NUREG-0693

Analysis of Ultimate Heat Sink Cooling Ponds

R. Codell, W. K. Nuttle

Office of Nuclear Reactor Regulation

U.S. Nuclear Regulatory Commission Available from

GPO Sal es Program Division of Technical Information and Document Control S. Nuclear Regulatory Commission U. Washington, C. D. 20555

and

National Technical Information Service Springfield, Virginia 22161 NUREG-0693

Analysis of Ultimate Heat Sink Cooling Ponds

Manuscript Completed: July 1980 Date Published: November 1980

R. Codell, W. K. Nuttle

Division of Engineering Office of Nuclear Reactor Regulation U.S. Nuclear Regulatory Commission Washington, D.C. 20656

ABSTRACT

A method to analyze the performance of ultimate heat sink cooling pond s is presented. A simple mathematical model of a cooling pond is used to scan weather data to determine the period of the record for which the most adverse pond temperature or rate of evaporation would occur . Once the most adverse

conditions have been determined, the peak pond temperature can be calculated . Several simple mathematical models of ponds are described; these could be used to determine peak pond temperature, using the identified meteorological record . Evaporative water loss may be found directly from the scanning a simp le and conservative heat-and-material balance . by

Methodology by which short periods of onsite data can compared with offsite records developed , so that the adequacy ofbe th e offsite datalonger pond performance iscomputations can be established . for

iii

CONTENTS

Page

ABSTRACT...... i ii ...... x SYMBO LS...... i I NTRODUCT I ON. . 1...... 1 2. HEAT AND TRANSFER RELATIONSHIPS IN PONDS...... MASS 3 2.1 Equil ibrium Temperature Heat Transfer Model...... 3 2.2 Devel opment of the Basis for Surface Heat and Mass Transfer From a Pond...... S 2.3 Conservatism of Equilibrium Temperature Formulation...... 10

3. POND MODELS...... 13 Mixed-Tank 3.1 Model...... 14 Heat Balance ...... 3.1.1 IS

Heat oa Into Pond...... 15 3.1.1.1 L d 3.1.1.2 Heat Out From Surface ...... 15 Heat Out in l ow own or Leakage Stream. .. 15 3.1.1.3 B d

3.1. 2 Mass Balance ...... 15

3.2 Stratified- Flow Model...... 16

Heat Balance ...... 16 3.2.1 ...... 3. 2.1.1 Heat Enteri ng From Above...... 16 d . 3.2.1.2 Heat Leaving From Segment by A vection . . 16 Change in Heat Content During Time 3.2.1.3 at.... 16 3.2.1.4 Heat Entering Segment 1 From Plant...... 18 H a A ...... 18 3�2.1.S e t Transferred to tmosphere . .

3.2.2 Mass Sal ance ...... 18

F ...... • ...... • . 3. 3 P 1 ug- l ow Mode 1 ...... 18

3.3.1 Heat Sal ance ...... 18 3. 3.1.1 Heat Enteri ng by Advection From Previous Segment. .... � ...... 18 t Advection...... 3.3.1.2 Heat Leaving Segmen by 19 3.3.1.3 Heat Transfer to Atmosphere From Segment. 19 3.3.1.4 Change in Segment Heat Content During Time at...... 19 3.3.1.S Heat Enteri ng From Plant...... 20

v CONTENTS (Continued )

Page

DATA SCREENING METHODOLOGy ...... 4. 21 4.1 Meteorological Inputs to Sc reening Model ...... 22 APPL ICABIL ITY OF WEATHER RECORD...... 5. 25 DESCR IPTION OF COMPUTER PROGRAMS AND THE IR OPERAT ION ...... 6. 29

6.1 Introduction ...... 6.2 Meteorological Data Sc reening Program UHSPND...... 29 29 6.2.1 Prog ram Ope ration ...... 29 6.2.2 Program Outputs ...... •...... 6.2.3 Prog ram Inputs ...... 30 31 6.2.3.1 Pond Data Card ...... 6.2,3 .2 Monthly Average Card ...... 31 6.2.3.3 End Card ...... 31 31 6.2.4 Data Input Examp e ...... 1 32

6.3 Program COMET ...... '...... 33

6.3.1 Prog ram Inputs ...... '...... 34 6.4 Prog ram UHS3 ...... 34 6.4. Prog ram Inputs ...... 1 35 6.4.2 Uti zati on of Prog ram UHS3 ...... 1 i 36 SAM PLE CA LCU LAT IONS ...... 7. 39

7.1 Finding the Pe riod of Worst-Case Cooling Perfo rmance and 30-Day Evapo rative Water loss--Prog ram UHS PND...... 40 7.2 Statistical Treatment of UHSPND Output ...... 7.3 Dete rmining the Applicability of the Offsite Data 41 Set--Prog ram COMET ...... 41 7.4 Final Design Basis Pond Tempe rature and Water Loss Computat ions- -Prog ram UHS3 ...... 50 Evaporative Loss ...... 7.4.1 67 7.4.2 Correction Factors fo r Peak Temperature and Water loss ...... 68

REFERENCES ...... ',' . . .. 73

vi CONTENTS (Continued)

Page

APPENDIX A--STATISTICAL TREATMENT OF OUTPUT...... 75 A.I Additional Statistical Manipulation...... 76 ...... •.. . A.2 Maximum Likeli hood Curve �...... A. 3 Error Bands...... 76 79 APPENDIX B"-COMPUTER CODES...... 81

vii LIST OF FIGURES

Page

2.1 Definition of Equ i libri um Coefficients...... · 4 4 2.2 Pond Temperature Computati ons (Steady State) ...... 2. 3 Heat Loads on a Pond...... 6 2.4 Steady-State Surface Temperatures ...... 12 3.1 Mixed -Tank Model ...... 14 Stratifi ed- Flow ModeL ...... 17 3.2 1 3.3 Pl ug-Fl ow Model...... 9 4. 1 Insolation as a Function of Time ...... '...... 24 7.1 sting of Input for Program ULTSNK...... 41 Li 7. 2 Output From Program UHSPND...... 42 Yearly Maximum Ambient Pond Tempera tures ...... 48 7.3 7.4 Yearly Maximum Ambient Po nd Temperatures, Max imum Likelihood Frequency Curve , 0.05 and 0.95 Error Bands...... 49 I nput to Program COMET...... 49 7.7.6 5 Output of Program COMET ...... 51 7.7 Correlation of Equilibri um Temperatures , Susquehanna River Site Versus Harrisburg Station ...... 59 7. 8 Program UHS3 Data Deck, rst Set...... 60 Fi 7.9 Output From Program UHS3 , First Set...... 61 7.10 Ambient Pond Temperature as a Function Time...... 66 of Pond Temperature With Externa l Plant Heat Load , 7.11 and Constant E i and as a Funct on of Time...... 66 ·7.12 Data Deck for ProgramK UHS3 , Second Set...... 67 7.13 Output From Program UHS3 , Second Set...... 68 7.14 Pond Temperature (Final Calculation) as a Function of Time...... 70 A.1 Pearson Type I II Coordi nates...... 77 A.2 Table of Versus P in Percent...... PN 00 78 Errors of Esti mated Va lues...... A. 3 8083 B.1 L isti ng of Program UHSPND ...... ·...... B.2 Listing of Prog ram COMET...... 99 B.3 Listing of Program UHS3 ...... 101 B.4 Li st i ng of Psychrometri c Subrout i nes...... 104

LIST OF TABLES

5.1 Estimated Correction Factor 6E(x) Compared to Actual Transient Model Response 6T True Correction Factors ...... 27 max ( } 6.1 Pond Data Card Input Parameters ...... 32 Monthly Average Card Input Parameters...... 33 6.2 6.3 Meteorological Input for Program UHS3...... 36 6. 4 NA LI T INLIST for Program UHS3 ...... 37 U ME3 FiSnal Temperature RUns Varying Starting Time ...... 7.1 HS 71

viii SYMBOLS

pond surface area, ft2 or acres A one-half the daily insolation , Btu/ft2 AO surface area of nth segment of the plug-flow model , ft2 AnC cloud cover in tenths of the total sky obscured Bowen's ratio, mm Hg/oF C1 �O.26 heat capacity of water , Btu/lb/oF Cp E equilibrium temperature, of estimation of equilibrium temperatures using data from offsite E2 E1, and onsite records, respectively , of E(x) estimation of equilibrium temperature using monthly average meteorologic data, of e saturation pressure of air above pond surface , mm Hg a e saturation pressure of air at surface temperature T ' mm Hg s S g skew coefficient H heat content, Btu HN heat transfer from segment N, Btu/day heat of vaporization of water , Btu/lb �vap H net heat flux, Btu/(ft2 day) net atmospheric longwave radiation, Btu/ (ft2 day ) HAN back radiation from pond surface , Btu/ (ft2 day) HBR conductive and convective heat loss , Btu/ (ft2 day) HC H evaporative heat loss , Btu/ (ft2 day) E H heat transfer from segment n, Btu/day n net plant heat rej ctio , Btu/ (ft2 day) HRJ e n gross solar radiation HS net solar radiation, Btu/ (ft2 day) HSN K equilibrium heat tr ansfer coefficient , Btu/ (ft2 dayOF ) k error band scale factor

M sample mean P probability probability of occurrence for an event from an infinite population PlIO probability of occurrence for an event from a finite population PN p atmospheric pressure, mm Hg q heat flow inside a pond, Btu/hr

ix

ULTIMATE ANALVSIS Of HEAT SINK COOLING PONDS

1. INTRODUCTION The l ate heat sink defined as the complex of our es of service u tim (UHS) is s c or house water supply necessary to safely operate, shut down, and cool down a nuclear power plant. l g ponds, spray ponds, and mechanical cooling Coo in draft towers are some examples of the types of 'Ultimate hea sinks in use today. t

The U. Nuclear Regulatory Co.i ssfon (NRC) has set forth in Regul atory S. o Guide 1.27 (Ref. I) the llowin positions on the design ultimate heat sinks: f g of

the (I) The ulti mate heat sink be able dissipate design-basis accident (e.g.,must loss-of-coolantto acc1dent} heatone ofaunit plus of the heat hu d n and cooldown all units serves. of a safe s t ow of other it The heat sink must provide 30-day supply of cooling water. at or below (2) a the desi gn-basis temperature for all safety-related equipment.

The system must shown to be able performing under the (3) be cap of et o o og c condi t ions ng the worst· coo performance m e r 1 i 1 eadi to 1i ng and under the conditions leading to the highest water loss.

This report identifies methods that may be used to select the mo severe st combinations of contro11in9 meteorologic paranaetersfor surface cooli ng pond heat transfer and evaporat1 ve water loss. The procedure scans a long weather record , which usually avai lable from the ation Weather Service for a is N a] nearby station, and it predicts the period for which either pond temperature or water loss woul maximized. for a hydraulically simple cooling pond. d be The pri nci p 1 e of near superpos it ion ass m d whi the 1i is u , allows peak ambient o d e ch p n temperature to be superimposed on the peak "excess" temperature due heat o to plant rejection. This pr ce ure determines the tiMing within the weather record of peak ambient pond d temperature. The true can the peak then be determined in a subsequent, more rigorous calculation. loss continuous Maximum evaporative water is determined by picking the30-day period of the record whi ch the highest evaporation losses and has aSSUMing that all heat rejected by the plant results the evaporation pond in of water. To effective the scanning procedure requires data record on the be data a order of tens years in length. Since these usually come from of data wi11 somewhere other than the site its (such as an airport), methods to compare el f these dat� with the limited onsite data are developed so that adequacy, or the at 1 east the conservatism of the te can be. estab i shed. ,_ 1 factors to offsadded i data results Conservative correction to the flnal are suggested. be

as These models and methods are provided useful tool s for UHS aoalyses of cool ng ponds. They are intended guidelines only. these methods i NRC as Use of does not automatically assure approval, nor are they required procedures

1 for nuclear power lant licensi ng. Furthermore, by publ ishing this guidance p do s not wi sh to discourage independent assessments of UHS performance or NRC e the furtherance of state of the art. the

2 2. HEAT AND MASS TRANSFER RELATIONSHIPS IN PONDS

The relationship used in this report for the transfer of heat and water vapor from the pond surface is developed along the lines of the "equi librium temperature" procedure of Brady et a1. (Ref. 2) and Edi nger et al. ( Ref. 3). The mai n reasons for the choice of this procedure are:

It is inherently simple.

It can be shown to be conservative.

It makes poss ible visual izati on of the concept "excess temperature. II of

This last poi nt serves as a basis for the separation of the pond temperature responses as a result of environmental forces from those which result from plant driving forces; this separation further facil itates the scanning weather data as described below. of

Other heat transfer relationships may be more accurate than the one used here ; however, the selection of the period of meteorological record giving the 'most adverse pond temperature or evaporation should be fai rly insensitive to the heat transfer relationship or pond model. Therefore, it is acceptable to use the proposed heat transfer and pond hydraul ic model to scan the weather record , and then to use that record with a more sophi sticated heat transfer and pond model for final determination of the maximum pond temperature and water losses.

2.1 Equilibrium Temperature Heat Transfer Model

The temperature the pond would reach at steady state without external heat inputs and under constant environmental conditions is known as the equil ibrium temperature E. The equi librium temperature is the temperature at which the removal from the pond balances the heat addition. Thi s relation grheatap hical ly illustrated in Figure 2.1. Equilibrium temperature , thereforeis , is a rigorously definable property, dependent on the meteorological conditions at an instant in time. The equi librium heat transfer coefficient K is al so illustrated i n Figure and is defined as the slope of the heat removal curve at pond temperature2.1 T E for a unit surface area: S =

aH K = aT (2-1)

3 SLOPE = aH (SOLAR) ) = aT • HEAT ADDITION E K HEAT H ------S ADDITION OR REMOVAL RATE, BTU/(FT2DAV)

SURFACE HEAT REMOVAL

E

Ts-SURFACE TEMPERATURE - of

Figure Definition of Equilibrium Coefficients. 2. 1

SLOPE = (TRUE) K' SOLAR + POWER PLANT LOAD / -/1 ­ HEAT ADDITION J./ OR I REMOVAL RATE. ,/'" BTU/(FT2DA V) I I • Hs I I I SLOPE = I K I I I I E T (T RUE) T (Predicted from s s K) TS - SURFACE TEMPERATURE - of

Figure Pond Temperature Computations (Steady State). 2.2

4 In this case, the heat transfer H can be described as

dT , K (�-2) providi ng that is reasonably constant in the interval T to E. This is, of K S course, approximately true only if T is very close to E. In a thermal ly heavily S , loaded pond, this assumption is not correct. The heat removal curve has an increasing slope at higher pond temperatures ; therefore , the heat transfer may be underestimated for high heat loadings , and the predicted pond temperature may be too high. This 'potential error is shown graphical ly in Figure 2. 2. The external heat load on the pond must, therefore , be factored into the deter­ mination of pond temperature .

2.2 Devel opment the Basis for Surface Heat and Mass Transfer From Pond of a Mechanisms of surface heat and mass transfer have been extensi vely studied in connection with large , lightly loaded bodies of water , such as lakes and reser­ voirs. Much less work exi sts on small, heavily loaded ponds. Ap�l ication of results from large water bodies must be applied to smal l, heavi ly loaded ponds cautiously and conservatively unti l further experimental evidence of pond per­ formance can be gathered. The NRC is sponsoring experiments on such ponds with Battel le, Pacific Northwest Laboratories.

A relationship for the rate of net heat flow into the pond can be devel oped through consideration of each heat source and heat loss. It is assumed that al l heat exchange with an i solated body of water takes pl�ce through its surface. The rate of heat exchange H is

2 ' Btu/(ft day) (2-3)

in which : -

H = net rate of heat flow into the pond · H = net rate of shortwave solar radi at ion enteri ng the pond , SN measured directly

· H = net rate of 10ngwave atmospheric radiati on entering the pond, AN measured directly

H = net rate of back radiation leaving the pond surface · BR H = net rate of he�t loss due to evaporation

· E H = net rate of heat flow from the pond due to conduction and con­ e vection

·

H = net rate of heat addi tion by the plant RJ Thi s relationship is illustrated graphical ly in Figure 2.3.

5 H• • H• H• H• H• SN HAN e BR E RJ

z Z I- w CJ-w Z w-0 > 1- 0 Zz wa::> 0 > « « « t= ...J-0 «a:: J: t= «::!; « 0.1- ...JI-� � wCJ �c a:: CJ o 85e" « a::W Oz > za::e,, 0a. W (1)0a:: �O Z O� «> o� � (I)J: ...J 0 ...JCJ a. a:: � CJ W «m

Figure Heat Loads on a Pond. 2.3

Of the heat flows into the pond as a result of radi ation and only the HSN HAN' net atmospheric radiation can be estimated from meteorologic parameters. The net atmospheric radiation term can be approxi mated usi ng air temperature T and cloud cover (in. tenths). Ryan and Harleman (Ref. 4) developed the A fol lowing formulaC for H AN:

13 2 2 H = 1. 2.10- (T 4 0)6 (1 + 0.17C ) Btu/(ft day) (2-4 ) AN A + 6

Three components of the heat exchange equation, and are functions HBR, HE' HC' of the pond surface temperature . The back radiation term may be expressed using the rel ation for radiation from a black body (Ref. 2):

Btu/(ft2 day) (2-5 ) where T is the surface temperature of the pond. Using the linear terms of S the Taylor series expansion of this relation gives

1801 15.7(T ) Btu/(ft2 day) HBR = + S (2-6)

The evaporative heat flow can be estimated by

Btu/(ft2 day) (2-7) in which e is the saturation vapor pressure at the temperature of the water s surface Hg) and e is the saturation vapor pressure of the air above the (mm a pond . The second term on the right is an empirical function of windspeed in mi les per hour, U. The wind function proposed by Brady (Ref. 2) is used:

2 2 feU) = 70 + 0.7U Btu/(ft day)/mm Hg (2-8)

6 where is measured at the 18-foot level . U . The quantity (e - e ) can be replaced by a relationship using the slope of s a the vapor pressure versus temperature curve for some temperature between the surface temperature of the pond and the dew point temperature TO'

mm Hg (2-9)

The following polynomial for p can be used in the temperature range normally encountered (Ref . 2):

0.255 - 0.0085T* + 0.00204 (T* )2 (2-10) p =

where

Making the appropriate substitutions ,

Btu/ (ft2 day ) (2-11)

The conduction and convection heat flow can be approximated by

Btu/ (ft2 day ) (2-12)

where

T air temperature A = Bowen's coefficient , 0.26 mm Hgl°F C1 =

Making the appropriate sUbstitutions in Eq . (2-3) , and neglecting the plant heat load for now , leads to

H + 1.2 x 10_13 (T + 460)6 (1 0.17C2) - (1801 A = SN A + + 15.7TS) - peT -T )f (U) - 0.26 (T -T )f(U) Btu/ (ft2 day) (2-13) S o S A

7 Equation (2-13) can be put into the equilibrium temperature form ,

. H = -T ) Btu/(ft2 day) (2-14) K(E S

Equation (2-13) is solved for by letting T E and 0: K S = H =

= H 1.2 x 10_13(T 460)6 + 0.17C2) - (1801 15 .7E) o SN + A + (1 + - P (E -T )f(U) - 0.26(E -T )f(U) (2-15) O A

Subtracting Eq . (2-15 ) from Eq . (2-13 ) gives

. H 15 .7(E -T ) + (P 0.26)(E -T )f (U) Btu/ (ft2 day) (2-16) = S + S

Comparison with Eq . (2-14) leads to a relation for K:

= 15 .7 (P 0.26)f (U) Btu/ (ft2 dayOF) (2-17) K + +

The pond is likely to have its lowest cooling capacity during the summer months , since ambient temperatures will be higher . It can be shown , using Eqs . (2-4) and (2-5) , �hat the components of atmospheric radiation and back radiation from the pond surface nearly balance in the warmer months . The error of neglecting both terms under these conditions is small . The elimi­ nation of the atmospheric- and back-radiation terms from Eq . (2-13) allows for the exp1 icit solution for the equi1 ibrium temperature . Equation (2-13) becomes

Btu/ (ft2 day ) (2-18)

Substituting E T ' 0, and solving for E gives = s H =

. H (PT 0.26T ) SN O A = + (2-19) (P 0.26)f(U) E + + (P + 0.26)

8 Equating Eq. (2-14) with Eq. (2-18),

. K(E - ) ( - (2-20) T H peT - f U ) - 0.26(T T )f(U) - S) = SN S TO S A

Eq. ( 19 Substituting from 2- ) for E and solving for K gives

K = + 0.26 )f(U) Btu/(ft2 day (2-21) (P oF)

This allows Eq. (2-19) to be put in its final form,

. ) H (P 0.26T E SN + TO + A (2-22) = � (P 2 + 0. 6)

Equation (2-23) is the alternate formulation of Eq. (2-17) which follows from the approximation H . So, the surface heat transfer equation as it is HAN � BR used in the model has the form

. (E -T ) Btu/(ft2 day) (2-14) H = K S Btu/(ft2 day) (2-17) K = 15.7 + (P + 0.26)f(U) )I( )Ie 0.00204(T)2 mm Hg/OF (2-10) P = 0.255 - O.0085T +

)I( TS ":"""'-+ T ------To..- 2

f(U)= Btu/(ft2 day)/mm Hg (2-8) 70 + O.7U2

. H ( T + O.26T ) SN P O (2-22) E = � + A (P + 0.26)

9 in which

T = pond surface temperature , S of T = air temperature , A of = dew point temperature , of TO U = windspeed , mph , measured at the IS-foot lev�l = net short wave solar radiation received by the pond, HSN Btu/ (ft2 day )

Evaporation is calculated directly from the evaporative heat flux:

(2-23)

where

W = evaporative flux per unit area of surface 'e H = heat of vaporization of water Btu/lb vap

2.3 Conservatism of Equilibrium Temperature Formulation

The formulation of the heat transfer formulae used has a number builtin conservatisms , which tend to overestimate pond temperature. One ofof the larger conservatisms is the choice of a wind dependence feU ). The Brady wind funct ion employed seems to underestimate the evaporative flux , even when compared to Brady's own data (Ref . 4).

Brady's wind function is derived empirically from large lake data . A more accurate , but less conservative formula was derived by Ryan (Ref. 4) on firmer physical grounds:

(2-24)

+ 460 --S - = T ..,,-=,..-- v _ 0.378e 0.378e L\6 1 s 1 - a p p

where U2 is expressed in mph measured 2 m above water surface, and = virtual temperature , of L\6V and where

p = atmospheric pressure , mm Hg

10 This formula accounts for an expected increase in natural convection with increasing pond temperature , whereas Brady·s wind function is not temperature dependent .

A simple example illustrates the different heat transfer formulations and how they can drastically affect the temperature calculations. The parame�ers refer to a one-sQuare-foot section of pond surface:

Solar input = 2100 Btu/ (ft2 day )

Dew point temperature = 70°F

Ambient air temperature = gOoF

Windspeed = 2 mph

Power plant load = 0 to 11, 000 Btu/ (ft2 day )

Four heat transfer formulas are used to calculate the steady-state pond temperature in response to these meteorological parameters:

(1) The equi 1 i bri um temperature and heat transfer coeffici ents based on unloaded pond conditions (not a function of pond temperature ).

(2) The equilibrium temperature and heat transfer coefficients based on pond temperature (method used in present models ).

(3) Rigorous formu1 a--each of heat transfer terms in Eq. (2-3) is explicitly calculated with Brady wind function used .

(4) Rigorous formula--same as case 3 but with Ryan wind function used .

The results of this calculation are presented in Figure 2.4. Although all of the four formulas are in good agreement at light pond loadings , they deviate substantially at high loadings . The conservatism of the Brady wind function over the Ryan wind function is evident , as is the conservatism of the approximation formula over the rigorous formula .

11 W= 2MPH 200 C=0.5 Hs: = 2100 BTU/(FT2DAY) T =90°F A 190 To= 70 OF

180

170

SURFACE 160 TEMP T -oF S 150

140

130

120

110

100

90 0 1 2 5 ·6 7 8 9 1 0 11 12 3 4 -BTU/(FT2DAY) HEAT LOAD FROM PLANT x 1000

Figure Steady-State Surface Temperatures. 2.4

12 POND MODELS 3. The hydrodynamics of small cooling ponds typically used for ulti mate heat sinks can be extremely compli cated. Because of its lower density, heated water may stratify on the surface of the pond. In many cases, this strati­ fication may be used to good advantage in order to segregate the heated upper water layer from the cooler underlying water. This m� be accomplished by designing and locating the intake from and discharges to the pond so as to minimize mixing. Mixing of the waters in the pond because of improper design, or mixing induced high winds will tend to lower the efficiency of the pond by IIshort-circuitinbygll the hot and cool layers.

Mathematical models capable of accurately simulating thermal hydraulics of ponds are becoming' increasingly available (Refs. and 6). The methods 5 s. described 'here, however I nvo 1 ve only very simp 1 e , ideal zed pond model Complicated mathematical modelsi are only as good as their i data input and the ability of the modeler to describe the pond and its environment. It has not been found necessary to employ sophi sticated pond models to the meteorological screening procedure.

Three of the simple models will be described.

(I) The mixed-tank model assumes total mixi ng of all heated effluent through­ out the volume of the pond.

(2 ) The stratifi ed-flow model assumes complete density strati fication with the heated effluent entering the surface layer and the cooled water being withdrawn from the bottom layer.

(3) The plug-flow model assumes that the thermal effluent is discharged to the pond and travels as a lip 1 ugll through the entire volume of the pond, all the whi le transferring heat to the atmosphere.

Only the mixed-tank model is used in the data scanning procedure.

well desi gned cooling pond will have hydraulic properties approaching those ofA the stratified- or plug-flow models, which are most efficient at dissipating heat (heated and cooled water do not mix in these designs). The mixed-tank model represents an inefficient design. Heated water entering the pond will be completely and instantly mixed with the total pond inventory. Therefore, part of the heated water will be recirculated before it has had the opportunity to be cooled; but part of the water will stay in the pond for a long period time. of

It is not necessarily true, however, that any of the three models would repre­ sent the prototype. In some cases, there could be conditions in the prototype pond that would lead to less effi cient operation than predicted by any of the three models described here. For example, "side arms" of irregularly shaped reservoirs used for power plant cooling � be less efficie'nt at N!jecting heat than is the main body of the reservoir because circulation in these regions can be poor. Also, there exi sts the possibility that stratificati on m� cause short-circui ting between the intake and discharge which would tend to isolate

13 the cold water of the lower layer from the intake and thereby effectively reduce the thermal inertia of the pond , that is , its capacity to absorb initially high heat loads . For example , see the analysis in Jirka (Ref . 7).

These pond models do not explicitly simulate the complicated hydrodynamic features of ponds . the possibility of factors that would reduce efficiency exist , arbitrary reductionsIf of surface area and pond volume can be made to assure conser­ vatism. Furthermore , the relative simplicity of the models allows their incorporation into a pond temperature computer program to be described later , in which all three pond configurations are considered"UHS3,1I simultaneously.

3.1 Mixed-Tank Model

The mixed-tank model depicted in Figure 3 .1 presumes that the heated effluent is instantaneously and uniformly mixed throughout the volume of the tank , and that the water in the tank is uniform in temperature . Heat transfer with the atmosphere occurs at the surface of the tank . This heat transfer is less efficient in the case of a completely mixed pond than in a pond where the hot and cool water do not mix . Atmospheric heat transfer is related to the pond surface temperature , which is diminished in the former case and preserved in the latter .

• H

SURFACE AREA A

VO LUME V

TEMPERATURE T

PLANT HEAT ADDITION • HRJ

Figure Mixed-Tank Model. 3.1

14 3.1.1 Heat Balance

heat and mass balance can be formulated for the mixed-tank model. terms Aof the heat balance are: The

3.1.1.1 ea Load Into Pond H t

Heat in H Btu/hr (3-1) = RJ 3.1.1.2 From Surface Heat Out

AK (3-2) H (T-E) Btu/hr = 24 where

A surface area of the pond, ft2. = 2 = equilibrium heat transfer coefficient, Btu/(ft day)/oF K mixed-pond temperature, of T = equilibrium temperature, E = of 3.1.1.3 Heat Out in B10wdown or leakage Stream

With reference to the mixed-pond temperature heat loss from blowdown is definition zero: T, by

q W C 0 (3-3) b = b (T - T) = P where

W f10wrate of the b10wdown or leakage stream b = density of water, 1b/ft3 p = C specific heat of water, Btu/lb/oF p = Combining all heat inputs to and outputs from the pond, and using the relationship relating temperature to heat, the following is obtained:

H d RJ _ AK T °F/hr (3-4) dt C V 24 C V (T - E) = p p

where V is the pond volume.

3.1.2 Mass Balance

The mass balance on the pond includes evaporative loss from the surface and the b10wdown or leakage. The terms of the mass balance are:

15 B10wdown on leakage flow = W ft3/hr Evaporative loss from surface = W 3/hr/ft2 e ft�'

(3-5)

where

slope of the vapor pressure-temperature curve , mm Hg/oF dew point temperature , of heat of vaporization of water , Btu/1b

Combining all terms of the mass balance yields the expression:

- peT -T ) f*U ) A dV S O - =-W (3-6) dt b 24 C H P p vap

3.2 Stratified-Flow Model

In the stratified�f10w model (Figure 3.2) the assumption is made that the heated eff1uent enters on the surface of the pond and cooled water is withdrawn from the bottom of the pond . Water does not mix vertically but simply moves from the surface layer to the bottom as a "plug. II Heat transfer occurs only from the surface layer .

The pond is segmented into N horizontal slices of thickness as shown in �N Figure 3.2. In the computer program subsequently described , = 10. The terms of the energy balance of segment n are:

3.2.1 Heat Balance

3.2.1.1 Heat Entering From Above q = W C T Btu/hr n-1 P p n-1 (3-7) where

= f10wrate through pond W

3.2.1.2 Heat Leaving From Segment by Advection Btu/hr (3-8)

3.2.1.3 Change in Heat Content During Time at

Btu/hr (3-9)

16

, H• + RJ T n p CpWin

SURFACE AREA A

PLU Gn_1 Tn-1

I

PLU T = Gn n Vn V/N lI

PLUGn+1 � T n+1 I V = TOTAL VOLUME T N = NO. OF SEGMENTS

TN % FlowW

PLANT HEAT ADDITION • H RJ

Figure Stratified-Flow Model. 3.2

Combining all terms yields the following expression for segment n:

(3-10)

17 The heat balance of the uppermost segme nt inc udes the atmospheri c heat transfer and the heat addition from the plant . 1 The additional terms of this heat balance are:

3.2.1 .4 Heat Entering Segment 1 From Plant

. q (W C T + H ) Btu/hr (3-11) o = p p N RJ 3.2.1.5 Heat Transferred to Atmosphere

. H = KA - E) Btu/hr (3-12) 24 (T1 combining Eqs . (3-8), (3-9), (3-11), and (3-12) yields the expression for the first segment:

H RJ - (T1 - E) + 24 - KA (3-13) C A P p III

3.2.2 Mass Balance

No mass balance is formulated for the stratified-flow model , or the plug-flow model subsequently described . Instead , the mass balance performed on the mixed-tank model is used to correct the volume of the stratified- and plug-flow models . This approach is justified because the amount of heat leaving the pond surface is roughly the same regardless of the model chosen . Since 50% to 80% of atmospheric heat transfer is by latent heat (evaporation ), the consumptive water use predicted by each model is assumed to be about the same .

3.3 Plug-Flow Model

The plug-flow model depicted in Figure 3.3 assumes that the heated effluent enters the pond and travels horizonta lly as a lip ug" of water through the entire volume of the pond , excha nging heat to the1 atmosphere . Water in the plug does not mix horizontally , but the temperature in the plug is assumed to be uniform vertically .

