WORKING PAPER NO. 46
STREAM TEMPERATURE PREDICTION METHODOLOGY
Date: March 1964 Distribution
Prepared by J. Seaders Project Staff
Reviewed by R. Zeller Cooperating Agencies
Approved by General
U. S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE
Public Health Service
Region IX
Water Supply and Pollution Control Program, Pacific Northwest
Room 570 Pittock Block
Portland, Oregon 97205
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This working paper contains preliminary data and information primarily
intended for internal use by the Columbia River Basin staff and
cooperating agencies. The material presented in this paper has not
been fully evaluated and should not be considered as final.
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METHODOLOGY FOR THE COMPUTATION OF STREAM TEMPERATURES
The purpose of this report is to describe the methods used to find
the increase in river water temperature as a parcel of water moves down
stream.
The elements of the problem are: (1) the mass of water affected
in. a given time period; (2) the energy input per unit of area for this
period; (3) the exposed area of the water surface. These three parts
when put in equation form give:
(Constant) (Area) (Energy Input) _
Mass = (Discharge) (Time) (Change in Temperature)
The problem then is to find the value of area and energy input for
a given set of weather and discharge conditions. This subject wil'l'-be
solved in parts as follows:
I. Development of Energy Budget Table and Its Application;
II. Development of Travel Time Curves for Constant Discharges;
III. Development of Exposure Area Curves for Constant Discharges,
The three subject areas will then be tied together to arrive at values
for specific conditions.
I. Development of the Energy Budget Table and Its Application (Table 1)
There are nine columns shown. Columns 7, 8, and 9 can be obtained
from standard physics textbooks and may be calculated from Stephan-
4
Boltzmann's Law: Qh = 0.97<^ T .
o w
Column 1 need not be discussed except that it is up to the inves-
tigators as to how many days to include in a given time period.
-------
(1)
(2)
(3)
(4)
EHEfiCT BUDGET TABLES
(5) (6)
(7)
mm
Jon. 1-10
11-20
21.31
V«V». 1.10
, 11-20
- 21-28
liar. 1.10
11-20
21-31
Apr. 1-10
11-20
21.30
Key J-10
21^31
Jyajc | =10
11.20
21-30
Jnly 1.10
11-20
31-31
Atig* 1»10
11-20
21.31
Sept. 1.10
11.33
21-30
Oct. 1-10
11»20
21.31
Nov. 1-10
11-20
21-30
Dsc. 1-10
11-20
Sf-. 21-30
Hot Solar
Hadiation
82
03
112
177
174
201
241
274
285
373
367
43G
442
510
533
535
523
E8D
630
ESS
598
B23
473
455
423
340
313
231
219
163
140
114
103
90,
. 71
78
1
E
osoo
b
EFKCST
MJIASK
1000
.IV .18
.17 .17
.19J .19
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1600
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2100
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1600
10
11
12
12
14
12
12
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2100
6
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7
6
6
7
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0800
53
54
ES
55
B7
B7
M.
53
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EUPISA
(A
1000
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6-3
69
71
72
70
63
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1600
72
73-
76
01
85
63
B2
,
J1
2100
31
G2
64.
70
63
67
65
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40
41
.42
4-i
45
"48
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4?'
50
51
52
£.3
54
!5F.
56
67
E3
59
.60
61
63
64
65
66 '
6?
68
69
70
71
72
T3
74
75
76
77
78
Radiation
for
Wator
Ly/day
674
60S
P91
693
702
707
713
719
734
720
73S
741.
Kfi .
Vfo
1
'. 7S9
; 7GS
; 771
;:777
'7^9
793s"
&02
807
813
819
826
833
833
851
853
8C4
871
878
834
631
833
805
Saturation
Vtspor
Fror-Eure
8.7
9.1
9.4
9.S
10.2
10.5
10.9
11.3
11.3
12^7
11U7
14.2
I
14.3
1£.3 :
IB. e
W«4
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17«7
315.3-
i«le
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22.5
23.3
2J.2
25.0
25.3
26.7
27.S
23.6
29.6
30.6
31.6
32.7
TABLE 1
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For the values tabulated under the remaining columns we proceed as
follows:
Column 2 (Solar Radiation)
For several stations the total incoming solar radiation is measured
directly by means, of a pyrheliometer, but the stations are far apart and
few in number. Solar radiation intensity charts may be used. See
reference to these charts in final Umpqua Report (page 2, reference A--
Appendix A). Nomographs have been prepared (see page 89, Proceedings
of the Twelfth Pacific Northwest Symposium on Water Pollution Research,
Corvallis, Oregon, November 7, 1963). Some work on correlation of
radiation and degree days seems to have some merit, but more for confirming
other methods than as a method in its own right. The quantities in the
Energy Budget Table, Column 2, are derived from several items.
Incoming solar radiation, as just discussed, is the total quantity
and not the effective radiation since part of this is reflected back by
earth and water. To obtain Che reflected radiation, we apply a percent
to the incoming solar radiation (see Data Tables for energy budget
computations). This percentage reflectivity to be applied is computed
by using the reflectivity of water surface which, in turn, is dependent
upon mean solar altitude and sky cover. (See Lake Hefner Studies--
Figure 63, page 87.) To obtain the net incoming solar radiation,
subtract the reflected from the total; this is the quantity entered in_
column 2.
