FEBRUARY 1987
ROADWAY -- A NUMERICAL MODEL FOR PREDICTING
AIR POLLUTANTS NEAR HIGHWAYS
User ' s Guide
ATMOSPHERIC SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NC
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ROADWAY -- A NUMERICAL MODEL FOR PREDICTING
AIR POLLUTANTS NEAR HIGHWAYS
User ' s Guide
by
Robert E. Eskridge
Meteorology and Assessment Division
Atmospheric Sciences Research Laboratory
Research Triangle Park, NC 27711
and
Joseph A. Catalano
Aerocomp, Inc.
3303 Harbor Boulevard
Costa Mesa, CA 92626
Contract No. EPA 68-02-4106
ATMOSPHERIC SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NC
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NOTICE
The information in this document has been funded by the United States
Environmental Protection Agency under Contract No. 68-02-4106 to Aerocomp,
Inc. It has been subject to the Agency's peer and administrative review,
and it has been approved for publication as an EPA document. Mention of
trade names or commercial products does not constitute endorsement or
recommendation for use.
AFFILIATION
Dr. Robert E. Eskridge is a meteorologist in the Meteorology
and Assessment Division, Environmental Protection Agency, Research
Triangle Park, North Carolina.. He is on assignment from the National
Oceanic and Atmospheric Administration, U.S. Department of Commerce.
ii
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PREFACE
One area of research within the Meteorology and Assessment
Division is development, evaluation, validation, and application
of models for air quality simulation, photochemistry, and
meteorology. The models must be able to describe air quality and
atmospheric processes affecting the transport and diffusion of
airborne pollutants on scales ranging from local to global.
Within the Division, the Environmental Operations Branch adapts
and evaluates new and existing meteorological dispersion models
and statistical technique models, tailors effective models for
recurring user application, and makes these models available
through the User's Network for Applied Modeling of Air Pollution
(UNAMAP) system of EPA.
ROADWAY is a numerical model for predicting air pollution
levels near highways. It solves a conservation of species
equation via finite-difference approximations. Temperature at
two heights and wind velocity upwind of the highway are required
inputs; surface layer similarity theory is used to produce wind
and turbulence profiles. A unique aspect of ROADWAY is the
treatment of vehicle wake effects which are superimposed on the
wind and turbulence fields. Chemical reactions due to exhaust
emissions near the roadway are simulated by a 2-step mechanism
that yields concentrations of NO, NO , and 0 in the very near
Zi o
field.
Although attempts are made to thoroughly check computer
p r o g r am s with a wide variety of input data, errors are
occasionally found. Revisions may be obtained as they are issued
by completing and returning the form on the last page of this
guide.
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The first four sections of this document are directed to
managers and project directors who wish to evaluate the
applicability of the model to their needs. Sections 5, 6, 7-, and
11 are directed to engineers, meteorologists, numerical analysts,
and other scientists who are required to become familiar with the
details of the model. Finally, Sections 8 through 11 are
directed to persons responsible for implementing and executing
the program.
Comments and suggestions regarding this publication should be
di reeled to:
Robert E. Eskridge
Terrain Effects Branch
Meteorology and Assessment Division (MD-80)
Environmental Protection Agency
Research Triangle Park, NC 27711.
or ,
Joseph A. Catalano
Technical Director
Aerocomp, Inc
3303 Harbor Boulevard
Costa Mesa, California 92626
Technical questions regarding use of the model should be directed
to (919) 541-4551. Users within the Federal Government may call
FTS 629-4551. Copies of the user's guide are available from the
National Technical Information Service (NT IS), Springfield, VA
22161.
The magnetic tape containing FORTRAN source code for ROADWAY
can be found (along with other diffusion models) in UNAMAP
Version 6 and up which is available from Computer Products, NTIS,
Springfield, VA 22161 (phone number: (703) 487-4763).
IV
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ABSTRACT
ROADWAY is a finite-difference model which solves a
conservation of species equation to predict pollutant
concentrations within two hundred meters of a highway. It uses
surface layer similarity theory to predict wind and eddy
diffusion profiles from temperature at two heights and wind
velocity upwind of the highway. A unique feature of the model is
its use of vehicle wake theory, which was originally developed by
Eskridge and Hunt (1979), and was modified by Eskridge and
Thompson (1982); and Eskridge and Rao (1983, 1985). It is
assumed that vehicle wakes affect the wind and turbulence fields
in a linear manner with wake intensity a function of vehicle
speed, downwind distance, and distance from the wake center. The
user has the option of considering NO, NO , and 0 chemical
2t o
reactions near the road. Output from the model consists of x-z
fields of wind components, eddy diffusion coefficients, and
concentration of pollutant species.
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CONTENTS
Preface iii
Abstract v
Figures ix
Tables x
Acknowledgments xi
Executive Summary 1
1. Introduction 4
2. Data-Requirements Checklist 6
3. Features and Limitations ' . ... 8
4. Basis for ROADWAY 11
Numerical approach 11
Similarity theory 13
Vehicle wake theory 13
5. Technical Description 15
Conservation of species equation 15
The boundary conditions 16
The grid 17
The numerical scheme 18
The basic-state atmosphere 19
Vehicle wake theory 23
Chemical reactions 28
6. Example Problem 31
7. iWodel Evaluation 38
Background 33
Evaluation results 39
8. Computer Aspects of the Model 42
Structure of ROADWAY 42
Program modules 42
v i i
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CONTENTS (continued)
9. Input Data Preparation 50
Record input sequence 50
Intricacies of the data 54
10. Execution and Interpretation of the Model .... 59
ROADWAY verification run 60
Example problem 68
11. Error Messages and Remedial Action 78
References 83
Appendix A - Listing of FORTRAN Source Code for ROADWAY . 86
Appendix B - Turbulent Diffusion Behind Vehicles:
Evaluation of ROADWAY Models 125
v i i i
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FIGURES
Number Page
1 Coordinate system used in the model 24
2 Geometry of the example problem 32
3 u and v wind fields for the example problem 33
4 Turbulence fields for the example problem 35
5 Pollutant concentration fields for the example
problem ....... 36
6 Comparative performance of highway models ...... 41
7 Structure of ROADWAY computational system ...... 43
8 ROADWAY flow diagram 48
9 Examples of several highway configurations and
their appropriate values of RDANGL 56
10 Sample job stream for ROADWAY 59
11 Printed output for the verification run 62
12 Printed output for the example problem 70
IX
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TABLES
Number Page
1 Algorithm Used to Set Grid Dimensions and
the Steady-state Time Period 17
2 Constants for the Polynomial Fits in Eqs. 47 and 49 . 26
3 Comparison of Model Results Using the GM Data .... 40
4 Record Input Sequence for ROADWAY 50
5 Roughness Lengths for Various Surface Types 54
6 Input Data for the Sample Test 61
? Input Data for the Example Problem 68
8 Error Messages and Remedial Action 78
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ACKNOWLEDGMENTS
The authors wish to express their appreciation to Mr. Brian
Eder and Mr. William Petersen for helpful comments regarding
aspects of the work presented here. Special mention is made to
Mr. Thomas Chico who optimized the source code. Most of this text
was excerpted from technical publications dealing with ROADWAY
over the past few years.
Support of Aerocomp by the Environmental Protection Agency
Contract No. 68-02-4106 is also gratefully acknowledged.
x i
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EXECUTIVE SUMMARY
ROADWAY is a numerical model for predicting air pollution
levels near highways. It solves a conservation of species
equation via finite-difference approximations. Temperature at
two heights and wind velocity upwind of the highway are
required. With these inputs surface layer similarity theory is
used to produce wind and turbulence profiles. A unique aspect of
ROADWAY is its treatment of vehicle wakes which are superimposed
linearly on the wind and turbulence fields. The vehicle wake
intensity is a function of vehicle speed, downwind distance, and
distance from the wake center. Additionally, the user has the
option of considering NO, NO , and 0 chemistry; reactions of
LI O
these pollutants are calculated by a 2-step mechanism applicable
to the very near field. Output from the model consists of fields
in the x-z plane for wind components, eddy diffusion
coefficients, and concentrations of four pollutant species.
To estimate concentrations for any simulated hour,
information on meteorology, highway configuration, and emissions
are required. The meteorological information needed for the
computation includes representative roughness length, temperature
at two heights upwind of the highway, and hourly average wind
speed and direction at the level of the upper temperature
sensor. If the chemistry- option is exercised, two photochemical
reaction rate constants, background for each species, and
conversion factors (gm/sec to ppm) are also required. The
following highway configuration data are needed for execution of
the mode 1:
number of traffic lanes,
width of each lane (m),
width of the traffic median (m),
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angle between highway and a line running
north-south (degrees),
traffic volume (veh/hr),
average vehicle speed (km/hr), and
average vehicle dimensions (m).
Air quality and emission data necessary for model execution are
background pollutant concentrations and vehicle emission rates.
No sampling grid or receptor information is required as these are
internally generated.
Since ROADWAY is a numerical model it has none of the
limitations generally associated with Gaussian algorithms. That
is,
it is a multilayer model which considers vertical
variation of both wind and diffusivity,
. it can treat calm or light wind conditions, and
. it can simulate chemical reactions of the emitted
pollutant species.
Also, the model can include up to ten traffic lanes and has
features to reduce execution costs (at the expense of accuracy)
and to provide intermediate output. ROADWAY was developed
independent of tracer data, and has been demonstrated to perform
as well as other highway models currently available.
ROADWAY has several limitations. A major restriction o£ the
model is the requirement that the vehicle speed be much greater
than the wind speed. This requirement, however, should be met in
most instances of significant pollutant impacts. More
importantly, the model is valid for all vehicle speeds when wind
speeds are light. Another limitation is that ROADWAY does not
consider wind meander which becomes important when the mean wind
is parallel to the highway. Also, because its use is restricted
to the very near field (within 200 m of the roadway), other
algorithms would be better suited for calculating impacts at
longer distances. Finally, since ROADWAY algorithms are
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SECTION 1
INTRODUCTION
The problem of automobile pollution has been of interest
since 1969 when the National Environmental Policy Act was
promulgated. The Act requires that construction of new highways
which are partially paid for by federal funds include an
environmental impact statement as part of the plans. Various
approaches including Gaussian solutions (Zimmerman and Thompson,
1975) and numeric solutions of conservation of species equations
(Danard, 1972) have been used to predict concentrations near
highways. A theory to predict vehicle wake effects did not
exist, however, and earlier models either ignored the vehicle
wake effects on the velocity and turbulence fields or
parameterized them in a simple manner (such as by enhancing
dispersion over the highway).
Eskridge et al. (I979b) developed a finite-difference model
for calculating pollutant concentrations on and near a highway
that incorporates the vehicle wake theory formulated by Eskridge
and Hunt (1979) from a perturbation analysis of the equations of
motion. The major restriction of the model is the requirement
that the vehicle speed be much greater than the wind speed.
Vehicle wake theory was evaluated and modified in wind tunnel
experiments by Eskridge and Thompson (1982) and Eskridge and Rao
(1983, 1986). The results of these wind tunnel investigations
are included in the version of ROADWAY described here. Because
certain pollutants emitted on the road are reactive, a simplified
chemical mechanism was added to the model. Chemical reactions
involving nitric oxide (NO), nitrogen dioxide (NO ), and ozone
2
(0 ) are simulated by a 2-step mechanism.
o
Recently, Rao et al. (1986) evaluated ROADWAY and two other
highway models, HIWAY-2 and CALINE3, using statistical techniques
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suggested by Fox (1981), Willmott (1982), extreme value
statistics (Tabony, 1983), and the "bootstrap" method (Diaconis
and Efron, 1983). Tracer data from the General Motors (GM)
Sulfate Dispersion Experiment were used for the evaluation. The
results indicate that all three models perform well but HIWAY-2
and ROADWAY fit the data better than CALINE3. It should be noted
that unlike HIWAY-2 and CALINE3, the ROADWAY model was developed
independent of the GM data set.
This document is directed toward three different readers:
managers, air pollution meteorologists, and computer
specialists. The first four sections are aimed at managers and
project directors who wish to evaluate the applicability of the
model to their needs. Sections 5, 6, 7, and 11 are directed to
meteorologists or engineers who must become familiar with details
of the model. Finally, Sections 8 through 11 are directed toward
persons responsible for implementing and executing the program,
and, if necessary, making modifications to the code. A listing
of the FORTRAN source statements are included in Appendix A;
Appendix B gives a reprint of an article on the performance of
ROADWAY against observed data and the two other highway models
no ted earlier.
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SECTION 2
DATA-REQUIREMENTS CHECKLIST
To estimate concentrations for any simulated hour, data for
program control, as well as information on meteorology, highway
configuration, and emissions are required. These are mentioned
briefly here; more detail on proper formatting for data entry
is given in Section 9.
The user must indicate whether the following features are
to be employed:
chemistry option,
antidiffusion calculation option, and
intermediate print option.
The meteorological information needed for the computations are:
« roughness length (m),
temperature at two heights upwind of the
highway (K), and
hourly average wind speed (m/sec) and
direction (degrees).
The following highway configuration data are required:
number of traffic lanes,
width of each lane (m),
width of the traffic median (m),
angle between highway and a line running
north-south (degrees),
traffic volume,
average vehicle speed (km/hr), and
average vehicle dimensions (m).
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The user must supply the following air quality and emission
data for each hour of simulation:
Background pollutant concentrations (ppm),
Vehicle emission rates (g/km*veh), and
Factor to convert grams per second (gm/sec)
to parts per million (ppm) for the pollutant.
If the user exercises the chemistry option, then background
concentrations, vehicle emission rates, and conversion factors
must be provided for nitrogen oxide (NO), carbon monoxide (CO),
and nitrogen dioxide (NO,,). Also, the background ozone (0.,) must
L
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SECTION 3
FEATURES AND LIMITATIONS
The diffusion equation derived from a statement of the
conservation of mass or species, forms the basis for the ROADWAY
computational system. This equation is one of three partial
differential equations used to describe distributed parameter
systems otherwise known as fields.
The conservation of species equation (i.e., a diffusion
equation), is used to predict pollutant concentration fields near
highways. The finite-difference method used in ROADWAY
represents the time-space continuum by a set of discretely spaced
points; the grid produced by these points is not evenly spaced
upon the field in ROADWAY since higher resolution is needed near
the road and lesser away from it. An algebraic equation
approximating the partial differential equation is derived for
each grid point. The solution is found by solving these
equations for all points in the grid after applying boundary
conditions and initial values to the field. Since ROADWAY is a
numerical model it has none of the limitations of Gaussian
solutions to the diffusion equation. That is,
ROADWAY is a multilayer model which considers vertical
variation of both wind and diffusivity,
it treats calm or light wind conditions, and
optionally computes chemical reactions of source
pollutant species.
As mentioned previously, ROADWAY requires a reduced
meteorological input data set. Realistic wind and turbulence
profiles can be calculated using surface layer similarity theory
as evidenced by a verification study using the GM data set
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(Eskridge and Binkowski, 1979). The model was developed on
theoretical grounds and using wind tunnel experiments and is
independent of tracer studies. It, nevertheless, performs as
well as the most accurate highway models today. Up to ten
traffic lanes can be simulated. The model can provide
intermediate output and, at the expense of accuracy, has features
to reduce execution costs.
Since the algorithms of ROADWAY are solved by a computer, the
calculations are subject to truncation and roundoff errors. In
the context of numerical analysis, truncation errors ' occur in
approximating infinite series by a finite number of terms.
Roundoff errors, on the other hand, are machine-dependent and
occur because computations are done on the precision of a
computer which introduces errors by the dropping off of digits.
Another source of error is that related to computational
instability. In solving the conservation of species equation,
both the time and space variables must be discretized by means of
finite-difference expansions. A small error made at one time
step of the calculation can result in a larger error at a later
time resulting in unbounded error growth. A segment of the
ROADWAY code tests conditions to ensure that calculations remain
s table-.
A mode"! limitation is that the vehicle speed must be much
greater than the ambient wind speed. Considering usual freeway
speeds and meteorological scenarios where significant pollutant
impacts would occur, this may not be a limitation. More
importantly, the model is valid for all vehicle speeds when winds
are light which is when Gaussian approaches breakdown. ROADWAY
does not consider wind meander; this becomes important when the
mean wind is nearly parallel to the highway. The use of ROADWAY
is restricted to the very near field -- within two hundred meters
of the roadway, beyond two hundred meters meteorological
processes that are not accounted for in the model become
impo r tant.
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Another limitation is costs related to computer execution.
Being a numerical model, ROADWAY is relatively expensive to run
when compared to Gaussian-based models. Execution time using the
chemistry option is on the order of 10 CPU minutes on a DEC
VAX-11/780. ROADWAY implementation on a personal computer is
entirely possible and execution costs in this environment would
be much less.
Due to its applicability in only the near field and because
of execution expense, ROADWAY is recommended for use in
conjunction with a Gaussian model such as 'HIWAY-2 (Petersen,
1980; Rao and Keenan, 1980).
10
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SECTION 4
BASIS FOR ROADWAY
This section gives a brief narrative highlighting important
aspects of the modeling approach. A detailed technical
description of the various algorithms that accomplish the
simulation is presented in Section 5.
NUMERICAL APPROACH
Three fundamental partial differential equations serve as the
mathematical model for virtually all problems of applied
physics. One of these is the conservation of mass or diffusion
equation which serves as the basis of the ROADWAY computational
system. A statement of the conservation of mass, this equation
is generically given as,
|£ = V-KV.P (1)
o t
where P is a scalar field and K is determined by the parameters
of the system. Where the medium is itself in motion, the equation
becomes
11 = -V'VP + V'KVP (2)
a t
which, in its modified form, is u-sed to predict pollutant
concentrations near a highway. In the Eulerian (or fixed)
coordinate system, the equation is,
3 C/ 3t = -V'VC + V'KVC + S, (3)
advection diffusion source/sink
term term term
where C represents concentration of a given pollutant species, V
is the wind vector, and K the three-dimensional eddy
11
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diffusivity. Eq. 3 is, therefore, a statement of the
conservation of species.
The finite-difference method used in ROADWAY represents the
time-space continuum by a set of discretely spaced points. The
grid produced by these points is not evenly spaced upon the field
since higher resolution is needed near the road and lesser away
from it. An algebraic equation approximating the partial
differential equation is derived for each grid point; the
solution is found by solving all these equations for all points
in the grid after applying boundary conditions and initial values
to the field. Four grid points define a. box, and the pollutant
mass within each box depends upon the advection of pollutant into
and out of the box (advection term), the diffusion of pollutant
mass through the sides of the box (diffusion term), and any
sources or sinks of effluent within the box (source/sink term).
In ROADWAY, vehicle exhaust is a source of effluent, while
chemical reactions act as both source and sink for certain
pollutant species.
Automobile exaust gases contain nitrogen dioxide which in the
presence of sunlight undergoes a chemical change forming ozone
and nitrous oxide. Simultaneously, reverse reactions take place
tending to convert the NO back to N00. The rate at which the
Lt
N02> NO, and 03 constituents form and dissipate are approximated
by the three partial differential equations. Therefore, to
simulate the system, the transport and diffusion of the three
constituents has to be represented by three coupled, simultaneous
diffusion equations.
In the numerical treatment of systems of partial differential
^equations, four unavoidable sources of error are encountered.
These are modeling errors, measurement errors, truncation errors,
and roundoff errors. Of these, the last two concern the
numerical analyst/meteorologist. Truncation errors are due to
the finite representation of what are otherwise infinite series.
Roundoff errors occur because calculations are made with the
12
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available precision of a computer whose internal representation
of numeric data fields cannot accommodate all the digits of a
calculation. Somewhat related to these is still another source
of error which is known as computational instability. In solving
the ROADWAY conservation of species equation, both the time and
space variables must be discretized by means of finite-difference
expansions. Unless the time interval d is sufficiently small
compared to the net spacing h and z, computational instability
can result (i.e., a small error at time t can propagate with each
successive calculation so that at future times unbounded error
growth occurs). Other ROADWAY errors relate to assumptions of
initial and boundary conditions and to uncertainties in the input
parameters.
SIMILARITY THEORY
The ROADWAY computational system uses the theory of surface
layer similarity to produce wind and turbulence profiles from
temperature at two levels and wind observed just upwind of the
highway. From the initial assumption of a horizontally
homogeneous atmosphere, similarity theory predicts the wind and
turbulence profiles from the friction velocity and Monin-Obukhov
length. These profiles comprise the basic-state atmosphere upon
which the vehicle wake effects are added. The reader is referred
to Busch (1973) for a review of surface layer similarity theory.
VEHICLE WAKE THEORY
Early attempts to predict pollutant concentration adjacent to
highways via line source algorithms yielded unsatisfactory
results because traffic-induced turbulence was not considered or
was poorly represented. A unique aspect of ROADWAY is its
treatment of vehicle wake effects. The theory was originally
developed by Eskridge and Hunt (1979) and modified by Eskridge
and Thompson (1982) and Eskridge and Rao (1983, 1986).
Vehicle wake theory predicts that turbulent mixing and hence
pollutant concentration near the highway are dependent on vehicle
13
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speeds. Vehicle wake turbulence is greatest over the highway and
decreases rapidly with increasing downwind distance and
increasing height above the highway. The theory finds that these
effects are more important during stable atmospheric conditions
than during neutral and unstable conditions.
14
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SECTION 5
TECHNICAL DESCRIPTION
In the prior section a brief description of the algorithm and
method was given to acquaint the reader with generic aspects of
the model. Presented here is the mathematical formulation of the
physical processes taking place near the road and their
simulation by the algorithms of ROADWAY. Equations are shown in
their final form for brevity, but references are given for those
readers interested in details of the derivations.
CONSERVATION OF SPECIES EQUATION
The conservation of species equation,' a modified form of the
diffusion equation, is expressed as follows
3C/3t + V-CV = V-KVC + E + R, (4)
whe-re V is the divergence operator in x and z coordinates, E is
an emission source term, X is the eddy diffusion coefficient, C
is a chemical species, and R is a corresponding set of chemical
reac t i ons .
One of the main assumptions made in the model is that a
reference atmosphere describable by surface layer similarity
theory exists and that upon this reference atmosphere the
perturbations due to the vehicles can be added. I.e.,
K = KS(z) + KW(x,z)
XX X
and (5)
K = KS(z) + KW(x,z),
2 Z Z
S W
where K. and K. are eddy diffusion coefficients from similarity
and wake theories, respectively. Likewise, the wake velocity
deficit is added to the wind field described by similarity theory
15
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to yield the total wind field.
The equation of continuity for an incompressible fluid,
V'Y = 0, is used to yield w, the vertical velocity, which is non
zero along the road in the presence of vehicle wakes. Because
there is no time dependence in this equation, the numeric
calculation is stable.
THE BOUNDARY CONDITIONS
The problem of imposing boundary conditions is always
difficult in atmospheric modeling, especially when the scale of
the problem is small. In this model, it is assumed that the
gradient at the surface is zero, i.e.,
3C/3z = 0 at z = 0, (6 )
which implies no losses at the surface. At the side boundaries
the following conditions are imposed:
3C/3x =0 at the outflow boundary
and (7)
C = background at the inflow boundary.
At the top boundary it is assumed that the concentration is at
background levels, i.e.,
C = background at z = z (8)
max
These boundary conditions are not perfect physical
constraints as they are imposed primarily for mathematical
reasons. It has been found in numerical experiments that the
model results are more sensitive to the height of the modeling
region than to any other boundary condition. Therefore, when
winds are light or nearly parallel to the roadway, the height of
the integration region is raised from 20 to 70 m.
16
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THE GRID
The finite-differencing scheme used by the model represents
the time/space continuum by a set of discretely spaced points.
The grid produced by these points is not evenly spaced upon the
field in ROADWAY since higher resolution is needed near the road
and lesser farther away. The numerical scheme of Steven Zalesak
(described in the Appendix of Eskridge et al., 1979) allows this
variable grid spacing in the horizontal and vertical directions.
The grid also varies according to the wind speed and direction
and the number of highway lanes. Table 1 summarizes how the grid
is set; (one should note the time assumed to reach steady-state
conditions and that u is the component of the wind perpendicular
to the road).
TABLE 1. ALGORITHM USED TO SET GRID DIMENSIONS AND THE
STEADY-STATE TIME PERIOD
Horizontal scale
Road-wind angle:
> 10°
<_ 10°
Vertical scale
Dimens ions :
scale begins 20 m upwind of -first lane;
scale ends 30 m downwind of last lane
scale begins 25 m upwind of first lane;
scale ends 25 m downwind of last lane
u (m/sec):
u < 0. 1
0.1 £ u < 0.5
u 2. 0.5
Steady-state time period
Dimens ions:
scale begins at 1 m; scale ends at 70 m
scale begins at 1 m; scale ends at 50 m
scale begins at 1 m; scale ends at 20 m
u (m/sec):
u < 0. 1
0.1 <_ u < 0.5
u > 0 . 5
Time to reach steady-state conditions
900 sec
600 sec
300 sec
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An algebraic equation approximating the partial differential
equation is derived for each grid point. The solution is found
by solving all these equations for all points in the grid after
applying boundary conditions and initial values to the field.
THE NUMERICAL SCHEME
Eq. 4 can be written in operator form as
3C/3t + B^ » B2C + B3C + B4C = E + R (9)
where B,, B0, B., , and B. are linear operators representing
1 2t o 4
9u( )/3x, 3w( )/3x, -(3/3x)K3( )/3 x, and -(3/3z)K 3( )/3z,
X Z
respectively. Eq. 9 can be approximated by
4
(Cn,+ 1 - Cn)/At + I L (C) = E., + R . (10)
ik ik , m ik ik ik
m= 1
where L (m = 1 4) are approximations of B using x = iA x,
m m
z = kAz - 0.5z, and t = nAt. Eq. 10 is solved by a fractional
step method (Marchuk, 1975). The procedure is as follows:
C1 = Cn + AtL^C11), (11)
C2 = C1 + AtL.-iC1) , (12)
Lt
C3 = C2 + AtL,(C2), (13)
3
C4 = C3 + AtL4(C3), and (14)
Cn+1 = C4 + At(E.k + R.k). (15)
I 4
If C ,...,C are eliminated, the system reduces to an equation of
the form
rn+^ - rn + At YT rn + At ( v +n 1 + ( Atl^f 1
\j -"w ^ ut/i^v ^ utlii..^!!..^ ^ \ia»^ V««»y
^ m i k ik
m -i- higher order terms. (16)
The operators L_ and L are approximations centered in space,
o 4
while the operators L and L , which solve the advection terms,
-L Li
are based on the flux-corrected algorithm of Zalesak which is an
upstream algorithm that ensures nonnegative values for the
18
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concentration at every grid point. As shown by Eskridge et al.
(I979b), this scheme reduces numerical diffusion and is stable
for
At < 0 . 5 Ax/ u
max
(17)
THE BASIC-STATE ATMOSPHERE
The basic-state for upwind atmospheric conditions are
determined by surface layer similarity theory which requires the
specification of the vertical temperature gradient and the wind
velocity. From this information, vertical profiles of u, v, K ,
X
and
theory.
K_ are generated. Binkowski (1979) gives details on the
z
The wind profiles used in the model are obtained from
similarity theory in the following manner. Since the Obukhov
length L is very difficult to measure directly, the bulk
Richardson number is used as a stability parameter
(18)
h h
where g is the acceleration due to gravity, h the height of the
wind observation, U the wind speed at height h, 9 the potential
temperature at h, and A0 the difference in potential temperature
between two tower points. The temperature difference is taken
over the height increment (h-z ), where the height z of the
lower instrument is assumed to be small enough relative to h so
that A9 is representative of a temperature difference over the
entire distance h. The Obukhov length L may be expressed as
hG(h)
F2 (h)R
(19)
where
F(h)
(20)
19
-------
Q(n) - Inl I + 0111 . (21)
n s u / T '\ _ i _ J r / -W 2 i i \ f -v J. 1 \ " / r r v" ^ i ~\ ( v _L 1 ^ ^ -i 1
P(h/L) = IntllXg + l)(Xfl + 1) /L(X + 1)IX + 1) J;
_i -i (22)
+ 2[tan X-tan X_],
where
X = (l-16h/L)4, XQ = (l-16z0/L)4 '(23)
for L < 0 (unstable),
P(h/L) = 5(h-z )/L for L>0(stable), (24)
Q(h/L) = 2 ln[(Y1 + 1)/(Y + 1)1, (25>
9 1
Y = X , Y = (l-16z]L/L)2 for L < 0 (unstable),
Q(h/L) = 5(h-z1)/L forL>0 (stable). (26)
Given a value of R,, Eq. (19) is solved by an iterative
process to return a value of L. The present method has an error
in reproducing a given L of at most 0.08% in the range -4
-------
where
G0 = k[ln(zl/Z0) + Q(z1/L)l , (30)
Qh1) = 2 ln[(YQ + 1)/(Y1+ 1)],
YQ = XA for L < 0, C31)
L
(32)
Once U^i T ^, and T are obtained, the profiles of u and T are
available from
u = u^FCz), (33)
T = TQ + T^GU) , (34)
where z replaces h, andz replaces z everywhere in
Eqs. (20)-(26).
The eddy diffusivity for vertical turbulent transfer of a
passive scalar is written
Kz = CiawX, - (35)
where X is a length scale and c a constant determined as
follows. For steady, neutral flow in the surface layer,
K = kzu*. (36)
Z
It follows from (35) and (36) that
kzu*
ci = 7TT- (37)
1 awX
and under neutral conditions
a /u# = 1. 28, zX =0.4,
hence c = 0.125. For simplicity, this neutral value will be
used in all the following calculations. The following
approximation is used for the surface layer
21
-------
w
u*
(38)
where = 1 + 5z/L
m
The length scale X in the surface layer is
X = zf
m
(39)
where f . the nondimensional frequency at which the maximum power
m
occurs in the w spectrum, is given by the empirical expression
m
0.4[0.4 + 0.6 exp(4z/L)], z/L <0
0.4[1.0 + 3.39z/L-0.25(z/L)2], 0 < z/L < 2.0
0.04 [6. 78 + 2.39(z/L-2.0). ] , z/L>2
(40)
which is based on the results of Kaimal (1973).
Estimating KS is much more difficult and is important only
when the winds have a large component parallel to the roadway.
It is assumed in this model that
rs
L
X
a cos9 + a sin9| . ,A X, z/L 2 0
u v ' z = 0 . 5Az
a cos9 + a sin9| ... X, z/L< 0
u v I z = 0 . 5Az
(41)
where 9 is the wind direction and where a and a are given by
u v a J
u
RlV
(42)
where
Rl = (3<2fm
R0 = 3 . 2f a
2 m w
1.4z/L,
(43)
(44)
The above formulation does not include the cross correlation
terms.
-------
VEHICLE WAKE THEORY
The vehicle wake theory was developed by Eskridge and Hunt
(1979) and modifications were made based upon wind tunnel
experiments by Eskridge and Thompson (1982) and Eskridge and Rao
(1983, 1986). All known constants in the wake theory are now
based upon wind tunnel measurements. A brief description of
those studies is given next.
Single Vehicle Wake
The wake velocity deficit of a-single vehicle is given by
UD = QA(-s)~°'75f(n/Ks),-z/l (s)), (45)
where
~s~ = s/h; "z= z/(yAh); n~= n/(XyAw );
h is the height of the vehicle; Q is the wind speed relative to
the vehicle; A is the strength of the wake determined by the
overturning moment acting on the vehicle; y and A are constants
with experimentally-determined (wind tunnel) values of 0.95 and
1.14, respectively; s is the coordinate along the centerline of
the wake; n is the coordinate in the horizontal plane
perpendicular to s; z is the vertical coordinate; l(s) is the
vertical scale length of the wake; and w is the width of the
vehicle. A and l(s) are given by
and
A4 = CJ(32TT/e~Ay'3) (46)
d
l(a) = yAhfs)174, (47)
where C , is the drag coefficient and the other variables are
given above. Figure 1 shows the coordinate system used in the
model.
The function f in Eq. 45 is the solution to a partial
differential equation which does not have a closed form solution
(Eskridge and Thompson, 1982). However, the equation is
separable as follows,
23
-------
Figure 1. Coordinate system used in the model
n,s,z pertain
to the vehicle wake; x,y,z are fi*ed coordinates
in the usual cartesian sense.
24
-------
f(n/i(s),zYl(s)) = Y(n/l(s))T(z/l(s)), (48)
where
Y(n/l(s)) = C exp(-n2/'(8' I2(s) ) .
T(z7l(s) was found by fitting a polynomial to wind tunnel
measurements of velocity deficit given by
T(z/l(s)) H T(C) = b0 + bi^ + " + be^5' (49)
where the coefficients b ,...,bfi are listed in Table 2.
The turbulent kinetic energy terms are given by
(u1 2,v' 2,w'2) = (a, ,a,,a )A2Q2s"1<2F (X,o>) (50)
j. 4 *i c
where
X = n/(wds°'4), u = z/(hs0'4),
and u and v are oriented in the s and n directions, respectively.
The constants a , a , and a were evaluated from wind tunnel data
J. Lt o
and were found to be 0.048, 0.040, and 0.030, respectively. The
function F was determined by a least-squares orthogonal
c
polynomial fit to wind tunnel data and is given by
F0(X,») = I I *2m,n""x2m, <»D
n=0 m=0
and subject to the restriction that F > 0.0. The constants in
c
Eq. 51 are listed on the right side of Table 2.
25
-------
TABLE 2. CONSTANTS FOR THE POLYNOMIAL FITS IN EQS. 47 AND 49
Equa t i on 4 7
Coef f .
b-
0
b,
1
DO
2
b_
3
b4
b.
5
b.
6
Va 1 ue
0.0179349
2. 5765870
-2 . 3062584
0.8951468
-0.1758604
0.0169970
-0.0006404
Coef f .
j,
0
0
]h
0
\b
0
0
1
2
3
^04
!h
2
2
2
2
0
1
2
3
Equa t
Va
0.
0.
-0 .
0.
-0.
-0.
-0.
-0.
0.
-0.
i on
49
1 ue
35
12
47
67
35
18
93
18
56
39
1
5
9
3
7
9
4
2
1
9
123
530
624
252
246
058
550
142
791
537
7
8
1
3
6
1
7
7
1
3
X
X
X
X
X
X
X
X
X
1
1
1
1
1
1
1
1
1
o'1
o2
o ^
2
0
2
0
o1
o
o3
24
4*
4
4
\|;
4
ijj
4
ill
0
1
2
3
0.
-0.
0.
-0.
0.
264
94
10
23
15
946
3406
3483
4
1
815
043
5
8
0
3
7
X
X
X
X
1
1
1
1
2
0
4
0
o4
o4
44
The observed wind velocity fluctuation at some fixed point
near a roadway are due to three distinct causes. Velocity
fluctuations are produced by vehicle wake turbulence as described
by Eq. 50 and they are also due to ambient turbulence.
Fluctuations also occur because of the time variation in the wind
velocity as the vehicle wake passes a fixed point. This
wake-passing effect is clearly not turbulence, but is an artifact
of the fact that the data are taken in the Eulerian rather than
the Lagrangian frame of reference.
Let the superscripts p and w and the subscript <» represent
the wake-passing effect, the wake turbulence, and the ambient
turbulence, respectively. The total velocity variance is
26
-------
assumed, as a first approximation, to be determined by adding the
components, so that
W
2 2 2 2
u1 = u' + u1 -»- u1 , (52)
oo
with similar expressions for v'^ and w'^ . Eq. 52 assumes there
are no interactions between the various scales of turbulence.
The total velocity variance energy is defined by
a2 = (u'2 + v'2 + w'2)/2, (53)
with similar definitions for the ambient, wake, and wake-passing
velocity variances. It should be noted that while the
wake-passing turbulence can be very large, it is nondiffusive,
and one is interested in it only as a feature of the vehicle wake
theory and in the analysis of roadway data. During the normal
execution of the ROADWAY model, the wake-passing effects are not
calculated.
