EPA/600/A-96/019
IMPROVED ALGORITHMS FOR ESTIMATING THE EFFECTS OF POLLUTION
IMPACTS FROM AREA AND OPEN PIT SOURCES
              William B. Petersen and Steven G. Perry1

              Atmospheric Sciences Modeling Division
              Air Resources Laboratory
              National Oceanic and Atmospheric Administration
              Research Triangle Park, NC 27711
INTRODUCTION

       The increasing environmental concern over hazardous emissions from landfills, landfarms,
settling ponds, agricultural fields, surface mines, and surface impoundments has renewed interest
in improving concentration estimates downwind from area sources. Simplistic and numerically
efficient methods (for estimating area source impacts) are  the virtual point  source approach
(Turner, 1970) as used in the models LONGZ (Bjorklund and Bowers, 1979) and VALLEY (Burt,
1977), and the finite line source approach as used in ISCST  (Bowers et al.,  1979). The virtual
point source and finite line segment algorithms are most appropriate for estimating concentrations
at downwind distances significantly larger than the side width of the area  source (Hwang, 1986
and Weber, 1982).  However, these constructs fail for concentration estimates within or near the
area source. Thistle and  Londergan (1989) showed  that these algorithms  behaved  in a manner
inconsistent with mathematical and physical principles.  They demonstrated that models that use
numerical techniques to approximate the Gaussian point source dispersion function over the area
source are more realistic although computationally intensive. One of the models that they found to
be mathematically and physically consistent was PAL (Petersen and Rumsey, 1987).
       Shortly after the Thistle and Londergan study, the Office  of Air  Quality Planning and
Standards in the U.S.  Environmental Protection Agency (EPA) decided to update the area source
algorithm in ISC2 (U.S. EPA, 1992) using the approach contained in PAL. At about the same time
the Office of Research and  Development in EPA  was involved  in a  project to  improve the
computational efficiency of the area source algorithm in PAL. It is this more efficient version of
the PAL area source algorithm that has been implemented in ISC2 and will be described in this
paper.  In addition, the improved area source algorithm is utilized in a new  approach to modeling
open-pit sources.
       Title II, Part  B, Section 234 of the Clean Air  Act Amendments of  1990 provide for a
reexamination of the current Environmental Protection  Agency's methods  for modeling fugitive
particulate (PMio) from open-pit surface coal mines. ISC2 is specifically  named as the method
that needs further study.
1 Both authors are on assignment to the National Exposure Research Laboratory, U.S. Environmental
Protection Agency.

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       To address the requirements of the Act, an open pit algorithm has been developed. Wind
tunnel experimentation (Thompson,  1993,  1994a  and Perry  et  al.,  1994) suggests that the
emissions within the pit are not uniformly released from the pit opening.  Rather, they show a
tendency to be emitted primarily from an upwind sub-area of the pit opening due to the general
recirculation flow within the pit.  The  algorithm uses the  pit depth and dimensions, height of
emissions above the pit floor, and the wind direction to 1) estimate the fraction of paniculate that
leaves the pit (escape fraction) and 2) to calculate the sub-area  dimensions.  The new integrated
area-source algorithm is used to model  emissions from this sub-area.   Initial vertical  dispersion
due to turbulence in the pit is also considered. Although the development work for the area source
and open pit algorithms was done with ISC2, both are incorporated in ISC3.  In this paper we will
refer to the model incorporating these algorithms as ISC3.
NEW AREA-SOURCE ALGORITHM

       Based on the results of an evaluation of area source algorithms performed for  EPA
(Thistle and Londergan, 1989), the finite line segment algorithm used in the ISCST model gives
physically unrealistic results for receptors located near the edges and corners of the area.  This is
not so much a deficiency in the algorithm as it is a problem in application.  The finite line segment
was developed as a simple approximation to the contribution at a receptor from an area  source.
Conceptually, it  is an improvement over the  virtual point source approach without the expense of
numerically approximating the point source function over an area source.  It was never the intent
of the developers that the area source algorithm would be applied for nearby receptors. However,
recent concern for environmental impacts from  nearby area sources and advancements  in high
speed data processing for PC's make  it reasonable to revisit the area source problem. This section
provides a brief description of the integration technique used in ISC2.
                                                        Wind Direction
                 Q
                 •o
                  s
                 u
                     0,0
                   Receptor
                               Xmin
                                                        Alongwind Direction
            Figure 1. xmin and xmax are the distances to the closest and furthest vertices from the area
            source, yj and^ arc *« crosswind distances at an arbitrary distance x upwind.

