EPA-660/3-75-037
JUNE 1975
Ecological Research Series
Improving the Statistical Reliability of
Stream Heat Assimilation Prediction
SB.
01
O
National Environmental Research Center
Office of Research and Development
U.S. Environmental Protection Agency
Corvallis, Oregon 97330
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development,
U.S. Environmental Protection Agency, have been grouped into
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technology. Elimination of traditional grouping was consciously
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1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the ECOLOGICAL RESEARCH STUDIES
series. This series describes research on the effects of pollution
on humans, plant and animal species, and materials. Problems are
assessed for their long- and short-term influences. Investigations
include formation, transport, and pathway studies to determine the
fate of pollutants and their effects. This work provides the technical
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EPA REVIEW NOTICE
This report has been reviewed by the Office of Research and
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EPA-660/3-75-037
JUNE 1975
IMPROVING THE STATISTICAL RELIABILITY OF
STREAM HEAT ASSIMILATION PREDICTION
by
Richard W. McLay
Mahendra S. Hundal
Kathleen R. Lamborn
Contract 68-03-0439
Program Element 1BA032
ROAP/Task No. 21 AJH/35
Project Officer
Bruce A. Tichenor
Pacific Northwest Environmental Research Laboratory
National Environmental Research Center
Corvallis, Oregon 97330
NATIONAL ENVIRONMENTAL RESEARCH CENTER
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CORVALLIS, OREGON 97330
For sale by the Superintendent of Documents, U.S. Government
Printing Office, Washington, D.C. 20402
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ABSTRACT
In response to an increased interest in water quality
by the public, a large effort has been mounted to develop
mathematical models for predicting heat assimilation in
bodies of water. The accuracy of these models has recently
come under scrutiny due to the need for temperature
predictions within 1 °C of the ambient. This work is
an evaluation of existing, one-dimensional stream tem-
perature prediction techniques for accuracy and precision.
The approach is through error estimates on a general
model that encompasses all of the models presently used.
A sensitivity analysis of this general model is used
in conjunction with statistical methods to determine the
solution errors. Data taken in 1973 at the Vernon, Vermont
nuclear plant are used as a data base. These data are
used in conjunction with Burlington, Vermont airport
weather station data to 1) gain insight into the orders-
of-magnitude of the various errors and 2) carry out a
detailed data analysis to establish the probabilities
of meeting given error requirements. This report contains
the model descriptions for the general stream model, the
sensitivity analysis model, and the data analysis models;
a description of the Vernon, Vermont site; the data for
four problems from the Vernon nuclear plant; an order-
of-magnitude error study; and the results of the four data
analyses. The four appendices contain 1) a description
of the input FORMAT specifications, 2) the input data
for the four problems, 3) program listings, and 4) the
theory of the sensitivity analysis.
This report was submitted in fulfillment of Contract
68-03-0439 by Richard W. McLay, P.E., Essex Junction,
Vermont, under the partial sponsorship of the Environmental
Protection Agency. Work was completed as of May 1975.
-------
CONTENTS
Section Page
I CONCLUSIONS 1
II RECOMMENDATIONS 2
III INTRODUCTION
PURPOSE 3
SCOPE 3
IV MODEL DESCRIPTIONS
THE GENERAL STREAM MODEL 5
THE SENSITIVITY ANALYSIS MODEL 7
THE DATA ANALYSIS MODELS 8
V STUDY AREA AND METHODOLOGY
THE VERNON NUCLEAR PLANT ""*
DATA BASE DESCRIPTION 14
EXAMPLE PROBLEMS 17
VI DISCUSSION OF RESULTS 18
ORDER OF MAGNITUDE ERROR ANALYSIS 18
RESULTS OF DATA ANALYSES 20
VII REFERENCES 25
VIII SYMBOLS AND VARIABLE NAMES 26
IX APPENDICES
A. FORMAT SPECIFICATIONS 28
B. INPUT DATA 34
C. PROGRAM LISTINGS 77
D. THEORY OF THE SENSITIVITY ANALYSIS 150
iii
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FIGURES
No. PagjS
1 Control Volume for Stream Model 6
2 Six Primary Meteorological and Site Variables 10
3 Model Using Site Water Temperature Data 11
U Model Using Site and Station 7 Temperature Data 12
5 The Vernon Nuclear Plant-Temperature Sampling
Stations 15
IV
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TABLES
No. Page
1 Probabilities of Meeting Given Error Requirements 21
by an Observer at the Vernon Site Averaging One
Day and Predicting One Day Ahead at a Distance of
25,000 Feet(7620 Meters) Downstream.
2 Probabilities of Meeting Given Error Requirements 22
by an Observer at the Vernon Site Averaging Two
Days and Predicting One Day Ahead at a Distance of
25,000 Feet(7620 Meters) Downstream.
3 Probabilities of Meeting Given Error Requirements
by an Observer at Station 7 One Day Ahead at the
Vernon Site(Same Position as for Table 2). 22
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SECTION I
CONCLUSIONS
1. One-dimensional stream temperature models are effective
for predicting average temperatures over a short period
of time.
2. Predictions made using site data averaged over a day
will be within 2 °F (1.11 °C) of the actual average
temperature of the following day over 90 percent of
the time.
3. The water temperature at the Vernon site is the most
important factor in the analysis. The Vernon study
indicates that meteorological factors affect the
Connecticut river predictions results very little.
Travel time thus appears to be a major factor since a
knowledge of the initial temperature is essential to
accurate predictions.
4. Seasonal effects on prediction accuracy are minor.
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SECTION II
RECOMMENDATIONS
The results of this study indicate that, in this case,
water temperature at the site is the most important
variable in the prediction of the downstream Connecticut
river temperature. In order to minimize the errors of
prediction, it is recommended that temperatures be
monitored upstream of the site and predictions be made
over as short a period of time as possible, i.e., average
the previous day's data to predict the following day's
average temperature. This is motivated by the need to
know the initial temperature in the analysis for the entire
travel time of water through that portion of the stream
being simulated.
These predictions are useful to a plant operator making
day-to-day decisions as opposed to a planner predicting
conditions to occur several years in the future using an
historical weather data base.
This work indicates that for the Vernon plant such pre-
dictions will have error within 2 °F (1.11 °C) 90 percent
of the time. Smaller streams may have greater effects from
meteorological parameters, which were not found from the
Vernon problems. It is also recommended that similar
sensitivity analyses be performed for two-dimensional models
used for predicting temperatures in lakes, estuaries, and
cooling ponds.
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SECTION III
INTRODUCTION
PURPOSE
Stream temperature is an important factor in water quality.
The temperature of the stream directly controls the types
and amounts of plant and animal life native to it. In
recent years there has been an increased interest in
water quality by the public. In response to this interest
a very large effort has been mounted to develop mathe-
matical models for predicting heat assimilation in
bodies of water.
Models have been developed for predicting temperatures
in streams, cooling ponds, reservoirs, estuaries, and
large lakes (See, for example, the review by Policastro
and Tokar [1972]). Usually, a stream model assumes a
one-dimensional problem with uniform mixing and with
various modes of heat transport at the air-water inter-
face simulated by semi-emperical expressions. In addition,
the problem is generally treated as one in a steady-state
condition, i.e., the formulation involves a relationship
between the flow rate and the position downstream from
an initial point, x , allowing the independent variable
to be chosen as the variable x while the time variable
becomes implicit to the problem. While the development
of stream models is straight-forward, their use is
subject to a great deal of interpretation and judgement
(See, for example, Asbury [1970]).
The purpose of this study is to determine the effects
of variations in initial temperature and meteorological
data on results of mathematical models for predicting
stream temperatures.
SCOPE
Three principal problems inherent in model use to predict
heat assimulation are:
1. The extrapolation of weather station meteoro-
logical data to the site under study is subject
to considerable variance.
-------
2. There is usually a lack of data from which to
compute the evaporation and other heat transfer
rates for a stream.
3. The temporal variations of the data cause large
variations in short-term predictions.
In addition to these, we find that the spatial and temporal
variations of temperature in the environment without the
addition of a heat load may be greater than either the
requirements set by a regulatory agency or the errors in-
herent in the model, i.e., there is a question as to what
the ambient values really are. Local variations in topog-
raphy and/or tree cover can shade the stream and cause
effective incoming and outgoing radiation areas to be
reduced. The accuracy of instruments used to measure
the various physical quantities is always subject to review.
Ground water advection can be an influential transport
process, but it is almost impossible to measure. Finally,
the large amount of data taken for any site provides a
good probability for human error in recording or trans-
position.
This study considered the three principal problems listed
above by using a sensitivity analysis of a general, one-
dimensional stream model. This was combined with data
analysis techniques to compute the probabilities of meeting
given error requirements. Data from the Vernon, Vermont
nuclear plant and the Burlington, Vermont weather station
were used to form a data base, from which four example
problems were obtained and evaluated.
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SECTION IV
MODEL DESCRIPTIONS
THE GENERAL STREAM MODEL
The stream model used for the study is one-dimensional with
the independent variable being the distance downstream, x .
This model is simple enough that a general version of it
can be considered that encompasses all one-dimensional
models now in existence. A discussion of this concept
is given in Appendix D.
All one-dimensional models take a basic form as shown
in Figure 1 and are described by the equation:
uA dT
~T dx [QRad ~ QRef ~ QBack ~ QEvap ~ QConv + QMis]
(1)
where the variables are as defined in Section VIII, Symbols
and Variable Names, and the water is fully mixed at each
cross section. Any departure from the form of equation (1)
due to direct integration, approximations to the heat
fluxes Q , etc., can be shown by a Taylor's expansion to
be proportional to some power of the mesh size. (See
Appendix D)- Put simply, as the number of stations or
data points in the models are increased they will all
produce results converging toward the same solution, pro-
vided that total heat fluxes and the heat transfer coeffi-
cients are the same. The fundamental heat flux expressions
used in this work are taken from Laevastu [1960], where the
processes are linearized in T . Not all authors use
linearized expressions (See for example Jaske [1971]).
However, numerical experience shows that if the temperature
variations are small, i.e., small with respect to absolute
temperatures, and of course they always will be, it is
justified to linearize the expressions, including the
fourth power terms in the back radiation fluxes.
The concept of using a simple, general model was considered
essential in this work, since it reduced the study from
a huge data handling problem for many models to the study
of a single, general model whose error analysis applies
equally well to all models in question, provided a con-
vergent mesh size (station length) is specified.
The expressions for the heat fluxes from Laevastu [1960]
are:
-------
UA
Figure 1. Control voluma for stream model
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Q^, . = 1.9 sin a (1 - 0.0006 C3) (0.061)
Solar
Q = 1 Q (0.061) ,
Reflected _ Solar
a
= (1.0 - 0.765 CM14.38 - 0.09 ( (T - 32)
(0.35)(1.0 + 9.8 x 10~3 W2)(ew - e ) ,
n =
Evaporation 240
Q . = 39.0(T - Ta)(0.26 + 0.077 W,) i (0.061)
Convection a 2 9
(2)
The definitions are given in Section VIII. It should be
noted here that the coefficients from these terms are
largely based on empirical data and in many cases will vary
considerably. However, as is seen in Section VI, the
sensitivity analysis reveals little change in temperature
decay rates with considerable change in these flux expres-
sions for the Connecticut River. For smaller streams, this
would not be the case.
THE SENSITIVITY ANALYSIS MODEL
In order to study the errors in stream temperature produced
by the errors in input data, it is necessary to develop
certain error expressions from equation (1). These are
developed in view of the two fundamental definitions from
Rosko [1972]:
1. Accuracy is defined as conformity of fact.
2. Precision is defined as sharpness of definition.
In the case of this work then, accuracy refers to the con-
vergence of the solution to the actual stream temperature.
Similarly, precision refers to the rate of convergence.
The sensitivity, or error, analysis required for the work
was developed from equation (1) by making a small change,
or variation, in the variables. Equation (1) can be
rewritten symbolically as
-------
A variation of both sides of this equation yields
Au
where it is assumed that the flow rate and stream width are
known and that the process described is linear in its varia-
tion. If the error in temperature, 6T(o) , is known at
the initial point, it is apparent that, given the errors in
the heat fluxes, 6Q , the error at any given point down-
stream can be computed from equation (4) by a direct
computation.
It is important to note that, if approximate values of the
coefficients in equation (4) are obtained as constants,
the equation can be solved in closed-form,
6T = A exp[-ax] + I C.j_
i
Results of an analysis of this type are presented in
Section VI.
THE DATA ANALYSIS MODELS
Previous sections have described the mathematical model
studied and the sensitivity analysis model. The first of
these models, or close variations of it, has been used
extensively to predict the mean temperatures of streams.
The sensitivity analysis model has the capability of pre-
dicting the error in the mean temperature at a point down-
stream, given the corresponding errors in the mean initial
condition for temperature and the mean meteorological con-
ditions. Thus, the mathematical models were available for
a study, setting the stage for the data analysis.
The philosophy of the data analysis emerged from the con-
cepts of probability. As has been shown by Hogan et al.
[1972J, it is unrealistic to establish the error in the
estimate of the mean temperature deterministically.
Rather, the statement must read to the effect:
If the errors in the heat fluxes \&Q\ and the
error in initial mean temperature |6T(o)| are
constrained in size to given values, then the
probability that the error in mean stream tem-
perature |6T| <_ 1/n °C will be P-J , |6T| <_ 1 °C
will be P2 (?2 > P1)
-------
Put simply, for given errors in the initial mean temperature
and the meteorological data, it is possible to determine
the probability of meeting a given error requirement. This
can be done by using the sensitivity analysis model, which
appears to be a very realistic approach to assessing the
effects of the introduction of a heat load.
The methods employed in the data analysis are best visualized
by using Figure 2, where the six primary variables are il-
lustrated. The effect of errors in these variables is shown
schematically in the figure, where the initial error 6T is
seen to decrease with increasing x . By collecting a data
base of these variables over a period of several months, it
was possible to make use of the sensitivity analysis to
compute the error in temperature for a number of trials,
based on moving averages. With an increasing number of
trials the probability, P , that |<5T| is less than some
given error in temperature can be estimated from:
_._ Number of trials with |6T| < given value
Total number of trials ' ( '
Figures 3 and 4 illustrate the methods for utilizing the
data base to evaluate equation (5). Figure 3 shows
schematically the data base at an airport weather station
remote to the site, in this case the Burlington, Vermont
weather station. These data are collected together with the
stream temperatures at the site every three hours, eight
points per variable per day. These data are averaged over
a specified number of previous days, then compared with the
respective averages over the day following to form the errors
in the input variables, 6 , etc. The sensitivity analysis
is then used to predict the errors in temperature down-
stream. These are then compared with the given temperature
error requirement and the components of equation (5) com-
puted. It should be noted here that this model simulates
the errors of an observer at the site attempting to predict
the temperature several days ahead.
Figure 4 shows schematically the second data analysis model,
where the data base includes 1) the remote weather station
data, 2) the stream temperatures at the site, and 3) the
average daily stream temperature above the site (See
Figure 5, station 7). In this case the daily average of
the station 7 temperature is compared with the following
day's daily average temperature at the site. Meteorological
data are averaged in an analogous manner, i.e., daily
averages compared for two consecutive days. These form the
errors in the input variables. The sensitivity analysis
is then used to predict the errors in temperature downstream,
these are compared with the given temperature error require-
ments, and the components of equation (5) computed. This
-------
I Cloud \
^ Cover/
Relative
\ Humidity/
'Air
W(Wind)
(Initial
\
V Temperature/
T 1.
/Stream \
1 Temper-)
\ tore /
tsi ( Error in \
\ Stream Temperature/
Figure 2. Six primary meteorological and sit* variables
10
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Process movts through all of data
Average Over
Several Day*
Compart With
Average Over Day
Following
"Airport Data and
Stream Temperature*
1
leverage Over Several Days |
=
[Average Over Doy Followlng|
w "
[compare Average*|
Compute 8T Downstream
Numerator of
., Probability
COMPUTE AND
PRINT PROBABILITIES
Figure 3. Model using site water tenperature data
11
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I
L
Compare T»aly~Av«rage
With Vernon Average
r. , ^Airport Data and
I - 1 Stream Temperatures
Average Vernon
Data
Average Over A Day|
Compare With Vernon Average
\
r
Compute 6T Downstream
Numerator of Probability
COMPUTE AND
PRWT PROBABILITIES
Figure 4. Model using site and station 7 temperature data
12
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model simulates the errors of an observer remote to the
site attempting to predict the site stream temperature
one day ahead.
13
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SECTION V
STUDY AREA AND METHODOLOGY
THE VERNON NUCLEAR PLANT
A program of ecological studies of the Connecticut river in
the vicinity of Vernon, Vermont was initiated in 1967, prior
to the operation of the Vermont Yankee Nuclear Powerplant.
The preoperational studies were enlarged in scope in sub-
sequent years and were continued after the plant became
operational in October 1972. The location of the plant is
shown in Figure 5, where the positions of short-term and
long-term sampling stations are shown. The particulars of
these sampling stations are as follows:
Station No. Location Relative to Vernon Dam Type
1 6.45 Miles (10.4 Km) South Short-term
2 4.70 Miles (7.56 Km) South Short-term
3 0.65 Miles (1.05 KM) South Long-term
4 0.55 Miles (0.89 Km) North Short-term
5 1.25 Miles (2.01 Km) North Short-term
6 4.10 Miles (6.60 Km) North Short-term
7 4.25 Miles (6.84 Km) North Long-term
8 8.70 Miles (14.0 Km) North Short-term
Stations 3 and 7 are permanently emplaced below and above
the site respectively. Stations 3 and 7 yielded the water
temperature data used in the study while meteorological data
were obtained from instruments at the plant and in Keene,
New Hampshire.
DATA BASE DESCRIPTION
The data base used in the project was taken from four
sources:
1) Measured water temperatures at the site
(See Aquatec [1974]),
2) Measured meteorological data at the site
(Personal communications) ,
3) Meteorological data from Brattleboro, Vermont
and Keene, New Hampshire (U.S. Weather Service),
4) Meteorological data at the Burlington, Vermont
weather station (U.S. Weather Service).
14
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CHESTERFIELD
r
Q l/fe I 2
SCALE IN MILES
NEW HAMPSHIRE
iNUCLEAR PLANT*
VERNON DAM
VERMONT
WINDHAM CO. U CHESHIRE CO.
FRANKLIN C0.\
MASSACHUSETTS
Figure 5. The Vernon nuclear plant-temperature
sampling stations
15
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The data base variables and dates for the Vernon plant
example problems are as follows:
1. Burlington, Vermont Weather Station data and Vernon,
Vermont water temperature data:
Variables
Cloud cover, air temperature, relative humidity/
wind speed, water temperature from stations 3 and 7.
pates of Available Data
a) May 1, 1973 to June 20, 1973
b) August 15, 1973 to August 31, 1973 and September
12, 1973 to September 26, 1973.
c) October 1, 1973 to October 3, 1973, October 17,
1973 to October 24, 1973, and October 27, 1973
to October 29, 1973.
d) October 17, 1973 to October 24, 1973, October 27,
1973 to October 29, 1973, and November 1, 1973
to November 14, 1973.
2. Vernon, Vermont (and vicinity) site meteorological
data:
Daily Average Variables
Cloud cover, air temperature, relative humidity,
wind speed.
Dates of Available Data
June 21, 1973
September 27, 1973
October 30, 1973
November 15, 1973
16
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EXAMPLE PROBLEMS
Four example problems were constructed from the data base
previously discussed. They represented spring, summer, fall
and winter conditions at the Vernon Nuclear Plant. The days
studied were June 21, September 27, October 30, and November
15, 1973. The dates of the data blocks were as labeled a),
b), c) and d) above in the previous section "Dates of Avail-
able Data." Computations were carried out to a point 25000
feet (7620 meters) downstream from the initial point in the
model (x = 0).
17
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SECTION VI
DISCUSSION OF RESULTS
In addition to the analyses described in Section IV, the
Data Analysis Models, an order-of-magnitude error analysis
was carried out using the closed-form solution developed
from equation (4).
ORDER-OF-MAGNITUDE ERROR ANALYSIS
In order to gain insight into the solution of equation (4),
it was logical to simplify the form of the equation and
obtain a closed-form solution
6T = A e~ax + Z Ci , (6)
i
where the C.; are the respective particular solutions
associated with the errors <5 , etc., and the constant A
is related directly to the error in water temperature 6T(o)
at the site, x = 0 . The coefficient a then reveals the
rate of decay of the error in temperature with distance.
The June 21, 1973 averaged data were taken as an example
problem:
uA (Rate of flow) = 13,503 ft3/sec ,
El (River width) = 400 ft ,
C (Cloud cover) = 8 tenths ,
cT (Sun angle) = 59° ,
(Relative humidity) = 71 percent ,
W2 (Wind speed) = 10 MPH ,
Tair (Air temperature) = 75 °F . (7)
These data were compared with the averaged data of May 31,
1973 to obtain the errors in the variables between these
two days. This was done arbitrarily to examine the
order-of-magnitude of the resulting errors in temperature.
The input errors are:
18
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6C (Error in cloud cover) = 2 tenths ,
6a (Error in sun angle) = 5° ,
6<|> (Error in relative humidity) = 29 percent ,
6W2 (Error in wind speed) = 5.2 MPH ,
(Error in air temperature) = 1 6 °F . (8)
Thus, the problem will yield approximate errors for predicting
the water temperature on June 21, 1973 given the meteoro-
logical data from May 31, 1973. Of interest are the solutions
Cj^ of equation (6) , which are due to the respective errors
in equation (8). They are found from equation (4) and
Appendix D to be
1.
2.
3.
4.
5.
6 TCp
6T
aP
6V
6Tw2P
6TT
airP
10.2 °F
1.71 °F
0.357 °F
1.33 °F
19.63 °F
(9)
Similarly, from the same source the coefficient a can be
found:
a = 0.947 x 106 . (10)
The corresponding value of x where the value of 6T falls
below 5 percent of the original value at x = 0. is
x = 3,170,000 feet ,
(966,000 meters)
= 600 miles
(11)
(966 kilometers)
This order-of-magnitude study indicates important facts
associated with the Vernon site:
19
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1. Modeling the Connecticut river, which has a large
flow rate in comparison with its width, produces
a solution that will have errors decaying over a
very long distance. This means that the error in
temperature will remain virtually constant near
x = 0 .
2. The computations are far less sensitive to the
environmental factors than thought previously.
3. Since the error in temperature is nearly constant
near x = 0 , the variable of primary concern is
the initial error in temperature 6T(o) . Thus, it
appears that records of upstream temperatures in the
Connecticut river would be useful for projecting
average temperatures downstream.
4. Since a is inversely proportional to the volume
flow Au it is possible to compute the value of
a. for the various flow rates, given a known flow-
rate A^U-| and associated a , a-) :
a = a
1
This expression will yield the stream flow for
which a given decay rate will exist.
RESULTS OF DATA ANALYSES
The results of the four data analyses are presented in the
form of probabilities for meeting given error requirements
with the variables averaged over a given number of prior
days. Tables I, II, and III contain results from all four
problems. It should again be emphasized that these results
relate to a plant operator making decisions as to the
operating conditions of a given plant as opposed to a site
planner predicting conditions several years in advance.
As indicated on the tables, the river temperatures and the
meteorological parameters are averaged over one and two
days respectively.
Results in Table I indicate that an observer at the site
attempting to predict the average stream temperature the
following day at a position 25,000 feet (7,620 meters)
downstream by averaging the previous day's meteorological
data and stream temperature data would compute an
20
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Table 1. PROBABILITIES OF MEETING GIVEN ERRO'R REQUIREMENTS BY AN OBSERVER AT
THE VERNON SITE AVERAGING ONE DAY AND PREDICTING ONE DAY AHEAD AT A
DISTANCE OF 25,000 FEET (7620 METERS) DOWNSTREAM
Error Requirement F (°C)
June 21 , 1973
September 27, 1973
October 30, 1973
November 15, 1973
1°F (0
0.
