r/EPA
PROPERTY OF
United States
Environmental Protection
Agency
Environmental Sciences Research
Laboratory
Research Trjangle Park NC 27711
EPA-600/8-80-016
April 1980
Research and Development
User's Guide for
MPTER
A Multiple Point
Gaussian Dispersion
Algorithm with
Optional Terrain
Adjustment
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U S Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are
1 Environmental Health Effects Research
2 Environmental Protection Technology
3 Ecological Research
4 Environmental Monitoring
5 Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7 Interagency Energy-Environment Research and Development
8. "Special" Reports
9 Miscellaneous Reports
This report has been assigned to the "SPECIAL" REPORTS series. This series is
reserved for reports targeted to meet the technical information needs of specific
user groups The series includes problem-oriented reports, research application
reports, and executive summary documents Examples include state-of-the-art
analyses, technology assessments, design manuals, user manuals, and reports
on the results of major research and development efforts.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/8-80-016
APRIL 1980
USER'S GUIDE FOR F1PTER
A Multiple Point Gaussian Dispersion Algorithm
With Optional Terrain Adjustment
by
Thomas E. Pierce* and D. Bruce Turner*
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
Research Triangle Park, NC 27711
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NC 27711
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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. Mention of trade names or commercial
products does not constitute endorsement or recommendation for
use.
AUTHORS' AFFILIATION
The authors are on assignment to the U. S. Environmental
Protection Agency from the National Oceanic and Atmospheric
Administration, U. S. Department of Commerce.
11
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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 capable of describing air
quality and atmospheric processes affecting the disposition
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 computer network system.
MPTER is an adaptation of the point source portion of
RAMR, using Gaussian point source modeling techniques.
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.
Comments and suggestions regarding this publication
should be directed to:
Chief, Environmental Operations Branch
Meteorology and Assessment Division (MD-80)
Environmental Protection Agency
RESRCH TRI PK, 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. The User's Guide is
available from NTIS, Springfield, Va. 22161.
The magnetic tape containing all Fortran source codes
for MPTER may be ordered from Computer Products, NTIS.
iii
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ABSTRACT
The information presented in this user's guide is directed
to air pollution scientists interested in applying air quality
simulation models. MPTER is the designation for Multiple Point
source algorithm with TERrain adjustments. This algorithm is
useful for estimating air quality concentrations of relatively
nonreactive pollutants; hourly estimates are made using the
Gaussian steady-state model. The algorithm is most applicable
for source-receptor distances less than 10 km and for locations
with level or rolling terrain where a single wind vector for
each hour adequately approximates the flow over the source and
receptor sites. The terrain adjustment option is limited in
application to receptors whose elevation is no higher than the
lowest stack top elevation of the sources considered. Calcula-
tions are performed on the hourly meteorological data that the
model requires: wind direction, wind speed, temperature, stabil-
ity class, and mixing height. Emission information required of
the point sources are source coordinates, emission rate, physi-
cal height, stack diameter, stack gas exit velocity, and stack
gas temperature.
In addition to terrain adjustment, options are available
for stack downwash, gradual plume rise, and buoyancy-induced
dispersion. All printed output is optionally available so the
user can avoid unneeded output volume. General information is
contained in the Executive Summary and the first three chapters.
The technical basis for the algorithm is given in Chapter 4 and
Appendices A and B. The remaining material herein relates to
use and understanding of the computer program for the algorithm.
iv
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CONTENTS
Preface iii
Abstract iv
Figures vi
Tables vi
Acknowledgments viii
Executive Summary 1
1. Introduction 3
2. Data Requirements 4
3. Recommendations 7
Uses 7
Assumptions 9
Sources of error and accuracy 13
4. Basis for MPTER 15
Gaussian modeling 15
Inputs 16
Plume rise 18
Dispersion Parameters 19
Gaussian plume equations 19
Other considerations 20
Special optional features 20
5. Overview of Computer Program 25
Program description 25
Additional comments 26
6. Discussion of Computer Aspects of MPTER 28
Description of source code 28
Data preparation 28
Running costs and output volume 41
Error messages and remedial action 44
7. Input Card, Input File and Output
File Specifications 49
8. Example Problems 65
References 144
Appendices 146
A. Point source computations 146
B. Plume rise 150
C. Source program listing 156
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FIGURES
Number Page
1 Adjustment of plume rise due to terrain 24
2 Subroutine structure in MPTER 27
3 Input data deck setup for MPTER 56
4 System flow for MPTER 57
5 Concentration as function of distance for
source 2, hour 1 for four runs of example 2 96
TABLES
Number Page
1 Wind Profile Power Law Exponents Corresponding
to a 0.03 m Roughness 17
2 Statistics Related to MPTER Source Code Size 26
3 MPTER Output Volume 42
4 Maximum Output: 5-day run for 250 sources
and 180 receptors 43
5 MPTER Card Type 1,2, and 3 - Title (3 cards) 49
6 MPTER Card 4 - Control and Constants (1 card) 50
7 MPTER Card 5 - Options (1 card) 51
8 MPTER Card 6 - Wind and Terrain (1 card) 52
9 MPTER Card Type 7 - Point Source (up to 250 cards). . . 52
10 MPTER Card Type 8 - Met. Data Identifiers 53
11 MPTER Card Type 9 - Specified Significant
Sources (1 card) 53
12 MPTER Card Type 10 - Polar Coordinate
Receptors (1 card) 53
13 MPTER Card Type 11 - Polar Coordinate
Receptor Elevations (36 cards) 54
14 MPTER Card Type 12 - Receptor (up to 180 cards) .... 54
15 MPTER Card Type 13 - Segmented Run (1 card) 54
VI
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TABLES Cont'd
Number Page
16 MPTER Card Type 14 - Meteorology 55
17 MPTER Optional Input File - Meteorological
Data (Unit 11) 59
18 MPTER Optional Input File -
Emission Data (Unit 15) 60
19 MPTER Optional Output Punched Cards - Average
Concentrations (Unit 1) 60
20 MPTER Optional Output File - Partial
Concentrations (Unit 10) 61
21 MPTER Optional Output File - Hourly
Concentrations (Unit 12) 62
22 MPTER Optional Output File - Averaging -
Period Concentrations (Unit 13) 63
23 MPTER Optional Temporary File - Values for
High-Five Tables (Unit 14) 64
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ACKNOWLEDGMENTS
The authors appreciate the discovery of errors and the suggestions for
change received from the regional meteorologists, especially Mick Daye, in
their provisional use of earlier MPTER versions; scientists in OAQPS, espec-
ially Jerome Mersch, are also thanked for their testing of MPTER.
The authors thank Barbara Gass of the State of Michigan, Department of
Natural Resources for suggesting the conditions of the source used in Example
2.
The assistance of Barbara Hinton, Hazel Hevenor, Erik Sieurin, and
especially that of Joan Emory is gratefully acknowledged.
viii
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EXECUTIVE SUMMARY
The MPTER computer code (Multiple Point source model with TERrain
adjustments) provides a method to estimate air pollutant concentrations
from multiple sources in rural environments, and can make optional
adjustments for slight terrain variations.
Although the algorithm is based upon Gaussian modeling assumptions
and incorporates the Pasquill-Gifford (P-G) dispersion parameter values,
several technical options and various parameter values may also be entered
as input. Hence, MPTER may be considered a research tool for exploratory
use of various assumptions and parameter values.
****************
* If estimates are to be submitted for review to satisfy regula- *
* tory requirements, certain parameter values and options may be re- *
* required. Under these circumstances, specific applications of MPTER *
* should be discussed with the appropriate regional meteorologist to *
* ensure that the calculations are performed in the most appropriate *
* way. *
****************
MPTER can estimate the resulting concentrations at a maximum of 180
receptors from a maximum of 250 point sources. Gaussian assumptions and
techniques are used to perform the estimates hourly, considering each
hour as a steady state period. Required input information consists of
point source and hourly meteorological data. Periods from one hour to
one year may be simulated, with all output controlled by the user through
selection of options.
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Features of the algorithm include:
o Averaging periods of longer than 1 hour, if selected by user.
o Hourly meteorological data that may be read off punched cards
for each hour, or from a tape (or disk) containing a
year's data (same data as used for RAM or CRSTER).
o An optional terrain adjustment as a function of stability
class.
o Inclusion or omission of stack downwash.
o Inclusion of gradual plume rise, or final rise only.
o Inclusion or omission of buoyancy-induced dispersion of
pollutant at the source using the method of Pasquill.
o Input of anemometer height.
o Input of wind profile power law exponents as functions of
stability.
o Concentration contributions that are available per hour
and/or for the selected averaging period at each
receptor from up to 25 sources.
o Concentrations available hourly and/or for the selected
averaging period at each receptor.
o Optional output of the following information: average
concentration over length of record, plus highest
five concentrations for each receptor for four
averaging times (1-, 3-, 8-, and 24-hour); and
an additional averaging time selected by the user.
o Optional output files for further processing of concentrations
that are available per hour and for each averaging
period.
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SECTION 1
INTRODUCTION
Although since the availability of UNAMAP (Version 3) in March of 1978
(EPA, 1978), there has been a model that will estimate impact from multiple
sources in rural areas over flat terrain, RAMR (The rural version of RAM,
Turner and Novak, 1978), and a model that will estimate impact from a single
plant for situations where terrain features are no higher than the elevation
of the lowest stack top for the plant, CRSTER (EPA, 1977), there has not been
a readily available model that will consider both multiple sources and adjust-
ments for slight terrain differences. The MPTER was assembled to fill this
need.
MPTER, Multiple Point source model with TERraln adjustments, essentially
bases its calculations for point sources on RAMR. The terrain adjustment
factors are entered as functions of stability class. This algorithm is
limited to terrain situations where receptor ground-level elevations are no
higher than the elevation of the lowest stack top.
Computations can be made for 180 receptors and 250 point sources with
the requirement that meteorological data be furnished for each hour that is
simulated. Either short-term (several hours) or long-term (one year) calcu-
lations are available to the user. A number of options allows the user
versatility in the amount of MPTER output; other options allow calculations
of stack downwash, gradual plume rise, and enhanced initial plume size due to
buoyancy induced turbulence.
Section 2 of this users guide gives the data requirements for employing
MPTER and Section 3 discusses uses, assumptions, and sources of error and
accuracy. These two sections should give the air pollution manager the
background to decide if this algorithm is useful to his needs. Section 4
presents the mathematical basis for the algorithm, and the remaining sections
provide information to the air pollution scientist or computer specialist
wanting to prepare data and run the algorithm.
3
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SECTION 2
DATA REQUIREMENTS
To estimate concentrations for any simulated time period, data for
emissions, meteorology, receptors, and for program control are needed. These
are discussed briefly here. More detail on proper formatting for data entry
to the program is covered in Chapter 7.
EMISSION DATA
The following information on each point source is required as input:
East coordinate of point source, user units
North coordinate of point source, user units
Sulfur dioxide emission rate, g s
Particulate emission rate, g s~
(Only one of the two emission rates given above will be used
in a given run.)
Physical stack height, m
Stack gas temperature, K
Stack inside diameter, m
Stack gas exit velocity, m s~
Stack ground-level elevation, user height units
(This last data entry is only needed if the terrain adjust-
ment option is used. Any height units can be selected by the
user if used throughout.)
The east-north coordinate system can be provided in any consistent
units.
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METEOROLOGICAL DATA
Meteorological data can be entered by use of a year's prepared data on
tape (or disk) or on punched cards with a separate card for each simulated
hour. Data on tape or disk are arranged with daily records. Meteorological
data prepared with RAMMET or the CRSTER preprocessor are quite acceptable to
the MPTER program. Hourly data on cards include the following:
Year
Julian day
Hour
Stability class
Wind speed, m s
Ambient air temperature, K
Wind direction, from which the wind blows, degrees
clockwise from north
Mixing height, top of the neutral or unstable layer, m
(not required for stable conditions)
RECEPTOR DATA
MPTER has the capability of generating an array of receptors in polar
coordinate form (explained in more detail later). For most applications,
information is entered on a separate punched card for each receptor.
The following information is required:
East coordinate of receptor, user units
North coordinate of receptor, user units
Receptor height above local ground-level, m
Receptor ground-level elevation, user height units
(The elevation is required only if the terrain adjust-
ment option is used.)
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CONTROL DATA
The following control information is needed for a run. Some additional
information, to be discussed later, may be required depending upon options
selected. Control information needed includes:
Headings (for output)
Year
Starting Julian Day
Starting Hour
Number of averaging periods to be run
Number of hours in each averaging period
Code for selecting the pollutant for this run (sulfur
dioxide or particulate)
Number of significant sources (used for contribution to
concentration from individual sources)
Additional averaging time for high-five table (explained
later)
Conversion for user units (east and north coordinates)
Conversion for user height units
Half-life of pollutant used in this run
Values to select each option
Anemometer height
Wind profile power law exponents (one for each stability)
Terrain adjustments, if used (one for each stability)
Further discussion of input data is given in Chapter 7.
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SECTION 3
RECOMMENDATIONS
USES
As stated in the introduction, MPTER is a multiple point source dis-
persion model for situations that would be considered rural. Because optional
adjustments can be made for slight terrain variations, careful study of model
inputs is required to ensure the user's problem is addressed, and to provide
proper output for the problem at hand. Also, since the model may be applied
to impact analyses in response to regulatory requirements, the user should
determine if certain options and/or parameter values are required by the
potential reviewer in order to be acceptable.
Its versatility allows MPTER to function as both a tool for research and
for more routine impact analysis. In research, numerous parameter variations
can be explored for comparisons with measured air quality data, and various
sensitivities can be determined.
A frequent use of the model will be to assess air pollutant impact to
compare with National Ambient Air Quality Standards. Since the short-term
standards are not to be exceeded more than once a year, extremes of the
frequency distribution must be determined. Brute force approaches may be
required to estimate these extremes through calculation of a full year's
data, as is done by CRSTER. Receptor locations are input by the user, except
when the model's option is used for generating a polar coordinate set of
receptors centered in a specified location.
