EPA/600/8-87/009
March 1987
NTIS Accession Number
PB87-168 787/AS
USER'S GUIDE FOR PAL 2.0
A GAUSSIAN-PLUME ALGORITHM
FOR POINT, AREA, AND LINE SOURCES
ATMOSPHERIC SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
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USER'S GUIDE FOR PAL 2.0
A GAUSSIAN-PLDME ALGORITHM
FOR POINT, AREA, AND LINE SOURCES
by
William B. Petersen
and
E. Diane Rumsey
Meteorology and Assessment Division
Atmospheric Sciences Research Laboratory
Research Triangle Park, North Carolina 27711
ATMOSPHERIC SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
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NOTICE
The information in this document has been funded by the United States
Environmental Protection Agency. It has been subject to the Agency's peer
and administrative review, and it has been approved for publication as an EPA
document,. Mention of trade names or commercial products does not constitute
endorsement or recommendation for use.
AFFILIATION
Mr. William B. Petersen and Ms E. Diane Rumsey are meteorologists in the
Meteorology and Assessment Division, Environmental Protection Agency, Research
Triangle Park, NC, on assignment from the National Oceanic and Atmospheric
Administration, U.S. Department of Commerce.
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PREFACE
The User's Guide for PAL 2.0 was written so that one need not understand
the mathematical formulation to apply the model. However, we strongly recom-
mend that the user carefully read Sections 2, 3, 7, and 8, which give valuable
insight into the model's flexibility and limitations, and the assignment of
values to input parameters.
While attempts are made to thoroughly check out computer programs with a
wide variety of data, errors are found occasionally, In case there is a need
to correct, revise, or update this model, revisions will be distributed in
the same manner as this report. If your copy was obtained by purchase or
special order, you may obtain revisions as they are issued by completing the
mailing form on the last page of this report.
Comments and suggestions regarding this document should be directed to
Chief, Environmental Applications Branch, Meteorology and Assessment Division,
(Mail Drop 80), Environmental Protection Agency, Research Triangle Park, NC
27711).
Technical questions regarding use of the model may be asked by calling
(919) 541-4564. Users within the Federal Government may call FTS 629-4564.
Copies of the user's guide are available from the National Technical Infor-
mation Service (NTIS), Springfield, VA 22161.
The magnetic tape containing FORTRAN source code for PAL 2.0 will be
contained (along with other dispersion models) in futrue versions of the
UNAMAP library, which may be ordered from Computer Products, NTIS, Springfield,
VA 22161 (phone number: (703) 487-4763).
This user's guide is intended to be a living document that is updated as
changes are required. Each page of the User's Guide to PAL 2.0 has a month
and year typed in the lower right hand corner. Future revisions to this
document will be indicated in the preface, and every page that is changed due
to the revision will have a new date printed in the lower right hand corner.
The current version number of PAL and the date associated with it will be
given in the preface of the user's guide. The version number is also main-
tained in the source code allowing the user to confirm that his user's guide
and source code are current.
Throughout the rest of this document PAL 2.0 will be referred to as PAL.
PAL 2.0 represents a significant modification to the original PAL model,
(Petersen, 1978). In the past, such a modification to one of our air quality
models would have been accompanied with a change in the name of the model.
However, the following convention will be used for PAL. Major modifications
to the model will be indicated by a change in the version number. Minor
modifications will be reflected by a change in the update number. The version
and update numbers are separated by a "." and appear after the name of the
model.
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ABSTRACT
PAL is an acronym for the Point, Area, and Line source algorithm. PAL
is a method of estimating short-terra dispersion using Gaussian-plume steady-
state assumptions. The algorithm can be used for estimating concentrations
of non-reactive pollutants at 99 receptors for averaging times of from 1 to
24 hours, and for a limited number of point, area, and line sources (99 of
each type).
Calculations are performed for each hour. The hourly meteorological
data required are wind direction, wind speed, stability class, and mixing
height. Single values of each of these four parameters are assumed repre-
sentative for the area modeled. The Pasquill-Gifford or McElroy-Pooler
dispersion curves are used to characterize dispersion.
This algorithm is not intended for application to entire urban areas
but is intended, rather, to assess the impact on air quality, on scales of
tens to hundreds of meters, of portions of urban areas such as shopping
centers, large parking areas, and airports. Level terrain is assumed.
The Gaussian point source equation estimates concentrations from point
sources after determining the effective height of emission and the upwind and
crosswind distance of the source from the receptor.
Numerical integration oC the Gaussian point source equation is used to
determine concentrations from the four types of line sources. Subroutines
are included that estimate concentrations for multiplelane line and curved
path sources, special line sources (line sources with endpoints at different
heights above ground), and special curved path sources.
Integration over the area source which includes edge effects from the
source region is done by considering finite line sources perpendicular to the
wind at intervals upwind from the receptor. The crosswind integration is
done analytically; integration upwind is done numerically by successive
approximations.
The PAL model can treat deposition of both gaseous and suspended
particulate pollutants in the plume since gravitational settling and dry
deposition of the particles are explicitly accounted for. The analvtical
diffusion-deposition expressions (Rao, 1982) listed in this report are easy
to apply and, in the limit when pollutant settling and deposition velocities
are zero, they reduce to the usual Gaussian plume diffusion algorithms.
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CONTENTS
Preface ill
Abstract iv
Figures vi
Tables vi
Symbols and Abbreviations vii
Acknowledgements viii
Executive Summary ix
1. Introduction 1
2. Data-Requirements Checklist 3
3. Features and Limitations 7
4. Basis for PAL 10
Point sources 10
Area sources 10
Line sources 11
5. Technical Description 13
Point source computations 13
Area source computations 15
Line source computations 19
Curved source computations 24
Special path sources 29
Settling and dry deposition 31
Settling and deposition velocities 35
6. Example Problems 36
Example 1 Test for basic use of PAL 36
Example 2 Test with deposition option ......... 40
7. Computer aspects of the model 43
General flow of the model 43
Description of subroutines and functions 46
8. Preparation of Input Data 50
Point sources 60
Area sources 62
Line sources 62
Meteorology 63
9. Sensitivity Analysis 65
10. Execution of Model and Interpretation of output 68
References 82
Appendix. Settling and Deposition Velocities 84
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FIGURES
Number
1 Upwind and crosswind distances of point sources from a receptor
2 Minimum, X}, and maximum, Xz upwind distances of an area source
from a receptor and croswind line sources
3 Line source and receptor relationships
4 Curved source and receptor relationships
5 Source types included in example problem 1
6 Schematic diagram of sources and receptors in example problem 2
7 General flow diagram for PAL
8 Structure of subroutines and functions in PAL program
9 Input data deck for the PAL model
10 Percentage difference in concentrations for PINL (PINA) values
of 0.001 to 0.1
11 Computer listing output for example 1
12 Computer listing putput for example 2
14
17
20
25
37
41
44
45
51
67
70
77
TABLES
Number
1
2
3
4
5
6
7
8
Meteorology Data for Example 1
Source Strengths for the Five Source Types in Example 1 . .
Three-Hour Average Concentrations (ji g/m3) for Both 3-Hour
Meteorology Periods
Description of Input Data ...
Exponents for Wind Profile
Percentage Difference in CPU time for PINL (PINA) Values of
0.001 and 0.1 . . .
Input Data for Example 1
Input Data for Example 2 , . .
38
38
39
52
64
66
69
76
VI
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SYMBOLS & ABBREVIATIONS
Dimensions are abbreviated as follows: m = mass, 1 = length, t = time.
a - acceleration of the vehicle
d - diameter of particle (1)
D - total line source length (1)
Df - surface deposition flux (m/1 t)
EF - emission factor (m/veh 1)
fp - point source dispersion function
fc - dispersion function corrected for finite length of line source
f - dispersion function for area sources
h - building height (1)
H - effective height of source emission (1)
Hb - width of building (1)
1 - length of line (1)
L - mixing height of inversion, top of unstable layer (1)
N - eddy reflection number
0 - point source emission rate (m/t)
q^ - line source emission rate (m/t 1)
q^ - area emission rate (m/1 )
t - total time of travel (t)
tp - time of travel to a point (t)
TV - traffic volume (veh/t)
U - mean wind speed (1/t)
Vj - dry deposition velocity of pollutant (1/t)
VL - average vehicle length (1)
Vg - minimum vehicle speed (1/t)
Vp - vehicle speed at a given point (1/t)
Vf - final vehicle speed (1/t)
V0 - initial vehicle speed (1/t)
W - gravitational settling velocity of pollutant particles (1/t)
X - upwind distance from a receptor to a point on a line source (1)
Xf - total distance of travel (1)
Xp - distance to travel to any point, P (1)
Y - crosswind distance from a receptor to a point on a line source (1)
YA - crosswind distance of a point from the receptor (1)
Yg - crosswind distance of a point from the receptor (1)
z - receptor height above ground (1)
p - radius of circle (1)
Xp - concentration from a single point (ra/1^)
(j) - azimuth from circle center to intersection (radians)
p - dynamic viscosity of air
Oy - standard deviation of plume concentration distribution in the
lateral (1)
az - standard deviation of plume concentration distribution in the
vertical (1)
9 - wind direction
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ACKNOWLEDGEMENTS
The authors wish to express their appreciation to Bruce Turner, who was
responsible for much of the development of the PAL model; to John Irwin and
Alan Huber for their helpful discussions and review. Much credit for PAL 2.0
also belongs to Dr. Shankar Rao and TRC for their development of PAL-DS and
PALU respectively. Portions of this text were excerpted from the PAL and
PAL-DS user's guides.
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EXECUTIVE SUMMARY
The Point A_rea Line source computer algorithm is designed to simulate
dispersion from continuous releases of six source types. The algorithm is
based upon Gaussian plume assumptions including a vertically uniform wind
direction field and no chemical reactions. PAL can provide concentration
estimates at up to 99 receptor locations.
The model requires hourly input of wind direction and speed, stability
class, mixing height and ambient air temperature. Source parameters include
physical stack height above ground, stack top inside diameter, stack gas
temperature, exit velocity and pollutant emission rate. Line source informa-
tion include number of lanes of traffic, vehicle speeds and line source emis-
sion rates.
PAL 2.0 incorporates two major enhancements from previous versions of
PAL. Rao (1982) provided an analytical solution of a gradient- transfer
model for dry deposition of gaseous and particulate pollutants which was
included in a version of PAL called PAL-DS. The deposition and gravitational
settling algorithm are included in PAL 2.0. The other major enhancement is
the inclusion of urban diffusion coefficients.
Features of the PAL computer code include:
o Wind speed extrapolated to release heights,
o Removal through gravitational settling and deposition,
o Optional control to include average concentrations,
o Optional control to include diurnal variation in emissions, and
o Optional control to include urban diffusion coefficients.