0.
0.
0.
.56°C)
6
613
769
75
2°F (1
0.
0.
0.
1 .
.11°C)
9
935
923
0
3°F (1
0.
0.
0.
1 .
.67°C) I
94
963
923
0
(4°F (2
1 .
0.
0.
1 .
.22
0
968
923
0
°0
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Table 2. PROBABILITIES OF MEETING GIVEN ERROR REQUIREMENTS BY AN OBSERVER AT
THE VERNON SITE AVERAGING TWO DAYS AND PREDICTING ONE DAY AHEAD AT A
DISTANCE OF 25,000 FEET (7620 METERS) DOWNSTREAM
Error Requirement °F (°
June 21 , 1973
September 27, 1973
October 30, 1973
November 15, 1973
3F (0.56°C)
0.469
0.533
0.5
0.522
2°F (1
0.
0.
0.
0.
.11°C)
694
867
833
957
3°F (1
0.
0.
0.
1 .
C)
.67°C)
898
933
833
0
4°F (2
0.
0.
0.
1 .
.22°C)
980
967
917
0
Table 3. PROBABILITIES OF MEETING GIVEN ERROR REQUIREMENTS BY AN OBSERVER AT
STATION 7 ONE DAY AHEAD AT THE VERNON SITE(SAME POSITION AS STATED
FOR TABLE 2)
Error Requirement °F (°C)
T
June 21 , 1973
October 30, 1973
°F (0.56°C)
0.520
0.846
9o M nio v
<£ r (, I . I I t_;
0.800
0.923
3°F (1.67°C)
0.880
0.923
4°F (2:22°C)
0.960
0.923
-------
approximate stream temperature within an error of 2 °F
(1.11 °C) between 90 and 100 percent of the time. He would
compute an approximate stream temperature within an error
of 1 °F (0.56 °C) between 60 and 77 percent of the time.
Table II shows that the same observer at the site making
the same prediction of an average temperature as made in
Table I but using the average of two prior days' data
would compute an approximate stream temperature within an
error of 1 °F (2.22 °C) between 92 and 100 percent of the
time. He would predict within an error of 3°F (1.67 °C)
between 83 and 100 percent of the time. Similarly, a 2 °F
(1.11 °C) error would be obtained between 69 and 96 percent
of the time. Finally a 1 °F (0.56 °C) error would be ob-
tained between 47 and 53 percent of the time.
Table III shows that an observer using data from station 7
above the Vernon dam, attempting to predict stream tem-
peratures at the Vernon site by averaging a day's station
7 water temperature would compute an approximate stream
temperature within an error of 4 °F (2.22 °C) between 92
and 96 percent of the time. He would predict within 3 °F
(1.67 °C) between 88 and 92 percent of the time, within
2 °F (1.11 °C) between 80 and 92 percent of the time.
Finally, he would predict within 1 °F (0.56 °C) between
52 and 85 percent of the time.
Thus, it is seen that predictions made at the site (with a
daily average) a short period of time into the future are
accurate over 90 percent of the time for a 2 °F (1.11 °C)
allowable error. Averaging data over a two day period of
time reduces the probability of meeting the 2 °F (1.11 °C)
error to around 80 percent, which appears to be a primary
influence of the travel time through this portion of the
Connecticut river system, one to two days. These studies
indicate that it is important to have good records of up-
stream temperatures from a site. With these it will be
possible to predict an average temperature within 2 °F
(1.11 °C). It is important to note, however, that short
term fluctuations are not predictable by these methods as
used in the project. Finally, the effects of season do
not appear to make appreciable differences in predictions.
23
-------
SECTION VII
REFERENCES
Aquatec, Inc. 1974. Ecological Studies of the Connecticut
River Vernon/Vermont, Report Hi Prepared for Vermont Yankee
Nuclear Power Corporation, Rutland, Vermont.
Asbary, J.G. 1970. Effects of Thermal Discharges on the
Mass/Energy Balance of Lakp. Michigan Argonne National
Laboratories, Argonne, Illinois Report No. ANL/ES-1.
Hogan, C.M., L.C.Patmore and H. Seidman 1973. Statistical
Prediction of Equilibrium Temperature from Standard Meteor-
ological Data Bases U.S. Environmental Protection Agency,
Corvallis, Oregon. Report No. EPA-660/2-73-003.
Jaske, R.T. 1971. Use of Simulation in the Development of
Regional Plans for Plant Siting and Thermal Effluent Manage-
ment Paper 71-WA/PWR-3, Presented at the Winter Annual Meeting
of the American Society of Mechanical Engineers.
Laevastu, T. 1960. Factors Affecting the Temperature of the
Surface Layer of the Sea Commentationes Phvsica-Mathematical
XXV, 1, Societas Scientiarum Fennica, Centraltryckeriet
Helsingfors, Helsinki.
Policastro, A.J. and J.V. Tokar 1972. Heated-Effluent Disper-
sion in Large Lakes: State-of-the-Art of Analytical Modeling
Part 1, Critique of Model Formulations Argonne National Lab-
oratories, Argonne, Illinois Report No. ANL/ES-11.
Rosko, J.S. 1972. Digital Simulation of Physical Systems
Addison-Wesley: Reading, Massachusetts p.2.
Salvador!, M.G. and M.L. Baron 1961. Numerical Methods in
Engineering Prentice-Hall, Inc.: Englewood Cliffs, New
Jersey.
25
-------
SECTION VIII
SYMBOLS AND VARIABLE NAMES
VARIABLE NAMES
a - General integration limit.
A - Stream cross-sectional area.
A,A - Amplitude of exponential decay function.
C - Cloud cover.
Cj_ - Constants.
c - Specific heat.
DT - Allowable error in stream temperature.
f - Function of several variables.
f - Derivative of f( f = df/dx)/
h - Integration step.
!•] , 12 - Integrals.
KJ_ - Kernel function.
H, EL - Stream width.
n - Integer number.
O(-) - Of order(Order of magnitude).
P, Pj_ - Probability of occurence.
Q - Total heat flux.
°-i' Q-ij ~ Particular heat fluxes.
Q-Back ~ Back radiation heat flux.
°-Conv Qconvection ~ Convective heat flux.
°-Evap' °-Evaporation ~ Evaporative heat flux.
°-Mis(c) ~ Miscellaneous heat flux.
Q-Rad' °-Solar ~ Radiative solar heat flux.
Q-Ref' QReflective ~ Reflective heat flux.
T - Stream temperature.
To - Initial stream temperature.
U,u - Average stream flow velocity.
W, W2 - Wind speed.
x - Distance downstream.
X-L - Particular position.
26
-------
x - Particular value of x.
xmax ~ Maximum value of x.
y - General function.
y - Derivative of general function.
y(0), yo - Initial value of general function.
Yj_ - Value of function at x-^.
z - Dummy variable of integration.
GREEK SYMBOLS
a - Decay rate coefficient.
a, a - Sun angle.
SC - Error in cloud cover.
SQ - Error in total heat flux.
6T - Error in stream temperature.
6T(0) - Initial error in stream temperature.
STair - Error in air temperature.
6Taj_rp - Particular solution for air temperature error.
6TCp - Particular solution for cloud cover error.
&Tj_ - Particular solution.
~ Particular solution for wind speed error.
6T~ - Particular solution for sun angle error.
6T(i)p - Particular solution for relative humidity error.
6W,6W2 - Error in wind speed.
6a - Error in sun angle.
6<(> - Error in relative humidity.
Ax - Increment in downstream distance.
<|> - Relative humidity in percent.
p - Density.
£ - Position.
27
-------
APPENDIX A
FORMAT SPECIFICATIONS
This appendix presents the procedures required for using the
three codes developed during the course of the project:
1. The general stream model code, STREAM.
2. The sensitivity analysis code, SENSIT.
3. The data analysis code, MONT.
STREAM
The digital computer code STREAM performs all the necessary
computations to predict the stream water temperature at any
distance downstream from a given initial station. The
principle of conservation of energy is applied to the stream
under steady-state, steady-flow conditions. Heat transfer
to and from the water in the various heat transfer modes is
computed. Numerical integration is used to compute the
stream temperature, with a choice of four algorithms
available to the user. A listing of the STREAM code is
given in APPENDIX C.
INPUT REQUIREMENTS TO STREAM
STREAM accepts the following information:
INTC: (1, 2, 3 or 4) in 6110 FORMAT. This parameter
respectively chooses Euler, Modified Euler, Runge
Kutta or Adams-Moulton integration routines.
X, DX, DXPR, XEND: in 6E10.0 FORMAT. These parameters are,
respectively, the initial value of the distance down-
stream in feet (usually 0.), the integration interval
in feet, the print interval in feet, and the final value
of the distance downstream in feet.
ERR0R, DXMAX: in 6E10.0 FORMAT. These parameters are used
by the integration routine only and represent the error
in the function in °F and the maximum integration step
size in feet allowed.
TEMP, U, AREA, EL: in 6E10.0 FORMAT. These parameters are,
respectively, the initial value of the temperature in
°F, the average velocity of the stream in ft/sec, the
cross-sectional area of the stream in ft^, and the
stream width in feet.
28
-------
RHO, WMPH, TAIR, CLD, RH, ALBAR: in 6E10.0 FORMAT. These
are, respectively, the density of the water (62.U
#/ft3, here), the wind speed in MPH, the air temperature
in °F, the cloud cover in tenths, the relative humidity
in percent, and the average sun angle in degrees.
The final information is read in a loop of 10 sets:
PTBL(I), TTBL(I), HFGTB(I) in 6E10.0 FORMAT. These tables
are, respectively, the water saturation pressure table
in PSI, the water temperature table in °F, and the
latent heat of evaporation table in BTU/pound, all
corresponding and in order. This information is
extracted from standard steam tables for the temperature
range 32 to 120 °F.
The code then computes the stream temperature downstream
from a given point. The output proceeds at each print
position with the position X itself, the integration step
DX , the stream temperature TEMP, and the derivative of
the stream temperature with respect to the position variable
DTEMP. Following this, other auxilliary variables are
printed out: EW, EVAP, HE, HFG, H0, EBR, and HC. These are
only important for diagnostics, not the solution itself.
SENSIT
The digital computer code SENSIT performs all necessary
computations to predict the error in the stream water
temperature (due to the difference between the actual and
approximate input data) at any distance downstream from a
given initial station. The variation in the original
equation is coded to examine the effects of errors of the
input variables. Numerical integration is used to compute
the error in stream temperature, with a choice of four
algorithms available to the user. A listing of the SENSIT
code is given in APPENDIX C.
INPUT REQUIREMENTS TO SENSIT
SENSIT accepts the following information:
INTC: In 6110 FORMAT. This variable is the integration
routine to be used (See STREAM for description).
29
-------
X, DX, DXPR, XEND: In 6E10.0 FORMAT (See STREAM for
description).
ERROR, DXMAX: In 6E10.0 FORMAT (See STREAM for description).
DT, U, AREA, EL: In 6E10.0 FORMAT. The initial temperature
error DT is read in at this point (other variables are
described in STREAM).
RHO, WMPH, TAIR, CLD, RH, ALBAR: In 6E10.0 FORMAT (See
STREAM for variable description).
PTBL(I), TTBL(I), HFGTB(I): In 6E10.0 FORMAT (See STREAM
for variable description).
DALP, DCLD, DRH, DTAIR, DWMPH: In 6E10.0 FORMAT. These
variables are the errors in the respective values of
the sun angle in degrees, the cloud cover in tenths,
the relative humidity in percent, the air temperature
in °F, and the wind velocity in MPH.
NTEMP: In 6110 FORMAT. This is the number of temperatures
given downstream.
STTBL(I), XTBL(I): In 6E10.0 FORMAT. These tables are,
respectively, the water temperature and the position
downstream in NTEMP sets.
The code then computes the error in the stream temperature
downstream from a given point. The output proceeds at each
print position with the position X itself, the integration
step DX , the stream temperature TEMP, the error in the
stream temperature DT, and the derivative of the error in
stream temperature DDT .
Following this some auxilliary variables are also printed
out: EW, DEW, EWAP, HE, HFG, H0B, HC, HLYMN, and HD, which
are important for diagnostics, not for the solution itself.
MONT
The digital computer code MONT performs all the necessary
calculations to obtain the probabilities for meeting a given
temperature requirement. The code takes prepared data and
makes a series of trials, forming data differences, and
uses the sensitivity analysis code, SENSIT, to obtain the
stream temperature difference at a prescribed distance
downstream (in this case 25,000 feet [7620 meters]). The
code makes three studies:
30
-------
1. Computes the probability of meeting given error
requirements given in both initial water tempera-
ture and meteorological data at the site.
2. Computes the probabilities of meeting given error
requirements given errors from water temperature
and meteorological time averaged data at the site.
3. Computes the probabilities of meeting given error
requirements given errors from water temperature
and meteorological data at a remote site, in the
case of this study, at station 7 above the nuclear
plant. A list of the MONT code is given in
APPENDIX C.
INPUT REQUIREMENTS TO MONT
MONT accepts the following information:
NLN, LOG1: In 6110 FORMAT. The first variable is the number
of lines of data (taken every 3 hours, 8 data points per
day, each day always complete); the second variable is
0 if no time averaged data appears, not zero if time
averaged data appears.
Following these integer variables the major part of the data
is read for the remote airport and the site water temperature
in a loop of NLN lines as follows:
C(I), TA(I), PHI(I), W(I), TW(I): In 6F10.3 FORMAT. The
variables are: 1) the cloud cover in tenths, 2) the
air temperature in °F, 3) the relative humidity in
percent, 4) the wind speed in knots, and 5) the site
water temperature in °F.
Next, the average data for the actual site and the particular
day are input:
UA, EL, CC, TAIR: In 6F10.3 FORMAT. These variables are 1)
the flow volumes of the river in ft3/sec, 2) the river
width in ft, the cloud cover in tenths, and the air
temperature in °F.
TWA, RH, WSP: In 6F10.3 FORMAT. These variables are 1)
the water temperature in °F, 2) the relative humidity
in percent and 3) the wind speed in knots.
31
-------
If LOG1 = 0 the next two sets of data are not necessary. If
LOG1 ^ 0 the next two sets of data for the dates of past years
prior to the date in question (the time-averaged data).
NTA: In 6110 FORMAT. This value is the number of lines of
time averaged data.
Following this NTA lines of data are read in as follows:
CTA(I), TATA(I), PHITA(I), WTA(I), TWTA(I): In 6F10.3
FORMAT. The variables are 1) the cloud cover in tenths,
2) the air temperature in °F, 3) the relative humidity
in percent, 4) the wind speed in knots, and 5) the
water temperature in °F.
Following this, the data describing the analysis are read in:
NCAS: In 6110 FORMAT. This is the number of cases of
temperature to be used in the trials.
DELT(I), 1=1, NCAS: In 6E10.3 FORMAT. These are input in
sequence, the first six values of allowed temperature
on the first line, the second six on the second line, etc.
NDAS: In 6110 FORMAT. This is the number of day cases to
be tried.
IDAS(I), 1=1, NDAS: In 6110 FORMAT. These are the number of
days of data to be averaged in each day case. They are
input in sequence, six values per line.
Following this, 10 lines of data are input for the sensitivity
analysis program, which is a subroutine in this case.
PTBL(I), TTBL(I), HFGTB(I): In 6E10.3 FORMAT (See STREAM for
variables description).
The next data to be input are 1) the number of days since
March 21 (the vernal equinox) which is required to estimate
the coefficient involved with the sun heating effect, and 2)
the latitude of the plant in degrees:
DM21, BETA: In 6E10.0 FORMAT.
The last data to be input are the daily average of the water
temperature at the remote site:
T7(I), 1=1, Number of Days in 6E10.3 FORMAT.
32
-------
The code then computes the errors in the stream temperature
downstream from a given point considering the days to be
averaged as requested. Three sets of input errors are
examined:
1. The airport meteorological data and stream temperature
against itself (simulating values at a site).
2. The time-averaged meteorological and stream tempera-
ture data against the site data.
3. The airport meteorological data and the remote site
water temperature data against the site data
water temperatures (simulating predictions from a
distance).
These are compared to the requirements on temperature for
each case. The number of cases for which the requirements
are satisfied are recorded and printed out in the form of
probability values.
33
-------
APPENDIX B
INPUT DATA
This Appendix contains the input for the four example
problems.
EXAMPLE PROBLEM INPUT
The input for the four example problems has the following
format:
1. The number of lines of data, 8 lines per day
(3 hour intevals).
2. The time averaged data logic parameter (1 means
time averaged data appears, 0 means no time
averaged data appears).
3. The data now appears by line as follows:
a) Cloud cover in tenths.
b) Air temperature in °F.
c) Relative humidity in percent.
d) Wind speed in knots.
e) Water temperature °F.
4. The average data (over a day) for the plant site
then is:
a) The flow volume, UA, ft^/sec.
b) The river width, EL, ft.
c) The cloud cover at the site in tenths.
d) The air temperature °F
e) The water temperature °F.
f) The relative humidity in percent.
g) The wind speed in knots.
-------
5. If time-averaged data appears the following then
is required:
a) The number of time-averaged data lines.
b) The lines of data as follows
1) Cloud cover in tenths.
2) Air temperature °F.
3) Relative humidity in percent.
4) Wind speed in knots.
5) The water temperature in °F.
6. The control data for the data analysis is next.
a) The number of cases of error in temperature.
b) The allowed errors in temperature.
c) The number of cases for days of data to be
averaged.
d) The actual number of days of data to be
averaged.
7. The tables of vapor pressure and latent heat (no
changes except for very unusual conditions).
8. The days to the date in question past March 21.
9. The latitude of the site in degrees.
10. The daily averages of the water temperatures at
the remote site. In this case station 7.
PRINTOUT FOR THE FOUR EXAMPLE PROBLEMS
35
-------
JUNE 21, 1973
MAY 1 to JUNE 20, 1973
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54.000
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59.000
55.000
54.000
54*000
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64.000
68.000
52.000
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100.000
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93.000
96.000
100.000
83.000
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_..3«000
3.000
3. COO
. 10.000....
9.000
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4. COO
4.000
9.000 ~
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10.000
8.000
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11.000.
10.000
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10.000
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10.000
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10,000
43.000
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42.000
42.000
41,000
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45.000
46.000
46.000
46.000
47.000
49.000
48.000
50.000
60,000
67.000
63,000
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51.000
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48,000
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96.000
93.000
93.000
93.000 ..
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80.000
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100.000
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96.000
96,000
100.000
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7.000
10. COO
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13.000
10.000
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b.OOO
3,000
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4.000
10.000
3.000
3.000
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6.000
11. CCO
13.000
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Ib.COO
14.000
13. COO
54*700
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54.500
54.000
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52.500
52.500
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51«500
51.200
51*000
51.000
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51-000
51« 000
51« 000
51*000
50«700
50-500
50*200
50-200
50-200
50*200
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3.000
47.000
47*000
47.000
50.000
54.000
58.000
56. COO
43. COO
39.000
37.000
45.000
60.000
67.000
68.000
63. COO
52.000
47.000
42.000
51.000
60.000
67,000
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63.000
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45.000
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47.000
54.000
100*000
100*000
100.000
86.000
75.000
65.000
62.000
96.000
100.000
100.000
100.000
. 70.000
40.000
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43.000
74.000
89.000
96.000
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55,000
51,000
50.000
83.000
96.000
100.000 "
100.000
86,000
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7*000
.. 2*000 ._ ..
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10. COO
4. COO
2*000
3* COO
2. COO
3. COO
3. COO
6.000
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7. CCO
4*000
7. COO
2*000
6. COO
8*000
12, COO
13.000
6. COO
3*000
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51*700
51*500
51*500
51*500
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53*500
53*700
53*700
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4.000
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2.000
8.000
7.000
9.000
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2.000
8.000
8.000
6.000
10.000
1.000
5,000
3.000
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10.000
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63.000
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61.000
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63.000
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57.000
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52.000
51.000
54.000
57.000
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61.000
63*000
65.000
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65.000
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75.000
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96.000
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93,000
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97*000
97.000
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3. COO
6. COO
7. COO
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6. COO
7. COO
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b.COO
4. COO
4. COO
7. COO
10. COO
7.000
8*000
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10. COO
13.000
6.000
7.000
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10. COO
10. COO,
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9.000
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13.000
10.000
10.000
54*000
54*000
54.000
54*000
54*000.
54*000
53*700
53*700
53«500
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54*000
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55*700
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55*200
-------
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8.000
7,000
10,000
10.000
10.000
10.000
10.000
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3.000
10.000
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10.000
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69.000
72.000
60.000
58.000
57.000
55.000
56.000
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64*000
63.000
58*000
56.000
56.000
56.000
59.000
60*000
64.000
62.000
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56.000
54.000
60*000
64*000
62*000
97,000
100.000
100.000
73.000
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100.000
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54.000
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96,000
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73.000
81,000
80.000
80,000
70*000
68*000
75*000
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9.000
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6*000
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2.000
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5.000
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3.000
3.000
4,000
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4.000
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6. COO
10.000
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14.000
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55*500
55*500
55*500
56*500
57*200
57*700
57*700
57*700
57*700
57*500
57*700
58*000
58*200
58*200 "
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58*500
58*500 ~
59*000
59*000
59*500
60*000
60*000
60*000
60*200
60*200
60*700
61*500
62*000
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8.000
6,000
6.000
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10.000
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10.000
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66*000
56.000
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62.000
68.000
70.000
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53.000
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60.000
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68.000
46.000
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36.000
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100.000
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100.000
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5.000
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10.000
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10.000
5.000
3,000
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10.000
5.000
8.000
2.000
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3.000
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9.000
6.000
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4.000
3. COO
3.000
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61«700
61*500 .
61-000
61.000
61.000
60«700
60«700
61.500
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61.500
61*200
61*200
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" 6*000
10.000
10.000
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8.000
8.000
10.000
10.000
7.000
7.000
10,000
7.000
7.000
10.000
8.000
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8.000
7.000
4.000
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65.000
77*000
80*000
76.000
76.000
68.000
67.000
71.000
74.000
78,000
85.000
71.000
72.000
72.000
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70.000
70*000
76,000
79.000
80*000
75.000
61.000
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68,000
77.000
81.000
84.000
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84.000
76.000
82.000
84.000
84.000
66.000
52,000
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45.000
75,000
93,000
93.000
68.000
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3.000
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8.000
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7.000
13.000
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10.000
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13.000
8.000
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3.000
10.000
11.000
12. COO
10.000
61*000
61*000
61*500
61*700
61*700
62*000
62*000
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62*200
62.700
63*000
63*100
63*500
63*000
62*700
62*700
62*500
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63*000
64*000
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64*700
64*500
64*200
64*000
64*000
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65*200
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79.000
71.000
73.000
71*000
71.000
72.000
79.000
82.000
77.000
72.000
67.000
61.000
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71,000
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79.000
70.000
63.000
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72.000
73.000
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78.000
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10.000
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2.000
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10,000
10,000
10,000
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78.000
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62.000
70.000
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75.000
70.000
61.000
53.000
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55.000
55.000
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58.000
55.000
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100.000
100.000
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90.000
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34.000
38.000
33,000
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55,000
60,000
55.000
59,000
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6.000
6. COO
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4.000
3. COO
5.000,
6.000
5.000
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3. COO
3.000
7.000
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14,000
13.000
13,000
8.000
8.000
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6.000
70*200
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72.200
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62.000
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43.000
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65.000
59.000
55.000
55.000
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65.000
80.000
89.000
96.000
96,000
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72.000
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12, COO
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3.000
2.000
3.000
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11,000
12,000
10.000
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68*000.