The pond is segmented into N vert ica s ices of ength as de pi cted in 1 1 1 ax Figure 3.3. In the computer program subsequently described , N = 10. The terms of the energy budget on segment n are:

3.3.1 Heat Balance

3.3.1.1 Heat Entering by Advection From Previous Segment

Btu/hr (3-14)

18

• TOTAL VOLUME V TOTAL SURFACE AREA A

An in W Cp in t t T W qn-1 qn qn+1 N' W - V - � ... n ... -. � � An PLUG 1 n -1 n n+ 1 N

Vn= V/N An= A/ N

PLANT HEAT ADDITION • HRJ

Figure Plug"Flow Model. 3.3

3.3.1.2 Heat Leaving Segment by Advection

Btu/hr (3-15)

3.3.1.3 Heat Transfer to Atmosphere From Segment

•

H - (T - E) Btu/hr , = KAN (3-16) 24 n

3.3.1.4 Change in Segment Heat Content During Time at

Btu/hr . (3-17)

combining all terms yields the expression for the temperature of segment n:

(T - E) K n °F/hr (3-18) ,24 C p p ax

The heat balance on the first segment includes the heat released from the plant and the recirculated heat from the pond. The additional term in this heat balance is:

19

1\ 3.3.1.5 Heat Entering From Plant

(3 -19)

Combining Eqs. (3-15), (3-16), (3-17), and (3-19) yields the expression for the temperature of the first segment:

(3-20)

20 4. DATA SCREENING METHODOLOGY

In this section, a method is described with which long-term weather records can be screened to find the period in which the cooling pond temperature will be maximized.

The "equilibrium temperature" heat transfer approach is used in a method that decouples the plant heat input effects from environmental effects on the pond. The temperature of the pond may be determined by the so ut i on of the differential equation for the mixed-tank model, 1

H dT = AK (E _ T) + RJ (4-1) dt C V C V P p P p

For the purpose of developing the model, E, and V are temporarily assumed to be constant. Equation (4-1) will, therefore,K, be linear with respect to T, the fully mixed pond temperature.

Since the equation is linear, it is possible to consfder that the pond . I �emperature is a sum of the unloaded pond temperature.T and an "excess" temperature o. I T = T + (4-2) 0

I But T would be determined by the solution of Eq. (4-1) without external loading:

I dT A ' = K (T - (4-3) dt C V E) p P E (4-1) Subtracting Eq. (4-3) from q. gives the differential equation for excess temperature

H dO _ (4-4) AKO + RJ dt - V C V p Cp P p

The determination of pond temperature has, therefore, been separated into two simpler probl ems, because now the ambient and excess pond temperatures can be determined independently of one another. The excess temperature does not depend on the meteorological record, so it can be solved directly0 from Eq. (4-4) using the plant heat rejection rate. The pond ambient temperature I T does not depend on the heat rejection from the plant, so it can be

21 calculated from Eq. (4-3) using only the long meteorological reco,rd . The peak pond temperature can , therefore , be found by summing (superimposing) the peak I T and a:

I (T) = (T ) a (4-5) peak peak + peak

Unfortunately, the basic premise that Eq. (4-1) is linear is incorrect. Both and E are functions of T. In addi t ion, the pond volume V wi change as wateK r on the pond is lost by seepage and evaporation. (Makeup wate11 r is assumed to be unavai lable during the operation of the pond. ) The thermal hydraulics of the pond and, therefore , how it responds to heat input, wi ll depend on how and when heat is rejected to the pond. If the pond can be represented by the I completely mixed model , the superposition of T and a may overestimate the peak pond temperature for very high loadi ngs.

The uti lity of the methods just described is to identify the timing of maximum I ambient pond temperature T and maximum exce'ss temperature so that more accurate computations can be made in which the pond temperatura e can be deter­ mined directly. A more sophisticated model of the pond may in factT be desirable for the actual pond temperature cal cul ations rather than the simpler models emp l oyed to screen the meteorological data. The initi al temperature and starting time for this computation is determined from the screening procedure . Since the heat transfer rel ationships are nonli near with respect to pond temperature, and since the model ultimately used for temperature calculations may be dif­ ferent from those used in the screening, there are no firm guarantees that the optimal starting time for peak temperature wi ll necessarily be found. Most likely, the optimal starting time wi ll fal l within hours of that determined by the screening procedure . A series of sensitivity runs spaced several hours apart, starting both before and after the starting time indicated by the screening procedure wi ll assure that the peak pond temperature has indeed been found.

4. 1 Meteorological Inputs to Screening Model

The screening model developed in Section 4 required two types of data: (1) weather data (dry bulb temperature , dew point" windspeed, and cloud cover) which may be obtained from National Weather Service records, and (2) rates of net solar radiation which do not exist for long periods of record . A method for synthesizing solar radiation using cloud cover data has been developed. National Weather Service tapes of Tape Data Fami ly-14 (TDF-14) are used by the model as a source of temperature and wi ndspeed data and the cloud cover obser­ vations. These tapes are avai lable for major observation poi nts throughout the United States.

The solar radiation term for the heat exchange relation must be either taken from direct measurements or estimated. The model estimates hourly solar radia­ tion rates in a three-step process. First, given the latitude of the pond and the time of year , the maxi mum solar radiation avai lable to the pond for the day under conditi ons is estimated. Second, this gross figure is fitted to a sinusoidal functi.on to find the rate of insolation for each hour

22 of dayl ight. Final ly, these hourly rates are modified to take into account the effect of cloud cover.

A subrouti ne based on the wo rk of R. W. Hamon (Ref. 8) is used to estimate the maximum dai ly solar radiation. This total dai ly radiation figure is fitted a sinusoidal function as shown in Figure 4. 1. The hourly variation of to radiation is

. H (t ) 2t1 [acos(wt ) - acos(wt1 )] Btu/(ft2 day) (4-6) S O = O where

A O a = 1 (4-7) sin (wt1 ) - t cos (wt ) w l 1

_1t hr (4-8) W - 12 and

A one-hal f the dai ly insolation O = t time of observation before or after midday , hr o = tl = hal f-l ength the time of dayl ight, hr Solar radiation ultimately reaching the earth 1s surface is greatly affected atmospheric conditions , especial ly by cloud cover. The amount of cloud covebyr in tenths of the total sky obscured is avai lable from the data tapes. This information is used in a rel ati onship developed by Wunderl ich (Ref. 9) to modi fy the insolation rates :

. . H H ( l - 0 .65 C2 )0. 94 Btu/(ft2 day) SN = S (4-9)

In which :

H net solar radiation Btu/(ft2 day) SN H = gross rate of solar radiation Btu/(ft2 day) S = cloud cover in tenths c = 0 . 94 factor that adjusts for the average 6% reflection = from the water surface

23 z o � ...I

iz

u. o w

a::�

o �------=- cx:cos(wt) HOURS BEFORE OR AFTER MIDDAY

Figure Insolation as a Function of Time. 4.1

24 5. APPLICABILITY OF WEATHER RECORD Long-term meteorological records at the site itsel f are not usually avai lable. Current NRC practice requires only limited onsite data col lection. Meteoro 1 og1 ca 1 data col l ected ons te may be inadequate for cool i ng pond analysis because measurements of isol ar radiation and cloud cover are not required by current regulations or guidel ines.

In the absence of long-term onsite data, the meteorological data for analyzing UHS performance must be obtained from offsite weather stations (such as ai rports) for which long-term records , including solar radiation or cloud cover, are avai lable. Additional ly, the site and offsite data may display s i gni fi cant di fferences because of orographi c effects� Because long-term records are absolutely necessary, some method to ensure applicabi lity of the offsite data is required.

To develop the method, several assumptions are required:

(1) A representative norm of the true pond temperature wi 11 be the equilibrium temperature E, which can be calculated from the monthly mean val ues of the meteorological variables, and

(2) The response of the pond hydrodynamics wi ll be fast compared meteorological changes. to

The val idity of the assumptions wi ll be subsequently shown by way of an illustrative example.

The ass umptions greatly simplify the analysis of the problem and allow a meaningful quantitative appraisal of the Oi'lsite and offsite data without a dynamic analys is of the pond itself.

• The principal tool in the ' methodology is the equilibrium temperature calculated by the transient mixed-pond model (UHS3) usi ng monthly average data. _The equi librium temperatures are determined using oftsite data [that is, E(x) ] and again using onsite data [that is, E(x) ]. Of offsite onsite course , the data cover the same period. * The difference,

AT = E(x) - E(x) offsite onsi te ' is ultimately added to the peak temperature T calculated by the UHS3 model max to reflect the bias induced by usi ng the available long-term offsite data verses th� onsite data.

The AT thus calculated represents the total bias induced by the different data sets . It may be of interest to know the relative effects of each meteorological parameter on the AT .

*The important differences are long term. * We assume that by using monthly ' (30-day) averages , the effects of short-term , local variations have been adequately included without having to deal analytical ly with such phenomena as thunderstorms. 25 The di fference of the pond temperature AE, in response to di fference in meteoro ogi ca data ons i te and offs i te , can be determi ned by cons i deri ng 1 1 E with respect to the independent variables T the partial. differential s of O ' T , U, and H A SN :

(5-1)

If the differences between offsite and onsite parameters ar e smal l, the difference AE can be approxi mated by the sum of the individual differences due to changes in a single meteorological parameter, holdi ng the others constant:

. II.E II.E + AE + + II.E (5-2) T ,U,H T U , H II.E T T H T T U � � � A SN � SN � A ' SN � A ' 0' 0' 0'

The sum of the four terms on the right-hand side of Eq. (5-2) wi ll probably not add up to the AE predi cted directly from the calculation of El and E2 because of nonli nearities. The breakdown into individual components should be largely indicative of the true differences between the data sets , 'however. A brief computer program , COMET (COmpare METeorology) , has been written which eval uates the differences in steady state temperatures between two data sets and their sensitivity to differences in the averages of dew point, air temperature , wi ndspeed, and solar radi at i on between the two sets of data. This program also cal culates the correction factor , in cubic feet of water, for the differences in evaporation between two sites based on the 30-day average meteorology. Resultant steady state temperatures and water loss rates between the two data sets are correl ated. The standard errors a and coefficients of determination r2 are calculated for temperature and . evaporation. The use of the correction factors from program COMET al leviates the ambiguity of location of the weather station instruments at either site. The conservatism using the di fference in equi librium temperatures E(x) from month ly averageof data ' to correct for peak temperature at the site can be demonstr�ted by example . Consi der that the "estimated" correction factor AT = E(x) -E (x) is to be added to the peak temperature 1 offs ite onsi te calculated by the UHS3 model of pond performance. A 40-day continuous record of meteorological data at Harrisburg , Pennsylvania, was used as the data base for the offsite location. To represent the onsite data base, the same 40-day record was used, but a bias was added to each of the val ues of T , T H and A O ' S ' U, one parameter at a time. Peak thermal ly loaded pond temperatures were then calculated for the onsite data base with no bias , and recalculated with a bias on each meteorlogical parameter. The "true" correction factor is observed from this calculation as the difference in the peak temperature of the biased and unbi ased case. / The true correction factor for peak temperature usi ng the mixed-tank model were compared with the differences in equi librium temperature based on a 40-day average of the meteorological parameters (estimated correction factor). The results of this comparison are presented in Table The table shows 5. 1.

26 x Table 5. 1 Estimated Correction Factor wE( ) Compared Actual Transient Model Response AT lII (True Correction Factorsto ) max

ATmax aE (x) lillie true (estimated correction Bias on meteorological termslle correction factors) factor) from + ++ +++ AT , 111111111 AT ' AH , AU , from program A O Bt�/ft2hr mph EcX) T UHS3 of of Eq. (5"2) max

0 0 0 0 74 .93 0 104. 36 0 10 0 0 0 77.44 2.51 106.01 1.65

0 10 0 0 80. 89 5. 96 109.14 5.03 5.78 0 0 1000 0 82.00 7.07 110.14 0 0 0 5 72. 49 -2.45 97.6 -6. 76

III is based on actual peak temperature wi th example heat load in examp le ATmax pond using mixed-tank model . lillie _ H ' AE(X) is based on 40-day average of S and rms U. lIeIllIll TA , TO ' T bias added to each hourly val ue of dry bulb temperature A = T . + A A T bias added to each hourly val ue of dew point temperature A O = T '

• O ++-. • b1as added to each hourly val ue of solar radiation H ' AHS = S

= bias added to each hourly value of wi ndspeed U. +++AU

that , as expected, the estimated correction factors AE(x) were always larger pos iti ve ly than the actual increases in pond temperature predi cted by the mixed-tank nsient m odel AT , (the "true" correction factor) and are , tra max therefore , conservative.

Table provides , in part, an indication of the �ias induced by an arbi trary variat5.io1n of each parameter. The variations [AE(x)] indi cate that, wi th the exception solar radiation, H Ill the most important factor is the dew poi nt. of S

"Unfortunately, the relative magnitude of the arbi trary variations (i.e. , we ll wi thi n the range of variati on potentially expected ATA of 10°F is AH between sites: the variation of S by 1000 Btu/ft2 hr) is a major change.

27

6. DESCRIPTION OF COMPUTER PROGRAMS AND THEIR OPERATION

6. 1 Introduction

Three separate computer programs are described which may be used for several facets of the cool ing pond analysis. The programs rely on 'the procedures and methods described in the previous sections. Al l programs are written in 7600 FORTRAN IV. Minor modifications may be necessary for other computeCDCr systems.

(1) Program UHSPND is used to scan the weather record tapes to predict the 1 i ke ly peri ods of lowest cool i ng performance and hi ghest evaporative loss.

(2) Program COMET compares the limited quantity of onsite meteorological data with summaries of offsite data provided by program UHSPND to determine if there are significant differences between the two which might lead to differences in predicted pond performance.

(3) Program UHS3 can be used to calculate the most pessimi stic cooling pond temperature using ideal i zed pond hydraulic models and the abbreviated weather record furni sh�d from program UHSPND. These programs are described in greater detail in the fol lowing sections.

6. 2 Meteorological Data Screening Program UHSPND

Program UHSPND can be used to scan long weather records to determi ne the period of lowest cooling performance and highest evaporation for small cool ing ponds in UHS service. A simple mixed-tank hydraul ic model and the Brady-Geyer heat transfer formulae are empl oyed in a running simulation for the enti re length of the weather record. The time of maximum ambient pond temperature and the 30-day period gi' ving maximum evaporation are determined from the simulation.

6. 2. 1 Program Operation

The program first reads and screens meteorological data from National Weather Service Tape Data Fami ly 14 (TDF-14) magnetic tapes. Hourly or three-hourly val ues of up to 48 meteorological variables are 'stored on these tapes in a compact alphanumeric code . Subroutine SUB1 interprets the code and extracts the values of windspeed, dry bulb temperature , dew pOint temperature , cloud cover, relative humidity, and atmospheric pressure. As a computational expedient, only the months May through September are scanned, since it is highly unlikely that either the peak temperature or evaporation losses occur in the other months. would

The stored data are checked for missing or inconsi stent val ues. If one or two consecutive observations of a meteorological parameter are missing, they be replaced by interpolated val ues. If, however, more than two consecutiwivell observations are missing or in error, the entire day of data is ski pped and an ' message to thi s effect is pri nted.

29 The program synthesizes solar radiation needed for subsequent calculations from the cloud cover, date , and latitude , since no direct observations of solar radiation are contained in the TDF-14 tapes. This procedure is discussed in Section Direct observations of solar radiation would be most desirable if available4. from other sources, but no provisions for their input . are presently incorporated in the program .

Subroutine SUB2 numerical ly calculates the ambient unloaded pond temperature and evaporative loss with the mixed-tank model and the Brady-Geyer heat transfer relationships using the meteorological variables generated in subroutine SUBl. The yearly maximum pond temperature and yearly maximum 30-day evaporative water loss are determined along with their dates of occurrence.

Subroutine SUBS statist'ical ly treats the data base consisting of the annual maximum pond temperatures and maximum annual 30-day evaporations for further manual analysis.

6.2.2 Program Outputs

The program provi des the fol lowi ng information, depending in some cases on the options selected:

(1) An informative message is printed if missing or inconsi stent data are encountered , so that it is clear that the record for that day has been skipped.

(2) A table of hourly val ues of windspeed, dry bulb temperature , dew point temperature , solar radiation, cloud cover, and relative humidity is printed and/or punched for the 35 days precedi ng the time of maximum ambient temperature and the 5 days fol lowing. This table may subsequently be used in a more rigorous computation of thermal ly loaded pond temperature wi th program UHS3, or may be used wi th some other dynamic temperature model . Although only the values of wi ndspeed, dry bulb temperature , dew point temperature and solar radiation are used in the UHSPND and UHS3 mode 1 s , other formu 1 at ions of the heat trans fer relationShips may require the cloud cover and relative humidity, so these are al so outputted.

(3) The dates and quantity of evaporation for the yearly worst 30-day ambient period in an unl oaded pond is outputted. The quantity of (unloaded) evaporated water loss may be added to a conservative estimate of excess evaporative loss from added heat to determine total evaporative water loss directly, without the need for an additional computer program as is necessary with the peak temperature calculations.

(4) Monthly averages of meteorological parameters for al l specified years the record are printed for the purpose of comparing offsite data withof limited quantities of onsite data using program COMET described later.

(5) The maximum annual ambient pond temperature and 30-day evaporation al l years on the tape are printed, ranked in order from highest to lofowerst magnitude. Approximate probabi lities are calculated so that the ranked outputs can be plotted on an arithmetic-probability scal e. The mean ,

30 standard deviation, and skew of the data are also printed. Further stati stical manipulation may be performed manual ly using the procedures outl i ned in Appendix A, Statistical Treatment of Output.

6.2.3 Program Inputs

The fol lowi ng input data are necessary to run program UHSPND:

(1) Pond surface area, ft2 or acres.

(2) Pond vol ume , ft3 .

(3) latitude , oN.

(4) A TDF-14 weather tape from a representative station near the site.

The TDF-14 weather tapes can be obtained from the National Cl imatic Center , Federal Bui 1 di ng, Ashevi 11e, North Caro 1jna 28801.

Computer and peripheral requirements to run program UHSPND on the Brookhaven National laboratories CDC 7600 computer are one magnetic tape drive , two di sk files, and about 12 ,000 (decimal ) words.

Specific instructions for running the program apply to the NRC version on the Brookhaven computer. Versions of UHSPND for use at other centers can be expected to differ in their use of tapes and job control cards. Minor modi fications to the program may be necessary for computer systems other than CDC.

The data deck required to operate program UHSPND consists of three types of data cards ; the pond data card , the monthly average card, and the end card. The input data are read in NAMElIST form named INPUT.

The fol lowing tables explain the meaning of each variables in the NAMElIST :

6.2. 3.1 Pond Data Card

This NAMElIST specifies the pond parameters for the mixed-tank models and specifies certain printing options as shown in Table 6.1.

6.2. 3.2 Monthly Average Card

This NAMElIST specifies the year and month to start computing monthly meteorological summaries to be used for comparison with onsite meteorological data.

6.2 .3.3 End Card

By specifying N = 0, the program terminates.

One set of output is generated from each pond data card or monthly average card . These cards are unrelated and may be inserted in any order.

31 Table 6. 1 Pond Data Card Input Parameters

Variabl e Value Type and description

N 1-99 Integer--card number used to identify the the card as a "pond data" card and to i denti fy the results in the output A >0 Real , pond surface area in square feet <0 Real , pond surface area in acres V >0 Real , pond volume in cubic feet <0 Real , pond volume in acre-feet lAT 2S-S0 Real , latitude of pond in decimal degrees north latitude IPRNT Integer--print option Prints and punches hourly meteorological data o 1 Printed output only -1 Punched output only

If a second pond data or monthly average card is used, say to test the sensitivity to a variation in a pond parameter, only the variable changed needs to be inputted on the NAMElIST card .

6. 2.4 Data Input Example

Consi der a pond with vol ume lo S x 107 ft3 and 8 x 105 ft2 surface area at latitude 4SoN. Determine the highest ambient temperature and evaporation rate , and print the worst case meteorology. Rerun the calculation with hal f the vol ume , determine the periods of highest temperature and evaporation, and print and punch the output for the worst temperature period. Final ly, compute the monthly averages of the meteorological data from June 1971 to the end of the tape.

The data input for this examp le wou ld be:

$INPUT N=1, A=8. 0ES , V=1. SE7 , lAT=4S .0, PRINT=l$ $INPUJ N=2, V=0. 7SE7 , ISRCH=l, IPRINT=O$ $INPUT N=101 , YRMODY(1)=71, YRMODY(2)=6$ $INPUT N=O$

32 Table 6.2 Monthly Average Card Input Parameters

Variable Value Type and description

N > 99 Integer--identified this card as a monthly average card . YRMODY(1) Real , the year of the beginning date for the computation of monthly averages meteorological data of

YRMODY(2) 5 - 9 Real , the month of the beginning date the computation of monthly averages. for LAT 25-50 Real , the latitude in decimal degrees north if di fferent from that previously speci fied.

6.3 Program COMET Program COMET (fQmpare METeorology) compares equi libri um temperature and evapora­ tion rates computed from monthly average val ues of solar radiation, dew pOi nt temperature , dry bulb temperature , and rms (root mean square) wi ndspeed for two data sets . It has been previously demonstrated in Section 5 that equi lib rium temperature computed from monthly average meteorological conditions can a meaningful norm for the comparison of two data sets used to compute peak tembe pera­ tures.

Program UHSPND computes the monthly averages of the meteorological parameters from the offsite weather station record provided on the National Climatic Center tape. The other data set would be taken from limited onsite measurements.

If onsite data are not complete (for example, if solar radiation is not available) , the offsite data can be substituted for t,!l e missing parameters. The program calculates the equi librium temperature E(x) and 30-day evaporation W (x) for e each data set, the di fference in calculated val ues of E, and the apparent dif­ ferences in E due to differences between each of the meteorological parameters. Therefore , if one of the meteorological parameters for the site is unknown , the apparent di fferences due to only the other three parameters can still determined. be

The output val ues of onsite and offsite equi librium temperature and tion rates are correl ated for as many months as avai lable to determievapone ra­ there is a significant difference b�tween the locations. The coefficientif of determination r2 is computed for 'E(x) onsite and offsite. A coefficient determination of 0.9 would indicate that 90%of the variance in one data sofet is accounted for by variation of the other data set, and that 10% of the varia­ tion is unexplained.

33 The average equi libri um temperature d; fference and avetage evaporati on rate difference between the two data sets the biases E(x) and W (x) , respec· are e tively. The biases may be used cautiously as correction factors to the loaded pond temperature and 30-day evaporation loss. coefficient peak The of determi nation r2 should be high. Lower val ues may indicate poor qual i ty data , real orographic differences between sites , or a combination of the two . Because the data bases are generally smal l and may be incomplete , we suggest that the. biases used o n y in the conservative sense ; that is, onsi te E(x) or be l if We(x) are greater than correspondi ng offsite values , the di fference should be added the oaded pond temperature or evaporation as a correction. the oppto ositepeak is thel case , no corrections should be made. If

6.3.1 Program Inputs

Program COMET requires mo nthly averages of dry bulb temperature , dew point temperature , solar radiation and rms wi ndspeed for each site. The first card speci fies the number of months of data and is read in IS format. The next cards contain the fol lowi ng informationI read in format: I 8F10 .0

i eld Vari able Descri t on F p i

I TD1 Dew point temperature , of, data set I TAl 2 Dry bulb temperature , of, data set 1 3 W1 Rms wi ndspeed , mph , data set 1 HI Solar radiation, Btu/( ft! day) , data set 4 I T Dew po n temperature , of, data set 5 D2 i t 2 TA2 6 Dry bulb temperature , of, data set 2 7 W2 Rms wind speed, mph, data set 2 8 H2 Solar radi ati on, Btu/( ft2 day) data set 2

If dew point temperature is not avai l a le directl y, it can be synthe s ed from dry bulb temperature , wet bulb temperbature , and atmospheric pressure izusing a psychrometric chart , or subroutine PSYI descr i bed in Appendix B.

6.4 Program UHS3

Program UHS3 calculates the temperature in the ultimate heat sink pond under com i ned influence of the meteorology the external plant heat load. the b and Hourly meteorological data are provided on cards from program UHSPND.

34 The pond is represented by three simplified hydraulic models simultaneously: the mixed-tank mode l as used in the screening 'program UHSPNO, the stratified­ flow model , and the plug-flow model. Heat transfer relationships are based on the Brady-Geyer method as in program UHSPNO.

The pond outl et temperatures and volume for al l three models are pri nted simultaneously. Maximum temperature for each pond model determined and time of occurrence of the maximum is printed. is the

6.4. 1 Program Input

Necessary input data for this program include a title card, the external heat input, meteoro logical conditions , volume and surface area, makeup , blowdown , leakage , and circulation flowrate of the pond:

(1) The first card of the data deck is a title card. Information entered on thi s card wi 11 be pri nted at the beginni ng of the program output. no information is to be printed out, this card should be left blank. If

(2) Meteorological data are general ly provi ded directly from program UHSPND . The first card in the meteorological deck specifies the number of time periods in the table (usual ly 960) and is read in IS format. The subsequent cards are read two time periods (usual ly 1 hour each) per card as illustrated in Table 6.3.

If constant meteorological conditions are specified, only the first val ues of W, TA , TO , and HSN need to be inputted. (3) The heat and flowrate table is inputted next. The plant heat rejection and UHS flowrate during the design accident should be plotted on a semi log plot, with heat and flowrate on the linear scale and time on the logarithmic scale. A table of heat and flowrate to the pond versus time should then be created from a straight line approximation of the graph. This procedure must be fol l owed because a log-linear interpolation of the heat and flowrate table is used in the program. Plant heat is often provi ded in this graphic form di rectly.

Heat and flowrate are inputted in a NAMELIST format named HFT. For example, a typical heat load and flowrate t�ble wou ld be:

$HFT HEAT(I) 0. 0, I. O , I. 6ES, I. OES , 4. 9E8; 5 .6E8 , 6.9E8, 5.IE8 , = ES . S I. 4E8 , 0 8E , 0.5E8, FLOW(I) = 40 , 50, 8*60, TH(I) 0.001, 0.025 , 0.04, 6, = 0. 08, 50 , 600, 1000 , NH = 9$

where

HEAT = array of plant heat input, Btu/hr FLOW array of flow inputs, ft3/hr = TH = array of corresponding times (relative to the start of accident) for the HEAT and FLOW arrays the

NH = number of entries in the table.

35 Table 6.3 Meteorological Input for Program UHS3 Format [13 , 2(3F5.1, F6. 1, F4. 0)]

Field Variable Description

ISEQ Sequence number-not used 1 2 W(!) Wi ndspeed, mph 3 TA( !) Dry bulb temperature , of TOO) 4 Dew point temperature , of 5 HSO) Solar radiation, Btu/(ft2 day) 6 CC Cloud cover--not used in this program but punched from UHSPND

7 RH Relative humidity--not used in this program , but punched from UHSPND W(I+1) Wi ndspeed--second set on card 8 TA(I+1) 9 Dry bulb temperature, of 10 TOO+1) Dew point temperature , of 11 HSO+1) Solar radiation 12 CC Cloud cover

13 RH Relative humidity

It should noted that the start of the heat and flowrate table does not necessarilybe have to correspond to the s�art of the meteorological input table. The time for the start of the heat and f10wrate table is del ayed by a variable TSKIP (HR) , described below. (4) Pond parameters and constants are read next in a NAMELIST format cal led INLIST. The variables in INLIST are described in Table 6.4. 6.4.2 Uti lization of Program UHS3 Program UHS3 is usual ly empl oyed to determi ne maximum pond temperature in the fol lowi ng manner:

(1) Two initi al pond simulations should be performed (in the same run): (a) The fi rst run simUlates the pond ambient temperature resulti ng only from meteorological inputs without the external heat load. This is most easily done by setting TSKIP to a large number of hours in INLIST (for example, TSKIP=5000). The peak ambient pond temperature and time of occurrence general ly wi 11 not be the same as those predicted from UHSPND.

36 Table 6.4 NAMELIST INLIST for Program UHS3

efault Variable valD ue Description

VZERO Pond vol umes , ft3- -if zero , termi nates program 0.0 BLOW Blowdown fl ow out, ft3/hr 0. 0 A Pond surface area , ft2 0.0 NSTEPS Number of timesteps to be performed 100 NPRINT Pri ntouts of pond temperatures every NPRINT 10 steps

DT Integration timestep , hours 0.2 TZERO Initial pond temperature , of 80 TSKIP Time after start of program that corresponds 0 start of heat and flow table. Shi fts thi s tabltoe relative to meteorology table which starts at time zero. For time less than TSKIP, evaporat ion is suppressed so that the pond vol ume does not decrease.

QBASE Bias to be added to al l HEAT in heat-flow table, 0 Btu/hr

FBASE Bias to be added to al l fl owrate in heat- flow 0 table, ft3/hr

E Constant equi i bri um temperature of, if so 80 specified by IME1 T=l

AK1 Constant surface heat exchange coeffi ci ent, 150 Btu/( ft2 day)/oF if IMET=l

IMET Opti onal constant E and AKI if IMET=l 0 BTA Bias to be added to al l TA in table (dry bulb 0 temperature), of

BTD Bias to be added to al l TO in table (dew point 0 temperature), of

BHS Bias to be added to al l HS (solar radiati on) , 0 Btu/(ft2 hr)

BW Bias to be called to al l in Table 0 (wi ndspeed) , mph W 6. 3

HEAT Same as Heat- fl ow table if different from that speci fi ed FLOW specified by previous input in NAMELIST HFT NH input in NAME LI ST HFT

Note : Mul tiple runs may be made by inserti ng several INLIST cards in succession. Only the variables which are di fferent from the previous namel ist card read are changed. The program termi nates setti ng VZERO=O . by

37 (b) The second simulation determines the peak pond temperature only froID TSKIP the effects of external heat input. This is done by resetting to zero , and specifying that E and AKl are constants namel ist INlIST (for example, IMET=l , TSKIP=O , AK1=120 , E=85 , TZEinR0=85 ). The choice of AKl and is somewhat arbitrary, but the initial pond E E. temperature TZERO should always be set equal to (2) A second run is prepared so that peak ambient pond temperature determined from the first simulation wi ll coincide wi th the peak excess temperature caused by plant input alone:

(a) By inspection of the two previous simulations , choose the model desired (for example, mixed tank) and the time of peak temperature for each.

(b) The approximate time to del ay the start of the heat input TSKIP is then defined:

TSKIP = time of peak ambient temperature minus time of peak excess temperature.

(d) Because of non1 i nearities in the pond mode1 s,·the peak temperature wi ll not necessarily concide with that of the direct linear superpositi on, and the time to the peak m� be shifted. Several simulations m� be made wi thin the same run , varying the parameters TSKIP by several hours to assure that the peak temperature has been found, although in general the differences should be minor.

An example run of al l programs from start to ·finish wi ll be covered in the next section.

38 SAMPLE CALCULATIONS 7. This section describes the analysis of a hypothetical UHS cool ing pond and shows how the computer programs and methods presented thi s paper can be used wi th hi stori cal weather records to determi ne the indes i gn bas is return temperature and worst-case 30-day evaporative water loss for a given pond.

The fol l owi ng i nformat ion is needed for computer programs UHSPND, COMET, and UHS3 order perform these analyses. in to (1) For UHSPND:

(a) Pond area and vol ume.

(b) Lati tude of the pond.

(c) National Weather Service data tape (TDF-14) for an observation Apo int near the pond site.

(d) Date the begi nning of onsite data col lection. of (2) For COMET: (a) Monthly averages for the months of May through September of onsi te observations of dai ly insolati on, dry bulb temperature , dew poi nt temperature ; and the monthly rms wi ndspeed. If onsite insolation is not avai lable, the offsi te insolation term generated by UHSPND can be used in its place as long as this fact is acknowl edged in the analys is of the results.

(b) Monthly averages as described above from the long-term (offsite) weather record for the peri od that corresponds to the peri od onsite meteorological observations. This information can be0-( obtai ned from UHSPND by using a monthly average card in the data deck.

(3) For UHS3:

(a) The punched output from UHSPND consisting of the meteorological parameters for the 40-day period that encompasses peak ambient pond temperature .

