EPA-660/3-75-002
JANUARY 1975
Ecological Research Series
Effect of Meteorological Variables on
Temperature Changes in Flowing Streams
National Environmental Research Center
Office of Research and Development
U.S. Environmental Protection Agency
Corvallis, Oregon 97330
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RESEARCH REPORTING SERIES
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EPA-660/3-75-002
January 1975
EFFECT OF METEOROLOGICAL VARIABLES ON
TEMPERATURE CHANGES IN FLOWING STREAMS
By
Robert W. Troxler, Jr.
Edward L. Thackston
Grant No. R-800613
Program Element 1BA032
ROAP 21AJH/Task 12
Project Officer
Bruce Tichenor
Pacific Northwest Research Laboratory
National Environmental Research Center
Corvallis, Oregon 97330
NATIONAL ENVIRONMENTAL RESEARCH CENTER
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CORVALLIS, OREGON 97330
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ABSTRACT
A mathematical model for predicting the change in water temperature
in a flowing stream as a function of stream geometry and standard
weather information was developed and tested. Five field tests were
conducted on cold water released from hydro-power stations as it
warmed up moving downstream over periods up to 38 hours.
Predictions of temperature changes were made based on (a) weather
data from a boat floating with the water, (b) data from a station
on the bank, and (c) data from a remote weather station 100 miles
away. Agreement between predicted and observed temperature changes
was good, even with remote data, when adjustments to compensate
for the local micro-climate were made. Computer programs and all
data are included. This reportvas submitted in fulfillment of
Project Number 16130 FDQ, Grant Number R-800673, by Vanderbilt
University, Department of Environmental and Water Resources Engineering
under the sponsorship of the Environmental Protection Agency. Work
was completed as of November 1974.
ii
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TABLE OF CONTENTS
INTRODUCTION
THE ENERGY BUDGET .................. 2
Solar Radiation
Atmospheric Radiation
Back Radiation
Evaporation
Conduction
EXPERIMENTAL WORK .................. 8
Tracer Measurements
Depth Determinations
Meteorological Readings
Water Temperature Measurements
CHARACTERISTICS OF STREAMS BELOW
HYDROELECTRIC INSTALLATIONS ............. 13
Air Temperature
Relative Humidity
Wind Speed
RESULTS OF THE STUDY ................. 17
Energy Transfer by all Mechanisms
Computed and Measured Solar Radiation
Water Temperature Predictions
CONCLUSIONS ..................... 37
BIBLIOGRAPHY ..................... 39
APPENDIX 1 ...................... 40
APPENDIX 2 ...................... 41
APPENDIX 3 ...................... 53
ill
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FIGURES
PAGE
1 VARIATION OF AIR TEMPERATURE OVER
CANEY FORK RIVER AT TWO ELEVATIONS 14
2 VARIATION OF LAPSE RATE OVER CANEY
FORK RIVER WITH TIME 14
3 VARIATION OF HUMIDITY AT TWO ELEVATIONS
OVER CANEY FORK RIVER 16
4 WIND SPEED ON CUMBERLAND RIVER VS. WIND
SPEED AT NASHVILLE 16
5 ENERGY BUDGET COMPONENTS DURING CUMBERLAND
RIVER SURVEY 2 18
6 ENERGY BUDGET COMPONENTS DURING CUMBERLAND
RIVER SURVEY 3 18
7 ENERGY BUDGET COMPONENTS DURING HOLSTON
RIVER SURVEY 19
8 ENERGY BUDGET COMPONENTS DURING CANEY
FORK RIVER SURVEY 19
9 ENERGY BUDGET COMPONENTS DURING
CUMBERLAND RIVER SURVEY 4 20
10 MEASURED AND COMPUTED (FROM BOAT DATA)
SOLAR RADIATION - CUMBERLAND RIVER SURVEY 2 20
11 MEASURED AND COMPUTED (FROM NASHVILLE DATA)
SOLAR RADIATION - CUMBERLAND RIVER SURVEY 2 21
12 MEASURED AND COMPUTED (FROM BOAT DATA) SOLAR
RADIATION - CUMBERLAND RIVER SURVEY 3 21
13 MEASURED AND COMPUTED (FROM NASHVILLE DATA)
SOLAR RADIATION - CUMBERLAND RIVER SURVEY 3 22
14 MEASURED AND COMPUTED (FROM BOAT DATA) SOLAR
RADIATION - CUMBERLAND RIVER SURVEY 4 22
15 MEASURED AND COMPUTED (FROM NASHVILLE DATA)
SOLAR RADIATION - CUMBERLAND RIVER SURVEY 4 23
IV
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FIGURES CONTINUED
PAGE
16 OBSERVED AND PREDICTED (FROM BOAT DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 2 28
17 OBSERVED AND PREDICTED (FROM BOAT DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 3 28
18 OBSERVED AND PREDICTED (FROM BOAT DATA)
TEMPERATURES, HOLSTON RIVER SURVEY 30
19 OBSERVED AND PREDICTED (WITH BOAT DATA)
TEMPERATURES, CANEY FORK RIVER SURVEY 30
20 OBSERVED AND PREDICTED (WITH BOAT DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 4 31
21 OBSERVED AND PREDICTED (WITH NASHVILLE DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 2 34
22 OBSERVED AND PREDICTED (WITH NASHVILLE DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 3 34
23 OBSERVED AND PREDICTED (WITH NASHVILLE DATA)
TEMPERATURES, CANEY FORK RIVER SURVEY 35
24 OBSERVED AND PREDICTED (FROM NASHVILLE DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 4 35
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TABLES
TABLE page
1 SUMMARY OF RIVER SURVEYS 9
2 CLOUD COVER ESTIMATES FROM
NASHVILLE AND BOAT 11
3 MEASURED AND COMPUTED SOLAR RADIATION 24
4 LEAST SQUARES FIT OF BOAT DATA WITH
VARIOUS CORRECTIONS FOR FOG 29
5 LEAST SQUARES FIT OF NASHVILLE DATA
USING VARIOUS CORRECTIONS 33
VI
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INTRODUCTION
The demand for energy, particularly electric power, has
increased sharply in recent years. As increased electri-
city is generated to meet this demand, larger amounts of
waste heat will be produced. This thermal energy, which
must be transferred to the environment, can cause undesi-
rable temperature rises in natural bodies of water when
heated cooling water is discharged to them.
This study had as its purpose the construction and veri-
fication of an energy budget model for the accurate pre-
diction of temperatures in flowing rivers, based solely
on the approximate geometry of the stream and on data
normally taken at U.S. Weather Bureau weather stations.
The particular model studied was first presented by
Raphael (1) and later modified by Thackston (2) for com-
puter analysis of cooling ponds. Further modifications
of the model were necessary to adapt it to conditions in
flowing rivers.
The original plan of attack was to study rivers which had
been heated by thermal discharges. However, no rivers
within reasonable distances of Nashville have a mixed tem-
perature rise of more than a few degrees above equilibri-
um temperature. Since experimental errors might be a
large fraction of the small temperature changes occur-
ring in the river, another situation with large tempera-
ture changes was sought. The warming of cold water re-
leased from the hypolimnion of stratified reservoirs
through hydroelectric plants was studied instead. The
water released from the stratified reservoirs had a tem-
perature of approximately 50°F in all six field surveys.
Since this was well below the equilibrium temperature,
which was 80° - 90°F during the daytime, changes in tem-
perature great enough to test the model were encountered.
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THE ENERGY BUDGET
The energy budget for water bodies can be written as
Qt " Qs + Qa + Qb + Qe + Qc U>
where Q^ equals total energy transferred, Q§ equals
absorbed solar radiation, Qa equals absorbea longwave
atmospheric radiation, QJ.J equals longwave back radia-
tion to space, Qe equals energy lost by evaporation,
and Qc equals energy gained or lost by conduction.
Following the standard thermodynamic convention, energy
transferred into the system, which in our case is a
small slug of water in the river, is considered posi-
tive, and energy lost is negative.
If the earth had no atmosphere, the solar energy re-
ceived on a flat surface would depend only on the alti-
tude of the sun and the slight fluctuations in total
energy radiated from the sun. Fluctuations in solar
output are minor and are neglected in this paper. Since
the earth has a relatively dense atmosphere, all of the
energy incident upon the top of the atmosphere is not
received at the surface of a body of water. Part of
the radiation is scattered or absorbed by solid parti-
cles, gases, and water vapor. In this manner, part of
the shortwave, or direct, radiation is transformed into
diffuse solar radiation and longwave radiation. Direct
solar radiation which is scattered becomes diffuse solar
radiation, and that which is absorbed and reemitted be-
comes longwave, or atmospheric radiation. For the pur-
pose of this study, all three types of incoming radia-
tion must be calculated separately.
