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


TABLE 5 - LEAST SQUARES FIT OF NASHVILLE
DATA USING VARIOUS CORRECTIONS

(0, ~ Piy2
n-k
Survey No Air Temp. Air Temp. Air Temp.
Correction -2°F -4°F -4°R
Wind Speed
= 1.5 mph
Cumberland
#2 1.89664 1.44248 1.06291 0.05161
Cumberland
#3 1.91275 1.09745 0.52697 0.91710
Caney Fork 14.87599 12.20794 9.88349 0.4415
Total 18.68538 14.74787 11.47337 1.41021

33


TABLE 4-LEAST SQUARES FIT OF BOAT DATA
WITH VARIOUS CORRECTIONS FOR FOG

2
(0; - Py)
Survey n-k
8 = .95 When No Corrections Cloud Cover
Fog Present For Fog =10 When Fog
Present
Cumberland 0.09232 0.03352 0.04719
#2
Cumberland 0.07046 0.11828 0.07785
#3
Holston 0.20695 0.20965 0.25019
Caney Fork 0.36281 0.36281 0.36252
Mis .73254 De .72246 d= £73775

29


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


Evaporation

Much effort has been applied to developing evaporation
formulas. Numerous empirical formulas are now in
existence. The equation used in this study was

Q, = - C Ule, - ea) (15)

Q, is the energy lost by evaporation, C is an empirical
coefficient, U is the wind speed in miles per hour, e
is the saturated vapor pressure of the air at the water
surface temperature in inches of mercury, and eg 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

e, = exp[17.62 - 9501/(T, + 460] (16)
where Ty is the temperature of the water. This equation
is the same as Equation 11 with T, substituted for Tw

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.

nr = 2c =(Co(Tw - Ta)\ (_P (17)
0 \e,- ea To00

P is the barometric pressure in inches of mercury, Q. is
the energy transferred by conduction, and Cy is a con-
stant with a value of 0.61. By making substitutions

6


163.
103,
163.
163,
163.
163.
163.
164.
164,
164,
164,
164.
164,
164,

164,
164,

Bez
7.5
13.6
1362
Lle2

72
Tel
6aP

603
6.1
10.5
1u.7
10.9
10.2
9.2
8.5
1G.
12.1
13.
13.6
12.8
10.
8.5
9.5
10.3
10.2
10.1

62.5
61.5
61.
Old
6165
Ole
61S
61.
60.5
Ole
6005
61.
600d
60.5
60.5
60.5
6065
60.5
61.5
64,
68.
7205
To.
TT.

81.5
82.
82.
80.5

294
le
le
le
le
le
le
le
le
de
le
le
le
le
le
le
l.
la
le
9G
208
o8L
072
209
297
63
26)

268

205

a oe ll od ol


109
110
144
112
113
WA
415
410
7
418

EAMEXP(17.62302"9500,E20/ ( WETT+460,))}
EWeEXP(17,6230209500,626/ (TWAT#46G) )
FAS a Ea
weCCtl)
TFCLFOG(1),ESe1)G0 TG 126
Su TA 196
120 SETAsU.95
U21 So TA 217
190 1F(K)19992509199
199 GO TS (20192924 20322042205 92008 207s 20892092210) 9K
269 LETAs( 5.15) #EAS 49,74
SG 12 217
201 SETAR(GL15)REAS#O,75
GO To Z17
262 SETAR( O15) #EASHO, 7S
GU TD 217
203 SETAR(0,1423)¥EAS46,771
60 TO 217
204 PETAm(ColBR) MEAS HU. TES
GO TO 217
205 BETAm(O,157)#EAS HO L793
co TM 217
206 BETAS(0.135) *EAS+O,¢
GG TO 217
207 BETAm(0e13)*EAS+0,.681
GO TO 217
208 SETAm(9.12)"EAS+0,825
GO TO 217
209 BETAs(0,105)#EAS0, 865
GO TO 217
210 BETAa(0,09)*EAS+0, 866
SCOKCAH ee eeatetHeeeet ete net EtErereseet agers HaseeteF et ener egeutere
QA IS LONG WAVE ATMOSPHERIC RADIATION
SIGMA IS THE STEFAN@BULTZMANN RADIATION CONSTANT
217 SIGMA#0,00000000166
GO TO 218


94

60
G1
62
63
64
65
Ge
GT
ob
67
70
uu
2

THETA IS THE TIME INCREMENT
SHADE IS THE FRACTIUN MF THE RIVER WHICK 18 SHADED
BLOCK 18 THE FRACTION OF THE SKY WHICH IS BLOCKED FRO THE RIVER
00 19 Jel,Na
READ(S,1LL DAY(S) sHOUR CI) ,DEPTHOS Ds TAIR( Sd 8 (Ud ,CO Cd eUl UN)» SHADE (I)
LoBLOCK(V),TFOG(Y)
1 FURMAT( 2F5e226F1lOeesF9e2aT1)
10 CONTINUE
vO 5260 JalyNu
5200 READ(5,5261) TWI( J)
5201 FORMAT(FIC.O)
aRITE (6359)
55 FURMATC(ILS)
WRITE (6231 )RLPRAZARAPR4sRSPROPRTMPRGAKGAKR I NSE L LPR 1 2aP Sek 1492, SROs
URLTeRLESR199R20
BL FORMAT(2044)
BRITE (69423012029 R32 AS RSs AOZATAABAIIALOSALIsAL22 br ALS ALS Al Os
lL ALT#A185A192A20
42  FURMAT(2644)
WRITE (694635 )B12 B22 632 B42 5s BOs BT Bb, 89s BI Os LL se 212k 5a Loe 8 LS Rb,
18179818s28199B20
43 FURMAT(20A4)
WRITE (S244) Cle C2sC Be Cos Ss COsC Te CBr COC DCL CLZ, C450 Lo, CLS eC Lb,
L 6479618619020
44 FURMAT(20A4)
WRITE (6939 )STAL»STAZsSTAZs STAGs STASpSTADSSTATSSTABZS IAIISTALOSLAT,
LLONGJELEV
39 FORMAT(ILOCATION IS 's1GAGs2X,I LATITUDE IS 'aFGe2e2xr'LUNGITUDE IS
Lo 'sFOe2s2Xs'ELEVATIUN IS !4F5.0)
LAT@LAT+0,5
LATSINTCLAT)
5 CONTINUE
TNDEX®O
TIME(1L)#HOUR(1)
00 41 Jma2,N0
TECHOUR (J) @HOURCJ@1)) 40041061


es

253
254
255
156
257
258
259

260
261

262
263

265
266
267

270
2n
272
273

275
21
am
278
27g
260

12
19

20
30

40

55

50
57

100
35

FORMAT(O9Xs,ITEMP.» DEG, FI)
WRITE (6,16) (TACK) sKets13)

FORMATCH TIMES 5XeTe912(8X072))

O26 19 Kelsl2.

LINE(K) 81

WRITE (S¢2G) LENE
FGRMAT(1L9X21214))
CUNTINUE

D0 LO Jwlst21

LINE( Jett

GB 40 Kslylelslo

LINE CK) FIL
PTLE(TY(T)@MINI ELC et Le
TPlsPT.

SaPTyoIP}
1F(S00,5)50955255
IPTlalPi42

GO TO 57

IPTLaIOL

CONTINUE
IPT2e(TWOCT)@MIN) #1001
LINE(IPTI)#IP
LINECIPT2Z) 810
TFCIPTI,EQTPT2)LINECIPTI)&IS
WRITE (6s35)HOUR( I), LINE
FORMAT(LXsF4,125Xs121Als/)
RETURN

ENO


9s

CUMEERLALG RIVER SURVEY Be

JULY

WEATREF CATA FRUN SASRVILEE

49,
37020

210.
210.
210.
210.
210.
210.
210,
210,
210,
210.
210.
210,
210.
210,
210.
210.
210.
220.
210,
210,
210.
210,
210.
210.
210.
210.

