly well below its long-term 

average due to reduced recharge to the surficial 

aquifer. Although the reduction due to drought 

conditions is not known, reduced ground-water inflow 

might be an important factor contributing to lake-level 

declines.

Leakage during the study year also was 

probably above average due to less recharge and 

increased irrigation pumping relative to other years. 

Long-term water levels in the Lake Alfred well 

indicate that the annual average head in the Upper 

Floridan aquifer was lower during 1986 than during 

the previous 4 years. The mean monthly head 

conditions for April and May 1986 also were below 

the means for these months in the previous 4 years. A 

significantly lower annual average head condition 

occurred during 1981, and average head conditions, 

lower but similar to 1986, occurred in 1976 and 1977. 

Therefore, although heads in the Upper Floridan 

aquifer during the 1986 water year were lower than in 

recent years, they were within the range of head values 

recorded between 1976 and 1986.

The drop in the stage of Lake Lucerne due to 

leakage induced by ground-water pumping during the 

1986 water year was estimated to be equal to 2.3 in. 

This quantity represented approximately a 20-percent 

increase in the annual leakage from Lake Lucerne 

compared with hypothetical nonpumping conditions. 

Ninety-two percent of this increased loss occurred 

Figure 38. Monthly and total annual net ground-water flow 

to Lake Lucerne for the 1986 water year.

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

1.2

0.5

0.2

-0.1

-0.4

-0.6

-1.1 -1.2

-0.1

-0.4 -0.3

0.2

NET FLOW, IN INCHES PER MONTH

TOTAL ANNUAL NET FLOW = -2.1 INCHES

3

2

1

0

-1

-2

-3

NET FLOW, IN CENTIMETERS PER MONTH

OCT NOV DEC JAN FEB MAR APR MAYJUNE JULY AUG SEPT 

1985 1986

1986 WATER YEAR

vsub
Influence of Evaporation, Ground Water, and Uncertainty in the Hydrologic Budget 49

during the months of April, May, and June 1986. In 

the short term, this recurring annual loss might appear 

to be compensated for if it is accompanied by average 

and above average annual rainfall and ground-water 

inflow. During drought periods, however, the 

accumulation of induced leakage losses over a 

succession of years will accelerate the natural decline 

in lake stage. As a result, the lake might decline well 

below minimum levels encountered during drought 

periods prior to pumping. Over the long-term average, 

induced leakage will result in less lake storage and, in 

turn, lower lake levels, than existed prior to pumping.

INFLUENCE OF EVAPORATION, GROUND 

WATER, AND UNCERTAINTY

IN THE HYDROLOGIC BUDGET

The hydrologic budget of Lake Lucerne is a 

statement of the conservation of water mass for the 

lake: the change in the volume of the lake is equal to 

the quantity of water added to the lake by rainfall and 

ground-water inflow minus the water removed from 

the lake by evaporation and leakage. Measured or 

computed flux rates for each of these processes allow 

the true hydrologic budget to be approximated and the 

relative importance of each of the fluxes to be 

compared. Monthly rates for each of these fluxes and 

associated measurement errors are presented in 

figure 39. The rainfall data are from daily 

measurements from a standard nonrecording rain 

gage. Lake storage changes are based on hourly stage 

data (Lee and others, 1991).

Hydrologic-Budget Results

Precipitation and evaporation are the major 

components of the hydrologic budget of Lake Lucerne 

on both a monthly and an annual basis, but groundwater fluxes are significant. Over the entire budget 

year (October 1, 1985, to September 30, 1986), 

precipitation was about 10 in. below the long-term 

average; however, it still composed about 80 percent 

of the total inflow (precipitation plus ground-water 

inflow). Ground-water inflow contributed 20 percent 

of the total annual inflow. On a monthly basis, ground 

water contributed a more varying amount of the total 

inflow to the lake, from 5 to 72 percent. It exceeded 

monthly precipitation only once, in November 1985, 

and was nearly equal to precipitation in March and 

April 1986.

Over the year, evaporation accounted for 

82 percent of the total outflow (evaporation plus 

leakage), and lake leakage accounted for 18 percent. 

For the study year, evaporation was about 8 in. higher 

than the estimated long-term average for the region. 

Reduced cloud cover and an associated increase in 

incoming solar radiation would be expected to 

increase evaporation during a drought year. Monthly 

leakage was more consistent than monthly groundwater inflow, varying only from 10 to 30 percent of the 

total outflow from the lake. Leakage made up the 

smallest percentage of the outflow in September 1986 

and made up the largest percentage of the total outflow 

in January and February 1986. Leakage rates were 

highest in May 1986 but represented a smaller 

percentage of the total outflow because evaporation 

was also highest in this month.

Pumping increased the relative importance of 

leakage in the annual budget only moderately (from 15 

to 18 percent of the total outflow) but caused a 

significant increase in certain months. Because 

evaporation was the dominant outflow, pumping did 

not translate into a large increase in the total annual 

outflow, but it did cause a substantial increase in 

monthly outflows between April and July 1986. 

Pumping increased the total monthly outflow by 

11 percent in May and by 7 and 8 percent, 

respectively, in April and June. Pumping increased the 

annual leakage rate by about 20 percent.

The large uncertainty in the ground-water flux 

terms contributes inaccuracy to the overall budget. 

