Front Cover
 Title Page
 Table of Contents
 I. Introduction
 II. Statistical evidence concerning...
 III. Thermal imagery of the Lake...
 IV. The energy balance of Lake...
 V. The modified lake
 VI. Air tamperature downwind of...
 VII. Conclusions
 Historic note

Group Title: Bulletin - Agricultural Experiment Stations, University of Florida ; 808 (technical)
Title: The Moderating effect of Lake Apopka on downwind temperatures
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00027450/00001
 Material Information
Title: The Moderating effect of Lake Apopka on downwind temperatures
Series Title: Bulletin Agricultural Experiment Stations, University of Florida
Physical Description: 48 p. : ill. (some col.), maps ; 23 cm.
Language: English
Creator: Bill, R. G ( Robert George ), 1949-
University of Florida -- Fruit Crops Dept
Publisher: Fruit Crops Dept., Institute of Food and Agricultural Sciences, University of Florida
Place of Publication: Gainesville Fla.
Publication Date: 1979
Subject: Atmospheric temperature -- Florida -- Lake Apopka   ( lcsh )
Temperature -- Apopka, Lake (Fla.)   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
non-fiction   ( marcgt )
Bibliography: Bibliography: p. 47-48.
Statement of Responsibility: R.G. Bill, Jr. ... et al..
 Record Information
Bibliographic ID: UF00027450
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: aleph - 000401149
oclc - 07223109
notis - ACE6967

Table of Contents
    Front Cover
        Front Cover 1
        Front Cover 2
    Title Page
        Title Page
    Table of Contents
        Table of Contents
    I. Introduction
        Page 1
    II. Statistical evidence concerning the lake effect
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
    III. Thermal imagery of the Lake Apopka region
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
    IV. The energy balance of Lake Apopka
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
    V. The modified lake
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
    VI. Air tamperature downwind of lake Apopka
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
    VII. Conclusions
        Page 46
        Page 47
        Page 48
    Historic note
        Page 49
Full Text

(Lcmber 1979

R. G. Bill, Jr., J. F. BArtholic, R. A. Sutherland,
J. Georg, and FAMiLe 1980

.J. dUv, o i-i ori-

Agricultural Experiment Stations
Institute of Food and Agricultural Sciences
University of Florida, Gainesville
F A. Wood, Dean for Research

Bulletin 808 (technical)

JAN 9-1, 1976 -' -50 DI- ECT
0500-0600 EST /

Thermal imagery downwind of Lake Apopka.

The Moderating Effect of Lake Apopka
on Downwind Temperatures

R. G. Bill, Jr., J. F. Bartholic, R. A. Sutherland,
J. Georg, and E. Chen

Fruit Crops Department
Institute of Food and Agricultural Sciences
University of Florida

This public document was promulgated at an annual cost of $3,430
or a cost per copy of $2.29 to present information on the effect of
lakes on local microclimates and to estimate effects of lake

All programs and related activities sponsored or assisted by the Florida
Agricultural Experiment Stations are open to all persons regardless of race,
color, national origin, age, sex, or handicap.



Chapter Page
I. Introduction ....................................... 1
II. Statistical Evidence Concerning the Lake Effect........... 2
Temperature Trends from Previous Lake Studies...... 2
"Cold Night" Temperature Trends in the Vicinity
of Lake Apopka ............................. 3
Lake Apopka Area Wind Study .................... 11
III. Thermal Imagery of the Lake Apopka Region ............ 13
Analysis of NOAA-3 Satellite Data 13
Analysis of Thermal Flights South of Lake Apopka ... 13
IV. The Energy Balance of Lake Apopka .................... 18
Measurement of Energy Fluxes ..................... 22
A Comparison of the "Lake Effect" with the
"Urban Heat Island"........................ 30
V. The Modified Lake .................................. 31
VI. Air Temperature Downwind of Lake Apopka ............ 38

The Governing Equations ....................... 38
The Constant Flux Layer ........................ 40
Energy Conservation at the Surface ................. 40
Boundary Conditions ............................. 41
Numerical M ethods .............................. 42
Numerical Results ................................42
VII. Conclusions ................... ..................... 46
References ................... ............................. 47

This work was supported by the U.S. Department of Interior, Office
of Water Research and Technology, as authorized under the Water
Resource Research Act; the Florida Department of Environmental
Regulation, Office of Lake Restoration; and NASA, Meteorology and
Climatology, Kennedy Space Center. We wish to acknowledge the expert
help of Meri A. Karafin in the preparation of this bulletin.


Moderating.effects of large bodies of water on surface temperatures of
coastal regions have been noted qualitatively by climatologists for many
years. Agriculturists have been aware of similar effects on a much
smaller scale produced by the plumes of lakes and have used this infor-
mation as an aid in the selection of growing sites for cultivars subject to
cold damage. Florida citrus growers, for example, have found that by
planting on the southern shores of lakes, they can obtain some
moderating effects on minimum temperatures which occur at night dur-
ing freeze conditions when winds are predominately from the north
(Lawrence, 1963; Bartholic and Sutherland, 1975). Although these prac-
tical effects are well known, surface temperature data are quite sparse
(see e.g. Geiger, 1965). No detailed quantitative data are available, con-
cerning energy transport and flow conditions associated with such con-
vective plumes.
Thermal protection of crops by lakes is only one of many benefits
from the abundant number of lakes in Florida. Recreational use of lakes
alone results in millions of dollars in revenues to the economy of Florida.
Furthermore, lakes are an important part of the hydrological cycle and
will become increasingly valuable as man continues to increase his
demands for water through agricultural, industrial, and residential uses.
Unfortunately, many lakes in Florida are undergoing severe eutrophic
processes, either through natural conditions or conditions aggravated by
man's use of water. The Florida Department of Environmental Regula-
tion and the Florida Fish and Game Commission have recommended
lake drawdown as a method of removing excess nutrients from water,
germinating lake bottom vegetation, and solidifying lake bottom sedi-
ments in studies of eutrophic lakes such as Lake Carlton and Apopka.
However, many of the lakes are in need of renewal in key agricultural
areas. Thus an assessment of lake elevation levels compatible with ther-
mal protection needs of agriculture is critical. A complete understanding
of the physical mechanisms involved in the advection of heat from lakes
is necessary in order to assess these needs.
Transport mechanisms include both turbulent and radiative transfer.
Lakes, being warmer than the air and surrounding land, release sensible
and latent heat under typical nocturnal cold front conditions. Sensible
and/or latent heat, depending upon the downwind dew point temper-
ature, is transferred by turbulent diffusion to the ground as the moist
buoyant plume is advected beyond the lake by the moving air mass. The
radiation energy balance of the surface downwind of the lake may also
be affected by advection of water vapor from the lake surface. That is,

local changes in vertical profiles of absolute humidity may change net
radiation loss from the ground.
Several different approaches have been used to quantify these many
effects. First, the statistical evidence of the moderating effect of lakes
has been summarized. A detailed evaluation of temperature and wind
data in the vicinity of Lake Apopka from freeze events of the last 43
years provided by the National Weather Service has been emphasized in
particular, because of the severe eutrophic state of Lake Apopka and the
lake's importance to the citrus industry. More detailed information is
necessary, however, to gain more insight into the specific thermo-
dynamic processes. These are provided in part by temperature data ob-
tained from satellite and aircraft mounted thermal scanners in the
Apopka region. Data are also provided on surface temperatures, radia-
tion, turbulent transport, and wind flow over Lake Apopka. Data were
obtained on nights of severe cold conditions. It was possible to delineate
flow conditions in which significant thermal effects could be expected to
occur downwind of lakes and to estimate the energy transport associated
with these effects.
Finally, the measured physical parameters characterizing the Lake
Apopka region were incorporated in a two-dimensional model simu-
lating air flow over the lake under various conditions of drawdown to
assess the effect of lake drawdown on downwind temperature.