Determining appropriate receptor locations where maximum impact might be
expected is a difficult user problem. Little guidance is available for
selecting optimum receptor positions, but the following three steps may prove
helpful: 1) use screening methods to locate distances to maxima; 2) at
chese distances, use polar coordinate locations about each source of significance,
analyzing a year's or more meteorological data, and then 3) make estimates
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using receptors at probable locations of source interaction.
In other diverse applications, MPTER can estimate concentrations from a
single source for one simulated hour for one or more receptors, either at
ground-level or varying heights above the ground, or it can simulate con-
centrations hour-by-hour for a year that result from 250 point sources at as
many as 180 receptors.
MPTER is most applicable within 10 km of the source. Its use beyond
this distance will be less accurate due to mesoscale influences, such as wind
change with height, and to meteorological conditions that may vary during the
time of transport.
The types of multiple-source applications for which MPTER is suited are
similar to single-source applications of CRSTER, and include:
o Stack design studies
o Combustion source permit applications
o Regulatory variance evaluation
o Monitoring network design
o Control strategy evaluation for SIPs
o Fuel (e.g., coal) conversion studies
o Control technology evaluation
o Design of supplementary control systems
o New source review
o Prevention of significant deterioration (within 10 km of sources)
Computer time and costs will in general be proportional to the number of
hours simulated, since each hour's simulation is done independently. Time
and costs will also vary in proportion to the number of sources. Regarding
receptors, time and costs will increase in proportion to the number of possible
source-receptor pairs, i.e., the number of sources times the number of
receptors. Use of a minimum number of receptors will therefore lower computer
costs.
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ASSUMPTIONS
The foundation of MPTER, including much of its computer code, is the
point source portion of RAMR.
Gaussian Modeling
The following assumptions are made: 1) continuous plumes are diluted
upon release by the wind speed at stack top; 2) dispersion from continuous
plumes results in time averaged Gaussian distributions in both the horizontal
and vertical directions through the dispersing plume; 3) concentration esti-
mates may be made for each hourly period using the mean meteorological condi-
tions appropriate for each hour; 4) the total concentration at a receptor is
the sum of the concentrations estimated at the receptor from each source,
i.e., concentrations are additive; and 5) concentrations at a receptor for
periods longer than an hour can be determined by averaging the hourly concen-
trations over the period.
The upwind distance x and the crosswind distance y of the source from
the receptor is determined as a function of the mean hourly wind direction.
Dispersion parameter values are determined as functions of stability class
and upwind distance. Equations to estimate concentration are selected de-
pendent upon stability class, and, for neutral or unstable conditions, upon
the relation of dispersion parameter value to mixing height (See Appendix A).
The location of the receptor relative to the plume position is a dominant
factor in the magnitude of the concentration.
Dispersion Parameter Values
The dispersion parameter values used in MPTER are the Pasquill-Gifford
(P-G) parameters (Pasquill, 1961; Gifford, 1960) representative for open
country (a roughness of approximately 0.03 m ). The subroutines used to
determine the parameter values are the same as in the UNAMAP programs PTDIS,
PTMTP, and RAMR.
Except for stable layers aloft, which inhibit vertical dispersion, the
atmosphere is treated as a single layer in the vertical that has the same
rate of vertical dispersion throughout. Complete eddy reflection is assumed
both from the ground and from the stable layer aloft, given by the mixing
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height for neutral and unstable stabilities.
Plume Rise
Plume rise is calculated using the methods of Briggs (See Appendix B).
Although the plume rise from point sources is usually dominated by buoyancy,
plume rise due to momentum is also considered. (Merging of nearby buoyant
plumes is not considered.) Stack downwash is an optional consideration.
Building downwash can not be considered.
Input Data
All input data are assumed to be representative for the area being
modeled. Since concentration estimates are proportional to emissions, con-
sideration of variations may be necessary, such as diurnal or weekday vs.
weekend. MPTER can utilize hourly emissions as an option. The meteorological
data consisting of wind direction, wind speed, temperature, stability class,
and mixing height for each hour should be representative of the region being
modeled. Representativeness and possible sources of error are discussed in
Section 4. Wind speed is measured at the anemometer height and then extra-
polated to the stack top, using power law wind speed profiles with the expo-
nent dependent upon stability.
Mixing Height
The entire plume is completely eddy-reflected if the effective plume
height is below the mixing height. The entire plume is assumed to be within
the stable layer aloft if the effective plume height is above the mixing
height.
MPTER does not include calculations for the transitional phenomenon of
fumigation, which is the elimination of an inversion layer containing a
stabilized plume from below (which causes mixing of pollutants downward,
resulting in uniform concentrations with height beneath the original plume
center!ine).
Removal or Depletion
Transformations of a pollutant resulting in loss of that pollutant
throughout the entire depth of each plume can be approximated by MPTER. If
the loss to be simulated is realistic and occurs through the whole plume
10
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without dependence upon concentration, then this exponential loss may provide
a reasonable simulation. If however, the loss mechanism is selective, the
loss mechanism built into the model will not approximate the atmospheric
chemistry very well. Examples of selective loss mechanisms include impaction
with features on the ground surface, reactions with materials on the ground,
or dependence on a given small parcel of air for concentration (requiring
consideration of contributions from all sources to this parcel).
SPECIAL FEATURES
The following four features are options in MPTER.
Option 1: Terrain Adjustments
Consideration of the differences between local ground-level elevation at
the stack and at the receptor is an option in MPTER. Terrain adjustment
factors are entered by the user for each of the six Pasquill stability
classes. These factors can be any real number between 0 and 1. Terrain
adjustments can be simulated as in CRSTER by entry of O's for all six stabil-
ities, resulting in plumes that level off and remain at the same mean-sea-
level elevation. Calculations are made by subtracting the difference, defined
as the elevation of receptor ground-level minus the elevation of the source
ground-level, from the effective plume height. More detail of the terrain
adjustment is given in Section 4.
Of note to the user is that calculation of terrain adjustment is limited
to receptors whose ground-level elevation is less than the elevation of the
lowest stack top used in the run.
The terrain adjustment incorporated in MPTER is obviously simplistic.
For the estimation of plume behavior in the vicinity of a single hill, the
stable-plume fluid modeling studies of Snyder and Hunt (1978) have shown the
importance of the Froude number, and of the location of the receptor and the
plume relative to hill base and top. None of these parameters is considered
here, but rather the relation of receptor and source ground-level elevations.
The reader is therefore cautioned against assigning too great a significance
to results obtained using the terrain adjustment option.
11
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Option 2: Stack Downwash
A second optional feature of MPTER is considerations of stack tip
downwash using the methods of Briggs. In such an analysis, a height increment
is deducted from the physical stack height before determining momentum or
buoyancy rise. This option primarily affects computations from stacks having
small ratios of exit velocity to wind speed.
Option 3: Gradual Rise
Gradual plume rise has been made an optional feature of MPTER, because
2/3
although the use of the x dependence for rising plumes will determine
average plume height with distances quite well, the plume axis is not horizontal
during the rising phase. Therefore, dispersion is taking place perpendicular
to the bent-over plume axis rather than vertically. The P-G dispersion
parameters represent horizontal and vertical dispersion about a horizontal
plume, which may not be appropriate for estimating dispersion of a rising
bent-over plume. By making computations with and without the gradual plume
rise, at least identification is possible of potentially high concentrations
during the gradual plume rise phase. When gradual rise is not employed,
computations are made using the final effective plume height.
Option 4: Buoyancy-Induced Dispersion
The final optional feature of MPTER is a method suggested by Pasquill
(1976) for determining the buoyancy induced dispersion in both the horizontal
and vertical directions. This feature is offered because emitted plumes
undergo a certain amount of growth during the plume rise phase, due to the
turbulent motions associated with the conditions of plume release and the
turbulent entrainment of ambient air. Such dispersion, however will generally
have little effect upon maximum concentrations unless the stack height is
small compared to the plume rise.
12
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SOURCES OF ERROR AND ACCURACY
The user would benefit appreciably if a given expected accuracy of the
output could be associated with each air quality dispersion model. Unfor-
tunately, such an association is not possible, since accuracy is dependent
upon not only the model, but on the quality of the input information used in
the application (including both emission information and meteorological
data),
Since concentrations are directly dependent upon emissions, inaccurate
emissions information is a source of error. The estimation of emission height,
which is obtained through the calculation of plume rise, is dependent upon
exit velocity and exit temperature. Correct specification of these para-
meters, as well as the physical characteristics of stack location, stack
diameter, and stack height, is important. When hour-to-hour comparisons are
made, hourly emission rates and exit velocities are important.
A second source of error is the representativeness of the meteorological
data available for input. Generally, the greater the distance from the site
to be modeled from the location at which the meteorological data are measured,
the less representative the data. Slight topographic differences between two
adjacent sites, however, may also cause the data at one site to be quite
nonrepresentative of the other site (for example, two valleys oriented in
different directions). Wind speed and direction are probably more subject to
terrain-induced nonrepresentativeness than are mixing height or stability
class.
Even if meteorological data from a site being modeled are considered to
be climatologically representative, the extrapolation of the wind speed to
the stack top of each source may still produce rather large errors on an
hour-to-hour basis. Possibly the greatest single cause of inaccuracy in the
model is incorrect input of the wind direction transporting the plume. Where
the primary meteorological data are from near-ground measurements (< 10 m
high), the taller and more buoyant a plume is, the greater the chance for
wind direction inaccuracies.
In MPTER no attempt is made to extrapolate wind direction to stack top
from a near-ground observation, since the deviation from the surface wind may
13
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be either clockwise or counterclockwise. Although surface wind direction
may have little effect upon long-term concentrations (such as annual average)
from single plants, and may not greatly alter estimates of extreme concentra-
tion values from such a source, use of surface wind direction to determine
plume transport direction usually causes large errors in hour-to-hour esti-
mates. This potential error is a very important consideration if attempting
to compare air quality measurements with the model estimates. The error is
also important in considering interactions of several sources where actual
wind directions are significant in determining the location of a plume from a
source passing over another source.
Since the P-G stability classes are used as input and the P-G dispersion
parameters are used for plume spreading, the fact should be recognized that a
change of only one stability class for input will cause large changes (factors
of 5 to 10) in concentration at a receptor. Such changes are especially
likely if the receptor is closer to the source than the distance to maximum
concentration.
Other potential causes of large inaccuracies in concentration at a given
point include wind speed errors, wind speed profile power law exponents that
differ from actual variations, and nonrepresentative stability classes.
However, if the user is searching for maximum impact and is relocating recep-
tors in order to find such maxima, there will be considerably less sensitivity
to wind speed differences and power law exponents, but still significant
sensitivity to stability class.
Not included in this model are situations where wind speed varies
markedly within the hour, whereby the effective plume height will fluctuate,
causing increased vertical dispersion of the plume.
Maxima even at the extreme ends of the frequency distribution will tend
to have more accuracy than hour-to-hour comparisons. Longer averaging
times, such as annual concentrations, will also have less error than short
averaging times. Background concentrations from sources not considered in
the emission inventory may become more important for the longer averaging
times.
24
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SECTION 4
BASIS FOR MPTER
As mentioned, the point source portion of RAMR is the basis of MPTER,
providing much of its computer code.
GAUSSIAN MODELING
The following assumptions common to Gaussian modeling are made in MPTER.
Plume Dilution
Continuous releases of pollutants from stacks are diluted by the mean
(hourly) wind speed at the stack top.
Gaussian Horizontal and Vertical Distributions
Dispersion is assumed to occur such that time-averaged plumes over 1-
hour periods have Gaussian (normal) distributions perpendicular to the plume
centerline in the horizontal and vertical.
Steady-State
Calculations are made as if the atmosphere had reached a steady state.
Concentrations for a given hour are calculated independently of conditions
for the previous hour or preceding hours.
Concentration, Sum of Contributions
The total concentration for a given hour for a particular receptor is
the sum of the estimated contributions from each source.
Average Concentrations
The average concentration over periods longer than 1 hour can be deter-
mined by averaging the hourly concentrations at the receptor over the period.
15
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INPUTS
Emission Inventories
Since, for similar meteorological conditions, the contribution from
a source to the concentration at a receptor is directly proportional to
emission rate from that source, emissions must be expressed accurately.
Attempts should be made to include time variations occurring from many
air pollution sources, such as hourly changes per day or weekdays vs
weekends. For cases that have complete emissions information, creation
of a system is usually necessary that will calculate and store hourly
emissions for the designated period to be simulated. This task can be
accomplished independently of MPTER; the model is designed to accept
hourly emissions in addition to annual emission rates that establish a
correspondence between emissions and exit velocity.
Meteorological Conditions Representative of Region
The meteorological input for each hour consists of a value for each
of five parameters: wind direction, wind speed, temperature, stability
class, and mixing height -- all of which should be representative of the
entire region containing the sources and receptors. Mixing height is
required only if the stability is neutral or unstable.
Wind Speeds and Directions
Wind speeds and directions should be hourly averages. (National
Weather Service hourly observations are actually averages of a few
minutes at the time of the observation, usually 5 to 10 minutes prior to
the hour.) Input winds should be representative of the entire region
being modeled.
Emissions from continuous sources are assumed to be stretched along
the direction of the wind by the speed of the wind at stack top. Thus,
the stronger the wind, the greater the dilution of the emitted plume.
In MPTER the input wind speed is assumed representative for the input
anemometer height above the ground. The wind speed uh at the physical
stack height h is calculated from:
uh - u2 (h/z/
16
-------
where u is the input wind speed for this hour, z is the anemometer
^ a
height, and the exponent p is a function of stability. If u. is determined
_1 n
to be less than 1ms , it is set equal to 1.