67*500
67*000
67*000
67*500
68*500
68*500
68*500
67*700
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67*000
67*000
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67*700
67*500
66*500
65*700
65*000
63*500
62*200
62*200
62*700
62*700
62*200
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60*200
59*500
59*000
-------
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10.000
10.000
4,000
3,000
7.000
10.000
10.000
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8.000
8.000
3.000
3,000
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W*TER
71.000
74.000
72.000
63,000
59.000
64.000
63*000
76.000
83.000
83.000
78.000
73.000
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• " 62*OCO«EL."
66,000
60*000
64,000
84,000
93.000
90.000
87.000
66.000
46,000
51,000
62.000
76.000
3*000
6*000
3,000
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3,000
4,000
10,000
12.000
16,000
11.000
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71.000WIND
59*000
59«000
59*000
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58*700
58*500
58*200
58*500
59*500
60*000
60*200
.60*200
8«OOOTEMP AIR"
SPEED- 8*700
UA« 13503,OOOK WIDTH* 4oo.ooocLD CQVER- S'OOOTEMP AIR» 75.000
TEMP
-------
\UMdER OF CASES- 4
ALLOWED QTS
•looroouE 01
tSOOCOOOE 01
•3000000E 01
•400POOOE 01
NUMBER OF DAYS AVEKAGED«
DAYS AVERAGED
1
8
PTBL1 TTBL1 HFGTB1
•b85E-01
122E OP
02 '108E.
02 «107E
•178E 00 «5UOE 02 tl07E
«256E 00 »60CE 02 «106E
•363E 00 »700E 02 -105E
•507E 00
•698E 00
•949E OC
•127E 01
t!69E 01
t800E 02
•900E 02
»10GE 03
•11GE 03
t!2GE 03
•105E 04
• 104E 04
• 104E 04'
•103E 04
•103E 04
DAYS SINCE MARCH 21«
41.QOOBETA"
45^000
-------
ADDITIONAL DATA FOR STATION 7 ABOVE THE DAM
TEMPERATURES AT STATION 7, °F, DAILY AVERAGES, MAY 1-JUNE 21
48.9, 50.7, 52.3, 52.4, 52.0, 51.8, 51.9, 52.9,
53.0, 53.1, 54.5, 55.2, 55.0, 54.5, 54.2, 54.2,
53.6, 52.4, 51.4, 50.8, 51.0, 50.6, 52.3, 53.9,
53.7, 54.1, 53.8, 54.3, 55.3, 56.3, 57.9, 59.0,
59.4, 58.8, 58.9, 60.0, 60.9, 62.3, 63.3, 64.6,
65.2, 66.8, 69.2, 69.3, 69.0, 67.3, 66.9, 66.1,
62.4, 59.3, 59.9
52
-------
NUMBER 6F
CLD C9VE.R
5.000
5.000
10.000
'' 10.000
9.000
10*000
10.000
4.000
.000
" " 9.000
_____ 10*000
10*000
1.000
1.000
.000
.000
.000
1.000
8.000
8.000
8.000
7.000
.. .. 9.000
9. COO
5. COO
5.000
ocr ir,n.
AUGUST
DATA LINES'
AIRTE^P REL
66*000
64*000
66*000
70.000
75.000
75.000
71.000
66*000
62*000
62*000
62*000
67*000
77.000
79.000
75.000
65*000
62*000
59.000
62* COO
75.000
82.000
83.000
79.000
68.UOC
66,000
64.000
DTK ii, it/j
15 to 31
256TJME AV
HIH rtlND
87.000
90.000
90.000
84.000
69.000..
66.000
76.000 "
.....87.000...
93.000
97*000
100.000
93,000.
62.000
47.000
b'8.000
87.000 ""
93.000.
97.000
97,000
71.000
55,000
bl.OOO
65,000
93*000
93.000
97.000
and SEPTEMBER
, L8GIC-.
SPD WATER
"b.COO
6. COO
7. COO
8*000
_..iq*ooo
10. COO
6*000
...5*000
3. COO
3*000
. ...*»coo
4.000
b.OOO
9.000
3.000
3.000
3.000
4. COO
4. COO
b.COO
b.COO
7. COO
4. COO
3*000
3. COO
3*000
12 to 26
0
TEMP
78*000
77*500
77*200
77.500
77*200 _ _
77*000
77*000
77« 000
76«700
76*700
76*000 .___
75*700
75*700 "" " "
76*500
77*000
76*500
76«200
76*500
76«bOO
76*500 _.
76.500
77*500
77*700
77t200
76*700
76»700
53
-------
t
t1"
r
i
t
t
I
t
3.000
8.000"
8.000
9.000
~' "10, COO
8.000
3.000
8.000
5.000
7.000
""" 5.000
9.000
9,000
"" 4.000""
3.000
3.000
.000
.000
4.000
2.000
1,000
.000
',000'
.000
.000
4,000
8.000
8,000
66.000
~ 76*000
85*000
85*000
67.000
66.000
65.000
63.00C
63.000
74.000
~ 80.000
69.000
72.000
67.000
63.000
60*000
63.000
74.000
79.000
81.000
73.000
67.000
63.000
61.000
62.000
75.000
80.000
80.000
97.000
71.000"
57«000
51.000
87.000
93.000
93.000
97.000
100.000
84.000
67.000
84,000
34,000
"93Tcbo"
97,000
97.000
97.000
71.000
60.000
54.000
69.000
84,000
90.000
93,000
97.000
69.000
49,000
56.000
54
3. coo
6*000
4*000
9* COO
11.000
5. COO
5. COO
6~.OGO
.. *«coo
4. COO
"" 4,OOG~
9.000
5.000
5.000
3.QOO
5.000
4.000
10. COO
5.QOO
5.000
6.00C
3.000
6.000
7. COO
3.000
11.000
1U.COO
10.000
76*700
~ 76*700
77*200
77*000
77*000
76*700
76*500
76*500
75*700
76*000
76*700
77*200
77*200
76*500
76*200
75*700
75*700
76*000
76*200
76*700
77.200
76.500
76*200
76*200
75*200
75*500
76*000
76*500
-------
i
r "~" 10.000
r
10.000
«[*
ui 10.000
V
: 10.000
10. 000
10. COO
" 10.000
lo.ooo
8. COO
1.000
2.000
.000
.000"
.000
9.000
7.000
9.000
lo.ooo
" ~ ' lo.ooo
10. COO
1.000
,000
,000
.000
1.000
.000
i .000
f
.000
• 000
70*000
63*000
69*000
67*000
66*000
65*000
61*000
_ 61*000
61*000
54.000
51.000
47.000
50.000
64.000
68.000
70.000
67.000
67.000
65.000
64.000
60.000
64.000-
68.000
71.000
65.000
55.000
52.000
49.000
51,000
79.000
84,000
76.000 *
73.000
81.000
84,000
93.000
90,000
75,000
90.000
93.000
100.000
100.000
65.000
55.000
49,000
66,000
61.000
73,000
75,000
81,000
58.000
49.000
48.000
61,000
90.0CO
93.000
96.000
100.000
55
6, COO
5. COO _
8.000
13.000
13.000
11.000
10. COO
_8.0QO
f.OOO
4.000
3.000
3.000
5.000"
6.000
9.000
5.000
4.000
3.000
8.000
b.QOO
/•COO
8.000
6. COO
8.000
4.QOO
5,000
3.000
t.QOO
5.000
76*700
76*500
75*500
75*200
75*000
75*000
75*200 "
_76*000
76«000
76 • 000 "
75.500
74.500
73.500
73.500
74*000
75*000
75.000
74*500
73*700
73.500
73*200
73»200
73*500
74.500
75*000
74*500
73*700
73*500
73*200
-------
1.000
-. -6(000
9.000
8*000
7.000
10.000
10.000
10.000
_ 10.000
10.000
10.000
10,000
10.000
10.000
10.000
10.000
^000
6.000
6.000
" " " 4.000
5.000
10.000
10.000
9.000
4.000
2.000
.000
10.000
69.000
76 •000"
77*000
69.000
"63.000
61.000
62.000
64.000
65.000
75.000
76.000
72.000
70.000
" 68.000
66.000
67.000
79.000
84.000
86.000
81*000
78.000
77.000
68.000
68.000
76.000
" 83.000
85.000
77.000
68.000
48*. 000
48.000
73.000
""90.6"60~~"
97.000
93,000
"90.000
93.000
69.000
"" 66 ,000
34.000
90.000
93.000
100.000
97,000
77.000"
65.000
63,000
79,000
88.000
88,000
93,000
100,000
97,000
74,000
b3.000
64.000
56
6.000
9.000
, 8. COO.
b.OOO
4.000
4.000
4.000
&.QOO
. 5*000 ..
b.COO
6.000
4.000
4.000
5.000
4. COO
4.000
8. COO
4. COO
4.000
4.QOO
9.000
9. COO
b.COO~~
4. COO
^•000
~ Ib.COO""""
9.000
b.OOO
73*200
74*000
74*000
73*500
73.000
.72*700
72*700
'72*700
73*<500
74*000
74*000
73*700 .
73*500
73*500
73*500.
73*500
"74*000 ~"
74*500
75*000
75*000
75*500
75*500
75*200
75*000
75*500
76*000
76*500
77*000
-------
" " " 5.000
: .coo
, .000
II
" "" 3.000
__4.000 __
2.000
" 2.000"
5.000
3.000
3.000
9.000
10.000
__ 8.000 ~
9.000
5.000
'10.000
4,000
2.000
9.000
5.000
2.000
4*000
.... „ 10.000
10. COO
10*000
_ 10.000
5.000
T..
a, ooo
7,000
69.000
64.000
61.000
63.000
77.000
85.000
87,000
81.000
76.000
72,000
73.000
75,000
84,000
90,000
91,000
' 79.000
74.000
70,000
68,000
69,000
83,000
88.000
74.000
74.000
71.000
60.000
56.000
b6,000
60,000
81.000
93.000
97.000
100,000
.__7*.000
61,000
57.000
79,000
82,000
93.000
87.000
85.000
67.000
56.000
bO.OOO
69.000
82,000
93,000
10-0.000
100,000
67.000
61.000
82.000
82.000
90.000
67.000
75.000
75.000
62,000
57
4.000
3.000 ._
3.000
4, COO
8*000 _
11.000
b.OOO
5 .000
5. COO
3.000""
_ 4*000
b.QCO
9.000
9«000
10. COO
8. COO
4. COO
3.000
4.000
b.COO
b.COO
b.OOO
12. COO
3.000
7.000
7.000
6. COO
7.000
9,000
76,500
76 • 000 _ _ __
75^700
75,500
75*500 __
76«000
77«000 ""
77 • 000
77«000
76*500
76«200
76«000
76«200
77«000
77*500
77«700
77.200
76*700
77*000
77«000
77«500
77*500
78*500
79*000
79*000
71.200
70.700
70*200
70*500
-------
10.000
10*000
10.000
10.000
~i o.ooo
4.000
9.000
5.000
9*000
4. COO
9.000
10.000
10.000
10.000
10.000
10*000
1 0.000
10.000
10.000
10.000
10.000
10.000
10.000
10,000
10.000
8.000
9.000
10.000
62.000
62»000
60.000
56.000
54.000
51.000
51.000
61.000
63.000
64*000
57.000"
52.000
51.000
50,000
51*000
59.000
59.000
55.000
54.000
54.000
54.000
54.000
54.000
55.000
57.000
59.000
57*000
57*000
48.000
50*000
58*000
?8*000
83.000 ~
90.000
93.000
58.000
.46.000
47.000
~ 69.000"
83,000
86.000
86.000
90.000
70.000
75.000
90.000
93.000
96.000
96*000
96.000
96.000
100.000
96.000
93*000
93.000
96.000
58
9.000
~" 8*000
6*000
3. COO
3. COO
3.000 ..
3.000
Ifch.COO
b.COO
8*000
3VOOO"
3. COO
6.000
4.000
7. OOP
8.000
5*000
5*000
8*000
4*000
6.QOO
4. COO
6.000
3.000
8*000
b.COO
5*000
7*000
70*500
70*500
70*500
70*500
70»200
70*000
69*500
6**5tfO
70*200
70*500
71*"000~~
70*500
70*200
69*700
69*500
69*500
68*500
68*200
68*000
68*000
68*000
67*700
67*500
67*700
67*700
67*700
67*700
67*700
-------
10*000
10.000
10*000
~ 9tOOO
9*000
9*000
6*000
. 9.000
10*000
.000
• 000
4.000
8.000
6.000
10. COO
1 0.000
10*000
10*000
10.000
10.000
1C. 000
10*000
10.000
2.000
8.000
4.000
9.000
2.000
.000
58.00C
58.000
56*000
54*000
54*000
53*000
51*000
51*000
50*000
42.000
41.000
52*000
55.000
56.000
50.CQO
48.000
50.000
50.000
52.000
52.000
54.000
51.000
51.000
47.000
41.000
39.000
40.000
54.000
61*000
93*000
90.000
83.000
'75.000
69.000
72*000
69.QOO
...71*000
71,000
86.000
96.000
55.000
53.000
_ 51.000
74.00.0
93.000
93,000
96.000
96,000
96.000
96.000
96.000
23.000
93.000
96.000
100.000
100.000
90,000
72.000
59
11*000
.._„ 1.1*000
12. COO
~ 13.QOO
12. COO
12*000
9*000
11*000...
10.000
3.000
4.000
8.000
11.000
5. COO.
4.C.OO
7.000
10.000
8.000
12.000
4. COO
6.000
13.000
13.000
4.000
3.000
3.000
3. COO
8.000
10*000
67*500
67*200_
67*000
67*000
67*000
67*000
66*700
66*700 ..._
66*500
66*000
65*500
66*000
66*700
__.66*700
66*200
66*000
65*700
65*700
65*000
65*000
65*500
65*200
64*700
64*200
64*000
_ 63«500
63*700
64*500
64*700
-------
V.
2.000
i.ooo
6. COO
10.000
.._ "10.000
10.000
10.000
10.000
9.000
5.000
.000
•000
5.000
.000
2.000
5.000
4.000
3.000
.000
.000
.000
10.000
10.000
10.000
10.000
10.000
10.000
9.000
63*000
55*000
55.000
54.000
54.000
54*000
55.000
55.000
51.000
47.000
43.000
35.000
33.000
34.000
48.000
53.000
54.000
44.000
38.000
35.000
34.000
41.000
44.000
48.000
51.000
54.000
57*000
58.000
60.000
69.000
62.000
64,000
~ 67~,000~
69.000
75.000
80.000
90*000
74*000
73.000
85.000
92,000
96.000
66.000
45,000
42.000
71.000
86.000
89.000
92.000
86.000
80.000
93.000
93.000
100.000
100.000
100.000
60
13.000
7. COO
12.000
11.000
13.~OC"0
16, COO
14.000
8. COO
. 12*000
9*000
6,000
.4,000
4.000
4.QOO
4. COO
6,000
7, COO
5,000
5.000
4.000
4. COO
10.000
7.000
12.000
23.000
1 7*000
i.o.ooo
8. COO
64*200
63*700
63*700
63*500
~ 63*500
63*500
64*000
64*200
64*000
63*500
63*000
63*000
62«700
63*000
63*500
63*200
62*700
62*500
62*200
62*200
62*000
61«700
61*500
61*500
61*500
61*000
61*000
60*700
-------
t'
f
'. ' """ 7.000
i!
10.000
Jl
, 1.000
11.
•"" " 10. 000
10.000
10.000
*" ~" 10. coo"
10.000
10.000
10.000
10.000
10.000
i o.ooo
10.000
5,000
7.000
• 000
1.000
' 3.000
3.000
7.000
8.000
4.000
.000
.000
_ 8,000
j 2.000
7,000
7,000
56*000
53.000
61.000
64.000
57*000
55*000
52.000
50.000
50.000
50*000
50.000
51*000
53.000
53*000
50*00.0
49*000
46*000
43*000
56*000
63*000
65*000
54*000
50*000
47*000
44*000
45.000
60*000
66*UOO
68*000
100.000
100.000
97.000
75*000
93*000.
96.000
100.000
100.000
100.000
100.000
100.000.
100.000
100.000
__100.000
93,«.OJaa
93.000
89,000
100.000
78,000
65,000
59.000
83.000
89.000
96.000
96.000
100.000
87.000
68*000
63.000
61
3. COO
3.QOO
9. COO
6.000
_ 7.-coo.
6.000
8.000
__8.000
7.000
6.QCO
.. 7.000.
7,000
4,000
; 4, COO
6, COO
4,000
4.000
3,000
/•OOO
10, COO
10.000
7.000
_..».? 000.
5.000
3.000
4,000
14,000
12.000
10.000
60*700
61*000
61*500
62*000
61*500
61*500
61*200
61*200.
61*200
61*000
.60*500
60*000
59*500
59*200
55*5-00-
59*500
_59*500.
60*000
60*700
60*700
60*000
59*500
59*200
59*000
' ~59«000
58*700
59*200
59*500
59*000
-------
.000 61.000 78.000 6.000 59*000
f.OOO 6l«000 78*000 7.000 58*700
UA» 77l8«OOOK rtlDTH- fOO.OOOCLD CQVER" 2.000TEMP AIR- 62.000
TEMP WATER- 60.000REL HUM- 72.000WIND SPEED- 8.700
NUMBER OF CASES- 4
ALLO^EP OTS
•100COOOE 01
.200rCOOE Cl
.3000000E 01
•fOOOOOOE 01
NUMdEK fcF DAYS AVERAGED- 2
£ CAYS AVERAGED
1
2
FTBLl TTBL1 HFGT81
*******»»*******«»*«*«****•»***«*«*«***«#»«<»*«•«*****«**»»«»**
.
.
*
.
•
.
.
*
*
*
885E-Q1 »32oE
122E
178E
256E
363E
5C7E
698E
9f9E
127E
169E
OC
00
00
cc
00
00
00
01
01
f
*
*
*
.
*
.
.
.
40CE
500E
600E
700E
800E
90CE
100E
11CE
12GE
02
02
02
02
02
02
02
03
03
03
.
.
.
.
.
*
*
•
•
*
1Q3E
107E
107E
106E
105E
105E
lOf E
lOf E
103E
103E
Of
Of
Of
Of
of
of
Of
Of
of
of
DAYS SjNCE MARCH Si' 75.000BETA* 45,000
-------
OCTOBER 30 , 1974
OCTOBER 1 to 3 , 17 to 24, and 27 to 29, 1973
NUMBER 6F DATA
CLD C9VER AIR
~ .000
. poo
.000
.000
3.000
8.000
5.000
5.000
5.000
3.000
10.000
10.000
10.000
10.000
10.000
10*000
10.000
10.000
10.000
10.000
10*000
10.000
10.000
10.000
10.000
10.000
LINES"
rEMp REL
38*000
37.000
38*000
56*000
65*000
66*000
59*000
55.000 ._
54*000
54*000
53.000
58.000
60*000
58.000
58*000
59.000
61.000
60*000
62.000
65*000
64.000
65.000
62*000
58*000
44*000
45.000
112TIME AV
HU^ WIND
96.000
100,000
100.000
72.000
.,..47*000..
37.000
56.000
_., 67.000..
75*000
75*000
74.000
72.000
84.000
96.000
100.000
97.000
97.000
100.000
100.000
97.000
100.000
100.000
100*000
100.000
65.000
65.000
63
. L8GIC-
SPO WATER
4.000
3.00.0.
3*000
6*000
8.*.000_.
8. COO
9.000
5.000__
11. COO
7.000
9.000
10.000
10.000
9*coo._
8*000
7*000
8.000
4.000
4.000
6.000
7.000
3.000
b.OOO
3.000
9. -000
6.000
0
TEMP
"60*000
60*000
60*000
60*700
_ 61*000
60*700
60*500
_. _ .,60*500
60*200
60« 200
60*200
60*500
60*500
_ 60*700. ._ „,
60*500
60*500
60*500. ...
60*500
60*500
60*700
61»000
60*700
60*500
60»5UO
54*700
54*700
-------
t "
I
1 10.000
1
\ ' "10.000
1
«u_ 10.000
10.000
1 0.6 oo
10.000
10,000
lo.ooo
9.000
8,000
loVooo
10,000
10.000
10,000
1.000
3,000
5.000
1.000
5.000
ic.ooo
10.000
10.000
10.000
lo. coo
10.000
10.000
I
1. 10.000
10.000
45.000
45*000
45*000
47.000
""45*000
45.000
43.000
42*000
38*000
46.000
47.000
46.000
45.000
43.000
37.000
32.000
32.000
43.000
48.000
50.000
44.000
45.000
44.00C
44.000
44.000
44.00C
46.000
46,000
68.000
" 77.000
80,000
56.000
58.000"
60.000
73,000
76,000
82.000
66.000
61,000
66.000
71.000
73.000
89.000
96.000
100.000
100.000
63.000
50.000
68.000
58.000
80.000
86.000
86.000
100.000
100.000
100.000
64
10. COO
10. 000
_ 14* 000
10.000
"""7.000
7*000
4.000
*»COO
5.000
7,000
6. COO
6.000
4. COO
3". 000
3.000
3.000
3.000
.000
3.000
5. COO
6. COO
8.000
11.000
11.000
7.000
3. COO
6 . 000
7.000
54*500
54'7UO -
55*000
55*500
55.500
55*500
55*000
55*000 ~
54*700
54*700
54*500
54*500
54*200
54,200
54*000
54*000
53*700 ""
53*700
53*700
54*200
54*000
54*000
53*700
53*500
53*200
53*000
53*000
53*500
-------
10.000
10.000
10.000
L — " "" StOOQ
8.000
2.000
" "" .000
__.. t000
.000
.000
.000
.000
4.000
.000
3.000
5.000
.000
.000
.000
_. .000
.000
4.000
3.000
7.000
8.000
, _. 4.000
, i
I 5.000
r
I i.
5.000
4.000
46.000
44.000_.
44.000
41.000
39.000
43.000
47.000
49.000
40.000
37.000
34.000
33*000
32*000
47*000_
56.00C
58.000
45.000
44.000
40*000
38.000
35*000
56*000
62.000
63.000
55.000
50*000
47.000
44.000
39.000
96.000
....IPO. 000.
100.000
100.000
._.. 89,000,
71.000
56. COO
50.000
86.000
89.000
92.000
96.000
100.000
93.000
64.000
60.000
93.000
86*000
96.000
100.000
100. OCO
72.00.0
58.000
54,000
69.000
86.000
93.000
96.000
96.000
65
10. COO
7.000
6.000
7.000
6.COO_
9.000
4.000
.4.000
3. CCO
3.000
5*000
4.00.0
3. -000
10. COP ___
6. COO
7. COO
_ b.COO
b.COO
3. COO
3. COO
b.COO
11.000
10.000
6. COO
b.COO
3. COO
3. COO
3.000
3,000
53*200
53*000
53> COO
52«700
52*500
52*200
52.700
53*200
53*000
52*700
52*500.
52.200
52*000
52*000
52*000
52*500
52.500.