Temperature Trends from Previous Lake Studies
Statistical data from previous studies on the moderating effects of
lakes in Florida are quite sparse (Davis, 1963; Davis, 1958; Benson,
1960). Results in Table 1 from a study of Santa Fe Lake (Davis, 1963) are

Table 1. Observed average minimum temperatures for Santa Fe Lake area,
Average minimum temperatures (OC) on all nights
Nov. Dec. Jan. Feb. Mar. Season
Lake Stations 9.4 5.1 6.2 5.3 11.9 7.0
Remote Stations 7.9 4.0 5.3 4.4 11.1 6.6
Difference 1.5 1.1 0.9 0.9 0.8 0.4
Average minimum temperatures on cold nights
Lake Stations 5.8 0.0 1.9 2.4 4.3 2.4
Remote Stations 3.3 -1.3 -0.2 1.1 2.3 0.5
Difference 2.5 1.3 2.1 1.3 2.0 1.9
Source: Davis, 1963.

averages for minimum temperatures during the 1962-63 winter season.
Three remote stations were used-one at the northwest edge of the lake,
two at the southern edge. Differences in temperature between lake and
remote locations were from 1.3 to 2.50C on "cold nights," i.e., nights
with temperatures 2.2C or below in peninsular Florida. The effect of
wind direction, however, is not taken into account. With winds from the
northwest it might be expected that the lake station at the northwestern
edge would function as a "remote station."

"Cold Night" Temperature Trends in the Vicinity of Lake

Lake Apopka is located in the central portion of the Florida peninsula
(Figure 1). The lake is approximately 13 km across and has a mean depth
of 1.65 m. Large areas of citrus exist both south and east of the lake.
These are low flat areas with sandy soils not normally well adapted for
citrus because of their freeze susceptibility from poor air drainage. There
is also a considerable area of citrus growth west of the lake, on land with
relatively high elevation. The area immediately north of the lake is
characterized by organic soils and is used for vegetable farming.
Data used herein were taken from the records of the Federal-State
Agricultural Weather Service in Lakeland, Florida. This service has
made winter temperature surveys of the Florida peninsula since 1935. A
number of the temperature survey stations have been located in
agricultural lands around the periphery of Lake Apopka. Data from
these form the basis of this report. Circumstances often necessitate
relocation of the temperature recording stations, and therefore the length
of record from station to station varies. Stations are listed in Table 2 with
their township, range and section number, and other pertinent notes.
Their approximate locations with respect to Lake Apopka are shown in
Figure 2.
Minimum temperature data are tabulated by the Weather Service for
all temperature survey stations for all "cold nights." A "cold night" is
defined as one when the minimum temperature was 2.2 C or lower at a
minimum of at least one station in the network. The average minimum
temperature for the history of the stations on all "cold nights" are
shown in Figure 3. Generally, these averages reflect a temperature
climatology imposed by air flow from the northwest quadrant. However,
calm nights are also a part of the data as well as nights with flow from a
direction other than the northwest quadrant.
Stations in Townships 21 and 22, Range 217, probably warrant closest
examination in any effort to discover the possible moderating effects of
Lake Apopka on the temperature of surrounding areas. Many of the
other stations may be influenced by numerous other lakes in the area,

particularly those north of Apopka. Also, station exposure, soil type,
elevation, the distribution of rainfall, and other more subtle influences
on daily variations in temperature at a discrete point become increasingly
difficult to separate from lake effects with increasing distance from the
lake. Effect of the soil type is probably an important factor in the dif-
ferences among averages at stations 5, 8, and 8A (muck) and station 18
(Leon sand). A first approximation may be deduced from stations 3, 4,
and 4A. The most obvious difference in the exposure of these stations is
that station 3 was exposed over sand while the others were over muck,

Figure 1. Lake Apopka, water depth (meters).

but the period of record for stations 3 and 4A is much shorter than for
station 4. Further, the record years for 3 and 4A are different periods.
Thus, an approximation of 1.6C difference in average minimum
temperature at these stations due to soil type would be reasonable. It
would appear, then, that stations 12, 18, and 21 still received some
moderating influence due to Lake Apopka on "cold nights" if average
minimum temperatures at stations 5, 8, and 8A were increased by 1.6 C.
Figure 3 may reveal the general "cold night" climatology of the area
around Lake Apopka, but it reveals nothing about the effect the lake
may have on potentially critical low temperatures or their duration.
Numerous thermographs from the stations within a few miles north and
south of the lake were reviewed for freeze events in an attempt to show
"typical" temperature tendencies and gain some insight into this aspect.
Thermographs from stations 8 and 18 for three freeze episodes are shown
in Figures 4 and 5. They appear representative of all others reviewed. The
average difference in the minimum temperature for the seven cases is
within 0.6 C of the historical difference (Figure 3). It is clearly evident
from the curves in Figures 4 and 5 that the freeze threat is less severe on
the south side of the lake where minima are higher and durations shorter
than those north of the lake. It would be reasonable, allowing for dif-
ferences in soil type, to assume that at least some of the difference in
freeze threat is attributable to the moderating effect of the lake. These
statistical data, however, do not permit estimation of the distance the ef-
fect extends and the rate at which the effect decays with distance.
Further information concerning the duration of critical temperature at
several locations around Lake Apopka is presented in Table 3, which
shows stations 8 and 12 to be of particular importance. Records from
these two stations span 21 years, while the others span 30 years. Station 8
(Zellwood) accumulated a total of 267 hours at below -3.3 C in the
21-year period while station 12 accumulated only 73 hours.' Seasonal ac-
cumulations for these two locations are plotted in Figure 6. Note that the
trend was reversed during 1959-60 and 1960-61. One possible cause of
this reversal might be that flooding or manipulation of the water table at
Zellwood effectively moderated the microclimate in these particular
Statistical probabilities for a few of the stations in Figure 2 are
available (Table 4). The method used to determine the probabilities is
described by Barger (1960). It may be deduced from the raw data that
probabilities for station 12 would be similar to station 2 and those for
station 8 a little greater than those for station 7, until those for stations 8
and 12 are determined.

1. Station 18 (closest to the lake) had even fewer hours below -3.3 C, but the
period of record did not lend itself to comparison with station 8.

Table 2. Locations of data point sources in Figure 2.
ID# Name Township Range Section
1 Astatula 20 26 4
1-A Astatula 20 26B 32
(These were averaged together-13 years, the first influenced some by Lake
Dora, the latter by Lake Harris)
2 Tangerine 20 27A 18
(group of lakes N, E, and W. Exposure: average low. Leon sand; 38 years.)
3 Zellwood Sand 20 27T-C 29
(5 years)
4 Zellwood 20 27T-B 27
(exposure: low, muck, 29 years)
4-A Zellwood 20 27T-B 21
(4 years)
5 Zellwood Ex. Sta. 21 27T-B 9
(18 years, exposure: low, muck)
6 Sorrento 20 28C 6
(11 years, frost pocket)
7 Plymouth 20 28A 29
(28 years, exposure: low, Norfolk sand)
7-A Plymouth 21 28 6
(7 years, Norfolk sand)
8 Zellwood 21 27T-A 12
(22 years, exposure: low, muck)
8-a Zellwood 21 27T 4
(2 years, exposure: low, muck)
9 Apopka 21 28T-A 9
(36 years, exposure: low, Leon sand)
10 Apopka 21 28B 30
(3 years)
11 Forest City 21 29 16
(33 years, exposure: low, Norfolk sand)
12 Fuller Crossing 21 29 16
(sometimes called Winter Garden. 18 yrs. as Fuller Crossing, 1 as Winter
Garden. Seemingly identical location, exposure: avg. low, Leon sand)
13 Orlo Vista 22 28B 26
(37 yrs., exposure: low, Norfolk sand)
14 Pickard 22 28C 26
(19 yrs., exposure: avg. high, Norfolk sand)
15 Avalon 23 27 18
(9 yrs., Johns Lake may influence)

Table 2.-Continued.