Solar Radiation
With clear sky conditions, solar radiation is primarily
a function of solar altitude. Moon (3) presented values
of direct and diffuse radiation on a flat surface as a
function of solar altitude. Upadhyaya (4) fit polyno-
mials to this data by non-linear least squares methods
to produce the equations
Qi = - 0.1470a + 0.3023a2 - 0.008546a3 (2)
+ 0.0001271^ - 0.000000001012a5
Q2 = 1.680a + 0.03178a2 + 0.0002414a3
- 0.000000004729a4 + 0.000000005858a5 (3)
2
-------
where Q is the direct solar radiation, Q2 is the dif-
fuse solar radiation, and a is the solar altitude in
degrees above the horizon.
The solar altitude is given by the equation
sin a = sin $ sin * 4- cos cos 6 cos h (4)
where is the latitude; <$ is the declination of the
sun; and h is the hour angle of the sun. Thackston (2)
used the above mentioned non-linear least squares method
to determine an equation for 6 . Data from a solar
ephemeris was used.
The equation obtained was
6 = - 23.28 cos[ (2irday/365) + 0.165] (5)
where day is the day of the year.
Once sin a was calculated using Equation 4, values ofQ.
were determined from the equation.
a = sin a+ sina3 + 3 sina5 , 15 sina? <6>
Total solar radiation is the sum of direct and diffuse
solar radiation, Q, and Q2. However, Equations 1 and 2
apply only to clear sky conditions. Furthermore, they
assume that no part of the river is shaded from the sky.
The net direct solar radiation becomes
Q3 *= QI (1 - s) (7>
where s is the portion of the river surface shaded from
direct sunlight. This shaded fraction was usually about
5% during daylight hours on the rivers studied.
Net diffuse radiation is corrected for the percentage
of the sky blocked from view of the river by the surround-
ing hills. This number was often substantial because the
rivers studied all flowed in rather deep and narrow val-
leys. Net diffuse radiation became
Q4 = Q2 (1 - b) (8)
where b is the portion of the sky blocked from view of
the river.
3
-------
Total clear sky solar radiation is the sum of diffuse
and direct solar radiation. Cloud cover was taken into
account by using the relationship
Qs = (Q3 + Q4)(1 - 0. 0071 C2) (9)
where C is the cloud cover in tenths of sky.
Atmospheric Radiation
Considerable difficulties arise in determining a re-
lationship for longwave atmospheric radiation. These
difficulties are encountered because the atmosphere is
far from homogeneous. Temperature gradients are quite
variable from day to day and the distribution of mois-
ture is seldom known to the observer.
Anderson (5) proposed an empirical relationship of the
form
Qa = a B (T + 460)1* (1 - r) (10)
in which Q is the longwave atmospheric radiation,
-------
Wet bulb temperature, T ,, may be calculated from the
relative humidity and air temperature by the equation
Twb = (0.655 + 0.36R) Ta (12)
Since the reflectivity of the water surface is usually
used as 0.03, Equation 10 becomes
Qa = 1.66 x 10"9e(T -I- 460)'* (13)
a a
Atmospheric radiation can easily be determined by a
computer utilizing Equations 11 - 13, given only rela-
tive humidity and air temperature. The sequence of
operations is as follows:
1. Determine Twb from Equation 12.
2. Plug T^ into Equation 11 to determine es,
which is also equal to ea.
3. Use the value of cloud cover to determine the
proper equation to use for calculating 0.
Insert the value of ea into the proper equa-
tion and find B.
4. Determine Qa from equation 13.
In earlier work with the model, the atmospheric radia-
tion was corrected for the percentage of the sky blocked
from view of the water surface. However, this procedure
gave temperature predictions which were too low. The
surrounding valley walls radiate to the water and the
attempted correction did not take this radiation into
account. By recognizing that the trees and rocks cover-
ing the valley slopes radiated just as the atmosphere,
better temperature predictions were obtained than by
assuming that all longwave radiation came from the visi-
ble portion of the sky.
Back Radiation
All bodies which have some thermal energy radiate to the
environment. The relationship is quantified by the
equation
Qb = eo(Tw + 460)4 (14)
where Qb is back radiation, e is the emissivity, about
0.97 for water, a is the Stefan-Boltzman constant, and
Tw is the temperature of the water surface in °F.
5
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Evaporation
Much effort has been applied to developing evaporation
formulas. Numerous empirical formulas are now in
existence. The equation used in this study was
Qe = - C U(ew - ea) (15)
Qe is the energy lost by evaporation, C is an empirical
coefficient, U is the wind speed in miles per hour, ew
is the saturated vapor pressure of the air at the water
surface temperature in inches of mercury, and ea is the
vapor pressure of the air in inches of mercury.
The constant C depends on the geometry of the water sur-
face and its surroundings, the height of wind measure-
ments, and probably other factors. The value of C was
determined by the Lake Hefner studies to be approxima-
tely 13.9 in the units used here. Note should be taken
of the fact that wind speeds at Lake Hefner were measured
at 8 meters. Adjustments which were made to correct for
different heights of wind measurements in this study are
discussed later.
The saturated vapor pressure at the water surface tem-
perature is determined from
ew = exp[17.62 - 9501/(TW + 460] (16)
where Tw is the temperature of the water. This equation
is the same as Equation 11 with Tw substituted for Twb
Conduction
Energy is transferred from air to water or water to air
by conduction if a driving force in the form of a tempera-
ture difference exists. Important factors in this mech-
anism of energy transfer are air temperature, water tem-
perature, and wind velocity.
Because of the similarity between evaporation and con-
duction, Bowen developed a relationship between the two
known as the Bowen ratio.
R =
P is the barometric pressure in inches of mercury, Q is
the energy transferred by conduction, and Co is a con-
stant with a value of 0.61. By making substitutions
-------
from tht' evaporation formula, Equation 17 becomes
Qc = 0.00543 UP (T - TW> (18)
Normal approximate barometric pressure can be computed
by the relationship,
29.92
P = -
<* n
p
1545
-15 E ^
(T + 460) J
3. *
(19)
in which E is the elevation of the site in feet above mean
sea level.
As previously stated, the total energy received on a
square foot of water surface is computed from Equation
1. This energy transfer is converted to a temperature
change by the equation
AT -
in which AT is the temperature change in °F, Q. is the
average rate of energy transfer in Btu/ft2-hr, 9 is
the time interval in hours, and d is the average depth
for the time interval.
The steps in the computer program to predict temperature
changes of the water body are the following:
1. The initial temperature is given.
2. The average rate of energy transfer by each
mechanism is computed using Equations 2 through
19.
3. The total rate of energy is obtained from
Equation 1.
4. Equation 20 is used to compute a temperature
change.
5. The computed temperature change is added to the
previous temperature to give a new water
temperature .
6. Steps 2-5 are repeated for the total time of
the survey.
Although 30-minute time intervals were used for this
study, savings in computer time could probably be realized
by employing hourly readings.
-------
EXPERIMENTAL WORK
Five field surveys were conducted to test the computer
model. Weather data and information pertaining to the
geometry of the stream were collected.
All of the surveys were conducted downstream from dams
having rather deep impoundments behind them. The dis-
charges had temperature of approximately 50°F. In each
case a slug of water was marked with Rhodamine WT dye
and followed downstream for up to 36 hours. (See Table
1 for a concise summary of each survey.)
Two boats were used, a weather boat and a dye boat. The
dye boat established the peak of the dye cloud as often
as possible, usually about every hour. Dye concentra-
tions were measured with a fluorometer. The fluorometer
was equipped with a pump which circulated river water
through the fluorometric cell continually. Two methods
were utilized to find the dye peak. The first method
was to position the dye boat downstream of the dye cloud
and take readings as the cloud passed. When the crew-
men felt the peak had been reached, they released a buoy
as a marker for the weather boat. The second method of
detecting the peak was to take the boat downstream of
the cloud and drive it back upstream through the cloud.
A buoy was released when the fluorometer readings peaked.
This method seemed to give slightly better results.
Additional dye was placed in the river whenever the peaks
of the dye curve began to flatten because of dispersion.
Plug flow was assumed in the prediction model. Con-
siderable dispersion took place in at least two of the
surveys, but this was determined to have no significant
effect on the results because of the slight longitudinal
temperature gradients in the streams.
River depths were measured by the dye boat with a re-
cording fathometer. A plot of the depth of the river
bottom from the water surface was created by driving
the boat from one bank of the river to the other. Since
only the average depth of the river was necessary, the
area within the plot was determined by planimetering and
this quantity was divided by the length of the plot
to obtain the average depth. Fathometer recordings
were made every 30 to 60 minutes.
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TABLE 1 - SUMMARY OF RIVER SURVEYS
Survey
Date
River
Location
Length of
River
Surveyed
(Miles)
Approx.
