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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