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SECTION 1
INTRODUCTION
PAL is a multisource Gaussian-Plume atmospheric dispersion algorithm for
estimating concentrations of non-reactive pollutants. Concentration estimates
are based on hourly meteorology, and averages can be computed for averaging
time from 1 to 24 hours. Six source types are included in PAL: point, area,
two types of line sources, and two types of curved path sources. As many as
99 sources may be included under each source type. PAL is not intended as
an urban-wide model but may be applied to estimate the contribution of part of
an urban area to the concentration. Portions of urban areas assessed by PAL
for impact on air quality are:
o Industrial complexes
o Sports stadiums
o Parking lots
o Shopping areas
o Airports
At the heart of PAL is the Gaussian-Plume point source equation (Gifford,
1960). The equation is used directly in the computations for point, line,
and curved path sources, and in a modified form for area sources. A unique
feature of PAL is the computational technique for estimating the concentra-
tion from area sources. This technique incorporates edge effects and is
theoretically more accurate than the methods used in the Climatological
Dispersion Model (COM) (Busse and Zimmerman, 1973) and the Air Quality Dis-
play Model (AQDM) (Martin, 1971). The horizontal line source algorithm is
similar to the Highway Air Pollution Model (HIWAY) (Zimmerman and Thompson,
1975). Input source types also include two types of curved paths, one of
which considers variation of emissions along the path. PAL will also esti-
mate concentrations from a line source which has a variation in emission
along the source. This line source may be slanted or elevated relative to
the ground. PAL offers considerable flexibility to the user. Any or all of
the six source subroutines may be utilized. The user also has the options of
employing an hourly variation to emission rates and of allowing the wind
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speed to change with height. Concentration estimates can be made at up to 99
user specified receptor locations.
Rao (1982) gave analytical solutions of a gradient-transfer model for
dry deposition of gaseous and particulate pollutants from a plume. These new
diffusion-deposition algorithms were presented as analytical extensions of the
Gaussian plume diffusion algorithms currently used in EPA. models under various
atmospheric stability and mixing conditions. The analytical gradient-transfer
model treats gravitational settling and dry deposition of pollutant in a
physically realistic and straightforward manner, and it is subject to the
same basic assumptions and limitations associated with all Gaussian plume-
type models.
This document is divided into three parts, each directed to a different
audience: managers, dispersion meteorologists, and computer specialists. The
first four sections are aimed at managers and project directors who wish to
evaluate the applicability of the model to their needs. Sections 5, 6, 9,
and 10 are directed toward dispersion meteorologists or engineers who are
required to become familiar with the details of the model. Finally, Sections
7 through 10 are directed toward persons responsible for implementing and
executing the program.
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SECTION 2
DATA-REQUIREMENTS CHECKLIST
The PAL algorithm can consider six types of sources. In any single
execution, any combination of these six source types can be used. However,
the maximum number of input sources for any given type cannot exceed 99. PAL
requires data on user options, sources, meteorology and receptors. The user
must indicate whether the following options are to be employed:
o Integration accuracy for area and line sources,
o Wind increase with height,
o Control for average concentrations,
o Option for diurnal variations in emissions,
o Option for urban diffusion coefficients, and
o Option for deposition and gravitational settling.
The treatment of point sources in PAL is similar to that in many other
air quality simulation models. In order to calculate plume rise, the stack
gas temperature in combination with stack gas volume flow, or stack inside
diameter and stack gas velocity are required. Point source information
consists of the following for each source:
o Point source strength (g sec~*),
o Physical stack height (m),
o Stack gas temperature (°K),
o Stack gas velocity (ra sec ),
o Stack inside top diameter (m),
O 1
o Stack gas volume flow (m sec ),
o East coordinator of stack (km),
o North coordinate of stack (km), and
o Initial dispersion parameters (m).
In PAL, the shape of area sources may be squares or rectangles.
Boundaries must be oriented north-south and east-west. There are no
special restrictions about source size. A unique feature of PAL is that
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negative area source strengths can be considered in order to account for
smaller areas with no emission within larger area sources. Area source
information consists of the following for each source:
o Area source strength (g sec m ),
o Area source height (m) (assumed to be effective height.),
o East coordinate of south-west corner (km) and,
o North coordinate of south-west corner (km).
Four types of line sources can be considered in PAL. All require similar
input data. Curved path sources require coordinates of three points to define
the path. Special line and path sources require information on vehicle speed
and size. Line source information consist of the following:
o Line source strength (g sec m ),
o Line source height (m),
o Number of lanes if multilane (dimensionless),
o East coordinate of point A (km),
o North coordinate of point A (km),
o East coordinate of point B (km),
o North coordinate of point B (km),
o Initial speed of vehicles (m sec"*) (at point A),
o Final speed of vehicles (ra sec"*) (at point B),
o Initial dispersion parameters (m),
o Gross estimate of vehicle size (m) and
o Vehicle volume (Veh/hr).
Receptors may be located at any position relative to the air pollutant
sources. However, common sense should be used so that receptors are not
positioned in the center of lanes of traffic, etc. The data required for
each receptor consist of the east and north coordinates of the receptor and
the height of the receptor above ground level. The height of a receptor is
the distance of that receptor above the local ground level, not the height of
the ground above some reference plane. The three receptor parameters are:
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o East coordinate of receptor (km),
o North coordinate pf receptor (km), and
o Height of receptor above ground (in).
The input of meteorological data for each simulated hour, up to 24 hours,
follows all required source and receptor data. Care should be taken to ensure
that the meteorological data are representative of the source-receptor locality.
Available airport data may not be representative of an urban or suburban site.
Wind speed and direction are especially sensitive to the local environment
especially in the vicinity of buildings. Depending upon the nature of the
problem being considered, special instrumentation may be established in the
field in order to gather representative meteorological data.
Mixing height will frequently be of little importance if source-receptor
distances are small. Mixing height is the top of the unstable or neutral
layer near the ground. Therefore, mixing height is not used if the lowest
atmospheric layer is stable. Mixing height is usually more nearly the same
over larger areas than wind speed or wind direction. However, urban influences
may cause the existance of a neutral layer at the surface and a mixing height
at night compared to stable conditions for this period in the rural area.
The ambient air temperature is used only for the calculation of plume
rise for the point sources.
Since a meteorological data card is read for each simulated hour, some
additional optional data related to diurnal emission rates are included with
the meteorological data. If the option is employed to vary the emission
rates of the sources, a dimensionless factor for each source type is read in
for each hour. The computations for each source are then multiplied by this
factor using the individual emissions previously read. For example, if infor-
mation indicates that for this hour the emissions from all point sources are
about half the emission rates previously read in, the factor would be 0.5.
Or, if the emissions are thought to be about 30 percent higher for this
hour, the factor would be 1.30.
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The meteorological and diurnal factor input parameters follow:
o Wind direction (deg),
o Wind speed (m sec ),
o Pasquill stability class (dimensionless),
o Mixing height (m),
o Ambient air temperature (°K),
o Diurnal variation for point sources (dimensionless),
o Diurnal variation for area sources (dimensionless),
o Diurnal variation for horizontal line sources (dimensionless),
o Diurnal variation for curved sources (dimensionless),
o Diurnal variation for specialized line sources (dimensionless), and
o Diurnal variation for specialized curved sources (dimensionless).
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SECTION 3
FEATURES AND LIMITATIONS
The analysis power available to the user of PAL cannot be appreciated
unless two features of the model are understood. One feature of the model
concerns the handling of the wind speed. While the user is specifying the
kinds of source types which will later be input in the problem, the user also
specifies whether the wind speed varies as a function of height. The wind
speed can be held constant or can be varied as a function of height and sta-
bility class. The manner In which the wind speed is handled within PAL is
specified for each source type, allowing considerable flexibility.
A second feature of the model concerns how the emission rates from the
various input sources are determined. Unlike some multisource models, such
as the Real-Time Air-Quality Model (RAM) (Novak and Turner, 1976), the
emissions data for each source type is Input into the model only once and Is
not initialized for each hour of meteorology. However, as each hour of
meteorology is input, the user can specifv, independently for each source
type, the fractional amount of the initial input emission rate to be applied.
For instance, say we had specified the maximum sulfur dioxide (803) emission
rate for a situation in which we had only point and area sources. From
insight into the situation, we might know that the point sources contribute
most during the daylight hours from factory emissions, and that the area
sources contribute most during the nighttime hours from home heating. We
could model the above hypothetical situation by appropriately varying the
emission factors, individually for each source type, for each hour of a
24-hour period. The wind speed feature and the emission rate feature are
extremely powerful when considered with the various restarting options of the
program.
PAL, as other Gaussian models, is subject to Gaussian dispersion assump-
tions, such as conservation of mass, steady state atmospheric conditions,
and relatively flat terrain. Complex aerodynamic effects, like downwash from
buildings, are not considered in PAL. However, enhanced dispersion can be
simulated by modifying the dispersion parameters to account for initial mixing
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caused by buildings. The detail which PAL considers, such as edge effects
from area sources and the finite length of line sources, generally prohibits
the application of PAL to an entire urban area due to excessive computer cost.
Also, since meteorological data are entered hour by hour, a normal run for
PAL would be to simulate a period of 1 to 24 hours. Calculations for more
than several 24-hour periods would also be costly. The principal use of PAL
is to estimate the increase in pollutant concentration over that due to other
sources not included in the PAL computation.
PAL treats gravitational settling and dry deposition of pollutants in a
physically realistic manner, and is subject to the same basic assumptions
and limitations associated with Gaussian plume models. The equations used
in PAL are the same as those used in PAL-DS (Rao, 1982).
In Gaussian models concentration estimates are inversely proportional to
the wind speed. Besides the unreasonably high concentration estimates
calculated during very low speed conditions due to this inverse relationship,
there are other modeling difficulties associated with low wind speeds. Wind
directions may be extremely variable. Thus, the hour average wind direction
used in the model may well not be a true representation of the wind direction
during the hour. The dispersion parameters used in PAL do not account for
this kind of variability in the wind. Because of the extreme variability of
the wind direction, actual concentrations might well be much lower than model
estimates. Gaussian models also assume that there is no build-up of pollutant
from hour to hour. That is, the concentration estimate made for a particular
hour is independent of the concentration estimate made for the meteorology of
the previous hour. However, during low wind speed conditions, pollutant
build-up may occur, particularly for an urban area or a section of an urban
area. A reasonable lower limit of wind speed to use as input into PAL is 1.0
m sec .
Care must also be exercised when computing high average concentration
estimates to compare with air quality standards, say for example 8 hours. It
would be unrealistic to assume that a combination of wind direction, wind
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speed, and stability class would persist during an 8-hour period. The persis-
tence of the above variables can be obtained from meteorological records and
should be used accordingly in the model.
PAL is designed to make estimates over relatively level terrain. Receptor
height should not be used in an attempt to simulate topographic differences.
The height of the receptor is the height of that receptor above the local
ground level, not the height of the ground above some reference plane.
