vvEPA
United States Environmental Sciences Research EPA-600/8-82-014
Environmental Protection Laboratory August 1982
Agency Research Triangle Park NC 27711
Research and Development
PTPLU—A Single
Source Gaussian
Dispersion Algorithm
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EPA-600/8-82-014
PTPLU - A SINGLE SOURCE GAUSSIAN
DISPERSION ALGORITHM
User's Guide
by
Thomas E. Pierce, D. Bruce Turner
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
Research Triangle Park, NC 27711
Joseph A. Catalano and Frank V. Hale III
Aerocomp , Inc.
3303 Harbor Boulevard
Costa Mesa, CA 92626
Contract No. EPA 68-02-3442
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NC
CHICAGO 1L 60604-3590
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DISCLAIMER
This report has been reviewed by the Environmental
Sciences Research Laboratory, U.S. Environmental Protection
Agency, and approved for publication. Approval does not
signify that the contents necessarily reflect the views and
policies of the U.S. Environmental Protection Agency, nor
does mention of trade names or commercial products constitute
endorsement or recommendation for use.
AFFILIATION
Mr. Thomas E. Pierce and Mr. D. Bruce Turner are
meteorologists in the Meteorology and Assessment Division,
Environmental Protection Agency, Research Triangle Park,
North Carolina. They are on assignment from the National
Oceanic and Atmospheric Administration, U.S. Department
of Commerce. (Mr. Pierce is now employed by NUS Corporation
Gaithersburg, Maryland) Mr. Joseph A. Catalano and Mr.
Frank V. Hale III are employed by Aerocomp, Inc., Costa
Mesa , Californ ia.
11
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FOREWORD
Within the Office of Air, Land, and Water Use, the
Environmental Sciences Research Laboratory conducts a research
program in the physical sciences to detect, define, and quantify
the effects of air pollution on urban, regional, and global
atmospheres and the subsequent impact on water quality and land
use. This includes research and development programs designed to
quantitate the relationships between emissions of pollutants from
all types of sources, air quality, and atmospheric effects.
The Meteorology and Assessment Division conducts research
programs in environmental meteorology to describe the roles and
interrelationships of atmospheric processes and airborne
pollutants in effective air, water, and land resource
management. Developed air quality simulation models (in the
FORTRAN computer language) are made available to dispersion model
users in computer-readable form by availability of a magnetic
tape from NTIS (see preface).
PTPLU is a dispersion algorithm made available in 1981. The
program is based upon Gaussian dispersion concepts of
steady-state modeling. Limitations are imposed on use of the
algorithm by the assumptions that pollutants are nonreactive and
that one wind vector and one stability class are representative
of the area being modeled. Despite these limitations, PTPLU
provides a useful short-term algorithm to obtain the highest
concentration and corresponding distance for point sources.
K. L. Demer j i an
Di rector
Meteorology and Assessment Division
i i i
ENVIRONMENTAL PROTECTIOH AGENCY
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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 dispersion 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 EPA's UNAMAP system.
PTPLU is a screening model that uses Gaussian plume modeling
techniques. PTPLU is designed for low-cost, detailed screening
of point sources to determine maximum one-hour concentrations and
also to determine if it is necessary to use one of the more
i nt r icate mode Is.
Although attempts are made to thoroughly check computer
programs with a wide variety of input data, errors are
occasionally found. Revisions may be obtained as they are issued
by completing and sending the form on the last page of this
guide.
This document is divided into three parts. Sections 1
through 3 are directed to managers and project directors who may
wish to become acquainted with the model. Sections 4 and 5 are
directed to engineers, meteorologists, and other scientists who
are required to become familiar with the workings of a model.
Since a number of nonmeteorologists will be using this screening
model, Appendix A, Modeling Concepts, presents some of the basic
concepts of air pollution meteorology. Together with a Glossary,
this should provide the less-experienced user sufficient
background to apply the model. Finally, sections 6, 7, and 8 are
directed to programmers and data processing professionals, who
are often required to implement and run the model. These
sections employ the standard terminology of the computer
i ndus t ry.
Comments and suggestions regarding this publication should be
d i rected to
IV
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Chief, Environmental Operations Branch
Meteorology and Assessment Division (MD-80)
Environmental Protection Agency
Research Triangle Park, NC 27711.
Technical questions regarding use of the model may be asked
by calling (919) 541-4564. Users within the Federal Government
may call FTS 629-4564. Copies of the user's guide are available
from the National Technical Information Service (NTIS),
Springfield, VA 22161.
The magnetic tape containing FORTRAN source code for PTPLU is
contained (along with other dispersion models) in UNAMAP (Version
4), which may be ordered as PB 81 164 600 from Computer Products,
NTIS, Springfield, VA 22161 (phone number: (703) 487-4763).
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ABSTRACT
PTPLU (from Po i nT PLUme) is an improved model for estimating
the location of the maximum short-term concentration from a
single point source as a function of stability and wind speed.
The algorithm is similar to PTMAX, which was first released in
May 1973. Among the improvements in this version are options for
the estimation of gradual plume rise, stack downwash, and
buoyancy-induced dispersion. Maximum concentrations and their
corresponding downwind distances are calculated for two sets of
wind speeds: winds assumed to be constant with height and winds
assumed to increase with height. For the latter case, wind speed
is extrapolated from anemometer height to stack top using a
power-law wind profile. PTPLU is based on the point-source
solutions of the Gaussian plume equations. It uses Briggs' plume
rise equations, Pasquill stability classes, and Pasqui11-Gifford
dispersion parameters. Multiple reflections are considered until
the vertical dispersion parameter is 1.6 times the mixing height;
uniform mixing is assumed thereafter. No fumigation or chemical
reactions are considered. A built-in test example is provided
with the interactive version of the program. This document
describes the input, processing, and output of both the batch and
interactive versions of the program.
v i
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CONTENTS
Foreword i i i
Preface iv
Abstract vi
Figures viii
Tables ix
Symbols and Abbreviations x
Acknowledgments xi
1. Introduction 1
2. Data-Requirements Checklist 3
3. Features and Limitations 4
4. Technical Description 6
5. Program Overview and Structure 10
6. Input Data Preparation 14
7. Execution of the Model and Sample Test 15
8. Example Calculation 29
References 32
Append ices
A. Modeling Concepts 33
Basic Concepts 33
Gaussian Equations for Estimating
Concentrations 37
Plume Rise for Point Sources 41
Dispersion Parameters 44
Buoyancy-Induced Dispersion 50
References 50
B. Indexed Listing of FORTRAN Source
Statements (Batch) 52
C. Sensitivity Analysis 87
Options 87
Plume-Rise-Related Parameters 89
Glossary 94
vi i
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FIGURES
Number Page
1 Iterative search routine used by PTPLU 8
2 Structure of batch version of PTPLU 13
3 Sample job stream for batch version of PTPLU 15
4 Schematic of batch output of PTPLU 17
5 Batch output of PTPLU 18
6 Output of unabridged interactive version of PTPLU . . 20
7 Batch output of example calculation 30
A-l Coordinate system showing Gaussian distributions
in the horizontal and vertical 39
A-2 Estimation of lateral dispersion parameter 49
C-l Sensitivity of maximum concentration and distance-to-
maximum to changes in stack gas temperature .... 90
C-2 Sensitivity of maximum concentration and distance-to-
maximum to changes in stack gas velocity 93
VI 1 1
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TABLES
Number Page
1 Record Input Sequence 14
A-l Key to Stability Categories 45
A-2 Basis and Scope of the Original P-G Curves 46
A-3 Constants for the Vertical Dispersion Parameter
Equation 48
C-l Plume Heights and Concentrations with and without
the Gradual-Rise Option 88
C-2 Maximum Concentrations with and without Stack
Downwash, for Stability Class D 88
C-3 Maximum Concentrations with and without BID 89
C-4 Percent Increase in Maximum Concentration with
Decreasing Stack Gas Temperature 91
C-5 Percent Decrease in Distance to Maximum Concentration
with Decreasing Stack Gas Temperature 91
C-6 Percent Increase in Maximum Concentration with
Decreasing Stack Gas Velocity 92
C-7 Percent Decrease in Distance to Maximum Concentration
with Decreasing Stack Gas Velocity 92
IX
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SYMBOLS AND ABBREVIATIONS
Dimensions are abbreviated as follows:
m = mass, 1 = length, t = time, T = temperature.
d -- stack inside diameter (1)
F -- buoyancy flux parameter (l"*/t3)
g -- acceleration due to gravity (1/t2)
H -- effective height of plume (1)
h -- stack height above ground (1)
h' -- stack height adjusted for stack downwash (1)
L --mixing height (1)
p -- wind-profile exponent
Q -- emission rate (m/t)
s --stability parameter (t~2)
T -- ambient air temperature (T)
Ts -- stack gas temperature (T)
u -- wind speed at stack top (1/t)
vs -- stack gas exit velocity (1/t)
x -- downwind distance (1)
Xf -- distance to final rise (1)
x* -- distance at which atmospheric turbulence begins
to dominate entrainment (1)
y -- crosswind distance (1)
z -- receptor height above ground (1)
Ah -- plume rise (1)
AT -- temperature difference between ambient air and
stack gas (T)
(AT)C -- temperature difference for crossover from momentum
to buoyancy-dominated plume (T)
80/9z -- vertical potential temperature gradient of a layer
of air (T/1)
IT -- pi , 3. 14159
e -- base of natural logarithms, 2.71828
ay -- lateral dispersion parameter (1)
Oye -- effective lateral dispersion (1)
cFyO -- buoyancy-induced lateral dispersion (1)
az -- vertical dispersion parameter (1)
crze -- effective vertical dispersion (1)
azo -- buoyancy-induced vertical dispersion (1)
Xp -- concentration due to a point source (m/13)
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ACKNOWLEDGMENTS
The authors wish to express their appreciation to Mr. William
B. Petersen and Mr. John S. Irwin for helpful comments regarding
aspects of the work presented here. Support of Aerocomp by the
Environmental Protection Agency Contract No. 68-02-3442 is also
gratefully acknowledged.
x i
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SECTION 1
INTRODUCTION
PTPLU (from Po i nT PLUme) provides a method for estimating
maximum ground-level concentrations from a single point source.
The algorithm is based on Gaussian plume modeling assumptions
incorporating the Pasqui11-Gifford (P-G) dispersion parameters.
Briggs' plume rise equations (Briggs, 1969) are employed by the
model to determine the effective height of pollutant release.
Three technical options are available with PTPLU. Stack
downwash may be considered, as well as buoyancy-induced
dispersion and gradual plume rise. In addition, anemometer
height, wind-profile exponents, and mixing height can be
specified on input.
The routines employed to estimate dispersion by PTPLU have
been extracted from MPTER (Multiple Point source algorithm with
TERrain adjustments) (Pierce and Turner, 1980), which is in turn
based on point-source segments of the rural version of RAM
(Turner and Novak, 1978). PTPLU provides an economical and
technically sound approach to estimating maximum concentrations
for comparison with ambient air quality standards and for use in
air pollution research.
Modeling the effects of the release of inert pollutants into
the atmosphere usually follows a three-step procedure. First,
simple screening steps are performed using a hand calculator or
air quality nomograms. This simple screening method is, as a
rule, sufficiently conservative to ensure that maximum
concentrations will not be underestimated. If results of the
simple screening indicate a potential air quality problem, a more
detailed screening is warranted. This intermediate step usually
involves the use of simple computer models to quantify the
effects of pollutant release on air quality. A more elaborate
procedure is followed when detailed screening indicates that a
more refined analysis is required. For sources with significant
potential effects, computation continues, using models better
suited for handling multiple sources, multiple receptors, and
topographic effects. The user is referred to the "Guideline on
Air Quality Models" (U. S. Environmental Protection Agency, 1978)
in selecting the models appropriate for regulatory applications.
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The model described herein is suited for the intermediate
step of detailed screening. If concentrations are low, no
detailed modeling will then be required. In this manner,
resources are conserved, and only potentially troublesome sources
are left for analysis with the more refined models.
The Environmental Operations Branch of EPA supports the
User's Network for Applied Modeling of Air Pollution — a set of
models commonly known by the acronym UNAMAP. A brief description
of the latest version of UNAMAP is available from the
Environmental Operations Branch.
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SECTION 2
DATA-REQUIREMENTS CHECKLIST
PTPLU requires data on options, sources, meteorology, and
receptors. The user must indicate whether any of three
options--gradua1 rise, stack downwash, or buoyancy-induced
dispersion--is to be employed. Information required on the
sources includes the following:
source strength (grams per second),
physical stack height (meters),
• stack gas temperature (kelvin),
stack gas velocity (meters per second), and
• stack inside diameter (meters).
The meteorological data needed to compute maximum concentrations
are as follows:
ambient air temperature (kelvin),
mixing height (meters),
wind-profile exponents, and
anemometer height (meters).
The only input required for receptors is the uniform height above
ground of the receptors (in meters).
Because the maximum concentration is directly proportional to
the emission rate of the source, care should be exercised to
accurately determine this parameter. The mixing height and
ambient air temperature should be representative of the vicinity
of the source.
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SECTION 3
FEATURES AND LIMITATIONS
As noted previously, PTPLU is an upgraded version of program
PTMAX released in mid-1973 (UNAMAP Version 1). Since then,
several larger models have been developed, such as CRSTER (U. S.
Environmental Protection Agency, 1977), RAM, and MPTER. Certain
features of these more complex models suitable for detailed
screening have been transferred to PTPLU. Hence, a number of
features not found in PTMAX are now available in PTPLU. These
improvements are as follows:
calculations using wind speeds at anemometer height
and wind speeds extrapolated to stack top;
optional gradual plume rise;
optional stack downwash;
• optional buoyancy-induced dispersion;
three modes of operation: batch, interactive with a
paper terminal, and interactive with a video display;
input of anemometer height;
input of mixing height;
input of wind-profile exponents;
calculations for any number of single sources in
one run; and
consideration of momentum-dominated as well as
buoyancy-dominated plumes.
PTPLU still retains some of the limitations of PTMAX, however.
Among these are the following:
predetermined wind speeds,
unsuitabi1ity for complex terrain,
no consideration of building downwash,
4
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no provision for calculating the effect of multiple
point sources,
• no consideration of fumigation, and
no consideration of pollutant removal or chemical
react i ons. '
The model is most applicable within 10 km of the source.
Beyond this distance, the estimates are expected to be less
accurate, due to mesoscale influences such as wind direction
shear with height and changing meteorological conditions during
the time of transport.
As a screening model, PTPLU can be applied to single sources
for the fo1lowi ng:
monitor ing-network design,
prevention of significant deterioration,
new source review,
fuel-conversion studies,
control technology evaluation, and
• combustion-source permit applications.
PTPLU is primarily useful in determining the maximum one-hour
concentration from a point source and the meteorological
conditions associated with the maximum. Maximum concentrations
are computed for 49 different combinations of wind speed and
stability.
PTPLU can also be used in selecting the distances used as
input into the models CRSTER and MPTER for generation of polar
coordinate receptor arrays.
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SECTION 4
TECHNICAL DESCRIPTION
PTPLU is a Gaussian plume dispersion model designed to screen
maximum concentrations from single point sources. Persons not
familiar with Gaussian point source modeling techniques and plume
rise estimates are referred to Appendix A.
PTPLU determines the distance to and the magnitude of maximum
concentrations from a point source for 49 internally generated
combinations of wind speed and stability. PTPLU is based on the
following modeling assumptions:
the wind speed existing at stack top applies to both
plume rise and dilution;
plume rise is calculated using methods suggested by
Briggs;
the pollutant release is continuous at a rate specified
by the user;
calculations are made as if the atmosphere has reached
a steady-state condition; and
• for unstable and neutral conditions, complete eddy
reflection is calculated both from the ground and from
the stable layer aloft given by the mixing height.
In calculating maximum concentrations, PTPLU is much like the
PTMAX algorithm (Turner and Busse, 1973). However, PTPLU
calculates concentrations for both wind speeds constant with
height and wind speeds extrapolated to stack top. In addition to
the user-supplied wind-profile exponents, PTPLU allows for
optional calculations due to the effect of 1) gradual plume rise,
2) stack downwash, and 3) buoyancy-induced dispersion. Any one
of these processes can alter the distance or magnitude of maximum
concentration. Thus, the user is offered more flexibility in
screening analyses.
The distance to maximum concentration is determined by an
iterative sequential search. For each combination of wind speed
and stability, the maximum concentration is selected from 16
fixed distances (0.1, 0.3, 0.5, 0.7, 1, 2, 3, 5, 7, 10, 15, 20,
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30, 40, 50, and 100 km). This distance then becomes the start
for the iterative search for the maximum. Calculations begin
with increments appropriate to the starting point (+0.1 km for
starting points 0.1-0.7 km, +1 km for starting points 1-7 km, +10
km for starting points 10-50 km, and -10 km for the 100-km
starting point). Iterations proceed back and forth in one-tenth
increments until the increment reaches one meter. If the
distance of the maximum exceeds 100 km, the search ceases and a
warning message is printed.
Figure 1 illustrates the technique used to find the maximum
concentration and the distance to the maximum. In the initial
step, a concentration is calculated sequentially at each of the
16 fixed distances noted above, and an absolute maximum is
selected from the 16 values. The chosen maximum is represented
by point 1 in Figure 1. The iterative search begins here, moving
from right to left in fixed increments along the curve.
Concentrations are computed using this increment until a lower
concentration is encountered. At this point the direction is
reversed and this point becomes the starting point for the next
iteration, with a new distance increment reduced by an order of
magnitude from the previous one. As indicated in Figure 1, the
next two iterations yield starting points at points 3 and 4. The
search for the absolute maximum ceases when the increment has
been reduced to one meter.
Gradual plume rise (option 1) is available as an optional
calculation in PTPLU. Although the 2/3 dependence for rising
plumes determines average plume height with distance quite well,
the dispersive processes that occur during buoyant rise are
thought to be different from those that occur during steady-state
transport. The P-G dispersion parameters represent horizontal
and vertical dispersion about a horizontal plume, which may or
may not be appropriate for estimating dispersion about a
bent-over plume. By making computations with and without gradual
plume rise, identification of potentially high concentrations is
possible. When gradual rise is not employed, computations use
only the final effective plume height.
Stack-top downwash (option 2) can be considered using the
methods of Briggs. In such an analysis, a height increment is
deducted from the physical height before momentum or buoyancy
rise is determined. Use of this option primarily affects
computations from stacks having small ratios of exit velocity to
wind speed.
Buoyancy-induced dispersion calculations (option 3) are
offered because emitted plumes undergo a certain amount of growth
during the plume rise phase. This is due to the turbulent
motions associated with conditions of plume release and the
turbulent entrainment of ambient air. During the initial growth
phases of release, the plume is assumed to be nearly symmetrical
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about its centerline; hence, the buoyancy-induced dispersion in
the horizontal direction is modeled as equal to that in the
vertical direction. The contribution by buoyant plume rise to
the total dispersion is small compared with the dispersion caused
by atmospheric turbulence. The maximum effects on ground-level
concentrations occur for short heights of release combined with
large plume rise, but, in general, buoyancy-induced dispersion
has little effect on maximum surface concentrations from elevated
re leases.
To simulate increased wind speed with height, PTPLU requires
the input of wind-profile exponents for each stability class.
With this feature, maximum concentrations are computed for both
wind speed at anemometer height and wind speed extrapolated to
stack top.
The three options and the additional calculations for
extrapolated wind speeds allow more flexibility and realism in
identifying maximum concentrations. When employing PTPLU as a
screening model for regulatory applications, the user is advised
to contact the regional meteorologist or modeling contact about
the proper specifications of options and wind-profile exponents..
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SECTION 5
PROGRAM OVERVIEW AND STRUCTURE
PTPLU may be run either in batch mode or interactively.
There are two interactive versions: one with minimal output,
quite useful for terminals using paper, and one with expanded
output useful for terminals with video display.
The interactive version consists of the batch version
(modified to serve as a subroutine) and a set of subroutines for
preparing the input to the model. The program is menu-driven so
that the user may select for execution any one of a number of
routines. Routines are available for entering or modifying (any
number of times) meteorology, receptor height, options, source
parameters, and run title. The user may also invoke a subroutine
to display the current input data. After the data have been
prepared in this interactive manner, the model may be executed.
When each subroutine has finished execution, the user is
presented with the original menu. The interactive session is
completed by selecting "END" on the menu.
There are two versions of the interactive routines within the
program, and the first action of the user is to select which
version is to be used. One version produces unabridged output
with full headings and data descriptions. The other produces
abridged output with little data description. The unabridged
version is designed for use with a visua1-display output device.
In such an output medium, length of output has little effect on
running time or cost. The abridged version is designed for use
with a hard-copy device, in which case length of output affects
both running time and cost. In addition, the output of the
unabridged version assists a new user by means of full data
descriptions, whereas the abridged version is more useful to an
experienced user who is familiar with the operation of the
program and can work with abbreviated output.
The program contains default data, which serve as both a
template for the user and a built-in test data set. The default
data represent a hypothetical source of medium height. The
default source parameters are as follows: source strength of
2750 g/s, physical stack height of 165 m, exit temperature of
425 K, exit velocity of 38 m/s, and inside stack diameter of 4.5
m. The remaining default data were selected as being typical.
All options default to 1 (use option). Ambient air temperature
10
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and mixing height default to 293 K and 2000 m, respectively.
Anemometer height is taken as 10 m. Wind-profile exponents
default to 0.07, 0.07, 0.10, 0.15, 0.35, and 0.55 for stability
Glasses A -through F, respectively. These values correspond to a
roughness parameter of 0.03 m. The height of the receptor
defaults to zero (ground level).
When the interactive routines are expecting numeric input
from the user, care must be taken that data of the proper type
are entered. The entry of alphabetic characters when numeric
data are expected can result in a FORTRAN error and termination
of the program. If this arrangement is not satisfactory, it may
be possible to add a routine that reads numeric data as
alphanumeric data, checks the format of the input, and either
converts the alphanumeric data to a number or produces an error
message under program control. Alternatively, on many systems,
the ERR= option of the FORTRAN language could be used to process
this error (the notable exception being IBM OS systems).
The subroutines of the model (PH, TPMX, PHX, RCON, and PSIG)
are identical in the batch and interactive versions. The main
routine of the batch version has been transformed into subroutine
PTPLU of the interactive version. The conversion involved
replacing read statements with subroutine parameters and
assignment statements. Also, the format of the output was
modified for use with a 79-character visual display. Aside from
these changes of input and output, subroutine PTPLU is identical
to the main routine of the batch version.
PROGRAM MODULES
IPTPLU -- Main module of the interactive version. IPTPLU invokes
either LPTPLU or SPTPLU depending on the type of output
desired--long form for CRT runs, short form for
hard-copy terminals.
IPLDIS -- Prints model input parameters as currently available in
memory.
IPLMET -- Allows substitution of meteorological parameters.
IPLOPT -- Allows changing of options.
IPLREC -- Allows changing of receptor height.
IPLSOR -- Allows modification of source parameters.
IPLTTL -- Provides a way to change the title.
LPTPLU -- Unabridged interactive version of PTPLU. Provides a
menu-driven means to prepare input and execute the
mode 1.
11
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PH -- Calculates specific plume rise parameters for a given
wind speed.
PHX -- Calculates gradual plume rise, if the option is
employed.
PSIG -- Calculates the lateral and vertical dispersion
parameters as a function of distance from the source
and stabi1i ty class.
PTPLU -- Main module of the batch version and a subroutine of
the interactive version. PTPLU produces all printed
output (input parameters, calculated parameters, and
output tables), calculates the plume rise as a function
of wind speed, and controls the input to TPMX in order
to produce the maximum concentration tables.
RCON -- Calculates the relative concentration (concentration
divided by source strength) under a given set of
conditions (solves the appropriate Gaussian equation).
SPLDIS -- Abridged display of interactive input data.
SPLMET -- Abridged modification of interactive meteorological
data.
SPLOPT -- Abridged modification of interactive options.
SPLREC -- Abridged modification of receptor height.
SPLSOR -- Abridged modification of source data.
SPLTTL -- Abridged modification of run title.
SPTPLU -- Abridged interactive version of PTPLU. Provides a
terse menu-driven means to prepare input and execute
the mode 1 .
TPMX -- Searches for the distance to the maximum concentration
by calling RCON, first at a set of fixed distances and
then at incremental distances.
Figure 2 shows the structure of the batch version of PTPLU.
12
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PTPLU
EXIT
READ AND CHECK INPUT DATA
CALCULATE PORTIONS OF PLUME RISE
LOOP FOR EACH STABILITY
LOOP FOR CONSTANT WIND SPEEDS WITH HEIGHT
PH
TPMX
- PHX
- RCON
' PSIG
ADD CAUTIONARY LABELS
LOOP FOR WIND SPEEDS VARYING WITH HEIGHT
PH
TPMX
— PHX
— RCON
I PSIG
ADD CAUTIONARY LABELS
WRITE OUTPUT
Figure 2. Structure of batch version of PTPLU,
13
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SECTION 6
INPUT DATA PREPARATION
Table 1 (below) applies to input preparation for the batch
execution mode. Data requirements are identical to those of the
interactive mode. Data fields follow a free form (i.e., they are
separated by commas). The input data should conform to the
variable-name type. That is, decimals should be included for all
values corresponding to real variables.
Record
type
TABLE 1. RECORD INPUT SEQUENCE*
Var iable
name
Variable description
1 IOPT(1) Gradual plume rise option
IOPT(2) Stack downwash option
IOPT(3) Buoyancy-induced dispersion option
(1 = use option, 0 = do not use option)
T Ambient air temperature (kelvin)
(default value is 293 K)
HL Mixing height (meters)
Z Receptor's elevation above ground (meters)
2 HANE Anemometer height (meters)
PL Wind-profile exponents (6 values)
3 ALP 80-character title
4 Q Source strength (grams per second)
HP Physical stack height (meters)
TS Stack gas temperature (kelvin)
VS Stack gas velocity (meters per second)
D Stack diameter (meters)
Record Types
t imes .