Flow cfs
Duration
of Survey
(Hrs)
Initial
Temperature
(6F)
Final
Temperature
July 29-
1970
Cumberland
Below Wolf
Creek Dam,
near
Burksville,
Kentucky
72.5
12,000-
20,000
32.5
49.5
*>
F 54.7
August 30-
31, 1970
Cumberland
Below Wolf
Creek Dam,
near
Burksville,
Kentucky
48.3
6,000
35.5
52.3
59.7
June 12-13-
1971
Holston
Below
Cherokee Dam
near
Jefferson
City, Tenn.
50.0
4,000-
12,000
28.5
51.8
60.5
June 26-
1971
Caney Fork
Below Center
Hill Dam
near
Carthage,
Tenn.
24.0
3,000
16.0
52.1
59.4
July 17-
18, 1971
Cumberland
Below Wolf
Creek Dam
near
Eurksville,
Kentucky
35.8
4,000
33.0
51.1
59.3
V£>
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Two major sources of error were possible with the measure-
ments taken from the dye boat. Dye tracer curves were
often quite elongated and the peaks were somewhat flat,
making the decision of picking the center of the dye
cloud a difficult one. Although errors in individual
water temperature measurements were possible because
the weather boat was not located on the peak of the
dye tracer cloud, the errors are not cumulative.
Through the course of a survey both small positive and
negative errors probably occurred, making the measured
temperature curve somewhat more uneven than it really
was.
Depth measurements for a particular stretch of river
were probably not representative at times. Wide varia-
tions in river depths were encountered within relatively
short distances. However, since both the depths and
measurements can be assumed to be normally distributed,
the average of many measurements should differ only
slightly from the actual average depth. Calculated
temperature changes are inversely proportional to the
depth, so erroneous depth measurements would lead to
serious errors in temperature prediction.
Meteorological readings and water temperature were
taken every 30 minutes by the crewmen in the weather
boat. This boat stayed as close to the dye peak as
possible. Since the surface velocities in rivers are
slightly higher than average velocities, the dye boat
occasionally had to anchor and wait for the peak of the
dye cloud to watch up. The weather variables that were
recorded were air temperature, relative humidity,
cloud cover, and wind speed. The elevation of the
horizon from the horizontal, which was used to compute
the fraction of the sky blocked from view of the river,
the percentage of the water surface shaded from direct
sunlight, and the actual water temperature were also
recorded. Descriptions of the meterological instru-
ments used are in the appendix.
Air temperature, both wet bulb and dry bulb, were
measured using a Bendix aspirated psychrometer. The
readings were taken about 18 inches above the water sur-
face. Relative humidity was calculated from wet bulb
and dry bulb temperatures by using a psychrometrie
chart.
Cloud cover was estimated by eye and reported as tenths
of the sky covered. Table 2 indicates that estimates
10
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TABLE 2 - CLOUD COVER ESTIMATES FROM
NASHVILLE AND BOAT
Survey
Day
Average Cloud Cover,
Tenths
Boat
Nashville
Cumberland #2
Cumberland #3
Caney Fork
July 29, 1970
July 30, 1970
Aug. 30, 1970
Aug. 31, 1970
June 26, 1971
1.36
2.42
2.90
5.80
0.30
2.46
2.74
6.66
5.35
0.70
11
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made from the boat were considerably lower than those
reported by a U.S. Weather Bureau weather station approxi-
mately 100 miles from the survey sites. Part of this
error can probably be attributed to lack of skilled
weather observers. A larger part of the error is prob-
ably due to the geometry of the situation. During the
survey considerable fractions of the sky were blocked
from view of the water surface by the surrounding hills.
Because of the vertical thickness of scattered clouds,
equally spaced clouds near the horizon will appear den-
ser than those directly overhead, because the observer
cannot see the sky through the holes between the clouds.
These denser looking clouds, which were visible to Weather
Bureau observers at the relatively flat terrain at the
weather stations, were blocked from the view of the
observers in the boats and on the river bank. Thus,
cloud cover reported by project observers was usually
lower than that reported at nearby U.S. Weather Bureau
stations.
Dense woods covered large portions of the banks of the
rivers studied. Since portions of the river were usually
shaded, some of the direct solar radiation was prevented
from reaching the water's surface. This fraction of the
water's surface shaded was estimated by eye and ranged
from 0 to 10 percent.
Weather stations were set up in the vicinity of the river
during each survey. Wind speed and direction, air tem-
perature, and relative humidity were measured and re-
corded with automatic instruments. Cloud cover was
estimated by an observer at the site. Since much of
this data was of rather low quality, and some was miss-
ing, primarily due to equipment failures, it was not
carefully analyzed. However, the estimated values of
cloud cover tended to be higher at the bankside stations
than estimates made from the boat on the river. This
could have been caused by the bankside observer's
ability to see more of the sky, particularly the portion
near the horizon, where scattered clouds look denser
than they actually are, than the observers in the boats,
whose view was partially blocked by trees on the river-
bank and the adjacent hills and bluffs.
12
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CHARACTERISTICS OF STREAMS BELOW
HYDROELECTRIC INSTALLATIONS
The project was undertaken with the view that the heat
transfer mechanisms for the warming up of cold water
should be the same as the cooling of heated water, with
the heat flowing in opposite directions. This appears
to be the case. However/ problems with discharges from
deep reservoirs in Tennessee and Kentucky were encounter-
ed which were not entirely anticipated.
The three streams studied have cut rather narrow and
steep-sided valleys. The valleys of the Cumberland and
Caney Fork rivers have maximum depths of approximately
400 feet, while the valley of the Holston River is no
more than 200 feet deep. All three streams exhibit
well-developed meander patterns, with nearly vertical
cliffs on the outside of the meanders and moderate areas
of flood plain within.
The cold discharges, approximately 50°F in the summer
months, radically change the microclimate of the river
valleys below deep reservoirs. A tremendous cooling
effect is exerted on the adjacent air by the cold water.
When the air is cooled to the dew point, fog banks
begin to form. As soon as the sun's energy is blocked
out by hills and vegetation, patches of fog begin to
form over the water surface. These patches rapidly
change to thick fog banks during the early evening hours,
By morning the entire valleys are covered with thick
blankets of fog. When the air is warmed to above the
dew point by solar energy in the morning, these fog
banks are dissipated.
Cooling of the lower layers of air within the river
valleys create temperature inversions with very stable
atmospheric conditions being the result. Temperature
measurements made on the Caney Fork River about 2
miles below Center Hill Dam are presented in Figure 1
and 2. These measurements were made in May, 1972.
Figure 1 indicates that relatively large differences in
air temperature exist within small vertical distances
adjacent to the river. Lapse rates on a rather typical
spring night are shown in Figure 2. Lapse rates are
highest in the late afternoon and early evening, as is
illustrated by both figures.
13
-------
I 1 1 1 1
ELEVATION •• 80 FEET ABOVE CANEY FORK RIVER
- ELEVATION = 5 FEET ABOVE CANEY FORK RIVER
'12 24 12 24 12 24 12 24
MONDAY | TUESDAY | WEDNESDAY | THURSDAY | FRIDAY
FIGURE 1 - VARIATION OF AIR TEMPERATURE OVER CANEY
FORK RIVER AT TWO ELEVATIONS
O<33
5»42
am.
68 TO 7264 66 6862 64 6660 62 6460 62 64
AIR TEMPERATURE, °F
FIGURE 2 - VARIATION OF LAPSE RATE OVER CANEY
FORK RIVER WITH TIME
14
-------
Since relative humidity at constant vapor pressure is
a function of air temperature, the relative humidity
would be expected to be greater at lower elevations in
the valley. That this is the case is illustrated by
Figure 3. Note that, although the relative humidity
is higher at lower elevations, the total amount of mois-
ture in the air at various heights can remain the same.
Wind speeds measured in the river valleys were much lower
than those at surrounding weather stations. There appear
to be two primary reasons for this phenomenon. Weather
stations are usually located at airports, which are
usually flat and treeless. In constrast, the rivers
studied were in relatively deep and tortuous valleys.
The atmospheric stratifaction in the valleys, parti-
cularly at night, also helped to reduce air movement.
Wind speeds at Nashville and on the Cumberland River
are contrasted in Figure 4.
15
-------
100
ELEVATION •• 80 FEET ABOVE CANEY FORK RIVER
ELEVATION = 5 FEET ABOVE CANEY FORK RIVER
12 24
MONDAY
24 12 24 12 24 12
WEDNESDAY | THURSDAY | FRIDAY
FIGURE 3 - VARIATION OF HUMIDITY AT TWO ELEVATIONS
OVER CANEY TGRK RIVER
8
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Jfr A^AO M A ^ —Ml
4 6 8 10
WIND SPEED IN NASHVILLE, MPH
12
FIGURE 4 - WIND SPEED ON CUMBERLAND RIVER VS
WIND SPEED AT NASHVILLE
16
-------
RESULTS OF THE STUDY
The computed rates of energy transfer are presented in
graphical form in Figures 5 through 15. From the figures,
several statements can be made.