(b) heat-flowrate table describing the heat rejected by the pl ant and Athe flowrate through the pond during the period of time fol lowing a

. des i gn bas f s acei dent. . (c) Pond initial vol ume and surface area.

(d) Blowdown and seepage rates for the pond.

39 C 7.1 Finding the Period of Worst- ase Cool ing Performance and 30-Day E aporati e Water Loss--Program UHSPND v v The first step in the analysis is to use UHSPND to find the periods of recorded weather data that wi ll result in the worst-case cool ing performance (that is, highest pond temperature) and highest 30-day evaporative water loss. UHSPND can also be used at this point to generate the monthly averages of the meteorologic parameters needed run program to COMET. hypothetical pond located at 4O .25°N and having a surface area of 40 acres A(1 ,742 ,400 ft2 ) and a o ume acre"'feet (13,939 , 200 is used in this v l of 320 ft3) sample analysis. The long-term (1948-75) weather record from Harri sburg, used. limited onsite data from a faci lity located on the SuPennssquehyl vanannai a, Ri veris are used as the ons i te record for the hypothet i ca 1 pond.

The data deck for UH$PND has been constructed as described in Section 6. he T period o nsite data avai lable at the time of this study was January 1, 1973 , to Deceofmber 31, Since UHSPND only scans the weather record during the months of May through1976. September, the fi rst month of the long-term record for which onsite data are avai la le is ay 1973. Entering this month and year on b M a m nthly average card in the UHSPND data deck causes the program to print the montho ly averages necessary to run COMET for each summer month , begi nning with 1973 , unt i1 the end the long-term weather record is reached. . May of Figure 7.1 shows the data deck for UHSPND used for this example. The fol lowi ng information is printed by UHSPND as a :resu1t the data suppl ied in the data deck: of

(1) A list of the dates ignored by UHSPND due to periods of bad data in the long- term record.

(2) A l i st of the pond parameters used by UHSPND to run its pond model .

(3) A table of the yearly maximum modeled pond temperatures and 30-day evaporat i ve losses , thei r dates of occurrence and thei r lip 1 ott i ng positi ons. oth the temperatures and e ap rati e losses have been II B v o v ranked from highest to lowest magnitude and their sample means , standard deviations , and skews ha been calculated. ve (4) The dai ly meteorological data consisting of hourly observations for each day in the period of the 35 days ending wi th the date of the mOdeled pond temperature and 5 days fol lowi ng it. This informahitigheonst is also punched on cards as a result of usi ng and a message indicating the number the cards punched folloIPRNT=Ows the pri nted output. of No printed or punched output is pro ded for the days ski pped because of bad data. vi

(5) A table of the monthly rms windspeeds and mean values of dry bulb temperature , dewpoint temperature , dai ly solar radiation, cloud cover in tenths, and relative humidity for the months of May through September duri ng the period begi nning May 1973 and conti nuing to the end of the long-term record in 1975.

40 ,LAT.ltO.2S, ISRCHat , IpICN-..--a-s­ SINPUT N_Na10t , 0,A=1YR74MOO24Y00.(1)a, V=113,393920YRMO OY0.(2 ).5,LATa40.25S SINPUT SINPUT NaOS Figure Listing of Input for Program Ul 1.1 TSN K.

A partial listing of the output gen-era ted by UHSPND in thi s e}

The stati stical methods of frequency analysis using Pearson type coor­ dinates , outl i ned in Appendix A, have been appl ied to the sample III of year ly maximum pond temperatures in order to gai n some insight into the trend in the data. The histogram in Figure 7. 3 gives some idea of the distribution of the yearly maximum temperatures. A frequency plot of the yearly maximum tempera­ ture data is presented in Figure 7.4. Here the temperatures were first plotted on arithmetic-probability paper usi ng the exceedence frequencies (plotti ng positi ons) computed by UHSPND. Next, the most likely probability curve and the 5% and 95% error bands were constructed from the mean and standard devi ati on computed by UHSPND and the methods and tabl es of Appendix A.

Note that the skew was taken to be zero because of the smal l size of the sample. The computed frequency curve can be used to extrapolate the 1% per year ambient exceedance pond temperature from the UHSPND results. This temperature is found to be 85.5° F. Since this is less than the maximum modeled temperature of 85. 7° F, no temperature correction factor wi ll be in subsequent calculations. Note , however, that the maximum fal ls within usethed 5% and 95% confidence limits and is not considered anomalous. These stati stical procedures can also be applied to the sample of yearly maximum 30-day evaporative loss. The predi cted loss is 992 ,000 ft3 • Agai n, the modeled maximum evaporative loss of 1,023,650 ft3 is larger than the 1% per year exeedence loss found by extrapolation and no correction wi ll be made for this in subsequent evaporation calculations.

7.3 Determining the Appl icabi lity of the Offsite Data Set--Program COMET

There is a potential for error because of the use of an offsite data record. The second step in the cool ing pond analysis is to compare the offsite record with the limited onsite record and generate some reasonable correction factors a significant difference exists between the two records. Program COMET usedif for this task. is

COMET compares equilibrium te�peratures generated from the monthly arithmetic mean val ues of dew point, dry bulb temperatures , dai ly solar radiation, the root mean square ( rms ) wi ndspeeds from two different sites. The rms wiandnd­ speed is used as the representative average because of the quadratic function of wi ndspeed in the model equations. This information is input to COMET in the form described in Section 6, one month per data card. In this case , a period of 15 spring and summer months , May 1973-September 1975 , was available for study. The offsite information was input as set 1 and the onsite information

41

• u.s. NUC L E A REGULATO Y COMMISSION- ULTIMATE A T SINK COOLING POND METEOROLOG ICAL SC ANN I NG MODEL R C O D E ll A N DR W � 1979 HE NUTTlE" NOVEMBER

********** S UBR OUTINE SUBt HAS BEEN C A LLED F O R LATIT UDE 40.25 D EG. ***** • NOR TH DISCONTINUITY IN DATA CAUSED 6/11/71 TO 8E SK IPPED DISCONTINUITY IN DATA C A USED 9/25/71 TO SK IPPED OISCONT INUITY I N D A T A CAUSEO 51 5/72 TO 8E SKIPPED BE DISCONT INUITY I N DATA CAUSED 51 6/72 TO 8E SK IPPED DISCONTINUITY IN DATA CAUSED 51 1112 TO SE SK IPPED DISCONT INUITY IN DATA CAUSED 51 8/72 T O BE SK IPPED DISCONT INUITY IN DATA CAUSED 8 1 7/72 TO HE SK IPPED' T N UIT Y DATA CAUSED 7/11/73 TO SK IPPED DIDlsSCONTCON INUII TY IN D A T A CAUSED 7/15/73 TO BESE SK IPPED DATA CAUSED 7/1&/73 ·TO HE S� IPPED DDISISCONTCONTININUITY IN CAUSED 7 /17/73 TO BE SK I PPED DATA DIS CONTINUITY IN DATA CAUSED 51 t/75 TO BE SK IPPED

POND HAS FOLLOWING � * ********* NUMBER 1 THE PARAMETERS ************************* I\) SURF ACE ARI A 1742400.00 FT**2 ( 40.00 ACRES)

VOLUME 1393Q200 .00 FT**] ( 320 .00 ACRE-FT)

ISRCH IPRNT ;; = 0

********** P O ND NUM8ER \ HAS BEEN MODELLEO TO OETERMINE THE wORST ************* PERIODS FO� COOL ING AND EVAPO RATIVE WATER LOSS

Figure Output From Program UHSPND. 7.2 ********- * THE SAMPLE OF V R Y MAXIMUM POND TEMPERATURES AND 3 0 DAY E A L *****-**** EVAPORATIVE BV THIS MODEL IS DESCRIBED BELOW • LOSSES GENERATED

• • • • •••• ••TfM PERATUR E • • • • •• ••• • ••• • • • • • EVA'ORA TIVE O 8 •••• ••• • � � * EXCEEDED D A TE EX D L S * /100 VR* *CVR. MO . DV.'* /l0CEE0 DYRE * DATE * F T u] * CYR. MO .DY.,* ••••••••• • • •CDE• • G.F)•••• • ••• • • ••••• ••• • •••••••••••• • • • •••••••••••• ••• • • * 2.45 * 85. 71 * * * 72. 7 . 2 3. ·l.4S .. * & ... * 5.9 * * 5.97 * 109 2434 8 61U.. 95 * 63. 1.7.23.10. 7 83. 50 .. 75. 3. * 8. 6 * * 9.49 * 83.15 * 52. 7 .23 - 9.49 * 043 7 1 . 5 * 55. 13.01 * 8 2.1te! * 68. 7.1'.. .. 1 . 0 9 51 . 8.7 97 . • t .. . . 1".'54 8 2 . 0 * 4 9 . 7 . 0. * t".53 4 .. 881870331364.3.8 * 74. 7.222 . * * .. 0 3 * - * 20.0& * 8 t.85 * 71. 7.10. 20,.06 - 8 7 0 2 . 1 - 71. 7 .28. U . - - 23.'58 - 81.29 * 57 . ".18. - 2 3.5 8 - 8 64591.4 * 54 . 8 .1l. - 27.10 - 81.15 - "4. 7.20. .. 27.tO 8551 4 2.4 - 61 . 7.12. - • - 30. & 3 .. 80. 9 8 - 63. 7. l. * 3 0 . ft 3 - 83,,959. 1 - 65. 7. 9. ..* * 34.15 * 80.90 - 59. 7. 1. - 3 4 .15 * 836561.6 * 62. 7.l7 . 8 * * J7 .&7 * 80.84 - 70. 8. l. - 37 .67 - 8261 2.2 - 7 . 9. - 41. 19 - 80.46 71. 7. 1. * • 823344.4 * 53S9. * * 41 .t9 9.13. 44.72 * 80.44 * 61. 7.l5. IUI.72 * 801589.5 64. 6.17 . • * * * 48 .24 80 . 38 48 . 8.29. * 48 . 24 * 9 4 7 0 . 2 * 73. 6. * • 7 5 8. • 51.7& * 80 .30 • 7 . 2 1. * 51 . 7 ft * 7 837 l 0 . 5 * 7 3 1 . � • * I;] 68. • w 55.28 * 2 * 70. 8.. 3 . * 55.28 * 8 0.l * 55. 7.l8. 7 5 . 7 1 * 5 * 8 40 * * 80. 12 * ft 5. 8.1 8 • 58 .81 * 764858 .0 60. 7. * 58 .81 • * ft . * 62.33 * 7 9.91 * 7 4 . 7 . 9. ft2.3] * 7 63910.1 - 56 . 7.15. * - fl5.8 S * 78.99 * 51. 7.11. * 65.85 * 754 " 8 2.3 7l. 8.l1 . * .. • 69. J7 • 78. 68 fl6• fI .2" . * fl9 .37 * 7 5 3 8 61 .1 * 7.l9 • * * • * 72.9 0 - 18. 42 - 61 . fI.211. * 7l.90 - 141 111 .9 " 5l75.. 8'.19. * * * 7 6.42 3 . * 1ft. 42 78.l3 "9. 7 . 1 . * 7]9849. fI - 51 . * - 7 9 .94 8. 9 5 0 . 8. 8 * 7 9.94 * 73"522.0 - 58 . 6.18.8. _ 7 * 3. - * 1 1 83.4" * 735030.0 - " 7 . 7 . 6 . .. 83.4& 17 .92 .. flO. 9 • . * - . 9 7 .88 58. 728814.0 * " 9. . 1 9 . * 9 - 7 7. 8. * 8".99 - " - 86 * - 90.51 * 7 1 . 6 * 6l. 8. * 90.51 - 7U320.1 * 4q . 6.23 . 8 * 5 0. * * 9 4.03 * 71.08 * 54. 7.37 . 1. * 94.03 * 6 9124 4.7 * 7. 3. .. * . 7.29 • * q7 . '5 C; * 7 " . - 5ft . 1!.18. • cH .55 "7 1605.5 * 48 8 • • • •••• • • • ••••• • ••••• • •9 •••••• •••••••• • •••••••••• ••••••••••••••• • •

ME AN 80.22 80]913.5

802qf>.12 SUf\40ARO OEV. 2.089

.113 SKEw .545

Figure (Continued). 7.2 • ••• •• 6 /1�/72 • ••••• •••• METEOROLOGY FOR *.* •• *****.***************************

• ••••• •••••••••••••••••••••••••• •••••••••••••••••••••••••••••••••• ••••• HOUR' , WIND SP .,DR Y BULB , EWP OINT ,SOLAR RAD CLOUD ,RELATIVE , D ,BTU/FlUO, COVER ,HUMI DITY , (MPH) (DE G.Fl , (DEG.Fl • ••••••••••••••••••••• •••••• •••• ••••••••••••••••••••••••••••••••••••••• O. 1.� 71.3 66.3 0 .0 , 1 .00 84.0 1 . 0 . 0 7 1 . 0 66 .0 0 . 0, 1.00 84. 0 2. 1.5 71.0 66 .0 0 . 0, 1.00 84. 0 3. 3 .1 , . 71.0 66.0 0.0 , 1 .00 84.0 4. 4 .6 71.0 66.0 0.0 , 1.00 5 . 5 .0 71.3 66.7 134.6 , 1.00 8854.0.0 ,. 6 . 5 .4 71. 7 67 .3 406.2 , 1.00 86.0 5.8 72.0 68.0 677. 8, 1.00 8 7 .0 7.8. 5.8 73.7 68.0 � 3 1.0 , 1.00 82. 7 9. 5.8 75.3 68.0 ,· 1148.3 , 1 .00 7 8.3 10. 5.8 77.0 68 .0 1315.1 , 1 .00 74.0 11. 6.9 78.7 68.7 1759 . 8 , .93 7 1.7 12. 8 .1 80.3 &9 .3 2128.5 , .87 6 9 .3 , 13. 9 . 2 82.0 , 70.0 2369 .2 , .80 67 . 0 1 4. 8.8 82.3 70.0 2321 .8 , .77 6�. 3 15. 8.4 82 .7 70.0 2134.0 , .73 65.7 1 6. 8.1 83.0 70. 0 1812.7 , .70 65.0 t 17. 8 .1 8 2 .0 69.7 125 9.7 , .73 66 .3 18. 8 .1 81 . 0 69.3 717. 2 , .77 67 . 7 lQ. 8.1 80.0 69. 0 �24.6 , .80 6Q. O 20. 8.1 78.0 67 .3 0.0 , .63 6�. 7 �l . 8.1 76.0 &5. 7 0.0 , .47 7 0.3 22. 8.1 74.0 64.0 0.0 , .30 71.0 23. 7 .7 73.0 64.0 0 .0 .20 7 3.7 , • ••• ••••••••••••••• • •••••••••••••••••••••••••••••••• •••••••••••••••••••

Figure (Continued). 7.2 ********* * METEOROLOGY FOR �/20/72* ***************** •• * ••• **************** ***•

••••••••••••••• • • ••••••••• •••••••••••••••••••••••••• •••••• ••••••••••••• HOUR , WIND SP.,DR Y BULB ,DEWPOINT ,SOLAR RAD CLOUD , , (DES.F) ,8TU/FT2/D, COVER ,R,HELU MIATIVDITYE , (MPH) (DES.F) • ••••••••••••••••••••• •••••••••• • • • •••••••• • •••••••••• •••• ••••••• •••• •• O. 7.3 72.0 64.0 0.0 , .10 76.3 t. 6 .9 71. 0 64.0 0.0 , 0.00 7 9 .0 2. 4.6 10.3 �4.3 0 .0 , . 2 7 8 1 .7 3 . 2.3 69. 7 64.7 0.0 , .53 84.3 4. 0.0 �9.0 65.0 0.0 , .80 87 .0 5. 3.1 70.3 65.7 213.4 , .83 85.3 6 . �.I 7 1.7 66.3 595.8 , .87 83. 7 7. 9.2 7 3.0 67 �0 918.4 , .90 8a.O 8. 9.2, 74.3 61 .3 1 154.7 , . 93 7 9 .3 9 . 9.2 75.7 6 7.7 .97 76.7 9 . 2 7 1.0 68.0 1 2883 .74 , 10. 1 5 . 1.00 11. 10.0 78.0 67 .3 14201 .2 , 1.00 74.070.0 10. 7 79.0 1.00 � 6.0 12. 66. 7 145 5.' , 13. 11.5 80.0 �6.0 1420. 2, 1.00 �2.0 14. 10.1 19.1 66.3 1315.4 , 1.00 63.1 T .. Con 1 0 .0 7 9 .3 6 6.1 114 8.8 , 1.00 65.3 15. 9.2 79.0 61 .0 931 .1 , 1.00 �7 .0 . 17.16. 10.7 . � 78.8 , 1 .00 6 9 .3 , 1 8 . 12.3 771.08.0 �677 .0 407 . 5 , 1.00 11.7 7 6 0 67 .0 3 . , 1.00 74.0 13. 8 . 1 � 2019.. 12.3 75.3 67 .0 0.01 , 1 . 00. 7 5.7 21 . 10.7 74.7 67 .0 1.00 77 . 3 , 0.0 , 22. , 9.2 74.0 6 7. 0.0 , 1.00 19.0 23. 11.1 74.0 66.70 0.0 , 1 .00 78.0 • ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••

Figure (Continued). 7.2 OUTPUT FROM PROGRAM UHSPND FOR THE PERIOD 6-21- 72 THROUGH 7-28-72 HAS BEEN OMITTED BECAUSE OF ITS LENGTH

********** ME TEOROLOG Y FOR 7/29/72* ***** *** ***** **** **************************

••••••••••••••••••••• • • • • • • • • ••• ••• • ••••• • • • • • • • • • • •••••••• • • • • ••• •••• • HOUR , WIND SP . , DRY BULB , DEWPOINT CLOUD ,RELATIVE , (DEG.Fl , (DEG.F) ,S,BOLARTU/F TUDRAD , COVER , HUMI DITY ,

• • •••••••••••••(MPH••••) • • • • • • • • ••• • • •••••••••• •••••• • • ••• • ••• •••• ••• • • ••• • • O. 0.0 61. 3 56.0 0.0 , .07 83.0 1. 0.0 60.0 56.0 '0.0 , 0.00 17 .0 . 5IJ.3 55 .7 11 . 0 2 • l.q . 0 , .07 0 3. 3.8 5 8.7 55.3 0.0 , . 13 8q.O 90. 4. 5.8 5 8.0 55.0 0.0 , . a o 0 5. 5.4 Sq .7 5 6.0 68. 0 , . 33 88.0 6 . 5.0 6 1.3 57 .0 726.0 , . 4 7 86.0 4.6 63.0 58 .0 , . 60 8 4 . 0 7 . .5 8 . 5.0 65.0 57 . 3 un , .73 77 .0 5.4 67 .0 5 6.7 152012.77 , 7 0 . 0 . . .87 \0.9 5 . 8 6q.O 56.0 1 00.6 , 1.00 63.0 .J:Io 5.0 7 . 7 5&.3 2 58 .7 0'\ 11. t 1617.2 , .q] 4.2 74.3 56.7 12. 14J(' 0 . 1 , .87 54.3 .80 13. 3 .5 77 . 0 57 .0 2177.3 , 50. 0 14. 2.3 56 .7 2 0 3.2 , . 80 , 48.0 78.07 56.3 0 . 8 0 46. 0 1"i. . 2 9.0 1726.3 ·, 1 8 44. 0 lb. 0.0 80.0 56 .0 1365.3 , . 0 3 56 .3 828 .1 47 .3 17. 0.0 78. , .87 18. 0.0 7 6.1 56.7 366.8 , . 9 3 50.7 0.0 75.0 57 .0 25.7 , 1.0 0 54.0 19. 5.0 5 0.0 1.00 5 3.3 20. 0 . 0 7 6.7 , 21. 0.0 75. 0 5& .3 0.0 , 1.00 5 2 .7 22. o�o 75.0 5 6.0 0.0 , 1.00 '2. 0 6 23. 0.0 71.7 C;& .7 0.0 , . 93 0 . 7 • • • • • ••••••• • •••••••• •••••••••••••••• • • • • •••••••••••••••• ••••••••••••••

*** *** *********** ******* * ***** *** * ****** * * ********III UMBER OF C.RDS PUNCHED :II 492

Figure (Continued). 7.2 • • •••••••• T"E MONTHLY AVERAGE VALUES FROM 51 1/7 3 TO OF DATA •••• •••••••• • END

••••••••• • • • •••••••• • • ••••••••• • • •••••• ••• ••••••• ••••• •••• ••• .DRY .DEWPOINT . SOLA R * RMS WIND BULB • CLOUD .RELATIVE . * SPEED • (DEG .F) • *RADIATION. COVER (DES .F) .HUMIDIT Y . 1973 •••••• ••••• ••• •••••• • •••••••• • ••• ••••••••••• •••••••••• ••••••• • • • • • • • * 57 .38 • 47 .1& • 1 3 81.& . .&8 72.0 MAY 8.91 • * • " * • * * * • JUNE &.12 .• 12.19 • 62 .&1 166 2.5 .&1 73.1 * • • * • * • * • * * • * 6.4 3 * 76.14 * 63.78 * • 61.1 JULY. 1888.2 .4& * • * • • • • * * 5.90 * • 64.59 1 54'. ' * .52 • 11. 2 AUGUST * 75.3 8 * * • • * * • • • SEPT E"'BER * 7.1l * 67 .87 * 55 .9.! * 1309.3 * .51 • 68. 0 • -,. * • • • • • • 197 4 ••••••• •••••••• • ••••• ••••••• • •••••••• •••••••••••••••••• • ••• •• * • • • * • • 8 .61 • 63.41 * 4&.71 * .57 * 56.8 * M A Y * • 165 3.4 * • * * * • • * * 70.60 • 57 .27 * 1687.0 * .61 • 6 4 .1 • -1=00 JUNE 1.5 9 ....., • • * • • • • * 77.27 * 5 9.89 • 17&6 .7 . 51 * 57 .6 • JULY * 7.5 4 • * * • * * • • * 5 . 74 76.47 * * .62 • * AUGUST • * 63.89 1 386 .5 66.3 • * * * * • • 7.46. 64.24 * • 119 9.1 * .62 • • SEPTE"'SER � * 55 .62 15.1 * • • * * • • 197 5 • • • • ••••••• ••••••• ••••••• •••••••••••••••••••••••••••••••••••• * • • • * * * • 64.14 • • 56 .1 * • * �AY 6.bS • 55.96 1 3 .6& 7&.2 * • • • * • • JUNE • 1.61 • 70.51 • 62.24 • 1636.& . . 58 • 7 7.0 • * • • * • * • * 6.84 * 15.01 66. 34 • 1750.1 * .50 * 7 .7 • JULY * * * • • * • & • • 6.15 • • &&.77 1517.8 .60 • 11.7 * AUGUST 75.12 • • • * • * • • • * 1.31 62 .82· . 56 .25 7 .4 • .&0 • * SEPTEM8ER * • 11 3 81.3 * • • • * * • • ••• • ••••• • • ••••••• ••••••• •••••• • ••••• ••••••••••••••••• • • • • • •

Figure (Continued). 7.2 ' 8 � w a:: � 7� etC a:: w 6"- ���<.J WW I- Q,. I- tn 5� W etJ:O

a:: . : . a:: : ': et Z w- ': : " . >i= 31- . . LL,- 0 tn3: 2 a:: et ...:. wIn 3: ...: � 1,­ � Z 7-,0 7SO 82 83

MAXIMUM POND TEMPERATUR ES, YEARLY o f

Figure Yearly Maximum Ambient Pond Temperatures. 1.3

as set 2. The latter record lacked two of the parameters needed , solar radia­ tion and dew point. The onsite information did include wet bulb temperature observations which al lowed calculation of dew point temperatures using sub­ routine PSY1 presented in Appendix B. The synthesized solar radiation values from the offs ite record provi ded by UHSPND were substituted for the onsite solar radiation. copy of the input fi le for COMET is shown in Figure Output is generatedA by COMET for each data card containing monthly average1. 5.s. This output consists of the fol lowing information:

(1) Monthly meteorologic averages as input for ea ch.

(2) Calculated monthly average equi librium temperature and evaporation.

(3) Differences between the average equilib rium temperatures and evaporations of the two data sets.

(4) Component differences in the equi librium temperature due to each meteoro­ logical parameter.

In addition to this output , the fo l lowing information is printed once al l the monthly data have been read: of

(1) Coeffi ci ents of determi nat ion r 2 for the equil i bri um temperatures and evaporations.

(2) Biases between the two data sets for the equi librium temperatures and evaporations.

48 900�------,

/' r:r;" / « MODELED TEMPERATURES A w > J: 1- CALCULATED POINTS o � 86° w a; o u.

I I I I I I I I I I I I I I I 99 95 0 80 70 60 50 40 30 20. 10 5 2 1 .2 .1 98 9 EXCEEDENCE PROBABILITY, PERCENT

Figure Yearly Maximum Ambient Pond Temperatures, Maximum Likeliho 7.4 od Frequency Curve, and Error Bands. 0.05 0.95 A copy of the COMET output generated for thi s example is presented in Figur� 7. 6. Tlie correlation coefficient for the two sets of equi librium temperatures is high (0.976) , indicati ng that the predicted effects of the offsite meteorology on the hypothetical pond's temperature correlates closely wi th the effects that wou ld have been produced by onsite meteorology had that been avai lable. This correlation is shown graphical ly in Figure 7.7.

The positive bias between the onsite and offsite equi librium temperatures indicates that the onsite 'equil ibrium temperatures are , on the average , higher than those predicted using offsi te meteorology. The primary reason for this bias is indicated from the differences due to individual meteorologic parame­ ters. Onsite wi ndspeeds are smal ler, which leads to lower evaporation and cool ing. This effect is partial ly offset by higher dew point and d� bulb temperatures onsite.

The positive (onsi te-offsite) temperature bias wi ll therefore be used as a temperature correction factor in subsequent calculations. Evaporation is on the average , higher for the offsite data , however, and no negative correction factor wi ll be applied.

7.4 Final Desi gn Basis Pond Temperature and Water Loss Computa' tions-- Program UHS3

The final step in the cool ing pond analysis is to combine the results of the programs COMET and UHS3 run from data provi ded by UHSPND, and the results of the manual statistical analyses to obtain a maximum water return temperature . Pond water loss is conservatively calculated manual ly.

Fol lowi ng the procedure of Section 6, two runs of UHS3 are made. The first run performs two simulations:

(1) Calculate the pond temperature in response only to the meteorologic variables with no emergency heat load.

(2) Calculate pond temperature in response only to heat load.

The input deck for the first run is shown in Figure Notice that in the 7.8. ' first INLIST input, TSKIP is set to a large time (5000 hours), to bypass the heat input table. The starting val ue of temperature TZERO is n�ncritical for this step and is set to 80°F. In the second INLIST input, TSKIP is reset to zero , and the val ues of K and are chosen on basis of experience to be 150 Btu/(ft2 day)/oF and 90°F, respecE tively. Notithece also that should be set equal to E which is 90°F. TZERO

The output from the first run is shown in Figure 7.9. If the mixed-tank model is chosen, the peak ambi ent pond temperature wou1 d be occurri ng 833 hours after the start. This is plotted graphical ly 86in. 32°Figur F e The analysis would be similar if either the strati fied- or plug-fl ow mode7.10.l had been chosen. The peak temperature due to pond heat load only would be or a rise of 18.8°F above the starting temperature of 90°F, and occurri10ng8. 8°F 191.6 hours after the start. This is plotted graphical ly in Figure at 7.11.

50 PROGRAM COMPARE EQUILIBRIUM TEMPERATUR ES FROM TWO DATA SETS A ND COMPUTE THE SENSITIVITY OF fACH VARI ABLE , TO

DEW POINT DRY BULB WIND SPEED S OLAR R AD . EQUILIBRIUM T E M P. E VAPORA lION (DEG. F) (MP H ) (BTU/FT**2/DY) (DEG. (FT**3/FT**2) F)

DATA SET 1 47. 2 0 8.tH 1381 .60 &4.80 .44 57 . 40

D ATA SET 2 4& .80 53.80 5.48 1381 . 60 & 6 . q q . 38

E2-£' 1 2.1q7 EVAP2-EVAP1 = II -.06

DIFFERENCES IN E BETWEEN DATA SET 2 A N D DATA SET 1 BY PARAMETE R

DIFFERENCE DEW DUE TO POINT • -.155 DEG . F DIFFERE NCE R Y DUE TO D BULB TEMP . = -1 .200 DEG. F DIFFE RENCE DUE T,O W INO S P EED . 3 . 48 1 DEG . F DIFFERENCE D U E TO INSOLATION . . 0 DEG. ,SUMMA TION OF INDIVIDUAL DIFFERENCES = 2.00126 DEG. F

� ******************************************************************************* ****************************** �

DEW POINT DRY BULB WINO SPEE D SOLAR RAD. EQUILIBRIUM TEMP . EVAPORATION (OEG. ( MPH) (BTU/ FT**2/DY) (DEG. F ) ( F T**3/FT**i!l F)

D ATA SET 2 . 70 72.80 & . 12 1 & 62 . 50 80.88 .Sq 6

DATA SET 2 1 . 3 0 67 .50 3.q O 1&62.50 81.11 . 5 3 6

E2-El EVAP2-EVAPt - . 0 & • .228 =

DIFFERE�CES IN E RETWEEN DATA S£ T 2 AND DATA SET 1 BY PARAMETER

DIFFERENCE DUE TO DEW PO I NT DEG. = -.&52 F DIFFERENCE BUL� -1 .244 DEG. F DUE TO DRY T EMP • • DIFFERENCE DUE TO WIND S PEED DEG . c 2.081 DIFFERENCE D UE INSOLATION F TO = DEG . F SUMMA�ION OF INDIVIDUAL DIFFERENCE S -.000 DEG. F = .18'5

Figure Output of Program COMET. 7.6 ***************** *********************************************************** .****** *************** ***********

DEW POINT DRY BULB WIND SPEED SOLAR RAD. EQUILIBR IUM TEMP . EVAPORATI O N F) ( M P H) (BTU/FT**2JDY) (D EG. F ) (FT**3/FT**2 ) (OEG.