3 and 4 may be repeated (as a pair) any number of
When one of the
entered by the user in
The same parameters
vers i ons.
interactive versions
response to requests
are required for the
is used, the data are
from the program.
batch and interactive
14
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SECTION 7
EXECUTION OF THE MODEL AND SAMPLE TEST
PTPLU produces an error-free compile on IBM MVS and Univac
EXEC 8 computers. Execution results are comparable to within
0.2% for these two systems. The program can also be used in mini
and microcomputers having comparable accuracy. A sample job
stream for the batch version is presented below.
i
END OF JOB
7
INPUT RECORDS
UNIT 5
DATA
UNIT 6
PRINTER
EXECUTE PTPLU
'JOB CARD
Figure 3. Sample job stream for batch version of PTPLU.
15
-------
Test data for the batch version are as follows:
0,1,1,278. ,1500. ,2.
7.,.07,.07,.10,.15 , .35 , .55
PTPLU EXAMPLE RUN - INPUT BY T. PIERCE 12/29/80
1000. ,200.,450. ,20.,5.
A job stream for a Univac EXEC 8 system might have the
fo1lowi ng form:
@RUN,R/R JOB-ID,ETC
@ASG,A MODELS*LOAD.
@XQT MODELS*LOAD.PTPLU
(input records shown above)
aFiN
The following is a sample job stream for an IBM system under
OS or MVS:
//JOBID JOB (PROJ,ACCT,OTHER),CLASS=A,TIME=1
//XPTPLU EXEC PGM=PTPLU,TIME=(,05)
//STEPLIB DD DSN=USER.MODELS.LOAD,DISP=SHR
//FT06F001 DD SYSOUT=A
//FT05F001 DD *
(input records shown above)
/*
//
A sample job stream for a CDC system under Scope 3.14 may
look as fo1 lows:
XX,T05,P4.
USER,HALE,EPA.
PROJECT,*PRJ*XX.
ATTACH,LIB,MODELSLIB,ID=XX.
LIBRARY,LIB.
PTPLU.
*
(input records shown above)
*
A schematic illustrating the various sections
output resulting from the batch version is shown
Model outputs include a heading (A in Figure
the program name and
Sec t i on
buoyancy
of the two-page
in F igure 4.
(A in Figure 4) that indicates
source. Section B displays the input
C gives two calculated values, volumetric
flux parameter used for plume rise.
parameters.
flow and the
Section D contains the output, with results for the assumption of
constant wind speed with height on the left and those for
extrapolated wind speed with height on the right. For each
combination of wind speed and stability, the maximum
concentration, the distance of the maximum, and the plume
16
-------
effective height at this
qualifying footnotes that
Figure 5 gives the batch run
distance are given. Section E contains
may be referred to in section D.
output of the sample test.
as.:; n
(B)
Figure 4. Schematic of batch output of PTPLU.
In the interactive version, a sample test is built into the
program. The only step involved in running the sample test is
selecting "RUN" from the main menu. The output resulting from
the unabridged interactive version using this built-in test data
set is given in Figure 6, where, as illustration, all interactive
options are exercised. Users may verify the proper execution of
the program by comparing their results with those given in Figure
6.
17
-------
riTi.u (VLHSION aiojb)
AN IMI'llOVLI) POINT SOUIM'L SCREENING MODEL
MODI F 1 Ell I1Y: JOt CATALANO AND FRANK IIAI.E
AEHOOOMP, INC. - INPUT PARAMETERS«<
PTPI.U EXAMPLE HUN - INPUT UY T. PIERCE 12/29/80
•'•OPTIONS** *
If - I, USt OPTION
IF ^ 0, IGNORE OPTION
IOPTI I ) - 0 (OHAD PLUME RISE)
IOI'I'(2) - 1 (STACK DOWNWASII)
IOPTU) = 1 (BUOY. INDUCED DISP. )
••-METEOROLOGY*••
AMBIENT AIR TEMPERATURE
MIXING HEIGHT
ANEMOMETER HEIGHT
WIND PROFILE EXPONENTS
278.00 (K)
= 1500.00 (M)
7.00 (M)
= A:0.07, B-.0.07, C:0. 10
DsO.15, E:0.3S, F:0.55
"•RECEPTOR IIEK1IIT"*
2.00 (M)
VOI.UMtTKIC H.OIV - JS2.70 (M**J/SEC)
»CALCULATED PARAMETERS<«
BUOYANCY FLUX PARAMETER =
•••SOURCE*"
EMISSION RATE -
STACK HEIGHT -
EXIT TEMP.
EXIT VELOCITY =
STACK D1AM.
1000.00 (G/SEC)
200.00 (M)
450.00 (K)
20.00 (M/SEC)
5.00 (M)
468.52 (M"4/SEC"3)
PIPI.U LXAMI'Lfc RUN - INPUT BY T. PIERCE 12/29/80
STABILITY
••••WINDS CONSTANT WITH HEIGHT*"*
WIND SPEED MAX CONC DIST OF MAX PLUME HT
1
1
1
1
1
1
1
(M/SbC)
0.50
0.80
1 .00
1 .50
2.00
2.50
3.00
(G/CU M)
O.OOOOE'OO
.OOOOE'OO
.OOOOE'OO
.9137E-04
.3549E-04
.1038E-04
3.1729E-04
(KM)
0.000
0.000
0.000
1 .664
1.551
1 .294
1.154
(M)
3299.5(2)
2137.2(2)
1749.7(2)
1233.2(2)
974.9(2)
819. «(2)
716.6(2)
"••WINDS CONSTANT WITH HEIGHT**"
STABILITY
2
2
2
2
2
2
2
2
2
WIND SPEED
(M/SbC)
0.50
0.80
1 .00
1.50
2.00
2.50
3.00
4.00
5.00
MAX CONC
(U/CU M)
O.OOOOE'OO
O.OOOOE'OO
O.OOOOE'OO
.5562E-04
.3268E-04
.3650E-04
.4472E-04
.5571E-04
.6101E-04
DIST OF MAX
(KM)
0.000
0.000
0.000
7.764
6.175
4.679
4.092
3.428
3.025
PLUME HT
(M)
3299.5(2)
2137.2(2)
1749.7(2)
1233.2(2)
974.9(2)
819.9(2)
716.6(2)
587.4(2)
509.9(2)
••"WINDS CONSTANT WITH HEIGHT""
STABILITY
3
J
3
3
3
3
J
3
3
WIND SPEED
(M/SEC)
2.00
2.50
3.00
4.00
5.00
7.00
10.00
12.00
15.00
MAX CONC
(G/CU M)
8.2078E-05
B.BJaUt-Oi
9.5617E-05
1.0570E-C4
1 . 1146E-04
1.I556E-04
1.1311E-04
1 .0928E-04
1.0373E-04
DIST OF MAX
(KM)
14.653
11.061
9.533
7.759
6.696
5.499
4.602
4.259
3.886
PLUME HT
(M)
974.9(2)
819.9(2)
716.6(2)
587.4(2)
509.9(2)
421 .4(2)
355.0(2)
329.1(2)
301 .6(2)
STACK TOP WINDS (EXTRAPOLATED FROM 7
WIND SPEED MAX CONC
(M/SEC) (G/CU M)
0.63 O.OOOOE'OO
1.01 O.OOOOE'OO
1.'26 4.2626E-04
1.90 3.4502E-04
2.53 3.I034E-04
3.16 3.2021E-04
3.79 3.2851E-04
DIST OF MAX
(KM)
0.000
0.000
.693
.582
.280
.130
.059
STACK TOP WINDS (EXTRAPOLATED FROM 7
WIND SPEED MAX CONC
(M/SEC) (G/CU M)
0.63 O.OOOOE'OO
1.01 O.OOOOE'OO
1.26 .7943E-04
1.90 .3483E-04
2.53 .3700E-04
3.16 .4700E-04
3.79 .5400E-04
5.06 .6120E-04
6.32 .6291E-04
DIST OF MAX
(KM)
0.000
0.000
8.001
6.628
4.634
3.957
3.535
3.006
2.684
STACK TOP WINDS (EXTRAPOLATED FROM 7
WIND SPEED MAX CONC
(M/SEC) (G/CU M)
2.80 9.2853E-05
3.50 I.0128E-04
4.19 1.0710E-04
5.59 1.1349E-04
6.99 .1555E-04
9.79 .I345E-04
13.98 .0538E-04
16.78 .0068E-04
20.97 .3312E-05
DIST OF MAX
(KM)
10.070
8.512
7.513
6.251
5.501
4.648
3.999
3.716
3.435
0 METERS)****
PLUME HT
(M)
2651.2(2)
1732.0(2)
1425.6(2)
1017.1(2)
812.8(2)
690.2(2)
608.5(2)
0 METERS)****
PLUME HT
(M)
2651 .2(2)
1732.0(2)
1425.6(2)
1017. 1(2)
812.8(2)
690.2(2)
608.5(2)
506.4(2)
445.1(2)
0 METERS)*"*
PLUME HT
(M)
754.2(2)
643.3(2)
569.4(2)
477.1(2)
421.7(2)
358.3(2)
310.1(2)
289.3(2)
268.4(2)
Figure 5. Batch output of PTPLU.
-------
••••WINDS CONSTANT WITH HEIGHT""
5 1 AH 1 1.1 IY
4
1
4
4
4
4
4
4
4
4
t
4
4
4
WIND SI'!. 1.11
(M/SLC)
11 50
0.80
1 .00
1 .50
2.00
2.50
3.00
4 00
5 00
7.00
10.00
12.00
15.00
20.00
0
0
0
9
9
1
1
2
2
3
}
J
3
3
MAX CONC
((i/CU M)
.OOOOE'OO
.OOOOEtOO
.OOOOEtOO
.9990E»09
.9990E'09
.6235E-05
.9170E-05
.4067E-05
.780IE-05
.2S4IE-05
.4767E-05
.4927E-05
.47I8E-05
.3S89E-05
DIST OK MAX
(KM)
0.000
0.000
0.000
999.999(3)
999.999(3)
91 .619
71.819
50.S8I
39.291
29.980
22.760
20.120
17.431
14.690
PLUME HT
(M)
1299.5(2)
2117 .2(2)
1 7 19 . 7 ( 2 )
1211.2(2)
974.9(2)
819.9(2)
716.6(2)
587.4(2)
509.9(2)
421.4(2)
355.0(2)
329.1(2)
101 .6(2)
272.5(2)
••••WINDS CONSTANT WITH HEIGHT"**
SI'AUILITY
5
5
5
5
5
WIND SPL'ED
(M/SLC)
2.00
2 50
1.00
4.00
5.00
3
3
3
2.
2.
MAX CONC
Ui/CU M)
.9085E-05
.S456E-05
.2630E-05
.844IE-05
.5432E-05
DIST OF MAX
(KM)
88.920(1)
80.118(1)
74.220
65.981
60.182
PLUME HT
(M)
180.0(2)
367.1(2)
1S7 .1(2)
142.9(2)
112.7(2)
••••WINDS CONSTANT WITH HEIGHT****
STABILITY
b
6
6
6
6
WIN!) SPEED
(M/SEC)
2.00
2.50
3.00
4.00
5.00
9.
9
9.
9
9.
MAX CONC
(G/CU M)
,9990E*09
.9990EI09
.9990E>09
,9990E>09
,9990E>09
O1ST OF MAX
(KM)
999.999(1)
999.999(3)
999.999(1)
999.999(1)
999.999(1)
PLUME HT
(M)
349.4(2)
118.7(2)
330.5(2)
318.6(2)
310.1(2)
••••STACK TOP WINDS (EXTRAPOLATED FROM 7
WIND SPEED
(M/SEC)
0.83
1.32
1.65
2.48
3.31
4.11
4.96
6.61
8.27
11 .57
16.51
19.84
24.80
31.07
MAX CONC
(O/CU M)
0. OOOOE<00
9.9990E<09
9.9990E«09
1.6I12E-05
2.0808E-05
2.4628E-05
2.7671E-05
1. 1917E-05
1.3882E-05
3.4949E-05
1.4511E-05
1.1640E-OS
3. 1826E-05
2.8586E-OS
DIST OF MAX
(KM)
0.000
999.999(1)
999.999(1)
92.609
63.590
48.590
39.601
30.000
26.220
20.591
16.401
14.770
11.201
11.691
••••STACK TOP WINDS (EXTRAPOLATED FKOM 7
WIND SPEED
(M/SEC)
6.47
8.08
9.70
12.91
16.16
MAX CONC
(G/CU M)
2.2232E-05
1.9687E-05
1.7767E-05
1.S021E-05
1 .3611E-05
DIST OF MAX
(KM)
54.680
50.490
47.282
42.942
40.000
••••STACK TOP WINDS (EXTRAPOLATED FROM 7
WIND SPEED
(M/SEC)
12.64
15.80
18.96
25.28
11 .60
MAX CONC
(G/CU M)
9.9990E«09
9.9990E«09
9.9990E*09
9.9990E»09
9.9990E+09
DIST OF MAX
(KM)
999.999(1)
999.999(1)
999.999(1)
999.999(1)
999.999(1)
. 0 METERS)""
PLUME HT
(M)
2074.6(2)
1371 .6(2)
1117.1(2)
824.9(2)
668.6(2)
574.9(2)
512.4(2)
434.3(2)
38T.5I2)
133.9(2)
290.8(2)
271.2(2)
255.5(2)
217.9(2)
.0 METERS)**"
PLUME HT
(M)
121.8(2)
113.0(2)
306.4(2)
296.6(2)
287.1(2)
.0 METERS)""
PLUME HT
(M)
280.8(2)
272.7(2)
266. 1(2)
257.0(2)
250.9(2)
(1) HIE DISTANCE TO THE POINT OF MAXIMUM CONCENTRATION IS SO OREAT THAT THE SAME STABILITY IS NOT LIKELY
TO PLKSIbT I.ONO ENOUGH FOR THE PLUME TO TRAVEL THIS FAR.
(2) Till. HI.UllL IS CALCULATED TO HE AT A HEIGHT WHERE CARE SHOULD BE USED IN INTERPRETING THE COMPUTATION.
(J) NO COMPUTATION WAS ATTEMPTED FOR THIS HEIGHT AS THE POINT OF MAXIMUM CONCENTRATION IS GREATER THAN 100 KILOMETERS
FROM THE SOURCE
Figure 5. (continued)
-------
DO YOU WISH TO USE THE ABRIDGED VERSION?
NO
IPTPLU - IMPROVED POINT SOURCE SCREENING MODEL - VERSION 81035
THE INTERACTIVE VERSION OF PTPLU DEVELOPED UNDER CONTRACT BY
AEROCOMP, INC. - COSTA MESA, CA FOR THE
ENVIRONMENTAL OPERATIONS BRANCH, EPA
1 CHANGE OPTIONS
2 CHANGE METEOROLOGY
3 CHANGE RECEPTOR ELEVATION
4 CHANGE SOURCE CHARACTERISTICS
5 CHANGE TITLE
6 DISPLAY INPUT DATA
7 RUN
8 END
ENTER SELECTION (1,2,3,4,5,6,7 OR 8)
1
PRESENT OPTIONS ARE:
1 COMPUTE GRADUAL RISE
2 COMPUTE DOWNWASH
3 COMPUTE BUOYANCY INDUCED DISPERSION
CHANGE WHICH OPTION? (4 TO DISPLAY; 5 TO RETURN TO MENU)
5
1 CHANGE OPTIONS
2 CHANGE METEOROLOGY
3 CHANGE RECEPTOR ELEVATION
4 CHANGE SOURCE CHARACTERISTICS
5 CHANGE TITLE
6 DISPLAY INPUT DATA
7 RUN
8 END
ENTER SELECTION (1,2,3,4,5,6,7 OR 8)
2
PRESENT METEOROLOGY:
1 AMBIENT AIR TEMPERATURE (K): 293.0
2 MIXING HEIGHT (M): 2000.0
3 ANEMOMETER HEIGHT (M): 10.0
4 WIND PROFILE EXPONENTS:
0.07 0.07 0.10 0.15 0.35 0.55
CHANGE WHICH ITEM? (5 TO DISPLAY; 6 TO RETURN TO MENU)
1
ENTER NEW AIR TEMPERATURE (K):
293. 0
CHANGE WHICH ITEM? (5 TO DISPLAY; 6 TO RETURN TO MENU)
2
Figure 6. Output of unabridged interactive version of PTPLU.
20
-------
ENTER NEW MIXING HEIGHT (M):
2080.0
CHANGE WHICH ITEM? (5 TO DISPLAY; 6 TO RETURN TO MENU)
3
ENTER NEW ANEMOMETER HEIGHT (M):
10.0
CHANGE WHICH ITEM? (5 TO DISPLAY; 6 TO RETURN TO MENU)
4
ENTER NEW WIND PROFILE EXPONENTS (SIX):
07,.07,.10,. 15, .35,.55
CHANGE WHICH ITEM? (5 TO DISPLAY; 6 TO RETURN TO MENU)
5
PRESENT METEOROLOGY:
1 AMBIENT AIR TEMPERATURE (K): 293.0
2 MIXING HEIGHT (M): 2000.0
3 ANEMOMETER HEIGHT (M): 10.0
4 WIND PROFILE EXPONENTS:
0.07 0.07 0.10 0.15 0.35 0.55
CHANGE WHICH ITEM? (5 TO DISPLAY; 6 TO RETURN TO MENU)
6
1 CHANGE OPTIONS
2 CHANGE METEOROLOGY
3 CHANGE RECEPTOR ELEVATION
4 CHANGE SOURCE CHARACTERISTICS
5 CHANGE TITLE
6 DISPLAY INPUT DATA
7 RUN
8 END
ENTER SELECTION (1,2,3,4,5,6,7 OR 8)
3
PRESENT HEIGHT OF RECEPTORS IS (M): 0.0
ENTER NEW RECEPTOR HEIGHT (M)
0.0
1 CHANGE OPTIONS
2 CHANGE METEOROLOGY
3 CHANGE RECEPTOR ELEVATION
4 CHANGE SOURCE CHARACTERISTICS
5 CHANGE TITLE
6 DISPLAY INPUT DATA
7 RUN
8 END
ENTER SELECTION (1,2,3,4,5,6,7 OR 8)
4
Figure 6. (continued)
21
-------
PRESENT SOURCE CHARACTERISTICS ARE:
1 SOURCE STRENGTH (G/SEC): 2750.0
2 PHYSICAL HEIGHT OF STACK (M): 165.0
3 STACK GAS TEMPERATURE (K): 425.0
4 STACK GAS VELOCITY (M/SEC): 38.0
5 INSIDE STACK DIAMETER (M): 4.5
CHANGE WHICH CHARACTERISTIC? (6 TO DISPLAY; 7 TO RETURN)
1
ENTER NEW SOURCE STRENGTH (G/SEC):
2750.0
CHANGE WHICH CHARACTERISTIC? (6 TO DISPLAY; 7 TO RETURN)
2
ENTER NEW PHYSICAL STACK HEIGHT (M):
165.0
CHANGE WHICH CHARACTERISTIC? (6 TO DISPLAY; 7 TO RETURN)
3
ENTER NEW STACK GAS TEMPERATURE (K):
425.0
CHANGE WHICH CHARACTERISTIC? (6 TO DISPLAY; 7 TO RETURN)
4
ENTER NEW STACK GAS VELOCITY (M/SEC):
38.0
CHANGE WHICH CHARACTERISTIC? (6 TO DISPLAY; 7 TO RETURN)
5
ENTER NEW INSIDE STACK DIAMETER (M):
4.50
CHANGE WHICH CHARACTERISTIC? (6 TO DISPLAY; 7 TO RETURN)
6
PRESENT SOURCE CHARACTERISTICS ARE:
1 SOURCE STRENGTH (G/SEC): 2750.0
2 PHYSICAL HEIGHT OF STACK (M): 165.0
3 STACK GAS TEMPERATURE (K): 425.0
4 STACK GAS VELOCITY (M/SEC): 38.0
5 INSIDE STACK DIAMETER (M): 4.5
CHANGE WHICH CHARACTERISTIC? (6 TO DISPLAY; 7 TO RETURN)
7
1 CHANGE OPTIONS
2 CHANGE METEOROLOGY
3 CHANGE RECEPTOR ELEVATION
4 CHANGE SOURCE CHARACTERISTICS
5 CHANGE TITLE
6 DISPLAY INPUT DATA
7 RUN
8 END
Figure 6. (continued)
22
-------
ENTER SELECTION (1,2,3,4,5,6,7 OR 8)
5
PRESENT TITLE IS:
*** TEST OF PTPLU «**
CHANGE TO: (NOT MORE THAN 60 CHARACTERS)
DEMONSTRATION OF INTERACTIVE SESSION SUBMITTED BY T. CHICO
1 CHANGE OPTIONS
2 CHANGE METEOROLOGY
3 CHANGE RECEPTOR ELEVATION
4 CHANGE SOURCE CHARACTERISTICS
5 CHANGE TITLE
6 DISPLAY INPUT DATA
7 RUN
8 END
ENTER SELECTION (1,2,3,4,5,6,7 OR 8)
6
CURRENT INPUT DATA:
OPTIONS:
COMPUTE GRADUAL RISE
COMPUTE DOWNWASH
COMPUTE BUOYANCY INDUCED DISPERSION
METEOROLOGY:
AMBIENT AIR TEMPERATURE (K): 293.0
MIXING HEIGHT (M): 2000.0
ANEMOMETER HEIGHT (M): 10.0
WIND PROFILE EXPONENTS: 0.07 0.07 0.10 0.15 0.35 0.55
RECEPTOR HEIGHT (M): 0.0
SOURCE CHARACTERISTICS:
SOURCE STRENGTH (G/SEC): 2750.0
PHYSICAL HEIGHT OF STACK (M): 165.0
STACK GAS TEMPERATURE (K): 425.0
STACK GAS VELOCITY (M/SEC): 38.0
INSIDE STACK DIAMETER (M): 4.5
TITLE:
DEMONSTRATION OF INTERACTIVE SESSION SUBMITTED BY T. CHICO
ENTER M TO RETURN TO MENU
M
1 CHANGE OPTIONS
2 CHANGE METEOROLOGY
3 CHANGE RECEPTOR ELEVATION
4 CHANGE SOURCE CHARACTERISTICS
5 CHANGE TITLE
6 DISPLAY INPUT DATA
7 RUN
8 END
ENTER SELECTION (1,2,3,4,5,6,7 OR 8)
7
Figure 6. (continued)
23
-------
PTPLU -- IMPROVED MODEL FOR SCREENING MAXIMUM CONCENTRATIONS -- VERSION 81035
***TITLE***
DEMONSTRATION OF INTERACTIVE SESSION SUBMITTED BY T. CHICO
"•OPTIONS***
IF = 1, USE OPTION
IF = 0, IGNORE OPTION
IOPTU) = 1 (GRAD PLUME RISE)
IOPT(2) = 1 (STACK DOWNWASH)
IOPT(3) = 1 (BUOY. INDUCED DISP.)
**'METEOROLOGY***
AMBIENT AIR TEMPERATURE
MIXING HEIGHT
ANEMOMETER HEIGHT
WIND PROFILE EXPONENTS
"•RECEPTOR HEIGHT"
293.00 (K)
2000.00 (M)
10.00 (M)
A:0.07, B:0.07,
C:0.10
D:0. 15 , E:0.35 , F-.0.55
0.00 (M)
**'SOURCE***
EMISSION RATE =
STACK HEIGHT =
EXIT TEMP.
EXIT VELOCITY =
STACK DIAM.
2750.00 (G/SEC)
165.00 (M)
425.00 (K)
38.00 (M/SEC)
4.50 (M)
»CALCULATED PARAMETERS<«
VOLUMETRIC FLOW = 604.36 (M**3/SEC)
BUOYANCY FLUX PARAMETER = 585.91 (M«*4/SEC**3)
DEMONSTRATION OF INTERACTIVE SESSION SUBMITTED BY T. CHICO
****WINDS CONSTANT WITH HEIGHT****
STABILITY
1
1
1
1
1
1
1
****STACK
STAB I L I TY
1
WIND SPEED
(M/SEC)
0.50
0.80
1 .00
1.50
2.00
2.50
3.00
MAX CONC
(G/CU M)
O.OOOOE+00
O.OOOOE+QO
8.5341E-04
7 .2139E-04
8.1207E-04
9.7610E-04
1 .0968E-03
TOP WINDS (EXTRAPOLATED
WIND SPEED
(M/SEC)
0.61
MAX CONC
(G/CU M)
O.OOOOE+00
DIST OF MAX
(KM)
0. 000
0.000
1.971
1 .839
1. 152
1 .042
0.967
PLUME HT
(M)
2276.0(2)
2380.3(2)
1937 .2(2)
1346.5(2)
900.2(2)
715.1(2)
601.1(2)
FROM 10.0 METERS ) * * * *
DIST OF MAX
(KM)
0.000
PLUME HT
(M)
2365.5(2)
Figure 6. (continued)
24
-------
1
1
1
1
1
1
*»**WINDS
STABILITY
2
2
2
2
2
2
2
2
2
****STACK
STABILITY
2
2
2
2
2
2
2
2
2
****WINDS
STABILITY
3
3
3
3
3
3
3
3
3
****STACK
STABILITY
3
3
3
3
3
0.97
1.22
1.83
2.43
3.04
3.65
CONSTANT WITH
WIND SPEED
(M/SEC)
0.50
0.80
1.00
1.50
2.00
2.50
3.00
4.00
5.00
8.6173E-04
7.9007E-04
7.4371E-04
9.5698E-04
1.1053E-03
1.2024E-03
HEIGHT****
MAX CONC
(G/CU M)
O.OOOOE+00
O.OOOOE+00
3.6782E-04
2.7921E-04
2.9739E-04
3.3243E-04
3.6094E-04
4.0207E-04
4.2822E-04
TOP WINDS (EXTRAPOLATED
WIND SPEED
(M/SEC)
0.61
0.97
1.22
1.83
2.43
3.04
3.65
4.87
6.08
CONSTANT WITH
WIND SPEED
(M/SEC)
2.00
2.50
3.00
4.00
5.00
7.00
10.00
12.00
15 .00
MAX CONC
(G/CU M)
O.OOOOE+00
3.7696E-04
3. 1362E-04
2 .8484E-04
3.2815E-04
3.6306E-04
3.8972E-04
4.2541E-04
4.4524E-04
HEIGHT****
MAX CONC
(G/CU M)
1.8735E-04
2.1485E-04
2.3785E-04
2.7289E-04
2.9702E-04
3.2415E-04
3.3578E-04
3 .3386E-04
3. 2435E-04
TOP WINDS (EXTRAPOLATED
WIND SPEED
(M/SEC)
2.65
3.31
3. 97
5.29
6 .62
MAX CONC
(G/CU M)
2.2207E-04
2.5008E-04
2.7203E-04
3.0253E-04
3.2060E-04
1.974
1.931
1.205
1.054
0.962
0.899
DIST OF MAX
(KM)
0.000
0.000
10.381
8.514
5.786
4.858
4.264
3.511
3.053
FROM 10.0 METERS
DIST OF MAX
(KM)
0.000
10.369
10.025
6.337
4. 954
4.222
3.728
3.103
2.723
DIST OF MAX
(KM)
14.212
11.631
9.980
7.956
6.750
5.389
4.380
3.990
3 .599
1985.6(2)
1621.5(2)
995.2(2)
734.4(2)
593.6(2)
506.4(2)
PLUME HT
(M)
2276.0(2)
2380.3(2)
1937 .2(2)
1346.5(2)
1051. 1(2)
873.9(2)
755.7(2)
608. 1(2)
519.4(2)
) * * * *
PLUME HT
(M)
2365 .5(2)
1985.6(2)
1621.5(2)
1136.0(2)
893.2(2)
747.6(2)
650.5(2)
529.1(2)
456.3(2)
PLUME HT
(M)
1051. 1(2)
873.9(2)
755.7(2)
608. 1(2 )
519.4(2)
418.2(2)
342.2(2)
312.7(2)
283. 1(2)
FROM 10.0 METERS ) * * * *
DIST OF MAX
(KM)
11 .084
9 .217
7 .996
6.483
5.582
PLUME HT
(M)
834.5(2)
700.6(2)
611.3(2)
499 .7(2)
432.8(2)
Figure 6. (continued)
25
-------
9.27
13.24
15.88
19.85
3.3497E-04
3.3062E-04
3.2074E-04
3.0259E-04
4.565
3.806
3.513
3.218
356.3(2)
298.9(2)
276.6(2)
254.3(2)
****WINDS CONSTANT WITH HEIGHT****
STABILITY WIND SPEED
(M/SEC)
0.50
0.80
00
50
00
2.50
3.