Multi-vehicle Velocity and Turbulence Fields
The equations describing multi-vehicle wind velocity,
turbulence, and wake-passing effect are presented below. The
derivations for these equations are given in Eskridge and Rao
(1983) .
The horizontal wind velocity components are computed by
N i-TV /2
u(xQlt) = U^Cz^t) - l/TVh IJ UD_(x0,y/Vh)sin« dy
~ J-llvh'^J~
and (54)
N fTV /2
v(x0,t) = Voo(z(),t) - l/TVh I J h UD (x0,y/Vh)cosa dy
j=l -TVh/2 J ~
where Vh is the average vehicle speed, XQ = (xQ,y0,z0), UD is
~ J
given by Eq. 45, N is the number of vehicles passing the point XQ
during the time interval (-T/2,T/2), a is the angle between the
relative wind Q and the highway, and U^tzjt) and V00(z,t) are
upwind ambient conditi'ons.
27
-------
The turbulent kinetic energy component along the x-axis is
given by
N
u"(x0,t) = l/TVh I } " u'^(x0,y/Vh) dy,
-TVh/2 ~ (55)
where u1^ is defined by Eq. 50 and similar expressions are found
for v ' ^ and w1 2 .
The velocity variance due to wake-passing is given by
- N rjiy I 2 _
u'2(x ,t)= I/TV I \ h [U.(xn,y/V. )sina - u(xn,t)]2 dy
~ i = l -TV. /2 J ~ ~
J n
and (56)
_ N TVh/2 _
V2(x0,t) = l/TVh if [U.(x0,y/Vh)cos a - v ( x Q , t ) ] 2 dy,
j=l rvh
where U. = |U ,V I - un Eqs . 54, 55, and 56 are integrated
j loo'ool \
using Simpson's method.
CHEMICAL REACTIONS
An automobile exhaust emits nitrogen dioxide ( NO ) as a
&
function of time. With sunlight, the NO- undergoes a chemical
L
change forming ozone (0 ) and nitrous oxide (NO).
O
Simultaneously, reverse reactions take place tending to convert
the NO back to NO . The basic reactions are:
Lt
kl
N0 + hv - ^> NO + 0
0 *-> 0
(57)
NO + 0. - -> NO
O- Ui
k4
NO + XO > NO + X
61
0. + X - a-> XO
Where XO represent organic radical reactants. The rate at which
the NO , NO, and 0- constituents form
I* O
by three partial differential equations
the NO , NO, and 0- constituents form and dissipate is expressed
I* O
28
-------
3(NO
-k.(N0) + k(0)(NO) + k.(NO)(XO)
~ .0 ,, .
o t 12 3 o 4
a, = k,(NO_) - k,(0.)(NO) - k.(NO.)(XO) (58)
at 1 L O O 4
T-p = k,(0) - k,(0.)(NO) - k,(0,)(X)
o I Z 0 O Do
Where k1, k , k , k,, and kc are chemical reaction rate
1 L O * b
constants. These equations show that the rate of change of N0_,
for example, at any point depends upon its own concentration and
those of NO, 0 , and the organic radical s. (Note that the 0 and
o o
M concentrations have been absorbed in the k rate constant).
Therefore, to simulate the system, the diffusion of the three
principal constituents must be represented by three coupled,
simultaneous diffusion equations with mass transfer.
ROADWAY assumes that the physical processes of interest occur
within approximately 200 m of the highway. For this length scale
and reasonable crosswind velocities, the length of time the
vehicle emissions are close to the road limits the applicable
chemistry. Because of this, it is-assumed that the following
reactions are the only important ones near the highway:
NO + 0_ ±-> N0_ (59)
O £ '
and
NO,, k2 > NO + 00. (60)
k^ and k2 are chemical reaction rate constants with values of
22.0 ppm'imin'1 and 0.46 min"1. The value for kg is a m-id-day
value; k2 varies diurnally (Note that 02 concentration has been
absorbed in the k2 rate constant). These reactions lead to the
following conservation of species equations:
29
-------
3A/3t + V-AV = V-KVA + EA - k1DA + k2C, (6l)
(62)
(63)
3C/3t + V-CV = V-KVC + En + kDA - k.C,
\j i . £
and
3D/3t + V-DV = V'KVD + En - knDA + k0C,
U JL &
where A, C, and D represent the concentration of NO, N02 , and O, ,
respectively; vehicle emissions are in units of g/km*veh.
30
-------
SECTION 6
EXAMPLE PROBLEM
This section presents a hypothetical problem to illustrate
the use of ROADWAY and the type of information provided by the
model. Details concerning input and output for this example are
given in Section 11 after the reader has become familiar with the
preparation of model inputs.
The geometry of the example problem is depicted in Figure 2
which also includes the required highway information. The area
upwind of the highway can be described as flat with medium to
long grass with a representative roughness length of 0.5 m. The
pertinent meteorological and air quality measurements just upwind
of the highway are as follows:
274.22 K at a height of 1.22 meters,
274.33 K at a height of 4.24 meters,
due westerly winds at 0.94 m/sec (measured at the same
height as the upper temperature instrument), and
* background NO, NO^, 0,, and CO concentrations of
0.052 ppm, 0.25 ppm, 0.10 ppm, and 40.0 ppm
respect ive1y.
All measurements represent hourly averages.
The horizontal wind fields are shown in Figure 3. The
vertical velocity field, also provided by ROADWAY, is not shown.
The u field is fairly uniform except for the expected increase of
speed with height. The v field shows, as expected, that the
southbound lanes contribute a southerly component to the wind
(negative sign); while the northbound lanes result in a northerly
component (positive sign). It should be noted that the traffic
influence decreases with height and distance downwind of the
31
-------
N
t
1
\ }
r
,
t
1
i
Wind
i
c
(
|
,
|
(
J
rrn
jj
i i
'i
ft
V:'
t
ii
1!
\^1
! D
LijlJ
« -I
kHIHfl '
1
(Vv. .. ;. .j
P '.- .-*
"' ' ' 1
'-"'... '
I''' ' ' '"..'
i '.
'*'' '
' ' ' ' :" . ./ .
!:.. .
! f .
.;... y ; .'.
- 1
1 .
r .
i ' ' . * - '
:,' . ' "
r< ' .. i
1.-
;";"" . '-.-.
r.;
.'.'
0- -i
f
I
f
B
IL
|
h-
L
-*-a4m »
r T Tl
l
I
^^nH
I'M
I M
1 ujj
ft]
^^^
1
'
I
i
i
i
i
i
1
I
.
Highway Data
Volume (veh/hr) 1366 1366 1366
Speed (km/hr 80 80 80
NO (g/km veh) 2.7 2.7 27
CO
(g/km veh) 90 90 90
NO2(g/km veh) 3.0 3.0 30
1366
80
2.7
90
3.0
Figure 2. Geometry of the example problem.
32
-------
15
Height
(m)
2.0
1.0
20 30 40
Downwind distance (m)
u(m/sec)
50 60
70
15
Height 10
(m)
v (m/sec)
10
20 30 40
Downwind distance (m)
50
70
Figure 3. u and v wind fields for the example problem.
33
-------
hi ghway.
The diffusivity fields are given in Figure 4. Vehicle wakes
associated with the traffic contribute significantly to both the
K and K ' fields. The wake turbulence decreases with height and
distance downwind of the highway.
The pollutant fields are provided in Figure 5. Because the
chemistry option was exercised, the four concentration fields are
given on output. Concentrations of the pollutants except 03 are
highest in the vicinity of the traffic lanes and decrease with a
skewed pattern in the downwind direction. The 0 concentrations,
O
on the other hand, are lowest near the highway since chemical
reactions are such that vehicle emissions combine to act as sinks
for 0 decreasing upward to the background value given by the
O
user in the input stream.
34
-------
10
20 30 40
Downwind distance (m)
15
Kz (mysec)
10
bo
as.
10
20 30 40 50
Downwind distance (m)
60
70
Figure 4. Turbulence fields for the example problem.
35
-------
15
NO(ppm)
S 10
JS
rt
93
0.25
0.50
20 30 40
Downwind distance (m)
50
60
70
15-
C O(ppm)
10
&
bfl
S3 5
10
20 30 40
Downwind distance (m)
50
Figure 5 .
60
70
Pollutant concentration field for
prob1 em.
the example
36
-------
Si
bfl
pH
o
a:
10
10
20 30 40
Downwind distance (m)
20 30 40
Downwind distance (m)
Figure 5. continued
50
70
37
-------
SECTION 7
MODEL EVALUATION
BACKGROUND
Rao et al . (1980) evaluated four Gaussian models (GM, HIWAY,
AIRPOL-4, and CALINE2) and three numerical models (DANARD,
MROAD 2, and ROADS) using tracer data from the General Motors
Sulfate Dispersion Experiment (Cadle et al., 1976). In general,
the numerical models as a group performed rather poorly compared
to the Gaussian models. Although the GM model (Chock, 1978)
performed best, it had a tendency to underpredict . For this
reason, it was found inappropriate for decision-making where
worst-case results are desirable to ensure compliance with the
standards. For regulatory applications, it was concluded that
the HIWAY model (Zimmerman and Thompson, 1975) was the most
useful since it had the highest percentage of overprediction in
most of the statistical tests considered.
Based on recent studies that quantified traffic-induced
turbulence and its influence on pollutant dispersion in the near
field, Rao and Keenan (1980) modified the Pasqui11-Gifford
diffusion curves used by HIWAY. They also added an aerodynamic
drag factor to handle dispersion under near-calm conditions.
With these refinements, model performance was improved
significantly giving results comparable to those of GM. Although
predictions are significantly improved in the new HIWAY model
(renamed HIWAY-2), a slight tendency to overpredict still
remains. This makes HIWAY-2 appropriate for screening regulatory
applicat ions.
Recently, Rao et al. (1985) have evaluated ROADWAY along with
HIWAY-2 and CALINE3 using statistical techniques suggested by Fox
38
-------
(1981) and Willmott (1982), extreme value statistics (Tabony,
1983), and the "bootstrap" method (Diaconis and Efron, 1983).
CALINE3 is based on the Gaussian equation and employs a mixing
zone concept to characterize diffusion over the road. Some of
the results of the evaluation are discussed here. A reprint of
the journal article describing the study is given in Appendix B.
This study used the SFg data taken in the GM Sulfate Dispersion
experiment for the model evaluations.
EVALUATION RESULTS
The paired statistical test parameters are given in Table 3.
HIWAY-2, ROADWAY, and CALINE3 explain respectively 70-, 65-, and
29-percent of the variance. The slopes of the regression lines
are close to 1.0 and the intercepts are small for all three
models. The index of agreement is a measure of the degree to
which model predictions are free from error. It shows that the
performance of ROADWAY and HIWAY-2 is similar and that both
predict considerably better than CALINE3. The mean difference
and mean fractional error, which are measures of overall model
bias, indicate that both ROADWAY and HIWAY-2 overpredict, while
CALINE3 has a slight tendency toward underprediction. One of the
better overall measures of model performance is the root mean
square error (RMSE). As shown in Table 3, the RMSE values for
the three models indicate that HIWAY-2 performs slightly better
than ROADWAY and both are considerably better than CALINE3. It
should be noted also that most of the error associated with the
three models is not systematic (i.e., MSES approach zero). This
indicates that the models are performing as well as possible
without major algorithm modification. figure 6 illustrates the
relative performance of the three models relating them to
observed data.
39
-------
TABLE 3. COMPARISON OF MODEL RESULTS USING THE GM DATA SET
Stat1st ic
Obse rved
HIWAY-2
CALINE3
ROADWAY
N
range
mean
s
r ^
s lope
, b
5
0.01
0
0
94
-4.92 0
. 96
. 74
intercept , a
D
d
MFE
RMSE
MSEU
MSES
MSE
N =
s =
r2 =
D =
d =
s amp 1 e si
s t andard
correlati
squared
index of
mean diff
ze
devi
a t i on
5
.01
1
0
0
0
0
0
0
-0
0
0
0
0
on coefficient
agreement
94
-4.68
.07
. 77
.70
.87
.23
. 91
.11
.12
.44
.18
.02
. 20
MFE
RMSE
MSE
MSEU
MSES
5
0.09
0
1
0
0
0
0
0
0
1
1
0
1
= mean f
94
-
.
.
t
.
.
.
9
i
.
r
17.97 0
96
31
29
96
04
64
00
04
11
22
00
22
ac t i ona 1
= root mean squar
= mean square err
= unsyst
emat i c MS
= sy sterna
tic MSE
5
.02
1
0
0
1
0
0
0
-0
0
0
0
0
er
e e
or
E
94
-5
. 2
.9
. 6
.'0
.2
. 8
.2
. 2
.6
. 2
.29
0
2
5
0
5
6
5
1
0
9
.06
.3
ro
5
r
r r o r
erence
For the following equations, P = predicted, M = measured, and
P. = a
i
bM. .
i
N
N
d = (1/N)Z(P. - M.) = (l/N)Zd. = P - M
D = 1
rN
- [£
(,
N
MFE = (/2/N)Z(M. - P. )//(M.
P. )
1
RMSE =
N
./2
N -
MSE = (1/N)Z(P. - P.)
u i i
N ~
MSE = (1/N)Z(P. - M.)
s i i
MSE = RMSE'
40
-------
CUMULATIVE
PROBABILITY
fX i X2J
3.0
SECOND HIGHEST CONCENTRATION
Figure 6. Comparative performance of highway models
41
-------
SECTION 8
COMPUTER ASPECTS OF THE MODEL
This section discusses ROADWAY from a system design and
programming perspective to give the reader a general view of the
computational system. The overall structure of the program, a
brief description of each subprogram, and the general processing
flow are given next.
STRUCTURE OF ROADWAY
ROADWAY consists of a main routine, 19 subroutines, and 8
functions as shown in Figure 7. All input data are read and
screened in subroutine READER. Output is provided by several
subroutines: ECHO prints the input data; the downwind grid points
and traffic lane locations are output in subroutine CENTER; tlie
velocity, turbulence, and concentration fields are all printed by
subroutine GRAPH. A brief description of the main program,
subroutines, and functions follows.
PROGRAM MODULES
Main -- The mainline program begins with introductory comments
including the program abstract, authorship, program
structure, and input/output units. After these
introductory comments, the program performs the
following tasks by subroutine call: read and echo input
data, initialize arrays, determine ambient atmospheric
conditions using similarity theory, initialize x-z grid
system, compute and add vehicle wake effects to the
turbulence fields, advect and diffuse the pollutants,
and write the results.
42
-------
ROADWAY
ZEiO
READER
ECHO
S.LAYR
UVCMP
MOVE
WHEREX
CENT6R
WAKE
NONDIV
G«Ar>H
ADVCHM
RIBST
RIBTOZ
GETSFC
PROFIL
TURBC
*
*
*
*
FILLIT
* Entry points in subroutine RI BULK
x Function col Is
FC
POLY
SIMPSN
TIMING
BNDRYC
ADU
BMOVE
ANTU
ADW
ANTW
DIFFX
DIFFZ
GRAPH
x
X
X
X
Figure 7. Structure of ROADWAY computational system,
43
-------
While error messages are printed from pertinent code
segments, control of program execution including
program termination occurs exclusively in the main
rout ine.
READER -- This module is called by the main routine and reads all
input data from FORTRAN unit 5. The data is screened
to detect gross errors. If an error is detected, then
a nonzero value is assigned to variable IERR, an error
message is printed, and control is returned to the main
routine. Input data is shared with the main and
subroutines via labeled common INCOM.
ECHO
ZERO
Called by the main program, this subroutine echoes the
input data. The data is passed to this module by
labeled common (INCOM).
Subroutine called by the main program to perform
initialization of arrays.
SBLAYR -- This module is called by the main routine and is the
driver for the surface layer model which uses
similarity theory to obtain surface boundary layer
parameters. It calculates the velocity profiles,
turbulence profiles, and the eddy diffusion
coef fie lents.
UVCMP -- Called by the main program, this subroutine converts
wind velocity into its u and v components.
MOVE -- Module called by the main routine to initialize the
grid in the x direction.
WHEREX -- This subroutine is called by the main program to
calculate the number and spacing of grid points in the
x direction. It also builds the arrays containing
emissions at each lane location.
CENTER -- This module determines the center of each traffic
lane. The x direction grid points and traffic lane
44
-------
locations are written here. This subroutine is called
by the main program.
WAKE -- Calculates the changes in the wind and turbulence
fields due to the vehicle wakes. It can also calculate
the wake passing effect (Eskridge and Rao, 1983); these
calculations are not normally done, however. WAKE is
called by the main routine.
NONDIV -- Subroutine NONDIV is called by the main program to find
the vertical velocity using the inflow and outflow in
the x direction from the u field and the vertical
inflow through the bottom of the box around each grid
point. The vertical velocity at a grid point is a
linear interpolation of the vertical velocity at the
bottom and top boundaries of the box.
ADVCHM -- Called by the main routine, this module controls the
advective, diffusion, and chemical calculations by
calling pertinent subroutiaes and functions.
RIBULK -- Entry points in this subroutine are called by SBLAYR to
calculate surface quantities such as u , and T.,. using
similarity theory. Entry points RIBST, RIBTOZ, GETSFC,
PROFIL, and TURBC are accessed by subroutine SBLAYR.
FILLIT Called by module WHEREX, it builds grid points in the x
direction using the specified indices and increment.
FC -- This function is called by subroutine WAKE to perform a
2-dimensional fit to wind tunnel data of the turbulent
kinetic energy terms in the y-z plane (Eskridge and
Thompson, 1982).
POLY -- Called by subroutine WAKE, this function calculates the
vertical variation of wake velocity deficit using a
curve fit to wind tunnel data in subroutine FC.
SIMPSN -- This module performs a numerical integration using
Simpson's method. It is called by subroutine WAKE.
45
-------
TIMING -- This subroutine is called by module ADVCHM and finds
the maximum allowable time step for advection and
diffusion to eliminate computational instability. It
also calculates a stable chemical reaction time step.
BNDRYC -- Subroutine called by module ADVCHM to set the boundary
conditions for a pollutant during the marching process.
ADU
BMOVE
ANTU
ADW
ANTW
DIFFX
DIFFZ
GRAPH
This function is called by subroutine ADVCHM to
determine transport in the x direction by an upstream
flux corrected-method.
Called by module ADVCHM, this subroutine initializes an
array passed in the argument list.
This function performs the antidiffusion or flux
delimiter calculation in .the x direction and is called
by subroutine ADVCHM.
This function is called by subroutine ADYCHM to obtain
transport in the z direction using an upstream flux
corrected method. This function is called by
subroutine ADVCHM.
This function performs the antidiffus ion or flux
delimiter calculation in the z direction and is called
by subroutine ADVCHM.
Function called by module ADVCHM to calculate diffusion
in the x direction by centered-in-space differences
making allowances for the unequal spacing of the grid.
Function called by module ADVCHM to calculate diffusion
in the z direction by differences centered-in-space
making allowances for unequal spacing.
This subroutine prints velocity, diffusivity, and
pollutant concentration fields. It is called by both
the main program and subroutine ADVCHM.
46
-------
Figure 8 presents a flow diagram of ROADWAY showing its major
loops and the relationships of the subroutines and functions to
each other .
47
-------
ROADWAY
Read input data (READER)
Echo input data (ECHO)
Initialize arrays (ZERO)
Calculate velocity and turbulence profiles (SBLAYR)
L R1BULK
Calculate pollutant source strengths
Complete grid point and emission arrays (WHEREX)
I FULIT
Determine center of traffic lanes (CENTER)
Calculate wake effects ( WAKE )
P FC
h POLY
I SIMPSN
Add vehicle wake effects to ambient wind
Remove divergence from wind field ( NONDIV )
Write velocity fields (GRAPH)
Add wake turbulence to eddy diffusion coefficients
Write eddy diffusivity f ields ( GRAPH)
Advect and diffuse pollutants (ADVCHM)
Determine advection/ diffusion/chemical time steps ( T I M I NC )
Figure 8. ROADWAY flow diagram,
48
-------
.,_, 1
-
-
EXIT
Loop over time to reach steady-state
Set boundary conditions ( BNDRYC)
Advect pollutants in x direction (ADD)
Set boundary conditions ( BNDRYC)
Remove artificial numerical diffusion ( A NTU )
Set boundary conditions! BNDRYC )
Advect pollutants in z direction ( ADW )
Set boundary conditions ( BNDRYC)
Rem-ove artificial numerical diffusion (ANTW/
Set boundary conditions ( BNDRYC)
Calculate diffusion in the x direction (Dl FFX)
Set boundary conditions ( BNDRYC)
Calculate diffusion in the z direction (DIFFZ)
Set boundary conditions (BNDRYC)
Perform NO, NC^, and O.^ chemistry
r- -*--- Loop over number of chemical time steps
»
H - P-erfom ch-*mkal reaetio-n simulation
|- --- --- Set boundary conditions (ENDRYC)
Print intermediate pollutant fields (GRAPH)
Print final results (GRAPH )
Figure 8. (continued)
49
-------
SECTION 9
INPUT DATA PREPARATION
RECORD INPUT SEQUENCE
There are 11 record types read by ROADWAY; 8 of these are
free format input. While the free format is simple to use, care
should be taken to ensure that variables are given values in the
correct order. Each variable should be separated by a comma and
should conform to the variable name type (i.e., integer or
real). One of the record types is optional, depending on the
options exercised on record type 4. A brief description of each
input parameter is given in Table 4 where correct units are also
displayed. Under the "Format" column in Table 4, FF represents
free format.
TABLE 4. RECORD INPUT SEQUENCE FOR ROADWAY
Record type &
Variable Column Format
Variable description
Record type 1
HEAD1 1-80 20A4
80-character title
Record type 2
HEAD2 1-80 20A4 80-character title
Record type 3
HEADS 1-80 20A4 80-character title
Record type 4
ZO
Zl
FF Surface roughness
FF Height of lower tempera-
ture instrument
(cont inued)
Units
m
m
50
-------
TABLE 4 (continued)
Record type &
Var i abIe
Column Format Variable description
Units
Z2
ICHEM
IANTI
INTPR
Becord type 5
Tl
T2
WSPD
WDIR
RDANGL
FF Height of upper temperature m
and anemometer
FF Chemistry option
0, include NO, CO, NO ,
and 0 chemistry
<>
1, do not include chemistry
FF Antidiffus ion calculation
opt ion
0, do antidiffusion
calculation
1, skip antidiffus ion
calculation
FF Intermediate print option
0, print fields of meteor-
ological variables and
intermediate concen-
tration fields
1, print only final con-
centration fields
FF Temperature at height Zl K
FF Temperature at height Z2 K
FF Hourly average wind speed m/sec
FF Hourly av'erage wind deg
di rec t ion
FF Angle between road and deg
line running north-south.
Counterclockwise is positive,
clockwise is negative and
always less than 90°.
(cont inued)
51
-------
TABLE 4 (continued)
Record type &
Variable Column Format Variable description Units
Record type 6 -- Background concentrations *
BACKGA FF Background concentration ppm
of NO
BACKGB FF Background concentration ppm
of CO
BACKGC FF Background concentration ppm
of NO2
BACKGD FF Background concentration ppm
of 03
Record type 7 -- Highway information
NLANE FF Number of traffic lanes. ---
Maximum of 10; minimum of 4.
Must be in increments of 2.
WIDL FF Width of one lane m
MEDN FF Width of traffic median m
Record type 8 -- Traffic information
NVEH --- FF Number of vehicles per veh.hr
southbound lane in an hour.
NVEH1 FF Number of vehicles per veh.hr
northbound lane in an hour.
VSPD FF Average vehicle speed in km/hr
southbound lanes
VSPD1 FF Average vehicle speed in km/hr
northbound lanes
VWID FF Average width of vehicles m
VHGH FF Average height of vehicles m
Record type 9 -- Emission information t
EMA FF NO emission rate for g/km/veh
southbound lanes
EMB FF CO emission rate for g/km/veh
southbound lanes
52
-------
TABLE 4 (continued)
Record type &
Var iabl e
EMC
EMA1
EMB1
EMC1
Column Format
FF
FF
FF
FF
Variable description
NO emission rate for
U
southbound lanes
NO emission rate for
northbound lanes
CO emission rate for
northbound lanes
N02 emission rate for
Units
g/km/veh
g/ km/ veh
g/ km/ veh
g/ km/ veh
Record type 10
CNA
CNB
CNC
CND
Record type 11
Kl
K2
northbound lanes
- Conversion factors **
FF Conversion from g/sec to
ppm for NO
FF Conversion from g/sec to
ppm for CO
FF Conversion from g/sec to
ppm for N00
Atf
FF Conversion from g/sec to
ppm for 0
- Reaction rates (read only if ICHEM = 0)
FF Reaction rate for
NO + 0,, > NO,, + 0,
ppm min
FF
Reaction rate for
mm
-1
NO
-> NO + 0-
FF = free format
If ICHEM = 1, then BACKGA is the background concentration
of the pollutant and BACKGB, BACKGC, and BACKGD are omitted.
If ICHEM = 1, then EMA and EMA1 are the pollutant emission
rates of the southbound and northbound lanes, respectively,
and EMB, EMC, EMB1, and EMC1 are omitted.
If ICHEM = 1, then CNA is the conversion factor for the
pollutant and CNB, CNC, and CND are omitted.
53
-------
INTRICACIES OF THE DATA
Most of the input data listed are straightforward. .However,
there are some input variables which require clarification to be
sure that values are assigned properly.
Record Type 4
The roughness length, ZQ, must represent the surface
characteristics immediately upwind of the highway.
lengths for model input are listed below.
Roughness
TABLE 5. ROUGHNESS LENGTHS FOR VARIOUS SURFACE TYPES
Land-use type
Roughness
ZQ (cm)
Source
cropland and pasture 20
cropland, woodland, and
graz i ng land 3 0
i rr igated crops 5
grazed forest and woodland 90
ungrazed forest and woodland 100
subhumid grassland and
semiarid grazing land 10
open woodland grazed 20
desert shrubland 30
swamp 20
mar sh1 and 5 0
metropolitan city 100
lake or ocean -0.01
from Sheih et al. (197.9)
from Sheih et al. (1979)
from Sheih et al. (1979)
from Sheih et al. (1979)
from Sheih et al. ( 1979)
from Sheih et al. (1979)
from Sheih et al. (1979)
from Sheih et al. (1979)
from Sheih et al. (1979)
from Sheih et al. (1979)
from Sheih et al. (1979 )
from Sheih et al . (1979 )
From Sheih et al. (1979)
If the chemistry option is exercised (i.e., ICHEM = 0), then
chemical reactions of NO,
NO.
and 0.
near the road are
2' "3
simulated. For exercising this option, the user must provide the
following additional information:
Background concentrations of NO, CO, N02> anQ< 0-;
NO, CO, and N00 emission rates for northbound and
u
southbound vehicles;
54
-------
Conversion factors (g/sec^to ppm) for NO, CO, NO 0,
Z
and Oo; and
Chemical reaction rates for
NO + 03 > N02 + 02 and
NO, + 00 > NO + 0,.
4 & o
The upwind differencing scheme for advection tends to diffuse the
concentration field artificially. By exercising the
antidiffus ion option (i.e., IANTI = 0), most of the numerical
dispersion is removed. Although execution time is increased, it
is recommended that this option be used.
The user may see the concentration fields evolve before
reaching steady-state conditions by using the intermediate print
option (i.e., INTPR = 0). The velocity and diffusivity fields
are also provided when this option is exercised. If the user
chooses not- to implement the intermediate print option (i.e.,
INTPR = 1), then ROADWAY simply echoes the input data and prints
the steady-state concentration fields.
Record Type 5
RDANGL is the angle between the highway and a line running
north-south. The angle is always less then 90°. Examples of
several highway configurations and their appropriate values of
RDANGL are given in Figure 9.
Record Type 6
If the chemistry option is exercised (i.e., ICHEM = 0), then
the background concentrations of NO, CO, N02, and 0~ must also be
given. When the chemistry option is not considered (i.e.,
ICHEM = 1), then only the background concentration of the
pollutant being simulated is required.
55
-------
RDANGL s -45
RDANGL =45
N
t
RDANGL = 0
N
f
90°
Invalid value for RDANGL
RDANGL must be less than 90°
Figure 9. Examples of several highway configurations and their
appropriate values of RDANGL.
56
-------
Record Type 7
MEDN, the width of the traffic median, should be treated as a
real number not as an integer; the value provided for the median
width should contain a decimal point.
Record Type 8
Northbound refers to lanes with a northerly component to the
traffic flow; southbound refers to lanes with a southerly
component to the traffic flow. While traffic volume and traffic
speed can differ between northbound and southbound lanes, NVEH
and VSPD apply to all northbound lanes and NVEH1 and VSPD1 apply
to all southbound lanes.
Values of VWID and VHGH for an intermediate size American
automobile are 1.8 m and 1.4 m, respectively.
Record Type 9
If the chemistry option is exercised (i.e., ICHEM = 0), then
vehicle emission rates for NO, CO, and NO for both north- and
2
southbound lanes must be given by the user. When the chemistry
option is not considered (i.e., ICHEM = 1), only the north- and
southbound emission rates for the pollutant being simulated are
required. Any inert pollutant can be simulated by placing the
emission rate in EM.
Record Type 10
The multipliers to convert emision rate in grams per second
to parts per million for each pollutant species can be obtained
from
Conversion factor = 83144 T/M*P (64)
where T is the ambient air temperature (K), M is the molecular
weight of the pollutant species, and P is the atmospheric
pressure (mb). The factor 83144 is the universal gas constant in
57
-------
appropriate units. If the chemistry option is requested (i.e.,
ICHEM = 0), then the conversion factors for NO, CO, NO2 , and 03
must be provided on the input stream. At a temperature of 25°C
and sea level pressure of 1013.25 mb , these conversion factors
are 815.24, 873.45, 531.74, and 509.69 for NO, CO, N02, and Og,
respectively. When the chemistry option is not used (i.e.,
ICHEM = l), only the conversion factor for the pollutant under
consideration is required.
Record Type 11
When the chemistry option is requested (i.e., ICHEM = 0),
the chemical reaction rates k , k for the chemical mechanism
NO + 03 --> N02 + 02
It o
N00 + 0 + hv > NO + 0,
U u U
need to be provided. These reactions are assumed to be the only
ones of importance near the roadway. Seinfeld (1975) gives the
values 22.0/(ppm min ) and 0.46/min as applicable to k and
k , respect i vely .
It
58
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SECTION 10
EXECUTION AND INTERPRETATION OF THE MODEL
ROADWAY produces an error-free compile on UNIVAC EXEC 8, IBM
MVS, and DEC VAX/VMS computers with comparable output results. A
sample job stream is shown below.
END OF JOB STATEMENT
INPUT RECORDS
UNIT 5=DATA
UNIT 6=PRINTER
EXECUTE ROADWAY
JOB STATEMENT
o
o
o
Figure 10. Sample job stream for ROADWAY
59
-------
Job control language (JCL) for model execution on a UNIVAC
EXEC 8 system would have the following form:
@RUN,R/R JOB -ID, ETC
@ASG,A MODELS*LOAD.
@XQT MOD ELS* LOAD. ROADWAY
(input records shown in Table 6)
On an IBM system under OS or MVS , the JCL would look as
f o 1 lows ,
//JOBID JOB (PROJ, ACCT, OTHER) ,CLASS=A,TIME=1
//XTROADWY EXEC PGM=ROADWAY, TIME= ( , 10 )
//STEPLIB DD DSN=USER. MODELS. LOAD, DISP=SHR
//FT06F001 DD SYSOUT=A
//FT05F001 DD *
(control information and model input data)
/*
ROADWAY VERIFICATION RUN
Sample test data (unit 5) for model verification are given in
Table 6; Figure 11 shows the resulting model output for the
sample test. proper execution of the program can be verified by
comparing results with those given in the figure. Using
identical inputs, any machine should produce output numbers
within 3% of those shown here. If this is not the case, either
the version of the code is different or the data was not properly
entered .
60
-------
TABLE 6. INPUT DATA FOR THE SAMPLE TEST
Record Record type
ROADWAY VERIFICATION RUN 1
INERT POLLUTANT SIMULATION 2
INTERMEDIATE PRINT OPTION EXERCISED 3
0.05,1.22,4.24,1,0,0 4
284.38,284.49,0.94,270. ,0.0 5
40.0 6
4,3.4,11.8 7
1366.,1366.,80.0,80.0,1.8,1.4 8
90.0,90.0 9
873.36 10
61
-------
« ROADWAY (VERSION 86010) * *
TITLE: ROADWAY VERIFICATION RUN
INERT POLLUTANT SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
OPTIONS
CHEMISTRY OPTION (ICHEM) 1
ANTIDIFFUSION CALCULATION OPTION (IANTI) 0
INTERMEDIATE PRINT OPTION (INTPR) 0
METEOROLOGY
SURFACE ROUGHNESS (ZO) O.OSOO M
HEIGHT OF TEMPERATURE INSTRUMENTS
LOWER (Zl) 1.22 M
UPPER (Z2) 4.24 M
TEMPERATURE AT HEIGHT:
Zl (Tl) 284.38 K
Z2 (T2) 284.49 K
WIND SPEED (WSPD) 0.94M/SEC
WIND DIRECTION (WDIR) 270.00 DEC
HIGHWAY INFORMATION
NUMBER OF TRAFFIC LANES (NLANE) 4
WIDTH OF EACH LANE (WIDL) ........ 3.40 M
WIDTH OF MEDIAN (MEDN) 11.80M
ANGLE BETWEEN ROAD AND LINE RUNNING N-S (RDANGL) 0.00 DEC
TRAFFIC VOLUME
SOUTHBOUND LANES (NVEH) 1366. VEH/HR
NORTHBOUND LANES (NVEH1) 1366. VEH/HR
AVERAGE VEHICLE SPEED
SOUTHBOUND LANES (VSPD) 80.00KM/HR
NORTHBOUND LANES (VSPD1) 80.00KM/HR
AVERAGE DIMENSIONS OF VEHICLES
WIDTH (VWID) 1.80 M
HEIGHT (VHGH) ... 1.40M
EMISSION INFORMATION
BACKGROUND CONCENTRATION (BACKGA) 40.0000 PPM
EMISSION RATES:
SOUTHBOUND LANES (EMA) 90.0000 G/KM/VEH
NORTHBOUND LANES (EMA1) 90.0000 G/KM/VEH
CONVERSION FACTOR FOR G/SEC TO PPM (CNA) 873.3800
*************************
J Input information and 5
* model parameters are *
* listed here *
*************************
Figure 11. Printed output for the verification run
62
-------
TITLE: ROADWAY VERIFICATION RUN
INERT POLLUTANT SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
GRID POINTS IN X DIRECTION FROM
LEFT TO RIGHT ACROSS ROADWAY
(METERS)
20.0
35.0
45.0
48
51
55
59
63
67
70
73
83
98
118
143.8
173.8
INDICATES LOCATION OF TRAFFIC LANE CENTER.
THE FOLLOWING GRAPHICAL OUTPUT IS A CROSS SECTION ACROSS THE HIGHWAY IN THE
X-Z PLANE. IN EACH FIELD, THE BOTTOM LINE IS AT Z = 1 METER, WITH HEIGHT
INCREASING TOWARD THE TOP OP THE PAGE. SUCCEEDING LINES REPRESENT Z = 2,
4.5, 10.5, 20, 50, AND 70 METERS. THE SPACING ACROSS THE ROAD IS DETERMINED
BY STARTING AT THE BOTTOM LEFT POINT, WHICH CORRESPONDS TO THE FIRST VALUE
OF THE X GRID PRINTED EARLIER, WITH INCREASING VALUES TO THE RIGHT. THE
LAST SET OP CONCENTRATION FIELDS REPRESENT THE STEADY-STATE VALUES AND THE
AVERAGES FOR THE 30 MINUTE PERIOD. THESE STEADY-STATE FIELDS OCCUR AT 300,
600, OR 900 SECONDS.