52*500
52*000
52*000
51*500
51*700
52*000
52*500
52*500
52*200
52*000
51*500
51*200
-------
7.000
4*000
tOOO
.000
:~"~,oou
10.000
10,000
10. LOO
10.000
10.000
lo.coo
10.000
4,000
2,000
5.000
8.000
" 8.000
10.000
9.000
10.000
10,000
10,000
8.000
5.000
8.000
10.000
10,000
10,000
50.000
61.000
62*000
52,000
43,000
54,000
47,000
" 45«OOC
44,000
44,000
44*000
40,000
38,000
31,000
30,000
27,000
39,000
42,000
43,000
37,000
41,000
42,000
40,000
36,000
45,000
49,000
43.000
47.000
96.000
67.000
67,000
93.000
100.000
96,000
96.000
83.000"
80*000
74.000
71.000
76.000
67.000
92.000
96.000
96.000
79.000
63.000
63.000
82.000
73.000
71.000
62.000
79,000
68.000
09.000
39 ,000
74.000
66
3,000
"6.000
5. COO
3.000
3,000
10,000
9.000
lo.Q&G
11.000
13.000
9.000
7.000
3.000
3.000
3.000
5.000
4.000
8.QOO
5,000
3. COO
6. COO
9.000
12.000
3.000
11.000
12.000
13,000
11.000
51*000
51*500" """"
52»000
52*000
52,000
52,000
51,700
" 51*5t>$
51*700
52*000
52*000
51*700
51,500
51*000
51 t QOO
50*700
~" 50*500
50*700
50*700
50«500
50*200
50*000
50*000
50*000
50*000
50*000 "
50*000
50*000
-------
10.000 47.000 93.000 8.000 50*000
UA- f240.000R WIDTH- fOO.OOOCLD C9VER* 1»OOOT£MP AlR»
TEMP W#TEr<» 50«OOOREL HUMi 68'OCOWIND SHEED» *000
NUMBER QF CASES- f
ALL8KET OTS
•looroooE 01
•200COOOE 01
•300COOOE 01
.fOcroouE 01
NUMBER 6F DAYS AVERAGED? 2
CAYS AVERAGED
1
2
PTBLl TTBL1 HFGT81
45*000
.
.
•
t
.
.
.
t
.
t
885E-01
122E
178E
256E
363E
507E
698E
9f 9E
127E
169E
00
OP
OC
OC
OC
OC
00
01
01
• 320E
•
t
.
.
.
.
.
»
.
400E
500E
600E
700E
8UOE
900E
100E
110E
12CE
02
02
02
02
02
02
02
03
03
03
.
.
.
.
.
•
.
.
.
.
108E
107E
107E
106E
105E
105E
lOfE
10f E
103E
103E
of
Of
Of
Of
of
Of
Of
Of
of
of
DAYS SINCE MARCH
103.000BETA*
45.000
-------
ADDITIONAL DATA FOR STATION 7 ABOVE THE DAM
TEMPERATURES AT STATION 7, °F, DAILY AVERAGES,
OCTOBER 1-3, 17-24, AND 27-29
60.1, 60.0, 59.8, 55.8, 55.0, 54.5, 53.6, 53.4,
53.0, 52.6, 52.9, 52.7, 51.9, 51.0
68
-------
NOVEMBER 15, 1973
OCTOBER 17 to 24 and 27 to 29, 1973
NOVEMBER 1 to 14, 1973
NUMBER er DATA LINES- BOOTiME AV. LSGIO. ,_o
CLO cevE9 AIRTEMP REL HU* WIND SPD ^ATER TEMP
10.000 44*000 65.000 9.00054*700
10*000 45*000 65.000 6.000 54*700
10.000
' ~ 10.000
10,000
10.000
10.000
10.000
10*000
10.000
9.000
8.000
10.000
10.000
10.000
10.000
1.000
3.000
5.000
1.000
5.000
10.000
10.000
10.000
10.000
10.000
45.000
45.000
45.000
47.000
45.000
45.000
43.000
42.000
38.000
46.000
47.000
46.000
45.000
43.000
37.000
32.000
32.000
43.000
48.000
50*000
44.000
45.000
44.000
44.000
68.000
~ 77.000'
80vQOQ_.
56.000
bS.OOO
60.000
73.000
" 76.000
82.000
66.000
61,000
A6'000
71.000
73.000
89.000
96.000
100.000
100.000
63.000
bO.OOO
68.000
58.000
80.000
86.000
10.000
10. COO
_14.000
10. COO
7. COO
7.000
4.000
"4.000
5.000
7.000
6.000
6 . 000
4.000
3.000
3.000
3.0.0.0
3.000
.000
3.000
5.000
6.000__
8. COO
11.000
11.000
54*500
54*700 ~~
55 » 000 .
55.500
55*500
55*500
55*000
5S«000
54*700
54«700
54*500 '
54*500 __
54*200
54*200
54*000
54*000
53*700
53«700.._
53*700
54*200
54*000 _
54*000
53*700
53*500
69
-------
1 10.000
ti. " io.ooo
I ! '
'',..._ _._. 10.000
10.000
lo. coo
10.000
10*000
9. COO
8.000
2. COO
_..___. tOQO
.000
.000
" .000
,, - .... .000
.000
4. COO
.000
3.000
5.000
.000
.000
.000
.000
.000
(f - '- - '4,000
1
> 3.000
7.000
44'OOC
44.000
46.0CO
46.000
46/000
44*000
44*000
41.000
39.000
43.000
47.000
49*000
40*000
37*000
34.000
33.000
32.000
47*000
56. COO
58.000
45.000
44.000
40.0UC
38.000
35.000
56.000
62. COO
63,000
86.000
100.000
ICO. 000
100,000
~~ 96,000
100,000
100.000
" " 100* 000
89.000
71. COO
"56.000
5Q.OOO
86.000
89,000
52,000
96.000
100.000
93.000
6.COO
6.000
9.000
~4.~000
4*000
3. COO
3.000
5. COO.
4,000
3,000
10,000
6,000
7.0CO
5, QCO
5.000
3.000" "
3.000
5.000
11. COO
10. COO
6. COO
53*200
53*000
53.000
53.500
53,200
53«000
53*000
52*7t30"
52*500
52*200
52*700
53*200
53*000
52*700
52*500
52*200
52*000
52*000
52*000
52*500
52*500
52*500
52*000
52*000
51*500
51.700
52*000
52*500
70
-------
" "8.000
4.000
5.000
5.000
4.000
7.000
" 4.000
.000
.000
.000
10.000
10.000
..__. . ..... --lotooo
10.000
10.000
lo.coo
10.000
4.000
2.000
5.000
8.000
8.000
lo.coo
9.000
~ '- 10". ooo
10.000
10.000
8.000
5.000
55.000
50.000
47.00C
44.000
39.000
50*000
" 61.000
62.000
52.00C
"" 43.000
54.000
47.000
45.000
44.000
44.000
44.000
40.000
38.000
31.000
30.000
27.000
39.000
42.000
43.000
37.000
41.000
42.000
40.000
36.000
69.000
86,000.
93.000
96.000
96.000
96.000
67.000
67.000
93.000
100.000
96.000
96.000
83.000
80.000
74.000
71.000
76.000
67.000
92.000
96.000
96,000
79.000
63,000
63-000
82.000
73.000
71.000
62.000
79.000
5.000
3.000
3. COO
3.000 "
3.000
3.QOO
6.QOO
5.000
3. COO
"3.000 ""
10.000
9.000
i if. ooo
11.000
13.000
9.000
7.000
3.000
3.000
3.000
5. COO
4.000
8.000
b.QOO
3.000
6,000
9.000
12.000
3.000
52*500
52*200. _ _ ....
52*000
51*500
51*200
51.000
51»500
52«000
52»000
52*000
52»000
51*700
51.500
51*700
52*000
52«000
51*700
51*500
51*000
51*000
50»7VO
50*500
50*700
50*700
50*500
50*200
50*000
50*000
50*000
71
-------
r
8.000
io.ooo
lOtOOO
10.000
"10.000
10*000
lOtOOO
10. COO
10.000
10.000
10.000
10.000
10.000
"ib.coo
6.000
4.000
5.000
8. COO
10.000
10.000
lo.ooo
10.000
3.000
3.000
3.000
9.000
9. COO
4,000
45*000
49*000
49*000
47*000
47,000
39*000
48*000
46.000 "
47*000
49.000
50*000
49*000
49*000
' 49.000
49*000
48.000
49.000"
54.000
52*000
50*000
45.000
43.000
42*000
42.000
44.000
44.000
42.00C
41.000
68*000
59*000
59.000
74.000
" 93,000
93.000
80*000
83.000
93.000
93.000
69.000
63.000
61,000
56,000
50.000
48.000
" "48.000
43.000
45.000
50.000
74-000
76.000
71.000
60,000
47.000
40*000
41.000
40.000
72
11*000
12.000
1.3.000.
11.000
8,000
3*000
5.000
e>»co6~
6.000
9.000
"~i2*ooo~
14.000
20.000
13.QOO
14.000
16.000
8. COO"
9.000
9.000
b.QOO
b.COO
6.000
" 14. COO
14.000
lb.000
17.000
12.000
15.000
50*000
50*000
50*000
50*000
50.000
... . 49*000
49*000
4.9».0-UO
.49*000
49«200
50*000
50*000
49*200
4 g". ooo
48*200
48*200
"48*500"
48*700
48*700
48*500
48*500
48*700
48*700
49*000
49*000
49*200
49*000
49*000
-------
: " 9tOOO
1 9.000
6.000
" " 8. COO
9*000
9.000
" 6.000
9. COO
1.000
2.000
2.000
3.000
5.000
9.000
6.000
""5.000
8.000
10.000
10.000
10.000
7tOOO
9.000
10.000
10.000
1C. COO
7.000
7.000
8.000
8*000
4o*ooo
39.000
37.000
36.000
36*000
38*000
39.000
37.000
33.000
31.000
32.000
31.000
34.000
35. COO
38.0.00
35.000
34.000
32.00C
31.000
30.000
28.000
31.000
32.000
29.000
28.000
27.000
£5.000
27.000
30.000
39.000
38.000
39.000
"40.000 "
40.000
37.000
36.000
41,000
44,000
'47.000 ~
43*000
43.000
42.000 "
37.000
31.000
32.000
37.000
33,000
36.000
41.000
53,000
40.000
36.000
58.000
61.000
bS.OOO
60.000
61,000
58.000
73
14.000
18.000
12.000
~ '14*000
17*000
11* COO
11.000
8.000
8.000
"" "6.000
7.000
7.000
~12rGOd "
9*000
10.000
11,000
7.000
11.000
lu.coo
12*000
14, COO
1U.COO
.17.000
8.000
12.000
7.000
9.000
b.OOO
4.000
48*500
48*500
48*500
48*200
48*200
48*2UO
48*200
47*500
47*000
47*000
46*700
46*700
47*000
47*000
46*700
46*500
45*700
45,500
45*200
45*000
45"* 000
45,000
45*000
44*700
44*500
44*500 __
44*500
44*500
44*500
-------
1 7.000
i
•;1 9.000
"... ,9. COO
1
10.000
10* COO
10.000
10.000
10.000
10.000
9.000
10.000
7. COO
9.000
9.000
6.000
7.000
"7 •000
9.000
9.000
10.000
9.UOO
10.000
10.000
10.000
8.000
t 7.000
1 5.000
10.000
36.000
33.000
38*000
33*000
36*000
36*000
36*000
36*000
33*000
40.000
41.000
38.000
36.000
35.000
32.000
32.000
34*000
33.000
31.000
29.000
26.000
25.000
25.000
25.000
30.000
33.000
31.000
31.000
52.000
46.000
46*000
53.000
67.000
62*000
62.000
57.000
50.000
45.000
45.000
57.000
42.000
42.000
45.000
43.000
"38.000
45.000
43.000
45.000
46.000
46.000
53.0'00
66.000
56.000
42.000
43.000
45.000
6. COO
12. COO
.._.io*coo
7.000
8. COO
7*000
10.000
15-.GOO
15. COO
14.000
13.000
8.000
12.000
7.QOO
7.000
12. COO
12. COO
12.000
Ib.COO
13. COO
14.000
12*000
12.000
10.000
9.000
9. COO
10. COO
11. COO
44*700
44»700
44*200
44*000
44*000
44*000
43*500
43f5-0«
43*500
43*500
43*500
43*500
43*200
43*000
43*000
43*000
43*000
43*000
42*500
42*200
42*000
41*700
41*500
41*500
41*500
41*200
41*200
41*000
-------
1
-------
8.000
6.000
3.000
57tOOO
48.000
45.000
42.000
63,000
71.000
12.000
4.000
4.000
42*000
42.000
42.000
UA* 7640.OCOR rtlDTH* 400.000CLD C8VER" 1»OOOTEMP AIR- 50.000
TEMP WATER* 41.700REL HUM- 68.000WIND SPEED" 4.400
NUMBER er CASES* 4
ALLOWED DTS
.100COOOE 01
•20CCOOOE 01
.300COOOE 01
-o .400COOOE 01
Ol
NUMBER &F DAYS AVERAGED- 2
CAYS AVERAGED
1
2
PTBL1 TTBL1 HFGTBl
• S85E-01 »32cE Q2 »108E 0**
.122E 00 »40CE 02 »107E 04
•178E 00 -500E 02 »107E 0^
.256E 00 »600E 02 .106E Q4
.363E OC »700E 02 »105E 0^
•507E GP »300E 02 »l05t 04
•698E OP «90CE 02 •104E Q4
»949t OC »10CE 03 «104E Q4
•127E 01 «11CE 03 .103E Q4
•169E 01 «1HOE 03 »103E 04
-------
APPENDIX C
PROGRAM LISTINGS
This appendix presents complete program listings for the
STREAM, SENSIT, and MONT codes.
77
-------
1
2
3
4
5
6
7
8
9
10
11
12
13
If
15
16
17
18
19
20
21
?2
?3
24
25
26
27
23
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
• 000
.000
,000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
r
C
C
C
C
C
C
C
4
5
10
20
100
250
STRFAM
STREAM THERMAL M9DFL
IMTC* IN* I9*EL* AREA*U
C9MMQN DTEMP.TE"1P* XPR* XFND, DXPR, X.DX*
C9MM6M ERRBR.DXMAX
C9MM8MRHfij I*MO*MD* TAI RjCLD* RH^ ALBAR* TWS,TAj EW^ EAj H9S*HS
C9MM9M HS^^ Hft3> P8R/EVAP,HEiHC/ HLYMN, PTBL ( 10 )*TTBL( 10) i WHS* CONST
CALL IM°UT
IF( 1NTC -4)4
XPR = DXPR
cgNTjNJUp:
D9 100 JF« l.INT
CALL DI-FFQ
G9 T9 (10*10.20)* INTC
CALL EULFR(OTEMPjTEMP*DX,l* JE*V->
G9 T8 100
CALL RK4(DTEMP*TEMP*DX*1.JE*X)
C9NTINUE
IF(X - XPR ) 5*250*250
CALL 9UPT
-------
29.000
30.000
31.000 105"
32.000 '.
33.000 110
34.000
35.000 120
36.000
37.000
33.000 130
39.000 131
40.000
41,000 140
42.000
43,000
44.000 150
45.000
46.000 300
47.000
48.000
'49.000
50.000
51.000
52.000
53.000
54.000 10
55.000 20
56.000 C
XPR « XPR + nxPf?
IF(X - XFND) 5*300*300
C9NTINUF
JJMP • -1
C8NT1MUE
XPR =• X +. DXPR
C9KTIMUC:
CALLN9RD(DTEMP*X* XPR* TEMP* ERR9R, t . DX* DXMAX* JUMP* KSTP*KC* 1 »E-6* 18 >
IFUuMPilSOj^O.lSO
(•RlTEdB.isi) X
F3RMAT(//i x *'Ei4.5i INTEGRATIBN FAILURE')
CALL EXIT
C9NTINUF
CALL 3IFFQ
G3 T8 IPO
CALL 9UPT
IF(X - XFND) 110*300.300
CALL .EXIT
END
SJB38UTINE INPUT
1 CSM^ISN OTEMP.TEMP, XPR. XEND, OXPR. X* DX* INT.INTC*
1 IN* I3*FI../ARFA*UjERR9RjDXMAX
CSMMBNRHSj WMD*.HD* TAI R* CLD* RH* ALBAR j TWS , TA* EW*EA*H8S*HS
C9MM6N HSR*HR3*FBR*EvAPjHE*HC*HLYMN,PTBL(lO). *TTBL(10) *WMSjC6NST
C9MMBN HFG/r.LDl*HFGTB(io)*CeNSV
FSRMAT(AFIO.O)
F9RMAT(6T10)
CHBlCE 8F INTEGRATI8N SUBR8UTINF
-------
CD
Q
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
.
.
.
.
.
.
»
,
.
.
.
.
.
«
*
.
.
.
.
.
«
«
.
.
,
.
t
•
«
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000.
000
000
000
000
30
40
50
60
110
115
120
125
130
135
140
H5
150
C
C
160
IF! INTC - 3)
INT . INTC
G9 T9 60
INT s n
G9 T9 60
C3NTINUF
INTC
30*40*50
C9NTINUF
G8 T9.
WRITE!
F3RMAT
G9 T9
(11
19.
( * 1
ISO
OjlP.0^130,
115
)
****
140)
.
FULFR
INTC
1NTERRATI9N *****!//)
C9NTINUF
WRITE!
FORMAT
G8 T9
WRITE!
F9RMAT
G8 T9
WR I TE (
F3RMAT
CgNT.j M
19,
( M
125
)
*****
M8D.
EULER INTEGRATI8N *****(//)
150
19.
( M
135
)
*****
Uf
TH
8RDER RUNGE-KUTTA ******DX,DX
ADAMS M8UI,TBN INTEQ. »**»***!//)
• PARAMETERS
XOX/DXPR,
'F6.pl
E10.3/
/)
EN
D
XE-ND.
DX
s'Eln.3! DXPR »'E10.3
READ(IN.IO) FRR9R,DXMAX
-------
86*000 WRlTE( 18.180) E9R8R.DXMAX
87.000 180 F3RMATP 'ERR8R a(El0.3» DXMAX o'E'.O.S//)
88.000 REAQdN.10) TEMP, U> AREA.F.L
89.000 REAO(IN.IO) RH8. WMPH, TAIRj CLP* RHj A-LBAR
90.000 09 .185 IsljlO
91.000 185 REAodN.10) PT3L(I)i TT8L(l)j MFGTB(1>
92.000 TA . (TATR - 32.)*5./9.
93.000 W » WV|PM»22./15.
9*iOOO IN^S 9 W * .3048
95.000 HMD B WMPH * 24.
96.000 C8NST >i FL/( RH9*U*ASE:A )
97.000 C3NS1 B (RH8#0.00328)/{P4«»3600.#Ot06l'M
98.000 SINA » STN(AL3AR^3.14159/180.)
93.000 CLDt « 1. • .07A5«CLO
103.000 C INCIDENT SSl-AR ^ADlATlSN
101 •'000 H8S a 1.9*SINA
102.000 H3 = H8S»(1» • .0006*CLD»*3)
103.000 c REFLECTED ssi.AR RADIATIBN
134.000 HSR s H3*3./AL3AR
10=»000 EA = ?^H*( 1013./147Q« )*SI ( TTBL, PTBLj TA IR» io>
106.000 WRlTEt18.200) TPMP
107-000 200 FSRMATM INITIAL STREAM TEMPERATURE *'F6.2i DEG F'/>
103«000 WRlTElI8j210) U,AREA.EL
109.000 210 F3RMAT(i STREAM VF.L9CITV = ' F6. ^' FT/SEC CR. SEC. AREA
110.000 1F10.2' SQ. FT. SURFACE WIDTH »'F6«ll FT'/)
111.000 WRlTEf19.220) RM8*CLD^RH.ALBAR
112.000220 F9RMAT(i RH8a'F5.2i LR/CU.FT. CLO=»F4.1' 'TENTHS'*
113.000 1» RH«'F5.1I PCTi/1 ALBAR 3iF4.1' OEGRFES'/)
-------
114.000 WRITE(I8,230) TAtR,TA/C8NST/ CBNS1
115.000 230 F3RMATP AIR TFMP. ='F5.1' DFC3 F'F8»1' DFG .C' i
116.000 1' C9NST siElO.3' CONSl «IEIO«3'/)
117.000 WRlTE(19*240) W.WMPH,WMS*WMD
118.000 240 FQRMAT(i WjND VELBCjTY «»F6.2i FT/sECIF8.2IMPH'F8.2' METERs1/
119.000 1 '/SEC'F8.2i MlLES/DAYl/)
120.000 WRlTE'(I8.260)
1P1.0QO 260 F9RMAT(/,T20tTTBL'T40'PTBL'T60lHFt5TB'/)
122.000 08 ?70 t »lj10
123.000 270 WRlTEt16.280) TTBL(I)* PTBL(I). HFGTB(I)
124.000 28a FQRMAT(inX/3F20.5)
125.000 WRlTF(Ifl*300) EAjH6S*HS.HSR
126.000 300 F5RMAT{//' FA ,»E12.4I HSS «IE12.4' HS B'E12.4j
1?7.000 1 ' HSR ='E12.4-' LY/MTNM
1P8.000 WRlTEC18.310)
129.000 310 F8RMAT(MM
S 130.000 RETURN
131.000 ENJD
132.000 SUBRBJT'INE 8UPT
133.000 C3MM8N DTEMP, TFMP, XPRjXFND*DXPR,X,DX* INT^INTC*
134,000 1 IN, 18,El *ARFA*LJf ERR3R*DXMAX
135.000 C3MM3MRHBJ WMD/MDjTAlRjCLDjRH* ALBAR* T^'SjTAj EW*EA*H6SjHS
136.000 C3MMBM HSR*HB3*FBRjevAP,HEjHCjHLYMNjPTBL(10)>TTBL(10)*W«S»CeNST
137.000 CQMneN rlFG^rLDl*HFGTB(lO)/C8N«;1
13B.OOO WRlTE(I8«10) X>DX
139.000 10 F9RMAT(i X =»'F7,H FT DX a'Ffe.l* /)
140.'000 WRlTE(I8.20) TE^Pj'DTtMP
1^1.000 20 'F9RMAT(i STREAM TEMP «IF6»2' DFG F DTEMP »
142.000 1' DEG F/FTl/)
-------
143.000
144.000 30 F9RMAT(i EH >'F13t5i EvAP/MMPD «'E12»5' HE «'
145.000 1E12.5' I Y/MIN HFG =iE12«5j/>
146.000 WRlTF(l9,50) H8q,F.BR,HC
147.000 50 F3RyiATM H8R ai£lP«5' EBR»iF12.5" HC »'E12.5' LY/MlNi/1
148-000 WRlTE(I9,60) HLYMN/HO
149.000 60 F3RMAT(' T9TAL HEAT TRANSFER • I.NT/1NTC*
157.000 1 IN,J9,Fl jARFA*U*ERR9R*DXMAX
S 158.000 cscNeNRMa, WMD,MDJTAIRJCLD*RHJALBARJTW.SJTA* EWJEA/HBS/.HS
159.000 C-JMM6M HSR' Hfl3i FBR^EVAP/HE^ HC, HLYMM, PTBu (10) i TTBL (10) • WMS^CBNST
1<,0«000 C3^MSM HFG*rLOl,HFGT
161.000 C 'THERMAL FXCHANQr WjT-l
162.000 TwS= (TFMP-3?.)»5./9.
163.000 E.-/=(1013./14.7)#SI(TTBL.PTBL,TFMP.10)
164.000' C EFFECTIVF BArK RADIATI8N.
165.000 H3B« (l4.38-.09*TWS-.04fi-#RH)/69.7?
166.000 ESR s H9R * rLOl
167.000 C EVAP63ATT8N HEAT TRAMSFF.P-.
168.000 EVA? « .35* (EW-EA)*(1. + .009R* WMD)
169.000. HFQ » SI(TTBl iHPGTB/TEMPjlO)
170.000 HE * EVAP*HFG*C^NS1
-------
171.
172.
173.
174 .
175,
176.
177.
178.
179.
180.
181.
182.
183.
184.
185.
186.
187.
188.
139.
190.
191.
192,
193.
194.
195.
196.
197.
198.
199.