4.
5.
7.
.00
.00
.00
.00
10.00
12.00
15.00
20.00
MAX CONC
(G/CU M)
0
0
9
9
9
3
4
6
7
9
1
1
1
1
.OOOOE+00
.OOOOE+00
.9990E+09
.9990E+09
.9990E+09
.8419E-05
.6683E-05
.1618E-05
.4276E-05
.2719E-05
.0637E-04
.1080E-04
.1334E-04
.1179E-04
DIST OF MAX
(KM)
0.
0.
999.
999.
999.
99.
76.
51.
38.
28.
20.
17 .
15.
12.
000
000
999(3)
999(3)
999(3)
338
209
671
990
710
774
950
293
771
PLUME HT
(M)
2276
2380
1937
1346
1051
873
755
608
519
418
342
312
283
253
.0(2
• 3(
.2(
.5(
.!(
.9(
.7(
.!(
.4(
.2(
.2(
.7(
.!(
.6(
2
2
2
2
2
2
2
2
2
2
2
2
2
)
)
)
)
)
)
)
)
)
)
)
)
)
)
FROM 10.0 METERS)****
****STACK TOP WINDS (EXTRAPOLATED
STABILITY WIND SPEED
(M/SEC)
4 0.76
4 1.22
4 1.52
4 2.28
4 3.05
4 3.81
4 4.57
4 6.09
4 7.61
4 10.66
4 15.23
4 18.27
4 22.84
4 30.45
****WINDS CONSTANT WITH HEIGHT*"**
STABILITY WIND SPEED MAX CONC DIST OF MAX
0
9
9
9
4
5
6
8
9
1
1
1
1
1
MAX CONC
(G/CU M)
.OOOOE+00
.9990E+09
.9990E+09
.9990E+09
.7410E-05
.8910E-05
.9087E-05
.5636E-05
.6420E-05
.0815E-04
.1339E-04
.1285E-04
.0937E-04
.0377E-04
DIST OF MAX
(KM)
0
999
999
999
74
55
43
30
26
19
15
13
11
10
.000
.999(3)
.999(3)
.999(3)
.688
.160
.631
.961
.493
.710
.131
.470
.871
.150
PLUME HT
(M)
2492
1619
1328
940
746
630
553
456
397
331
281
262
242
220
.7(2)
.8(2)
.9(2)
.9(2)
.9(2)
.5(2)
.0(2)
.0(2)
.8(2)
.3(2)
.4(2)
.0(2)
.6(2)
.9(2)
(M/SEC)
2.00
2.50
3.00
4.00
5.00
(G/CU M)
1.3457E-04
1.2444E-04
1.1633E-04
1.0392E-04
9.4705E-05
(KM)
68.893(1)
61 .581
.252
.083
56.
49 .
44.291
PLUME HT
(M)
362.4(2)
348.2(2)
337.4(2)
321.7(2)
310.4(2)
****STACK TOP WINDS (EXTRAPOLATED FROM 10.0 METERS)****
STABILITY WIND SPEED MAX CONC DIST OF MAX PLUME HT
(M/SEC) (G/CU M) (KM) (M)
5 5.34 9.2100E-05 42.981 307.3(2)
Figure 6. (continued)
26
-------
6.67
8.00
10.67
13.34
8.3409E-05
7.6437E-05
6.5760E-05
5.7935E-05
40.000
40.000
40.000
39.984
297 .1(2)
289.3(2)
278.0(2)
269.9(2)
****WINDS CONSTANT WITH HEIGHT****
STABILITY WIND SPEED
(M/SEC)
00
50
00
00
5.00
MAX CONC
(G/CU M)
9.9990E+09
9.9990E+09
9.9990E+09
9.9990E+09
9.9990E+09
DIST OF MAX
(KM)
999.999(3)
999.999(3)
999.999(3)
999.999(3)
999.999(3)
PLUME HT
(M)
328.8(2)
317.1(2)
308. 1(2)
295.0(2)
285.7(2)
****STACK TOP WINDS (EXTRAPOLATED FROM 10.0 METERS)****
STABILITY
6
6
6
6
6
WIND SPEED
(M/SEC)
9.35
11 .68
14.02
18.69
23.37
MAX CONC
(G/CU M)
9.9990E+09
9.9990E+09
9.9990E+09
9.9990E+09
9.9990E+09
DIST OF MAX
(KM)
999.999(3)
999.999(3)
999.999(3)
999.999(3)
999.999(3)
PLUME HT
(M)
263.0(2)
256.0(2)
250.6(2)
242.8(2)
237.2(2)
(1) THE DISTANCE TO THE POINT OF MAXIMUM CONCENTRATION IS SO
GREAT THAT THE SAME STABILITY IS NOT LIKELY TO PERSIST
LONG ENOUGH FOR THE PLUME TO TRAVEL THIS FAR.
(2) THE PLUME IS CALCULATED TO BE AT A HEIGHT WHERE CARE
SHOULD BE USED IN INTERPRETING THE COMPUTATION.
(3) NO COMPUTATION WAS ATTEMPTED FOR THIS HEIGHT AS THE POINT
OF MAXIMUM CONCENTRATION IS GREATER THAN 100 KILOMETERS
FROM THE SOURCE.
1 CHANGE OPTIONS
2 CHANGE METEOROLOGY
3 CHANGE RECEPTOR ELEVATION
4 CHANGE SOURCE CHARACTERISTICS
5 CHANGE TITLE
6 DISPLAY INPUT DATA
7 RUN
8 END
ENTER SELECTION (1,2,3,4,5,6,7 OR 8)
3
PTPLU RUN TERMINATED AT USER REQUEST
8
Figure 6. (continued)
27
-------
Three cautionary messages are given by the program: one
pertains to the probability that the stability will change before
the plume can reach the estimated point of maximum concentration;
one is for elevated plumes; and one pertains to maximum
concentrations occurring at extreme distances. Effective heights
of more than 200 m are regarded as extreme and are tagged with a
cautionary message. Distances to maximum concentrations greater
than 100 km are considered to be beyond the scope of this model.
These calculations are tagged; the concentrations are shown as
9.9990E+09 g/m3, and the distances are shown as 999.999 km.
To determine the probability that the stability will change
before the plume can travel to the estimated point of maximum
concentration, the distance to the maximum is divided by the wind
speed (assuming a uniform wind speed at all points under
consideration), yielding an estimated travel time. If this
travel time is greater than the threshold value for the stability
considered, the corresponding distance is tagged. Travel-time
threshold values employed by the program are as follows:
Stabi1i ty Travel time
A 4.0 hours
B 6.0 hours
C 8.0 hours
D 277.5 hours
E 8.0 hours
F 8.0 hours
28
-------
SECTION 8
EXAMPLE CALCULATION
The following example illustrates the application of PTPLU.
A 40-meter stack emits 151 g/s of a pollutant. The stack
diameter is 2.68 m, the exit velocity is 20.0 m/s, and the stack
gas temperature is 350 K. It is desired to determine the maximum
concentration, to find the distance at which it occurs, and to
see, in general, how concentration varies with wind speed and
stability. For the options, ambient temperature, mixing height,
receptor elevation, anemometer height, and wind speed power-law
exponents, users are referred to the batch output of Figure 7.
The maximum concentration is selected as the largest
concentration in column 7 of output section D (see Figure 4 for
designation of output sections). The concentrations in this
column can also be plotted as a function of wind speed, to give
an overall picture of the dependency of pollutant concentrations
on wind speed and stability.
Portions of this example are used in the sensitivity analysis
presented in Appendix C.
29
-------
•TITLE""
IMPI.U (VhUSION 8IOJ6)
AN IMPROVED I'OIN'I SOUIlCh SCREENING MODEL
MODI Fl Ell BY: JO1£ CATALANO AND FRANK HALE
ALKOOOMP, INC. - CUSTA MESA, CA FOB THE
ENVIRONMENTAL OPERATIONS BRANCH, EPA
>» INPUT PARAMETERS<«
EXAMPLE CALCULATION - SECTION 8 OF USER'S GUIDE
•"OPTIONS"*
IF = I, USL OPTION
IF - 0, IGNORE OPTION
101'1(1) - I (GltAD PLUME KISE)
IOI'I'(2) - 0 (STACK IJOWNWASII)
101'l'(l) = 0 (UUOY. INDUCED DISP. )
•••METEOROLOGY•••
AMUIENT AIR TEMPERATURE
MIXING HEIGHT
ANEMOMETER HEIGHT
WIND PROFILE EXPONENTS
293.00 (K)
1500.00 (M)
10.00 (M)
A:0.07, B:0.07, C:0.10
DiO.15, E:0.35, F:0.55
"•SOURCE"*
EMISSION KATE
STACK HEIGHT
EXIT TEMP.
EXIT VELOCITY
STACK DIAM.
151.00 (G/SEC)
40.00 (M)
350.00 (K)
20.00 (M/SEC)
2.68 (M)
•"HtTLPTOH HEIGHT*" -
0.00 (M)
VOLUMLTKIC KI.OW - 112.82 (M"3/SEC)
>»CALCULATED PARAMETERS<«
BUOYANCY FLUX PARAMETER =
57.35
-------
••••WINIIS CONSTANT WITH HEIGHT***'
STAUII.ITY
4
4
4
4
4
4
4
4
4
4
4
4
4
4
WIND SPLE1)
(M/SbC)
11.50
0.80
1 .00
1 .50
2.00
2.50
3.00
4.00
5 .00
7.00
10.00
12.00
15.00
20.00
a
1
2
J
5
7
8
1
1
MAX CONC
(G/CU M)
9990E»09
65IIE-05
3036E-05
9940E-05
660IE-05
29I5E-05
7243E-05
I252E-04
3348t 04
6431E-04
8725E-04
9439E-04
98IOE-04
9449E-04
DIST OF MAX
(KM)
999.999(3)
60.481
40.220
21 .551
13.842
10.000
8.086
5.618
4.314
3.000
2.252
1 .953
1.669
1 .402
••••WINDS CONSTANT WITH HEIGHT
SI'AHILI I'Y
5
5
5
5
5
WIND SPtED
(M/StC)
2.00
2.50
3.00
4.00
5.00
MAX CONC
(G/CU M)
8946E-04
7455E-04
6286E-04
4512E-04
325IE-04
DIST OF MAX
(KM)
9.923
8.963
8.280
7.298
6.644
PLUME HT
(M)
919.0(2)
589.4(2)
479.5(2)
333.0(2)
259.7(2)
215.8(2)
186.5
149.9
127.9
102.8
83.9
76.6
69.3
62.0
«* • •
PLUME HT
(M)
131 .0
124.5
119.5
112.2
107.0
••••WINDS CONSTANT WITH HEIGHT"**
STAUII.ITY
b
6
6
e
6
WIND SPttD
(M/StC)
2.01)
2.50
3.00
4.00
5.00
I
1
1
1
9
MAX CONC
(G/CU M)
2707E-04
2I43E-04
1662E-04
0748E-04
893IE-05
DIST OF MAX
(KM)
19.741
17.010
15.082
14.999
14.410
Pl.UME HT
(M)
115.5
110.1
105.9
99.9
95.6
••••STACK TOP WINDS (EXTRAPOLATED FKOM 10.0 METERS)'
WIND SPEED
(M/SEC)
0.62
0.98
1.23
1.85
2.46
3.08
3.69
4.92
6.16
8.62
12.31
14.77
18.47
24.62
1
2
3
5
7
e
i
i
i
i
i
i
i
i
MAX CONC
(G/CU M)
1091E-05
2524E-05
1073E-05
I505E-05
1708E-05
9369E-05
0524E-04
3204E-04
5290E-04
7899E-04
9511E-04
9803E-04
9640E-04
8654E-04
DIST OK MAX
(KM)
98.419
41 .362
29.491
15.612
10. 160
7.619
6.197
4.390
3.429
2.553
1.916
1 .686
1 .468
1 .260
••••STACK TOP WINDS ( EXTKAPOLATED FKOM 10
WIND SPEED
(M/SEC)
3.25
4.06
4.87
6.50
8.12
MAX CONC
(G/CU M)
5788E-04
4443E-04
3395E-04
1837E-04
07I1E-04
DIST OF MAX
(KM)
7.988
7.259
6.715
5.968
5.466
••••STACK TOP WINDS (EXTKAPOLATED FROM 10
WIND SPEED
(M/SEC)
4.29
5.36
6.43
8.57
10.72
i
9
8
7
7
MAX CONC
(G/CU M)
0491E-04
6261E-05
9407E-05
9123E-05
1622E-05
DIST OF MAX
(KM)
14.999
13.952
12.821
11.280
10.241
Pl.UMt HT
(M)
754.0(2)
486.2(2)
397.0(2)
278.0(2)
218.5(2)
182.8
159.0
129.2
111.4
91.0
75.7
69.7
63.6
57.8
0 METEKS)*'
PLUME HT
(M)
117.4
111.8
107.6
101 .4
97.0
0 METERS!**
PLUME HT
(M)
98.5
94.4
91. 1
86.5
83.1
(1) HIE DISTANCE TO THE POINT OK MAXIMUM CONCENTRATION IS SO GREAT THAT THE SAME STABILITY IS NOT LIKELY
TO PERSIST LONG ENOUGH FOR THE PLUME TO TRAVEL THIS PAH.
(2) lilt Pl.UME IS CALCULATED TO BE AT A HEIGHT WHERE CARE SHOULD BE USED IN INTERPRETING THE COMPUTATION.
U) NO (IMPUTATION WAS ATTEMPTED FOR THIS HEIGHT AS THE POINT OF MAXIMUM CONCENTRATION IS GREATER THAN 100 KILOMETERS
FROM THE SOURCE.
Figure 7. (continued)
-------
REFERENCES
Briggs, G. A. 1969. Plume Rise. USAEC Critical Review Series.
TID-25075, National Technical Information Service,
Springfield, VA. 81 pp.
Pierce, T. E., and D. B. Turner. 1980. User's Guide for MPTER:
A Multiple Point Gaussian Dispersion Algorithm with Optional
Terrain Adjustment. EPA-600/8-80-016, U. S. Environmental
Protection Agency, Research Triangle Park, NC. 247 pp.
Turner, D. B., and A. D. Busse. 1973. Users' Guides to the
Interactive Versions of Three Point Source Dispersion
Programs: PTMAX, PTDIS, and PTMTP. U. S. Environmental
Protection Agency, Research Triangle Park, NC.
Turner, D. B., and J. H. Novak. 1978. User's Guide for RAM,
Volume I, Algorithm Description and Use. EPA-600/8-78-016a,
U. S. Environmental Protection Agency, Research Triangle
Park, NC. 70 pp.
U. S. Environmental Protection Agency. 1977. User's Manual for
Single Source (CRSTER) Model. Monitoring and Data Analysis
Division, EPA-450/2-77-013. Research Triangle Park, NC.
U. S. Environmental Protection Agency. 1978. Guideline on Air
Quality Models. EPA-450/2-78-027, Office of Air Quality
Planning and Standards, U. S. Environmental Protection
Agency, Research Triangle Park, NC. 83 pp.
32
-------
APPENDIX A
MODELING CONCEPTS
BASIC CONCEPTS
Meteorological factors of wind and turbulence are important
in the dispersion process. The dispersion of pollutants emitted
into the atmosphere depends on the turbulent mixing that takes
place between the polluted air and its cleaner surroundings.
This turbulent mixing occurs primarily through eddy dispersion by
the circular motions (eddies) that exist in many sizes in the
atmosphere, which tend to break portions from the volume of
polluted air and mix them with clean air.
In addition to meteorological factors, other factors are
significant in modeling the dispersion process and pollutant
concentrations. Source characteristics and surface roughness
features, as well as topography, are among the interrelated
factors that determine the pollutant concentration field.
Source-Related Factors
An important parameter related to pollutant concentrations is
the rate of emission of the pollutant from the source.
Concentrations are directly proportional to emission rate,
usually expressed as mass per unit time. The effective height of
release is also important. Roughly, the maximum ground-level
concentration is inversely proportional to the square of the
height of release. The effective height of release is the
combination of physical release height and any additional rise
due to buoyancy or momentum effects. The buoyancy of a hot plume
will usually dominate over the effect of momentum. Buoyant plume
rise is affected by the excess of the stack gas temperature above
the ambient air temperature and the volume flow of stack gases.
Buoyant rise also decreases with increasing wind speed and is
affected by the thermal stability of the air above the plume.
Momentum rise is important for plumes with little excess
temperature and is proportional to stack gas velocity and stack
d i ame t e r .
Over relatively flat terrain, a higher effective stack height
decreases ground-level concentrations and causes the maximum
concentration to occur farther from the source. Effective
heights are raised by increasing the physical stack height, the
33
-------
'•••-stack gas temperature, the volume of exit gases (without
decreasing the exit temperature), or the stack gas exit velocity.
Meteorological Factors
Wind direction is a primary variable in determining
concentrations at specific receptors, because it determines
whether transport takes place from the source towards the general
direction of the receptor. Concentrations from line and area
sources are less sensitive to wind direction than are
concentrations from point sources.
Wind speed dilutes air pollutants from continuous sources as
the plume emerges from the stack. With increasing wind speed,
the pollutant concentrations in the plume become more dilute.
Both mechanical production of turbulence and buoyant
production or loss of turbulence are important in pollutant
dispersion. Mechanical turbulence results from wind flow over
objects. The number, size, and spacing of the objects or
roughness elements influence the growth of mechanical
turbulence. When roughness elements are close together, like
trees in a forest, mechanical turbulence is not enhanced, because
a new interface forms, allowing the air to flow smoothly over the
objects. Mechanical turbulence is enhanced in regions where
large objects like mountains or skyscrapers disturb the general
air flow. In general, an increase of wind speed will increase
the mechanical turbulence.
In light-wind situations, the heating or cooling of the
earth's surface increases the importance of buoyantly produced
turbulence to dispersion processes. As the sun heats the
surface, the air next to the surface is heated and rises
buoyantly. During times of strong surface heating, commonly
referred to as unstable conditions, buoyant turbulence is
produced by the rising thermals of heated air, further amplifying
the mechanical turbulence. Furthermore, strong surface heating
leads to superadiabatic lapse rates (see Glossary) which
encourage the formation of convective cells. Rising thermals are
carried upwards in narrow convective updrafts. A general region
of subsiding air surrounds these narrow columns. Thus, in
unstable conditions, a plume spreads over a relatively large
vertical distance.
At nighttime, radiant heat loss at the surface cools the air
near the ground. In such situations, commonly referred to as
stable conditions, a temperature inversion exists. Further,
buoyant turbulence is not produced, and mechanically induced
turbulence is suppressed. Thus, a plume spreads little
vertically in stable conditions.
34
-------
In a temperature structure where the air is neither heated
nor cooled, turbulence is neither amplified nor suppressed.
These conditions are commonly referred to as neutral.
Pasquill (1961) devised a method for classifying turbulence
in terms of atmospheric conditions into six stability categories,
ranging from very unstable (class A), to neutral (class D), to
moderately stable (class F) (see Table A-l). For PTPLU, the
dispersion due to atmospheric turbulence is assumed to be related
to the Pasquill stability classes.
Wind speed generally increases with height above the surface,
and this increase depends on both surface roughness and
atmospheric stability. A power-law profile of the form
u(z) = u(za)(z/za)p
is frequently used to approximate this increase. The wind speed
at a height z above the ground is u(z); u(za) is the wind speed
measured at the anemometer height, za, above the ground; and p is
a function of stability. For a more detailed discussion of wind
profiles, see Irwin (1979).
Another condition that affects vertical dispersion is the
thickness of the neutral or unstable layer, often referred to as
the mixing layer. At the top of the convective layer, an
inversion usually exists, tending to damp out vertical motions
and limiting the extent to which pollutants can spread
vertically. The strength and depth of the inversion are also
important; if the inversion is weak or shallow, pollutants may
still diffuse through it.
The mixing height varies both seasonally and diurnally. It
is typically high in summer and at mid-day and low in winter, and
it frequently is undefined at night (when a surface-based
inversion exists). For a clima tologica1 summary of mixing
heights across the United States see Holzworth (1972).
Further Considerations
Usually, the wind turns with height, due primarily to
friction of the wind with the ground. Friction causes slowing of
the wind near the surface, which causes the low-level flow to
deviate toward low pressure. This results in a clockwise turning
of the wind with height. Other forces also cause turning of the
wind with height. Within a barotropic atmosphere (in which the
surfaces of constant pressure are also surfaces of constant
density), the wind direction is constant with height, except near
the surface, where frictional effects take place. The atmosphere
is usually not barotropic; when surfaces of constant pressure and
constant density do not coincide, the atmosphere is said to be
baroclinic. In such an atmosphere, the wind direction must vary
35
-------
with height, since colder air is advected (transported
horizontally) into warmer surroundings (or warmer air into colder
surroundings). During cold-air advection, the wind direction
backs (counterclockwise rotation) with height, and during
warm-air advection, the wind direction veers (clockwise rotation)
with height. Vertical wind shear causes portions of a polluted
plume that has dispersed to different altitudes to be transported
away from the source in different directions, resulting in
additional horizontal spreading or dispersion. Because effects
of wind direction shear are ignored in the model presented here,
estimates of concentration directly downwind of sources are
likely to be higher than concentrations actually observed at
distances greater than 10 km from the source. Methods to account
for the effect of wind direction shear are discussed by Pasquill
(1976) .
Besides causing wind direction shear, the frictional effect
also causes a wind speed shear, with the wind speed decreasing
near the earth's surface (to zero at the surface). Under stable
conditions, the increase of speed with height to the wind speed
of the free atmosphere may take place through a shallow layer,
only 100 to 200 m thick. This also tends to be the case if the
surface is smooth. Under conditions of instability or large
surface roughness, the transition takes place through a much
deeper layer. The combined effects of stability and surface
roughness result in different patterns of wind speed with time of
day at different heights. For example, wind speeds near the
ground (10 m) generally exhibit a nighttime minimum and a daytime
maximum. At greater heights (e.g., 200 m above ground), wind
speeds may reach a minimum (maximum surface friction effect)
during mid-afternoon and a maximum (nearest the free atmosphere
speed) at n ight.
In considering buoyant production or suppression of
turbulence as reflected in the vertical temperature structure, it
is important to realize that the layer adjacent to the ground
surface characterizes the state of the atmosphere. For instance,
when conditions are very unstable, the temperature structure
through the well-mixed convective layer (typically on the order
of 1000 to 2000 m thick) is nearly adiabatic, indicating that
turbulent motion is neither suppressed nor enhanced. Only within
the near-surface layer (typically 100 m thick or less) is the
temperature structure superadiabatic. If one attempted to
specify the state of the atmosphere using the temperature
structure in the higher layers, one would erroneously conclude
that the atmosphere was nearly neutral, when in fact it was
convectively unstable. During stable conditions, the temperature
structure above the surface-based inversion is often nearly
adiabatic. Hence, during stable conditions, the temperature
structure within the layers aloft may not truly reflect how
stable the entire dispersion layer is. Therefore, in considering
ground-level concentrations from point sources, it is important
36
o
-------
to examine the surface layer near the ground to properly
determine the influences of buoyant production or loss of
turbulent kinetic energy on dispersion through the surface layer.
Information about conditions above the ground is by no means
useless. On the contrary, detailed structures of temperature and
wind velocity with height are extremely useful for assessing air
pollution transport and dispersion; but they are most useful when
interpreted with near-surface measurements.
Air pollution simulations are frequently complicated by local
flows. Uneven solar heating on the sides of valleys or cold-air
drainage at night can cause small-scale circulations that may
make analysis of meteorological measurements difficult. For
example, during the Lewiston, Idaho -- Clarkston, Washington
study (U. S. Department of Health, Education, and Welfare, 1964),
maximum ground-level concentrations were observed at a receptor
down-valley from the source at the time when surface wind
measurements indicated an up-valley flow. Thorough analysis,
revealed that the high concentrations were due to the fumigation
(rapid downward mixing) of the detached plume, which had been
flowing down-valley during the night. The plume was not mixed
downward to the valley floor until the winds had already shifted
to up-va11ey.
Another cause of local circulations is land-water interfaces,
which can produce land and sea breezes, due to horizontal
temperature differences, especially during periods of light
general wind flow.
The effects of local flow are sufficiently complex to require
a special modeling approach for each condition.
