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STATE OF FLORIDA
DEPARTMENT OF NATURAL RESOURCES
Harmon Shields, Executive Director




DIVISION OF INTERIOR RESOURCES
Charles M. Sanders, Director




BUREAU OF GEOLOGY
Charles W. Hendry, Jr., Chief




Report of Investigations No. 73




WATER BALANCE OF LAKE KERR A DEDUCTIVE STUDY
OF A LANDLOCKED LAKE IN NORTH- CENTRAL FLORIDA




By
G. H. Hughes






Prepared by the
UNITED STATES GEOLOGICAL SURVEY
in cooperation with the
BUREAU OF GEOLOGY
FLORIDA DEPARTMENT OF NATURAL RESOURCES


Tallahassee, Florida


1974






DEPARTMENT
OF
NATURAL RESOURCES



REUBIN O'D. ASKEW
Governor


DOROTHY W. GLISSON
Secretary of State



THOMAS D. O'MALLEY
Treasurer



RALPH D. TURLINGTON
Commissioner of Education


ROBERT L. SHEVIN
Attorney General



FRED O. DICKINSON, JR.
Comptroller



DOYLE CONNER
Commissioner ofAgriculture


HARMON W. SHIELDS
Executive Director






LETTER OF TRANSMITTAL


Bureau of Geology
Tallahassee
October 10, 1974


Honorable Reubin O'D. Askew, Chairman
Department of Natural Resources
Tallahassee, Florida

Dear Governor Askew:

We are pleased to make available Report of Investigations No. 73
entitled "Water Balance of Lake Kerr a Deductive Study of a Land-locked
Lake in North-central Florida" by G. H. Hughes.


This study demonstrates the
developed with a minimum amount of
value in the analysis of future lake
accumulated in detail and time may
realistically acquired.


hydrologic parameters that can be
data. This technique should prove of
problems where data has not been
be such that these data cannot be


Respectfully yours,



Charles W. Hendry, Jr., Chief
Bureau of Geology















































Completed manuscript received
July 29, 1974
Printed for the
Department of Natural Resources
Bureau of Geology


Tallahassee
1974


iv







CONTENTS

Page
Abstract ............................................................ 1
Introduction ........................................................ 2
Environmental setting of lake ........................................... 5
Water level fluctuations ................... ............................ 11
Water balance computations .......................................... 12
Basic equation ................................................. 12
Rainfall ................................................. ..... 13
Evaporation ..................................................... 15
Leakage ........................................................ 16
Surface water and ground water inflow .............................. 16
Results ......................................................... 18
Analysis of monthly results ............................................ 18
Nature of expected error of estimate of rainfall .......................... 18
Analysis of scatter of water balance results ............................ 20
Search for probable cause of large deviations ............................ 21
Error of estimate of evaporation ................................. 21
Error of estimate of leakage ..................................... 23
Error of estimate of ground water inflow ......................... 26
Combined error of estimate of rainfall and surface-water inflow ......... 32
Analysis of yearly results ............................................... 36
Summary ................................................ .......... 45
References........................................................ 59










WATER BALANCE OF LAKE KERR A DEDUCTIVE STUDY
OF A LANDLOCKED LAKE IN NORTH- CENTRAL FLORIDA

By
G. H. Hughes


ABSTRACT

Accurate measurements of the many factors that make up the water
balance of a lake almost always are lacking. However, enough information may
be available to permit speculation about a lake's water balance. Landlocked lakes
require less information than other lakes because surface-water outflow is zero.

Of the other parameters required, records of rainfall at National Weather
Service offices provide some basis for estimating yearly and monthly rainfall on
a lake. Estimates of average yearly lake evaporation for a given area and records
of pan evaporation provide a basis for making realistic estimates of yearly and
monthly evaporation from a specific lake. Estimates of other factors in a lake's
water balance sometimes can be made for selected conditions when the
... hydrologic characteristics of an area are known.

When such estimates are used in a water-balance equation, the difference
between the computed and observed changes in lake level may be large or small
and may vary erratically or systematically. If the equation is applied for a wide
enough range in lake level, an analysis of these differences may tell which of the
estimated factors are causing the bulk of the errors. At least, such an analysis
will lead to a better -understanding of why the lake. level fluctuates than
previously existed.

The analytical process just described was used to approximate the water
balance of Lake Kerr, which is landlocked. The monthly change in lake level was
computed for 1962 69 from estimates of rainfall evaporation, leakage,
surface-water and ground-water inflow. Although leakage is known to vary, it
was assumed to be constant at 0.1 foot per month. Surface-water and
ground-water inflows were estimated as zero, even though they may occur at
times.

The computed monthly change in level was within 0.10 foot of the
observed change in level about 70 percent of the time. Errors substantially
greater than 0.10 foot were somewhat erratically distributed in time. Almost all
of the large errors indicated inflow not accounted for by the estimates. Because
rainfall estimates were based on records from rainfall stations some 20 30 miles
from the lake, at least some large errors substantially larger than 0.10
foot -were expected; however, errors of this type were expected to balance






BUREAU OF GEOLOGY


over a period as long as 8 years. Because the large errors were related to periods
when the lake level rose, the errors were presumed to stem from faulty estimates
of rainfall or surface-water inflow.

The reasons why it was concluded that the large errors were caused almost
entirely by faulty estimates of rainfall rather than of surface-water inflow are the
manner in which the large errors varied when the rainfall estimate was based on
different combinations of rainfall stations in the same general area, and from the
fact that the lake in 1 year rose greatly when the quantity and seasonal
distribution of rainfall were about normal for all stations. The absence of
pronounced seasonal variation in errors less than 0.10 foot suggested that
ground-water inflow played a relatively minor role in the water balance of Lake
Kerr.

Analysis of the yearly water-balance data showed that overall for
1962 69 the computed change in lake level was in error by 5.29 feet. Part of
the error was readily attributed to the fact that surface-water and ground-water
inflows were estimated as zero, for the cumulative effect of small quantities of
either could be appreciable over an 8-year period. The error was reduced from
5.29 feet to 3.65 feet when variations in leakage and ground-water inflow were
accounted for by regression methods wherein the net of leakage and
ground-water inflow was related to the difference between the lake stage and the
level of water in a well tapping the same aquifer that underlies Lake Kerr. The
remainder of the error was attributed to faulty estimates of surface-water inflow,
which conceivably could average from 0.2 to 0.3 foot per year rather than
zero and of rainfall on Lake Kerr which during 1962 -69 apparently was
appreciably greater than estimated on basis of rainfall at Crescent City and
Ocala- Over the long term, however, the average of rainfall at Crescent City and
Ocala may be more closely representative of rainfall at Lake Kerr.

Based on the long-term averages for Crescent City and Ocala, rainfall at
Lake Kerr averages about 54 inches per year. Lake evaporation is estimated to
average about 46 inches per year. During 1962 69, leakage from Lake Kerr was
about 12 inches greater than ground-water inflow to Lake Kerr. If this 12-inch
difference is representative of the long-term average, surface-water inflow
averaging about 4 inches per year is required to maintain the water balance of
Lake Kerr. Ground-water inflow is indicated to be relatively small, probably in
the same order of magnitude as surface-water inflow.

INTRODUCTION

Accurate definition of the water balance of a lake requires measurement of
quantities of water that move into the lake from various sources and that move






REPORT OF INVESTIGATIONS NO. 73 3

out of the lake to various sinks. For most lakes in Florida, data from which a
water balance can be accurately computed are lacking. For many of the lakes,
however, measurements of lake-level fluctuations are available. For some of
these lakes enough additional information is available to permit some
speculation about the lake's water balance. Less information is needed for
landlocked lakes than for other types of lakes because surface-water outflow is
eliminated as a factor by definition. Records of rainfall at National Weather
Service offices provide some basis for estimating rainfall on a lake. Data are
available for making realistic estimates of evaporation from shallow lakes in
Florida. From general knowledge of the hydrology of an area, reasonable
estimates sometimes can be made of other water-balance factors for selected
conditions, such as a drought.

When such estimates are used in a water-balance equation, the difference
between the computed and observed changes in lake level may be large or small
and may vary erratically or systematically. If the equation is applied for a wide
enough range in lake level, analysis of these differences may tell which of the
estimated factors are causing the bulk of the errors.

The purpose of this report is to apply the analytical process just described
to Lake Kerr, a landlocked lake located in north-central Florida as shown in
figure 1. In scope, the water balance is computed from sparse data for months
spanning 1962 69. Computed changes in lake level are compared with observed
changes in level. Differences are then examined for significance.

The objective of the study is to provide a basis for understanding why the
lake level fluctuates precisely as it does rather than to formulate a method for
predicting-precisely what thealtitude of the lake level will be at any given time.
Where adequate lake-level records are available, use of the analytical techniques
described in this report or variations of them may lead to increased
understanding of other lakes in Florida.

For the convenience of those readers who prefer to use International
System (metric) units rather than English units, the conversion factors for terms
used in this report are listed below:

Multiply English Unit By To obtain metric unit

feet 0.3048 meters
miles 1.609 kilometers
square miles 2.590 square kilometers







4 BUREAU OF GEOLOGY





BRADFORD CLAY




,I ./ ST. JOHNS

ALACHUA ES



II
GAINESVILLE PUTNAM PAATa i







I LFLAGLER


CRESCENT CITY

LSL



SLAKE
MARION GEOwa___


SOCALA
SHARPS NATIONAL
WELL VOLUSIA
FOREST








-- --------- ME fga1* r
\ A1 W^ LAKE WrAE

LA\ E LtSBN
-GW-- __ LAKE


LAKE



S~\ \r SEMINOLE
STJODY AEA I \


Figpe I. Map showing location of Lake Kerr in north-central Florida.