Name Township
Montverde 22
(38 yrs., exposure: high, Norfold sand)
Howey 21
(38 yrs., exposure: low, Norfolk sand)
Winter Garden 22
(19 yrs., exposure: avg. low, Leon sand)
Clarcona 21
(7 yrs., Norfolk sand)
Clarcona 21
(11 yrs., Norfolk sand)
Ocoee 22
(very short)







25 26 27 28 29

Figure 2. Data source locations.







21 3{3

2.8 3.9

Z *6.1
22 -5.

23 *
Scale : I-1.6 km

25 26 27 28 29

Figure 3. Average minimum temperatures for "cold nights."

1957 1962

\ Dec. 12 13 Dec. 14

minima 4 5.1 -3.6
-4.4 -7.2 -7.2


Figure 4. Comparison of thermographs north and south of Lake Apopka dur-
ing freeze episodes.


FEB 18

-- -I.I

-2.5 -0.5 -0.4 -2.7 MINIMA

------ -6.0 -3.9 -4.3 -6.0 MINIMA


Figure 5. Comparison of thermographs north and south of Lake Apopka
during freeze episodes.

Table 3. Seasons with a total of 10 hours or more at or below -3.30C.
Boldface type indicates seasons with 20 hours or more at or below -3.30C.
Station # Name Yeart

Zellwood #1
Forest City
Orlo Vista


8 Zellwood 48,50,55,57,58,61,62,65,68.
12 Fuller Crossing 57,59,62.
1The year is that of the beginning of the season; i.e., 37 denotes the 1937-38 season, etc.

Table 4. Probability (%) the air temperature (%) will be as low or lower
than indicated temperatures at least one in any season.

Station # Name -8.9 -7.8 -6.7 -5.6 -4.4 -3.3 -2.2 -1.1 0.0C
2 Tangerine Nil 3 6 13 26 48 78 96
7 Plymouth Nil 4 7 18 33 58 84 981
11 Forest City Nil 4 9 16 34 48 85 98t
17 Howey Nil 8 16 31 56 82 98t
tTheoretical value



AI \
10 \I \ /
I \ //
I \

ti on iA 1 F e CI i
Fgo 6 ronlt tcD r-e oo n Of q- 2N r.2 Ioo r- aloe 0
0 LOLo 0 U- Lo ) L o (D c (D (D w 0 0 (D o ( (D

Sri IO O C)U) ) ) 0 co 9 D ID W (0 W (D (D


Station 8 Zellwood 2127T-A
Station 12 Fuller Crossing 2228T D

Figure 6. Seasonal accumulations of -2.20C and lower.

Lake Apopka Area Wind Study
Characteristics of the wind speed and direction in the vicinity of Lake
Apopka were examined for periods of freeze episodes that had a high
probability of damaging some part of citrus trees. The period covered in
this report are January 1934 through March 1977. There are some scanty
records of damaging freezes before 1934 to the middle of the last cen-
tury, but there are no wind records available.
The only systematic wind records available from the vicinity of
Apopka are those of the National Weather Service at Orlando. These
form the basis for this report and are plotted in the form of a windrose in
Figure 7. The number of hours and average wind velocity are tabulated
in Table 5. Frequency of wind observations occasionally changed over


w E

Figure 7. Number of hours wind was from designated direction at Orlando,
Florida during 72 freeze episodes in the period 1934-77.

the record period. The time period used for a freeze episode in this report
was 1800 EST to 0700 EST. Observations ranged from as few as three to
nine or more within this time period. Hourly observations were available
for nearly 80% of the cases. The cases with fewer observations probably
did not introduce any error, as the variability of the wind direction in all
cases was seldom more than 25 degrees from the prevailing direction.

Table 5. Number of hours and average velocity of wind at each
direction during 72 freeze episodes in the period 1934-1977,
Orlando, Florida.
Wind Total Velocity

NNW 207 4.8
NW 192 4.2
N 135 3.8
WNW 86 5.5
W 34 4.6
NNE 28 3.3
WSW 11 3.4
SW 9 3.1
NE 8 3.1
SSW 5 3.1
SE 4 1.5
ESE 3 1.5
ENE 2 3.9
S 2 2.3
SSE 2 1.3
47 0 (calm)
tWind velocities were observed in an unobstructed area and doubtless are greater than
would have been observed in a grove.

Table 6. Number of freeze events by years from 1934 to 1977t.
1934 2 1943 1 1955 1 1960 6 1966 3
1937 1 1947 4 1956 3 1961 2 1967 1
1938 2 1948 2 1957 4 1962 3 1970 1
1940 6 1950 2 1958 12 1964 2 1971 1
1941 2 1954 1 1959 5 1965 2 1977 3

Total = 72
t42'%o of the years-1935, 1936, 1939, 1942, 1944, 1945, 1946, 1949, 1951, 1952, 1953,
1963, 1968, 1969, 1972, 1973, 1974, 1975, 1976-had no freezes affecting citrus.

The 43.5-year record had 25 years with freezes with a high probability
(57%) of damaging citrus in the Lake Apopka area (see Table 6). There
were 72 freeze events in those 25 years, an average of about three per
year. Of the 72 freeze nights, 20 occurred on two consecutive nights, 15
on three nights, 8 on four nights, and 5 over five consecutive nights dura-
tion. About 67% of the freezes were more than one night in duration.

Analysis of NOAA-3 Satellite Data
The NOAA series of satellites pass over Florida at approximately 2200
EST. These satellites have thermal scanners with a resolution of about
0.8 km on the ground. Thus, it is possible to analyze the data from the
NOAA satellite to determine temperature patterns in the vicinity of Lake
General weather conditions characteristic of radiation freeze nights oc-
curred on the night of 4 March 1975, i.e. clear skies and wind speed of
1.0 to 3.0 m/sec. Temperature patterns from the NOAA satellite were
analyzed at Kennedy Space Center. General temperature patterns show
the lowest temperatures are usually in low flat areas west of Lake
Apopka and in the central ridge area of Florida (Figure 8). The higher
temperature patterns are shown to occur in areas characterized by hilly
terrain directly west of Lake Apopka. A cold region in the muckland
north of the lake is readily apparent. This cold region would be expected
from the low thermal diffusivity properties of organic soils. The region
directly south of the lake is in sharp contrast to this cold region. A cold
surface the size of the muckland clearly results in cold air moving onto
the lake from the north; however, the region south of the lake is the
warmest in this scene. The temperature difference between the warmest
and coolest areas is about 6 C even though the exact temperatures in
each zone are not known. These temperatures are not truly quantitative,
but they do clearly show temperature patterns in the whole vicinity of
Lake Apopka and are in good agreement with climatic data presented in
Section II.

Analysis of Thermal Flights South of Lake Apopka
Satellite data portraying the general temperature patterns shown in the
previous section has two shortcomings. First, the resolution of the scan-
ner does not allow detailed temperature patterns south of the lake, and
second, the information is qualitative. Thus, an aircraft-mounted ther-
mal scanner flown at a height of 1.6 km was employed to provide data
with high resolution and greater accuracy.




- -


Figure 8. NOAA satellite data for 4 March 1975.



MINNEOLA 2 point Winter
O CLERMIO gordon

I.E Km

Figure 9. General map of the Lake Apopka area. Flight lines were made in the
general region outlined south of the lake.