GAUSSIAN EQUATIONS FOR ESTIMATING CONCENTRATIONS
In using the Gaussian plume model, one assumes that pollutant
concentrations from a continuously emitted plume are proportional
to emission rate, and are diluted by the wind at the point of
emission at a rate inversely proportional to the wind speed. One
also assumes that the time-averaged (over approximately one hour)
pollutant concentrations crosswind and in the vertical near the
source are closely described by Gaussian or normal
distributions. The standard deviations of a plume concentration
in these two directions are empirically related to the levels of
turbulence in the atmosphere and increase with distance from the
source.
In its simplest form, the Gaussian model is based on the
assumption that the pollutant does not undergo chemical reactions
or other removal processes during its transport from the source.
Furthermore, pollutants reaching the ground or the top of the
mixing height as the plume grows are assumed to be eddy-reflected
37
-------
back toward the plume center-line.
The three Gaussian equations given below are based on a
coordinate scheme with the origin at the base of the stack, x
downwind from the source, y crosswind, and z vertical; Figure A-l
illustrates the coordinate system. These equations include four
components, from left to right in Eq. Al: 1) concentrations are
proportional to emission rate, 2) the released effluent is
diluted by the wind passing the point of release, 3) the effluent
is spread horizontally, resulting in a Gaussian or normal
(be 11-shaped) crosswind distribution downwind, and 4) the
effluent is spread vertically. Vertical spread also results in a
normal vertical distribution near the source, which at greater
downwind distances is modified by eddy reflection at the ground
and, if appropriate, by eddy reflection at the mixing height.
The following symbols are used:
Xp -- concentration (grams per cubic meter),
Q -- emission rate (grams per second),
u -- wind speed (meters per second),
av -- standard deviation of plume concentration distributed
in the horizontal (evaluated at distance x and for
the appropriate stability) (meters),
az -- standard deviation of plume concentration distributed
in the vertical (evaluated at distance x and for the
appropriate stability) (meters),
L -- mixing height (meters),
H -- effective height of emission (meters),
z -- receptor height above ground (meters), and
y -- crosswind distance from plume centerline (meters).
The concentration, Xp> &t a receptor at (x,y,z) from the
continuous emission from a point source located at (0,0,H) is
given by one of the three following equations.
For stable conditions or unlimited mixing,
Xp = Q • 1/u • g1/(/?F oy) • g2/(/2rF az) , (Al)
where
%l = exp(-0.5 y2/ay), and
38
-------
Figure A-l.
Coordinate system showing Gaussian distributions
in the horizontal and vertical.
39
-------
g2 = exp[-0.5(z-H) 2/oz] + exp [ -0 . 5 ( z+H) 2 /a| ] .
Note that if y = 0, or z = 0, or both z and H are 0, this
equation simplifies greatly.
For unstable or neutral conditions, where az is greater than
1.6 L,
Xp = Q • 1/u • g!/(/2iT ay) • 1/L. (A2)
For unstable or neutral conditions, provided that both H and
z are less than L, where az is less than or equal to 1.6 L,
Xp = Q • 1/u • gi/(/TF ay) • g3/(/TiT az ) , (A3)
where
oo
g3 - y texp[-0.5(z-H+2NL)2/a|] + exp [ -0 . 5 ( Z+H+2NL) 2 /a| ] } .
N---<"
(This infinite series converges rapidly, and evaluation with N
varying from -4 to +4 is usually sufficient.)
When estimates are calculated by hand, Eq . Al is frequently
applied until az = 0.8 L, and then Eq . A2 is applied for all
distances where az exceeds 0.8 L. This causes an inflection
point in a plot of concentrations with distance. Adding Eq . A3,
which includes multiple eddy reflections, and changing the
criteria for use of Eq . A2 to situations where az is greater than
1.6 L results in a smooth transition to uniform mixing,
regardless of source or receptor height. Values must be obtained
for the dispersion parameters in the above equations. In his
original discussions of dispersion and in his subsequent
writings, Pasquill (1961, 1974, 1976) emphasized the desirability
of using direct measurements of turbulent intensity to
characterize atmospheric dispersion. Typically, we lack the
required turbulence measurements and resort to other methods of
estimating the parameters. Although not expressed as standard
deviations for use with Gaussian equations, Pasquill (1961)
provided some estimates of dispersion qualified by, "for use in
the likely absence of special measurements of wind structure
there was clearly a need for broad estimates of 6 and h in terms
of routine meteorological data." Pasquill's parameters of
spreading are 9 and h. Gifford (1960) transformed Pasquill's
parameters to ay and az for use with Gaussian equations.
Commonly referred to as the Pasqu i 1 1 -Gi f f ord (P-G) dispersion
parameters, these are discussed later in this appendix.
By differentiating Eq . Al with respect to distance, x, and
setting the derivative equal to zero, an equation for maximum
concentration can be derived:
40
-------
Xmax = 2Qaz/ayeTTuH2;
the distance to maximum concentration is the distance where az =
H//2". However, this equation is correct only if the ratio of
az/ay is constant with distance (see Pasquill (1974), p. 273, for
further details). For the P-G parameter values, the ratio is not
constant, and maximum concentrations, if required, are determined
using iterative methods.
PLUME RISE FOR POINT SOURCES
The use of the methods of Briggs to estimate plume rise and
effective height of emission are discussed below.
First, actual or estimated wind speed at stack top, u(h), is
assumed to be available.
Stack Downwash
To consider stack downwash, the physical stack height is
modified following Briggs (1973, p. 4). The h' is found from
h' = h + 2{[vs/u(h)] - 1.5}d for vs < 1.5u(h), (A4)
h1 = h for v"s > 1.5u(h) ,
where h is physical stack height (meters), vs is stack gas
velocity (meters per second), and d is inside stack-top diameter
(meters). This h1 is used throughout the remainder of the plume
height computation. If stack downwash is not considered, h1 = h
in the following equations.
Buoyancy Flux
For most plume rise situations, the value of the Briggs
buoyancy flux parameter, F (mVs3) is needed. The following
equation is equivalent to Briggs1 (1975, p. 63) Eq. 12:
F = (gvsd2AT)/(4Ts), (A5)
where AT = Ts - T, Ts is stack gas temperature (kelvin), and T is
ambient air temperature (kelvin).
Unstable or Neutral; Crossover Between Momentum and Buoyancy
For cases with stack gas temperature greater than or equal to
ambient air temperature, it must be determined whether the plume
rise is dominated by momentum or buoyancy. The crossover
temperature difference (AT)C is determined for 1) F less than 55
and 2) F greater than or equal to 55. If the difference between
stack gas temperature and ambient air temperature, AT, exceeds or
equals the (AT)C, plume rise is assumed to be buoyancy dominated;
41
-------
if the difference is less than (AT)C, plume rise is assumed to be
momentum dominated (see below).
The crossover temperature difference is found by setting
Briggs' (1969, p. 59) Eq. 5.2 equal to the combination of Briggs1
(1971, p. 1031) Eqs. 6 and 7 and solving for AT. For F less than
55,
(AT)C = 0.0297v^/3Ts/d2/3. (A6)
For F equal to or greater than 55,
(AT)C = 0.00575vs:/3Ts/d1 /3. (A7)
Unstable or Neutral: Buoyancy Rise
For situations where AT exceeds or is equal to (AT)C as
determined above, buoyancy is assumed to dominate. The distance
to final rise xf (in kilometers) is determined from the
equivalent of Briggs1 (1971, p. 1031) Eq. 7, and the distance to
final rise is assumed to be 3.5x*, where x* is the distance at
which atmospheric turbulence begins to dominate entrainment. For
F less than 55,
xf = 0.049F5/8. (A8)
For F equal to or greater than 55,
xf = 0.119F2'5. (A9)
The plume height, H (in meters), is determined from the
equivalent of the combination of Briggs1 (1971, p. 1031) Eqs. 6
and 7. For F less than 55,
H = h' + 21.425F3M/u(h). (A10)
For F equal to or greater than 55,
H = h1 + 38.71F3/5/u(h). (All)
Unstable or Neutral: Momentum Rise
For situations where the stack gas temperature is less than
the ambient air temperature, it is assumed that the plume rise is
dominated by momentum. Also, if AT is less than (AT)C from Eq.
A6 or A7, it is assumed that the plume rise is dominated by
momentum. The plume height is calculated from Briggs1 (1969,
p. 59) Eq. 5.2:
H = h' + 3dvs/u(h). (A12)
Briggs (1969) suggests that this equation is most applicable when
42
-------
vs/u is greater than 4. Since momentum rise occurs quite close
to the point of release, the distance to final rise is set equal
to zero.
Stability Parameter
For stable situations, the stability parameter s is
calculated from the equation (Briggs, 1971, p. 1031):
s = g(39/az)/T. (A13)
As an approximation, for stability class E (or 5), 96/3z is taken
as 0.02 K/m, and for stability class F (or 6), 36/3z is taken as
0.035 K/m.
Stable; Crossover Between Momentum and Buoyancy
For cases with stack gas temperature greater than or equal to
ambient air temperature, it must be determined whether the plume
rise is dominated by momentum or buoyancy. The crossover
temperature difference (AT)C is found by setting Briggs' (1975,
p. 96) Eq. 59 equal to Briggs' (1969, p. 59) Eq. 4.28, and
solving for AT. The result is
(AT)C = 0.019582vsT s1/2. (A14)
If the difference between stack gas temperature and ambient air
temperature (AT) exceeds or equals (AT)C, the plume rise is
assumed to be buoyancy dominated; if AT is less than (AT)C, the
plume rise is assumed to be momentum dominated.
Stable; Buoyancy Rise
For situations where AT is greater than or equal to (AT)C,
buoyancy is assumed to dominate. The distance to final rise (in
kilometers) is determined by the equivalent of a combination of
Briggs' (1975, p. 96) Eqs. 48 and 59:
Xf = 0.0020715u(h)s~1/2. (A15)
The plume height is determined by the equivalent of Briggs'
(1975, p. 96) Eq. 59:
H = h' + 2.6{F/[u(h)s]}1/3. (A16)
The stable buoyancy rise for calm conditions (Briggs, 1975,
pp. 81-82) is also evaluated:
H = h' + 4FlMs-3/8. (A17)
The lower of the two values obtained from Eqs. A16 and A17 is
taken as the final effective height.
43
-------
By setting Eqs. A16 and A17 equal to each other and solving
for u(h), one can determine the wind speed that yields the same
plume rise for the wind conditions (A16) as does the equation for
calm conditions (A17). This wind speed is
u(h) = (2.6/4)3F1Ms1/8
= 0.2746F1'"s1/8. (A18)
For wind speed less than or equal to this value, Eq. A17
should be used for plume rise; for wind speeds greater than this
value, Eq. A16 should be used.
Stable; Momentum Rise
When the stack gas temperature is less than the ambient air
temperature, it is assumed that the plume rise is dominated by
momentum. If AT is less than (AT)C as determined by Eq. A14, it
is also assumed that the plume rise is dominated by momentum.
The plume height is calculated from Briggs1 (1969, p. 59) Eq.
4.28:
H = h' + 1.5{(v|d2T)/[4Tsu(h)]}1/3s-1/6. (A19)
The equation for unstable or neutral momentum rise (A12) is
also evaluated. The lower result of these two equations is used
as the resulting plume height.
All Conditions; Distance Less than Distance to
Final Rise (Gradual Rise)
Where gradual rise is to be estimated for unstable, neutral
or stable conditions, if the distance upwind from receptor to
source x (in kilometers), is less than the distance to final
rise, the equivalent of Briggs' (1971, p. 1030) Eq. 2 is used to
determine plume height:
H = h' + (160F1 /3x2 /3)/u(h). (A20)
This height is used only for buoyancy-dominated conditions;
should it exceed the final rise for the appropriate condition,
the final rise is substituted instead.
DISPERSION PARAMETERS
PTPLU uses the method presented by Pasquill (1961) to
estimate the dispersion potential of the atmosphere. In this
method, six stability categories are specified in terms of wind
speed and solar radiation. Stability categories are given in
Table A-l. Class A is the most unstable and class F the most
s table.
44
-------
TABLE A-l. KEY TO STABILITY CATEGORIES FROM PASQUILL (1961)*
Day
Nightt
Surface wind Incoming solar radiation Thinly overcast 3/8 or
speed (at 10m) —— or 4/8 or more less
(m/s) Strong Moderate Slight low cloud cloud
< 2
2-3
3-5
5-6
> 6
A
A-B
B
C
C
A-B
B
B-C
C-D
D
B
C
C
D
D
_
E
D
D
D
_
F
E
D
D
* The neutral class, D, should be used for overcast conditions
during day or night.
t Night refers to the period from one hour before sunset to one
hour after sunrise.
The lateral and vertical dispersion parameters are those
computed by Gifford (1960) from the original plume spreading
parameters reported by Pasquill (1961). The relevant background
of the P-G curves is summarized by Pasquill (1976) and is given
in Table A-2. It should be noted from Table A-2 that vertical
dispersion estimates were based on surface release of material.
The algorithms employed by PTPLU to evaluate the horizontal
and vertical dispersion parameters are discussed next. Similar
algorithms are employed by MPTER, RAM, PTDIS, and PTMTP.
One of the assumptions of Gaussian plume modeling is that
concentrations within the plume vary vertically and horizontally
according to a normal distribution, with the maximum
concentrations along the plume centerline. In converting plume
dimensions to standard deviations, Gifford assumed that the edge
of the plume is equivalent to the point where the concentration
is 1/10 of the centerline concentration at the same distance from
the source. This is equivalent to 2.15 a.
Vertical Dispersion
The P-G curves describing the vertical spread of plumes
been shown to fit an exponential equation of the form
az = ax ,
have
where x is the downwind distance. Values of a and b vary with
stability class and range of downwind distance. The vertical
dispersion parameter is set to 5000 m for stability class A at
distances greater than 3.11 km and for stability class B at
45
-------
TABLE A-2.
BASIS AND SCOPE OF THE ORIGINAL P-G CURVES FROM
PASQUILL (1976)
Crosswind spread
Source height
Samp 1i ng t ime
Basis for x = 0.1 to 1 km
Any (within mixed layer).
3 mi n.
Preliminary statistics of wind
direction fluctuation for a surface
roughness length of 3 cm.
Bas is for x =
10 to 100 km Extrapolation of short-range data
in the light of limited special
observations of tracer dispersion
over level terrain of mixed
roughness (implied roughness length
of 30 cm).
Ver t i cal spread
Source height
Samp 1i ng t ime
Basis for x = 0.1 to 1 km
Basis for x = 10 to 100 km
Effectively zero (surface release
of material), but offered as
usable for any height in a mixed
layer, in the absence of strong
evidence to the contrary.
Any. For elevated sources up to
about 100 m, the limiting sampling
time is roughly proportional to
the height of the source; if the
height of the source is above
100 m, the sampling time is roughly
10 min.
Properties of the wind profile over
a surface of small roughness
(roughness length of 3 cm), with
guidance from dispersion studies,
especially in regard to the effect
of thermal stratification.
As for the crosswind spread, with
guidance from early data on
the properties of the vertical
component of turbulence at heights
throughout the mixed layer.
46
-------
distances greater than 35 km. Table A-3 shows the constants
employed by PTPLU. It should be noted that the program limits
the vertical dispersion parameter to 5000 m.
Lateral Dispersion
Lateral dispersion has been estimated at 0.1 km and 100 km by
measuring the half-angle from the plume centerline to the edge of
the plume at 2.15 standard deviations. Lateral dispersion for
any downwind distance less than 100 km can be estimated by linear
interpolation, with the half-angle as the ordinate and the
logarithm of the downwind distance as the abscissa. The tangent
of this angle is 2.15 standard deviations divided by the downwind
distance. Using these facts, the horizontal dispersion parameter
(in meters) can be obtained from the interpolated half-angle as
fo1 lows:
ay = 1000 x tan(9)/2.15,
where x is the downwind distance in kilometers.
The half-angles (degrees) employed by the model at 0.1 km and
100 km for each stability class are
0.1 km
100 km
Stabi1i ty
class
A
B
C
D
E
F
Figure A-2 graphically represents the equations for the
half-angle. Although commom logarithms are used in this figure,
the program employs the natural logarithm of downwind distance
for the abscissa. Therefore, the corresponding values to 0.1 and
100 km are -2.30 and 4.6. As an example, the equation used to
determine the half-angle for stability A is obtained as follows:
30.0
22.5
15.0
10.0
7.5
5.0
12.50
10.00
7.50
5.00
3.75
2.50
where
and
9 = a ln(x) + b,
a = [(12.50 - 30.0)/(4.6 + 2.3)]
b = 30 + 2.3a,
9 = -2.5334 ln(x) + 24.167.
47
-------
TABLE A-3.
CONSTANTS FOR THE VERTICAL DISPERSION PARAMETER
EQUATION
Stability Di
class
A
0.1
0.15
0.2
0.25
0.3
0.4
B
0.2
C
D
0.3
1
3
10
E
0.1
0.3
1
2
4
10
20
F
0.2
0.7
1
2
3
7
15
30
s t ance
(km)
< 0.1
- 0.15
- 0.2
- 0.25
- 0.3
- 0.4
- 0.5
> 0.5
< 0.2
- 0.4
> 0.4
< 0.3
- 1
- 3
- 10
- 30
> 30
< 0.1
- 0.3
- 1
- 2
- 4
- 10
- 20
- 40
> 40
< 0.2
- 0.7
- 1
- 2
- 3
- 7
- 15
- 30
- 60
> 60
a
122.80
158.08
170.22
179.52
217.41
258.89
346.75
453.85
90.673
98.483
109.300
61.141
34.459
32.093
32.093
33.504
36.650
44.053
24.260
23.331
21.628
21.628
22.534
24.703
26 .970
35.420
47.618
15.209
14.457
13.953
13.953
14.823
16.187
17.836
22.651
27.074
34.219
0
1
1
1
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
b
.9447
.0542
.0932
.1262
.2644
.4094
.7283
.1166
. 93198
.98332
.09710
.91465
. 86974
.81066
.64403
.60486
.56589
.51179
.83660
.81956
. 75660
.63077
.57154
.50527
.46713
.37615
.29592
.81558
. 78407
.68465
.63227
.54503
.46490
.41507
.32681
.27436
.21716
48
-------
2.15 oy
— *• plume
centerline
INTERPOLATION OF HALF-ANGLE
FOR CALCULATION OF HORIZONTAL
DISPERSION PARAMETER
0y = (x/2.15) tan(Q)
X (km)
100
Figure A-2. Estimation of lateral dispersion parameter.
-------
The constants a and b for each stability class are as follows:
Stabi1ity
class a b
A
B
C
D
E
F
BUOYANCY-INDUCED DISPERSION
-2.5334
-1.8096
-1.0857
-0.72382
-0.54287
-0.36191
24.167
18.333
12.500
8.3333
6.2500
4.1667
For strongly buoyant plumes, entrainment as the plume ascends
through the ambient air contributes to both vertical and
horizontal spread. Pasquill (1976) suggests that this induced
dispersion, crzo, can be approximated by the plume rise divided by
3.5. The effective dispersion can then be determined by adding
var iances:
Jze
= (a2
2 \ 1 / 2
zo
a*)
where aze is the effective dispersion, and az is the dispersion
due to ambient turbulence levels. At the distance of final rise
and beyond, the induced dispersion is constant, based on the
height of final rise. At distances closer to the source, gradual
plume rise is used to determine the induced dispersion.
Since in the initial growth phases of release, the plume is
nearly symmetrical about its centerline, buoyancy-induced
dispersion in the horizontal direction, QyO, equal to that in the
vertical direction, is used:
Jyo
Ah/3.5.
To yield an effective lateral dispersion value, °~ye >
express i on is
turbulence:
combined with that for dispersion due to'
this
amb i ent
ye
a',) l
*
/2
REFERENCES
Briggs, G. A. 1969. Plume Rise. USAEC Critical Review Series,
TID-25075, National Technical Information Service,
Springfield, VA. 81 pp.
50
-------
Briggs, G. A. 1971. Some Recent Analyses of Plume Rise
Observation. In: Proceedings of the Second International
Clean Air Congress, H. M. Englund and W. T. Beery, eds.
Academic Press, New York. pp. 1029-1032.
Briggs, G. A. 1973. Diffusion Estimation for Small Emissions.
NOAA Atmos. Turb. and Diff. Lab., Contribution File No.
(Draft) 79. Oak Ridge, TN. 59 pp.
Briggs, G. A. 1975. Plume rise predictions. In: Lectures on
Air Pollution and Environmental Impact Analysis, D. A.
Haugen, ed. Amer. Meteorol. Soc., Boston, MA. pp. 59-111.
Gifford, F. A. 1960. Atmospheric dispersion calculations using
the generalized Gaussian plume model. Nucl. Safety 2:
56-59.
Holzworth, G. C. 1972. Mixing Heights, Wind Speeds, and
Potential for Urban Air Pollution Throughout the Contiguous
United States. Office of Air Programs, U. S. Environmental
Protection Agency, Research Triangle Park, NC. 118 pp.
Irwin, J. S. 1979. A theoretical variation of the wind profile
power-law exponent as a function of surface roughness and
stability. Atmos. Environ. 13: 191-194.
Pasquill, F. 1961. The estimation of dispersion of windborne
material. Meteorol. Magazine 90: 33-49.
Pasquill, F. 1974. Atmospheric Diffusion, 2nd ed. John Wiley
and Sons, New York. 429 pp.
Pasquill, F. 1976. Atmospheric Dispersion Parameters in
Gaussian Plume Modeling. Part II. Possible Requirements
for Change in the Turner Workbook Values.
EPA-600/4-76-030b, U. S. Environmental Protection Agency,
Research Triangle Park, NC. 44 pp.
U. S. Department of Health, Education, and Welfare. 1964. A
Study of Air Pollution in the Interstate Region of Lewiston,
Idaho, and Clarkson, Washington. Public Health Service Pub.
No. 999-AP-8, Cincinnati, OH. 154 pp.
51
-------
APPENDIX B
INDEXED LISTING OF FORTRAN SOURCE STATEMENTS (BATCH)
The source code and a cross-referenced listing of the batch
version of PTPLU follow. The cross-referenced listing contains
all references to statement labels, subprograms, and variables
that appear in the source program. Statement numbers appear
first in the listing and are in numerical order. Variables,
arrays, etc., appear second and are in alphabetical order.
52
-------
INDEX
PAGE
PTPLU VERSION 81036
01
co
00001*
00002*
00003*
00004*
00005*
00006*
00007*
00008*
00009*
00010*
0001 1*
00012*
00013*
00014*
00015*
00016*
00017*
00018*
00019*
00020*
00021*
00022*
00023*
00024*
00025*
00026*
00027*
00028*
00029*
00030*
00031*
00032*
00033*
00034*
00035*
00036*
00037*
00038*
00039*
00040*
00041*
00042*
00043*
00044*
00045*
00046*
00047*
00048*
00049*
00050*
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
c
c
PTPLU VERSION 81036
THIS IS THE BATCH VERSION OF PTPLU .
PTPLU ABSTRACT:
PTPLU FEATURES SEVERAL IMPROVEMENTS OF THE PTMAX
ALGORITHM. THE ANALYSIS OF CONCENTRATION HAS BEEN
EXPANDED TO INCLUDE COMPUTATIONS BASED ON INCREASED
WIND SPEED WITH HEIGHT FROM USER INPUT WIND PROFILE
EXPONENTS. OTHER FEATURES INCLUDE OPTIONS FOR CALCULATION
OF GRADUAL PLUME RISE, STACK DOWNWASH, AND INITIAL
PLUME SIZE DUE TO BUOYANCY INDUCED DISPERSION.
PTPLU AUTHORS :
THOMAS E. PIERCE AND D. BRUCE TURNER
(ON ASSIGNMENT FROM NOAA)
ENVIRONMENTAL OPERATIONS BRANCH (MD - 80)
METEOROLOGY AND ASSESSMENT DIVISION, ESRL
ENVIRONMENTAL PROTECTION AGENCY
PTPLU MODIFIED BY:
JOE CATALANO AND FRANK HALE
AEROCOMP, INC.
3303 HARBOR BLVD.
COSTA MESA, CA 92626
PTPLU SUPPORTED BY:
ENVIRONMENTAL OPERATIONS BRANCH
MAIL DROP 80, EPA
RESRCH TRI PK , NC 27711
PHONE: (919) 541-4564 FTS 629-4564
PTPLU INPUT:
DATA IN CARD TYPES 1,2 AND 4 MUST BE SEPARATED BY A SPACE
OR A COMMA TO BE COMPATIBLE WITH UNIVAC'S FREE FORMAT.
ADDITIONAL SOURCES CAN BE COMPUTED WITH EXTRA INPUT OF CARD
TYPES 3 AND 4. TWO BLANK DATA CARDS FOLLOW TO TERMINATE
EXECUTION.