The Pasquill-Gifford horizontal dispersion parameter values used in PAL
are strictly applicable only to concentration estimates with a 3-minute
averaging time (Pasquill, 1976). An increase would be expected in horizontal
dispersion for averaging times of 1 hour. As on-site measurements of turbulence
statistics become more routinely available and the state-of-the-art in dis-
persion modeling improves, PAL could be easily modified to incorporate such
advances. The dispersion parameters in PAL are applicable for rural or urban
environments depending on the value of IURB on card type 4.
Finally, PAL does not require any tape drives or external files for
storage. Storage requirements are approximately 49K words. The example
problem 1 (Section 6) used 21.6 seconds of computer time on the tiNIVAC 1110.
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SECTION 4
BASIS FOR PAL
The following assumptions are made: 1) Dispersion from points, and area
and line elements result in Gaussian distributions in both the horizontal and
vertical directions through the dispersing plume from that point or element,
and therefore steady-state Gaussian plume equations can be used for point
sources and the integration of these equations for line and area sources.
2) Concentration estimates may be made for each hourly period using the mean
meteorological conditions appropriate for each hour. 3) The total concentration
at a receptor is the sum of the concentrations estimated from all point and
area sources, that is, concentrations are additive.
POINT SOURCES
The basis for the point source calculations is the point source form of
the Gaussian diffusion equation. A computation is made for each source-receptor
pair. The upwind distance of a source from an individual raceptor is first
calculated. If this distance is negative, indicating that the source is down-
wind of the receptor, no calculation for this source-receptor pair is needed.
For positive upwind distances, the crosswind distance of the source from the
receptor Is also determined. Plume rise for each source Is calculated once
for each hourly simulation period. The plume rise is added to the physical
stack height to give effective height of emission. The dispersion equation
is then evaluated. The standard deviations of plume spreading are determined
as functions of the Pasquill stability class and of the source-receptor
distance. As each concentration from a point source at a receptor is
calculated, it is added to the accumulated concentrations from point sources
for that particular hour.
AREA SOURCES
The calculation of concentrations from area sources is simulated by a
number of finite crosswind line sources. If all four corners of the area
source have positive upwind distances from the receptor, an integration will
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be performed starting from the corner of minimum distance to the corner of
maximum distance. If some but not all of the corners have a negative upwind
distance, then the integration will be performed from an upwind distance of
zero to the greatest distance. If all four corners have negative distances
from the receptor, this indicates the entire area source Is downwind of the
receptor position. A number of crosswind (that is, perpendicular to the
upwind direction) line sources at various distances from the minimum to the
maximum distance are considered. Concentrations for each of these distances
are calculated using the infinite line source form of the Gaussian equation.
This concentration from an infinite line source Is corrected for the finite
extent of each individual line by considering the distance in units of oy of
each end of the line from the upwind azimuth line through the receptor. The
fraction of the area under a Gaussian curve between these limits determines
the correction. An integration is performed using the concentration contri-
bution from a number of lines and considering the distance between lines.
This integration is the first estimate of the concentration from the area
source. A second estimate is made by using the first estimate with additional
calculations made for lines lying half-way between all the previously calculated
lines. This second estimate is compared with the first and if the second
falls within a set criteria the second estimate is taken as the final concen-
tration. If the second estimate is not within the criteria, additional calcu-
lations are made, each time choosing additional lines lying half-way between
lines of the previous total set.
LINE SOURCES
The calculation of concentrations from line sources is done by an
integration of the point source equation in the same manner as in Zimmerman
and Thompson (1975). Distances to the end points of the lines are determined
in terms of upwind and crosswind distances. The line source is limited to
those parts of the line which contribute concentrations to the receptor. Cal-
culations are made for a number of points on the line, and, assuming linear
change in concentration between these points, an estimate of the concentration
from the line is determined. This first estimate is then compared to a second
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estimate, made by taking additional points between the existing ones and then
assuming linear changes of concentrations between each of the adjacent points.
The second estimate is compared to the first, and if it falls within a set
criteria, the second estimate is taken as the concentration. If the second
estimate is not within the criteria, third and subsequent estimates may be
required by taking additional points. Estimates for curved sources are
determined similarly by evaluating for locations on the curve and integrating.
For the specilized line and curved sources, provisions are included to determine
the height and emission rate for each location evaluated.
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SECTION 5
TECHNICAL DESCRIPTION
These expressions are used in the discussions that follow:
2 2
g! =» exp (-0.5 y /ay)
g2 = exp [-0.5(z-H)2/a2] + exp [-0.5(z+H)2/a2I
g3 = £ { exp [-0.5(z-H+2NL)2/a2] + exp [-0.5(z+H+2NL)2/a2]}
N=-»
(This infinite series converges rapidly, and evaluation with the integer, N,
varying from -4 to +4 is usually sufficient.)
Where: H = effective height of emission (m),
L = mixing height, the top of the unstable layer (m),
y = crosswind distance (m),
z = receptor height above ground (m),
Oy = standard deviation of plume concentration distribution in the
lateral (m), and
az * standard deviation of plume concentration distribution in the
vertical (m).
POINT SOURCE COMPUTATION
The upwind distance, X, and the crosswind distance, Y, of a point source
from a receptor (see Figure 1) are given by:
X = (Sp-Sr) cos y + (Rp-Rr) sin o (1)
Y = (Sp-Sr) sin 0 - (Rp-Rr) cosy (2)
13 9/86
-------
NORTH
SOURCE
WIND
SOURCE 2
RECEPTOR
EAST
Figure 1. Upwind and crosswind distances of point sources from
a receptor.
14
9/86
-------
where Rp, Sp are the coordinates of the point source; Rj. , Sr are the coordi-
nates of the receptor, and 0 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 coordi
nate system R, S. Frequently a conversion is required in order to express x
and y in meters or kilometers.
The contribution, to the concentration, Xn» from a single point source to
a receptor is given by one of the three following equations where xp is in g
O _1 1
m , 0 is point source emission rate in g sec , u is wind speed in m sec ,
and av and az are evaluated for the upwind distance x, and the stability
class.
For stable conditions or unlimited mixing:
Xp = ° Si g2/(2yazu) (3)
In unstable or neutral conditions and if az is greater than 1.6 times
the mixing height, L, the distribution below the mixing height is uniform
with height provided that both the effective height, H, and the receptor
height, z, are below the mixing height:
(4)
(If H or z is above the mixing height, Xp = °«)
In all other unstable or neutral conditions, that is, if az is less than
1.6 times the mixing height:
Xp = 0 g! g3/(2Traya2u) (5)
AREA SOURCE COMPUTATIONS
Equation (1) is used to determine the upwind distance, X, of a corner of
the area source with coordinates Rp, Sp from a receptor with coordinates Rr, Sr.
15
9/86
-------
By evaluating X for the four corners of the area source, the maximum and
minimum upward distances of the area source from the receptor are determined
(see Figure 2). If the X's are negative for all four corners, indicating the
entire area source is downwind, no calculation is performed. If the minimum x
is negative, the minimum considered is zero, as no computations need to be
performed for that portion of the area source downwind of the receptor.)
For a given upwind distance, X, from a receptor at point Rr, Sr, the
north coordinate, SL, of the intersection of a crosswind line with a north-
south boundary given by R = R^ is:
SL - (Rh - Rr) sin 9 + Sr (6)
cos 0
The coordinates of this intersection are then R^, S^.
Similarly, for a given upwind distance, X, from a receptor at Rr, Sr,
the east coordinate, RL, of the intersection of a crosswind line with an east-
west boundary given by S = S^ is:
RL = x - (Sy, - Sv) cos 0 + Rr (7)
sin 0
The coordinates of this intersection are then RL , S^.
Using the above relationships and special tests for sin 0=0 and cos y =
0, along with the equations for the four boundaries of the area source, the
two intersetions (A and B) of the crosswind line and the boundaries of the
area source can be found.
The two crosswind distances, Y^ and Yg, of these points from the receptor
can be found using Equation (2).
Assuming that the distances Y^ and Yg are in km, the number of standard
deviations in the Gaussian distribution of these points from the upwind azimuth
16 9/86
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NORTH
WIND
AREA
SOURCE
©
RECEPTOR
EAST
Figure 2. Minimum, X^, and maximum, X£, upwind distances of
crosswind line sources related to an area source from a receptor.
17
9/86
-------
through the receptor are given by:
SA = (1000 YA) / ay (8)
SB = (1000 YB) / av (9)
where Oy is in meters and is determined for the distance X and the atmospheric
stability. SA and SB can be used to determine the fractional portion of the
area under a Gaussian curve between these limits. In PAL this is accomplished
by interpolating between values in a table. The values in the table are from
-3.8 s to 3.8 s at intervals of 0.1 s.
To account for the finite length of the line source, the fraction deter-
mined above is used to correct the calculation for a crosswind line source,
infinite in extent.
The first .estimate, C^, for the concentration, X^, from an area source
is given by:
9
GI = ^A F£cOWn) + fcttmax) + I *c
-------
The second estimate is compared with the first estimate and if the ratio
of the two are within a set criteria, *A = C2« If not, a third estimate is
made, by evaluating fc for additional lines, then comparing with the second
estimate. The notation fc means each f as defined below is corrected for the
finite length of each line. The following defines the function, f, which is
related to the concentration contribution from an infinite crosswind line
source.
For stable conditions or unlimited mixing:
where g2 was defined before.
In unstable or neutral conditions and if az is greater than 1.6 times
the mixing height, L, the distribution below the mixing height is uniform
with height provided that both the effective height, H, and the receptor
height, z, are below the mixing height:
f - 1/L (13)
(If H or z is above the mixing height, f = 0.)
In all other unstable or neutral conditions, that is if az is less than
1.6 times the mixing height:
f - g3/ [ az(2Tr)1/2 ] (14)
LINE SOURCE COMPUTATIONS
The line source and receptor relationships are shown in Figure 3. Points
A and B are the beginning and ending points of the line. X and Y are the
19 9/86
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NORTH
WIND
RECEPTOR
(Rr,Sr)
Figure 3. Line source and receptor relationships.
20
9/86
-------
upwind and crosswind distances from a receptor to a point on the line source.
X and Y are given by Equations (1) and (2).
Rp and Sp are the coordinates of any point on the line and are functions
of length, it., along the line and total length of the line, D:
Rp - L (RB - RA) + RA (15)
D
SP - 1
-------
and R = (S - Sr) tan 6 + Rr (20)
The resulting intersection R, S (see point I, Figure 3) must be tested to
see if it is upwind of the receptor by testing for positive X using Equation
(1), and if it lies on the line source between points A and B. If both of
these conditions are met, the line source is considered to be made up of two
segments: The first segment from point A to the intersection point, and the
second segment from the intersection point to point B. The point directly
upwind has a significant contribution to the concentration at the receptor.