REPORT OF INVESTIGATIONS NO. 73


ENVIRONMENTAL SETTING OF LAKE

Lake Kerr is in Marion County. Although almost entirely surrounded by
Ocala National Forest, most of the land adjacent to the lake is privately owned.
The lake occupies an irregularly shaped depression that probably was formed by
subsidence of the land surface owing to the dissolution of limestone at some
depth below the surface. A remnant of the former land surface remains as an
island, as shown in figure 2. The lake covers about 4 square miles or about 7
percent of the 60 square-mile surface-drainage area.

Lake Kerr connects with Lake Warner (fig. 1) at times of low water by
means of a canal dug an unknown number of years ago and at times of high
water by the canal and a natural water course. Except for the interconnection
between the two lakes, neither Lake Kerr nor Lake Warner have an established
outlet for surface-water outflow. Neither lake is known to have spilled or to have
been dry. If both lakes were full enough to spill, water would move from Lake


DASHED LINES INDICATE
SHORELINE


0 3000 FEET
EXPLANATION
CONTOUR LINE SHOWING DEPTH OF WATER, REFERENCED TO LAKE LEVEL
10 239 FEET ABOVE MEAN SEA LEVEL. CONTOUR INTERVAL IS FIVE FEET.
x16 NUMBER INDICATES DEPTH AT INDICATED POINT.

Figure 2. Map showing shape and general configuration of bottom of Lake
Kerr.






BUREAU OF GEOLOGY


Kerr to Lake Warner and then to the St. Johns River. Because Lake Kerr and
Lake Warner are so close together in the same hydrologic environment, their
levels tend to fluctuate together irrespective of the interconnecting channels.
Should their levels differ temporarily, the altitude of the common level after
equalization would be determined largely by the altitude of Lake Kerr's level
before equalization, because Lake Kerr is so much the larger of the two.
Consequently, whether Lake Kerr and Lake Warner are considered as poorly
connected parts of the same lake, or Lake Kerr is considered as a lake standing
alone, as if the interconnecting channels did not exist, is inconsequential to the
purpose of this report.



Much of the area immediate to Lake Kerr remains a wilderness. Several
homes have been built along the shore and, on the south side, a handful of small
groves or orchards are farmed. The area may not long remain a wilderness; some
evidence can be seen of plans for additional settlements around the lake.



The drainage area of Lake Kerr is largely covered by pine forest. The
surficial materials are dominantly thick to moderately thick, well drained, acidic
sands (Florida Agricultural Experiment Stations, 1962) that readily absorb rain
of moderate intensity. Much of the absorbed water is retained as soil moisture
and in time is returned to the atmosphere by evapotranspiration. When more
water is absorbed than can be retained as soil moisture, water moves downward
to the water table. Intense rain may cause sheet runoff that is temporarily
impounded in local depressions, but the terrain is somewhat uniquely marked by
the absence of a throughgoing system of streams.


In the area of Lake Kerr two principal and clearly different aquifers
commonly exist. The upper aquifer, the shallow aquifer of this report, is
basically the water-table aquifer, which consists of permeable sand at shallow
depths and clayey sand interbedded with some clay lenses at greater depths. The
shallow aquifer is generally underlain by a layer of material of low permeability
that confines or partly confines water in the lower aquifer, a limestone aquifer,
hereafter in this report called the Floridan aquifer, following the usage of Parker
and others (1955, p. 189) and Faulkner (1970, pp. 89-117). The confining bed
in many places is missing or has been fractured or breached by its collapse into
solution cavities in the limestone. Such gaps or breaks in the confining bed
locally permit downward movement of water from the shallow aquifer to the
Floridan aquifer. Water moves down gradient through the Floridan aquifer to
emerge as seepage or spring flow in stream valleys or other low areas.









J 24
tJ


Ow
J,






' ,
22




-1 21


APR MAY JUNE JULY


AUG SEPT OCT


---- I ----,- ',!? :

DE
R,;


FEB MAR


JAN





































MAN APR MAY JUNE JULY AUG PSPT OCT NOV DEC


0S
rJJ
04
0


J 26





25



1 24


JAN Fr8












26 r,:
LII
L"', --I e" -,-







. 26 .
25 -







P 1 11111111 1


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












I&
I '25




24







2 5- -6
0 I


JAN FEB MAR APR MAY JUNE JULY


OCT NOV DEC







REPORT OF INVESTIGATIONS NO. 73


WATER- LEVEL FLUCTUATIONS

The level of Lake Kerr has been measured at monthly or weekly intervals
since 1936, except from mid-1952 to mid-1955 when no measurements were
made. A water-level recorder has been in operation since October 1961. Because
a continuous water-level record is more useful than an intermittent one for
water-balance studies, only the data for years subsequent to 1961 are used in the
more detailed analyses of this report. Data for the preceding years are used in
some broad comparisons of conditions during different yearly periods. Unless
otherwise stated, the years referred to in this report are calendar years.

Daily lake-level fluctuations of Lake Kerr from 1962 to 1969 are shown in
figures 3 6. Casual study of the daily hydrograph of Lake Kerr and the record


1962 63 64--: 65 66 67 68 69

Figure 7. Graphs showing month-end level of Lake Kerr and estimate of
monthly rainfall the generalareaof Lake Kerr, 1962- 69






12 BUREAU OF GEOLOGY

of daily rainfall in the general area of Lake Kerr (U. S. Weather Bureau,
1961 70) suggest that the level of the lake rises abruptly during storm periods
but tends otherwise to decline. This implies that the rise of. the lake level is
caused by rainfall on the lake and possibly by surface-water inflow to the lake.
Because surface-water outflow does not occur, any decline in level must be
caused by evaporation and probably also by leakage. The decline of the lake
level may be modified by ground-water inflow. Month-end and year-end levels of
Lake Kerr are shown in figures 7 and 8.





E MAXIMUM LEVEL OF RECORD: 27.00 FEET, OCT. II, 1966
5 28 uMINuIIu I PVFI nO RFEnRn: 19.92 FEET. MAY 10.1957


1935 1940 1945 1950 1955 1960 1965 1970


Figure. Graph showing year-end level of
1955 69.


Lake Kerr, 1936-51 and


WATER -BALANCE COMPUTATIONS

BASIC EQUATION

Of all the components required for accurate definition of the water
balance of Lake Kerr, only the change in lake level has been measured. The
water balance of the lake can be approximated, however, if rational estimates of
the other components involved can be made and substituted in the water-balance
equation:







REPORT OF INVESTIGATIONS NO. 73


H H=P-E-S+ Isw g (1)

wherein, H = change in lake level,

P = rainfall on lake,

E = evaporation from lake,

S = leakage from lake,

Isw = surface-water inflow to lake, and

Igw = ground-water inflow to lake.


Equation 1 can be used for any period for which the different components
can be evaluated. The changes in level computed in this report are for each
month during 1962 69 and the change is expressed in feet without regard for
the fact that the lake area varies with the lake level. Error that results from
variations in lake area is inconsequential to the purpose of this report, because,
as figures 2 and 7 indicate, the change in lake area during the study period was
small relative to the total area of the lake.



RAINFALL

For the computations that follow, rainfall on Lake Kerr was estimated as
the average of rainfall recorded at the National Weather Service stations in
Crescent City and Ocala (fig. 1). For the time spans indicated in figure 9, yearly
rainfall averaged 53.48 inches at Crescent City and 53.98 at Ocala. Figure 7
shows the average of the monthly rainfall at these two stations for 1962 69.

Records of rainfall are available for several stations in the general ares of
Lake Kerr, but not all of the stations are currently active and some of the
stations have been operative for only a few years. Records for the stations at
Crescent City arid Ocala were selected for use in the basic computations of the
report because, as a pair, these stations appear to represent Lake Kerr as well as,
or better than, any two of the other stations. In addition, the stations at
Crescent City and Ocala are currently (1973) active, and the records for these
stations are almost complete for the time span of the lake-level record of Lake
Kerr. Records for the other rainfall stations in the area were used in
supplemental computations.






14 BUREAU OF GEOLOGY
RAINFALL INCHES RAINFALL INCHES

N) o 0o Do%) b oo 0
0 0 0 0 0 0 0 0



1890 1890


1895 1895


1900 1900


1905 1905


1950 1910
r m

1915 1915


1920 1920


1925 1925


1930 0 1930


1935 t 1935


1940 1940


1945 5 1945 -
".
1950 1950


1955 1955 ..


1940 1960


1965 1965


1970 1970



Figre 9. Graphs showing yearly rainfall at Crescent City and Ocala, Fla,
1892 -1969. Cross (x) indicates years for which rainfall was
estimated for part of year, usually only 1 or, 2 months, on basis of
records for other rainfall stations in the same general area.