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
.000
000
boo
000
000
.000
000
000
000
000
000
000
c
c
c
c
ccccc
ccccc
ccccc
ccccc
c
c
c
c
c
c
120
130
150
160
180
C8NVECTI8N HFAT TRANSFER
HC = 39. #(.26 + .Q77*WMS)*(TWS - TA )/l440«
T3TAL HFAT TRANSFER T9 -WATER/ LY/MIN
HLYMN » HS -
-------
200.000 GS T8 254
201.000 C FIND X IN TABLE.S IN TABLE
202.000 210 03 220 IKa2*M
203.000 II • IK
204.000 IF(XTBLdK)-X)
205.000 2.20
206.000 254 Xl
207.000 X2
208.000 Yl
209-000 Y2
210.000 SI
XTBl" dI-1)
XTBIJII)
YTBf dl-l)
YTBLdl)
Y1 +
-------
2?S
2?9
230
231
232
233
234
235
236
237
238
233
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
.
.
.
•
.
..
.
.
.
.
•
.
,
.
.
.
.
.
.
.
.
.
.
.
.
.
•
25 5 •
256
•
000
000
000
000
000
000
000
000
000
000
000
000
0-0 0
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
20
200
CCCCC
CCCCC
CCCCC
c
CCCCC
CCCCC
CCCCC
10
100
20
T.T+DT
RETURN
CONTINUE
09 POO InliNp-
Y( i )»• sYtn + (YP( i >+SYP*DT/?.
C9NTINUF.
RETURN
END
F3URTH 9RDER RUNGE-KUTTA INTEGRATTSN
SUBRQUTIME RK4(YP*YiDTjNE:j J*T)
DIMFNSI9M YP(5') .Y(5)*AK<5*4) jSYfS)
G9 T6( 10»20*30*40)> J
cgNjiNUp;
D9 1-00 i = l/NF
SY( T ) = Yd)
A<( T j'l ) = DT*YP( I )
Y.d ) = Yd ) +AK( I'jl }#.5
CaNTIMUR
ST » T
T ST +'nT*«H
RETURN
C9NTINUF
09 POO I»liNF
-------
2=57tOOO AK(tjE) . DT*YP(I)
25S..OOO Y(I) =. SY(I> + AK< I j ? U.5
259.000 200 C9NTINUF.
260.000 RETURN
261.000 30 C9NTINUE
263.000 D9 300 i « 1,NE
263-000 AK(Tj3) . DT*YP(I)
26^.000 Y(I) = SY (I) + AKH.3)
265.000 300 C9NT1NUE
2^6tOQO T = ST + DT
267.000 RETURN
26SOOO 40 C8NTINUE
269.000 09 *00 T * 1,NE
270.000 AK(I^) = DT.#YP(I)
271.000 Y(I)sSY(T) + (
272.000 ^00 C9NTINUE
273.000 RETURN
274.000 END
275.000 CCCCC
276.000 CCCCC
277.000 CCCCC
278.000 C ADAMS-M9ULT9N INTEGRAT19N
279.000 CCCCC
280.000 CCCCC
281.000 CCCCC
282.000 SUBRBUTlNE
233.000 DlMENSrSN STARY(5)/Y(5),SY<5),SAVEY(5)/F(5).FP(5>,DELTA{5)tDALTA(5
23ft000 l>'A<5)/B(5)jr<5)»D<5)iAA<5)»BB<5)jCC<5)jDD(5)/SF(5)
-------
235.000
286.000
287.000
288-000
239.000
290.000
291.000
292.000
293.000
•294.000
295.000
296.000
297.000
293.000
299.000
300.000
301.000
302.000
303.000
304.000
305.000
306.000
307.000
308.000
309.000
310.000
311.000
312.000
313.000
IF ( 803 ) » I A
C JUMP P9S. REST6RE VALUES
999 T=SAVET
993 JUMp=0
09 901 I»1/NF
F( I )=SF( T )
901 Y(I)=SAVFY(I)
G3 T.8 10?
C J'JMP SJEG. INITIALIZE.
1 03 5 I»1»NE
3TARY! I )sY( I>
A( I 1=0.001
Bf I 1*0.001
C{ I } «0.0nl
50(1) lO.onl
KSTp=0
KDELY=0
KCBMsO
XT=95«/(?88.»64. )
Ua8A,3»/M 2.*R040. )
V995tO/?88.0
P«HR. 0/34.0
Q*35.0/7?.0
R«5. 0/48.0
S»1.0/l?0.0
-------
314.000 IAM
315.000 JjMpsO
316.000 G8 T8 1101
317iOOO C BEGIN INTEGRATION STrP
318.000 1000 D9 1111 T=1*NE
319.000 SF(I)=F(M
320.000 llll SAVFY(I)«Ytn
391.000 C H T90 SMALL RETURN WITH JUMP NFG
322.000 600 IF(A9S(T+H)-ABS'+D(I) >
328.000 10 FP( I)«F(T)+2.3*A(n+3«6«B
S 329.000 IA»?
330.000 G3 T8 1101
331-000 11 D3 12 Isl^NE
332.000 12 SY(I)=Y(T)
333.000 D9 20 I»1*NE
3-34.000 DELTA CT)»F(I)-FPm
3^b..OOO 20 Y(I>aY(n+V#OELTA < t > *H
336.000
337.000
338.000 G9 T8 1101
339.000 21 KCSMsO
3*0.000 D3 30 I»1/NE
341.000 DALTA ( T ) «.F( I) -FP( I)
-------
342,000 29 Y{I)s5Y(I)+V*DALTA (IUH
343.000 3.0 C9NTIMUC
344.000 C TEST F9R STARTING SEQUENCE
34b.OOO 31 IFUsTP-?8)3Ri40.*40
3^6'OOp C APPLY TEST 2 9N ZER9TH STEP
347.000 35 IF«sTP>FiO*50*60
3^8.000 C HALVING TESTS
3^9«000 40 D8 45 I=1*NE
353.000 IF(ABS(DALTA ( T ) ) -ERRQR/ABS ( H n*Rj 45* 5g
351tOOO 45 C8NTINUF
352*000 50 IF(v*H*r.L!F-0.lP5)60,60,55
353.000 55 T=T-H
354.000 C FAIL TESTSj HALVE H
355.000 ?23 H=H/2.0
356.000 KOELY»0
357.000 D9 56 I=1/NE
35S.OOO A( I )sAm/2.n
353.000 B(I)*3(11/4.0
3#.o.ooo cducm/s'.n
361.000 F(I)=SF(T)
362.000 Y(I)sSAVFY(I)
363.000 56 D(I)*D(I 5/16.0
364-000 G9 T8 1000
365-000 C PASS TESTS' T.6RRECT AjB*OD
366.000 60 KSTpsKSTp+1
367.000 D9 65 IM/NE
368.000 A( I UA( I ^+3«0»8( 1 )+6.0*C( I )*10.n#0( I )-t-P*DALTA (I)
369.000 62 B( I )«3< I )+4.*0*C( I > + 10«0*D(I )+Q#OALTA(I >
370tOOO 64 C(I )»C(I)+5*n*0'I)+R*DALTA(I)
-------
371»000 67 D(I )-3
372.000 65 CONTINUE
373tOOO C IF IN! STARTING SEQUENCE* BRANCH
3770*90*100
375*000 70 G9 TS "(1.000*1000*1000*7**1000*1DOO*1000*78*1000*1000*1000*7mlOOOj
376*000 11000,1000*86.1000.1000j1000*74,1000*1000*I000)*KSTP
377.000 C 4TH, 12TH* 2nTH STEP, G9 BACK
378.000 74 H--H
379«000 09 75 I»1jNE
380.000 A(I)a-A(T)
331.000 75 C(I).-Cm
3S2.000 G8 T6 1000
3S3.000 C 8TH STEP G8 FBWARO
33<*pOOO 78 Hs-H
3S5.000 09 79 I=1*NE
386.000 Y(I)«STARY(I)
387.000 A(I)a-A(t)
33S.OOO 79 C(I)»-C(T)
339.000 G8 T8 1000
390.000 c I&TH STEP/ HALV? H* APPLY TEST 1
391.000 86 H»H/2«0
39a»000 D9 S7 IsliNE
393.000 A.( I )=A( I 1/2.n
391.000 B(I)=3(I)/^.n
395.000 C(I)=C(I 1/8.0
396.000 87 D( I )O< U/l.6.0
397.000 •D9 88 I=1*N£
398.000 IF(ABS(DALTA (T ) )-ERR8R/ABS(M))8Rj88^89
-------
399.000 88 C9NTIMUC
400.000 C PASS TEST S8 F8WARO WITH HALVFD H
401.000 G9'T8 78
402.000 C FAIL TEST BEGIN AGAIN WITH HALVFD H
403.000 89 H«-M
404.000 D8 9? I*1/NE
405.000 92 Y(I)=STARY( 1 >
406.000 G9 T8 1
407.000 C 24TH STEP* DflUBLE H, STARTING SFQUENCE ENDS
408.000 90 H*H*p.O
409.000 D3 91 I^i^NiE
410.000 A(I>=/UI)*2.0
411.000 B(1)*3(T)*4.0
412.000 C(I)sC(T)*8»0
4l3"000 91 D(IlOm*16.0
414.000 G3 TB 7«?
415.000 100 KDELYa:OFLY*1
416.000 C WILL \EXT STFP ^8yE PAST TLIK
417.000 102 IF(AB5(TI.IM-T)-ABS(H))1034103J110
418.000 C YES ....SAVF T AMD Y, INTEGRATE T8 TlIM.RETURN,
4i9.ooo 103 ENDH»TLIM-T
420.000 D9 105 IsljNF
421.000 AA(T)=ENDH«A(I)/H
4?2.000 B3(I)«ENDH**?*B(I)/H**2
423.000 CC( I )=ENDH**3*C(I)/H**3
424.000 105 DD( t )»ENDH**4*D( I')/H**4
425.000 SAVFT'T
426.000 D3 800 Tsl-iNF
427.000 SF
-------
428.000 800 SAVPY{IJ«Y(I)
4?9,000 806 ToTtn
430,000 0:3 106 Isl>NF
431.000 Y( I )=Y( I )+ENDH*(F(I HAAd )+BB( I J+CC(.I )+DD(I) )
432.000 106 FP( I )«F( I >+2'.0#AAfI )+3.0#BB( I >+4.0*CC ( I )+5.0*DD( I)
G9 T8 1101
435.000 802 D3 805 tsl^NP
436,000 805 SY(I)«Y(T)
437.000 D3 107 lel^NF
433.000 DELTA (T)«F(I>-FP{I)
439.000 107 Y(I)»Y(Ii+V»OELTA (I)*FNDH
440«000 IA=5
441.000 Q3 T8 1101
442,000 803 09 103 I»1*NF
443.000 DALTA (T )=F( 1 )-FP(1 )
444.000 108 Y( I )=3Y(t )+V*DALTA (I)*EMDH
445.000 JUMP«1
446.000 G9 TB 1101
447.000 C N9.......TEST FBR DOUBLING. IF flK, BEGIN NEST STE- AFTER D8UBLING
443.000 110 IF(ABS(TlIM-T>-ABS(2.0*H))1000.1000*111
449.000 111 IFUDEl_Y-4)1000.1?Ojl20
450.000 120. IF(ABS(?.0#H1-ABS(HMAX)1121J121,1000
451.000 121 Da 125 1=1,IMF
452,,000 IFUBStDALTA ( I ) ) -ERR8R/ (128. 0»ABS ( H ) > ) 125, 125* 1000
453.000 125 CSN'TINUC
454*000 lF(V*H*CLlF-
'455.000 130 C9NTINUF.
-------
456-000 335 H=2.0*H
457.000 09 135 T»1*NF
458.300 A( I )»2.0»A(I)
459.000 B(I>»4,o*B(I)
463.000 C{ I )s3.0»Cm
461.300 135 D(I>=16.n*DFlQ.6*l4V,IKSTP «'t2X.I3t10X/'DAL3A(I)>,/
466.000 1151 F8RMAT(5(2X^I2jtXiE14.7))
467.000 RETuRNI
468.000 .END
vo
-------
1.000 C
2.000 C
3.000 C SENSIT
4.000 C
5.000 C
6.000 c SENSITIVITY ANALYSIS
7.000 c
3.000 C
9.000 C
10.000 CgMMSSDDT^DT. XPR, XF.N3, DXPR,X,DX. INT,!NTo IN.IB,ELiAREA*U
11.000 CSMwieN ERR8R,DX"iAX,TrMP,HFQTBMn),C9NSl
12.000 C8MMBMRH8>WMn,HO,TAIR*CLD/RH-, A| BAR, TWS>TA,Ew,EA,H8S,HS
13.000 C9MMBN HRR,HeB*EBR>EVAP,HE*HC,HLYMN,PTB|_(10),TT3L(10),
14.000 C9MM0N HF-GjH8C^CLDljCLO?/CLD3*DALpjDALp'??jDCLD^DRH^DTAIRi
15.000 iDTA.D'
16.000 IN»5
17.000 I9»6
18.000 CALL INPUT
19.000 IFdNTC - 4)
?0.000 4 XPR » DXPR
?1.000 5 C9NJIMUF
?2.000 09 100 JF= 1,1NT
P3.000 CALL DIFFQ
24.000 G9 TB (10*10,20>j INTC
25.000 10 CALL EULFR(ODTjOTjDX.ljJE*X)
26.000 Ga T0 100
27.000 20 CALL RK4 t DDT , DT . DX, 1, JE,-X )
23.000 100 CaNTlNUE
29.000 IF(X - XPR ) 5,250,250
30.000 250 CALL 9UPT
51.000 XPR s XPR * DXP9
32«000 IF(X - XFND) 5
33.000 105 CaNrlNUF.
34.000 JUMP = -1
35.000 110 C8NTINJE
36.000 XPR s X + DXPR
-------
37.000 120 C8NTIMUF
38t000 CALLN9RDX*DXMAX*jUMP,KS*KC/l.E-6(JlMP)l30*140.150
40-000 130 WRlTE<19.131) X
41.000 131 F9RMAT(//t X «iE14.5i iNTEGRAT r8NI FAjLURpi)
42.000 CALL EXIT
43.000 140 C9NTINUF
44.000 CALL DIFFQ
45.000 G9 T9 1?0
46.000 150 CALL 8UPT
47.000. IF(X - XFND) 110*300.300
43.000 300 CALL EXIT
49-000 END
50.000 SUBR8JTINE iNJoUT
51,000 caMMe^ obij OT. XPR*XENOJDXPR.X,DX>INT*INTC*
55.000 1 IN, I9,tl.*ARFA*LJjERR9RjDXMAXjTEMP.HFGTB(10).C8NSl
53.000 CSMMeMRHH^WMnjHDjTAIR^CLD^RH/A
54.000 C8MM9N HSR/h99jFBR^EVAP.HEjHCjHLYMN,PTBL(10)iTTBL(10)jWMS*CONST
55.000 C8MM8N HFGjriRCiCLD1jCLD?>CLD3/DALP.DALPR,DCLD>DRHiDTAIR*
56.000 lDTA^DW.nwMS.nirJMD/DEA.DEW*DLYMNJ
57.000 10 F9RMATC6F10.0)
58.000 20 F3Rv|AT(6TlO)
59-000 RATI8 » 3.14159/180.
60-000 C CHOICE 8F INTEGRATI9NI SUBR9UTINF
61.000 READ(IN.PO) IMTC
62.000 IFdNlTC - 3) 30.40'SD
63-. 000 30 IsjT « INTC
64.000 Q8 T8 60
-------
65.000 40
66.000
67.000 50
AS. 000 60
.69.000
73.300 110
71.000 115
72-300
73.000 120
74.000
75.300 125
76,300
77.300 130
73.300 135
79.000
80.000 140
81.000 If 5
82.000 I5o
83.300 C
84.000 C
85.000
86.000
87.000 160
8S.OOO
89*000
93.000
91.000 180
92.000
93.000
INT a 4
G8 T8 60
C9NTINUF
C9NTINUE
G9 T8 (110, IPO/130,
WRlTE( la, 115)
F9R.MAT(!1 *»»»
G3 T6 150
C9NTINUF
WRlTE(IS,125)
F9RMAT( I 1 *»*##
G8 T9 IRQ
WRlTEH^lSB)
F9RMAT(M *»**#
GB T3 150
WRlTE(IS,145>
FSRMAT(M *##*#
C9NTINUE
INTPQRATISN CQNTR8L
REAr5(IN,lO) XjDX,DX
UO), INTC
JTULFR INTEfiRAT18N *»»**i//)
M8D. EULER INTEGRATI8N »*#**
r//)
4 TH 8RDER RUNGE-KUTTA **##**»//)
ADAMS M8ULT8N INTEQ. #****#*
PARAMETERS'
PR/ XEND
'//)
WRlTFt IS,160)X/TX«DXPRjXEND
F9RMAT1 i X =(Ff .?i
1 ' XENiD ="E10.3,
READ(IN,1Q) FRRf?R,D
WRlTE(I8.180> ERRSR
FBRflAT( ' ERR89 B»
READ(IN,10) DT,U,A
DX ='E10.3i DXPR ='E10.
/)
XMAX
,DXMAX
E10.3I DXMAX ««E10.3>/)
R!TA,EL
3
READ( IN, 10) RH8,WMPH.TAIR/CLD,RH, ALBAR
-------
94.000 D9 185 1 = 1*10
95.000 185 READ(IN»10) PTBUlJj TTBL(l)j HFGTB(I)
96.000 TA = (TATR • 32O»5./9.
97.000 W * W*1PH*22./15.
98.000 WHS a W * .3048
99.000 WMD 6 WMPH * ?4.
100.000 C0NST o Fl_/(RH9*U*AR-A)
101.000 C9NS1 » {RHe*0.r>03PS)/C?4.*3600.»0.06t4)
102.000 REAO(lNilO) DALP*DCLD^DRHjDTAIR,DWMPH
103.000 DTA a DTAlR*B«/9.
104.000 H3S = lt9*SlN(ALBAR*RATI-8)
105.000 H3C 9 1.9*C6S(ALaAR*RATI8)
106.000 CLDl B i. - ,0765*CLD
107.000 OLD? * -.OOIR*CLD«*?
108.000 CL.D3 » 1. - iOOr)6*CLD**3
109»000 DAlPR =. HALP * RATI9
110.000 D^ a DWMPH*p?./i5.
111.000 D-KMs s DW- * .30^8
112.000 D/JMD = DWMPH#?4.
113.000 C IMClOENT SSLAR 9ADIATI8N
114.000 HS = H8S * Cl D3
115.000 C REFLECTFD S0I AR RADIATION
116^000 HSR a HS » 3./ALBAR
117.000 FTA = SI{JTBl jPTBL^TAlR^lQ)
118.000 EA = RH*(101:WU70. )*FTA
-119.000 TAlRP « TAIR+DTAIR
120.000 F-TAP « SI (TTRL*PT3L*.TAIRPjlO)
121.000 DEA «..(1013./1470. )*(DRH»FTA + RH#
-------
123.000 200 F8RMATM INITIAL DT »'F.12.4 ' OEQ F1/)
124.000 WRlTE(I8j210) U.AREA,EL
1P5.000 210 F8RMAT(i STREAM VFL8CITY ,'F6.3t FT/SEC CR. SEC. AREA «'
126*000 1F10.2' .SO. FT. SURFACE WIDTH »»F6.i' FT'/)
197.000 WRlTE(I8,220) RH8,CLD,RHjALBAR
138.000220 F8RMATM RH8«'F5.2l LB/cU.FT. CLD-'F4.1' TENTHS'4
1P9.000 1» RH««F5.1' PCTi/' ALBAR =»F4.1' OEGRKES'/)
130.000 WRlTE( 19.230) TA I R, TA^ C3NST> C0N551
Igl.OOO 230 F8RMAT(i AIR TFMP. s'FR.l' OFQ FiFS'l' DEG C1/
132.000 1» CSiMRT slElO.31 C8NS1 «iF10.3j/)
133.000 WRlTE(I8.240!l W, WMPH. WMS> WMO
131.000 2^fO F9RMAT(" WIND VELOCITY «'F6.2» FT/SEC'F8.2iMPHIF8.2' METERS'*
l35'300 l'/SEC'F8.2l MlLES/DAYl/)
136.000 W3ITET< 18,260)
137.000 260 F3RMAT(/,T20iTTRLtT40'PTBL'T60«HFf3TBi/)
133.000 D8 270 I -1*10
139.090 270 WRlTE(I8,280) TTBLdli PTBLd), HFGTB(I')
1*0.000 28Q F9RMAT(tnXj3F30.5)
141.000 WRlTEtI9,300)DCLDjDRHjDTAIR
142.000 300 FaRMATf/i D.CLD ="F6.3i. DRM »iF5.3' DTAIR .'F6.2)
1*3.000 WRlTEtIB,310) DALP/OWMPH
H^.OOO 310 FaRMATt/l DALP s'F6.2i DW^IPH ni-F6.2)
145.000 WRlTEt 18*320) Hf}S> HBC* HS, HSR
146.000320 F3RMAT(/i HfiS=(E12.4l H8C*'l E1 ?. 41 HSa'El?.4' HSR»'E12.4l LY/MIN')
147.000" IN')
148.000 WRlTE(18,330) EA,DEA
149.000 330 F8RMAT(/l EA »'El2.4" DEA BiF!1?.4)
150*000 WRlTE(I9/34o>
-------
o
°
151.
152.
153.
154.
155.
156.
157.
153.
159.
160«
161.
162.
163.
164»
165.
166.
167.
168.
U9.
170.
171.
172.
173.
174,
175.
176.
177.,
178.
179.
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
ooo
000
000
000
000
000
340
350
360
10
20
30
50
60
F9RMAT(/,T20iSTTBL'T40iXTBL'/>
READ(IN,?0) NTEMP
D3 350 I =1>NTEMP
REAO(INMO) STTBL ( I ) * XT8L( I)
WRITE( 18.280) STTBL ( I > , XTBl ( 1)
C9NTINUF
WRlTEt 18,360)
F9RMAT( M ' )
RETURN
C9MM8N
NJE 6UPT
DDT..
XPR, XEND. DXPR* X^ Dx* INT>
C8MN)SM HfiR>
TW3/ TA* EW> EA/ H3S* HS
FBR^EVAP^HE/ HC* HI. YMN, PTBL ( 10 ) t TTBL { 10 ) « WMS/CgNST
C9MMSN HFG/HBCjCLDli f.LDP> CLD3J
DCLD*DRH> DTAlRj
iDTA.DN/DWMSjD^MOjDEAf'DEWjDLYMN.DBTUS^NTEMP* STTBl ( 10 )t XTBL (10)
WRlTE(I8jlO> X^ OX
F8RMATH X ='F7»1» FT DX s'Ffc.i */)
WRlTE(i8^20) TEMP
F8RMAT(» STREAM TFMp
WRlTni8,70) DT.DDT
IM'RITE(IB.30) EW, DEWj
F9RMAT(i EW »(fl?.5i
1E12.51 fY/MTN HFG
=iE12«4' DEc5 F'/)
F9RMAT(i HBR ?»E1P.R'
WRITE(I8*60) HLYMM/HO
F8RMAT(i T8TAL HEAT TRANSFER
HFt5
'DEW siF12.5t
»»E12»5j/)
C
EBR='F1?.5'
EvAP aiE12.5i
HE
»IE12.5'
-IE12.5' LY/MIN »
-------
183.000
1«1.
182.
133.
184.
135.
186«
187.
183.
189.
190.
191.
19?.
193.
194.
195.
196.
197.
198.
199.
200.
201.
.202.
203.
204.
205.
206.
207.
000
000
000
000
000
000
000
OQO
000
000
000
000
000
000
000
000
ooo
000
000
000
000
000
000
000
000
000'
000
70
80
90
C
C
C
' BTU/SEC-FT2t/j
F9RMAT(i DT .«iFl?.5i DDT »iFl
W3lTE(I9,80) DLYMN,DBTUS
F8RMATM DLYMN «»£!?. 5» DBTIJS «»E12,5*/»
WRlTE(19.90>
XPR. XFND* DXPRj X, DX,
RETURN
END
SUBR8JTINE DIFEO
C3MMBN DDTjDT^
C9MMBM
THERMAL F.XCHANGF WITH ENV IR9-NMFNT .