««« CARD TYPE ONE (FREE FORMAT) »»»
VARIABLE DESCRIPTION
lOPT(l) GRADUAL RISE OPTION 0: DO NOT COMPUTE GRADUAL RISE
1: COMPUTE GRADUAL RISE
IOPT(2) STACK DOWNWASH OPTION 0: DON'T COMPUTE DOWNWASH
1 : DO COMPUTE DOWNWASH
IOPT(3) BUOYANCY INDUCED DISPERSION
0: NONE COMPUTED
1: USE PASQU ILL'S TECHNIQUE
T AMBIENT AIR TEMPERATURE (DEC, K)
HL MIXING HEIGHT (METERS)
PLB00010
PLB00020
PLB00030
PLB00040
PLB00050
PLB00060
PLB00070
PLB00080
PLB00090
PLB00100
PLB00110
PLB00120
PLB00130
PLB00140
PLB00150
PLB00160
PLB00170
PLB00180
PLB00190
PLB00200
PLB00210
PLB00220
PLB00230
PLB00240
PLB00250
PLB00260
PLB00270
PLB00280
PLB00290
PLB00300
PLB00310
PLB00320
PLB00330
PLB00340
PLB00350
PLB00360
PLB00370
PLB00380
PLB00390
PLB00400
PLB00410
PLB00420
PLB00430
PLB00440
PLB00450
PLB00460
PLB00470
PLB00480
PLB00490
PLB00500
-------
I N I) bi X
OOU51*
00052*
00053*
00054*
00055*
00056*
00057*
00058*
00059*
00060*
00061*
00062*
00063*
00064*
00065*
00066*
00067*
00068*
00069*
00070*
00071*
00072*
00073*
00074*
00075*
00076*
00077*
00078*
00079*
00080*
00081*
00082*
00083*
00084*
00085*
00086*
00087*
00088*
00089*
00090*
00091*
00092*
00093*
00094*
00095*
00096*
00097*
00098*
00099*
00100*
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
C
C
PAGE
PTPLU VERSION 81036
Z RECEPTOR ELEVATION (ABOVE GRND SFC, IN METERS)
««« CARD TYPE TWO (FREE FORMAT) »»»
******************************************************
* IMPORTANT MESSAGE *
* CALCULATIONS SUBMITTED TO SATISFY REGULATORY *
* REQUIREMENTS MAY REQUIRE CERTAIN PARAMETER VALUES *
* FOR WIND PROFILE EXPONENTS AND THE USE OF CERTAIN *
* OPTIONS. CHECK WITH THE APPROPRIATE EPA REGIONAL *
* OFFICE TO INSURE THAT ACCEPTABLE PARAMETER VALUES *
* ARE USED IN YOUR RUN. *
******************************************************
HANE ANEMOMETER HEIGHT (METERS)
NORMAL HEIGHT IS TEN METERS
PL(I,I=1,6) WIND PROFILE EXPONENTS
(SIX VALUES CORRESPONDING TO EACH STABILITY CLASS)
««« CARD TYPE THREE (20A4) »»»
ALP ALPHANUMERIC DATA FOR OUTPUT HEADING (80 CHARACTERS)
««« CARD TYPE FOUR (FREE FORMAT) »»»
Q
HP
TS
VS
D
SOURCE STRENGTH (G/SEC)
PHYSICAL STACK HEIGHT (M)
STACK GAS TEMPERATURE (DEC K)
STACK GAS VELOCITY (M/SEC)
STACK DIAMETER (M)
PTPLU FLOW RELATIONS
PTPLU
* READ AND CHECK INPUT DATA
* CALCULATE PORTIONS OF PLUME RISE
- IJOOP FOR EACH STABILITY
- LOOP FOR CONSTANT WIND SPEEDS WITH HEIGHT
* * PH
* * TPMX
I
* * PHX
I
* * RCON
I
* * PSIG
* ADD CAUTIONARY LABELS
PLB00510
PLB00520
PLB00530
PLB00540
PLB00550
PLB00560
PLB00570
PLB00580
PLB00590
PLB00600
PLB00610
PLB00620
PLB00630
PLB00640
PLB00650
PLB00660
PLB00670
PLB00680
PLB00690
PLB00700
PLB00710
PLB00720
PLB00730
PLB00740
PLB00750
PLB00760
PLB00770
PLB00780
PLB00790
PLB00800
PLB00810
PLB00820
PLB00830
PLB00840
PLB00850
PLB00860
PLB00870
PLB00880
PLB00890
PLB00900
PLB00910
PLB00920
PLB00930
PLB00940
PLB00950
PLB00960
PLB00970
PLB00980
PLB00990
PLB01000
-------
INDEX
PAGE
PTPLU VERSION 81036
CJl
o>
00101*
00102*
00103*
00104*
00105*
00106*
00107*
00108*
00109*
00110*
00111*
00112*
00113*
00114*
00115*
00116*
00117*
00118*
00119*
00120*
00121*
00122*
00123*
00124*
00125*
0 0 1 2 6 *
00127*
00128*
00129*
00130*
00131*
00132*
00133*
00134*
00135*
00136*
00137*
00138*
00139*
0014U*
00141*
00142*
00143*
00144*
00145*
00146*
00147*
00148*
00149*
00150*
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
- LOOP FOR WIND SPEEDS VARYING WITH HEIGHT
* * PH
TPMX
I
* *
I
PHX
RCON
* * PSIG
ADD CAUTIONARY LABELS
I
EXIT
WRITE OUTPUT
1 COMV1ON /MS/ KST,X,SY,SZ
2 COMMON /MH/ HP,VS,XFUN,DHU,ME,XFOUSE,DHUTE,DHAUE,DUTE,DHCAE,DHCAF
IMF,XFOUSF,DHUTF,DHAUF,DUTF,D
3 COMMON /ALL/ IOPT(3),U,HL,H,Z,Y,XF,DELH,HF,CMAX,XMAX,RC,PDHX,HPRM
4 DIMENSION ANOT(4), UA(14), CM(6,14), XM(6,14), HE(6,14), AD(6,14)
1 AH(6,14), ALP(20), CM2(6,14), XM2(6,14), HE2(6,14), AD2
2(6,14), AH2(6,14), UZ(6,14), PL(6), WI(6)
5 DATA UA /.5,.8,1.,1.5,2.,2.5,3.,4.,5.,7.,10.,12.,15.)20./
6 DATA ANOT /' I,1(l)l,'(2)',1(3)1/
7 IRD=5
8 IWRI=6
9 WRITE(IWRI,5432)
10 5432 FORMAT('1' ,21X, 'PTPLU (VERSION 81036 ) '/22X, 'AN IMPROVED POINT1,
.' SOURCE SCREENING MODEL'/22X,'MODIFIED BY: JOE CATALANO AND ',
.'FRANK HALE1/22X,'AEROCOMP, INC. - COSTA MESA, CA FOR THE1/
.22X,'ENVIRONMENTAL OPERATIONS BRANCH, EPA1)
C READ CARD TYPE 1, OPTIONS, TEMP, MX HT, AND RECEPTOR HT
11 READ (IRD, * ) (IOPT(I),I=1,3),T,HL,Z
C READ CARD TYPE 2, ANEMOMETER HT AND WIND SPEED EXPONENTS
12 READ (IRD, * ) HANE,(PL(I),I=1,6)
C ENTRY POINT FOR CALCULATIONS OF ADDITIONAL SOURCES.
C READ CARD TYPE 3, OUTPUT HEADING
13 10 READ (IRD,430,END=400) ALP
C READ CARD TYPE 4, SOURCE INFORMATION
14 READ (IRD, * ,END=400) Q,HP,TS,VS,D
PLB01010
PLB01020
PLB01030
PLB01040
PLB01050
PLB01060
PLB01070
PLB01080
PLB01090
PLB01100
PLB01110
PLB01120
PLB01130
PLB01140
PLB01150
PLB01160
PLB01170
PLB01180
PLB01190
PLB01200
PLB01210
PLB01220
PLB01230
PLB01240
PLB01250
PLB01260
.PLB01270
PLB01280
PLB01290
,PLB01300
PLB01310
PLB01320
PLB01330
PLB01340
PLB01350
PLB01360
PLB01370
PLB01380
PLB01390
PLB01400
PLB01410
PLB01420
PLB01430
PLB01440
PLB01450
PLB01460
PLB01470
PLB01480
PLB01490
PLB01500
-------
INDEX
PAGE
PTPLU VERSION 81036
00151*
00152*
00153*
00154*
00155*
00156*
00157*
00158*
00159*
00160*
00161*
00162*
00163*
00164*
00165*
00166*
00167*
00168*
00169*
00170*
00171*
00172*
00173*
00174*
00175*
00176*
00177*
00178*
00179*
00180*
00181*
00182*
00183*
00184*
00185*
00186*
00187*
00188*
00189*
00190*
00191*
00192*
00193*
00194*
00195*
00196*
00197*
00198*
00199*
00200*
15 DO 20 K=l,6 PLB01510
16 20 WI(K)=(HP/HANE)**PL(K) PLB01520
C WI WILL BE USED TO CALCULATE THE WIND AT STACK TOP PLB01530
C THE FOLLOWING 3 STATEMENTS CHECK TO INSURE THE REASONABLENESS PLB01540
C OF THE INPUT PARAMETERS. PLB01550
17 IF (HL.LE.0.0) HL=5000.0 PLB01560
18 IF (Z.LE.0.0) Z=0.0 PLB01570
19 IF (Q.GT.O.) GO TO 530 PLB01580
C CHECK ON EMISSION VALUE PLB01590
20 WRITE (IWRI,410) Q PLB01600
21 STOP PLB01610
C IF NO AMBIENT AIR TEMP IS INPUT 293 KELVIN IS ASSUMED. PLB01620
22 530 IF (T.EQ.O.) T=293. PLB01630
23 VF=0.785398*VS*D*D PLB01640
C CALCULATE VOLUME FLOW (VF) PLB01650
C PRINT INITIAL INFORMATION PLB01660
24 WRITE(IWRI,440)ALP PLB01670
25 WRITE(IWRI,460)T,Q PLB01680
26 WRITE(IWRI,461)HL,HP,IOPT(1),HANE,TS PLB01690
27 WRITE(IWRI,462)IOPT(2),(PL(I),1=1,3),VS PLB01700
28 WRITE(IWRl,463)IOPT(3),(PL(I),I=4,6),D,Z PLB01710
29 DELT=TS-T PLB01720
C DELT (TEMPERATURE DIFFERENCE) PLB01730
30 F=3.1214*VF*DELT/TS PLB01740
C CALCULATE F (BUOYANCY FLUX PARAMETER) PLB01750
C WRITE CALCULATED PARAMETERS. PLB01760
31 WRITE(IWRI,465)VF,F PLB01770
32 WRITE (IWRI,470)ALP PLB01780
33 PDHX=160.*F**0.33333 PLB01790
C PDHX = PARTIAL DELH(X) PLB01800
C THIS EQUATION IS PART OF THAT IN BRIGGS(1969) P. 57 PLB01810
C CHECK TO SEE IF BUOYANT OR MOMENTUM FLOW;STABLE OR UNSTABLE PLB01820
34 IF (TS.LT.T) GO TO 40 PLB01830
35 IF (F.GE.55.) GO TO 30 PLB01840
C DETERMINE DELTA-T FOR BUOYANCY-MOMENTUM CROSSOVER (F<55) FOUND PLB01850
C BY EQUATING BRIGGSU969) EQ 5.2,PAGE 59 WITH COMBINATION OF PLB01860
C BRIGGS (1971) EQUATIONS 6 AND 7, PAGE 1031 FOR F<55. PLB01870
36 DTMB=0.0297*TS*VS**0.33333/D**0.66667 PLB01880
37 IF (DELT.LT.DTMB) GO TO 40 PLB01890
C THE FOLLOWING VARIABLES HAVE BEEN NORMALIZED WITH RESPECT TO U PLB01900
C E.G. XFUN = FINAL DISTANCE (X) AS A FNCN OF U. PLB01910
C (0.049 IS 14*3.5/1000)BRIGGS(1971) EQUATION 7,F<55, AND PLB01920
C FINAL DISTANCE AS A FUNCTION OF U IS 3.5*XSTAR PLB01930
38 XFUN=0.049*F**0.625 PLB01940
C USED A COMBINATION OF BRIGGS(1971) EQNS. 6 AND 7, P. 1031 FOR PLB01950
C F<55 - DHU IS AGAIN A FUNCTION OF WIND SPEED. PLB01960
39 DHU=21.425*F**0.75 PLB01970
40 GO TO 50 PLB01980
C DETERMINE DELTA-T FOR BUOYANCY-MOMENTUM CROSSOVER (F>55) PLB01990
C FOUND BY EQUATING BRIGGS(1969) EQ. 5.2, PAGE 59 WITH PLB02000
-------
INDEX
PTPLU VERSION 81036
PAGE
00201*
00202*
00203*
00204*
00205*
00206*
00207*
00208*
00209*
00210*
00211*
00212*
00213*
00214*
00215*
00216*
00217*
00218*
00219*
00220*
00221*
00222*
00223*
00224*
00225*
00226*
00227*
00228*
00229*
00230*
00231*
00232*
00233*
00234*
00235*
00236*
00237*
00238*
00239*
00240*
00241*
00242*
00243*
00244*
00245*
00246*
00247*
00248*
00249*
00250*
C COMBINATION OF BRIGGS(1971) EQNS. 6 AND 7, PAGE 1031 FOR F>55. PLB02010
41 30 DTMB=0.00575*TS*VS**0.66667/D**0.33333 PLB02020
42 IF (DELT.LT.DTMB) GO TO 40 PLB02030
C DISTANCE TO FINAL BUOYANT RISE AS A FUNCTION OF U PLB02040
C ( 0.119 = 34*3.5/100 ) PLB02050
C FROM BRIGGSU971) EQN. 7, F>55, AND DISTANCE TO FINAL RISE IS PLB02060
C 3.5 XSTAR. PLB02070
43 XFUN=0.119*F**0.4 PLB02080
C USING A COMBINATION OF BRIGGS (1971) EQNS. 6 AND 7, PAGE 1031 PLB02090
C FOR F > 55. ' PLB02100
44 DHU=38.71*F**0.6 PLB02110
45 GO TO 50 PLB02120
C UNSTABLE-NEUTRAL MOMENTUM RISE FROM BRIGGSU969) EQN.5.2, P.59 PLB02130
C NOTE: MOST ACCURATE WHEN VS/U>4 IT TENDS TO OVERESTIMATE RISE PLB02140
C WHEN VS/U<4 (SEE BRIGGS(1975) PAGE 78, FIG. 4) PLB02150
46 40 XFUN=0. PLB02160
47 DHU=3.*VS*D PLB02170
C PREPARE PLUME RISE CALCULATIONS FOR STABLE CONDITIONS PLB02180
C SE- STABILITY E SF- STABILITY F PLB02190
C 0.196123 = 9.80616 * 0.02 PLB02200
48 50 SE=0.196123/T PLB02210
C 1.75 = 0.035/0.02 PLB02220
49 SF=1.75*SE PLB02230
C ME AND MF ARE INDICATORS FOR MOMENTUM PREDICTORS UNDER PLB02240
C STABILITIES E AND F, RESPECTIVELY. PLB02250
50 ME=0 PLB02260
51 MF = 0 PLB02270
52 IF (TS.LT.T) GO TO 60 PLB02280
C DETERMINE DELTA-T FOR BUOYANCY-MOMENTUM CROSSOVER (STABLE) PLB02290
C FOUND BY EQUATING BRIGGSU975) EQ. 59, PAGE 96 FOR STABLE PLB02300
C BUOYANT RISE WITH BRIGGS(1969) EQ. 4.25, PAGE 59 . PLB02310
C STABILITY E CALCULATIONS PLB02320
53 DTMB=0.019582*T*VS*SQRT(SE) PLB02330
54 IF (DELT.LT.DTMB) GO TO 60 PLB02340
C STABLE BUOYANT RISE (DELTA-H WILL BE DETERMINED LATER IN THE PLB02350
C PROGRAM AFTER THE WIND SPEED IS INPUT)(WIND WILL BE ALLOWED TO PLB02360
C BE LOW ENOUGH TO REQUIRE STABLE RISE IN CALM CONDITIONS) PLB02370
C BRIGGSU975) EQ. 59,PAGE 96. PLB02380
55 DHUTE=2.6*(F/SE)**0.33333 PLB02390
56 DHCAE=4.0*F**0.25/SE**0.375 PLB02400
C PLUME RISE UNDER CALM CONDITIONS, EQ 56 AND TOP P82 (BRIGGS 75) PLB02410
C COMBINATION OF BRIGGS(1975) EQNS. 48 AND 59, DISTANCE TO FINAL PLB02420
C RISE WILL BE DETERMINED AFTER THE WIND SPEED IS INTRODUCED. PLB02430
57 XFOUSE=0.0020715/SQRT(SE) PLB02440
58 GO TO 70 PLB02450
C STABLE MOMENTUM RISE FOR E STABILITY PLB02460
5» 60 ME=1 PLB02470
60 DHAUE=3.*VS*D PLB02480
C THE FOLLOWING TWO EQNS. ARE TAKEN FROM BRIGGS EQNS. 4.28, P. 59-PLB02490
C DUM IS A DUMMY EXPRESSION USED IN CALCULATING DELTA-H. PLB02500
-------
I N D E X
PAGE
PTPLU VERSION 81036
00251*
00252*
00253*
00254*
00255*
00256*
00257*
00258*
00259*
00260*
00261*
00262*
00263*
00264*
00265*
00266*
00267*
00268*
00269*
00270*
00271*
00272*
00273*
00274*
00275*
00276*
00277*
00278*
0 0 2 7 9 *
00280*
00281*
00282*
00283*
00284*
00285*
00286*
00287*
00288*
00289*
00290*
00291*
00292*
00293*
00294*
00295*
00296*
00297*
00298*
00299*
00300*
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
C
70
C
C
C
80
90
C
C
C
C
C
C
C
C
C
C
C
C
C
100
C
C
no
C
C
120
C
C
130
DUM=1 . 5*(VS*VS*D*D*T/(4.*TS))**0.33333
DUTE=DUM/SE**0. 166667
F STABILITY CASE
DTMB=0.019582*T*VS*SQRT(SF)
THE FOLLOWING EXPRESSIONS ARE SIMILAR TO THOSE USED IN THE
E-STABILITY SECTION.
IF (DELT.LT.DTMB) GO TO 80
DHUTF=2.6*(F/SF)**0.33333
DHCAF=4.0*F**0.25/SF**0. 375
PLUME RISE UNDER CALM CONDITIONS, EQ 56 AND TOP P82 (BRIGGS 75
XFOUSF=0.0020715/SQRT(SF)
GO TO 90
MF=1
DHAUF=3.*VS*D
IF (ME.EQ.O) DUM=1.5*(VS*VS*D*D*T/(4.*TS) )**0. 33333
DUTF=DUM/SF**0. 166667
DO 330 KST=1,6
GOTO (100,110,120,130,140,150), KST
SET DO LOOP LIMITS AND TEST TIME (THOUSANDS OF SECONDS) AS A
FUNCTION OF STABILITY.
IA AND IB ARE INDICIES WHICH RESTRICT THE WIND SPEEDS
PLB02510
PLB02520
PLB02530
PLB02540
PLB02550
PLB02560
PLB02570
PLB02580
PLB02590
)PLB02600
PLB02610
PLB02620
PLB02630
PLB02640
PLB02650
PLB02660
PLB02670
PLB02680
PLB02690
PLB02700
PLB02710
FOR EACH STABILITY CLASS. TM, THE TRAVEIL TIME OF THE PLUME, ISPLB02720
THE MAXIMUM TIME A PLUME IS EXPECTED TO REMAIN AT A PARTICULAR
STABILITY. THE LIMITS FOR EACH STABILITY CLASS ARE
A - 4 HOURS
B - 6 HOURS
C - 8 HOURS
D - UNLIMITED
E - 8 HOURS
F - 8 HOURS
IA=1
IB=7
TM=14.4
14.4 IS EQUIVALENT TO 4 HOURS. (IN THOUSANDS OF SECONDS)
GO TO 160
STABILITY B (60)
IA=1
IB=9
TM=21.6
21.6 IS EQUIVALENT TO 6 HOURS.
GO TO 160
STABILITY C (70)
IA=5
IB=13
TM=28.8
28.8 IS EQUIVALENT TO 8 HOURS.
GO TO 160
STABILITY D (80)
1A=1
PLB02730
PLB02740
PLB02750
PLB02760
PLB02770
PLB02780
PLB02790
PLB02800
PLB02810
PLB02820
PLB02830
PLB02840
PLB02850
PLB02860
PLB02870
PLB02880
PLB02890
PLB02900
PLB02910
PLB02920
PLB02930
PLB02940
PLB02950
PLB02960
PLB02970
PLB02980
PLB02990
PLB03000
-------
INDEX
PAGE
PTPLU VERSION 81036
00301*
00302»
00303*
00304*
00305*
00306*
00307*
00308*
00309*
00310*
00311*
00312*
00313*
00314*
00315*
00316*
00317*
00318*
00319*
00320*
00321*
00322*
00323*
00324*
00325*
00326*
00327*
00328*
00329*
00330*
00331*
00332*
00333*
00334*
00335*
00336*
00337*
00338*
00339*
00340*
00341*
00342*
00343*
00344*
00345*
00346*
00347*
00348*
00349*
00350*
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
C
C
C
140
C
150
C
C
160
C
C
170
180
C
C
C
C
C
200
240
C
C
C
C
IB=14
TM=999.
999. IS MORE THAN 24 HOURS SINCE THE MET CONDITIONS PRODUCING
D-STABILITY CAN PERSIST FOR EXTENDED PERIODS OF TIME.
GO TO 160
STABILITY E (90)
IA=5
IB=9
TM=28.8
28.8 IS EQUIVALENT TO 8 HOURS.
GO TO 160
STABILITY F (100)
IA=5
IB=9
TM IS STILL EQUAL TO 28.8 (8 HOURS).
CALCULATE FOR EACH APPROPRIATE WIND SPEED.
DO 240 I=IA,IB
U=UA(I)
DETERMINE PLUME HEIGHT.
CALL PH
H=HF
DETERMINE MAXIMUM CONCENTRATION FOR THIS EFFECTIVE HEIGHT.
CALL TPMX
DETERMINE IF CAUTIONARY NOTES ARE NEEDED.
IF (CMAX.NE.9.999E+9) GO TO 170
CM(KST, I )=CMAX
GO TO 180
CM(KST, I )=CMAX*Q
XM(KST, I )=XMAX
HE(KST,I)=H
TI IS THE TRAVEL TIME FROM SOURCE TO DISTANCE OF MAX.
TI=XMAX/U
SECTION FOR CAUTIONARY MESSAGES.
INITIALIZE CAUTIONARY FLAGS.
AH(KST.I) = ANOT(l)
AD(KST.I) = ANOT(l)
TEST FOR EXCESSIVE TRAVEL TIME.
IF(TI .GT.TM)AD(KST, I ) =ANOT(2)
CHECK FOR DIST TO MAX GREATER THAN 100 KM.
IF(XMAX.LT. 100. )GOTO200
CM(KST, I )=9.999E+9
XM(KST, I )=999.999
AD(KST, I )=ANOT(4)
TEST FOR EFFECTIVE HEIGHT MORE THAN 200 M.
IFUI.GT. 200. )AH(KST, I )=ANOT( 3)
CONTINUE
END OF LOOP FOR EACH WIND SPEED.