The line is broken into two segments so that this point will be considered in
the integration estimate that follows. If there are two segments to the line
source, the total concentration is given by the sum of the two concentrations
from the segments.
The concentration from a line source is then given by the following
equation.
D
X- f dH (21)
U
where:
q^ = line source emission rate (g sec~ m~ ) ,
U = wind speed (m sec"l)
D = line source length (m) , and
fp = point source dispersion function.
The point source dispersion function is given by one of the three
following equations where ay and az are evaluated for the upwind distance
X, and the stability class.
For stable conditions, or unlimited mixing:
22 9/86
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fp = gig? (22)
2 IT Oy az
where gj and g2 have been previously defined.
In unstable or neutral conditions, if az is greater than 1.6 times the
mixing height, L (meters), the distribution below the mixing height is uniform
with height regardless of source or receptor height, provided both are less
than the mixing height.
L (2*)172 (23)
In all other unstable or neutral conditions:
fp
ay az
(24)
It should be noted that in PAL, initial oy's and oz's, such as to account
for intial dispersion in the turbulent wake behind vehicles, are input values.
The virtual distance for the given stability class is calculated within the
algorithm. These virtual distances are added to the physical distances prior
to determining ay and az for each concentration computation.
The integral, Equation 21, is evaluated using the trapezoidal rule by
making first estimate, Cj, given by:
9
Cl =
A£
U
1 [ fp(o) + fp (10A*) ] + I fp (iAJt)
(25)
where AJl = D/10, and f is defined above. For each of the 11 evaluations of
fp, the upwind distance, X, of the point on the line from the receptor is
determined as a function of AX,, and X is used to determine az and
-------
the line is redefined. Then Equation (25) is again evaluated.
A second estimate, C2, is determined from:
10
r cl + from this line source.
For line source with an intersection point upwind from the receptor, the
contribution from the second segment must also be determined. If the point
directly upwind was not used to break the line into two segments, and the
entire line source is considered as one segment, it is possible for the entire
portion of the line that contributes significantly to the concentration to be
between two of the eleven points, and thus an erroneous concentration of
zero would result.
For line sources with multiple lanes, the integral would be evaluated for
each lane and the concentration summed to represent the total concentration
at that receptor from the line source.
CURVED SOURCE COMPUTATIONS
Figure 4 shows the curved source and receptor relationships. Points A
and C are the end points of the curved path. Point B is an arbitrary point
on the curve between A and C. The curve is assumed to be of constant radius.
24 9/86
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NORTH
WIND
C
(RC.SC)
(Rp.Sp)
RECEPTOR
(Rr.Sr)
©
EAST
Figure 4. Curved source and receptor relationships.
25
9/86
-------
The radius of the circle, of which the curve is a part, is determined in
the following way: The coordinates of point D midway between A and B on a
chord are found by averaging the R and S coordinates of A and B. Similarly,
the coordinates of point E midway between B and C on a chord are found. The
perpendicular bisector of a chord of a circle will pass through the center of
a circle. Also, the slope of the perpendlcuar bisector is the negative
reciprocal of the slope of the chord. The slope of chord AB is:
(RB - RA) / (SB - SA)
and the slope of chord BC is::
(Rc - RB) / (Sc - SB)
The slope of the bisector through D, call this m^, is:
- (sB - SA) / (RB - RA) = mi
The slope of the bisector through E,.call this ra2, is:
- (Sc - SB) / (Rc - RB) = m2
The resulting equation of the bisector through D is:
R0 - RD = mi (S0 - SD) (27)
and the equation of the bisector through E is:
R0 - RE = m2 (S0 - SE) (28)
Ro and So can be determined from these two equations, for example:
S0 = (miSD - m2 SE - RD + RE) / (mi - m2) (29)
and R0 = mi (So - SD) + RD (30)
26 9/86
-------
The radius of the circle can be determined from the coordinates of the center
(Ro, So) and any one of the three points on the curve, for example:
p - /(SA - SQ)2+ (RA -R0)2 (31)
In order to provide a proper estimate of the concentrations from the
curved source at a receptor, it is desirable to determine if a line in the
upwind direction from the receptor intersects the curve. The equation of the
line through the receptor in the direction of the upwind azimuth is:
R - Rr - (S - Sr) tan 0 (32)
The equation of the circle of which the curve is a part is:
p2 = (S - SQ)2 + (R - RQ)2 (33)
The two possible intersections of the line and the circle are found by
solving a quadratic equation for one of the two variables, for example, of
the form:
a R2 +b R + c = 0 . (34)
where a = 1 + cot20 (35)
b = -2 Rr cot2y + 2 Sr coto -2 So coty - 2 RQ (36)
2 2
and c = Rr cot 0 - 2 Rr Sr coto - 2 Rr SQ cote ~ 2 so sr
7 o 7 o
+ S/ + S/ + RQZ -p2 (37)
Two possible values of R are found from:
27 9/86
-------
-bt /
b2-4ac , (38)
2a
If b -4ac is negative, R has imaginary roots and there is no intersection of
f\
the circle and the line. If b^-4ac is zero, the line is tangent to the circle
f\
and there is one intersection. If b -4ac is positive there are two inter-
sections and both roots of the equation are found. If one or two values of R
are found, then one or two values of S are found from:
S = (R-Rr) coto + Sr (39)
If one or more intersections were found for the line and circle, the
upwind distance of this (these) point(s) from the receptor can be determined
using Equation (1). If this value is negative, indicating the point is
downwind from the receptor, it need not be considered further. However, for
a point with a positive x, it must be determined if this intersection on the
circle is also on the curve, that is, between points A and C.
The direction from the center of the circle (R0, S0) to a point (Rp,
Sp) on the circle is:
<|> -tan'1 [ (Rp-R0) / (Sp - SQ) ] (40)
The directed azimuth from the circle's center to any intersection and to points
A, B, and C can then be found. With some logic to consider the crossover point
(from 360° to 0"), it can be determined if the for the intersection is within
the range of 4> swept out by the curve.
After determining if any intersections are on the curve, the curve is
considered in three pieces if there are two intersections, two if there is one
intersection, and as a single curve if there are no intersections. The
computation is done very similarly to that for line sources. Whereas the
length along the line is used to make calculations at intervals for the line
source, the variation of the azimuth from the center of the circle, $, is
used for the curved source. The coordinates of a point on the curve for which
28
-------
the concentration contribution is being evaluated are found from:
Rp = R0 + p sin 4 (41)
Sp = S0 + p sin 4 (42)
The upwind and crosswind distances, x and y, of a given point on the curve
with coordinates (Rp, Sp) for the receptor (Rr, Sr) are calculated as previously
using Equations (1) and (2). The same point source dispersion function, fp
as given in the "Line Source Computations" section is used.
SPECIAL PATH SOURCES
The slant (or special line) and special curved path source calculations
are made in a similar way as the line source and curved source calculations,
respectively. Unlike Equation 21, the concentration from special sources is
given by
y = 1 D
U ^o q£ fp d l (43)
where q^ is now no longer a constant but varies along the source. This
section will describe how q£ is calculated for special sources.
The acceleration of the vehicles is assumed constant and equal to
a = vf ~ vo (44)
where a = acceleration of the vehicles,
Vo = initial vehicle speed at point A (see Figures 3 and 4),
Vf = final vehicle speed at B or C (see Figures 3 and 4), and
t = total time of travel.
29 ' 9/86
-------
The vehicle speed at any point "P" on the source is given by
Vp = atp + V0 (45)
where vp = vehicle speed at P, and
tp = time of travel to P.
The vehicle acceleration can also be expressed as
V2 - V2
a = f o
2Xf (46)
where Xf = total distance of travel.
The distance of travel to any point "P" can be expressed as
?
XI a t- V t
J. d u _i_ » A I-..
P = p T O P
2
where Xp = distance of travel to P.
Solving for tp in Equation 47 and substituting in Equation 45,
1/2 (48)
The emission rate q^ [g/(sec m)] is now given by
TV (veh/hr) EF [g/(sec veh)]
3600 (sec/hr) Vp (m/sec)
where TV = traffic volume.
30 9/86
-------
The emission rate is inversely proportional to Vp. In order to ensure that
q^ will not approach infinity as Vp goes to zero, a simple tecnhique is used
to set a minimum vehicle speed. The minimum speed (Vs) is calcualted using
the traffic volume and a gross estimate of average vehicle length (VL).
v m TV (veh/hr) VL (m/veh) (5Q)
3600 (sec/hr)
Vs is then in m/sec and physically it is the slowest speed the vehicles
could be going and still maintain the traffic volume. If Vp is less than Vs ,
then Vp is set equal to Vs.
For most applications this change in vehicle speed will have negligible
effect on the concentration estimates.
SETTLING AND DRY DEPOSITION
The analytical expressions for atmospheric concentration of a gaseous or
suspended particulate pollutant, subject to deposition and/or gravitational
settling, in a plume released from an elevated continuous point source are
given by Rao (1982). These algorithms are based on a gradient-transfer (K-
theory) model. Details of the model and the solutions can be found in that
reference. Here we only list the plume diffusion-deposition algorithms
applicable to the PAL model under various stability and mixing conditions.
The expressions to be used in the discussions that follow are
§1 = exp (-y2) (51)
§2 = exp{-2W(£ - H)x- - W2 x2}
exp{-(z' + H)2}
(1 - 4/₯ VL x exp U2} erfc {5} )] (52)
31 9/86
-------
' r A A A A AO
g3 = zlexp{-2W (z - Hj) x - W^
N=-«
[exp{-(£ - H)2} + exp{-(z
o ^
(1 - 4/7 Vi £ exp { Ci } erfc 5i>l (53)
A
For V2 = 0,
g'4 = (1 + 2 x\2) erfc (x^) - (2xy/7) expC-^^) (54)
For V2 ^ 0,
gi = (V!/^2) . exp(4Vd V2 erfcCZVj x)
- (W/2 V2) . erfc(W x) - (55)
I T >
In the above, gy, go, and g/ are the modifications of the nondi-
mensional functions g2, g3, and §4 defined previously. Though g4 was not
explicitly defined, it can be easily seen that g4 = 1. The capped quantities
denote the nondimensional variables defined below.
H - H//2~'oz H! = H!//2 az
L - L//2 az Vd = Vd/U
A A A A A A
Vj = Vd - W/2 V2 = Vd - W
W = W/U x = x//2" az
y = y/vT az z = z//2~ az
AAAA AAAA
5 = z + H + 2 Y x E, = z :
32 9/86
-------
where
H = effective height of source emission,
HX = H + 2 N L,
L = mixing depth or height of inversion lid,
N = eddy reflection number,
U = mean wind speed,
Vj = dry deposition velocity of pollutant,
W = gravitational settling velocity of pollutant particles,
X = horizontal upwind distance of source from receptor,
Y,z = horizontal crosswind and vertical coordinates of receptor, and
Oy,0z = Gaussian plume dispersion parameters in y and z directions
A A til
In the limit of W = V, = 0, the expressions for g2» go, and g/
reduce to the expressions for g2, g3, g4«
Depending on the atmospheric stability and mixing conditions, the
contribution to the receptor concentration, xp, due to a single point source
is given by one of the following equations.