1. Atmospheric radiation and back radiation almost
balance each other, at the water temperatures found,
2. Evaporative and conduction energy transfers
are of minor importance with the low wind
speeds encountered,according to the equation
used, Equation 15. The median wind speed en-
countered near the water was about one mile
per hour.
3. Because of the facts noted above, solar radia-
tion accounted for almost all of the energy
transfer.
Should the river be above rather than below equilibrium
temperature, the following would be true.
1. Back radiation would be considerably greater
because of higher water temperatures.
2. Evaporative and conductive heat transfers
would, of course, be negative rather than
positive.
3. The total energy transfer would be negative.
The only component of the energy budget which could easily
be recorded on the field surveys was solar radiation. It
was measured with an Eppley pyroheliometer located at the
bankside weather station. Results from only three of the
five surveys are presented in Table 3 because the in-
strument was out of service when the studies were made
on the Caney Fork and Holston rivers.
Agreement between the measured and calculated solar
radiation was reasonably good. An analysis of variance
test at the 95 percent confidence level showed that
there was no significant difference in the three differ-
ent methods of obtaining solar radiation data listed in
Table 3. The computed values of solar radiation from the
boat data of July 29, July 30, and August 30 of 1970 were
17
-------
400
1 1
TOTAL ENEMY TRANSFER
SOLAR RADIATION
ATMOSPHERIC RADIATION
EVAPORATIVE AND CONDUCTIVE
ENERGY TRANSFER
BACK RADIATION
CUMBERLAND SURVEY 2
JULY 29-30,1970
-100
15
19 23 3
SUN TIME, HOURS
15
FIGURE 5 - ENERGY BUDGET COMPONENTS DURING
CUMBERLAND RIVER SURVEY 2
400
300-
.TOTAL ENEMT TRANSFER
-SOLAR RADIATION
-ATMOSPHERIC RADIATION
EVAPORATIVE AND CONDUCTIVE
ENER8Y TRANSFER
RADIATION
CD
200-
85
u.
CO
I
111
100
CUMBERLAND SURVEY 3
AUGUST 30-31, 1970
-K>0-
JL
15 19 23 3 7
SUN TIME, HOURS
15
19
FIGURE 6 - ENERGY BUDGET COMPONENTS DURING
CUMBERLAND RIVER SURVEY 3
18
-------
400
HOUSTON SURVEY
JUNE , 1971
II
23
SUN TIME, HOURS
FIGURE 7
400i r
K
300
oc
Id
£
>-
u
100
0
°
-100-
ENERGY BUDGET COMPONENTS DURING
HOLSTON RIVER SURVEY
. TOTAL ENEMY TRANSFER
-30LM RADIATION
-ATMOSnCKK RMXATON
-BACK RAOMTWN
CANEY FORK SURVEY
JUNE 26, 1971
15 19 23 3
SUN TIME, HOURS
15
FIGURE 8 - ENERGY BUDGET COMPONENTS DURING
CANEY FORK RIVER SURVEY
19
-------
400
SOO
ZOO
100
f •
.TOTAL EMOWT TMMPIM
-SOUk* HAOIATION
-ATWMMMC MDMTON
-MCK MAOMTION
\
CUMBERLAND SURVEY 4
JULY 17-18,1071
IB
» Z8 3
SUN TIME. HOURS
II
15
FIGURE 9 - ENERGY BUDGET COMPONENTS DURING
CUMBERLAND RIVER SURVEY 4
400
CUMBERLAND SURVEY 2
MEASURED
COMPUTED, BOAT DATA
15
19 23 3
SUN TIME, HOURS
FIGURE 10 - MEASURED AND COMPUTED (FROM BOAT DATA)
SOLAR RADIATION - CUMBERLAND RIVER
SURVEY 2
20
-------
400
CUMBERLAND SURVEY 2
MEASURED
COMPUTED, NASHVILLE DATA
16 (9 23 3
SUN TIME. HOURS
15
FIGURE 11 - MEASURED AND COMPUTED (FROM NASHVILLE DATA)
SOLAR RADIATION - CUMBERLAND RIVER SURVEY 2
400
CUMBERLAND SURVEY 3
-COMPUTED. BOAT DATA A
A
23
SUN TIME, HOURS
15
FIGURE 12 - MEASURED AND COMPUTED (FROM BOAT DATA)
SOLAR RADIATION - CUMBERLAND RIVER
SURVEY 3
21
-------
400
300
200
100
CUMBERLAND SURVEY 3
-MEASURED
•COMPUTED, NASHVILLE DATA
23 3
SUN TIME, HOURS
19
FIGURE 13 - MEASURED AND COMPUTED (FROM NASHVILLE DATA)
SOLAR RADIATION - CUMBERLAND RIVER SURVEY 3
i i i i
CUMBERLAND SURVEY 4
MEASURED
COMPUTED, BOAT DATA
400|
J_
19
23 37
SUN TIME, HOURS
15
19
FIGURE 14 - MEASURED AND COMPUTED (FROM BOAT DATA) SOLAR
RADIATION - CUMBERLAND RIVER SURVEY 4
22
-------
400
CUMBERLAND SURVEY 4
MEASURED
COMPUTED. NASHVILLE DATA
19
23 3
SUN TIME, HOURS
15
19
FIGURE 15 - MEASURED AND COMPUTED (FROM NASHVILLE DATA)
SOLAR RADIATION - CUMBERLAND RIVER SURVEY 4
23
-------
TABLE 3.- MEASURED AND COMPUTED SOLAR RADIATION
Survey
Cumberland
#2
Cumberland
#3
Cumberland
#4
Day
July 29
1970
July 30
1970
Aug. 30
1970
Aug. 31
1970
July 17
1971
July 18
1971
Btu/ft2 - day
Measured
Near
Survey
Site
1843
1768
1463
1661
2253
1991
Computed
From
Boat
Data
2189*
1987*
1676*
1508
2152
1756
computed
From
Nashville
Data
2003
2005
1110**
1477
2159
1229
* Probably high because of low estimates of cloud cover.
** Heavy cloud cover over Nashville.
24
-------
probably too high because the estimates of cloud cover
were too low. Solar radiation computed from the Nashville
data was close to the measured values when values of cloud
cover were approximately the same at Nashville and the
survey site. The large difference of August 30, 1970,
was due to a heavy cloud over Nashville which was not
present at Burksville, Kentucky. (See Table 2. ) It
should be noted that errors in river temperature pre-
dictions using boat data for Cumberland River surveys 2
and 3 correspond to errors in computed solar radiation.
For reasons yet unknown, the temperature predictions for
Cumberland River survey 4 were too high even though computed
values of solar radiation were low.
Difficulties with the energy budget due to the unusual
microclimatology were encountered, especially the confusing
effects of the dense fog at night. Back radiation from the
surface of the water is a function of water temperature alone,
but there is a possibility that some of the back radiation
might have been reflected back to the water surface by the
fog.
Effects of the fog upon the incoming atmospheric radiation
were also unknown. Atmospheric radiation is a function of
cloud cover, air temperature, and relative humidity. The
fog was, in effect, a low-lying cloud, covering the entire
water surface for the entire night, and partially during the
day. However, the thickness of the fog blanket was only
about 20 to 40 feet. Therefore, there was a question as to
whether or not the fog should be treated as complete cloud
cover. The fog certainly covered the water, and undoubtedly
contributed longwave radiation to the water surface, but
whether or not the radiation was more or less than would
have been received from a complete cover of normal clouds was
not known.
Another problem was associated with the air temperature
reading used in the longwave radiation calculation. Actually.
the entire vertical air column radiates to the water surface.
The air temperature measured 18 inches above the water surface
is not necessarily representative of the entire air column,
especially in light of the data shown in Figure 1. However,
if it is assumed that, because of the presence of the dense
fog and the generally clear skies above the fog, the major
contribution of longwave radiation is from the fog, then the
air temperature measured in the boat would be the correct
one.
The above questions have not yet been satisfactorily answered
during this study. Another project, using better instrumen-
25
-------
tation, could perhaps provide answers. However, a least
squares method of curve fitting was used in an attempt to
resolve the problem with the fog for the purpose of this
project. Since 4 of the 5 surveys gave temperature pre-
diction curves which closely matched the curves of observed
temperature, data from these 4 surveys was used in an
attempt to obtain the best fit. The data from the Cumber-
land River surveys 2 and 3 were used in its entirety.