TEMP * ST»5./9.
n DT*5./9.
SI(TTBL»PTBL*TFMPjio)
TFMP + DT .
SI (TTBl jPTBL^TTWjlO)
(101.3. /14.7)#FTA
(inl3./14.7)*(FTB - FTA)
EFFCCTIVF BACK RADIATI9N,
H8B= (14.38-.09*TWS-.046*RH)/6q.7?
EBR » H8R#CLD1
EVAPSRATIQN HEAT TRANSFER.
FTA
TTW
FTB
EW
-------
20S.OOO
209.000
210«000
211.000
212.000
213.000
21 t » 000
215*000
216.000
217.000
218-000
219.000
220.000
2P1.000
222.000
2?3.000
224.000
2?5«OoO
226.000
2?7.000
2>a»ooo
229.000
230.000
231.000
232.000
233.000
234.000
235.000
EVAP a .35* (EW-EA)*(1. + «009R* WMD )
HFG > SKTTBl ..HFGTB/TEMPjlO)
HE a EVAP*HFfi*C^NSl
C CQNVECTjftN HFAT TRAMgFER
HC » 39.*(.2ft + .077*WMS)*(TWS - TA J/H40*
C T9TAL HFAT TRANSFER TS WATER* I.Y/MIM
HLYMN B HS • (E^R + HSR + HC + HE >
C TSTAL HFAT TRANSFER* BTU/SEC-FT?
HD » HLYMM * «0f>i4
Fl « CLO?*DCl D*H8S
F2 a CLO^*H3r»DALPR
F3 a .0765*Dr.LD»H8R
F4 » -CLnl#(-.09*DT'.'JS • .046*DRH>/69.72
F5 = "(F1+F2i*3./AL3AR
F6 = HS*3«#DALP/ALPAR*#P
F7 a ••( .35#HF3/tf400. )*( (!• + . 0098*WMD ) # (DFW - DEA ) +
1 .0098*DwMD*(EW - EA 1 )
FS a • { .19 ./I 4^0. ) *( ( .26 -f i077*WMS ) * (DTwS - DTA) +
1 .077*DWMS*(TWS -TAJ)
DLYMN > Fl + F2 + F3 + F4 + >5 + F6- + F? + F8
DBTUS = DLYMN».0614
DDT « CBNST*DBTUS
RETURN
END
CCCCC
ccccc
CCCCC
CCCCC
-------
236.000
237.000
238.000
239.000
240.000
241.000
242.000
243.000
244.000
245.000
246.000
247.000
243.000
249.000
253.000
251.000
252.000
253.000
254.000
P55.000
256
257
258
259
260
261
262
263
264
*
t
.
•
.
.
•
•
•
000
000
000
000
000
000
000
ooo
000
FJNCTI8N .SKXTBLjYTBLjXjN)
C LINEAR INTERP8LATI8N 8R EXTRAPOLATION 6p SINGLE VARIABLE FljNCTI8N1
C XTBL « INDEPFNDFNT VARIABLE TABLE
C YTBL « DEPENDENT VARIABLE TABLF
C IND « INDICAT.QR 8F EXTRAPSLATIBN
C 8*No EXTRAP8I ATT8N, 1=L6WER EXTRAP8LATI8N* ?.4PPER E73RAP8LATI8N
DIMEN518N XTBL(40.)*YTBL<40)
C CHECK T8 SEE IF EXTRAP8LATI8N !S NEEDED.
IFtX-XTBl (1 ) ) 1?0*130*150
120 IND » 1
.130 II . 2
G8 T6 254
150 IF(XT3L(N)-X) 160*180*210
160 'IND ' 2
180 II « N
G9 T8 ?54
C FIND X IN TABLE. S IN TABLE
?10 DO ?20 IKs2*N
II = IK -
IF(XTBL( TKJ-X) 920*254*354
220 C9NT1NUC
254 XI
X2
Yl
Y2
SI
XT3I
XTSI
YTBI
YTBL
Yl-H
(
(
(
(
I
1
I
I
Y2
I-
I)
I-
I)
1)
1)
-Y1)*(X-X1
)/rx2-xi>
RETURN
END
CCCCC
-------
265.000 CCCCC
266.000 C EULER AND M8D1FTEO EULER
267.000 CCCCC
26S-000 CCCCC
269.000 CCCCC
273.000 SUBRBUTINE EULER ( YP> YJ DT
271.000 DIMFN5I3N YP ( 20 ) , Y( 20 ) >
272.000 Gg T0(10j?0)jJ
273.'000 10 C^NTlNUe
27*«000 D9 100 I=1*NF
275.000 SY( T)= Y( I J
276.000 SYP£I )= YP( I )
277.000 Y(I)= Y( T )+DT*YP( I )
278.000 100 C3NTIMUE
279.000 T=T+DT
230.000 RETURN!
281-000 20 C9NT1MUF
285.000 D9 ?00 Isl^NF
283.000 Y(I)= SY( I )+(YP( I )+SYP(I
28^.000 POO C9NTINUF.
2S5.000 RETURN!
286.000 ENID
287.000 CCCCC
288.000 CCCCC
2^9.000 CCCCC
290-000 C F8URTM 8RDER RUMGE-KUTTA
291.000 CCCCC
292.000 CCCCC
293.000 CCCCC
INTEGRATTftN
,NEj J>T)
SY(20),SYP(?!0)
) )*OT/?.
INTEGRATT8N
-------
294.000 SUBR8UTINE RK4(YPjV.DT*NE>JiT)
295.000 DlMCNSIflN YP(5)iY<5).AK(5*4)jSY(5>
296'OQO . G9 TB(10j20*30'*0)*J
297.000 10 CgNTiMUC
298.000 09 100 I»1/NET
299.000 SY( I ) B Y(I)
303.000 A<(!,!> = DT»YP(I)
301-000 Y(I> = Yd) +AK(I*l->*»5-
302.000 100 C9NTINJUE
303.000 ST = T
301.000 T = T + DT*.R
305.000 RETURN
306-000 20 C9NTIMUE
307.000 D3 POO TaliNF
308-000 AK(1*2) » DT#YP(1)
309.000 Y(I) i SY(I) * AK t DT*YP{I)
315.000 Y(I) « SY (1) •»• AK1I.3)
316.000 300 C9NTIMUE
317.000 T * ST + DT
318-000 RETURN
319.000 40 C3NTINUE
3PO.OOO D8 400 I i IjNE
351.000 AK(I^) * DT #YP(I)
-------
3P2
3?3
3?4
3?5
326
327
3^3
3?9
330
331
312
313
314
315
336
337
3.13
3.19
340
341
342
343
344
345
'346
347
348
349
350
.000
.000
.000
.000
.000
'•000
.000
.000
.000
.000
.000
.000
.000
.000
• coo
.000
.000
• 000
.000
.000
• 000
• 000
.000
.000
.000
.000
• 000
.000
• 000
400
ccccc
ccccc
ccccc
-c
ccccc
ccccc
ccccc
991
c
993
998
c
999
992
901
C
1
Y(I)sSY(T) + (AKlT*l)+AKUj4)+?t*(AKU*2)4'AK(T*3)))/6.«
CONTINUE
RETURN
END
ADAMS-M9ULTSN INTEGRATI8N
£UBR9UTINEN8RD(C-,TjTLlMjY,E3R9R,NF,H*HMAX* JUMP* KSTP* KCSN* CLlF* 18)
DIMEN5I8N STARY (5 ) • Y ( 5 ) ,SY (5 ) , SAVEY ( 5 ) * F ( 5 ) ,FP ( 5 ) /DELTA (5 ) t DALTA (5
1 ) j A < 5 ) * 3 < 5 ) , r ( 5 5 ' D'( 5 > ' AA ( 5 ) * B3 t R > j CC ( 5 > *- DD ( 5 ) * SF ( 5 )
IF(KsTP-32767)993j991*991
KSTP=28
TEST F9R TYPF BF ENTRY
IF (JIMP ) 1 *99R*999
G8 T8 (1000*1 1*?1*80?*803)/IA
JUMP P8s. RE
-------
351.000
352.000
353.000
354.000 5
355.000
356.000
357.000
358.000
359.000
360.000
361.000
362.000
363.000
364.000
365.000
366.000
367.000
368.000 C
363.000 1000
370.000
371.000 1111
372.000 C
.373.000 600
374..000 601
375.000
376.000 605
377.000
378.000
A( I )»0.0nl
B( I ) sQ.noi
C( I )*o.noi
D( I i «o«oni
KSTP=0
KOELY*O
KCBN=0
XT=95./(?88.»64. )
Ue863«/(12.*R040. )
V«95.0/?R8.0
P"2s.0/?4.0
Q=35.Q/7?.0
R«5. Q/48.0
S»l .0/120.0
IA«l
JUMPED
G9 T9 1101
BEGIN INTEGRATION STFP
09 1111 T«ljNE
SF( T )«F( T )
SAVEYd JeYdl
H TBS 'SMALL RETURN WITH JUMP NPG.
IF(ABS(T4-H)-ABS(T) >6o5j 60 1*605
JjMps-1
G9 T6 1101
T?T+H
09 10 I»1jNE
Y( I )»Y( I1+H*+B(I)+C(T)+D
-------
10 FP( M*F< T >+2.o*A( n+3.o*8(i
00
380
3S1
382
333
334
335
336
387
388
339
393
391
393
393
394
395
396
397
393
399
400
401
402
403
404
405
406
407
.000
.000
.000
.000
.000
.000
.000
.000
.000
• 000
• 000
oOOO
• coo
.000
.000
.000 c
• 000
.000 c
.000
.000 C
.000
.000
.000
.000
• 000
.000 C
.000
.000
IAS?
G3 T8 Unl
11 D9 12 I»1*NE
12 SY( I )=Y( M
03 ?0 I»1*NE
DELTA ( T )«F(I )-FP( I )
20 Y{ I )sY< I )+V*DElTA (I ) »H
IA*T
KC8N=1
G9 T9 linl
21 KCBN.O
D9 30 U1/NE
DALTA (T)sFm-FPm
29 Y( I 5=3Y( I)+V#OALTA (I)*H
30 C9NTINUF!
TEST F8R STARTIMG SEQUENCE
31 IF(KSTP-?8)3Rj40>40
APPLY TfST 2 9N ZER9TH STEP
35 IFUsTP)50/5r>j60
HALviNs TESTS
40 D9 45 1=1 >NE
IF (ABS (DALTA ( T ) ) -ERRSR/ABS (M ) >45* 45/55
45 C8NTIMUF
50 IF(V*H*CLlF-'n.l?5)60. 60*5$
55 TsT-H
FAIL fESTSj HALVE H
?23 H=?H/2.0
KD£LY«O
-------
408.000
409.000
410.000
411.000
412.000
413.000
41 4.000
415.000
416.000 C
417-000
41 8.000
419.000
423.000
431.000
422.000
423.000
424.000 C
4?5.000
436«000
427.000
42S.OOO C
429.000
410.000
431.000
432.000
433.000
434.000 C
435*000
56
60
62
64
67
65
70
74
75
78
09 56 I«1*NE
A( )»Am/a«n
B( )"B(M/4.0
C( >»cm/8.n
F( )=SF(T)
Y( laSAVFYU)
D.( 1=3(11/16.0
G9 T9 1000
PASS TESTS* T.9RRECT A*B*C*D
K3TP =
C( I )aC( T )+5.n*D(I 5+R*DALTA(I )
D( I 1»D( I H.S#nALTA(I i
C9NTINUF
IF IN STARTING SEQUENCE* BRANCH
IFUSTP- 24)70*30*100
G9 T9 (1 000* 1 000* 1000* 7^* 1000* 1 000* 1 000*78* 1 000* 1000* 1000*74* 10CO/
1 1 000* 1000/86* 1000*1000*'! 000* 74* 1000*1000*1 000 )*KSTP
4TH, 12TH* 20TH STEP* G9 BACK.
Ha-H
09 75 I»1*NE
A( I )*-A(I)
C(I )»-C( t )
G3 TB 1000
8TH STEP G8 F9WARD
H^-H
-------
436.000 D9 79 I«1JNE
437.000 Y(I)oSTARYU)
438*000 A(I)S-A(T)
439.000 79 C(I1«-C(T)
4^0.000 G9 T8 1000
441.000 c I&TH STEP^ HALVP- H> APPLY TEST 1
44?.000 86 HsH/p.Q
443.000 03 '87 1 = 1 >NE
444.000 A(I)iA(n/2.0
445.000 B( I >«3( D/4.0
446.000 C( I )»C( M/8.0
447.000 87 D( I J*D( D/16.0
448.000 D1? 88 I»t*NE
449-000 IF(ABS(DALTA ( T ) )-ERR8R/ABS(HnR«J ,88>89
450.000 88 C9NTINUE
4"51iOOp C PASS TEST G6 F8WARD WITH HALVFD H
452.000 G6 T6 78
453.000 C FAIL TEST BEGIN AGAIN WITH HALVFD H
454.000 89 H="H
455.000 D9 92 I=UNE
456.000 92 Y( I )=STARY-( I )
457.000 G8 TB 1
453.000 C 24TH STEP/ DfiUBLE H, STARTING SEQUENCE ENDS
455.000 90 H=H»2,Q
460.000 D3 91 I=1*NE
461.000 A< H*A( I )*2«n
462.000 B(I)»B(t1*4.0
463.000 C(I)sCm*8.0
464.000 91 0(I)>0(T)*16.0
-------
465.000 GS T8 78
466.000 100 KDELY»KDFLY+1
467,000 C WILL NEXT STFP *IQVF PAST TLIM
468.000 102 IF(ABS(TIIM-T)-ABS(H))103/103*110
469.000 C YES...,,., t.SAVE T AND YJ INTEGRATE T8 TLJMjRETURN*
470.000 103 ENDH'*TLIM-T
471.000 D3 105 I=1*NF
472.000 AA( I )=ENDH*A(1)/H
473.000 B8( I )*ENinH»*?*8(I)/H#«2
474.000 CC( I )=ENnH*#3*CU >/H«*3
475.000 105 D0( I )-ENJDH##4*D(l )/H*»4
476.000 SAVET=T
477.000 D3 800 T»1*NF
478.000 SF(I)=F(T>
479.000 800 SAVFY(I)SY(I)
480.000 806 TsTun
481.000 03 106 t«l*NF
482.000 Y(D»Y(i)+ENOH*(F(I)+AA(I>+BB(T1+CC(I)*DD(p)
483.'000 106 FP(I)=F(t)+2.0»AA(I)+3.0*BB(I)+4.0*CC(IJ+5.0»DD{I>
4S4.000 IA«4
485.000 G3 TB 1101
436,300 802 D9 805 I«ljNF
487.000 805 SY(I)»Y(T)
488.000 D8 107 ,I,ljNF
489.000 DELTA (T ) =F(I)-FP(II
490.000 107 Y(I )»Y( I )+V*RELTA (I-)*ENDH
49i.OOO IA«B
492.000 GQ T8 1101
-------
1.000 CCCCC C( 1000)*rLBUr> C
2.000 CCCCC TA(1000'>=AIR TEMP.
3.000 C PHI(10001= RFL MUMIOITY
4.0CO C MlOCO'l* WIND S°EF.D
5«OoO C TW(10001= 'WATER TFMP
6..000 C NCAS*'N9. 8F C.ASES
7'000 C N3A= MS. .SF D'AY1? TB BE TRIES
S-OCO C- DELjlSOlr E3R9R CRlTt^I?R T^ 3F SATISFIED
9*000 C IOAS(.50)= N9. 3F DAYS IN TRIAL
ib.ooo c NLN= Me. SF LI NFS
11.000 C OT= FRW9R CRITE^I&R F9R THE S=FCIFTC CASE
12OOO C N'TAa NI3. Qf TI'MF AVERAGED DATA PBt.MTS
13.000 C UA^EL/CC. ... ..*'Yl (S)-*XPR1 jXE JDl/DXPR1 / XI j DX1 j NE1 / INTlj INTCl/INl* 181
17.000 l*ELijARFAl>U1
15.000 CaM-iS'j' FRR9iRliOVMAyiiTE^Pl*HFGT^l (lO)^CBNSll
19.000 CSMvisM RMeijWlf WMDl>HDl,TAI3ljrL01 jRHl/ AL3AR1, T^Sl j TA1> TWSA1, EW1>
PO.OOO 1EAUH3S1.HS1
31.000 C.JMMSN HSftljHQBl jFBRUEVAPljHEl . Hri^ HL YMN1/ PTBL1 (1 0 ) / TTBL 1 ( 10 ) t
=2.000 IwMSljCSMsTl
53.000 C3MM5N Cl IFl,HFTl,M3CljCLDlljCl D?1,CL03lfDALP1jOALPR1*DCLD1jDRH1>
•34.000 IDTAlRlOTA'lyD'/Jl.DWMSl/DUIMDlOEAl ji3t^l>-DLYMNljD3TUSl/MTEMP.l*
P5.-OCO PSTTiLldnJ/XT^LKlO)
?6«000 C3MM8N C ( 1COO 1 > TA ( 1 000 } t PHH lOnn 1 j *i (1000 )> TW ( 1000 )
?7.0CO C3NM6N Nf.AS/ NDA> DELT(BO)/ IDAStSC)
P5.000 C9M.MBM MI-N>INjI«^U>OT,.NTA* IDA
?9-.000 C3MMSN CTA(50) jTATA ( 50 1 / PHITA ( BO 1 j I«TA (5o)/TWTA (50)
-------
30.
31.
32.
33.
34,
•35 •
36.
37.
355-
33.
40-
41.
45.
43 .
44,
45.
45.
47.
4S .
43.
50.
51.
52,
53.
54.'
55 «
56.
000
000
000
000
000
000
ooo
ooo
ooo
000
ooo
^ ^ o
«J ^ *J
000
030
000
000
000
000
000
000
ooo
000
•*N —, /">
JUvJ
000
000
000
OO'O
ccccc
ccccc
ccccc
ccccc
20
c
ccccc
ccccc
ccccc
ccccc
ccccc
C9M.MPM
Cf5hMBM
COMMON
CdMMBM
C9MM6^
CALL ^F
DT>1 .
Dfl ?0 I
CALL PR
C9NTIMU
CALL PR
CAUL VE
CALL EX
END
SUBRBJT
SJBRBJT
.'C9MMBN
UAiEL,CC.TAlR,TWAjRHjWSp
T"JT2^ TNT3/DC/DTA,DPHI^OW.DTWji INVS/ IFl
DM21,BETA
LRGl.iNDAq
ir.ASiP^PfSO* 10.)
FAD
DA = 1/NOA«!
3R
(T
3D
RN!9M
IT
TMi.FflR READING IN DATA
INE RFEAO
YP1 (5)»Y1 (S)*.XPRl«XENDljnXPRl*XljDXl
liELl.jARE'Al>Ul
NE1> INTli INTCIMNI^ 181
-------
=57.000 .C3MM9N 'F.RRBR1 ', DVMAX1, TEMPI, HFGTql M 0 )> CONS11
53.000 C3M-M6N RH31,l
59OOO 1EA1,H9S1,HS1
60.000
61-000
62,000 C^MMSM Cl IFl,HFGl,HdCl,CLDl.l,CI D2'l , CLDSl^DALPl/DALPRl^CLDlj
63.000 lPTAlRl,DTAl,DWl,DWMSl,D^M0.1,DEAt,DFl'o)
67.ooo C5K^SN NI N,IN,I^U/DT,NTA.J IDA
68-000 C3M:M9M CTA ( 50 ) , TATA ( 50 ). PHI TA ( Rn >, W.TA ( 50) t TWTA ( 50)
69OOO C3MM8N UA, EL, CC/.TA I R, TWA, RH, v*ISP
70.000 C3MMf3M I MT?, T NTT, DC, DTA, DPHI , DW, DTW, IN.VS* I FLAG
71.000 C'JMMBN DM21,RETA
72.000 C3MM6N LRG1.
73.000 C3MM8M
7(,.000 IM*101
75.000 lau^io;
.76.000 1000 F9RMATi
77.000 1001 F3RMAT(6T1'0)
73.000 READ (INMOOn MLN,L93l
79.000 iN^lTEf IBlJ,2000)NLNjL9Gl
30.'000 2000 F3RM.AT(iwo,2x, INUMRER OF DATA I I NFS= I / 15, I TIME AV. LSQIC='M5)
31.000 WRITE!I9U,POOD
82.000 2001 FORMAT (1 HO, 2X, i.CLD CSVER AIRTFMP =?EL HUM. WIND SPD WATER TEMP')
33..000 D3 10 I« 1,NLN
H^.OOO REAQ(IN,1000) C(I),TA(I V,PHI(I>>W(I)/TW(I )
85,000 ^ITECCi),TAi
-------
CTl
36,000
87.0CO
SB.000
39.330
90.000
91.000
92.330
93.000
3
95.
96.
97.
9s.
99.
100.
101.
102.
103-
•000
'000
• 000
.000
.000
.'000
.000
.000
. 000
•000
10^.300
105-000
136.060
13/.330
108.000
109,000
110.000
111.000
112,030
113tOOO
2002 F9RMATUHQ;2X,5(F10.3* IX.) )
10 CONTINUE
c PLANT DATA
c UA»vftL* FL=RTVER ^IOTH, cL=CL9uo CBVER/ TAIR
C" T'JA = wATER TEMP, RH*REL HUMIDITY, WSP^lND SPEED ('KM8T3)
REAOt IN. 1 003)iJA»'EL»CC/TATR
MR
|R WIDTHei^ix/FlO.S,»CLD C9VER=
2003 FORMAT(
11X/F13.3.'TEMP AIR=';lXjF10.3)
READ( I.M, 1 000)TWA,PH/wSP
HUM*' /.1X*F10»3* 'WIND
15
)NT4
2005 FORMAT(lH0^2Xj'NUMBER 9F TIME AV. DATA P8INTS='>IX*15)
WR'ITE( I9U.2006)
2006 F3RMAT('n',2X, 'CLD C3VFR TA AIR TEMP TA REL HUM TA WlNiD TA
1 TEMP dATER TA'i )
0 '3 ? 0 I = 1 i N T A
READ( IN, 1000) CTA(I ), TATA ( I ) , PH T T A ( I ) / WTA (I ) , TiA/TA ( I )
WRlTEf I9U,20n7)rT'A( I )^TATA(J ),PHITA(I )
2007 F^RMATC tMC>2x*S(Fio.3^ ixn
20 CONTINUE
16 C3NTIMUE
READ(IM,1001)NCAS
-------
114.000 WRITET
11-5 • POO 2008 F9RMAT{lwOf2x» 'MUMBER 9F CASES.* 11 1 X* I 4 )
116.000 READfJN1300C)(DFLT(J>i
117,000 3000 F3R"!AT(6F10.3>
1.18.000 WRlTF(IBiJj3010)
119.000 3010 FORMAT(IHO/2X*'ALLP^ED DTS')
•120.030 '.V'RITF( 1911*2009) (Df=
121,000 2009 F9RMAT(1HO/2V,EH, . .