For stable conditions or unlimited mixing,
XP - 0 gl . £2
U Ly L2 (57)
For unstable or neutral conditions, with az < 1.6 L,
U Ly Lz (58)
For unstable or neutral conditions, with uniform vertical mixing (az > 1.6L),
Xp'Q iL fl
U L L (59)
33 9/86
-------
In the above,
Ly = /2"ir ay, L2 = /2V az, (60)
L is the mixing depth, and Q is the point source emission rate; Oy and az are
evaluated for the given distance x and the atmospheric stability class.
Equations 57 to 59 are directly used in the computations for point, line, and
curved path sources.
The equations given above are used in modified form for area sources.
Integration over the area source which includes edge effects from the source
region is done by considering finite line sources perpendicular to the mean
wind at intervals upwind from the receptor. The concentration due to a finite
line source is obtained by correcting the function f related to the concentration
contribution to a receptor from an infinite crosswind line source. Depending
on the atmospheric stability and mixing conditions, the function f is given by
one of the following equations:
For stable conditions or unlimited mixing,
f - g/L (61)
For unstable or neutral conditions, with az < 1.6 L,
. f - g3/Lz (62)
For unstable or neutral conditions, with uniform vertical mixing (az > 1.6 L),
f - g^/L (63)
In the above, L is the mixing depth and Lz is defined in Equation 60.
Surface Deposition Flux
The surface deposition flux Df is calculated directly from the ground-
level concentration as
Df(x,y) = Vd . x(x,y,0) (64)
This is the amount of pollutant deposited per unit time per unit surface
34 9/86
-------
ey
area. Df is usually expressed as kg/km^-hour. In the PAL program, the
deposition flux is calculated only at ground-level receptors; these are
defined as the receptors which are not higher than 1 meter above local ground-
level elevation.
SETTLING AND DEPOSITION VELOCITIES
The values of the settling and deposition velocities primarily depend on
the particle diameter d. In the trivial case of W = V 0. For small
particles (d = 0.1~50 ym), 0 < W < V^; deposition is enhanced here beyond
that due to gravitational settling, primarily due to increased turbulent
transfer resulting from surface roughness. For larger particles (d > 50 pra),
it is generally assumed that V^ = W > 0, since gravitational settling is
the dominant deposition mechanism. When W > V 0, re-entrainment of the
deposited particles from the surface back into the atmosphere is implied, as
in a dust storm, for example. The first four types of model parameters given
above are widely used in atmospheric disperison and deposition of particulate
material. The deposition of gases is a special case of the particulate
problem with W = 0. Thus, one has to carefully select the values of W and V
-------
SECTION 6
EXAMPLE PROBLEMS
In this section, problems are provided to illustrate different modeling
scenarios and to demonstrate several unique features of PAL. Details con-
cerning input and output of the example problems are discussed in Section 10
after the reader has become familiar with PAL input data preparation.
EXAMPLE 1
This example problem demonstrates the basic use of PAL. The sources
path and receptor locations are shown in Figure 5: one point source, two area
sources, three line sources, one curved path source, and two special line
sources. This example is intended to be a simplified model of an airport;
none of the emissions and physical dimensions should be considered realistic.
Also, not all of the sources of emissions, such as taxiways, are included in
this example problem. Notice that the two area sources are overlayed. In
this paricular example the hatched area represents a building with no emis-
sions and the other area source is a parking lot with its associated emissions.
The area source strength for the building is the same as that for the parking
lot but negative in sign. The effect of the negative area source strength is
to make the concentration from the building equal to zero. Also, using the
negative area source strength reduces the number of area source inputs from
three to two in this case. The point source is an incinerator. Line sources
one and two are fourlane highways with a fourlane curved path source in
between. Line source three is a two-lane entrance road. The special line
sources are active runways.
This example consists of two, three-hour meteorology periods. Each period
has a unique set of meteorology shown in Table 1. During the first three
hours a transition from neutral (stability class 4) to unstable (stability
class 2) atmospheric stability is simulated. Also, the height of the mixed
depth layer increases from 500 m to 1100 m. During the second three-hour
period the major change is the increase in wind speed during the second hour.
36 9/86
-------
.fl
O
I"
c
0)
t>C
""( '31VMOH003 HinOS HiaON
37
9/86
-------
TABLE 1. METEOROLOGICAL DATA FOR EXAMPLE 1
Hour
I
2
3
1
2
3
Meteorology
Wind Angle
(Deg)
0
350
345
Meteorology
30
45
50
Period 1
Wind Speed
(m/sec)
2
2.5
3.0
Period 2
3.0
6.1
3.8
Stability
Class
4
3
2
4
4
3
Mixing Ht.
(m)
500
900
1100
1000
1000
1000
Ambient Air
Temp
(Deg-K)
285
289
294
290
300
298
TABLE 2. SOURCE STRENGTHS FOR THE FIVE SOURCE TYPES IN EXAMPLE 1.
Horizontal Curved Slant or
Point Areas Lines Horizontal Path Vertical Lines
(Lane) (Lane)
(1) (2) (3) (4) (1) (2) (3) (4)
(No.) g/sec g/sec-nr g/sec-m g/sec-m
1 5. .0002 .0001 .0002 .0009 .0010 .001 .002 .0009 .001
2 -.0002 .0018 .0018 .0009 .0007
3 .0002 .002.0
g/sec
30.
10.
38
'9/86
-------
Five of the six possible source types are included in this problem.
Table 2 illustrates their individual source strenghts. These strengths remain
constant throughout both meteorology periods.
PAL computes the contribution to the concentration at each receptor for
each source type. This output is produced for each hour of simulation. The
average concentration for each of the two three-hour meteorology periods is
also displayed as a part of the output and is summarized here in Table 3.
During the first three hours area source 1 has a major impact at receptors
3, 4, and 5. Maximum line source contributions are about an order of magnitude
lower. During the second 3 hours major impact occurs from the area source
and special line source.
TABLE 3. THREE-HOUR AVERAGE CONCENTRATION (yg/m3) FOR BOTH 3-HOUR METEOROLOGY PERIODS.
First 3-Hour Meteorology Period
Receptor From From From From From From Total
No. Points Areas Hor. Lines Cur. Lines Spec. Lines Spec. Paths Cone.
10 00 0 140.6 0 140.(
20 00 0 65.0 0 65.(
3 10.5 1890. <1 0 37.7 0 1938.:
4 12.3 527.9 <1 0 29.1 0 569.!
5 7.6 310.7 1.1 76.8 26.4 0 422.1
Second 3-Hour Meteorology Period
10 0 <1 0 102.7 0 102.;
20 0 <1 0 43.2 0 43.;
3 0 264.8 32.7 0 12.9 0 310.'
40 0 30.4 <1 3.0 0 33.:
50 0 21.5 51.9 <1 0 13.(
39 9/86
-------
EXAMPLE 2
Example 2 is intended to illustrate all six types of sources available
in PAL. It does not pretend to represent a realistic situation. The lo-
cations of the sources and receptors are presented in Figure 6. Some of the
receptors are above ground-level. The pollutant is assumed to be total
suspended particulate (TSP) matter with a deposition velocity V
-------
en
o:
LJ
o
N
M
tt
O
LJ
U
a:
o
CO
n
o
Q_
LJ
^ 3NI1 IBlNOZiaOH
in
a
OJ
Q
en
CD
7
LJ
H
CE
2
>-4
O
o:
co o
o
o
i__
w
u
2:
_ I
^ I-
en
OJ
cn
u
e
-------
Example two differs from problem I in that the concentrations at the
receptors are affected by gravitational settling and deposition loss of the
pollutant. In this example, no average concentrations are calculated. The
concentrations for each receptor within each of the four hours are computed
along with deposition flux quantities. Deposition fluxes are computed only
for surface receptors. Figure 12 in Section 10 shows the output from the
model run.
42 9/86
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SECTION 7
COMPUTER ASPECTS OF THE MODEL
The general framework of PAL Is discussed in this section. It is intended
to give the reader a general knowledge of the computer program, rather than a
detailed description of each subroutine. The general flow of PAL, the struc-
ture of the computer subroutines and the computer functions, and a brief de-
scription of each subroutine and function are included in this section.
GENERAL FLOW OF THE MODEL
Figure 7 depicts the general flow of the model. The main routine reads
the following types of information.
o integration accuracy for area and line sources,
o options to be employed concerning wind speed changes with height and
variation of emission factors,
o source types to be used,
o options for urban coefficients,
o control for average concentration,
o options for deposition or gravitational settling,
o source types and characteristics,
o receptor coordinates,
o meteorological data, and
o options for diurnal variation in emissions.
Up to a maximum of 99 sources of each type or any combination of the source
types may be used.
Figure 8 shows the structure of the subroutines and functions. "PAL" is
the main routine; it reads input data and stores the appropriate data in
common with the six major subroutines. All input data for each hour are read
before execution begins on any source type. A brief description of the main
program, subroutines and functions follows.
43 9/86
-------
52
p-l
i-l
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3
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-------
PAL-
POINT
AREA
HRZLN
CRVLN
SPCLN
SPCCR
RP
FPLUME
XPLUME
RCONCP
or
RCONPD ~
HIND
URBNYZ
or
PGSIG
RCONCA
or
RCONAD
HIND
XV?
XVZ
INTEGL
RCONCP
or
RCONPD
WIND
XVY
XVZ
ANGARC
DIFANG
INTEGL
CURLIN
RCONCP
or
RCONPD
HIND
XVY
XVZ
INTEGL
RCONCP
or
RCONPD
HIND
XVY
XVZ
ANGARC
INTEGL
CURLIN
RCONCP
or
RCONPD
URBN-YZ
or
PGSIG
URBNYZ
or
PGSIG
ARGCHK
EXPO
EXPO
ARGCHK
. F
URBNYZ
or
PGSIG
URBNYZ
DIFANG
RCONCP
or
PGSIG
or
RCONPD
URBNYZ or PGSIG
ARGCHK
EXPO
- F
URBNYZ
or
PGSIG
URBNYZ
or
PGSIG
ARGCHK
EXPO
URBNYZ
DIFANG
RCONCP
or
PGSIG
or
RCONPD
URBNYZ or PGSIG
ARGCHK
EXPO
- F
URBNYZ
or
PGSIG
URBNYZ
or
PGSIG
ARGCHK
EXPO
DIFANG
RCONCP
URBNYZ
or
PGSIG
or
RCONPD
URBNYZ or PGSIG
ARGCHK
EXPO
. F
URBNYZ
or
PGSIG
URBNYZ
or
PGSIG
ARGCHK
EXPO
DIFANG
URBNYZ
or
RCONCP PGSIG
or
RCONPD URBNYZ
or
PGSIG
URBNYZ or PGSIG ARGCHK
ARGCHK
EXPO
EXPO
Figure' 8. Structure of subroutine and functions in PAL program.