During the Holston River survey, approximately 0.8 inches
of rain fell in the area of the survey during a heavy
afternoon thunderstorm. Because the amount of local in-
flow to the Holston River could not be determined, and the
temperature of this inflow was unknown, the predictive
model was unable to accurately determine temperature changes
after the storm runoff entered the river. Thus, the portion
of the Holston survey that was used in fitting the curve was
that part unaffected by the storm runoff. An arbitrary cut-
off was established at 19.0 hours on June 12.
Data from the Caney Fork survey was used up to 20.75 hours.
The fluorometer ceased to function at about this time and
the peak of the dye curve was lost.
The formula
T = P
n-k
was used for determining best fit, with 0^ being the obser-
ved temperature at a particular time, P.^ the predicted
temperature at that time, n the total number of observa-
tions, and k the number of independent variables being mani
pulated to obtain a fit. The values of T for the four sur-
veys were added to give a quantity which was an indicator
of goodness of fit.
The above procedure was used in an attempt to determine the
effect of various methods of handling the fog problem in
the predictive model. The first method was to set the B
term in the equation for longwave radiation equal to .95.
The value of & is rarely this high under normal conditions
in Raphaels (1) equations, but Anderson's (5) original data
showed low- lying dense clouds to give a value of 8 equal to
0.95. Therefore, it was felt that the dense fog might
radiate more energy to the surface of the water than would
be normally received from complete cloud cover. The second
method was to make no corrections for the fog, and simply
to use the value of cloud cover observed in the upper
atmosphere.
26
-------
Thirdly, the value of cloud cover was set to 10 when-
ever fog was present. As Table 4 shows, the results were
inconclusive. The summations of the values of T were
not significantly different for the three methods.
Figures 16 through 20 illustrate the curves of observed
and predicted temperature using the boat data with B
set equal to .95 when fog was present. As has previously
been stated, the errors in the predictions for the Holston
River survey are largely due to local inflow, and the dye
cloud was lost on the Caney Fork due to the failure of the
fluorometer. The errors in the predictions for the Cumber-
land River survey of 1971 have not been satisfactorily
explained. Errors in depth measurements would have re-
sulted in a proportional error in temperature change, but
that all of the error was due to incorrect depth measure-
ments seems unlikely.
Weather data from the airport at Nashville, Tennessee,
was also used to predict the temperature changes in the
rivers. Nashville is approximately 100 miles west of
the Cumberland and Caney Fork Rivers, and 200 miles west
of the Holston River.
It is obvious that the temperature prediction model developed
in this project would be worthless if the weather data to
be used as input had to be gathered by a boat on the river
itself. If this had to be done, it would be just as easy
to measure the water temperature itself. The model could
not then be used for predictive purposes.
One of the objectives of this research was to see how easily
data from "nearby" weather stations could be used to pre-
dict the temperature changes in a stream. Comparison of
the boat data with that from Nashville showed that there
were consistent differences of the type discussed earlier
in the section on "Characteristics of Streams Below Hydro-
electric Installations." If data from Nashville or some
similar station is to be used to predict changes in the
water temperature of streams similar to the ones studied
in this project, the air temperature and wind speed will
have to be modified (reduced) to correspond to conditions
at the water surface. Also, the relative humidity may
need to be raised.
Comparison of the boat data with Nashville data showed that
the Nashville air temperature was usually 2° to 3° higher
than the air temperature measured on the boat during the
27
-------
UJ
rr
£
CL
cr
UJ
I
PREDICTED WITH
BOAT DATA
20 0 4
SUN TIME
FIGURE 16 - OBSERVED AND PREDICTED (FROM BOAT DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 2
UJ
Cfl
i
s
UJ
CC
UJ
I
IiriiJIii ' I
i i i i
FIGURE 17 -
0 4
SUN TIME
OBSERVED AND PREDICTED (FROM BOAT DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 3
28
-------
TABLE 4-LEAST SQUARES FIT OF BOAT DATA
WITH VARIOUS CORRECTIONS FOR FOG
Survey
Cumberland
#2
Cumberland
#3
Holston
Caney Fork
B = .95 When
Fog Present
0.09232
0.07046
0. 20695
0. 36281
Z= .73254
5T(01 - P^2
n - k
No Corrections
For Fog
0.03352
0.11828
0. 20965
0. 36281
£= .72246
Cloud Cover
=10 When Fog
Present
0.04719
0.07785
0.25019
0.36252
X = .73775
29
-------
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OU
LL
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oo
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if]
I52
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3U
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8
•
^
•
.
^
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• ,
4
i
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R
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8
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RE
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X
tR
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X
VE
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D
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t wrr
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H
II
. : .
•«
— i —
2(
-
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.
D
FIGURE 18 OBSERVED AND PREDICTED (FROM BOAT DATA)
TEMPERATURES, HOLSTON RIVER SURVEY
s
I
60
58
56
54
52
50
_^__
n:u
"H-
•
• •••••OBSERVED
:DICTED WITH
VT DATA
8 12
FIGURE 19
12 16 20
16 20 0 4 8
SUN TIME
OBSERVED AND PREDICTED (WITH BOAT DATA)
TEMPERATURES, CANEY FORK RIVER SURVEY
30
-------
LJ
E
i
UJ
or
UJ
I
60
58
56
54
52
50
• ! -i "
1
i i
••••••••••....•
• * •
OBSERVED
PREDICTED WITH
BOAT DATA
,
I II i I II I
8
12
16 20
0 4
SUN TIME
8
12
16 20
FIGURE 20 - OBSERVED AND PREDICTED (WITH BOAT DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 4
31
-------
daytime, and 5° - 10 F higher than the boat-measured air
temperature at night. The Nashville wind speed was also
determined to have been consistently higher than that
measured on the boat, but no clear relationship could be
determined, as was shown by Figure 4. Therefore, the
final adjustment simply set the wind speed at 1.5 mphf
which was the approximate average wind speed actually
observed.
Various combinations of adjustments to Nashville data
were tried before it was used to predict temperatures in
the streams studied. The same least squares procedure
that was used to try to determine the best method of
handling fog was also used to determine the effect of the
various combinations of adjustments. The results from
4 such adjustments are shown in Table 5.
Figures 21-24 show the observed water temperature, the
water temperature predicted using unadjusted Nashville
data, and the water temperature predicted using the
adjustment shown in the last column of Table 5. The re-
sults show that generally good agreement between observed
and predicted temperatures can be realized if appropriate
adjustments to the Weather Bureau data can be made. On
the other hand, unadjusted data from even nearly weather
stations is not likely to give good results because of the
great differences between the microclimates of airport
weather stations and river valleys. Even bankside weather
stations must be checked carefully.
Obviously, the particular adjustments found to be appro-
priate in this case are not necessarily typical. In
particular, rivers used for power plant discharges are
likely to be wider, flatter, and more exposed, with a
wider flood plain terrace than the ones studied, so that
their microclimate would likely be more similar to nearby
weather stations than the deep, narrow, sheltered valleys
encountered in this study. Thus, the necessary adjust-
ments might not be as great as the ones found necessary
in this case. The important point is that there are
differences that must be taken into account, but that,
when these differences are accounted for, reasonable pre-
dictions can be made.
In each case, a preliminary study of the weather in the
vicinity of the stream, as compared with that of the
weather station to be used, must be made. The approximate
depth of the stream for various flows and the influence of
32
-------
TABLE 5 - LEAST SQUARES FIT OF NASHVILLE
DATA USING VARIOUS CORRECTIONS
Survey
Cumberland
#2
Cumberland
#3
Caney Fork
Total
No
Correction
1.89664
1.91275
14.87599
18.68538
<°i - Pi)'
n - k
Air Temp.
-2°F
1.44248
1.09745
12.20794
14.74787
Air Temp .
-4°F
1.06291
0.52697
9.88349
11.47337
Air Temp .
-4°F
Wind Speed
= 1.5 mph
0.05161
0.91710
0.4415
1.41021
33
-------
LL
o
UJ
Q:
ul
ce
OBSERVED
PREDICTED WITH
NASHVILLE DATA
PREDICTED WITH ADJ.
NASHVILLE DATA
.'... i . i .: I .
20 0 4
SUN TIME
FIGURE 21 OBSERVED AND PREDICTED (WITH NASHVILLE DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 2
UJ
0=
CL
I
cc
UJ
I
PREDICTED WITH
NASHVILLE DATA
SHVILLE DATA
i "»•'• i i i
50
8
20 0 4
SUN TIME
FIGURE 22 OBSERVED AND PREDICTED (WITH NASHVILLE DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 3
34
-------
OBSERVED
PREDICTED WITH
NASHVILLE DATA
12 16 20
0 4
SUN TIME
8
12
16 20
FIGURE 23 - OBSERVED AND PREDICTED (WITH NASHVILLE DATA)
TEMPERATURES, CANEY FORK RIVER SURVEY
[H
jjj
j
ijj
•
1
&
•
&
"
*•
.