Figure 11. (continued)
63
-------
TITLE: ROADWAY VERIFICATION RUN
INERT POLLUTANT SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
U FIELD (M/SEC)
4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18
2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14
1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44
0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.92 0.92 0.92 0.93 0.93 0.93
0.65 0.65 0.65 O.S4 O.S2 0.61 0.63 0.64 0.63 0.61 0.61 0.63 0.63 0.64 0.64 0.64
0.49 0.49 0.49 0.4S 0.42 0.44 0.45 0.46 0.43 0.40 0.42 0.44 0.46 0.47 0.47 0.47
20.0 35.0 4S.O 48.4 SI.8 55.2 59.4 63.6 67.0 70.4 73.8 83.8 98.3 118.8 143.8 173.8
V FIELD (M/SEC)
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.02
0.00 0.00 0.00 0.00 -0.11 -0.28 -0.27 -0.27 -0.28 -0.17 -0.01 0.01 0.04 0.03 0.02 0.01
0.00 0.00 0.00 -0.52 -1.32 -1.37 -0.99 -0.82 -0.22 0.6S 0.75 0.26 0.12 0.07 0.04 0.03
0.00 0.00 0.00 -1.63 -2.98 -2.28 -1.58 -1.25 0.55 2.02 1.42 0.49 0.21 0.11 0.06 0.03
20.0 35.0 43.0 48.4 51.8 55.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
W FIELD (M/SEC)
0.00 0.00 0.01 0.02 0.01 -0.01 -0.01 0.01 0.02 0.01 -0.01 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.01 0.02 0.01 -0.01 -0.01 0.01 0.02 0.01 -0.01 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.01 0.02 0.01 -0.01 -0.01 0.01 0.02 0.01 -0.01 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.01 0.02 0.01 -0.01 -0.01 0.01 0.02 0.01 -0.01 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.02 0.01 -0.01 -0.01 0.01 0.02 0.00 -0.01 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00
20.0 35.0 45.0 48.4 51.8 55.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
The input wind direction
and speed and the assump-
tion of non-divergence
are used to generate
J these wind components
Figure 11. (continued)
64
-------
TITLE: ROADWAY VERIFICATION RUN
INERT POLLUTANT SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
KX FIELD (M"2/SEC)
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.26
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.27 0.28 0.29 0.30 0.32 0.30 0.29 0.28
0.25 0.2S 0.25 0.25 0.45 0.83 0.53 0.44 0.40 0.57 0.73 0.49 0.36 0.31 0.29 0.28
0.25 0.25 0.25 0.91 1.49 1.06 0.57 0.44 1.05 1.60 1.14 0.47 0.34 0.29 0.27 0.26
0.25 0.25 0.25 2.24 2.80 0.99 0.49 0.38 2.33 2.87 1.05 0.39 0.30 0.27 0.26 0.26
20.0 35.0 45.0 48.4 51.8 55.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
KZ FIELD (M««2/SEC)
0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12
0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.10 0.10
0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.08 0.10 0.11 0.11 0.13 0.15 0.13 0.11 0.10
0.05 0.05 0.05 0.05 0.25 0.43 0.34 0.25 0.20 0.37 0.53 0.29 0.17 0.12 0.09 0.08
0.03 0.03 0.03 0.57 1.04 0.69 0.30 0.19 0.69 1.13 0.76 0.21 0.11 0.07 0.05 0.05
0.02 0.02 0.02 0.83 1.06 0.32 0.12 0.07 0.86 1.09 0.34 0.08 0.04 0.03 0.03 0.02
20.0 35.0 45.0 48.4 51.8 55.2 59.4 63.8 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
* Diffusivity fields computed *
* in subroutine SBLAYR are *
* qiven here *
*»%»*************»**********»**
Figure 11. (continued)
65
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TITLE: ROADWAY VERIFICATION RUN
INERT POLLUTANT SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
POLLUTANT CONCENTRATIONS (PPM) AT TIME 150.597061 SEC
40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00
40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.01 40.03 40.04 40.04
40.00 40.00 40.00 40.00 40.01 40.06 40.16 40.21 40.33 40.35 40.91 41.05 41.89 42.53 42.57 42.57
40.00 40.00 39.98 40.22 44.04 46.39 47.45 47.42 49.03 54.08 56.44 56.31 56.30 53.95 50.46 50.46
40.00 40.00 40.16 54.25 58.56 56.53 54.99 55.27 65.67 68.60 65.43 61.08 61.12 55.03 49.61 49.61
40.00 40.00 44.23 59.24 61.97 59.49 57.37 59.53 70.58 71.95 87.89 62.57 62.59 54.89 48.62 48.62
20.0 35.0 45.0 48.4 51.8 55.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
POLLUTANT CONCENTRATIONS (PPM) AT TIME 300.751068 SEC
40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00
40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.01 40.01 40.03 40.05 40.05
40.00 40.00 40.00 40.00 40.00 40.07 40.15 40.24 40.29 40.44 40.65 41.38 41.67 42.51 42.90 42.90
40.00 40.00 39.98 40.22 44.03 46.39 47.44 47.48 48.90 54.34 56.60 56.44 56.33 54.83 53.70 53.70
40.00 40.00 40.16 54.25 58.56 56.53 54.99 55.27 65.74 68.82 65.79 61.28 60.01 57.49 56.14 56.14
40.00.40.00 44.23 59.24 61.97 59.49 57.38 59.55 70.68 72.16 68.29 62.74 61.14 58.34 56.81 56.81
20.0 35.0 45.0 48.4 51.8 55.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
POLLUTANT CONCENTRATIONS (PPM) AT TIME 450.905060 SEC
40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00.40.00
40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.01 40.01 40.03 40.05 40.05
40.00 40.00 40.00 40.00 40.00 40.07 40.15 40.24 40.29 40.44 40.65 41.38 41.67 42.51 42.90 42.90
40.00 40.00 39.98 40.22 44.03 46.39 47.44 47.48 48.91 54.33 56.59 56.45 56.33 54.64 53.79 53.79
40.00 40.00 40.16 54.25 58.56 56.53 54.99 55.27 65.73 68.80 65.77 61.35 59.99 57.49 56.37 56.37
40.00 40.00 44.23 59.24 61.97 59.49 57.38 59,55 70.68 72.15 68.26 62.83 61.10 58.33 57.13 57.13
20.0 35.0 45.0 48.4 51.8 55.2 59.4 83.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.3
* Pollutant concentrations are *
* listed at each of four pro- *
* , K *
* qram steps
**********
Figure 11. (continued)
66
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TITLE: ROADWAY VERIFICATION RUN
INERT POLLUTANT SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
POLLUTANT CONCENTRATIONS (PPM) AT TIME 800.173218 SEC
40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00
40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.01 40.01 40.03 40.05 40.05
40.00 40.00 40.00 40.00 40.00 40.07 40.15 40.24 40.29 40.44 40.65 41.38 41.67 42.51 42.90 42.90
40.00 40.00 39.98 40.22 44.03 46.39 47.44 47.48 48.91 54.33 56.59 56.45 56.33 54.64 53.79 53.79
40.00 40.00 40.16 54.25 58.56 56.53 54.99 55.27 65.73 68.80 65.77 61.35 59.99 57.49 56.38 56.38
40.00 40.00 44.23 59.24 81.97 59.49 57.38 59.55 70.68 72.15 68.26 62.83 61.10 58.33 57.13 57.13
20.0 35.0 4S.O 48.4 51.8 55.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
NORMAL TERMINATION.
This message is printed at the
end to inform the user that no
anomalies occurred during
program execution
Figure 11. (continued)
67
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EXAMPLE PROBLEM
In Section 6, a problem was discussed to illustrate model
application to a four-lane highway; the chemistry option was used
and most other options were exercised. Using model output,
scalar fields of wind, diffusivity, and concentration were
displayed. In this section, the same problem is considered but
in more detail; intricacies of the input data are discussed and
the output listing is displayed with annotations for ease of
interpretat ion.
The unit 5 input stream is tabulated below. Unlike input for
other models, no records are repeated (excepting title); record
types 4 through 11 are unique and must be ordered as given.
TABLE 7. INPUT DATA FOR THE EXAMPLE PROBLEM
Record Record type
EXAMPLE PROBLEM 1
NOX - 03 SIMULATION 2
INTERMEDIATE PRINT OPTION IMPLEMENTED 3
0.05,1.22,4.24,0,0,0 4
284.38,284.49,0.94,270.0,0.0 5
0.052,40.0,0.25,0.1 6
4,3.4,11.8 7
1366. ,1366. ,80.0,80.0,1.8, 1.4 8
2.7,90.0,0.3,2.7,90.0,0.3 9
813.01,873.36,531.91,509.68 10
22.0,0.46 11
As noted in record 4, both the chemistry and intermediate print
options are exercised: IGHEM and INTPR are set to zero. By using
the chemistry option, the following applies:
Background concentrations of NO, CO, NO , and 0 are
2' 3
. needed and should be provided in record type 6;
68
-------
NO, CO, and NO emission rates for northbound and
2
southbound vehicles are needed as in record type 9;
Conversion factors (g/sec to ppm) for NO, CO, NO , and 0
it O
have to be supplied as in record type 10; and
Optional record type 11 should be present and contain
appropriate chemical reaction rates.
Output for the problem is given in Figure 12. The printed
output consists of five parts: input data, grid information, wind
velocity fields, diffusivity fields, and concentration fields.
The velocity and diffusivity fields are printed optionally,
depending on the value of INTPR as noted in Table 4. If the
intermediate print option is not exercised (i.e., INTPR = 1),
then only the steady-state concentration fields are printed.
Because the intermediate print option was used, all the available
output is printed.
69
-------
* ROADWAY (VERSION 86010) « *
TITLE: EXAMPLE PROBLEM
NOX-03 SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
OPTIONS
CHEMISTRY OPTION (ICHEM) ' 0
ANTIDIFFUSION CALCULATION OPTION (IANTI) 0
INTERMEDIATE PRINT OPTION (INTPR) 0
METEOROLOGY
SURFACE ROUGHNESS (ZO) O.OSOO M
HEIGHT OF TEMPERATURE INSTRUMENTS
LOWER (Zl) 1.22 M
UPPER (Z2) 4.24 M
TEMPERATURE AT HEIGHT:
Zl (Tl) 284.38 K
22 (T2) 284.49 K
WIND SPEED (WSPD) 0.94 M/SEC
WIND DIRECTION (WDIR) 270.00 DEG
HIGHWAY INFORMATION
NUMBER OF TRAFFIC LANES (NLANE) 4
WIDTH OF EACH LANE (WIDL) 3.40M
WIDTH OF MEDIAN (MEDN) 11.80 M
ANGLE BETWEEN ROAD AND LINE RUNNING N-S (RDANGL) 0.00 DEG
TRAFFIC VOLUME
SOUTHBOUND LANES (NVEH) 1366. VEH/HR
NORTHBOUND LANES (NVEH1) 1366. VEH/HR
AVERAGE VEHICLE SPEED
SOUTHBOUND LANES (VSPD) 80.00KM/HR
NORTHBOUND LANES (VSPD1) 80.00 KM/HR
AVERAGE DIMENSIONS OF VEHICLES
WIDTH (VWID) 1.80 M
HEIGHT (VHGH) 1.40M
TITLE: EXAMPLE PROBLEM
NOX-03 SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
EMISSION INFORMATION
BACKGROUND CONCENTRATIONS:
NO (BACKGA) 0.0520 PPM
CO (BACKGB) 40.0000 PPM
NO2 (BACKGC) 0.2500 PPM
O3 (BACKGD) 0.1000 PPM
EMISSION RATES FOR THE SOUTHBOUND LANES:
NO (EMA) 2.7000 G/KM/VEH
CO (EMB) 90.0000 G/KM/VEH
NO2 (EMC) 0.3000 G/KM/VEH
EMISSION RATES FOR THE NORTHBOUND LANES:
NO (EMA1) 2.7000 G/KM/VEH
CO (EMB1) 90.0000 G/KM/VEH
NO2 (EMC1) 0.3000 G/KM/VEH
CONVERSION FACTORS (G/SEC TO PPM) FOR:
NO (CNA) 813.0100
CO (CNB) 873.3600
NO2 (CNC) 531.9100
03 (CND) 509.6800
CHEMICAL REACTION RATES FOR THE FOLLOWING:
NO + 03 > N02 + 02 22.0000 I/(PPM MIN)
NO2 * O2 > NO +03 0.4600 1/M1N
Figure 12, Printed output for the example problem.
70
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TITLE: EXAMPLE PROBLEM
NOX-03 SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
GRID POINTS IN X DIRECTION FROM
LEFT TO RIGHT ACROSS ROADWAY
(METERS)
20.0
35. 0
45. 0
48.4
51.8
55.2
59.4
83. 8
87.0
70.4
73.8
83.8
98.8
118.8
143.8
173.8
INDICATES LOCATION OF TRAFFIC LANE CENTER.
THE FOLLOWING GRAPHICAL OUTPUT IS A CROSS SECTION ACROSS THE HIGHWAY IN THE
X-Z PLANE. IN EACH FIELD, THE BOTTOM LINE IS AT Z = I METER, WITH HEIGHT
INCREASING TOWARD THE TOP OF THE PAGE. SUCCEEDING LINES REPRESENT Z = 2,
4.5, 10.5, 20, 50, AND 70 METERS. THE SPACING ACROSS THE ROAD IS DETERMINED
BY STARTING AT THE BOTTOM LEFT POINT, WHICH CORRESPONDS TO THE FIRST VALUE
OF THE X GRID PRINTED EARLIER, WITH INCREASING VALUES TO THE RIGHT. THE
LAST SET OF CONCENTRATION FIELDS REPRESENT THE STEADY-STATE VALUES AND THE
AVERAGES FOR THE 30 MINUTE PERIOD. THESE STEADY-STATE FIELDS OCCUR AT 300,
600, OR 900 SECONDS.
Figure 12. (continued)
71
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TITLE: EXAMPLE PROBLEM
NOX-03 SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
0 FIELD (M/SEC)
4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18 4.18
2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14 2.14
1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44
0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.92 0.92 0.92 0.93 0.93 0.93
0.85 0.65 0.65 0.64 0.82 0.62 0.63 0.64 0.63 0.61 0.61 0.63 0.63 0.64 0.64 0.64
0.49 0.49 0.49 0.45 0.42 0.44 0.45 0.46 0.43 0.40 0.42 0.44 0.46 0.47 0.47 0.47
20.0 35.0 45.0 48.4 51.8 55.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.3 143.8 173.8
V FIELD (M/SEC)
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 D.00 O.OO O.OO 0.00 O.OO O.OO 0.00 0.00 0.00 0.00 0.00 0.00 -0.02
0.00 0.00 0.00 0.00 -0.11 -0.28 -0.27 -0.27 -0.28 -0.17. -0.01 0.01 0.04 0.03 0.02 0.01
0.00 0.00 0.00 -0.52 -1.32 -1.37 -0.99 -0.82 -0.22 0.65 0.75 0.26 0.12 0.07 0.04 0.03
0.00 0.00 0.00 -1.63 -2.98 -2.28 -1.58 -1.25 0.55 2.02 1.42 0.49 0.21 0.11 0.06 0.03
20.0 35.0 45.0 48.4 51.8 55.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
W FIELD (M/SEC)
0.00 0.00 0.01 0.02 0.01 -0.01 -0.01 0.01 0.02 0.01 -0.01 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.01 0.02 0.01 -0.01 -0.01 0.01 0.02 0.01 -0.01 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.01 0.02 0.01 -0.01 -0.01 0.01 0.02 0.01 -0.01 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.01 0.02 0.01 -0.01 -0.01 0.01 0.02 0.01 -0.01 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.02 0.01 -0.01 -0.01 0.01 0.02 0.00 -0.01 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00
20.0 35.0 45.0 48.4 51.8 55.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
Figure 12. (continued)
72
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TITLE: EXAMPLE PROBLEM
NOX-03 SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
KX FIELD (M«»2/SEC)
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.2S 0.25 0.25 0.25 0.25
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.2-5 0.25 0.25 0.25 0.25 0.2S
0.25 0.25 0.25 0.25 0.23 0.25 0.25 0.25 0.27 0.28 0.29 0.30 0.32 0.30 0.29 0.28
0.25 0.25 0.25 0.25 0.45 0.63 0.53 0.44 0.40 0.5? 0.73 0.49 0.36 0.31 0.29 0.28
0.25 0.25 0.25 0.91 1.49 1.06 0;57 0.44 1.05 1.60 1.14 0.47 0.34 0.29 0.27 0.26
0.25 0.25 0.25 2.24 2.30 0.99 0.49 0.38 2.33 2.87 1.05 0.39 0.30 0.27 0.26 0.26
20.0 35.0 45.0 48.4 51.8 55.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
KZ FIELD (M*»2/SEC)
0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12
0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.10 0.10
0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.08 0.10 0.11 0.11 0.13 0.15 0.13 0.11 0.10
0.05 0.05 0.05 0.05 0.25 0.43 0.34 0.25 0.20 0.37 0.53 0.29 0.17 0.12 0.09 0.08
0.03 0.03 0.03 0.57 1.04 0.69 0.30 0.19 0,69 1.13 0.76 0.21 0.11 0.07 0.05 0.05
0.02 0.02 0.02 0.83 1.06 0.32 0.12 0.07 0.86 1.09 0.34 0.08 0.04 0.03 0.03 0.02
20.0 35.0 45.0 48.4 51.8 55.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.3 143.8 173.3
Figure 12. (continued)
73
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TITLE: EXAMPLE PROBLEM
NOX-03 SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
NITROGEN OXIDE, NO (PPM) AT TIME 150.597061 SEC
0.05 0.05 0.05 O.OS O.OS 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05 0.05 0.05 0.05 O.OS 0.05 0.05 0.05 O.OS 0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.06 0.06 0.06 0.07 0.08 0.09 0.09 0.09
0.05 0.05 0.05 0.06 0.12 0.17 0.19 0.19 0.24 0.36 0.43 0.42 0.42 0.36 0.27 0.27
0.05 0.05 0.06 0.37 0.48 0.43 0.39 0.40 0.68 0.76 0.67 0.55 0.56 0.39 0.25 0.25
0.05 0.05 0.12 0.50 0.58 0.51 0.46 0.51 0.81 0.85 0.74 0.60 0.60 0.39 0.22 0.22
20.0 35.0 45.0 48.4 SI.8 SS.2 S9.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
CARBON MONOXIDE, CO (PPM) AT TIME 150.597061 SEC
40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00
40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.01 40.03 40.04 40.04
40.00 40.00 40.00 40.00 40.01 40.06 40.16 40.21 40.33 40.35 40.91 41.05 41.89 42.53 42.57 42.57
40.00 40.00 39.98 40.22 44.04 46.39 47.45 47.42 49.03 54.08 56.44 56.31 56.30 53.95 50.46 50.46
40.00 40.00 40.16 54.25 S8.S8 56.53 54.99 55.27 65.67 68.60 65.43 61.08 61.12 55.03 49.61 49.61
40.00 40.00 44.23 S9.24 61.97 59.49 57.37 59.53 70.58 71.95 67.89 62.57 62.59 54.89 48.62 48.62
20.0 35.0 4S.O 48.4 51.8 55.2 59.4 63.8 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.3
NITROGEN DIXO1DE, NO2 (PPM) AT TIME 150.597061 SEC
0.25 0.25 0.25 0.25 0.2S 0.2S 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
0.25 0.2S 0.25 0.2S 0.25 0.25 0.25 0.2S 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
0.25 0.2S 0.25 0.25 0.2S 0.25 0.25 0.25 0.26 0.26 0.27 0.27 0.28 0.29 0.29 0.29
0.25 0.25 0.2S 0.2S 0.30 0.32 0.33 0.33 0.34 0.36 0.37 0.37 0.37 0.36 0.34 0.34
0.25 0.2S 0.2S 0.36 0.37 0.37 0.36 0.36 0.39 0.40 0.39 0.38 0.38 0.36 0.34 0.34
0.2S 0.2S 0.31 0.37 0.38 0.37 0.37 0.37 0.40 0.41 0.40 0.38 0.38 0.36 0.34 0.34
20.0 35.0 45.0 48.4 51.8 SS.2 59.4 63.6 67.0 70.4 73.8 83.8 98.3 118.8 143.8 173.8
TITLE: EXAMPLE PROBLEM
NOX-03 SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
OZONE, 03 (PPM) AT TIME 150.597061 SEC
0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.09 0.09 0.09 0.08 0.07 0.07 0.07 0.07
0.10 0.10 0.10 0.10 0.05 0.04 0.04 0.04 0.03 0.02 0.02 0.02 0.02 0.02 0.03 0.03
0.10 0.10 0.10 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.02 0.03 0.03
0.10 0.10 0.0$ 0.02 0.01 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.02 0.03 0.03
20.0 3S.O 45.0 48.4 51.8 5S.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.3 173.3
Figure 12. (continued)
74
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TITLE: EXAMPLE PROBLEM
NOX-03 SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
NITROGEN OXIDE, NO (PPM) ' AT TIME 300.751068 SEC
O.OS 0.05 0.05 0.05 0.05 0.05 0.05 O.OS 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.05 0.05 O.OS 0.05 0.05 0.05 0.05 O.OS 0.05 0.05 O.OS 0.05 0.05 0.05 0.05 0.05
0.05 0.05 0.05 O.OS 0.05 0.05 0.05 O.OS 0.06 0.06 0.06 0.07 0.08 0.09 0.10 0.10
0.05 0.05 0.05 0.06 0.12 0.17 0.19 0.19 0.23 0.37 0.43 0.43 0.42 0.38 0.36 0.36
O.OS 0.05 0.06 0.37 0.48 0.43 0.39 0.40 0.68 0.77 0.68 O.S6 O.S3 0.46 0.42 0.42
O.OS O.OS 0.12 0.50 O.S8 O.S1 0.46 O.S1 0.82 0.86 0.7S 0.60 O.S6 0.48 0.44 0.44
20.0 35.0 4S.O 48.4 SI.8 SS.2 S9.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
CARBON MONOXIDE, CO (PPM) AT TIME 300.751068 SEC
40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00
40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.01 40.01 40.03 40.05 40.05
40.00 40.00 40.00 40.00 40.00 40.07 40.IS 40.24 40.29 40.44 40.85 41.38 41.67 42.51 42.90 42.90
40.00 40.00 39.98 40.22 44.03 46.39 47.44 47.48 48.90 54.34 56.60 56.44 S6.33 54.63 53.70 53.70
40.00 40.00 40.16 S4.2S 58.56 S6.S3 54.99 S5.27 6S.74 88.82 65.79 61.28 60.01 S7.49 56.14 56.14
40.00 40.00 44.23 59.24 61.97 S9.49 S7.38 59.55 70.68 72.16 68.29 62.74 61.14 58.34 56.81 56.81
20.0 3S.O 4S.O 48.4 51.8 55.2 59.4 63.6 87.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
NITROGEN DIXOIDE, NO2 (PPM) AT TIME 300.751068 SEC
0.25 0.25 0.25 0.25 0.2S 0.25 0.25 0.25 0.2S 0.25 0.25 0.25 0.25 0.25 0.25 0.25
0.25 0.25 0.25 0.2S 0.2S 0.2S 0.2S 0.25 0.25 0.2S 0.2S 0.2S 0.25 0.25 0.25 0.25
0.25 0.25 0.2S 0.25 0.2S 0.25 0.2S 0.25 0.26 0.28 0.28 0.27 0.28 0.29 0.29 0.29
0.25 0.25 0.2S 0.2S 0.30 0.32 4.33 0.33 0.34 0.36 0.37 0.37 0.37 0.36 0.36 0.36
0.25 0.2S 0.25 0.36 0.37 0.37 0.36 0.36 0.39 0.40 0.39 0.38 0.38 0.37 0.36 0.36
0.2S 0.2S 0.31 0.37 0.38 0.37 0.37 0.37 0.40 0.41 0.40 0.38 0.38 0.37 0.37 0.37
20.0 35.0 4S.O 48.4 SI.8 55.2 59.4 63.8 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
TITLE: EXAMPLE PROBLEM
NOX-03 SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
OZONE, 03 (PPM) AT TIME 300.751068 SEC
0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.09 0.09 0.08 0.08 0.07 0.06 0.06
0.10 0.10 0.10 0.10 0.05 0.04 0.04 0.04 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02
0.10 0.10 0.10 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02
0.10 0.10 0.05 0.02 0.01 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02
20.0 35.0 43.0 48.4 51.8 55.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
Figure 12. (continued)
75
-------
TITLE: EXAMPLE PROBLEM
NOX-03 SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
NITROGEN OXIDE, NO (PPM) AT TIME 450.905060 SEC
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.06 0.06 0.06 0.06 0.07 0.08 0.09 0.10 0.10
0.05 0.05 0.05 0.06 0.12 0.17 0.19 0.19 0.23 0.37 0.43 0.43 0.42 0.38 0.36 0.36
0.05 0.05 O.OS 0.37 0.48 0.43 0.39 0.40 0.68 0.78 O.S8 0.56 O.S2 0.46 0.43 0.43
O.OS 0.05 0.12 O.SO 0.58 O.S1 0.46 0.51 0.82 0.86 0.75 0.60 0.56 0.48 0.45 0.45
20.0 35.0 4S.O 48.4 51.8 55.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
CARBON MONOXIDE, CO (PPM) AT TIME 450.905060 SEC
40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00
40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.01 40.01 40.03 40.05 40.05
40.00 40.00 40.00 40.00 40.00 40.07 40.15 40.24 40.29 40.44 40.85 41.38 41.67 42.51 42.90 42.90
40.00 40.00 39.98 40.22 44.03 46.39 47.44 47.48 48.91 54.33 56.59 56.45 56.33 54.64 53.79 53.79
40.00 40.00 40.18 54.25 58.58 58.53 54.99 55.27 65.73 88.80 65.77 31.35 59.99 57.49 56.37 58.37
40.00 40.00 44.23 59.24 61.97 59.49 57.38 59.55 70.68 72.15 68.26 62.83 61.10 58.33 57.13 57.13
20.0 35.0 45.0 48.4 51.8 55.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
NITROGEN DIXOIDE, N02 (PPM) AT TIME 450.905060 SEC
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.26 0.26 0.26 0.27 0.28 0.29 0.29 0.29
0.25 0.25 0.25 0.25 0.30 0.32 0.33 0.33 0.34 0.36 0.37 0.37 0.37 0.36 0.36 0.36
0.25 0.25 0.2S 0.36 0.37 0.37 0.36 0.36 0.39 0.40 0.39 0.38 0.38 0.37 0.37 0.37
0.25 0.25 0.31 0.37 0.38 0.37 0.37 0.37 0.40 0.41 0.40 0.38 0.38 0.37 0.37 0.37
20.0 35.0 45.0 48.4 51.8 55.2 S9.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
TITLE: EXAMPLE PROBLEM
NOX-03 SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
OZONE, O3 (PPM) AT TIME 450.905060 SEC
0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
0.10 0.10 0.10 0.10 0,10 0.10 0.10 0.10 0.10 0.09 0.09 0.08 0.08 0.07 0.06 O.OS
0.10 0.10 0.10 0.10 0.05 0.04 0.04 0.04 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02
0.10 0.10 0.10 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02
0.10 0.10 O.OS 0.02 0.01 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02
20.0 35.0 45.0 48.4 SI.3 5S.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
Figure 12. (continued)
76
-------
TITLE: EXAMPLE PROBLEM
NOX-03 SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
NITROGEN OXIDE, NO (PPM) AT TIME 600.173218 SEC
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.06 0.06 0.06 0.06 0.07 0.08 0.09 0.10 0.10
0.05 0.05 0.05 0.06 0.12 0.17 0.19 0.19 0.23 0.37 0.43 0.43 0.42 0.38 0.36 0.36
0.05 0.05 0.08 0.37 0.48 0.43 0.39 0.40 0.68 0.76 0.68 0.56 0.52 0.46 0.43 0.43
0.05 0.05 0.12 0.50 0.58 0.51 0.46 0.51 0.82 0.86 0.75 0.60 0.56 0.48 0.45 0.45
20.0 3S.O 45.0 48.4 51.8 55.2 S9.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
CARBON MONOXIDE, CO (PPM) AT TIME 600.173218 SEC
40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00
40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.00 40.01 40.01 40.03 40.05 40.05
40.00 40.00 40.00 40.00 40.00 40.07 40.15 40.24 40.29 40.44 40.85 41.18 41.67 42.51 42.90 42.90
40.00 40.00 39.98 40.22 44.03 46.39 47.44 47.48 48.91 54.33 56.59 56.45 56.33 54.64 53.79 53.79
40.00 40.00 40.16 54.25 58.56 56.53 54.99 55.27 65.73 88.80 65.77 61.35 59.99 57.49 56.38 56.38
40.00 40.00 44.23 59.24 61.97 59.49 57.38 59.55 70.88 72.15 68.26 62.83 61.10 58.33 57.13 57.13
20.0 35.0 45.0 48.4 51.8 55.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
NITROGEN DIXOIDE, NO2 (PPM) AT TIME 600.173218 SEC
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.26 0.26 0.26 0.27 0.28 0.29 0.29 0.29
0.25 0.25 0.25 0.25 0.30 0.32 0.33 0.33 0.34 0.36 0.37 0.37 0.37 0.36 0.36 0.36
0.25 0.25 0.25 0.36 0.37 0.37 0.36 0.36 0.39 0.40 0.39 0.38 0.38 0.37 0.37 0.37
0.25 0.25 0.31 0.37 0.38 0.37 0.37 0.37 0.40 0.41 0.40 0.38 0.38 0.37 0.37 0.37
20.0 35.0 45.0 48.4 51.8 55.2 59.4 63.6 67.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
TITLE: EXAMPLE PROBLEM
NOX-03 SIMULATION
INTERMEDIATE PRINT OPTION EXERCISED
OZONE, 03 (PPM) AT TIME 600.173218 SEC
0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.09 0.09 0.08 0.08 0.07 0.06 0.06
0.10 0.10 0.10 0.10 0.05 0.04 0.04 0.04 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02
0.10 0.10 0.10 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02
0.10 0.10 0.05 0.02 0.01 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.02
20.0 35,0 45.0 48.4 51.8 55.2 59.4 63.6 87.0 70.4 73.8 83.8 98.8 118.8 143.8 173.8
NORMAL TERMINATION.
Figure 12. (continued)
77
-------
SECTION 11
ERROR MESSAGES AND REMEDIAL ACTION
ROADWAY can generate up to 20 error messages, each of which
causes program termination. Table 7 lists each message, along
with error description and suggested corrective action. The
table is ordered by error number.
TABLE 8. ERROR MESSAGES AND REMEDIAL ACTION
MESSAGE: *** ERROR 1: SURFACE ROUGHNESS, ZO, IS LESS THAN
ZERO.
*** EXECUTION TERMINATED.
Surface roughness must be greater than zero.
Modify variable ZO in record type 4.
DESCRIPTION
ACTION:
MESSAGE:
DESCRIPTION
ACTION:
*** ERROR 2: HEIGHT OF LOWER TEMPERATURE, Zl,
IS LESS THAN ZERO.
*** EXECUTION TERMINATED.
The instrument must be located above ground level.
Modify record type 4 so that Zl is positive.
MESSAGE:
DESCRIPTION:
ACTION:
*** ERROR 3: HEIGHT OF UPPER TEMPERATURE INSTRU-
MENT, Z2, IS BELOW OR EQUAL TO THAT OF THE LOWER
INSTRUMENT.
*** EXECUTION TERMINATED
The height of the upper instrument must be greater
than that of the lower instrument.
Modify record type 4 so that Z2 is greater than
Zl.
78
-------
TABLE 8. (continued)
MESSAGE:
DESCRIPTION:
ACTION:
*** ERROR 4: INPUT OPTIONS MUST EQUAL ZERO OR
ONE.
*** EXECUTION TERMINATED.
Branches in the source code assume that the input
options are either equal to zero or one.
Modify record type 4. Make sure variables ICHEM,
IANTI, and INTPR are initialized' to either zero
or one.
MESSAGE:
DESCRIPTION:
ACTION:
MESSAGE:
DESCRIPTION:
ACTION:
*** ERROR 5: TEMPERATURE AT HEIGHT Zl IS NOT
IN DEGREES KELVIN.
*** EXECUTION TERMINATED.
The temperature at height Zl given by the user
is not in Kelvin units.
Make sure temperatures given in record type 5
are in Kelvin degrees.
*** ERROR 6: TEMPERATURE AT HEIGHT Z2 IS NOT
IN DEGREES KELVIN.
*** EXECUTION TERMINATED.
The temperature at height Z2 given by the user
is not in Kelvin units.
Make sure temperatures given in record type 5
are in Kelvin degrees.
MESSAGE:
DESCRIPTION:
ACTION:
*** ERROR 7: INPUT WIND SPEED IS IN ERROR.
*** EXECUTION TERMINATED.
The wind speed provided is either negative o-r
too 1 arge.
Modify variable WSPD in record type 5.
79
-------
TABLE 8. (continued)
MESSAGE: *** ERROR 8: INPUT WIND DIRECTION IS IN ERROR.
*** EXECUTION TERMINATED.
DESCRIPTION: The input wind direction must be between 0° and
360° .
ACTION: Modify variable WDIR on record type 5.
MESSAGE:
DESCRIPTION:
ACTION:
*** ERROR 9: HIGHWAY ORIENTATION IS INCORRECTLY
SPECIFIED.
*** EXECUTION TERMINATED.
The absolute value of RDANGL must be between
0° and 90°.
Modify variable RDANGL on record type 5.
MESSAGE:
DESCRIPTION:
ACTION:
MESSAGE:
DESCRIPTION:
ACTION:
*** ERROR 10: BACKGROUND POLLUTANT CONCENTRATIONS
CANNOT BE LESS THAN ZERO.
*** EXECUTION TERMINATED.
Background pollutant concentrations must be greater
than or equal to zero.
Modify record type 6 so that all background con-
centrations are greater than or equal to zero.
*** ERROR 11: NUMBER OF TRAFFIC LANES IS. INCOR-
RECTLY SPECIFIED.
*** EXECUTION TERMINATED.
The number of traffic lanes must be between 4
and 10 (inclusive) and must be evenly divisible
by 2.
Modify variable NLANE on record type 7.
MESSAGE:
*** ERROR 12: WIDTH OF A TRAFFIC LANE CANNOT
BE LESS THAN OR EQUAL TO ZERO.
*** EXECUTION TERMINATED.
80
-------
TABLE 8. (continued)
DESCRIPTION: The width of a traffic lane must have a positive
va1ue.
ACTION: Modify WIDL on record type 7.
MESSAGE: *** ERROR 13: THE TRAFFIC MEDIAN CANNOT BE LESS
THAN ZERO.
*** EXECUTION TERMINATED.
DESCRIPTION: The variable MEDN cannot be less than zero.
ACTION: Modify MEDN on record type 7.
MESSAGE: *** ERROR 14: TRAFFIC VOLUME CANNOT BE LESS THAN
OR EQUAL TO ZERO.
*** EXECUTION TERMINATED.
DESCRIPTION: Variables NVEH and NVEH1 must be greater than
zero.
ACTION: Modify traffic volume input on record type 8.
MESSAGE: *** ERROR 15: AVERAGE VEHICLE SPEED IS INCORRECTLY
SPECIFIED.
*** EXECUTION TERMINATED.
DESCRIPTION: The average vehicle speed must be a positive number
less than 200 km/hr.
ACTION: Make sure variables VSPD and VSPD1 on record type
8 meet this criteria.
MESSAGE: *** ERROR 16: AVERAGE VEHICLE DIMENSIONS ARE
INCORRECTLY SPECIFIED.
*** EXECUTION TERMINATED.
DESCRIPTION: The user specified the vehicle dimensions to be
either too large (i.e., greater than WIDL) or
negat i ve .
81
-------
TABLE 8. (continued)
ACTION: Modify variable VWID and VHGH on record type 8.