DATA SE T 1 63.80 6.43 1888.20 83.54 .6q 16.10 DATA SET 2 63. QO "'7 . 80 3 . 70 1 888. 20 84.58 '5 q /' •

E2-E l . 1.0 46 -.t o EVAP2-EVAPI •

DIFFERENCES I N E BETWEE� D ATA SET 2 AND OAT A SE T 1 BY PARAMETER

DIFFERENCE DUE TO DEw POINT .04 6 DEG. F = DIF FERENCE DUF DRY BUL� TEMP. = -1 .856 OEG. F TO DIF FERENCE DUE TO W I ND S PEED = 2.770 OEG. F D IFFERENCE DUE TO INSOL ATION . .000 DEG . F DIfFERENCES SUMMAT ION OF INDIVIDUAL = .q60 OEG. F

� **************************************************** ******** ************************************************ * �

DEW POINT DRY �IND SPEED S OLAR RAD. EQUILIBRIUM TEMP. EVAPORATION .(OEG. F) BULB ( MPH) (BTU/FT**2/DY) (DEG. F) (FT**3/FT**2)

7 DAT A SET 1 6 4 . 6 0 7 5 .40 '5.QO 154 Q.QO 81. 2 .56

DAT A SET 2 64 .80 6Q.4 0 3.20 lS4 Q .QO "2.72 .09

E 2-E l. EVAP2- EVAPI • 1.00t -.07

DIFFERENCES IN E BETwE E N DATA SET 2 AND DATA SET t BY PARAMETER

DIFFERENCE DUE TO DEW POINT • .09Q DEG. F DIFFERENCE OUE T O DRY BULB TEMP. -1 .381 OEG . = F DIFFERENCE DUE TO WIND SPEED 2.231 DEG . F = DIFFERENCE DUE TO INSOLA TION = .000 DEG. F SUM MATION OF INDIVIO�AL DIFFERENCES = .Q4Q OEG. F

Figure (Continued). 7.6 ***** * * ***** ******************** *** ************* ***** * * *** *********************** ****************************

DEw POINT DRY B ULB wIND SPFEO SOLAR RAD. T EMP . EVAPO RATInN (OEG. F) ( MPH) (BTU/FT**21DY) EQUILIB( DEGRIU. FM ) (FT**3/FT**2)

DA TA SET t 5 '5.90 &7 .90 7.3 1 3 0 9 . 3 0 72.45 7 .47 DATA SE T 2 54.70 60.40 4.00 1309.30 72.75 .38

E2-E l .30 6 EVAPi!-EVAPI -.09 • •

DIFFERENCES I N E BETWEEN DATA SET 2 AND DATA SET 1 BY P ARAMETE R

-. 530 DIF FfRENCE DUE TO DEW POINT • DEG. F DIF FERENCE DUE TO DRY BULB TEMP -2. 123 DEG. F .... •• DIFFERENCE DUE TO WIND SPEED = D EG . F DIF FERENCE DUE TO INSOL ATION = 2.8. 00063 DEG. F SUMMA TION OF INDIVIDUAL DIFFERE NCES . .21 1 DEG. F

� ***** *** ***** ********************** * * * *** *** ********* ******** *************** * * *********** ******************** �

DEW POINT DRY WINO .SPEED SOLAR RAD . TEMP . EVAPORATION (OEG. BULB (MPH) (BTU/FT**2IDY) E QUIL(DIBEGRIU. M (FT**3/FT**2) FL F)

DA TA SET 4 6.70. 63. 5 0 . & 1 1&53.40 69. 11 . 59 8 DATA SET 2 45.00 56.70 5 .&0 1&53.40 69.98 .49

E 2-El .8&7 EVAPi!-EVAPI -.10 • •

DIFFEHENCES IN BETWEEN DATA SET 2 AND DATA S ET 1 BY PARAMETER E DIF FERENCE DUE TO DEW POINT • DEG . F DIFFER ENCE DUE T O D RY RULB TEMP -.572 • • - 2. 107 DEG. F DUE DIFFERENCE TO WIN D SPEED • 3.432 DEG. F DIFFERENC E DUE INSOLATION . -. 000 DEG . F TO SU�MA TION OF INDIVIDUAL DIF FERENCES = DEG . F .753

Figure (Continued). 7.6 •••••••••••••••••••••••••••••••••••••• **••• *.***.*. * •• ****.*.*.**.*.*****************************************

D EW POINT DRY BULB WINO SPEED SOLAR RAD. EQUILIBRIUM TEMP . EVA PORATION ( DEG. F) ( MPH) (BTU/FT**2/0Y) (OEG. (FT**3/FT**i!) F)

DATA SET 7 . 59 1 & 87 . 00 57 .30 70.EtO 76.58 .ft1 DATA SET 2 54.50 &3. 10 1&87 .00 7&.47 . 52 4.80

E2-El . - .103 EVAP2-EVAPl -.09 •

DIFFERENCES IN E BETWEEN DATA SET 2 AND DATA SET 1 PARAMETER BY DIFFER ENCE DUE TO DEW P O N T -1 . 1&2 OEG. I E DIFFER E N CE D UE DRY TEMP -1 .941:1 . F TO BUL8 • • D EG F DIF FERENCE DUE TO WIND SPEED OEG. • 2 DIF F ERE N CE DUE TO I NSOLATION . 2.9.0000 DEG . F SUMMATION OF INOIVIDUAL DIFFERENCES . -.1 91 OEG . F .******.**********.*********.********************************************************************************

OEW POINT DRY BULB WIND SPEED SOLAR RAD. EQUI LIBRIUM TEMP. EVAPORAT ION (OEG. F ) (MPH) (BTU/FT* *2/DY) (DEG. (FT**3/FT* *i!) F)

DATA SET 1 '59.90 7.54 17&& .70 7 9.99 .70 77.30 SE T 2 59 .90 4 .12 1 7 && .70 81.4'5 OUA &8.40 .57

E 2-El . 1.4 &3 EVAP2-EVA Pl -.13 :I

DIFFEREN CES IN E BETWEEN �ATA SET AND DATA SET 1 BY PARAMETER 2 DIFFERENC E OUE TO DEW POINT . DEG . F D IFFERENCE D UE DRY BULB TEMP - 2.1.05200 DEG. F TO •• DIF FERENCE DUE TO WIND S PEED : 3.489 DEG . F DIFFERENCE D Uf F TO INSOLATION . -.000 DEG. SUMMATION I N DIVIDUAL = DEG. OF DIFFERENCES 1.3 37 F Figure (Continued). 7.6 * * * **** ******* **** **** ******* *** **************************** ********** **************************************

OEW POINT BUL B WIND S P EEO SOLAR RAO. EQUILI BR IUM TEMP . EVAPORATION DRY ( MPH) CRTU/FT**2/0Y) ( DEG . (FT**3/FT**2) (OEG. Fl F)

DATA SET 1 7 &.50 1386.50 80. 4 5 .52 63.'0 5.7'4 DATA SE T 62.40 68 .00 3.3' 1386 .50 7'.53 .44 2

E2-E l . -.91' EVAP2 -EVAPl -.08 •

DIF FERENCES IN E BE TWEEN DATA SET A ND DATA SET t BY PARAMETER 2 DIF FERENCE DU� TO DEw POINT = -.72' OEG . F DIFFERENCE DUF TO DRY Blll B TEMP . = -2 . 020 DEG . F DIFFERENCE DUE TO SPEED OEG WIND • 1.1 86 . F DIFFERENCE DUE TO INSOLATION 0 0 0 DEG . 11 - F SUMMATION OF INDIVIDUAL DIFFERENCES = -.9. 63 DEG. F

(It (It ************************************************************************************************************

DEw POI NT DRY BULB WINO SPEED SOLAR RAD. EQUILIBR IUM TEMP . EVAPORATION (DEG. F) ( M PH ) (BTU/FT**2/DY) (DEG. F) (FT**3/FT**2)

OATA SE T 1 55.60 64.20 7.46 1 70 70.25 .41 n'. DATA SET 58 .50 4.18 119 '.70 7 0.22 2 53.20 .34

E2-El -.03 1 EVAP2-EVAPI - .06 11 •

DIFFERENCES IN E BETWEEN DATA SET 2 AND DATA SET 1 BY PARA METER

DIFFERENCE DUE TO D EW POINT = -1 .085 DEG. F DIFFERE NCE DUE T O TEMP -1.680 D E G F •• . DIF FERENCE DUE TO DRYWIN D BULBSPEED 2.664 DEG. • F DUE TO INSOLATION . -.000 DEG . F DIFFERENCE DIFFERENCES . SU�MATION OF INDIVIDUAL -,100 OEG. F Figure (Continued). 7.6 '****************************************************************************** *******************************

DEW POINT DRY BULB W IND S PEED SOLAR RAD. EQU ILIBR I UM TEMP . EVAPORATION (OEG. F) (MPH) (BTU/FT**21DY) F) (FT**3 /FT**2) (OEG. .

DATA SET 1 56.00 6 4.70 .6. 65 156 3.70 74.47 .51

DUA SET 2 53.60 &1.00 4.36 156 3 .70 74.78 . 47

E2-E l z 3 09 EVAP2-EVAPI - .04 • •

O iFFERENCES IN E BETwfEN DATA SET 2 AND DATA SET 1 8, PARAMETER

i' D IFF EHENCE TO POINT z -1 .014 DEG. F DIFFER ENCE DUE TO DEWR Y BULB TEMP -.998 •• DEG. F DIF FERENCE DUE TO DWIND S P EED DEG. F • 2.278 DIFFERENCE DUE TO INSOLATION = .000 DEG. F SUt.1MATION OF INOIVIDIJAL DIFFERENCES . .2&& DEG. F tn ****************************** � **************************************************************** ************** '

DEW POINT D RY 8ULY WIND SPEED SOLAR RAD. EQUILIBR IUM TEMP. eVAPORATION (OE G. (MP H) (BTU/FT**lIDY) (DEG . (FT**3/F T**2) F) F)

DATA SE T 1 &2.20 70.60 7.6 1 163&.60 78.42 . 57 SET 2 59.90 65. 70 4 . 53 1636 .&0 79.24 .51 OATA

V A P 2 E V A P1 • 0 6 E2-E l - - • .815 E .

DIFFtRENCES IN E BETWEEN D ATA SET 2 1 B Y PAR AMETER AND DATA SET DIFFERENCE DUE TO DEW P O NT -1 .090 DEG . F I • D I F E R E N C E DUE T O D�Y BULB T E M P -1 .204 DEG . F F • • DIFF ERENCE DUE TO WIND SPEED • 3.031 DEG . DIFFERENCE DUE TO INSOLA TION = .000 DEG . F SUMMATION OF INDIVIDUAL DIFFERENCES . .737 D E G. F

Fillure 7.6 (Continued). ***�********************************************************************************************************�

OEW DRY aUlR WINO SPEED SOLAR RAD. TE�P . EVAPORATION POINT BR ( DEG. F1 ( �PH) R T U / F T * * / D Y EQUILI(DEGI. U� (FT**3/FT**2) ( 2 ) F) ·

OATA SET 1 66. 30 7 5.00 6.84 175 0.10 8 3 0 7 .63 .

DAU SET 2 63.C)0 6C).40 3.54 1750 .10 83.85 .56

E2-E l .780 EVAPa-EVAPl -.07 I: •

DIFFERENCES IN E BETWEEN DATA SET 2 AND DATA SET 1 BY PA RAMETER

DIFFERENCE DUE TO DEW POINT -1 . 178 DEG. I: F DIFFERENC E DUE TO DRY BULB TE�P . = -1 . 248 DEG. F DIF FERENCE DUE TO W I N D S P E D 3 . 123 E g OEG . F DIFFERENCE DUE TO INSOLATION .000 DEG . • F S MMA T I O N OF INDIV I D U A L DIFF E RENCES . .696 DEG . F U tTl ****************************************************************************************** � *******************

DRY BULK WIND SOLAR R AD. TEM P. EVAPORATION DEW(DEG PO. I FN T) SPEED (RTU/FT**21DY) EQUIL(DIBEGRIU. MF) (FT**3/FT**21 (MP H)

D ATA SET 66.80 7 5 . 1 0 6.75 1517.80 81 .75 .55

DATA SE T 2 &2 .60 68 .20 3.94 151 7 .80 80.52 .48

E2-El -1 .230 EVAP2-EVAP1 -.07 = •

DIFFERENCfS E BETwEEN DAT A SET 2 AND DATA SET 1 BY PARAME TER I N DIFFERENCE U DEw -2. 110 DEG. F f TO POINT • DIFFERENCE D TEMP . = DUE TO BULB -1 .580 DEG. F DIFFERENCE TO DRYWIN D SPEED 2.402 F DUE I: OEG. DIfFERENCE DUE TO INSOLATION = .000 DEG. f SUMMATION OF INDIVIDUAL DIFFfRENCES = -1 .288 DEG. F Figure (Continued). 7.6 ******************************************** *****************************************************************

DEW P O INT DRY BULB WIND SPEED SOLAR RAD. EQUILIBRIUM TEMP . EVAPORATION (DEG. F) ( M PH) (ATU/FT**2/DY) (DEG. F ) (FT**3/FT**Z)

OATA SET 1 56.30 62 .80 7 .31 1173 .40 .38 70.07 DATA SET 2 52 .90 57 .90 4.47 1173.40 69. 40 . 3 3

E2-E1 . -.67 3 EVAPZ-EVAP1 • -.05

DIFFER ENCES IN E BETWEEN DATA SET 2 AND DATA SET 1 BY PARAMETER

DIFFERENCE DUE TO DEW POINT • -1 .564 DEG. F DIF FERENCE DUE TO DRY BULB TEMP . = -1 .444 DEG. DIFFERENCE DUE TO WIND SPEED = 2.288 DEG. F DIFFERENCE DUE TO INSOLATION = -.000 DEG. F SUMMA TION OF INDIVIDUAL DIFFERENCES -.7 21 DEG. F • '" � **************************************** ************************************************ *********************

SAMPLE R SQUARED FOR EQUILIBRIUM TEMP . .976 SUNDARD ERROR .932 DEG.F = • SAMPLE R SQUARE D FOR EVAPORATION .956E+OO SUNDARD E RROR = .177E-01FT**3/FT**2 • AVERAGE E, D ATA S ET 1 76.5 02 • AVERAGE E, DATA SET 2 76.906 • AVERAGE E 2 - AVERAGE E1 .4036 AVERAGE EVAP2 - AVERAGE E= VAP 1 0 7 6 2 • -.

Figure (Continued). 7.6 80

<.... e( wc .... 75 e;; e( Z Z e(:I: w :J 70 0 en :J � ur

65

(HARRISB E, URG DATA SET)

Figure Correlation of Equilibrium Temperatures, Susquehanna 7.7 River Site vs. Harrisburg Station.

The second run of program UHS3 is set up after inspection of the first run. The parameter TSKI P, which del ays the start of the heat input table, is adjusted so that the temperature peaks would be superimposed:

TSKIP 833 - 191. 6 641.4 hours = =

The data deck for this run is shown in Figure 7.12. The output from thi s run is shown in Figure 7. 13, and shown graphical ly in Figure 7.14. The calculated peak pond temperature is 105. 22°F occurring at 810. 6 hours after start. Note that the predicted peak temperature by direct superposition of the preliminary

runs is 86 .32°F + 18 .8°F = 10S.12°F, and would occur at 833.0 hours. The close agreement is partial ly due to the good choice of K and for the excess temperature calculation in the fi rst run , and must not be Edeemed to be necessari ly true in every case.

Because of non1 i nearities in the heat transfer terms of the model , the true maximum wi 11 not necessari ly occur at the time predicted for direct superposition. In fact, the calculated peak in the above example actual ly

59 960 66.3 0 . 01.00- 84. 0.0 11.0 66.0 0.01 .00 84. 1 1.1 . CJ5 71.011.3 66.0 0.01.00 84. 3.1 71. 0 66.0 0 .01.00 84. 2 71 .0 66. 0 0.01.00 8 4 . 5.0 71.3 66.7 '13 4.61.00 3 4 . 6 71.7 61 .3 406.21 .00 86. 68. 0 677.81.00 8 5. ,. 5.85 •• 68.0 .5.85.8 7275..03 68.01148.31.00 8778.. 5 5.8 73.7 68.01315.9 31 .0111..0000 83.74. 6.9 78.1 68.71759 .8 72. 6 8077.0. 3 69.32128 .5' 69. 8 2.0 70.02369 . 2 . 9803 67 • • . T 8.1 10.02321 .8 .,81 9.28.4 12.7 70.02134.0 . 66. I' 8.8 . 8 8382.3.0 70.01812.7 77 65.66. , 82.0 69.11259 .7 .13 66. 1 . 7 3 1 ,0 81.0 .10 68. 8.8.11 8 0.0 69.0 224.6 .80 69. 11 8.8.11 78.0 6169.3· 1 17.2 .17 10. 8.1 0.0 70. . .47 8.1 64.0 O.Q0.0 .· 3630 7 .7 167 3.0.0 64.65.10 0.0 . 2 0 12' 7.3 74.072.0 64.0 0.0 ,. 10 11. 6.9 11.0 64.0 0.00.00 774.9 . 1413 4.6 64.3 0.0 . 27 7 6 . 2.3 . 0.0 .53 70.3 65.0 0 . 0 .80 82·. 3 . 1 10.369 .. 7 6645.71 85.84. 15 0.0 ".0 81 . 213.4 .83

*** CARDS 16 TO 47Q ARE NOT SHOW ***

66;0 0.01.00 84. 67 . 3 61.' 60.1 30.61.�O 8b. 474712 3.5 60.3 300.91.00 75. 2.30 .0 10.0 60.0 571.11.00 0.01.2 7168 ..7 3 60.01203�3 .87 68. 0.0 60.0193 1.3 71., 474134 0. 0 74.0 60.02637 .6 62. 1.9 7275.3�7 58 .32960.5 .73 566 5 .. 41� .60 78.0 55.03133� 4 .570 .45. 3.8 76.7 56.73132.5 .53 51 . 5.8 55 . 3288-3.8 . 5 0 45. 9.6 79.3 55.72486 .7 • 47671 7.1 78.1 56.01969.2 .50 .67.50 44 • 11.5 80.0 78.3 55.71160.4 .83 44. 9.6 46. 418 76.7 47 1.6 48 . 5.8 75.0 55.0 30.61.00 50. 1.3.87 7t .3 55.3 .73 58. r.9 55.1 0.0 67.1 0.0 479 0.0 64.0 56.0 .20 0.0 .47 6779. 480 •• NH= 14.TH(1)=O, .0.0 0 1, 1 ,1.1,t.l5. 9,3.0.09,5 62,8,.7 12,256.04 , 29, 1 40,8.1340 , 2000, SHFHET AT( 1 )-0,O,. 85E9,2* .51E9, .5E9, .68E9, .6E 9, .4E 9, .31E9, .27E9,.21E9, .1 8E9,. lE9,FLOW(1)-1 4*3.6E5S DETER�INE POND TEMPERA TURE SINRUNLIS TTO VZERO=t . 39392EA�8 7IENT,A-t .7424E6,NSTEPS=4500,NPR INT =lOO, T ZERO=80,TSKIP-5000 ,D T-0 .2S FORCED POND TEMPERATURE EFFECTS RUN TO DETERIP=O�IN, E 1-150, E.9Jt.l:J.. ERO-9WI0 . NPRTHOUTINT= AMl 8IENT SINL 1ST T5K IMET-t ,AK � OOS TERMINAVZT EERO=� RUN S SINLIST ,Figure Data Deck for Program UHS3. First Set. 7.8

occurred about one earl ier than predicted (an error of a day is reasonable because of the varidayati on of meteorology on a 1-day cycle). Table 7. 1 illustrates the peak temperature predi cted by varying the parameter TSKIP over a range of up to 30 hours.

The results indicate that, in this case , the maximum temperature is very nearly predicted at the time indicated by the direct superposition of the peaks .

60 RUN TO DETERMINE AMB IENT POND TEMP ERATURE

VZERO . 17424E+07A BLOW AMAI

NPRINT NSTEPS 100 DT TZ80ERO.0 50T8K00.0lP . 4500 .200

QBASE F8ASE E 15Al<0.0l IMET O. O. 80.0 0

8TA0.0 BT0.0O 8HS0.0 BW 0 .0

...... � ...... • : • HEAT IN Tl�1E FROM FLOW • IN •

BTU/HR• : START FT**3/HR ••••••••• • ••••••••••• • • ••••••• • •

• O. 0 . 00 .360E+06 � .360E+06 • • O. .01 • . 850E+09 1.00 .360E+06 • .51 0E+09 .360E+06 : 1.10 • • .510E+09 1.90 .360E+06 .360E+06 : .500E+09 3.90 .680E+09 . 360E+06 : 5.00 ' .360E+06 • .600E+09 8.00 • : .400E+09 12.00 .360E+06 24.00 .360E+06 • .31 0E+09 • .270E+09 I .360E+06 29.00 I I 140 .00 : .210E+09 .36 0 E+06 • .180E+09 I 840.00 • .360E+06 • I 2000.00 .360E+06 • .100 E +09 • • •••••••••••••••••••• •••••••••• •

Figure Output From Pro gram UHS3, First 7.9 Set.

61 ************* MO DEL ********** *** RESULTS

•• •• • • ••• TEMPERATURE •••••••• VO LUME •••• TIME • STRAT • (F) • • • I FT**3 • I HR I MIXED PLUG ...... , I 20.0 I 7 9.9 : 79.9 I 79.9 I .13920E+08 : • I 40.0 I 78. 7 • 79.6 78.7 .13895E+08 60.0 : : •: I I 77.0 • 7 7 . 0 I .138 6 8E+08 • 80.0 73.8 I 78.5 I 77.1 73.8 . 1 3 8 8 E + 0 8 : • • : : 2 I 100.0 • 68 .2 7 4 . 8 • .13765E+08 •: • 120.0 66. 1 : 68.2 • I 66. 1 I . 137 37E+08 1_40.0 65.7 70.0 : : I I 68 .2 .137 23E+08 I : 65.7 : 1 60.0 I 65.7 67 .3 • 65.7 . 137 1 3 E + 0 : • : 8 : 1 180.0 6 5.9 67 . 1 • 65.9 I .13705E+08 I : I 2 0 0.0 I 66 . 3 6 7 . 2 66.3 .13692E+08 • : : I 220.0 68.3 67 . 8 I 6 8 .3 . 1 82E+0 I : 36 8 • I 2 4 0 . 0 69 .6 I 70.2 1 .13 672E+08 • 7 0.2 I 260. 0 70.3 I 70.6 . 70.3 . : .13661E+08 1 : I 280.0 70.7 I 70.3 1 7 0 . 8 .136 50E+08 • : • 3 00.0 7 0 . 8 70.6 70.9 1 3 3 E 0 8 �• I . + • I : •: 6 5 .. 320 .0 7 2 . I 1 72.2 . 1 6 2 2 E + 0 8 • I 1 70 .8 3 1 3 40. 0 73.2 72.4 I 7 3.2 1 .13612E+08 • : • I 360.0 7 4.5 73.2 74.5 I .135,)7E+08 I : : 380.0 74 74.3 • I . 5 I I • I .135 6 ,)E+08 400.0 72. 5 73.7 74.5 • I I I .13541E+08 • • 72.5 : • 420.0 70.8 1 72.1 .,. 70.8 I .13519E+08 • : 440.0 I 70. 1 1 70.8 • I .13503E+08 I • 70.1 : 1 I 7 0 7 70.6 : 7- 0.7 I . 3 4 8 8 E + 0 8 46-0.0 . : 1 : ;1 480.0 I 71. 3 I 71.3 I .13 4 7 2E+08 'I : 71.3 1 500.0 1 71.6 I I 71.6 I .13458E+08 I 71.5 • I 520.0 I 73.1 71.3 I I .13444E+08 • : 73.1 I 540.0 : 74.0 I 1 74.0 . 343 1 + 0 8 • 72.4 : 1 E • -.• 75. 1 1 73.3 7 5 .1 I .134 20E+08 I 560.0, . : I 580 .0 I 75.9 I 75.0 I I .13409E.08 : 75.9 I 600.0 • 75. 8 I I I . 133 83E+08 1 75.6 75.8 620.0 . 1 I 7'7.4 I . 1 3 3 + 0 : 77.4 7 5 . 5 I 71£ 8 : 640.0 78.9 I 1 18.9 I .13356E+08 1 '1 : 76.7 I 660 .0 1 79.4 I 7 7 .5 7 9 .4 I .13340£+08 I : I 680.0 I I 7 9 .0 1 .13322E+08 I 79 0 78.2 -. ·1 700.0 I 79.6. 78.6 I 79.6 I .1330·8£+08 1 I I 720.0 I I 79.. • 80.6 I 1 3299'E+ 08 • 80.6 1 • .• I 740.0 I 80.0 I 82.5 1 ..• 82 .5, . .13288E+08 J 760.0 I 8 1 .5 83.7 • 1 3273E+08 83.1 I : • : I .780.0 I 83.8 1 8 2.4 I 83.9 I .13259E+08 I 1 800.0 83.6 I 8 . . 1 83. 6 1 1 I. 2 8 .13240E+08 I I 1 83 .3 I 84 .6 I . 1 3220E+08 820.0 84.6 : I 840.0 I 85. 2 I 1 85.2 I .131')3E+08 I 84.4 • I 860.0 t 84.8 I 84.6 I I .13159E+08 • 84.8 I 880.0 I 83.8 I 83.8 I .13125E+08 I 900. 0 80.0 84.0 I 80. 0 . 1 3068E+08 I ' . 8� .8 1 I ...... I . ... . I ...... : . � � . � .. . .

MODELLED T E MP-ERATURES I MAXIMUM )(ED MODEL I: 833.20 ."MI 85.90 AT HOURS a 855.80 STRAT MODEL 84.69 AT HOURS MODEL • 833.00 PLUG 8 5.91 AT HOURS Figure (Continued). 7.9

62 R UN T O DETERMINE FORCED POND T�MPERATUR£ WITHOUT AM8lE�T EFFECTS

VZERO A BLOW AMAKE .13939E+08 .17424£+07 O. o.

NSTEP45 0 0 a NPRINT OT.200 TZERO TSKIP 100 90 .0 0.0

QBASE FBASE E AKl IMET o. o. 90.0 150.0 1

STA BTD SHS0.0 BW0 .0 0.0 0 • .0

. ...•...... � ...... : I a HEAT IN a TIME F R OM FLOW IN I I I BTU/HR START FT **3/HR I • •••••••••••••••••••••••••• •••••••• .' : 0 . 0.00 I .3&OE+0& • a . 0 1 I : a o. a .360£+06 I I 1.00 I . 3&OE+06 • . 8 50E+09 • • .510E +09 : I I • 1.1 0 .360£+06 : .510E +09 I : I 1 90 .360E+06 • I .500E+09 . I .360E+06 • : 3.90 .680E+09 • . 360E+06 I • : 5.00 • : I .600E+09 I 8.00 • .360E+0&- I • .400E+09 12. 00 . 3&OE +06 • I I .31 0E+09 :• .360E+06 I • •: 24.00 • : I .27 0E+09 29.00 .360E+06 • • : .c!10E+09 I 140.00 • .360E+06 I : • . 1 80E+09 , 840.00 .360£+06 : : : I 200 0.00 I + .100E+09 I 3 60E 06 a ••• •••• ••• • • ••• •••••••••••••. • ••••• •

Figure (Continued). 7.9

63 *** ********** ************ * MODE L RESULTS

�VOLUME • ••••••• • •••••• • • • TIME • TEMPERATURE (F) • FT**,3 HR • MIXE D STRAT : Pl,.UG • •••••• •••• ••••• ••• •••••••••• ••••••• •••••••• • : 9 9.b 90.8 • 91.b • . 13878E+08 20.0 • • 40.0 103.2 q9.4 • .13 799E+Oe • • 100.4 • & 1 5. 101.7 I • .137 tbE+08 bO.O 0 4 101.5 I 1 0 3 .9 : 103.5 : .13620E+08 80.0 • 10b.8 107.7 1 0 5 . • 104.4 . 13496E+08 • I I 100.0 3 • 120.0 • 108.3 10b.4 105. 1 .13365E+08 • • 140 .0 J 107.1 I 105.4 .13240E+08 108.6 -- • 108.7 1 0 7 . & : 105 . b .13120E+Oe lbO.O • 180.0 : 108 .8 107.9 : 105.7 . 130 06E+08 200.0 • 108.8 108.1 • : : 105.8 .12888E+08 J 108.7 J 108.2 • 105 . 8 .1277&E+08 220.0 • : 108.7 108.3 • 1 0 5.7 .12 675 E+08 • 240.0 260. 0 : 108 . 3 : 105.7 . 12576E+08 108.b 280.0 I 108.5 108.4 105.6 .1247bE+08 : • 300.0 I 108.4 108.3 I 105 . 5 : .123 71E+08 I 320.0 108.3 108.3 : 105.4 I .J2275E+08 • 340. 0 108.3 • 108.2 I 1 05_. 4 : .12184E+08 • 3bO. 0 108.2 • 108.2 : 105.3 : .1209I1E+08 : 380.0 108.1 1 0 8.1 I : .119 7bE+08 • 105.2 1 08.0 108.0 : 105.1 : .118 57E+08 • 1100.0 : 420.0 1 07 . 9 108.0 105.1 • .117111E+08 : • I 440.0 107 . 8 107 . 9 I 105.0 I 1 1 625E+0-8 • • • 11&0.0 107.7 107 .8 104.9 • • I .11513E+08 1 • 1180 .0 1 07. 6 107.7 • : 104.8 I .11404E+08 : 500.0 I 107 .·-6 107 .7 I 104 . 8 : I 520 .0 .1l301E+08 : 107.5 107.6 : 104.7 I I 5 110. 0 .11207E+08 : 107.4 107.5 : 1011 . 7 I . 1 1 114E+08 I • 5& 0 .0 107 . 4 107.4 • : I 1 0 4 .6 J .110 25E+08 : 5 80.0 : 107.3 1 0 7.4 : 104.5 I . 1 0 94'()E+08 I • &00.0 I 1 07.2 107.3 I 1 04. 5 I -.10851E+ 08 • • 0-20 0 • 107.2 107.3 1011.4 1 . 0765E+08 .• : 1 I 640.0 : 107.1 107.2 : 1 04.4 I .10680E+08 : 660.0 10 . : 107.1 7 1 I 1011.3 I .1059 9E+08 I 680.0 107.0 1 0 7.1 104.3 • . 1 0 5 1 7E+08 : I I • 700. 0 I 107.0 107.0 104.3 -. .10 438E+08 I I • I • 720.0, : 106.9 107.0 1 04.2 .10365E+08 • • I • 740.0 I 1 06.9 1 06.9 1104.2 .1029.1 E+08 • I � 760.0 : .10 6.8 106.9 • 104.1 • • .102 21E+08 • 780.0 106.8 106.8 104.1 • .10151E+Oe I • • : 800.0 -. : 106.7 106.8 • 104.1 I .100-78E+0 8 I 820. I 0 I 106.7 106.7 • 104.0 I .10005E+08 I • 8 40.0 1 06.6 • I 1 06.7 : 104.0 I .99302E+07 I • 860.0 106.6 106.1 • : I I . 9 8 446E+07 I • 880.0 106 . 5 0 103.9 • : 1 &.6 I 103.9 I .97 57 1E+07 I 900.0 • 106.3 106.5 03.8 t • I 1 I 1 .961182E+07 •••••••• •••••••• ...... � ......

MAXIMUM MODELLED TEMPERA TUR ES: MIXED ,MODEL I: 108.78 194.20 108.35 AT 212.20 HOURS STRAT MODEL l: MODEL I: 105.03 209.60 PLUG AT HOURS Figure (Continued). 7.9

64 WITHOUT AMBIE NT EFFECTS RUN TO DETERMINE FORCED POND . T�MPERATURE

A AMAKE VZERO BLOW .1'3939E+08 .174 24£+07 o. o. TZEAO NSTEPS NPA10IN0 T DT.200 9 0.0 TSKIP 4500 0.0 IMET o. QBASE o. FBASE 90E .0 AKI 150.0 1.