Since the P-G dispersion parameters used in MPTER have greatest
validity for a surface roughness of approximately 0.03 m (Pasquill,
1976), wind speed power law exponents for each stability for this roughness
are based on Irwin (1979), given in Table 1.
TABLE 1. WIND PROFILE POWER LAW EXPONENTS
CORRESPONDING TO A 0.03 METER ROUGHNESS
Stability Exponent
A 0.07
B 0.07
C 0.10
D 0.15
E 0.35
F 0.55
As stated in the previous chapter, directional shear with height is
not included, which means that the direction of flow is assumed to be
the same at all heights over the region. The taller the effective
height of a source, the larger the expected error in direction of plume
transport. Although the effects of surface friction are such that wind
direction usually veers (turns clockwise) with height, the thermal
effects (in response to the horizontal temperature gradient in the
region) can overcome the effect of friction and cause backing (turning
counterclockwise with height) instead of veering.
In the program RAMMET, which processes National Weather Service
hourly observations, the wind directions (reported to the nearest 10°)
are altered by a randomly generated number from 0 to 9 used to add -4°
to +5° to the wind vector. An extreme overestimate of concentration
17
-------
is thus prevented at a point downwind of a source during a period of
steady wind, when sequential observations are from the same direction.
Rather than allow the plume centerline to remain in exactly the same
position for several hours, the changing wind allows for some variation
of the plume centerline within the 10° sector. Although this step can
in no way simulate the actual sequence of hourly events (wind direction
to 1° accuracy cannot be obtained from wind direction reported to the
nearest 10°), such variations can be expected to produce more representative
concentrations over a period of record than those obtained using winds
to only the 10° increments. (Sensitivity tests of this alteration for
single sources have indicated that, where a few hours of unstable conditions
are critical to producing high concentrations, the resulting concentrations
are extremely sensitive to the exact sequence of random numbers used.
Such a sequence might be two wind directions 1° apart versus two wind
directions 9° apart. Differences of 40 to 50 percent in 24-hour concentrations
from a single source have appeared in the sensitivity tests, due to the
random wind direction variation alone.) Use of the most accurate wind
information available for input is therefore necessary.
Mixing Height
If vertical temperature soundings are available from a representative
location, they should be used with hourly surface temperatures to estimate
hourly mixing heights for periods with neutral or unstable stability.
If a series of National Weather Service hourly data are being processed
by the program RAMMET, two values of mixing height per day are required.
These are the maximum and minimum mixing heights as defined by Holzworth
(1972). RAMMET provides a crude interpolation to obtain hourly mixing
heights. This interpolation does not consider hourly surface temperatures.
PLUME RISE
Plume rise from point sources is calculated using the methods of
Briggs (see Appendix B). Although the plume rise from point sources is
usually dominated by buoyancy, plume rise due to momentum is also considered.
Stack downwash can optionally be considered, though building downwash
and the merging of nearby buoyant plumes cannot.
18
-------
In ranking the point sources by the significance of their expected
impact, only the rise due to buoyancy is processed, since it is expected
to be the dominant plume rise factor. In the computation of the effect
of each point source upon receptors for each simulated hour, however,
all three of the above mentioned effects -- stack downwash, momentum plume
rise, and buoyant plume rise -- can be considered. These computations are
discussed in detail in Appendix B. Of note is that since wind speeds are not
allowed to be less than 1ms", the stable buoyancy plume rise for calm
conditions is not required and is therefore not included in the program code
for MPTER.
DISPERSION PARAMETERS
The dispersion parameter values in MPTER are the P-G values (Pasquill,
1961; Gifford, 1960), which appear as graphs in Turner (1970) and in
Gifford (Figure 2; 1976). These are most applicable to a surface roughness
of 0.03 m (Pasquill, 1976). The subroutines used to determine these
open-countryside parameter values are the same as in the UNAMAP programs
PTDIS and PTMTP (EPA, 1978).
Except for stable layers aloft that inhibit vertical dispersion,
the atmosphere is treated as a single layer vertically, with the same
rate of vertical dispersion throughout the layer. Complete eddy reflection
is assumed both from the ground and from the stable layer aloft, which
is given by the mixing height.
GAUSSIAN PLUME EQUATIONS
The upwind distance x of the point source from the receptor and the
crosswind distance, y, of the point source from the receptor are calculated
using Equations (Al) and (A2) in Appendix A, for each source-receptor
pair per simulated hour. Both dispersion parameter values a and a are
determined as functions of this upwind distance x and stability class.
One of three equations is used to estimate concentrations under
various conditions of stability and mixing height. Equation (A3) in
Appendix A is used for stable conditions or for unlimited mixing; eddy
reflection at the ground is assumed. For unstable or neutral conditions
where vertical dispersion is so great that uniform mixing is assured beneath
19
-------
an elevated inversion, Equation (A4) in Appendix A is used. Finally,
for unstable or neutral conditions where vertical dispersion is still
small compared to the mixing height, Equation (A5) in Appendix A is
used. This equation incorporates multiple eddy reflections from the
ground and the base of the stable layer aloft. Simplifications to the
above equations, valid if the height of the receptor z is assumed at
ground level, are incorporated into the appropriate subroutines.
OTHER CONSIDERATIONS
Fumigation
The transitional phenomenon of fumigation, defined in Section 3, is
not included in calculations made by MPTER. Conditions specified for
each hour are calculated as if a steady-state had been achieved for
those specified conditions.
Removal or Chemical Reactions
Transformations of a pollutant resulting in its loss throughout the
entire depth of each plume is accomplished by an exponential decrease
with travel time from the source. The input parameter is the length of
time expected for loss of 50% (half-life) of the emitted pollutant.
MPTER does not have the capability to change this parameter value during
a given run. If the loss to be simulated occurs throughout the whole
plume, without dependence upon concentration, then the exponential loss
may provide a reasonable simulation if the loss rate is realistic.
However, if the loss mechanism is selective, the loss rate will not be
adequately modeled. Selective loss mechanisms include impaction with
features on the ground surface, reactions with materials on the ground,
or dependence on the concentration in a given small parcel of air (requiring
consideration of contributions from all sources to this parcel).
SPECIAL OPTIONAL FEATURES
The following four special features, mentioned in Section 3, are
options in MPTER.
20
-------
Option 1: Terrain Adjustments
Consideration of the differences between local ground-level elevation
at the stack and at the receptor is an option in MPTER. Terrain adjustment
factors are entered by the user for each of the six P-G stability classes.
These factors can be any real number between 0 and 1, which allows
terrain to be regarded as in CRSTER by entry of O's for all six stabilities.
Plumes that level off and remain at the same mean-sea-level elevation
can thus be simulated, despite terrain influences. Calculations are
made by subtracting the difference, defined as the elevation of receptor
ground level minus the elevation of the source ground level, from the
effective plume height.
The terrain adjustment can calculate for the elevations for which
MPTER is limited using the same methods as the model Valley by entry of
1's for the first four stabilities (unstable and neutral) and O's for
the stable classes 5 and 6. The 1's allow full response of the plume to
terrain factors, i.e., they simulate the plume rising over terrain
features. (The entry of a 1 for the terrain adjustment factor for a
given stability will compute as if the source and receptor were on a
level surface.)
The equation used for the inclusion of the terrain adjustment is
HA = H - AE + FT AE
where
HA = adjusted effective height
H = effective height
AE = ER - Es
ER = ground level elevation of receptor
ES = ground level elevation of source
FT = terrain adjustment factor.
Shown below are the adjusted effective heights for four values of
the terrain factor:
21
-------
HA = H for FT = 1
HA = H - AE for FT = 0
HA = H - 0.7 AE for Fy = 0.3
HA = H - 0.1 AE for FT = 0.9
The manner in which the terrain adjustment is simulated is depicted
in Figure 1 for three values of the factor.
Of note to the user is that calculation of terrain adjustment is
limited to receptors whose ground-level elevation is less than the
elevation of the lowest stack top used in the run.
The terrain adjustment incorporated in MPTER is obviously simplistic.
For the estimation of plume behavior in the vicinity of a single hill,
the stable-plume fluid modeling studies of Hunt et al (1978) have shown
the importance of the Froude number, and of the location of the receptor
and the plume relative to hill base and top. None of these parameters
is considered here, but rather the relation of the receptor and source
ground level elevations. The reader is therefore cautioned against
assigning too great a significance to results obtained using the terrain
adjustment option.
Option 2: Stack Downwash
A second optional feature of MPTER is consideration of stack tip
downwash using the methods of Briggs. In such an analysis, a height
increment is deducted from the physical stack height before determining
momentum or buoyancy rise. Use of this option primarily affects computations
from stacks having small ratios of exit velocity to wind speed.
Option 3: Gradual Rise
Gradual plume rise determination has been made an optional feature
2/3
of MPTER, because although the use of the x ' dependence for rising
plumes will determine average plume height with distance quite well, the
plume axis is not horizontal during the rising phase. Dispersion is
thus taking place perpendicular to the bent over plume axis rather than
vertically. The P-G dispersion parameters represent horizontal and
vertical dispersion about a horizontal plume, which may not be appropriate
22
-------
for estimating dispersion about a bentover plume. By making computations
with and without the gradual plume rise, at least identification is possible
of potentially high concentrations during the gradual plume rise phase. When
gradual rise is not employed, computations are made using the final effective
plume height.
Option 4: Buoyancy-Induced Dispersion
The buoyancy-induced dispersion feature is offered because emitted
plumes undergo a certain amount of growth during the plume rise phase, due
to the turbulent motions associated with the conditions of plume release and
the turbulent entrainment of ambient air. Pasquill (1976) suggests that this
induced dispersion, a , can be approximated by AH/3.5, and the effective
dispersion can be determined by adding variances, i.e.,
/2 2~~
a = a + a
ze 20 z
where a is the effective dispersion and a is the dispersion due to
ambient turbulence levels. At the distance of final rise and beyond, a is
a constant using AH of final rise. At distances closer to the source, the
AH used to determine aZQ is itself determined using gradual rise.
Since in the initial growth phases of release the plume is nearly
symmetrical about its centerline, buoyancy-induced dispersion in the horizon-
tal direction equal to that in the vertical is used, a = AH/3.5. This
expression is combined with that for dispersion due to ambient turbulence in
the same manner as is shown above for the vertical.
In general, buoyancy-induced dispersion will have little effect upon
maximum concentrations unless the stack height is small compared to the plume
rise. Also, it is most effective in simulating concentrations near plume
center!ines close to the source, where treating the emission as a point
source confines the plume to a volume much smaller than the actual plume. It
should be clarified here that the buoyancy-induced dispersion close to the
source is calculated using the gradual rise in MPTER, even if the gradual
plume rise option is not being used to determine the effective plume height.
23
-------
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SECTION 5
OVERVIEW OF COMPUTER PROGRAM
With the exception that meteorological data output from RAMMET can be
input, MPTER is a stand-alone program. Numerous options within MPTER allow
control of its output, rather than relying upon numerous peripheral programs.
PROGRAM DESCRIPTION
A brief description of the main program and each subroutine used in
MPTER is given. Some of the subroutines and various lines of code are cited
directly from RAMR.
MPTER - Main Program: reads and checks input parameters, initializes
variables, writes out initial information, determines significant
sources, calls PTR for point source concentrations, reads and
writes tapes/discs, calls OUTHR to print concentration contributions
arid summaries.
PTR - Subroutine called by MPTER to calculate the point source contri-
bution to each receptor. Briggs plume rise equations are solved
in this routine.
RCP - Subroutine called by PTR, RCP returns values of relative concentra-
tions, a , and a .
PGYZ - Subroutine called by RCP, PGYZ calculates a and a for a given
downwind distance and stability classification.
EXPOS - Block data containing coefficients and exponents used in determining
high ground level concentrations that are used to rank the signi-
ficant sources.
ANGARC - Function determining the appropriate arctan of east resultant wind
component over the north resultant wind component with the resulting
angle between 0° and 360°.
25
-------
OUTHR - Subroutine which arranges and then prints tables of concentration.
Number of tables that is output depends on the option combination
specified.
RANK - Subroutine called by MPTER that ranks concentrations for four or
five averaging times so that highest five concentrations are printed
for each receptor.
ADDITIONAL COMMENTS
Figure 2 is an abbreviated flow diagram of MPTER showing its major
loops and the relationships of the subroutines to each other and the main
program.
The main program of MPTER primarily exists for input and bookkeeping;
most technical calculations are performed by subroutine PTR. PTR calls
subroutine RCP, which in turn obtains dispersion parameter values from
subroutine PGYZ, then selects and solves the appropriate Gaussian equation.
Subroutine RANK orders the highest five concentrations for each averaging
time for each receptor. Subroutine OUTHR essentially provides the printed
output.
The executable program for MPTER requires 48 k core on EPA's UNIVAC 1110.
Table 2 gives information on the lines of code in MPTER and its subroutines.
TABLE 2. STATISTICS RELATED TO MPTER SOURCE CODE SIZE
ROUTINE
Main
Block Data
ANGARC
PTR
RCP
PGYZ
RANK
OUTHR
MPTER SYSTEM
Total
Lines of
Code
1428
38
29
275
228
85
58
307
2448
Number
of Program
Statements
564
6
22
120
119
66
30
191
1118
Number
of Comment
Lines
741
13
7
152
108
14
25
98
1158
Number
of Defined
Variables
189
4
4
83
48
34
31
45
262
26
-------
MPTER
, READ INPUT DATA
. LOOP FOR CALENDAR DAYS
. LOOP FOR AVERAGING TIME
•READ MET DATA
•ANGARC
. LOOP ON HOURS
PTR
LOOP ON RECEPTORS
LOOP ON SOURCES
•RCP
PGYZ
L
•RANK
OUTHR
• OUTAVG (ENTRY POINT IN OUTHR)
EXIT
Figure 2. Subroutine structure in MPTER.
-------
SECTION 6
DISCUSSION OF COMPUTER ASPECTS OF MPTER
A numbering system has been adopted for this section to provide a ready
reference to the following discussion.