Also make sure variable WIDL on record type 7
is properly initialized.
MESSAGE: *** ERROR 17: VEHICLE EMISSION RATES MUST BE
GREATER THAN ZERO.
*** EXECUTION TERMINATED.
DESCRIPTION: The vehicle emission rates must be greater than
zero .
ACTION: Make sure all the vehicle emission rates on record
type 9 meet this criteria.
MESSAGE: *** ERROR 18: CONVERSION FACTOR FOR G/SEC TO
PPM IS INCORRECTLY SPECIFIED.
*** EXECUTION TERMINATED.
DESCRIPTION: The conversion factors supplied by the user are
negative.
ACTION: Make sure all conversion factors on record type
lOarepositive.
MESSAGE: *** ERROR 19: CHEMICAL REACTION RATES CANNOT
BE LESS THAN ZERO.
*** EXECUTION TERMINATED.
DESCRIPTION: The chemical reaction rates (rate constants)
supplied by the user are unrealistic.
ACTION: Check variables Kl and K2 on record type 11 in
units of ppm min andmin
MESSAGE: *** ERROR 20: N - M + 1 IS NOT ODD.
*** EXECUTION TERMINATED.
DESCRIPTION: Values of the indices passed in subroutine SIMPSN
were incorrectly specified.
ACTION: Check SIMPSN calls in subroutine WAKE.
82
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REFERENCES
Binkowski, F. S. 1979. A simple semiempirica1 theory for
turbulence in the atmospheric surface layer. Atmos. Environ.
13:247-253.
Busch, N. E. 1973. On the mechanics of atmospheric turbulence.
In: Workshop on Micrometeorology, 0. A. -Haugen, Ed., Amer.
Meteor. Soc. pp. 1-61.
Cadle, S. H., D. P. Chock, J. M. Heuss, and P. R. Monson. 1976.
Results of the General Motors Sulfate Dispersion experiments.
GMRP GMR-2107. Warren, MI.
Chock, D. P. 1978. A simple line source model for dispersion near
roadways. Atmos. Environ. 12: 823- 829.
Danard, M. B. 1972. Numerical modeling of carbon monoxide
concentrations near a highway. J. Appl. Meteor. 11: 947-957.
Diaconis, P. and B. Efron. 1983. Computer-intensive methods in
statistics. Sci. Am. 248: 116-130.
Eskridge, R. E. and F. S. Binkowski, 1979a. Surface layer
similarity for highway modeling: a comparison of two
approaches. Presented at the Fourth Symposium of Turbulence,
Diffusion, and Air Pollution of the American Meteorological
Society on January 15-18, 1979 in Reno, Nevada.
Eskridge, R. E., F. S. Binkowski, J. C. R. Hunt, T. L. Clark, and
K. L. Demerjian. 1979b. Highway modeling. Part II: Advection
and diffusion of SFg tracer gas. J. Appl. Meteor. 18: 401-412.
Eskridge, R. E. and J. C. R. Hunt. 1979. Highway modeling. Part I:
Prediction of velocity and turbulence fields in the wakes of
vehicles. J. Appl. Meteor. 18: 387-400.
83
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Eskridge, R. E. and S. T. Rao. 1983. Measurement and prediction
of traffic-induced turbulence fields near roadways. J. Appl.
Meteor. 22: 1431-1443.
Eskridge, R'. E. and S. T. Rao. 1986. Turbulent diffusion behind
vehicles: experimentally determined turbulence mixing
parameters. Atmos. Environ. 20: 851-860.
Eskridge, R. E. and R. S. Thompson. 1982. Experimental and
theoretical study of the wake of a block-shaped vehicle in a
shear-free boundary flow. Atmos. Environ. 16: 2821-2836.
Fox, D. G. 1981. Judging air quality model performance. Bull. Am.
iVIeteorol. Soc. 62: 599-609.
Marchuk, G. I. 1975. Methods of Numerical Mathematics. Translated
by Jiri Ruzicka. Springer.Verlag. 316 pp.
Petersen, W. B. 1980. User's Guide for HIWAY-2, A Highway Air
Pollution Model. EPA-600/8-80-018, U. S. Environmental
Protection Agency, Research Triangle Park, 'NC. 69 pp.
Petersen, W. B., R. E. Eskridge, S. T. Rao, and V. Pagnotti.
1984. Effects of traffic speed on the ambient pollutant
concentration near roadways. Presented at the 77th Annual
Meeting of the Air Pollution Control Association on June
24-29, 1984 in San Francisco, California.
Rao, S. T. and M. T. Keenan. 1980. Suggestions for improvement of
the EPA-HIWAY model. JAPCA 30: 247-256.
Rao, S. T., G. Sistla, M. T. Keenan, and J. S. Wilson. 1980. An
evaluation of some commonly used highway dispersion models.
JAPCA 30: 239-246.
Rao, S. T., G. Sistta, R. E. Eskridge, and W. B. Petersen. 1985.
Turbulent diffusion behind vehicles: evaluation of roadway
models. Atmos. Environ. 20: 1095-1103.
84
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Seinfeld, J. H. 1975. Air Pollution: Physical and Chemical
Fundamentals McGraw-Hill, NY. 523pp.
Sheih, C. M., M. L. Wesely and B. B. Kicks. 1979. Estimated dry
deposition velocities of sulfur over the eastern United States
and surrounding regions. Atmos. Environ. 13: 1361-1368.
Tabony, R. C. 1983. Extreme value analysis in meteoroloy. Meteor.
Mag. 112: (No. 1329) 78-98.
Willmott, C. J. 1982. Some comments on the evaluation of model
performance. Bull. Am. Meteorol. Soc. 63: 1309-1313.
Zimmerman, J. R. and R. S. Thompson. 1975. User's Guide for
HIWAY, a Highway Air Pollution Model. EPA-650/4-74-008, U. S.
Environmental Protection Agency, Research Triangle Park, NC.
59 pp.
85
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APPENDIX A
LISTING OF FORTRAN SOURCE CODE FOR ROADWAY
A listing of the FORTRAN source statements for ROADWAY is
given here. The model consists of a main module, 19 subroutines,
and 8 functions. Error-free compilations have been obtained
using ANSI FORTRAN compilers running under Univac EXEC 8 and DEC
VAX/VMS.
86
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PROGRAM ABSTRACT ROADWAY (VERSION 86010) KWY00010
RWY00020
ROADWAY IS A FINITE DIFFERENCE MODEL WHICH PREDICTS RWY00030
POLLUTANT CONCENTRATIONS NEAR A ROADWAY. THIS PROGRAM SHOULD RWY00040
BE USED AS AN ADJUNCT TO THE STANDARD GAUSSIAN HIGHWAY MODELS RWY00050
SINCE IT IS MORE EXPENSIVE TO RUN. RWYOOOSO
RWY00070
THIS PROGRAM USES SURFACE LAYER SIMILARITY THEORY TO RWYOOOSO
PRODUCE VERTICAL WIND AND TURBULENCE PROFILES. TEMPERATURES RWY00090
AT TWO HEIGHTS AND WIND VELOCITY ARE REQUIRED. THESE VALUES RWY00100
ARE USUALLY OBTAINED FROM INSTRUMENTS LOCATED ON A TOWER RWY00110
UPWIND OF THE ROADWAY. RWY00120
RWY00130
ROADWAY IS UNIQUE IN THAT IT USES THE VEHICLE WAKE THEORY RWY00140
DEVELOPED BY ESKRIDGE AND HUNT (1979) AND AS MODIFIED AND RWY001SO
VERIFIED BY ESKRIDGE AND THOMPSON (1982) USING WIND TUNNEL RWY00160
EXPERIMENTS. THIS THEORY PREDICTS THE VELOCITY AND TURBULENCE RWY00170
ALONG A HIGHWAY. RWY00180
RWY00190
RWY00200
REFERENCES RWY00210
RWY00220
ESKRIDGE, R. E. AND J. C. R. HUNT. 1979. HIGHWAY MODELING. RWY00230
PART I: PREDICTION OP VELOCITY AND TURBULENCE FIELDS IN THERWY00240
WAKES OF VEHICLES. J. APPL. METEOR. 18: 387. RWY002SO
RWY002SO
ESKRIDGE, H. E., ?. S. BINKOWSKI , J. C. R. HUNT, T. L. CLARK, RWY00270
AND K. L. DEMERJIAN. 1979. HIGHWAY MODELING. PART II: RWY00280
ADVECTION AND DIFFUSION OF SF8 TRACER GAS. RWY00290
J. APPL. METEOR. 18s 401-412. RWY00300
RWY00310
ESKRIDGE, R. E. AND R. S. THOMPSON. 1982. EXPERIMENTAL AND RWY00320
THEORETICAL STUDY OF THE WAKE OF A BLOCK-SHAPED VEHICLE IN RWY00330
A SHEAR-FREE BOUNDARY FLOW. ATMOS. ENVIRON. 18: 2821. RWY00340
RWY003SO
ESKRIDGE, R. E. AND S. T. RAO. 1983. MEASUREMENT AND PREDIC- RWY00360
TION OF TRAFFIC- INDUCED TURBULENCE FIELDS NEAR ROADWAYS. RWY00370
J. APPL. METEOR. 22: 1431-1443. RWY00380
RWY00390
RWY00400
PROGRAM WRITTEN AND SUPPORTED BY RWY00410
RWY00420
BERT ESKRIDGE RWY00430
DIVISION OF METEOROLOGY (MD-80) RWY00440
0. S. ENVIRONMENTAL PROTECTION AGENCY RWY00450
RESEARCH TRIANGLE PARK, NC 27711 RWY00460
PHONE: (919) 541-4351 RWY00470
RWY00480
RWY00490
STRUCTURE AND MODULE SUMMARY RWYOOSOO
RWYOOS10
ROADWAY RWY00520
READER READ INPUT DATA RWY00530
ECHO ECHO INPUT DATA RWYOOS40
ZERO INITIALIZE ARRAYS RWYOOS50
SBLAYR SURFACE LAYER MODEL DRIVER . RWYOOS60
RIBST « INITIALIZE SURFACE LAYER MODEL RWY00570
RIBTOZ « ESTIMATE ZETA RWY00580
GETSFC CALCULATE U» , T* , AND TO RWYOOS90
PROF I L DETERMINE PROFILES OF WIND SPEED AND RWYOOSOO
TEMPERATURE RWY00810
TURBC CALCULATE TURBULENT MOMENTS RWY00620
UVCMP CONVERT WIND TO U AND V COMPONENTS RWY00630
MOVE « INITIALIZE GRID IN X DIRECTION RWY00640
WHEREX DETERMINE GRID SPACING IN X DIRECTION. FILL IN RWY00850
EMISSION GRID. RWY006SO
FILLIT FILL GRID POINT ARRAY RWY00870
CENTER DETERMINE CENTER OF. TRAFFIC LANES RWY00680
WAKE ADD VEHICLE WAKE EFFECTS TO WIND TURBULENCE FIELDS RWY00690
» FC -- 2-DIMENSIONAL FIT (X-Z PLANE) OF TURBULENT RWY00700
KINETIC ENERGY TERMS TO WIND TUNNEL DATA RWY00710
I POLY « CURVE FIT OF VELOCITY DEFICIT BEHIND RWY00720
VEHICLES TO WIND TUNNEL DATA RWY00730
SIMPSN NUMERICAL INTEGRATION USING SIMPSON'S RWY00740
METHOD RWY00750
-------
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NONDIV -
GRAPH -
ADVCHM
REMOVE DIVERGENCE FROM THE WIND FIELD
PRINT 2-DIMENSIONAL FIELD
ADVECT AND DIFFUSE POLLUTANTS. CHEMISTRY PERFORMED
HERE, IF SPECIFIED.
TIMING DETERMINE THE ADVECTION/DIFFUSION AND
CHEMICAL REACTION TIME STEPS
BNDRYC « ESTABLISH BOUNDARY CONDITIONS FOR THE
POLLUTANT DURING THE MARCHING PROCESS
-- CALCULATE TRANSPORT IN X DIRECTION
ADU
BMOVE
ANTU
ADW
ANTW
DIFFX
DIFFZ
GRAPH
PERFORM ANTIDIFFUSION CALCULATION
CALCULATE TRANSPORT IN Z DIRECTION
PERFORM ANTIDIFFUSION CALCULATION
DIFFUSION IN X DIRECTION
DIFFUSION IN Z DIRECTION
PRINT 2-DIMENSIONAL FIELD
ENTRY POINT IN SUBROUTINE RIBULK
» FUNCTION
INPUT/OUTPUT INFORMATION
DATA SET
FORTRAN
UNIT
S
6
CONTROL INPUT
OUTPUT
I/O UNIT
READER OR DISK
PRINTER OR DISK
C
C«
C
C
C»*«
C""'
C
c
c«
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c
c*
REAL K1,K2,NVEH,NVEH1,MEDN,KX,KXP,KZ,KZP
REAL KXPAS.KYPAS.KYP
DIMENSION XVUO),X(24),Z(8),DU(24,8),C1(24,8),C2(24,8),C3(24,8)
DIMENSION UPRO(8),VPRO(8),DV(24,a),KX(8),KZ(3)
DIMENSION SA(24),SB(24)
-------
C*"
c*»*
C
C*"*
C
C
C»»«
C
40
C
c«
C
so
ROAD. THE HOAD IS TREATED A3 IF IT IS ORIENTATED IN A NORTH-
SOUTH DIRECTION.
WDIR = WDIR * RDANGL
DETERMINE VELOCITY AND TURBULENCE PROFILES AND CALCULATE
EDDY DIFFUSION COEFFICIENTS.
CALL SBLAYR(ZO,Z1,Z2,T1,T2,WSPD,WDIR,8,Z,KX,KZ,RIB,WDPRO)
CONVERT WIND TO U AND V COMPONENTS.
DO 40 K = 2,8
CALL UVCMP(WDIR,WDPRO(K),UPRO(K),VPRO(K))
CONTINUE
NUMBER OF VERTICAL GRID POINTS IS A FUNCTION OF THE NORMAL
WIND VELOCITY.
0 » ABS(UPRO(2))
KMAX > 8
IF (U .LT. 0.5) KMAX * 7
IF (U .LT. 0.1) KMAX » 8
TMSTOP » 300.
IF (KMAX .EQ. 7) TMSTOP = 800.
IF (KMAX .EQ. 8) TMSTOP » 900.
CALCULATE THE SOURCE STRENGTH FROM THE EMISSION STRENGTH.
EA =» VSPD EMA/3800.
EA1 » VSPD1 * EMA1/3600.
IF (ICHEM .EQ. 1) 00 TO SO
EB = VSPD EMB/3SOO.
EB1 - VSPD1 * EMB1/3800.
EC = VSPD EMC/3800.
EC1 » VSPD1 EMC1/3800.
CONTINtJE
VSPD » VSPD/3.8
VSPD1 » VSPD1/3.8
DDX » WIDL
DDZ * Z(2) * 0.5 (Z(3) - Z(2))
DVOL » DDX DDZ ABS(-VSPD + VPRO(2))
DVOL1 » DDX DDZ » ABS(VSPD1 + VPRO(2))
EA * EA/DVOL
EA1 » EA1/DVOL1
IF (ICHEM .EQ. 1) GO TO 80
EB1 » EB1/DVOL1
EB ' EB/DVOL
EC! « EC1/DVOL1
EC * EC/DVOL
CONTINUE
QVA * EA NVEH/3800.
QVA1 * EA1 NVEH1/3800.
IF (ICHEM .EQ. 1) GO TO 70
QVB a EB
QVB1
QVC
70
EB1
EC
QVC1 » EC1
CONTINUE
NVEH/3600.
KVEH1/3600.
NVEH/3800.
NVEH1/3800.
C
C*
C
CALCULATE NUMBER AND SPACING OF GRID POINTS IN X DIRECTION.
NX » 13 + NLANE
IR1 3 4
IF (WDIR .GT. 10. .AND. WDIR .LT.
IF (WDIR .GT. 190. .AND. WDIR .LT.
IF (IR1 .EQ. 4) CALL IVOVE(XD2,XD)
(IR1 .EQ. 3) CALL MOVE(XD3,XD)
170.)
350.)
IR1
IR1
C
C^**
c**«
IF
IF
(IR1 .EQ. 5) CALL NDVE(XD1,XD)
FILL IN GRID POINT ARRAY ACCORDING TO THE NUMBER OF TRAFFIC
LANES AND FILL IN THE CORRESPONDING EMISSION ARRAYS.
RWY01510
RWYO1520
RWY01530
RWY01540
RWY01550
RWY01560
RWY01570
RWY01580
RWY01590
RWYO1600
RWY01810
RWY01S20
RWY01830
RWY01640
RWY01650
RWY01660
RWY01870
RWY01880
RWY01890
RWY01700
RWY01710
RWY01720
RWY01730
RWY01740
RWY01750
RWY01760
RWY01770
RWY01780
RWY01790
RWY01800
RWY01810
RWY01820
RWY01830
RWY01840
RWY01850
RWY01860
RWY01870
RWY01380
RWY01890
RWY01900
RWY01910
RWY01920
RWY01930
RWY01940
RWY01950
RWY01960
RWY01970
RWY01980
RWY01990
RWY02000
RWY02010
RWY02020
RWY02030
RWY02040
RWY020SO
RWY02060
RWY02070
RWY02080
RWY02090
RWY02100
RWY02110
RWY02120
RWY02130
RWY02140
RWY02150
RWY02160
RWY02170
RWY02180
RWY02190
RWY02200
RWY02210
RWY02220
RWY02230
RWY02240
RWY02250
89
-------
c
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CAL.L WHEREX(NLANE,IR1,WIDL,MEDN,XD,QVA,QYA1,QVB,QVB1,QVC,
1 QVC1,X,SA,SB,SC)
DETERMINE CENTER OF LANES FOR WAKE CALCULATION.
CALL CENTER(HEAD1,HEAD2,HEAD3,IR1,NLANE,WIDL,X,NX,XV,HWAYL)
INITIALLY SET WIND FIELD TO AMBIENT CONDITIONS.
c*
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DO 90 I = 1,NX
DO 80 K * l.KMAX
C1(I,K) * UPHO(K)
C2(I,K) = VPRO(K)
80 CONTINUE
90 CONTINUE
DETERMINE VEHICLE WAKE EFFECTS (DU, DV) AND ADD TO AMBIENT
WIND (01, C2).
CALL WAKE(UPRO,VPRO,VSPD,VSPD1,VHCH,NVEH,NVEH1,VWID,X,Z,NX,
1 KMAX,XV,NLANE,DU,DV,KXP,KZP,KXPAS,KYPAS,KYP,IEHR)
IF (IERR .EQ. 0) CXI TO 95
WRITE(10,1000)
GO TO 999
95 CONTINUE
DO 110 1 = l.NX
DO 100 K » l.KMAX
C1(I,K) > Cl(I.K) + DU(I,K)
C2(I,K) * C2(I,K) + DV(I,K)
100 CONTINUE
110 CONTINUE
REMOVE DIVERGENCE FROM THE WIND FIELD IN THE X-Z PLANE.
CALL NONDIV(C1,NX,KMAX,X,Z,C3)
SET WINDS AT SURFACE TO ZERO.
DO 120 I a 1,NX
01(1,1) = 0.0
C3(I,1) » -C3(t,2)
120 CONTINUE
C
C»«« OUTPUT VELOCITY FIELDS (U * 01, V * C2, W * C3).
C
WRITE(IO.1020)
WRITEUO.1025)
TIME » -1.0
IF (INTPR .EQ. 1) GO TO 130
WRITE(10,1030) HEAD1.HEAD2,HEADS
WRITE(10,1040)
CALL GRAPH(C1,1,TIME,NX,KMAX,X,HWAYL)
WRITE!10,1050)
CALL GRAPH(C2,1,TIME,NX,XMAX,X,HWAYL)
WRITE(IO,1060)
CALL GRAPH(C3,1,TIME,NX,KMAX,X,HWAYL)
130 CONTINUE
C
C««» ADD WAKE .TURBULENCE TO EDDY DIFFUSION COEFFICIENTS.
C
DO 150 K = KMAX,1,-1
DO 140 I = 1,NX
KXPU.K) = KXP(I,K) * KX(K)
KZP(I.K) = KZP(I,K) + KZ(K)
140 CONTINUE
150 CONTINUE
C
C»*» OUTPUT EDDY DIFFUSION COEFFICIENT FIELDS.
C
IF (INTPR .EQ. 1) GO TO 180
WRITEC10,1030) HEAD1,HEAD2,HEAD3
WRITEC10,1070)
CALL GRAPH(KXP,1,TIME,NX,KMAX,X,HWAYL)
RWY02260
RWY02270
RWY02280
RWY02290
RWY02300
RWY02310
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RWY02SSO
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RWY02S80
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RWY02610
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RWY02860
RWY02S70
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RWY02890
RWY02700
RWY02710
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RWY02730
RWY02740
RWY02750
RWY02760
RWY02770
RWY02780
RWY02790
RWY02800
RWY02810
RWY02S20
RWY02830
RWY02340
RWY02850
RWY02880
RWY02870
RWY02880
RWY02890
RWY02900
RWY02910
RWY02920
RWY02930
RWY02940
RWY02950
RWY02960
RWY02970
RWY02980
RWY02990
RWY03000
90
-------
WRITE(IO.1080)
CALL GRAPH(KZP.l,TIME,NX,KMAX,X,HWAYL)
160 CONTINUE
>*. PERFORM CHEMISTRY, IF APPLICABLE, AND CALCULATE DIFFUSION.
CALL ADVCHM(SA,SB,SC,A,B,C,D,HWAYL)
GO BACK AND GET DATA FOR NEXT HOUR.
C
C«*»
C
GO TO 10
C
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999 STOP
FORMAT STATEMENTS.
1000 FORMAT('0»«* EXECUTION TERMINATED.1)
1010 FORMATCO"' NORMAL TERMINATION.')
1020 FORMATUHO,//////////, 25X.8K''),/,
1 25X,'",79X,'',/,
2 25X,' THE FOLLOWING GRAPHICAL OUTPUT IS A CROSS SECTION'
3 ' ACROSS THE HIGHWAY IN THE ',/,
4 25X,' X-Z PLANE. IN EACH FIELD, THE BOTTOM LINE IS AT '
5 'Z = 1 METER, WITH HEIGHT ',/,
8 25X,' INCREASING TOWARD THE TOP OP THE PAGE. SUCCEEDIN'
7 'G LINES REPRESENT Z = 2, »',/,
3 25X,' 4.S, 10.5, 20, SO, AND 70 METERS. THE SPACING AC'
9 'ROSS THE ROAD IS DETERMINED ')
1025 FORMAT(25X,' BY STARTING AT THE BOTTOM LEFT POINT, WHICH CORRE'
1 'SPONDS TO THE FIRST VALUE ',/,
2 2SX,' OF THE X GRID PRINTED EARLIER, WITH INCREASING VA'
3 'LUES TO THE RIGHT. THE ',/,
4 25X,'» LAST SET OF CONCENTRATION FIELDS REPRESENT THE ST1
5 'EADY-STATE VALUES AND THE ',/,
, 8 25X,' AVERAGES FOR THE 30 MINUTE PERIOD. THESE STEADY-1
7 'STATE FIELDS OCCUR AT 300, ',/,
8 25X,' 600, OR 900 SECONDS. '
9
A
B
25X,'" ,79X,'',/,
25X.8K"'))
1030 FORMATUH1,'TITLE: ' , 20A4, 2( / , 9X, 20A4)/ )
1040 FORMATUHO,'U FIELD (M/SEC)1)
1050 FORMATUHO,'V FIELD (M/SEC)')
1080 FORMATUHO,'W FIELD (M/SEC)')
1070 FORMATUHO,'KX FIELD (M*«2/SEC) ' )
1080 FORMATUHO,'KZ FIELD (M»«2/SEC)')
END
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SUBROUTINE READER(IERR,IEOF)
PARAMETER LIST:
OUTPUT: IERR - INPUT ERROR INDICATOR (0 = NO ERROR)
IEOF - END OF FILE INDICATOR (1 = END OF FILE)
CALLING ROUTINE:
MAIN
DESCRIPTION:
THIS MODULE READS ALL INPUT DATA FROM FORTRAN UNIT 5. THE
INPUT DATA IS SCREENED TO DETECT ERRORS. IF AN ERROR IS
DETECTED, THEN A NONZERO VALUE IS ASSIGNED TO IERR, AN ERROR
MESSAGE IS PRINTED, AND CONTROL IS RETURNED TO THE MAIN
ROUTINE. INPUT DATA IS PASSED TO THE MAIN ROUTINE VIA
COMMON /INCOM/.
CONTROL INPUT DATA (UNIT 5)
RECORD TYPES 1-3: ALPHANUMERIC DATA FOR TITLES. FORMAT (20A4)
HEAD1 - 80 CHARACTER TITLE
HEAD2 - 80 CHARACTER TITLE
HEADS - 30 CHARACTER TITLE
RWY03010
RWY03020
RWY03030
RWY03040
RWY03050
RWY03060
RWY03070
RWY03080
RWY03090
RWY03100
RWY03110
RWY03120
RWY03130
RWY03140
RWY03150
RWY03160
RWY03170
RWY03180
RWY03190
RWY03200
.RWY03210
RWY03220
.RWY03230
RWY03240
.RWY03250
RWY03260
.RWY03270
RWY03280
.RWY03290
RWY03300
.RWY03310
RWY03320
.RWY03330
RWY03340
.RWY03350
RWY03360
.RWY03370
RWY03380
RWY03390
RWY03400
RWY03410
RWY03420
RWY03430
RWY03440
RWY03450
RWY03460
RWY03470
RWY03480
=RWY03490
RWY03SOO
RWY03S10
RWY03520
RWY03S30
RWY03S40
RWY03S50
RWY035SO
RWY03570
RWY03580
RWY03S90
RWY03600
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RWY03S30
RWY03640
RWY03SSO
RWY03660
RWY03S70
RWY03680
RWY03690
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RWY03710
RWY03720
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RWY03740
RWY03750
91
-------
c
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c«»
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<:*
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C«"
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C*9*
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c***
RECORD TYPE 4: FORMAT (FREE)
ZO - SURFACE ROUGHNESS (METERS)
Zl - HEIGHT OF LOWER TEMPERATURE INSTRUMENT (METERS)
22 - HEIGHT OF UPPER TEMPERATURE INSTRUMENT AND
ANEMOMETER (METERS)
ICHEM - CHEMISTRY OPTION
0, INCLUDE NO, CO, NO2 , AND O3 CHEMISTRY
1, NO CHEMISTRY
IANTI - ANTIDIFPUSION CALCULATION OPTION
0, DO ANTIDIFFUSION CALCULATION
1, SKIP ANTIDIFFUSION CALCULATION
INTPR - INTERMEDIATE PRINT OPTION
0, PRINT FIELDS OP METEOROLOGICAL VARIABLES AND
INTERMEDIATE CONCENTRATION FIELDS
1, PRINT ONLY FINAL CONCENTRATION FIELDS
RECORD TYPE S: FORMAT (FREE)
Tl - TEMPERATURE AT HEIGHT, Zl (KELVIN)
T2 - TEMPERATURE AT HEIGHT, Z2 (KELVIN)
WSPD - HOURLY AVERAGE WIND SPEED) (M/SEC)
WDIR - HOURLY AVERAGE WIND DIRECTION (METEOROLOGICAL
COORDINATES )
RDANGL - ANGLE BETWEEN ROAD AND LINE RUNNING NORTH-SOUTH.
THE ANGLE STARTS AT ZERO DEGREES NORTH. COUNTER-
CLOCKWISE IS POSITIVE AND CLOCKWISE IS NEGATIVE.
THE ANGLE IS ALWAYS LESS THAN 90 DEGREES.
RECORD TYPE 6: BACKGROUND CONCENTRATIONS. FORMAT (FREE)
BACKGA - BACKGROUND CONCENTRATION OF NO (PPM)
BACKGB - BACKGROUND CONCENTRATION OP 00 (PPM)
BACKGC - BACKGROUND CONCENTRATION OF NO2 (PPM)
BACKGD - BACKGROUND CONCENTRATION OF 03 (PPM)
IF ICHEM = i, THEN i
(1) BACKGA IS THE BACKGROUND CONCENTRATION OF THE POLLUTANT
(PPM) AND
(2) BACKGB, BACKGC, BACKGD ARE NOT PROVIDED.
RECORD TYPE 7: HIGHWAY INFORMATION. FORMAT (FREE)
NLANE - NUMBER OF TRAFFIC LANES. MAXIMUM IS 10; MINIMUM IS
4. MUST BE IN INCREMENTS OF 2.
W1DL - WIDTH OP ONE LANE (METERS)
MEDN - WIDTH OF TRAFFIC MEDIAN (METERS)
RECORD TYPE 8s TRAFFIC INFORMATION. FORMAT (FREE)
NVEH - NUMBER OF VEHICLES PER SOUTHBOUND LANE IN AN HOUR
PERIOD
NVEH1 - NUMBER OF VEHICLES PER NORTHBOUND LANE IN AN HOUR
PERIOD
VSPD - AVERAGE VEHICLE SPEED IN SOUTHBOUND LANES (KM/HR)
VSPD1 - AVERAGE VEHICLE SPEED IN NORTHBOUND LANES (KM/HR)
VWID - AVERAGE WIDTH OF VEHICLES (METERS)
VHGH - AVERAGE HEIGHT OF VEHICLES (METERS)
RECORD TYPE 9: EMISSION INFORMATION. FORMAT (FREE)
EMA - NO EMISSION RATE FOR SOUTHBOUND LANES (G/KM/VEH)
EMB - CO EMISSION RATE FOR SOUTHBOUND LANES (G/KM/VEH)
EMC - NO2 EMISSION RATE FOR SOUTHBOUND LANES (G/KM/VEH)
EMA1 - NO EMISSION RATE FOR NORTHBOUND LANES (G/KM/VEH)
EMB1 - CO EMISSION RATE FOR NORTHBOUND LANES (G/KM/VEH)
EMC1 - NO2 EMISSION RATE FOR NORTHBOUND LANES (G/KM/VEH)
IF ICHEM = 1, THEN:
(1) EMA » POLLUTANT EMISSION RATE FOR SOUTHBOUND LANES
EMA1 = POLLUTANT EMISSION RATE FOR NORTHBOUND LANES
(2) EMB, EMC, EMB1, EMC1 ARE NOT PROVIDED.
RECORD TYPE 10: CONVERSION FACTORS. FORMAT (FREE)
RWY03760
RWYQ3770
KWY03780
RWY03790
RWY03800
RWY03810
RWY03820
RWY03830
RWY03840
RWY03850
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RWY04100
RWY04UO
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RWY04470
RWY04480
RWY04490
RWY04SOO
92
-------
c
c
c
c
c
c
c
c
c
c
c«
c
c
c
c
c
c
c
OJB
CNC
CND
- CONVERSION FROM G/SEC TO PPM FOR NO
- CONVERSION FROM G/SEC TO PPM FOR CO
- CONVERSION FROM G/.SEC TO PPM FOR NO2
- CONVERSION FROM G/SEC TO PPM FOR 03
IF ICHEM = 1, THEN:
(1) CNA * CONVERSION FROM G/SEC TO PPM FOR THE POLLUTANT
(2) CNB, CNC, CND ARE NOT PROVIDED
RECORD TYPE 11: CHEMICAL REACTION RATES.
READ ONLY IF ICHEM = 0
FORMAT (FREE)
Kl - CHEMICAL REACTION RATE (I/SEC) FOR THE FOLLOWING:
NO + 03 - NO2 + 02
K2 - CHEMICAL REACTION RATE (I/SEC) FOR THE FOLLOWING:
N02 + 02 NO + 03
REAL K1,K2,NVEH,NVEH1,MEDN
DIMENSION HEAD1(20),HEAD2(20),HEAD3(20)
COMMON /INCOM/ BACXGA,BACKGB,BAaCGC,EACXGD,CNA,CNB,CNC,CND,EMA,
c
c
c
c
c
c
DATA IN/5/,
EMA1,EMB,EMB1,EMC,EMC1,Kl,K2,MEDN,NVEH,NVEH1,
RDANGL.Tl,T2,VHGH,VWID,VSPD,VSPDl,WDIR,WIDL,WSPD,
ZO,Zl,Z2,HEAD1,HEAD2,HEADS,IANTI,ICHEM,INTPR,NLANE
IO/6/
IERR
I EOF
INITIALIZE.
0
0
C
C»
C
READ RECORD TYPE 1-3.
READ(IN,1000,END-990) HEAD1,HEAD2,HEAD3
READ RECORD TYPE 4 AND PERFORM SCREENING.
READ(IN,») ZO,Z1,Z2,ICHEM,IANTI,INTPR
IF (ZO .GT. 0.) GO TO 20
IERR = 1
WRITE(10,2010) IERR
GO TO 999 -
20 CONTINUE
IF (Zl .GE. 0.) GO TO 30
IERR » 2
WRITEtIO.2020) IERR
GO TO 999
30 CONTINUE
IP (22 .GT. Zl) GO TO 40
IERR ' 3
WRITE(IO,2030) IERR
GO TO 999
40 CONTINUE
IF ((ICHEM .NE. 0) .AND. (ICHEM .NE. D) IERR = 4
IF ((IANTI .NE. 0) .AND. (IANTI .NE. 1)) IERR = 4
IF ((INTPR .NE. 0) .AND. (INTPR .NE. D) IERR = 4
IF (IERR .EQ. 0) GO TO 50
WRITEtIO,2040) IERR
GO TO 999
50 CONTINUE
READ RECORD TYPE 5 AND PERFORM SCREENING.
READtIN,*) T1,T2,WSPD,WDIR,RDANGL
IF (Tl .GT. 200.) GO TO 80
IERR = s
WRITEt10,2050) IERR
GO TO 999
80 CONTINUE
IF (T2 .GT. 200.) GO TO 70
IERR = 8
WRITEt10,2060) IERR
GO TO 99*
70 CONTINUE
IF ((WSPD .GT. 0.) .AND. (WSPD .LT. 99.)) GO TO 80
RWY04510
RWY04S20
RWY04530
RWY04540
RWY04550
RWY04560
RWY04570
RWY04S80
RWY04590
RWY04600
RWY04610
RWY04620
RWY04630
RWY04640
RWY04650
RWY04SSO
RWY04670
RWY04680
RWY04690
RWY04700
RWY04710
RWY04720
RWY04730
RWY04740
RWY04750
RWY04760
RWY04770
RWY04780
RWY04790
RWY04800
RWY04810
RWY04820
RWY04830
RWY04840
RWY048SO
RWY04860
RWY04870
RWY04880
RWY04890
RWY04900
RWY04910
RWYQ4920
RWY04930
RWY04940
RWY049SO
RWY04960
RWY04970
RWY04980
RWY04990
RWY05000
RWY05010
RWY05020
RWY05030
RWY05040
RWY050SO
RWY05080
RWY05070
RWY05080
RWY05090
RWY05100
RWYO 5110
RWY05120
RWY05130
RWY05140
RWY05150
RWY05160
RWYOS170
RWY05180
RWYOS190
RWYOS200
RWY05210
RWY05220
RWY05230
RWY05240
RWY05250
93
-------
c
c«
c
c
c«
c
c
c«
c
IERR = 7
WRITE(10,2070) IERR
GO TO 999
80 CONTINUE
IF ((WDIH .GE. 0.) :AND. (WDIR .l£. 360.)) GO TO 90
IERR * 8
WRITE(10,2080) IERR
GO TO 999
90 CONTINUE
IF ((ABS(RDANGL) .GE. 0.) .AND. (ABS(RDANGL) .LT. 90.)) GOTO 100
IERR = 9
WRITE(10,2090) IERR
GO TO 999
100 CONTINUE
READ RECORD TYPE 8 PERFORM SCREENING.