/
1
•
*
11
t|
i
ii
ii
: iTTTl
/
1
/ jT
/ *
MIT
501
>
*•
<•
•*
••
ir~*
•*
•:
;
—
1
*•—
,<••
...
j
—
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— -
— -
_—
.—
.
-—
••*•
• •
_
—
1
^
• •
x
••
.
X
..
— •
X
•••*
1
x* •
••••OBSERVED
.PREDICTED WITH
NASHVILLE DATA
__ PREDICTED WITH
NASHVILLE DATA
1
; , . ' ,
•
'••
....
•
ADJ.
:
_—
••
1
,
.
|
j
.
--
-
r
i
Lu
o
60
58
s
CL
CE
UJ
I
56
54
52
50
8
12
16 20
8
12
16 20
0 4
SUN TIME
FIGURE 24 - OBSERVED AND PREDICTED (FROM NASHVILLE DATA)
TEMPERATURE, CUMBERLAND RIVER SURVEY 4
35
-------
bank shading and blockage of the sky must also be
determined. After this data is accumulated, then present,
historical, derived, or predicted weather data, with the
appropriate adjustments, should be usable in the model
presented herein for prediction of the downstream water
temperature for various water conditions and power plant
loadings. The model should thus be a valuable management
tool for managing the quality of our nation's waters.
36
-------
CONCLUSIONS
This study has demonstrated that temperatures of flow-
ing rivers can be rather accurately forecast if the
river depth, river valley geometry, and weather varia-
bles are known. Solar radiation, which is primarily
influenced by cloud cover, is by far the most impor-
tant factor in the energy budget of flowing streams.
Although some difficulties were encountered in pre-
dicting stream temperatures with weather data from
stations other than in the river valley, appropriate
modifications can be made to account for the clima-
tological differences between the two locations.
The problems encountered by studying rivers below
equilibrium temperature appear to be considerably
greater than studying those above equilibrium tempera-
ture. Air temperatures exhibit considerable lapse
rates in river valleys below hydroelectric installa-
tions. These vertical temperature differentials are
primarily due to the stratification resulting from
density differences. In contrast, the air above
heated rivers would tend to be unstable with low
lapse rates. The temperature at weather stations in
the area would tend to be much more indicative of
air temperatures in valleys through which warm rivers
flow.
Adjustments for wind speeds are necessary to use any
data from local weather stations. This adjustment should
be relatively easy to make, given the geometry of the
river valley. Wind speeds measured in the river valleys
were much lower than those recorded at nearby weather
stations, and this pattern would probably be similar
in most instances.
Average depths for use in the model could possibly be
determined from relatively few cross-sections. Great
care had to be used in determining river depths in the
studies conducted because unsteady flow conditions were
encountered. Releases from the dams were variable,
often being almost constant during the daytime and com-
pletely shut off during the late evening and early
morning hours. Unsteady flow conditions presented no
problem to the weather boat, because it followed a
tagged slug of water, but the dye boat (which measured
depth) had to be careful to measure depths at a parti-
37
-------
cular river mile near the time when the weather boat
passed, because the depth at a particular river mile
changed with time.
The temperature predictions determined by the model
can only be as accurate as the weather data used for
input. Highly accurate weather predictions are diffi-
cult to obtain. However/ the model studied appears to
be a useful tool. It should be of value in defining
the consequences of critical weather conditions, as
well as temperature changes during ordinary circum-
stances.
38
-------
BIBLIOGRAPHY
1. Raphael, J. M. "Prediction of Temperatures in
Rivers and Reservoirs." Journal of the
Power Division/ American Society of Civil
Engineers, 88, P02, 157-181 (July, 1962).
2. Thackston, E. L. Effect of Geographical Location
on Cooling Pond Requirements and Performance.
Environmental Protection Agency. Water Pollution
Research Series, No. 16130 FDQ 03/71, U.S.
Government Printing Office, Washington, March,
1971.
3. Moon, Perry. "Proposed Standard Radiation Curves
for Engineering Use." Journal of the Franklin
Institute, CCXXX, 5 (November, 1940) .
4. Upadhyaya, Ajeya K. Predicting Temperature Changes
of Cold Water Released From a Dam.Unpublished
M.S. thesis, Vanderbilt University, 1971.
5. Anderson, E. R. "Energy Budget Studies. Water Loss
Investigation: Lake Hefner Studies." Pro-
fessional Paper 269, U.S. Geological Survey,
Washington, D. C.: Government Printing Office,
1954.
39
-------
APPENDIX 1
Equipment Used For Measuring Variables In Model
Variable Description
Depth
Air Temperature
and Wet Bulb
Temperature
3. Cloud Cover
4. Wind Velocity
Shaded Fraction
of Water Surface
Blocked Fraction
of Solar Hemi-
sphere
Water Temperature
Fathometer, Raytheon Model DE-719.
Uses sonar principle. Four ranges:
0-55, 50-105, 100-155, 150-205
feet. Built-in power supply. Re-
corder chart speed ranges from 1 -
4 inch/ min.
Bendix aspirated psychrometer.
Contains matched wet and dry bulb
mercury thermometers and a mina-
ture electric fan powered by 3
standard D-cell flashlight batter-
ies. Air velocity of greater
than 15 ft/sec created by fan.
Thermometers graduated from 10°
to 110° and accurate to .7°F.
Estimated by eye and reported as
tenths of sky covered by clouds.
*
Stewart Electronic Odometer. Five
digit non-reset electromagnetic
counter designed for remote wire
connection to a contacting anemo-
meter .
Estimated by eye.
Average angle of the sky blocked
by hills and bluffs determined by
measuring in four directions with
a Navy sextant. Blocked fraction
of sky is sine of average angle.
Whitney model TF-20 portable
underwater thermometer. Range of
30°-110°F in four increments.
Accuracy of +.2°F. Resolution of
.1°F. Powered by 8 standard D
cell flashlight batteries.
40
-------
APPENDIX 2
Computer Program and User's Manual
The computer program uses the energy budget approach to
calculate water temperatures in non-stratified water bodies,
The equations discussed in Chapter I are utilized with the
general procedure being that described on page 7.
The program is written in Fortran IV and was run on the
Vanderbilt University XDS Sigma 7 computer.
41
-------
Line See Equation Comment
Number Page Number
1 Common statement allows certain
variables to be used in both the
main program and a subroutine.
2-4 Dimension statement for other
variables used.
5 Real statement allows variables
lat, long, netsum, netsky to be
used as real variables.
6-8 Variables initially set equal
to zero.
9-20 Read statements to get general
information about survey into
the program.
21-23 Initial water temperature is
fifth card in data deck.
25-29 Latitude, longitude, elevation,
number of data points, and
general location specified.
31-39 Comment cards defining variables.
40-44 Routine to read all meteorological
information.
45-47 Routine to read all water
temperatures
48-65 Information on first six data
cards printed.
66-67 Latitude set to an integer value.
69-76 Routine to handle time when
changing days.
77-225 Routine to compute water tempera-
ture changes.
77-81 Variables for particular time
interval printed.
42
-------
Line
Number
82
83-86
87-88
92-96
97
98-100
101
See
Page
3
3
3
2
3
2
3
Equation
Number
5
4
6
2
7
3
8
Comment
Declination of the sun calculated.
Sine of solar altitude calculated.
Solar altitude calculated.
Direct solar radiation uncorrected
for clouds or shaded fraction
calculated.
Correction for part of river
shaded applied to direct solar
radiation.
Diffuse solar radiation calculated
Correction for part of the sky
blocked applied to diffuse solar
radiation.
103 4 9 Total solar radiation calculated
by applying correction for cloud
cover.
105-147 Routine to calculate atmospheric
radiation.
106-108 5 12 Wet bulb temperature calculated
from relative humidity and air
temperature.
109
Air vapor pressure calculated.
110 6 16 Vapor pressure air would have
at water temperature calculated.
112-139 4 10 Routine to pick equation for g
for each value of cloud cover.
141-147 4 10 Atmospheric radiation calculated.
149-153 5 14 Back radiation from water
calculated.
155-158 6 15 Energy transfer by evaporation
or condensation calculated.
43
-------
Line See Equation
Number Page Number Comment
160-164 6 17 Energy transfer by conduction
calculated.
166-179 2 1 Total energy transfer rate
calculated.
180-183 7 20 Temperature change for time
interval calculated.
185-189 New water temperature calculated,
77-225 If not at end of data, new rate
of energy transfer computed for
the next time interval.
240-279 Subroutine to plot observed and
predicted water temperatures
versus time.