Eom AUV SIG

5
5

7.5
6.0
bed
960
965
1.0
10.5
11-0
11.6
1zZ

13.66
13.5
1460
14.5
15.0
15.5
16.0
16.5
17.6
17.5
18.0
18.8
1960
19.5
2000
20.5
21.0
21.5
22.0

85.36

13.5
iz.
iC.
i3-G
bCek
Ga
14.6

1G.
13.5
1265
1405
13,23
1366
16.2
4400
1262
14046
1461
1566
14.0
1202
11-7
1500
14.0
15-0
1920
19.0
23.9
20.06
20.0

360,

78.
ele
e245
64.
65.8
€7.
6B,
5Ge
85,F
GGe
Fle
926
Gl.
FOet
91.5
936
9205
Gin
Fle
GOs
€9.5
89,
6705
86.6
65,5
65.
63,
79,
7965
80.

+70
163
59

052
Se
250

043
039
037
039
936
037

027
o2g
rs)
30
232
034
36
046
045
740
048
260
072
266
261

S6bURKESVILLE KENTUCKY

wuwucus

004
+04
eS
020
Pree)
ued
Ved

rate)
Yed
Ved
005
We0
202

005
005
2995
005
005
010
950
250
260
406
420
400
400
4.0
4.0
4.0
400

wee ee


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


RELATIVE HUMIDITY , %

ELEVATION : 80 FEET ABOVE CANEY FORK RIVER

—eeeene ELEVATION: 5 FEET ABOVE CANEY FORK RIVER
1 1 1 1 1 1 1
2 24 12 24 12 24 12 24
MONDAY | TUESDAY =| WEDNESDAY =| = THURSDAY ~—s‘|.- FRIDAY

WIND SPEED ON CUMBERLAND RIVER, MPH

FIGURE 3 - VARIATION OF HUMIDITY AT TWO ELEVATIONS

OVER CANEY i‘GRK RIVER

>

n

© -CUMBERLAND SURVEY 2
®-CUMBERLAND SURVEY 3

2

2 4 6 8 0 12
WIND SPEED IN NASHVILLE, MPH

FIGURE 4 - WIND SPEED ON CUMBERLAND RIVER VS.