IF (ICHEM .EQ. 0) GO TO 105
READ(IN,*) BACKGA
IF (BACKGA .GE. 0.) GO TO 110
IERR = 10
WRITEU0.2100) IERR
GO TO 999
105 CONTINUE
R£AD(IN,«) BACKGA,BACKGB,BACKGC,BACKGD
IF (BACKGA .LT. 0.) IERR = 10
IF (BACKGB .LT. 0.) IERR = 10
IF (BACKGC .LT. 0.) IERR = 10
IF (BACKGD .LT. 0.) IERR = 10
IF (IERR .EQ. 0) GO TO 110
WRITE(IO,2100) IERR
GO TO 999
110 CONTINUE
READ RECORD TYPE 7 AND PERFORM SCREENING.
READ(IN,«) NLANE.WIDL.MEDN
IF ((NLANE.GE.4) .AND. (NLANE.LE.10) .AND.
1
-------
READ RECORD TYPE 11 IF APPLICABLE AND PERFORM SCREENING.
C«»» READ RECORD TYPE 9 AND PERFORM SCREENING.
C
IF (ICHEM .EQ. 0) GO TO 175
READUN,') EMA.EMA1
IF ((EMA .GT. 0.) .AND. (EMA1 .GT. 0.)) GO TO 130
IERR * 17
WRITEUO.2170) IERR
GO TO 999
175 READUN,*) EMA.EMB, EMC, EMA1, EMB1 ,EMC1
IF ((EMA .LE. 0.) .OR. (EMA1 .LE. 0.)) IERR = 17
IF ((EMB .LE. 0.) .OR. (EMB1 .LE. 0.)) IERR = 17
IF ((EMC .LE. 0.) .OR. (EMC1 .LE. 0.)) IERR = 17
IF (IERR .EQ. 0) GO TO 180
WRITEUO.2170) IERR
GO TO 999
C
C*** READ RECORD TYPE 10 AND PERFORM SCREENING.
C
180 IF (ICHEM .EQ. 0) GO TO 18S
R£AD(IN,«) CNA
IF (CNA .GT. 0.) GO TO 999
IERR * 18
WRITE(10,2180) IERR
GO TO 999
18S READUN,*) CNA,CNB,CNC,CND
IF (CNA .LE. 0.) IERR a 18
IF (CNB .LE. 0.) IERR ' 18
IF (CNC .LE. 0.) IERR = 18
IF (CND .LE. 0.) IERR = 18
IF (IERR .EQ. 0) GO TO 190
WRITE(IO,2130) IERR
GO TO 999
C
C*«*
C
190 READUN,*) K1.K2
IF ((Kl .GE. 0.) .AND. (K2 .GE. 0.)) GOTO 999
IERR a 19
WRITEU0.2190) IERR
GO TO 999
C
C«*» END OF PILE PROCESSING.
C
990 I EOF « 1
C
999 RETURN
C
C««« INPUT FORMATS.
C
1000 FORMAT(20A4/20A4/20A4)
C
ERROR STATEMENT FORMATS.
C
2010 FORMATCO*** ERROR ',12,': SURFACE ROUGHNESS, ZO, IS LESS THAN '
1 'ZERO.')
2020 FORMATCO*** ERROR ',12,': HEIGHT OF LOWER TEMPERATURE ',
1 'INSTRUMENT, Zl, IS LESS THAN ZERO.')
2030 FORMATCO*** ERROR ',12,': HEIGHT OF UPPER TEMPERATURE ',
1 'INSTRUMENT, Z2, IS BELOW OR EQUAL THAT OF THE LOWER ',
2 'INSTRUMENT.')
2040 POHMATCO*** ERROR ',12,': INPUT OPTIONS MUST EQUAL ZERO OR ',
1 'ONE.')
2050 FORMATCO*** ERROR ',12,': TEMPERATURE AT HEIGHT Zl IS NOT IN ',
1 'DEGREES KELVIN.')
2060 PORMATCO*** ERROR ' ,12, ': TEMPERATURE AT HEIGHT Z2 IS NOT IN ' ,
1 'DEGREES KELVIN.')
2070 FORMATCO*** ERROR ',12,': INPUT WIND SPEED IS IN ERROR.')
2080 PORMATCO*** ERROR ',12,': INPUT WIND DIRECTION IS IN ERROR.')
2090 FORMATCO*** ERROR ',12,': HIGHWAY ORIENTATION IS INCORRECTLY ',
I 'SPECIFIED.')
2100 FORMATCO*** ERROR ',12,': BACKGROUND POLLUTANT CONCENTRATIONS '
1 'CANNOT BE LESS THAN ZERO.')
2110 PORMATCO*** ERROR ',12,': NUMBER OF TRAFFIC LANES IS ',
1 'INCORRECTLY SPECIFIED.')
2120 PORMAT( '<) ERROR ' ,12, ' : WIDTH OF A TRAFFIC LANE CANNOT BE ' ,
RWY0601Q
RWY06020
RWY06030
RWY06040
RWY060SO
RWY06060
RWY08070
RWY06080
RWY06090
RWY06100
RWY06110
RWYOS120
RWY06UO
RWY06140
RWY061SO
RWY08160
RWY06170
RWY06180
RWYOS190
RWY06200
RWY08210
RWY06220
RWY06230
RWY06240
RWY082SO
RWY062SO
RWY06270
RWY08280
RWY08290
RWY06300
RWYOS310
RWY08320
RWY06330
RWY06340
RWY063SO
RWY08360
RWY06370
RWY06380
RWYOS390
RWY06400
RWY08410
RWYOS420
RWY06430
RWY06440
RWY064SO
RWYOS460
RWYOS470
RWYQ6480
RWY08490
RWY06SOO
RWY08510
RWY06S20
RWY06S30
.RWY06540
RWY08550
RWY06S60
RWY06570
RWY08530
RWY06590
RWY06600
RWY06610
RWY06620
RWY06S30
RWYOS640
RWY06650
RWY06660
RWY06670
RWY08680
RWY06890
RWY06700
.RWY06710
RWY08720
RWY06730
RWY06740
RWY08750
95
-------
1 'LESS THAN OR EQUAL TO ZERO.') RWY06760
2130 FORMATCO'" ERROR ',12,': THE TRAFFIC MEDIAN CANNOT BE LESS', RWY08770
1 ' THAN ZERO.') RWY06780
2140 FORMATCO'" ERROR ',12,': TRAFFIC VOLUME CANNOT BE LESS THAN ', RWY06790
1 'OR EQUAL TO ZERO.') RWY06800
2150 FORMATCO'" ERROR ',12,': AVERAGE VEHICLE SPEED IS INCORRECTLY',RWYO6810
1 ' SPECIFIED.') RWY06820
2160 FORMATCO"' ERROR ',12,': AVERAGE VEHICLE DIMENSIONS ARE ', RWY06830
1 'INCORRECTLY SPECIFIED.') RWY06840
2170 FORMATCO"' ERROR ',12,': VEHICLE EMISSION RATES MUST BE ', RWY06850
1 'GREATER THAN ZERO.') RWY06860
2180 FORMATCO*" ERROR ',12,': CONVERSION FACTOR FOR G/SEC TO PPM ', RWY06870
1 MS INCORRECTLY SPECIFIED.') RWY06880
2190 FORMATCO"' ERROR ',12,': CHEMICAL REACTION RATES CANNOT BE ', RWY08890
1 'LESS THAN ZERO.') RWY06900
END RWY08910
RWY06920
=====*RWY06930
RWY06940
RWY06950
RWY06960
RWY06970
RWY06980
RWY06990
RWY07000
RWY07010
RWY07020
RWY07030
REAL K1,K2,NVEH,NVEH1,MEDN RWY07040
DIMENSION HEAD1(20),HEAD2(20),HEAD3(20) RWY07050
COMMON /INCOM/ BACXGA,BACKGB,BACKGC,BACKGD,CNA,CNB,CNC,CND,EMA, RWY07060
EMAl,EMB,EMBl,EMC,EMCl,Kl,K2tMEDN,NVEH,NVEHl, RWY07070
RDANGL,T1,T2,VHGH,VWID,VSPD,VSPD1,WDIR,WIDL,WSPD, RWY07080
ZO,Z1,Z2,HEAD1,HEAD2,HEADS,IANTI,ICHEM,INTPR.NLANE RWY07090
RWY07100
RWY07110
RWY07120
RWY07130
RWY07140
RWY07150
RWY07160
RWY07170
WRITE(10,1010) ICHEM,IANTI,INTPR
C
c
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SUBROUTINE ECHO
CALLING ROUTINE:
MAIN
DESCRIPTION:
THIS MODULE ECHOES THE INPUT DATA. THE DATA
THIS SUBROUTINE VIA COMMON /INCOM/.
IS PASSED TO
C
c.
C
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C*
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c*
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C*"*
c
DATA IN/5/, IO/8/, IVER/88010/
PRINT TITLE.
WRITE( IO.1000) IVER,HEAD1,HEAD2,HEAD3
PRINT OPTIONS.
PRINT METEOROLOGICAL INFORMATION.
WRITE( IO.1020) ZO,Z1,Z2,T1,T2,WSPD,WDIR
PRINT HIGHWAY INFORMATION.
WRITE( IO.1030) NLANE,WIDL,MEDN,RDANGL
WRITE( 10,1035) NVEH,NVEH1,VSPD,VSPD1,VWID,VHGH
PRINT EMISSIONS INFORMATION.
IF (ICHEM .EQ. 0) GO TO 10
WRITE(IO,1040) BACXGA,EMA,EMA1,CNA
GO TO 999
10 CONTINUE
WRITE(10,1005) HEAD1,HEAD2,HEAD3
WRITE(IO,10SO) BACKGA,BACKGB,BACKGC,BACKGD
WRITE(IO.1060) EMA,EMB,EMC,EMA1,EMB1,EMC1
WRITEU0.1070) CNA,CNB,CNC,CND,K1,K2
999 RETURN
FORMAT STATEMENTS.
1000 FORMAT(IX,33X, " » ROADWAY (VERSION ',15,') ',///,
1 IX,'TITLE: ',20A4,2(/,9X,20A4)/)
1005 FORMATUH1,'TITLE: ' , 20A4, 2( / , 9X, 20A4) / )
1010 PORMATUHO, '0 P T I 0 N S1,/,
I 1H0.4X,'CHEMISTRY OPTION (ICHEM) ' , 29C . ' ) , 4X, I 8 , / ,
2 IX,4X,'ANTIDIFFUSION CALCULATION OPTION (IANTI)
3 4X.I8,/,
RWY07180
RWY07190
RWY07200
RWY07210
RWY07220
RWY07230
RWY07240
RWY07250
RWY07280
RWY07270
RWY07280
RWY07290
RWY07300
RWY07310
RWY07320
RWY07330
RWY07340
RWY07350
RWY07380
RWY07370
RWY07380
RWY07390
RWY07400
RWY07410
RWY07420
RWY07430
RWY07440
RWY07450
RWY07480
RWY07470
RWY07480
,13('.').RWY07490
RWY07500
96
-------
4 IX,
1020 FORMAT(1HO,
1 1HO,
2 IX,
3 IX,
4 IX,
5 IX,
S IX,
7 IX,
3 IX,
9 IX,
1030 FORMAT(1HO,
1 1HO,
2 IX,
3 IX,
4 IX,
S
1035 FORMAT( IX,
1
2
3
4
S
8
7
8
9
A
IX,
IX,
IX,
8X,
8X,
IX,
IX,
IX,
1040 FORMATdHO,
1HO,
IX,
IX,
IX,
IX,
1050 FORMATdHO,
1 1HO,
2 IX,
3 IX,
4 IX,
5 IX,
1080 FORMAT( IX,
1 IX,
2 IX,
3 IX,
4 IX,
S IX,
8 IX,
7 IX,
1070 FORMAT( IX,
IX,
IX,
IX,
IX,
IX,
IX,
END
IX,
4X,'INTERMEDIATE PRINT OPTION (INTPR) ',20('.'),4X,I8/
'METEOROLOGY',/,
4X,'SURFACE ROUGHNESS (ZO) ',31('.'},2X.F10.4,' M',/,
4X,'HEIGHT OF TEMPERATURE INSTRUMENTS',/,
7X,'LOWER (Zl) ',40('.'),2X,F10.2,' M1,/,
7X,'UPPER (Z2) ',40('.'),2X.F10.2,' M1,/,
4X,'TEMPERATURE AT HEIGHT:',/,
7X,'Z1 (Tl) ' ,43C .'),2X,F10.2, ' K',/,
7X,'Z2 (T2) ',43<'.'),2X,F10.2,' K',/,
4X,'WIND SPEED (WSPD) ',38('.'),2X.F10.2,' M/SEC',/,
4X,'WIND DIRECTION (WDIR) ',32('.'),2X.F10.2,' DEG1,/)
'HIGHWAY INFORMATION1,/,
4X,'NUMBER OF TRAFFIC LANES (NLANE) ',22('.'),4X,18,/,
4X,'WIDTH OF EACH LANE (WIDL) ',28('.'),2X.P10.2,' M1,
4X,'WIDTH OF MEDIAN (MEDN) ',31('.'),2X.F10.2,' M',/
4X,'ANGLE BETWEEN ROAD AND LINE RUNNING N-3 (RDANGL) '
SO.'),2X,F10.2,' DEG1)
4X,'TRAFFIC VOLUME1,/,
7X,'SOUTHBOUND LANES (NVEH) ',27('.'),4X.F8.0,
' VEH/HR',/,
7X,'NORTHBOUND LANES (NVEH1) ',28('.'),4X.F8.0,
' VEH/HR',/,
4X,'AVERAGE VEHICLE SPEED',/,
'SOOTHBOUND LANES (VSPD) ',27('.'),2X.F10.2,' KM/HR',/
'NORTHBOUND LANES (VSPD1) ',28('.'),2X.F10.2,' KM/HR'/
4X,'AVERAGE DIMENSIONS OF VEHICLES',/,
7X,'WIDTH (VWID) ' ,38( ' . ' ), 2X.F10. 2, ' M', / ,
7X,'HEIGHT (VHGH) ',37('.'),2X,F10.2,' M',/)
'EMISSION INFORMATION',/,
4X,'BACKGROUND CONCENTRATION (BACKGA) ',20('.'),2X,
F10.4,' PPM',/,
4X,'EMISSION RATES;',/,
7X,'SOOTHBOOND LANES (EMA) ',27('.'),2X.F10.4,
1 G/KM/VEH',/,
7X,'NORTHBOUND LANES (EMA1) ',27('.'),2X,F10.4,
' G/KM/VEH',/,
4X,'CONVERSION FACTOR FOR G/SEC TO PPM (CNA) ' ,13('.' )
-2X.F10.4)
'EMISSION INFORMATION',/,
4X,'BACKGROUND CONCENTRATIONS:',/,
7X,'NO (BACKGA) ',38('.'),2X.F10.4,' PPM',/,
7X,'CO (BACKGB) ',38('.'),2X.F10.4,' PPM',/,
7X,'NO2 (BACKGC) ',38('.'),2X,F10.4,' PPM',/,
7X,'O3 (BACKGD) ',38('.'),2X.F10.4,' PPM')
4X,'EMISSION RATES FOR THE SOUTHBOUND LANES:',/,
7X,'NO (EMA) ',41C.'),2X.F10.4,' G/KM/VEH',/,
7X,'CO (EMB) ',41C.'),2X,F10.4,' G/KM/VEH',/,
7X,'NO2 (EMC) ',41('.'),2X.F10.4,' G/KM/VEH',/,
4X,'EMISSION RATES FOR THE NORTHBOUND LANES:',/,
7X,'NO (EMA1) ',40('.'),2X,F10.4,' G/KM/VEH',/,
7X,'CO (EMB1) ',40('.'),2X,F10.4,' G/KM/VEH',/,
7X,'NO2 (EMC1) ',40('.'),2X.FIO.4,' G/KM/VEH')
4X,'CONVERSION FACTORS (G/SEC TO PPM) FOR:',/,
7X,'NO (CNA) ',41('.'),2X,F10.4,/,
7X,'CO (CNS) ',41('.'),2X,F10.4,/,
7X,'NO2 (CNC) ',41('.'),2X,F10.4,/,
7X,'O3 (CND) ',41('.'),2X,F10.4,/,
4X,'CHEMICAL REACTION RATES FOR THE FOLLOWING:',/,
7X,'NO * 03 - NO2 » O2 '28('.'),2X.F10.4,
' 1/(PPM MIN)1,/
7X,'NO2 + 02 MO + O3 '28<'.'),2X.F10.4,' 1/MIN')
C
C
C
C
C
C
C
C
C
SUBROUTINE ZERO(ICHEM,SA,SB,SC,A,B,C,D)
PARAMETER LIST:
INPUT: ICHEM - CHEMISTRY OPTION
OUTPUT: SA - NO EMISSION GRID (G/M»«3/SEC).
IF ICHEM = 1, THEN SA IS THE POLLUTANT
EMISSION GRID AND SB AND SC ARE IRRELEVANT.
SB - CO EMISSION GRID (G/M««3/SEC)
SC - NO2 EMISSION GRID (G/M»»3/SEC)
A - NO CONCENTRATION FIELD (PPM).
)RWY07510
RWY07520
RWY07530
RWY07540
RWY07550
RWY07560
RWY07570
RWY07580
RWY07S90
ROT07SOO
RWY07S10
RWY07620
RWY07630
/RWY07640
RWY07650
.RWY07660
RWY07870
RWY07S80
RWY07890
RWY07700
RWY07710
RWY07720
RWY07730
.RWY07740
.RWY07750
RWY07760
RWY07770
RWY07780
RWY07790
RWY07800
RWY07810
RWY07820
RWY07830
RWY07840
RWY07350
RWY07880
.RWY07870
RWY07880
RWY07890
RWY07900
RWY07910
RWY07920
RWY07930
RWY07940
RWY07950
RWY07960
RWY07970
RWY07980
RWY07990
RWY08000
RWY08010
RWY08020
RWY08030
RWY08040
RWY08050
RWY08060
RWY08070
RWY08080
RWY08090
RWY08100
RWY08110
RWY08120
RWY08130
=RWY08UO
RWY08150
RWY08160
RWY08170
RWY08180
RWY08190
RWY08200
RWY08210
RWY08220
RWY08230
RWY08240
RWY08250
-------
c
c
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10
20
100
200
300
C
C
C
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IF ICHEM = 1, THEN A IS THE POLLUTANT
CONCENTRATION FIELD AND B, C, AND D ARE
IRRELEVANT.
8 - CO CONCENTRATION FIELD (PPM)
C - NO2 CONCENTRATION FIELD (PPM)
D - O3 CONCENTRATION FIELD (PPM)
CALLING ROUTINE:
MAIN
DESCRIPTION:
THIS MODULE PERFORMS THE NECESSARY INITIALIZATION PRIOR TO
CALCULATIONS.
DIMENSION A(24,8,2),B(24,3,2),C(24,3,2),D(24,8,2)
DIMENSION SA(24),SB(24),SC(24)
DO 300 I a 1,24
SA(I) * 0.0
IF (ICHEM .EQ. 1) GO TO 10
SB(I) a 0.0
SCU) » 0.0
CONTINUE
DO 200 K » 1,8
DO 100 L =» 1,2
A(I,K,L) * 0.0
IF (ICHEM .EQ. 1) GO TO 20
8(1, K,L) a o.Q
C(I,K,L) = 0.0
D(I,K,L) » 0.0
CONTINUE
CONTINUE
CONTINUE
CONTINUE
RETURN
END
RWY08260
RWY08270
RWY08280
RWY08290
RWY03300
RWY08310
RWY08320
RWY08330
RWY08340
RWY08350
RWY08360
RWY08370
RWY08380
RWY08390
RWY08400
RWY08410
RWY08420
RWY08430
RWY08440
RWY084SO
RWY08460
RWY08470
RWY08480
RWY08490
RWY08SOO
RWY08510
RWY08S20
RWY08S30
RWY08S40
RWY08SSO
RWY08S80
RWY08S70
RWY08S80
RWY08590
RWY08SOO
RWY08810
RWY08620
RWY08630
RWY08650
SUBROUTINE SBLAYR(ZO,Z1 ,H,T1 ,T2 ,WSP,WDIR,KMAX,2,KX,KZ,RIB,WSPD)
PARAMETER LIST:
INPUT: ZO - SURFACE ROUGHNESS (METERS)
Zl - HEIGHT OF LOWER TEMPERATURE INSTRUMENT
(METERS)
H - HEIGHT OF UPPER TEMPERATURE INSTRUMENT AND
ANEMOMETER (METERS)
Tl - TEMPERATURE AT HEIGHT, Zl (KELVIN)
T2 - TEMPERATURE AT HEIGHT, H (KELVIN)
WSP - HOURLY AVERAGE WIND SPEED (M/SEC)
WDIR - HOURLY AVERAGE WIND DIRECTION (RELATIVE TO
THE HIGHWAY)
KMAX - NUMBER OF VERTICAL LEVELS (KMAX * 8)
Z - ARRAY CONTAINING HEIGHTS OF VERTICAL LEVELS
(METERS)
OUTPUT: KX - HORIZONTAL EDDY DIFFUSION COEFFICIENTS
(M««2/SEC)
KZ - VERTICAL EDDY DIFFUSION COEFFICIENTS
(M'»2/SEC)
RIB - BULK RICHARDSON NUMBER
WSPD - VELOCITY PROFILE ARRAY (M/SEC)
CALLING ROUTINE:
MAIN
SUBPROGRAMS CALLED:
RIBST*. RIBTOZ*, GETSFC*. PROFIL*. TURBC*
INDICATES ENTRY POINT IN SUBROUTINE RIBULK
DESCRIPTION:
THIS NODULE IS THE DRIVING ROUTINE FOR THE SURFACE LAYER
MODEL WRITTEN BY FRANK BINKOWSKI USING SIMILARITY THEORY.
THIS SUBROUTINE FINDS THE VELOCITY PROFILE, TURBULENCE
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C9**
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c»««
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PROFILES, AND CALCULATES EDDY DIFFUSION COEFFICIENTS.
REAL LAMDA,KX,KZ,L
DIMENSION KX(8) ,KZ(8) ,WSPD(8) ,Z(8)
DATA G/9.80616/, GAMD/.00976/
INITIALIZE SURFACE LAYER MODEL.
DELZ = H - Zl
THETA1 « Tl * GAMD Zl
THETA2 » T2 + GAMD H
DTEMP » THETA2 - THETA1
RIB * H G « DTEMP/ (THETA2 WSP»«2)
IF(HIB .GT. 0.20) RIB * 0.20
CALL RIBST(H,Z1,ZO,1)
GET ESTIMATE OF ZETA.
CALL RIBTOZ< RIB, ZETA)
CALCULATE U«, T», AND TO.
CALL GETSFC(ZETA,WSP,THETA2, DTEMP, USTAR.TSTAR, TO )
L » H/ZETA
CALCOLATE VERTICAL WIND PROFILE AND EDDY DIFFUSION
COEFFICIENTS.
DO 20 K « 2,KMAX
ZL * Z(K)/L
OBTAIN WIND SPEED, TEMPERATURE, AND GRADIENTS OF THESE
PARAMETERS AT HEIGHT ZL.
CALL PROPIL(Z(K) ,ZL, USTAR.TSTAR, TO, WSPD(K) , TH , DUDZ , DTHDZ )
ZETA « Z(K)/L
OBTAIN TURBULENT MOMENTS USING BINKOWSKI7S CLOSURE MODEL.
CALL TURBC(ZBTA,SU,SV,SW,ST,UT,SQ,FM)
SU » SU USTAR
3V m SV USTAR
SW * SW * USTAR
IF (WDIR .LT. 90.) WD1 « 90. - WDIR
IF (WDIR .GE. 90. .AND. WDIR .LT. 180.) WD1 » WDIR - 90.
17 (WDIR .GE. 180. .AND. WDIR .LT. 270.) WD1 = 270. - WDIR
IF (WDIR .GT. 270.) WD1 * WDIR - 270.
WD1 * WDl 3.14159285/180.
SU1 * SO COS(WDl) * SV SIN(WDl)
SV1 « -SU SIN(WDl) + 3V COS(WDl)
LAMDA » Z(K)/FM
KZ(K) > .125 SW * LAMDA
IF (ZETA .LT. 0. .AND. K .GT. 2) GO TO 10
KX(K) * ABS(SUl) * LAMDA
CONTINUE
CONTINUE
DO 30 K * 3.KMAX
KX(K) * KX(2)
CONTINUE
KX(1) a KX(2)
RETURN
END
SUBROUTINE RIBULK(H,Z1 ,ZO,NTYPE,ZZ,RIB)
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THIS ROUTINE CALCULATES SURFACE QUANTITIES SUCH AS U" AND T« USINGRWY09720
USING SIMILARITY THEORY.
REFERENCES :
NICKERSON AND SMILEY JAM(14) 297-300 197S.
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BENOIT JAM(IS) 359-860 1977
NOTE: THE STABLE PROFILES ARE INTEGRATED FROM ZO/L TO Z/L ALSO.
THIS IS AN EXTENSION OF NICKERSON 4 SMILEY( 1975 ), BENO!T( 1977 ).
THE CALLING SEQUENCES ARE:
CALL RIBST(H,Z1,ZO, NTYPE)
WHERE:
H IS ANEMOMETER HEIGHT (METERS)
Zl IS THE LOWEB THERMOMETER HEIGHT (METERS)
ZO IS THE ROUGHNESS HEIGHT (METERS)
NTYPE IS A PROFILE INDICATOR.
NTYPEsl; DYER PROFILES
NTYPE=2; BUSINGER PROFILES..
THIS INITIALIZES THE ROUTINE.
NOW TO OBTAIN AN ESTIMATE OF ZETA FROM A VALUE OP RIB:
CALL RIBTOZ(RIB,ZETA)
TO OBTAIN U», T« AND TO:
CALL GETSFC(ZL,UH,THETA,DT,DSTAR,TSTAR,TO)
WHERE:
ZL IS A VALUE OR ESTIMATE OF ZETA.
UH IS THE WIND SPEED AT H (METERS /SECOND)
THETA IS THE POTENTIAL TEMPERATURE AT H (DEGREES KELVIN)
DT IS THE TEMPERATURE DIFFERENCE BETWEEN H AND Zl (DEGREES)
USTAR IS U* AT ZO (METERS/ SECOND)
TSTAR IS T« AT ZO (DEGREES KELVIN)
TO IS THE EXTRAPOLATED TEMPERATURE AT ZO (DEGREES KELVIN)
TO OBTAIN VALUES OP WIND SPEED, TEMPERATURE AND THE GRADIENTS
OF THESE QUANTITIES AT VARIOUS HEIGHTS:
CALL PROFIUHZ.ZL.USTAR.TSTAR.TO.UP.TP.DUDZ.DTHDZ)
WHERE:
HZ IS THE HEIGHT (METERS) AND MOST BE GREATER THAN ZO.
ZL IS THE VALUE OP ZETA AT HZ.
USTAR, TSTAR, TO ARE AS ABOVE.
UP IS THE PREDICTED WIND SPEED AT HZ ( METERS/ SECOND ).
TP IS THE PREDICTED POTENTIAL TEMPERATURE AT HZ (DEGREES KELVIN)
DUDZ AND DTHDZ ARE THE PREDICTED WIND SHEAR (I/SECONDS) AND
POTENTIAL TEMPERATURE GRADIENT (DEGREES /METER) AT HZ.
TO OBTAIN TURBULENT MOMENTS USING BINKOWSKI'S CLOSURE MODEL:
CALL TURBC(Z,SU,SV,SW,ST,UT,SQ,FM)
WHERE:
Z IS Z/L
SU.SV.SW ARE THE NORMALIZED RMS TURBULENT VELOCITY COMPONENTS.
THEY ARE NORMALIZED BY USTAR AND THUS ARE NON-DIMENSIONAL.
ST IS THE NORMALIZED RMS TURBULENT TEMPERATURE FLUCTUATION.
IT IS NORMALIZED BY TSTAR AND IS NON-DIMENSIONAL.
UT IS NORMALIZED LONGITUDINAL KINEMATIC HEAT -FLUX. IT IS NORMAL-
IZED BY USTAR-TSTAR AND IS NONDIMEN3IONAL.
3Q IS THE NORMALIZED RMS TURBULENT VELOCITY FLUCTUATION. IT IS
NORMALIZED BY USTAR AND IS NON-DIMENSIONAL.
FM IS THE NON-DIMENSIONAL FREQUENCY OF THE PEAK IN THE W SPECTRUM
THIS CALL SHOULD ONLY BE USED WHEN NTYPE =! ABOVE.
CODED BY DR FRANCIS 3. BINKOW3KI 1977.
DATA GRAV/9.80618/, ONE3/0. 3S3333/
FAC1(X1,X2)*ALOG( (X1«X1+1 . 0 )«(X1+1. 0 ) «(X1+1. 0 )/ (
1 (X2«X2+1.0)«(X2+1.0)»(X2+1.0) ) )
PAC2(Y1,Y2)=2.0»(ALOG( (Y1+1.0)/(Y2+1.0) ) )
ENTRY RIBST(H,Z1,ZO, NTYPE)
COMMENT: INITIALIZE THE CONSTANTS AND PARAMETERS.
C
IF(NTYPE .EQ. 2) GO TO 1
DYER PfcOFILES.
GAMA1= 1S.O
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.RWY10310
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GAMA2=18.0
BETA =3.0
VK=0.4
R=1.0
ARIB2=8.S12
GO TO 3
BCSINGER PROFILES
GAMA1=15.0
GAMA2=9.0
BETA=4.7
VK=0.35
R=0.74
ARIB2*6.424
ALNZ*ALOG(H/ZO)
ALNZT-ALOG(H/Z1)
ALNZ1»ALOG(Z1/ZO)
F2GN»ALNZ«ALNZ/(R'ALNZT)
Z1H»Z1/H
ZOH=ZO/H
ZOlaZO/Zl
GM1HZO»GAMA1*ZOH
GM2HZ1*GAMA2«Z1H
GM2HZO=CAMA2»ZOH
VKGH»VK«GRAV«H
RETURN
ENTRY ZTORIB(ZL,RIB)
HL'ZL
ASSIGN 5 TO ISTAT
GO TO 109
BB*HL«G/(VK«P«P)
RIB*BB
RETURN
ENTRY RIBTOZCRIB,ZEST)
ACC=0.0
ITERM=3
IP( RIB .LT. 0.04 ) GO TO 85
ITERM=5
ACC=ARIB2
HL=F2GN"(1.0 + ACC»RIB)*RIB
ITERATE TO RECOVER Z/L.
DO 81 ITERal.ITERM
ASSIGN 8 TO ISTAT
GO TO 109
ZEST»(VK«P»F/G)«RIB
HL'ZEST
CONTINUE
RETURN
ENTRY GETSFC(ZI,,OH,THETA,DT,USTAR,TSTAR,TO)
HL=ZL
ASSIGN 8 TO ISTAT
GO TO 109
IF(HL.LT. 0.0 ) GO TO 4
BYTO=>BETA«HL«Z1H» (1. 0-Z01)
GO=(R«ALNZ1 + BYTO)/VK
GO TO 7
ETAO*SQRT(1.0 -GM2HZO»HL)
GO=R«(ALNZ1 + FAC2(ETAO,ETA1) )/VK
USTAR=UH/F
TSTAR=DT/G
TO=THETA - DT - TSTAR'GO
RETURN
IF(HL .LT. 0.0 ) GO TO 101
STABLE
BYU=»BETA»HI,«( 1.0-ZOH)
BYT=BETA«HL«(1.0-Z1H)
Fa(ALNZ + BYU)/VK
G=( R'ALNZT + BYT)/VK
GO TO 105
UNSTABLE
ZETAO=SQRT( SQRTt 1.0 - GMIHZO'HL ) )
ETA1=SQRT(1,0-GM2HZ1»HL)
avmosio
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ZETAH=SQRT(SQRT(1.0-GAMA1*HL) )
ETAH=SQRT(1.0-GAMA2«HL )
F=(ALNZ + FACl(ZETAO,ZETAH)-f2.0*(ATAN(ZETAH)-ATANUETAO)))/VK
G=R«( ALNZT * FAC2(ETA1,ETAH) )/VK
GO TO ISTAT,(5,6,8)
ENTRY PBDFIL(HZ,ZL,USTAR,TSTAR,TO,UP,TP,DUDZ,DTHDZ)
HL»ZL
VKHZ=VK*HZ
ALNXaALOGtHZ/ZO)
IF( HL .LT. 0.0 ) GO TO 44
BY»BETA*HL* ( 1 . 0 -ZO /HZ )
F=(ALNX + BY)/VK
G=( R'ALNX + BY)/VK
DUDZ=USTAR«(1.0 + BY)/VKHZ
DTHDZ»TSTAR«(R +BY)/VKHZ
GO TO 55
UNSTABLE
GMAHZO*GAMA1 »ZO/HZ
GMBHZO=GAMA2»ZO/HZ
ZETAO=SQRT( 3QRT( 1.0 - GMAHZO'HL ) )
ETAO~SQRT( 1 . 0-GMBHZO*HL)
ZETAH»SQRT(SQRT(1.0-GAMA1*HL) )
ETAH"SQRT(1.0-GAMA2»HL )
F»(ALNX + FAC1(ZETAO,ZETAH)+2.0»(ATAN(ZETAH)-ATAN(ZETAO)))/VK
G»R»(ALNX * FAC2(ETAO,ETAH) )/VK
DUDZ*USTAR/ (VKHZ»ZETAH)
DTHDZ=R«TSTAR/ (VKHZ'ETAH)
UP - USTAR'F
TP»TO + TSTAR*G
RETURN
ENTRY TURBC(Z,SU,SV,SW,ST,UT,Sq,FM)
IF( Z .LT. 0.0 ) GO TO 91
STABLE
PHIM = 1.0 + 5.0'Z
GO TO 95
UNSTABLE
PHIM=1.0/SQRT( SQRT( 1.0-18.0»Z ) )
RF=Z/PHIM
GAMMA > RF/(1.0 - RF)
ALFAT=2.83»( ( 0.30«PHIM-Z)/( 0.79«PHIM-Z) )
PHIH>PHIM/ALFAT
USE INTERNAL ALFAT TO GET PHIH.
SCALE" 1.0
IF( Z .GT. 0.0 ) SCALE * 1.0 * 3.39«Z - 0.25»Z«Z
IF( Z .GE. 2.0 ) SCALE » 8.78 + 2.39»( Z - 2.0 )
THIS MAKE FM PROPORTIONAL TO Z/L FOR LARGE Z/L.
IF( Z .LT. 0.0 ) SCALE * 0.40 + 0. 80«EXP(4.0"Z)
SCALE2*SCALE*SCALE
FM» 0.4 'SCALE
D1=1.0/FM
SW=( ( PHIM-Z) /( 1 . 20»FM) ) "0. 333333
SWFM»0.4«3W
W2»SW«SW
Q2=W2"(3.0 + 0.75«(1.0 * Dl) * 1.80«GA\WA)
V2aONE3«Q2 - W2 ( 0 . 0 8 GAWHA * 0. 13*(2. 0-D1 ) )
U2=<32 - ( V2 * W2)
T2«2.5»PHIH/SWFM
IF( Z .GT. 0.0) T2-T2/SCALE2
SU=3QRT(U2)
UT"O.S3»(PHIH + 1.9»PHIM)/SWFM
IF( Z .GT. 0.0 ) UT=UT/SCALE2
ST=SQRT(T2)
SV=SQRT(V2)
3Q=SQRT(Q2)
RETURN
END
33=3333333333=333333=333333 33333=3333333333=3333333333=3=333333:
SUBROUTINE UVCMP(DIR,SPD,U, V)
PARAMETER LIST:
INPUT: DIR - WIND DIRECTION (RELATIVE TO HIGHWAY)
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SPD - WIND SPEED (M/SEC)
OUTPUT! U - EAST -WEST COMPONENT (RELATIVE TO A N-S
HIGHWAY) OF THE WIND (M/SEC)
V - NORTH-SOUTH COMPONENT (RELATIVE TO A N-S
HIGHWAY) OF THE WIND (M/SEC)
CALLING ROUTINE:
MAIN
DESCRIPTION:
THE SUBROUTINE CONVERTS WIND VELOCITY INTO ITS U AND V
COMPONENTS.