6.1 DESCRIPTION OF SOURCE CODE
Although few readers will have the need or desire to examine the source
code in detail, several comments will be made about its organization. For
the main program and most subroutines, explanatory statements and details on
inputs are given prior to the first program statements. For the main program,
a flow diagram is also given indicating the relationships of the subroutines
and the major loops. Programs have been partitioned in sections when lengthy,
and an outline of the sections follows the format statements.
6.2 DATA PREPARATION
Users preparing to make a run with MPTER should rely most heavily on
Section 7, which details the specification of input, and Section 8, which
gives runstream examples. This section discusses those elements that may
require further explanation to some users and, in effect, might serve as a
"troubleshooting" reference.
6.2.1 Control and Specification of Constants
6.2.1.1 Starting Date and Time —
The two-digit year and the three-digit Julian day for the start of the
run are entered in the two portions of the indexed variable IDATE. The hour
for the start of the run (between 1 and 24) is entered in IHSTRT. These
data are used somewhat differently depending upon whether the meteorological
data are entered through a file prepared by RAMMET, or upon hour-by-hour
punched cards. (See discussion of this option below, 6.2.2.3.) If data are
entered on cards, all three values are replaced and are relatively unimportant.
If data are read from the preprocessed file, these variable values are used
28
-------
to position the file so that the first meteorological data read are for the
proper day.
6.2.1.2 Number of Periods, Number of Hours --
Any run of MPTER will be for a given simulated length of record from
one hour to one year. The simulation is done hour-by-hour, with an optional
printout of concentration estimates at each receptor for each hour (see
6.2.3.3 below). Printout of concentration estimates for one other averaging
period is also available, the length in hours of which is a data entry, the
variable, NAVG. The number of these averaging periods in the run is the
value entered for NPER.
6.2.1.2.1 Example -- Simulation is desired of a three-day (72-hour)
length of record, obtaining 24-hour averages as part of the run. NPER will
equal 3, and NAVG will equal 24.
6.2.1.2.2. Example -- Simulation is desired of a one-year (not leap
year) length of record, obtaining eight-hour averages as part of the run.
NPER will equal 2920 (365 x 3), and NAVG will equal 8. (This example is not
very practical if options are selected to obtain printed output, as tremendous
amounts will be generated; see 6.2.3.3 and 6.3.2 below.)
6.2.1.3 Pollutant Indicator ~
The variable IPOL (See Card Type 4, Section 7) is set on the point
source card (Type 7) to either 3 for use of the emission rate in columns 29
to 36, or 4 for use of columns 39 to 44. IPOL is also used to select
the proper headings "S0211 or "PART" on output. The dispersion is treated
identically for the two pollutants whose emissions are in the above fields
on the point source card. Calculations may be made for pollutants other
than sulfur dioxide and particulate matter by substituting their emissions
in either above defined field. However, without altering the program, all
headings will still read "S02" or "PART." Pollutants whose emissions are
substituted should be relatively nonreactive, or have a loss rate describable
by an exponential loss with time.
6.2.1.4 Number of Significant Sources --
The variable NSIGP is specified primarily to obtain printed information
29
-------
on contributions to the concentration at each receptor from up to 25 individual
sources. The value entered is the number of sources for which contributions
will be printed for each hour (optional, see 6.2.3.3.3 below) and for each
averaging time (again optional, see 6.2.3.3.9 below). The output is printed
such that the same number of pages is required for 1 to 10 significant
sources; twice this number is required for 11 to 20 significant sources, and
three times this number for 21 to 25 sources. Care should thus be exercised
to specify only the number of sources that is actually necessary.
6.2.1.5 Fifth Averaging Time for High-Five Concentration Table --
The value of the variable, NAV5, is significant only if the run is
lengthy, say, a simulation of five days or more. If the option to produce
and write the high-five table is used (see 6.2.3.3.11 below), this value
will be the length in hours of an additional averaging time that will be
used to list the five highest concentrations over the period of this run.
Since high-five tables are already produced for 1-, 3-, 8-, and 24-hour
averaging times, none of these values will be used if entered for NAV5.
Also, the value entered should be evenly divisible into 24. Only 2, 4, 6,
and 12 meet all these criteria. If, then, a need exists for knowing the
highest five concentrations for any of these averaging times (2-, 4-, 6-,
or 12), enter the proper value; otherwise enter zero.
6.2.1.6 Multiplier Constant — CONONE
The multiplier constant CONONE is used to convert distances in the user
units to distances in kilometers. These units are subsequently used for
obtaining dispersion parameters and relating receptors to plume locations.
If the user coordinate system is in kilometers, CONONE =1. If user coordinate
system is in miles, CONONE = 1.609344.
6.2.1.7 Multiplier Constant — CELM
The multiplier constant CELM will convert the user height units to meters.
If the elevations are reported in meters, CELM =1; if the elevations are in
feet, CELM = 0.3048. CELM is used only when terrain adjustments are made
with Option 1. In this option, heights are entered for both source ground-
level elevations and receptor ground-level elevations, in height units conven-
ient to the user.
30
-------
6.2.1.8 Pollutant Half-Life -- HAFL
An exponential loss of the considered pollutant with travel time is
included in the model. At a travel time equal to the half-life, 50% of the
pollutant will remain. Although this view of chemical or physical depletion
processes is overly simplistic, it may be useful under certain circumstances.
Note that the half-life is entered in seconds. If the user wants no depletion
to be considered, entering zero for the half-life will cause skipping of
those portions of the code calculating pollutant loss.
6.2.1.9 Values of Variables Related to Increase of Wind with Height --
The anemometer height in meters for the meteorological data used is
entered on CARD TYPE 6. Six values for the wind profile power law exponent,
one for each stability class, are also entered on CARD TYPE 6. In Section
4, values were given from Irwin (1979) consistent with the surface roughness
that corresponds to the P-G dispersion parameter values. For computations
submitted in response to regulatory requirements, certain values for this
parameter may be required; the appropriate EPA regional office should be
consulted prior to performing calculations.
If Option 1 is employed to make terrain adjustments, six terrain adjust-
ment factor values (one for each stability class) that are read in on CARD
TYPE 6 are used in subsequent computations (see 6.2.3.1.1 below). The
values must be real numbers between 0 and 1.
6.2.2 Input Data
Comments on emission, receptor, and meteorological data are made here.
6.2.2.1 Emission Data — (See CARD TYPE 7)
The alphanumeric name and the eight variables of point source information
are the same as used in most dispersion models. Only one of the two emission
rates will be used in a given run (see 6.2.1.3 above). If only one pollutant
is of interest, the other field may be left blank. If Option 6 to enter
hourly emission rates (see 6.2.3.2.2 below) is not used, the emission rates
should provide the best estimate of the emission for the length of record
being run. If maximum or design emissions are used, concentration estimates
may be somewhat larger than actual concentrations. However, Irwin and
31
-------
Cope (1979) have demonstrated that maximum operating conditions may not
necessarily produce the highest modeled concentrations. If the option is
exercised to input hourly emissions from a separate file (see 6.2.3.2.2
below), the input emission on each source card can be either average (normal)
emission or maximum design, with the exit velocity appropriate for that
condition. In MPTER, the hourly emissions input are compared with the
emissions initially input on CARD TYPE 7 and that comparison is used to
scale the exit velocity upwards if the hourly emission is greater, or down-
wards if the hourly emission is less.
In MPTER, no provision exists for altering the stack gas temperature.
The value entered on the point source card is used throughout, even if
hourly emissions are entered. Since Irwin and Cope (1979) have shown that
variation in exit temperature is a sensitive parameter for maximum concen-
tration, and if sufficiently detailed information is available for estimating
hourly stack gas temperatures, we would recommend alteration of the model to
accept hourly stack gas temperature. Along this same line, with at least
the pollutant SCu, a constant scaling does not necessarily exist between
emission rate and exit velocity due to changes in sulfur content of the fuel
(and also heat content of the fuel). Here again, alteration of the model
may be desirable so that the three parameters (emissions, stack gas tempera-
ture, and exit velocity) are all entered hourly. Under the present procedure,
only emissions are entered hourly; exit temperature is left constant through-
out the run, and exit velocity is scaled by emission rate.
If Option 1 for terrain adjustments is employed, the ground-level
elevation of each point source is an element of the point source card, CARD
TYPE 7, and is input in units chosen as convenient by the user (see 6.2.1.6
above).
6.2.2.2 Receptor Data — (See CARD TYPES 10, 11, and 12)
If Option 8 is employed (see below), polar coordinate receptor positions
are generated internally in MPTER about a specified location for one to five
radial distances. Thirty-six receptors are generated for each distance. If
all five distances are used, 180 receptors are generated -- the maximum number
of receptors allowed in MPTER. Note that the distances (and also the center
32
-------
of the polar coordinate grid) are specified in user units. If Option 8 is
employed to generate the polar coordinate receptors and Option 1 is employed
to include terrain adjustments, the ground-level elevations of these receptors
must be entered using CARD TYPE 11. A separate card is used for each azimuth,
with from one to five elevations per card (see 6.2.3.1.1 below).
An alternative method of entering receptors into an MPTER run is to
specify receptor locations (again, in user units) on individual cards for
each receptor (CARD TYPE 12).
Note that the receptor height above local ground level must be in
meters. Although in many applications the height will be zero (receptor at
the ground), other situations may occur where determining concentrations
above the ground is desirable, such as at plume centerline. Although no
restriction on this height exists, careful thought should be given to the
assignment of receptor heights far removed from the ground surface. A
cautioning statement in subroutine RCP will be generated if both the effective
plume height and the receptor height are above the mixing height. This may
cause many useless lines of output.
6.2.2.2.1 Receptor ground-level elevation -- Values for this parameter
are required only if Option 1 to employ terrain adjustments is used (see
6.2.3.1.1 below). Note that elevations are entered in the user height
units. Estimations in MPTER are limited to receptors whose ground-level
elevation is lower than the lowest elevation of all the stack tops in the
run. If numerous sources and receptors exist, it is not necessarily easy to
inspect the input data to see if this criterion is met. A receptor whose
elevation is above this low stack top value will not have a concentration
estimate calculated; instead, the concentration will be set to an extremely
high value that will cause asterisks to appear on the output for this receptor
(at least on EPA's UNIVAC 1110). Also, double asterisks will appear beside
the receptor numbers in the initial output listing receptors. Single asterisks
will appear beside receptor numbers whose elevations are below the ground-
level elevation of the source having the highest ground-level elevation.
Caution should be used in interpretation of these concentrations.
33
-------
Users who want to make a run for a significant length of simulated time
are thus advised that when employing the terrain adjustment option, they
must first make a run for a short period (one hour -- meteorological data are
unimportant)-to see if double asterisks appear on the receptor list. Then
these receptors should be eliminated before making the long-term run.
6.2.2.3 Meteorological Data — (See CARD TYPE 14)
Meteorological data files prepared by the CRSTER Preprocessor or by the
similar program from the RAM system, RAMMET, are acceptable by MPTER.
Proper running of these preprocessor programs results in a one-year period
of record with one record for each calendar day. Twenty-four values of each
of the following parameters are contained in this record: Pasquill-Gifford
Stability Class, wind speed (at anemometer height), ambient air temperature,
wind flow vector (wind direction +_ 180°), and mixing height. The user
should be reminded that if using either of these programs to process meteor-
ological data, a complete set of data must be input to either program. Any
"holes" in the data set must be filled by the user. In using this data for
input to MPTER one record is read for each simulated day. If making a run
for a period of record of less than a year and starting after Day 001 (January
1st), MPTER will skip records to arrive at the proper day based upon the
variable IDATE(2) on CARD 4 (see 6.2.1.4 above).
If using meteorological data from the preprocessed file, Option 5 will
be zero. Also, the four variables on CARD TYPE 8 are to be read in and will
be checked against the data on the input file.
Alternatively, when employing Option 5, meteorological data is read
from punched cards (see CARD TYPE 14) with one card for each simulated hour
in the run. The wind speed on this card again is for the anemometer height.
The wind direction is the direction from which the wind blows.
6.2.3 Options
There are four technical options, four input options, 11 print options,
and five other options either for control or for output to files. To employ
the particular option, a 1 is entered as input to the element of the array
IOPT with the same number as the option number. Otherwise, a zero is
34
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entered for this variable. Values of 0 or 1 are entered for all options on
CARD TYPE 5.
6.2.3.1 Technical Options --
6.2.3.1.1 Option 1: Terrain Adjustment -- Since terrain adjustment is
a major feature of this model, this is Option 1. Terrain adjustment is made
if the option is employed, that is IOPT(1) = 1. The use of this option re-
quires input of source ground-level elevation on CARD TYPE 7 (see 6.2.2.1
above) and receptor ground-level elevation on CARD TYPE 12 (see 6.2.2.1
above). If Option 8 for generation of polar coordinate receptors is used,
CARD TYPE 11 with elevations for the polar coordinate receptors are also
read (one card for each of 36 azimuths). Also, this option requires that six
terrain adjustment factors, one for each stability class be entered on CARD
TYPE 6. These values must be real numbers between zero and one. This allows
the model to be used for research with various values. Of note to the user is
that if the run results are to be submitted in response to regulatory require-
ments, certain values may be required for these parameters. If zeros are
entered for all six stabilities, this will have the effect of doing the
terrain adjustment the same as done by CRSTER. If ones are entered for all
six stabilities the concentration estimates will be the same as if terrain
is not considered (the option not employed) for 1's will cause the plumes to
rise fully over the terrain which is equivalent to elevated plumes over a
level surface. Therefore where use of Ts for all stabilities is contem-
plated, the use of the terrain option is unnecessary.
6.2.3.1.2 Option 2: No Stack Downwash -- With IOPT(2) = 0, stack down-
wash is used if applicable using the procedure given in Appendix B. With
IOPT(2) = 1, stack downwash is not estimated.