WIND SPEED AT NASHVILLE
16

2


WATER TEMPERATURE, °F

WATER TEMPERATURE, °F

PREDICTED WITH
~~~ NASHVILLE DATA

ED WITH ADy. led :

PP cette aah oA |
‘a i |g a AR Ss
16 20 4 8 l2 I6 20

SUN TIME

FIGURE 21 - OBSERVED AND PREDICTED (WITH NASHVILLE DATA)

‘

62

60)

58

56

54

52

50L

FIG

TEMPERATURES, CUMBERLAND RIVER SURVEY 2
7 TTT

—FSRRTER A
Oe eee
8 12 16 20 fe) 4 8 !2 I6 20

SUN TIME

URE 22 - OBSERVED AND PREDICTED (WITH NASHVILLE DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 3

34



$9

Tie

62.5

206

oN

rite TERA AVI
COSC* eee esa eas wee

oe

JORRE RI
a7? eu?
7? .
ox ai
1.4 od
Ze fe
2a” ea
cares ue
Ger ad
4, Ud
268 ce
4° ve
Aah oe
2? a
20? 42
bet hl
Bat 2Ue
le? wut
LaF ef
Be 2id
4eé ade
le® re)
Le? af
Le? 140
le? 2?
8 ?
ed 7?
3 Le
rr le
or le

CITY TENNESSEE

oi7
eat
237
037
041
ah
sel
eal
enh
sol
eal
ool
ead
236
24
2i7
eaZ
034
017
oi?
eee
23?
eal
22?
el?
eel
0i4
034
226


TABLE OF CONTENTS

INTRODUCTION . 2. 6 2 2 ee ee we ee we we we ee 1

THE ENERGY BUDGET . « «2 2 e+ © © © ee ee ee ee 2

Solar Radiation
Atmospheric Radiation
Back Radiation
Evaporation
Conduction

EXPERIMENTAL WORK . . «© 2 © «© © © © © © © © © ee ee 8
Tracer Measurements
Depth Determinations
Meteorological Readings
Water Temperature Measurements

CHARACTERISTICS OF STREAMS BELOW
HYDROELECTRIC INSTALLATIONS . . 2. « © «© © © © © © © © 13

Air Temperature

Relative Humidity

Wind Speed
RESULTS OF THE STUDY . . . 2 6 6 ee ee ee ew ew ew OL?

Energy Transfer by all Mechanisms

Computed and Measured Solar Radiation

Water Temperature Predictions
CONCLUSIONS . 2... 2 6 ee ee ew ee ee ee te we 87
BIBLIOGRAPHY . . . 1. 1 ee ee ee ew ee et ew we 8D
APPENDIX 1... 1 we ee ee ee eee we ee ee ee 40
APPENDIX 2... 1 6 6 ee ee ee ee ee ee ee ww we 4

APPENDIX 3. 1 6 ew ee ee eee ee te ee ee eee 5B


89

3903
5944
59.44
59.5
5944
5944
390%
39.5
59.5
59,5
59.5
5905
59.0
89.0
59.0
5946
59.7
5907
59.75
6001
60.3
6004
6005


“9

WATER TEMPERATURE HOLSTON RIVER SURVEY
53.3
53.3
5304
53.6
53.8
53.9
54,
54.4
5541
$55.1
55.7
56.3
5004
57s
5702
57,3
57.6
57,8
58.1
$8.2
58,3
50,4
50.5
58,5
58.6


02

CANCY FORK RIVER S'IRVEY
JUNE Zee 1971
AIR TEMPERATURE, CLUUD COVER, & RELATIVE dusloTr¥Y FaOm wASIVILLE, TENNESSEE

S2ei

360e 25,9 409, 3S CARTHAGEs TENNESSEE

177, 7.5 4.9 79. 095 3. 3 230 235
177. 7.75 &e7 Bie od Qe 3 22d 12k
177. 6.23 3.9 B36 277 Ze 0 oat 148
V77e GATS Teh B50 072 Ze i) 220 eae
177. G25 4,5 a7. 208 Re Le? 7 012
77. Ge75 5a? 8405 093 2 Len 020 029
177, i0.294,7 90. 127 le Let 005 129
L177, 16,79529 9405 252 le 1.9 ous 216
177, 11625467 93 047 le leh ev 31
177. 11679503 9462 «42 Oe 1.9 or) 31
177. 12025501 90. .37 Me 1eG eu +39
L772 12475406 96. 038 Ge 200 25 eal
177. 13629704 96. a3A le 207 ous 221
177. 136751009 96. 039 le 205 or) 126
177, 14.25606 956 239 le 12 ous 229
177. 14.75601 95. 240 Qe lel 240 241
LTT. 15025526 95 041 20 Le? 020 034
177. 1575604 95. 042 2° 1.7 210 2222
177. 16625600 Snes 043 le 1.4 005 22?
177. 16.755.3 Dae 043 le 1 200 047
LTT, 17025425 94, 044 le 7 200 224
177. 17575403 936 045 fe 7 +30 029
177. 16.25503 936 046 Oe 24 200 19
177, 18.7548 9105 049 Cs 06 +4 224
177. 19625428 9060 152 Oe 7 200 031
177 — 19075404 8b. 255 Oe 05 120 024
177, 20.257.8 87. 059 %e oo 1.0 042

477, 200757.9 85 262 Oe 8 120 042


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 8B

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


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


400 T + T T +
HOLSTON SUI
JUNE , 1971
f& 300;
=
2
au
Ss
E 200+
6s
3
a
100 _ _ ee _ _
1 5 r) Fa) $ 7

SUN TIME, HOURS

FIGURE 7 - ENERGY BUDGET COMPONENTS DURING
HOLSTON RIVER SURVEY

4 T T “T T T T T
300]
+
x
- 200}
a
wW
100) CANEY FORK SURVEY
JUNE 26, 1971
E
>
2
¥
Ww
“I
ar —— 1 1 n
7 WW 15 19 23 3 7 W

SUN TIME, HOURS

FIGURE 8 - ENERGY BUDGET COMPONENTS DURING
CANEY FORK RIVER SURVEY
1



Since relative humidity at constant vapor pressure is

a function of air temperature, the
would be expected to be greater at
the valley. That this is the case
Figure 3. Note that, although the
is higher at lower elevations, the
ture in the air at various heights

relative humidity
lower elevations in
is illustrated by
relative humidity
total amount of mois-
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


WATER TEMPERATURE, °F

WATER TEMPERATURE, °F

55

54

53

52

5I

PREDICTED wi
BOAT DATA TH

|i} —

50

Pat ar :
ESN YO Wat Wa

1
8 2  & 20

SUN TIME

FIGURE 16 - OBSERVED AND PREDICTED (FROM BOAT DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 2

62

eof

58

56

54

52

50"

SUN TIME

FIGURE 17 - OBSERVED AND PREDICTED (FROM BOAT DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 3

28


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 psychrometric
chart.

Cloud cover was estimated by eye and reported as tenths
of the sky covered. Table 2 indicates that estimates

10


69

GANEY FURK Riven SURVEY

JUNE
BOAT

S2ek
3600
1
177
177.
177.
177.
177.
177.
177,
177.
177,
177.
177.
177.
177.
177,
177.
177.
177,
177.
177.
177.
w77.
177.
u77.
177.
177.
u77.
i177.
477.

26019Th
DATS

12.255.)
12075405
13625704
136721005
44023606
44075601
15425566
15075604
16,2565
16.75553
17025405
17,754.3
18,255.63
18.75468
19425448
19,754.04
20225748
20.7579

20

Ge

CARTRAGEs TENNESICE

3
3
or]
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162
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ree


9S

CUMEERLANO RIVER SURVEY #2

JULY
BDAT

49.5
37029

216.
210.
210.
210.
210.
210.
210,
210,
210,
210.
210.
210,
210.
210.
210,
210.
210.
210.
210,
210,
210.
210,
210.
210.
210,

B5R 2021570

LATA

7.8

FeO

€.5

9.00
945

1060
16.5
11.6
11.5
1200
12.5
13.0
13.5
14.0
14.5
15.0
15.5
16.0
16,5
17.0
17.5
18.9
16.5
19.0
19,5
2000
20,5
21.0
21.5
22.0

65.30

13.5
12.0
16.0
134u
Lue>

166%
10.0
13.5
léeo
14.9
13.3
1366
16062
14.0
1202
14.4
146)
15.6
14.6
12.2
11.7
15-0
14.0
15-0
19.0
19.0
23.9
20.0
20.0

360,

61a
66.0
7005
7500
T16G
Teed
7745
76e6
82.0
560d
8200
89.0
83.0
83.0
73.5
800
79.0
7600
T7660
7000
7000
T10G
64.5
7520
6520
6345
60.0
60.5
6200
5955

099
236
238
7h
299
265
«76
79
270
009
207
232
258
272
a3]
004
73
208
275
276
084
093
295
293
1.00
1.00
1.0
1.0
1.0
1.0

66

209
109
1.0
1.0
00
000
000

AURKSVILLESKY,

1.46
1.73
1.23
«77
107
1.33
2.4
Te
1.93
2.23
1.8
1.27
2.0
2elt
2e0
2.47
1.27
1.13
1.27
235
223.
1647
le67
1649
053
0.9
eo7
1,27
e77
7

004
204
«05
020
Ged
ed
O66

ariel
ed
105
Grae
242
2U5
ous

ud

290

Me EP Peer re ree


THE ENERGY BUDGET
The energy budget for water bodies can be written as
% = Of +0 + ® +O, + Q (1)