                                             2

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       The area source algorithms in  PAL and ISC3 are functionally the same; the pollutant
impact from an area source is  approximated by  a  number  of finite  crosswind line sources.
However, the integration techniques are different. To illustrate the integration technique we apply
it for a rectangular area source. Let x be the upwind distance and y the crosswind distance.  For a
given source receptor pair, there is a xmin and a x^ (see Figure 1) which coincides with the x of a
vertex. That is, a vertex is represented  by (x/.y,) with *„+/ = */, for closure.  If we \e\.f(x) be the
dispersion from a point source at a distance x and let y(x) be the crosswind distance to the ih side,
then the integration proceeds as follows:  In Figure \,xmin> *„ xb, and x^ are the upwind distances
from the  nearest to furthest vertex from  a downwind receptor and the four vertices are Xj, A^, Aj,
and Xj. The concentration can be expressed as;

         X=
           = —  Pi = —.
             a.,        a
where;
               y         "* y
and e(pi) and e(pj) are defined as follows,
                 Pi    j
        e(p,) =   f  -p= exp M).5 p
                                                                 exp £-0.5
The integrals from -o> top/ and -oo top2 are the cumulative distribution of the standardized normal
distribution  and can be determined  from tables.  Each  side  of the area  source can  now  be
integrated independently.    Figure  2  provides  a simplified  graphical  representation  of the
integration by sides.  In the actual integration only those portion of the sides that contribute to the
concentration at the receptor are included, that is  IX*)/^*) I <4.0.  This criteria is a function of
source-receptor geometry, wind direction, and atmospheric stability. f(x) has  the following forms:
For stable conditions or unlimited mixing:
            /(*) =
                                    exp
+ exp
In unstable or neutral conditions and if cz is greater than 1.6 times the mixing height, L, the
distribution below the mixing height is uniform with height.
                                               /•>
                                  /(*) =
In all other unstable or neutral conditions, that is if az is less than 1.6 time L:
   /(*) =
                               exp
                          = -00
                                    -Q5(z-H+2NL)2
     exp
This infinite series converges rapidly, and evaluation with the integer, N, varying from -4 to +4 is
usually sufficient.
AREA REPRESENTATION ALGORITHM FOR OPEN PIT MINING

       The method for modeling particulate impacts from open-pit, surface coal-mine activities is
based on the analysis by Perry et al. (1994) and Thompson (1994a, 1994b) of two wind-tunnel
studies recently performed at the EPA Fluid Modeling Facility in which the impacts of emissions

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                                Wind Direction
                                                                                 Wind Direction
                                                 I
                                                5
                                                13
                                Alongwind Direction     Receptor
        Xm*

Alongwind Direction
                                                                                 Wind Direction
                                Alongwind Direction
Alongwind Direction
Figure 2 Graphical representation of the integration by sides. The shaded areas represent a positive contribution. The
horizontal-line pattern represents a negative contribution. The positive and negative contribution cancel everywhere
except the area source.

from a variety of scale model open pits  were  examined.  Perry et al. concluded that,  due to
recirculations  within the pit, particles  that escape show a tendency to be emitted toward the
upwind portion of the pit opening.  The pit-mining algorithms determine the escape fraction (for
each particle size group); and  establish the location and size of the sub-area from which the
escaped paniculate is modeled with ISC3.  It is important to preface that the open-pit algorithms
are designed only for the modeling of impacts outside of the  pit caused by emissions within the
pit, that mines are assumed generally rectangular in shape, and that the emissions within the pit are
assumed to be at least somewhat scattered.