The maximum probable errors associated with the 

ground-water inflow and leakage estimates are large 

(106 and 102 percent, respectively) and broaden the 

interpretation of the role of ground water in the 

hydrologic budget of the lake. Because of these large 

confidence limits, a smaller probability exists that 

ground-water inflow could contribute negligibly to the 

total inflow, or it could contribute as much as 

58 percent. Similarly, leakage could potentially range 

from a negligibly small amount to 53 percent of the 

annual outflow. The large errors in the ground-water 

fluxes primarily indicate the uncertainty in the 

hydraulic conductivity of the geologic materials 

surrounding and underlying the lake. They do not 

indicate uncertainty in the overall patterns of groundwater inflow and leakage around the lake, which are 

based on the head distribution around the lake.
50 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

Figure 39. Monthly values of hydrologic-budget components of Lake Lucerne for the 1986 water year: (

A) precipitation, (

B) evaporat

(D) leakage, and (

E) ground-water inflow.

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

02468

1012

PRECIPITATION, IN INCHES

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

 OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

02468

1012

EVAPORATION, IN INCHES

 OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT

024

LEAKAGE, IN INCHES OCT NOV DEC JAN FEB MAR 

-10

-8-6-4-2

0246

CHANGE IN STORAGE, IN INCHES

1985 1986 1985 1986

1985 1986 1985 1986

1985 

GROUND-WATER INFLOW,

IN INCHES

A. B. C.

D. E. 5

31

024531

EXPLANAT

 MAXIMUM P

 IN HYDROL

COMPONEN

1986 WATER YEAR

1986 WATER YEAR

1986 WATER YEAR

1986 WAT

1986 WATER YEAR

2824201612840

2824201612840

12840

12840

PRECIPITATION, IN CENTIMETERS

EVAPORATION, IN CENTIMETERS

LEAKAGE, IN CENTIMETERS

GROUND-WATER INFLOW,

IN CENTIMETERS
Influence of Evaporation, Ground Water, and Uncertainty in the Hydrologic Budget 51

Evaluation of Budget Error

The error in the hydrologic budget is the 

difference between the observed change in storage and 

that predicted by the right-hand side of the hydrologicbudget equation (eq. 1). When the annual values for 

budget terms are put into the right side of equation 1, 

the predicted annual change in storage is a decline 

(indicated by a negative sign) of –19.1 in. During this 

period, however, the measured decline in lake stage 

was only –9.2 in. The result is an error in the annual 

hydrologic-budget equation of –9.9 in. Referring to 

equations 1 and 3,

ERbudget, annual = ∆S – P + E – GI + GO

= – 9.2 – 40.9+57.9 –10.5+12.6 = – 9.9 in.

The annual budget error is much smaller than the 

probable error in the hydrologic budget, which is 

computed from the probable measurement errors of 

terms in the hydrologic budget. Referring to equations 

1 and 4,

The errors in the annual rainfall and change in 

storage are estimated to be 10 percent and 5 percent, 

respectively (Winter, 1981b). Error in the annual 

energy-budget evaporation term is 16.4 percent, and 

errors in the ground-water inflow and leakage terms 

are 106 and 102 percent, respectively.

Knowledge of the overall hydrologic budget can 

provide insight into how well individual terms are 

quantified. The calculation for probable error 

indicates that the error in the hydrologic budget is 

dominated by the error in the ground-water terms. 

Thus, the budget error term could contain useful 

information about the ground-water flux terms, but 

this information must first be extracted from the 

remaining, randomly distributed error.

To investigate the possibility that the budget 

error term is not entirely random, a correlation matrix 

was defined between monthly values of all of the 

terms in the hydrologic budget and the monthly error 

term. Only two terms had a correlation with the error 

of 50 percent or higher: leakage and net ground-water 

flow. Leakage (GO) was linearly correlated with error 

(R = 0.70, probability level = 0.01, Se = 0.82 in.). A 

poor correlation exists between ground-water inflow 

and error, but because of the correlation with leakage, 

net ground-water flow (ground-water inflow minus 

leakage) has the next best correlation with the error 

term. This correlation is weak and of questionable 

statistical significance (R = 0.60, probability level = 

0.04, Se = 0.90 in.); however, it does indicate a 

positive correlation between these two variables.

The weak correlation between monthly budget 

error and any budget term is not surprising, 

considering the potentially random nature of the error 

component. The correlation is significant from a 

qualitative viewpoint, but the rather poor regression 

relation prohibits strong quantitative interpretation. 

Nonetheless, the correlation with leakage does explain 

49 percent of the variance in the error term. If the net 

ground-water flow to Lake Lucerne was computed as 

the residual term to the hydrologic-budget equation, 

the influence of this correlation would be incorporated 

into the result.

To explore the possible physical significance of 

the budget error term, monthly net ground-water flow 

was derived as the residual term to the hydrologicbudget equation, and this estimate was regressed 

against the calculated net ground-water flow. The 

relatively high correlation between net ground-water 

flow estimated by these two markedly different 

methods (R = 0.83, probability level = 0.001, Se = 0.90 

in.) implies that the physical significance of net 

ground water derived as a budget residual is not 

overwhelmed by the errors that the term contains 

(fig. 40). This occurs in spite of the fact that the errors 

associated with calculating net ground water as a 

residual term are often larger than estimates of 

monthly net ground-water flow (table 5).