where Q, equals total energy transferred, Q, equals
absorbed solar radiation, Q, equals absorbed longwave
atmospheric radiation, Q, equals longwave back radia-
tion to space, Q, equals energy lost by evaporation,
and Q, 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

Q) = - 0.1470a + 0.302302 ~- 0.008546a3 (2)

+ 0.0001271a% - 0.00000000101245
Qo = 1.680G + 0.031780? + 0.000241443

- 0.000000004729a% + 0.000000005858a5 (3)
2


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


19

262,
242,
242,
242.
242.
242,
243,
243,
243,
243,
243.
243,
243.
243.
243,
243,
243,
243,
243,
243,
243,
243,
243.
243.
243.
243,
243.
243,
243,
243,
243,
243.
243,
243.
243,
243,

Oke
el.
Ole
Obs
Gis
ate
6u03
Soe
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bed
59.5
56.9
Dt,
2b
See

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83.
BG,
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83,
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ee ee eee
One enone
ww

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a eR ek SO ol


9

WATER TEMPERATURE CUMBERLAND RIVER SURVEY #3
52.3
5205
32.5
52.5
52.6
32.9
3302
53.5
53.8
54.0
5402
5403
54.8
5502
55046
3567
55,8
55.8
3509
56,0
3602
5603


99

56,5
56.5
56.5
56,5
56.5
5606
56,5
36.5
5605
56.7
36.7
56.6
56.7
56,7
56.7
56.8
56.9
57.0
57.3
5704
57.5
57.8
57,9
58.3
58.6
56,8
58.9
5901
59.2
5943
5944
5944
5957
59.7
5907
5907


CUMBERLAND SURVEY 3

-—--—--- MEASURED 4
COMPUTED, NASHVILLE DATA

:

8

SOLAR RADIATION, BTU/FT?/HR
T

a
23 3
SUN TIME, HOURS

FIGURE 13 - MEASURED AND COMPUTED (FROM NASHVILLE DATA)
SOLAR RADIATION - CUMBERLAND RIVER SURVEY 3

§

ew

SOLAR RADIATION, 8TU/FT?/HR

23 3
SUN TIME, HOURS

FIGURE 14 - MEASURED AND COMPUTED (FROM BOAT DATA) SOLAR
RADIATION - CUMBERLAND RIVER SURVEY 4

22


oL

CUMBERLAND RIVER SURVEY #%
JULY 17-18, 1971
WEATHER DATA FROM NASHVILLE

51.1
37.20

198,
198,
198,
198,
198,
198,
198,
198,
198,
198,
198,
196,
198,
198,
198,
196,
198,
198,
198,
198,
198,
198,
198,
198,
198,
198,
198,
198,
198,
198,

7275 509
3225 864
3275 8.8
9e25 728
9675 345
2562560
10,7201
12.256.6
11.757.
42025565
120754.35
13-257.2
13.754.7
142253561
140 757el
45225802
15.754.9
1602563
16275766
17025601
170757075
14025802
18,757.66
49025609
196756005
20025549
20.75603
21225607
21075701
22025764

€5.30

560.
69.5
68,
74.9
74.8
79,
856
87.5
85.
83,
55,
83.
BS.
BG,
85.
82.
8].
84,
79.5
8205
TBs
7305
70+
69,
876
6565
65.
6305
6265
6205
6145

+83
78
282
274
oS

053
ool
259
055
056
099
072
57
+62
074
063
267

079
285
195

395
098
095
095
095
095
093

66

BURKSVILLE, KY.

094
1444
1.79
1.79
1072
1.35
lel
2022
3,22
3.19
2274
1947
1.18
2023
202
1043
1043
LeF2
1648
6
4
038
«6
1226
1651
1e4
14
104
164
104

2379
226
228
el?
«34
226
rt:)
02h
<2)
04
«14
033
125
019
34
232
032
224
126
126
022
226
028
228
042
039
244
a3]

034

eee


16

17

18

19

20

21

22

23

24

FIGURES CONTINUED

OBSERVED AND PREDICTED (FROM BOAT DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 2

OBSERVED AND PREDICTED (FROM BOAT DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 3

OBSERVED AND PREDICTED (FROM BOAT DATA)
TEMPERATURES, HOLSTON RIVER SURVEY

OBSERVED AND PREDICTED (WITH BOAT DATA)
TEMPERATURES, CANEY FORK RIVER SURVEY

OBSERVED AND PREDICTED (WITH BOAT DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 4

OBSERVED AND PREDICTED (WITH NASHVILLE DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 2

OBSERVED AND PREDICTED (WITH NASHVILLE DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 3

OBSERVED AND PREDICTED (WITH NASHVILLE DATA)
TEMPERATURES, CANEY FORK RIVER SURVEY

OBSERVED AND PREDICTED (FROM NASHVILLE DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 4

PAGE

28

28

30

30

31

34

34

35

35


10

11

12

13

14

15

FIGURES

VARIATION OF AIR TEMPERATURE OVER
CANEY FORK RIVER AT TWO ELEVATIONS

VARIATION OF LAPSE RATE OVER CANEY
FORK RIVER WITH TIME

VARIATION OF HUMIDITY AT TWO ELEVATIONS
OVER CANEY FORK RIVER

WIND SPEED ON CUMBERLAND RIVER VS. WIND
SPEED AT NASHVILLE

ENERGY BUDGET COMPONENTS DURING CUMBERLAND
RIVER SURVEY 2

ENERGY BUDGET COMPONENTS DURING CUMBERLAND
RIVER SURVEY 3

ENERGY BUDGET COMPONENTS DURING HOLSTON
RIVER SURVEY

ENERGY BUDGET COMPONENTS DURING CANEY
FORK RIVER SURVEY

ENERGY BUDGET COMPONENTS DURING
CUMBERLAND RIVER SURVEY 4

MEASURED AND COMPUTED (FROM BOAT DATA)
SOLAR RADIATION - CUMBERLAND RIVER SURVEY 2

MEASURED AND COMPUTED (FROM NASHVILLE DATA)
SOLAR RADIATION ~ CUMBERLAND RIVER SURVEY 2

MEASURED AND COMPUTED (FROM BOAT DATA) SOLAR
RADIATION - CUMBERLAND RIVER SURVEY 3

MEASURED AND COMPUTED (FROM NASHVILLE DATA)
SOLAR RADIATION - CUMBERLAND RIVER SURVEY 3

MEASURED AND COMPUTED (FROM BOAT DATA) SOLAR
RADIATION - CUMBERLAND RIVER SURVEY 4

MEASURED AND COMPUTED (FROM NASHVILLE DATA)
SOLAR RADIATION - CUMBERLAND RIVER SURVEY 4

iv

PAGE
14
14
16
16
18
18
19
19
20
20
21
21
22
22

23


TABLE 2 - CLOUD COVER ESTIMATES FROM
NASHVILLE AND BOAT

Average Cloud Cover,

Survey Day Tenths
Boat Nashville
Cumberland #2] July 29, 1970 1.36 2.46
July 30, 1970 2.42 2.74
Cumberland #3] Aug. 30, 1970 2.90 6.66
Aug. 31, 1970 5.80 5.35
Caney Fork June 26, 1971 0.30 0.70

11


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.


9L

WATER TEMPERATURE CUMBERLAND RIVER SURVEY #4
51.1
Sled
51.2
5le3
Sled
B5leo
320i
52.5
52.7
33.
53.7
54,
54.3
54,5
55,
55.2
55.4
53.6
55.8
355,48
36,
5601
5001
5002
5602
36.1
56.2
5602
56.2
5602
56.2
3602
56.2

52


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


EPA-660/3-75-002
JANUARY 1975

Ecological Research Series



APPENDIX 1

Equipment Used For Measuring Variables In Model

Variable

Description

Depth

Air Temperature
and Wet Bulb
Temperature

Cloud Cover

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


Total clear sky solar radiation is the sum of diffuse
and direct solar radiation. Cloud cover was taken into
account by using the relationship

Qe = (Q3 + Q4) (1 - 0.0071 Cc?) (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

Q, =o 8 (T+ 460)* (1 - x) (10)

in which Q_ is the longwave atmospheric radiation, gis
the Stefafi-Boltzman constant, 8 is a constant which
is a function of vapor pressure, and the height and
type of cloud cover, being higher for greater vapor
pressure, greater cloud cover, and lower clouds, T is
the air temperature in °F, and r is the reflectivity
of the water surface.

Plots of 8 versus vapor pressure, eg, for particular
values of cloud cover were developed by Raphael from
Anderson's data. These plots were straight lines of