44
-------
1 CQMMHN
Z 01 MEMS I ON OePTH(15C)#TA.iPU50)jkU50)/eCU50>,yU$0)* SHADE (150) /DA
5 REAL LATjLDNG/NETSUN/NETSKY
fe ALPH4*Jf
7 H«0,
8 D£ltA«Of
9 REAOO*30)
10 117/K19/K19
ft 30 FURMA7C20A4)
U READ(5/32
13 1 AX7/A1B/A19/A20
It 32 FOHMA7UOA4)
17 33 FQ<».MAT<20A4J
18
20 34 FQRMA7(20A4)
tf C TWAT IS THE "INITIAL WATfcR ' TEMPERATURE WHICH lit RfiA" JH AT THIS PT,
2Z R£AO(5/46) TWAT
23 46 FOR«AT(FIO,5)
24 930 CONTINUE
25 C NQ J$ THE TOTAL NUMBEK OF CBSfcRVATIOMS
jZ6 RE AD (5/25) LAT^LQNi,ELfcV/NO*STAl/5TA2/STA3*STA4*STA>/5TA6j5TA7/5T
2,7 iA8/STA9/STAiO
28 23 FORMAT(3F10.2/I10/10A4)
21 IFUAT)17*17*940
30 940 CONTINUE
31 C TAIR.TEMPERATURE QF AIR IN DEGREES F
32 C R-RELATJVE HUMIDITY AS ^RACTIO^
33 C UNWIND SPEED IN MjLt5 PC* HOUR
3^- c CC.CLOUD COVE* IN TENTHS OF SKY
3S C DAY IS THE DAY QF THE YEAR
?6 C HOUR IS THE HOUR OF DAY
-------
31 C THETA IS THfc TIME
38 C SHADE IS THE FRACTION Dp THt KIVER WHICH IS SHADED
39 C 31QCK, IS TnP FKACTIPN OF ThE SKY WHICH IS BIOCKEU P*Q* THE RIVER
40 DO 10 J-l/NO
41 READ {»/ 1 U DAYU ),HDUR tJ},QEPTH(j),TAIK(J),5-'N)(»CC(J)/U(0)^ SHADE U)
43 H
44 10 CONTINUE
45 DO 5200 jal,»MU
46 5200 REAQ(5f52Cl)TwQ{ J)
47 5201 FQRflATtFio.bJ
48 WRITE «**?»>
49 55 rURMATC '1 » )
50
51
52 31 FQRMAT(20AAJ
53
^4 1
55 *2
57 1817*818*619,820
ifl 43 FQRMAT(20A4)
FURMAT(20A4)
WRITE(6*39)
ILONGjELEV
39 FORMAK ILDCATION IS »/10A4/ZX/ 'LATITUDE IS i*F6.2*2X" UUNGITUDE IS
UN IS I/F5.0)
I.AT-INTUAT)
5 CONTINUE
69 INDEX.O
70 TIM6(1)»HDURU)
-71 00 41 J-2/NO
71 IF
-------
75 40 JNDEX«INDEX+l
74- 41 Tr*g(g )sHD'JK( J) + ( I
75 OQ 3 IsljiNP
77 15 *RITE(6,12> PAY ( I ) ,tiPUP i I), DEPTH ( I }, TAIR ( I )>* ( I) >CC ( i ) , u ( I ) ,SHAUE (
fln 1/F5 lj2X,'PEL HUH« «, F4.?/2X^ «CC- '/F4,l^X*'Up '/F>,1/' SHAD, FR
2; 2.. i,P4,2j2X/l3LDCKb
82 4 oeLTA»-23.2S*COSU.*
g3 C H.hQUR ANCLE UF THE
^8? tr
-1 90 107 il-O.O
21 C 5UNTI51UJKFCT SuLAR RMHIATIDN UNCi-RRECTEO PCJR CLU^OS
flf C 130 SUN«Io.11469996*ALPHA*0.3023495*ALPHA**2-O.CU85400A3*MLPHA*J(,3*(0,lZ
^ 2PHA**6
J2 c sKrioiFouRATiQN UNCORRECT.D
49 SKY»1.6802983*ALPHA-(Ofil777075E-01)*AtPH
inn 1A**3-1 0.4729434. IE-OS )*ALPHA**4-(0.585B371bF'-06)*ALpHA**5
NETSKY"SKY*( 1 .-BU&CM I ) }
C QI IS ACTUAL SOLAR RADIATION
QUiNETSKY+NETSUNJ*jl.-0,0071*CC(l)**2)
C ....... ...... P •••..•,•••••••••• 1 1 ••• 1 1 ......... • • • • ' • *
C EW U THE COMPUTED VAPH? PRESSURE DP THE «ATER IN
D C AIR AT TEMPERATURE UF THE WATER
707 109 RATJQfO. 655+0. 36*R£i)
108 WETT»RATIO*TAIR(IJ
-------
109 EA.EXPt 17. 62302-9500, fc2o/ ( WfcTT+^60, ) >
110 Ew»EXPU7.6Z302-9500ta*6/(ThAT+460) )
111 cAS a EA
112 K»CC(I>
113 IF( JFQC(l). E3.l)GQ TG 120
11* Gu Til 190
H5 120 :;ETA«U.*5
416 121 :-0 TO 217
117 190 IFCK)i9-?jiOO>l99
118 199 &G TO (20i*2
119 2&0 i>.ETA«(0.1£)*
120 GU TO 217
201 KeTA«CO.lS)*
&U TD 217
ZQ2 ti£TA«(0.1&)*
124 i»U TD 217
125 203 &ETA«(0, 143J*EA5+0.771
Mb GO TO 217
U7 204 PtTA«tC,13BJ*EAS+0.783
128 GC TD 217
130 GU TO 217
131 206 3ETA«CO.;35)*EA5+O.B
152- &Q TO 217
133 2&7 S£TA«t0.13)*EA5*O.Bl
t3f GO TO 217
135 203 6ETA»tO,12?*EAS+0.825
13> GO TO 217
137 209 BETA»t0.1C5)*EAS+0.845
136 GO TO 217
139 210 BETA«(0,09)*EAS+0,e&6
1fO C ... .............. ... ....... . i ......... ..... ..»*.
Ifl C QA IS LONG ^AVB ATMQSPHERiC RADIATION
142 C SIGMA IS THE 3TEFAN-BULTZMANN PAOUTIQN CD^'STA^T
M 117 SIGMA'O. 00000000166
14f CO TD 218
-------
145 »001 UUTPUT BETA
Hfe 218 TA4«(TAIP(I)+459,67)**4
147 wA*0,y7v$lG"lA#BETA*'U4
146 C , ,., •
149 C 3d IS THF EFFbCTlVE ftAC* RAUIATIHN
150 C IT IS A FUNCTION OF SI5MA/ bETA* AIR TEMPERATURE* AfjU WATER
151 C TEMPERATURE.
152 21*» T*4.«(T«'AT+4J>9.67)**4
153 220 w6«-0.«7*SJ<3«A*Tl«!4
154 C , ,
155 C S£ IS ThE PVAHQRATEU HCfeT
156 C IT IS A FUNCTION OF Ui^-0 VELOCITY ANH TMF nlFFERfci^t efcTV/EEf
157 C VAPOR PRFSSuRE uF SATwRATEn /MP A^C ACTUAL AlK
168 310 3fc»-13.9*u(I)*(6W-eA)
159 C ..**....*..*.. i.. * «•«
1*0 C Qh IS THE CONDUCTED HEAT bETWEEN «ATEK-Alk INTFRPACfc
10,1 C IT IS A FUNCTION Of- mJN? VELOCITY/ BA^Ur-tTKIC FKgSSVir-f: AND
*. 162 C OIFFERE^CE SgTWEEN TfcMPEKATURFS QF -ATc^ AND AJR
*° 1W P«29,92/EXP( (3
164 400 QH«0I00543*U(I
165 C
C <3T IS THE TOTAL SURFACE HEAT TRANSFER
500 QT««I*QB+Q6*QH*QA
C SUREN IS THE ENERGY CHANGfc UU£ TD SURFACE
AREAvl.O
170 C THETA IS THE TIME INCRFMEuT IN HOURS
171 IF(I.EQ.l) GO TO 550
172. GO TD 560
173 550 THEtA«(TJMEt2?-TIMEli»/2.
n4- GO TO 600
175 560 !F(i,EQ.NO) GO TO 570
176 GO to 580
117 570 THETA«(TIME(NO)-TlME(NO-lM/2.
118 GO fO 600
17THETA/62.4
-------
181 C
184 C TQTEN IS TH£ TOTAL 6NEK&Y CHANGE
183 800 TQT6N-SUREN
184- C • ..........