A NASA aircraft using a thermal scanner flew routes south of the lake
(Figure 9). The path scanned is shown schematically in Figure 10. Infor-
mation from the scanner was recorded on analog tape in the aircraft.
These tapes were then taken to Kennedy Space Center where the data
were processed on film in which each color represents a specific
temperature interval.
A number of flights have been flown south of Lake Apopka. A color
print of thermal scanner data from one such flight is reproduced as the
frontispiece of this bulletin. Interpretation of the scanner map is given in
Figure 11. Winds were 2 4 m/sec from the north-northeast on this par-
ticular night. The temperature pattern south of Lake Apopka is shown
clearly. The bands of highest temperatures are immediately south of the
lake, and the thermal effect from the lake appears to reach beyond the 6




Figure 10. Schematic showing the thermal scanner in
relation tn the underlvino tfPrrin


JAN 9-10 1976 .67
0500- 0600 -1.67-0..........

r 1 r l An HULL POINT p toroor po

--.. :, .:_. :,_- .. .. _._[ .< '
A K ,- ,'., .", S- -. _:, ..
/ .- -_ : . -. : : -... '
Figure~ ~ ~ ~ ~ ~ ~~~~~~~~-;~' I hra sanrdtasuho Lk ppa.(e rntsic orclrmp rdcdfom scanner data.

km covered with the thermal scanner. The effect of the plume of warm
air moving over the land which modifies temperature south of the lake is
seen clearly. Temperatures both to the east and west of the lake are as
much as 5 C lower than those for similar land south of the lake. Thus,
there is an obvious dramatic temperature modification south of the lake
as shown from this composite of thermal scanner information.
Data from the thermal scanner were also analyzed statistically
(Sutherland and Bartholic, 1976). A grid was used to develop a matrix of
temperatures south of the lake, and the values were statistically analyzed.
Data points falling on or near smaller lakes were eliminated from the
analysis. Results from this study are shown in Figure 12. A cursory view
of the raw data indicated that there was little, if any, effect due to eleva-
tion on this night. This was corroborated by correlation coefficients
showing elevation to be statistically insignificant. Such results are to be
expected on nights with high wind conditions.

Thermal effects documented in previous sections result from the abili-
ty of the lake to store radiant energy received during the day and to
release part of this energy to the air at night in the form of sensible and
latent heat. The ability to store large quantities of energy stems from the
relatively high heat capacity, c, of water and the large volume of water in
the lake. Similar effects, although much larger in scale, are seen in
coastal areas during the winter where convection currents from the warm
oceans produce moderate temperatures as compared with those found on
the inland continental land masses. The energy balance over land and
over bodies of water is discussed below in order to understand these ef-
fects better.
Energy flow patterns found on land and on a lake for typical condi-
tions during a "freeze period" are illustrated schematically in Figures 13
and 14 following Munn (1966). Daytime conditions are shown in Figure
13 and nocturnal conditions in Figure 14. The energy balance during the
day is quite similar for the land and lake cases. The net radiation, R., the
resultant of long wave terrestial radiation and short wave solar radiation,
is a positive flux heating the soil and lake. Both the soil and water sur-
faces are typically warmer than the incoming air associated with the cold
front. Furthermore, the vapor pressure of water, which increases with
temperature, is also typically higher at the surface than within the air
mass. Some of the radiant energy received goes into increasing the
temperature and relative humidity of the air; that is, the amount of ra-
diant energy that the land and lake may absorb is reduced by the sensible
heat, H, and latent heat, LE, flux to the air. Another possible energy
term in the case of the lake is the heat flux received from the muck at the

0 0 O

0 0

0 0




5 -







0 a 0100

o 0 o

o o

E" 0

0 o o o

0 0

0 0 0l

0 0

o o

o o

0 0


I I I I I f I I I I -I I I I I I
5 10 15 20 25 30 35


Figure 12. Statistical analysis of temperature patterns south of Lake Apopka, 8-9 February 1974.

Figure 13. Daytime energy patterns over lake and land,
where H = sensible heat flux,
LE = latent heat flux,
R. = net radiation, and
A- = time rate of change of internal energy.

bottom of the lake. Calculations have indicated this energy flux may be
neglected due to the small temperature gradient and low thermal conduc-
tivity of the muck. The net balance of the energy flux, R, + H + LE,
equals the time rate of change of internal energy, Au/AT, of the lake and
control volume associated with the land. Thus, the intensity of solar
radiation is such that internal energy increases with time for most of the
day, and'the control volumes become warmer under conditions typical of
freeze periods; that is, when the sky is clear.



Figure 14. Nocturnal energy patterns,
where H = sensible heat flux,
LE = latent heat flux,
R. = net radiation, and
A- = time rate of change of internal energy.

Similarities between the two cases disappear rapidly close to sunset
(Figure 14). The equivalent blackbody temperature of the sky is quite low
on clear nights. The net radiation becomes a substantial energy flux from
the lake and land. Low heat capacity of the soil causes the soil surface
temperature to decrease rapidly below the air temperature in the case of
the land control volume. Thus, the land control volume receives energy
in the form of sensible heat from the air. Additional energy is gained
from the latent heat released by the condensation of water vapor if the
surface temperature falls to the dew point temperature. Typically, the
sum of fluxes (H+LE+R,) is less than zero, and the land control
volume decreases in internal energy (Au/Ar <0). Obviously, the danger
of freeze damage is greatest on clear nights when the outgoing net radia-
tion flux is large.
The temperature of the lake on a "freeze night" is warmer than the air
above it in contrast to the rapidly falling temperatures within the land
control volume. Energy leaves the lake as radiant energy as well as sensi-
ble and latent heat. The source for this energy flux is stored internal
energy at the lake, i.e. R, +H+LE = Au/Ar. The lake then contributes
to an increase in the temperature and vapor content of the air moving
over the lake. Fronts associated with severe freezing conditions are usual-
ly dry air masses; hence, air advected downwind of the lake can increase
the energy flux to the land control volume by increasing H through a rise
in air temperature and increasing condensation, LE, by raising the dew
point temperature of the air.

Measurement of Energy Fluxes
Measurements of net radiation, air and lake temperatures, and relative
humidity were obtained in addition to surface temperatures in an in-
strumented boat on Lake Apopka on the "freeze night" of 19 January
1977. Profiles of air temperature to a height of 15 m were also obtained
for the night of 19 January 1977 at locations north and south of Lake
Apopka. Locations of these observation points are shown in Figure 15.
The instrumented boat provided by the Earth Resource Center of
NASA (Kennedy Space Center) was located on the east of Lake Apopka
since the prevailing winds for the two "freeze nights" were west to north-
westerly. This location provided ample distance for the local surface
boundary layer to become fully developed; hence, measurements from
this location can be considered typical for most of the lake. Depth of the
lake at this location was 1.70 m as compared to an average lake depth of
1.65 m. Instrumentation in the boat included a wet bulb-dry bulb
psychrometer, an Atkins thermistor for measuring water temperature, an
epoxy-encased copper-constantan thermocouple for measuring muck
temperatures, a Swissteco S-1 net radiometer, and a cup anemometer and

w---.50 -

Figure 15. Observation sites on Lake Apopka.

wind vane. Instrumentation to determine the Bowen ratio, B =H/LE,
was mounted on a boom extending approximately 2 m beyond the bow
of the boat to estimate the amount of energy released by the lake through
sensible and latent heat. The Bowen ratio instrumentation consisted of a
Brady array humidity sensing device and a 38 gauge copper-constantan
thermocouple referenced to an ice water reference junction. The


temperature and humidity array were attached to the belt of a pulley
system and continuously traversed up and down a distance of approx-
imately 1.5 m. The bottom point of the traverse was approximately 0.4 m
above the mean surface level of the lake. The time for a complete
traverse was 40 seconds. Changes in relative humidity and temperature
levels were recorded continuously on Esterline Angus chart recorders. A
switch at the top of the traverse triggered an event marker so that a
record of the position of the array could be maintained. Calculated dif-
ferences of vapor pressure and temperature across the 1.5 m traversed,
coupled with measurements of net radiation and the rate of change of the
lake temperature are used to estimate LE and H as below.
The Bowen ratio technique relies on the use of turbulent transport
coefficients of heat, KH, and vapor, K,, (which are analogous to thermal
and mass diffusivities used in laminar flows) to estimate sensible and la-
tent heat from vertical gradients of temperature, dt/dz, and vapor densi-
ty, dQ,/dz, as follows:
H c.KH(dt/dz)
LE L K,(dQv/dz)
where o, is the vapor density, c, is the specific heat of air at constant
pressure, and L is the latent heat of vaporization. In finite difference