the form 8 = a + be, for each value of cloud cover in
tenths of sky. Thackston utilized these plots by writ-
ing them in equation form for each value of cloud cover
from 1 to 10. These equations were built into a com-
puter program along with instructions to pick the pro-
per equations for a particular cloud cover.

Since vapor pressure of ambient air is equal to the
saturated vapor pressure at the wet bulb temperature,
an equation between the latter quantities was obtained
by the non-linear least squares procedure, The equa-
tion is

e, = exp(17.62 - 9501/(T,, + 460)] (11)

with the units of e, being inches of mercury.

4


where Q, is the direct solar radiation, Qj is the dif-
fuse sotar radiation, and o is the solar altitude in
degrees above the horizon.

The solar altitude is given by the equation

sin a = sin ¢ sin & + cos ¢ cos 6 cosh (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[(2mday/365) + 0.165) (5)

where day is the day of the year.

Once sin owas calculated using Equation 4, values of 4
were determined from the equation.

a= sina Sina? , 3 sine? | 15 sina’ (6)

40 + 337

Total solar radiation is the sum of direct and diffuse
solar radiation, Q, and Qj. However, Equations 1 and 2
apply only to cleat sky conditions. Furthermore, they
assume that no part of the river is shaded from the sky.

The net direct solar radiation becomes

Q3 = Q) (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 = 2 (1- b) (8)

where b is the portion of the sky blocked from view of
the river. 3


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


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


$0.2
Se.1

56,1

LL



TABLE 3.- MEASURED AND COMPUTED SOLAR RADIATION

Btu/ft? - day

Survey Day Measured Computed Computed
Near From From
Survey Boat ;
Site Data Nashville
Cumberland July 29 1843 2189* 2003
#2 1970
July 30
1970 1768 1987* 2005
Cumberland Aug. 30
#3 1970 1463 1676* 1110**
Aug. 31
1970 1661 1508 1477
Cumberland July 17
#4 1971 2253 2152 2159
July 18
1971 1991 1756 1229

* Probably high because of low estimates of cloud cover.

** Heavy cloud cover over Nashville.

24


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


;

T T T T T

CUMBERLAND SURVEY 4

:

----~---MEASURED
COMPUTED, NASHVILLE DATA que
iv

g

SOLAR RADIATION, 8TU/FT2/HR

.
a
a

‘SUN TIME, HOURS

FIGURE 15 - MEASURED AND COMPUTED (FROM NASHVILLE DATA)
SOLAR RADIATION - CUMBERLAND RIVER SURVEY 4

23


09

CUMPERLAYS sIvik
AUGUST Soe312197°
LATA

BOLT

52.2
37ee0

242,
242.
242,
242.
242.
242.
242.
242,
2426
2425
242,
242.
242.
242.
242.
242,
242,
242,
242,
242,
242,
242.
242,
242,
242,
242,
242.
242,
242.

16.8
ll.
11.5
12.9
1é.?
13,
12.5
+e
16.5
18.
15.5
le,
16.5
17.
17.8
18,
1.8
19.
19.5
20.
20.5
21.

2.36

6,5
16.5

7.5
1209
lae

l2ei
léel
leel
14.4

5.5
7.7

SURVEY 52

3026

Soe
heb
$1.5
O4eG
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Ts.
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75
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8b.
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61.

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lel elt ek et oe oo


TABLE

TABLES

SUMMARY OF RIVER SURVEYS .

CLOUD COVER ESTIMATES FROM
NASHVILLE AND BOAT .......

MEASURED AND COMPUTED SOLAR RADIATION

LEAST SQUARES FIT OF BOAT DATA WITH
VARIOUS CORRECTIONS FOR FOG ..........

LEAST SQUARES FIT OF NASHV
USING VARIOUS CORRECTIONS

ILLE DATA

11
24

29

33


9 T T T T T T T
ELEVATION: 80 FEET ABOVE CANEY FORK RIVER
seem ELEVATION: 5 FEET ABOVE CANEY FORK RIVER =

8

AIR TEMPERATURE, °F
8 3

12 24 2 24 12 24 12 24 2
MONDAY | TUESDAY =| WEDNESDAY =| = THURSDAY = | FRIDAY

FIGURE 1 - VARIATION OF AIR TEMPERATURE OVER CANEY
FCRK RIVER AT TWO ELEVATIONS

m4 Ty 7 TO
-
Ww
# oot L
4
Ww
>
&
w 40F q r F 4
8
<
$
8:05) 0:33} 842!
Z wm! | Sel aa] |/ a] | 728
70 66 68 ow 60 62 6460 62 64

AIR TEMPERATURE, °F

FIGURE 2 - VARIATION OF LAPSE RATE OVER CANEY
FORK RIVER WITH TIME

14


TECHNICAL REPORT DATA
(Please read lastructions on the reverse before completing)

T AIPORT NO. i IS. RECIPIENT'S ACGESSIONNO.
|___EPA-660/3-75-002... ...._1-_
= EPA=660/3-75 |S. REPORT DATE

January, 1975 (issued)
}. PERFORMING ORGANIZATION CODE

Effect of Meteorological Variables on Temperature
Changes in Flowing Streams

7, AUTHOR(S) 8. PERFORMING ORGANIZATION REPORT NO.
Robert W. Troxler, Jr.and
Edward L. Thackston

9, PERFORMING ORG \NIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT NO,
Department of Environmental and Water Resources 1BA032
Engineering 11. CONTRACT/GRANT NO,
Vanderbilt University
Nashville, Tennessee 37235 R-800613
12, SPONSORING AGENCY NAME AND ADDRESS 13. TYPE OF REPORT AND PERIOD COVERED
National Environmental Research Center Final
Office of Research and Development 14. SPONSORING AGENCY CODE

U.S. Environmental Protection Agency
Corvallis, Oregon 97330

18. SUPPLEMENTARY NOTES

16. 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 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 b.1DENTIFIERS/OPEN ENOED TERMS |c. COSATI Field/Group
Water temperature, heat budget, River temperature 13/13B
mathematical models, climatology prediction

TR. DISTRIBUTION STATEMENT 19. SECURITY CLASS (This Report) fat. NO. OF PAGES]
Release unlimited 20. SECURITY CLASS (This page) 22. AR.

EPA Form 2220-1 (9-73)
4 U.S. GOVERNMENT PRINTING OFFICE: 1975-697-996193 REGION 10


Ts

70

80

99
24
2001

64

7

TIME LSHOUR (NO) @THETA

TIME2SHOUR (ND)

Su 77 90

TIME LSHLUR ( HOUR(L)eHGUR(1=1))/2.)

Le ( (HG

TIME2eHOUR(E) +¢ (HGUR( I+) -HOUR(T) )/2,)

60 TO 2001

WRITE(6224) TIMELs TIME?

FORMAT(EGURING THE TIME INTERVAL FROM 'yFE,3e1Xe'TO 'shO,3s////)

TwCL) © TRAT

CONTINUE

WRITE (6964)

FORMAT(I1!)

WRITE (6s DLIRLaRZpRIPP4, RS, POPRTPROPRG,KL yp SLL ZLZ PL I,K L4yRISPRLG,

URL TARIIsRIIARZO

WRITE (Os4ZIALPAZs ABI A4s DSc AGS ATSABP AGS ALOPALI VAL Zo Irae ALS eb Oy

1 AL724185A19sA20

WRITE (6243)819829 83084 B5sBOeB 7p BG 2 BI, FL CoP LIAL ZeF 14221 4s RL S2B Lb,

18172B18s8195820

WRITE (6264 CLs Cos C Br CG, FS COsC Te Cos COs ClosCllsClasC pss Clare Ci5eCley

1 €17261846199C20

CALL GRAPH

CALL EXIT

END

SUBROUTINE GRAPH

COMMON HOUR(150)sTW(159)sTWOL150)4N0

DIMENSION LINE(121)214(13)

DATA IPsTOsTOsTSsTBsIL/IP Is IOlyt, ty tmlyt Wyt hts

MINS TWO(L)

00 400 IslyNo

TFC $~L)15915,30

AXIS LABELLING

15
16

22

OO 16 Ke1s13
TACKY EM ING (Kel)

WRITE (6922)
PORMATCIHL)
TFCPeEQeLWRITE (6017)


SL

198,
198,
198,
199.
199.
199,
199.
199,
199.
199,
199,
199,
199.
199,
199.