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       ISC3 first estimates the escape fraction as a function of incident wind  speed and the
particle size distribution of material released within the pit (Thompson, 1994b). The computation
of escape fraction is particularly important for modeling large particles susceptible to gravitational
settling and less important for PMjQ analyses where the vast majority of material escapes.  As
implemented in ISC3, for each of up to 20 particle size  categories, an  escape  fraction (e) is
computed as:
                                =1.0/1 + -
where
        Ur
        a
               is the settling velocity,
               is the approach wind speed at a height of 10m,
               is the proportionality constant in the relationship between flux from the pit
               and the product of Ur and concentration in the pit (Thompson, 1994a).
v,  is already computed in ISC3 (as is done in ISC2) for each size category. Thompson (1994a)
used  laboratory measurements of pollutant residence  times  in a  variety of  pit  shapes  and
determined that a single value of a = 0.029 worked well for all pits studied.
       The adjusted emission rate (q,) for each particle size category is then computed as:
                                9i =  e i• • f{  • Q
where q is the total emission rate (for all particles) within the pit,/ is the original mass fraction for
the i-th size category, and e, is calculated from the above equation.   The adjusted total emission
rate, for all particles escaping the  pit, is the sum of the qt.  In summary, the amount of particulate
that leaves the open pit mine and  is available to impact air quality downwind is a function of the
total emissions within the pit, wind speed, and the particle size distribution of emitted material.
       Secondly, ISC3 computes the location and size of a sub-area of the actual pit opening from
which the pit emissions will be modeled.  This sub-area source  is assumed to be  at surface level.
Given an arbitrary rectangular-shaped pit with an arbitrary wind direction as shown in Figure 3,
ISC3  determines the sub-area source in the  following way. Based on the wind direction and pit
orientation, the model determines the upwind sides of the pit; in the case of Figure 3, the upwind
sides are 1 and 2. The model then computes the along wind length of the pit (/). / varies between
the lengths of the two sides of the  rectangular pit as follows:
                            /  =  L»(l  - Q/90) + W.(Q/90)
where 6 is the wind direction relative to the long axis of the pit (therefore 6 varies between 0° and
90°).  / is the scaling factor that is  used to normalize the depth of the pit.
                          Wind direction
                      W
                                                    AW
                                                       alongwind
                                                          length (I)
           Figure 3. The effective area for a wind direction of about 45 degrees from the long axis of
           the pit.  AL and AW (and thus the area) vary with wind direction.

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       The model user must specify the average height (H) of emissions from the floor of the pit
and the pit volume (V). With these, ISC3 calculates the effective pit depth (de) and the relative pit
depth (dr) as:
                                de  = V/(L.W)
                                d,  = (d.-H)/l
       Based on observations and measurements in the wind runnel study, it was clear that the
emissions within the pit are not uniformly released from the pit opening.  Rather, the emissions
showed a tendency (based on smoke releases) to be emitted primarily from an upwind sub-area (or
effective area, Ae) of the pit opening and the sub-area size and location depended on the relative
pit depth and the wind direction.  The wind tunnel data indicate that if dr £ 0.2, then the effective
area is about 8% of the total opening of the mine (i.e. ^,=0.08). If dr< 0.2, then the fractional area
increases as:
                             At  =  (L0-1.7d'r'3)ln
When dr = 0, the effective area is equal to the total area of the mine opening (i.e. Ae=\ .0).
       The specific dimensions of this assumed rectangular sub-area are calculated as a function
of 6 such that (see Figure 3):
                              AW =  dJ-^t'W
and,
                               AL  = A(ec^Q)'L
W is defined as the short dimension of the pit and L is the long dimension; AW is the dimension
of the effective area aligned with the short  side of the pit and AL is the  dimension of the effective
area aligned with the long side of the pit.  In the way of a few examples, if Ae = 0.36 at 9 = 45°,
then AW = 0.6-W and AL = 0.6-L; at the extreme of 6 = 0° (wind along the long axis of the pit),
AW = W and AL = Ae-L;  at 6 = 90° (wind along the short axis of the pit), AW = /le-W and  AL =
L.
       The emission rate, qe, for the effective area is such that;
                                  
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run scale dimensions oi Hi m in tne along now direction and 4DU m in the cross flow direction
(the wind is perpendicular to the  long dimension of the pit, i.e.  6 = 90 degrees).  The pit is 45 m
deep and the emissions are from the pit floor (H = 0).  Therefore the effective pit depth, de , is
simply 45 m and the relative pit depth, dr , is equal to 45/225 = 0.2. With this relative depth, the
effective area for emissions, Ae ,  equals 0.08 (8 %), and the dimensions of the area are 18 m in the
alongwind  direction and 450 m  in the crosswind directions. In addition, the pit-induced initial
dispersion is equal to 45 m/ 4.3 = 10.5 m.
                     MODEL COMPARISONS WITH WIND TUNNEL
            z
            o

            I
            111
            o
            o
            o
            o
            UJ
            N
            Q:
            O
                 101
••  ISC2-Full Area
'—  ISC3- Fractional Area
—  Wnd Tunnel
                                    CROSSWIND WIDTH OF PIT
                   -300      -200      -100      0        100
                                    CROSSWIND DISTANCE (m)
                                    200
300
            Figure 4.  Horizontal concentration distributions at the downwind edge of a 225m X 450m
            pit with effective depth of 45m and source at the pit floor. ISC2 Full Area is the
            distribution from the 1SC2 model and ISC2 Partial Area is from ISC3.