REPORT OF INVESTIGATIONS NO. 73 15

EVAPORATION

Estimates of monthly evaporation from Lake Kerr in this report are keyed
to the estimate of average yearly lake evaporation of 46 inches given for the
Lake Kerr area by Kohler, Nordenson, and Baker (1959). Measurements of
evaporation from a standard, 4-foot diameter, Weather Bureau type pan at
Lisbon, Fla., (U. S. Weather Bureau, 1961 70), about 35 miles south of Lake
Kerr (fig. 1), were used to determine the distribution of evaporation during the
months and years of the investigation. Means and extremes of monthly pan
evaporation are shown in figure 10 for 1960 69, when yearly pan evaporation
averaged 58.80 inches. From the estimate of average yearly lake evaporation (46
in.) and the average yearly pan evaporation (58.80 in.), a yearly pan coefficient
of 0.78 was obtained. For estimates of monthly evaporation, this pan coefficient
was varied between 0.66 (for February) and 0.87 (for July and August) to adjust
for seasonal variation of the relation between pan and lake evaporation, in
accordance with findings for Lake Okeechobee, Fla. (Kohler, 1954, p. 128). This
distribution of evaporation gave the same yearly evaporation as would have been
obtained by uniform application of a yearly pan coefficient of 0.78. No attempt
was made to adjust for the fact that such seasonal variations are not precisely the
same each year.



10
EXPLANATION
C6 '- -MAXIMUM

S 8 -AVERAGE
L) 8
S-MINIMUM


z


0 4
4

W

z



J F M A M J J A S N D


Figure 10. Graph showing monthly evaporation from standard, 4-foot
diameter, Weather Bureau type pan at Lisbon,Fla., 1960 69.
r// ii/ f ~. ;"'1, f/






BUREAU OF GEOLOGY


Data from the Lisbon evaporation pan were selected because the pan is in
a relatively low area surrounded by lakes and because it is slightly closer to Lake
Kerr than is the only other pan in the area, which is at Gainesville (fig. 1).
Because the estimates of monthly evaporation are keyed to Kohler's estimate of
average yearly lake evaporation, however, any pan in the area would have served
about equally well to define the seasonal distribution of evaporation.



LEAKAGE

Leakage from Lake Kerr was determined as a residual of equation 1 by
use of the observed change in lake level and related estimates of evaporation and
rainfall determined as previously described. Surface-water and ground-water
inflow were assumed to be zero, for reasons to be explained in the following
paragraph. Leakage was determined for a few selected winter months in which
rainfall was minimal and which followed periods of relative drought. The reasons
for selecting these winter months are as follows: (1) Evaporation is small during
winter months; hence, a possible error of 10 20 percent in the pan coefficient
used does not cause a large absolute error in estimated lake evaporation. (2)
Surface-water inflow does not occur at Lake Kerr when rainfall is light. (3)
Ground-water inflow would be least during droughts, if it occurs at all. The
monthly leakage indicated by these computations averaged about 0.1 foot per
month. Although leakage from the lake is known to vary in magnitude between
wet and dry periods, the value of 0.1 foot per month was used in the
water-balance computations for all months.

SURFACE WATER AND GROUND WATER INFLOW

In the water-balance computations that follow, surface-water and
ground-water inflow to the lake are tentatively estimated as zero for the
following reasons: (1) In terrain such as that surrounding Lake Kerr, runoff
usually does not result from light or moderate rainfalls. If and when sheet runoff
does result from a storm, its duration is not much longer than the storm period.
(2) In areas where sinkholes result from solution of limestone some depth below
the land surface, and the subsequent collapse of surficial materials into the
solution cavity, the level of water in the shallow aquifer has been found at times
to be below the level of water in lakes and ponds in the same areas, especially
during dry spells (Clark and others, 1964, pp. 15 31; Hendricks and Goodwin,
1952, pp. 180, 204, 205). Conceivably, therefore, both surface-water and
ground-water inflow to Lake Kerr might be zero or nearly zero much of the
time. (3) For times when surface-water and ground-water inflow are not zero,
monthly estimates of these quantities cannot be made from the available data.






REPORT OF INVESTIGATIONS NO. 73


Allowing that surface-water and ground-water inflow occur at times, and
proceeding on the assumption that they do not occur, might lead to errors in the
results of water-balance computations. If such errors are found, study of them,


COMPUTED LAKE-LEVEL -CHANGE.- ("A'), 'FEET


Figure 11. Graph showing relation between observed and computed monthly
chanl gei a ie kleve ofLake Kerr, 1962 -69.





BUREAU OF GEOLOGY


or of the trends that they follow, may reveal that surface-water and
ground-water inflow are, indeed, appreciably different from zero.

RESULTS

By use of equation 1, and previously described estimates of rainfall,
evaporation, leakage, surface-water and ground-water inflow, the monthly
change in lake level was computed for Lake Kerr for 1962- 69. Figure 11
compares the computed change in lake level to the observed change in lake level.

ANALYSIS OF MONTHLY RESULTS

The scatter of the data in figure 11 relates to incorrect estimates or
assumptions used in the water-balance computations. For example, if the
estimated rainfall on the lake was greater than actual, if surface-water outflow
actually occurred, or if estimated evaporation and leakage from the lake were
less than actual, data would tend to plot to the right of (below) the equal-value
line. On the other hand, if estimated rainfall on the lake was less than actual, if
surface-water and ground-water inflow occurred, or if estimated evaporation and
leakage were greater than actual, data would tend to plot to the left of (above)
the equal-value line.

NATURE OF EXPECTED ERROR OF ESTIMATE RAINFALL

In this report, errors that result from estimates of rainfall at Lake Kerr are
likely to be random. This randomness is demonstrable. For example, consider
the relation between rainfall recorded at Crescent City and the average of rainfall
recorded at DeLand and Palatka, as shown in figure 12. Except for differences in
direction, Crescent City lies between DeLand and Palatka in about the same way
that Lake Kerr lies between Crescent City and Ocala (fig. 1). Thus, rainfall at
DeLand and Palatka provides about the same basis for estimating rainfall at
Crescent City that rainfall at Crescent City and Ocala provides for estimating
rainfall at Lake Kerr. Consequently, the difference between rainfall recorded at
Crescent City and the average of rainfall recorded at DeLand and Palatka
represents the error that might be expected in the estimates of rainfall at Lake
Kerr.

Figure 12 shows that the estimate of monthly rainfall is greatly in error on
the average of 2 to 3 months of the year. Over a long enough time, the errors
tend to balance; but the cumulative error still can be large for periods as long as
a year. During 1962 -69, for example, the average of rainfall at DeLand and
Palatka differed from that recorded at Crescent City by as much as 0.75 foot per
year. Over the 8 years, however, the difference averaged only 0.08 foot per year.







REPORT OF INVESTIGATIONS NO. 73 19

Analysis of the scatter of the rainfall data in figure 12 shows that about 70
percent of the rainfall data plot within 0.10 foot of the equal-value line. A
similar analysis showed that for the 47 months having less than 0.30 foot rainfall
(based on the average of rainfall at DeLand and Palatka) scatter of the data
decreases and that about 85 percent of the data points fall within 0.10 foot of
the equal-value line.


AVERAGE OF RAINFALL AT DELAND AND PALATKA ("B"), FEET

.o ro o oo

o8 \


\ 0 8'00 0 0
\o \o \ o


0 0-0
\\ O
o \




0 0 \D

o \ \

\\,,

3 0 o \

\ \ jk\ \\


P0 9 0
N (
DIFFERENCE BETWEEN "A" AND
"B", FEET


Figure 12. Graph showing relation between average of monthly rainfall at two
stations some distance apart (DeLand and Palatka) and monthly
rainfall at a station midway between the two (Crescent City) for
1962--69.






BUREAU OF GEOLOGY


ANALYSIS OF SCATTER OF WATER- BALANCE RESULTS

The scatter of the lake-level data in figure 11 resembles the scatter of
rainfall data in figure 12. About 70 percent of the lake-level data plot within
0.10 foot of the equal-value line; however, most of the lake-level data points that
deviate greatly from the equal-value line fall to the left of the line. The summary
of lake-level data in table 1 indicates that the errors (differences between
observed and computed change in lake level) tend to balance for all months
except June, July, and August. Although some inconsistencies are apparent, the
seasonal distribution of the errors shown in table I roughly parallels the seasonal
distribution of monthly rainfall shown in table 2.

TABLE 1
SEASONAL DISTRIBUTION OF DIFFERENCE BETWEEN OBSERVED AND
COMPUTED MONTHLY CHANGE IN LEVEL OF LAKE KERR, 1962-69, IN FEET.

Month Average Median
difference difference
January +0.04 +0.02
February .02 .01
March + .05 + .03
April + .05 + .03
May + .04 + .00
June + .13 + .08
July + .14 + .11
August + .20 + .17
September + .02 .02
October .00 .00
November .02 .03
December + .02 .00

TABLE 2
SEASONAL DISTRIBUTION OF AVERAGE OF MONTHLY RAINFALL
AT CRESCENT CITY AND OCALA, 1962-69, IN FEET

Month Average Median


January
February
March
April
May
June


0.20


0.22
.45
.20







REPORT OF INVESTIGATIONS NO. 73


TABLE 2 Continued
SEASONAL DISTRIBUTION OF AVERAGE OF MONTHLY RAINFALL
AT CRESCENT CITY AND OCALA, 1962-69, IN FEET.