8TA BTD 8HS0 .0 BW0 .0 0.0 0 .9

• • ••••••••••••••••••••• ••••••••••• • 1 I TIME IN I HEAT IN FROM FLOW I I FT**3 /HR • STAIlT ••••••••BTU/HR••• ••••• •••• ••• ••••••••••• 10. a 0.00 .360E+06 .360£+06 I 10. .01 I 850E+09 1� .360E+06 I I .• 1.00 1 .510£+09 I 1.10 .360E+06 : I .51OE+09 I 1.90 .360£+06 I 1 .500E+0 9 3.90 .360E+06 I I I .680E+09 I 5.00 .360E+06 : t .600E+09 I 0 .360E+06 8 . 0 : .400E+09 r .360E+06 • : 12.00 • I .310E+09 I 24.00 • : • . 270E+09 29.00 .360E+06 • I I I • I I 140.00 • .360E+06 .210E + 09 • : I • 1801+09 840.00 0 + 0 6 I : . 36 E : I . 100E+09 I 2000.00 .360E+06 : : •••••••••••••••••••••••••••••••••••

Figure (Continued). 7.9

65 90.0

II. 0 I w 80.0 a:: ;:) I- oe( a:: w a.. :E 70.0 w I-

60.0 '-- ..L...... --' .L- ...L...... L ---JL..... -'- ______...1..._.....J 0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000.0 TIME - HOURS

Figure Ambient Pond Temperature as a Function of Time. 7. 10

II. o .I w a:: ;:) a::� w a.. :E w I-

______60.0 � � � � � � �____ L_ _L____ L_ __ � 0.0 100.0 200.0 300.0 400.0 500.0 600:0 700.0 800.0 900.0 1000.0 TIME - HOURS

Figure Pond Temperature With External Plant Heat Load and Constants 7.11 and as a Function of Time. E K

66 96O 1 1-.9 66 .3 0.01 .00 84. 0 .0 71.0 66.0 0.01.00 1.5· 771.3 1 .0 66.0 0 . 01. 0 0 84. 7 1.0 66.0 0 . 01.00 84.' a. 71.0 66.0 0 . 01.·0 0 8 4 . 3.1 71.3 66.7 134 . 61. 00 84. 3 4.6 71.7 406.21.00 86. 5.80 7 2 . 0 68.0 6 77. 81.00 85. 4 5.4 6678.0.3 93-1 .01 .00 75.3 68.011 48 .31.00 8787 . 65 5.8 7'7.073.7 68. 01315.11.0 0 83. 6.!.98 78.7 68.71 7 59.8 9 3 • 7 2 • 7 80.3 69.32128.5 . 8 7 67 94.. 82. 0 70.02369.2 .80 67 . 8.1 70.02 321 .8 . 77 66_ 89.2 . 4 82.1 7 0 .02 134 . 0 66. .13 89 8.8 838 2..03 7 0 . 018 1 2.7 .70 65. 8 . 1 82.0 6 9 . 71259.7 66. 1 0 8.1 81 .0 69.3 717. 2 .77 68. 8.1 8 0.0 69.0 224 .6 .80.13 69. 1 1 8.1 6'7 . 3 0 . 0 . 6 3 70. 8 . 1 76. 0 65.7 0.0 .47 70. 8 .1 7 8.0 64.0 0.0 7 1 . 7.7 73.0 64.0 0 . 0' .20 7 4. 131 2 8.17.3 74.07 2 .0 0.0 .1. 3 0 76. 6.9 71. 0 64.0 0.00.00 79. 4.6 7 0.3 64.64.03 0.0 .27 82. 2.3 69.7 64.7 0.0 .53 •. 14 69.0 65.'() 0.0 .80 8 7 . 10.3 65. 1 213.4 8845 . 1 5 0.0 3.1 .83

*** CARDS 16 TO 47Q ARE NOT SHOWN ***

66.0 61.0 0.01.00 84. 2.3 67 .3 60.7 30.61.00 80. 412471 3.51.2 68.7 60.3 300.91 .00 75. 0.0 7 0.0 57 1 . 1 1 .00 473 60.01203.3 .87- 68 . 0.0 60.019.0 31 .3 .73 65.71. 474 00.0 . 0 74.071.3 60. 02637 .6 .60 62. 75.372.7 58. 32960 .5 475 76.7 56.73t32.5 .53 51..89 78.0 55.03133.4 .5.507' 5645.. 476 3.8 .50 4551 . 9.6 7 9 .3 .50 44. 477 7.7 80.78.70 5655.019.3286983.8.2 .50 4 4. 9.6 78.3 55.7248116 6.70.4 .67 478 11.5 7 6.1 55.3 .83 5.8 75.0 55.0 30 .61 .00 5046. 7.1 71. 55.3 470.01.6 .73 48. , 1 .9 67 .7 55.7 0 . 0 .4 67 . 479 3 7 4 80 0.03.8 64.0 56 .0 0.0 .20 58 . 62 .7 56 .0 0.0 .13 79. SHFT NH=1 4,TH(1)=0 ,.0 1,1,1.1,1.75.9, 0.03 . 9 ,5,8, 12,2 4,29, 140 ,84 0,2000, HEAT (1)=0,0,.85 E9,2*.51E9, .5E9, . 6 8 E 9 ,.6E9 , .4E 9, .31E9, .27E9, .21E9; .18E9, .lE9,FLOW(1)=14*3.6E5S RUN TO VZERODETERM=1 . 39392E7INE PEAK,A=1 POND. 742 4E6TEMPER, NSTEPS=450ATURE 0 , NPR INT =tOO,TZER0=80, SINTSKLISTIP= 639 .0,DT = 0.2 1

IINTERLISMINAT TE RUN VIERO=OI Figure Data Deck for Program UHS3, Second Set. 7.12

7 .4.1 Evaporative Loss

A conservative water loss cal culation wi ll be empl oyed in which the maximum amb ient 30-day water loss wi ll be added to the 30-day seepage loss and the evaporative loss due to heat addition assuming 100% of the excess heat is lost by evaporation :

67 RUN TO DETERMIN E PEA K POND TEMPERATURE

VZERO A BLOW AMAKE • .13939E+08 11424E+01 O. o •

NSTEPS4500 NPR100INT OT TZ80ERO.0 TSK IP .200 639.0

O. QSASE O . FBASE 80E .0 15AKl0.0 IM0 ET

8TA0.0 BTO.0 BHS0 .0 BW0.0 0

• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • : : HEAT IN TIME FROM FLO W IN • BTU/HR STA RT FT'Iu3/HR •••••••••••• ••••• ••••• • ••••••••• I 6 6 O. 0.00 . 3 0E+0 I .360E+06 O. . 0 1 I 1.00 .360E+06 .850E+09 .51 0E+09 I .360E+06 .510E+09 1.10 1.90 .360E+06 .360E+06 : .500E+09 3.90 .360£+06 • .680E+09 5.00 " 8.00 .360£+06 • • .600E+09 • I • • .400E+09 12.00 .360£+06 .31 0E+09 • • • 24.00 .360E+06 • • .360E+06 • .27 0E+09 29.00 • .210E+09 .. • • 140.00 .360E+06 • : .180£+09 840.00 • • .360E+06 • • : 2000.00 • .100E+09 .360£+06 •••••••••••••••••••••••••••••••••••

Figure Output From Program UHS3, Second Set. 7.13

68 R E SUL T S ************* MOOEL * * **** ****** *

• • • •••••• TE�PE R ATURE • • • • • ••• •••• TIMH R E : S TRAT : (F)PLU G : VOlUNE

•••: MIXED ** ••••••••• • •• • •••••••• • • • ••••••••••••FT 3•••• : • : 2 0 . 0 79.9 7 9.9 : .13920E+08 : : 4 0 . 0 7 8.7 7979.9.6 : 7 8 .7 : .13895E+08 : : 60 . 0 77.0 7 8.5 : 7 7.0 . 1 3868E+08 : : 80. 0 7 3 .8 11 .1 : 73.8 .13828E+08 r : 100.0 6 8.2 7 4.8 : 68. 2 .13 7 65E+08: : 120.0 66. 1 70.0 I 66 .1 .137 3 1E+08 : 1 4 0 .0 65.7 6 8.2 : 65. 7 .13723E+08 :

• 0 n E+ 0 0 - • 1 3 i�� f& :- -- & 5�7 :- --'6-'r;3 �� 37 1 8 : : 180.0 : 6 7 . 1 b565-;1.9 .13705E+08 I 65.9 : 200 .0 .: 6 6 . 3: �7 .2 66. 3: .13692E+08 : I : 2 20.0 : 68 .3 : b7.8 6 8 . 3 :.13b82E+08 : 6 9 .6 70.2 : .13672E+08 = : 240.0 : 70.2 : r 70.3 : 10.6 7 0 . 3 r .13661E+08 : 260.0 : 70.7 I 70.3 70.8 : .13650E+08 : 280.0 : 70.8 70.6 I . 1 3 6 3 5 E + 0 : 300.0 : 7 0 .9 8 320 . 0: 7 2 . 1 70. 8 7 2.2 . 1 3 6 2E 0 8 : 340.0 : 73.2 7 3 .2 :r .13612 2E+08+ : 72.4 360.0 I 74.5 73.2 74. 5: .13597E+08 : 380.0 : 74.5 7 4 . 3 I 7 4.5 : . 13569E+08 : 73.7 : .135 41E+08 : �OO.O420.0 : 72.5 72.5 : .13519E+08 7 0.8 72.1 : 70.8 : : 70 1 70.8 : 70.1 r . 1 350 +08 440 .0 : � 3E r : 4bO .0 : 7 0.7 7 0 .6 I 70.7 I .13488E+08 : : 480.0 · 71.3 71.3 4 2 E 0 8 : 5 O.0 7 1.6 . 71.371.5 : 71.6 : I .133Q57 8E+08+ )I Q I I I 520 .0 7 3 .1 : ·71.3 t 73.1 I .13444E+08 : I 540.0 74.0 I I .13431E+08 7 2 .4 74.0 : 6 . 75. 1 I 73.3 I 75. 1 I .13420E+08 I: 55800 .00 75.9 : 15.0 .13409E+08 I 75.9 : : 600.0 75.8 : 75.6 I 75.8 : .13383E+08 · : 620.0 77. 4 I 15.5 I .13371E+08 77.4 I '640.0 . 79.7 I 76.7 : 1 8 .9 3 3 5 6 E 8 I .1 +0 : 660.0 : 89.8 I 78.6 : 81 .8 : .1332 5 E+08 · : 680.0 : 9 2.� : 88 .5 I �O.O I .13277E+08 a 700.0 I 95.9 I 90.8 : 91 .9 : .13 3 0 E+0 2 8 : 720.0 98.8 : 94.0 I I .13184E+08 · I 95.3 I 7 4 . 0 I 101. 9 : 96.6 I 98.6 131 3 0 0 I . 3 E+ 8 : 760.0 1 0 2.8 99 .7 I 99.7 .13 0 63E+08 I I I I : 780.0 : 103.3 : 100.5 t I .13003E+08 a 100.1 I 800.0 I 102.8 101.4 I 99.7 I I .12931 E+08 : : 820.0 : 103. 8 : 101.8 : 100 . 7 I .12 863E+08 : : 840.0 I 103.0 : 103. 1 100.0 : . 2 2 E + 0 I I 1 71 8 I 860 .0 • 102.1 102.2 I 99.1 8 5 0 I I .126 E+ 8 : I I 100.4 I 101.7 9'.5 : 880.0 I .12596E+08 : I I 94.9 : 99.8 I 92. 0 I .12 477E+08 : 9 00.0 • • ••• • •• •• • • •• •••• • • • • • • ••••• • • •••• •• ••• • • • •• •

-ODELLED TEMPERATURES. MIMAXEDXIM UM 104�61 810.80 HOURS STRAT MODEL : 103.19 AT 836.20 HOURS = MODED E L 100.77 AT 810.60 HOURS PLUG MO L : AT

Figure (Continued). 7.13

69 110.0 r------,

100.0

IL 0 I 90.0 w II: ::l l- e:( II: 80.0 w Q.. :!E w I- \START OF HEAT INPUT 70.0

�o . 0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.00 1000.0

TIME - HOURS

Figure Pond Temperature (Final Calculation) as a Function of 7.14 Tima.

3 Maximum ambient 30-day loss 1.024 X 06 ft = 1 3 + 30-day seepage •. X 106 ft = 1 44 153 x 109 Btu = X 106 ft3 + 1000 Btu/lb x 62. 4 l b/ft3 2.45

Total 30-day water loss X ft3 = 4. 91 106 The total vol ume of the pond is 13.9 x ft3 , so 65% of the pond water be left after 30 days. 106 would

7.4. 2 Correction Factors for Peak Temperature and Water Loss

To the peak temperature and 30-day water loss should added the correction be factors due to (1) stati stical extrapolation of the offsite data to the 1% year exceedence val ues and (2) the onsite versus offsite comparison per meteorologlcal data. of

The statistical extrapolation performed with the results of the program indicate that the maximum ambient pond temperature and 30"day evaporatioUHn SPNDare greater than the extrapolated 1% per year exceedence val �es. Since only positive (conservati ve) correction factors are taken , no correction necessary for (1). is

70 Table 7.1 UHS3 final Temperature Runs Varyi ng Starting Time

Hours Peak Time of Run TSKIP, from best tempera- peak No. hours estimate ture , of hours

1 641. 4 0 lOS. 22 810.6

2 617.4 -24 lOS. 08 810.6 3 +24 10S. 29 810.8 66S.4 4 629.4 -12 lOS. 14 810.6 S 6S3.4 +12 lOS. 26 810.8 . 63S.4 10S.19 810.6 6 - 6 7 647.4 + 6 lOS. 24 810.8 8 639 -2.4 lOS. 21 810.6 643 +1. 6 lOS. 810.6 9 23

The onsi te-offsite com arison of meteorological data from program COMET indicates that the onsitp e data would predict about a 0.4°F higher pond equilibrium temperature . Therefore , the maximum pond temperature should be raised accordi ngly:

Maximum pond temperature = 10S. 12°F+ 0.4°F= lOS. 52°F.

Offsite evaporation is predicted to be higher than that onsite , so correction factor for evaporation should be taken. no

71

REFERENCES

1. U. S. Nucl ear Regul atory Commi ssion, Regul atory Guide 1.27, Revision 2, "Ultimate Heat Sinks for Nucl ear Power Plants ," January 1976.*

2. D. K. Brady, W. L. Graves , and J. C. Geyer, Surface Heat Exchange at Power Plant Cooling Lakes , Report No. 5, Edison Electri c Institute , EEl Publ ication 69-401 , New York, N.Y. 1969.

3. J. Edi nger et a1 ., "Generic Emergency Cool ing Pond Analysis," May 1972E., United States Atomic Energy Commi ssion , Washington , D.C. October 1972.**

Ryan and D. Harleman , IIAn Analytical and Experimental Study 4. P.of J.Trans ient CooliR.ng F.Ponds Behavior," Report No. 161, R. Parsons Laboratory for Water Resources and Hydrodynami cs , DepartmentM. Ci vil Engineering, Massachusetts Institute of Technology, Cambridge01, Mass. , January 1973.

5. G. H. Jirka, Abraham , and D. R. F. Harleman , "An Assessment of Techniques of G.Hy drothermal Prediction," Technical Report No. 203, R. Parsons Laboratory for Water Resources and Hydrodynamics , Department M. Civil Engineering, Massachusetts Institute of Technology, Cambridge ,01 Mass. , July 1975 (also avai lable as NUREG-0044**).

Edinger and E. M. Bushak, "A Hydrodynamic Two-Dimensional 6. J.Re sour E. ces Model ," J. Edinger Associates , Wayne, 1 975. E. Pa. , G. H. Jirka, D. W. Wood, and D. R. F. Harleman , "Transient Heat Releases 7. From Offshore Nucl ear P1ants ," Journal of the Hydraulics Division, American Society of Civil Engi neers , No. HY2 , 151-168, February 1977.

8. R. W. Hamon , L. L. Wi ess, and W. T. Wi l son, "Inso1ation as an Empirical Function Dai ly Sunshine Duration," Monthly Weather Revi ew 82(6): 141-146 , June 1954of.

9. W. O. Wunderl ich , "Heat and Mass Transfer Between a Water Surface and Atmosphere ," Report No. 14, TVA Engi neering Laboratory , Norris, Tennesthesee , 1972.

10. L. R. Beard , "Statistical Methods in Hydrology," Engineering Memo. EM 1110-2- 1450 , U. S. Army Engineer District , Corps of Engineers , Sacramento , Cal ifornia, January 1962.

*Avai 1ab1e for purchase from the NRC/GPO Sales Program, U.S. "Nucl ear Regul atory Commi ssion , Washington, DC 20555. **Available for purchase from the NRC/GPO Sales Program , U. S. Nuclear Regulatory Commi ssion , Washington, DC 20555 , and/or the National Technical Information Service, Springfield, VA 22161

73

,

APPENDIX A Statistical Treatment of Output

" Program in addition to determining the peak ambient pond temperature for the UHSentirPNDe , length of record, determines the maximum ambient temperature and evaporation for each year of the record. Subrouti ne SUBS performs sever al simple manipulations of the yearly maximums to faci litate graphic analyses :

(1) The data are ranked from highest to lowest temperature. (2) Their "pr obabi lity" or plotting position is determined based on the number of years in the data set using the formul ae (Ref. 10):

Pl - I/N = 1 (O. S) (A-I) I/N (O.S) P == (A-2) N P Pl (i-l)AP i == - (A-3) where

lIN _ 2(0. S) uII.p - N-l where

N number data poi nts in the set == of

Pl == plotting position of the highest yearly maximum

P plotting position of the lowest yearly maximum N == P plotting position of each indivi�ual point i == (3) The first three moments of the distribution (mean , standard deviation, and skew) are determined from the formulae (Ref. 10):

(mean) M == !:T (A-4) T

2 S2 - (!:T)2/N (standar d devi ation) == !:T2 (A-S) N-l

N2L:Ts - 3NL:TL:T2 + 2(!:T)3 (skew) g (A-6) == ------N(N-l) (N-2)s3

7S

I where

I: implies the sum over al l N val ues in the data set

A. I Additional Stati stical Manipulation The ranked annual maximum ambient temperature and evaporation data should be plotted in arithmetic-probability coordinates directly from the output from step 2 in order to get a qual itative look at the trends in the yearly maximum temperatures. A histogram of the same output may al so be useful . A maximum likelihood curve and error bands should be drawn on the probability graph fol lowi ng standard stati stical procedures such as those outl i ned in Reference

For convenience , several of the necessary tables and procedures described in this reference for Pearson type III coordi nates are dupl i cated in the present report and wi ll be described.

A. 2 Maximum Likeli hood Curve

The maximum likel ihood frequency curve in probability coordi nates is described by the fol lowing equation:

T=M +kS (A-7) where

the mean M = s = the standard deviation

k = a tabulated factor dependent on probability and skew

The procedures shown here involve only temperatures , but evaporation may be treated in exactly the same way. The maximum likel ihood frequency curve should be computed using the fol lowi ng steps:

(1) Arbitrari ly select val ues of P� , the probability of occurrence if the data set were drawn from an infinite populati on, to cover the range of interest on the graph. Suggested val ues would be P = 0. 1, 1, 10 , 50 , � 90 , 99 and 99. 9%. (2) For each selected val ue of P , find the k val ue corresponding to the � adopted skew coefficient using Figure A. 1. ( Note: Beard suggests that skew cannot be rel iably determined from smal l data sets , so zero skew is usual ly adopted.)

(3) Calculate T from Eq. (A-7) fQr each val ue of k determined.

(4) Find the corresponding val ue of PN ' the probability corrected for the limited size N of the data set, for each val ue of P� using Figure A.2. Plot T vs P for each val ue selected on the same probability plot that (5) N the raw data were plotted.

76

I ', '

1JAB8(JI 'nrJ xu �

, 8 • Mep1tude _� (Skew k 1D ataDd&rd 4evie.ticma trcm tor .�llce ptl"CeIl�' at:· 0.01 0.1 1.0 5 10 70 coettic1ent) 30 50 90 95 99 99.9 99.99 ' "

1 .0 5.92 4.54 3.03 1 . 87 1.34 0.38 '-0.16 ..0.6 1 .. .1 12 ",1.31 .1 ",,1 .80 ' ..1. 88 0.8 5.48 '4.25 1 . 83 1 . 34 .1 . .5� - " ' 2.90 ' 0.42 ..1 3 -0.60 ..1.16 - 2,O -2�18 0 . 6 1.79 1.33 0.45 ·0 � l 5.04 3.96 2·77 -0.09 -0.58 -1.19 -1·. -2.2 a -2.53 0.4 4.60 3.67 1.74 '-0 .06 -�. 5 n 2.62 1 .32 0.48 , �0 .'7 ' .1.22 l"1 ,51 -2 ·03 -a.54 -2.�

0.2 1.69 1.30 0.51 ..0.0 3 ..1.2 5 ·2 81. 4.16 3.38 2.1ta -0.55 . -1.58 ..-2 .18 . -3.32 0.0 3 . 13 2.33 1.64 -1.28 -1 .64 2 . 3 ' · 09 .09 1.28 '0.52 ' 0.00 -0.- 52 -3. -l·7] -0.2 . 32 1 . 5 1.25 0.55 0.03 0. 51 - 3 3 2.81 2.18 8 ..1 . 30 ..1·69 .�. U · 38 - .16 ' 0. 2 . 92 2.54 2.0 1.51 0 5 0.06 2 62 3 67 "'-I - 4 3 1.22 � 7 . -0.48 -1. -1.14 '- . "-. '" -4.60 , -.....t 32 9 -0.6 2.53 2 2 1.88 1.45 1.19 0.58 0.09 0 4 ' 1 . 3 -1 . '-' . 8 - . - 7 -5 .04 -0.8 2.18 2.03 1.7 4 1.38 1.16 0.60 0.13 5 ,.1. 343 1 -2.7.901 , .�.96 · ,-0.42 - . 8 .. . 25 - .48 - 3 5 -1.0 1.80 1.59 1.31 1.12 0.61 0.16 ,-0. 38 1 1 . 81 . -5 1.88 , - . 34 ",3.03 " .. 4.54 · 92

Skew Coett1c1ent� C�nly Uae4 - 3.13 3 . 09 2.33 1.28 0.52 0.52 ..1.64 ·2 33 1.64 0.00 ..1.2 8 · -3 .09 -3.73 .00 3.03 2.30 1.63 1.27 0 01 -0. 52 -1.65 -2.36 -.04 3.65 0. 53 . ..1.2 8 ..3 .15 ..3.82 -.12 3 .48 2.92 2.24 1.60 1.26 0.54 0.02 0 51 -1.29 -1 .67 ,-3.26 99 - . -2.42 ·3·

- - . 3 .26 2.16 1.5 1.25 0.55 0.03 -0. 50 -1.10 . 50 3.42 23 2 . 1 ..1. 30 -2 -4.23 2.6811 2.091.54 1.23 0.56 0 5 -0.49 1 1 . 7 -2.56 - . 3.08 . 0 - 31 - 2 -3.55 . -4.42 - 32 1.52 ',0.5 . ' 53 . 31 2.58 1 -1 73 2.98 2.05 1.22 0.06 -0.48 ,1.)2 . -2.60 ..3.6 3 -4. -.40 1.51 1.22 0 .0 6 -1 . 32 ..1.7 4 ..3.6 7 ...4.60 2 . 92 2.54 2.03 0 . 51 -0.48 -2 . 62 (X) NOTE : Approximate transformations between normal deviate and Pearson 'l'ype III deviate k can be ac compli sheti ·,rith the following eq llation :

+ (x .. t) 3�1} k. i{[t 1]

A.1 Type III Coordinates (After 10, Exhibit 39). ' , Figure Paanon Ref. .�. .. ; .' 'lAiD or PJrvEastB'llo III PitcD.r

a '. For useV1th �B draw �r_ 'normal population' , . t

. . .0 30 0 10 .0 · . CD 50 ', · 5 0 1.0' 0.1, .' O.Ol., If-I , .

37·2 , I ' 50.0: 24.3 20.4- 15.'" '12�1 " 10 .2 " 2 50 .0 3,4.7' 19·3: 14 .6 9.0 5.7 4.3> . . .. 3 50 0 33� 6 16.9- 11 ·9 6 4-, 3�5 '. 2 ·1 . 10.4- 5.0 4 50.0 33·0 ' 15.4.c 2.4< 1�37 . .' . 5 ' 50.0 32 ·' 14.6 .9.4- 4 2 1.·79 ·92 ; . 50.0 '32.2 1 .8 6 3 8.8 3'.6 1·38' .66 50.0 . 1.·9 ' 3 13 8. 2 1.. 7 50 .0 .5' 3 .23· 13 ·50 .. 31 .7 13·l. � 9 S 0 7·9 - .94, · 39,', 50· 31 .6 12 .7' 7.6, 2 .7 .82 ' ·31 9 .. 1O- 50 0' 31·· 5: 12. � 1 · 3 2 ., ·72:' . .25 50.0 . 12'.3 1· 1 2 3, .64.. 11 31.4 6 . · .21 50 .0 31 ·3 '12.1 9 2.2' · 58 12 ·5 .i8 1.2 2 'L3· 50..00 331 .1 11.9 6.8 2.1 .16 . 6 . .48 14- 50.0 31 .1 u .& . 7- 2.0 , .45 .14-3 , 15 11 .7 6.6 1 .96 31 . 0 6 � 5 .42 16 50.0 11 .6. 1 ·90 .12 17 50 .0 31 .0' 11 .5 1.84., .40 6.4-: .3A' .10'1 18 . 50 .0, 30.9 ' 11 .4 6.3 1 .79 50 .0 0.9 6 ... · 36 19 3 11 ·3 2 1.74, · 091 50.0 30 .8 . . .084 20 11 .3 6�2 1.70 ]4 50.0 30 . .078 21 8 11 .2 6.1 1.67 5 . 0 30 .8 11 .1 1.63 ··3331 .073 ' 22' 0 6.1 50 .0 30 .7 6.0 . 1 · 30 . 23 ' U.l 1 6 068 24 50.0 30 .7 11 .0 1·58 .29 . - 064 50.0 30 ·7 6.5·09 1 . 55 .28 .060 25 11 .0

0 . 0 30.6 10 .9 5·9 1.53 . 27 .057 2726 505 .0 30 .6 10·9 ·5 .054 5.9 1 28 50.0 30 .6 10 .9 5.8 1.491 .26 .051 30 .6 10 .8 .26 �04-9 5.8 1.4-7 .25 2930 50 .0 10.8 1.4-5 .24- 50.0 30. 6 5.8 .04.6 50.0 30.4 10 .6 1 . 33 40 5.(l .20 .034 50 .0 30 ·3 10 .4- 5.4 .025 (.,0 1.22 .16 50.0 10 .2 5 . 2 120 30 .2 1.11 .13 .017

«> 50.0 30·0 10.0 5·0 .010 1.00 .10

are ars HarE : Px values above usable approximatel7 with Pe on 1'ype III distributions baving ,small skew coefficients .

A. (After Figun. 2 Tabieof PN VersulP' :;in-Percent Ref. 10, Exhibit 40).

78

t A. 3 Error Bands

Error bands for the 5% and the 95% confidence limits may also be plotted using the fol lowi ng procedure:

(1) For the same values of P selected in the computation of the maximum i ke 1 i frequency cu e, select the error of est imat i on from 1 hood � Figure for the 0.05 and 0.95 levels of confidence £ 5 and £95' respectiA.vely.3

(2) Determine the coordinate of the error band lines usi ng the formulae:

TO •95 M + (k+£9 s = s ) (A-B)

To . os = M + ( k+£s )s for each val ue of P�. and (3) Plot TO •95 To . os vs p� on the same plot as the maximum likel ihood curve and the raw data. (Note: Do -not plot To •9s and To . o s vs as i n the maximum likel ihood curve. ) PN

The error limit curves express the probability of a value fal ling outside the error bands any given year. For the 95% and 5% bands , therefore , therofe is 1 chance in 20in that the ambient temperature val ue for any given recurrence interval is greater than indicated by the 5% curve and 1 chance in 20 that it is less than the 95% curve.

An example of the statistical procedure is offered in Section 7.

The maxi mum like lihood curves for temperature T and 30-day evaporation rate W e are extrapolated to the 100-year recurrence interval (0.01 probability per year) to determine T1 00 and W1 00. * Correction factors for peak temperature AT and evaporation aWe are determi ned by compari ng T 1 00 and W1 00 wi th thei r corresponding highest observed values from the record, T and W max max:

(A-10)

(A-11)

Only correction factors greater than zero are consi dered. If the maximum observed temperature or evaporation is higher than the 100-year recurrence val ues , no correction factor is taken. These correction factors may be added di rect ly to the peak l oaded pond temperature evaporations determi ned in subsequent calculations. and

*Other recurrence intervals may be used.

79 - . / " '

EBR

- Aa-Coetf'ic1en.ta-; at Stan'ard-, Deviatiou' -

-,- >

Years; - _ Level ot at ixceedeDce- PrequellCY - ill Percent �1gD1ti RecoreJ.; (Il, 0.1 1 10; 50 90 99; 99.9 C8llce* - -

.. 4.41. 41 , .76 .05 5 � 3�� 2 12 .95 1.00 1 .22 ' · - - 10, - 2.U 1.65 1·07 .58 57 .76 .94 .. 15 - 1. 52 1:.19 .79 .� .48 . 65 .80 20 1.23 .tT(, .64 .39 .42 .58 ·71 . 30 .93 .74, 5Oc ·31 ·35 . 49 .60 -4<} .77 .61 .42 ' .27 ·31 .43 .53 · 3 50 .67 .54 .36 .24 �28 .49 · 30 9 70 .55 ...... 20' .24 .34 .42 · 100 .45 .36 .25 .17 .21 .29 37

- . · 3 .25 - � 1.41 1.09 68 3 ·31 . 41 , . 49 10 .77 .60 · 39 .22 .24 ·32 · 39 . · 15 . - .57' 45 29 .18 . 20 . 27 · 34 · ' 3 20 .41 · 37 .2 .15 .18 .24 0 _ : 30 .. 36 .29 .19- .12 .15 .20 .25 . 2 , . 40 ·30 4 .16 .11 13 .18 .22 . 50 .27 .21- 14- .10 .12 .16 ' .20 70 .22 .17 .l2' .08 .,10 .14 .18 100 .18 .14 .10 .07 .09 .12 .15

- - - - .41 �31 -·33 .68 - -1.41 5 - ·7 .49 - - -1.09 ,5 - · . - - · - .24 ' ·39 · 3 - - - ' 32 - .60 10 · 9 - 22 77 . . 4 . .34 - 2 · 15 .27 - .20 18 - . 9 5 - 57 20 - · - .24 - .15 - 4 - . 7 - . - - 30 - - .18 - . 25 · 37 30 . 2 . 15 5 . . 2 - .20 - 1 - · 6 - 12 9 9 3 40 - .18 - 1 .16 .22 - - . 3 -.11 - - .24 - · 30 50 - .16 -.10 . .20 - .12 .14 - .21 - 27 - -.18, . .1 ·.08 - . 70 - - 4 - .10 - .12 - 17 - .22 100 . 15 .12 .09 - .07 .10 .14 .18

- - - 1 . .76 . 5 -2.12 -3 .41 -4 .41 ·95 5 -1- .22 - 00 - 9 - 10 5 -·58 -1 ·07 . - .911- . 7 - - 1 6 -2 .11 . 76 . 5 15 - .6 - .48 ·79 - i - - 1.1 --1 .52 - .80 46 - 9 . - .58 .. 42 1 .7l .64 - - -·39 - 2 20 - - .97 3 30 - .60 . 3' -·31 ·50 · .49 - - - - - .74 93 · · 40 5 3 - . - . 4 - . 3 - . 4� - 1 27 - 2 - .61 - 77 5 . 3 -.24 · 0 .49 - .28 - 36 - .54 - . 67 · 70 . . � - .2_ - . ·30 .44 - .34 - 20 - - 55 100 - . 37 .29 .21 - . 17 - .25 .36 . 45

* true BUID Chance ot value be1l3g greater tbaD of normal -curve value and given error . Figure A.3 Erronof Estima18d Values (After Ref. 10, Exhibit 6).