Typically, the transport of heat and mass are assumed to be the same,
KH/K, = 1.
S(Au/A) R, B (Au/A R,)
LE = and H =
1+B I+B
if R. and Au/Ar are known. The primary results for the freeze nights are
detailed below.
Wind speed and direction, the 2-m air temperature, and specific
humidity are plotted as a function of time for the period 0000 0530
EST, 20 January 1977 (Figure 16). The air temperature, t, and the
specific humidity, q, for the period are compared in Table 7 with data
supplied by NOAA from Gainesville and Orlando.
Windspeed, air temperature, and specific humidity were relatively con-
stant throughout most of the night. The wind direction varied gradually
from the west at midnight to the north at 0400 EST. Turbulent transport
of sensible heat was sufficient at wind speeds above approximately 4
m/sec to keep the temperature of the air mass moving across the lake
above 0.5 C. This contrasts markedly with Orlando and Gainesville
mean temperatures at 0300 when temperatures were respectively 5.0C
and 4.4 C. The air temperature recorded for Orlando (Table 7) would






E 0
-2 O ,


S-2 'I I I
O N-0-- ---0--c---O__o


a 0

0 -0


~o I I-I I I
0100 0200 0300 0400 0500 0600


Figure 16. Meterological data from observation site.

seem to indicate temperature effects of Lake Apopka have been
eliminated by diffusion by distances of the order of 20 km downwind of
the lake.
Wind speed decreased simultaneously with the reduction in air
temperature from 0300 to 0600 EST, until it was reduced below the stall
speed of the cup anemometer (40 cm/sec). This result is expected since a
reduction in wind speed would reduce turbulent diffusivity and, hence,
the amount of sensible heat available to maintain the temperature of the
air mass at an elevated level.
A plot of temperature as a function of location with respect to Lake
Apopka (Figure 17) indicates the effect of wind speed on turbulent
transport even more dramatically. Temperature data are shown here for
the period of 0218 to 0303 EST and 0548 to 0611 EST for 20 January
1977. Wind speed fluctuated between 4 and 5 m/sec for the time period
of 0219 to 0303 EST. A zone of warm air is readily apparent downwind
of the lake in contrast to regions east and west of the lake. No such warm
region was observed, however, for the time period of 0548 0611, when
the wind was well below 1 m/sec. Fluctuations in temperature for this
time period appear to be the result of local thermal effects.
Similar temperature plots along with dew point data are shown for
0100, 17 February 1977, when the wind was from the northwest direction
at = 6 m/sec (Figure 18). A region of warm moist air is clearly visible
downwind of the lake. Air temperatures are strongly correlated with the
axis of wind movement across the lake.
High temperatures observed on and downwind of Lake Apopka
resulted from the transport of sensible and latent heat from reduction in
the internal energy of the lake. Lake temperature at midnight 19 January
1977 was 5.6 C. A vertical traverse of the lake indicated the lake could
be considered to be isothermal to a depth of 1.5 m. A thermal boundary
layer with a temperature gradient existed below this level. The
temperature in the isothermal region changed at a rate of 0.14 C/hour

Table 7. Air temperature and specific humidity for 20 January 1977.
Gainesville Lake Apopka Orlando
Time temp humidity temp humidity temp humidity
(EST) (0C) (g/kg) (0C) (g/kg) (0C) (g/kg)
0000 1.1 3.1
0100 -5.6 1.8 0.6 2.3 -3.9 2.4
0200 0.8 2.2 -4.4 2.3
0300 -4.4 1.7 1.1 2.3 -5.0 2.2
0400 -0.6 2.2 -4.4 2.3
0500 -3.9 2.3 -1.1 2.3 -6.1 2.1

over a period, AT, of 5 hours. However, no change in the boundary layer
temperature was detected.
The time rate of change of the internal energy of the lake may be ex-
pressed as follows:
au aT
= pc-dz, where depth, d = 1.5 m,
9u AT
= QC d.
or AT
Observed temperature change in the lake corresponds to a time rate
of change of internal energy of 0.35 cal/(cm2'min). Net radiation, which
was nearly constant for this time period, was 0.20 cal/(cm2omin). Thus,
the energy available for sensible and latent heat was 0.15 cal/(cm2 min).
An estimate of the ratio of sensible heat to latent heat for the period
was obtained from the recorded analog outputs of the Brady array and
Typical results for the high-wind period of 20 January 1977 are shown
in Figure 19. Increasing voltage indicates increasing temperature and in-
creasing relative humidity; hence, a pattern of increasing vapor pressure
and temperature with decreasing heights is discernable. Precise estimates
of the Bowen ratio are difficult; however, calculations from an inspec-
tion of the analog records indicate the Bowen ratio is approximately 1.
A comparison of the result with the theoretical results of Penman
(1948) would seem to indicate the transport of sensible and latent heat at
the lake surface occurs at approximately saturation conditions. Penman
(1948) showed the functional form of the temperature dependence of the
Bowen ratio under saturation conditions is the ratio of the psychrometric
constant, 7 = CpP/0.622L (P = total pressure), to the slope of the
saturation pressure vs. temperature curve, A. = .66 mb/C is not a
strong function of temperature. However, A varies from 0.46 mb/ C at
0 oC to 1.9 mb/ C at 25 C and y/A = 0.66/0.549 = 1.2 under the condi-
tions for which the data were taken.
It is now possible to estimate the sensible heat transfer, h, and total
heat transfer, hr, coefficients from the above considerations.
H + LE = H(1 + A/y) = h(1 + A/y) (t, t),
where t, = average lake temperature and t, = average air temperature.
h = 0.018 cal/(cm2.min.00C) taking t, = 5.60C and t. = 1.1 C.
These coefficients will be used in discussing the energy balance of the
lake during drawdown.

0100 EST



I-I 1 KM


o o 0218-0303
* 0548-0611

Figure 17. Air temperature south of Lake Apopka for 20 January 1977.


FEBRUARY 17, 1977
0100 EST




2- /0 0
I --0-0 / .
-i -. /-


Figure 18. Air and dew point temperature south of Lake Apopka for 17
February 1977.

TIME ----

Figure 19. Thermocouple and Brady array analog outputs from lake obser-
vation site.