Month Average Median
July .76 .75
August .69 .72
September .56 .56
October .26 .17
November .16 .16
December .25 .21


Rainfall at Lake Kerr was estimated to be less than 0.30 foot per month
for 47 of the 96 months investigated. For these 47 months, 81 percent of the
lake-level data plotted within 0.10 foot of the equal-value line and 89 percent
plotted within 0.11 foot. The average deviation for these 47 months was slightly
less than 0.01 foot to the left of the equal-value line. For the 49 months when
estimated rainfall was greater than 0.30 foot per month, the lake-level data for
only 25 months fell within 0.10 foot of the equal-value line; the average
deviation for these 25 months was about zero.

The large errors in the lake-level data of figure 11 occur somewhat
erratically in time, as indicated in figure 13, and often are preceded or followed
immediately by small errors. The small errors show some indication of cyclic
variation that may be related to alternate wet or dry periods.

SEARCH FOR PROBABLE CAUSE OF LARGE ERRORS

ERROR OF ESTIMATE OF EVAPORATION

The number of possible sources of large and erratic errors was reduced by
process of elimination. The nature of the evaporation process generally precludes
large and erratic variations in the monthly evaporation from a shallow lake. Lake
evaporation follows a fairly consistent seasonal pattern determined largely by
solar radiation. Deviations from the norm for a month are usually less than 0.10
foot. The estimates of lake evaporation appear to serve adequately well in the
water-balance computations about 70 percent of the time, often for months
immediately preceding or following months having large errors. If pan-based
estimates of evaporation from a shallow lake are about. correct for a particular
month, they are not likely to be greatly in error for the preceding or following
months of the same year or for the same month of the preceding and following






BUREAU OF GEOLOGY


years. Thus, the estimate of evaporation is not a likely source of large and erratic
errors.


DIFFERENCE


BETWEEN OBSERVED AND


COMPUTED CHANGE IN LAKE


LEVEL, FEET


0 0 I
b & o a


Figm 13. Graph showing time distribution of difference between observed
and computed monthly change in lake level of Lake Kerr.







REPORT OF INVESTIGATIONS NO. 73


ERROR OF ESTIMATE OF LEAKAGE

Although leakage of water from natural lakes is known to vary, the
assumption that leakage from Lake Kerr occurred uniformly at 0.1 foot per
month is not a likely source of large and erratic errors in the monthly
water-balance computations. Leakage to the Floridan aquifer is directly
proportional to the permeability of the confining bed underlying the lake, the
viscosity of the Water moving through confining bed, and the difference between
the lake level and the hydrostatic level of water in the Floridan aquifer.
Although the permeability of the confining bed may change in time, with the
formation of new sinkholes or the sealing off of existing sinkholes, for example,
it can be considered as being essentially constant for periods lasting several years
or even several decades. The viscosity of water does vary with seasonal changes
in temperature, but in Florida monthly changes in leakage from this cause can
only be small. Both the lake level and the hydrostatic level of water in the
Floridan aquifer fluctuate appreciably but they trend alike, as indicated in figure
14. (See fig. 15 for well locations.) Thus, the difference between the lake level


40,0


35.0


30.0' -


25.0


20.0 1-


1964 1965 -1966 1967 1968 1969 1970
Figure 14. Graphs show, variation in level of water in wells near Lake Kerr.
Wells A, B, and C tap the Floridan aquifer; Well F bottoms in the
shallow aquifer. Well locations are shown in figure 15.


I I I I i- -I


WELL A








WELL 8
LAKE KERR "
WELL C


I I I


I I I I I ...


.


I


I





BUREAU OF GEOLOGY

0 5 MILES
I I


MAY 15, 1968: LAKE LEVEL, 23.66 FEET


JANUARY 20, 1967: LAKE LEVEL, 26.25 FEET


EXPLANATION
CONTOUR LINE REPRESENTING
HYDROSTATIC LEVEL OF WATER IN
FLORIDAN AQUIFER.
OBSERVATION WELL (WELLS A-E TAP
FLORIDAN AQUIFER; WELL F BOTTOMS
IN SHALLOW AQUIFER). NUMERALS
GIVE WATER LEVEL IN FEET ABOVE
MEAN SEA LEVEL.


Figuze 15. Maps showing relation between level of water in Lake Kerr and
hydrostatic level of water in Floridan aquifer for contrasting
water-level conditions. Maps adapted from Fauilker (1970, fig. 23).








REPORT OF INVESTIGATIONS NO. 73


and the hydrostatic level of water in the Floridan aquifer does not change from
month to month as much as might be presumed from the change in either level
alone. For example, the hydrostatic level of water in the Floridan aquifer
declined about 4 feet between January 20, 1967 and May 15, 1968, as indicated
in figure 15, whereas the lake level declined about 2.6 feet. Hence, the difference
between the two levels changed only 1.4 feet.

The effective difference between the lake level and the hydrostatic level of
water in the Floridan aquifer is not readily determinable because the hydrostatic
level evidently decreases from west to east in the area of Lake Kerr, and in May
1968 was about at the level of the lake at the western edge of the lake, and
about 8 feet lower than the lake level at the eastern edge. If the permeability of
the materials underlying the lake is uniformly distributed across the lake
bottom, the difference between the lake level and the hydrostatic level in effect
would average about 4 feet. If the difference between the two levels changed 1.4
feet, therefore, the leakage from the lake would change by the ratio of 1.4 to 4,
or by 35 percent. In relation to the average leakage from the lake, estimated to
be 0.1 foot per month, such a change would amount to less than 0.04 foot per
month. The contrast in water-level conditions involved in this example is far
greater than any that is likely to occur within a span of 2 months.

The extent of the variation in leakage from Lake Kerr also was appraised
as follows: In 1956 57 Lake Kerr declined in level a total of 1.88 feet, from an
initial altitude of about 22 feet above msl (mean sea level); in 1962 63 Lake
Kerr declined in level a total of 1.55 feet, from an initial altitude of about 24
feet above msl (fig. 8). In each case the lake level declined steadily the year
before and the seasonal trend of the lake level was about the same in both
periods. The average of rainfall at Crescent City and Ocala totaled 8.00 feet in
1956- 57 and 7.78 feet in 1962 63. On the assumption that lake evaporation
and surface- and ground-water inflow were the same for both periods, it follows
from the differences in rainfall and lake-level decline that the lake leaked about
0.55 foot more in 1956 57 than in 1962 63. Thus, for a difference in lake
level that averaged about 2 feet, the difference in leakage averaged about 0.02
foot per month. If an estimate of regional rainfall based on 6 to 9 rainfall
stations in the general area of Lake Kerr is used in the preceding example,
leakage is indicated to average about 0.03 foot per month greater in 1956 -57
than in 1962 63.

Although the level of Lake Kerr averaged about 2 feet higher in 1962 63
than in 1956 57, the maximum level in 1962 63 was about 4 feet higher than
the minimum level in 1956 57. The difference in leakage occurring at times of
the maximum and minimum levels presumably was about twice as great as the
0.02 to 0.03 foot per month average difference indicated for the 2-year periods.







BUREAU OF GEOLOGY


For 1962 -69, therefore, when the range in lake level was about 4.7 feet
(fig. 7), leakage from the lake might have varied slightly more than 0.04 to 0.06
foot per month between the wettest and driest periods, but it could not have
varied enough to cause errors substantially greater than 0.10 foot per month in
the water-balance computations.

ERROR OF ESTIMATE OF GROUND-WATER INFLOW

The assumption that ground-water inflow was zero might at times lead to
large errors in the results of water-balance computations for Lake Kerr but such
errors are not likely to occur in one month and not occur in the following
month. For example, ground-water inflow might increase substantially and
somewhat abruptly from a rapid buildup of water in the shallow aquifer during
an extended period of several intense rainfalls. Once increased, however, the rate
of ground-water inflow would be sustained by water stored in the aquifer. Thus,
the effect of an appreciable increase in ground-water inflow would be expected
to linger long enough to decrease the rate of lake-level decline for one or more
months after any such buildup occurred. If this effect is large enough to cause
large errors in the results of the water-balance computations, it should be easily
detected.

As a test for large variations in ground-water inflow, a study was made of
the decline in level of Lake Kerr using selected rainless periods. The periods used
involve parts of 54 months and are widely enough dispersed timewise to
represent the full range of the lake level during 1962 69.

An equivalent monthly rate of lake-level decline was computed on the
basis of the observed lake-level decline during periods lasting from a few to
several days when the lake-level decline apparently was uninterrupted by rainfall,
and when little or no rainfall was recorded at rainfall stations in the general area
of the lake. In table 3 the equivalent monthly observed lake-level decline is
compared with the lake-level decline attributed to evaporation and leakage from
the lake as previously estimated. Without regard to algebraic sign, the difference
between the two is as much as 0.16 foot, but is 0.10 foot, or less, for all except
3 of the 54 months, and is 0.05 foot, or less, for 40 months. When the algebraic
sign of the difference is taken into account, the differences for all months fall
within a range of 0.25 foot; differences for all but 3 of the 54 months fall within
a range of 0.16 foot; and, differences for any given month of the year fall within
a range of 0.14 foot.

The range of the difference between the equivalent monthly observed
lake-evel decline and the lake-level decline attributed to evaporation and leakage
reflects the combined effects of variations in leakage and ground-water inflow.








REPORT OF INVESTIGATIONS NO. 73


DECLINE IN


TABLE 3
LEVEL OF LAKE KERR DURING


SELECTED PERIODS OF LITTLE OR NO RAINFALL, IN FEET.