45
9/86
-------
DESCRIPTION OF SUBROUTINES AND FUNCTIONS
Each subroutine and function of PAL is briefly described in the following
pages.
PAL - PAL is the main program that reads in all input data. Source in-
put data cards include point, area, horizontal line, special
line, horizontal curved path, and special curved path sources.
Subroutines are called for each source type. Any combination, or
all, of the above subroutines can be called by PAL. Input data
cards for receptor location and hourly meteorology are required
and not optional input as the above. PAL prints out all input
data and concentration estimates.
POINT - This subroutine is called by PAL and makes concentration estimates
for point sources. POINT calls subroutines XPLUME and FPLUME for
plume rise calculation. Subroutine RCONCP is called by POINT to
estimate the relative concentration for a receptor at a given
downwind and crosswind distance.
AREA - This subroutine is called by PAL and makes concentratibn estimates
from area sources. AREA calls RCONCA, which calculates the rela-
tive concentration for a receptor downwind of an infinite line
source. PGSIG is also called by AREA to determine sigma y (ay)
and sigma z (oz) for a given stability class and downwind distance.
The concentration from area sources is approximated by numerical
integration in the upwind direction of the concentration from
infinite crosswind line sources corrected for finite length.
HRZLN - This subroutine is called by PAL and makes concentration estimates
for multilane horizontal line sources. Functions XVY and XVZ are
called by HRZLN to calculate the virtual distance necessary to
account for initial crosswind and vertical dispersion, which
is specified by the user. Subroutines RCONCP, called by HRZLN,
estimates the relative concentration for a receptor at a given
downwind and crosswind distance.
46 9/86
-------
CRVLN - This subroutine is called by PAL and makes concentration estimates
from multilane horizontal curved path sources. CRVLN calls two
subroutines, CURLIN and RCONCP. CURLIN calculates the coordi-
nates, if any, of the intersection points of the curved path and
the upwind projection from the receptor coordinates. Subroutine
RCONCP and functions XVY and XVZ are called by CRVLN and have the
same function as they do in HRZLN. The shape of the curved path
is approximated by an arc from a circle, determined from the
three points on the curved path specified by the user.
SPCLN - This subroutine is called by PAL and makes concentration estimates
from special line sources. SPCLN calls subroutine RCONCP and
functions XVY and XVZ, which are used in the same manner as in
HRZLN. The line sources do not have to be horizontal and emissions
per unit length are allowed to vary.
SPCCR - This subroutine is called by PAL and makes concentraion estimates
from special curved path sources. Subroutines CURLIN and RCONCP
and functions XVY, XVZ, DIFANG and ANGARC are called by SPCCR
and are used in the same manner as in CRVLN. The special curved
path sources must be horizontal but will allow emissions per unit
length to vary along the curved path.
XPLUME - This subroutine is called by POINT and calculates the plume rise
at a given downwind distance x.
FPLUME - This subroutine is called by POINT and calculates the final plume
rise.
RCONCP - This subroutine is called by POINT, HRZLN, CRVLN, SPCLN, and
SPCCR. RCONCP calls PGSIS. RCONCP determines the relative
concentration at a receptor from a point source at a given upwind
and crosswind distance.
PGSIG - This subroutine is called by RCONCP and calculates ay and az for
a given stability and downwind distance.
47 9/86
-------
RCONCA - This subroutine is called by AREA and calculates the relative
concentration normalized for wind speed for a receptor downwind
of a crosswind infinite line source.
CURLIN - This subroutine is called by CRVLN and SPCCR. CURLIN determines
the coordinates of the intersetion points, if any, of a curved
path source and the line in the direction of the wind through the
receptor coordinates.
XVY - This function is called by POINT, HRZLN, CRVLN, SPCLN, and SPCCR.
XVY calculates the virtual distance necessary to account for the
initial crosswind dispersion.
XYZ - This function is called by POINT, HRZLN, CRVLN, SPCLN, and SPCCR.
XVZ calculates the virtual distance necessary to account for the
initial vertical dispersion.
DIFANG - This function is called by CRVLN and SPCCR. DIFANG determines
the angular difference between two angles.
ANGARC - This function is called by CRVLN and SPCCR. ANGARC determines
the angle specified by a given slope. The resulting angle is
between 0 and 360 degrees.
WIND - This subroutine causes wind speed to be constant with height
below and above minimum and maximum aboveground heights. It
also allows wind speed to be no lower than a user input minimum
speed.
URBNYZ - This subroutine incorporates Briggs urban (McElroy-Pooler) dis-
persion coefficients. Calculates urban sigmas from the stability
and downwind distances.
48 9/86
-------
F - This function, called by INTEGL, calculates the concentration of a
single point source on a special line source, a'horizontal line
source, a. curved path source, or a special curved path source,
depending on the option chosen.
INTEGL - This subroutine calculates the approximate value of a definite
integral, and a relative error-bound for that value. The inte-
gration algorithm is an application of the Richardson extrapo-
lation to the composite trapezoidal rule.
RCONAD - This subroutine, called by AREA, calculates xu/Q» the relative
concentration normalized for wind speed, at any downwind receptor
location due to the dispersion and deposition of gaseous or
particulate pollutants from a crosswind infinite line source.
RCONPD - This subroutine, called by POINT and F, calculates xu/°-» the
relative concentration normalized for wind speed, at any downwind
receptor location due to the dispersion and deposition of gaseous
or particulate pollutants from a continuous point source.
ARGCHK - This subroutine, called by RCONAD and RCONPD, limits the arguments
of exp(p2)-erfc(p) arising in the deposition algorithms to avoid
overflow/underflow errors in the program.
EXPO - This subroutine, called by RCONAD and RCONPD, calculates and re-
turns q = e , if p is given. EXPO checks and limits the argumen
p to avoid overflow/underflow errors in the program.
49 9/86
-------
SECTION 8
PREPARATION OF INPUT DATA
The sequence of input data cards is shown in Figure 9. The formats for
the input data cards are shown in Table 4. All input data are in free format,
except card 1 which is an alphanumeric 20A4 format. While the free format is
very easy to use, care should be taken to make sure every variable is given a
value in the correct order. Each variable should be separated by a comma or
blank. A complete description of the free format can be found in any Fortran
reference manual. Integer variable names begin with the letters I - N. Those
input cards which are optional are noted below the card type number. A brief
description of each input parameter is given in Table 4 with the appropriate
units. The metric system of units is used in PAL. Horizontal coordinates of
sources are given in units of kilometers. Temperatures are given in units of
degrees kelvin. Emission rates are given in mgs units (meter-gram-second).
Input data cards for source types, receptor locations, and hourly
meteorology have, as a first variable, an integer called ICARD. If ICARD
equals one, more cards of this type are expected. If ICARD equals two, then
the last card of this type is expected. At card type 13 the program will
terminate if KTL = 0. Three other options are also available:
o To start a new problem giving all the input information.
o To leave all sources the same but input new information on receptors
and meteorology.
o To input new information on meteorology.
There are two other options available to the user, IDEP and IURB. If
IDEP = 1, deposition effects are ignored. If IDEP = 2, deposition effects are
considered using the specified values (in centimeters/sec) of pollutant set-
tling and deposition velocities W and VD, respectively. If IURB = 1, Pasquill-
Gillford dispersion curves are used for rural dispersion. If IURB = 2,
Briggs urban (McElroy-Pooler) dispersion curves are used for urban dispersion.
50 9/86
-------
OPTIONAL,
DEPENDING UPON
CONTROL INFORMATION
Figure 9. Input data dedc for the PAL model. Card type
numbers are in parentheses.
51
9-86
-------
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9/86
-------
Table 4 should be helpful in organizing data for input into PAL. How-
ever, there are several variables that may need further explanation. The
balance of this section will be concerned with explaining the use of these
input variables and should aid the user in assigning values to them.
POINT SOURCES
In the point source subroutine (POINT) the stack gas velocity (VSP) and
stack inside diameter (DP) are ignored if the stack gas volume flow (VFP) is
greater than zero. However, VSP and DP must still be specified with dummy
values since the free format requires values for all variables. If there are
no point sources in a particular run, then the ambient air temperature (WTA)
from the meteorology input card type 12 is ignored. If WTA equals zero, then
a value of 293°K is assumed in the program.
In subroutine POINT the initial dispersion parameters SYOP and SZOP
allow for initial dispersion in the horizontal and vertical, respectively.
For a tall stack these parameters would generally have little influence on
downwind concentrations. The initial disperion parameters would be helpful
in accounting for the initial mixing of a plume in the building wake. Due to
the complex turbulence in the building wake, plume dispersion is best modeled
using physical models. However, there are some simple cases where the initial
dispersion parameters would be applicable. The values suggested for SYOP and
SZOP in this report should be considered preliminary in nature. It is beyond
the scope of this report to undertake a detailed discussion of aerodynamic
effects in the wake of a building. Some pertinent points are discussed below
concerning the circumstances in which aerodynamic effects are a problem and
where SYOP and SZOP might be useful.
For a squat building, whose width is >^ its height, a sufficient stack
height and exit velocity for the effluent to escape the influence of the
building is given by the familiar 2 1/2 times rule. The rule simply states
that if the stack height is greater than 2 1/2 h (where h is the building
height) and the exit velocity of the plume is greater than 1.5 u (where u is
the mean wind speed), then the plume will escape from the influence of the
60 9/86
-------
building. Stack height always refers to the height of the stack above the
ground. For a tall building, whose height is greater than its width, the 2 1/2
rule can be relaxed. Briggs (1973) suggested that a sufficient stack height
would be the building height plus 1.5 times the smaller of either the building
height, or the maximum width of the building perpendicular to the wind direc-
tion. If the criteria in either one of the above rules are met, then the
stack can be considered a tall one, and building influences may be ignored.
In a wind tunnel study, for a squat building, whose width was twice its
height, Huber and Snyder (1976) suggested that the plume was strongly affected
by the recirculating flow in the wake "cavity" region behind the building
during the following conditions: (1) When the stack height was _< 1.2 h and
(2) When the exit velocity was _<_ 1.5 u. The buoyancy of the plume is generally
not a factor in the initial plume capture within the "cavity" region. If the
above criteria are met, then SYOP and SZOP can be used to model the initial
mixing. Huber (1984) suggests that appropriate initial dispersion parameters
might be
ayo = .35 Hb
azo = 0.7 h
where: H^ is the width of the building and h is the building height.