199,
199.
199,
199.
199,
199.
199,
199,
199,
199,
199,
199,
199.
199,
199,
199.
199.
199.
199,
199,
199,
199,

220757.2
23029609
23.7978

025

279

1:25
1-73
2se8
“e75
Baad
3BeTR
4e28
4-78
502%
3075
6028
6275
7025
7.75
6.23
Ge75
9025
9.75

8.6
7.9
8.7
lued
lied
106
244
Te.
7.73
8.9
10.6
Lied
9.32
6073
Tee
9%.
9.25
9.8
8.3
602

10,258.8
10,7395
11225902
11.75605
12.258.3
12,759.2
134251003
13475904
14.2571
14.758.5
15425907
15,7510.6
160251168
16.7511.

62.
60+
60.
Oe
$0.
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Oe
Su.
Bue
Ode
O98
O56
O15
$002
6000
6205
65.6
bbe
68.
TT.
83.5
84.5
88,
Bo.
8a,
8765
63.5
83.
84,
84,5
8405
900
856
Bl.
89,
87.
83.

Qe

1.33
275
+14
+28
76
le
748

016
021
045
+37
045
28?
265
057
o3P
024
1696
20?
2043
204
2236
1e7
2.71
4.36
4.72
5.00
3528
5.75
502
4.28
2.56
265
1.05
1,76
1.9

de
de
le
de
de
le
le
le
Le
le
Vs
le
l-

oT
236

049
ol

005
005
005

O
ot
ot
Oe

Oe
Oe
Os
V5
ot
or)
oe
od
rd

el?

004

a NN a ol ol ol ad


8s

WATER TEMPERATURE
49.5
49.6
49.6
50.6
S00z
$0.4
5005
5007
500
$1015
$1.40
5105
$1.65
$1.6
52.0
S202
5203
52.35
52040
52045
52.45
52050
52.5
52.5
5205
52.5
$205
52.5
5206
$2.7
$a.5
5805
92.5
52.5
$2.5

CUMBERLANM RIVER SURVEY #2


WATER TEMPERATURE, °F

8

a
@

|
j clea
sesecies cp aetlt

a
o

an
BS

a
i)

a
fe}

SUN TIME

FIGURE 20 - OBSERVED AND PREDICTED (WITH BOAT DATA)
TEMPERATURES, CUMBERLAND RIVER SURVEY 4

31


TL

WATER TEMPERATURE CANEY FURK RIVER SURVEY
S2ei
S2ee
5205
52.5
52.75
5301
53.3
5307
54e2
54.6
556
$503
35.6
5O0z
5% 0%
5Te4
3716
5709
58ez
58.2
50.4
58.6
58.7
56,8
59.
59.
5%.
59,


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 mph,
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


Ltt

13
1%
15
10
11
78
19
80
81
82
83

85

86
87
88
89
90
a1

42
43
94
95
6

98

100
101
102
103

105
106
107

108

an

ang a

40
41

15

42

4

107

130

109

INDEXSINDEX#1

TIAB CJ) BROUR (Ye CI NDEX#Z4,)

vO 3 lelsnr

G60 719 4

WRITE (612) DAY( LT) sHOUPR GT), DEPTR( Ts TAIR( 1 a RC 1) s0C (4d sulle SHAVE (
L1),8LUCK(1)

FOOMATCIDAYS 'sF5,022Xe THOUR® VFO, 392Xa 1UFPTH@ 'yF5sj2e%e VTAIRS !
Le F 5g ls2kyIPEL Hume 1,FG,202Xe'CCe Mealy c¥o'Um 'sFoele! SHAD, FR
Zee bak e2e2Xe I BLOCKED Fa, wm ta Fa,2e/)}

DELTAs=23,25%*COS(2,¥*3. 14159*DAV(1)/365e40.104)

rlaHQUR ANGLE UF THE Sun

hs 360,%( (12 .9NTUR(T12/24,)

SINAL BC SINCLAT/D 7 e296) MSINCLELTA/ 576296) wu SCLAT/S7 CSE I*CTSEDELTS
1/576296)*COS(H/57.296))

ALPHABCSI NAL) + (STN ALMA) /O4 6 BC STNAL HHS) D/4U eFC LS eR (DINALRHT) )/320,

ALPHASALPHAMS 70296

TF CALPHAILOTs LO7s132U

arse0,0

Go TO 109

SUN n weet SOLAR RADJATION UNCURRECTED FOR CLULOS GR SmADEL

FRACT

SUNKA Os 1 4699964AL PHASO, BOZB495 HAL PHAmae 290, UBS400 4 Sul Fri Akm de (Onl
L70G045E 903) HALPHAMH4e (9, LOLZ5OS ZEROS) MALP MARRS 4H (0, 329034526 —08 FAL
Z2PHAMHO

NE TSUN@SUN*(1.=SHADE(1))

SKY IS DIFFUSE SOLAR RADIATION UNCORRECTED FUR BLUCKEU SKY FRACTION

SKYm} 680298 3¥ALPHAw( 0, S177 TOTS EMO] ) ALPHA MHZ 4 (0024141 90E@03 ) HALPH
LA#H2— (0547294341 E605) HAL PH AMHG@ (0, 5858371 OF M06 ) RALPH NERD

NETSKY@SKY*(Le*BLUCK(1))

QI IS ACTUAL SGLAR RADIATION

QI a (NETSKY+NETSUN ) (1.90, 0071"CC (1) eeZz)

TPHOHAH EH RH REEF HHT eH es EH RE THEFT ERersrereseasterevetatottseotaretre

EW JS THE COMPUTED VAPOR PRESSURE OF THE wATER IN SATURATED

AIR AT TEMPERATURE GF THE WATER

RAT{[O80.65540,36eR 61)

WETTSRATIOWTAIR(1)


ENERGY TRANSFER, 8TU /FT®/HR

SOLAR RADIATION, BTU/FT?/HR

5

T

7:
W 1S iT) 2 3 Tv u
SUN TIME, HOURS

FIGURE 9 - ENERGY BUDGET COMPONENTS DURING
CUMBERLAND RIVER SURVEY 4

T T — T T T T

CUMBERLAND SURVEY 2

a 1

7 iH) iS 19 23 3
SUN TIME, HOURS

FIGURE 10 - MEASURED AND COMPUTED (FROM BOAT DATA)
SOLAR RADIATION - CUMBERLAND RIVER
SURVEY 2

20



os

181
182
183
184
185
186
187
188
189
190
194
192
193
194
195
196
197
198
499
200
204
202
4203
204
205
206
207
208
209
a10
244
22
ELK}
att
aS
ale

Cc
i

¢
¢

¢
¢

805

900

950

1900

13

18

20

2\
22
23
2000
50

60

eeetaeseecvaeneseseetate eons OO eee eran eteseeseretoercasegentee

oe eee
TOTEN IS THE TOTAL ENERGY CHANGE
TOTENSSUREN

POORER Hee EME TEST AER HETHOH HOHE HOR er ener HHOHH eh et or teortseonton
TEMP IS THE TEMPERAIUK® CHANGE JN DEGREES FARERHE{T
VOLMAREAKLEPTH(T)

TEMPSTATEN/ VOL

TWAT 1S TRE CALCULATED WATER TEMPERATURE GURIWG THIS TIME INTERVAL
TWATSTAAT+ TEMP

POMPE Herne e eee Re Reet HORT HOHE EHEC ETE RD er een HBastataMaeHnoresrantas
ARITE (6s LCODI ALPHA, Ms DELTA, EW, EA, WETT

FURMATCHALPHAE! y FAD Se 2he HEIs FLO. Se 2Xs GE! Tasty FLO, 22s TEWe ly PLU
Lede 2Xe EAS teFlLGeSee¥a te ET BULAB IZFR,35//)

WRITE (6913) QT 9 GAs GRA QE, UH, OT

FORMAT CISGLARS' DFT, Le 2Xe ATNO oF T el e2rs (CACKElpFe,lsZas EVAR EIDFB,
Lls2Xka! CONG aN sF 7 La 2he I TUTAL BIS FE gle 2X se! BTUSSQ ET miR tes)

*RITE( 6,16) TOTEN

FORMATCITOTAL ENERGY CHANGESI,FR2.3s2ks ICECKEES FAHKED SEL Tab T MHZ,
/)

WRITE (6920)

FORMATCITRE COMPUTED TEMPERATURE INCSEMELT IN CEGREEY FAREVHEILT Is
v4)

WRITE (6221) TEMP

FORMAT(F12.69/)

WRITE (6922)

FORMAT(ITHEREFORE THE CALCULATED WATER Teste PR ATURE IY UEGREES FARE
UNHEIT 1S!)

WRITE(6923) TWAT

FORMAT(F12.6)

TF(%.EQ,1) GO TO 50

GO TA 460

TIMELsHOUR(1)

TIME2SHOUR(1)+THETA

GO TO 90

TEC}.EQ.NO) GU TO 70

GO TO 80


6S

5205
5204
5204
5206
B20%
3203
5208
52.2
52.3
3223
5203
3203
32.5
32.5
$2.55
5206
3807
52,85
5320
5902
5364
3306
53575
53.8
5309
54el
54035
Shee
54.5
5406
5407


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 reportws 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.

ii


BIBLIOGRAPHY

Raphael, J. M. "Prediction of Temperatures in
Rivers and Reservoirs." Journal of the
Power Division, American Society of Civil
Engineers, 88, PO2, 157-181 (July, 1962).

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.

Moon, Perry, "Proposed Standard Radiation Curves
for Engineering Use." Journal of the Franklin
Institute, CCXxXx, 5 (November, 1940).

Upadhyaya, Ajeya K. Predicting Temperature Changes
of Cold Water Released From a Dam. Unpublished
M.S. thesis, Vanderbilt University, 1971.

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


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


ca)

243,
243.
243,
243,
243,
243,
243.

81.5
8G
78,5
T6s
T4.
68.5
67.5

1.7
1.7
del

«07
90?
02

045
oR5

le
de
le

a9
026
033
029
036
033
226


from the: evaporation formula, Equation 17 becomes
Qg = 0.00543 U P (Ty - Ty) (18)

Normal approximate barometric pressure can be computed
by the relationship,

29.92
a 32.15 E (19)
*P\ 545 | (tT, + 460)

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