6.2.3.1.3 Option 3: No Gradual Plume Rise -- With IOPT(3) = 0, gradual
plume rise from stack top to the distance of final rise is determined using
the procedures in Appendix B. With IOPT(3) = 1, only the final plume height
is used for effective height.
6.2.3.1.4 Option 4: Use Buoyancy-induced Dispersion — With IOPT(4) = 0,
sources are treated as point sources. With IOPT(4) = 1, buoyancy-induced
plume size is determined in both the horizontal and vertical dependent on
35
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plume rise using the techniques suggested by Pasquill (see Section 4). It
should be pointed out that even if Option 3 is employed, resulting in use of
only the final plume height for effective height of emission, the gradual
plume rise is determined internally to determine the buoyancy-induced plume
size. (It would not be the least bit appropriate to use the final plume
rise to determine the initial size close to the stack.)
6.2.3.2 Input Options —
For the four following input options, specific action is taken if the
value of 1 is entered.
6.2.3.2.1 Option 5: Met. Data on Cards -- If IOPT(5) = 1, met data are
entered on cards with one card for each simulated hour (see 6.2.2.3 above).
If option 5 is 0, meteorological data is entered using records on unit 11. The
specification of the records on this input file are given in the next section.
6.2.3.2.2 Option 6: Read Hourly Emissions — If IOPT(6) = 1, hourly
emissions for each point source are read from unit 15 in the main program,
then are compared with the emissions input on the point source card for
scaling the exit velocity (see 6.2.2.1). Subroutine PTR performs these
tasks; Section 7 specifies the records on this input file.
6.2.3.2.3 Option 7: Specify Significant Sources -- The number of signi-
ficant sources, given as NSIGP on Card 4, is ranked when the emissions data
are processed according to expected ground-level impact under B stability,
with a wind at stack top of 3 m s~ . This option can be employed if the
contribution of a source is sought for a subsequent run that is outside this
list or too far down it to be included among the significant sources, NSIGP
on Card 4 (see 6.2.1.5 above). When IOPT(7) = 1, an additional input card is
read (CARD TYPE 9) that indicates how many sources will be specified (NPT),
then gives their source numbers (the array MPS) corresponding to the source
numbers in the printed output list. Source numbers are assigned according to
the order of the source input. For example, consider an application having 30
sources, where a run is deemed useful that shows contributions from 10 sources
(NSIGP on CARD 4 will be set to 10). Specifically, the contributions from
sources 7 and 22 are desired. The 12 most significant of the 25 sources, in
order are: 3, 8, 23, 11, 2, 15, 4, 27, 1, 5, 28, and 14. Since 7 and 22 are
36
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not among these 12, and further are not in the first 10, Option 7 is set
equal to 1, and CARD TYPE 9 contains 2 for NPT and the two numbers 7 and 22
for the two entries to MPS. Sources 7 and 22 will occupy the first two
columns in the contribution table. The program will fill the other eight
positions of the significant source list (to total 10) with the first eight
sources of the list of 25, i.e., 3, 8, 23, 11, 2, 15, 4 and 27.
6.2.3.2.4 Option 8: Input Radial Distances and Generate Polar Coordi-
nate Receptors -- For the user's convenience in making computations at an
array of receptors that are positioned about a specific source or some other
point, Option 8 provides for reading an additional input card (CARD TYPE 10)
with from one to five non-zero distances in user units. Additionally, the
east and north coordinates (also in user units) of a center position are
provided. The program generates the east and north coordinates of each
receptor in a polar coordinate array, generating 36 receptors for each non-
zero distance (one for each 10 degrees of azimuth). A five-value distance
array is read from the card with distances entered for the number of distances
desired. Zeros are added to fill the array. For example, to produce a
receptor array with two distances, two distances and three zeros are entered.
This step will generate 72 receptors (36 for each distance). Putting non-
zero values for all five distances will generate 180 receptors, which is the
maximum number that MPTER can compute. Thus using Option 8 in this manner
will not allow the input of any additional receptor cards with positions
specified by the user.
Of note to the user is that if both Option 8 and Option 1 for terrain
adjustment are used, elevations of the polar coordinate receptors must be
read in using CARD TYPE 11. These can best be obtained by drawing 36 radials
from the designated center point on a topographical map, and drawing circles
for each distance. Then the elevations can be determined from the map by
reading elevations outward from the center, starting with the 10-degree azimuth
radial. If all five distances are used so that 180 receptors are generated,
a card with ENDREC in Columns 1-6 must be read following CARD TYPE 10 (or
the last card of CARD TYPE 11 if used).
37
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6.2.3.3 Printed Output Options —
When employed, the eleven printed output options will cause portions of
the computer code to be skipped. A normal run will generally use at least
some of these options.
6.2.3.3.1 Option 9: Delete Emissions with Height Table — Option 9 will
be left zero only if it is desirable to look at the distribution of physical
stack heights of the sources being modeled. This table is printed at the end
of Section E in the main program, and is shown in Example 4.
6.2.3.3.2 Option 10: Delete Averaging Time Meteorological Summary —
Option 10 will be left zero when the user desires to obtain a listing of the
hourly meteorological data for each simulated averaging time, and the resul-
tant or average conditions for that period. If the run is for a long period
of record, such as a year, a similar record more than likely has already been
made for the meteorological data. One output page for each averaging time
will be required; Section N of the main program prints this table.
6.2.3.3.3 Option 11: Delete Hourly Contributions -- Option 11 will be
left zero only when the value of NSIGP on CARD TYPE 4 is one or more, when
the user wishes to examine on an hour-by-hour basis the contributions to the
receptor concentrations of significant sources. If IOPT(11) = 1, Sections B,
C, D, and E of Subroutine OUTHR are skipped.
6.2.3.3.4 Option 12: Delete Meteorological Data on Hourly Contribu-
tions -- Option 12 will be left zero only when the meteorological data for
the hour should be listed with the contribution (see Example 2). If
IOPT(12) = 1, Section C in Subroutine OUTHR is skipped.
6.2.3.3.5 Option 13: Delete Final Plume Height and Distance to Final
Rise on Hourly Contributions — Option 13 will be left zero only when the
hourly calculated final plume height and the distance to final rise is
desired with the hourly contributions. Information on effective plume
height of specific sources can be invaluable in trying to determine distance
to maximum concentrations, or in trying to arrange receptors vertically. If
IOPT(13) = 1, Section D in Subroutine OUTHR is skipped.
38
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6.2.3.3.6 Option 14: Delete Hourly Summary — Option 14 will be left
zero when it is desirable to have the hourly summary printed for each hour
in the run. The hourly summary contains the sum of the contributions to the
concentration at each receptor. In addition to this sum, two components of
the concentration are given: that due to all significant sources, and that
due to all other sources, (i.e., those not considered in the sources selected
as significant for this run). If IOPT(14) = 1, Sections F, G, H, and I in
i
Subroutine OUTHR are skipped.
6.2.3.3.7 Option 15: Delete Meteorological Data on Hourly Summary --
Option 15 will be left zero when the meteorological data are required for
the hour printed with the hourly summary. This information is the same as
discussed in 6.2.3.3.4 above, Option 12. Seldom should the meteorological
data be needed on both of these outputs. If IOPT(15) = 1, Section G in
Subroutine OUTHR is skipped.
6.2.3.3.8 Option 16: Delete Final Plume Height and Distance to Final
Rise on Hourly Summary — Option 16 will be left zero when the final plume
height and distance to final rise are needed on the hourly summary. This
information is the same as on the contributions (see 6.2.3.3.5 above), and
should not be needed on both outputs. If IOPT(16) = 1, Section H in Sub-
routine OUTHR is skipped.
6.2.3.3.9 Option 17: Delete Averaging-Time Contributions -- Option 17
will be left zero when examination of the contributions from the significant
sources is desired for each averaging time. If IOTP(17) = 1, Section J in
Subroutine OUTHR is skipped.
6.2.3.3.10 Option 18: Delete Averaging-Time Summary -- Option 18 will
be left zero when printout of the averaging-time summary is needed. This
table is similar to the hourly summary (see 6.2.3.3.6 above), except for the
simulation period covered. If averaging over these hours would be meaningless
due to a run being made for a number of independent hourly periods, Options 17
and 18 should both be set to 1. If IOPT(18) = 1, Section K in Subroutine
OUTHR is skipped.
6.2.3.3.11 Option 19: Delete Average Concentrations and High-Five
,'able -- Option 19 will be left zero in order to produce average concentrations
39
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for the duration of the run and to list the five highest concentrations for
four or five averaging times. (See discussion concerning the variable NAV5
in 6.2.1.5 above.) For this table to be useful, at least two periods of the
concentration averaging period should be run. Any run less than 5 days will
have some zeros in the output table, since one output will be the highest
five concentrations for the 24-hour averaging time. If IOPT(19) = 1,
Sections Q and S in MPTER will be skipped.
6.2.3.4 Other Control and Output Options --
The five other control and output options cause portions of the code to
be executed only if the option is employed.
6.2.3.4.1 Option 20: Run as Part of a Segmented Long Run — Option 20
is used to segment a run into several pieces. CARD TYPE 13 is read and
appropriate input and output files are set to the correct record. Also,
data for the average concentration and high-five are read from the previous
segment and written for the next segment using unit 14.
To properly break a large run into segments, the number of averaging
periods, NPER on CARD 4, should be set to the total number for the sum of
the segments. This step will allow the variable LDRUN, from CARD TYPE 13,
to control the program flow and temporarily store the proper data on unit 14.
For example, to break a one-year run into two segments, let NPER equal 366,
and NAVG equal 24 for both segments. On Card 13 for the first segment, IDAY
is zero and LDRUN can be 180; for the second segment, IDAY is 180 and LDRUN
is 366 (for a leap year). The proper date and time should be entered on
Card 4 for each run.
6.2.3.4.2 Option 21: Write Partial Concentrations to Disk -- Option 21
provides for all concentration contributions from each source to each receptor
for each hour using unit 10. One record is written in Section PTR.F for
each receptor for each hour; thus a large number of records will be written
even for a relatively short length of simulated period. The specifications
for these records are given in Section 7, The user should proceed with
knowledge of the amount of data generated before using this option.
40
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6.2.3.4.3 Option 22: Write Hourly Concentrations to Disk -- Option 22
provides for writing a record once each hour on unit 12 containing the
concentration for each receptor. This option is written at the end of
Section P of MPTER. The specifications for these records are given in
Section 7.
6.2.3.4.4 Option 23: Write Average Concentrations to Disk -- Option 23
provides for writing a record once each averaging period on unit 13, con-
taining the concentration for each receptor. This option is written at the
end of Section OUTHR.K; specifications for these records are given in
Section 7.
6.2.3.4.5 Option 24: Punch Average Concentrations on Cards -- Option 24
provides for punching cards at the end of each averaging period of the
concentration for each receptor for the averaging time (one card per receptor).
Unit 1 is used for punching. The format for these output cards is given in
Section 7.
6.3 RUNNING COSTS AND OUTPUT VOLUME
6.3.1 Running Costs
The examples to be shown in Section 8 will give the user some idea of
running costs. Below are examples of time and costs for runs on EPA's UNIVAC
1110.
Example 1 1.178s 8
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TABLE 3. MPTER OUTPUT VOLUME
Output
No, of lines No. of pages
Mandatory Output on All Runs
Emissions with Height Table
Met. Data for Avg. Period
Met. Data on Hourly Contributions or Hourly Summaries 5
3 - 6
1/2
1
Final Plume Rise and Distance to Final Rise
less than 10 sources 3
250 sources 51
(1 line plus two lines for each 10 sources or fraction of 10 sources)
Hourly Contributions (for each hour)
for 1 to 10 significant sources
about 30 receptors
about 31 to 83 receptors
about 84 to 136 receptors
about 137 to 180 receptors
for 11 to 20 significant sources
for 21 to 25 significant sources
1
2
3
4
twice that for 1 to 10
three times that for 1 to 10
Hourly Summaries (for each hour)
(See above for number of lines to add for met. data and for plume data.)
about 45 receptors
about 46 to 98 receptors
about 99 to 151 receptors
about 152 to 180 receptors
1
2
3
4
Averaging Period Contributions (for each period)
for 1 to 10 significant sources
46 receptors 1
47 to 99 receptors 2
100 to 152 receptors 3
153 to 180 receptors 4
for 11 to 20 significant sources twice that for 1 to 10
for 20 to 25 significant sources three times that for 1 to 10
Averaging Period Summary (for each period)
44 receptors
45 to 78 receptors
99 to 151 receptors
152 to 180 receptors
1
2
3
4
Average Concentrations and High-Five Table
for 180 receptors
(Proportionately less for less than 180 receptors.)
17
42
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Consider the following example run and the estimate of maximum output.
Five averaging periods of 24 hours each are to be simulated, using 250 sources
and 180 receptors (both of these are maximum values). The number of signif-
icant sources is 25, also the maximum. Table 4 gives an estimate of the
number of pages of output.
TABLE 4. MAXIMUM OUTPUT: 5-DAY RUN FOR 250 SOURCES AND 180 RECEPTORS.
Output No. of Pages
Mandatory output (because of number of sources and receptors) 11
Emissions with Height Table (1/2 page, included above)
Met. Data Summary for Avg. Period 5
Hourly Contributions with Met. Data and Plume Height Info.
(an additional page is added because of 51 lines of plume info.)
13 pages x 5 periods x 24 hours = 1560
Hourly Summaries, 4 pages x 5 periods x 24 hours = 480
Averaging Period Contributions, 12 pages x 5 periods = 60
Averaging Period Summaries, 4 pages x 5 periods = 20
High-Five Table 17
Total 2153
Obviously most users will want to delete much of this output. Consider-
ing that the above proposed run is only of 5 days duration, the user must be
very generous in the use of options to delete unneeded output.
43
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6.4 ERROR MESSAGES AND REMEDIAL ACTION
Fourteen error messages can be generated by MPTER. Each of these will
terminate program execution with STOP.