A Comparison of the "Lake Effect"
with the "Urban Heat Island"
Thermal effects similar to those discussed above have been reported
for many years in urban areas at night during the winter season. The ad-
ditional source of energy is supplied in these cases not only through the
release of internal energy, but also by the waste heat added to the at-
mosphere by man's utilization of energy for industrial and residential
purposes. Bornstein (1968) reported combustion during the winter in
Manhattan Island, New York, released a flux heat of more than 0.28
cal/(cm2*min). This is of the same order of magnitude as the released
sensible and latent heat from Lake Apopka (0.15 cal/(cm2-min) over a


- 115 km2 surface area). Thus, one would expect to observe temperature
modification patterns similar to those observed in urban areas.
Gutman (1974) gave a complete survey of the thermal effects of cities.
Briefly, the "urban heat island" in comparison with surrounding rural
areas is characterized by increased surface temperatures, lower humidity,
lower wind speeds, and increased turbulence. Bornstein (1968) reported
elevated temperatures of about 4 C for Manhattan. No surface inver-
sions were observed in contrast to suburban areas; however, a slight in-
version elevated above the city was detected.
A study by Preston-White (1970) of the heat island surrounding Dur-
ban, South Africa, has indicated the center of the heat island may be
displaced from the central business district by a sea breeze. Such an ef-
fect would be quite similar to the thermal effects observed under high
wind conditions downwind of Lake Apopka. Angell et al. (1971) ob-
served in a study of Columbus, Ohio, heat island advection of heat from
the urban area to rural areas caused an elevated inversion quite similar to
those observed south of Lake Apopka. Thus, the above discussion sug-
gests that a model used to predict flow parameters for the "urban heat
island" would be appropriate with slight modifications for predicting
temperature and humidity profiles in the Lake Apopka region.
Numerous one-dimensional models of the "urban heat island" exists
(e.g. Estoque, 1963, and Myrup, 1969). However, these models inherent-
ly neglect advection terms and cannot give an accurate account of the
downwind development of temperature and humidity. The two-
dimensional model of Gutman (1974) was employed to model the effect
of a drawdown of Lake Apopka on downwind temperatures.
Gutman (1974) uses a finite difference scheme, internally consistent
with conservation of mass, momentum, and energy, to solve a set of dif-
ferential equations, including the Navier-Stokes equations, a turbulent
diffusion equation for water vapor, and the heat equation for the soil
substrate. Surface temperatures are not prescribed as boundary condi-
tions; instead, they are predicted from an energy balance at the surface
which is consistent with boundary conditions imposed at 1500 m and at a
depth of 0.1 m in the substrate. Such a model is necessary to determine
surface temperatures downwind of the lake as well as contours of
temperature and humidity. Upwind conditions may be varied to model
changes in front conditions.


The proposed drawdown of Lake Apopka reduces the total heat
capacity of the lake, thus drastically decreasing the ability of the lake to
store energy and maintain relatively stable temperatures. Certainly, a
cursory inspection of the temperature field upwind of the lake, as

discussed in Section III, indicates that the lake cannot be completely
drained during the winter season without risking extensive freeze damage
to crops south of the lake. Beyond this, the question concerning the
volume of water necessary to provide adequate thermal protection is
quite-difficult and may be answered only in a probabilistic sense.
The data of 20 January 1977 were used to develop a one-dimensional
time-dependent model of energy flow and lake temperature in order to
determine the effect of decreased water volume on the fall of the lake
temperature during the passage of a cold front. Data from that night
were used to provide information of radiation and turbulent transfer
coefficients. The lake is assumed to be an isothermal body of constant
depth, d, exchanging energy to the air in the form of radiation and latent
and sensible heat. The bottom of the lake is assumed to be an adiabatic
surface. The equations describing these conditions are developed below
(notation as in the previous section).
From the first law of thermodynamics,
cdr = R, + (H + LE)
where H + LE = h(l + A/*y) (t. t,), at any time r. Air temperature, t.
= 2.20C from 0700 1800 EST and t. = 1.1 C from 1800 0700 EST,
was determined from temperature data taken from Orlando and observa-
tions on the lake. The day temperature corresponds to the average hourly
temperatures in Orlando, which were approximately constant.
The radiation term is separated into two functions. A sinusiodal varia-
tion with a period, P, of 24 hours is assumed during the daytime (0700
-1800); that is, R, = Ro Sin (2HT/P), where the amplitude R, is chosen to
give an average radiation for an 11-hour period of 0.44 cal/(cm2'min).
This radiation constant corresponds to the average net radiation
measured at the IFAS Horticultural Unit on 22 January 1977 during a
clear day. The net outgoing radiation between 1600 and 0700 EST is
calculated as the difference between sky temperature and the graybody
radiation emitted by the lake surface. The equivalent blackbody sky
temperature was calculated as 242 K or -31 C from net radiation data
of 20 January 1977. Thus, taking the emissivity, c, of the lake to be 0.98,
R, = o[(242)4 0.98(t, + 273)4]
where a is the Stefan-Boltzman constant.
The equation in finite difference form for the lake temperature t, at
time, T + AT, in terms of the lake temperature at time r is

t, (7 + Ar) = f
f = R. sin ( 2- ) + h(1 + a) (t, t) for 0700 5 r < 1800
f= a [2424 0.98 (t,+273)4] + h(1 + -) (t t,) for 1800 r 0700.

The time step used for calculations was 1 hour. Data collected since
1974 indicates typically the lake temperature is approximately 10 C prior
to the passage of a cold front. Thus, the algorithm was started with the
initial condition t1(0700) = 10C. Results of the calculation are shown
for a 2-day period in Tables 8, 9, 10, with d = 150, 100, and 50 cm
An inspection of Table 8 indicates that the one-dimensional model
predicts relatively closely the patterns of lake temperatures observed dur-
ing the passage of the cold front of 19-20 January, 1977. The 0600
temperature for the second day is predicted as 5.7 C while the observed
lake temperature low was 5.6 C. The rate of temperature decrease for
the second day between 2400 and 0500 was 0.18 C/hr as compared with
a measured rate of 0.14C/hr.
The discrepancy noted in the rate of decrease in temperature is due to
the higher predicted levels of sensible and latent heat as compared with
measured levels. These increased heat transfer levels were specifically in-
corporated into the model to take into account the dependence of the
transfer coefficient, h, on downwind distance, x. Few data are available
on the effect of distance on transfer coefficients; however, h is propor-
tional to x- 0.2 for a turbulent boundary layer on an isothermal flat sur-
face (e.g. Gebhart, 1971). It may be shown that the total coefficient, h, is
related to the coefficient, hL, at the end of the plate by the simple rela-
tion, h = 1.25hL; hence, the transfer coefficient was augmented by 25 %.
Effects of decreasing the total heat capacity of the lake are indicated in
Tables 9 and 10, where the average depth is taken as 100 and 50 cm,
respectively. Variations in day and nighttime lake temperatures become
greater with decreasing depth, d, due to the small heat capacity of the
lake. Higher temperatures in the day result in increased levels of latent
and sensible heat. Increases in these modes of heat transfer reduce the
proportion of radiant energy which may be stored during the day and
may then be available to be advected downwind of the lake at night.
The rate at which the lake temperature drops with time increases with
decreasing dat night, for the 2-day period. The temperature drop rate on
the second day between 0000 and 0600 is 0.23 oC/hr for the case d = 100
cm. One might expect the temperature drop rate to decrease since the rate
of energy loss by latent and sensible heat has decreased. However, the
relatively constant radiation loss coupled with the sharply decreased heat
capacity results in the higher predicted nighttime temperature drop-rates.
Eventually, the rate of temperature drop must decrease as the
temperature of the lake approaches the air temperature, since heat
transfer is proportional to the temperature difference. However, this
model indicates the temperature-drop rate for the lake increases with
decreasing average lake depth, while the lake temperature is in the range
critical for freeze protection.

Table 8. Lake temperature evolution with lake depth 150 cm.