1?2.000 READMN.1001 l.MDAS
123.300 WRlTE'(I9il,2010>MDAS
1'4.000 2010 F3R^IAT( »fi'j2Xj'DUMBER 8F .DAYS AVERAQEDs i / 2Xj 14 )
1?5.000 READ(IM.100l)(nAS(i)j I«1*NDAS)
126.330 W3lTE< I9IJ/301.1)
127.000 3011 F1RMAT(lwO/2X*'DAYS AVERAGEOi)
123.000 W=?ITE( IS.ll/2050) MDA3(I )*I«1>NDAS)
129.030 2050 F9RMAT(iwO^2X*15)
13J.OOO WRlTF.(lSlJj201l)
1-31.000 201.1 F9RMAT(1HO>2X^'PTBL1 TTBLl HFQT.Bl i > //, 2X/ 60< i* I ) )
132.000 D=) 185 lal'/ln
133.000 READ(IMM002) PTBLl ' I > ' TTBLl (I ), HFG'TBl ( 1 )
134.000 WRlTE FlO. 3/ I BETA= 11 2X/ FlO.3 )
1.42.000 09 30•••" •••-•-
-------
143.000 D<5 40
144.000 P3P( IDA.. TCASlaO,
1'jo.COu 40 Cf^Tr>lUE
!<+&*000 30 CcNTHUF
147.000 RETURN
143.OuO END
1.49*000 CCCCC
150-000 CCCCC
151.000 CCCCC
152.000 CCCCC
133.00'Q CCCCC
154.000 SUBROUTINE PR9B
155.000 ;C3MM8N YP'l (5)/Yl ( 5 ) / XPR1 * XEND1. DXP91/ Xl/ DX1, NE11 INT1/JNTC1MN1/I81
1^6.000 1/EL1/A3FA1/U1
->. 157. OuO C.^MIBV ERP0K1 j DXMAX1/TEI1P1/HFGTR1
OT 1=53.000 -C3MM8M RHOl/Wl*iA)MDl/HDl,TAIRljrLD
159.000 lEAl/H^Sl'/HSl
160*000 C9MMRN HSR1>H93t/EP^1/EVAP1>HE1.HC1,HLYMN1/PTEL1(10)/TTBL1(10)>
161 .000 IW'^51 /C9NST1
162.000 CfjMMRM Cl IF 1, HFT1, HdCl / CLDl 1 / Cl 021 * CLD31/ DALP1/ DALPR1» DCLD1/-DRH1/
163.000 IDTAlRl/DTAl/OWlf D/JM31/D'^MD1/DEA1 , DE!/J1/ DtYMNl/ DBTUS1/NTEMP1/
164rOoO 2STT-BL1 (ln)jXT-3L1 (10)
165 «000 CeM^lSM C( 1 000 ) / TA ( 1 000 ) . PHI (1000) , M 1000 )/'TW ( 1000)
166.000 C.3MfiN NfAS^ NDA/ DELT'(RO)/ pASC^O)'
167.000 C^h^BN Nl N, IN/ IRU/DT» NTA/'lDA
16S«000 C9MMSN. CTA(5-0)/TATA(50)jPHITA(sn)*WTA(5Q)/TWTA(50)
169-000 C3MM8N UA/EL.CC.TAIR,TWAj«H/WSP
170.00'0 C9MM8V INT2/ T NT^/ DC> OTA/ DPHI / DW. DTK/ JNVS/ IFLAG
-------
171.000 CdM^eVl OMJ31, RET A
173.000 Cftl-MSN LRGl/NlOAS
173-000 .Ca«:i6NI irAS>P3
17^.000 DIMENSION P3I10)
175.. 000 C NOA= 'MUMRER ftr DAYS jN THE CAgF
1.7= • 000 IDM3A
177.000 NDA=IDAS(ID)
178.000 -NClsNLN/R
173.. 000 F'>lDAa\IDA»3
1^1.000 iF(NDA-Nrl) 10*999/999
1B2.000 1
183.000
ooo DENP=O.
187.000 D'5 ?0
i3S,:co cs*o.
is9.ooo TAS=O.
1 9LOQO 1*3 = 0.
192. 000 T'/JSsOt
193.000 Da .^C. 1 = 1 /N'OA.
194 -.0.00 D9 to J=1 »3
195.000 IMT, = fi*( IPO+I-1 l-i-J-8
196.000 C3 = CS + r'( INT)
197.000 TAS = TAS 4. TA(INT)
198.000 PHIS=PHIR + PHI(INT)
-------
193.030 wS* gs + W( INT )
200-300 T*S = T-A'S + TW(INJT)
201.000 40 C3N-TIMUF
202.000 30
203.000 cs
SQt.O'OO TAS= TAS*FKDA
203*000 PHlS=DHIR*FNnA
307.0CO TA'S=
203.000 C lNT?s F3I LS^TNG DAy
503.000 HT?= I?n + NDA
210. OCO C1S='C.
211.000 TAlS=0.
212.000 P^I1S=2.
213,000 klS=D.
21'MOOO T'J13 = 0.
21 5.300 D9 '^0 1 = 1/8
216.000 C I\T.3= JHF ACTUAL PfiSlTIBN IN THR DAY
217.000 INT3=IMT?*8-R+I
218.000 CiSIClS+r< INT3)
219.00.0 TAlS = TAlR + TAUNT3)
2^0.000 PHllS=PHTlS+pHI ( INT3)
2?1.00C Wl.S = i'jlS + l*( INT3)
2^2-000 TWlSaTWlS+TW( INT3)
2P3.QOO SO C9NTINUF
2?4.0GO C1S3C1S».125
2^5.000 TA13'=TA1K*.1?5
PHI iS = PiHT lS*
WlSaWl'S*»125
-------
223. COO. T.nSsTWTfi*. l?5
2?9.JCO DC°C.1S-CS
230.000
'
2^3.000
23^.000
E;53.0SO STT-3Ll(?)=Tw1S
?'36rOoO XTBt.1 (1 )S0.
2S7.00.0 XTBL1 (?) =25000.
233-000
2*o«ooo CALL '
09 60 ICASsl*MCAS
IF(Art3(Y1 (1) )-DrLT(ICAS))
2*3.000 65 C9NTINJF
2^5.000 70
246.000 60
247.000 ?_0
2*3.000
2*9.0.00 D=» 75
251. coo 75 C^N
252.000 IF(L6Gl )?00^?01 .200
253.000 gOO C3NT1MUF.
2=5*. 000 ENUM = 0.
253-000 DENcO*
256.000 DF.NPsO.
-------
.257,000 C('l303)«rC
2=5S.OJO TA(1000)«TAIR
2=53.000 PHI (1000) s-RH
260.000 w(1000)»wSP
261.000 T'/l
262.000 Dd
264.000 ?05
2&5.000
266.000 DOCTA(I)-CC
267.000 DTA.TATAM J-TA1R
263.000 DPHl«P.HfTA( D-RM
263.0'jO •D«I = WTA( I ,.lvSP
270.0.00 DTW.T'x'T^n )-TWA.
271. OCO '•STT^LimsT1*'? 10DO)
272.000 STT8L1 (?)"!•/,• (1000)
273,000 XTBLl(l)=b.
274.000 XTBu(?)=25000.
275.000
276.000
277.000 CAUL C
27^.000 D3 HO ICAS=1
-------
to
LO
2S5-. 000
23S
237
238
283
290
231
292
293
29*
293
206
297
298
239
300
375
376
.377
378
37-9
330
331
332
3-53
384
3S5
336
337
•
•
•
•
•
t
*
*
*
t
•
*
*
*
*
•
•
f
•
•
*
•
*
*
t-
t
%
f
000
ooo
DOO.
000
OOP
000
000
ooo
000
oco
000
0-0 0
000
000
000
000
000
000
000
000
000
Ooo
ooo-
coo
000
000
000
000
90
?01.
999
4000
ccccc
ccccc
ccccc
ccccc
ccccc
2000
•recce
ccccc
ccccc
ccccc
J
D3 90 ICAS*1>^CAS
P3( tCAS) =PR( TCA.s)/FNTA
CALL 9aTTO6u*pR( ICASJ* IDAI
C3NTtNjr
C3NTIMUE
^tTuRM
C9NTIMUE
'^ITF.'J. I9lJj 4000V
F3RMAT{1H8/2X/-'T83 SMALLI)
CALL EXIT
EMD
SUBSBJTINE eiJTT(l3U*P*l J
W^lTEt I9iJj2000) IiP
FaR;-1AT(lM9i?X^ 'CASri, I^^PXj 'PRMARTLITY'*EU.7)
RETURN
END
SUBRRJTINiE C6MP(ENUM/DFN)-
C9M-1SM YP1(5),Y1 t =5 ) / XPRl , XENO-t , OXPfU, XI, DX1 , Nt \, INTl/INTCl* INI, I 91
L^ELljAREAl^Ul
CgMMeN ERR8R1*OXMAX1, TEMPI jHFQTSK 10) /CwNSll
-------
3SS.OGO
'3P.9.00Q 1EA1/H3S1.HS1
393OOO CStfMSM HSR1/H9B1 /£RRl/EVAPl/Ht1 *HC1 j HLYMN1 > PTEL3 (10 ) / TT8L1 (10 )*
391.000, 1WMS1,C3\IST1
392.030 C9MMSM Cl IFl,HFT1,H8C1*CLD1\,Cl 0?1.CLD31/DALP1*DALPRl,DCLD1/ORH1*
393.000 lDTAitRljDTAl/nWl.DV!MSl/DWMDl/DEA1 PHI (1000) . W (1,000 ), TW (1000)
396-000 C^M^tsN IMP AS/ MDA* DELTfFJO)/
397.000 C3MM9M Nl N/IN/I^U/DT.NTA»IDA
39S.OOO
399.000
40J.OOO C3MMSM I \'T2, TNT-?/ DC/ DTA/ DP.HI /DW. DTW/ INVS/ IFLAG
431 OOO C3MM6N DM21/RETA
402.000 C3MM6N .LBS1/NDAS
!^ '403-000 C9MMQSJ
4:')4iOJO RHBl=6?.4
405.000 XI=0.
406.000 Yl(l)«DTw
407.000 Xc.NOl=25nOO.
408.000 DXPRl=XFNfDl
403.300 DXlslOOO.
430.OuO N'Eilsl
411.000 INlalNl
412.OOP I31' = I?U
413.000 ELl-EL
414.000 AREA1=UA
.415.000 Ul«l.
-------
417.000 DXMAX1-2ROOO.
418.. 0.00
419.000
423.000
4?6.000
4?3«-000 TAIS1=TA(
CLDi=C(INJVSJ
.
4P3.000 TwSl«5'.*{TEi1Pl-32. 1/9.
4^9.000 TAl=5'*(TAIRl-33.
431.0.00 DAL3R1.0A.LP1/57.296
432-000 DCL01=OC
433.000 DRH1=2PH|
434.000 DTA1RUTDTA
43.6.000 DWMsi = D^l «.3048
437.00.0 D*IMD1 = D.«/1 *36'oO» *24.
43S.OQO CCCCC
.4^9-000 CCCCC
440.000 CCCCC
4
-------
445
446
'447
443
443
453
451
452
453
454
455
456
45 /
453
459
460
461
462
463
464
465
466
467
•468
469
470
471
472
• 000
• 000
.000
.030
.030
.030
• 300
« 0 00
• 300
.300
.000
.300
• 000
.000
.000
.000
.330
.030
.000
.000
•000
.000
.000
.000
.300
.000
.000
.000
ccccc
.10
20
ccccc
ccccc
ccccc
ccccc
ccccc
ccccc
IpUAGsQ
IF"( AB3 ( Y1 ( 1 ) ) »DT ) 10 J 10* ?0
CONTINUE
EMUMsENUM+l t
I?LAG»1
C3NTINJE
DENsQEiM + 1 •
RETURM'
END
FUKC.TISN ALNAPfTM^l/BETA)
S\1»SIN(RETA)
Trll= 6. ?R*Divi'?l/ ',36F«
DEL= A3I\i(slN( (?3. 45/57. ?96) )*RTNI(TH1 ) )
pHY = AC9S(TA,\i(DEL)^TAM(BETA) )
•JO=?4«*?HY/6.P8
TI =P4» -Tn
AV= (Tl-TO ) *STN (DEL) *SNl/34«
Av»Av-C3S'(DEl ) #C8S( 3ETA ) » f SI N( 6,2R*Tl/24« ) -SIN ( 6»28*TO/24 . ) 5/6.28
Al_NAP = ASTN( AV)
RETURN
ENID
-------
473.000
474.000
470.000
476,000
477.000
473.QOO
^79.000
430.000
4*51.000
432.000
4S3.000
1^.000
485.000
456.000
437.000
488.000
433.000
490.000
491. -000
^92.000
493,000
494.0-00
495.000
496.000
497.000
498.000
499.000
500.000
501.000
CCCCC
CCCCC
CCCCC
c
1
4
5
1.0
20
100
250
105
5JB39UTINE HuNOl
STREAM THERMAL M6DFL **** SENSITIVITY ANALYSIS **»«
C3MM8N YP(5)*Y( DXPR
CSNTI^'JF
D'3 100 JF* l.INT
CALL DIFFQ
G3 TP. (in*10*30)* IMTC
CALL EULFRf YP* Y»OX*^-:*.JE*X}
3g Te 100
CALL ^;<4 ( YP* Y'DX*NF* JE*X)
C3NTINUE
IF'(X • XPR+ DX/4.J 5*250*250
C3NTIMJ^
XPR = X.P5 + OXPR
IF-(X - XFND) 5*300*300
C9NTINUF
jJi^P = rl
* 4LBAR>TWS'TA«TWSA'E:w*EA'Hes>-HS
HLYMN*pTBL( 10)jTTBL( 10) iwMS/JC8.NST
rLD-?*DALP*DALPR*DCLD*DRH*DTAIR*
jDBTUS*N'TEMP*STT3L(10)*-XTBL(10)
-------
NJ
OO
502
5)3
50
515
516
517
518
519
5?0
521
522
523
5?*
525
526
5?7
528
529
,000
• 000
.000
•00.0
• 000
.030
.000
.Q'_)0
.000
• 000
.000
.000
.000
^ r- "~]
. WlJVJ
.000
.000
• 000
.000
.000
.000
.000
.000
.000
• 000
.000
.000
• 000
• 000
110
C9MINJE
XPR = X 4. DXP-3
lao
130
131
140
150
300
ccccc
ccccc
'•CCCCC
ccccc
C3NTINUF
CALLN3RO(YP*
IF( JU1PJ1 30*
W=?ITE( 1-3,131
F'3R^IAT(//'
RETURN
C3NTINJF
CALL 3IFVQ
Q3 T8' 1?6
C9NT1MUE
IF(X • XFND)
CONTINUE:
RETURN
END
SJBR8JTINE I
X*XPR/Y*£RReRjNE>DXjDxMAX*JUMP^KSTP*KC8N*CLIF*l8]
lfO.150
) X
X ='E14.5.i IsjTEGpATT8M FAILURE')
110*300*300
NPUT
DIMENSION PTRL(101*TTSLMO)
CSM^iBV YP'(5)
, DT* DUM(4)^XPR*XFMD*DXPR*X*DX*NE* INT* INTCj
1 JN*19*EI *ARFA*U*EPR5R*DXMAX,TFMP,HFGTB(1Q).C8NS1
C8f1M8MRHfi*W*
C3MM8N' HRR*H
CSh^SN CL If,
1DTA,D^*DWMS*
WMD,Hp*TAlR,CLD*RH,ALRAR*T^S*TA,TWSAjE^*EA*H8S*H:
8R'*FBR*EVAP,HEjHC*HLYMN/PTbL *TTBL /WMS*C8'NST
HFQ.H8C*CLDl.*CLD2*rLD3*'OALP,DALPR*DCLD/DRH*DTAlR
DWMD*DEA,DEW*DLYM.N,DBTU'S>NTEMP>STT3L(10)*XTBLC10
-------
NJ
IO
530.000 10
531.000 20
533.000
533.000 C
534 i 000
535.000
536.000
537.000 33
538-. 000
539.000 40
5*0.000
541.000 50
542.000 60
544 V 300
5i»3'000 65
.545.000
547.000 110
548. COO 115
550.000 120
551.000
552.000 125
5n3.000
5'StiOOO 130
555.000 135
556.000
557.000 140
553.000 145
F9R~1AT(*>F10.0)
F9RMAT.(M10)
RAT 18. « 3«14159./1«0.
NJM3ES 8'F E3UATI8NS- AND. CHBICE frF INTEGRATION SUBR6UTINE
NE»t
rjToi
IFtlMTC - 3> 30*40*50
INT = iNlTC
G3 T8 60 '
IMT = *
G9. T8 60
C9IMTINUF
C9NTINUF
IF(JFLA-n6S,.150j65
CSNTINJF.
Gg.Te* ( 11 0*.1?0* 130* 140)* iNTC
W^ I TEH 9* 115V
F3RMAT(«r »*** EULFR IMTERRAT19N »*»»*1//)
CONTINUE
.H3ITEU9.125)
F9RMAT(M *»#** M8D. EULFR INTEGRATI9N **»«»!//)
38 T9 1=50
h ^ 1 T F ( I S • 1 3 5 )
F8RMATM1 ***»* 4 TH 8RDER RUNQE-KUTTA •******»//}
G6 T9 ISO
kvR I TE( 18.145)
F9RMAT(M *»*** ADAMS M8UI T8N INTEG. *»*****i//)
-------
5o9.3oO 150
5O.300 C
561.000 C INTEGRATION r.SNTRGL PARAMETERS
562*000 C^NST * Fl/(RH9*U*AR'.E:A)
563.000 C.9NS1 • (RH8*0.003?S)/(?4«*360n.*0.06it)
56^.300 DTA = DTAIR*B«/T.
565OOO H9S , 1, 9*S I N.( ALBAR'R'AT 18 )
566.000 H9C = 1 . 9*CSS ( ALBA'R'*=?A'Tie )
567.300 CLDl =•!. - ,0765*CLD
568.300 CLD? « -.001J»»CID**2
569-000 CLD:3 » 1. - .0006»CLD**3
570.000 DALPR = HALF5 * RAT19
571.000 D-J » D', TA IR, .\ Q )
579.000 EA = 3HMl01'3*/U70t )*FTA
5SO.OGO fAlRP = TAIR+DTAIR
5S1.000 FTAP = STtTTRL*PTRL*TAIRP/10)
5S2-000 DEA a ( 1013./1470O*(DRH*FTA + RH*(FTAP - FTA))
5*3.000 IFLAsl
58^.000 IF(IFLA-1) 198^199^198
585.000 198 CONTINUE
536.000 WRITE CIO-2.0,01 OT
-------
5^7.000 200 F9RMAT(» .INITIAL DT .1^13.4 ' DEG F'/>
.
5*9.000 210 F6RMATM STREAM VFL3CITY * CSN2;!
59:5-000 230 F3RMAT(' AIR TFM'P. «'FS.J' OF-3 FiF8»l» DEG C'*
53b«000 li C9MST "iE-10.3" CBNS1 aipio.3//)
597.000 WRITF(.I8*2*0) W. WfPHj WMSj KMD
593.000 240 F9RMA.T"(" WIND VELOCITY «iF6.2i FT/SEC ' F8.2 ' MPH 'F8.2 ' METERS «J
5C>9>000 li/SEC'F8.2' ^IILES/DAYI/)
600. 300 W^lTF(I^i?60)
601.000 260 F9R.1AT(yJT20lTTRL'T40'PTBL'j60tHFST!3'/J
603.000 270 W^ITF.(I5.280) TTBL(T)/ PTBLM). HFGTB(I)
634.000 23O FSR^AT < 1 OX/3F20.5 )
6.15.000 1N3ITE:(13..300)QCLD,D'3H,DTAIR
635-000 300. F^K^AT(/i OrLD =!F6.3', ORH »IF5.S'- DTAIR a'F.6.2)
60.7.030 WRliF'l IS.310) DALP/OWMPH
638.000 310 F3RMAT(/» DALP »iF6.2i- DWIP'H .« • F6.2 )
639.000- W^ITE( 13.320) 'H^Sf H3C» HSjHSR
610.000 320 F^R^lA1'/" .H8S»''El?.4' H9C=iEi?..fti HS»'E12«*' HsR»'E12«'4» LY/MjN1)
611-000 IN' )
612.000 W=ilTF(I3.330) EA^DFA
61'3'OQO 3.30 F3RMAT(/i EA =iEl/?«4' DEA
614.000 W-?ITF(I3.340J
615.030 .340 F9RvtAT
-------
616.300 199
617.00.0 RETURN
6 IS. 000 END
619.000 CCCCC
630.000 CCCCC
6?1-000 CCCCC
652.000 CCCCC
6^3.000 S'JBRSJTIME 6UPT
654.000 C9MM9N DOT,YPU)> DT* DUM ( 4 ) , XF9, x'c.MDj. D*PR, X> OX/ NE j I NT*
6°3«000 llNiTCj IN, IB/FL/ ARfTA, U>» ERR8R; DXMAX, TEMP> HFGTB ('10 )
626,000 C9MMagRHR/w'/WMa,HD.TAlR*CLD*RH* ALPAR/TWg*TAjTWsA
627.000 C"?M'M9M HSR, Hflg, =-BR^ E\/Ap^ HE, HC, HLYMM/ pTBL ( 10 \> TTfiL ( 10 ) , WMS* CBNST
6'S.OOO C3MM8N Cl IF> HFG, H6C/ CLDl , CLO?j rLQr^j DALP, DALPR/DCLD/ DRH>
63^.000
630.300 W-mFUS.lO) X^OX
'631.000 10 F9RMATM x ciF7.li FT
633.000 2-0 FaRMATt"" STREA-I TFMP =»E12«4' DES F1/)
6^4«OnO wi:?l.TE( 19^70) OT.DD.T
635,000 W9ITF( 16.30) EW.DEW* rvAP, HE* HFfi
636.000 30 F3R-1ATM E^ a'FlP.5' DEw e'FIP.51 E.VAP = ' E12 .5 ' HE ='
637- OCO Itl'S.B'' I. Y/rtTN HFG a'E12»5*/i
638. OQO WRlTF( I9.5Q) H9R*EPRiHC
639,000 50 F9R^AT(i KSR ='E1?«5' FBR='F12.=;' HC .IE12.51
640.000 W3lTF(l3.60> HLYMN*HD-
641.000 60 F5R,JIAT(! T6TAL HEAT TSAMSFER B'F12.5' LY/MIN ' E15«5j
642,000 1' BTO/S.F.C-FT2!./)
643.000 70 F9RMAT(' QT'»'Fl?.5t QDT B»F1?.5>/)
-------
w
64 4 -000
6^5.000 SO
t , c - "i A n
D lf.3 * wUw
6^7.000 90
648.000
649.000
650.000 CCCCC
651.000 CCCCC
632.000 CCCCC
653.000 CCCCC
654-.000
655.000
6 — ' ~ -i PI i
-•O • -J JU
657.000
658.000.
659.000
660.000 :
661.000 C
662-000
663.000
664.000
665-000.
666.000
667.000
668.000
669.000
670.000
6-71.000 C
672.000
n3lT£(ia.30> DLYMN,Oet(JS
F9RMA.K' DLYMM «YP(4), DT/ DUM(4)^XPRjXEND/DXPR>X^DXiNE*
ITMT T^lTr- T,\l TQ n A 3 C7 A II r^DQC) ^VMAV.TCMP UiCf^TRMn^aPflNIQI
L 1-N r > 1 J| C* 1'Nj ID»bL? "^LAiUit-^KaKfL/XnAA-/ 1 1 1 '• / rtr u i DV IU^/UDINOI
C3MM6MRHfl«WjWHO.HDtTA-IR.Cj5H* Al ^AS, TWS' TAj T'*lsA* EW> EA,H6S' HS
C3I^^19M .Hficr/H93,>3R>cVAPjHE/HCil4LYMN*PTBL(10)/TTBL(10)»WMS*CeNST
C3fNTEMP,SITBL(10)^XT8L(lO)
THERMAL FXCHANGC- WITH ENV IR9NMFNT .
TEMP «.' si
T"/S= (TFMP-3?. ) *5./3.
TWSA s T'wS + ?.7^.