ERprob %e

∆S ( ) •∆S 2 %eP ( ) •P 2 %eE ( ) •E 2 = + + +

%e

GI ( ) •GI 2 %eGO + ( ) •GO

2

ERprob ( ) 0.05 9.2 • 2 ( ) 0.10 40.9 • 2 + 0.164 57.9 +( ) • 2 = +

( ) 1.06 10.5 • 2 ( ) 1.02 12.6 • 2 +

= ( ) 0.21 +++ + ( ) 16.7 ( ) 90.2 ( ) 123.9 (168.4 )

= 20.0 in.
52 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

The residual net ground-water term unavoidably 

includes random errors as well as additional physical 

information. The fact that a significant part of the 

budget error is correlated with a physical process, 

namely leakage (and, thus, net ground-water flow), 

however, encourages some reevaluation of our 

independent estimates of ground-water inflow and 

leakage.

The monthly residual net ground-water flow 

indicates that both ground-water inflow and leakage 

rates are greater than those estimated by flow-net 

analysis. For example, the residual net ground-water 

flow indicates net inflow occurred in 7 months as 

opposed to only 4 months using flow-net-derived 

values (fig. 41). In addition, for most months when 

the residual net ground-water flow indicated net 

inflow, this net inflow is greater than the gross groundwater inflow estimated by flow-net analysis (compare 

table 5 with fig. 32). Thus, these larger residual net 

inflows cannot be arrived at by simply reducing 

leakage. Alternatively, the negative residual net flow 

for May 1986 indicates substantially greater outflow 

than was estimated by flow-net analysis (fig. 41).

Revised Estimates of Ground-Water Inflow 

and Leakage

Monthly ground-water inflow and leakage were 

recomputed on the basis of the relation shown in 

figure 40 and assuming a simple physical model. 

Revised ground-water inflow and leakage rates were 

each defined as the product of the original estimate 

and some constant coefficient. To determine these 

coefficients, the monthly residual net flow was 

regressed against monthly values of GI and GO by 

using multiple linear regression. This regression, 

which was forced through the origin (R = 0.82, 

probability level = 0.004, Se = 1.0 in.), predicts a 

coefficient of 2.2 for ground-water inflow and a 

coefficient of 1.4 for leakage. The monthly net 

ground-water flows derived from these revised 

estimates of ground-water inflow and leakage are 

shown in figure 41.

Table 5. Monthly residual net ground-water flow to Lake 

Lucerne and the associated error

[P, precipitation; ei , error in term i; E, evaporation; ∆S, change in storage; 

RNGW, residual net ground-water flow. All values are in inches]

Year and 

month P eP E eE ∆S e∆S RNGW eRNGW

1985:

October 3.27 0.33 4.70 1.26 1.68 0.08 3.11 1.30

November .55 .05 3.49 .98 – .84 .04 2.10 .98

December 2.29 .23 2.65 .61 – .60 .03 – .24 .65

1986:

January 3.44 .34 2.29 .63 1.92 .10 .77 .72

February 2.41 .24 2.56 .51 0 0 .15 .56

March 2.74 .27 4.32 .67 –1.56 .08 .02 .73

April .61 .06 7.16 1.17 –7.20 .36 – .65 1.22

May .93 .09 7.12 1.35 –8.52 .43 –2.33 1.42

June 7.97 .80 5.63 .72 2.76 .14 .42 1.08

July 3.97 .40 6.04 .82 –2.28 – .11 – .21 .92

August 9.89 .99 6.08 .82 5.40 .27 1.59 1.31

September 2.81 .28 5.83 .91 0 0 3.02 .95

Total 40.88 57.87 –9.24

-1.5 -1.0 -0.5 0 0.5 1.0 1.5

-3

-2

-1

0

1

2

3

4

NET GROUND-WATER FLOW, IN INCHES

RESIDUAL NET GROUND-WATER FLOW, 

IN INCHES

RESIDUAL NET GROUND-WATER FLOW, 

IN CENTIMETERS

8

6

4

2

0

-2

-4

-6

Figure 40. Monthy relation between the residual net 

ground-water flow and the calculated net ground-water flow 

to Lake Lucerne for the 1986 water year. Figure 41. Monthly calculated, residual, and revised net 

ground-water flow to Lake Lucerne for the 1986 water year.

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT 

-3

-2

-1

0

1

2

3

4

CALCULATED

RESIDUAL

REVISED

1985 1986

1986 WATER YEAR

8

6

4

2

0

-2

-4

-6

NET GROUND-WATER FLOW,

IN INCHES

NET GROUND-WATER FLOW, 

IN CENTIMETERS
Summary and Conclusions 53

Reevaluation of the ground-water inflow and 

leakage terms on this basis indicates that leakage 

would increase by about 40 percent over the original 

estimate (17.5 instead of 12.6 in/yr). Ground-water 

inflow would more than double, an increase of 

120 percent. Ground-water inflow would total 

23.6 in/yr, and net ground-water flow would be 

+6.1 in. The remaining error in the annual hydrologic 

budget would be greatly reduced, from −9.9 in. to 

+1.7 in. The monthly budget error also would no 

longer correlate with terms in the hydrologic budget.

The importance of ground-water inflow to the 

hydrologic budget is significantly increased using the 

revised values. As a result, ground-water inflow 

would contribute about 37 percent of the total annual 

inflow. Annual leakage increases moderately from 18 

to 23 percent of the total outflow, and leakage ranges 

from 13 to 35 percent of the total monthly outflow. 

