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.

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(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
' ..El
.50
.21
.21.
.20
.20





.20
.20
.21
.20
.19
.19




.
n
CV2 BAI
B (%{
1600
•




.17
.17
• .1.9
.SO
.20
.23
.20
.20
.20




t
3C '
5bs)
2100
"I


-

.17
.17
.19
i20
.20
.21
.20
.19

,

\
i
t
, ISMI VAroa MSKSBEE
0300 1COO 1GCO 2100 OSOO




12.5
1S.7.
13. i
12,-?
3.1.3
ilia










	

—

r


1
13M ibv? 13.4 ' ' S
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is.3 is.o ia.i- 2
14.2 115.0 13.3 3
13.6 12.3. 13.3 3
1 i
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13.0 11.9
13.0 i2.2
.



/


/
/

L?Il ' 2
12.3 :-3
.' J
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1
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ME.
1000





6
6
8
6
7
6
7
7
7





Us)
1600





10
11
12
12
14
12
12
12





2100





6
S
7
6
6
7
J





0800





53
54
ES
55
B7
B7
M.
53


/
/

MF
EUPISA
(A
1000





P5
6-3
69
71
72
70 •
63





AH
StEI °
ir).
1600





72
73-
76
01
85
63
B2

,•



J1
2100





31
G2
64.
70
63
67
65





\Sster-
Tesrp.
ox
40
41
.42
4-i
45
"48
.4E
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
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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 ..time—s-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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