6.4.1 Error Message 1
The first error message occurs if the user specifies the number of
sources to be significant as more than 25 on CARD 4. The following error
message is printed:
NSIGP (THE NO. OF SIGNF POINT SOURCES) WAS FOUND TO EXCEED
THE LIMIT (25). USER TRIED TO INPUT xxx SOURCES *********
EXECUTION TERMINATED **********
where xxx is the value put on CARD 4 for the variable NSIGP.
The corrective action is to change the value of NSIGP on CARD 4 to a
value of 25 or less.
6.4.2 Error Message 2
The second error message occurs for situations using Option 1. If any
of the six values of the terrain adjustment factor are outside the acceptable
range of between 0. and 1., the following error message is printed:
CONTER VALUE IS OUTSIDE OF RANGE: ZERO TO ONE. EXECUTION
TERMINATED.
The corrective action is to change the offending value(s) of CONTER
(input values that were entered on Card 6 are printed prior to the error
statement).
6.4.3 Error Message 3
The third error message occurs if the user attempts to input more than
the maximum number of point sources (250), or forgets to place an 'ENDPOINT'
card following the last point source. The following error message is printed:
USER TRIED TO INPUT MORE THAN 250 POINT SOURCES. THIS GOES
BEYOND THE CURRENT PROGRAM DIMENSIONS.
44
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The corrective action is to reduce the number of sources to 250 and/or
to put the 'ENDPOINT1 card behind the 250th source.
6.4.4 Error Message 4
The fourth error message is printed if no sources were specified:
NPT = xxx I.E., EQUAL OR LESS THAN ZERO RUN TERMINATED
CHECK INPUT DATA
where xxx will be zero.
The corrective action is to revise the run stream so that it includes
data for at least one point source.
6.4.5 Error Message 5
The fifth error message is written when Option 7 is employed by the
user to specify numbers of sources he wants to be considered as significant,
but he specifies a number larger than the number of significant sources
allowed for the run (NSIGP). The following error message is printed:
***ERROR — USER TRIED TO SPECIFY xxx SIGNIFICANT SOURCES,
BUT IS ONLY ALLOWING yyy TOTAL SIGNIFICANT SOURCES IN THIS RUN.
*** RUN TERMINATED - CHECK INPUT DATA! ***
where xxx is the value of INPT from CARD TYPE 8 and yyy is the value of
NSIGP from CARD 4.
The corrective action is to increase NSIGP (not to exceed 25) 0£ to
decrease the value of INPT to equal or less than NSIGP, and to eliminate all
but that number (INPT) of sources on CARD TYPE 8 following the value of
INPT.
6.4.6 Error Message 6
The sixth error message is written when Option 5 is zero, requiring
meteorological data to be read from a tape or disk file. If the surface
station identification and the year read from CARD TYPE 9 do not match those
given in the first record on the file, the following error message is printed:
SURFACE DATA IDENTIFIERS READ INTO MODEL (STATION = xxxxx, YEAR = yy)
DO NOT AGREE WITH THE PREPROCESSOR OUTPUT FILE (STATION = wwwww,
YEAR = 22)
45
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where xxxxx and yy are read in on CARD TYPE 9, and wwwww and zz are
from the file.
Corrective action is to substitute the proper desired file or to change
the identifiers on the card to match the data. The user should be careful
to use the most representative meteorological data available.
6.4.7 Error Message 7
The seventh error message is similar to message six, occurring when
meteorological data are read from a file when Option 5 is zero. If the
upper air station identification for the station used to calculate mixing
height and the year read from CARD TYPE 9 do not match those given in the
first record on the file, the following error message is printed:
MIXING HEIGHT IDENTIFIERS READ INTO MODEL (STATION = xxxxx,
YEAR = yy) DO NOT AGREE WITH THE PREPROCESSOR OUTPUT FILE
(STATION = wwwww, YEAR = zz)
Corrective action is to substitute the proper desired file or to change
the identifiers on the card to match the data. The user should be careful
to use the most representative meteorological data available.
6.4.8 Error Message 8
The eighth error message occurs if both Option 1 for terrain and Option
8 to generate receptors equal 1 and the 36 elevation cards (TYPE 11) are out
of sequence, or have been punched incorrectly. If the numbers 1 through 36
on the cards do not match the internally generated numbers 1 through 36, the
following message is printed:
WRONG RECEPTOR ELEVATION CARD READ. READ CARD FOR AZIMUTH
xxx SHOULD HAVE BEEN yyy.
The corrective action is to check the sequencing and formatting of all
TYPE 11 cards and to correct any errors.
6.4.9 Error Message 9
The ninth error message occurs if the user attempts to enter more than
180 receptors or failed to place an 'ENDREC1 card after the 180th receptor
was generated or read. In other words, the user failed to put this card
46
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behind the last TYPE 11 card if 180 polar coordinate receptors were generated,
or behind the CARD TYPE 12 which generates the 180th receptor. The following
message is printed:
**** USER EITHER TRIED TO INPUT MORE THAN 180 RECEPTORS OR
ENDREC WAS NOT PLACED AFTER THE LAST RECEPTOR CARD **** ********
EXECUTION TERMINATED *******
The corrective action is to reduce the number of receptors to no more
than 180 and to place an ENDREC card at the proper place.
6.4.10 Error Message 10
The tenth error message occurs if no receptors have been generated or
read in:
NO RECEPTORS HAVE BEEN CHOSEN
The corrective action is to restructure the input runstream so that
receptors are generated or read.
6.4.11 Error Message 11
The eleventh error message occurs if Option 20 to segment a run is
used, and in the second or greater segment of such a run, the number of days
previously processed (IDAY, read from CARD TYPE 13) does not match the
number of days written to an external file after processing. The following
message is printed:
*** DAYS DO NOT MATCH, IDAY = xxx, IDAYS = yyyy
The corrective action is to replace CARD TYPE 13 with the proper value
of IDAY to match the information from the previous run.
6.4.12 Error Message 12
The twelth error message occurs if Option 5 is zero, requiring meteor-
ological data to be read from a file. If either the year or Julian day in
the program execution does not match the year or day on the record on the
meteorological data, the following message is printed:
DATE ON MET. TAPE, yyddd, DOES NOT MATCH INTERNAL DATE,
wwzzz
47
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where yyddd are the year and day from the meteorological file and wwzzz are
the year and day generated in the execution of the program.
The corrective action is to determine the cause and correct the runstream,
or the meteorological file, or both.
6.4.13 Error Message 13
The thirteenth error message occurs if a value for the start hour of a
period becomes zero or negative. The following message is printed:
HOUR xxx IS NOT PERMITTED. HOURS MUST BE DEFINED BETWEEN
1 and 24
where xxx is the value of IHSTRT.
The corrective action is to check the value of IHSTRT in CARD 4.
6.4.14 Error Message 14
The fourteenth error message occurs using Option 6 to read hourly
emissions. If the combined year, Julian day and hour from the internal
execution of the program do not match the similar date time group from the
file, the following message is printed.
DATE BEING PROCESSED IS = byydddhr DATE OF HOURLY POINT EMISSION
RECORD IS = bxxeeeff *** PLEASE CHECK EMISSION RECORDS***
The corrective action is to check the emission records or determine the
reason why the internal date is in error.
48
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SECTION 7
INPUT CARD, INPUT FILE, AND OUTPUT FILE SPECIFICATIONS
CARD INPUT
Tables 5 through 16 list the card input necessary to execute MPTER. Since
some card types are read in UNIVAC's free format, individual values on a card
must be separated either by a comma or a space. Up to 250 point sources and
180 receptor cards are allowed; more than this number will result in runstream
termination. Meteorology data can be input on cards or through a preprocessed
file of the same type used for RAM and CRSTER. Hourly emissions can also be
read in as an option.
The ordering of the cards in the input deck is shown in Figure 3. The
systems flow for MPTER is shown in Figure 4.
TABLE 5. MPTER CARD TYPE 1, 2, and 3 - TITLE (3 cards)
Variable Format Description Units
LINE1 20A4 80 alphanumeric characters for heading
LINE2 20A4 80 alphanumeric characters for heading
LINE3 20A4 80 alphanumeric characters for heading
49
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TABLE 6. MPTER CARD 4 - CONTROL AND CONSTANTS (1 card)
Variable Format
Description
Units
IDATE(l) Free
IDATE(2) Format
IHSTRT
NPER
NAVG
I POL
NSIGP
NAV5
CONONE
CELM
HAFL
2 digit year (see 6.2.1.4)
starting Julian day for this run
starting hour for this run
number of averaging periods to be run
(see 6.2.1.2)
number of hrs in an averaging period
pollutant indicator: 3 = S02
4 = Suspended Particulars (see 6.2.1.1)
number of significant point sources,
max = 25. (see 6.2.1.5)
number of hrs in the user specified period
for which a high-five concentration
table is generated, (see 6.2.1.3)
multiplier constant, user units to km
(see 6.2.1.5)
multiplier constant, user ht units to m
(see 6.2.1.6)
pollutant half-life (see 6.2.1.7)
seconds
50
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TABLE 7. MPTER CARD 5 - OPTIONS (1 card) - integer values: 0 or 1
Variable Format
Description
TECHNICAL OPTIONS (see 6.2.3.1)
Free Use Terrain Adjustments
Format No Stack Downwash
No Gradual Plume Rise
Include Buoyancy Induced Dispersion
INPUT OPTIONS (see 6.2.3.2)
Met. Data on Cards
Read Hourly Emissions
Specify Significant Sources
Input Radial Distances and Generate Polar Coordinate
lOPT(l)
IOPT(2)
IOPT(3)
IOPT(4)
IOPT(5)
IOPT(6)
IOPT(7)
IOPT(8)
IOPT(9)
IQPT(IO)
lOPT(ll)
IOPT(12)
IOPT(13)
IOPT(14)
IOPT(15)
IOPT(16)
IOPT(17)
IOPT(18)
IOPT(19)
IOPT(20)
IOPT(21)
IOPT(22)
IOPT(23)
IOPT(24)
Receptors
PRINTED OUTPUT OPTIONS (see 6.2.3.3)
Delete Emissions With Height Table
Delete Resultant Met. Data Summary for Averaging
Period
Delete Hourly Contributions
Delete Met. Data on Hourly Contributions
Delete Final Plume Height and Distance to Final Rise
on Hourly Contributions
Delete Hourly Summary
Delete Met. Data on Hourly Summary
Delete Final Plume Height and Distance to Final Rise
on Hourly Summary
Delete Averaging-Period Contributions
Delete Averaging-Period Summary
Delete Average Concentrations and High-Five Table
OTHER CONTROL AND OUTPUT OPTIONS (see 6.2.3.4)
Run is Part of a Segmented Run
Write Partial Concentrations to Disk or Tape
Write Hourly Concentrations to Disk or Tape
Write Averaging Period Concentrations to Disk or Tape
Punch Averaging Period Concentrations on Cards
51
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TABLE 8. MPTER CARD 6 - WIND AND TERRAIN (1 card)
Variable
Format
Description
Units
HANE Free
PL(I),I=1,6 Format
CONTER(I),I=1,6
anemometer height
wind increase with height exponents for
each stability class (see 6.2.1.8)
terrain adjustment factors for each
stability class (real numbers
from 0 to 1)
meters
TABLE 9. MPTER CARD TYPE 7 - POINT SOURCE* (up to 250 cards) (see 6.2.2.1)
Variable
RNAME
SOURCE(l.NPT)
SOURCE(2,NPT)
SOURCE(3,NPT)
SOURCE(4,NPT)
SOURCE(5,NPT)
SOURCE(6,NPT)
SOURCE(7,NPT)
SOURCE(8,NPT)
ELP(NPT)
Format
2A6
F8.2
F8.2
F8.2
F8.2
F8.2
F8.2
F8.2
F8.2
F4.0
Description
12 alphanumeric characters for source
identification
east coordinate of point source
north coordinate of point source
sulfur dioxide emission rate
parti cul ate emission rate
physical stack height
stack gas temperature
stack inside diameter
stack gas exit velocity
source ground-level elevation
Units
.
user units
user units
gs-1
meters
Kelvin
meters
m s"1
user ht units
*Card with ENDPOINTS in columns 1-9 is read in after the last point source
card.
52
-------
TABLE 10. MPTER CARD TYPE 8 - MET. DATA IDENTIFIERS (used with option 5=0)
Variable
ISFCD
ISFCYR
IMXD
IMXYR
Format Description
Free sfc met station identifier
Format year of sfc met data
upper-air station identifier
year of mixing-height data
Units
5 digits
2 digits
5 digits
2 digits
TABLE 11.
MPTER CARD TYPE 9 - SPECIFIED SIGNIFICANT SOURCES (1
(used with option 7=1)
card)
Variable
Format Description
Units
NPT
MPS
13 number of user specified significant
point sources
2513 point source numbers user wants to be
considered significant
TABLE 12. MPTER CARD TYPE 10 - POLAR COORDINATE RECEPTORS (1 card)
(used with option 8=1)
Variable
Format
Description
Units
RADIL(I),I=1,5 5F4.0
CENTX
CENTY
F8.3
F8.3
up to five radial distances which each
generate 36 receptors around points
CENTX, CENTY on azimuths 10 to 360
degrees user units
east coordinate about which radials
are centered user units
north coordinate about which radials
are centered user units
53
-------
TABLE 13. MPTER CARD TYPE 11 - POLAR COORDINATE RECEPTOR ELEVATIONS (36 cards)
(used if options 1 and 8 are both 1)
Variable Format Description Units
IDUM 12 azimuth indicator (1 to 36)
8X (8 blank columns)
ELRDUM 5F10.0 receptor ground-level elevations for this
azimuth for up to five distances user ht units
TABLE 14. MPTER CARD TYPE 12 - RECEPTOR* (up to 180 cards) (see 6.2.2.2)
Variable
RNAME
RREC
SREC
ZR
ELR
Format
2A4
F10.3
F10.3
F10.0
F10.0
Description
8 alphanumeric characters for station
identification
east coordinate of receptor
north coordinate of receptor
receptor height above local ground-level
receptor ground-level elevation
(see 6.2.2.2.1)
Units
.
user uni
user uni
meters
user ht uni
ts
ts
ts
*Card with ENDREC in columns 1-6 should follow the last receptor card
(a maximum of 180 receptors are allowed input to MPTER for both those
generated by option 8 and those entered on card type 12.)