80 APPENDIX B

Computer Codes

81

P ROGRAM UHSPND ( INP U T , OUTPUT, TAPEq ,TA P E8=/4Q 5,TAP E5=I N PUT U L TSIN K2 1,TAPt6 =OllTPUT ,PUNCH, UL TSINK 3 TAPEa:PUN CrI) C UL TSINK4 C P R OG�AM UHSPND IS A PRUGRAM UNDER DEVELOPMENT 8Y T HE STAFF THE UL TSINK5 OF C H Y � ROLOG IC E N G I NEE�ING S ECTION OF THE U.S. NUCLEAR �EGULATORY ULTSINK & C COMMISSIO� FO� USE I� EVALUATING THE D ESIGN BASI S ME TEOROLOGY OF IILTSINK7 C �MALL C OUL ING PONDS USED AS THE ULT IMATE �EAT SINK O F A NUCLEAR ULTSlhK8 C POWER P L ANT. THE PROGRAM USES HISTORI CAL �EATHER DATA P�OVIDED ULTSINK9 C O N TAPE H Y T HE NATIONAL WEATHER SERVICE A ND A SIMPL IfIED POND U L T S I N 10 C T E M P E R A T U E MODEL TO DET EHMtNE THE PER IOO OF RECORn WH ICH WOULD UL TSINl l R C RESULT IN EITHER THE LOwEST COOL ING PERFORMANCE OR HIG�EST ULTSIN12 C EVAPO RATIVE �ATER LOSS IN A GIVE N POND. THE f THE PROGRA M ULTSIN13 USE O C A N D THE ANALYTICAL TECHN I QUES WH ICH IT EMP L O Y S ARE fULLY DESCRIBEDULTSIN1 4 C IN LITERATURE AVAILABLE THROUGH THE HYDROLOGIC ENG INE E�ING ULTSIN15 C SEC TION. ALL QUESTIONS AND COMM£NTS SHOULD BE ADDRESSED TO ULTSIN1& C R. COOELL . lJLTSINt 7 C ULTSIN18 R EAL L AT\,LA T,YRMODY (3),Y RMAX(40,8) JUL yq 1 LAT1=0. . ULTSIN 21 ULTSIN2 2 100 FOw R RMAITET(6,(tHl100),2 0(/ ) ,lO X, 'U.S. NUCLEAR REGULATO R Y ULTIM A TEULTSIN23 COMMISSION- 1 HEAT S IN� COOL ING POND METEOHO L OGICAL S CANNING MODEL',/10X, 'R CODULTSIN24 2ELL AND W NUTTLE, NOVEMBER lq7Q',/1Hl) ULTSIN25 N A MEL IST/INPUT/N, A , V ,LAT,ISRCH, IPRNT ,YRMODY ULTSIN 2& DATA N , ISR C H , I PRNT/l , 1,01 ULTSI�27 C ULTSIN28 C R EAD DATA C ARD ULTSINZ9 C ULTSIN30 REAO (5, INPUT) ULTSIN31 IF (N. EQ.O) STOP ULTSIN32 C ULTSINJ3 C If THI S IS THE FIRST DATA CARD OR IF LAT HAS CHANGE , A ULTSIN34 p GENERATE C NEW INTERMEDIATE FILE. ULTSIN35 C ULTSIN3& IF(ABS(LATI-L A T).GE CALL SU8 1 ( L A T) UL TSIN37 ••OOl ) L AT1=LAT ULTSIN38 IF (N.GT .qQ) GO TO ULTSIN]9 IF (V.LT.O.)V =V. ( -43SbO4 .) ULTSIN40 IF (A.LT.0.)A:A.(-435 & 0.) ULTSIN41 A 1 =A/435&0. ULTSIN42 Vl=V/435bO. ULTSIN43 C ULTSIN44 C P RINT POND PARAMETERS . UL TSIN45 C UL TSIN4& WR ITE ( 6,510)N, A,Al ,V,Vl , JSRCH, IPR NT ULTSIN47 510 FORMA T(S(/), T20, 10('.'),' POND N UMBER ',12 ,' HAS THE FOLLOWING PARULTSIN48 l A M ETERS ',�5(A.·),II,T35, 'SURFACE AREA '2X,F12.2, ' FT**2 ( ',FQ.2, ULTSIN49 ?' ACRES) ',II,T35, 'VOLUME',8X,F12.2, ' FT**3 (',FQ.2, ' ACRE-FT) ',II,UL TSIN50 3T35, 'ISRC H ',I2,T&5, ' IPRNT = ULTSIN51 = ',12) ULTSIN5Z WR ITE (&,5 50)N S50 FOR MAT(S(/) ,T2 0,1 0 ('* '),' PON D NUMBER ',12, ' HAS BEEN MODELLEO TO ULTSIN53 1DfTERMINE THE WORST ',13(' *') ,I,T38, 'PERIODS COOLING AND EVAULTSINS4 2PORATTVE WATER LOSS',I,tHl) FOR ULTSINS5 C ULTSINS& C MODEL TO FINO YEAHL Y MAXIMUM TEMP ERATURES AND DAY EVAPORATIVE ULTSINS7 C LOSSES. · 30 U LTSI�S8 C ULTSINS9 CALL SUB2 (A,V,YRMA X) JULyq 2 C U�TSIN&l C RAN K YEARLY MAXIMU M TEMP ERATUR ES AND 30 DAY EVAPORATIVE L OSSES' ULTSIN&2 C C OMPUTE 100 YEAR �XCEEPE NCES, SAMP LE MEANS , STANDARD DEVIAT IONS , ULTSIN&3 C A ND S�EwS . ULTSIN&4

Figure B.1 Listing of Program UHSPND.

83 C ULTSIN&5 CALL S U85C Y R M A X ) ULTSIN&6 IF CIsRCH.LE.O.OH.ISRC H.GE .6) GO TO 1 ULTSIN &1 C ULTsIN&8 C P R INT PUNCH DAILY ME TEOROLOGY FOR THE PER IOD S OF RECOR D UlTSIN�q C PRECEfDINA N OIOG RTHE HIGHEST ISRCH POND TEMPERATURES. (ISRCH ) &) UlT SIN 70 C ULTSIN71 ULTSIN12 DO l=t ,Is RCH DO 23 J:l ,3 ULT8IN7 ULTSIN14� 3 Jl=YRMOJ+lOY ( J )=YRMAX CI,Jl) ULTSIN75 sUB3( YRMOoY,IPRNTl JUlyq 3 CIFA LL(I PRN T.EQ. l ) WRI TE Cb,5 20) ULTSIN17 520 F O R M A T (lHl ) ULTSIN78 ULTSINqZ 2 GOC ONT TOIN UE1 UL TSINq3 Y R M O D ( . ULTSINQ4 C 4 Y 3)=I ULTSINQS C CAL CULATE A ND PRINT MONTHLY AVERAGES OF EACH P ARAMETER IN METABL. ULT SINQ & C ULTSINQ7 CALL SUB4( YRMODY , LAT ) ULTSINQ 8 GO TO TSINQQ UL END 1 ULT5ItOO 'SUBROUTINE 5uBt elAT) SU8t SUBt lJ c 5U81 4 REAL ME TAB l(2 7,10) , sRAO (2S) ,LAT 5 COMMON IOATE( 3) , IHOUR ( &) ,WI NDSP (6) , TEMPD8 (6) , TEMPWB (6) ,TE MPOP (&) ,SSUBU8t1 6 tHUMIO(&) ,PRESSR (&) ,SKY(&) SUB t 7 METAB L/210*O. 1 SUB t 8 DATA DATA sRAD 125*0.1 SUBI Q W R ITE(b,520) LAT S t U8 10 520 FORMATCS(/) , T20,10('*'),' SUB R O I N E SUBI HAS BEEN C A LLED FOR lATISUBI UT SU81 11 1TUDE = ',F 5.2, ' DEG. NORT H ' , 5(' * '),/) C SUBI 1213 C POSITION FIRST OF M A Y SUBI . C TAPE TO 8U81 1 4 CALL REAORC SU 15 I:(121-IOATE C3»*4-2 SUB81I 1 6 DO 2 J=I ,I SU81 1118 2 READ (S) SU8t lq 3 CALL REAORC SUBt 2 0 IF (I HOUR ( I ).NE.O) GO TO 3 SU81 2221 IF (lD ATE(2) .LT.5) GO TO 3 S UB I C SU8 t 23 C READ IN I R S T b LINES OF DATA SU8t 24 c F SU81 25 DO 4 SUBI 26 ME TABL(I,1-1,&I)= IDATE Ct) SURI META8L(I, Z )_IDATE(Z) SU81 21 ME TA8L (I,3)=lDATE ( �) SUBI 282Q METABL(I,4)=IHOUR(I) s UBt 30 META8L (I,5):WINDSPCI) SU81 3 1 ME TA8L (I,6) =TEMPDB (I) SU81 32 METABl ( I,7)=TEMPDP (I) SUBt 33 ME T A SL (I,8)=SKY (I) SUBI 34 MET ABL(I,q )=SKY (I) SUB 135 4 ME TABL(I,10)=HUMID (I) SUR t 36 C SUBt 31 C MAKE SURE THA T THE FIRST l INE OF DATA 15 COM�LETE. SUBt 38 C IF DATA ARE M S SI G , SUBST I TUTE FROM THE SECOND OR THIRO L I ES SUBt 3Q FIRST I N S THE N C THREE L I N E ARE �AD, SK IP TO NEXT DAY . SU81 C IF SU81 40 41 Figure (Continued). B.1

84 INDE X:1 SUB t 42 tyR:IOUU 1) SUB 43 SUBt 44 I MON: IDA TE (2) lOA Y: I DA SUBt 45 1=1 n: (H SUBt 4& GO TO & S UB t 47 4 8 5 GO TO 12 SUBt IF(I.EQ.3) SUBI 4q 1=1+1 S U B I DO 7 J::5. l 0 50 7 IF (ME TABLC1,J) .GE .Qq q.) ME TARL (1,J)ZME TA8L CI,J) SUB t SUB t 51 '6 DO 1 J=5. tO IF (ME TABLC1,J) .GE.QQQQ.) GO TO 5 SUBI 52 CONTINUE SUBt 53 INOEX=2 SUB t 5S54 C SUBt 5& C READ IN R�ST OF F IRST DAY 'S DATA. SUBt C SUB t 57 58 DO 8 K:7.19 , & SUBt K 5 = K + 5 SUBt Sq CAL L REAORC SUSt &0 DO J=I< ,K5 SUBt &1 8 &2 IK1 =1-1<+1 SUBt &3 DO 8 SUBt I=I<,K <; &11 11<1 = 1-1<+1 SUBt M ETABL CI, 1)=IDATE C1) SUBt &S �ETABL(I,2) =IOATEC 2) SUBt &6 ME TABLCI,3)=IDATE C]) SUB t &7 METABL (I,4 ) =IHOURCIK1) SUBt &9&8 METABL (I,5)=WINOSP(IK1) SUBt ME TABL CI,&)=T EMP OB CIK1) SUBt 70 M E TABL C I,7) =TEMPDP CIK1) SUB t 71 METABLCI,8)=SI

Figure B.1 (Continued).

85 c T O NEXT D A Y . SUB t 105 c T HE. SUBt 106 IF CMElAB L(I2,�). G E . qqqq.) GO TO SUB t 107 10=1-1 Ii SUBt 108 ME TASL ( I,K)=ME TABL (12 , Kl- CMETASL CI2,K)- MElAB LCIO,K» *.&6&1 SUB I 109 MF TAAL(ll,Kl=ME TABL C I 2 , K ) - C METABL CI2,K ) -MfTABL CIO" K» *.3333 SUBI 1 1 0 10 CONTINUE SUBI 111 SUBt 112 C UBt -1 1 3 C 'GENERATE SOLA R RADIATION TERM. S C SUBt 114 CALL SOLA RCLAT,IYR, IMO N, IOAY,SRAO) SUBt 115 C I SUB 116 'C A P PLY CLOUD COVER ADJUSTMENT (AFTER AND READ SOLA R RADSUB I 111 �UNDERLICH) U C IATION TERM INTO METABL . S BI 1189 S_UBl. SUBSVBtt 120 121 C S B I 122 U 00 1=1 ,25 SUBI ti!3 METAR13lCI ,8):SRAD (I)*.94*(I.-.65*META8l (I,8) **Z) SUB I U" C 13 SUBI SUBI 12U&5 C WRITE ONE D A Y'S WEA THER RECORD IN TO INTERMEDI ATE STORAGE . C SUBI wR ITE MEr ABl U B I 1218 S C (9) S U BI 1 2 9 C NEXT DAY IS FIRST OF OC TOBER,SKIP MAY SUBI 130 C IF TO NEXT FIRST. SU81 20 IF (METABL C2b,2) .lE.9) GO TO 14 t3Ut2 SUBI C SUB I 133 C SEPARATE Y EAR S BY BLANK DATA RECORD . S I C SUUBB I 13. 135 00 15 1-1,27 SUB I DO SUBI 1 36 METABL15 J_l(I, J),I=OO . S B 1387 1 5 WRI TE METABl SUUBIt 139_ (9) SUBI 00 1& R EAD (8)1- 1 ,847 140 SUBSU8 I1 141 c 142 C IF END OF RECORD ENC OUNTERED, RETURN MAIN PROGRAM. S U BI 143 C TO 144 SUBI IF (EOF(8) .NE.0) GO TO S UB I 145 (7 16 CONT I N UE SUBt S B t 1.14'1 GO TO 3 C SUBU I 1 48 C READ IN NE X T DAY'S DATA. S UB I C UB t 14IS9O S DO 8 3 SUB I 1 1=1, Ul 14 124=1+24 U Bt lSi! S I DO 18 1(1;1 .10 S SUUBB t 153 18 METABL CI,K)=METABL CI24,K) ME TABL(1,4)=O. S U B I IS15"5 DO 1 9 S U t t56 ME TABL1=(I,4,&l ) =IDAT E (t) 'SUBB t META8L CI,2)=IOATE (2) SUBI 15B7 ME T A BL (I,3)= IOATE (]) SUBI 159 METABL (I, 4)a IHOUR(I) SUB I 1 0 METAR L ( I ,5)=WINDSPCI) 6 META8L (I,6 )aTEMPOB (I) SSUUBI 1&1 METABLCI,1)aTEMPOP (I) SUBIB I 162 METABL CI,8)=SKY (I) SUBI 163" META8L CI, 9)=SKY (I) S t UB 1&5 19 METABLCI,1 0)=HUMIOCI) SUB1 , 16& INDEX=l S U Figure (Continued). BI 161 B.1

86 IYR = IOHH 1 ) SUBI 168 IMONz IDUE SUB t 169 (CD SUB I 170 10Hz IDUE n) SUB I SUBI 17171Z GOI=t TO 6 SU8 1 1 7 3 C WR ITE ERROR MESSAGE W�EN OA TA ARE SK IPPED SUB I 174 SU8 1 C 1 15 12 IMON,IOAV, IYR SUB I 176 500 FOWRRMITEAT(6,CT35 5,00)'OIS CONTINUITY I� DATA C AUSED ',Il, '/ ',I2, '/',I2, ' TO BSU81' ITT IE SK IPPED ') SUB 1 178 c .SUB I 179 180 C FLAG RECORD CONTAINING BAO DATA. SUBI C SUBt 181 META8L C2, 1 ) =QQQ9. SUB I 18Z WR ITE Cq) ME TABL SUB I GO TO C3,20) , INDEX SUB 1 118834 1 7 REWIND 9 SUB I 185 RE..., IND 8 SUB I RETURN SUB I 18& END SUBI 1 87 8 8 SUBROUTINE SUB 2CA,V,YR MA X) JULY9 1 4 I�PROVED VERSION OF NUTTLE PROGRAM U SING 2ND ORDER R� SU8Z J c R CODELL,SEPT 19, 197 9 SUBZ . 4 c SUBZ c MODELS POND TEMP ERATURE RESPONSE USING D ATA IN INTERMEDIA TE SUBZ 5 C SUB 6 STORAGE . RETURNS YE� RLY MAXIM UM TEMPERATURES AND 30 DAY EVAPOR­ Z 7 C ATIVE lOSSES WITH THE IR DATES OF OCCURENCE. SU82 8 C SU82 COMMON/ TFUNC/ CON1 , CON2 SU8Z 109 REAL ABSMA X (4) ,META8L C27 ,10) , TIME C25) ,SRAO C2S) , TEM PD8 C25) , SU82 11 t TEMPDP C2S) ,WINDSP CZS) , KN(4) ,EV (4) ,EVAP (30) ,TE MPMX'CS ) SUBZ 2 , EVPMAX(4) , YRMAXC40 ,81,MA XT JULY9 125 COMMON/COEF/ CEH (6) , CELt 6 ),C H{6) ,CL C6) SU8Z 14 DATA TSTEP/l.0/ SU82 15 DAU STEP/ .5/ SUBZ DATA OT02,OT06,OT/.5,.16666667,1.0/ SUB2 1716 DO 39 1=1 ,40 SU8Z DO J=I , 8 SU82 1819 39 YRMA39X CI,J).O. SUB2 20 CON1=A/ (t4Q 8*V) SUBZ 21 CON28A/ 14Q 7&OO. SUBZ SUB2 22 MAl(T=OlNOX=O . JUL Y9 26 3 ABSM AX(t).O. SUBZ EVPMAXCl)=O. SU82 29 30 TEMPMl( =0. SUBZ EVTOT=OCl. ) SUBZ 3231 10 READ eQ) ME TABL SUB2 33 I F(EOF C Q) .NE.O) GO TO 12 SUBZ 34 IF CMETABl CZ, l).GE.QQQq.) GO TO 10 SU8Z 35 PONDTP=ME TABl C t , 7 ) SUBZ DO 3 SUBZ 3& EVAP 0C 1=1 , 30 SUBZ 37 301 COIliTI NUE1)- 0 SUB2 38 39 DO 13t .J = t SU8Z SR A OCJ,:ME TABL,25 C J,8) SUBZ 40 TEMP08 C J)·METABL ( J,6) SUBZ 4 1 TEMPOP { J ) = MET ABL(J , 7 ) SUB2 42 �INOSP CJ)=MEtABL CJ,5) SUBi 4443 131 CONTINUE S UBZ 45 DO J=I ,24 SUBZ J Pt=13J+l2 SUBZ 4ft 47 FigureB. 1 (Continued).

87 c SU8Z 48 c CALCuL ATION OF PO�O TEMPERATURE A ND EVAPORATIVE WATER LOSS USING SUBZ 49 c THE LINE AR HEAT EXCHANGE EQUATIONS IN A SECOND ORDER RUNGE-KUTTA S 8 2 50 c NUMER ICAL INTEGRATION. SUB2U 51 c SUB2 52 C ALL TfUN (PONOTP , TEMPOB (J) ,wINDSP(J) ,SRAD (J) , TEMPOP (J) , Suei! 51 1 KN(l) , EV( t ) SUBZ 54 P T P 1 =PONOTP+KN(1)*OT SU82 55 CALL TFUN (PTP1 , TEMPOB (JPt " wINOSP (JP1),S RAD(JP1),TEM�DP (JP1), SUB2 1 KN(2) ,EV( 2 » 5657 PONDTP =PONDTP+ (KN(1)+KN(2» *OT02 SUB2SUBZ 58 EVAP ( 1 ) =EVAP(1)+(E V(l'+ EV(2»*DT02 c SUBZSUBZ . 59 c COLLECT MAXIM UM TlMPERATURE 60&1 c SUBZ IF CPONDTP.GT.MAXT) MAIT. PONDTP .SU�Z 62 132 C ONT I NUE JULnSUBi! 7 c S UBZ 6. 65 c SEA RCH FOR YEARLY MAXIM UM TEM PERATURE AND EVAPORATIVE WATER LOSS. SUB2 C 66 SUBZ 67 00 B 1=1 ,:30 &8 33 EVTOT=EVTOT+EVAP (I) SUB i! IF CEVTOT.LT .EVPMAX(11) GO TO SUB2B2 69 7 0 EVPMAX ( 1 ) -EVTOT 1 3 EVPMAX(2 ,aMETABL(1,1) SUB2 7172 EVPM AX(3)=METABL (1,2) SUUBZB S 2 7 3 E VPMAX(4)aMETABL (1,3) SUBi! 7. 75 1 3 00 2 9 l=l ,2Q S U 130=30-1 SUBi!8Z 76 11=130+1 SUBZ 71 29 EVAP(Il)=EVAPCI:3 0) SUB2 78 EVAEVTOT=OP(l)=. O. SUSU8Z8Z 79 IF (MAXT. LT. ABSM AX(l» GO TO JULn 80 8 JULV9 8 ABSMAX (l ) ;;MAX T 9 A BSMAX(21= MET A BL (1, l'. SUBZ ABSMAX(3)=METARl (I,2 ) SUB2 8483 ABSMAX(4 )=MET A 8L C1, ] ) SUBZ 85 8 CONTINUE JUL MAXTzO . JULnyq 10 C SUBZ It C READ IN NEIT DAY'S DATA. SUB2 90 SUBZ 91 C 92 1 1 R EAD (9) META BL SUU IF(EOF(9) .NE.0.O) GOTO 12 93 IF (MET ABL ( l,l).GT.O.) GO TO SU8ZSU81 94 LNOX=LNDX+l 14 SUBi! 95 YRMAXCLN DX, I)=ABSM AX (l) SU82 96 Y�MAX (LNDX,2).A8SMAX(2) SUB2 97 Y�MA X(LNOX ,]) =A8SM A XC3) SUBZ 98 Y RMAX (LNDX,4)=A8SM AX(4) SUB2 99 YRMAX(LND X,5) =EVPMAX (1) SU82 1 0 0 Y RMAX(LNDX,&) =EVPMAX(2) SUB2 10110Z YRMAX (lND X,7)=EVPM4X (3) SUB2 YRMAX(LNDX,8)= EVP MAX(4) UBZ 10.3 S 1=1 S U I F (ABSM AX(l).GE . TE�P MI ( l» GO TO 16 SUB2B2 105 1=6 • S UB2 106 107 GO TO 20 SUB2 108 16 IF (I.GE . S ) GO TO 1 7 SUBi! 109 1 5=5-1 SUB2 110 DO 18 J=l ,IS SUB2 111 L=S J SUBi! 112 .. Figure (Continued). B. 1

88 l� Ll=TEMPMXL+t (Ll)=TE�PMX (L) SUSUBZBZ 113 1 7 TEM PMX C I )=ABSMAX ( I) S U 114 BZ 117 20 ABSMAX(t)zO . suez 2 0 EVPMAlCC 1)= 0. SURZ 1,1 21 MAXT=O. O J q ULy lZ GO TO to SUBZ 14 If CMETABL(2, 1).LT.QQQq. ) GO TO 1 124 SUBZ li5 DO 37 1=1 ,35 S U Z 1 1=1+1 SUBZB 126 1�7 3 7 CONTINUE J UL q y 13 GO TO SURZ '130 C 11 SUBZ 131 C END OF DATA FILE ENCOUNTERE D. R E T U R N TO MA IN PROGRA M. SUBZ C SUB2 13Z 12 REWIND q SUB2 1334 RE TU RN SUR2 END SUBZ 135 SUBROUTINE TFUN (PT,OB,W,S RAD,DP,OT,OE) TFUN 1362 COMMON/TFUNCI CON1, CON2 TFUN DATA HSPRAY,HIN,ES PRAY/3*O.OI TFUN 3 4 TSTAR= CDP+PT)*.S TFU� BETA=.255 00�5*TSTAR+. 000204*TSTAR**2 TFUN 5 • • WINFUN =7�+.7*W**2 TFUN 6 RK=15.7+C.2 6+BETA )*WINFUN TFUN '7 E:SRAD/RK+(. 2&*OB+BET A*DP) /(.2&+8ETA ) T F U N 89 DT= (RK* CE-PT)+HI N-HS PRAY)*CONI TFUN OE=BETA* C PT-OP)*WINF UN*CONi-ESPRAY TFUN 10 RETURN TFUN 11 E ND TFUN 13Ii SUBROUTI N E SU83CYRMOOY, I PRNT) JULyq 14 C J U L YCJ 15 . C PRINTS AND/OR PRNC HES DATA FROM INTERM EDI ATE JULYCJ 16 C FILE FOR PERIOD OF 'NDYS' D AYS BEFORE AND 5 JULY' C DAYS YRMODY . JULY' 17 C FOLLOWING JULY' 18 I' C IF IPRINT=l , DATA IS PR I NTED · J ULYCJ ZO C IF IPRINTa.l, DATA IS PUNCHED J U Y CJ C IF I P R I N T = O , DATA IS BOTH PRI NTED AND PUNCHE D JULY9L 2221 C JULyq "Z3 REAL YRMODY (3), �ETA8L( 21, 10) ,JNDX JULY' 2 4 INTEGER IOATE (!) JULY9 N =O JUL ' 2625 OA NOVS/3':;1 JULYY ' JNDX=OT A . U LYCJ 2 7 IPNCH=O J L 28 U YCJ Z9 IF C IPRNT.EQ.l) GO TO 40 J U CJ IF ( IPRNT.EQ.O) IPRNT�l ULYCJ 30 IPN CH=l JUJ LYCJ 31 40 CONT INUE L Y CJ C JUUL Y CJ 3433 C POSITIO N TAPEQ TO 'NoyS' D A YS DATE J UL Y CJ 35 BEFORE C PROVIDED IN YRMODY. IF DATA IS NOT AVAILA BLE , JULYCJ 36 THE C POSITIO N TAPECJ TO FIRST DA� OF DATA IN YCJ C SAME YEA R A S YRMODY. JULYCJL 37 38 C JUL CJ READ (q) �E U8L JULYCJY 39 YRI:METABL ( JULYCJ 4041 REWIND Q 1,t) 42 JULY9 IF CYR MOOY (l).LE.YR) GO TO 4 3 N z(Y RMODY (1)-YR'*154. t JULY'LY9 DO 2 I=l,N 44 2 READ Cq) JULYCJLyq 45 ME TABL Figure (Continued). 4 6 B.1

89 N�O JUL Y9 07 t IF (YR MODY (2) .LE. 5.)GO TO 3- JUL Y9 48 N a ((Y RMODY (2) -5. )*31 .) JUL Y ' 49 IF ( YRMODY (2) .GT.6.)NaN-l JULY9 50 3 CONTINUE JULY9 51 N � YRMOD Y(3)+N-NDYS JULY9 52 TO 4 JULY' 5] NIFDY(N.GTS =NDY.O)GS+N O JULY' 54 GO TO & JUL Y9 55 I 00 5 I=l,N JULY9 R EAD ( 9) META8L JULY' 56 5 7 65 CO�TINUE J ULY ' 58 NDY S6=NOYS+& JULY9 59 N=O JULY9 .0 C JULY' 61 C GENERATE OUTPUT JULY' C JULY' &2.3 DO 35 I-l ,NDYS. -JULY9 READ (9) MET A8l JULY' .4 IF ( ME T A8l ( 2, t ).GE ." ". )GO TO 35 JUL Y' 65 66 IF (IPNCH. NE .l) GO TO 41 J UL Y' 6 7 IF (I. EQ.l) PUNCH (4, 610)ND Y S&, ME TABl(l, 2 )�METABL (I,3),METABL �t,11 JUlY9 610 FORMAT ('* * APPROXIMATE LY DAYS OF MET. DATA FOL L OW. DATA A REJULY' 68 ' 6' 1 PUNCHED 2 HOURS TO A',I,' ****, 1 2, ' CARD BEGINNING WIT H HOUR ON ',]F]SU8] ' 2 . 0 , THE FORMAT FOR T�E DATA I S 13,2(' ,1, '**** ]F 5. 1,F6.0 1 �F4.2, F4SU83 43 WHERE FIELD 1 THE CA RD N U MBE R AND THE F OLLOW ING ',I, ' **** VASU8] 4.45 2.0)]RIAB lE SEQUE�CE ISIS REP EATED- wIND SPEED, DRY BUlB,OEWP DINT,SOlAR 50-',1,'**** IATION , CLOUD COVER ,ANO RE LATIVE H U MIDITY .') A.SUB] 446 7 DO 42 SUB] 48 lS-L + l Lcl,2],2 SUB] ., N=N+l SUB] 50 42 WRITE (4,590)N, ((ME TAB l ( J,K) , K-S, 101,J -l ,ll ) 5'0 FORMAT (I3,2(]F5.1,F&.t,F4. 2 , F 4.0» SUB]SU8] 525t IF ( IPR NT.N E.l) GO ]5 SU8] 41 C ONT1 NUE TO SUB] 55S4 IDATE (1)=METABLC1,2) SUB] 55 IDATE (2)=META8l (1,]) SUB] 56 IDATE (3)D METABL(l,l) SUB] WRITE (6,500) I O A TE SUB ] 57 DO 3' J=I ,24 SUB] 58 39 WRITE (&,52 0) (META8L (J,K),K=4, tO) SUB] 5960 WRITE (6,510 ) SUB] 61 FORMAT (IHl,5( /) ,T20, lO('*'),' METEOROLOGY '2(IZ, 'I '),I2,4 �( '*� SUB] SOO 1),III,T 25,71 ('. '),I, T25, ·, HOUR , WIND FORSP ., DRY BULB , DEWPOINT , SUB] 62 2S0lAN RAO CLOUD ,RE L A TIVE ,', I,T25, ',' ,T35, ', (MPH) , (DE G.F)SUB] 63 ] , (DEG.F) ,BTU/FT 2/D, COVER ,HUMIDITY ,',I,T25,71('.'» SUB] 64 510 FORMAT(Ti5, 7 1(' .'» SUB] 65 520 FORMAT (T25, ',',3X,F3.0,] X, ',',i X,F 4 . l,3X,',',2X,F5 .1,aX ,', ',2 X , SUB] 66 � tF5.1,2 X ,', ·,2X,F 6.1,lX, � , ',3X,F 4.2,2X, ',',2X,F5 .1,2 X, ', ) SUB] 6867 35 CONT I NUE SUB] 69 20 CONT INUE S UB] 100 I F (IP NCH.EQ.l) WR ITE (&,600)N SUB] 101 600 FOR M lT (IH t , 5(/) ,T20, 10(' * '),' IMBER OF CARDS PUNCHED - ',I], ' " SUB3 102 140('*'» SUB] 10] REWIN D 9 SUB] t04 RETURN SUB] 105 END JULY' SU8ROUTI NE SUB4 ( YRMOD Y,LAT) S UB. 72 0 C SUB. ] E C PRI NTS OUT AVERAG MONTHLY VAL UES FOR METEOROLOGI C PARAME TERS S UB4 4 BEGIN�ING WITH DATE GIVEN IN YRMODY AND ENDING WITH THE LAST SUB4 5 C DAY ON THE DATA TA PE . - SUB4 S UB4 67 C Figure (Continued). B.1

90 R EAL YRMOOY (!1 ,MET_SL(2 7,lO' ,LA T S U B 4 INTEGER IDAT E (3) , MON ( 5) , MO� ; H (5) SU84 98 , DATA MON/121 , 152, 182 ,�13, 2441 SUB4 10 DATA MONTH/ 'MAY', 'JUNE', 'JULY ',' AUGUST', 'SEPTEM8ER '1 SU84 11 INOx=O SU84 12 W INo S P-O. SU84 i3 TEMPDP=O . SUB4 14 TEMPOB=O . SUB4 15 SOLARozO. SU8. 16 IOATE = Y R MOD Y SUBII CL OUD=G(l). (2) S U B4 181'1 HUMID=O. S UB4 19 I OUE (2) = R M O D Y S UB4 2 0 IO_TE (3)=Y RMODY (1)n) SUB4 21 WR ITE (6,500) IOATE SU84 22 500 FOR MATC 5(/) ,T20 , 10C'*'),' THE MONTHLY AVERAGE VALUES FROM ' , SUB4 23 12(12, '1'),12, ' TO END OF DATA ' , 13( '*'),1 /) SUB4 24 WR ITE (6, �10 ) SU 4 510 FORM_ TCT30 , &I ('.'),I, T30 '*R MS BULB *DEWPOINT * SOLAR *SUB48 25 1 CLOUD *RELATIVE *',I, T30, '*WIN S PEEDD *DR Y * CDEG .F) (DEG.F) *RADIATSUB4 26 2ION* COVER *') * SUB4 21 I Y R=1 900+IOATE* HU(3MID) ITY SUB4 2928 WR ITE (&, 520 ) I YR SUB4 3 0 520 FORMATCT20, I 4,T30,61 ('.'), I,T30, '*',T40, '*',T50, '*',T60,'* ',T10, SUB4 3 1 SUB4 32 l '* ',T8 o ,'*',r 9 0 , ' * ' ) C SUB4 3� C POSITION TAPE9 TO FI1 sT D A Y OF O T H PROVIDED IN YRMDOY. SUB. 3. C M N S U 4 B 35 READ (9) ME T A B L SUB. 36 YR.MEUBL 1,1 ) SUB. J1 REWINO q C SUB4 38 IF (YRMOOYCt). LE .YR) GO TO 1 SUB4 3' N= (YR MOOYCt)-YR) *15 4.+1.· S UB4 40 00 2 Izl , N SUB4 41 2 READ (9)METABl SUB4 42 1 N . C C Y R � O D Y ( 2 ) -� . ) * 31 . ) SUB4 43 IF (N.LE.O) GO TO & S UB. II. 00 4 I=l ,N SUB' .5 4 REAO (9) META8L 8UB. •• 6 IF (METABL(I,]) .LE . l . ) GO TO 5 SUB ••, 8ACKSPACE 9 SUB. ., REAO (9) METABL SUB. ., GO T O , SUB4 50 5 IF (METARL (2, 1).GE.9999.) GO TO 9 SUB. 51 C S UB 4 C READ IN ONE MONTH 'S DATA SU84 52 C SUB4 5 ' 8 INDX=INOX+l 8UB4 54 IOAT EC1,=ME TA8L C 1,Z) SUB4 55 5. IDATE (2)=METABL ( I,]) SUB4 57 I OATE (])= METABL (l,ll S U B 4 5' D AYNUM=MON (IO A TE C1)-4 ) + I OATE (2)-1 SUB4 IF (MOD ( IDATE C3) ,U) .fQ.O) O A YNUM sOAYNUM+l. 8UB4 '059 DAYLEN= OAYLIT(L AT,DAYNUM) SUB. 6 1 00 .7 1 = 1,2 4 SUB. 62 WIND SP=META8L (I,5)**a+WINDSP SUB4 63 TEMPoezMETABL CI,&) +TEMPOR SUB4 64 TEMPOP= ME TABL (I,�)+TEMPDP 8UB4 CLOUo.ME T A BL (I,9)+CLOUO SUB. 65.•• HUMIO=ME TAB LCI,i O)+ H UMIO SUB. SOLARD=SOLARO+ME TABL (I,S) /DAYLEN SUB4 6' 7q REA D (9) META8L .8 IF (META8L(1,1).LE.0.) GO T O SUB4S UB. 6. 11 70 FiSJure B. 1 (Continued).