DO-LOOP WITH WIND PROFILE EXPONENTS
PLB03010
PLB03020
PLB03030
PLB03040
PLB03050
PLB03060
PLB03070
PLB03080
PLB03090
PLB03100
PLB03110
PLB03120
PLB03130
PLB03140
PLB03150
PLB03160
PLB03170
PLB03180
PLB03190
PLB03200
PLB03210
PLB03220
PLB03230
PLB03240
PLB03250
PLB03260
PLB03270
PLB03280
PLB03290
PLB03300
PLB03310
PLB03320
PLB03330
PLB03340
PLB03350
PLB03360
PLB03370
PLB03380
PLB03390
PLB03400
PLB03410
PLB03420
PLB03430
PLB03440
PLB03450
PLB03460
PLB03470
PLB03480
PLB03490
PLB03500
-------
INDEX
PAGE
PTPLU VERSION 81036
02
o
00351*
00352*
00353*
00354*
00355*
00356*
00357*
00358*
00359*
00360*
00361*
00362*
00363*
00364*
00365*
00366*
00367*
00368*
00369*
00370*
00371*
00372*
00373*
00374*
00375*
00376*
00377*
00378*
00379*
00380*
00381*
00382*
00383*
00384*
00385*
00386*
00387*
00388*
00389*
00390*
00391*
00392*
00393*
00394*
00395*
00396*
00397*
00398*
00399*
00400*
118 DO 320 I=IA,IB PLB03510
119 U=UA(I)*WI(KST) PLB03520
C CALCULATE THE EFFECTIVE STACK HEIGHT PLB03530
C CALL THE PLUME RISE ROUTINE PLB03540
120 CALL PH PLB03550
121 H=HF PLB03560
C CALCULATE MAXIMUM CNCENTRATION AND PLB03570
C LOCATE THE DISTANCE TO MAX CONCENTRATION FOR THIS PLB03580
C WIND SPEED AND STABILITY BY CALLING TPMX PLB03590
122 CALL TPMX PLB03600
123 IF (CMAX.NE.9.999E+9) GO TO 250 PLB03610
124 CM2(KST,I)=CMAX PLB03620
125 GO TO 260 PLB03630
126 250 CM2(KST,I)=CMAX*Q PLB03640
127 260 XM2(KST,I)=XMAX PLB03650
128 HE2(KST,I)=H PLB03660
129 UZ(KST,I)=U PLB03670
130 TI=XMAX/U PLB03680
C SECTION FOR CAUTIONARY MESSAGES. PLB03690
C INITIALIZE CAUTIONARY FLAGS. PLB03700
131 AH2(KST,I) = ANOT(l) PLB03710
132 AD2(KST,I) = ANOT(l) PLB03720
C TEST FOR EXCESSIVE TRAVEL TIME. PLB03730
133 IF(TI.GT.TM)AD2(KST,I) = ANOT(2) PLB03740
C CHECK FOR DIST TO MAX GREATER THAN 100 KM. PLB03750
134 IF(XMAX.LT.100.)GOTO201 PLB03760
135 CM2(KST,I)=9.999E+9 PLB03770
136 XM2(KST,I)=999.999 PLB03780
137 AD2(KST,I)=ANOT(4) PLB03790
C TEST FOR EFFECTIVE HEIGHT MORE THAN 200 M. PLB03800
138 201 IF(H.GT.200.)AH2(KST,I)=ANOT(3) PLB03810
139 320 CONTINUE PLB03820
C END OF LOOP FOR EXTRAPOLATED WIND SPEEDS. PLB03830
140 330 CONTINUE PLB03840
C END OF LOOP FOR EACH STABILITY. PLB03850
C PLB03860
C WRITE OUTPUT SUMMARY TABLE. PLB03870
141 KST=1 PLB03880
142 WRITE (IWRI,480)HANE PLB03890
143 WRITE(IWRI ,482) PLB03900
144 WRITE (IWRI,485) PLB03910
145 DO 340 N=l,7 PLB03920
146 WRITE (IWRI,490) KST,UA(N),CM(KST,N),XM(KST,N),AD(KST,N),HE(KST,N)PLB03930
1,AH(KST,N),UZ(KST,N),CM2(KST,N),XM2(KST,N),AD2(KST,N),HE2(KST,N).APLB03940
2H2(KST,N) PLB03950
147 340 CONTINUE PLB03960
148 KST=2 PLB03970
149 WRITE (IWRI,480)HANE PLB03980
150 WKITE(IWRI,482) PLB03990
151 WRITE (IWRI,485) PLB04000
-------
INDEX
PAGE
PTPLU VERSION 81036
00401*
00402*
00403*
00404*
00405*
00406*
00407*
00408*
00409*
00410*
00411*
00412*
00413*
00414*
00415*
00416*
00417*
00418*
00419*
00420*
00421*
00422*
00423*
00424*
00425*
00426*
00427*
00428*
00429*
00430*
00431*
00432*
00433*
00434*
00435*
00436*
00437*
00438*
00439*
00440*
00441*
00442*
00443*
00444*
00445*
00446*
00447*
00448*
00449*
00450*
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
163
184
185
186
187
188
189
350
360
370
380
390
400
C
410
430
DO 350 N=l,9 PLB04010
WRITE (IWRI ,490) KST,UA(N),CM(KST,N),XM(KST,N),AD(KST,N), IIE(KST,N)PLB04020
1,AH(KST,N),UZ(KST,N),CM2(KST,N),XM2(KST,N),AD2(KST,N),HE2(KST,N),APLB04030
2H2(KST,N) PLB04040
CONTINUE PLB04050
KST=3 PLB04060
WRITE (IWRI,480)HANE PLB04070
WRITE(IWRI,482) PLB04080
WRITE (IWRI,485) PLB04090
DO 360 N = 5, 13 PLB04100
WRITE (IWRI,490) KST,UA(N),CM(KST,N),XM(KST,N),AD(KST,N),HE(KST,N)PLB04110
1 ,AH(KST,N),UZ(KST,N),CM2(KST,N),XM2(KST,N),AD2(KST,N),HE2(KST,N).APLB04120
2H2(KST,N) PLB04130
CONTINUE PLB04140
KST=4 PLB04150
WRITE (IWRI,480)HANE PLB04160
WRITE(IWRI,482) PLB04170
WRITE (IWRI,485) PLB04180
DO 370 N=l, 14 PLB04190
WRITE (IWRI,490) KST,UA(N),CM(KST,N),XM(KST,N),AD(KST,N),HE(KST,N)PLB04200
1,AH(KST,N),UZ(KST,N),CM2(KST,N),XM2(KST,N),AD2(KST,N),HE2(KST,N).APLB04210
2H2(KST,N) PLB04220
CONTINUE PLB04230
KST=5 PLB04240
WRITE ( IWRI ,480 )HANE PLB04250
WR1TE(IWRI,482) PLB04260
WRITE (IWRI,485) PLB04270
DO 380 N=5,9 PLB04280
WRITE (IWRI,490) KST,UA(N),CM(KST,N),XM(KST,N),AD(KST,N),HE(KST,N)PLB04290
1,AH(KST,N),UZ(KST,N),CM2(KST,N),XM2(KST,N),AD2(KST,N),HE2(KST,N).APLB04300
2H2(KST,N) PLB04310
CONTINUE PLB04320
KST=6 PLB04330
WRITE (6,480)HANE PLB04340
WRITE(IWRI,482) PLB04350
WRITE (6,485) PLB04360
DO 390 N=5,9 PLB04370
WRITE (IWRI,490) KST,UA(N),CM(KST,N),XM(KST,N),AD(KST,N),UE(KST,N)PLB04380
1,AH(KST,N),UZ(KST,N),CM2(KST,N),XM2(KST,N),AD2(KST,N),HE2(KST,N).APLB04390
2H2(KST,N)
CONTINUE
WRITE (IWRI,500)
WRITE (IWRI,510)
WRITE (IWRI,520)
GO TO 10
STOP
FORMAT (IX,1 EMISSION OF '.F10.4,1 G/SEC NOT ACCEPTABLE.'/1
1 EXECUTION TERMINATED - CHECK INPUT DATA *** ' )
FORMAT (20A4)
PLB04400
PLB04410
PLB04420
PLB04430
PLB04440
PLB04450
PLB04460
PLB04470
PLB04480
PLB04490
PLB04500
-------
INDEX
PAGE 10
PTPLU VERSION 81036
00451*
00452*
00453*
00454*
00455*
00456*
00457*
00458*
00459*
00460*
00461*
00462*
00463*
00464*
00465*
00466*
00467*
00468*
00469*
00470*
00471*
00472*
00473*
00474*
00475*
00476*
00477*
00478*
00479*
00480*
00481*
00482*
00483*
00484*
00485*
00486*
00487*
00488*
00489*
00490*
00491*
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
440
460
461
462
463
465
470
480
482
485
490
500
510
520
C
C
FORMAT(/49X, '»> INPUT PARAMETERS <«'/' *** TITLE*** ',20A4) PLB04510
FORMAT(/IX,'***OPT1ONS***',24X, PLB04520
1 '* "METEOROLOGY***' ,33X,'***SOURCE***'/1X,'IF = 1, USE OPTION', PLB04530
219X,'AMBIENT AIR TEMPERATURE =',F9.2,' (K)',12X, PLB04540
3'EMISSION RATE =',F9.2,' (G/SEC)') PLB04550
FORMATdX,'IF = 0, IGNORE OPTION',16X,'MIXING HEIGHT1,11X, PLB04560
5'=',F9.2,' (M)',12X,'STACK HEIGHT =',F9.2,' (M)'/1X, PLB04570
6'IOPTd) = ',11,' (GRAD PLUME RISE)',8X,'ANEMOMETER HEIGHT', PLBQ4580
77X,'=',F9.2,' (M)',12X,'EXIT TEMP. =',F9.2,' (K)') PLB04590
FORMATdX, ' IOPT( 2) = ',11,' ( STACK DOWNWASH)', 9X, PLB04600
9'WIND PROFILE EXPONENTS = A:',F4.2,', B:',F4.2,', C: ' , PLB04610
.F4.2,2X,'EXIT VELOCITY =',F9.2,' (M/SEC)') PLB04620
FORMATdX,'IOPT(3) = ',11,' (BUOY. INDUCED DISP.)',SOX, PLB04630
.'D: ' ,F4.2,' , E:',F4.2,1, F:' ,F4.2,2X,'STACK DIAM. =', PLB04640
.F9.2,' (M)'/'0***RECEPTOR HEIGHT*** =',F9.2,' (M)') PLB04650
FORMAT (/47X, ' >»CALCULATED PARAMETERS <«',/1X,'VOLUMETRIC FLO' , ' PLB04660
1W =',F9.2,' (M**3/SEC)',11X,'BUOYANCY FLUX PARAMETER =',F9.2, PLB04670
2' (M**4/SEC**3)') PLB04680
FORMAT(//1X,20A4) PLB04690
FORMAT (1H0.20X,'****WINDS CONSTANT WITH HEIGHT****', PLB04700
.9X,'****STACK TOP WINDS (EXTRAPOLATED FROM ',F5.1,' METERS)', PLB04710
.'****') PLB04720
FORMAT(' STABILITY',3X,'WIND SPEED', PLB04730
13X,'MAX CONC',3X,'DIST OF MAX',3X,' PLUME HT ',7X,'WIND SPEED', PLB04740
23X,'MAX CONC',3X,'DIST OF MAX',3X,' PLUME HT') PLB04750
FORMATdSX,'(M/SEC) (G/CU M)',7X,4H(KM),10X,3H(M),12X, PLB04760
4'(M/SEC) (G/CU M)1,7X,4H(KM),10X,3H(M)) PLB04770
FORMAT (4X,II,10X.F6.2,3X,1PE10.4,4X,OPF8.3,A3,IX,F8.1,A3,9X, PLB04780
1F6.2.3X,1PE10.4,4X,OPF8.3,A3,1X,F8.1,A3) PLB04790
FORMAT (1HO,1 (1) THE DISTANCE TO THE POINT OF MAXIMUM CONCENTRATIPLB04800
ION IS SO GREAT THAT THE SAME STABILITY IS NOT LIKELY'/1H , PLB04810
2' TO PERSIST LONG ENOUGH FOR THE PLUME TO TRAVEL THIS FAR.'PLB04820
3) PLB04830
FORMAT CO (2) THE PLUME IS CALCULATED TO BE AT A HEIGHT WHERE CARPLB04840
IE SHOULD BE USED IN INTERPRETING THE COMPUTATION.1) PLB04850
FORMAT (1HO,1 (3) NO COMPUTATION WAS ATTEMPTED FOR THIS HEIGHT AS PLB04860
1THE POINT OF MAXIMUM CONCENTRATION IS GREATER THAN 100 KILOMETERS'PLB04870
2/1H ,' FROM THE SOURCE.1) PLB04880
PLB04890
END PLB04900
PLB04910
-------
OJ
CO
INDEX
SYMBOL
10
20
30
40
50
60
70
80
90
100
110
120
130
140
ISO
160
170
180
200
201
240
250
260
320
330
340
350
360
370
380
390
400
410
430
440
460
461
462
463
465
470
480
482
485
490
500
510
520
PAGE 11
PTPLU VERSION 81036
REFERENCES
13*
15
35
34
40
52
58
64
68
74
74
74
74
74
74
78
102
104
112
134
97
123
125
118
73
145
152
159
166
173
180
13RD
20WR
13RD
24WR
25WR
26WR
27WR
28WR
31WR
32WR
142VVR
143WR
144WR
146WR
183WR
184WR
185WR
186
16*
41*
37
45
54
63*
69*
73*
75*
79*
83*
87*
91*
95*
82
105*
106*
116*
138*
117*
126*
127*
139*
140*
147*
154*
161*
168*
175*
182*
14RD
188*
189*
190*
191*
192*
193*
194*
195*
196*
149WR
150WR
151WR
153WR
201*
202*
203*
42
48*
59*
46«
86
90
94
97'
187*
156WR
157WR
158WR
160WR
163WR
164WR
165WR
167WR
170WR
171WR
172WR
174WR
177WR 197*
178WR 198*
179WR 199*
181WR 200*
-------
05
INDEX
530
5432
AD
AD 2
AH
All 2
ALL
ALP
ANOT
CM
CM 2
CMAX
D
DELH
DELT
DHAUE
DHAUF
DHCAE
DIICAF
DHU
DHUTE
DIfUTF
DTMB
DUM
DUTE
DUTF
F
H
HANE
HE
HE2
HF
HL
HP
HPRM
I
1A
IB
I OPT
IRD
IWRI
PAGE 12
PTPLU VERSION 81036
19
9WR
4DI
4DI
4DI
4DI
3OO
4DI
4DI
137
4DI
4DI
SCO
2CO
61
3CO
29 =
2CO
2CO
2CO
2CO
2CO
2CO
2CO
36 =
61 =
2CO
2CO
30 =
65
300
12RD
4DI
4DI
3CO
SCO
2CO
SCO
11RD
103
116
133
75 =
76 =
SCO
7 =
8 =
142WR
158WR
178WR
22»
10*
110 =
132 =
109 =
131 =
13RD
6 DA
138
103 =
124 =
102
14RD
70
30
60 =
70 =
56 =
66 =
39 =
55 =
65 =
37
62
62 =
72 =
31WR
66
100 =
16
107 =
128 =
100
11RD
14RD
11RD
105
118
135
79 =
80 =
11RD
11RD
9WR
143WR
160WR
181WR
111 =
133 =
116 =
138 =
24WR
109
105 =
126 =
103
23
71
37
44 =
41 =
71 =
33
107
26WR
146WR
146WR
121
17
16 '
12RD
106
119
136
83 =
84 =
26WR
12RD
20WR
144WR
163WR
183WR
115 =
137 =
146WR
146WR
32WR
110
113 =
135 =
105
23
71
42
47 =
42
72
35
116
142WR
153WR
153WR
17 =
26WR
12RD
107
124
137
87 =
88 =
27WR
13RD
24WR
146WR
164WR
184WR
146WR
146WR
153WR
153WR
111
146WR
146WR
123
28WR
54
53 =
38
121 =
149WR
160WR
16 OWli
26WR
27WR
109
126
138
91 =
92 =
28WR
14RD
25WR
149WR
165WR
185WR
153WR
153WR
160WR
160WR
115
153WR
153WR
124
36
64
54
39
128
156WR
167WR
167WR
27WR
110
127
95 =
96 =
26WR
150WR
167WR
160WR
160WR
167WR
167WR
116
160WR
160WR
126
41
63 =
43
138
163WR
174WR
174WR
28WR
111
128
97
97
27WR
151WR
170WR
167WR
167WR
174WR
174WR
131
167WR
167WR
47
64
44
170WR
181WR
181WR
28VVR
113
129
118
118
28WR
153WR
171WR
174WR
174WR
181WR
181WR
132
174WR
174WR
60
55
177WR
97
114
131
31WR
156WR
172WR
181WR
181WR
133
181WR
181WR
61
56
98
115
132
32WR
157WR
174WR
-------
01
INDEX
K
KST
PAGE 13
PTPLU VERSION 81036
ME
MF
Mil
MS
N
PDHX
PH
PL
Q
RC
SE
SF
SQRT
SY
sz
T
TI
TM
TPMX
TS
U
UA
UZ
VF
VS
Wl
X
XF
XFOUSE
15
ICO
113
131
146WR
148 =
153WR
160WR
167WR
174WR
174WR
181WR
20O
2CO
200
ICO
145
146WR
153WR
160WR
167WR
167WR
174WR
181WR
3CO
99
4DI
14RD
SCO
48 =
49 =
53
ICO
ICO
11RD
63
108 =
77 =
101
14RD
SCO
4DI
4DI
23 =
2CO
61
4D1
ICO
3CO
2CO
16
73
114
132
146WR
153WR
153WR
160WR
167WR
174WR
174WR
181WR
50 =
51 =
146WR
146WR
153WR
160WR
167WR
167WR
174WR
181WR
33 =
120
12RD
19
49
63
57
22
71
111
81 =
122
26WR
98 =
5 DA
129 =
30
14RD
63
16 =
57 =
16
74
115
133
146WR
153WR
153WR
160WR
167WR
174WR
176 =
181WR
59 =
69 =
146WR
146WR
153WR
160WR
167WR
173
174WR
181WR
16
20WR
53
65
63
22 =
130 =
85 =
29
108
98
146WR
31WR
23
70
119
103
1 16
135
146WR
153WR
155 =
160WR
167WR
174WR
181WR
181WR
71
146WR
152
153WR
160WR
167WR
174WR
174WR
181WR
27WR
25WR
55
66
67
25WR
133
89 =
30
119 =
119
153WR
27WR
71
105
119
136
146WR
153WR
160WR
160WR
167WR
174WR
181WR
181WR
146WR
153WR
153WR
160WR
167WR
174WR
174WR
181WR
28WR
105
56
67
29
93 =
34
129
146WR
160WR
36
71
106
124
137
146WR
153WR
160WR
160WR
167WR
174WR
181WR
146WR
153WR
153WR
160WR
167WR
174WR
180
181WR
126
57
72
34
111
36
130
153WR
167WR
41
107
126
138
146WR
153WR
160WR
162 =
167WR
174WR
181WR
146VVR
153WR
159
160WR
167WR
174WR
181WR
181WR
62
48
133
41
160WR
174WR
47
109
127
141 =
146WR
153WR
160WR
167WR
167WR
174WR
181WR
146WR
153WR
160WR
160WR
167WR
174WR
181WR
181WR
52
52
167WR
181WR
53
110
128
146WR
146WR
153WR
160WR
167WR
167WR
174WR
181WR
146WR
153WR
160WR
160WR
167WR
174WR
181WR
53
61
174WR
60
111
129
146WR
146WR
153WR
160WR
167WR
169 =
174WR
181WR
146WR
153WR
160WR
166
167WR
174WR
181WR
61
71
181WR
61
-------
INDEX
PTPLU VERSION 81036
PAGE 14
XFOUSF -
XFUN
XM
XM2
XMAX
Y
Z
2CO
2OO
4DI
41)1
3CO
3CO
3OO
67 =
38 =
106 =
127 =
106
11RD
43 =
114 =
136 =
108
18
46 =
146WR
146WR
112
18 =
153WR
153WR
127
28WR
160WR
160WR
130
167WR
167WR
134
174WR
174WR
181WR
181WR
Oi
05
-------
INDEX
PAGE 15
SUBROUTINE RCON
00492*
00493*
00494*
00495*
00496*
00497*
00498*
00499*
00500*
00501*
00502*
00503*
00504*
00505*
00506*
00507*
00508*
00509*
00510*
00511*
00512*
00513*
00514*
00515*
00516*
00517*
00518*
00519*
00520*
00521*
00522*
00523*
00524*
00525*
00526*
00527*
00528*
00529*
00530*
00531*
00532*
00533*
00534*
00535*
00536*
00537*
00538*
00539*
00540*
00541*
SUBROUTINE RCON
C
C->->->->SECTION RCON.A - COMMON.
COMV10N /MS/KST,X,SY,SZ
COMMON /ALL/IOPT(3),U,HL,H,Z,Y,XF,DELH,HF,CMAX,XMAX,RC,PDHX,HPRM
C
C
C->->->->SECTION RCON.B - EXPLANATIONS AND COMPUTATIONS
COMMON TO ALL CONDITIONS.
RCON DETERMINES RELATIVE CONCENTRATIONS, CHI/Q, FROM POINT SOURCES.
RCON CALLS PSIG FOR THE DISPERSION COEFFICENTS.
THE INPUT VARIABLES ARE:
U WIND SPEED (M/SEC)
Z RECEPTOR HEIGHT (M)
H EFFECTIVE STACK HEIGHT (M)
HL MIXING HEIGHT- TOP OF NEUTRAL OR UNSTABLE LAYER(M).
X DISTANCE RECEPTOR IS DOWNWIND OF SOURCE (KM)
Y DISTANCE RECEPTOR IS CROSSWIND FROM SOURCE (KM)
KST STABILITY CLASS
DELH PLUME RISE(METERS)
THE OUTPUT VARIABLES ARE
HORIZONTAL DISPERSION PARAMETER
VERTICAL DISPERSION PARAMETER
RELATIVE CONCENTRATION (SEC/M**3)
OUTPUT UNIT CONTROL
PLB04920
PLB04930
PLB04940
PLB04950
PLB04960
PLB04970
PLB04980
PLB04990
PLB05000
PLB05010
PLB05020
PLB05030
PLB05040
PLB05050
PLB05060
PLB05070
PLB05080
PLB05090
PLB05100
PLB05110
PLB05120
PLB05130
PLB05140
PLB05150
PLB05160
PLB05170
PLB05180
PLB05190
PLB05200
SY
SZ
RC RELATIVE CONCENTRATION (SEC/M**3) ,CHI/Q
IWRI
4 IWRI=6
C THE FOLLOWING EQUATION IS SOLVED --
C RC = (1/(2*PI*U*SIGMA Y*SIGMA Z))* (EXP(-0.5*(Y/SIGMA Y)**2))
C (EXP(-0.5*((Z-H)/SIGMA Z)**2) +• EXP(-0.5*((Z+H)/SIGMA Z)**2)PLB05210
C PLUS THE SUM OF THE FOLLOWING 4 TERMS K TIMES (N=1,K) -- PLB05220
C FOR NEUTRAL OR UNSTABLE CASES: PLB05230
C TERM 1- EXP(-0.5*((Z-H-2NL)/SIGMA Z)**2) PLB05240
C TERM 2- EXP(-0.5*((Z+H-2NL)/SIGMA Z)**2) PLB05250
C TERM 3- EXP(-0.5*((Z-H+2NL)/SIGMA Z)**2) PLB05260
C TERM 4- EXP(-0.5*((Z+H+2NL)/SIGMA Z)**2) PLB05270
C NOTE THAT MIXING HEIGHT- THE TOP OF THE NEUTRAL OR UNSTABLE LAYER- PLB05280
C HAS A VALUE ONLY FOR STABILITIES 1-4, THAT IS, MIXING HEIGHT, PLB05290
C THE HEIGHT OF THE NEUTRAL OR UNSTABLE LAYER, DOES NOT EXIST FOR STABLEPLB05300
C LAYERS AT THE GROUND SURFACE- STABILITY 5 OR 6. PLB05310
C THE ABOVE EQUATION IS SIMILAR TO EQUATION (5.8) P 36 IN PLB05320
C WORKBOOK OF ATMOSPHERIC DISPERSION ESTIMATES WITH THE ADDITIONPLB05330
C OF THE EXPONENTIAL INVOLVING Y. PLB05340
C IF STABLE, SKIP CONSIDERATION OF MIXING HEIGHT. PLB05350
5 IF (KST.GE.5) GO TO 50 PLB05360
C IF THE SOURCE IS ABOVE THE LID, SET RC = 0., AND RETURN. PLB05370
6 IF (H.GT.HL) GO TO 20 PLB05380
7 IF (Z-HL) 50,50,40 PLB05390
8 20 IF (Z.LT.HL) GO TO 40 PLB05400
9 WRITE (IWRI,470) PLB05410
-------
I N D E X
PAGE 16
SUBROUTINE RCON
CTV
oo
00542*
00543*
00544*
00545*
00546*
00547*
00548*
00549*
00550*
00551*
00552*
00553*
00554*
00555*
00556*
00557*
00558*
00559*
00560*
00561*
00562*
00563*
00564*
00565*
00566*
00567*
00568*
00569*
00570*
00571*
00572*
00573*
00574*
00575*
00576*
00577*
00578*
00579*
00580*
00581*
00582*
00583*
00584*
00585*
00586*
00587*
00588*
00589*
00590*
00591*
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
THIS AVOIDS
40 RC=0.
RETURN
C IF X IS LESS THAN 1 METER, SET RC=0. AND RETURN.
C PROBLEMS OF INCORRECT VALUES NEAR THE SOURCE.
50 IF (X.LT.0.001) GO TO 40
C CALL PSIG TO OBTAIN VALUES FOR SY AND SZ
CALL PSIG
C SY = SIGMA Y, THE STANDARD DEVIATION OF CONCENTRATION IN THE
C Y-DIRECTION (M)
C SZ = SIGMA Z, THE STANDARD DEVIATION OF CONCENTRATION IN THE
C Z-DIRECTION (M)
C IF IOPT(3) = 1, CONSIDER BUOYANCY INDUCED DISPERSION
IF (IOPT(3).EQ.O) GO TO 70
DUM=DELH/3.5
IF(IOPT(1).EQ.O. .AND. X.LT.XF)DUM=PDHX*X**0.666667/(3.5*U)
DUM=DUM*DUM
SY=SQRT(SY*SY+DUM)
SZ=SQRT(SZ*SZ+DUM)
70 Cl=l.
IF (Y.EQ.0.0) GO TO 100
YD=1000.*Y
C YD IS CROSSWIND DISTANCE IN METERS.
DUM=YD/SY
T£MP=0.5*DUM*DUM
IF (TEMP.GE.50.) GO TO 40
C1=EXP(TEMP)
100 IF (KST.GT.4) GO TO 120
IF (HL.LT.5000.) GO TO 200
C IF STABLE CONDITION OR UNLIMITED MIXING HEIGHT,
C USE EQUATION 3.2 IF Z = 0, OR EQ 3.1 FOR NON-ZERO Z.
C (EQUATION NUMBERS REFER TO WORKBOOK OF ATMOSPHERIC DISPERSION PLB05720
C ESTIMATES.) PLB05730
120 C2=2.*SZ*SZ PLB05740
IF (Z) 40,130,150 PLB05750
C NOTE: AN ERRONEOUS NEGATIVE Z WILL RESULT IN ZERO CONCENTRATIONSPLBO5760
C PLB05770
C->->->->SECTION RCON.C - STABLE OR UNLIMITED MIXING, Z IS ZERO. PLB05780
C PLB05790
130 C3=H*H/C2 PLB05800
PLB05810
PLB05820
PLB05830
PLB05840
PLB05850
PLB05860
PLB05870
PLB05880
PLB05890
PLB05900
PLB05910
PLB05420
PLB05430
PLB05440
PLB05450
PLB05460
PLB05470
PLB05480
PLB05490
PLB05500
PLB05510
PLB05520
PLB05530
PLB05540
PLB05550
PLB05560
PLB05570
PLB05580
PLB05590
PLB05600
PLB05610
PLB05620
PLB05630
PLB05640
PLB05650
PLB05660
PLB05670
PLB05680
PLB05690
PLB05700
PLB05710
C3=H*H/C2
IF (C3.GE.50.) GO TO 40
A2=l./EXP(C3)
C WADE EQUATION 3.2.
RC=A2/(3.14159*U*SY*SZ*C1)
RETURN
C
C->->->->SECTION RCON.D - STABLE OR UNLIMITED MIXING, Z IS NON-ZERO.
C
150 A2=0.
A3 = 0.
CA=Z-H
-------
INDEX
PAGE 17
00592*
00593*
00594*
00595*
00596*
00597*
00598*
00599*
00600*
00601*
00602*
00603*
00604*
00605*
00606*
00607*
00608*
00609*
00610*
00611*
00612*
00613*
00614*
00615*
00616*
00617*
00618*
00619*
00620*
00621*
00622*
00623*
00624*
00625*
00626*
00627*
00628*
00629*
00630*
00631*
00632*
00633*
00634*
00635*
00636*
00637*
00638*
00639*
00640*
00641*
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
170
C
190
SUBROUTINE RCON
CB=Z+H
C3=CA*CA/C2
C4=CB*CB/C2
IF (C3.GE.50.) GO TO 170
A2=1./EXP(C3)
IF (C4.GE.50.) GO TO 190
A3 = l ./EXP(C4)
WADE EQUATION 3.1.
RC=(A2+A3)/(6.28318*U*SY*SZ*C1)
RETURN
C
C->->->->SECTION RCON.E - UNSTABLE, ASSURED OF UNIFORM MIXING.
C
C
C
C
C
200
C
IF SIGMA-Z IS GREATER THAN 1.6 TIMES THE MIXING HEIGHT,
THE DISTRIBUTION BELOW THE MIXING HEIGHT IS UNIFORM WITH
HEIGHT REGARDLESS OF SOURCE HEIGHT OR RECEPTOR HEIGHT BECAUSE
OF REPEATED EDDY REFLECTIONS FROM THE GROUND AND THE MIXING HT
IF (SZ/HL.LE.1.6) GO TO 220
WADE EQUATION 3.5.
RC=1./(2.5066*U*SY*HL*C1)
RETURN
C INITIAL VALUE OF AN SET = 0.
C AN - THE NUMBER OF TIMES THE SUMMATION TERM IS EVALUATED
C AND ADDED IN.