Number Observed Equivalent Estimated
Calendar Starting Ending of days lake-level monthly evaporation
year date date in period 1/ decline decline plus leakage


1962


Jan. 12

Jan. 28
Feb. 16


Apr. 1
Apr. 8


Apr. 30
May 12
May 23


Oct. 3
Oct. 22


Nov. 30
Dec. 12


Mar. 31
Apr. 7


May 2

June 1
June 9


Aug. 3
Aug. 25


Sept. 6
Sept. 17


Oct. 1
Oct. 19


0.08

.13
.10
.23


0.16


0.25


Jan. 27

Feb. 9
Feb. 28
Total

Apr. 6
Apr. 25
Total

May 10
May 21
May 28
Total

Oct. 21
Oct. 30
Total

Dec. 11
Dec. 22
Total

Apr. 5
Apr. 30
Total

May 20

June 5
June 22
Total

Aug. 12
Aug. 30
Total

Sept. 16
Sept. 19
Total

Oct. 13
Nov. 1
Total:


1_/ Periods start and end at 1200 hours.


.29



.53




.59



.39



.25



.59

.58



.55



.58



.42



.40


1963


--








28 BUREAU OF GEOLOGY

TABLE 3- Continued
DECLINE IN LEVEL OF LAKE KERR DURING
SELECTED PERIODS OF LITTLE OR NO RAINFALL, IN FEET.

Number Observed Equivalent Estimated
Calendar Starting Ending of days lake-level monthly evaporation
year date date in period--/ decline decline plus leakage


1964


















1965


Mar. 5
Mar. 13
Mar. 20


Mar. 29
Apr. 9
Apr. 16


May 3
May 14


June 1
June 7
June 19


Mar. 31
Apr. 28


Apr. 30
May 13


Aug. 31
Sept 18


Oct. 2
Oct. 7
Oct. 22


Oct. 31
Nov. 13
Nov. 23


Nov. 30
Dec. 20


Nov. 29
Dec. 15


Dec. 11
Dec. 22
Total

Mar. 9
Mar. 15
Mar. 25
Total

Apr. 7
Apr. 13
Apr. 23
Total

May 12
May 31
Total

June 5
June 15
June 23
Total

Apr. 20
Apr. 30
Total

May 17
May 26
Total

Sept. 13
Sept. 25
Total

Oct. 5
Oct. 12
Oct. 30
Total

Nov. 5
Nov. 21
Nov. 27
Total

Dec. 10
Dec. 24
Total


1' Periods start and end at 1200 hours.


.34


.12
.09
.21

.04
.02
.07
.13

.13
.08
.12
.33

.15
.32
.47

.08
.15
.08
.31

.32
.04
.36

.21
.27
.48

.20
.08
.28


.23




.39




.55



.58




.60



.53



.64



.46




.32




.27



-27


.37




.50



.56




.58



.49



.60



.42




.37




.28



517








REPORT OF INVESTIGATIONS NO. 73 29

TABLE. 3 ;Continued
DECLINE IN LEVEL OF LAKE KERR DURING
SELECTED PERIODS OF LITTLE OR NO RAINFALL, IN FEET.

Number Observed Equivalent Estimated
Calendar Starting Ending of days lake-level monthly evaporation
year date date in period-1 decline decline plus leakage


1966


1967


Mar. 5
Mar. 15


Mar. 31
Apr. 5
Apr. 15


June 1
June 10
June 23


Aug. 31
Sept. 12
Sept. 22


Oct. 11

Nov. 2
Nov. 15


Nov. 28
Dec. 13
Dec. 18
Dec. 24
Dec. 29


Jan. 31
Feb. 22


Mar. 1
Mar. 8


Mar. 31
Apr. 25


May 7
May 16
May 24


Mar. 11
Mar. 31
Total

Apr. 3
Apr. 12
Apr. 26
Total

June 5
June 12
June 29
Total

Sept. 5
Sept. 17
Sept. 25
Total

Nov. 1

Nov. 11
Nov. 27
Total

Dec. 10
Dec. 16
Dec. 22
Dec. 28
Jan. 1
Total

Feb. 5
Feb. 28
Total

Mar. 5
Mar. 27
Total

Apr. 24
Apr. 30
Total

May 15
May 21
May 31
Total


SPeriods start and end at 1200 hours.


.09
.06
.06
.21

.31

.11
.16
.27

.10
.03
.02
.04
.02
.21

.04
.11
.15

.03
.28
.31

.44
.15
.59

.17
.12
.11
.40


.41




.49




.62




.49

.46



.39






.25



.38



.42



.61




.62


.40




.53




.54




.47

.37



.31






.26



.28



.39



.62




.62







30 BUREAU OF GEOLOGY

TABLE 3 Continued
DECLINE IN LEVEL OF LAKE KERR DURING
SELECTED PERIODS OF LITTLE OR NO RAINFALL; IN FEET.

Number Observed Equivalent Estimated
Caendar Starting Ending of days lake-level monthly evaporation
year date date in period-V/ decline 'decline plus leakage


1968




























1968


I I
j Periods


Aug. 31
Sept 15


Sept 30
Oct. 10
Oct. 18


Nov. 2

Jan. 1
Jan. 9
Jan. 24


Jan. 31
Feb. 7


Feb. 29
Mar. 13


Mar. 31
Apr. 7
Apr. 11


June 29
July 23


Aug. 1
Aug. 6
Aug. 21


Sept 28
Oct. 25


Oct. 31
Nov. 6


Sept. 6
Sept. 26
Total

Oct 8
Oct. 15
Oct. 31
Total

Nov. 30

Jan. 8
Jan. 22
Jan. 31
Total

Feb. 5
Feb. 17
Total

Mar. 5
Mar. 31
Total

Apr. 4
Apr. 9
Apr. 30
Total

July 1
July 31
Total

Aug. 3
Aug. 11
Aug. 27
Total

Oct. 5
Oct 31
Total

Nov. 1
Nov. 8


28

7
13
7
27

5
10
15

5
18
23

4
2
19
25

2
8
10

2
5
6
13

7
6
13

3
2


.46




.48

.36


.44.




.38

.32




.27



.27



.39




.55



.57




.54



.38


-' ____________ I A


start and end at 1200 hours.








REPORT OF INVESTIGATIONS NO. 73


DECLINE IN


TABLE 3- Continued
LEVEL OF LAKE KERR DURING


SELECTED PERIODS OF LITTLE OR NO RAINFALL, IN FEET.

Number Observed Equivalent Estimated
Calendar Starting Ending of days lake-level monthly evaporation
year date date in period decline decline plus leakage


Nov. 12
Nov. 19


Nov. 30
Dec. 4
Dec. 14
Dec. 23


Jan. 31
Feb. 3
Feb. 9
Feb. 16
Feb. 23


Feb. 28
Mar. 9
Mar. 19
Mar. 25


Mar. 31
Apr. 6
Apr. 19


May 3
May 22
May 28


June 6
June 17
June 21
June 25


Oct. 5

Nov. 1
Nov. 15

Nov. 30
Dec. 11
Dec. 26


Nov. 17
Nov. 30
Total

Dec. 3
Dec. 13
Dec. 19
Dec. 27
Total

Feb. 2
Feb. 7
Feb. 14
Feb. 21
Feb. 28
Total

Mar. 2
Mar. 11
Mar. 23
Mar. 31
Total

Apr. 5
Apr. 14
Apr. 30
Total

May 13
May 26
May 31
Total

June 9
June 20
June 24
June 30
Total

Oct. 15

Nov. 12
Nov. 26
Total
Dec. 6
Dec. 20
Dec. 30
Total


.03
.11
.05
.04
.23

.01
.05
.06
.05
.05
.23

.02
.08
.02
.09
.21

.05
.15
.21
.41

.19
.06
.05
.30

.04
.06
.05
.11
.26

.13

.12
.11
.23
.08
.08
.03
.19


.27





.34






.31





.38




.51




.55





.56

.40



.31




.31


.28





.29






.28





.34




.54




.56





.60

.35



.25




.31


- Periods start and end at 1200 hours.


1969


--







BUREAU OF GEOLOGY


The variation in the monthly rate of leakage in 1962- 69 was previously
presumed to be about 0.04 to 0.06 foot. Based on the range of 0.25 foot that
encompasses the differences for all of the 54 months investigated, variation in
the monthly rate of ground-water inflow would be about 0.20 foot. In analyses
of hydrologic data, however, the outliers seldom are given full weight because of
the possibility that they reflect the effects of peculiar errors. Hence, the range of
0.16 foot that encompasses the differences for 95 .percent of the months
investigated is assumed to give the best indication of the combined effect of
variations in ground-water inflow and leakage. This puts the variation in the
monthly rate of ground-water inflow at about 0.10 foot. Nothing in the analysis
indicates that variations in ground-water inflow are a likely source of large errors
in the results of the water-balance computations.

The small indicated variation in monthly rate of ground-water inflow to
Lake Kerr requires that ground-water inflow be small. The potential for water to
move into the lake from the shallow aquifer is proportional to the difference
between the lake level and the level of water in the shallow aquifer. The
difference between the lake level and the water level in Well F (figs. 14, 15),
which taps the shallow aquifer, suggests that the potential for water to move
into the lake increased about fourfold between July and November 1969. The
change in potential corresponding to the extremely dry and wet periods in 1963
and 1966 (fig. 7) had to be much greater than indicated for July- November
1969. For the rate of monthly ground-water inflow to change in magnitude by
several times and still vary within a range of about 0.10 foot, ground-water
inflow has to be extremely small (relative to 0.10 foot) during dry periods and
cannot be appreciably greater than 0.10 foot during wet periods.