185 C T£MP is THE T6*1PE»AIUR? CHANGE JN DEGREES
Ifcfc VOL«AREA*L'6PTH(I)
187 ^00 TfcMPaTDTEN/v'DL
168 C TWAT IS ThE CALCULATED mATER TEKPE&.ATuRfc yi'RIhG Tnlb TIME INTERVAL
189
190 C
i T * • ** v- * » '• " " ^ * c. r\ it. ' > ^ t
1=RITE(6/U}Tbt£,N
198 18 Ftj^riATMTCjTAL ElNtRGY CMAKuE" «t Pi? .Bj 2X> ' rfcr KEE^ FAHKtr*t IT-H**3
o iqq I/)
WRITE (6*20)
20 FO°.MAT( i ThE
201 1 ' )
21
505
*0* 22 FORMAT( ITMEKEFORE THE CALCULATED WATER TEi-^f-ATuRE P! i^fcORgfcS FAPfc
101 1NHEIT IS')
30^ 23 FOB«AT(FU.6)
^10 2000 IFfI.EQ.l) GO TO 50
411 CO TO 60
50 TIM61-HDURU)
TIME2"HOUR(1)+THETA
J114 GO TO 90
60 IFCJ.EQ.NQ) GO TO 70
GO TO 80
-------
217 70 TIMEl-HOURtNOJ-THfcTA
JLH GCJ TT 90
130 80 TIM6l«HUUK(l)-((HCUK(I)-40UR(I-m/2i>
M TIME2-HDUMI ) + C (HGUK< I+i)-HOUR< I) }/2. )
222, 50 TO 200 i
93 KRITE16/34) TIMEl^TIME?
24 FORrtAT(l0l/PING TH£ TIMP iNTfcRVAL
2001 Tw(I) • Tv»AT
3 CONTINUE
230 1
I Ai7/A18jAl9/A20
I Cl7/Ci8/Cl9/C20
237 CALi, GRAPH
.238 17 CALI. EXIT
23f END
34O SUBROUTINE GRAPH
241 COMMON HOURCl50)/
DIMENSION LINE(l2i)*lA(l3>
DATA
MIN«TWOtl)
245 DO
AXIS LABELLING
15 DQ 16 KP1,13
16 IA(KJ«MIN-KK-1)
SSO WRITC(6/22)
22 FORMAT UHi)
IF(|.EQ
-------
263 1? FQ*MAT(69X, ITEMP,, UE&. F'>
IB
166 00 19
257 19 LIN6(K)«Iu
^58 WRITE (6/20) LINE
359 20 Fu
260 30 CDNTJ
261 DQ 10
10 Llivl£
40
IP1-PT1
.2*7 SaPTl-IPl
55 IPT1-IP1+1
470 G0 TO 57
^71 30 IPTl^IPl
272 57 CONTINUE
273 IPTZ*(TWOtI?-
*?4 LINBUPTD-IP
475 LINEUPT2)»IQ
J7f» IF(IPTl,EQ.lPT2)LINfe(IPTU«IS
577 100 WRltE(6/35)HDUR(I)*LINE
57g 35 FQRMAT
^79 RETURN
480
-------
APPENDIX 3 - DATA
Two sets of data are necessary to execute the program. The first
is the stream geometry and weather data. The second is the set of
measured stream temperatures. The first water temperature measure-
ment corresponds with the first stream geometry and weather variable
measurement. The format for the data is at line 41 in the computer
program.
53
-------
CUMfcEF.LAND MVFis 5'JKVEY
JULY ?^
BOAT I-ATA
Ul
*»
49. :>
97.20
210. 7.5
210.
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JULY
TATA FF;L»-'
in
49.5
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TEMPERATURE CUMBERLAND RIVER SUPVEV
49,5
49,6
49,6
50,C
30,2
50,4
30,3
50,7
50,9
31,15
51,40
51,5
51,65
51,6
52,0
52,2
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52,35
52,40
32.45
32,45
52,30
32,5
52,5
32,5
32,3
32,5
52,3
32,6
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11,5
32.5
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52.5
52,4
52,4
52.4
52.2
52.3
52.3
52,2
52.3
52.3
52.3
52.3
52.3
52.5
32,55
52*6
52*7
52,85
53,0
53,2
53.4
53,6
53.75
93.8
53.9
94.1
94.35
94.4
94,5
94.6
94.7
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MATER TEMPERATURE CUMBERLAND RIVSR SURVEY #3
92,3
52,5
52.5
52.5
52,6
52.9
59.2
53,5
53,6
54,0
54,2
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56,9
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58,6
99,8
58,9
99,1
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WATER TEMPERATURE HOUSTON RIV6R SURVEY
53,3
53,3
53.4
53,6
53,a
53,9
54,
54,4
59,1
55,1
55,7
56,3
96,4
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57,3
57,6
57,8
58,1
98,2
98,3
98,4
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98,9
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39,3
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39,0
39.6
39,6
39.7
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39,75
60.1
60.3
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60,3
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TcHH£RATU,U- CftNfcY FUR* KUEK SURVEY
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-------
JULY 17-18,1971
BUAT DATA
51.1
36,75
198.
198.
198.
198.
198.
198.
198.
198.
198.
198,
198.
198.
198.
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15,754.9
16,256.3
16.757,6
17.256.1
17,757.75
18. 258. 2
18.757.6
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20.255.9
20.756.3
21.256.7
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-------
CUMBERLAND BIVEB SUEVK1
JULY 17-18. 1971
WEATHER DATA PBOM NASHVILLE
51.1
37.20
198.
198.
198.
198.
198.
198.
198.
198
198
198
198
198
198
198
65.30
7,75 3.9
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11,737.
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198, 15.258.2
198. 15.754.9
198. 16.256.3
198, 16.757.6
198. 17.236.1
198. 17.7*7,75
198. ia.259.2
198. 18,757.6
198. 19.256.9
198, 19.756.05
198. 20.255.9
198. 20.756.3
198. 21.256.7
198, 21.757.1
198, 22.257.4
560.
69,5
68.
74.5
74,3
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37.5
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65.
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79,5
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1.79
1.72
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3,22
3,19
2.74
1,47
1.18
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-------
CUMBERLAND RivtR SURVEY
51,1
31,1
51,2
51,3
51. d
31.0
52.1
52,?
52,7
33,
53.7
55,
55,2
55,4
55,6
55, 6
55,6
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96,2
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-------
It. Z
5*.l
96,1
56,1
36,1
56.1
56,2
56,3
56,4
56,4
56,4
56.4
56,5
56,6
56,6
56,6
56,0
56,9
57,1
57,2
57,5
57,7
57,9
51,2
51,4
51,6
91,1
ff.l
ft, 2
-------
TECHNICAL REPORT DATA
(I'lrase read titXructitms on the reverse before completing)
NO.
__ EPA-66Q/3--75--OQ2-
4. TITLE ANOSl/BMTLE
2.
5. REPORT DATE
Effect of Meteorological Variables on Temperature
Changes in Flowing Streams
6. PERFORMING ORGANIZATION CODE
I. RECIPIENT'S ACCESSION-NO.
January. 1975 (issued)
AUTHOR(S)
Robert U. Troxler, Jr.and
Edward L. Thackston
8. PERFORMING ORGANIZATION REPORT NO.
9, PERFORMING ORG '\NIZATION NAME AND ADDRESS
Department of Environmental and Water Resources
Engineering
Vanderbilt University
Nashville, Tennessee 37235
10. PROGRAM ELEMENT NO.
1BA032
11. CONTRACT/GRANT NO.
R-800613
12. SPONSORING AGENCY NAME AND ADDRESS
National Environmental Research Center
Office of Research and Development
U.S. Environmental Protection Agency
Corvallis, Oregon 97330
13. TYPE OF REPORT AND PERIOD COVERED
Fi nal
14. SPONSORING AGENCY CODE
IB. SUPPLEMENTARY NOTES
ACT
16. ABSTI
A mathematical model for predicting the change in water temperature
in a flowing stream as a function of stream geometry and standard
weather information was developed and tested. Five field tests were
conducted on cold water released from hydro-power stations as it
warmed up moving downstream over periods up to 38 hours.
Predictions of temperature changes were made based on (a) weather
data from a boat floating with the water, (b) data from a station
on the bank, and (c) data from a remote weather station 100 miles
away. Agreement between predicted and observed temperature changes
was good, even with remote data, when adjustments to compensate
for the local micro-climate were made. Computer programs and all
data are included. This report was submitted in fulfillment of
Project Number 16130 FDQ, Grant Number R-800613, by Vanderbilt
University, Department of Environmental and Water Resources Engineering
under the sponsorship of the Environmental Protection Agency. Work
was completed as of November 1974.
7.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
Water temperature, heat budget,
mathematical models, climatology
b.lDENTIFIERS/OPEN ENDED TERMS
River temperature
prediction
c. COSATt
13/13B
:LASS (This Report)
Release unlimited
20. SECURITY CLASS (This page)
21. NO. OF PAGES
.as.
22. PRICE
EPA Form 2220-1 (9-73)
6 U.S. GOVERNMENT PRINTING OFFICE: 1975-697-996(93 REGION 10
------- |