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 ------- 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. ------- 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 ' ..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 11* 13 1° ** *"* 3 *K is.3 is.o ia.i- 2 14.2 115.0 13.3 3 13.6 12.3. 13.3 3 1 i .1:5.0 J2.7- 13.0 11.9 13.0 i2.2 . / / / L?Il ' 2 12.3 :-3 .' J / 1 / j 1 - '-* i 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 J7.0 17«7 315.3- i«le Sl°8 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 ------- 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. ------- 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. ------- 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 ------- 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 ------- 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. ------- 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. ------- ;:Ataospheric Radiation: Factor,A.'.I :: . .;i;::;'!: j: ':' ' ':....: :, ....;.::i:: jjuji-jjiiij jjH iili!;!;: U.;::;..U::;; i. : ...:.:.(\.:.;._:Jn-UUftijLjiilH-!"^-?1 ..l.,;....,,-..;;.. :.---t::!:i; " '* c (a-ouD - COVER-TENTHS) "'':"' '''''" .-itii-.v;;:;-:!:;:;};.; ;:..;::..<;.::!:::'.{.::;... |.^ llh!!l=:!lii;ill!!li!!l:;;:;i;i;:;!;H|;i::ii:jteiill;ii; 'T j:r''i [ '';':' ' -'l--;r| ;t?.<-: , ; -.tlj!:''; ."::,t;!:]";-.!'it*!:!::::;;:»:::.;".t^J^Jj";*.i.'^:4.r;;:.. . ' .: >", I' .:^;;;tl^;j;:rJ.::i!V;.|:;=-;!'V:::.|.:::ii::ux-4^=::^.:iai4; - ^Ji-iiiLili-U-:^^! fr- liiiM ,: '_' i||::-t Vapor Pressur^;[i;;l|:jj:|:;{j|;jji||;ii. eJ YIN.; OF w-Y^ii: -1'- i '-. :.:'" .t-'!:H:l|rrhHS-;ir:!i};;t7t!t'?H'l!:i-r:; J ::!::.. ::.':jrt:r-! J ^i:^..:;::-::ji:iiLi^ipiiJim'^HpfHi^iiMU^1^ ..vFIG:' J ^IGt;:3j::f:;:!ii?iffiniHjijg;lffpHJHi^^ BEE M/M ------- "' ' """"'::1 (;:iit!!;:LL.:'":H:-'* ":| it:: .^vliil^lUuiiiiuiiii: lUlinJJthJtjHjfrijjjj;;; ii::j::!: .|l:ihi: .__^.. ,. ixijpMjyZHulluhuiiliu--:.. Jllli^lMiiliJLiiM^il'i; SliUJiii. ii-ffl ':'; iiiiliiiiJtitiilliiiiiHi'lt^^ :;:;:;;!.-::!;:::;;':;.:;..::'. : : !':::.::[' ; .::.: DOWHSTRgAK: . ..'.."!!.'; »-::l!li^ 'I; irHHinilr::!1. ii::!ltin! T77TTT7T7I::.: jrrpy;;rj7;: ; ^"t't'l'T" lift River' ;.:fi nrti:i:{::.;:;ti ,:;;'i'jj :n:Hi:: ,. > ;i!..r;1 ,t.:nj:iiii;:;;;=i!. .^HHSjniH:!?;, Hi«fli ,).: :.. i"-.!:i:d; U:iajt itilf TP iiii f:!i hit it;: if!! rnrtntr Mill iilM w. M iilM rtttTtt it iir; Hl't-ffi BEE M/M ------- ir;:!-T] :!i:!tH:ir ;: Velocity,.-;.'Discharge Curves: for Threei:Reache3'L.:JlL!i|Jl V . ... '.::';"' ::u:li-L;'-t::!:l':;i!::;:jii ; .. 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I.:... .-., : .:. :;...-. . ..: . i :;. :..' : '... .. . :!::.!::" '' '^1 J' I '' -. ~ri~-.->- ;-: -10 i-.;;: ;:: :.; '§ : r;;r.-:::t::-:"- :.;; 3" !:'vi:":;:Ci.:::i'!':.:" >-:;1 ^ i ' ', ]_', ' ^j t^ ,_, ] .' J.J '.! '..i- jj ' i * ! " " ':;:;::!.,'.!' .; i J!;;11-.j j.. ' i . .j, ^4^;J.-M.' :J . ' .. .::.' "^ >*'.*; "..-. "i!. :";];::.;r.;.!;;:.!-*.I.::^ir;:| .,''. ;'.:'. - i , ..'.;:;..,.;:;,,: .:' ' ! * * i;;,': * t'';: 11 *.: j - ;;n ,T"'!<: i: :i;!i;j:-.: ^i-nttr^F7!;^::! -r^LQ| -;:.i-;':;:::ti:;i' ;: 'ili^iii:!::^!]:;! ;:'L;i!:;:;:!|;i:;:;;.:::r.::::;;::.;.:f::--:ifH!!;:ii:;iif:i:Tj -.+ '.._: -.:- I: :;" -j«.i;ti;.-'':i :u:..i ' ~ ;.! ; ' ---!....*.; .,__ _*. .;;;;;;.mi?ll -.' . ;:'; :' ...;;:i-i: .'.....':":;I1I";;, '.-.Ti*; " Qt--:;:: ;/:-p^:i::~;l;i'.^ ,:-;:!;|::|.;;.;:;i;i, ; t:;.... t :::l.'':: a: ^^iiiiiii t: "i . (:;. [:"' ::;....{.:;. ::|-t;': }:v.I ------- 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. ------- |