COMBINED ERROR OF ESTIMATE OF
RAINFALL AND SURFACE- WATER INFLOW

The preceding discussion indicates that the errors in the water-balance
computations for Lake Kerr that are substantially greater than 0.10 foot are
attributable to errors in the estimates of rainfall or surface-water inflow. That
this is so can be established by comparing the sum of individual lake-level rises
during a month (disregarding the intervening lake-level declines) with the
estimate of monthly rainfall, as shown in table 4. The comparison is made for
months when the error of the water-balance computations was substantially
greater than 0.10 foot and was in the direction that indicates inflow not
otherwise accounted for. These are the months for which large positive errors (or
differences) are shown in figure 13. Data for July and August 1965 could not be
included in the analysis because of uncertainties as to how the lake behaved
when the lake-level record was incomplete. For 12 of the 16 months included in
table 4 the sum of the daily lake-level rises (adjusted for evaporation and







REPORT OF INVESTIGATIONS NO. 73


leakage) is substantially greater than the estimated rainfall at the lake. Allowing
for the difference between the sum of the daily lake-level rises and the estimated
monthly rainfall, the residual error for 13 months is rendered to something less
than 0.10 foot. The usual lake-level decline due to evaporation and leakage,
which ranged from about 0.01 to 0.02 foot per day, obscures in the record of
the lake level the effect of daily rainfalls smaller than about 0.01 0.02 foot.
Thus, for most of the months listed in table 4, the true lake rise probably was a
few hundredths of a foot greater than the indicated sum of the daily lake-level
rises.

Whether the substantial differences between the estimated monthly
rainfall and the sum of the daily lake-level rises is caused primarily by faulty
estimates of rainfall or by faulty estimates of surface-water inflow is not directly
determinable. For some months, all or a large part of the difference certainly can
be attributed to faulty rainfall estimates, but these months are not readily
distinguishable from months in which the difference cannot be so attributed.

The average of rainfall at Crescent City and Ocala does not always provide,
as shown earlier, an accurate estimate of rainfall at Lake Kerr. For any given
month, rainfall at any one station may better represent the rainfall at Lake Kerr
than would the average of rainfalls at other stations in the same general area. For
example, in September 1963 and September 1969, rainfall at Crescent City was
much greater than rainfall at Ocala (table 4), and was great enough to account
for the entire rise of the lake level for these months. As long as the potential
exists for such rainfalls to occur in the area, the possibility of their occurring at
Lake Kerr also exists and must be recognized.

The water-balance computations were repeated using estimates of rainfall
based on records for other rainfall stations in the general area of Lake Kerr,
taken singly and in different combinations, both including and excluding the
records for Crescent City and Ocala. The scatter of the results and the extent of
large errors in each set of computations were about the same, but for several of
the months in which large errors occurred, the size of the errors tended to vary
with the choice of rainfall stations. This indicated that the large errors for these
months are probably attributable to faulty estimates of rainfall. For some 7
months -- July 1962, May August 1965, August 1966, and July 1967 -- the
large errors persisted regardless of the rainfall station selected. Because of this
persistence, the possibility that surface-water inflow may at times contribute
substantially to the lake-level rise cannot be ruled out.

A study of yearly rainfall and lake-level data for 1936 69 shows
conclusively that rainfall must have been much greater at Lake Kerr during 1965
than was indicated by the catch at each of several rainfall stations in the area.








BUREAU OF GEOLOGY


TABLE 4
ESTIMATED MONTHLY RAINFALL COMPARED TO SUM OF DAILY
RISE IN LEVEL OF LAKE KERR FOR SELECTED MONTHS, 1962 69, IN FEET
Estimated monthly rainfall Number of days
Month _rainfall occurred
and Crescent Ocala Average Crescent Ocala
Year City City

(1) (2) (3) (4) (5) (6)


July
1962

Aug.
1962

May
1963

Sept
1963

Jan.
1964

1964

Apr.
1964

Dec.
1964

May
1965

Jume
1965

Aug.
1966
xuly
1967

Aug-
1968

OctL
1968

June
1969

ept.
969


0.76

33

.23

1.03

.55

.33

.46

39

.07


.80

.89

.80

.71

.78


33

.75


0.70

.31

.39

.43

.67

.33

.36

.45

.07

.72

.65

.80

.85

.66

.14

.43


0.73

.32

.31

.73

.61

.33

.41

.42


.07

.76

.77

.80

.78

.72

.24

.59


18

12

13

15

15

12

6

9

4

18

20

21

14


16

12

17








REPORT OF INVESTIGATIONS NO. 73


TABLE 4 -Continued
ESTIMATED MONTHLY RAINFALL COMPARED TO SUM OF DAILY
RISE IN LEVEL OF LAKE KERR FOR SELECTED MONTHS, 1962-69, IN FEET
Adjusted Magnitude
Number Sum of Estimated sum of Column 10 of
of days daily evaporation daily minus difference
of lake lake plus leakage, lake Column 4 shown in
rise rises feet per day rises 1/ figure 13
(7) (8) (9) (10) (11) (12)


0.67

.30

.50

.79

.60

.38

.39

.46

.15

.98

.72

.76

.81

.83

.16

.56


0.020

.018

.019

.014

.008

.013

.018

.009

.020

.018

.018

.018

.017

.012

.020

.014


0.95

.39

.65

.97

.70

.51

.44

.52

.19

1.27

.97

..99

.98

.92

.28

.72


1/Column 8 plus the product of values in columns 7 and 9.


0.22

.07

.34

.24

.09

.18

.03

.10

.12

.51

.20

.19

.20

.20

.04

.13


0.30

.25

.38

.23

.19

.22

.19

.17

.20

.55

.27

.35

.24

.19

.19

.20






BUREAU. OF GEOLOGY


For 1936- 64, yearly lake-level rises ranging from 1 to 2.4 feet occurred in 6
years During these 6 years the average of rainfall at Crescent City and Ocala
ranged from 64.50 to 72.54 inches, compared to the long-term average of about
54 inches. Regional rainfall as determined by the average of rainfall at from 6
to 9 stations within a distance of 40 miles from Lake Kerr in these same 6
years ranged from 5828 inches to 67.21 inches, compared to a long-term
average ofabout 53 inches. In 1965, however, Lake Kerr rose 1.52 feet when the
average of rainfall at Crescent City and Ocala was only 54.86 inches, and the
regional rainfall was only 53.10 inches. The indicated seasonal distribution of
rainfall during 1965 was not markedly different from that of 1964, for example,
when the lake rose substantially (fig. 4) or from that of many other years when
an equal or greater amount of rainfall was recorded in the area. Thus, the only
plausible explanation for the 1.52-foot lake rise in 1965 is that substantially
more rain fell at Lake Kerr than fell at any of the rainfall stations in the area,
including Crescent City and Ocala. On this basis it is concluded that all of the
large errors in the water-balance computations resulted primarily from faulty
estimates of rainfall. Surface-water inflow may have been a small contributing
factor during the most intensive rainfalls.

ANALYSIS OF YEARLY RESULTS

The monthly water-balance computations previously discussed were based
on the assumptions that leakage from Lake Kerr was constant at 0.1 foot per
month and that ground-water and surface-water inflows were zero. Use of these
ass-amptions did not produce the type of obvious, persistent, and seasonally
distributed errors that would be expected to crop up if the assumptions were
grossly wrong much of the time. However, assumptions that for some purposes
may be adequate for monthly computations are not necessarily adequate for
annual computations because in annual computations the cumulative effect of
small but persistent errors becomes increasingly important. For example, the
general disarray of the monthly water-balance data in figure 11 would be little
improved or worsened if ground-water inflow, rather than being assumed zero,
were assumed to vary from 0.01 foot per month in some months to 0.05 foot
per month in others. Yet, when the monthly results are summed for a year a
difference of 036 foot would accumulate if ground-water inflow were to average
0-03 foot per month rather than zero, and for 10 years the difference would
grow to 3.60 feet.

The cumulative effect of small but persistent errors may be indicated in
table 5, which summarizes the monthly water-balance computations by years.
The computations indicate that from 1962 to 1969 the level of Lake Kerr
declined 3.89 feet whereas the level actually rose 1.40 feet. The difference
between the two represents and error-of +5.29 feet, which is large in relation to







TABLE 5
APPROXIMATE YEARLY WATER BALANCE OF LAKE KERR, 1962 69, IN FEET;


CONSTANT LEAKAGE ASSUMED.


Estimated Estimated Change in lake level
Estimated ground-, surface-
Calendar Estimated lake Estimated water water Computed Observed Error-j
year rainfall evaporation leakage inflow inflow


1962 3.37 3.83 1.2 0 0 -1.66 -1.32 +0.34
1963 4.40 3.92 1.2 0 0 .72 .23 + .49
1964 6.04 3.88 1.2 0 0 + .96 +1.92 + .96
1965 4.57 3.87 1.2 0 0 .50 +1.52 +2.02
1966 4.60 3.75 1.2 0 0 .35 + .35 + .70
1967 3.70 3.99 1.2 0 0 -.1.49 -1.20 + .29
1968 4.75 3.84 1.2 0 0 .29 + .10 + .39
1969 5.12 3.76 1.2 0 0 + .16 + .26 + .10
Total 36.55 30.84 9.6 0 0 -3.89 +1.40 +5.29
Average 4.57 3.86 1.2 0 0 + .66


-I Error is the difference between observed and computed change in lake level.