91 GO TO 10 SUB4 71 IF CMETABLC1,�) .LE.l.) IF (METARL(?,I).GE.9 99Q.) GO TO SUB. 1Z 9 73 GO TO 8 SUB4 10 OAYS=IND X SUB4 7. 1 c SU84 5 sua. 1 6 C CALCULATE AND P� INT AVERAGES C SUB4 71 INOX=O SUB4 18 AVGWS= ( WINDSP/oAYS/24 .)**.5 SUB4 AVGD P=TEMPDP/oAYS 124. SUB4 8019 AVG Oe=TEMPOB/DAYS/24. SUB4 A VGCL=CLOUo/DAY S/24. SUB4 81 AVGHM=HUMIo/OAYS/24. SUB4 8]82 AVGSR=SOLARD/DAYS SUB4 84 I =IO ATE ( 1 ) -4 SUB. 85 WR ITE (6,530) MONTH(I),AVGWS, AVGDB,AVGOP ,AVGSA,A VGCl, AVGHM SUB4 8 6 5 30 FORMAT (T20, A10,'*·,2X,FS.2,2X ,'*',2X,F5 . l,lX, '*',2X ,F5.l,2X, '*', l XSUB4 81 1,F 6 .t,lX, '*',�X,F4.2,3X,·* ',tx,F5.1,]X, '*', I.T30, ' *',T40, ' *',T50, 8 8 3'*',TbO, '*',T7 0, '*', T 8 0, ' * ' ,T� 0, ' * ' ) SSUBUB44 8' WINOSPzO. SUB4 TEMPDP =O . SUB4 90 91 T EMPo8=O . SUB4 CLOUO-O. SUBI 9Z HUMID=O. SUBI 93 SOlARD =O. SUB4 94 GO TO 5 SUB4 95 OAYS=INOX SUB. 96 II 91 C SUB. 98 C CAlCULAT PRINT AVERAGES FOR THE LA ST MONTH OF E ACH DATA SUB. � AND 99 C PERIOD SUB. 1 00 C SUB4 INDX=O SUB. 101 AVGWS= ( WINDSP/DAYS/24 .)** . 5 SUB4 102] AVGDP=TEMPOP/OAYS/24. SUB. AVGOB=TEMPD�/DAYS/24. SUB4 104 A VGCL=CLO UD/DAYS/24. SUB4 106! AVGHM=HUMIO/DAYS/24. SUB. 101 AVGSR=SOLARD/DAYS S UB4 1 WR ITE (6,530) MONTH (5),AVGWS, AVGOB,AVGDP,AVGSR,AV Gtl ,AVGHM SUB4 08 WINDSP-O. SuB. 109 TE MPOP=O. SUB. 110 TEMPOS-O. SUBI 111 SOlA R O-O. SUB. III ClOUO=O. SUB. 11113. HUMIOzo. SUB. 115 RHO (9) META BL SUB. 116 IF (EOF (9) .NE.O) GO TO 12 SUB. IYR:190 0 + M ETA BL CI,I) SUB. 1178 WR ITE(6 ,52 0 ) IYR SUB. 119 IF (ME TABL ( 2,1).GE.Q999.) GO TO 9 SUB. 120 GO TO 8 SUB. 121 12 wRITE (6, 540) SUB. 540 FORMAT( T30,&l C'.'» SUB. 1221 RETURN SUB. 12. END SUB. SUBROUTIN E SU85 ( YRMAX ) SUB5 125 2 c SUB5 J C COMPUTES S A MPLE MEAN, STANOA�D DEViATION, SKEW, AND SUB5 �XCE�DENCE ¥OR • C Y�ARLY MAXIM U M TEMPERATURES AND WATER LOSSES GENERA TED BY SUBZ SUBS 5 CI SUB5 6 REAL YR MAX(40, 8) ,JUNK ( 4 ) , (40) ,M , M E SUB5 1 SUMT=O. _ i SUB'S 8 SUMT2=O. SUBS S UMT 1=O. SUB5 9 Figure (Continued). 10 B.l

92 �- 1 1 SUSUHMtE2=O=O. . SUB5 12 SUHE 3=0. SUBS 00 SUB5 13 20 l=l,40 1 4 'IF ( �RMAX ( l. l).lE. O.) GO 21 SUBS 15 20 CONTINUE TO SUB5 1617 Lal+l SUBS 21 L=L -l SUB5 C SUBS 118 . CRANK OATA IN ORDER OF DECRfASING M A GNITUDE SUBS 20 C SUBS 21 DO 1 SUB5 22 00 1 J=II=2,L,S ,. SUBS SUB5 2423 11=1-1 ' IF(YRMA MCI,J) .LE . YRMAX(ll.,J . » GO T O SUB� 2 5 2 M= l,. 1 SUBS 26 MJ=DO M+J-l SUBS 27 J UNK (M)=YRMA X(I,M J ) SUBS 28 2 SUBS 2. DOIF ( J3 UNM=K(I)I ,1. GT. YRMAXCM ,J» GO TO 4 SUBS 30 3 CONT INUE SU8S 31 4 00 5 K =M , ll SUB5 32 K M=I -K+M SUB5 33 KMI=KM- I SUB5 3 4 00 l2� 1 ,4 SUB5 3 5 L J=L2+5 J- l SUB5 36 5 YRMAM(K M , lJJ aYRMAX(K � I ,LJ) SUB5 37' 00 SUBS 38 LJ =L26 l2+ J :1-l ,. SUBS 3. 6 YRMA X(M,LJ)=J UNKCL2) SUBS 40 tCONTI NUE SUBS 41 C SUBS 42 C COM PUTE EXCEEOENCES SUBS 4] C SUBS 44 RL=L SUBS 45 P(1)= ( 1.- C.5) ** Cl./RL »*oo. SUBS X=�.*CSO.-P ( t ) l/ C AL-l . ) i SUA5 4647 1=2,L SUB5 DO 7 SUBS 48 11-1-1 4. 7 P(I)=P (ll) +X SUB5 50 DO I=I,L SUB5 51 SUM22T=SUM T+YRMAX(I,I) SUB5 52 SUM TZ=SUMT2+YRMAXCI,1 )** 2 SUBS SUMT3=SUMT3 +YAMAXCI,I,** 3 S UB5 53 SUME=SUME+YRMAX CI,S) SUB5 5545 SUMEZ=SUM E2+y A MA X CI,5)** 2 SUB5 56 2 2 SUME3=SUME3 + Y � M A X(I,S) * * ] SUBS 51 MT=SUMT/Al SUBS 58 ST=SQAT(CSUMT2- (SUMT **2/RL»/ (Rl - t .» . SUB5 5. GT= C R L**2*SUMT3-3.*Rl*SUMT *SUMT2+2.*SUM T** 3)/ (ST**3*Rl* CRl-l. )* SUB5 60 I(R l -Z . » SUB5 61 ME=SUME/Rl SUB5 62 SEaSQRT ((SUMEZ-CSUME **2/ Nl» /(AL-I .» SUB5 GE= ( R l**Z* SUM E3-3.*R L*SUME*SUM E2+2.*S UME**3) / (SE**J*A L* (Rl-l .)* SUB5 63 S UB5 64 I(WRRl-2ITE(.»6, 5 JO) SUB5 6665 530 FORMAT(IIII) SUB5 67 �R ITE Cb, 500) SUB5 500 FORMU ( T 20, l O('*',,'T H E O F Y EARLY M A X I MUM POND TEMPEAATURE SSUB5 68 1 AND 30 DAY ' , lO('*'), SAMI,TPLE3 1 ,' EVAPOAATIVE LOSSES BY THIIUB5 6" 2S MODEL IS DESCRIBED BElOW. ',II I,T28, 10(· .'),·TE MPGENEAATUERAR ETED� ,l "(·.� ) SUB5 7071 3 , E V A PORA TI V E S l T ' * E XC EDE 0 � 1 • _ _tUUE .s.tJ.B..!L_--'L.L • L.P S...!_,_��l ...... 28 . E « 5 X .!JlA.l.E__ 4DED',15X , 'OATE * ' ,1, T28, '*/l00 VR* (DES,F) *(YR. MO . DY.)*/l00SUB5 73

. R FT**3 *(YH.MO. DY.)*' ,I,T2 8 ,&5 C','». SUB5 � Y * -. " . . ... 74i Figura (Continued). B.1

93 D O to I�t ,L SU85 15 �RITE (&, 510) P ( I), (YRMAX CI,J) ,J=1 , 4 ),P(I),CYR� AXCI,K) ,K= 5,8) SUBS 16 5tt oO FORMA TCT 28, '*',l X,FS.2 ,lX, '*',3X,F5.2,3X, '*',tx, 3F3.0, tX, '*;,lX, S U85 iF5.i, lX, ' *',IX, F9.t,IX, '*',tX;3F 3.0, 1�,'*') SUB5 7178 WA ITEC&,5 20) MT,ME,ST,SE ,GT , GE SUBS 79 520 FORMAT CT28 ,&SC'.'), I I ,T26, ;MEAN ',T40,F5.2,T70,F9.t,ll, T17, SUBS 8 0 l 'STAND A RD O EV. ',T40,F6.],T70,F10 .2,II,T 26, 'SKEW· ,T40,F6.3,T70, SUBS 8 1 SUBS ' 82 2FR ETt'U.])RN SUB5 � NO SUBS 8483 SUBROUTINE RfA O RC R EAORC 2 C REAORC C READS WIND SPEED, DRY B U LB TEMPERATURE , WET BULB TEMPERA1uRE , R f AORC 3 4 POI N T, RELATIVE HUMIDITY, S TATION PRESSURE, AND TENTHS OF REAORC C DEW l C CLOUD COVER FROM NAT I O N AL wEATHER SERV I CE OATA TAPES. WIND SPEED REAORC 6 C I S RETUR NED IN MPH , TEMPERATURE IN DEGREES FARENHE IT, AND PHESSUREREAORC 7' C I N M M-HG . INPUT RECORD IS 495 CH�RAC TERS LONG . REAORC 8 C REAORC I NTEGER JUNK (&,9) , ISTAT (2) , IWIND (6,4) ,IT EMP(6,6) , I H U MID C6,�) , RElORC 109 lIP RESS (6,4) ,IS KY(6,6) RElORC" COMMON IDATE (]) , IHOUR (6),W I NDSP (6) , TEMPD8 (6) , TEMPW (6) , TEMP D P(6 ),R EAORC 1Z lHUMID(6) ,PRESSR C6) ,�KY (6) � REAORC !! R EAO(8 ,500) ISTAT,IDAT E, CIHOURCI), (JUN K (I,K),K_l ,4" RfAORC t. lCI wINDCI,K),K:l , 4 ) , CITEMP(I,K),K-l,6),IH UMIDCI,1),IHUMIOCI,2) r RfAORC 1! 2(IPRESS CI,K) ,K:l, 4) ,CI SK Y CI,K),Ka l,6) ,(J UNKCI,K ),K .S,9 ),1-, , 6) RfAORC 1 6 500 FORMAT C 14, 15, 3I2,6(IZ,I �,IZ,AI,IX,I Z,Al,It,Al,.(IZ ,Al), lX, REAORC l7 lI2 ,Al,I4,Al,I3,Al,1� ,&Al, Z(A10),A 2,A 8 , A2,4X») REAORC l8 00 100 I=I �6 RElORC l9 CALL SIGNCk CIWIND(t,3),IW IND(I , 4» REAORC20 WINOSPCI):IwINDCI,3) REAORCZl C A LL SIG NCK (ITEMPCI,1), ITEMPCI, 2» REAORCZ2 W I N O S PCI).WINOSPCI)*1 .15 0 7 8 REAORCi] CALL S IGNC K (IT EMPCI,]),ITEMP C I,4» RfAORCZ. CALL S IGNC K ( ITEMP(I,S),ITEMP(I,&» REAORCZ5 TEMPD8 C I )=ITEMPCI,1) , RfA ORC26 TEMPWB C I)aITEMP(I,3) REAORC27 TEMPDPCI)=ITEMPCI, 5 ) RflORCZ8 C A LL S IGNCK CIHUMIDCI,l),IH UM IDC I,l RElORCZ9 , » HUMIOCI)=IHU MIDCI,I) REA ORC30 CALL SIGNCK (IPR ESSCI,3 ),IPRESS CI,4» RElORC]! PRESSR C I )=IPRE5SCI,3) REAORC]i P RESSR CI).PR.E S S�(I)*.Ol RElORC]3 ICOVER=O REAORC]. CALL SIGNCK CICOVER, ISKY( I , S » RElORC]5 100 SKY (I).I COVER* .l REAORC!6 R ETURN RfAORC]7 END REAORC!8 S UBROUTINE SIG NCK (IFLn, ISG N) . SIGNCK Z C THI S SUBROUTINE FURNI SHED BY NATIONAL CLI M ATIC CENTER, A SHEVILLE SIGNCK ] C � I LL TEST A NY PSYCHROM ETR IC WITH A SIGN-OVER-UNITS SIGNCK C POSITIO� READ AS At AND THE HIGH ORDER POSITION AS AN SIGNCK 54 C I SPEC IFICATION OF PROPER WIDTH SIGNCK 6 THE SIGN S H O ULD ENTER TH� PARAME TER LIST AS ISGN, S I GNCK C 7 C T H E REMA INING PORTION AS IFLD SIGNCK 8 C U PON RET URN THE SUaROUTINE THE VALUE IFL D SIGNCK 9 C AN I�TEGERFRO WITM H PROPER SIGN· OF WILL BE SIGNCK10 ,C I t wILL BE THE USER 'S RES PONSIBILI T Y TO CDNVERT THIS SIGNCK II C TO DEC IMAL WITH PROPER DEC IMAL ALIGNMENT SIGNCK 12 C INVAL ID CONDITIO N CAUSES IFLD TO BE SET TO 9�99 SIGNC K1] DIMENSION IP(10) ,MI NCIO) ,NUM (10) 81GNCK14 DIMENS ION INU M(10) SlGNCK l5 D NUMI ' 1 , 7 , 8 ' , , I A T Al ' , , 2' , f 3' , ' ,, ' , , S' , • 6' , f , , 9 ' , 0 ' S IGNCK C NOTE • SOME GOMPUTE� SYSTEMS MA Y REQUIRE OIFFE�E N T CHARAC TERS AS .S I GNC K1716 C THE LAS� CH�RACT�RS IN AR�AYS IP AND MIN S IGNCK18 Figure (Continued). B.1

94 D A T A M I N/ 'J' , 'K' , ' L ' , ' M ' , ' N ' , 'O', ' P ' , ' Q ' , ' R ' , '1'1 S IGNCK19 D T P ' ' ' , F ' G , ' A A I I A , , B , , C' , '0' , 'f·', ' , ' , H , , I ' , SIG N CK20 1 725555555555 55555555BI S IGNCK;!1 OATA NUM/1,2,3,4, 5,6, 7,8,Q,01 SIGNCK22 D A TA UST/ ' *'I SIGNCK23

DATA MINUS/ ' .. 'I SIGNCK24 nATA NULL/ ' 'I SIGNC K 25 tF ( ISGN. EQ. NULL. A N D.IFLD. N E.O) GO T O 125 SIGNCK26 I F (IS GN.EQ.IAST) TO 105 SIGNCK27 GO IF (IS GN.EQ.MINUS) GO TO 1 10 SIGNCKi8 00 100 SIGNCK2Q IF ( ISGNK=I. E�,10. lP ( K» GO T O 115 SIG�CK 3 0 I F (ISGN.EQ.MINCK» GO TO 120 SIGNCK31 IF (IS GN.EQ. I N UM (K» GO TO 115 SIGNCK]2 ' 100 C ONT INUE SIGHCK]) 105 IFLO= QQ9qqq RETURN JULSIGNY 9CK3 7 51 110 IFLO=tO SIGNCK3& RETURN SIGNCK37 125 IFLO=IFLD*lO SIGNCK38 RETURN SIGNCK3Q 115 IFLD= IFL D*J O+NUM (K) SIGNCK40 RETURN SIGNCK41 120 IFLD=-CIFLO* 10+ NUM ( K» SIGNCK42 RETURN SIGHCK 43 END SIGNCK44 SUBROUTINE SOLAR (LAT, V�,MONTH,DAy,SR AO) SOLAR 2 C SOLAR 3 C RETURNS INSOLATION IN 8TU/ FT**2/DAY A T EACH HOUR OF THE SOLAR 4 DAY . SOLAR 5 C INTEGER y�, MONTH,OAy,MONDAT(1 2) SOLAR 6 REAL L A T,SR AO ( 25) SOLAR 7 DATA MOND AT/0, 31 ,5Q,QO,IZ 0 , 151 ,181,212,243 , 273, 3G4,3341 SOLAR 8 LP=MOD (YR , SOLAR 9 IU I F(L P .NE.O)GO TO 1 20 SOLAR 0 DO 100 1=3,.12 SOLAR 111 M O NDAT ( I):MONDAT(I)+l SOLAR 12 12100 NUM=MONOAT (MO NTH) +DAY SOLAR C SOLAR 1314 C FIND TOTA L POSSIBLE D A ILY RADIA TION AND LEN GTH OF DAYLIGHT. SOLAR 15 C SOLAR 16 TOTRA D = HAMN(L AT,VR , NUM) SOLAR DAYNUM=N UM SOLAR 1 7 DAY LEN=DAYLIT( L AT,OAYNUM) SOLAR 18 C SOLAR 20lQ C CALCU LATE THE SINUSOInAL VARIATION IN DAILY RADIATION. SOLAR 21 C SOLAR 22 Tl=.5*DAY LEN SOLAR 23 A=.5* TOTRAO SOLAR 2 4 W= .2618 SOLAR 25 ALPHA = l./(l./ (A*� ) *SIN( W*Tl)·Tl/A*COS ( W*Tl» SOLAR 26 A L P T O=ALPH A*COS Cw*Tt) SOLAR DO 130 1=1 ,25 SOLAR i827 TO=I-l . SOLAR 29 SIUO O)= O. SOLAR 30 TO=ABS (TO-12.) SOLAR C S OLAR 331 2 C C ALCULATE RAT E OF INSOLATION FOR EACH HOUR OF DAY LIG HT . SOLAR 3 3 C SOLAR 34 IF (TO.LE.Tl)SRAO(I) =(ALPHA* COS ( W*TO)-ALPT O)*aA YLEN SOLAR 35 CONT I NUE SOL AR 36 1.50 IF ( lP.NE.O) RE TURN SOLAR 37 00 140 1=3, 12 SOLAR 38 MONDAT (J)= M O NDA T ( I)·l SOLAR n 140 RETURN SOLAR 40 Figure (Continued). SOLAR 41 END . B.1

95 FUNCTION D4YL ITCLAT , OAYNUM ) DAVLI T i! C DULIT ] C RETURNS HOURS OF D AYL IGHT GIVE N LATITUDE OF oaSERV4TION A�D 'D A YLIT- ,. C � U MaER DAY OF THE YEAR. LATITUDE MUST 8E 8ETWEE� 25 AND DAYLI T 5 C 50 DEGREOFES T NORHE TH. THE SOURCE FOR LENGTH OF D4YL IGH T JNFOR- D A YLIT THE 6 C MA TION (STORED IN 4RRAY 'LENGTH ') IS THE SNI THS ONIAN ME TEOROLO G- OAYLIT D A YL I T. 87 C ICAL T A BLES . C DAnlT � REAL LAT, LATBL (&) ,LENGTH C 6, 1 0) ,OAY(10) DAYLl'10 DATA LAT8L/25.,30 . ,35. ,40.,45., 50.011 D A YLlTll DATA OAY /·10.,t3 .,7�.,1 45. ,172.,197., Z 63.,333.,35 5.,378.1 D A YLIT1Z DATA (LENGTH(I,I),I= t,tO) DAVLlT13 1 110.58 ,10.13, 12.15�13 .50, 13.68,13.53. 1Z. 17,10.7], 10.58. 1 0.131 D A YLIT14 DATA CLENGTH(2, I), I.t,10J D A YLI T15 2/10.20, 1 0.4 0,12.15, 11.83,14 .08,1 3.81, IZ.11,10.40 , 10.20, 10.401 D A Y LIT16 D A T A C LENGT H(3, I)� I.I,10 ) OAnlTU 3/�. 8 0, 1 0.0], 12.15, 14.23, 1 4.S2, 14.26, 12.20, 1 0 .02,�. 80, 10.0]1 DAYL IT18 DATA (LENGTH ( 4 ,I) ,I=I,10) DAYL IT 19 DAYLIT20 4/�.33,�.60, ll.18, 14. &7,15 .02, 14.70 ,12.. Z2,q.60,9.3J,9.601 DATA CLENGTH (5, I),I= t,10) DAYLJT21 5/8.7S,9.10, 12. 1Q, 15.28,15.&1, 15. Z3, 12. Z3,q.0.,8.75,9.1 01 DAnIT2! D A TA CLENGTH (b,I),Ial,IO) DAYLI T!] &/8.01 , 8 . 50,12.22 , 15.83, 1 6 .38, IS.88, 12.2 8,8.48,8.07,8.501 DAYLITZ4 00 100 1=2, 10 DAnIT2S DAYlITZ6 IFU·CDAI -lYNUM . GE . D4Y CI1).A ND .DAYNUM .LT.DAY (I» GO TO 110 DAYLIT21 1 00 CONTINUE DAYLIT28 110 DO 120 K=2,6 DAYLITZ9 I

96 25 DATA L 40 11103 .0,�0 9.7, 1103.0, 151 4 .0, lq47.0,2397 .0,2&55.0, HAMN 212 9.0,2&03.0,2342.0, 1951 .0,14 19.0, 1103.0,9 09.1, H H N 1 A 2& 2' 1103.0, 1514 .01 HAMN 28Z 1 DATA L 4 5 1882.7,&8 1.3,881.0,1311 .0, 1 778.0,Z289.0,2&18.0, HAMN 2729. 0 ,25 71.0,224 7.0,11�9 .0, 1274.0,88 2.7,681 .3,881 .0, 1311.01 HAHN 1 ·9 DATA L 50 1&82.3, 4&3.3,b31 .0, 1053. 0, '5 8.0,Zl&5.0 , 2581 . 0� HAHN 230 & 3.1 1 2729.0,2527 .0,213 6.0, 1584 .0,10&0.0,682.3,4 63. 3,&3 1.7,1053.01 HAMN HAMN 32 DATA LT 125.0,]0 .0,3 5.0,40.0,45.0,50.01 D A TA 1M 11,]2,&0,91 ,121, 152, 182,21�,244,274,305, 3351 HAHN DATA 131,28,31 ,30,31 ,30,3 1,31,30,3 1,30,3 1 1 HAMN 33 N 3. OAYC :MODA H A MN 35 LEAP=MOO (YR , 4) H A HN HAHN 3]&7 (LEAP.NE.O) GO TO tl0 IF 38 DO 100 1:4, 16 HAMN OATE (l)aDATE (l)+l.O HAMN ' 3940 100 CONT INUE HAHN HAHN 41 DO 105 1=2, 11 IM(I)=IMCI)+1 HAMN-.Z + 1 HAMN (I) = N 4 3 105 CON NT I NUE(1) HAMN 44 110 SUM=O.O HAHN 45 (MODA.GT.O) GO TO 115 IF RADIATION MONTH -MODA HAHHAHNN 4' C F O R MOOA)O FINO AVERAGE SOLAR 41 MO=_MO'o A FOR HAHN 48 11 =IM H HN 4 9 A ID=N (MO)(MO ) H AHN 50 12=11 +10-1 HAHN H H 5251 DAYS: 10 A OAY=I1 N GO TO 120 HAHAMMNN 53 A N 54 c FOR MOOA>O FIND RADIATION FOR DAY #DAYCI H H 55 DAYC IS TO MODA A MN 5& C EQUIVA L ENCED H 115 1111:1 HAHN HAHN 5758 10=1 HAHN 12-1 DAYaDAYC A HN &059 H OAYS=l.O H A H 61 HAMN &Z 120 00 180 II= I1,I 2 C DETERMINE IF DAY TABULAR IS HAHN 63 C IF D AY NOT TABULAR, INDEX OF DAY H AHN MO=OOF &4 MI=O HAHN &5 && 130 HAHHAHNN 00 1 = 2, 14 &7 DATEI:DATE (I) HAMN 6 8 HAMN ' 9 IF .(DAY.NE.DATEI) GO TO 125 MOaI HAMN 70 GO 140 H A HN TO 11 c M D HAS INDEX IF DAY.oATE (I) HAHN 7a I 125 (DAY.GT.DATEI.A�D .nAY.LT.D ATE(I+l» GO TO 435 130 CONTIF INU� HAHHA.MNN 73 GO TO 140 HAHN 7. 135 MI=I ' HAMN 75 1& C M I=I FOR DATE(I» DAY)oATE ( I +l) HAHN 71 C DETERMINE IF LAT IS TASULAR VALUE HAHN 18 1 40 {MoDA .LT.O.ANO .II.GT.I1) GO TO 150 HAHN 79 ML=OIF 80 HAMN 00 1 45 1=1,& HA_H_� - 8L IF TO l45 HAMN (LAT.NE.LT(I») GO 82 ML= I HAHN 83 c ML= I FOR L A T TABU L A R VALUE A MN 84 H TO 1 5 0 HAHN 85 ' GO 145 CONU NU� HAHN 8& i I�O IF ·(M.D*ML .EQ.O) TO 155 GO Figure (Continued). HAMN .81 B.1

97 HAMN c TABULAR DATE + LATI1UOE 8 8 J= (ML -! ) *lb+�D H.HN 8q HAMN=L ( J ) HAMN 9 01 GO TO 175 HAHN qZ 155 IF (ML. EQ.O) GO TO 160 HAHN HAHN 93 c NON TA BU'AR DATE + TABUL AR LATITUDE Mll:Ml-t HAMN 9 4 J: (ML-\ )·l"+�I l HAHN C)5 H A MN:YLAG(DAY,DA TE CMI1) ,LCJ ),4 ) HAHN 9 & GO TO 175 HAHN '97 1&0 CLAT.LE. 32.5) LATF=l HAHN 98 IF CLAT.GT. 32 .5.ANO .LAT.LE .37 .5) LATF: 2 HAHN C)CJ IF CLAT.GT.37.5.AND .LAT.lE.42 .S) LATF=3 HAHN 100 IF (LAT. GT.42.5) L ATF:4 HAMN 101 X(l ) :LT(LATF) HAHN 102 X HLATF+l ) HAHN 103 X((2)3)=aL LT CLATF+2) HAHN 104 105 IF CMO .EG. O) GO TO 1 65 HAHN LAR DAY NON TABULAR LATI T UDE HAHN 1 06 c TABU + Y ( I'=L(CLATf-t )*l&+ MO ) HAHN 107 Y(2)= L C LATf*16+ MO l HAHN 108 Y(3) = L« LATF+ll*1&+ MO ) HAHN 10C) HAHN 110 GO T O 110. NON TABULAR DATE NON TABULAR LATI TUDE HAHN 111 C + 165 Ml=MI-l HAHN 112 YC11:YL AG COAY,DATECM 1" LCCl A TF-l )*lb+Ml ),4) HAHN Y(2):YLAGCDAY,DA TE (Ml) ,LCLA TF*1&+Ml 1 ,4) HAHN 1 13 4 Y(3)= Y LAG CDAY,O ATE C M 1),LC(LATF+l'*1&+Ml ),4' I1AMN 11 11US& 1 10 HAMN=YLAG CLAT, X,Y,3 ) HAHN O A Y:aDAY+l.0 H A HN HAMN 11U78 175 OAY=D AY+l .O SUM:SU M+HAMN HAHN 180 HAM�=AMINt (2729 .0,AMAX1 (SUM/DAYS,O.O» HAHN 119 IF CLEAP.NE. O) RETURN HAHN 121210 DO HAHN 122 DATE18CI):5 1 DAT=4,EC1&I)- l .O HA HN 123 185 C ONTINUE HAHN 1 2 4 DO 190 1=2, 11 HAHN 125 IM(I ):IM( I)-l HAHN 12& N(I)=NCI) -1 HAMN 121 190 CONT INUE HAMN 128 RE TURN HAHN 129 END HAHN 1 3 0 FUNCTION YLAGCXI,XtY , N) YLAG 2 C N-POINT LAGRANG IAN I NTERPOLATION WHERE I -l , N L A G 3 SPEC IAL VERS ION FOR USE WITH FUNC TION *HAMN* VYLAG ' C 4 C PROGRAM AlITHOR - -E .C.LONG . COMPUTER SCIENCES DIVISION--ORNL OAK VLAG 5 C UNION CARBIDE NUCLEAR DIVISION . RIDGE, TENN ESSEE VI-AG DIME NSI ON X ( N) , Y(N) VI-AS 61 S=O .O Y L A 8 Pal.0 VLAGG 9 10 DO 110 J:al , N VLAG P:P *(xt-X CJ» Y L A 1 1 G 0=1 .0 YLAG 12 DO 105 I=l ,N YI-AG 13 IF CI�NE.J) GO TO 100 YLAG 14 XO=XI YLAG 15 GO rO l OS YLAG 111 b 100 YLAG XD=X(J ) VLAG 18 (0 5 YI-AG 1 9 110 D=S=S+YD *(XO-X(J) /D(I ) 20 YI-AG=S * P YLAG RETURN YLAG 21 YLA . 22 END Figure (Continued). � B.1