These findings are applicable for cubical or squat buildings. For a
building much wider than it Is tall, it would be expected that avo would
reach a maximum. Concentrations very close to the building are extremely
sensitive to the shape and orientation of the building with respect to the
location of the source. Concentration estimates using the above initial
dispersion parameters are more likely applicable for distances beyond ten
building heights downwind. The last case that remains is a most difficult
one: either the stack Is not tall enough or the exit velocity of the plume
not great enough for the plume to escape the Influence of the building, but
the plume Is not totally affected by the building wake. The plume may be
totally or partially captured in the displacement zone where it may be brought
near the ground at some distance downwind. In such cases, physical models
should be used to examine plume dispersion. More research is needed to deter-
mine the extent of the displacement zone and cavity behind a variety of shapes
61 9/86
-------
of buildings. The above initial dispersion parameters are intended to provide
some guidance until more complete analyses can be obtained.
AREA SOURCES
It is not mandatory that variables BEST and DNOR on card type 6 have the
same dimensions. Area sources can be either squares or rectangles. A special
feature in PAL allows for the area source to be negative. The advantage of
this feature is demonstrated in the example problem 1 in Section 6.
LINE SOURCES
In all of the line and curved path source subroutines the height of
emissions must be specified. The variables HLN, HLNS, and HCL on card types
7, 8, and 10, respectively, represent the height of the line or curved path
above the surrounding terrain. For a highway it is not the height of the
highway above the surrounding terrain, but the height of the emissions above
the highway. It is assumed that the height of the highway and surrounding
terrain are nearly the same.
A uniform emission rate, q^, must be specified for each line source in
subroutines HRZLN and CRVLN. For vehicles this line-source emission rate
can be found if the emission factor, EF(g veh~* mi~*), and the traffic volume,
TV(veh hr ), are known.
q^ (g sec"1 m~l) = EF(g veh mi"1) TV(veh hr"1)
1609.3 (m mi-1) 3600 (sec hr~l)
= 1.726 x 10~7 (EF) (TV)
A value of the emission factor for automobiles can be obtained from supplement
No. 5 for Compilation of Air Pollutant Emission Factors (EPA 1975). If the
special line or special path sources are used, both of which allow the
emission rate to vary, the user must specify the traffic volume (veh hr~^)
and the emission factor (g sec~M since these parameters are used internally
62 9/86
-------
to derive the variable emission rate as a function of location along the
source. The emission factors for aircraft, where traffic volumes are low,
should be 1-hour average values. PAL is not intended to predict peak con-
centrations that are likely to occur from aircraft emissions but rather is
intended to estimate the average concentration over a 1-hour time period. The
variables VSSL and VSCL on card types 9 and 10 respectively, are a rough
estimate of the length of the vehicles being considered.
METEOROLOGY
The stability of the atmosphere (MKST) is specified on card type 12.
The atmospheric stability is used to estimate the horizontal and vertical
dispersion parameters, av, az. The dispersion parameters were developed from
data most applicable to open country (Pasquill, 1961). When PAL is used in
urban areas (IURB on card type 4 should be 2) the dispersion parameters
suggested by McElroy-Pooler (1968) are used and account for the increase in
the roughness elements and the generally more unstable air over urban environ-
ments.
The wind-increase-with-height option allows the user to either specify
the wind speed (constant for all heights) or to use the option and let the
program estimate the wind speed for different heights. To account for an
increase of wind with height a power law of the form
is used in PAL. Irwin (1977) suggested a theoretical variation of the wind
profile power law exponent as a function of surface roughness and stability.
The exponents given in Table 5 are appropriate for a surface roughness typical
of urban areas.
63 9/86
-------
TABLE 5., EXPONENTS FOR WIND PROFILE
Rural Urban
Stability class Exponent (p) Exponent (p)
A
B
C
D
E
F
.07
.07
.10
.15
.35
.55
.15
o!5
.20
.25
.30
.30
On card type 4 of the input data, UHGT is the height applicable to the
wind speed, generally anemometer height. This variable is only used if the
wind increase with height option is used for one or more of the source types,
However, if the option is not used, a value for UHGT is required due to the
free format input. The usual anemometer height for airport data is in the
range of 7-10 meters.
64 9/86
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SECTION 9
SENSITIVITY ANALYSIS
The area source and four line source algorithms estimate the concentration
at each receptor through an interative process. The convergence criteria are
specified by the user through the PINA and PINL values. In the past we have
recommended a value of 0.02 (2%) for these values but no sensitivity test
were performed to establish the sensitivity of CPU time and concentration
estimates to the PINA and PINL values. A brief description of the sensitivity
of CPU time and concentration estimates for PINA, PINL values from 0.001 to
0.1 are provided in this section. A 1 km area source and two line sources
were considered in this sensitivity test. The line sources differed only in
their length. One was 100 km while the other was 1 km. Receptor distances
varied from 2 m to 10 km downwind of the source. Wind direction, atmospheric
stability, and source receptor geometry all effect the number of iteration
necessary for convergence.
Table 6 shows the percentage difference in CPU time for three wind di-
rection and two source types. The percentage difference was computed between
the PINA (PINL) values 0.001 and 0.1. Table 6 as well as other computations
not shown indicate the run time is more sensitive for the line source algo-
rithm. The PINA value can be assigned a very small value without the sacri-
fice of excessive run time.
The sensitivity of concentration estimates are shown in Figure 10. The
percentage difference versus the PINA (PINL) values are plotted for three wind
direction orientations and three stability classes (P-G classes A, D, and F).
The percentage difference was computed for the nearest receptor since it was
the most sensitive. This figure clearly shows the sensitivity to wind direc-
tion, stability and source receptor geometry. It is difficult to generalize
these results since a slight change in wind direction or source receptor
geometry could significantly change the results.
65 9/86
-------
TABLE 6. PERCENTAGE DIFFERENCE IN CPU TIME FOR
PINL (PINA) VALUES OF 0.001. and 0.1.
Difference [(CPU 0.001 - CPU 0.1)/CPU 0.001] *100
Wind
Direction
Area
Source
Long Line
Source
Perpendicular
Oblique
Parallel
14.5
14.6
9.1
1.36
26.9
22.1
66
9/86
-------
SHORT LINE SOURCE
O.C
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2
ui
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10 0.02 0.04
i i i i i i i i i i i i
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PER. WIND * * *
PAP ) WIND .
0 0.02 0.04
0.06 0.08 0.10 0.1
iiiiiiiiiititiiii
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PINL
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z
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JO 0.02 0.04 0.06 0.08 0.10 0.1
1 t 1 1 1 1 1 1 1 1 1 1 | | 1 1 1 l 1 | | | | | | | | | |
nni wiijn
PER. WIND » * «
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^ D
2
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-
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0.00 0.02 0.04 0.06 0.08
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AREA SOURCE
0.00 0.02 0.04 0.06 0.08 0.10 0.12
I.I 1 «^_
M -
UJ
It! 10~
5
u 5-
1 =
o 0-
oe
a. -
i i i i i i i i i i i i i i i i i i i i i i i i i i i i i
ORI WIND
PER. WIND * * » ^ * f
PAR WIND ^
/^
S _ _ _ A A
*rl* -'<. «^r »_*=: A 0 F
i i i i 1 i i i i I i i i i 1 i i i i f i i i ^ 1 i i i i
1 O
-
r10
-
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-0
0.00 0.02 0.04 0.06 0.08 0.10 0,12
PINA
Figure 10. Percentage difference in concentration versus
integration accuracy. The P-G stability for each
simulation is indicated by A,D, or F.
67
9/86
-------
SECTION 10
EXECUTION OF THE MODEL AND INTERPRETATION OF OUTPUT
PAL produces an error free compile on the UNIVAC 1110 computer. The code
should be transportable to other systems with little or no change. The output
of PAL has eleven parts, two of which are optional. The output begins with
printing the title of the run, which can be up to 80 characters in length.
The next printed information is a list of options beginning with the urban
(IURB) option and the user designated PINA (area integration accuracy) and
PINL (line integration accuracy) values. Following the option list, the
levels of constant wind are printed along with the minimum wind value. If
the user has exercised the option for deposition the output prints a statement
confirming the choice along with its corresponding velocity values next. The
rural or urban wind profile exponents are then listed with either their
default or user specified values. The next output section is the source
type, then all receptor information is listed followed by a printing of the
current meteorology conditions. Finally, a table of total concentrations is
output giving totals for each receptor for all meteorological periods.
The optional outputs available to the user Include concentration averages
and deposition flux tables. If the option for concentration averages is
used, a table listing average concentrations for each source type is printed
out for each set of meteorology. Average concentrations are indicated by
zeros in the column entitled "Hour". If the deposition option is exercised,
the output prints a listing of deposition fluxes for each receptor for all
meteorology periods.
A job stream on the UNIVAC 1110 system might have the following form:
@RUN, R/R 12 JOB-ID, ETC
@SYM PRINT $., 1, PR
@ASG, A PAL.
@XQT PAL.
68 9/86
-------
The input and output listing of example problems 1 and 2 of section 6
are presented in this section. The sample test data for example 1 is as
follows:
TABLE 7. INPUT DATA FOR EXAMPLE PROBLEM 1
CARD
TYPE
1 EXAMPLE PROBLEM FOR PAL
2 0.02,0.02,2,2,2,2,2,1
3 1,1,1,1,1,1,2,1
4 1,1,0.0,0.0,5.,10.,200. ,1
5 2,5.0,10.0,320.,0.,0.,12.,4.26,3.14,1. ,1.
6 1,0.0002,0.,4.2,2.6,0.6,0.8
6 2,-0.0002,0.,4.2,2.8,0.2,0.4
7 1,0.,4,0.2,0.5,4.0,0.5,3.0,1.5,16.,0.,0.0001,0.002,0.0009,0.001
7 1,0.,4,5.45,1.3,7.3,4.,3.,1.5,16.,0.,0.0018,0.0018,0.0009,0.0007
7 2,0.,2,4.8,3.,6.52,3.,3.,1.5,8.,0.,0.002,0.002
8 2,0.,4,4.,0.5,4.6,0.58,5.45,1.3,3.,1.5,16.,0.,0.001,0.002,0.0009,0.001
9 1,30. ,3.,3. ,3.2,4.5,6.4,4.5,0.,80.,15.,6.,60.,30.
9 2,10. ,3.,3.,0.8,1.5,4.,1.5,80.,0.,15.,6.,60.,30.
11 1,4.6,4.2,1.
11 1,4.6,3.6,1.
11 1,4.6,2.4,1.
11 1,4.6,1.2,1.
11 2,4.6,0.2,1.
12 1,0. ,2. ,4,500. ,285.
12 1,350.,2.5,3,900. ,289.
12 2,345.,3.,2,1100.,294.
13 3
12 1,30. ,3.,4,1000. ,290.
12 1,45.,6.1,4,1000.,300.
12 2,50.,3.8,3,1000.,298.
13 0
The numbers in the left hand column of table 4 are the input card type
numbers. For a complete description of each input card type see Table 1. In
this example there is no input card type 10, since there are no" special curved
path sources. Table 5 is a computer listing of the output for example 1.