BUREAU OF GEOLOGY


the total range in stage over the time involved. The direction of the error
indicates that the estimated inflow was consistently less than actual or that the
estimated outflow was consistently greater than actual. The first of the two
possibilities would be consistent with the fact that both ground-water and
surface-water inflow were estimated as zero.

Regression methods (Riggs, 1968) were used to evaluate the possible effect
of ground-water inflow to Lake Kerr. Terms of the water-balance equation
(equation I) were rearranged to obtain a monthly residual from values of the
observed change in lake level, estimated rainfall on the lake, estimated lake
evaporation, and estimated surface-water inflow (estimated as zero). The
water-balance residual represents the net effect of leakage from the lake and
ground-water inflow to the lake plus the net effect of errors in the estimates of
all the other factors involved.

The water-balance residual was related by a linear-regression equation to
the level of Lake Kerr and to an index of ground-water levels in the vicinity of
Lake Kerr. The best index of ground-water levels available for the 8 years
involved was the level of water in Sharps Ferry well, which taps the Floridan
aquifer about 8 miles east of Ocala (fig. 1). The level of water in Sharps Ferry
well represents the potentiometric surface of the Floridan aquifer at that point.
Because the aquifer integrates the effect of rainfall over a fairly large area, the
fluctuations of the potentiometric surface at Sharps Ferry well generally should
be proportional to the fluctuations of the potentiometric surface of the Floridan
aquifer at or beneath Lake Kerr, or, at least, the potentiometric surface at the
two points of concern should follow the same general trend through pronounced
wet and dry periods. Figure 16 shows a general comparison of fluctuations in the
water levels of Lake Kerr and Sharps Ferry well.

The equation used in the regression analysis was as follows:

Y = a + b (X2 X1) (2)

wherein Y is the monthly water-balance residual, X1 is the monthly average level
of Lake Kerr, and X2 is the monthly average level of water in Sharps Ferry well.
The constants a and b are determined by regression.

Leakage from Lake Kerr varies inversely with the X2 X1 term; that is,
when the X2 X1 term takes on its largest values, the potentiometric surface of
the Floridan aquifer at Lake Kerr is highest in relation to the lake level -- but
not necessarily above the lake level and the potential for water to leak from
Lake Kerr to the Floridan aquifer is at its smallest. Conversely, when the X2 -
X1 term takes on its smallest values, the potentiometric surface of the Floridan







REPORT OF INVESTIGATIONS NO. 73


aquifer at Lake Kerr is lowest in relation to the lake level and the potential for
water to leak from Lake Kerr is at its greatest.

Variations in ground-water inflow to Lake Kerr from the shallow aquifer
run counter to variations in leakage from the lake to the Floridan aquifer; that
is, when the potentiometric surface of the Floridan aquifer is high in relation to
the level of Lake Kerr, the level of water in the shallow aquifer is also high in
relation to the lake level because the two aqufers are recharged by the same



ALTITUDE OF WATER LEVEL, FEET ABOVE MEAN SEA LEVEL


P N N
0 0
b b 0 0


b 0 o
b b o


Graphs showing monthly average level of water in Lake Kerr and
Sharps Ferk well.


Figure 16.








I


WATER -BALANCE RESIDUAL (Y) OBSERVED CHANGE IN LEVEL OF LAKE KERR RAINFALL + EVAPORATION
3 0 Y *-0.642 + 0,0227 (Xg -XI,



0 0 0 0 0 0 0 0



rit
00a 0
-0 0 00 0 0


21 2 2 23
I I I I I I I I
S '21 22 23 24 25 26 27 28 29 30
r WATER LEVEL AT SHARPS FERRY WELL (X,) MINUS STAGE AT LAKE KERR (X,)

16 ,







REPORT OF INVESTIGATIONS NO. 73


rainfall; Consequently, when the potential for leakage to the Floridan aquifer is
small, the potential for ground-water inflow from the shallow aquifer is large,
and vice versa. Thus, variations in ground-water inflow also are related to the X2
- X1 term butin the opposite way that variations in leakage are related to the
term. The X2 X1 term therefore reflects the combined effect of variations in
leakage from Lake Kerr to the Floridan aquifer and ground-water inflow to Lake
Kerr from the shallow aquifer.

The data used to determine the regression coefficients of equation 2 were
restricted to that for months having estimated rainfall less than 0.30 foot
because (a) errors due to the estimate of surface-water inflow (estimated as zero)
would have minimal effect; (b) the selected data provided a fairly large sample
(about half the available data) consisting of data for 47 months that were widely
enough dispersed in time to be fairly representative of both wet and dry periods;
(c) data for months having rainfall greater than 0.30 foot per month lacked the
homogeneity required for valid regression analyses because of large and
apparently uncompensated errors in the estimates of rainfall for some months.
The resulting regression equation was

Y = -0.642 + 0.0227 (X2 X1). (3)


Figure 17 shows a plot of the data.

The monthly change in level of Lake Kerr was recomputed using the
regression equation (equation 3) to determine the net of leakage from Lake Kerr
and ground-water inflow to Lake Kerr, hereafter called net ground-water inflow.
Monthly values of rainfall, lake evaporation, and surface-water inflow were the
same as used in the previous computations. Net ground-water inflow ranged
from +0.03 foot per month in October 1964 to -0.14 foot per month in
April- June 1968, and averaged -0.083 foot per month overall. The range of
variation of net ground-water inflow (0.17 foot) agrees closely with the range of
0.16 foot deduced previously from the analysis of the observed lake-level
declines during rainless periods (table 3).

The monthly errors as indicated by the difference between the observed
change in lake level and the recomputed change in lake level differed
somewhat from the errors of the results of the previous computations, the
maximum difference being 0.13 foot in October 1964. For the most part,
however, monthly errors that were large in the previous computations remained
large and those that were small in the previous computations remained small. In
general appearance, the time distribution of the monthly errors shown in figure
18 is about the same as the distribution shown in figure 13.



























1963 1964 1965 196 1967 1968 169


Z
-J

S01



z


ew

Q!


1.0



.5



0



-.5


Jul"






i~i







Li


-,1.0


1962







TABLE 6
APPROXIMATE YEARLY WATER BALANCE OF LAKE KERR, 1962-69, IN FEET;
NET OF LEAKAGE AND GROUND-WATER INFLOW DETERMINED BY REGRESSION EQUATION

Estimated Estimated Change in lake level
Estimated leakage minus surface-
Calendar Estimated lake ground-water water Computed Observed Error1/
year rainfall evaporation inflow inflow

1962 3.37 3.83 1.43 0 -1.89 -1.32 +0.57
1963 4.40 3.92 1.37 0 .89 .23 + .66
1964 6.04 3.88 .55 0 +1.61 +1.92 + .31
1965 4.57 3.87 .43 0 + .27 +1.52 +1.25
1966 4.60 3.75 .78 0 + .07 + .35 + .28
1967 3.70 3.99 1.07 0 -1.36 -1.20 + .16
1968 4.75 3.84 1.25 0 .34 + .10 + .44
1969 5.12 3.76 1.08 0 + .28 + .26 .02
Total 36.55 30.84 7.96 0 2.25 +1.40 +3.65
Average 4.57 3.86 1.00 0 + .46


-/ Error is difference between observed and computed change in lake level.






BUREAU OF GEOLOGY


When the monthly water-balance results based on the regression equation
are summed by years (as shown in table 6) the resulting error is reduced for
some years in relation to the errors shown in table 5 and increased for
others- The reduction in error was greatest for years when the level of Lake Kerr
rose the most. The cumulative error for 1962 69 was appreciably reduced from
+5.29 feet to +3.65 feet.

As was true in table 5, the persistency of the positive sign of the yearly
errors in table 6 again indicates that estimated inflow to Lake Kerr was less than
actual or that estimated outflow from Lake Kerr was greater than actual. Part of
the error doubtlessly can be attributed to surface-water inflow which was
estimated as zero. Some surface-water inflow must result from intense rainfalls
around the lake. Although the inflow from any one storm might be small and
relatively inconsequential, inflow from the several intense storms that occur each
year might be expected to add water averaging from 0.2 to 0.3 foot per year.

Although the estimate of yearly lake evaporation conceivably could be
incorrect by a few inches, this would not produce a persistent error in the yearly
water-balance results because of the computational procedures used. For
example, if actual lake evaporation is 43 inches or 49 inches rather than 46
inches per year, as estimated, the difference is distributed almost uniformly
among the estimates of monthly lake evaporation. The error-in monthly-
evaporation consequently appears in the monthly water-balance
residual making them greater or less than they should be and, hence, in the
regression equation which is based on the residuals. When the regression
equation is used to determine net ground-water inflow, therefore, the resulting
values are in error in a positive direction if estimated lake evaporation is larger
than actual and they are in error in a negative direction if estimated lake
evaporation is smaller than actual. Thus, the error in the estimate of lake
evaporation is compensated for by an error of the opposite direction in the
estimate of net ground-water inflow.