The relative effect of pumping on leakage increases 

for the revised ground-water fluxes. Pumping would 

induce an additional 3.2 in/yr of leakage instead of the 

original estimate of 2.3 in/yr.

These revised estimates also have substantial 

uncertainty, as there is a substantial standard error in 

the regression relation between the net flows derived 

from flow-net analysis and those derived as a residual 

to the hydrologic-budget equation. At the least, this 

relation implies that the flow-net estimates of the 

ground-water fluxes are too low. A more conservative 

conclusion might be that ground-water fluxes lie 

within the bounds defined by the two estimates.

Differences between the two estimates of 

ground-water inflow and leakage could be explained 

easily by the large uncertainty in the estimates of Kh

and Kv sub . The use of a constant coefficient to GI and 

GO is analogous to a constant increase in a nonvarying 

value such as hydraulic conductivity. The effect of 

other time-varying factors that influence ground-water 

inflow and leakage (for example, transient inflows, the 

number of stream tubes, estimated depth of groundwater inflow, and area of leakage) would not be 

expected to be improved by a constant correction 

factor. In addition, the error in these terms is 

considered to be less than that in the hydraulic 

conductivity.

The justification for reinterpreting ground-water 

fluxes on the basis of the hydrologic-budget equation 

is founded on the conclusion that the budget error is 

not completely random, but instead is significantly 

correlated with the estimate of ground-water leakage 

and net ground-water flow. This correlation supports 

the other lines of evidence that indicate part of the 

budget error could be associated with systematic error 

(bias) in estimates of ground-water fluxes. The 

outcome of the analysis indicates that, although still 

second in importance to direct precipitation and 

evaporation, ground-water fluxes probably are more 

important to the hydrologic budget of Lake Lucerne 

than first determined. Leakage is estimated to have 

contributed about 23 percent of the total outflow from 

Lake Lucerne, and ground-water inflow about 

37 percent of the total inflow to the lake during the 

period of study.

SUMMARY AND CONCLUSIONS

Constructing descriptive hydrologic budgets of 

lakes requires better estimates of short-term 

evaporative losses and the ground-water interactions 

with lakes. This is particularly true for the many 

seepage lakes in Florida for which leakage and 

evaporation are the only water losses from the lake. 

Understanding both of these processes also is a critical 

step toward determining the added influence of 

leakage induced by pumping from the underlying 

Upper Floridan aquifer.

In a hydrologic budget computed for the 1-yr 

period from October 1, 1985, through September 30, 

1986, evaporation was the dominant outflow from 

Lake Lucerne on both a monthly and an annual basis. 

Annual evaporation computed by the energy-budget 

method was 57.87 in. and was nearly equal to the 

estimate of 57.39 in. from the simpler, theoretically 

based mass-transfer method. The annual energybudget estimate had the smallest maximum probable 

error, 16.4 percent, and was the most accurate method. 

This error was considerably less than the error in the 

annual mass-transfer estimate (31 percent), even when 

the effects of atmospheric stability were accounted for 

(21 percent). Evaporation for this 52-week period was 

higher than the long-term average (estimated from pan 

evaporation), probably as a result of the climatological 

conditions that resulted in the drought. The annual 

rainfall of 40.88 in. for the study period was about 

10 in. below the long-term average.

The energy-budget method provided the most 

accurate short-term estimates of evaporation. Shortterm evaporation estimates were made for daily, 

weekly, and monthly time periods. April had the 

highest monthly evaporation rate (7.16 in.) and 

January had the lowest (2.29 in.). Errors in energybudget evaporation ranged from 12.8 percent to 

27.6 percent of monthly values.
54 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

Daily evaporation rates calculated by the 

energy-budget method were affected by unrealistic 

Bowen ratios for 21 days, or 5.8 percent of the period 

of record. This occurred mostly during the winter 

months of the study, when evaporation rates were low. 

Evaporation rates for the remaining days were 

expected to have a maximum probable error higher 

than the annual error because of the higher errors in 

defining daily climatic conditions.

Pronounced seasonal differences existed 

between the energy-budget and mass-transfer 

methods, primarily as a result of the effects of 

atmospheric stability on the mass-transfer method. As 

a result, the mass-transfer evaporation overpredicted 

the energy-budget evaporation in the winter and 

underpredicted it in the summer. At Lake Lucerne, 

accounting for the effects of atmospheric stability in 

the mass-transfer method reduced the error in the 

annual evaporation.

Free water-surface evaporation from a pan at 

Lake Lucerne (FWSp) was a better predictor of actual 

lake evaporation (energy budget) than it was of its 

theoretical counterpart, the free water-surface 

evaporation computed for Lake Lucerne (FWS1). 

FWSp evaporation was 54.54 in/yr, and it 

underestimated lake evaporation calculated by the 

energy budget by 6 percent on an annual basis. On an 

annual basis, the pan coefficient calculated for the 1986 

water year using the Lake Lucerne pan data, or the data 

from the Lake Alfred NOAA site, was 0.73. These 

results agreed well with the long-term annual average 

coefficient of 0.74. The pan coefficient derived from 

the corrected energy-budget evaporation (FWS1) was 

higher, the average for the year being 0.75. 

Significantly larger differences appeared between pan 

coefficients calculated on a monthly basis.