Time Temperature ( cal \ ( cal cal
(0C) cm2*min k\cm2.min cm-2min

First day














- .236


Second day
0700 7.235 -.115 .000 -.120
0800 7.220 -.113 .195 -.118
0900 7.278 -.113 .374 -.117
1000 7.393 -.114 .522 -.119
1100 7.549 -.117 .629 -.122
1200 7.724 -.120 .684 -.127
1300 7.895 -.124 .684 -.132
1400 8.040 -.128 .629 -.138






Table 8.-Continued.
Time Temperature ( cal ) ( cal ) cal
(C) \cmt2min / \ cm2min I cm'*min /
Second day
2300 6.996 -.137 -.213 -.142
2400 6.804 -.133 -.211 -.136
0100 6.617 -.128 -.210 -.130
0200 6.434 -.124 -.209 -.124
0300 6.255 -.120 -.207 -.119
0400 6.081 -.116 -.206 -.114
0500 5.911 -.112 -.205 -.109
0600 5.744 -.108 .204 -.104

Table 9. Lake temperature evolution with lake depth 100 cm.
Time Temperature / cal cal / cal
(C) \cm.*min/ cmz.min \cm'min/
First day
















Time Temperature







Table 9.-Continued.
cal cal
cm2'min cm- min
Second day
-.090 .000
-.088 .195
-.088 .374
-.091 .522
-.095 .629
-.101 .684
-.108 .684
-.114 .629

-.120 .522
-.123 .374
-.125 .195
-.124 .000
-.145 -.215
-.138 -.213
-.138 -.211
-.125 -.209

-.119 -.207
-.113 -.205
-.107 -.204
-.102 -.202
-.096 -.200
-.091 -.199
-.086 -.197
-.081 -.196

Table 10. Lake temperature evolution with lake depth 50 cm.

Time Temperature cal
(C) \cm'.min/
First day
















- .202

2I min

Table 10. Lake temperature evolution with lake depth 50 cm.
Temperature / cal cal (c
(C) \cm'min \cm2-min /
First day
11.212 -.201 .522
11.109 -.203 .374
10.798 -.200 .195
10.278 -.193 .000
9.448 -.206 -.235
8.685 -.188 -.229
7.983 -.171 -.223
7.334 -.155 -.218

- .097

Second day
0700 3.479 -.030 .000 -.025
0800 3.650 -.029 .195 -.024
0900 4.026 -.033 .374 -.027
1000 4.562 -.041 .522 -.035
1100 5.196 -.053 .629 -.047
1200 5.862 -.067 .684 -.062
1300 6.489 -.082 .684 -.079
1400 7.012 -.097 .629 -.096





- .201


- .094






The low temperature for the 2-day period was predicted as 4.5 C for
the case d = 100 cm. A more critical concern is the amount of energy
that could be advected downwind of the lake, H + LE. The total latent
and sensible energy was summed for the period of the second day of the
cold front from Tables 8 through 10 and was reduced by only 22%. The
effect of the decrease in advected energy on the air mass south of the lake
will be discussed in the next section.
The lake temperature fell to 3.5 C for the case d = 50 cm by sunrise of
the second day at 0600. The temperature has further decreased to 2.3 C
at 0600 the following day. The latent and sensible heat released between
2400 to 0600 of the second day of the front is only 41% of the energy
released in the d = 150 cm case, the model for the unmodified lake.

The Governing Equations
A brief discussion of the equations governing a two-dimensional flow
over the Lake Apopka region and the boundary conditions necessary for
these equations is given in the following paragraphs.
The Gutman model consists of three layers: the soil substrate or lake
surface, the constant flux layer, and the transition layer. It is a two-
dimensional model where the ordinary Cartesian coordinate system is
used. The x-axis is at all times aligned to the geostrophic wind, the y-axis
is considered infinitely long, and the z-axis is in the vertical direction.
The Navier-Stokes equation governing the conservation of momentum
is used in the transition layer. The final form of the momentum equation
a aa ~8O fv g aO + 2(K)
at +ax az a z O ax az2
where r is the y component of vorticity defined by a" = (1)
O = the potential temperature (absolute),
g = acceleration due to gravity,
f = 20 sing, wherefis the Coriolus parameter,
0 is the rotation of the earth and 3 the latitude.
and K is the turbulent diffusion coefficient.
Traditional boundary layer assumptions were made in arriving at this
final form of the momentum equations. The vorticity form of the equa-
tions is introduced to remove the pressure term (e.g. Byers, 1959). Vor-
ticity is defined as the curl of the momentum equation in vector notation.
Temperature, t, is replaced by the potential temperature, 0, by assuming
adiabatic processes. That is,
0 = t(1000/P) R/.

The boundary layer approximation is that the horizontal diffusion is
small compared to vertical diffusion. The final assumption is that of in-
compressibility, where
V V = 0. (2)
The energy equation for an incompressible fluid in laminar flow is
given by Schlichting (1968),
lae ae ae
T-97 9+ 9x +
eC4 +uT +v^I = (3)

aK + + K b + R,
az ax Oz Oz
where K is the thermal conductivity and 4 is the viscous dissipation and /
is the kinematic viscosity of air, Q is the density of air, and R. is the flux
due to radiation. The equation for the two-dimensional boundary layer
flow simplifies to

eC, + u + w- -Ka + R.. (4)
S x Iz 8 az az
This equation is applicable to turbulent flows if K is taken as the eddy
The quantity q, which is the specific humidity, is used to describe the
transport of water vapor. Thus, the equation for vapor transport is
Oq aq .- a. (q
S+ u- + w = -=-A (5)
Wt ax az Qz Qz
(The turbulence coefficient K, is assumed to be the same for transfers of
momentum, energy, and water vapor.)
The y component of the cross-wind momentum takes the form
av av av a av
+ u- + w- = -f(u-u,) + -K-, (6)
at ax a z az '
where u, is the geostrophic wind speed and f the coriolus parameter.
The set of equations (0), (1), (2), (4), (5), (6) contains six unknowns,
namely, u, v, w, 0, and q.
K and R, have to be defined for the system to be closed. K, following
Gutman (1974), is defined as:
u(1 + ocTJ) for Ri < 0
K = PI-
(1- oRi)-' forRi >0

where the windshear term au is

Qu \(u + ] Q
aZ ~ rZ/ (Q)2

The eddy length scale I is defined as
I K(z + Zo)
K(z + z)

oc is a constant equal to 3 and is empirically determined by Estoque
(1963). Richardson's number Ri is defined as

i-g [ao/ (au)2
0 a9z az
The flux, R,, under nocturnal conditions is simply the resultant of long
wave radiation at any level. The method of Zdunkowski and Johnson
(1965) is employed in the model.

The Constant Flux Layer
The constant flux layer is a region above the ground where the fluxes
of energy, momentum, and water vapor are approximately constant with
height. The height of the constant flux layer influences the accuracy of
the numerical prediction (Gutman, 1974). As in Gutman (1974), the con-
stant flux layer, h, is taken as 10 m. Within this layer, flow variables may
be expressed as follows:

n(z+z) + Kz
In z) + -z
> = c o + (4), rbo)
In (h+z) + h

Here, 4 is a dummy variable for profiles of u, v, 0, or q. Gradients of u,
v, 0, and q are
1 K
a$ z+z.
5T In (h+z,) + Kh
Zo X
Energy Conservation at the Surface
The soil surface heat balance is governed by the equation
R. + LE + S + H = 0. (13)
Heat transfer below the surface is governed by the equation
aT 82T
at K, 2 = 0 (14)
where K, is thermal diffusivity.

The preceding equation implies one-dimensional conduction. This is
assumed since vertical temperature gradients are large as compared to
horizontal gradients. K, is assumed to be constant with depth.
To model LE, Gutman assumes that there is moisture available from
vegetative surface and this moisture represents a fraction, M, of the total
saturation; thus q, = Mq,,. LE is calculated as

LE = KL (15)

where L is the latent heat of vaporization of water.
Thus, the temperature can be found by solving simultaneously equa-
tions (14) for the substrate layer, (13) for the surface, (12) for the con-
stant layer, and (4) for the transition layer.

Boundary Conditions

The no-slip condition of a viscous fluid over a solid boundary surface,
u = v = w = 0, is applied at z = 0 (Figure 20). Water vapor content is
estimated as q. = Mq,o, at z = 0. At the top of the boundary layer, z =

z= 1400 U=Ug, v=0, e=const, q=const, =0

---> wind direction


z0 x u=v=w=o q=qsot

z=-I Substrate Lake o=const. Substrate
x-= x=50

At x=O, -= 0

Figure 20. Computing region and boundary conditions.

h, the wind is specified to equal the geostrophic wind u = us, v = 0, =
0, and the absolute humidity q = constant. The flow is assumed uniform
upstream. Conditions for the latter are calculated using the model with
the advection terms removed.