220 AN=0.
IF (Z) 40,380,230
C
C->->->->SECTION RCON.F - UNSTABLE, CALCULATE MULTIPLE EDDY
C REFLECTIONS, Z IS NON-ZERO.
C
C STATEMENTS 220-260 CALCULATE RC, THE RELATIVE CONCENTRATION,
C USING THE EQUATION DISCUSSED ABOVE. SEVERAL INTERMEDIATE
C VARIABLES ARE USED TO AVOID REPEATING CALCULATIONS.
C CHECKS ARE MADE TO BE SURE THAT THE ARGUMENT OF THE
C EXPONENTIAL FUNCTION IS NEVER GREATER THAN 50 (OR LESS THAN
C -50).
C CALCULATE MULTIPLE EDDY REFLECTIONS FOR RECEPTOR HEIGHT Z.
230 Al=l./(6.28318*U*SY*SZ*C1)
C2=2.*SZ*SZ
A2 = 0.
A3 = 0.
CA=Z-H
CB=Z+H
C3=CA*CA/C2
C4=CB*CB/C2
IF (C3.GE.50.) GO TO 250
A2=1./EXP(C3)
250 IF (C4.GE.50.) GO TO 270
A3=1./EXP(C4)
270 SUM=0.
PLB05920
PLB05930
PLB05940
PLB05950
PLB05960
PLB05970
PLB05980
PLB05990
PLB06000
PLB06010
PLB06020
PLB06030
PLB06040
PLB06050
PLB06060
PLB06070
PLB06080
PLB06090
PLB06100
PLB06110
PLB06120
PLB06130
PLB06140
PLB06150
PLB06160
PLB06170
PLB06180
PLB06190
PLB06200
PLB06210
PLB06220
PLB06230
PLB06240
PLB06250
PLB06260
PLB06270
PLB06280
PLB06290
PLB06300
PLB06310
PLB06320
PLB06330
PLB06340
PLB06350
PLB06360
PLB06370
PLB06380
PLB06390
PLB06400
PLB06410
-------
INDEX
PAGE 18
SUBROUTINE RCON
00642*
00643*
00644*
00645*
00646*
00647*
00648*
00649*
00650*
00651*
00652*
00653*
00654*
00655*
00656*
00657*
00658*
00659*
00660*
00661*
00662*
00663*
00664*
00665*
00666*
00667*
00668*
00669*
00670*
00671*
00672*
00673*
00674*
00675*
00676*
00677*
00678*
00679*
00680*
00681*
00682*
00683*
00684*
00685*
00686*
00687*
00688*
00689*
00690*
00691*
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
280
300
320
340
•360
C
C->->
C
C
C
C
380
400
410
THL=2.*HL
AN=AN+1 .
A5 = 0.
A6 = 0.
A7 = 0.
C5=AN*THL
CC=CA-C5
CD=CB-C5
CE=CA+C5
CF=CB+C5
C6=CC*CC/C2
C7=CD*CD/C2
C8=CE*CE/C2
C9=CF*CF/C2
IF (C6.GE.50.) GO TO 300
A4=1./EXP(C6)
IF (C7.GE.50.) GO TO 320
A5=1./EXP(C7)
IF (C8.GE.50.) GO TO 340
A6=1./EXP(C8)
IF (C9.GE.50.) GO TO 360
A7=1./EXP(C9)
T=A4+A5+A6+A7
SUM=SUM+T
IF (T.GE.0.01) GO TO 280
RC=A1*(A2+A3+SUM)
RETURN
->->SECTION RCON.G - UNSTABLE, CALCULATE MULTIPLE EDDY
REFLECTIONS, Z IS ZERO.
CALCULATE MULTIPLE EDDY REFLECTIONS FOR GROUND LEVEL RECEPTOR
HEIGHT.
A1=1./(6.28318*U*SY*SZ*C1)
A2 = 0 .
C2=2.*SZ*SZ
C3=H*H/C2
IF (C3.GE.50. ) GO TO 400
A2=2./EXP(C3)
SUM=0.
THL=2.*HL
AN=AN+1.
A4 = 0.
A6 = 0.
C5=AN*THL
CC=H-C5
CE=H+C5
C6=CC*CC/C2
C8=CE*CE/C2
PLB06420
PLB06430
PLB06440
PLB06450
PLB06460
PLB06470
PLB06480
PLB06490
PLB06500
PLB06510
PLB06520
PLB06530
PLB06540
PLB06550
PLB06560
PLB06570
PLB06580
PLB06590
PLB06600
PLB06610
PLB06620
PLB06630
PLB06640
PLB06650
PLB06660
PLB06670
PLB06680
PLB06690
PLB06700
PLB06710
PLB06720
PLB06730
PLB06740
PLB06750
PLB06760
PLB06770
PLB06780
PLB06790
PLB06800
PLB06810
PLB06820
PLB06830
PLB06840
PLB06850
PLB06860
PLB06870
PLB06880
PLB06890
PLB06900
PLB06910
-------
INDEX
PAGE 19
SUBROUTINE RCON
00692*
00693*
00694*
00695*
00696*
00697*
00698*
00699*
00700*
00701*
00702*
00703*
00704*
00705*
00706*
00707*
00708*
00709*
00710*
00711*
00712*
00713*
00714*
00715*
00716*
00717*
00718*
00719*
00720*
00721*
110
111
112
13
14
15
16
17
18
119
120
430
450
C
C
C***
C
C
C
C
C
C
C
C
C
C
C
C
C->-
470
C
C
IF (C6.GE.50.) GO TO 430
A4=2./EXP(C6)
IF (C8.GE.50. ) GO TO 450
A6=2./EXP(C8)
T=A4+A6
SUM=SUM+T
IF (T.GE.0.01) GO TO 410
RC=A1*(A2+SUM)
RETURN
SECTIONS OF SUBROUTINE RCON.
SECTION RCON. A - COMMON.
SECTION RCON.B - EXPLANATIONS AND COMPUTATIONS COMMON TO ALL
CONDITIONS.
SECTION RCON.C - STABLE OR UNLIMITED MIXING, Z IS ZERO.
SECTION RCON.D - STABLE OR UNLIMITED MIXING, Z IS NON-ZERO.
SECTION RCON.E - UNSTABLE, ASSURED OF UNIFORM MIXING.
SECTION RCON.F - UNSTABLE, CALCULATE MULTIPLE EDDY
REFLECTIONS; Z IS NON-ZERO.
SECTION RCON.G - UNSTABLE, CALCULATE MULTIPLE EDDY
REFLECTIONS; Z IS ZERO.
SECTION RCON.H - FORMAT.
>->->SECTION RCON.H - FORMAT
PLB06920
PLB06930
PLB06940
PLB06950
PLB06960
PLB06970
PLB06980
PLB06990
PLB07000
PLB07010
PLB07020
PLB07030
PLB07040
PLB07050
PLB07060
PLB07070
PLB07080
PLB07090
PLB07100
PLB07110
PLB07120
PLB07130
PLB07140
PLB07150
PLB07160
FORMAT (IHO.'BOTH H AND Z ARE ABOVE THE MIXING HEIGHT SO A RELI ABLPLB07 170
IE COMPUTATION CAN NOT BE MADE.1)
END
PLB07180
PLB07190
PLB07200
PLB07210
-------
INDEX PAGE 20
SYMBOL
20
40
SO
70
100
120
130
ISO
170
190
200
220
230
2SO
270
280
300
320
340
360
380
400
410
430
4SO
470
Al
A2
A3
A4
AS
A6
A7
ALL
AN
Cl
C2
C3
C4
C5
C6
C7
C8
C9
CA
6
7
5
14
21
27
30
30
42
44
28
48
52
61
63
67*
81
83
85
87
52
98
102*
110
112
9WR
53 =
33 =
117
37 =
68 =
69 =
70 =
71 =
300
51 =
20 =
29 =
80
31 =
98
41 =
72 =
77 =
78 =
79 =
80 =
38 =
8*
8
7
20*
27*
29*
31*
36*
44*
46*
48*
51*
53*
63*
65*
91
83*
85*
87*
89*
94*
100*
116
112*
114*
119*
92
34
45 =
82 =
84 =
86 =
88 =
67 =
26 =
31
96 =
32
99
44
73
81
83
85
87
40
10*
7
94 =
36 =
46
89
89
89
89
67
34
40
97
33
45
74
82
84
86
88
40
SUBROUTINE ROON
— — — D K"I?PT} CNJf'CQ _______________
12 25 30 32 52
12*
117
43= 46 55= 62= 92 95= 9
56= 64= 92
103= 111= 114
104= 113= 114
72 102= 102 105
46 49 53 94
41 54= 59 60 77 78 7
108 109
40= 42 43 59= 61 62 9
60= 63 64
75 76 105= 106 107
108= 110 111
109= 112 113
57= 59 59 73 75
-------
INDEX PAGE 21
SUBROUTINE RCON
CB
CC
CD
CE
CF
CMAX
DELH
DUM
EXP
H
HF
HL
HPRM
I OPT
1WRI
KST
MS
PDHX
PSIG
RC
RCON
SQRT
SUM
SY
SZ
T
TEMP
THL
U
X
XF
XMAX
Y
YD
Z
39 =
73 =
74 =
75 =
76 =
SCO
SCO
15 =
26
99
300
106
SCO
SCO
SCO
SCO
4 =
2OO
2CO
SCO
13
SCO
1EY
18
65 =
2CO
2OO
54
89 =
24 =
66 =
SCO
200
SCO
SCO
SCO
22 =
3CO
41
77
78
79
80
15
16 =
33
111
6
107
6
14
9WR
5
16
10 =
19
90 =
18 =
19 =
54
90
25
72
16
12
16
21
23
7
41
77
78
79
80
17 =
43
113
31
7
16
27
34 =
90
18
19
94
91
26
101 =
34
16
22
8
58 =
106 =
107 =
17
45
31
8
46 =
92
18
19
96
114 =
105
46
16
30
-4---I 1-_4-
60
108
109
17
62
38
28
49 =
100 =
23
29
96
115
49
38
60 74 76
108
109
18 19 23= 24
64 82 84 86
39 57 58 97
48 49 66 101
_,
92= 117=
115= 115 117
34 46 49 53
29 34 46 48
116
53 94
39 52 57 58
24
88
97
94
53
-------
INDEX
SUBROUTINE TPMX
PAGE 22
00722*
00723*
00724*
00725*
00726*
00727*
00728*
00729*
00730*
00731*
00732*
00733*
00734*
00735*
00736*
00737*
00738*
00739*
00740*
00741*
00742*
00743*
00744*
00745*
00746*
00747*
00748*
00749*
00750*
00751*
00752*
00753*
00754*
00755*
00756*
00757*
00758*
00759*
00760*
00761*
00762*
00763*
00764*
00765*
00766*
00767*
00768*
00769*
00770*
00771*
1 SUBROUTINE TPMX
C SUBROUTINE TPMX LOCATES THE DISTANCE TO MAX CONCENTRATION.
C THE PROXIMITY OF THE MAXIMUM CONCENTRATION IS DETERMINED BY
C SCREENING THE CALCULATED CONCENTRATIONS OF 16 PRESET DISTANCES
C THEN AN ITERATIVE PROCEDURE IS EMPLOYED TO PINPOINT THE
C DISTANCE TO MAX CONCENTRATION TO WITHIN ONE METER.
2 COMMON /MS/KST,X,SY,SZ
3 COMMON /ALL/IOPT(3),U,HL,H,Z,Y,XF,DELH,HF,CMAX,XMAX,RC,PDHX,HPRM
4 DIMENSION XV(16),DX1(16 )
5 DATA XV/.1,.3,.5,.7,1.,2.,3.,5.,7.,10.,15.,20.,30.,40.,50. ,100./
6 DATA DX1/4*-!.,5*-10.,6*-100.,100./
7 DUM = DELH
8 CMAX=0.
9 RC=0.0
10 Y=0.
11 XMAX=0.0
C DO LOOP DETERMINING THE DISTANCE OF MAX CONG AMONG THE
C FIXED DISTANCES.
12 DO 5 I =1,16
13 X = XV(I)
C OPTION 1 EMPLOYS THE GRADUAL RISE ROUTINE
14 IF(lOPT(l).EQ.O)GOTO15
15 DELH=DUM
16 H=HF
17 IF(X.GE.XF)GOTO15
18 CALL PHX
19 15 CALL RCON
20 IF (.NOT.(H.GT.HL.AND.KST.LE.4)) GO TO 347
21 CMAX = 0. '
22 XMAX = 0.
23 RETURN
24 347 CONTINUE
25 IF(RC.LT.CMAX)GOT05
26 CMAX=RC
27 XMAX=X
28 JB=!
29 5 CONTINUE
C CMAX IS THE HIGHEST OF THE 16 CONCENTRATIONS OCCURRING
C AT DISTANCE XMAX. JB IS THE INDEX (1-16) FOR THE MAX.
30 X=XMAX
C SET X EQUAL TO XMAX FOUND FROM PRESET X'S
31 CLST=CMAX
32 XLST=XMAX
C THE FOLLOWING INCREMENTS ARE USED:
C 0.1 KM FOR X LESS THAN 1 KM
C 1 .0 KM FOR X 1 KM TO 10 KM
C 10. KM FOR X 10 KM TO 100 KM
33 DX=DX1(JB)
34 8 IF(ABS(DX) .LE. .OODRETURN
C INCREMENT NOT ALLOWED TO BE LESS THAN 1 METER
PLB07220
PLB07230
PLB07240
.PLB07250
PLB07260
PLB07270
PLB07280
PLB07290
PLB07300
PLB07310
PLB07320
PLB07330
PLB07340
PLB07350
PLB07360
PLB07370
PLB07380
PLB07390
PLB07400
PLB07410
PLB07420
PLB07430
PLB07440
PLB07450
PLB07460
PLB07470
PLB07480
PLB07490
PLB07500
PLB07510
PLB07520
PLB07530
PLB07540
PLB07550
PLB07560
PLB07570
PLB07580
PLB07590
PLB07600
PLB07610
PLB07620
PLB07630
PLB07640
PLB07650
PLB07660
PLB07670
PLB07680
PLB07690
PLB07700
PLB07710
-------
INDEX
PAGE 23
SUBROUTINE TPMX
00772*
00773*
00774*
00775*
00776*
00777*
00778*
00779*
00780*
00781*
00782*
00783*
00784*
00785*
00786*
00787*
00788*
00789*
00790*
00791*
00792*
00793*
00794*
00795*
00796*
00797*
00798*
00799*
00800*
35 DX=-0.1*DX PLB07720
C REVERSE DIRECTIONS, REDUCE INCREMENT BY ONE-TENTH PLB07730
C THE ITERATIVE PROCESS CONTINUES IN THIS MANNER PLB07740
C WITH CALCULATIONS GOING BACKWARDS AND FORWARDS PLB07750
C IN SMALLER AND SMALLER INCREMENTS UNTIL A 1 PLB07760
C METER INTERVAL IS REACHED. PLB07770
36 9 IF(X.GT.100.)RETURN PLB07780
C IF X REACHES 100 KM CEASE COMPUTATIONS FOR THIS WIND SPEED. PLB07790
37 X=X+DX PLB07800
C OPTION 1 EMPLOYS GRADUAL PLUME RISE ROUTINE PLB07810
38 IF(lOPT(l).EQ.O)GOTO7 PLB07820
39 DELH=DUM PLB07830
40 H=HF PLB07840
41 IF(X.GE.XF)GOTO7 PLB07850
42 CALL PHX PLB07860
43 7 CALL RCON PLB07870
44 IF(RC.LE.CLST)GOT050 PLB07880
C NEW CONCENTRATION IS HIGHER, KEEP GOING TO FIND MAX. PLB07890
45 CLST=RC PLB07900
46 XLST=X PLB07910
47 GOTO9 PLB07920
48 50 CMAX=CLST PLB07930
C NEW CONCENTRATION IS LOWER, RETURN TO REVERSE DIRECTIONS PLB07940
49 XMAX=XLST PLB07950
50 CLST=RC PLB07960
51 XLST=X PLB07970
52 GOTO8 PLB07980
53 END PLB07990
C PLB08000
-------
OS
INDEX
SYMBOL
5
7
8
9
15
50
347
ABS
ALL
CLST
CMAX
DELH
DUM
DX
DX1
H
HF
ML
HPRM
I
I OPT
JB
KST
MS
PDHX
PHX
RC
RCON
SY
SZ
TPMX
U
X
XF
XLST
XMAX
XV
Y
Z
SUBROUTINE TPMX
PAGE 24
12
38
34*
36*
14
44
20
34
SCO
31 =
SCO
300
7 =
33 =
4DI
3CO
SCO
SCO
SCO
12
SCO
28 =
2CO
2CO
3CO
18
SCO
19
2CO
2CO
1EY
3CO
2CO
51
SCO
32 =
SCO
4DI
SCO
SCO
25
41
52
47
17
48*
24*
44
8 =
7
15
34
6DA
16 =
16
20
IS
14
33
20
42
9 =
43
13 =
17
46 =
11 =
5DA
10 =
------- KKtfK
29*
43*
19*
45= 48 50=
21= 25 26=
15= 39=
39
35= 35 37
33
20 40 =
40
28
38
25 26 44
17 27 30=
41
49 51 =
22= 27= 30
13
31
48 =
27 30= 36 37= 37 41 46
32
49 =
h- + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + _ + _ + _ + _ + _ + _ + _ + _ + _ + _ + _ + _ + _ + _ + _4._ + _ + _+._ + _ + _ + _ + _.1._.(._.f_.(._.(.
-------
INDEX
PAGE 25
SUBROUTINE PH
00801*
00802»
00803*
00804*
00805*
00806*
00807*
00808*
00809*
00810*
00811*
00812*
00813*
00814*
00815*
00816*
00817*
00818*
00819*
00820*
00821*
00822*
00823*
00824*
00825*
00826*
00827*
00828*
00829*
00830*
00831*
00832*
00833*
00834*
00835*
00836*
00837*
00838*
00839*
00840*
00841*
00842*
00843*
00844*
00845*
00846*
00847*
00848*
00849*
00850*
1 SUBROUTINE PH PLB08010
C ROUTINE FOR DETERMINING PLUME RISE. PLB08020
2 COMMON /MS/ KST,X,SY,SZ PLB08030
3 COMMON /MH/ HP,VS,XFUN,DHU,ME,XFOUSE,DHUTE,DHAUE,DUTE,DHCAE,DHCAF,PLB08040
IMF,XFOUSF,DHUTF,DHAUF,DUTF,D PLBO 8 050
4 COMMON /ALL/ IOPT(3),U,HL,H,Z,Y,XF,DELH,HF,CMAX,XMAX,RC,PDHX,HPRM PLB08060
C THE FOLLOWING PARAMETERS ARE INPUT TO SUBROUTINE PH: PLB08070
C DHAUE: DELTA-H*U MOMENTUM RISE USING UNSTABLE RISE FOR E PLB08080
C DHAUF: " " " " " " " F PLB08090
C DHCAE: DELTA-H CALM BUOYANT RISE FOR E-STABILITY PLB08100
C DHCAF: " " " " " F-STABILITY PLB08110
C DHU: DELTA-H*U (UNSTABLE AND NEUTRAL) PLB08120
C DHUTE: DELTA-H*U*».3333 STABLE BUOYANT RISE FOR E PLB08130
C DHUTF: " " " " " " " F PLB08140
C DUTE: DELTA-H*U**.3333 STABLE MOMENTUM RISE FOR E PLB08150
C DUTF: " " " " " " " F PLB08160
C HP: PHYSICAL STACK HEIGHT (FROM CARD INPUT) PLB08170
C ME: MOMENTUM INDICATOR FOR E-STABILITY PLB08180
C MF: " " " F-STABILITY PLB08190
C VS: STACK GAS VELOCITY (FROM CARD INPUT) PLB08200
C XFOUSE: DISTANCE TO STABLE BUOYANCY RISE/U FOR E PLB08210
C XFOUSF: " " " " " " F PLB08220
C XFUN: DIST(KM) TO FINAL BUOYANT RISE (UNSTABLE AND NEUTRAL) PLB08230
C PLB08240
C THE FOLLOWING PARAMETERS ARE OUTPUT FROM SUBROUTINE PH: PLB08250
C XF: DISTANCE OF FINAL RISE PLB08260
C DELH: FINAL PLUME RISE PLB08270
C HF: FINAL EFFECTIVE HEIGHT PLB08280
C PLB08290
5 HPRM=HP PLB08300
6 IF (IOPT(2).EQ.O) GOTO 10 PLB08310
C OPTION FOR STACK DOWNWASH PLB08320
7 DUM^VS/U PLB08330
8 IF (DUM.LT.1.5) HPRM=HP+2.*D*(DUM-1.5) PLB08340
9 IF (HPRM.LT.O.) HPRM=0. PLB08350
10 10 GOTO (20,20,20,20,30,50), KST PLB08360
C NEUTRAL OR UNSTABLE PLB08370
11 20 XF=XFUN PLB08380
12 DELH=DHU/U PLB08390
13 HF=HPRM+DELH PLB08400
14 RETURN PLB08410
C E STABILITY PLB08420
15 30 IF (ME.EQ.l) GO TO 40 PLB08430
16 XF=XFOUSE*U PLB08440
17 DELH=DHUTE/U**0.33333 PLB08450
18 IF (DHCAE.LT.DELH) DELH=DHCAE PLB08460
C COMPARE CALC PLUME RISE WITH CALM WIND PLUME RISE PLB08470
19 HF=HPRM+DELH PLB08480
20 RETURN PLB08490
C MOMENTUM RISE FOR E STABILITY PLB08500
-------
INDEX
00851*
00852*
00853*
00854*
00855*
00856*
00857*
00858*
00859*
00860*
00861*
00862*
00863*
00864*
00865*
00866*
00867*
00868*
00869*
00870*
00871*
00872*
00873*
00874*
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
C
50
C
60
C
C
SUBROUTINE PH
XF = 0.
DHA=DHAUE/U
DELH=DUTE/U** 0.3 3 3 3 3
IF (DHA.LT.DELH) DELH=DHA
HF=HPRM+DELH
RETURN
F STABILITY
IF (MF.EQ.l) GO TO 60
XF=XFOUSF*U
DELH=DHUTF/U**0.33333
IF (DHCAF.LT.DELH) DELH=DHCAF
COMPARE CALC PLUME RISE FOR CALM WIND PLUME RISE
HF=HPRM+DELH
RETURN
MOMENTUM RISE FOR F STABILITY
XF = 0.