Ground-water interactions with Lake Lucerne 

are controlled by the geologic setting of the lake, 

recharge to the surficial aquifer, and the head in the 

Upper Floridan aquifer. Modeling the steady-state 

ground-water flow patterns along a cross section 

through the Lake Lucerne basin provided a simple tool 

for testing the conceptual and physical model of 

ground-water interactions in a sinkhole-type seepage 

lake. Model results corroborated the presence of 

breaches in the confining unit beneath the lake that 

were inferred from a marine seismic-reflection survey. 

These breaches (where the confining unit is replaced 

by material 200 times more conductive) result in an 

increased hydraulic connection between the Upper 

Floridan aquifer and the surficial aquifer below the 

lake and also provide a preferential flow path for water 

in the surrounding basin to recharge the Upper 

Floridan aquifer.

A model anisotropy of 100 in the surficial 

aquifer best simulated the observed head distribution 

around the lake and the ground-water inflow and 

leakage rates calculated by flow-net analyses. With 

this anisotropy value, the ground-water basin was 

simulated for the seasonal extremes in observed 

ground-water level conditions (May and October). 

The potentiometric surface of the Upper Floridan 

aquifer, which is primarily controlled by local 

pumping for citrus irrigation, showed the largest 

differences between seasonal extremes.

Leakage was more than doubled under the low 

water-level condition compared with the high waterlevel condition, and the rate of ground-water inflow 

was reduced by approximately one-third. Low waterlevel conditions (May) were dominated by leakage 

outflow from 88 percent of the length of the lake cross 

section. Ground-water inflow from the surficial 

aquifer occurred only to a depth of 6 to 8 ft below the 

lake surface. At high water-level conditions 

(October), ground-water inflow occurred to a depth of 

about 16 ft below the lake surface, and leakage was 

predicted to occur from approximately 74 percent of 

the length of the lake cross section. Under both high 

and low water-level conditions, the majority of the 

ground-water inflow occurred near the shallow margin 

of the lakebed.

Low-permeability organic sediments could 

function like a confining unit and inhibit leakage rates 

through deeper, and thus more thickly covered, areas 

of the lake bottom. However, higher leakage rates 

could still occur through elevated regions of the 

lakebed where sediments are thin or absent. 

The conclusions derived from the use of a twodimensional model would be subject to refinements 

using a three-dimensional model. The use of a twodimensional model could explain the inability of the 

model to reproduce the magnitude of upward head 

gradients observed in the surficial aquifer around Lake 

Lucerne. The two-dimensional model also might 

overpredict the length of the lakebed that is 

experiencing leakage and underpredict the depth and 

magnitude of ground-water inflow. Alternately, the 

use of a three-dimensional model could require the use 

of higher vertical hydraulic conductivity in the 

sublake region.
References 55

Monthly ground-water inflow to Lake Lucerne 

calculated by flow-net analysis was highest during and 

for several months after the summer rainy season in 

1985. The highest monthly inflow of 2.0 in. occurred 

in October 1985, although the highest monthly rainfall 

occurred in July and August 1985. Ground-water 

inflows steadily decreased to a minimum value of 

0.4 in. in March 1986. Transient recharge conditions 

resulted in a twofold increase in the ground-water 

inflow to the lake in June over May 1986, but was 

followed in July by lower ground-water inflow rates 

after the transient recharge mounds dissipated. The 

annual ground-water inflow was estimated to equal 

10.5 in/yr. Rainfall was well below normal during the 

1986 water year, particularly July through September 

1986, and probably resulted in ground-water inflow 

rates that were significantly less than the long-term 

average. The error in the independent estimates of 

ground-water inflow was estimated to be 106 percent.

Monthly leakage outflow was directly 

proportional to the downward head gradients below 

the lake and ranged from a minimum of 0.7 in. in 

September 1986 to a maximum of 1.8 in. per month in 

May 1985. Annual leakage was estimated to be 

12.6 in. The annual leakage induced by manmade 

drawdown of the Upper Floridan aquifer was 

estimated to be 2.3 in., or a 22-percent increase in the 

estimated annual leakage without pumping effects. 

Ninety-two percent of the induced leakage occurred in 

April, May, and June 1986. The area of the lake 

bottom that experienced leakage was assumed to be 

constant; however, modeling results indicated that this 

area varies considerably between the seasonal 

extremes of head conditions at Lake Lucerne.

Ground-water inflow is a significant part of the 

hydrologic budget of Lake Lucerne. The flow-net 

estimate of ground-water inflow made up 

approximately 20 percent of the total annual inflow to 

Lake Lucerne. Ground-water inflow would 

presumably make up an even greater part of the total 

inflow in wetter years, as the fraction of ground-water 

recharge lost to evapotranspiration would be smaller.

The flow-net estimate of leakage made up 

18 percent of the annual outflow from the lake and 

ranged from 10 to 28 percent of the monthly outflow. 

Without pumping, leakage would have been reduced 

to 15 percent of the total outflow for the 1986 water 

year. The maximum leakage and evaporation rates 

occurred concurrently in May 1986, causing the 

largest monthly drop in stage, 8.5 in.

The error in the monthly hydrologic budget was 

not random but was correlated with monthly leakage 

and with net ground-water flow. Reinterpreting 

ground-water inflow and leakage from the residual net 

ground-water flow indicates that ground-water inflow 

to Lake Lucerne might be more than twice as high as 

the independent estimate derived from flow-net 

analysis, for a total of 23.6 in/yr. The difference, 

120 percent, between these two estimates of groundwater inflow was slightly greater than the 100-percent 

error attributed to the horizontal hydraulic 

conductivity in the surficial aquifer.