PI = 3.141592854
U m -3PD SIN(DIR PI/180.)
V * -SPD COS(DIR PI/180.)
RETURN
END
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SUBROUTINE TVDVE(XX,YY)
PARAMETER LIST:
INPUT: XX - INITIALIZING ARRAY
OUTPUT: YY - ARRAY TO BE INITIALIZED
CALLING ROUTINE:
MAIN
DESCRIPTION:
THIS MODULE INITIALIZES THE GRID IN THE X DIRECTION.
DIMENSION XX(8),YY(8)
DO 10 I = 1,8
YY(I) = XXU)
10 CONTINUE
RETURN
END
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SUBROUTINE WHEREX(NLANE, IR1 .WIDL.RMEDN.XD.QVA.QVAl ,QVB,QVB1 ,QVC,
1 QVC1,X,3A,SB,SC)
.
PARAMETER LIST:
INPUT: NLANE - NUMBER OF TRAFFIC LANES
IR1 - WIND DIRECTION INDICATOR
WIDL - WIDTH OP ONE LANE
RMEDN - HALF WIDTH OP TRAFFIC MEDIAN (METERS)
XD - GRID SPACING PARAMETERS (METERS)
QVA - NO SOURCE STRENGTH OF SOUTHBOUND LANES
(G/SEC/M"3)
QVA1 - NO SOURCE STRENGTH OF NORTHBOUND LANES
-------
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SUBPROGRAMS CALLED:
FILLIT
DESCRIPTION:
THIS M3DULE CALCULATES THE NUMBER AND SPACING OF GRID POINTS
IN THE X-DIRECTION AND FILLS THE ARRAYS CONTAINING THE
EMISSIONS AT EACH LANE LOCATION
DIMENSION SA(24),SB(24),SC(24),X(24),XD(8)
CALCULATE THE NUMBER OF LANES ON EACH SIDE OF THE MEDIAN.
MLANE a NLANE/2
FILL IN GRID POINTS TO THE LEFT OF THE HIGHWAY.
X(l) a 0.0
DO 10 I » 1.IR1
X(I>1) * X(I)
10 CONTINUE
XD(I)
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c
C'
c
c
c«
c
c
c=
c
c
c
c
> FILL IN GRID POINTS THRU LEFT LANES AND LEFT SIDE OF MEDIAN.
NSTART * IR1 + 2
NMAX * NSTART * MLANE
CALL FILLIT (WIDL, NSTART, NMAX, X)
X(NMAX*1) = X(NMAX) + (RMEDN - WIDL/ 2)
' FILL IN EMISSION GRID FOR LEFT LANES.
DO 30 K » 1, MLANE
SAUR.l+K+1) * QVA
IF (ICHEM .EQ. 1) GO TO 20
SBUR1+K+1) = QVB
SCUR1+K+1) = QVC
20 CONTINUE
30 CONTINUE
' FILL IN GRID POINTS THRU RIGHT SIDE OF MEDIAN AND RIGHT LANES
XCNMAX+2) = X(NMAX+l) + (RMEDN - WIDL/ 2)
NSTART * NMAX + 3
NMAX * NSTART + MLANE
CALL FILLIT(WIDL, NSTART, NMAX, X)
FILL IN EMISSION GRID FOR RIGHT LANES.
INDX = IR1 + MLANE + 3
DO SO K * 1, MLANE
SA(INDX+K+1) * QVA1
IF (ICHEM .EQ. 1) GO TO 40
SB(INDX+K+1) * QVB1
SC(INDX*K*1) = QVC1
40 CONTINUE
50 CONTINUE
FILL IN GRID POINTS TO THE RIGHT OP THE HIGHWAY.
NSTART * NMAX * 1
NMAX * NSTART * 3 - IR1 - 1
K * 1R1
DO 80 I » NSTART, NMAX
K = K + 1
X(I) = X(I-l) + XD(K)
60 CONTINUE
RETURN
END
SUBROUTINE FILLIT(ADDTV,IBEG,IEND.POINTX)
PARAMETER LIST:
INPUT: ADDTV - THE AMOUNT TO BE ADDED
RWY12760
RWY12770
RWY12780
RWY12790
RWY12800
RWY12810
RWY12820
RWY12830
RWY12840
RWY12850
RWY12860
RWY12870
RWY12880
RWY12890
RWY12900
RWY12910
RWY12920
RWY12930
RWY12940
RWY12950
RWY12960
RWY12970
RWY12980
RWY12990
RWY13000
RWY13010
RWY13020
RWY13030
RWY13040
RWY13050
RWY13060
KWY13070
RWY13080
RWY13090
RWY13100
RWY13110
RWY13120
RWY13130
.RWY13140
RWY13150
RWY13160
RWY13170
RWY13130
RWY13190
RWY13200
RWY13210
RWY13220
RWY13230
RWY13240
RWY132SO
RWY13260
RWY13270
RWY13230
RWY13290
RWY13300
RWY13310
RWY13320
RWY13330
RWY13340
RWY133SO
RWY13380
RWY13370
RWY13380
RWY13390
RWY13400
RWY13410
RWY13420
RWY13430
RWY13440
=RWY134SO
RWY13480
RWY13470
RWY13480
RWY13490
RWY13SOO
104
-------
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
IBEG - BEGINNING INDEX
I END - ENDING INDEX
I/O: POINTX - ARRAY TO BE FILLED
CALLING ROUTINES:
WHEREX
DESCRIPTION:
THIS MODULE FILLS IN THE GRID POINTS USING THE SPECIFIED
INDICES AND THE SUPPLIED AMOUNT TO BE ADDED.
DIMENSION POINTX(24)
DO 10 K = I BEG, I END
POINTX(K) * POINTX(K-l) * ADDTY
10 CONTINUE
RETURN
END
RWY13510
RWY13520
RWY13S30
RWY13540
RWY13550
RWY13560
RWY13570
RWY13S80
RWY13590
RWY13600
RWY13610
RWY13620
RWY13630
RWY13840
RWY13650
RWY138SO
RWY13670
RWY13880
RWY13890
RWY13700
RWY13720
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
C
C«
C
C
C«
C
C
C»*»
SUBROUTINE CENTER(HEAD1,HEAD2,HEAD3,IR1,NLANE,WIDL,X,NX,XY,HWAYL) RWY13730
RWY13740
10
PARAMETER LIST:
INPUT: HEAD! - 80 CHARACTER TITLE (1ST LINE)
HEAD2 - 80 CHARACTER TITLE (2ND LINE)
HEADS - 80 CHARACTER TITLE (3RD LINE)
IR1 - WIND DIRECTION INDICATOR
RWY13750
RWY13780
RWY13770
RWY13780
RWY13790
NLANE - NUMBER OF TRAFFIC LANES (AT LEAST 4; MAXIMUMRWY13800
OF 10; INCREMENTS OF 2 ONLY)
WIDL - WIDTH OF ONE LANE (METERS)
X - GRID POINTS IN THE X DIRECTION. CONTAINED
IN THIS ARRAY ARE THE LANE LOCATIONS.
NX - NUMBER OP GRID POINTS IN THE X DIRECTION
OUTPUT: XV - ARRAY CONTAINING CENTER OF TRAFFIC LANES
(METERS)
HWAYL - OUTPUT ARRAY CONTAINING LANE LOCATIONS
CALLING ROUTINE:
MAIN
DESCRIPTION]
THIS SUBROUTINE DETERMINES THE CENTER OF EACH TRAFFIC LANE.
THE X DIRECTION GRID POINTS AND TRAFFIC LANE LOCATIONS ARE
OUTPUT HERE.
DIMENSION HEAD1(20),HEAD2(20),HEAD3(20)
DIMENSION X(24),XV(10),HWAYL(24),HWAYST(24)
DATA BLNKL/' '/, BLNKST/' '/, XLANE/' '/, STAR/'*'/
DATA IN/5/, IO/8/
INITIALIZE.
DO 10 I > 1,24
HWAYL(I) ' BLNKL
HWAYST(I) = BLNKST
CONTINUE
DETERMINE THE NUMBER OF LANES ON EITHER SIDE OF MEDIAN.
MLANE a NLANE/ 2
FIND THE CENTER OF THE LEFTMOST LANE.
XV(1) * X(IR1*2)
HWAYLUR1 + 2) = XLANE
HWAYSTUR1 + 2) = STAR
FIND THE CENTER OF THE REMAINING LEFT LANES. FLAG THEIR
LOCATIONS.
I = 0
DO 20 K = 2, MLANE
XV(K) = XV(K-l) + WIDL
RWY13810
RWY13820
RWY13830
RWY13840
RWY13830
RWY13860
RWY13870
RWY13880
RWY13890
RWY13900
RWY13910
RWY13920
HWY13930
RWY13940
RWY139SO
RWY13960
RWY13970
RWY13980
RWY13990
RWY14000
RWY14010
RWY14020
RWY14030
RWY14040
RWY14050
RWY14060
RWY14070
RWY14080
RWY14090
RWY14100
RWY14110
RWY14120
RWY14130
RWY14140
RWY14150
RWY14180
RWY14170
RWY14130
RWY14190
RWY14200
RWY14210
RWY14220
RWY14230
RWY14240
RWY14250
105
-------
1 = 1 + 1
HWAYLUR1 + 2+I) = XLANE
HWAYST(IR1+2*I) = STAR
20 CONTINUE
C
C»*« DETERMINE NEXT ELEMENT TO BE PILLED IN THE LANE CENTER ARRAY
C«*» (XV) AND THE CORRESPONDING INDEX IN THE GRID ARRAY (X).
C
INDX * MLANE + 1
INDX2 » MLANE + IR1 + 5
C
C»«» FIND THE CENTER OF THE LANE JUST TO THE RIGHT OF THE MEDIAN.
C
XV (INDX) » XUNDX2)
C
C««* DETERMINE THE BEGINNING AND ENDING INDICES TO COMPLETE
C*** FILLING THE RIGHT LANE CENTERS. FILL THE LANE CENTER ARRAY.
C
I BEG INDX * 1
I END a INDX * MLANE - 1
HWAYLUNDX2) = XLANE
HWAYST(INDX2) - STAR
C
I - 0
DO 30 K » IBEG.IEND
XV(K) - XV(K-l) + WIDL
I » I + I
HWAYL(INDX2 + I) » XLANE
HWAYST(INDX2 + I) » STAR
30 CONTINUE
C
C"« OUTPOT THE X GRID DISTANCES AND LANE LOCATIONS (METERS).
C
WRITE(IO.IOOO) HEAD1,HEAD2,HEAD3
WRITB(IO.IOIO) (X(K).HWAYST(K), K = 2, NX)
WRITEC IO.1020)
C
RETURN
C
C«« FORMAT STATEMENTS.
C
1000 FORMATdHl, 'TITLE: ' ,20A4, 2(/, 9X.20A4)/ )
1010 FORMAT UHO, 5 OX, 'GRID POINTS IN X DIRECTION FROM',/,
1 IX, SOX, ' LEFT TO RIGHT ACROSS ROADWAY',/,
2 1X.50X,' (METERS)',/,
3 1HO,82X,FS.1,1X,A1,23(/,83X,F9.1,1X,A1))
1020 FORMATUHO.SOX, ' INDICATES LOCATION OF TRAFFIC LANE CENTER.')
END
C
C
SUBROUTINE WAKE(UB,VB,VSPD,VSPD1 ,H,NV,NV1 ,WID,X,Z,NX,
1 KMAX,XV,NLANE,DU,DV,KXP,KZP,KXPA3,KYPAS,KYP,IERR)
C
C PARAMETER LIST:
C INPUT: UB - VERTICAL PROFILE OF U COMPONENT OP WIND
C (M/SEC)
C VB VERTICAL PROFILE OF V COMPONENT OF WIND
C (M/SEC)
C V3PD - AVERAGE VEHICLE SPEED IN SOUTHBOUND LANES
C (M/SEC)
C VSPD1 - AVERAGE VEHICLE SPEED IN NORTHBOUND LANES
C (M/SEC)
C H AVERAGE HEIGHT OF VEHICLES (METERS)
C NV - SOUTHBOUND TRAFFIC VOLUME (VEH/HR)
C NV1 - NORTHBOUND TRAFFIC VOLUME (VEH/HR)
C WID - AVERAGE WIDTH OF VEHICLES (METERS)
C X - GRID POINTS IN THE X DIRECTION (METERS)
C Z GRID POINTS IN THE Z DIRECTION (METERS)
C NX - NUMBER OF GRID POINTS IN X DIRECTION
C KMAX - NUMBER OF GRID POINTS IN Z DIRECTION
C XV - LANE CENTER ARRAY
C NIANE - NUMBER OF TRAFFIC LANES
C DU VEHICLE WAKE EFFECTS ON THE U FIELD
C DV VEHICLE WAKE EFFECTS ON THE V FIELD
RWY142SO
RWY14270
RWY14280
RWY14290
RWY14300
RWY14310
RWY14320
RWY14330
RWY14340
RWY14350
RWY143SO
RWY14370
RWY14380
RWY14390
RWY14400
RWY14410
RWY14420
RWY14430
RWY14440
RWY14450
RWY14460
RWY14470
RWY14480
RWY14490
RWY14SOO
RWY14S10
RWY14520
RWY14S30
RWY14540
RWY14550
RWY14580
RWY14570
RWY14S80
RWY14S90
RWY14600
RWY14610
RWY14820
RWY14830
RWY14640
RWY148SO
RWY14680
RWY14870
RWY14880
RWY14890
RWY14700
RWY14710
RWY14720
RWY14730
RWY14740
sDWVI d. 7 ^ A
B HW I i t I 3 U
RWY14780
RWY14770
RWY14780
RWY14790
RWY14800
RWY14810
RWY14820
RWY14830
RWY14840
RWY14850
RWY14860
RWY14870
RWY14880
RWY14890
RWY14900
RWY14910
RWY14920
RWY14930
RWY14940
RWY14950
RWY14980
RWY14970
RWY14980
RWY14990
RWY1SOOO
106
-------
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
C"
c
KXP - WAKE TURBULENCE IN X DIRECTION (M»*2/SEC)
KZP - WAKE TURBULENCE IN Z DIRECTION (M*»2/SEC)
KXPAS - WAKE PASSING EFFECT IN X DIRECTION
(M»«2/SEC)
KYPAS - WAKE PASSING EFFECT IN Y DIRECTION
(M»«2/SEC)
KYP - WAKE TURBULENCE IN Y DIRECTION (M»»2/SEC)
IERR - ERROR INDICATOR (0 * NO ERROR)
CALLING ROUTINE:
MAIN
SUBPROGRAMS CALLED:
FC«, POLY*, SIMPSN
INDICATES FUNCTION CALL
DESCRIPTION:.
THIS SUBROUTINE CALCULATES THE CHANGES IN THE WIND AND
TURBULENCE FIELDS DUE TO THE VEHICLE WAKES. IT CAN ALSO
CALCULATE THE WAKE PASSING EFFECT (ESKRIDGE AND RAO, 1983),
BUT IT DOES NOT DO THESE CALCULATIONS NORMALLY.
DEFINITIONS OF IMPORTANT VARIABLES:
ALP - ANGLE BETWEEN Y-AXIS AND S-AXIS
BETA - ANGLE BETWEEN X-AXIS AND S-AXIS
RHO - DENSITY OF AIR
RX - ARRAY OF X-AXIS GRID POINTS PROJECTED ON R-AXIS
REAL KPX,KPY,NV,NV1,KXP,KZP,KXPAS,KYPAS,OMEGA,KYP
REAL KXI.KYI.KZI
DIMENSION KPX(41),KPY(41),UB(8),DV(24,8),VB(8),DU<24,8),XV(10)
DIMENSION KXP(24,8),KYP(24,8),KZP(24,8),RX(41)
DIMENSION KXI141),KY1(41),KZI(41),X(24),Z(8),YV(41)
DIMENSION 3(41),DQ(41),KXPAS(24,a),KYPAS(24,8)
DATA PI/3.141592854/,GAMA/.095/
DATA CD/.45/,Al/.048/,A2/.040/,A3/.030/
DATA IN/5/, IO/8/
INITIALIZE.
IWAKEP » 0
WAKE PASSING EFFECT TURNED OFF.
DO 20 I » l.NX
DO 10 K » l.KMAX
KXP(I.K) 0.0
KZP(I.K) 0.0
KYP(I,K> 0.0
KXPAS(I.K) 0.0
KYPAS(I,K) 0.0
DU(I,K) 0.0
DV(I.K) 0.0
10 CONTINUE
20 CONTINUE
VSP » -VSPD
FNV a NV
DO 250 J a l.NLANE
IF (J .GT. NLANE/2) VSP
ABS(VSPDl)
NV1
C
C
C»
C*
C«
C«
C
C*
C*
c«
c«
c«
C'
c»
IF (J .GT. NLANE/2) FNV
BETA » ATAN
-------
C
c
30
c
c
c
c***
C*'*
c
so
DO 200 I = 1,NX
XDST = X(I) - XV(J)
XLRG = 2.
XDL = XDST - XLRG
XDR = XDST * 2.
IF (XDL'XDR .GT. 0.0) GO TO 30
CASE WHERE X( I ) = XV(J) MUST BE HANDLED SEPARATELY.
IF (UB(2) .LT. 0.0) XDR » -0.1
IF (UB(2) .LT. 0.0) XLRG = 1.8
IF (UB(2) .GT. 0.0) XLRG = 0.1
IF (UB(2) ,GT. 0.0) XDL = 0.1
XRNG * ABS(XDR - XDL)
DX * XRNG * 0.025
DELY = ABS(DX/TAN(ALP))
SLOPE - ((VSP + VB(2))/(-UB(2)))
TEST TO SEE IF VEHICLE IS UPWIND OF X-AXIS GRID POINT.
B2 * -SLOPE (X(I))
YVEH » SLOPE XV(J) * B2
IF ((VSP * VB(2)) YVEH .LT. 0.0) GO TO 200
DO 50 N » 1,41
XD * (X(I) - XLRG) + (N-l) DX
Y » SLOPE X * BO, SOLVE FOR BO WHICH IS THE Y-AXIS
INTERCEPT, XD IS THE X-AXIS INTERCEPT, YO THE VEHICLE
POSITION. Y =« -I/SLOPE + Bl LINE THRU X(I) NORMAL TO
CENTERLINE OF WAKE.
BO * -SLOPE XD
YO * SLOPE XV(J) + BO
81 * X( I) /SLOPE
INTERSECTION OF THE TWO LINES DETERMINES S AND RX
S » DIST( (XV(J),YO),(XI,YI) )
RX « DIST( ( X(I), 0),(XI,YI) )
XI * (Bl - BO)/ (SLOPE * 1. /SLOPE)
Yl * SLOPE XI * BO
S(N) * SQRTUXI - XV(J))»«2 * (YO - YI)«2)
RX(N) « SQRT((X(I) - XI)»*2 + YI««2)
CONTINUE
THE FOLLOWING CODE DOES THE WAKE CALCULATION AND SUMS THE
EFFECTS OF THE WAKES.
QB « SQRT((VSP + VB(2))««2 + UB(2)"2)
A * (CD/(32. PI EXP(.5) 1.14 GAMA"3) ) «0. 25
DO ISO K » 2.KMAX
SCALNZ ' Z(K)
IF (Z(K) .GT. 2.45) SCALNZ * 2.45
DO 100 M » 1,41
IF (S(M) .LE. 0.0) S(M) » 1.E8
PAC » 1.0
IF (ABS(RX(M)) .LT. WID) FAC * 0.48 + 0.52 * AB3(RX(M) ) /WID
ZETA » (Z(K)/H)/((S(M)/H)".2S GAMA A)
IP (ABS(ZETA) .LT. l.E-20) ZETA » 0.0
ETA = RX(M)/(1.14 GAMA WID A (S(M) /H) .25 )
IF (ABS(ETA) .LT. l.E-20) ETA * 0.0
CHI - RX(M)/(WID (S(M)/H)*«.4)
IF (ABS(CHI) .LT. l.E-20) CHI = 0.0
OMEGA » Z(K)/(H (S(M)/H) .4)
IF (ABS(OMEGA) .LT. l.E-20) OMEGA = 0.0
KXI(M) = FAC ((A QB)««2 (S(M)/H) (-! .2)
RWY15760
RWY1S770
RWY15780
RWY15790
RWY15800
RWY15810
RWY15820
RWY1S830
RWY15840
RWY15850
RWY15860
RWY15870
RWY15880
RWY1S890
RWY1S900
RWY15910
RWY15920
RWY1S930
RWY15940
RWY15950
RWY159SO
RWY15970
RWY1S980
RWY15990
RWY16000
RWY16010
RWY16020
RWY16030
RWY16040
RWY1SOSO
RWY18060
RWY1S070
RWY16080
RWY16090
RWY18100
RWY18110
RWY18120
RWY16130
RWY1S140
RWY16150
RWY161SO
RWY16170
RWY18180
RWY18190
RWY18200
RWY1S210
RWY1S220
RWY1S230
RWY18240
RWY182SO
RWY1S280
RWY16270
RWY16280
RWY18290
RWY1S3QQ
RWY18310
RWY18320
RWY18330
RWY16340
RWY16350
RWY16380
RWY1S370
RWY16380
RWY16390
RWY16400
RWY16410
RWY16420
SIN(ALP) * A2 FC(CHI,OMEGA)RWY16430
RWY18440
RWY18450
1 (Al PC(CHI.OMEGA)
2 COS(ALPH) WtD
KYI(M) = FAC ((A * QB)««2 (S(M)/H)(-!.2)
1 (Al FC(CHI,OMEGA) COS(ALP) + A2 FC(CHI,OMEGA)RWY16480
2 SIN(ALP))) WID RWY18470
KZI(M) = FAC ((A * QB)"2 (S(M)/H) *(-1.2) * RWY16480
1 A3 FCtCHI,OMEGA)) SCALNZ RWY1S490
DQ(M) = FAC QB A (H/S(M))»«0.75 POLY(ZETA) * RWY16500
108
-------
1 EXP(-ETA**2/8.)
100 CONTINUE
CALL SIMPSN(1,41,DELY,KXI,AN1,IERR)
IF (IERR .HE. 0) GO TO 999
CALL SIMPSN(1,41,DELY,KYI,AN2,IERR)
IF (IERR .NE. 0) GO TO 999
CALL SIMPSN(1,41,DELY,KZI,AN3,IERR)
IF (IERR .NE. 0) GO TO 999
CALL SIMPSN(1,41,DELY,DQ,AN4,IERR)
IF (IERR .NE. 0) GO TO 999
KXP(I.K) a KXP(I.K) * FNV
KYP(I.K) » KYP(I,K) + FNV
KZP(I.K) a KZP(I,K) + FNV
DU(I.K) - SIGN(1.,UB(2))
ABS(VSP))
DV(I,K) * SIGN(1.,VSP)
ABS(VSP))
DU(I.K)
1
DV(I,K)
1
ISO CONTINUE
DO 170 N a
RX(N)
YV(N)
KXI(N)
KYI(N)
KZI(N)
S(N)
170 CONTINUE
200 CONTINUE
2 SO CONTINUE
IF (IWAKEP
= DU
(3
a DV
(3
1,41
0.0
0.0
0.0
0.0
0.0
0.0
EQ.
AN1/(3600
AN2/(3600
AN3/(3600
ABS(VSP))
ABS(VSP))
« ABS(VSP))
FNV AN4 COS(BETA)/
FNV AN4 « SIN(BETA)/
0) GO TO 999
RWY16510
RWY15520
RWY16530
RWY16540
RWY16550
RWY1S560
RWY16570
RWY16580
RWY16590
RWY16600
RWY16610
RWY16620
RWY16630
RWY16640
RWY16650
RWY18660
RWY16870
RWY18680
RWY16690
RWY18700
RWY18710
RWY16720
RWY16730
RWY16740
RWY16750
RWY16780
RWY16770
RWY18730
RWY16790
RWY16800
THE FOLLOWING SECTION OF CODE HAS BEEN IMMOBILIZED VIA IWAKEP.RWY16810
IT CAN BE USED TO CALCULATE THE WAKE PASSING EFFECTS BY RWY16820
SETTING IWAKEP TO 1 (SEE FIRST EXECUTABLE STATEMENT IN MODULE)RWY1S830
RWY16840
RWY16850
RWY16860
RWY16870
VSP * -VSPD
FNV = NV
DO 850 J a l.NLANE
IF (J .GT. NLANE/2) VSP
IF (J .GT. NLANE/2) FNV
ABS(VSPDl)
NV1
C
C"'
C«'
BETA * ATAN(ABS((VSP * VB(2))/UB(2)))
ALP « 0.3 PI - ABS(BETA)
C
C
RWY16880
RWY16890
RWY16900
RWY18910
RWY18920
RWY16930
RWY1S940
AT THE POINT (X,Z) THE INTEGRAL THAT YIELDS THE WAKE
PROPERTIES HAS AN INTEGRATION RANGE OVER WHICH THE FUNCTION
THAT IS BEING INTEGRATED IS MAINLY ZERO. THERFORE A MODIFIED RWY18950
APPROACH IS TAKEN. AN INTEGRATION RANGE OF (X-2, X+2) AROUND RWY18980
THE X GRID POINT IS CHOSEN, ASSUMING WHEN WAKE CENTERLINE IS RWY1S970
C
C«
C
3SO
C
c«
OUT OF THIS RANGE THE WAKE DOES NOT HAVE AN EFFECT AT THE
POINT, AND THEN THE POSITION OF THE VEHICLE IS DETERMINED.
DO 800 I » l.NX
XDST * X(I) - XV(J)
XLRG * 2.0
XDL * XDST - 2.0
IF (UB(2) .GT. 0.0) XLRG * 0.1
XDR * XDST + 2.
IF (XDL'XDR .GT. 0.0) GO TO 3SO
CASE WHERE X( I) = XV(J) MUST BE HANDLED SEPARATELY.
IF (UB(2) .LT. 0.0) XDR = -0.1
IF (UB(2) .GT. 0.0) XDL = 0.1
XRNG = ABS(XDR - XDL)
DX = XRNG 0.025
SLOPE » ((VSP + VB(2))/(-UB(2)))
TEST TO SEE IF VEHICLE IS UPWIND OF X-AXIS GRID POINT.
B2 « -SLOPE X(I)
YVEH * SLOPE XV(J) + B2
IF ((VSP+VB(2))»YVEH .LT. 0.0) GO TO 600
DO 400 N = 1,41
XD = (X(I) - XLRG) + (N - 1) DX
Y » SLOPE X + BO, SOLVE FOR BO WHICH IS THE Y-AXIS
RWY16980
RWY18990
RWY17000
RWY17010
RWY17020-
RWY17030
RWY17040
RWY17050
RWY17060
RWY17070
RWY17080
RWY17090
RWY17100
RWY17110
RWY17120
RWY17130
RWY17140
RWY17150
RWY17160
RWY17170
RWY17180
RWY17190
RWY17200
RWY17210
RWY17220
RWY17230
RWY17240
RWY17250
109
-------
£
c*
c
BO
YO
Bl
INTERCEPT, XD IS THE X-AXIS INTERCEPT. RWY17260
Y = -I/SLOPE + Bl LINE THRU XD NORMAL TO CENTERLINE OF WAKERWY17270
RWY17280
= -SLOPE XD
= SLOPE * XV(J) + BO
= XD/SLOPE
**
**
**
INTERSECTION OF THE TWO LINES DETERMINES S AND RX
S = DIST( (XV(J) ,YQ),(XI,YI) )
RX = DIST( ( X(I), 0),(XI,YI) )
1. /SLOPE)
400
C
c«
c»
c
XI » (Bl - BO)/(SLOPE
YI » SLOPE XI * BO
S(N) =» SQRTUXI - XV(J))««2
RX(N) = SQRT((X(I) - XI) "2 +
CONTINUE
(YO - YI)»«2)
YI«»2)
THE FOLLOWING CODE DOES THE WAKE PASSING TURBULENCE
CALCULATION.
DO 500 K = 2.KMAX
DO 450 M * 1,41
I? (S(M) .LE. 0.0) S(M) =» 1.B8
FAC si.o
IF (ABS(RX(M)) .LT. WID) FAC = 0.48 * 0.52
ZETA * (Z(K)/H)/((S(M)/H)»*.25 GAMA A)
IP (ABS(ZETA) .LT. l.E-20) ZETA = 0.0
ETA » RX(M)/(1.14 GAMA WID A (S(M)/H)
IF (ABS(ETA) .LT. l.E-20) ETA * 0.0
DQ1 » FAC QB A * (H/S(M) )»«0. 75 POLY(ZETA)
EXP(-ETA««2/8.)
.25)
C
C=
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
KPX(M) - ((UB(K)
1 (UB(K)
KPY(M) * «VB(K)
1 (VB(K)
450 CONTINUE
CALL 3IMPSN(1,41,DELY,KPX,AN8,IERR)
IF (IERR .NE. 0) GO TO 999
CALL SIMPSN(1,41,DELY,KPY,AN7,IERR)
IF (IERH .NE. 0) GO TO 999
KXPAS(I,K) * KXPASd.K) +
KYPASd.K) » KYPASd.K) +
500 CONTINUE
DO 520 N » 1,41
KPX(N) » 0.0
KPY(N) » 0.0
520 CONTINUE
800 CONTINUE
850 CONTINUE
999 RETURN
END
SIGN(1.,UB(2)) DQ1 COS(BETA)) -
DU(I,K)))"2
SIGN(1.,VSP) DQ1 SIN(BETA)) -
DV(I,K)))"2
FNV AN8/(3800. « ABS(VSP))
FNV AN7/(3800. ABS(VSP))
FUNCTION FC(Y,Z)
PARAMETER LIST:
INPUT; Y - SIMILARITY COORDINATE IN Y DIRECTION
Z - SIMILARITY COORDINATE IN Z DIRECTION
OUTPUT: FC - TURBULENT KINETIC ENERGY IN THE Y-Z PLANE
CALLING ROUTINE:
WAKE
DESCRIPTION:
THIS FUNCTION DOES A 2-DIMENSIONAL FIT TO WIND TUNNEL DATA
OP THE TURBULENT KINETIC ENERGY TERMS IN THE Y-Z PLANE (SEE
ESKRIDGE AND THOMPSON, 1982)
DATA AOO/ .3SU237B-1/, A01/ .1255308E+2/, A02/-.4798241E+2/,
A03/ .8732523E+2/, A04/-.3572486E+2/, A20/-.1890581 /,
1 A21/-.9345507E+1/, A22/-.18I1427E+3/, A23/
2 A24/-.3995373E+3/, A40/ .2649465 /,
3 A42/ .1034830E+4/, A43/-.2348153E+4/, A44/
RWY17290
RWY17300
RWY17310
RWY17320
RWY17330
RWY17340
RWY17 3'5 0
RWY17380
RWY17370
RWY17380
RWY17390
RWY17400
RWY17410
RWY17420
RWY17430
RWY17440
RWY17450
RWY17460
RWY17470
RWY17480
RWY17490
ABS(RX(M))/WID RWY17500
RWY17510
RWY17520
RWY17530
RWY17540
RWY17550
RWY17560
RWY17570
RWY17580
RWY17590
RWY17600
RWY17610
RWY17620
RWY17630
RWY17640
RWY17850
RWY17660
RWY17870
RWY17680
RWY17690
RWY17700
RWY17710
RWY17720
RWY17730
RWY17740
RWY17750
RWY17780
RWY17770
RWY17780
RWY17790
RWY17800
RWY17810
RWY17820
RWY17830
RWY17840
RWY178SO
RWY17880
RWY17870
RWY17880
RWY17890
RWY17900
RWY17910
RWY17920
RWY17930
RWY17940
RWY17950
RWY17980
RWY17970
RWY17980
RWY17990
5617911E+3/,
A41/-.9434068E+2/,
.1510437E-I-4/
RWY18000
110
-------
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
1000
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c«»«
c
100
c
c«»»
PC * AOO * Z * (A01 + Z * (A02 + Z (A03 + Z * A04))) +
1 Y»Y « (A20 + Z (A21 + Z (A22 + Z (A23 + Z A24))
2 + Y«4 (A40 + Z (A41 + Z (A42 + Z * (A43 + Z « A44))
IF ((ABS(Y) .GE. 0.55) .OR. (ABS(Z) .GE. 0.64)) FC = 0.0
IF ((Y .LT. 0.0) .AND. (Z .GT. ( 1 . 82*Y+1. 15) ) ) FC = 0.0
IF ((Y .GT. 0.0) .AND. (Z .GT. (-1 . 82»Y+1 . 15 ) ) ) FC = 0.0
IF (FC .GT. 1.0) FC = 1.0
RETURN
END
FUNCTION POLY(Z)
PARAMETER LIST:
INPOTs Z - SIMILARITY COORDINATE VALUE IN Z DIRECTION
OUTPUT: POLY - DETERMINES VERTICAL VARIATION OF WAKE
VELOCITY DEFICIT
CALLING ROUTINE:
WAKE
DESCRIPTION:
THE MODIFIED THEORY OF ESKRIDGE AND THOMPSON WAS STILL
INADEQUATE TO DESCRIBE THE VELOCITY DEFICIT BEHIND THE
VEHICLES. THUS, A CURVE FIT WAS MADE TO WIND TUNNEL DATA.
CURVE FIT TO NORMALIZED VELOCITY AT X/H=30 OM CENTERLINE.
DATA IN/5/, IO/8/
POLY » .0179349 + Z (2.576587 * Z (-2.3082534 * Z
1 (.8951488 * Z (-.1758804 + Z (.018997 - Z
2 .0006404)))))
IF (Z .GT. 8.2) POLY = 0.0
IF (POLY .GT. 1.1) WRITE( 10,1000) Z.POLY
RETURN
FORMATdX, 'ZETA=' ,F10.5,5X, 'UNORM-1 ,F10.S)
END
SUBROUTINE SIMPSN(M,N,DH,F,ANS, IERR)
PARAMETER LIST:
INPUT: M - STARTING INDEX
N - STOPPING INDEX. N - M * 1 MUST BE ODD.
DH - LENGTH OF EQUAL INTERVALS.
F - ARRAY CONTAINING FUNCTIONAL VALUES TO BE
INTEGRATED
OUTPUT: ANS - VALUE OF INTEGRAL
IERR - ERROR INDICATOR ( 0 * NO ERROR)
CALLING ROUTINE:
WAKE
DESCRIPTION:
THIS MODULE PERFORMS NUMERICAL INTEGRATION USING SIMPSON'S
METHOD.
DIMENSION P(N)
DATA IN/5/, IO/6/
TEST FOR M - N + 1 ODD.
ITST » MOD(N-M+1.2)
IF (ITST .EQ. 1) GO TO 100
IERR » 20
WRITE( 10,1000) IERR
GO TO 999
CONTINUE
PERFORM NUMERICAL INTEGRATION.
RWY18010
RWY18020
))RWY18030
))RWY18040
RWY18050
RWY18060
RWY18070
RWY18080
RWY18090
RWY18100
RWY18110
RWY18120
RWY18130
B WV 1 A 1 A n
tin I 1 0 1 4 U
RWY18150
RWY18180
RWY18170
RWY18180
RWY18190
RWY18200
RWY18210
RWY18220
RWY18230
RWY18240
RWY18250
RWY18260
RWY18270
RWY18280
RWY18290
RWY18300
RWY18310
RWY18320
RWY18330
RWY18340
RWY18350
RWY133SO
RWY18370
RWY18380
RWY18390
RWY18400
RWY18410
RWY13420
RWY13440
RWY13450
RWY18480
RWY18470
RWY18480
RWY18490
RWY13SOO
RWY18510
RWY18S20
RWY18530
RWY18S40
RWY18550
RWY18S60
RWY18570
RWY18580
RWY18590
RWY18600
RWY18610
RWY18620
RWY18830
RWY18S40
RWY18850
RWY18660
RWY18870
RWY18S80
RWY18S90
RWY18700
RWY18710
RWY18720
RWY18'T30
RWY18740
RWY18750
111
-------
c
105
110
C
999
C
1000
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
10
20
c
30
c
SUM =0.0
SUM = F(M) + F(N)
K = 0
JJ = M * 1
KK = N - 1
DO 110 I 3 JJ.KK.l
IF (K .EQ. 1) GO TO 105
SUM = SUM + 4.0 * F ( I )
K * 1
GO TO 110
CONTINUE
SUM = SUM * 2.0 * P(I)
K = 0
CONTINUE
ANS = SUM * OK/3.