Q
avo = gst ey (20)

in which AT is the temperature change in op, Q, is the
average rate of energy transfer in Btu/ft“-hr, @ 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.

7


64

945
146
147
148
199
150
4164
162
153
154
155
156
157
158
1549
160
161
162
143
164
105
166
167
168
469
110
111
172
193
414
195
176
111
4118
419
180

aaana

Oaan Aang

ano AA

3001
218

219
229

310

400

500

550
560
570

580
600

QUTPUT BETA

TAGR(TAIR (1) 4459067) #*4

the, 97S] GHARBET ART AG

Cosham ersevneeeeaet ert ete tHe HeFeet er eeeoat atte Htate*seenenegeeteg

G8 1$ THE EFFECTIVE BACK RADIATING

IT IS A FUNCTION GF SIGMAy BETA, wIR TEMPES ATURE, Al ATER

TEMPERATURE.

Tw43(THAT4459,607) x4

SB EHO STHST GMAT UG

Peete esegarereeetert stat eset eeasetoneterarereeortat ef oeenepageetgee

SE L$ ThE FVAPORATEW HET

IT 18 A FUNCTION GF KIND VELOCITY AND THe CIFFERENWCE GeTWEEN
VAPGR PRESSURE UF SATURATEN AIF AnC ACTUAL AIK

Geen ls. Feu LEC EWREA)

FeeH aoe ae as ee seteeter ee eset ee eeetntsneeeaset FH HRREet es FEHR ARE Etes

On 1S THE CONDUCTED HEAT bETWEEN WATEReAlS INTERFACE

IT TS A FUNCTION OF wit VELOCITY, BakoreTKIC FRESSURE AND

DIFFERENCE BETWEEN TEMPERATURES OF “ATc# AND GIR

PE29,9Z2/EXP( (S201 SMELEV)/ (1545.8 TAIR(1)46608)))

QHeO,O05434UCT)MPH(TAIRCI)=THAT)

SOTHO HEHE AH HERE RH ETRE H EEE EH Et HER HEHEHE HHH HEAT eT eH enone geatann

GT IS THE TUTAL SURFACE HEA] TRANSFER

QTaQI+QB+QCE+QH+Qd

SUREN IS THE ENERGY CHANGE DUE To SURFACE MEAT TRaNSrE®

AREA#1.0

THETA IS THE TIME INCREMEWT IN HOURS

IF(1,EQ.1) GO TO 850

GO TO 560

THETAM(TIMEC2)@TIME(1II/2.

GO TO 600

TF(T,EQ9eNO) SO TO 570

GO TO 580
THETAs(TIME(NO)@TIME(NOTM1) )/20

GO TO 600

THETAMCTIMEC T+ LI @TIME(T#1) 0/2.

SURENBQTMAREA#THETA/62.4



ss

20.0
» 2000
2001
16.0
13.4
1560
17et
LP eb
15.0
176G
140
L360
136u
1360
1360
9.7
11-6
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11.U
13.0
11.2
2060
17-5
1761
1260
1607
1403
1206
llel
13.8
1be0
16.0
13.0
1009
11.0
10.0

58.5
58.0
6006
56.0
57.5
58.0
Seay
57.5
59.0
5705
5865
60.0
3705
56.0
5605
6100
6360
6860
6940
7100
7820
T7900
8200
8320
8145
8520
86,5
88.0
7960
9160
9000
9005
9000
84.0
81.0
7700

120
1.0
97
169
1.0
1.9
1.9
1.9
1.0
1.90
1.0
1.0
1.0
1.9
1.0
Wie)
209
205
095
208
074
208
270
eT]
268
203
264
258
275
253
253
256
053
057
009
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0.0
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949
000
09
900
100
909
020
99
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1.0
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5.0
4.0
220
200
1.0
200
300
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.
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ene
of2J4

nn
ee
a2

nnn
eeee
woaofa
Ld

2.77
2.63
1293
3.23
2027
2.27
2443
4.43
2e07
3.47
1230
201

1.93
2.03
206

3.13
3.9

1,0
120
129
120
1.0
29
leo
320
dec
1.0
124
1.0
1e0
1.0
1.0
rs)

45
ous
U5
ous
005
005
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340
05
O06
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205
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005
203
0u5
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BREE PP PPR Pr HPP


TABLE 1 - SUMMARY OF RIVER SURVEYS
Survey July 29- August 30- June 12-13- June 26- July 17-
Date 1970 31, 1970 1971 1971 18, 1971
River Cumberland Cumberland Holston Caney Fork Cumberland
Location Below Wolf Below Wolf Below Below Center} Below Wolf
Creek Dam, Creek Dam, Cherokee Dam Hill Dam Creek Dam
near near near near near
Burksville, Burksville, Jefferson Carthage, Burksville,
Kentucky Kentucky City, Tenn. Tenn. Kentucky
Length of
River
Surveyed
(Miles) 72.5 48.3 50.0 24.0 35.8
Approx.
Flow cfs 12,000- 6,000 4,000- 3,000 4,000
20,000 12,000
Duration
of Survey
(Hrs) 32.5 35.5 28.5 16.0 33.0
Initial
Temperature
(“F) 49.5 52.3 51.8 52.1 51.1
Final b.
Temperature[F 54.7 59.7 60.5 59.4 59.3



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


8

oF
an
@

a
io2)

an
+

WATER TEMPERATURE,
B

8

SUN TIME

FIGURE 18 - OBSERVED AND PREDICTED (FROM BOAT DATA)
TEMPERATURES, HOLSTON RIVER SURVEY

Teta teint Te) Pt he tt ht ich tte te ett
| ficial i sidltts|sad |

i a

f°)
°o

oF

a
@

a
[))

a
ay

WATER TEMPERATURE,
8

3

8 12

SUN TIME
FIGURE 19 - OBSERVED AND PREDICTED (WITH BOAT DATA)
TEMPERATURES, CANEY FORK RIVER SURVEY

30


Ze

CUMBERLAMY RIVER SURVEY HG

JULY
BUAT

51,1
36079

198,
198,
198,
196,
1968,
196,
198,
196,
196,
198,
198,
198,
196,
198,
198,
198,
198,
198,
1968,
196,
198,
198,
198,
198,
198,
198,
198,
198,

98,

96,

L7-1622971
bATA

7275 G09
Be25 Bed
8.75 3.8
9.25 7.8
9,75 Bee
10.256.
16.75601
11.25605
11.757.
12.255.5
12.7546.35
13.25762
13.754.7
14625561
14075701
15425862
15.754.9
16.256.3
16,757.46
17.25601
17,757.75
38.25802
18.757.6
19.2569
192756005
20,255.09
20275603
21.25607
2107571
22025704

5OS6

77.
1S.
BGe5
BZ
Bae
34
Baad
350
3605
Be,
8Beb
39.
39.5
cer
8905
8G
88.5
65.
8705
87.
86,
85.
82.5
80.
76.
76,
7405
73.
7205
720

269
265
«59
256
2146
238
035
ack
se5
022
rr
129
227
0e5
«26
126
030
033
034
035
036
236
544
194
264
075
260
267
287
286

EUAKSVILLEs RY

7.0

7.9

aed
G5
(re
re
aud
Ce
Ce
Ge
Oe
te
o
20
oud
sue
on
005
aah
33
205
aus
oe)
de
de
le
de
1
de
de

y
ie

le

0379

126
eat

032

028

031

034

eee


2

T T T T T T T T

CUMBERLAND
JULY 29°30, 19” ey 2

——— —— ATMOSPHERIC RADIATION

EVAPORATIVE AND, CONDUCTIVE.
ENERGY TRANSFER

ENERGY TRANSFER, BTU /FT2/HR

-100b.

I
15 i) 23 3 7 u" 15
SUN TIME, HOURS

FIGURE 5 - ENERGY BUDGET COMPONENTS DURING
CUMBERLAND RIVER SURVEY 2

ENERGY TRANSFER, BTU/FT2/HR
ie}

SUN TIME, HOURS

FIGURE 6 - ENERGY BUDGET COMPONENTS DURING
CUMBERLAND RIVER SURVEY 3

18



RESEARCH REPORTING SERIES

Research reports of the Office of Research and Development,

U.S. Environmental Protection Agency, have been grouped into
five series. These five broad categories were established to
facilitate further development and application of environmental
technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in
related fields. The five series are:

1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research

4. Environmental Monitoring

5. Socioeconomic Environmental Studies

This report has been assigned to the ECOLOGICAL RESEARCH STUDIES
series. This series describes research on the effects of pollution

on humans, plant and animal species, and materials. Problems are
assessed for their long- and short-term influences. Investigations
include formation, transport, and pathway studies to determine the