Leakage revised from the analysis of the 

residual net ground-water flow term was 40 percent 

higher than the independent estimate, for an annual 

total of 17.5 in/yr. When using the revised estimates, 

ground-water inflow would increase to 37 percent of 

the total inflow to Lake Lucerne during the 1986 water 

year and would exceed monthly rainfall in October 

through December 1985. Leakage would increase 

only moderately to 23 percent of the total outflow and 

would never approach the monthly loss by 

evaporation.

The revised estimates of ground-water flow also 

had substantial uncertainty in them; however, they 

indicate that ground-water fluxes were greater than the 

independent estimates. The increases indicated by this 

analysis are comparable to the range of uncertainty 

associated with the estimates of hydraulic conductivity 

in the surficial aquifer and sublake region.

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———1983, The interaction of lakes with variably 

saturated porous media: Water Resources Research, 

v. 19, no. 5, p. 1203–1218.

Winter, T.C., and Pfannkuch, H.O., 1984, Effect of 

anisotropy and groundwater system geometry on 

seepage through lakebeds, 2. Numerical simulation 

analysis: Journal of Hydrology, v. 75, p. 239–253.
58 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

APPENDIX A. Energy-Budget Components and Evaporation Calculations for Each 

Thermal Survey Period

Table A1. Summary of energy-budget components and evaporation calculations for each thermal survey period

[Qs, incident shortwave radiation; Qr, reflected shortwave radiation; Qa, incident longwave radiation; Qar, reflected longwave radiation; Qbs, emitted longwave radiation; Qv, advected heat; Qx, change in stored heat; T0, water-surface temperature; EEB, energy-budget evaporation; cal/g, calories per gram; °C, 

degrees Celsius; cm/d, centimeters per day; Q values given in calories per square centimeter per day]