DTrtS = 3^*5 i/9i
FTA- = SI (TT3L»PTBL/T=:MP410)
Jfrt a TFMP •*• 'Of
FIB = SI (TTBl .PTBLjTTWjIO)
ifi' = ( 13'1 3./14.7)*FTA
DEW a (10l3./H.7)*(FTB - FTA)
EFFECTjVF BAC.< RA°IATl8N.
H9B« (l*.38-.09*TWS-.046*RH)/6q.7.?!
-------
673.000
674.000
•675« 000
-676. OdO
677OOO
673.000
673-000
680.000
631.000
6S2OOO
633.000
6S-'^
686.000
687.000
68S-OCO
633.Q30
690.000
691, OGO
692,000
693.000
694. COO.
695.000
696. OCO
697.000
693.000
693.000
700.000
E3R « H'3R*CLnt
C EVAP8RATT6N HEAT TRANSFER.
EvAp » ..75* (EW-EA)*( 1. + .009R* 'WMD
HF'3 a SI fTT3|. •MFGTB,TEMP,10)
HE » EVAP*HFfi*C3NSl
c CONVECTION HFAT TRANSFER
HC a 39. #(.26 -H .077#WMS)*(TWS - TA
C T9TAL HFAT TRANJSFFR T9 WATER, I.Y/MIN
HLYMNi = nS - (E3R 4--HSR + HC + HE)
C T3TAL..HFAT TRANSFER, 3TU/SEC-FT?
HD » HLYMM * «0<:>1'*
FI 3 CL3?*DCl. D*HSS
F3 = « 0765*DrLD*Hf?fa
F4 » -CL01* ( - «09*DTWS - .046*DRH)/69
F5 a -(n +F2)*3./ALBAR
F6 = - Hs*7. *DALP/ALPAR**?
F7 3 -C'«S5*HFG/t 440-0. )#(.(!• * .nO^S*
1 . Ou93#DwMD>-»(EW • FA ) )-
F3 = - ( ^g ./1440. ) *( ( . 2ft + »077*WMS)»
1 ..077*DWMs*(TWs - TA) )
DLYMN = FI +'F2 + F3 + F4 +-FB + F&
D3TUS n DLYMM*.0614
DOT .= -C9NST*n3TUS
RETURN!
END
CCCCC
CCCCC
) * ( DEW - DEA) •+
- DTA ) +
+ F7 + F8
-------
701.
702.
703.
70*.
705 »
706.
707.
70S.
703.
710.
711.
712.
713.
7lt.
715.
71b.
717-
71S.
719.
723«
72-r.
7? 2''
723.
72 4 •
725.
72.5.
727.
723.
729.
000
000
000
000
000
000
000
000
000
000
000-
000
000.
000
000
OOP
000
000
000
•000
-ooo
000
000
ooo.
000
000
-QOO
'000
-000
ccccc
'ccccc
c
c
r
c
c
c
c
120
130
•550
160
180
210.
220
25*-
FUNCT19S> SI (XT3L.J YT3!_/X,N)
LINEAR IMTE3PSLATIBN' 9R. FXTRAPftLATTflN 8-F
XTBu - K'OEP'FNDENT' VARIABLE TARLE
YTBL .= DFPENDEMT ,VA?!IA3LF TABLF
IMD *• INDICATOR 9F EXTRAP8LAT I ftN
dsN9 EXTK.APSLATI8N, 1*L9WER EXT^AP'SLAT I 9
DIMEN3I9M XTRL(401* YT3L(40)
CHECK T3 SEE" IF EXi^ei-AT I3^ TS' NEEDED.
lF
-------
730
731
732
733
7.34
735
735
737
73S
7.39
740
741
7*2
743
744
745
746
747
74S
749
750
751
752
753
754
755
756
757
f
•
*
•
t
«
•
*
•
•
ff
t
•
*
.
•
f
•
•
•
*
•
«
V
«
•
*
*
000
000
000
000
000
000
ooo
0-)0
000
0 jO
.000
000
JCO
000
000
ooo
000
000
ooo
ooo
000
ooo
000
030
000
OJO
oob
000
CCCCC
CCCCC
CCCCC
CCCCC
10
100
?0
200
CCCCC
CCCCC
CCCCC
CCCCC
ENID
SjBRe'JTTNJE EULER(YPjYjDTjNE*JjT)
DIMEM3I9N YP(20)/Y(2C.>J SY (20 > . SYP ( 20 )
G3 T6 ( 1 Oi 20 } t J
C3NTIMJE
D3 .100 I =l/i\IF
SY( n= Y(,I )
.SYP(I)= YP(n
Y( IU Y( t )+DT*YP( M
C.^NTI \UE
TsT+OT
RETjR\J
CSN'TINUE
D9 ?00 Is.ljNF
Y( I ) = SYH )•*•( YP( I.)+SYP( I ) )«D.T/?.
C3NTINUE.
RETU9M
END
SjeReJTIiVJE RK4 ( YPj Y>OT^NF* Jt T )
DIMEMSI9N YP(5),Y(5)j.AK(5^,4)>SY(5)
-------
758.000
759.000 10
760.000
761.000
762.000
7*3.000
764.000 100
765.000
766.000
7*7.000
763.000 20
763.000
770,000
771.000
772,000 200
773.0-00
.774.000 30
775.000
776,000
777.000
773.000 300
773.000
730.000
731,000 40
782,000
733*000-
734,00.0
785.000 400
736.000
03 Te(rO.;;0*30*40>*J
C9NTIMUP!
Dd 100 I=1*NF
SY( I ) « Yd )
A1<(I*1) a OT*YPdV
Y(I) * Yd) + AKd*l)**.5
CgNTlNlUE
ST = T
T • T + HT».R
RETURN
C3NTINUE
D'9 200 Id*NF
A<( 1*2) = DT*YP(1 1
Y( I ) = SY(.r) • .+ AXd*2)*
C^NTjNUP
RETURN
C3NTINUC
03 '300 I a.l*.SE'
AK( 1*3) a DT*YP( I )
Yd ! = 3Y ( I ) + AKd*3)
CSNT-INUF:
T = ST + DT
RETURN
C3NTINUE
D9 409 I - 1*NE
A<( 1*4) = DT *Y=( I)
Y( I )=SY( T ) + (AK( 1* t)+AK(
C8NTINUE
RETURN •
h(AKd*2)+AKd*3)
-------
7*7.
7*3.
759-
790.
791.
792.
793*
794.
795.
795.
797.
798.
799.
800.
801.
802.
803 t
804,
80?.
806.
807.
808.
809.
810.
811.
812.
813.
814.
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
.000
000
000
CCCCC
CCCCC
CCCCC
CCCCC
1
991
C
993
998
C
999
992
90.1
C
1
5
END
SJBR9JT
D I KENS I
L),A(5),
IpUSTP
KSTP.28
TEST re
IF(JUMP
G9 T8 (
JUMP =9
TaS'AVET
JJMP»0
D9 901
F( I )»SF
INEN3RD(F,T,TLlM,Y^ERR
9M STA^Y(5)>Y(5)jSY(5)
ac5ijC(5)*D(5)>AA<5.)*B
-.^2767)9^3,991/991
R TYPF Qf ENTRY
)1./998/999
1000* 11* PI/ 802/803)* I A
3. REsTQRE VALUES
Ial*NP
( T )
Y( l')aSAVPY( I.I
G9 T8 1
JUMP NE
D9 5 1 =
STARY( I
A( I UO.
B{ I )=0.
C( I )=0.
D{ I )=0i
KSTpsO
0?
G. INITIALIZE
l/NE
UY( I )
oni
oni
001
001
.NJFjH,HMAX, JUMP*KSTP>KC8N,CLIF/ 18)
AVFY ( 5 >> F( 5 ) • FP (5 ) > DELTA (5 )' DALT'A (
(5>jCC<5)jDD(5>*SF(5)
-------
815.000
816.000
S17OOO
813.000
819.000
8?1.000
KOELY-0
KC8N.O
XT«95«/t?88«*64. )
U«863«./( 1 2.*5040.
V»95.0/?S8.0
P«35. 0/24.0
G»35.0/7?.0
10
ID
8?3;.OOQ
8?4.00.d
825.000
856,000
8?7.000
^358.000
8=9.000
830.000
831,000
832.000
STEP
834.000
835.000
836.000
837.000
833.000
839.000
840.000
841.000
842.000
843.000
JUNPaO
G3 TB 1101
B£Gl*J INTEGRATION
1000 D9 1111 T=1*NE
SP(!)»F(T)
1111 SAVEY(I)=V(I J
C H T9B SMALL RETURN WITH JUMP MFG
600 lF(ABS(T-t-H)-ABS(T!>605j60lj6o5-
601
605
10
11
12
.
Gg Te Hnl
09. 10 I»1 *NE
Y( I)*Y( I )+H*(F( I ) +A ( I ) +B(I )+C( T J.+ D ( I ) )
FP(I)«F(T )+2.0*A(I)+3»0*B(I)+4.0*C(I)+5,0#D(I)
IA = ?>
G9 TS 1101
D9 12 I='ljNE'
SY(I)»Y(I)
Dd. 20: I*1^N£
-------
844.000
845,000
846. '000
847,000
848.000
849.000
850.000
851.000
852.000
853.000
.854.000 C
855.000
856.000 C
S57.-GOO
85S.OOO C
859.000
860.000
861.000
862.000
86^.000
864.000 C
865.000
866.000
867,000
868.000
869-000
870.000
871.000
20.
21
29
30
31
35
40
45
50
55
?23
DELTA { T )sF( I )-FP( I)
Y< M«Ym+V*DELTA U ) *H
IA»3
KCBM*1
G3 T9 llnl
KCSNsO
D9 30 I»1>N£
DALTA ( T )«F( I )-FP< I )
Y.( I )s3Y< T )+V*DALTA (I)*H
C9NT1MUF
TESj F8R STARTI^ SEQUENCE
lF«STP-?8)3R/40/40
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904.
905.
906.
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909.
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911.
912.
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950.030 IA*5
951.000 G9 TB linl
952.000 803 D9 108 I=1*NF
933.000 DALTA (T)=F (I)-FP(I)
934.000 108 Y( I)«SY( t')-»-V*DALTA d)*ENDH
95-5«000 .JUMp = l
-956.000 39 TS llnl
957.000 C N9........TEST F9R D6JBLING. IF'SK, BEGIN MEST STE- AFTER D8UBLING
-------
958,000. 110 IF(ABS(TI IM-T)-ABS(2.0*HniOOO.1000*111
959.000 111 IF«OELY-4)1000.»1PO>120
963.000 120 IF(AQ3(?.0*H1-A^S(HMAX))121»131*10QO
961.000 121 03 125 I,1*NF
962.000 IF(ABS(DALTA (!))-ERR8R/{128.0*ABS(H)))125*125*1000
963.000 125 C9NTIMUE
964.000 IF (V*-UCI. IF"0.0625) 130^.1000* 10.00
965.000 130 C3NTINJE
966.000 335 H = c.0*rl
967.000 05 135 I«1*NF
963.000 A(I)s2.0*A(I V
.969.000 B( I)s^»0*B( I)
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977.000 RETURN
973.OCO END'
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C3MMSM C ( 1000 ), TA (1000 Y, PHI (1 Onr».W( 1000 ),TW( 1000)
C9MM9vj NT.AS* NDA, OELT(SO), TOAc(FiO)
C3MiM8N' NI.NV1N, I^U,DT,NTAj IDA
C9MM9N CTA(50)»TATA(50)fPHITA(«5n),WTA(5Q),TWTA(50)
C3MM6N IMT2* TMT^*DC>DTA,DPHI,DW,DTWjINVs*IFLAG
C9MM9N
C9MM9M-
C9MMSN
2000 FgRMATdWO/aXi'PR5BABILTTV CHART ' /> 2XJ 60 ('*'))
WRITE! 1911,2001) (OELT( I ),I«»1,NCAS)
2001 F9RMAT(lwO,lOX,10(E10.3il.X).)
D-9 10 1-.
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5. 03.0 WRITE( I9U*2002) IP AS (I.)* (PRP( I / .1 ) , J« 1 1 NCAS )
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1517.000 C9MM8N !^^121
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15a0..020 PR(D»0.
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15=n.060 C -N3A. DUMBER BF DAYS IN THg CASF
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1532.000
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15^7.000
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1539.000
15*0.000
1541,000
1542.000
1543.000
1544.000
1545.000
1546.000
1547.000
D3 2C I
C-3 = 0.
TAS=O.
PHIS=0.
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D9-. ifO J
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CS'CS +
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?n«i*MOIF
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IPO+.I-D+J
r ( I'MT)
. + TAf I NT-)
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00
15tfi..OOO PHlSsPHIR + PHI(INT)
15«*9»'OCO W,3 = .gS + w( INT.)
1551 .00.0 40
1552. OCO 30
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15H«f.OQO TAS= ,TA3*FNDA
1555,000
15 tjo. OCO
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1553.000 C INT?= F.3lL8>,IMG DAY
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156J.OOO
1561.000
1562.000
1565.000 D3 =50 1,1*8
15^6.000 C iMT.^i THr ACTUAL PfiSlTISN IN THF DAY
15S7.000 I.MT3»INT?*8"R+I
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1570.000 PHllS'P^T IStPHI ( INT3)
1571. DOO lMS = WlS + i*/( INT3)
157?. 000 T"J1S = TW1 S + TW( IMT3)
•1573OOO 50 C^NTINJF
1574'. 000 C1S = C1S*.125
1575.000 TA15=TA1S*.1?5
1576. DOO PHllS
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1579'.000
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15S2.000
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1538.000
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1591.000
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15 95. '000
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1600.000
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STT3L1 »Trt1 S
X'TBLl (1 J = 0.
XTBL1 (2)-=25000«
NT£MPI«?
I.\lVS = IvjT?»8-Jf
CALL C9MP(EN.uicbr>EN)
'05 60 ICA3«1..NCA'S
IF(ABS(Y1 (in-DPLK ICASn 65j6R/70
65' C3NTJMJF
P3< tt!AS)=PR(ICAS)+l.
70 C3NTINJC
.60 C9NTINUE
20 C3NT1NJE
DENPaNQlF
03 75 ICASoljNCAS
PR( ICAS)=PR(JCA,S)/DE^P
75 CONTINUE'
W^lTEf ISiJj^OOO) (PR( I-J/ I = t^NCA'S)
2000 F8RMAT(/.2X* !SHTi:8N.'7 RESULTS I . in «F6
RETURN
999 C3NT1NJE
WRl TE(- ISJIJ* 4.000)
4000 F3RMAT(/,2X* »T89 SMALL')
CALL EXIT
RETURN
END
IX) )
-------
APPENDIX D
THEORY OF THE SENSITIVITY ANALYSIS
In this appendix the development of the equation (1) is
discussed together with the problems of convergence and
averaging of the data. The sensitivity analysis is further
discussed with the exact solution being developed for the
constant coefficient equation.
THE GENERAL STREAM MODEL
The equation ( 1 ) is developed from the energy equation
heat fluxes shown in Figure 1 . The development of this
equation is based on a Taylor's expansion of the dependent
variable, T , about the position, x , downstream:
T(x + dx) = T(x) + ^ (x) dx . (D-1)
QX
Use of this Taylor's expansion together with the conserva-
tion of energy for the control volume in Figure 1 yields:
uA T(x) - uA [T(x) + $2L (x) dx] +
dx
+ * dx [QRad - QRef - QBack ~ QEvap + QConv + QMisc] = °
(D-2)
The first term is the enthalpy transport into the control
volume; the second term is the analogous transport out of
the control volume; the third term is the total heat flux
at the air/water interface. Some minor algebra on equation
(D-2) yields equation (1), assuming that the quantities u,
A, and £ vary slowly along the stream.
The equation (1) holds between points at which flows and/or
heated effluents are added to the stream. Many authors
directly integrate equation (1) over a station length, Ax ,
assuming the fluxes and u, A, H to be constant over that
distance. The result is simply
x+Ax x+Ax
7uA dT C
— d? dx = J
°-Conv + °-Misc] dx
QRef QBack + QEvap
x x
150
-------
uA
- [T(x + Ax) - T(x>] = [QRaa - QRef
Ax
QConv + Q] Ax
T(X + Ax) = T(X) +
It is possible to then incorporate heat fluxes not covered
by those at the air/water interface in the Qwisc term»
simplifying the coding and the model considerably. Two
aspects of this concept should be emphasized: 1) all models
are similar to this model and are within a small error that
is a function of the mesh size, and 2) the convergence of
the procedure can be shown from previous literature.
Suppose that an alternate model is used in which the fluxes
are redistributed, i.e., the total flux may be the same but
the model assumptions causes a difference in the flux at
any position x . Then this difference can be represented
as a quantity proportional to the station length, Ax .
For example:
QRad(x + Ax) = QRad(x) + 0(Ax) ' (D~4)
But the introduction of this expression into equation (D-3)
will introduce a term of order Ax2 (O(Ax2)), which can be
made appropriately small by a suitable choice of Ax . Thus,
all correctly formulated models will be a measurable error
away from the general model described by equation ( 1 ) .
The question of numerical convergence of the solution is
discussed in general by Salvador! and Baron [1961], p. 116.
Much of the information provided by them can be directly
applied to this problem.
Suppose a general problem stakes the; form
151
-------
y = f(x, y) ,
y(0) = y0 . (D-5)
If Euler's method is taken as an example the form for the
integration is
Yi+1 = YI + f U± , y±)h , (D-6)
which is seen to be identical in form to equation (D-3).
From p. 91 in Salvador! and Baron
y(x) = /f(z) dz
y(x) = f(x)
•
y(x) = f(x)
(n)
y
(x) = f (n-1) (x) . (D_7)
A Taylor's expansion about x yields:
y(x±h) = y(x) ± J^f (x) + ^ |(x) ± £- f (x) + ---
*' ' (D-8)
From this the following expressions can be evaluated
x+h
I -I = f f(z) dz = y(x+h) - y(x)
x
= h[f (x) + y f (x) + JT f (x) + — ] , (D-9)
and
152
-------
x+h
ift/h
I2 = / f(z) dz = y(x+h) - y(x-h)
= [2 hf(x) + f (x) + f(IV) (x) + --- ] .
(D-10)
From Taylor's theorem and equation (D-6)
h2 '
y(x+h) = y(x) + hf(x) + jj- f(x) (D-11)
and the error is proportional to the maximum value of the
second derivative. With these fundamentals set down the
error for the equation
dT = _QL_ (D-1
dx uApc
can be readily found. From the general analysis the error
is bounded by the expression
IT - T < I—I Ax
1 Approximate Exact1 — uApc 'dx' /Am
max v D- i J j
An expression similar to (D-13) is easily developed for
.bounding the station length
Ax < I ^allowable I _ (D_14)
nnax idQi
uApc 'dx1
max
From experience, a convergent Ax can easily be obtained
for this differential equation since the heat fluxes are
generally very small and have small derivaties.
153
-------
DATA AVERAGING
For small changes in temperature the equation (1) will be
quasi-linear. Thus, the theory of linear equations can be
applied to the problem. This is very important since
average data will produce average output to such a model,
while a nonlinear model will not yield results of this
type.
To prove this it is necessary to examine the theory from a
different viewpoint. For example, the temperature at any
point x downstream from the disturbance can always be
represented from the linear equation in the form
x
T(x) = £]
i 0
where the integral occurs over the domain of interest and
the kernel function K^(x, £) relates the effect of the
i'th heat flux 0^(5) at the position £ to the temperature
T(x) at the position x ; the sum produces the effects of
all of the heat fluxes. Since the expression is linear , it
can be summed over several sets of heat fluxes to obtain the
sum of temperatures as follows
n
vx) =
(D-16)
Suppose that equation (D-16) is rearranged and both sides
of the equation divided by the number of temperatures n
n
(D-17)
This proves that the effects of the heat fluxes can be
averaged and the equation used to compute an average tem-
perature. This would not be true for a nonlinear equation
and is a significant result.
-------
THE SENSITIVITY ANALYSIS
The fundamental equation for the sensitivity analysis is
developed by varying both sides of the solution equation
(1):
d6T H
~dx" = Au" 6Q ' (D
where 6Q is the change in the heat fluxes and 6T the
resulting change in the stream temperature. The initial
condition for the equation is
6T(0) = <5TQ , (D-19)
i.e., an initial error in temperature <5T0 is known at a
point in the stream, which allows the computation of the
error at points downstream.
On closer examination of 6Q the linearity of the solution
emerges. The individual terms are
&Q = 1.9 sin a (-0.0018 C2 6C)(0.61)
Solar
+ (1.0 - 0.0006 C3)(1.9 cos of 6a) (0.061)
6Q0 *i x. ^ = - ) ,
155
-------
f
^Evaoration = ^fo (0-35) (1.0 + 9.8 x 10~3 w2) (6ew - 6ea)
"^Evaporation
Ph
240
(0.35) (9.8 x 10~3 ,5^) (ew _ e&)
^Convection = 39.0 (0.077 SW2) (T - Ta) (f) (0. 061)
+ 39.0 (0.26 + 0.077 W2) (&T - 6T&) (|) (0.061)
(D-20)
Note that small changes in the heat fluxes imply like changes
in 6T. Thus, the justification in linearizing the analysis.
The equation (D-18) is solved in this investigation using
numerical analysis procedures. However, for constant coef-
ficients in equation (D-18), the equation can be solved in
closed form. Symbolically the equation can be written as:
— r _ f1 ' i^ rp .L ^ j- r~* _i_ __ /""I Y T~\ o 1 \
— -— L C-i 01 + Cn + Co + WnJ , lD-/!1;
ax Au ' ^ o "i
where the C^ are constants. The solution to this equation
is found in two parts, a homogeneous solution decaying with
distance and particular solutions that are constant. The
homogeneous solution is found by assuming it in the form
6T = A e~ax , (D-22)
where A is an initial amplitude and a is the decay rate.
Substitution into equation (D-21) yields
-(a) A e~ax = JL [- c.| A e"ax] , (D-23)
which finds a to be
(D-24)
156
-------
The particular solutions are found from
C
(D-25)
where i = 2, --- , m . It is on this basis that the
sensitivity analysis is completed.
157
-------
TECHNICAL REPORT DATA
(Please read Inunctions on the reverse before completing)
1. REPORT NO.
EPA-660/3-75-037
2.
3. RECIPIENT'S ACCE88ION>NO.
4, TITLE AND SUBTITLE
5. REPORT DATE
Improving the Statistical Reliability of
Stream Heat Assimilation Prediction
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Richard W. McLay
Mahendra S. Hundal
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMIN
Richard W. McLay, P.E.
18 Redwood Terrace
Essex Junction, Vermont
05452
10. PROGRAM ELEMENT NO.
1BA032
11. CONTRACT/GRANT NO.
68-03-0439
12. SPONSORING AGENCY NAME AND ADDRESS
National Environmental Research Center
Office of Research and Development
U.S. Environmental Protection Agency
Corvallis, Oregon 97330 ^_____
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
16. SUPPLEMENTARY NOTES
16. ABSTRACT
This work is an evaluation of existing, one-dimensional stream temper-
ature prediction techniques for accuracy and precision. A sensitivity
analysis of a general model is used in oonjunction with statistical
methods to determine solution errors. Data taken in 1973 at the Vernon,
Vermont nuclear plant are used as a data base. These data are used with
Burlington, Vermont airport tfeafeher station data to 1) gain insight intc
the orders-of-magnitude of the various errors and 2) carry out a de-
tailed data analysis to establish probabilities of meeting given error
requirements.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Accuracy
Stream temperature prediction
18. DISTRIBUTION STATEMENT
19. SECURITY CLASS (TM&.Report)
21. NO. OF PAGES
163
20. SECURITY CLASS (Thispage)
22. PRICE
EPA Form 2220-1 (9-73)
U.S. GOVERNMENT PRINTING OFFICE: 1975-699-072 111 REGION 10
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