Although in the general area of Lake Kerr errors due to faulty estimates of
rainfall normally would be expected to balance closely over a period as long as 8
years, part of the large cumulative error indicated in table 6 probably is
attributable to the estimate of rainfall on the lake. The previous analysis of
monthly results indicated that the large errors substantially greater than 0.1
foot per month were primarily attributable to faulty estimates of rainfall. The
direction of the large errors indicated that estimated rainfall on the lake
frequently was substantially less than actual and seldom was substantially greater
than actual. Thus, for 1962- 69 the yearly rainfall at Lake Kerr may have
averaged from 2 to 3 inches more than was indicated by the average of rainfall at
Crescent City and Ocala, even though rainfall at the three points may average
about the same over the long term.







REPORT OF INVESTIGATIONS NO. 73


If an appreciable part of the cumulative error in table 6 is due to faulty
estimates of rainfall and if over the long term the yearly rainfall averages
about the same at Lake Kerr, Crescent City, and Ocala then water-balance
computations based on factors estimated as described herein (including the use
of equation 3 to determine net ground-water inflow) should in time produce a
greater proportion of negative errors than was produced for 1962 69. An
analysis of the monthly water-balance data for 1970 71 (not presented herein)
indicates that the yearly error in the computed change in level of Lake Kerr is
-0.70 foot from 1970 and -0.06 foot for 1971. A similar analysis of the yearly
data for 1956 61 indicates that the resulting yearly error is positive for 3 years
and negative for 3 years and that the cumulative error for the 6 years is only
slightly positive. This indicates that a greater proportion of negative yearly errors
can be expected over a longer time and that during 1962 69 rainfall at Lake
Kerr was somewhat anomalously greater than rainfall at Crescent City, Ocala,
and other stations in the general area.

SUMMARY

The monthly change in level of Lake Kerr was approximated for 1962 69
by use of a water-balance equation and estimates of rainfall, evaporation,
leakage, surface-water and ground-water inflow. Rainfall was taken as the
average of rainfall at Crescent City and Ocala. Estimated yearly lake evaporation
was distributed on basis of the seasonal variation of monthly pan evaporation.
Although leakage is known to vary, leakage was assumed to occur uniformly at
0.1 foot per month. Although surface-water and ground-water inflow occur at
times, these factors were tentatively estimated as zero.

The computed monthly change in lake level was within 0.10 foot of the
observed change in lake level about 70 percent of the time. Because of the
distance between the lake and the rainfall stations used for the estimate of
rainfall at the lake, some large errors were to be expected. Because of the usual
randomness of rainfall, however, errors from this cause were expected to balance
one another over a period as long as 8 years. Instead, most of the errors
substantially greater than 0.10 foot were of the same direction and indicated
inflow to the lake not accounted for by the various estimates. Because of their
magnitude and because they were traced to periods of lake-level rise, the large
errors presumably were caused by faulty estimates of rainfall or surface-water
inflow.

A similar array of large errors resulted when the estimate of rainfall was
based on records for other rainfall stations in the vicinity of Lake Kerr, taken
singly and in different combinations, both including and excluding those for
Crescent City and Ocala. In these computations, for some of the months







BUREAU OF GEOLOGY


associated with large errors the size of the errors varied with the choice of
rainfall stations, suggesting that the large errors of the computations based on
rainfall at Crescent City and Ocala probably were caused by faulty estimates of
rainfall. For 7 months, especially for 1965, but for other years as well, large
errors persisted regardless of the choice of rainfall stations used; however, for
1965 rainfall was shown to be substantially greater at Lake Kerr than indicated
by rainfall stations in the general area. Thus, it was concluded that all the large
errors of the water-balance computations resulted primarily from faulty
estimates of rainfall. Surface-water inflow probably is a small contributing factor
during the most intensive rainfalls.

The use of a constant rate of leakage from the lake and an estimate of zero
for ground-water inflow to the lake did not lead to large cyclical errors in the
analysis of the observed lake-level declines during rainless periods involving 54
months in 1962 69. Such errors would be expected to occur if either leakage
from the lake or ground-water inflow to the lake were both large and highly
variable between wet and dry periods. The combined effect of variations in the
monthly rates of leakage and ground-water inflow was indicated to be 0.16 foot
for 95 percent of the months involved. In a separate analysis, variation in the
monthly rate of leakage in 1962 69 was indicated to be about 0.04 0.06 foot.
Thus, the variation in the monthly rate of ground-water inflow apparently fell
within a range of about 0.10 foot.

Analysis of the difference between the level of water in a well tapping the
shallow aquifer and the level of water in the lake suggested that the relative
magnitude of ground-water inflow to the lake from the shallow aquifer varied
greatly between wet and dry periods; for this to occur within a variation in the
monthly rate of ground-water inflow of about 0.10 foot, the monthly rate of
ground-water inflow had to be small (relative to 0.10 foot) during dry periods
and not appreciably greater than 0.10 foot during wet periods.

The yearly water-balance data showed that for 1962 69 the computed
change in lake level was in error by +5.29 feet. The direction of the error
indicated inflow to the lake that was not accounted for by the estimates of the
various factors involved. Part of the error is easily explained by the fact that
both surface-water and ground-water inflows were estimated as zero. The
accumulation of small quantities of either could be appreciable over a period of
8 years.

The effect of ground-water inflow to Lake Kerr was investigated by use of
regression methods wherein net ground-water inflow (the net of leakage and
ground-water inflow) was related to the difference between the lake stage and
the level of water in Sharps Ferry well, which taps the same Floridan aquifer







REPORT OF INVESTIGATIONS NO. 73


that underlies Lake Kerr. After net ground-water inflow was determined by the
regression equation, the cumulative error in the computed change in level for
1962- 69 was appreciably reduced from +5.29 feet to +3.65 feet. Net
ground-water inflow ranged from +0.03 foot per month to -0.14 foot per month,
and averaged -0.083 foot per month for 1962 69, leakage being greater than
ground-water inflow for all but a few months near the end of 1964.

The remainder of the cumulative error in the computed change in level for
1962 69 was attributed to faulty estimates of surface-water inflow (estimated
as zero) and rainfall. Small quantities of surface-water inflow resulting from the
several intensive rainfalls that occur most years conceivably could total, on the
average, from 0.2 to 0.3 foot of water per year.

The analysis of large errors in the monthly water-balance results indicated
that during 1962 69 estimated rainfall at Lake Kerr frequently was
substantially less than actual and seldom was substantially greater than actual.
Thus, during 1962 69 the actual rainfall at Lake Kerr may have averaged 2 to 3
inches more than was estimated on basis of rainfall at Crescent City and Ocala,
even though rainfall at these two stations may be closely representative of
rainfall at Lake Kerr over a longer period of time. Analyses of water-balance data
for 1956 61 and 1970 71 (not included herein) indicated that rainfall at Lake
Kerr was anomalously high in 1962 69.

Based on the long-term averages for Crescent City and Ocala, rainfall at
Lake Kerr averages about 54 inches per year. Lake evaporation is estimated to
average about 46 inches per year. During 1962 69, leakage from Lake Kerr was
about 12 inches greater than ground-water inflow to Lake Kerr. If this 12-inch
difference is representative of the long-term average, surface-water inflow
averaging about 4 inches per year is required to maintain the water balance of
Lake Kerr. Ground-water inflow is indicated to be relatively small, probably in
the same order of magnitude as surface-water inflow.






48 BUREAU OF GEOLOGY







REPORT OF INVESTIGATIONS NO. 73


REFERENCES

Clark, W. E., Musgrove, R. H., Menke, C. G., and Cagle, J. W., Jr.
1963 Hydrology ofBrooklyn Lake near Keystone Heights, Florida: Florida State
Board of Conserv., Div. of Geol., Reptt. Iv. 33, 43 p -

Faulkner, G. L.
1970 Geohydrology of the Cross Florida Barge Canal area: U. S. Geol. Survey,
Tallahassee, Fla., open-file report, 222 p.

Florida Agricultural Experiment stations
1962 General soil map of Florida: Univ. of Florida, Gainesville, 1 sheet

Hendricks, E. L., and Goodwin, M. H., Jr.
1952 Water-level fluctuations in limestone sinks in southwestern Georgia in
Contributions to the hydrology of the United States: U. S. Geol. Survey
Water-Supply Paper 1110, pp. 157-245.

Kenner, W. E.
1964 Maps showing depths of selected lakes in Florida: Florida State Board of
Conserv., Div. of Geol., Inf. Circ. 40, 82 p.

Kohler, M. A., Nordenson, T. J., and Baker, D. R.
1959 Evaporation maps for the United States: U. S. Weather Bureau Tech. Paper 37,
13 p., 5 plates.

Kohler, M. A.
1954 Lake and pan evaporation in Water-loss investigations Lake Hefner studies,
technical report: U. S. Geol. Survey Prof. Paper 269, pp. 127 148.

Parker, G. G., Ferguson, G. E., Love, S. K., and others
1955 Water resources of southeastern Florida: U. S. Geol. Survey Water-Supply
Paper 1255, 965 p.

Riggs, H. C.
1968 Some statistical tools in hydrology: U. S. Geol. Survey, Tech. Water-Resources
Inv., Book 4, Chap. Al, 39 p.

U. S. Geological Survey
1962-1970 Water resources data for Florida, part 1, surface-water records, vol. 3, lakes,
annual summaries for 1961 69 water years: U. S. GeoL Survey, Water
Resources Div., Tallahassee, Fla., ann. ser.

U. S. Weather Bureau
1961-1970 Climatolotical data, Florida, monthly and annual summaries, 1960 69: U. S.
Dept. Commerce, Environmental Sci. Services Adm., Asheville, N. C.