98 PROGRAM COMET(INPUT, OUTPUT,TAPE5aINPUT ,TAPE&=OUTPUT) C C THIS _MOGRAM CALCULATES THE DIFFE RENCE BETWEEN THE EQUILIBRIUM TEMP- C ERATU RES OF TWO DATA SETS AND THE SENS ITIVITY TO T HE VARIOUS PARA- C ME TERS. e R. CODEll AND W. NUTTLE , USNRC , OCTOBER, 1 '78 C C TD1- DEw P OINT TEMP . FOR DATA SET 1 (F) e T A l a DRY �Ul8 TEMP. FOR DATA SET 1 (F) C W I- WIND SPEED FOR DATA SET 1 (MPH) HI- RATE OF I N SOLATION FOR D ATA SET 1 (8TU/FT**2/0AY) � . C TDZ- DEW POINT TEMP� FOR DATA SET Z CF) C TAZ= DRY BULB TEMP . FOM DATA. SET Z CF) C W2- WIND SPEED F OR DATA SET Z (MPH) e HZa RATE OF INSOLATION FOR DATA SET Z (8TU/FT**2/DAY) C COMMON/EVAP/Ak ,B DATA QX,QY,QXZ,QY Z,QCROSS/S*O.OI OATA ERR/l .0E-301 DATA S X,SY,SXZ,SYZ,SC R OSS/S*O .I WR ITE e&,lO O) 100 FORMAT C1Hl,10X, ' PROGRAM TO COMPARE EQUILI8RIUM TEMPERATURES 'ROM T tWO DATA S ETS AND C O MPUTE THE SENSITIVITY OF EACH VARI ABLE i ,ll) READ (5,499) I 499 FORMAT C U) DO Z Jal ,I READ CS,500) TD 1 ,TA1,Wl,Hl , TDZ,TA2,WZ,HZ 500 FORMAT(8Fl0.l) . IFCHZ.EQ.O.) HZ-HI C e CALCULATE EQUILI8R IUM TEMPERATURES e El-E (TOi,TA1,W l,Hl) . EVAPl a30.*(AK-15.7)*a* CE1-TD1)/(&Z.4*( .Z&+B) *1000) EZ-E CTDZ,TAZ,WZ,HZ) EVAPZ-30.*(AK-15.7)*B* CEZ-TDZ)/(&2.4*( .Z6+8)*100 0) ·DE-EZ-U DEV AP-EVAPZ-EVAPI "'RITE e6,99) WR ITEC6,101)TD1,TA1 ,Wl ,Hl, E l,EVAPI W RITE (6,200) TDZ,TAZ,W2,HZ,EZ,EVAPZ 99 FORMAT (TZ&, 'DEW POINT',T4Z, 'DRY 8UlB ',T56, 'WIND SPEED ',T•• , I'S OLAR RAD.',T8 Z, 'EQUILI ARIUM TEMP.',Tl04 ,'EVAPORA T ION',/tT27, Z' CDE G. F) ',T5','CMPH ) ',T67 , 'CBTU/FT**Z/DY) ' ,T86, ' CDEI . ') ',TIOI, 3'CFT**3/'T**Z) ',II) 101 F ORMAT (10X , 'OATA S ET 1 ',F1Z.Z,4FI5.Z,FZ O.Z,/ ) ZOO FORMAT elOX, 'DATA SET 2 ',F I2.2,4 FI5.2,F20.2,11) WR ITE C6,10Z) DE , DEVAP 10Z FORMATCT77, 'EZ-E l - " F6.3,5X, 'EVAPZ-EVAPI ',F7.Z) _ C C CALCULATE SUMS FOR CORRELATION COEFFICIENT S C SX-ShU SXZ-SXZ+El"Z SY-ShU SYZ-SYhU ..Z SeROSS =SCROSS+E l*EZ QxaQX+EVAPI QXZaQXZ+EVAP1"Z QY-QY+EVAPZ gyzaQY2+EVAPZ"Z QCROSSaQCROSS+EVAP1*EvAP2

�igure Listing of Program ET. B.2 COM

99 C C DIFFER ENCES I� EQUILIBRIUM TEMP D UE TO EAC H P ARAME TER. C OTO=E (T0 2,TA1, W l,Hl)-El OTA=E (T01, TA2,Wl ,Hl)-El OW =E CTD 1,TA1,w2,H l)-El O�.E ( T 01 ,TAI,Wl ,H2 )-El OTOT=OTo+OTA+DW+OH WR ITE C6,5 ) 5 F O RMAT( 1 110X, 'DIF FERENCES IN E BETwEEN DATA SET 2 AND DATA SET 1 lBV PARAMETER ' ,/) WR ITEC6,&) OTD & FORMATC10X, 'OIFFERENCE DUE TO DEW PO INT . ',T50,F10.J, ' DEG. WR ITE (&,7 )DTA F') 7 FORM AT ClOX, 'DIFFERENCE DUE TO DRY BULB TEMP ',T50,Fl"0.J, · DES . • • 1 F') WRITE l&,8) OW 8 FORMAT ( l OX, 'OIFFERENCE DUE TO WIND SPEED . ',T50,Fl0.J, ' DEG. WRITEC &,Cf)OH F') ; FORMAT ( l OX, 'DIFFERENCE D UE TO INSOLATION �T50,Fl0.3, ; DEI . F ) q • I'IRITEC&,tO)OTOT 1 0 FORMAH10X, 'SU MMATION O'F INDIVIDUAL OIF ERENCES ',T 50 ,Fl0.3, ' DE • lG. F',II, lX,130C' * '),III) � 2 coronIN UE C C CORRELATION ANALYSIS C S XX=hSlC2-SU*2 sn-I *SV2-SY**2 SXYal*SCROSS-SX*SY RSQ_ (SXY**2+ERR)/(SlClC*SYY+ER�) QXX- I*QX2-QlC**2 Q YV-I*QY2- QY**2 QXV-I*QCROSS-QhQY QRSQ- CQXY**2+ERR)/CQXX*QYY+ER R) SERR-SQRT(CCSlClC*SYY)-SlCY**2)/(I*CI-2 )*S lClC» QSERR-SQRT (C(QXX *QYY)-QlCY**2) / (I*(1 - 2) *QXlC» WR ITE (&, 300) RSQ, SERR WRITE C&,310) QRSQ,QSE RR 300 FORMAT C10lC, 'SA MPLE R SQUARED FOR EQUIL BRIUM TEMP • • ',Fl0.S, 1 10l, ' STANOARD ERROR - ',F10.J, ' D ES . F')I 310 FORMAT (lO X, 'SAMPLE R SQUARED FOR EVAP.ORATION E1S.S, ; • . " 1 10l,' STANoARD ERRQR - ',EI3.3, 'FT**3/ FT**2 ) SXXI-SX II Svn- sy II BIAS-SnI-SUI WRITE( &,250) SXXI,SYYI, BIAS ' 250 FORMAT (10X, ' AVERAGE E, DATA SET 1 ' ,FI2.3,I,10X, AVERAQI I, DATA i _ 1 SET 2 ' ,F12.3,1,10X, AVERAGE E2 - AVERAGE E ',FI2.4) • • l • EBllS= (QY-QX)/1 W RITEC&,251) EBIAS 251 F ORMAT (lOX, 'AV ERAGE EVAP2 - AVERAGE EVAPI ',FI2.4) • STOP END FUNCT ION E(To ,TA,W,H ) C C CALCULATES THE EQUILIBR I UM TEMPERATU R E BY THE BRADY METHOD C AN ITERATIVE PROCESS. IN C COMMON/EVAP/AK,B DATA A K,ES/IOO.,lOO.1 DO 1 1-1 ,50 TS TAR- (ES+TO) IC!.

B=. 255-.0085*TSTAR +.000204*TSTAR**2 AK:15. 7+ (S+.26) *(7 0.+.7*w**2) E=H/AK+C 8 * To+.2&*TA)/CB +.26 ) IF ( ABSCES-E) .LT 001) G O TO • • c ES-E 1 C ONTINUE 2 RETURN END Figure (Continued). B.2

100 PROG RAM UHS 3 CINPUT.OUTPUT.T APE5-INPUT . TAPE6-0UTPUT . I TAPER) 0001 10 C PROGRAM TO CALC UL ATE �AX T E MPERATURE IN A UHS PO�O 000120 C BY PLUG.M IXEO .iNO STRATIFI ED MODELS 000130 C R C OOELL USNRC NOV 191 8 000140 DIMENSI ON RCIO) .SCIO) .BCIO) .C CII) T I ME (20 ) .ITITLE C80) . • LOGICAL F LAGI 000160 C OMMO N AKI.E ,E2 ,BETA, TSK I P , QBA SE ,FBA SE, M I ,Ml,B TA,BT D,BHS,BW, I I ME T ,BL O W, FI,QI,TD, TA,HS,W,GC IOOO,4) , H EATClO) ,FLOW ClO). rTHClO) , l NME T,NH,A,DTME T NAMELIST/HFTI NH , H EAT,FL O�,TH 0 00135 O ATA M4 ,NSTEPS,NPRINT/O, 100. 101 DATA DT,TZERO/0.l,80.01 DATA TIMEM, T IMEST, T IMEPL/3*0. 01 II�LISTI VZER O,ALOW, A,NH,N TEPS, NPR OOOUO NAMELIST INT,DT,TZ. ER. O,DTMET I , TSK IP.Q8ASE,FBASE,E,AK I,I MET,AMAKES I ,8TA,BTD,BHS,8- 0001 55 l ,HEAT,FLOW,TH 00025. REAOC5, 101) NMET 101 F OR� ATCI5 ) , 000Z80 C READ IN MET TABLE C_IND SP .,DRY 8UL8,DE� PT,SOL RAD) OOOln READ CS, I) C CI, O) , GCI,l) ,G(I,l) , G(I , 3) ,CC,RH, I.\,N ME T) I FORMATC 3 X ,3F5� .0,F6.0 , lFO .0,3F 5.0,F6.0,lF 4.0 ) . C VZERO -V OLUME OF POND FT**3 C B L Ow . BLOWDOW N RATE OUT FT**3/HR C A = SURFACE AREA FT**l C NSTEPS - � UMBER OF INTEGRATION STEPS C NPR INT = P R INT EVERY NPRINT STEPS C DT = INTEGRATION TIMESTE P , HRS C TZERO INITIAL P OND TEMP OEG.F = C GCI,I,=TD-DEW POINT, OEG.F C GCI,l)=TA- DRY BUL8 DEG.F C G(I,3) aHS a SOLAR RAOI ATION BTU/ (FT**l DAY) C G(I,4)= = wIND SPEED MP H W C TSKIP = DELAY STAMT OF HEAT TA8LE BY T SK IP HRS C QBASE = BASE HEAT LOAD, �TU/HR C FBASE = B ASE FLOW, FT**3/HR C E C ONST EQUILIBRIUM T EMP , nEG.F IF U SED C AKI = C O�STANT H .T.CDEFF, HTU/ CFT**l DAY DES.F) , IF USED C IME T OPTIONAL C ONSTANT E A ND AKI IF IMET • = I C BTA,BTD,BHS,BW BIASES TO ADDEO T O ALL MET TABLE VALUES • 8E C OF TA ,TD,HS,AN D W RESPECTIVELY C NH = �UMBER OF ENTRIES IN HEAT TABLE C HEAT . ARRAY OF HEAT INPUTS, 8 TU/HR C FLOW = ARRAY OF FLOW R ATES, FT **3/HR TH ARRAY OF CORRESPOND ING TIMES F O R HEAT AND FLOW ARRA YS C • B L OUO 000310 AMAKE=O DTMET=' 000360 TSK IP =O 000310 QUSE=O 000380 FBASE=O 000390 BTA=O 000393 8 TD=0 000394 BHS=O 000395 Bw=O 000396 E=8 0 000400 AKI='SO 000410 I MET-O 000410 TO=GCI,I) 000430 T&=GCI,i!) 000440 HS=G Cl, 3) 0001150 W8S U , .) 000.. 0 1t1A 0 ( 5 , HF T ) DO • 1 8 1 , NH 000510 TlNEU)·TH (I ) TH( I)-TH ( I).I.OE-ZO 0005.0 • T H el).ALOS (TH(I» OOOSSO I'(NH.&T.�). &6TO 110 0005.0 'LOW(Z ) 8'LOWel) . 00OS1O HIA T eZ) 8HEAT (1) oooseo fIIH82 OOOS" TH(Z)8 1.0U 000.00 110 CONTl NU! 000.10

Figure B.3 Listing of Program UHS3. ,

101 .000 CONTINUE READ CS,.I O) I TITLE .10 FORMAT CIOA1) Il EADCS,I NLIIT) IF CYZEAO.LE.O.O) STOP WR ITE ( 6," 0) ITITLE •• 0 FOAMAT (IH l,5(/) �TIO,IOA1 ) WR ITE ( 6 ,SOO) YZIRO,A,8Low,AMA K E,NSTEPS,NPRINT,OT,TZERO, lTSK IP,Q8 ASE,F8ASE,E,AK1,IMET,8 TA,8TO,8HS,8W 500 FOA MAT ( 5(/),T.3, 'YZ E II0',T57 , · A · ,T66 . · 8LOW·.T76, 'AMAKE ·,I. T3•• lEl1.S .l• • Ell.5 , 3 •• E •• 3. I X.E•• 3 . II.T.3. 'NSTEPS ' ,T53. 'NP IIINT·.T65 . I·OT·.T 73. ·TZEIIO ·.T••• ·TSKIP'.I.T'3. 15. T5•• I • • T6•• F5.3.T73 ,F5.1. � ' T .3.F6.1.II�T ••• ·g8ASE ' .T5., ·F8 ASE .T65. ·E·.T7 • • ·AK1' .T.'. 'IMET'.I • • T'I .E• • 3. 1 •• E ••3. 3.,F5.1.5•• '5 .1,7•• ll.II.T. 5. ·8T A·,T55. ' 8TO · . T6. 5. · 8HS'.T75. ·8W' .I.T••• F'.1.6•• ' • • 1 .5• • F6. I.S.,F'.1 .6(Il .T.3. 635 ( ·.·).I.T'3. ·, HEAT IN ME FROM F L Ow IN 1;.I.T.3. ·1 8TUI I TI I 7HII T A T F T 3 / H 1 '.I.T'3.3 5('.'» • I A I •• A DO if I-I , NH I WII ITE (6.510)HEAT(I),TIME(I),F LOW(I) , 510 FORMAT ( T.3. ·,·. E • • 3. 1 •• ,·,I•• F 7.1.1 •• ·,;, E'.3. 1., ' I ' ) . wtUTE (6,510) 510 FOAMAT C T ,. 3, 3 5 ('.·) .5(1) . U l . l l ( '.').' MODEL IIEIUL TS ' .Il( ' . ' ) ,III. IT38,'•• TIME •••••••TEM PEIIATUAE (F) ••••••••Y OLUME •••• · .I.T3., ·. H II I MI.EO STRAT PLUG FT 3 1 ·.I.T38.46C'.'» • • • I •• FLAG1-.FALS.E . 000f>/l5 T5-0 OOObSO TMUn-O OOOb&O TMUPL-O 000f>70 M l -1 OOOftlO MI- I 000&90 . - . 0 01 000700 DO 3 1 - 1 . 1 0 000710 I (I) -TZEII O 000720 3 C(1+ U - T ZERO 000730 T aTZEIIO 000740 V_VZEAO 00074S c B E GIN NUMEIIICAL INTEGRATIONS 0007.0 DO b ioi_I . NSfEPS ooono c MIXED TANK SOL U TIO N S 000800 CALL MIXEO (FI,F3.T.V.X) 000810 CALL MIXEO CF7.F8.T+OT.F2,V+oT*F3.X+OT) 000820 TaT+oT. CF2+F7 )/2 000830 Vay+oT* (F3+F8 )/2 00084 0 c FIND MAX TEMPERATURE FOR MIXED MOOEL 0008S0 IF CT.LT. TS) GOTO b3 0 0 0 8 b O TS-T 000870 T I E 000880 M M _ . b3 CONTINUE 0008qO M4-M4+ 1 OOOqOO c STRAT IFIED MODEL OOOqlO A L l aY/ A 000q20 A L 3aY/ l0 OOO Q30 ALUA L111 0 000Q40 ALb a D T ( 4 * A L ) 000950 / f>2 . 3 A L 2 a F 1 1 A OOOQbO A L S I: AL2 *DT / A L 4 000Q70 CALL EQTEMP ( SCI» 000980 AK =AK 1 *A/24 0009QO RCI)aS(1)+ALS* (S(10 )-S(I» +(�I- AK. ( S (I)-f » *ALb 0010 Cl O 00 q 1=2,1 0 001010 q RCI)=S(I)+ALS* (S(I-ll-S(I» 001020 DO 10 1 = 1010 001030 10 SO)= k(J) 001 0 40 C P L UG FLOw MODEL 001 1110 C(l)=C(II) 001150 00 2 0 1=1 010 001160 8(1)=C(I+I )+AL5* (C CI)-C(I+I ») 001170 CALL EQTEMP CC C I) 001 t80 A K = A K I*'012110 00\ 190 8CI)=ACI )-'K*CBCI)-� ) *ALb 001200 20 ' RCI)= 8Cl)+ALb*Ql 001210 DO 21 1=1 010 001220 21 CCI+l )=IHll 0 0t230 IF CS(tn) .LT.TMA�ST) GOlD �, 00t 2 110 T M A XST=SCIO) 001250 TIMEST=X 0012&0

Figure (Continued). B.3

102 Itl CONTINUE 00 l10' IF (C (l1).Lf . TMU PL ) GOTO ItZ 0011i 80 TMA. P LaC (ll) OOll'O ' TIME PLalt 001 300 Itl CON TINUE 001310 . a .+OT 001310 IF (NP RINT.Gt.Ma) GOTO & 001 330 M 4 = 0 001 ' 40 WR ITEC&,51) It,T,SCIO),C(I O) ,V 51 FORMAT (T3 8 ,'I ',aCl.. ,F�.I,IX, ' I') ,E11.5,IX,'I') It CONTINUE 001370 WR ITE (&,55) T5, TIM EM, TMA XST,TI MEST,TMAXPL,TIMEPL 5 5 FORMA T ( T 38 ,4& C'.'),III,T 40, ' MAltIMUM MODELL EO T EMPERATUR ESI ',I ,T40 I,'M I XED MODEL = ·,FR.l, ' AT ',F8.l ' HOURS',I,T40, 'STRAT MODEL 8 ' l,F8.2, ' AT ', �.2, ' HOURS ',I,T40, 'PLUG MODEL ' ,F8.l, · AT . , a 3F8.l, ' HOURS ')� GOTO & 000 001430 END 001440 SUBROUTINE MIX ED (FA,F8 ,T,V,X) 0014 50 C MIXED TANK MOD EL COMMON AK1,E , El,"ETA,TS KIP,QBASE . FBASE,MI,Ml ,BTA,BTD,�HS,8W , I IME T ,BLO�,FI,QI,TD, T A ,HS,W,G(I OOO, 4) ,HE A T(lO) ,FLOW (lO) ,TH(2 0) , 2 NMET,NH ,A,DT MET C L OG-L I NEAR INTERPOLATI ON OF HEAT T A BLE 001530 DO I M l aMi ,NH 001540 X l = X-TSK I P 001550 IF (XI .LE.O.O) xI=.OOOOI 0015&0 X'''LOG C . . ) 001510 IF (X'.LT.TH(MI » GOTO I 001580 IF (X'.LT . TH C MI+I » GOTO IllO 0015.0 I CONTINUE 0011t00 1210 F4= C X,-TH CMI1)/CT hCMI+Il-TH (MI » 0011t10 Mi=MI 001&20 C EXTERNAL HEAT IN PUT TO P OND Q I 8HEAT (MI) +F4* ( HE AT(MI +I)-HE AT(MI » 001&30 C CIRCULATION THROUGH POND FI=FLOW CMI )+F4* C F L O W ( MI+I)-FLOW CMI » 001&40 C ADO BASE HEAT LOAD AND F L OW, IF ANY Q I =QI+QBASE 001&50 FI=FI+FBASE 00 1 660 C LINEAR INTERPOLATION OF MET T A BLE 001&70 I F ( N ME T.EQ . I) GOTO 100 001&80 M I =X/DTMET +I 001&'0 F4= (X-CMI-I ) *OTMET 1 /DTHE T 0 01100 TD=G ( MI ,I)+F4* (GCMI+I,11- G ( M I ,I» 001710 TA=G C M I , 2 ) + F4* CG CMI+I , 2 )-GCMI ,2» 001720 H S =G (MI ,3)+F4*CGCM I+I , 3)-G (MI , 3) 1 001730 w8GCMI ,4)+F4* CGC M I+I,4)-GCM I , 4» 001740 TDaTD+8TD 001 74l TA= TA+BTA 001 743 H S=HS+BHS 001144 W=w+BW 001745 100 CONT I NUE 001150 CALL EQTEMP ( T ) 0011&0 AK=AKI*A/24 001110 C RAT E OF TEMPERATURE CHANGE , OEG F/HR FA=(QI-A K*(T-E » /(&2 .4*V) 001180 C EVAPORATION RATE, FT**3/HR E 2a (AKI-15.71*8ETA* CT-TO)*A/(1t2.4* C .2&+8ETA)*24000) 0011'0 C RATE OF VOLUME CHANGE, FT**3/HR Fa=-BLOw-El 001810 R ETURN 001810 END 001830 SUBROUTINE EQTEMP C ) . 00lS40 C CALCULATE EQuILI8RIUiM T EMP ERATU R E A ND HEAT TRANSF E R COEFF C OMMON AKI,E,E2,8E TA, TSKIP,Q8ASE,FBASE , M l,M2,8TA,BTD,BHS,BW, I IMET,BLOW,FI, Q I ,TO,TA,HS,W,GC I OOO,4) ,HEAT(lO) ,FLOW (lO) ,TH(lO) , l NME T , N H,A,DTMET IF( IMET.EQ.I) RETURN 001'20 C WIND FUNCTION G7=70+.7*W **2 oOlno G5=(TD + T )12 OOIUO 8ETAa . 255-.0085*G5+.000204 *G5**2 001.50 C SURFA C E HEAT TRANSFER 001 .&0 AKI815.7+(.l&+BETA1*G7 001.10 EaHS/AK1+(.llt*T A+8ETA*TO)/ (.l&+BETA) oOlno RETURN 001 .. 0 END 002000

Figure B.3 (Continued).

103 SU8ROUT INE PSY1 (08,�B,PA,OP,PV,W,H,V,RH ) psn I THIS ROUTINE C A LCULATES' VAPOR PV, HUMID ITY R ATIO PSYI 2 C PR�SSURE � , C E�THALPY VOLUME V , REL ATIVE HUMIDITY RH, AND PSY1 3 C D EW POINT�, TEMP ERATURE DP\ PSYI 4 C WH E THE DRY BULB TEMP ERATURE 08, WET 8UL8 TEMPERATURE w8 , PSYI 5 C AND � BAR OMETRIC PR ESSURE P8 A R E G IVEN P SYI 6 C UNI T S' 08, wa , + D P )F> \ PS,. + P V )IN OF MG>\ W)= WATER VAP OR PSYl 7 C PER = DRY A I R>\ H )BTU/= O F DRY AIR>\ V )FT**3/= O F DRY P SYI 8 C AIR\ R H IS A FRAC T I ON, NOT ( PSYI 9 C (F )=(F -32.0E O)/l.�EO P S Y l 1 0 PVP= PVSF( 1'I8) PSYI II W S TAR=0. &22*PVP/(P B-PVP) PSYI 13 IF (W8.GT.32.0) GO TO 105 P SYl 14 PV=PVP-5 .10aE-a*PB* (D8-WB)/l.8 PSYl 15 GO TO 110 PSYI 16 100 PV=.P VP PSYI 17 GO TO 110 PS Yl 18 105 C08=C (DB) PSYl 19 CW8=C (WB) PSYl 20 HL=591 .31+0.aa09*CD8-Cw8 PSYI 21 CH=0 .2402+0. 4a09*WSTAR PSYl i!2 E X= ( WSTAR-CH* (CD8-CNB)/HL)/0.622 PSYI i!3 PVaPhEX/ Ct.+EX) PSYI 2. 110 W=0 .622*PV/ (PB-PV) PSYl 25 V=0 .154* C D8+4S9 .7)*(1 . 0+1000.0*W/ 436 0.0)/ PB PSYl 26 H=0 . 2 4 *DB+ (1061.0+0 .444*D8) * W P SYl 27 IF (PV .GT.O.O) GO TO 115 PSYI 28 PV= O.O PSYl n DP=O .O PSYI ]0 R H=O.O PSYl 31 RETURN PSYI n 115 I F (DB.NE.W B) GO TO 120 PSYl ] ] DP=oe PSYI ]4 RHal .0 PSYl 35 RETURN PSYl 36 1 20 opaOPF (PV) PSYl 57 RH=PV/PVSF (OB) PSYl ]8 RETURN PSYl n END PSYl 40 SUBROUT INE PSY2 (DB,OP,P B,WB,PV,W,H,V,RH) PSYi! 1 C THIS ROUT INE CALCULATES' wE T BULB TEMPERATURE WB , HUMIDITY Psv2 2 C RAT IO 1'1, ENTHALPY H, VOLUME V, VAPOR PRESSURE PV, PSY2 3 C A ND RELATIVE HUMIDITY RH\ PSY2 • C WHEN DRY BULB TEMPER ATURE DB , DEW POINT TEMPERATURE DP, PSY2 5 C AND 8AROMETRIC PRESSURE P8 ARE GIVEN p sn 6 C UNITS' 08, 1'18 , + DP IF>\ PB , + PV )IN OF HG>' 1'1). WATER VAPOR PSY2 7 C PE� = DRY A R>' � )8TU/. OF DRY Al R>' V )FT**3/= OF DRY PSY2 8 C A IR' RH IS AJ FRAC TION, NOT ( PSY2 CJ IF (OP.GT.OB) DP=De PSYi! 10 PvaPVSF (DP) Psv 2 II PVS=PVSF (DB) psn 12 RH=PV/PVS PSYi! 13 W = 0.622*PV/ ( PB-PV) PSY2 1. V=0. 154* (OB+4 9.1)*Cl.0+1000. 0*W/ 436 0.0)/ P B PSY2 1 5 HaO .24*D8+ (I0S61 .0+0.444*DB)* W PSY2 16 IF (H .GT.O.O) GO TO 100 PSY2 17 w8=DP PSY2 18 RET RN PSY2 19 1 00- WB=W8FU (H,P8) psn . 20 RETURN . psn 21 E ND PSY2 22 FUN CTION PVSF (X ) PVSF 1 PVSF D IMENSION A(&) , 8(Q) ,P(q) 2 DATA A� -7 . 902q�,5.02808,-I . �8 16E-7,11.3Q 4.8.1328E- 3,-3.4q1491 PVSF 3 PVSF DATA B/- 9 . 09118,-�.56654,O.87679 3,O.00602731 4 T = ( X+459. 6 88)/l.8 P VSF 5 PVSF 6 IF (T.LT.273.1&) GO TO 100 Z=373.161T PVSF 7 P(l)=A (I)* (Z-l . O) PVSF 8 P(2)=A (2)*ALOG10(Z) PVSF 9 ZI=A(4 ) *(1.0- 1 .011) PVSF PVSF 110 1 P ( 3) A (3) * ( 10.0** t • 0 ) = �1" Figure Listing of Psychrometric Subroutines. 8.4

104 Z1=A (&)*(2-1 .0) PVSF 12 P(4)=A C5)*CI0.0**21-1.0) PVSF 1 3 GO TO 105 PVSF 14 100 2=273.1&/T PVSF 15 P(1)=8Cl)*CZ-l .0) PVSF 1& P(2)=AC2 )*A L OGI0(Z) PVSF 17 P(3 )Z8C3) * (1.0-1 .0/Z) PI/SF 1 8 P(4)=ALOGI0CB(4» PVSF 19 105 SUM:aO.O PVSF 20 D O 110 1=1 ,4 PI/SF 2 1 110 SUM=SUM+P (I) PVSF 22 PVSF=29.921*10.0**SUM PVSF 23 RET URN PVSF 24 END PVSF 25 FUNCTION OPF (PV) OPF 1 C THIS ROUTINE CALCULATE S DEW-.POINT TEMPERATURE FO� A GIVEN OPF 2 OPF C VAPOR PRESSURE PV 3 OP (A,B,C, Yl=A+( B+C*Y)*Y OPF 4 UALOG (PV) O PF 5 I F ( P V.G T.0.183&) GO TO 100 OPF & OPF=OP(71.9S,24.873,0.8Q27,Y) OPF 7 RET URN OPF 8 1 00 OPF=OP (79.047, 30.S79, 1.8 893, Y ) OPF 9 RETURN O PF 10 END OPF 11 FU�CTION W8f (H,PB) WBF 1 C THIS ROUTINE APPROXIMATES THE w ET BUL8 TEMPERATURE FROM weF 2 C ENTHALPY H, AND BAROMETRIC PRESSURE PB WBF 3 WB ( A ,B,C,D,Y)=A+ (B+(C+O *Y) *Y)*Y weF 4 W (PV, PB)=0.&22*PV/(PB-PV) WBF 5 X(WB12,W12)=0.24*�8t2+(10bl.0+0. 444*wB1 2)*W12 WBF & IF (H.LE.O.O) GO TO 105 W BF 7 yzA LOG ( H ) WBF 8 IF (H.GT.l1.7 5S) GO TO 100 WBF 9 wBF=wB (0.&0 41 , 3.4841 ,1. 3&Ol,O.97307,Y) WBF 10 RETURN wBF 11 1 00 WBFzW8 (30.91S5,-39.&82,20.5841 ,-1.75S,Y) wBF 1 2 RETURN weF 13 105 WB 1=150.0 WBF 14 PV1:aPVSF CW81) W BF 1 5 Wl=W(P V1 ,PB) WBF 1& Xl=X(W81 ,wl) WSF 17 n=H-Xl WBF 18 110 WB2=we l-l .0 WBF 19 PV2=PVSF (wB2) WBF 20 w2zW (PV2,PB) WSF 21 X2zX ( WB2 , W 2) WBF 22 Y2=H-X2 WBF 23 I F (Yl*Y 2 ) 130, 120, 115 WBF 24 115 wB l =we2 WBF 25 Y1=Y 2 W8F 2& GO TO r110 WBF 27 120 I F (Yl. NE .O.O) GO TO 125 WBF 28 WBF= W8 1 I'/BF 29 RETURN WBf 30 125 WBF=I'IA2 wElF 31 RETURN wBF 32 130 Z=ABS (Yl/Y2) I'fBF 33 W8F= (WB2*Z+�Bl)/(1.O+Z) wBf 34 RETURN waF 35 END wBF 3"

Figure B.4 (Continued).

.u.s. GOVERIII!EIiT PRIHTIlfG OFFICE. 1980-0-,341-742/581

105

•

NRC 335 ' 1. REPORT NUMBE R (A ssigt1e d by DOC) FORM U.S. NUCLEAR REGULATORY COMMISSION 17-77) NUREG-0693 BIBLIOGRAPHIC DATA SHEET 4_ TITLE AN D SUBTITLE (Add Volume ND., if IIPpropria lll) 2_ (Leave blank)

Analysis of Ultimate Heat Sink Cool ing Ponds 3_ RECIPIENT'S ACCESSION NO_

7_ AUTHOR IS) 5. DATE REPORT COMPLETED Ri chard B. Code1 1 and William Nuttle YEAR K. fVJ�Nr I 1980 U Y PE RFORMING ORGAN I ZATI ON NAME AND MAILING ADDRESS (Include DATE REPORT ISSUED 9_ - Zip Code) -- _._------_._-- --- _._ .. -- . _. �NTH I YEAR I Re.ctor gu l-rio n ovember 1980 Office of Nuc lear � Nuc lear Comm1ss on 6_ (L eIWe blank) atory U.S. Regul �'. r Washington , . 2,555 • "r' DC - .� 8_ (L eave blan k)

12. SP ONSORING ORGAN I ZATION NAME AND MAI LING ADD RESS (Include Zip Code) 10_ PROJECT/TASK/WORK UN IT NO. N A 11. COI NTRACT NO. Same as 9, above .

N/A 13. TYPE OF REPORT PE RIOO COVE RED (I nclusive da lllS)

Technical Report I N /A 15. SU PPLEMENTARY NOTE S 14. (LeIWe blank) Computer Programs Avai labl e 16. ABSTRACT (200 words or less) method to analyze the perfonnance ·of ultimate heat sink cool ing ponds .i s A presented . A simple mathematical mode·1 a cool ing pond is used to scan of weather data to determine the period of the record for whi ch the most adverse pond temperature or rate of evaporation wou ld occur. Once the most advers e conditions have been detenni ned., the peak pond temperature can be calculated. Severa l simple mathematical models -of ponds are described ; these could be u sed to detennine peak pond temperature , us ing the identi fi ed meteorological - record . Evaporative water loss may be found direct1Y ' from the scanning'by a simple and conservative heat:'and-material ba lance.

Methodol ogy by which short peri ods of onsite data can be compared wi th longer offsite records is developed , so that the adequacy of the offs ite data for pond perfonnance co mputations can be establ i shed.

17. KEY WOR DS AND DOCUMENT ANALYSIS 17a. DESCRIPTORS

Ultimate Heat Sink Cool ing Poi'lds , Mathematical Models Evaporation

17b. IDENTI FIERS/OPE N-ENDED TE RMS

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