DHA=DHAUF/U
DELH=DUTF/U**0.33333
IF (DHA.LT.DELH) DELH=DHA
HF=HPRM+DELH
RETURN
END
PAGE 26
PLB08510
PLB08520
PLB08530
PLB08540
PLB08550
PLB08560
PLB08570
PLB08580
PLB08590
PLB08600
PLB08610
PLB08620
PLB08630
PLB08640
PLB08650
PLB08660
PLB08670
PLB08680
PLB08690
PLB08700
PLB08710
PLB08720
PLB08730
PLB08740
-------
INDEX
SYMBOL
PAGE 27
SUBROUTINE PH
= = REFERENCES
10
20
30
40
50
60
ALL
CMAX
D
DELH
DHA
DHAUE
DHAUF
DHCAE
DHCAF
DHU
DHUTE
DHUTF
DUM
DUTE
DUTF
H
HF
HL
HP
HPRM
I OPT
KST
ME
MF
MH
MS
PDHX
PH
RC
SY
SZ
U
VS
X
XF
XFOUSE -
XFOUSF -
XI-UN
XMAX
Y
Z
6
10
10
15
10
27
4CO
4OO
SCO
4CO
25
22 =
SCO
SCO
3CO
SCO
SCO
3CO
SCO
7 =
SCO
300
4CO
4CO
4CO
SCO
4CO
4CO
2CO
SCO
SCO
SCO
2CO
4CO
1EY
4CO
2CO
2CO
4CO
3CX)
2CO
4CO
SCO
SCO
SCO
4OO
4CO
4CO
10*
10 10 10 11*
15*
21*
27*
33*
8
12= 13 17= 18 18= 19
29= 30 30= 31 35= 36
24 24 34= 36 36
22
34
18 18
30 30
12
17
29
8 8
23
35
13= 19= 25= 31= 37=
5 8
5= 8= 9 9= 13 19
6
10
15
27
7 12 16 17 22 23
7
11= 16= 21= 28= 33=
16
28
11
23= 24
36= 37
25 31
28 29
24=
37
34
35
-------
INDEX
PAGE 28
SUBROUTINE PHX
00875*
00876*
00877*
00878*
00879*
00880*
00881*
00882*
00883*
00884*
00885*
SUBROUTINE PHX PLB08750
THIS ROUTINE CALLED WHEN EMPLOYING THE GRADUAL RISE OPTION. PLB08760
COMMON /MS/KST,X,SY,SZ PLB08770
COIVMON/ALL/IOPT(3),U,HL,H,Z,Y,XF,DELH,HF,CMAX,XMAX,RC,PDHX.HPRM PLB08780
PDHX IS 160.*F**0.3333 PLB08790
DELH = PDHX*X**0.6666667/U PLB08800
HX =HPRM + DELH PLB08810
IF (HX ,LT. HF) H = HX PLB08820
RETURN PLB08830
END PLB08840
PLB08850
CO
o
INDEX
PAGE 29
SUBROUTINE PHX
SYMBO1
ALL
CMAX
DELH
H
HF
HL
HPRM
HX
I OPT
KST
MS
PDHX
PHX
RC
SY
sz
u
X
XF
XMAX
Y
Z
SCO
SCO
SCO
SCO
SCO
SCO
3CO
5 =
3CO
2CO
2CO
SCO
1EY
SCO
2CO
2CO
SCO
2CO
3CO
3CO
SCO
3CO
= = = = = = = = = = = KtrbKtNUtO = = = = = = = = = = = = = = =
4= 5
6 =
6
5
6 6
4
4
4
h-t_ + --|._ + - + _ + - + -4._ + - + - + - + _ + - + - + --(-_ + _-)-_ + _ + _ + . + _ + _ + _ + _ + _+ +_+ + + + + +
-------
INDEX
PACK 30
SUBROUTINE PSIG
00886*
00887*
00888*
00889*
00890*
00891*
00892*
00893*
00894*
00895*
00896*
00897*
00898*
00899*
00900*
00901*
00902*
00903*
00904*
00905*
00906*
00907*
00908*
00909*
00910*
00911*
00912*
00913*
00914*
00915*
00916*
00917*
00918*
00919*
00920*
00921*
00922*
00923*
00924*
00925*
00926*
00927*
00928*
00929*
00930*
00931*
00932*
00933*
00934*
00935*
1 SUBROUTINE PSIG PLB08860
C VERTICAL DISPERSION PARAMETER VALUE, SZ DETERMINED BY PLB08870
C SZ = A * X ** B WHERE A AND B ARE FUNCTIONS OF BOTH STABILITY PLB08880
C AND RANGE OF X. PLB08890
C HORIZONTAL DISPERSION PARAMETER VALUE, SY DETERMINED BY PLB08900
C LOGARITHMIC INTERPOLATION OF PLUME HALF-ANGLE ACCORDING TO PLB08910
C DISTANCE AND CALCULATION OF 1/2.15 TIMES HALF-ARC LENGTH. PLB08920
2 COMMON /MS/KST,X,SY,SZ PLB08930
3 DIMENSION XA(7), XB(2), XD(5), XE(8), XF(9), AA(8), BA(8), AB(3), PLB08940
1BB(3), AD(6), BD(6), AE(9), BE(9), AF(10), BF(10) PLB08950
4 DATA XA /.5, .4, .3, .25, .2,.15, .!/ PLB08960
5 DATA XB /.4,.2/ PLB08970
6 DATA XD /30. ,10. ,3. ,1. , .3/ PLB08980
7 DATA XE /40. ,20. ,10. ,4. ,2. ,1 . , .3, .!/ PLB08990
8 DATA XF /60. ,30. , 15. ,7. ,3. ,2. ,1.,.7 , .2/ PLB09000
9 DATA AA / 453 . 85 , 346 . 75 , 258 . 89 , 217 . 41 , 1 79 . 52 , 170 . 22 , 1 58 . 08 ,1 22 . 8/ PLB09010
10 DATA BA /2.1166,1.7283,1.4094,1.2644,1.1262,1 .0932,1.0542, .9447/ PLB09020
11 DATA AB 7109.30,98 .483.90.673/ PLB09030
12 DATA BB /1.0971,0.98332,0.93198/ PLB09040
13 DATA AD /44.053 , 36 . 650 , 33.504,32.093,32.093 , 34.459/ PLB09050
14 DATA BD /O . 5 1179 , 0 . 56589,0.60486,0.64403 , 0 . 81066 , 0 . S6974/ PLB09060
15 DATA AE /47.618,35.420,26.970,24.703,22.534,21.628,21.628,23.331,2PLB09070
14.26/ PLB09080
16 DATA BE /O.29592,0.37615,0.46713,0.50527,0.57154,0.63077,0.75660,OPLB09090
1.81956,0.8366/ PLB09100
17 DATA AF /34.219,27.074,22.651,17.836,16.187,14.823,13.953,13.953,1PLB09110
14.457.15.209/ PLB09120
18 DATA BF /O. 21716 ,0. 27436,0.32681,0.41507,0.46490,0.54503,0.63227,OPLB09130
1.68465,0.78407,0.815587 PLB09140
19 XY=X PLB09150
20 GOTO (10,40,70,80,110,140), KST PLB09160
C STABILITY A (10) PLB09170
21 10 TH=(24.167-2.5334*ALOG(XY))/57.2958 PLB09180
22 IF (X.GT.3.11) GOTO 170 PLB09190
23 DO 20 ID=1,7 PLB09200
24 IF (X.GE.XA(ID)) GO TO 30 PLB09210
25 20 CONTINUE PLB09220
26 ID=8 PLB09230
27 30 SZ=AA(ID)*X**BA(ID) PLB09240
28 GO TO 190 PLB09250
C STABILITY B (20) PLB09260
29 40 TH=(18.333-1.8096*ALOG(XY))/57.2958 PLB09270
30 IF (X.GT.35.) GOTO 170 PLB09280
31 DO 50 ID=1,2 PLB09290
32 IF (X.GE.XB(ID)) GO TO 60 PLB09300
33 50 CONTINUE PLB09310
34 ID=3 PLB09320
35 60 SZ=AB(ID)*X**BB(ID) PLB09330
36 GO TO 180 PLB09340
C STABILITY C (30) PLB09350
-------
INDEX
SUBROUTINE PSIG
PAGE 31
oo
CO
00936*
00937*
00938*
00939*
00940*
00941*
00942*
00943*
00944*
00945*
00946*
00947*
00948*
00949*
00950*
00951*
00952*
00953*
00954*
00955*
00956*
00957*
00958*
00959*
00960*
00961*
00962*
00963*
00964*
00965*
00966*
00967*
00968*
00969*
00970*
37 70 TH=(12.5-1.0857*ALOG(XY))/57.2958
38 SZ=61.141*X**0.91465
39 GO TO 180
C STABILITY D (40)
40 80 TH=(8.3333-0.72382*ALOG(XY))/57.2958
41 DO 90 ID=1,5
42 IF (X.GE.XD(ID)) GO TO 100
43 90 CONTINUE
44 ID=6
45 100 SZ=AD(ID)*X**BD(ID)
46 GO TO 180
C STABILITY E (50)
47 110 TH=(6. 25-0.54287*ALOG(XY))/57 . 2958
48 DO 120 ID=1,8
49 IF (X.GE.XE(ID)) GO TO 130
50 120 CONTINUE
51 ID=9
52 130 SZ=AE(ID)*X**BE(ID)
53 GO TO 180
C STABILITY F (60)
54 140 TH=(4.1667-0.36191*ALOG(XY))/57.2958
55 DO 150 ID=1,9
56 IF (X.GE.XF(ID)) GOTO 160
57 150 CONTINUE
58 ID=10
59 160 SZ=AF(ID)*X**BF(ID)
60 GO TO 180
61 170 SZ=5000.
62 GO TO 190
63 180 IF (SZ.GT.5000.) SZ=5000.
64 190 SY=465.116*XY*S1N(TH)/COS(TH)
C 465.116 = 1000. (M/KM) / 2.15
65 RETURN
C
66 END
PLB09360
PLB09370
PLB09380
PLB09390
PLB09400
PLB09410
PLB09420
PLB09430
PLB09440
PLB09450
PLB09460
PLB09470
PLB09480
PLB09490
PLB09500
PLB09510
PLB09520
PLB09530
PLB09540
PLB09550
PLB09560
PLB09570
PLB09580
PLB09590
PLB09600
PLB09610
PLB09620
PLB09630
PLB09640
PLB09650
PLB09660
PLB09670
PLB09680
PLB09690
PLB09700
-------
INDEX
PAGE 32
SUBROUTINE PSIG
a I1VUKJL
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
AA
AB
AD
AE
AF
ALOG
BA
BB
BD
BE
BF
COS
ID
KST
MS
PSIG
SIN
SY
sz
TII
X
XA
XB
XD
XE
XF
XY
20
23
24
20
31
32
20
20
41
42
20
48
49
20
55
56
22
36
28
3DI
3DI
3DI
3DI
3DI
21
3DI
3DI
3DI
3DI
3D!
64
23
41
55
2CO
2OO
1EY
64
20O
2GO
21 =
2CO
45
3DI
3DI
3DI
3DI
3DI
19 =
21*
25*
27*
29*
33*
35*
37*
40*
43*
45*
47*
50*
52*
54*
57*
59*
30
39
62
9DA
11DA
13DA
15DA
17DA
29
10DA
12DA
14DA
16DA
18DA
24
42
56
20
64 =
27 =
29 =
19
49
4 DA
5DA
6 DA
7 DA
8 DA
21
; ------- Kfcr tKtNUbS __-____-_-____
61*
46 53 60 63*
64*
27
35
45
52
59
37 40 47 54
27
35
45
52
59
26= 27 27 31 32 34= 35
44= 45 45 48 49 51= 52
58= 59 59
35= 38= 45= 52= 59= 61= 63
37= 40= 47= 54= 64 64
22 24 27 30 32 35 38
52 56 59
24
32
42
49
56
29 37 40 47 54 64
35
52
63
42
-------
INDEX
SYMBOL
Al
A2
A3
A4
A5
A6
A7
AA
AB
ABS
AD
AD 2
AE
AF
AH
AH2
ALOG
ALP
AN
ANOT
BA
BB
BD
BE
BF
Cl
C2
C3
C4
C5
C6
C7
C8
C9
CA
CB
CC
CD
CE
CF
CLST
CM
CM2
CMAX
COS
D
DELH
DELT
PAGE 33
RCON
RCON
RCON
RCON
RCON
RCON
RCON
PSIG
PSIG
TPMX
MAIN P
MAIN P
PSIG
PSIG
MAIN P
MAIN P
PSIG
MAIN P
RCON
MAIN P
PSIG
PSIG
PSIG
PSIG
PSIG
RCON
RCON
RCON
RCON
RCON
RCON
RCON
RCON
RCON
RCON
RCON
RCON
RCON
RCON
RCON
TPMX
MAIN P
MAIN P
MAIN P
PSIG
MAIN P
PH
MAIN P
PSIG
TPMX
PH
PHX
"******** SUPER INDEX **********
ROUTINES IN WHICH THE SYMBOL IS USED
RCON
TPMX
-------
INDEX
PAGE 34
'** SUPER INDEX **********
00
Ol
DMA
DHAUE
DHAUF
DHCAE
DHCAF
DHU
DHUTE
DHUTF
DTMB
DUM
DUTE
DUTF
DX
DX1
EXP
F
H
I1ANE
HE
HE2
HF
HL
HP
HPRM
HX
I
IA
IB
ID
I OPT
IRD
IWRI
JB
K
KST
ME
MF
N
PDHX
PH
PHX
PL
PSIG
Q
RC
RCON
SE
SF
SIN
SQRT
- PH
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- TPMX
- TPMX
- RCON
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- PH
- PHX
- MAIN
- MAIN
- MAIN
- PSIG
- MAIN
- MAIN
- MAIN
- TPMX
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- TPMX
- MAIN
- RCON
- MAIN
- RCON
- TPMX
- MAIN
- MAIN
- PSIG
- MAIN
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
PH
PH
PH
PH
PH
PH
PH
PH
PH
PH
PHX
PH
RCON
PH
PHX
TPMX
PH
RCON
PH
PH
PH
PHX
TPMX
RCON
RCON
RCON
PHX
TPMX
RCON
PSIG
RCON
TPMX
TPMX
PSIG RCON TPMX
-------
INDEX
PAGE 3 5
oo
cr.
SUM
SY
SZ
T
TEMP
TH
THL
TI
TM
TPMX
TS
U
UA
UZ
VF
VS
WI
X
XA
XB
XD
XE
XF
XFOUSE
XFOUSF
XFUN
XLST
XM
XM2
XMAX
XV
XY
Y
YD
Z
******
- RCON
- PS 1C,
- PSIG
- MAIN
- RCON
- PSIG
- RCON
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- MAIN
- PHX
- PSIG
- PSIG
- PSIG
- PSIG
- PH
- MAIN
- MAIN
- MAIN
- TPMX
- MAIN
- MAIN
- MAIN
- TPMX
- PSIG
- RCON
- RCON
- MAIN
*********
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
* * *
RCON
RCON
RCON
PH
PH
PSIG
PSIG
PH
PH
PH
TPMX
TPMX
RCON
*******
********** SUPER INDEX
**********
PHX
RCON
ROON
RCON
TPMX
TPMX
>*********************a
INDEX
END OF ANALYSIS
JPL FORTRAN V VERSION
-------
APPENDIX C
SENSITIVITY ANALYSIS
This section presents a simple analysis designed to acquaint
the user with the magnitude of changes expected in surface
concentrations when certain model inputs are varied.
OPTIONS
PTPLU has three technical options: gradual plume rise, stack
downwash, and buoyancy-induced dispersion. The effects of
employing each of the options are discussed next, using as a base
the calculation presented in Section 8.
Gradual Plume Rise
The gradual plume rise option alters the assumptions made
about the height of the plume up to the distance of final rise.
If the option is not employed, calculations are made as if the
plume is always at the effective height. If the option is
employed, the plume is assumed to rise gradually to the final
height as the distance downwind increases. The effect of
employing the option is to decrease the plume height between the
point of release and the point of final rise, which results in
higher ground-level concentrations.
In the example presented in Section 8, the maximum
concentration occurs at a point beyond the distance of final rise
(see Figure 7). Thus, the gradual plume rise option has no
effect for stabilities B or D with a wind speed of 4 m/s.
Despite the fact that the option has no effect on the maxima, it
should be noted that in the process of searching for the maximum,
the option affects calculations for locations between the source
and the distance to final rise. Table C-l shows the plume
heights and concentrations with and without the option for some
of the distances for which calculations were performed, for
stability B with a wind speed of 4 m/s. It can be seen that
beyond 0.6 km, which is the distance to final rise, the option
has no effect. Also note in Figure 7 that the maximum
concentration for stability A with a wind speed of 3.0 m/s is
affected by the option, as this maximum occurs before final rise.
87
-------
TABLE C-l.
PLUME HEIGHTS AND CONCENTRATIONS WITH AND
WITHOUT THE GRADUAL-RISE OPTION*
Wi th gradual r ise
Without gradual rise
Di s t ance
(km)
0.1
0.3
0.5
0.7
Height
(m)
73.3
109.2
137.2
150.0
Cone .
(yg/m3)
0
11
77
190
He ight
(m)
150.0
150.0
150.0
150.0
Cone .
(yg/m3)
0
0
38
190
* For stability B and wind speed of 4 m/s.
Stack Downwash
The stack downwash option simulates lowering of the plume
just after it leaves the stack, as a result of low pressures on
the leeward side of the stack. The model carries out this
simulation by using a modified value for the physical height,
which lowers the effective height of the plume. Again, decreased
plume height results in higher ground-level concentrations.
The stack downwash option is important if •
of the effluent is less than 1.5 times the wind
example considered here, the wind speed is only
stack gas velocity is 20 m/s; therefore stack
have a minimal effect. As can be seen in Table
he exit veloc i ty
speed. In the
4 m/s, wh i1e the
downwash should
C-2, this is the
case. However, if the wind speed in this example was 15 m/s or
greater, the option becomes important and should be implemented.
TABLE C-2.
MAXIMUM CONCENTRATIONS WITH AND WITHOUT
STACK DOWNWASH, FOR STABILITY CLASS D
With stack downwash
Distance to
Cone. max. cone.
.3
Without stack downwash
(yg/m3)
204
(km)
1.64
Cone.
(yg/m3)
198
Distance to
max. cone.
(km)
1.67
88
-------
Buoyancy- ]j_nduc_e_d _Di_s_^er_s_i on (BID)
Buoyancy-induced dispersion is estimated by an increase in
the dispersion parameters proportional to the plume rise under
the assumption that the more buoyant a plume, the more the
buoyancy contributes to dispersion. In the two cases considered,
this increase in the dispersion parameters results in an increase
in the maximum ground-level concentrations. However, use of this
option will not always produce higher concentrations. For
stability A with a wind speed of 0.5 m/s, concentration is
reduced 23%. In general, the effect of buoyancy-induced
dispersion on concentration is negligible, except when the stack
height is small compared with the plume rise (as in this
example). It should be noted that multiple concentration peaks
are possible when this option is used along with the gradual
plume rise opt ion.
TABLE C-3. MAXIMUM CONCENTRATIONS WITH AND WITHOUT BID
With BID Wi thout BID
Stabi 1 i ty
class
B
D
Cone .
(ug/m3)
282
122
Distance to
max. cone.
(km)
0.97
4.79
Cone .
(ug/m3)
278
112
Di s tance
to
max. cone.
(km)
1.02
5.63
PLUME-RISE-RELATED PARAMETERS
Of several parameters that can influence plume rise, two are
varied here. The results of these variations are discussed next.
Stack Gas Temperature
Sensitivity to variations in stack gas temperature was
studied using the program's built-in sample test as a base.
Figure C-l shows the percent change in maximum concentration and
the percent change in distance to maximum concentration resulting
from decreases in stack gas temperature under three wind and
stability conditions. These results are also presented in Tables
C-4 and C-5 with an additional wind and stability condition
analyzed.
89
-------
% Change in Distance
% Change in Concentration
c
T
ft)
o
I
r+ GO
O (C
I 3
3 <»
PS —
X «-!•
I' <'
c —
3 ~
o o
>-«v
o
=*• 3
P ps
3 X
n> 3
en C
_ 3
3 ra
o
en 3
f O
O 3
gq p
en «.
O
r* 3
(D
3 P
'a 3
(D a
P Q.
3
Q
0)
I
I
10
o
•o
^*
I
Ul
O —
-------
TABLE C-4. PERCENT INCREASE IN MAXIMUM CONCENTRATION
WITH DECREASING STACK GAS TEMPERATURE
Stabi 1 ity
class
B
C
C
D
Wind
(m/s)
4.0
4.0
2.0
4.0
Decrease in stack gas temperature
5%
10.26
11.08
12.91
15.01
10%
24.57
26.66
31.69
36.97
15%
45.95
50.21
61.35
71.93
20%
81.70
90.22
115.04
135.35
TABLE C-5.
PERCENT DECREASE IN DISTANCE TO MAXIMUM CONCENTRATION
WITH DECREASING STACK GAS TEMPERATURE
Stabi 1 ity
class
B
C
C
D
Wind
(m/s)
4.0
4.0
2.0
4.0
Decrease in stack gas temperature
5%
-4.70
-5.47
-6.47
-9.13
10%
-10.17
-11.88
-14.30
-19.37
15%
-16.83
-19.52
-23.22
-30.85
20%
-25.23
-29.02
-34.22
-41.94
From Tables C-4 and C-5, it is apparent that decreased stack
gas temperature, which makes the plume less buoyant, generally
results in a higher maximum closer to the source. The specific
changes, however, also depend on the stability and wind speed.
Stack Gas Velocity
Sensitivity to variation in stack gas velocity was studied
using the built-in sample test as a base. Tables C-6 and C-7
show the percent change in maximum concentration and the percent
change in distance to maximum concentration resulting from
decreases in stack gas velocity under four wind and stability
conditions. Figure C-2 graphically depicts some of these
changes. It is apparent from Tables C-6 and C-7 and Figure C-2
that decreased stack gas velocity, which decreases plume rise,
generally results in higher maximum concentrations closer to the
source. However, the specific change in the results depends on
the stability and wind speed as well. In general, for a given
stability, higher wind speed counters the effect of increasing
the stack gas velocity.
91
-------
TABLE C-6. PERCENT INCREASE IN MAXIMUM CONCENTRATION
WITH DECREASING STACK GAS VELOCITY
Stabi 1 i ty
class
B
C
C
D
Wind
(m/s)
4.0
4.0
2.0
4.0
Decrease in stack gas ve
5%
4.14
4.46
5.15
5.98
10%
8.66
9.33
10.85
12.62
15%
13.59
14.68
17.19
20.00
loc i ty
20%
19.00
25.58
24.28
28.30
TABLE C-7. PERCENT DECREASE IN DISTANCE TO MAXIMUM CONCENTRATION
WITH DECREASING STACK GAS VELOCITY
Decrease in stack gas velocity
otaui j. i i y
class
B
C
C
D
VY 1 IIU
(m/s)
4.0
4.0
2.0
4.0
5%
-1.94
-2.30
-2.68
-3.95
10%
-3.99
-4.65
-5.78
-7.88
15%
-6.04
-7.05
-8.64
-11.85
20%
-8.15
-9.55
-11.52
-15.68
92
-------
CD
co
TJ
oq
C
<-i
(0
O
I
to
«•+ co
O c&
I 3
3 w
as -.
X rf
i' <'
c ~.
3 ~
O O
l-b
O
^ 3
» JB
3 X
(K? -.
CD 3
W C
3
o
en 3
S3 CD
O 3
<~s
Cfq fo
03 .-1
CO —.
O
< 3
-------
GLOSSARY
Some of the following definitions are taken from "Glossary of
Meteorology," Ralph E. Huschke, editor. American Meteorological
Society, Boston. 1959. 638 pp.
ADIABATIC PROCESS—A thermodynami c change of state of a system in
which there is no transfer of heat or mass across the
boundaries of the system. In an adiabatic process,
compression always results in warming, expansion in cooling.
ADVECTION--The process of transport of an atmospheric property
solely by the mass motion (velocity field) of the
atmosphere. Refers to predominantly horizontal large-scale
motions of the atmosphere.
AIR MASS--A widespread body of air that is approximately
homogeneous in its horizontal and vertical properties,
particularly with reference to temperature and moisture
d i s tr ibut ion.
ATMOSPHERIC STABILITY--State of the atmosphere with respect to
vertical motions. Atmospheric conditions may be classified
as stable, neutral, or unstable. In stable conditions, the
potential temperature increases with height, and vertical
motions are inhibited. Under these conditions, pollutants
emitted at the ground tend to accumulate, while effluents
from elevated sources normally remain aloft for long
distances. In unstable conditions, the potential
temperature decreases with height, and vertical motions are
enhanced. Low-level emissions are dispersed rapidly upward,
and high-level emissions are dispersed rapidly in the
vertical. Elevated sources frequently make their maximum
contribution to short-term ambient pollutant concentrations
under unstable conditions. Between stable and unstable
conditions is the situation in which the vertical
temperature profile decreases nearly adiabatica1ly. This
condition, called "neutral stability," is quite frequent in
most locations. For sources with tall stacks, the high wind
speed neutral condition suppresses plume rise, and high
ground-level concentrations are often observed. For
ground-level emissions, near-neutral conditions usually
result in concentrations between those for stable and
unstable conditions.
94
-------
BUOYANCY FLUX--A parameter related to the buoyant vertical
motions of a released volume of effluent due to its excess
of temperature over the surrounding air.
CONING--Spreading to produce a cone-shaped plume with its apex at
the source. This usually occurs under windy conditions, and
when the vertical temperature is near dry adiabatic or
somewhat subadiabatic.
DOWNWASH--Rapid mixing downward of a plume by strong winds;
usually observed in the lee of buildings and stacks.
DRY ADIABATIC LAPSE RATE--The rate of decrease of temperature
with height of a parcel of dry air lifted adiabatica1 ly to
lower pressures; 9.8°C/km.
EFFECTIVE STACK HEIGHT--The physical stack height plus plume
rise. The point above the ground at which the gaseous
effluent becomes essentially level.
ELEVATED INVERSION--An inversion layer above the ground surface
that inhibits the dispersion of buoyant plumes. Elevated
inversions are initiated by subsiding air from upper
atmospheric levels or are the transitional zones between
dissimilar air masses. Elevated inversions can also result
from radiation inversions (which start at the surface) that
are partially eliminated from below, due to surface heating.
FANNING--Spreading of a plume to give the appearance of a fan
spread horizontally. This occurs under stable conditions
when the vertical dispersion is greatly suppressed due to
the vertical thermal structure but does not impede
horizontal direction variations.
FUMIGATION--The rapid mixing downward to the ground of material
previously emitted into a stable layer. Commonly occurs
when the nocturnal temperature inversion is rapidly
dissipated by solar heating of the surface; also occurs in
sea breeze circulations during late morning or early
afternoon.
INSOLATION--Incoming solar radiation received at the earth's
sur face.
INVERSION—A layer of air in which temperature increases with
altitude; that is, inverted with respect to the more usual
decrease of temperature with altitude.
LAPSE RATE--Adiabatic lapse rate is the rate of temperature
change with height of a parcel displaced vertically in the
atmosphere adiabatically. The parcel becomes cooler with
lifting as it expands upon encountering less pressure;
95
-------
conversely, the parcel becomes warmer with descent as it is
compressed due to higher pressures. The adiabatic lapse
rate is a decrease of about 1°C/100 m rise. When the
temperature structure of the atmosphere (the environmental
lapse rate) is subadiabatic (i.e., cooling is less rapid
with height than the adiabatic rate), the atmosphere damps
out vertical motion. When the temperature structure is
superadiabatic, (i.e., cooling with height is more rapid
than the adiabatic rate), rising parcels continue to
accelerate upward. When the environmental lapse rate is
near the dry adiabatic rate, vertical motions are neither
damped out nor enhanced.
LOFTING--Upward spreading of the plume in the vertical above the
plume centerline, but minimum spreading downward, because
the plume is unable to penetrate an inversion below the
plume centerline.
LOOP ING--Plume spreading with the instantaneous appearance of
large loops; the emitted plume is caught in thermals and
rises, and a few seconds later, the newly emitted plume is
caught in descending air and moves downward from the point
of emission. Occurs in strongly unstable air; usually, the
vertical thermal structure is superadiabatic near the
ground.
MIXING HEIGHT--Height of the unstable or neutral layer that is
well-mixed. Usually the height of the first significant
inversion above the surface delimits the depth available for
vertical dispersion of pollutants.
.NOCTURNAL INVERSION—Surface-based inversion induced by radia-
tional cooling.
PHYSICAL STACK HEIGHT—ACtua 1 height (above ground) of a stack or
effluent source.
PLUME RISE--The height of a plume centerline above the point of
release at a distance downwind from a source due to buoyancy
and momentum effects. (The height above the point of
release where the plume becomes level is the final plume
rise.)
SUBSIDENCE INVERSION—A temperature inversion produced by the
adiabatic warming of a layer of descending air. Results in
a limited mixing volume below the subsiding layer.
SURFACE-BASED INVERSION--An inversion layer of stable air close
to the ground, usually a radiation inversion. Inhibits
dispersion of low-level releases of fugitive dust and other
pollutants.
96
-------
SURFACE BOUNDARY LAYER--The thin layer of air immediately above
the earth's surface. (In this layer, shearing stresses are
nearly cons tant.)
SURFACE ROUGHNESS--Irregular ities in or
that increase mechanical turbulence
d i spers i on.
on the earth's surface
and enhance pollutant
TRAPPING--Plume spreading is moderate to rapid near the point of
emission, but is impeded vertically (trapped) by an elevated
stable layer. Usually, thermal conditions in the lower
layer are adiabatic or subadiabatic.
97
-------
Date
Chief, Environmental Operations Branch
Meteorology and Assessment Division (MD-80)
U. S. Environmental Protection Agency
Research Triangle Park, NC 27711
I would like to receive future revisions to the
"PTPLU User's Guide."
Name
Organ izat ion
Address
City
State
Zip Code
Phone (Opt ional) (
99
« US GOVERNMENT PRCNTINO OFFICE 1982-559-092/0513
------- |