RETURN
FORMAT( ' O"* ERROR ',12,': N-M+1I3 NOT ODD. ')
END
SUBROUTINE NONDmu,NX,KMAX,X,Z,VO
PARAMETER LIST:
INPUT: U - U COMPONENT FIELD (M/SEC)
NX - NUMBEK OF GRID POINTS IN X DIRECTION
KMAX - NUMBER OP GRID POINTS IN Z DIRECTION
X - GRID POINTS IN THE X DIRECTION (METERS)
Z - GRID POINTS IN THE Z DIRECTION (METERS)
ODTPOT: W - VERTICAL VELOCITY FIELD (M/SEC)
CALLING ROUTINE:
MAIN
DESCRIPTION:
THE VERTICAL VELOCITY IS COMPUTED BY CALCULATING THE INFLOW
AND OUTFLOW IN THE X-DIRECTION FROM THE U FIELD AND THE
VERTICAL INFLOW IN THE BOTTOM OF A BOX ABOUND EACH GRID
POINT. THE VERTICAL VELOCITY AT THE GRID POINT IS A LINEAR
INTERPOLATION OF THE VERTICAL VELOCITY AT THE BOTTOM AND TOP
BOUNDARIES OF THE BOX. TO THE DEGREE THAT THE WIND FIELD
CONTAINS DIVERGENCE, ERROR IS INTRODUCED IN THE COMPUTATIONS
DIMENSION WTOP(24),WBOT(24),X(24),Z(8),W(24,8),U(24,8)
NX1 » NX - 1
KM » KMAX - 1
DO 20 K » 2, KM
DO 10 I » 2.NX1
X2 » (X(I>1) + X(I) )/2.
XI » (X(I) + X(I-l))/2.
DELX * X2 - XI
U2 » (UU+l.K) * U(1,K) )/2.
Ul = (U(I,K) + U(I-l,K))/2.
DELU * 02 - Ul
Z2 » (ZCK+1) + Z(K) )/2.
Zl - (Z(K) + Z(K-l))/2.
DELZ * Z2 - Zl
IF (K .GT. 2) WBOT(I) = WTOP(I)
IF (K .EQ. 2) WBOT(I) = 0.0
WTOP(I) * WBOT(I) - DELZ " DELU/DELX
W(I,K) = (WTOP(I) + WBOT(I))/2.
CONTINUE
CONTINUE
DO 30 K = l.KMAX
W(1,K) » W(2,K)
W(NX,K) = W(NX1,K)
CONTINUE
DO 40 I = 1,NX
W(I.KMAX) = W(I,KMAX-1)
RWY18760
RWY18770
RWY18780
RWY18790
RWY18800
RWY18810
RWY18820
RWY18830
RWY18840
RWY18850
RWY138SO
RWY18870
RWY13330
RWY18890
RWY18900
RWY18910
RWY18920
RWY18930
RWY13940
RWY18950
RWY189SO
RWY18970
nwvi A on n
-AW I 1 0 9 O U
RWY18990
RWY19000
RWY19010
RWY19020
RWY19030
RWY19040
RWY19050
RWY190SO
RWY19070
RWY19080
RWY19090
RWY19100
RWY19110
RWY19120
RWY19130
RWY19140
RWY19150
RWY19160
RWY19170
RWY19180
RWY19190
.RWY19200
RWY19210
RWY19220
RWY19230
RWY19240
RWY19250
RWY19260
RWY19270
RWY19280
RWY19290
RWY19300
RWY19310
RWY19320
RWY19330
RWY19340
RWY193SO
RWY193SO
RWY19370
RWY19380
RWY19390
RWY19400
RWY19410
RWY19420
RWY19430
RWY19440
RWY19450
RWY19460
RWY19470
RWY19480
RWY19490
RWY19500
112
-------
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c«
C
c«
C
40 CONTINUE
RETURN
END
SUBROUTINE ADVCHM(SA,SB,SC,A,B,C,D,HWAYL)
PARAMETER LIST:
INPUT: SA - NO EMISSION GRID (G/M"«3/SEC) .
IF ICHEM = 1, THEN SA IS THE POLLUTANT EMIS-
SION GRID AND SB AND SC ARE IRRELEVANT.
SB - CO EMISSION GRID (G/M»«3/SEC)
SC - NO2 EMISSION GRID (G/M«»3/SEC)
A - NO CONCENTRATION FIELD (PPM).
IF ICHEM * 1, THEN A IS THE POLLUTANT
CONCENTRATION FIELD AND B, C, AND D ARE
IRRELEVANT.
B - CO CONCENTRATION FIELD (PPM)
C - N02 CONCENTRATION FIELD (PPM)
D - O3 CONCENTRATION FIELD (PPM)
HWAYL - OUTPUT ARRAY CONTAINING LANE LOCATIONS
CALLING ROUTINE:
MAIN
SUBPROGRAMS CALLED:
TIMING, BNDRYC, ADU«, BMOVE, ANTU«, ADW , ANTW* , DIFFX»,
DIFFZ*, GRAPH
INDICATES FUNCTION CALL
DESCRIPTION:
THIS MODULE IS A CONTROLLING ROUTINE WHICH CALLS VARIOUS
ADVECTION AND DIFFUSION ROUTINES. THE CHEMICAL CALCULATIONS
ARE ALSO PERFORMED HERE.
REAL K1,K2,KX?,KZP,KX,KZ
DIMENSION AA(24,8),BB(24,8),CC(24,8),DD(24,8)
DIMENSION AI(24,8),BI(24,3),CI(24,3),DI(24,8)
DIMENSION U(24,8),W(24,3),A(24,8,2),B(24,3,2)
DIMENSION JCCP(24,8),KZP(24,8),C(24,8,2),D(24,8,2)
DIMENSION 3A(24),3B(24),3C(24),DCNWY(24),X(24),Z(8),KX(8),KZ(3)
DIMENSION HEADK20) ,HEAD2(20),HEAD3(20)
DIMENSION HWAYL(24)
COMMON /CALOOM/U,W,XMAX,KX,KZ,X,Z,TMSTOP,NX,1CCP,KZP
COMMON /INCOM/ BACXGA,BACKGB,BACKGC,BACKGD,CNA,CNB,CNC,CND,EMA,
1 EMA1,EMB,EMB1,EMC,EMC1,K1,K2,MEDN,NVEH,NVEH1,
2 RDANGL,T1,T2,VHGH,VWID,VSPD,VSPD1,WD,WIDL,WSPD,
3 ZO,Z1,Z2,HEAD1,HEAD2, HEADS, lANTI , ICHEM, INTPR.NLANE
DATA N/1/.NP/2/
DATA BB/ 192*0. /,CC/ 192*0. /,DD/ 192*0. /,BI/ 192*0. /.CI/1 92 »0./
DATA DI/192«0./
DATA DUMMY/24«0./
DATA IN/5/, IO/8/
FIND MAXIMUM VELOCITY AND THEN DETERMINE THE ADVECTIVE AND
CHEMICAL TIME STEPS.
JTEST ' 1
IF (WD .LE. 180.) JTEST * 2
CALL TIMINC( ICHEM, Kl,K2,DTADV1DTCHM,mJMCHM)
NZ1 a KMAX - 1
NX1 a NX - 1
I PRINT * 0
NPRINT = (TMSTOP/4.)/DTADV + 1
TIME = DTADV
KOUNTP » o
ESTABLISH BACKGROUND VALUES OF POLLUTANTS.
DO 50 I -» 1,NX
DO 40 J = l.KMAX
DO 30 K = 1,2
RWY19510
RWY19520
RWY19530
RWY19540
RWY19550
-BWV1 Q ^ fi ft
IfcH 1 A ,7 9 O U
RWY19570
RWY19580
RWY19590
RWY19600
RWY19610
RWY19620
RWY19630
RWY19840
RWY196SO
RWY196SO
RWY19670
RWY19630
RWY19690
RWY19700
RWY19710
RWY19720
RWY19730
RWY19740
RWY19750
RWY19780
RWY19770
RWY19780
RWY19790
RWY19800
RWY19810
RWY19820
RWY19830
RWY19840
RWY19850
RWY19860
RWY19870
RWY19880
RWY19890
RWY19900
RWY19910
RWY19920
RWY19930
RWY19940
RWY199SO
RWY19960
RWY19970
RWY19980
RWY19990
RWY20000
RWY20010
RWY20020
RWY20030
RWY20040
RWY20050
RWY20060
RWY20070
RWY20080
RWY20090
RWY20100
Rvmouo
RWY20120
RWY20130
RWY20140
RWY20150
RWY20160
RWY20170
RWY20130
RWY20190
RWY20200
RWY20210
RWY20220
RWY20230
RWY20240
RWY20250
113
-------
C
c»
C
A(I,J,K) = BACKGA
IF (ICHEM .EQ. 1) GO TO 20
B(I,J,K) = BACKGB
C(I,J,K) = BACKGC
D(I.J.K) = BACKGD
20 CONTINUE
30 CONTINUE
40 CONTINUE
50 CONTINUE
» THE ADVECTION CALCULATION IS PERFORMED USING FRACTIONAL
STEPS. THE PROCEDURE USED IN THIS PRGRAM IS TO: FIRST,
CALCULATE THE ADVECTION, SECOND DO A FLUX CORRECTION.
»* CALCULATE ADVECTION ALONG THE X-AXIS AND ADD EMISSIONS.
100 DO 120 I « I,NX
A(I,2,N) - A(I,2,N) * SA(I) DTADV CNA
IF (ICHEM .EQ. 1) GO TO 110
B(I,2,N) = B(I,2,N) * SB(I) DTADV CNB
C(I,2,N) » C(I,2,N) * SC(I) DTADV CMC
110 CONTINUE
120 CONTINUE
CALL BNDRYC(BACKGA,N,NX,KMAX,JTEST.A)
IF (ICHEM .EQ. 1) GO TO ISO
CALL 8NDRYC(BACKG8,N,NX,KMAX,JTEST,B)
CALL BNDRYC(BACKGC,N,NX,KMAX,JTEST.C)
CALL BNDRYC(BAOCGD,N,NX,KMAX,JTEST,D)
130 CONTINUE
DO 200 K = 2,NZ1
DO 190 I * 2.NX1
AA(I.K) => ADU(A,N,U,X,DTADV,I,K)
IF (ICHEM .EQ. 1) GO TO 180
BB(I,K) * ADUtB.N.U.X.DTADV.I.K)
ADU(C,N,U,X,DTADV,I,K)
ADU(D,N,U,X,DTADV,I,K)
130
190
CC(I,K)
DD(I,K)
CONTINUE
CONTINUE
200 CONTINUE
C
c*
C
C
<;»
c«
C
SET SIDE AND TOP BOUNDARY CONDITIONS.
CALL BNDRYC(BACKGA,1,NX,KMAX,JTEST,AA)
IF (ICHEM .EQ. 1) 00 TO 210
CALL BNDRYCtBACKGB,1,NX,KMAX.JTEST.BB)
CALL BNDRYC(BACKGC,1,NX,KMAX,JTEST,CC)
CALL BNDRYCtBACKGD,1,NX,KMAX,JTEST,DD)
210 CONTINUE
THE FLUX LIMITER CALCULATION ELIMINATES MOST OF THE ARTIFICAL
DIFFUSION.
IF (IANTI .EQ. 0) GO TO 22S
CALL BMOVECAA,192.AI)
IF (ICHEM .EQ. 1) GO TO 220
CALL BMOVE(B8,192,81)
CALL BMOVE(CC,192,CI)
CALL BMOVE(DD,192,DI)
220 CONTINUE
GO TO 280
225 CONTINUE
DO 250 K = 2.NZ1
DO 240 I = 2.NX1
AI(I.K) * ANTU(AA,U,X,I,K,DTADV,A,N,NX,SA)
IF (ICHEM .EQ. 1) 00 TO 230
BIU.K) = ANTU(BB,U,X,I,K,DTADV,B,N,NX,SB)
CKI.K) = ANTU(CC,U,X,I,K,DTADV,C,N,NX,SC)
DI(I.K) = ANTU(DD,U,X, I,K,DTADV,D,N,NX,DU1VMY)
230 CONTINUE
240 CONTINUE
250 CONTINUE
RWY20260
RWY2027Q
RWY20280
RWY20290
RWY20300
RWY20310
RWY20320
RWY20330
RWY20340
RWY20350
RWY20360
RWY20370
RWY20380
RWY20390
RWY20400
RWY20410
RWY2Q420
RWY20430
RWY2Q440
RWY20450
RWY20460
RWY20470
RWY20480
RWY20490
RWY20500
RWY20510
RWY20520
RWY20S30
RWY20540
RWY20550
RWY20SSO
RWY20570
RWY2QSSO
RWY20590
RWY20600
RWY20810
RWY20S20
RWY20630
RWY20840
RWY20650
RWY20660
RWY20670
RWY2Q880
RWY20690
RWY20700
RWY20710
RWY20T20
RWY20730
RWY20740
RWY20750
RWY20760
RWY20770
RWY20780
RWY20790
RWY20800
RWY20810
RWY20820
RWY20830
RWY20840
RWY20850
RWY20860
RWY20870
RWY20880
RWY20890
RWY20900
RWY20910
RWY20920
RWY20930
RWY20940
RWY209SO
RWY20960
RWY20970
RWY20980
RWY20990
RWY21000
114
-------
c«
c
c
c«
c
SET SIDE AND TOP BOUNDARY CONDITIONS.
CALL BNDRYC(BACKGA,1,NX,KMAX,JTEST,AI)
IF (ICHEM .EQ. 1) GO TO 260
CALL BNDRYC(BACKGB,1,NX,KMAX,JTEST,BI)
CALL BNDRYC(BACKGC,I,NX,KMAX,JTEST,CI)
CALL BNDRYCfBACKGD.l.NX.KMAX.JTEST.DI)
260 CONTINUE
CALCULATE ADVECTION IN Z DIRECTION.
DO 300 K = 2.NZ1
DO 290 I = 2.NX1
AA(I.K) = ADW(AI,W,Z,DTADV,I,K)
IF (ICHEM .EQ. 1) GO TO 280
ADW(BI,W,Z,DTADV,I,K)
ADW(CI,W,Z,DTADV,I,K)
ADW(DI,W,Z,DTADV,I,K)
280
290
BB(I,K)
CC(I,K)
DD(I,K)
CONTINUE
CONTINUE
C
C«
C
300 CONTINUE
C
C*
C
C
C*
C
SET SIDE AND TOP BOUNDARY CONDITIONS.
CALL BNDRYC(BACKGA,1 ,NX,KMAX, JTEST.AA)
IF (ICHEM .EQ. 1) GO TO 310
CALL BNDRYC(BACKGB,1,NX,KMAX,JTEST,BB)
CALL BNDRYC(BACKGC,1,NX,KMAX,JTEST,CC)
CALL BNDRYC(BACKGD,1,NX,KMAX,JTEST,DD)
310 CONTINUE
ANTIDIFFUSION CALCULATION FOR Z-AXIS.
IF (IANTI .EQ. 0) GO TO 325
CALL BMOVE(AA,192,AI)
IF (ICHEM .EQ. 1) GO TO 320
CALL BM3VE(BB,192,BI)
CALL BMQVE(CC,192.CI)
CALL BMOVE(DD,192,01)
320 CONTINUE
GO TO 360
325 CONTINUE
DO 350 I.« 2.NX1
DO 340 K * 2.KMAX
AI(I.K) » ANTW(AA,W,Z,I,K,DTADV,AI,KMAX)
IF (ICHEM .EQ. 1) GO TO 330
BI(I,K) = ANTW(BB,W,Z,I,K,DTADV,BI,KMAX)
CI(I,K) » ANTW(CC,W,Z,I,K,DTADV,CI,KMAX)
DI(I.K) * ANTW(DD,W,Z,I,K,DTADV,DI,KMAX)
330 CONTINUE
340 CONTINUE
350 CONTINUE
C
C«
C
SET SIDE AND TOP BOUNDARY CONDITIONS.
CALL BNDRYC(BACXGA,1,NX,KMAX,JTEST,AI)
IF (ICHEM .EQ. 1) GO TO 380
CALL BNDRYC(BACKG8,1,NX,KMAX,JTEST,BI)
CALL BNDRYC(BACKGC,1,NX,KMAX,JTEST,CI)
CALL BNDRYC(BACKGD,1,NX,KMAX,JTEST,DI)
360 CONTINUE
CALCULATION DIFFUSION IN X DIRECTION.
DO 400 I » 2.NX1
DO 390 K = 2,NZ1
AA(I,K) = AI(I,K) * DIPFX(AI,X,DTADV,I,K,KXP)
IF (ICHEM .EQ. 1) GO TO 370
BB(I,K) a BI(I,K) + DIPFX(BI,X,DTADV,I,K,KXP)
CI(I,K) + DIFFX(CI,X,DTADV,I,K,KXP)
DKI.K) + DIFFX(DI,X,DTADV,l,K,KXP)
370
390
CC(I,K)
DD(I,K)
CONTINUE
CONTINUE
400 CONTINUE
RWY21010
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115
-------
c
C"«
c
C
£
C
SET SIDE AND TOP BOUNDARY CONDITIONS.
CALL BNDRYC(BACKGA,1,NX,KMAX,JTEST,AA)
IF (ICHEM .EQ. 1) GO TO 410
CALL BNDRYC(BACKGB,1,NX,KMAX,JTEST,BB)
CALL BNDRYC(BACKGC,1,NX,KMAX,JTEST,CC)
CALL BNDRYC(BACKGD,1,NX,KMAX,JTEST,DD)
410 CONTINUE
CALCULATION DIFFUSION IN Z DIRECTION.
DO 450 I = 2.NX1
DO 440 K = 2.NZ1
AI(I,K) 3 AA(I,K) + DIFFZ(AA,Z,DTADV,I,K,KZP)
IF (ICHEM .EQ. 1) GO TO 430
BKI.K) » BB(I,K) + DIFFZ(BB,Z,DTADV,I,K,KZP)
CC(I,K) * DIFFZ(CC,Z,DTADV,I,K,KZP)
DD(I,K) + DIFFZ(DD,Z,DTADV,I,K,KZP)
430
440
CKI.K)
DKI.K)
CONTINUE
CONTINUE
C
C'
C
450 CONTINUE
SET SIDE AND TOP BOUNDARY CONDITIONS.
CALL BNDRYC(BACKGA,1,NX,KMAX,JTEST,AI)
IF (ICHEM .EQ. 1) GO TO 480
CALL 8NDRYC(BACKG8,1,NX,KMAX,JTEST,BI)
CALL BNDRYC(BACKGC,1,NX,KMAX,JTEST,CI)
CALL BNDRYC(BACKGD,l,NX,KMAX,JTEST,Dl)
460 CONTINUE
DO ROADWAY CHEMISTRY VIA EXPLICIT METHOD FOR NO, N02, 03, CO
NUMERICAL STABILITY FOR THE CHEMICAL CALCULATIONS GENERALLY
REQUIRES A SMALLER TIME STEP THAN THE ADVECTION TIME STEP.
HENCE THE METHOD IS TO DO THE ADVECTION AND THEN DO THE
CHEMISTRY IN SMALLER TIME STEPS TO CATCH UP (SEE ESKRIDGE
AND DEMERJIAN, 1977 ATMOS. ENVIRONM.).
IF (ICHEM .EQ. 1) GO TO 540
DO 530 L = l.NUMCHM
DO 520 I » 2.NX1
DO 510 K » 2.NZI
A(I,K,NP) - AKI.K) * DTCHM
1 (-K1 01(1,K) * AI(I.K) * K2 CId.K))
Bd.K.NP) - BI(I.K)
C(I,K,NP) « CUI.K) + DTCHM
1 ( Kl AI(I,K) DKI.K) - K2 CI(I.K))
D(I,K,NP) = DKI.K) * DTCHM
1 (-K1 DKI.K) AKI.K) + K2 CI(I.K))
AI(I.K) * Ad.K.NP)
BKI.K) = B(I.K.NP)
CId.K) - Cd.K.NP)
DKI.K) = D(I,K,NP)
510 CONTINUE
520 CONTINUE
530 CONTINUE
CALL BNDRYC(BACKGA,NP,NX,KMAXtJTEST,A)
CALL BNDRYC(BACKGB,NP,NX,KMAX,JTEST,B)
CALL BNDRYC(BACKGC,NP,NX,KMAX,JTEST,C)
CALL BNDRYC(BACKGD,NP,NX,KMAX,JTEST,D)
GO TO 560
C
c«
c
540 DO 580 I > l,NX
DO 550 K * l.KMAX
A(I,K,NP) = AKI.K)
550 CONTINUE
560 CONTINUE
PRINT INTERMEDIATE RESULTS.
IF (ICHEM .EQ. 1) GO TO 585
RWY21760
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RWY22260
RWY22270
RWY22280
RWY22290
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RWY22340
RWY22350
RWY223SO
RWY22370
RWY22380
RWY22390
RWY22400
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RWY22440
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RWY224SO
RWY22470
RWY22480
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RWY22500
116
-------
C
C-
C
IFdPRINT .LT. NPRINT) GO TO 580
IF (INTPR .NE. 0) GO TO 570
WRITEdO.1000) HEAD1,HEAD2,HEADS
WRITEdO.1010)
CALL GRAPH(A,NP,TIME,NX,KMAX,X,HWAYL)
WRITE(IO,1020)
CALL GRAPH(B,NP,TIME,NX,KMAX,X,HWAYL)
WRITEdO.lOSO)
CALL GRAPH(C,NP,TIME,NX,KMAX,X,HWAYL)
WRITEt10,1000) HEAD1.HEAD2,HEADS
WRITE(IO,1040)
CALL GHAPH(D,NP,TIME,NX,KMAX,X,HWArL)
570 CONTINUE
IPRINT = 0
580 CONTINUE
GO TO 600
585 IF (IPRINT .LT. NPRINT) GO TO "600
IF (INTPR .EQ. 1) GO TO 595
IF (KOUNTP/4«4 .NE. KOUNTP) GO TO 590
WRITE(10,1000) HEAD1.HEAD2,HEADS
590 WRITEdO.lOSO)
CALL GRAPH(A,NP,TIME,NX,KMAX,X,HWAYL)
KOUNTP » KOUNTP + 1
595 CONTINUE
IPRINT = 0
800 CONTINUE
NP * NP + 1
IF (NP .EQ. 3) NP » 1
N * N + 1
IF (N .EQ. 3) N = 1
TIME * TIME * DTADV
IF (TIME .GE. TMSTOP) GO TO 700
IPRINT * IPRINT + 1
GO TO 100
700 CONTINUE
NP * NP - 1
IF (NP .EQ. 0) NP * 2
PRINT FINAL RESULTS.
IF (ICHEM .EQ. 1) GO TO 750
WRITE(IO.IOOO) HEAD1.HEAD2,HEADS
WRITE(IO.IOIO)
CALL GRAPH(A,NP,TIME,NX,KMAX,X,HWAYL)
WRITE(IO,1020)
CALL GRAPH(B,NP,TIME,NX,KMAX,X,HWAYL)
WRITEdO.lOSO)
CALL GRAPHIC,NP,TIME,NX,KMAX.X.HWAYL)
WRITE(IO.IOOO) HEAD1.HEAD2,HEADS
WRITE(IO,1040)
CALL GRAPH(D,NP,TIME,NX,XMAX,X,HWAYL)
GO TO 999
750 CONTINUE
WRITE(IO.IOOO) HEAD1.HEAD2,HEADS
WRITEdO.lOSO)
CALL GRAPHU.NP.TIME.NX.KMAX.X.HWAYL)
C
999
C
C*»*
C
1000
1010
1020
1030
1040
1050
C
C33S33
RETURN
FORMAT STATMENTS.
FORMATdHl,'TITLE: ' , 20A4, 2( / , 9X, 20A4)/)
FORMATdHO,'NITROGEN OXIDE, NO (PPM)')
FORMATdHO,'CARBON MONOXIDE, CO (PPM)')
FORMAT(1HO,'NITROGEN DIXOIDE, NO2 (PPM)')
FORMAT(1HO,'OZONE, O3 (PPM)')
FORMAT(1HO,'POLLUTANT CONCENTRATIONS (PPM)')
END
RWY22510
AWY22S20
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RWY22950
RWY22960
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RWY22990
RWY23000
RWY23010
RWY23020
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RWY230SO
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RWY23080
RWY23090
HWY23100
RWY23110
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RWY23140
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RWY23190
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RWY23230
RWY23240
117
-------
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
SUBROUTINE TIMINC( ICTEM.K1.K2, DTADV, DTCHM.NUMCHM)
PARAMETER LIST:
INPUT: ICHEM - CHEMISTRY OPTION (IF ICHEM = 1, THEN Kl ,
K2, DTCHM, AND NUMCHM ARE IRRELEVANT)
Kl - CHEMICAL REACTION RATE (I/ (PPM M1N) FOR:
NO + 03 N02 + O2
K2 - CHEMICAL REACTION RATE (1/MIN) FOR:
NO2 + O2 --- NO + 03
OUTPUT: DTADV - ADVECTIVE/DIFPUSION TIME STEP (SEC)
DTCHM - CHEMICAL REACTION TIME STEP (SEC)
NUMCHM - NUMBER OF CHEMICAL REACTION TIME STEPS PER
ADVECT1VE/D1FFUS10N TIME STEP
CALLING ROUTINE:
ADVCHM
.
DESCRIPTION:
THIS SUBROUTINE FINDS THE MAXIMUM ALLOWABLE TIME STEP FOR
ADVECTIVE AND DIFFUSION TO ASSURE STABILITY. IT ALSO
DETERMINES THE CHEMICAL REACTION TIME STEP AND THE NUMBER OF
TIME STEPS PER ADVECTI YE/DIFFUSION TIME STEP.
REAL KXP,KZP,KX,KZ,K:,K2
DIMENSION X(24),Z(8),KXP<24,8),KZP(24,8),U(24,8),W(24,S),KX(8)
DIMENSION KZ(8)
COMMON /CALCOM/U,W,KMAX,KX,KZ,X,Z,TMSTOP,NX,KXP,KZP
DTI » 1000.
DT2 " 1000.
DT3 " 1000.
DT4 » 1000.
DO 20 I » 2, NX
DO 10 K = 2, UMAX
DX = X(I) - X(I-l)
DZ = Z(K) - Z(K-l)
Dl » 0.9S DX/ABS(U(I,K))
IF (Dl .LT. DTI) DTI = Dl
D3 - 0.5 DZ DZ/KZPU.K)
IF (D3 .LT. DT3) DT3 = D3
D4 » 0.5 DX DX/KXPU.K)
IF (D4 .LT. DT4) DT4 * D4
10 CONTINUE
20 CONTINUE
DTADV * AMIN1(DT1,DT3,DT4)
IF (ICHEM .EQ. 1) OO TO 30
FK * AMAXKK1.K2)
DTCHM - l./FK
NUMCHM * DTADV/DTCHM + 1.
DTCHM * DTADV/FLOAT(NUMCHM)
30 CONTINUE
RETURN
END
RWY23260
RWY23270
RWY23280
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RWY23700
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RWY23740
RWY237SO
RWY23780
RWY23770
RWY23730
RWY23790
RWY23800
RWY23810
RWY23820
RWY23840
SUBROUTINE BNDRYC(BACKGR,L,NX,KMAX,JTEST,RHO)
PARAMETER LIST:
INPUT: BACKGR - BACKGROUND POLLUTANT CONCENTRATIONS (PPM)
L - INDEX
NX - NUMBER OF GRID POINTS IN X DIRECTION
KMAX - NUMBER OF GRID POINTS IN Z DIRECTION
JTEST - WIND DIRECTION INDICATOR
I/O: RHO - ARRAY FOR WHICH BOUNDARY CONDITIONS ARE TO
BE ESTABLISHED
CALLING ROUTINE:
ADVCHM
DESCRIPTION:
THIS SUBROUTINE ESTABLISHES BOUNDARY CONDITIONS FOR A
RWY23850
RWY23860
RWY23870
RWY23830
RWY23890
RWY239QQ
RWY23910
RWY23920
RWY23930
RWY23940
RWY23950
RWY23960
RWY23970
RWY23980
RWY23990
RWY24000
118
-------
c
c
c
c*
c
c
C'
c
c
c*
c«
c*
c
c
c<
C'
c
c
C'
c«
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
POLLUTANT DURING THE MARCHING PROCESS.
DIMENSION RHO(24,8,2)
'«» LOWER BOUNDARY CONDITION IS THAT THE GRADIENT IS ZERO.
DO 10 I = l.NX
RHO(I,1,L) « RHO(I,2,L)
10 CONTINUE
' TOP BOUNDARY ASSUMES BACKGROUND.
DO 110 I a 1,NX
RHO(I,KMAX,L) = BACKGR
110 CONTINUE
'* THE OUTFLOW CONDITIONS ARE JUST AN EXTROPLATION OF INSIDE
VALUE TO THE BOUNDARY POINTS ASSUMING EQUAL GRADIENT OF
'» POLLUTANT.
IF (JTEST .EQ. 1) GO TO 300
' SET OUTFLOW CONDITION TO CONSTANT GRADIENT AT WEST
' BOUNDARY INFLOW TO BACKGROUND.
DO 210 K * 2.KMAX
RHO( 1,K,L) = RHO(2,K,L)
RHO(NX,K,L) a BACKGR
210 CONTINUE
GO TO 999
' SET OUTFLOW CONDITION TO CONSTANT GRADIENT AT EAST BOUNDARY
BOUNDARY INFLOW TO BACKGROUND
300 DO 310 K a 2.KMAX
RHO(NX,K,L) a RHO(NX-1,K,L)
RHO( 1,K,L) a BACKGR
310 CONTINUE
999 RETURN
END
FUNCTION ADU(RHO,L,U,X,DT,I,K)
PARAMETER LIST:
INPUT: RHO - ARRAY OF SUBSTANCE TO BE ADVECTED (PPM)
L - LIMITING INDEX (TIME LEVEL 1 OR 2)
U - U COMPONENT FIELD (M/SEC)
X - GRID POINTS IN X DIRECTION (METERS)
DT - ADVECT1VE TIME STEP (SEC)
I - INDEX FOR X DIRECTION
K - INDEX FOR Z DIRECTION
OUTPUT: ADU - CONCENTRATION FIELD ADVECTED IN X DIRECTION
FOR ONE TIME STEP
CALLING ROUTINE:
ADVCHM
DESCRIPTION:
TRANSPORT IN THE X DIRECTION IS DETERMINED USING AN UPSTREAM
FLUX CORRECTED METHOD. THE METHOD IS PREFERRED SINCE ONLY
ONE BOUNDARY POINT IS REQUIRED.
DIMENSION X(24),RHO(24,8,2),U(24,8)
DX(I) = X(I) - X(I-l)
XL(I,K) a X(I) + U(I,K) DT
UP(I,K) a .5 (U(I,K) + U(I+1,K»
RHOP(I.K) a (RHO(I,K,D) DX(I+1)/(XL(I+1,K) - XL(I,K))
RHOMd.K) = (RHOd.K.D) DX( I ) /(XL(I.K) - XL(I-1,K))
RWY24010
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RWY24140
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RWY2419Q
RWY24200
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RWY24220
RWY2423Q
RWY24240
RWY242SO
RWY24260
RWY24270
RWY2428Q
RWY24290
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RWY24320
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RWY24340
RWY24350
RWY24360
RWY24370
RWY24380
RWY24390
RWY24400
RWY24410
RWY24420
DWV9 A. A 1 ft
HIV I * 4 4 J U
RWY24440
RWY244SO
RWY24480
RWY24470
RWY24480
RWY24490
RWY24SOO
RWY24S10
RWY24S20
RWY24S30
RWY24S40
RWY24550
RWY24S60
RWY24570
RWY24S80
RWY24S90
RWY24600
RWY24610
RWY24S20
RWY24630
RWY24640
RWY246SO
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RWY24680
RWY24690
RWY24700
RWY24710
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RWY24730
RWY24740
RWY24750
119
-------
c
10
20
C
110
120
C
C
C
C .
C
C
C
c
c
c
c
c
c
c
c
c
c
10
c
c
c
c
c
c
c
c
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c
IF (UP(I,K) .GE. 0.0) GO TO 10
DMP = UPU.K) DT RHOM(I+1,K)
GO TO 20
CONTINUE
DMP = UP(I,K) * DT RHOPU.K)
CONTINUE
IF(UP(I-1,K).GE. 0.0) GO TO 110
DMM * UP(I-1,K) DT RHOMU.K)
GO TO 120
CONTINUE
D\M = UP(I-l.K) * DT RHOP(I-1,K)
CONTINUE
FM » RHO(I,K,L) .5 (DXU+1) + DX(I»
ADU » (FM + DMM - DMP)/(.5 (DXU + 1) * DX( I ) ) )
RETURN
END
RWY24760
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RWY2494Q
RWY24950
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RWY24970
RWY24990
SUBROUTINE BM>V£(A,N,B)
PARAMETER LIST:
INPUT: A - ARRAY USED FOR INITIALIZATION
N - ENDING INDEX
OUTPUT: 3 - ARRAY TO BE INITIALIZED
CALLING ROUTINE:
ADVCHM
DESCRIPTION:
THE PURPOSE OF THIS MODULE IS TO INITIALIZE AN ARRAY.
DIMENSION A(N),B(N)
DO 10 I = 1,N
B(I) * A(I)
CONTINUE
RETURN
END
FUNCTION ANTU(RHOT,U,X, I ,K,DT,RHO,L,NX,S)
PARAMETER LIST:
INPUT: RHOT - POLLUTION FIELD WHICH HAS BEEN ADVECTED IN
X DIRECTION
U - U COMPONENT FIELD (M/SEC)
X - GRID POINTS IN X DIRECTION (METERS)
I - INDEX FOR X DIRECTION
K - INDEX FOR Z DIRECTION
DT - ADVECTIVE TIME STEP (SEC)
RHO - POLLUTANT FIELD (PPM) WITHOUT ADVECTION IN
X DIRECTION
L - LIMITING INDEX
NX - NUMBER OF GRID POINTS IN X DIRECTION
S - EMISSION GRID (G/M»«3/SEC)
OUTPUTS ANTU - NUMERICAL DISPERSION TENDS TO "DIFFUSE" THE
RWY2SOOO
RWY25010
RWY25020
RWY25030
RWY2S040
RWY2SOSO
RWY25060
RWY2S070
RWY25080
RWY25090
RWY2S100
RWY25UQ
RWY25120
RWY25130
RWY25140
RWY25150
RWY25160
RWY25170-
RWY2S180
RWY2S190
RWY2S200
RWY2S210
PWVJ ^ o 9 n
ItrrI *0 L * U
RWY2S230
RWY2S240
OWY2S250
RWY2S280
RWY25270
RWY2S280
RWY2S290
RWY2S300
RWY25310
RWY2S320
RWY25330
RWY2S340
RWY2S350
RWY25360
RWY25370
RWY25380
RWY25390
CONCENTRATION FIELDS ARTIFICIALLY, THE OUTPUTRWY25400
OF THIS FUNCTION IS THE CONCENTRATION FIELD
WITH "MOST" OF THE NUMERICAL DISPERSION
REMOVED
CALLING ROUTINE:
ADVCHM
DESCRIPTION:
THIS FUNCTION PERFORMS THE ANTIDIFFUSION OR FLUX UMITER
CALCULATION.