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The quantities shown in column 2 are for Roseburg, Oregon; and
/
quantities for other regions have to be determined independently using
/
the above-suggested data. Correlation studies are needed, using one
or several methods, to determine the values for a given area.
f
Column 3
This column lists the factor/^ which influences the back radiation
of the water surface. This factor is determined for varying sky coverv.
and vapor pressure conditions. See Figure 1. (Jerome Raphael, ASCE
Journal, Power Division, July 1962, page 169, Figure 6.)
Sky cover is obtained from U. S. Weather Bureau records for daylight
conditions only. See Column A below for discussion of vapor pressure.
Column 4
This column lists the mean vapor pressure in millibars which may be
obtained from vapor pressure records -at meteorological stations. Usually
these records are kept in terms of relative humidity, dry-and wet-bulb
temperatures. The mean vapor pressure may be computed from such data.
Column 5 (Wind--U. S. Weather Bureau Records)
' An adjustment may be necessary to adjust the mean wind values to
effective wind values as follows: USWB data list all winds below..three
miles per hour (mph) as "no wind." According to McAlister, stream
motion of about one mph will give apparent wind speed even with still
air. To account for the above phenomenon, add "+2" to wind speed of
two mph; "+1" to.three and four mph; ^and no corrections above five mph.
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Wind speeds below three mph are, of necessity, estimates using
total wind travel/day and known values/hour.
Column 6 (Temperatures by Hour from U. S. Weather Bureau Records)
The computations using this information to find the energy input
function for a given temperature of a parcel of water are discussed in
the Umpqua Report, Appendix A, pages 1-4. To facilitate making repeated
computations, nomographs may be prepared to. obtain the energy input
quantity for any temperature for specific periods of the year (i.e.,
June 1-10; 7 a.m. to 12 noon; temperature of the water, 45 F). Such a
computation is shown on page 73, Proceedings of the Twelfth Pacific
Northwest Symposium on Water Pollution Research. Repeated computations
for various starting temperatures will give the values for the nomographs
desired.
A list of tables showing the data requirements for the preparation
of the Energy Data Table is shown in Appendix B.
II. Development of Travel Time Curves for Constant Discharges
Travel time studies are necessary to determine the length of time
a given parcel of water is in transit. (See Appendix C.) Travel time
«
studies are executed under conditions of increasing discharge in down-
stream direction, Figure 2.
For purposes of study, however, a reach of river may be assumed, to
have a constant discharge. If three travel time studies at incremental
discharge values, have been executed, an arithmetical or logarithmic plot
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of the velocity (from travel ..times-tudi-cs) versus discharge can be made.
When this is executed for each reach, a line drawn af the discharge
level of interest will give the corresponding travel time for each
reach, Figure 3.
Dividing the velocities thus found into the length of the reach, we
find'the time of travel for a given discharge for the reach-,
Thus 11=1,
Vl" *
A plot of T^, Ij, To, etc., versus river mile starting at the
source then gives the travel time curves for constant discharge. This
can be repeated for any number of discharge values, Figure 4.
III. Development of Exposure Area Curves for Constant Discharges
The exposure area for constant discharges is developed as follows:
^"\
The physical configuration of the river is determined fromaerial
photographs or direct measurement. Knowledge of mean depth and discharge^
velocity values may provide a coarse estimate, but it should be kept in
mind that the accuracy of the forecast is directly proportional to the
accuracy of the estimated area of water exposed. In the energy exchange
processes, as well as the estimate of the energy input function, a ten
percent, error on the area-exposed estimate means an "X + 10%" on the
temperature rise estimate. The sensitivity of each error fades as the
temperature rises because of the exponential nature of the temperature
gain process ("X" represents percent error of energy estimate). The
* .
manner of area determination from aerial photographs is to take five to
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6
six width measurements per mile of river and average them. The tabulated
values are then dated by their photographs and an estimate made of the
hydrological condition of each reach, i.e., discharge estimates for each
mile are made from a discharge versus river mile curves such as shown .in
Figure 5.
The discharge values may be obtained from U. S. Geological Survey
Water Supply Papers for the dates obtained from photographs. Correlation
studies for streams having little or no discharge flow data may be
required. Where no photographs are available, X-sections at representative
intervals should be taken.
It is desirable to have four or more different discharge values for
each reach and miles within the reach so that the discharge versus area
curve may be plotted for each river.mile or reach.
A curve, as shown.in Figure 5, will be obtained for rivers having
banks as shown in Figure 6.
From the series of curves such as Figure 6, a summation of width
or area curve with river mile is prepared by entering the curves for
each mile a-t selected discharges and finding the corresponding width,
Figure 7.
It is now possible to find the exposure area for any given time
period. We plan to find an area that is exposed for Q in five hours.
Enter the travel time versus river mile curve at five hours, move
horizontally to Q curve, FiguTre~~3.
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From here drop to^-width curve for Q~ below, then move left
horizontally to find .the area exposed. At this stage, all the components
for solving the problem are complete to find^/^T of the parcel of water.
K (E) (A)
Q t Ai
K = constant to make the equation dimensionally and
numerically homogeneous
E = energy input function/unit of area
A = area of the mass exposed to E
Q = discharge of mass 'affected
t = time
_XVr = temperature change
These computations may be performed by use of a digital computer.
This enables the investigator to obtain a wide range, of values on which
to base his recommendations. Such a program is described in Appendix D.
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-------
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APPENDICES
A. Water Temperature Prediction and Control Study, Umpqua River Basin;
Oregon State Water Resources Board; February 1964.
B. Meteorological Data--Roseburg, Oregon.
C. Travel Time Study of Rivers Using Fluorometric Techniques, by
John Seaders.
D. Stream Temperature Prediction by Digital Computer Techniques,
. Oregon State University, 1963.
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