United States
Environmental Protection
Agency
Atmospheric Sciences
Research Laboratory
Research Triangle Park NC 27711
Research and Development
EPA/600/S8-87/009 May 1987
SERA Project Summary
User's Guide for PAL 2.0, A
Gaussian-Plume Algorithm for
Point, Area, and Line Sources
William B. Petersen and E. Diane Rumsey
PAL is an acronym for the Point,
Area, and Line source algorithm. PAL is
a method of estimating short-term dis-
persion using Gaussian-plume steady
state assumptions. The algorithm can
be used for estimating concentrations
of non-reactive pollutants at 99 recep-
tors for averaging time 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 representative for the area
modeled. The Pasquill-Gifford or
McElroy-Pooler dispersion curves are
used to characterize dispersion.
The PAL model can treat deposition
of both gaseous and suspended par-
ticulate pollutants in the plume since
gravitational settling and dry deposition
of the particles are explicitly accounted
for. In the limit when pollutant settling
and deposition velocities are zero, they
reduce to the usual Gaussian-plume
diffusion algorithm.
This Project Summary was developed
by EPA's Atmospheric Sciences Re-
search Laboratory, Research Triangle
Park, NC, to announce key findings of
the research protect that Is fully docu-
mented In a separate report of the same
title (see Project Report ordering In-
formation at back).
Introduction
PAL 2.0 incorporates two major en-
hancements from previous versions of
PAL. The analytical solutions of a gradient-
transfer model for dry deposition of
gaseous and paniculate pollutants which
was included in a version of PAL called
PAL-DS are included in PAL 2.0. The
other major enhancement is the inclusion
of urban diffusion coefficients. This docu-
ment supersedes EPA-600/4-78-013 and
EPA-600/8-82-023.
PAL is a multisource Gaussian-Plume
atmospheric dispersion algorithm for
estimating concentrations of non-reactive
pollutants. Concentration estimates are
based on hourly meteorology, and aver-
ages 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:
• Industrial complexes
• Sports stadiums
• Parking lots
• Shopping areas
• Airports
At the heart of PAL is the Gaussian-
Plume point source equation. The equa-
tion 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 computa-
tional technique for estimating the con-
centration from area sources. This
technique incorporates edge effects and
is theoretically more accurate than the
methods used in the Climatological Dis-
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persion Model (COM) and the Air Quality
Display Model (AQDM). The horizontal
line source algorithm is similar to the
Highway Air Pollution Model (HIWAY).
Input source types also include two types
of curved paths, one of which considers
variation of emissions along the path.
PAL will also estimate 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 speed to change with
height. Concentration estimates can be
made at up to 99 user specified receptor
locations.
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 analytical
diffusion-deposition expressions listed in
this report are easy to apply and, in the
limit when pollutant settling and deposi-
tion velocities are zero, they reduce to
the usual Gaussian plume diffusion
algorithms.
Basis for PAL 2.0
The following assumptions are made:
1) Dispersion from points, and area and
line elements result in Gaussian distribu-
tions 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 esti-
mates 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 calcula-
tions is the point source form of the
Gaussian diffusion equation. A computa-
tion is made for each source-receptor
pair. The upwind distance of a source
from an individual receptor is first cal-
culated. If this distance is negative,
indicating that the source is downwind
of the receptor, no calculation for this
source-receptor pair is needed. For posi-
tive upwind distances, the crosswind dis-
tance 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 effec-
tive height of emission. The dispersion
equation is then evaluated. The standard
deviations of plume spreading are deter-
mined 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 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 dis-
tance 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 ay
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 contribution 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 cal-
culated 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 concentra-
tion. If the second estimate is not within
the criteria, additional calculations 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. Distances to
the end points of the lines are determined
in terms of upwind and crosswind dis-
tances. The line source is limited to those
parts of the line which contribute con-
centrations to the receptor. Calculations
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 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 specialized line and curved
sources, provisions are included to deter-
mine the height and emission rate for
each location evaluated. i
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William B. Petersen and E. Diane Rumsey from the National Oceanic and
Atmospheric Administration, U.S. Department of Commerce, are on
assignment to the Atmospheric Sciences Research Laboratory, U.S.
Environmental Protection Agency, Research Triangle Park, NC27711.
D. Bruce Turner is the EPA Project Officer (see below).
The complete report, entitled "User's Guide for PAL 2.0—A Gaussian-Plume
Algorithm for Point, Area, and Line Sources," (Order No. PB 87-168 787/
AS; Cost: $13.95, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Atmospheric Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
Official Business
Penalty for Private Use $300
EPA/600/S8-87/009
000032*
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