RWY25410
RWY25420
RWY2S430
RWY2S440
RWY25450
RWY2S460
RWY25470
RWY25480
RWY25490
RWY25SOO
120
-------
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
DIMENSION 3(24) ,X( 24) ,RHOT( 24, 8 ) ,U( 24, 8 ) ,RHO(24,8,2)
DXd) = xd) - xd-n
XL(I,K) * X(I) + U(I,K) » DT
UP(I.K) = .5 (U(I,K) * 0(1+1, K))
RHOP(I.K) = (RHOd.K.L) + F DT 3(1)) DX(I + 1)/
1 (XLd+l.K) - XL(I,K))
RHOMd.K) = (RHOd.K.L) + F DT « S(I-D) DX(I ) /
1 (XLd.K) - XL(I-l.K))
ASP(I.K) * (RHOM(I+1,K) - RHOPd.K)) . 5 DT ABS(UPd.K))
1 (l.-DT ABS(UP(I,K))/(XLd+l,K) - XL(I.K)))
DELd.K) = RHOT(I+1,K) - RHOTd ,K)
P » 1.
IF (K ,GT. 2) F * 0.0
NX1 NX - 1
XI « SIGN(1.,ASP(I,K))
Yl » SIGN(1.,ASP(I-1,K))
ZZ1 '0.0
IF (I .LT. NX1) ZZ1 a DEL(I+1,K)
ZZ2 = Q.o
IF (I .GT. 2) ZZ2 a DEL(I-l.K)
XX * XI AMAXKO.O.AMINKX1 ZZ2 (.5 (X(I + 1) - X(I-l))),
1 ABS(ASPd,K)),Xl ZZ1 (.5 (X(I+2) - X(I ) ) ) ) )
IF (I .GT. 2) GO TO 10
Zl > 0.0
Z2 » X(2) - X(l)
GO TO 20
10 CONTINUE
Zl = DEL(I-2,K)
Z2 * .5 (X(I) - X(I-2))
20 CONTINUE
Y * Yl AMAXKO.O.AMINHYl Zl (Z2),
1 ABS(ASP(I-1,K)),Y1 DEL(I.K) (.5 « (X(I+1) - X(I-l))))
ANTU » RHOTd, K) + (Y -XX)/(.S (X(I+1) - X(I-l)))
RETURN
END
FUNCTION ADW(RHO,W,Z,DT,I,K)
PARAMETER LIST:
INPUT: RHO - POLLUTANT CONCENTRATION FIELD (PPM)
W - W COMPONENT FIELD (M/SEC)
Z - GRID POINTS IN Z DIRECTION (METERS)
DT - ADVECTIVE TIME STEP (SEC)
I - INDEX FOR X DIRECTION
K - INDEX FOR Z DIRECTION
OUTPUT: ADW - POLLUTANT CONCENTRATION FIELD (PPM) ADVECTED
IN Z DIRECTION FOR ONE TIME STEP
CALLING ROUTINE:
ADVCHM
DESCRIPTION:
THIS FUNCTION CALCULATES TRANSPORT IN THE Z DIRECTION USING
AN UPSTREAM FLUX CORRECTED METHOD. THE METHOD IS PREFERRED
SINCE ONLY ONE BOUNDRY POINT IS NEEDED.
DIMENSION Z(8),RHO(24,8),W(24,8)
DZ(K) = Z(K) - Z(K-l)
ZL(I,K) = Z(K) + W(I,K) DT
WP(I,K) = .5 (W(I,K) +W(I,K+D)
RWY25510
RWY25520
RWY25530
RWY2 5540
RWY25550
RWY2S560
RWY25570
RWY25S80
RWY25590
RWY25600
RWY2SS10
RWY2S620
RWY2S630
RWY25640
RWY2S650
RWY25660
RWY25870
RWY25680
KWY2S690
RWY2S700
RWY25710
RWY25720
RWY25730
RWY25740
RWY25750
RWY25760
RWY25770
RWY25780
RWY25790
RWY2S800
RWY2S810
RWY2S820
RWY2S830
RWY25840
RWY2S3SO
RWY2S860
RWY25870
RWY25880
RWY2S390
RWY25900
)RWY25910
RWY2S920
RWY2S930
RWY25940
RWY25950
RWY25960
RWY2S980
RWY2S990
RWY26000
RWY26010
RWY26020
RWY26030
RWY28040
RWY280SO
RWY26060
RWY26070
RWY28080
RWY2S090
RWY26100
RWY28110
RWY28120
RWY26130
RWY2S140
RWY26150
RWY281SO
RWY28170
RWY26180
RWY2S190
RWY2S200
RWY2 6210
RWY26220
RWY26230
RWY26240
RWY28250
121
-------
c
c
c
RHOPd.K) = RHO(I.K) » DZ(K+1)/(ZL(I,K+1) - ZL(I,K))
RHOMd.K) = RHOd.K) « DZ(K) /(ZL(I,K) - ZL(I,K-D)
IF (WP(I.K) .GE.
DMP = WPd.K)
GO TO 20
10 CONTINUE
DMP = WP(l.K)
20 CONTINUE
IF (WP(I,K-1) .GE.
DMM * WP(I,K-1)
GO TO 120
110 CONTINUE
DMM = WP(I,K-1)
120 CONTINUE
.0) GO TO 10
DT * RHOM(I,K+1)
DT « RHOP(I.K)
0.0) GO TO 110
DT RHOM(I,K)
DT BHOP(I.K-l)
C
C=
C
C
C
C
C
C
C
C
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
FM » RHOd.K) .5 (DZ(K+1) * DZ(K))
ADW = (FM + DVM - DMP)/(.5 (DZ(K+1) + DZ(K)))
RETURN
END
FUNCTION ANTW(RHOT,W,Z,I,K,DT,RHO,KMAX)
PARAMETER LIST:
INPUT:
SHOT - CONCENTRATION FIELD WHICH HAS BEEN ADVECTED
IN Z DIRECTION
OUTPUT:
W - W COMPONENT FIELD (M/SEC)
Z - GRID POINTS IN Z DIRECTION (METERS)
I - INDEX FOR X DIRECTION
K - INDEX FOR Z DIRECTION
DT - ADVECTIVE TIME STEP
RHO - CONCENTRATION FIELD WITHOUT ADVECTION IN
Z DIRECTION
KMAX - NUMBER OF GRID POINTS IN Z DIRECTION
ANTW - NUMERICAL DISPERSION TENDS TO "DIFFUSE" THE
CONCENTRATION FIELDS ARTIFICIALLY, THE OUTPUTRWY26670
OF THIS FUNCTION IS THE CONCENTRATION FIELD RWY28680
WITH "MOST" OF THE NUMERICAL DISPERSION
REMOVED
RWY26260
RWY26270
RWY26280
" RWY26290
RWY26300
RWY2 6310
RWY26320
RWY26330
RWY26340
RWY26350
RWY26360
RWY26370
RWY28380
RWY26390
RWY26400
RWY26410
RWY28420
RWY26430
RWY26440
RWY26450
RWY26460
RWY26470
RWY26480
RWY26490
RWY26500
====RWY26510
RWY26520
RWY26S30
RWY26S40
RWY265SO
RWY26SSO
RWY26570
RWY28580
RWY28590
RWY26600
RWY28610
RWY26620
RWY26630
RWY2S640
RWY26650
RWY28660
CALLING ROUTINE:
ADVCHM
DESCRIPTION:
THIS FUNCTION PERFORMS THE ANTIDIPFUSION OR FLUX DELIMITER
CALCULATION.
DIMENSION Z(24),RHOT(24,3),W(24,3),RHO(24,3)
STATEMENT FUNCTIONS
DZ(K) = Z(K.) - Z(K-l)
ZL(I,K) » Z(K) + W
-------
XX = XI
AMAXKO.O.AMINKXl
ABS(ASPC,K)),X1
ZZ2
ZZ1
(.5
(.5
(Z(K+1) - Z(K-l))),
(Z(K+2) -
C
C*
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c=
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
IF (K .GT. 2) GO TO 10
Zl = 0.
Z2 = Z(2) - Z(l)
00 TO 20
10 CONTINUE
Zl = DEL(I,K-2)
Z2 = .5 (Z(K) - Z(K-2))
20 CONTINUE
PARAMETER LIST
INPUT: RHO
X
DT
I
K
KXP
RWY27010
RWY27020
RWY27030
RWY27040
RWY27050
RWY27060
RWY27070
RWY27080
RWY27090
RWY27100
RWY27110
RWY27120
Y » Yl AMAXKO.O.AMINKYl Zl * (Z2), RWY27130
1 ABS(ASP(I,K-1)),Y1 * DEL(I.K) (.S (Z(K+1) - Z(K-1)))))RWY27140
ANTW = RHOTU.K) * (Y - XX)/(.S » (Z(K+1) - Z(K-l))) RWY27150
RWY27180
RETURN RWY27170
END RWY27180
RWY27190
'RWY27200
RWY27210
FUNCTION DIFFX(RHO,X,DT,I,KtKXP) RWY27220
RWY27230
RWY27240
RWY27250
RWY27260
RWY27270
RWY27280
RWY27290
RWY27300
RWY27310
RWY27320
RWY27330
RWY27340
RWY27350
RWY27380
RWY27370
RWY27380
RWY27390
RWY27400
RWY27410
RWY27420
RWY27430
RWY27440
RWY274SO
RWY27480
RWY27470
RWY27480
(RHO(I+1,K) -RHO(I.K)) /DXK RWY27490
(RHO(I.K) - RHO(I-1,K))/DXH)RWY27500
RWY27510
RWY27520
RWY27530
RWY27S40
RWY27SSO
RWY27580
333333333333333333333333333333RWY27S70
RWY27S80
RWY27S90
RWY27800
RWY27610
- CONCENTRATION FIELD (PPM) RWY27820
- GRID POINTS IN THE Z DIRECTION (METERS)
- DIFFUSION TIME STEP (SEC)
- INDEX FOR X DIRECTION
- INDEX FOR Z DIRECTION
- VERTICAL EDDY DIFFUSION COEFFICIENTS
(M"2/SEC)
CONCENTRATION VALUES DIFFUSED IN THE Z
DIRECTION
CONCENTRATION FIELD (PPM)
GRID POINTS IN THE X DIRECTION (METERS)
DIFFUSION TIME STEP (SEC)
INDEX FOR X DIRECTION
INDEX FOR Z DIRECTION
HORIZONTAL EDDY DIFFUSION COEFFICIENTS
(M*«2/SEC)
OUTPUT: DIFFX - CONCENTRATION VALUES DIFFUSED IN THE X
DIRECTION
CALLING ROUTINE:
ADVCHM
DESCRIPTION:
THIS FUNCTION CALCULATES THE DIFFUSION IN THE X DIRECTION
BY CENTERED IN SPACE DIFFERENCES MAKING ALLOWANCES FOR
UNEQUAL SPACING.
REAL KXP
DIMENSION X(24),RHO(24,8),KXP(24,8)
DXH '
DXK '
DXD a
DIFFX
DIFFX
RETURN
END
X(I) - X(I-l)
XU+1) - X(I)
X(I+1) - X(I-l)
=((KXP(I+1,K) +
- (KXP(I.K) *
/DXD
* DIFFX DT
KXP(I.K))
KXP(I-l.K))
FUNCTION DIFFZ(HHO,Z,DT, I ,K,KZP)
PARAMETER LIST:
INPUT: RHO
Z
DT
I
K
KZP
OUTPUT: DIPFZ -
CALLING ROUTINE:
ADVCHM
DESCRIPTION:
RWY27630
RWY27840
RWY27850
RWY27860
RWY27870
RWY27880
RWY27S90
RWY27700
RWY27710
RWY27720
RWY27730
RWY27740
RWY27750
123
-------
c
c
c
c
THI3 FUNCTION CALCULATES THE DIFFUSION IN THE Z DIRECTION
BY CENTERED IN SPACE DIFFERENCES MAKING ALLOWANCES FOR
UNEQUAL SPACING.
REAL KZP
DIMENSION Z(3),RHO(24,8),KZP(24,3)
C
c
c
DZK = Z(K+U - Z(K)
DZH = Z(K) - Z(K-l)
DZD » Z(K+1) - Z(K-l)
DIFFZ =((KZP(I,K+1) +
1 - (KZP(I.K) +
2 /DZD
DIFFZ * DIFFZ DT
RETURN
END
KZPU.K)) (RHO(I,K+1) - RHO(I,K)) /D
KZPU.K-U) (RHOU.K) - RHO(I,K-1))/D
SUBROUTINE GRAPH (PRTARR.L, TIME, NX, KMAX.X.HWAYL)
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
PARAMETER LIST:
INPUT: PRTARR -
L
TIME
NX
KMAX
X
HWAYL -
CALLING ROUTINES:
MAIN, ADVCHM
DESCRIPTION:
THIS SUBROUTINE
POLLUTANT FIELD TO BE PRINTED (PPM)
LIMITING INDEX
TIME OF THE POLLUTANT FIELD (SEC)
NUMBER OF GRID POINTS IN THE X DIRECTION
NUMBER OF GRID POINTS IN THE Z DIRECTION
GRID POINTS IN THE X DIRECTION (METERS)
OUTPUT ARRAY CONTAINING LANE LOCATIONS
OUTPUTS VELOCITY, DIFFUSIVITY, AND
POLLUTANT FIELDS.
DIMEN3ION PRTARR(24,3,2),X(24),HWAYL(24),DASH(24)
DATA DASH/24*1 '/
DATA IN/5/, IO/8/
C
IF (TIME .GT. 0.0) WRITE(10,1000) TIME
DO 10 K * KMAX,2,-1
WRITE(10,1010) (PRTARR(I,K,L), I * 2,NX)
10 CONTINUE
WRITE(IO,1020) (DASH(I), I = 2,NX)
WRITE(IO,1030) (X(I), I - 2,NX)
WRITE(IO,1040) (HWAYL(I), I * 2,NX)
RETURN
C
C"**
C
1000 FORMAT(1H+,73X,'AT TIME',F12.8,IX,'SEC')
1010 FORMAT(1HO,22(1X,PS.2))
1020 FORMATt IX,'-',22(A4,''))
1030 FORMAT( IX,22(1X.F3.1))
1040 FORMAT( IX,ZX,22(A4,2X))
END
FORMAT STATEMENTS.
RWY27780
RWY27770
RWY27780
RWY27790
RWY27800
RWY27810
RWY27820
RWY27830
RWY27840
RWY27850
/DZK RWY27860
iZH)RWY27870
RWY27880
RWY27890
RWY27900
RWY27910
RWY27920
RWY27930
===RWY27940
RWY27950
RWY27960
RWY27970
RWY27980
RWY27990
RWY28QQO
RWY28010
RWY28020
RWY28030
RWY23040
RWY28050
RWY28060
RWY28070
RWY28080
RWY28090
RWY28100
RWY23UO
RWY28120
RWY28130
RWY28140
RWY28150
RWY28160
RWY28170
RWY28130
RWY28190
RWY28200
RWY28210
RWY28220
RWY28230
RWY28240
RWY282SO
RWY28280
RWY28270
RWY28280
RWY28290
RWY2830Q
RWY28310
RWY28320
RWY28330
RWY28340
124
-------
APPENDIX B
PERFORMANCE COMPARISON OF ROADWAY, HIWAY-2 AND CALINE3
The article in this appendix is reprinted from Atmospheric
Environment Yo1 20 Number 6, with the authors' permission.
125
-------
Atmosphtnc Environment Vol 20. No 6. pp 1095-1103, 1986.
Printed in Great Bntain.
0004-698 1 /86 J3.00 -t- 0 00
Pergamon Journals Ltd.
TURBULENT DIFFUSION BEHIND VEHICLES:
EVALUATION OF ROADWAY MODELS
S. T. RAO* and G. SISTLA
Division of Air Resources, NYS Dept. of Environmental Conservation, Albany, NY 12233, U.S.A.
and
R. E. ESKRIDGEf and W. B. PETERSENt
Atmospheric Sciences Research Laboratory, U.S. Environmental Protection Agency, Research Triangle
Park, NC 27711, U.S.A.
(First received 24 June 1985 and in final form 21 October 1985)
AbstractThis paper presents a statistical evaluation of three highway air pollution models (CALINE3,
HIWAY-2, and ROADWAY) using the tracer data from the General Motors Sulfate Dispersion Experiment.
Since the models predict the ensemble mean whereas any given observation reflects a single realization or an
event from a population, it should be recognized that the model predictions will almost always differ from the
corresponding observations, even if the models and the input data for the models are perfect The bootstrap
resampling procedure is used to quantify the variability in the observed concentrations due to the stochastic
nature of the atmosphere. The results suggest that the variability in the observations due to the random
nature of the atmosphere is about 30 %. Therefore, if the predicted values are within ± 30 % of the measured
concentrations, the differences between model predictions and observations should not be considered to be
significant. Thus a 'perfect* air quality model should predict to within ±30% of its corresponding observed
concentrations. Comparisons of the model predictions paired and unpaired in time with measurements
suggest that HIWAY-2 and ROADWAY perform best, but the performance of CALINE3 is acceptable.
Application of the extreme value theory and the bootstrap resampling procedure to the modeled and
measured data (unpaired) shows that all three models are capable of predicting the extreme concentrations
within the model performance criteria set forth above.
1. INTRODUCTION
The passage of the National Environmental Policy Act
of 1969 initiated modeling of pollution due to vehicles.
This act requires that for new highways that are
partially funded by federal funds an environmental
impact statement should be prepared before construc-
tion begins. A number of highway air pollution models
were developed in the early 1970s such as CALINE
(Beaton et al., 1972), EGAMA (Egan et al, 1973), and
HIWAY (Zimmerman and Thompson, 1975).
Attempts to validate and evaluate these models with
experimental data taken near highways were not
satisfactory because of the uncertainty in the estimate
of the emissions from vehicles. In field experiments the
background of measured pollutants was nonhomoge-
neous. Also, the statistical tests used in previous model
evaluations were rather simple. In 1975 General
Motors, with the cooperation of Ford Motor Co., the
Chrysler Corp. and the U.S. Environmental Protection
Agency, conducted a well conceived and controlled
highway experiment at the General Motors test facility
(Cadle el al., 1976). The tracer data from this exper-
Supported by U.S. EPA Grant CR-810475-01.
tOn assignment from NOAA, and to whom correspon-
dence should be addressed.
iment furnished for the first time an outstanding data
set for model evaluation and development.
The Environmental Protection Agency funded the
American Meteorology Society to establish a group of
scientists to evaluate and recommend techniques for
use in model evaluation. The recommendations of this
group are given by Fox (1981). In a response to the
recommendations of the American Meteorological
Society, Willmott (1982) made a number of important
suggestions.
In the late 1970s and early 1980s a number of
highway models were developed, and many of these
were evaluated by Rao et al. (1980) using the General
Motors data and many of the techniques recom-
mended by Fox (1981). In this paper three highway
models (CALINE3, HIWAY-2 and ROADWAY) will
be evaluated using the General Motors tracer data and
the statistical techniques suggested by Fox and
Willmott, extreme value statistics (Tabony, 1983), and
the 'bootstrap' methoc (Diaconis and Efron, 1983).
2. HIGHWAY MODELS
(a) The CALINE3 model
CALINE3 is a line source model developed by the
California Department of Transportation (Benson,
1979). It is based on the Gaussian diffusion equation
1095
126
-------
1096
S. T. RAO et al.
and employs a mixing zone cpncept to characterize
pollutant diffusion over the roadway. The model
divides individual highway sections into a series of
elements from which incremental concentrations are
computed from an approximation to the crosswind
finite line source equation and summed to form a total
concentration estimate at a particular receptor lo-
cation. Each element is modeled as an equivalent finite
line source positioned normal to the wind direction
and centered at the element midpoint. The region
directly over the highway is treated as a zone of
uniform emissions and turbulence.
The vertical diffusion parameter is a modification of
the curves suggested by Pasquill (1974) to incorporate
the initial diffusion over the highway. The horizontal
diffusion curves are identical to those suggested by
Turner (1970) except for averaging time and surface
roughness power law adjustments similar to those
made for the vertical diffusion curves.
(b) The HIWAY-2 model
The HIWAY-2 model (Rao and Keenan, 1980) is
basically a Gaussian diffusion model developed for at
grade and cut section roadway configurations.
Highway emissions are considered to be equivalent to
a series of finite line sources. Each lane of traffic is
modeled as if it were a straight, continuous, finite line
source with a uniform emission rate. A highway is
simulated with an increasing number of point sources
with the total contribution of all points computed by a
trapezoidal integration of the Gaussian point source
equation- over a finite length until the solution
converges.
The diffusion parameters used in HIWAY-2 were
determined from the tracer data collected during the
General Motors Experiment and the Long Island
Expressway Experiment (Sistla et d., 1979).
Downwind diffusion is a function of initial diffusion
and stability class. Three stability regimes are utilized
to characterize downwind diffusion. The initial spread
has incorporated in it a vehicle-induced drag factor
that accounts for the initial dilution of the pollutant
over the roadway, and allows the model to make
reasonable estimates of concentrations when the wind
speed is low and the wind direction is parallel to the
roadway.
(c) The ROADWAY model'
The ROADWAY model solves a conservation of
species equation via finite-difference approximations.
The model assumes a surface layer descnbable by
surface layer similarity theory with the superposition
of the effects of vehicle wakes. The vehicle wakes affect
the wind field and the turbulence fields, and it is
assumed in the model that the effect is linear. The
unique part of the ROADWAY model is the vehicle
wake theory, which was originally developed by
Eskridge and Hunt (1979), and modified by Eskridge
and Thompson (1982) and Eskridge and Rao (1983,
1986).
A vehicle wake is a region of increased turbulence
and decreased velocity relative to the vehicle. The
intensity of the wake is a function of vehicle speed,
downwind distance, and distance from the center of
the wake. An averaged velocity and turbulence field is
calculated across the highway based upon the number
of vehicles, vehicle speeds, and ambient, atmospheric
(upwind) conditions. Using the calculated velocity and
turbulence fields, pollutant concentration predictions
are made over, upwind and downwind of the highway.
It is worth noting that unlike CALINE3 and HIWAY-
2, the ROADWAY model development was indepen-
dent of the General Motors data.
3. EVALUATION AND COMPARISON OF HIGHWAY
POLLUTION MODELS
In this section the performance characteristics of
three diffusion models, HIWAY-2, CALINE3 and
ROADWAY, will be determined using the data from
the General Motors Sulfate Dispersion Experiment. It
should be borne in mind that HIWAY-2 and
CALINE3 are expected to perform well when tested
against the data from which they were developed.
Further, it is worth noting that the physics of the
problem is handled differently in all three of these
models. By making intercomparison of model results it
is possible to make an assessment of each model's
simulation capability as a function of different treat-
ments of modeling of pollutant transport and diffusion
near roadways.
Two techniques are used to compare the predicted
and measured concentrations, namely paired and
unpaired comparisons. A paired analysis allows a
direct comparison of. individual predictions with
measured values, while unpaired techniques determine
model behavior on a statistical basis, without regard to
the spatial and temporal correspondence between
measured and predicted concentrations. The tech-
niques used in the paired and unpaired analysis are
described in Fox (1981) and Rao et al. (1985), and the
unpaired (bootstrap) is described below. The results
from the paired analyses, summarized in Table 1,
indicate that HIWAY-2, ROADWAY and CALINE3
explain about 70%, 65% and 29% of the variance,
respectively. The slopes of the regression lines are close
to unity with small intercept values for all three
models. The Index of Agreement, which reflects the
degree to which the observation is accurately simulated
by the model, shows that HIWAY-2 is 5 % better than
ROADWAY and both are considerably better than
CALINE3. A second st ong measure of model per-
formance is the root-mean-square error (RMSE)
which indicates the size of the error produced in the
model; Table 1 shows that HIWAY-2 and
ROADWAY perform considerably better than
CALINE3. The mean fractional error shows that
CALINE3 tends to underpredict slightly and HIWAY-
2 and ROADWAY tend to overpredict. Mean frac-
tional error is not a good measure by itself, as it would
127
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Turbulent diffusion behind vehicles
1097
Table 1. Comparison of model results using the GM data
OBSERVED HIWAY-2 CALINE3 ROADWAY
Range
Mean
Standard deviation
R2
Slope
Intercept
Mean of (P/0)
Standard Deviation of (P/O)
Mean difference (d)
Variance of the difference (Sj)
Average absolute gross error (Idl)
Root-mean-square error (RMSEd)
Index of agreement (D)
Mean fractional error (MFE)
Unsystematic mean square error ( MS£U)
Systematic mean square error (MSES)
Mean square error ( M SE)
MSEJMSE
MSEJMSE
0.01^.92 0.01-4.68
0.% 1.07
0.74 0.77
0.70
0.87
0.23
1.30
0.99
0.11
0.18
0.30
0.44
0.91
-0.12
0.18
0.02
0.20
89%
11%
0.09-17.97
0.96
1.31
0.29
0.96
0.04
1.23
1.20
0.00
1.23
0.41
1.11
0.64
0.04
1.22
0.00
1.22
100%
0%
0.02-5.29
1.20
0.92
0.65
1.00
0.25
1.40
1.02
0.25
0.29
0.41
0.60
0.86
-0.21
0.29
0.06
0.35
83%
17%
N = 594.
indicate here that CALINE3 is the best model, but the
other statistical tests indicate otherwise. The mean
fractional error could be small if there are large
overpredictions balanced by large -inderpredictions.
The average errors between predictions and measure-
ments are similar for ROADWAY and HIWAY-2,
although the simulation of HIWAY-2 is slightly better
than that of ROADWAY. Particularly noteworthy is
the fact that the errors of all three models are mostly
unsystematic. For a good model the systematic dif-
ference should approach zero and the unsystematic
difference should approach the -oot-mean-square
error. The fact that similar results are found for both
HIWAY-2 and ROADWAY is indicative of the ap-
propriateness of the methodologies utilized in these
models, even though they are based on completely
different treatments of the physics of the problem. The
ROADWAY model uses vehicle wake theory, while
HIWAY-2 uses simple parameterizations of traffic-
induced turbulence from a Gaussian approach to
handle the transport and diffusion of pollutants near
roadways.
In the following analysis, account is taken of the fact
that the observations include measurement error, as
well as the variability due to the stochastic or random
nature of the atmosphere. It is imperative that this
variability be considered in model evaluation. Any
model prediction represents an ensemble average,
while any given observation reflects a specific realiz-
ation from a population that will almost always differ
from the prediction, even if the model and the input
data are perfect. Thus, it should be recognized that
there is no significant difference between model predic-
tions and observations as long as the predictions are
contained within the natural variability of the observed
concentrations. Assuming that the concentrations are
directly proportional to the emission strength and
indirectly proportional to the wind speed, the van-
ability in the normalized concentration CU/Q (where
C is the tracer gas concentration, U is the wind speed,
and Q is the emission strength) can be determined
using the General Motors data at the nearest roadside
ground level receptor under nearly perpendicular
wind-road orientations. Since previous investigations
(Eskridge and Rao, 1983; Eskridge et al., 1979; Rao et
al., 1979) on the role of traffic-induced turbulence
imply the concentrations immediately adjacent to the
roadway in the downwind direction are independent of
the atmospheric stability, and that pollutant diffusion
is dictated by the locally generated turbulence, it is
reasonable to combine all data from the nearest
roadside ground level (0.5 m height) monitor in the
downwind direction to investigate the
atmospheric-experimental variability. Furthermore,
the data are restricted to the 18 cases with wind
direction nearly perpendicular to the roadway, since
then the transport and diffusion from the source to the
receptor are well defined. The design of the General
Motors experiment ensures that the mechanical turbu-
lence generated by the moving vehicles will be ap-
proximately the same for all tracer experiments, be-
cause of constant vehicle speed as well as spacing of
vehicle packs and vehicles in the packs. Thus, the
analysis of the normalized concentration CU/Q for all
perpendicular wind-road orientation cases allows an
estimation of the magnitude of the
atmospheric-experimental variability (stochastic
process).
The cumulative probability plot of normalized
concentration is shown in Fig. 1. The computed mean
for CU/Q, the standard deviation of CU/Q, and the
coefficient of variation (ratio of the standard deviation
to the mean) about the mean are 0.587,0.154and 26 °0,
respectively. Thus, the mean for this sample can be
reported as p = 0.587 + 0.154. This indicates that the
best guess of the unknown true value p is p = 0.587,
128
-------
1098
S. T. RAO et al.
CUMULATIVE PLOT PERPENDICULAR WIMO DIRECTION
°
O O
« o t£th o o o O o 84th o
- p« * «i i* N oi
CUMULATIVE PROBABILITY
co 31
a,
-------
Turbulent diffusion behind vehicles
GM DATA , PERPENDICULAR WIND-ROAD CASES , N = 18
1099
340 -
J20 -
3OO -
2*0-
2«O-
240 -
220 -
2OO -
o
U. 140 -
O
120-
1 too-
M^
"
«0-
40 -
20-
o
i wvj ouvj i a
i rTMr-
rrcruiv-
M 1 IVJI1!^
.._--.,
MMIII I f )
S tondord Otv.gt.OB 1 r- )
Cotl(ici«ilo(Voriot«o (9 = «-//)
"****
»mn-
-OI2 -010 -O.O* -00« -0.04 -002 0.0 002 004 OO6 008 0.10
INTERVAL((p -p). (a -cr'}. (6 -6')]
Fig. 2. Uncertainty distribution for the selected parameters using 1000 bootstrap replications.
50-1
1 0
20 30 40
OBSERVED CONCENTRATION (PP8)
Fig. 3. Scatter plot of model predictions and measurements.
130
30 %
5 0
-------
1100
S. T. RAO et al.
Table 2. Comparison of model predictions with CM data
Data subset
Model
Percent of predktions
within ±30% of
observed concentration
Percent of predictions
< 30% of the
observed concentrations
Percent of predictions
> 30% of
observed concentrations
GM data ground
level downwind
receptor
nearest to roadway
where maximum is
observed (N "61)
All GM data from
all runs
HIWAY
HIWAY-2
CALINE3
ROADWAY
HIWAY
HIWAY-2
CALINE3
ROADWAY
40%
75%
42%
71%
28%
55%
44%
46%
7%
17%
53%
21%
14%
10%
29%
13%
53%
8%
5%
8%
58%
35%
27%
41%
concentrations has not been determined. To evaluate
the simulation capability of the models in predicting
the maximum concentrations, asymptotic extreme
value theory is used. In this method the marimnip
observed and predicted concentrations in each of the
18 tracer experiments are rank-ordered and the cumu-
lative probabilities are determined by
prob(x aS x2) = exp[ -exp( -y)],
(1)
where y = (x- u)/a and y is called the reduced variate,
x is the maximum concentration in each experiment, a
is the Gumbel slope, and u is the mode of the extreme
value distribution (see Gumbel, 1962).
The maxima of the observations and predictions for
each of the General Motors experiments for 4he
CALINE3, HIWAY-2, and ROADWAY models are
plotted in Figs 4,5 and 6, respectively, as a function of
the reduced variate, y. The figures show the best fit to
the model predicted data and the 95% confidence
interval to the fit, which is determined by the method of
maximum likelihood estimation. This fit has the
character of a type I double exponential distribution
(see Tabony, 1983).
The maximum observed concentrations are also
plotted to provide a comparison between the observa-
tions and model predictions. The measured data above
the mode of the distribution fall within the confidence
band for the model predicted values for ROADWAY
and almost for HIWAY-2, which indicates that the
model simulates the physical processes leading to the
maximum concentrations quite well. A large number
of the observations fall outside the confidence bands
for the CALINE3 model Good agreement was found
between the predictions and observations as far as the
extremes of the maxima (upper tail of the extreme
value distribution) are concerned for all three models
SO -
O
a.
a.
O
o
00 10 20 30
REDUCED VARIATE
Fig. 4. Maxima of the observations (stars) and predictions (triangles) of CALINE3.
Dashed lines are the 95 % confidence limits for the best fit line through the predictions. The
reduced variate is defined in Equation (1).
131
-------
Turbulent diffusion behind vehicles
110
50-
CD
u
I
u
-2.0
-10 00
10 20 30
REDUCED VARIATE
Fig. 5. Same as Fig. 4 except for HIWAY-2 and model predictions are shown using boxes.
60-
-.90-
2
0.
a.
00
-10
00 10 20 30
REDUCED VARIATE
Fig. 6. Same as Fig. 4 except for ROADWAY and model predictions are shown using
diamonds.
as shown in Figs 4-6. The statistical pararr^ters for the
extreme value distributions for the three models are
presented in Table 3. The second highest of the
observed maximum concentration is well within the
predicted second highest concentrations, indicating
that all these models are capable of simulating the
atmospheric processes quite well
The extreme value distribution discussed above is
dependent on the distribution of the data. An alternate
approach is to use the bootstrap method to evaluate
each model's ability to simulate the maximum concen-
tration. The bootstrap method is applied to the sets of
second highest concentration from the General
Motors data and the predictions of the three models.
The cumulative distributions of these concentrations
based on 1000 bootstrap replications are presented in
Fig. 7. It is evident that all of the models predict
somewhat larger values (within 1.0 ppb) of the concen-
132
-------
1102
S. T. RAO et al.
Table 3. Model comparison of second highest concentration (ppb)
Model
HIWAY-2
CALINE3
ROADWAY
Mode
1.839
1.525
1.895
Sample size
61
60*
61
Predicted $
4.219 ±1.057
4.207 ±1.191
4.665 ± 1.230
Observed
3.770
3.770
3.770
Boot strap 95 %
confidence interval
3.4CM.37
3.10-4.80
3.56-4.69
95 % confidence limit to the model predicted second highest concentration based on the extreme
value distribution.
One tracer run with very low wind speed is removed from this analysis.
1 o -
0.9 -
o a -
_ 07 -
M
X
VI
X
0 6
CD
2 0 5
O
CC
Q.
§03
(J
0 Z -
0 1 -
ROAOWAY
23 30 32 34 36 39 40 42 44 46 48
SECOND HIGHEST CONCENTRATION (PPB)
Fig. 7. Cumulative frequency distribution of model-based and the observation-based
second highest concentration using 1000 bootstrap replications.
5 0
tration than that measured for a given probability. The
ROADWAY model provides a more conservative
estimate (i.e. higher) of the concentration than the
other models. At 50% probability, the observed data
indicate that the second highest of the maximum
concentration is 3.62 ppb, while for the ROADWAY
model it is 4.58 ppb. Given that there is no significant
difference between model predictions and measure-
ments as long as the predictions are contained within
plus or minus 30 % of the measured concentrations, the
above result indicates that the predictions from the
ROADWAY model, as well as the other two models,
are in agreement with the measurements. Thus, these
models are seen to provide slightly conservative and
realistic estimates of the concentrations. Not only the
central tendencies, but also the extreme values pro-
duced by these models (especially HIWAY-2 and
ROADWAY) are observed to be in good agreement
with the measured data.
4. SUMMARY
The performance of CALINE3, HIWAY-2 and
ROADWAY has been assessed using the tracer data
133
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Turbulent diffusion behind vehicles
1103
from the General Motors Sulfate Dispersion
Experiment. The model predictions were first paired in
time with the observations and various statistical
parameters were evaluated. These tests indicate all
three models perform well with the General Motors
data, but HIWAY-2 and ROADWAY simulate the
data better than CALINE3.
Using the bootstrap method and the normalized
observations immediately downwind of the road, it
was shown that there is an expected variation in the
data of about ± 30 %. This variability in the observed
concentrations is due to measurement errors and the
randomness of the atmosphere. The implication of this
natural variability is that model predictions within
±30% of the observations can not be improved upon
with this data set.
To test how well the models predict extreme values,
asymptotic extreme value theory and the bootstrap
method were used. The results indicate that all three
models performed well in predicting the extreme
concentrations.
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