 1985

 1 Oct. 1-7 400.76 17.56 866.33 955.00 20.35 -21.21 580.34 0.26 28.47 0.44

 2 Oct. 8-15 347.03 15.04 872.29 953.37 .53 52.23 580.62 .18 27.96 .28

 3 Oct. 16-21 376.72 16.43 879.36 953.17 4.64 -31.32 580.60 .19 28.00 .45

 4 Oct. 22-28 314.97 13.53 869.35 936.50 .85 -21.31 581.09 .16 27.11 .37

 5 Oct. 29-Nov. 4 311.08 11.76 837.62 929.75 3.63 -139.26 581.49 .29 26.37 .45

 6 Nov. 5-11 329.76 14.07 757.89 888.15 .20 -22.99 583.23 .65 23.21 .21

 7 Nov. 12-18 328.89 14.69 825.71 901.91 .47 23.02 582.70 .09 24.18 .33

 8 Nov. 19-25 221.76 8.09 860.21 905.83 2.43 12.45 582.57 .09 24.42 .24

 9 Nov. 26-Dec. 2 264.12 11.09 838.26 908.16 1.65 -42.03 582.43 .15 24.67 .33

10 Dec. 3-9 239.96 10.79 716.53 868.37 7.49 -129.60 584.07 .68 21.69 .21

11 Dec. 10-16 251.95 11.26 726.73 853.96 2.15 -106.76 584.73 .50 20.49 .25

12 Dec. 17-23 257.14 11.80 640.14 800.77 0 -115.59 586.55 .65 17.19 .20

13 Dec. 24-30 301.69 13.79 621.82 777.42 2.33 -50.58 587.76 .64 14.98 .19

14 Dec. 31-Jan. 6 250.06 10.54 729.26 818.15 7.00 95.26 586.59 .03 17.12 .10

 1986

15 Jan. 7-12 193.19 7.17 752.57 816.71 16.73 21.64 586.77 .04 16.78 .19

16 Jan. 13-20 283.27 12.68 666.90 807.50 .11 .27 586.85 .22 16.63 .18

17 Jan. 21-27 298.88 11.67 675.56 812.29 1.06 -101.66 586.36 .35 17.52 .31

18 Jan. 28-Feb. 3 358.09 14.60 656.39 791.29 0 106.39 587.08 .38 16.23 .12

19 Feb. 4-12 260.61 11.96 771.76 863.23 10.69 43.06 584.91 .02 20.17 .20

20 Feb. 13-17 423.68 19.06 651.82 822.80 0 47.09 586.01 .33 18.17 .23

21 Feb. 18-24 339.92 15.11 779.29 879.43 2.03 60.21 584.32 .07 21.24 .26

22 Feb. 25-Mar. 3 420.94 22.61 638.33 822.57 .70 -133.19 585.52 .75 19.05 .33

23 Mar. 4-10 418.59 19.60 707.44 834.00 1.38 103.70 585.91 .16 18.35 .24

24 Mar. 11-17 350.87 13.89 820.29 892.57 14.45 119.31 584.04 - .05 21.75 .28

25 Mar. 18-24 505.64 22.73 729.03 870.71 .85 -115.11 583.95 .40 21.92 .55

26 Mar. 25-31 463.40 21.36 770.63 865.11 1.71 111.44 584.40 .10 21.09 .36

27 Apr. 1-7 561.76 23.67 810.84 895.51 0 62.02 582.90 .15 23.81 .56

28 Apr. 8-14 541.73 24.06 781.07 895.17 3.81 -29.60 582.89 .28 23.84 .57

29 Apr. 15-21 601.92 25.61 785.53 897.39 0 -21.64 582.79 .26 24.02 .64

30 Apr. 22-28 660.43 27.37 761.80 899.93 0 36.82 582.66 .19 24.25 .64

31 Apr. 29-May 5 590.07 24.30 837.42 930.01 0 26.00 581.46 .10 26.44 .67

32 May 6-12 502.55 22.33 815.14 924.93 4.12 -25.43 581.67 .17 26.06 .57

33 May 13-19 540.71 22.95 817.97 930.86 .22 20.44 581.42 .19 26.51 .53

34 May 20-26 542.04 24.11 844.01 948.30 2.78 49.20 580.70 .15 27.82 .53

35 May 27-June 2 627.53 25.45 866.79 965.95 3.64 44.53 579.97 .15 29.14 .67

36 June 3-9 492.95 23.36 913.60 967.73 2.17 11.75 579.94 .16 29.19 .58

37 June 10-16 415.81 18.57 900.57 977.29 37.58 -1.85 579.78 .44 29.50 .42

38 June 17-23 431.43 19.99 895.71 969.29 18.94 11.40 579.80 .51 29.46 .38

39 June 24-30 549.90 24.27 888.29 980.43 4.96 52.24 579.28 .34 30.40 .48

40 July 1-7 479.43 22.72 904.43 981.00 11.42 -21.02 579.25 .43 30.46 .48

41 July 8-14 525.47 23.05 911.58 990.86 2.73 32.10 578.75 .31 31.36 .50

42 July 15-21 508.48 22.61 965.60 1,003.57 10.05 2.30 578.30 .30 32.18 .58

43 July 22-28 431.41 18.65 914.28 983.86 5.84 -54.15 578.97 .48 30.97 .45

44 July 29-Aug. 4 433.56 21.33 931.71 984.72 37.09 63.73 579.05 .30 30.82 .42

45 Aug. 5-11 555.86 24.61 914.71 991.52 4.14 -16.90 578.68 .33 31.50 .60

46 Aug. 12-18 467.17 22.44 920.38 986.29 14.75 23.46 579.18 .46 30.58 .42

47 Aug. 19-26 480.26 21.29 910.52 987.94 12.67 13.93 579.10 .30 30.72 .48

48 Aug. 27-Sept. 1 511.09 23.05 923.48 995.12 24.29 -9.58 578.82 .37 31.23 .55

49 Sept. 2-8 475.94 21.35 919.99 988.53 13.92 -16.95 587.98 .35 30.95 .51

50 Sept. 9-15 415.61 19.04 920.03 1,022.41 9.57 1.98 579.34 .30 30.28 .41

51 Sept. 16-22 435.83 22.08 897.43 973.29 .67 -61.20 579.95 .24 29.19 .54

52 Sept. 23-30 483.73 22.14 908.29 976.43 .25 28.90 579.54 .19 29.93 .51

Thermal

survey

period

Dates Qs Qr Qa Qar + Qbs

Qv Qx

Latent

heat

(cal/g)

Bowen

ratio

T0

(

oC)

EEB

(cm/d)
Appendix 59

Table A2. Annual average values, weighted average errors, 

and relative errors for energy-budget components and 

evaporation, October 1985 to September 1986

[Values are in calories per square centimeter per day unless otherwise 

noted. Qs , incident shortwave radiation; Qr, reflected shortwave radiation; 

Qa, incident longwave radiation; Qar, reflected longwave radiation; Qbs, 

emitted longwave radiation; Qv, advected heat; |Qx|, absolute value of the 

change in stored heat; T0, water-surface temperature; EEB, energy-budget 

evaporation; cal/g, calories per gram; °C, degrees Celsius; cm/d, centimeters per day]

Term Average 

value

Weighted

average 

error

Relative

error

(percent)

Qs 419.4 19.9 4.8

Qr 18.5 .33 1.8

Qa 819.2 23.0 2.8

Qar + Qb s 915.4 21.5 2.3

Qv 6.3 .68 10.8

|Qx| 48.6 29.5 60.7

Latent heat

(cal/g)

582 6.4 1.1

T0 (°C) 25.2 .29 1.1

Bowen ratio

(unitless)

.327 .080 24.4

EEB (cm/d) .390 .064 16.4

150

100

50

0

-50

-100

-150 OCT NOV DEC JAN FEB MAR APR MAYJUNEJULYAUG SEPT

TOTAL STORED HEAT

CHANGE IN STORED HEAT

1985 1986

CHANGE IN STORED HEAT, IN CALORIES

PER SQUARE CENTIMETER PER DAY

9,000

8,000

7,000

6,000

5,000

4,000

TOTAL STORED HEAT, IN CALORIES

PER SQUARE CENTIMETER PER DAY

1986 WATER YEAR

Figure A1. Total stored heat and daily average change in 

stored heat in Lake Lucerne by thermal survey period for the 

1986 water year.

Figure A2. Total stored heat and daily change in stored heat 

in Lake Lucerne for the 1986 water year.

400

200

0

-200

-400

-600

1985 1986

TOTAL STORED HEAT

CHANGE IN STORED HEAT

9,000

8,000

7,000

6,000

5,000

4,000

TOTAL STORED HEAT, IN CALORIES

PER SQUARE CENTIMETER PER DAY

CHANGE IN STORED HEAT, IN CALORIES

PER SQUARE CENTIMETER PER DAY

1986 WATER YEAR

MISSING DATA

OCT NOV DEC JAN FEB MAR APR MAY JUNEJULY AUG SEPT
60 Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Fla.