TABLE 15. MPTER CARD TYPE 13 - SEGMENTED RUN (1 card)
(used with option 20 = 1)
Variable Format
I DAY Free
LDRUN Format
Description
number of days already processed
last day to be processed in this run
Units
-
54
-------
TABLE 16. MPTER CARD TYPE 14 - METEOROLOGY (see 6.2.2.3)
(used with option 5=1)
Variable
JYR
DAY!
JHR
IKST
QU
QTEMP
QTHETA
QHL
Format Description
Free year of met data
Format Julian day of met data
hour of met data
stability class for this hour
wind speed for this hour
ambient air temperature for this hour
wind direction for this hour
mixing height for this hour
Units
2 digits
3 digits
2 digits
-
m s~]
Kelvin
degrees azimuth
meters
55
-------
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HOURLY
EMISSION
DATA
CARD
INPUT
SEE
FIGURES.
AVG. PERIOD
CONC.
LISTING
OF
INPUT
EMISSIONS
WITH
HEIGHT
TABLE
OPTION 9 = 0
MPTER
HOURLY
PARTIAL
CONC.
• --I
1
T
HOURLY
PARTIAL
CONC.
OPTION 11 =0
HOURLY
MET
DATA
OPTION 12 = 0
FINAL
PLUME
HEIGHT
AND
DISTANCE
OPTION 13 = 0
^
*^
I
I
I
. ,
I
T
HOURLY
SUMMARY
OPTION 14 = 0
HOURLY
MET
DATA
OPTION 15 = 0
FINAL
PLUME
HEIGHT
AND
DISTANCE
OPTION 16 = 0
_^J
I
I 1
Y
AVG. PERIOD
PARTIAL
CONC.
OPTION 17 = 0
'I
I
AVG. PERIOD
SUMMARY
OPTION 18 = 0
HIGH-FIVE
TABLE
OPTION 19 = 0
MANDATORY FLOW
OPTIONAL FLOW
Figure 4. System flow for MPTER.
-------
FILE INPUT
Table 17 shows the file structure for the meteorological data that is
read from unit 11 if option 5=0. This file is unformatted and normally
is obtained as output from RAMMET or the CRSTER preprocessor.
Table 18 shows the file structure for the emission data that is
read from unit 15 if option 6=1. This file is unformatted and must be
generated by the user.
CARD OUTPUT
Table 19 shows the card format of punched cards containing concentra-
tions for each receptor for each averaging period. These are punched on
unit 1 if option 24 = 1. These cards can be used as input to special
purpose programs, such as plotter programs to contour the field of con-
centrations.
FILE OUTPUT
Table 20 shows the file structure for the partial concentrations
that are written on unit 10 if option 21 =1; this file is unformatted.
Output can become quite lengthy because so much information is available,
so care should be exercised to ensure the allocated storage space can
accommodate the amount of data generated.
Table 21 shows the file structure for the hourly concentrations
that are written on unit 12 if option 22 = 1. This file is unformatted.
These data can be quite useful v^hen processed to both give average
concentrations over any selected averaging time, and determine highest
and second highest concentrations of these over the length of record.
The processing of this file must be accomplished by user-devised programs.
Table 22 shows the file structure of the averaging-period concentra-
tions that are written on unit 13 if option 23 = 1. This file is unfor-
matted.
Table 23 shows the file structure of information related to high-
five tables that are written on unit 14 if option 20 = 1, i.e., if a run
is segmented. This file is unformatted and is read in upon execution of
the next segment of the run.
58
-------
TABLE 17. MPTER OPTIONAL INPUT FILE - METEOROLOGICAL DATA (Unit 11)
(input if option 5=0)
Variable
RECORD 1
ID
IYEAR
I DM
IYR
Dimensions Description
sfc station identifier
year of surface data
mix ht station identifier
year of mix ht data
Units
5 digits
2 digits
5 digits
2 digits
RECORD TYPE 2 (one for each day of year)
JYR year
IMO month
DAY! Julian day
IKST 24 stability class
QU 24 wind speed m s~
QTEMP 24 ambient air temperature K
DUMR 24 flow vector to 10° deg-azimuth
QTHETA 24 randomized flow vector deg-azimuth
HLH 2,24 mixing ht m
59
-------
TABLE 18. MPTER OPTIONAL INPUT FILE - EMISSION DATA (Unit 15)
(input if option 6=1)
Variable
Dimensions
Description
SOURCE(IPOL, I), I - 1, NPT
Emission rate for the
pollutant IPOL for each
source
Units
RECORD TYPE 1 (one for each hour of simulation)
IDATP - date-time indicator
consisting of:
year
Julian day
hour
2 digits
3 digits
2 digits
-1
TABLE 19. MPTER OPTIONAL OUTPUT PUNCHED CARDS - AVERAGE CONCENTRATIONS
(Unit 1) (punched if option 24 = 1)
Variable
Card Columns
Description
RREC
SREC
GWU
K
ZR
ELR
IDATE(l)
IDATE(2)
NB
6-15
16-25
26-35
36-45
46-50
51-60
61-70
72,73
75-77
79,80
east coordinate of receptor
north coordinate of receptor
concentration for averaging time
blank
receptor number
receptor height above ground
receptor ground-level elevation
year
Julian day
beginning hour of this period
Units
CARD TYPE 1 (One for each receptor for each averaging time)
1-4 word CNTL punched
5 blank
user units
user units
-3
m
user height
units
60
-------
TABLE 20. MPTER OPTIONAL OUTPUT FILE - PARTIAL CONCENTRATIONS (Unit 10)
(output if option 21 = 1)
Variable
Dimensions
Description
Units
(from main program)
RECORD 1
NRECEP
NPT
RREC(I), 1=1, NRECEP
SREC(I), 1=1, NRECEP
number of receptors
number of sources
east coordinate of
receptor
north coordinate of
receptor
RECORD TYPE 2 (one record for each receptor for each
simulated hour, from PTR)
I DATE
LH
K
PARTC(J), J = 1, NPT
user units
user units
year and Julian day
hour
receptor number
concentration at receptor ~
K from source J g m~
61
-------
TABLE 21. MPTER OPTIONAL OUTPUT FILE - HOURLY CONCENTRATIONS (Unit 12)
(output if option 22 = 1)
Variable
RECORD 1
NPER
NAVG
LINE!
LINE2
LINES
Dimensions
14
14
14
Description
number of periods
number of hours in
averaging period
80 alphanumeric
characters for title
80 alphanumeric
characters for title
80 alphanumeric
Units
-
_
_
_
RECORD 2
NRECEP
RREC(I), 1=1, NRECEP
SREC(I), 1=1, NRECEP
RECORD TYPE 3
IDATE(2)
LH
PHCHI(I), I
characters for title
number of receptors
east coordinate of
receptor
north coordinate of
receptor
(one for each simulated hour)
Julian Day
hour
1, NRECEP
user units
user units
hourly concentration for each _.,
receptor g m
62
-------
TABLE 22. MPTER OPTIONAL OUTPUT FILE - AVERAGING-PERIOD CONCENTRTIONS
(Unit 13) (output if option 23 = 1)
Variable
RECORD 1
NPER
NAVG
LINE1
LINE2
LINE3
Dimensions Description Units
number of periods
number of hours in
averaging period
14 80 alphanumeric
characters for title
14 80 alphanumeric
characters for title
14 80 alphanumeric
RECORD 2
NRECEP
RREC(I), 1=1, NRECEP
SREC(I), 1=1, NRECEP
RECORD TYPE 3
IDATE(2)
NB
PCHI(K), K =
characters for title
number of receptors
east coordinate of
receptor user units
north coordinate of
receptor user units
(one for each simulated averaging period)
Julian Day
ending hour of period
1, NRECEP averaging period concentration
for each receptor g m
-3
63
-------
TABLE 23. MPTER OPTIONAL TEMPORARY FILE - VALUES FOR HIGH-FIVE TABLES
(Unit 14) (output if option 20 = 1)
Variable
Dimensions
Description
Units
ONLY RECORD
I DAY (on write)
IDAYS (on read)
SUM 180
NHR
DAY1A
HR1
HMAXA
3,5,180,5
number of days processed
number of days previously processed
cumulation of long-term concentration
number of hours processed
Julian day number of start of period of
record
start hour of period of record
Highest five concentrations (g m~ ), and
associated day and hour, for each receptor,
for five different averaging times
64
-------
SECTION 8
EXAMPLE PROBLEMS
Four problems have been chosen to demonstrate some of the uses of MPTER
and to also show the various types of output.
EXAMPLE ONE
The first problem concerns one source for a single one-hour period. The
option to adjust for terrain is selected. Receptors are input so that five
receptors are stacked vertically above each of four downwind positions. When
using the terrain adjustment, MPTER is limited to making concentration esti-
mates at receptors whose ground-level elevation is no higher than that of the
lowest source stack top. The user tries to apply the model for a situation
outside this restriction.
Receptors 16 through 20 all have a ground-level elevation of 10 meters
higher than the stack top. Encountering this situation, the model sets the
concentration to a number too large to be printed in the format allocated for
the concentration. Asterisks thus appear on the output, signifying that no
estimates can be made for these receptors.
Only the hourly summary of concentrations is printed. The meteorological
data, used for the computation, the final effective height, and the distance
to the final height are printed as part of the summary.
Note that since the terrain option is employed in this run, receptors
whose ground-level elevations are lower than the source ground-level eleva-
tion are tagged with one asterisk, although computations are made for these
receptors. Receptors whose ground-level elevations exceed that of the stack
top are tagged with two asterisks, and no computations are attempted for
these receptors.
This problem also shows that receptors can be at the same position and
stacked in the vertical.
65
-------
EXAMPLE TWO
The second example, in four parts, is a sensitivity study. For esti-
mating concentrations directly downwind of an atypical source (low stack with
high buoyancy), four situations can be described by using different parameters:
A) final effective height, B) gradual plume rise, C) buoyancy-induced disper-
sion with final plume height, and D) buoyancy-induced dispersion with gradual
plume rise. This problem shows that with some sources and meteorological
conditions, multipeak concentrations with distance can be obtained, when
using the options of gradual plume rise and buoyancy-induced dispersion in
combination. A number of runs were made using various wind speed and stability
class configurations to find this phenomenon. Other combinations of meteoro-
logy and source parameters will not exhibit multipeaks in the concentration
profiles so vividly.
Concentrations are determined at various distances downwind from the
source over a level surface. The receptors are directly east of the source
and the wind is specified from the west (270 degrees).
Although two sources are used in this example, they are actually simu-
lating a variation in stack gas temperature at the same source. Therefore
the two sources are located at the same position. *
In Run A considering only final rise, note that concentrations for both
sources for both hours climb rapidly to a peak at a distance in the vicinity
of 1.0 to 2.0 km from the source and then decrease slowly with distance.
In Run B, which considers the gradual rise of the plume, concentrations
are somewhat higher near the source, but reach the same peak for the first
hour since this peak is at a distance beyond the distance of final rise, 1.35
km for source 1, and 1.08 km for source 2. However, for the second hour,
higher concentrations (30% higher for source 1) than in Run A are obtained
closer to the source than the distance to final rise.
In Run C, which returns to consideration of final rise, but also includes
buoyancy-induced dispersion, maximum concentrations (though slightly lower)
are virtually unchanged for hour one. For hour two the maximum concentrations
occur at the same distances as for Run A, but are about 80% of those for Run
A.
66
-------
In Run D, in which both gradual plume rise and buoyancy-induced dispersion
are considered, maximum concentrations for hour one occur nearer the source
and of higher magnitude, 26 to 38% higher, than in Run B. Also, source one
has a secondary and a tertiary peak about the primary maximum. Source two
has a secondary peak beyond the primary maximum. However, for hour two both
sources display single maxima of lower magnitude, 84 to 90%, than that given
by Run B, and at approximately the same distance from the source.
For these four runs, only the hourly contribution printouts are obtained;
they include the meteorological data, plume height, and distance information.
Figure 3 is a log-log plot of concentration as a function of distance
for source 2 for hour 1 for the four runs.
EXAMPLE THREE
The third example is a long term run in that calculations are made using
hour-by-hour meteorological data for a full year. This is the only example
where the high-five table (option 19 is left zero) is given. Also all
receptors in this run are generated using option 8. Since the terrain option
(option 1) is also employed, elevations on 36 cards of TYPE 11 are read in.
All printout, with the exception of the high-five table, is deleted, (i.e.,
options 9 through 18 are employed resulting in a savings of many pages of
output).
Note that asterisks relating to notes about receptor elevations are
given on the receptor lists, but not in the high-five table. Asterisks in
the high-five table are used to label the receptor with the highest and
second-highest concentrations.
EXAMPLE FOUR
The fourth problem is included primarily as an example of all types of
printed output except the high-five table. Also, more sources than can be
considered as significant occur, and two sources are specified, (8 and 27) to
obtain contribution information, even though they are not among the top 10 in
ranking of expected impact. This step employs option 7. Meteorological data
and plume height data are given on the hourly contribution printout, but not
on the hourly summaries.
The runstream and output for the four examples follow:
67
-------
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EXAMPLE 4, PAGE 21
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Turner, D. B., and Novak, J. H., 1978: User's Guide for RANI. Vol. I.