fate of pollutants and their effects. This work provides the technical
basis for setting standards to minimize undesirable changes in living
organisms in the aquatic, terrestrial and atmospheric environments.

EPA REVIEW NOTICE

This report has been reviewed by the Office of Research and
Development, EPA, and approved for publication. Approval does
not signify that the contents necessarily reflect the views and
policies of the Environmental Protection Agency, nor does mention
of trade names or commercial products constitute endorsement or
recommendation for use.


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


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
(Ox - Piy?
n-k

T=

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 8
term in the equation for longwave radiation equal to .95.
The value of 8 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 woulda
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


WATER TEMPERATURE, °F

WATER TEMPERATURE, °F

aa
60 |
58
56
54
52 ED

LLe i
50 — FIRST

i ec
8 12 16 4 8 12
SUN TIME

FIGURE 23 - OBSERVED AND PREDICTED (WITH NASHVILLE DATA)

TEMPERATURES, CANEY FORK RIVER SURVEY

60
58
56
54
52 ‘eeeees OBSERVED
— —PREDICTED WIT!
NASHVILLE DATA
50L —— RS Sat A
jouer
lL Lt i

8 l2 16 20 ie} 4
SUN TIME

i.
8 12

FIGURE 24 - OBSERVED AND PREDICTED (FROM NASHVILLE DATA)
TEMPERATURE, CUMBERLAND RIVER SURVEY 4

35



SOLAR RADIATION, BTU/FT7/HR

n
7 ut 15 9 23 3
SUN TIME, HOURS

FIGURE 11 - MEASURED AND COMPUTED (FROM NASHVILLE DATA)

SOLAR RADIATION, 8TU/FT/HR

SOLAR RADIATION - CUMBERLAND RIVER SURVEY 2

8

7—§
|
:
5

8

5

SUN TIME, HOURS

FIGURE 12 - MEASURED AND COMPUTED (FROM BOAT DATA)
SOLAR RADIATION - CUMBERLAND RIVER
SURVEY 3

21


Wet bulb temperature, Ty
relative humidity and ai

,» May be calculated from the
temperature by the equation

Twp = (0.655 + 0.36R) T, (12)

Since the reflectivity of the water surface is usually
used as 0.03, Equation 10 becomes

Q, = 1.66 x 107 %8(T, + 460)% (13)

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 Twp from Equation 12.

2. Plug Typ into Equation 11 to determine es,
which is also equal to eg.

3. Use the value of cloud cover to determine the
proper equation to use for calculating 8.
Insert the value of e, into the proper equa-
tion and find B.

4. Determine Q, 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

Op, = eo(T, + 460)4 (4)

where Q) is back radiation, e is the emissivity, about
0.97 for water, o is the Stefan-Boltzman constant, and
T, is the temperature of the water surface in OF,

5


Ls

Lad
-
~
.

Pe be PO FO
220 & o Oo
eee
enes

Gbeenrrn
Coen
ore rere

eaoecee

22.5 20.0 19, 260 Oe 6.5 400
23.0 20.0 78, 260 Oo 8. 1.0
23.5 200k 77,5 262 Q, 7.5 2.0
0.0 1606 77. «63 QO. Tr 1.0
05 1344 17. 063 Oe 6.5 400
100 15.6 77. 063 Oo. 6, 4.0
105 17.6 16. 267 Oe 6.5 200
200 18.6 75. °70 Oe 7. 400
205 1866 74,8 070 O00 6,5 4,G
320 17.0 Th. 070 Oe 6. 4.0
305 1406 7305 072 Cr 6.0 400
4, 13. 73. 74 Oe Oe de

4e5 i36 T2058 076 Or 6.5 he

5. 13. T2e 075 Os Te i

525 136 736 070 Or Te i.

be 9.7 14. 074 Oe 7 025
605 dle The 7) Oe Te 25

Te lle 76, 268 O. Te elS
705 lle 806 263 Oe Be 005
Be 13.6 82. 258 Oe 9. 005
8.5 1102 84, 059 3, de 005
9 20. 86. 054 Oe % 905
9,5 17.5 87. «52 Oe 8.5 05
10. 17el 88, 049 Or g, Ve

1005 126 66,5 046 ae 190 Oe

dle 16.7 89, 044 4, 11.5 205
103 1403 908 039 4, 10. Oe

12. 11.8 91. 038 4, 8. Ue

1265 dlel 91.5 036 4. 9 205
13. 1348 92. 033 4 Te 105
1305 lle 92. 034 4% 8, 005
14. 166 926 236 4 9. 2038
14.5 15. 91,5 237 a. 10. 205
18. 1009 91. 238 4 11,9 905

15.3 Jie 91.8 035 a. 10. 205
16. 100 920 232 2. 9. 905

PRR PRR PRP PRP Pre Eres


€Z

198,
198,
198,
199,
199.
199,
199.
199,
199,
199,
199,
199,
199,

199.

22,7572
232254.9
23.757.8
225 8a
075 709
1.25 8.7
4-75 10.6
2025 Llet
2.75 10.
3.28 84
3275 7.9
4.25 7.75
4075 8.9
5025 106
5075 Lhel
6025 9.85
6075 6075
7025 To2
7.75 9
8225 9025
8.75 905
9.25 8.3
9,75 6e2
10.2588
10.759.
116235902
11275665
12.258.3
12675902
33,251003
13575904
14025701
14,758.05
15625907
15,731006
165251168
16675116

Tee
72e
72s
72.
Te
72.
T2e
72s
TZe
Tas
Ths
100
71e5

75.
77s
796
Ble
8205
Bae
85,
86,
87,
8b.
BBS
89,
8945
906
906
90»
9005

89.5
88,
88,
88.
8655

065
s6L
065
266
067
290
099
09D
290
099
094

296
96
090
83
076
+69
254
257
292
249
048
047
046
244
045

245
045
143
238
244
047
e47
247
150

NNENFEO TRIG OHHABDA
AWEDIVOANONWVOOOW

econ eee e wees eee

i]
.

~t
w

10.5

026
024
4)
028
el?
al?

226
226
ol2
eh2
el?
eal
042
234
26
ei?
el?
134
023
022
022
022
aZ8
03?
126
219
ai?
el?
e215
aa7
el7
216

226

022

025
014

PRR RP RP PRP PREP Pre RPE rr ere


Line See Equation

Number Page Number Comment

82 3 5 Declination of the sun calculated.

83-86 3 4 Sine of solar altitude calculated.

87-88 3 6 Solar altitude calculated.

92-96 2 2 Direct solar radiation uncorrected
for clouds or shaded fraction
calculated.

97 3 7 Correction for part of river
shaded applied to direct solar
radiation.

98-100 2 3 Diffuse solar radiation calculated.

101 3 8 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 8
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


SY

DANE HAW p—

a1 ¢

25 €

COMMAN MOUR( 150. eTHIL50)s TWOCL 50) sNO
DIMENSTON OEPTH(15G), TALE (150) 9K 6150) ,C0 (180), 0150) +SHADE (180) sDA
LY¥(150) 4 TIME( 150) s BLOCKC150) s TAIRA(150)sRA( 159) s DFOG( 150) -UA(150) 00
2CAC180),QCT (199)
REAL LATs LONGANETSUN, NETSKY
ALPHAsu,
Hed,
GELTASS.
READ (Sa 3C Rp R2,R Za RGs RoenGsRT Res RG eh LOgn tls RLZsRlZenloaRLSyR1lOsk
L17eRL92K1G9sR20
BO FURMAT( 2044)
READ(593Z) ALI AZs AZ2ASs AS a AOS ATA AG DAIS ALODALIZALZ AID ALSSALSs ALG,
1 A172A1894199420
32 FoamaT(20a4)
REOD(5433)812B2053984,6 5s BOsBTy BGs KI KLOs deh leash lS, Plo, R150 16,
181723189819,820
33 FOPRMAT( 2004)
READ( 5934) Clo C2sC3aCosl Ss Cal ToC Bs CM Clos Lie Cl2sClssClosCl5sChby
1 C17s018,C190020
34 FORMAT(20A4)
TWAT US THE INITIAL WATER TEMPERATURE “HICH IS READ liv AT THIS PT,
READ(5s46) TWAT
46 FORMAT(F1O,5)
930 CONTINUE
NO I$ THE TOTAL NUMBEK OF CBSERVATIONS
READ(5225) LAT, LONGSELEVsNUsSTALsSTAZsSTASa5 TAGS TAIZ STAG, STATAST
LABsSTASsSTALO
25 FORMAT(3F10.22110,10A4)
IF (LAT)179172940
940 CONTINUE
TAIR@TEMPERATURE GF AIP IN DEGREES F
ReRELATIVE HUMIDITY AS FRACTION
UsWIND SPEED IN MILES PER HOUR
CCmCLOUD CoyER IN TENTHS OF SKY
DAY IS THE DAY OF THE YEAR
HOUR JS THE HOUR OF NAY


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 ana
this quantity was divided by the length of the plot

to obtain the average depth. Fathometer recordings

were made every 30 to 60 minutes.