Numerical Methods: Grid Systems
The largest gradients generally occur near the surface when calculating
boundary layer flow; thus, the more finely spaced grid points are placed
near the surface. Variables u, v, w, 0, and q are all placed on the same
grid points. Vorticity, ', is expressed as a derivative of u, and therefore it
is desirable to place at grid points vertically displaced from u. The K
model, which is also based on vertical derivatives of variables, is
therefore placed on the same grid point as vorticity. The grid is shown in
Figure 21.
The equations are formulated centering on I, J. For example, the con-
vective derivatives
,$ 84 9(u@b) 9(w<)
ax az a(ux a(wz
u--x + W z ~ 5x + az
a(uf) 1 u(I+ ,J) 4(I,J)-u(I- /2,J) I(I-1,J) for u 0
ax Ax u(I+ ,J) ,(I+1,J)-u(I- ,J) '(I,J) for u < 0
u(I+ ,J) = '/[u(I+1,J) + u(I,J)]
Ax = V2[x(I+1) x(I- 1)]
Az = [z(J+ 1) z(J- 1)].
Similarly, an equation can be written for terms such as a(w?)/az.
Analogous expressions for other derivatives are detailed by Gutman

Numerical Results
The numerical simulation discussed in the previous section was
evaluated for four critical cases as follows: (1) the unmodified lake under
high wind conditions, (2) the unmodified lake under low wind condi-
tions, (3) the modified lake (average depth = 1.0 m) under high wind
conditions, and (4) complete drawdown conditions. Physical parameters,
such as soil diffusivities, and boundary conditions, such as the 100 cm
soil temperatures, needed to be specified to simulate the Lake Apopka
region. These parameters are given in Table 11. The soil diffusivities
were calculated from Van Wijk (1966), and roughness parameters were
obtained from Chang (1960). Temperatures and moistures at the top of





I ,J


I, J- 1/2

I, J-1



u V w e, q

Figure 21. Grid system.

1 J 1/2





Table 11. Physical parameters used in numerical simulations.
Temperature at the bottom of the soil substrate: 11.50C
Potential temperature at the top of the boundary layer: 2C
Moisture content at the top of the boundary layer: 0.35 g/kg
Upwind roughness parameter: 0.01 m
Lake roughness parameter: 0.06 m
Downwind roughness parameter: 0.6 m
Muck diffusivity: 7.4 x 10-7 m2sec
Sand diffusivity: 1.15 x 10-6 m/sec

the boundary layer (1400 m) were supplied by the National Weather Ser-
vice, Ruskin, Florida. Temperatures for the lake were supplied from
measurements and from results of the one-dimensional model discussed
The one-dimensional model indicated the lake temperature would be
reduced by only about 1C if the average depth of the lake was 1 m under
typical cold front conditions. A drawdown to 1 m would result in a
reduction in sensible and latent heat transported from the lake of 22%.
The relationship between average lake depth and energy transported
from the lake as calculated by the one-dimensional model is shown in
Figure 22.
The net effect on downwind air temperature due to a change in the
lake temperature is related to the reduction in energy transported from
the lake and to possible changes in the trajectory of the thermal plume
from the lake. Less energy is available to be advected downwind as the
lake temperature decreases. Decreasing the lake temperature, however,
also acts to decrease the vertical ascent of the air mass across the lake.
This occurs in two ways: 1) decreases in air temperature increase the air
density, and 2) the reduced temperature of the lake reduces the transport
of water vapor, which is quite buoyant. Thus, there are competing
mechanisms to consider when analyzing the effects of decreased lake
The results of the model are most easily seen in terms of Figure 23 in
which surface temperature vs. downwind distance is plotted. Conditions
simulating a high wind condition (5.4 m/sec) and a low wind condition
(2.3 m/sec) were run with a lake temperature of 5.6C to check the
validity of the model. This corresponds to the conditions observed the
morning of 20 January 1977 (see Section IV). Surface and air
temperatures predicted by the model at a location corresponding approx-
imately to route 50 are 2 C under high wind conditions but approx-
imately -4.5 C under low wind conditions. These results are in good
agreement with results shown in Figure 16. The model is a steady-state
model, but it appears to simulate conditions downwind of the lake quite

W 80-

o- o

Figure 22. Energy transported from lake as a function of depth.
Sa 60


well. This may be explained in terms of the rapid response of the air
z 40


temperature to changes in the wind speed (Figure 16) and the relatively
slow variation in lake temperature.

0.0 0.5 1.0 1.5

Figure 22. Energy transported from lake as a function of depth.

well. This may be explained in terms of the rapid response of the air
temperature to changes in the wind speed (Figure 16) and the relatively
slow variation in lake temperature.
The lake temperature was reduced to 4.5 C (see Table 9), the coldest
temperature for the two-day simulation to simulate the condition of
drawdown to 1 m. The net effect is to decrease the surface temperature
by about only 0.5 C, as seen in Figure 23. Such a decrease would pro-
bably not affect growers seriously. Next, the lake under total drawdown
conditions was simulated. The effect is quite dramatic under low wind
conditions. The low diffusivity of the organic soil acts to insulate the sur-
face. The lake bed then becomes the coldest area in the region. The
model indicates temperatures would drop to -6.3 C at the southern
edge of the lake, and the thermal effect of an extended muckland created
by complete drawdown would extend 5 km from the present edge of the


o -4



O 5 10 15 20


S5.4 5.6
----E 5.4 4.5
0----0 2.3 5.6
---- X 2.3 Complete drawdown

Figure 23. 2-D numerical model results for surface temperature.


The results from the climate study, measurements, and the numerical
model indicate that Lake Apopka is a significant aid to citrus. Specifical-
ly, observations show downwind surface and air temperatures may be
higher than surrounding temperatures by as much as 5 C when wind
speeds are 3 m/sec or higher, and the area of thermal protection extends
more than 6 km downwind of the lake. However, the thermal protection
afforded by the lake is greatly diminished with wind speeds below 1

m/sec. Thus, variations in wind speed not only affect the rate at which
energy may be transported from the lake but also the rate at which
energy is advected.
The two-dimensional model indicates that in regard to lake drawdown
during the winter season a total drawdown to the lake bottom would
disastrously affect climate downwind of the lake with respect to citrus.
As seen in Figure 23, the numerical model predicts surface temperatures
near the lake would decrease as much as 8 from normal under total
drawdown conditions. Nevertheless, the numerical model does suggest
that a compromise on lake water levels for the winter could be effective.
The model predicts that decreases in downwind surface temperature
would be less than 0.5 C if the depth of Lake Apopka were maintained
at approximately 1 m. Furthermore, the surface area at the lake would
remain substantially unchanged at this level; hence, the land area under
protection of the lake should remain the same for any given wind direc-
tion. In addition, the heat capacity of the lake at the 1 m level would be
sufficient to maintain lake temperatures substantially unchanged from
those of typical conditions. This would assure that the partition of
energy between sensible and latent heat would remain the same. Finally,
it should be stated as a cautionary note, results from methods used in this
study apply to large bodies of water where much of the area can be well
described by two-dimensional models. Effects of lake drawdown on
smaller bodies of water which interact with the environment in a fully
three-dimensional manner are more complex and cannot be inferred
from these results.


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The publications in this collection do
not reflect current scientific knowledge
or recommendations. These texts
represent the historic publishing
record of the Institute for Food and
Agricultural Sciences and should be
used only to trace the historic work of
the Institute and its staff. Current IFAS
research may be found on the
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