Algorithm Description and Use, Vol. II. Data Preparation and
Listings. EPA-600/8-78-016 a and b, U. S. Environmental Protection
Agency, Research Triangle Park, NC. 60 and 222 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: User's Network for Applied
Modeling of Air Pollution (UNAMAP) (Version 3). (Computer programs
on magnetic tape for eleven air quality simulation models) NTIS PB
277-193, National Technical Information Service, Springfield, VA.
145
-------
APPENDIX A
POINT SOURCE COMPUTATIONS
Given an east-north coordinate system (R, S), then the upwind distance,
x, and the crosswind distance, y, of a point source from a receptor are given
by:
x = (Sp-Sr) cos 9 + (Rp-Rr) sin 6 (Al)
y = (Sp-Sr) sin 9 - (Rp-Rr) cos 9 (A2)
where R , S are the coordinates of the point source; R , S are the coordi-
nates of the receptor, and 9 is the wind direction (the direction from which
the wind blows). The units of x and y will be the same as those of the
coordinate system R, S. In order to determine plume dispersion parameters,
distances must be in kilometers or meters. A conversion may be required to
convert x and y above to the appropriate units.
The various forms of the Gaussian equation given below are based upon
the coordinate scheme with the origin at the ground, and x upwind from the
receptor, y crosswind, and z vertical. The Gaussian equations for continuous
releases have four components: 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 (bell-shaped) crosswind distribution at downwind distances, and 4) the
effluent is spread vertically. This latter component 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. Equations A3, A4 and A5 are broken
into these four components (see below).
The following symbols are defined:
XD» concentration, g m~
Q , emission rate, g s"
146
-------
u , wind speed, m s"
a , standard deviation of plume concentration horizontal
distribution (evaluated at the distance x and for
appropriate stability), m
o , standard deviation of plume concentration vertical
distribution (evaluated at the distance x and for
appropriate stability), m
L , mixing height, m
H , effective height of emission, m
z , receptor height above ground, m
y , crosswind distance, m
The contribution to the concentration, xp» from a single point source
to a receptor is given by one of the three following equations where the
expressions g, , g^, g^, are defined below.
Component: (1) (2) (3) (4)
*D = Q • IT 9l • °2 (A3)
^ / 2 TT a
(A5)
For stable conditions or unlimited mixing use equation (A3).
For unstable or neutral c
than 1.6 L, use equation (A4).
For unstable or neutral c
equation (A5), provided that both H and z are less than L.
For unstable or neutral conditions, where a is equal to or greater
For unstable or neutral conditions where o is less than 1.6 L, use
147
-------
Sensitivity tests using equation (A5) have indicated that for all H and
all z between the ground and the mixing height, the vertical distribution of
concentration with height is uniform when °" has increased to 1.6 L. Therefore,
when o is equal to or greater than 1.6 L for neutral or unstable conditions,
use equation (A4). For special cases such as z = 0, equation (A4) may give
appropriate concentrations for a much less than 1.6 L. However, the above
recommendation covers the more general case. (Note that this recommendation
differs from that of Pasquill (1976) and the Stability Workshop (Hanna, 1977),
which indicate that a should not be allowed to increase beyond 0.8 L.) For
ground level receptors, z = 0, the use of a^ = 0.8L in equation (A3) reduces
to equation (A4). However, the above recommendation allows a to increase
beyond the value of L, specifically as large as 1.6 L; it also allows for a
smooth transition to a uniform vertical profile for receptors above the
ground, z f 0, and for effective heights of emission approaching the mixing
height.
Definitions for expressions g-| , g£, g, follow:
g1 = exp (-0.5 y2/a2)
g2 = exp [-0.5(z-H)2/a2] + exp [-0.5(z+H)2/a2]
00 99 99
93 = I (exp [-0.5(zH+2NLr/a^] + exp [-0.5(z+H+2NL) /a*]}
(This infinite series converges rapidly and
evaluation with N varying from -4 to +4 is
usually sufficient.)
148
-------
REFERENCES -- APPENDIX A
Hanna, S. R., G. A. Briggs, J. Deardorff, B. A. Egan, F. A. Gifford and
F. Pasquill, 1977: AMS Workshop on Stability Classification Schemes
and Sigma Curves - Summary of Recommendations. Bull. Am. Meteorol.
Soc.. 58: 1305-1309.
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, N.C. 44 pp.
149
-------
APPENDIX B
PLUME RISE FOR POINT SOURCES
The manner in which the methods of Briggs are used 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
In order to consider stack downwash, modification of the physical stack
height is performed following Briggs (1973, p. 4). The h1 is found from:
h' = h + 2 [ ( v_/u(h)) - 1.5 1 d for vc < 1.5 u(h) (Bl)
I •> ) s
h1 = h for vs >_ 1.5 u(h)
where h is physical stack height, v is stack gas velocity, m s , and d is
inside stack-top diameter, m. This h' 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
4 -3
fieter, F, in m s is needed. Tl
equation (12), (Briggs, 1975, p. 63):
parameter, F, in m s~ is needed. The following equation is equivalent to
vc d2 AT (B2)
where AT = T - T, TS is stack gas temperature, K, and T is ambient air
temperature, K.
150
-------
Unstable or Neutral Crossover between Momentum and Buoyancy
For cases with stack gas temperature greater than ambient air temperature,
whether the plume rise is dominated by momentum or buoyancy must be determined.
The crossover temperature difference (AT) 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 the (AT) , the plume
rise is assumed to be buoyancy dominated; if less than this amount, the plume
rise is assumed to be momentum dominated (see below).
For F less than 55, the crossover temperature difference is found by
setting Equation (5.2) (Briggs, 1969, p. 59) equal to the combination of
Equations (6) and (7) (Briggs, 1971, p. 1031) and solving for AT. The
result is:
(AT)c = 0.0297 Ts VS1/3/ d2/3 (B3)
For F equal to or greater than 55, the crossover temperature difference
is found by setting Equation (5.2) (Briggs, 1969, p. 59) equal to the combina-
tion of Equation (6) and (7) (Briggs, 1971, p. 1031) and solving for AT. The
result is:
(ATL = 0.00575 T vc2/3/d1/3 (B4)
(c s s
Unstable or Neutral Buoyancy Rise
For situations where AT exceeds (AT) as determined above, buoyancy is
assumed to dominate. The distance to final rise xf in kilometers, is deter-
mined from the equivalent of Equation (7), (Briggs, 1971, p. 1031), and the
distance to final rise is assumed to be 3.5 x*, where x* is the distance at
which atmospheric turbulence begins to dominate entrainment.
For F less than 55:
xf = 0.049 F5/8 (B5)
For F equal to or greater than 55:
xf = 0.119 F2/5 (B6)
151
-------
The plume height, H, in meters, is determined from the equivalent of
the combination of Equations (6) and (7) (Briggs, 1971, p. 1031):
For F less than 55:
H = h1 + 21.425 F3/4/u(h) (B7)
For F equal to or greater than 55:
H = h1 + 38.71 F3/5/u(h) (B8)
Unstable or Neutral — - Momentum Rise
For situations where the stack gas temperature is less than or equal to
the ambient air temperature, the assumption is made that the plume rise is
dominated by momentum. If AT is less than (AT) from Equation (B3) or (B4),
c
the assumption is also made that the plume rise is dominated by momentum. The
plume height is calculated from Equation (5.2) (Briggs, 1969, p. 59):
H = h1 + 3d vs/u(h) (B9)
Briggs (1969, p. 59) suggests that this equation is most applicable when v /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 - 9- (BIO)
As an approximation, for stability class E, or 5, 96/9z is taken as 0.02 K
m" , and for stability class F, or 6, 96/9z is taken as 0.035 Km.
Stable - Crossover between Momentum and Buoyancy
For cases with stack gas temperatures greater than ambient air temper-
ature, determining whether the plume rise is dominated by momentum or buoyancy
is necessary. The crossover temperature difference (AT) is found by setting
Equation (59) (Briggs, 1975, p. 96) equal to Equation (4.28), (Briggs, 1969,
p. 59) and solving for AT. The result is:
(AT) = 0.01958 T vc s1/2 (BIT)
(- S
152
-------
If the difference between stack gas temperature and ambient air temper
ature, AT, exceeds the (AT) , the plume rise is assumed to be buoyancy domi
nated; if less than this amount, the plume rise is assumed to be momentum
dominated.
Stable : — Buoyancy Rise
For situations where AT exceeds (A)_ as determined above, buoyancy is
(*r
assumed to dominate. The distance to final rise, in kilometers, is deter-
mined by the equivalent of a combination of Equations (48) and (59) in
Briggs, (1975), p. 96):
xf = 0.00207 u(h) s ~1/2 (B12)
The plume height is determined by the equivalent of Equation (59)
(Briggs, 1975, p. 96): 1/3
H ' h' + 2'6 - (B13)
The stable buoyancy rise for calm conditions (Briggs, 1975, pp. 81-82)
is also evaluated:
H = h1 + 4 F1/4 s"3/8 (B14)
The lowest value of these two obtained from Equations (B13) and (B14) is
taken as the final effective height.
By setting equations (B13) and (B14) equal to each other and solving for
u(h), the wind speed can be determined that yields the same plume rise for
the wind conditions (B13) as does the calm equation. This rise is:
u(h) . ZjS FV4 ,1/8
= 0.2746 F1/4 S1/8 (B15)
For wind speed less than or equal to this value, use equation (B14) for
plume rise; for wind speeds greater than this value, use equation (B13).
153
-------
Stable —- Momentum Rise
Where the stack gas temperature is less than or equal to the ambient
air temperature, the assumption is made that the plume rise is dominated by
momentum. If AT is less than (AT)C as determined by (Bll), the assumption
is also made that the plume rise is dominated by momentum. The plume height
is calculated from Equation (4.28) of Briggs (1969), p. 59):
H = h1 + 1.5
2 2
vs d T
s'1/6 (B16)
The equation for unstable-neutral momentum rise (B9) 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 Equation (2)
(Briggs, 1972, p. 1030) is used to determine plume height:
Ififl F1/3 v 2/3
H = h' + 16°- Fu(h)x (B17)
This height will be used only for buoyancy dominated conditions; should it
exceed the final rise for the appropriate condition, the final rise is sub-
stituted instead.
154
-------
REFERENCES -- APPENDIX B
Briggs, Gary A., 1969: Plume Rise. USAEC Critical Review Series, TID-25075,
National Technical Information Service, Springfield, Va. 81 pp.
Briggs, Gary A., 1971: Some recent analyses of plume rise observation. In:
Proceedings of the Second International Clean Air Congress, H. M. England
and W. T. Beery, eds. Academic Press, New York. pp. 1029-1032.
Briggs, Gary A., 1972: Discussion on chimney plumes in neutral and stable
surroundings. Atmos. Environ. 6; 507-510.
Briggs, Gary A., 1973: Diffusion Estimation for Small Emissions. Atmos.
Turb, and Diff. Lab., Contribution File No. (Draft) 79. Oak Ridge, Tenn.
59 pp.
Briggs, Gary A., 1975: Plume rise predictions. In: Lectures on Air Pollution
and Environmental Impact Analysis, Duane A. Haugen, ed. Amer. Meteorol.
Soc., Chapter 3 (pp. 59-111). Boston, Mass. 296 pp.
155
-------
APPENDIX C
SOURCE PROGRAM LISTING
156
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1 REPORT NO
EPA-600/8-80-016
4 TITLE AND SUBTITLE
USER'S GUIDE FOR MPTER
A Multiple Point Gaussian Dispersion Algorithm With
Optional Terrain Adjustment
5. REPORT DATE
April 1980
6. PERFORMING ORGANIZATION CODE
3. RECIPIENTS /'CC^SSIGf+NO.
7. AUTHOR(S)
Thomas E. Pierce and D. Bruce Turner
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
(same as block 12)
10. PROGRAM ELEMENT NO.
C05A1A 10- 0008 (FY-80)
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory - RTF, NC
Office of Research and Development
U. S. Environmental Protection Agency
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Tn-hrmae
14. SPONSORING AGENCY CODE
EPA/600/09
15. SUPPLEMENTARY NOTES
16. ABSTRACT
ine information presented in this user's guide is directed to air pollu-
tion scientists interested in applying air quality simulation models. MPTER is the
designation for Multiple Point source algorithm with TERrain adjustments. This
algorithm is useful for estimating air quality concentrations of relatively non-
reactive pollutants; hourly estimates are made using the Gaussian steady-state model.
Ihe algorithm is most applicable for source-receptor distances less than 10 km and
for locations with level or rolling terrain where a single wind vector for each hour
adequately approximates the flow over the source and receptor sites. The terrain
adjustment option is limited in application to receptors whose elevation is no higher
than the lowest stack top elevation of the sources considered. Calculations are
performed on the hourly meteorological data that the model requires: wind direction,
wind speed, temperature, stability class, and mixing height. Emission information
required of the point sources are source coordinates, emission rate, physical height
stack diameter, stack gas exit velocity, and stack gas temperature. In addition to
terrain adjustment, options are available for stack downwash, gradual plume rise, and
buoyancy-induced dispersion. All printed output is optionally available so the user
can avoid unneeded output volume. General information is contained in the Executive
lummary and the first three chapters. The technical basis for the algorithm is given
in Chapter 4 and Appendices A and B. The remaining material herein relates to use and
understanding of the computer prooram for the alaorithm.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
*Air pollution
*Atmospheric models
Algorithms
*Atmospheric diffusion
b. IDENTIFIERS/OPEN ENDED TERMS C. COSATI FieUl/GtOUp
13 B
04 A
12 A
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (This Report)
UNCLASSIFIED
21. NO. OF PAGES
247
20. SECURITY CLASS (Thispage)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
239
-------
Date
Chief, Environmental Operations Branch
Meteorology and Assessment Division (MD-80)
U.S. Environmental Protection Agency
RESRCH TRI PK, NC 27711
I would like to receive future revisions to the
User's Guide for MPTER.
Name
Organization
Address
City State Zip_
Phone (Optional) ( ) -
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