Sources included are indicated by "YES's" under the column titles "Sources
Included" in the options list. Average concentrations are calculated for two
3-hour meteorology periods. The hourly variations in emissions option is
not used in this problem. Concentrations at the receptors are in units of
gm
-3
69
9/86
-------
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Table 8 lists the input data cards for example problem 2. Figure 12 is
a computer listing of the output. As in the previous problem, the output
begins with a listing of all the input parameters and options used. All
source types are included here. The output continues with the same format
f\
except that deposition flux tables are listed in kg/km -hour following the
concentration tables. Also, no average concentrations are printed. It should
be noted that calculated concentrations are less when including the effects
of deposition loss as compared to those of the similar case not considering
deposition loss.
TABLE 8. INPUT DATA FOR EXAMPLE PROBLEM 2
CARD
TYPE
1 TEST OF PAL USING ALL SOURCE TYPES FOR TSP
2 .02,.02,2,2,2,2,2,2
3 1,1,1,1,1,1,1,1
4 1,2,10. ,10. ,5. ,10.,200. ,1.
5 2,10. ,50. ,310.,0.0,0.0,12. ,6.25,5.,3.,2.
6 2,.05,1.,6.,4.,.5,.5
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7 2,.5,2,2.75,.5,2.75,5.25,3.,2.,10.,0.0,.001,.001
8 2,.5,2,2.75,5.25,3.04,5.96,3.75,6.25,3.,2.,10.,0.0,.001,.001
9 2,10.,.2,10.,2.752,4.25,6.,4.25,40.,40.,3.,1.5,60.,5.
10 2,8.,.5,2.75,2.25,4.27,2.73,4.75,4.25,50.,50.,2.,1.5,40.,5.
11 1,5.5,2.,!.
11 1,4.5,5.5,8.
11 1,10.,8.5,1.
11 1,7.5,2.5,5.
11 2,1.,8.,1.
12 1,315.,4.,3,1000.,280.
12 1,45.,4.,3,1000.,280.
12 1,135. ,4. ,3,1000. ,280.
12 2,225.,4.,3,1000. ,280.
13 0
76 9/86
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REFERENCES
Briggs, G. A. 1973. Diffusion Estimation for Small Emissions. NOAA Atmos-
pheric Turbulence and Diffusion Laboratory, Contribution File No. (Draft)
79. Oak Ridge, TN. 59 pp.
Busse, A. D., J. R. Zimmerman, 1973: User's Guide for the Climatological
Dispersion Model. EPA-R4-73-024, U.S. Environmental Protection Agency,
Research Triangle Park, North Carolina. 131 pp.
Gifford, F. A., Jr., 1960: Atmospheric dispersion calculations using the
generalized Gaussian plume model, Nuclear Safety, 2 (2):56-59.
Huber, A. H., W. H. Snyder. 1976: Building Wake Effects on Short Stack
Effluents. In: Proceedings of the Third Symposium on Atmospheric
Turbulence, Diffusion and Air Quality, American Meteorological Society.
Raleigh, North Carolina, pp. 235-242.
Huber, A. H. 1984: Evaluation of a Method for Estimating Pollution Concen-
trations Downwind of Influencing Buildings. U.S. Environmental Protection
Agecny, Research Triangle Park, Nc. 26 pp.
Irwin, J. S., 1977: A Theoretical Variation of the Wind Profile Power-Law
Exponent as a Function of Surface Roughness and Stability. Unpublished
manuscript. Environmental Sciences Research Laboratory, U.S. Environmen-
tal Protection Agency, Research Triangle Park, North Carolina. 10 pp.
Martin, D. 0., 1971: An Urban Diffusion Model for Estimating Long-Terra Value
of Air Quality. J. Air Pollution Control Assoc., 21(1):16-19.
McElroy, J. L., Pooler, F. Jr., 1968: St. Louis Dispersion Study, Volume II -
Analysis. U.S. Department of Health, Education and Welfare, Arlingrton,
VA. 51 pp.
Novak, J. H., D. B. Turner., 1976: An Efficient GAussian-Plume Multiple-
Source Air Quality Algorithm. J. Air Pollution Control Assoc., 26 (6):
570-575.
Pasquill, F. 1961. The Estimation of the Dispersion of Windborne Material.
Meteorol. Magazine, 90: 33-49.
Pasquill, F. 1976. Atmospheric Dispersion Parameters in Gaussian Plume
Modeling. Part II. Possible Requirements for Change in the Turner Work-
book Values. EPA-600/4-76-030b, U.S. Environmental Protection Agency,
Research Triangle Park, NC. 44 pp.
Petersen, W. B., 1978: User's Guide for PAL: A Gaussian-Plume Algorithm for
Point, Area, and Line Sources. EPA-600/4-78-013, U.S. EPA., Reserch
Triangle Park, N.C. , 163 pp.
Rao, K.S., 1982: Analytical Solutions of a Gradient-Transfer Model for plume
deposition and sedimentation. EPA-600/3-82-079, U.S. Environmental Pro-
tection Agency, Research Triangle Park, NC., 75 pp.
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Rao, K. S., and H. F. Snodgrass. 1982. PAL-DS Model: The PAL Model Including
Deposition and Sedimentation. EPA-600/8-82-023, U. S. Environmental
Protection Agency, Research Triangle Park, NC 49 pp.
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1975: U.S. Environmental Protection Agency, Research Triangle Park,
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Zimmerman, J. R. , R. S. Thompson., 1975: User's Guide for HIWAY, a Highway Air
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Research Triangle Park, North Carolina. 59 pp.
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APPENDIX
SETTLING AND DEPOSITION VELOCITIES
This appendix is a reproduction of Appendix B in Rao (1982)
For a monodisperse particulate cloud, the individual particles have a con
stant gravitational settling velocity. This terminal velocity is given by
Stokes1 equation (Fuchs, 1964):
w -
18 |J
where d is the diameter of the particle, g is acceleration due to gravity, p is
density of particles, and p is the dynamic viscosity of air. For d > 100 jjm,
the terminal fall velocity is sufficiently great that turbulence in the wake of
the particle cannot be neglected, and the viscous drag force F, on the particle
is greater than given by the Stokes' law, F, = 3nd^W. For a particle with d =
400 pm, the actual value of W is about one-third the value given by Eq. (B-l).
Stokes' expression for the drag force describes the effects of collisions be-
tween air molecules and a particle, assuming air to be a continuum. This
assumption is not valid for very small particles, since the mean free path
between molecular collisions is comparable to the particle size; under these
conditions "slippage" occurs, and the particles undergo Brownian motion and
diffusion, which give a terminal velocity greater than that predicted by Eq.
(B-l). A discussion of the slip correction factor for th,e Stokes' equation
can be found in Fuchs (1964) and Cadle (1975).
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The values for the terminal gravitational settling velocities for different
particulate materials are given in a tabular form by Lapple (1961) based on
particle diameter and Reynolds number. These values, which account for the
deviations from Stokes' equation discussed above, are given for spherical
particles with a specific gravity of 2.0 in air at 25°C and 1 atm. pressure.
This table has been reprinted in Sheely et a]L (1969) and Stern (1976).
The dry deposition pollutant-removal mechanisms at the earth's surface
include gravitational settling, turbulent and Brownian diffusion, chemical absorp-
tion, inertial impaction, thermal, and electrical effects. Some of the deposited
particles may be re-released into the atmosphere by mechanical resuspension.
Following the concept introduced by Chamberlain (1953), particle removal rates
from a polluted atmosphere to the surface are usually described by dry deposition
velocities which vary with particle size, surface properties (including surface
roughness (z ) and moisture), and meteorological conditions. The latter include
wind speed and direction, friction velocity (u.u), and thermal stratification of
the atmosphere. Deposition velocities for a wide variety of substances and
surface and atmospheric conditions may be obtained directly from the literature
(e.g., McMahon and Denison, 1979; Sehmel, 1980). Sehmel and Hodgson (1974)
gave plots relating deposition velocity (V.) to d, z , Uj., and the Monin-Obukhov
a o "
stability length.
Considerable care needs to be exercised in choosing a representative deposi-
tion velocity since it is a function of many factors and can vary by two orders
of magnitude for particles. Generally, V, should be defined relative to the
height above the surface at which the concentration measurement is made. The
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particle deposition velocity is approximately a linear function of wind speed
and friction velocity, and its minimum value occurs in the particle diameter
range 0.1 - 1 |Jm.
In the trivial case of W = V = 0, settling and deposition effects are neg-
ligible. For very small particles (d < 0.1 pm), gravitational settling can be
neglected, and dry deposition occurs primarily due to the nongravitational
effects mentioned above. In this case, W = 0 and V. > 0. For small particles
(d = 0.150 (Jm) , 0 < W < V,; deposition is enhanced here beyond that due to gravi-
tational settling, primarily due to increased turbulent transfer resulting from
surface roughness. For larger particles (d > 50 |Jm), it is generally assumed
that V = W > 0, since gravitational settling is the dominant deposition mech-
anism. When W > V > 0, re-entrainment of the deposited particles from the sur-
face back into the atmosphere is implied as, for example, in a dust storm. The
first four sets of model parameters given above are widely used in atmospheric
dispersion and deposition of particulate material. The deposition of gases is
a special case of the particulate problem with W = 0. Thus, one has to care-
fully select the values of W and V for use in the model.
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REFERENCES
Cadle, R. D., 1975: The Measurement of Airborne Particles. John Wiley & Sons,
New"York, 342 pp.
Chamberlain, A. C., 1953: Aspects of travel and deposition of aerosol and vapor
clouds. A.E.R.E. Report H.P.-1261, Atomic Energy Research Estab., Harwell,
Berks., U.K., 32 pp.
Fuchs, N. A., 1964: The Mechanics of Aerosols. The Macmillan Co., New York,
408 pp.
Lapple, C. £., 1961: J. Stanford Res. Inst. 5, p. 95.
McMahon, T. A., and P. J. Denison, 1979: Empirical atmospheric deposition para-
meters - a survey. Atmospheric Environment 13, 571-585.
Sehmel, G. A., and W. H. Hodgson, 1974: Predicted dry deposition velocities.
Atmosphere-Surface Exchange of Particulate and Gaseous Pollutants. Avail-
able as CONF-74Q921 from NTIS, Springfield, VA-. , 399-423.
Sehmel, G. A., 1980: Particle and gas dry deposition: a review. Atmospheric
Environment 14, 983-1011.
Sheeny, J. P., W. C. Achinger, and R. A. Simon, 1969: Handbook of Air Pollution.
Public Health Service Publication No. 999-AP-44, U.S. E.P.A., Research
Triangle Park, N.C.
Stern, A, C., 1976: Air Pollution. Academic Press, New York, Vol. I, 3rd ed.,
715 pp.
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