APPENDIX B. Conversion Tables for Calculation of Free Water-Surface Evaporation 

Rates

Table B1. Conversion table for calculating monthly total free water-surface evaporation from monthly total pan evaporation at 

Lake Lucerne

[in/d, inches per day; °F, degrees Fahrenheit; mi/d, miles per day; in/month, inches per month; αp, ratio of advected energy used in evaporation to total 

energy advected from the pan; FWSp, free water-surface evaporation from the pan]

Year and

month

Pan

evaporation

(in/d)

Mean pan

temperature

(°F)

Mean air

temperature

(°F)

Mean wind 

speed

(mi/d)

αp

FWSp

(in/d)

FWSp

(in/month)

1985

October 0.19 79.6 77.6 36.61 0.66 0.141 4.38

November .15 73.0 72.2 39.99 .64 .108 3.23

December .11 58.5 58.7 42.42 .56 .078 2.41

1986

January .11 59.5 59.6 47.50 .57 .080 2.47

February .16 66.6 63.4 60.94 .62 .124 3.46

March .20 65.8 65.1 62.31 .62 .140 4.35

April .26 72.5 69.5 46.36 .64 .192 5.75

May .29 78.8 77.3 41.99 .67 .208 6.44

June .25 83.6 78.4 34.82 .68 .188 5.65

July .24 84.1 80.9 49.72 .70 .181 5.60

August .26 85.0 80.2 34.91 .69 .197 6.10

September .21 83.1 79.9 27.09 .68 .157 4.70

Total 54.54

Table B2. Conversion table for calculating monthly total free water-surface evaporation from monthly total pan evaporation at 

Lake Alfred National Oceanic and Atmospheric Administration site

[in/d, inches per day; °F, degrees Fahrenheit; mi/d, miles per day; in/month, inches per month; αp, ratio of advected energy used in evaporation to total 

energy advected from the pan; FWSp, free water-surface evaporation from the pan]

Year and

month

Pan

evaporation

(in/d)

Daily mean pan

temperature, T0

(°F)

Daily mean 

air temperature, Ta

(°F)

Mean daily

wind run

(mi/d)

αp

FWSp

(in/d)

FWSp

(in/month)

1985

October 0.21 80.55 78.9 43.81 0.68 0.151 4.69

November .16 72.55 72.0 53.07 .65 .113 3.38

December .14 58.70 58.0 49.29 .56 .098 3.04

1986

January .13 58.65 58.3 55.23 .55 .094 2.91

February .18 66.05 64.2 52.64 .61 .131 3.68

March .22 66.35 64.2 63.10 .61 .163 5.07

April .31 71.45 67.8 58.50 .65 .229 6.87

May .34 78.65 76.1 57.71 .68 .247 7.64

June .26 84.10 81.0 37.57 .69 .194 5.82

July .26 85.15 81.7 36.61 .69 .192 5.96

August .27 85.95 82.2 36.26 .70 .204 6.32

September .24 84.25 80.7 35.97 .69 .175 5.26

Total 60.64
Appendix 61

Table B3. Conversion table for calculating monthly free water-surface evaporation from monthly energy-budget evaporation

[αl, ratio of advected energy used in evaporation to total advected energy from lake; Qx, change in stored heat in the lake; Qv, heat advected to the lake; Qw, 

energy advected by evaporating water; L, latent heat of evaporation; EEB, energy-budget evaporation; ∆E, energy-budget correction factor; FWSl

, free watersurface evaporation from corrected lake evaporation; (cal/cm2

)/d, calories per square centimeter per day; cal/g, calories per gram; cm/d, centimeters per day; 

in/d, inches per day; in/month, inches per month]

Year and 

month αl 

Qx

[(cal/cm2)/d]

Qv

[(cal/cm2)/d]

Qw

[(cal/cm2)/d]

L

(cal/g)

EEB 

(cm/d)

∆E

(cm/d)

FWSl 

(cm/d)

FWSl

(in/d)

FWSl

(in/month)

1985

October 0.60 –15.66 6.17 10.68 580.74 0.38 –0.01 0.37 0.147 4.56

November .58 -22.66 1.48 7.28 582.59 .30 – .02 .28 .110 3.30

December .51 -90.53 3.04 4.19 585.59 .22 – .08 .14 .055 1.70

1986

January .49 13.47 4.86 3.20 586.70 .19 .01 .20 .078 2.42

February .53 29.67 4.04 4.56 585.28 .23 .03 .26 .102 2.86

March .56 36.64 4.22 7.40 584.66 .35 .04 .39 .154 4.79

April .57 12.84 .89 14.65 582.72 .61 .03 .63 .249 7.46

May .61 21.36 2.19 15.84 581.09 .58 .04 .62 .244 7.57

June .61 20.13 15.09 14.10 579.72 .48 .02 .50 .196 5.87

July .62 – 3.04 10.37 15.48 578.84 .50 .00 .50 .196 6.07

August .63 11.75 16.24 15.43 578.97 .50 .01 .51 .201 6.22

September .61 –11.74 6.73 14.86 579.43 .49 .00 .49 .193 5.79

Total 58.61
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Lee and Swancar—HYDROLOGIC BUDGET OF LAKE LUCERNE, POLK COUNTY, FLA.—U.S. Geological Survey Water-Supply Pa