       The concentration distribution at the  downwind edge of the pit for the wind  tunnel
measurements and two modeling scenarios are shown in Figure 4.  The  results  labeled FULL-
AREA are those  provided by the ISC2 model. The results labeled FRACTIONAL AREA are
those provided by ISC3.  For ISC2 where it is assumed that the entire opening of the rectangular
pit  acts as a surface level  area source with  emissions  uniform over that area, the  modeled
distribution is nearly  three times larger than that observed.
       In contrast, the ISC3 model is releasing the same total emissions over a much smaller area
on the upwind edge of the actual pit opening (only covering 8% of the pit opening); the  plume is
initially dispersion  by  pit  generated  turbulence.   ISC3   is  showing  a slight  tendency to
overpredicting the distribution particularly near the center of the pit.  However, it is clear that the
modified area-source approach is  a great improvement over  that of ISC2  for  impacts  at the
downwind edge of the pit where concentrations are expected to be highest. For large downwind
distance (many times the dimensions of the pit), the ISC2 and ISC3 approaches are not expected to
give very different results.
ACKNOWLEDGMENTS

The authors would like to acknowledge Richard A. Strelitz who did the original development work on the
integration technique used for the new area source algorithm and Roger W. Erode who provided review and
refinements to the area source and open pit algorithms and implementation in ISC3.

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This paper has been reviewed in accordance with the U.S.  Environmental Protection Agency's  peer and
administrative review policies and approved for presentation and publication.  Mention of trade names or
commercial products does not constitute endorsement or recommendation for use.
REFERENCES

Bjorklund J.R. and Bowers J.F., 1979, User's instructions for the Shortz and Longz computer programs
(Volume I), TR-79-131-01. H.E. Cramer Company, Inc., University of Utah Research Park, POB 8049, Salt
Lake City, Utah.

Bowers, J.F., Bjorklund J.R., and Cheney C.S., 1979, User's guide for the Industrial Source Complex (ISC)
dispersion models, Volume I -User Instructions, EPA-450/4-79-030, U.S. Environmental Protection Agency,
Research Triangle Park, North Carolina.

Burt E.W., 1977, Valley model user's guide, EPA-450-2-77-018, U. S. Environmental Protection Agency,
Research Triangle Park, North Carolina.

Hwang S.T., 1986, Methods for estimating onsite ambient air concentrations, ACS Annual Meeting
Anaheim, California.

Perry S.G., Thompson R.S., and Petersen W.B., 1994, Considerations for modeling small-paniculate impacts
from surface coal mining operations based on wind-tunnel simulations, Eight Joint AMS/AWMA
Conference on Applications of Air Pollution Meteorology, Jan. 23-28, 1994, Nashville, Tennessee,
American Meteorological Society, Boston, Massachusetts.

Petersen W.B. and Rumsey E.D., 1987, User's guide for PAL 2.0 - A Gaussian-plume algorithm for point,
area, and line sources, EPA-600-8-87-009, U.S. Environmental Protection Agency, Research Triangle Park,
North Carolina.

Thistle H. and Londergan R.J., 1989, Review and evaluation of area source dispersion algorithms for
emission sources at superfund sited, EPA-450-4-89-020, U.S. Environmental Protection Agency, Research
Triangle Park, North Carolina.

Thompson, R. S., 1993, Wind tunnel simulations of dispersion from surface coal mines. Internal Data
Report, Fluid Modeling Facility, U.S. Environmental Protection Agency, Research Triangle Park, North
Carolina.

Thompson, R. S., 1994a, Residence time of contaminants released in surface coal mines - a wind-runnel
study. Eighth Joint AMS/AWMA Conference on Applications of Air Pollution Meteorology, Jan. 23-28,
1994, Nashville, Tennessee, American Meteorological Society, Boston, Massachusetts.

Thompson, R. S., 1994b, Personal Communication.

Turner D. B., Workbook of atmospheric dispersion estimates, U.S. Environmental Protection Agency,
Research Triangle Park, North Carolina, pp 84.

U.S. Environmental Protection Agency, 1992, User's guide for the Industrial Source Complex (ISC2)
dispersion models, Volume I -User Instructions, EPA-450-4-92-008a, U.S. Environmental Protection
Agency, Research Triangle Park, North Carolina.

Weber E., 1982, Air Pollution Assessment Methodology and Modeling,  Plenum Press, New York.

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                                   TECHNICAL  REPORT  DATA
1.  REPORT NO.
  EPA/600/A-96/019
   TITLE AND  SUBTITLE
Improved Algorithms for Estimating the Effects of
Pollution Impacts  from  Area  and Open  Pit Sources
                                                                  5.REPORT DATE
                                                                  6.PERFORMING ORGANIZATION CODE
7. AUTHOR (S)

William B.  Petersen and Steven G.  Perry
                                                                  8.PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS

Atmospheric  Sciences Modeling Division
Air Resources  Laboratory
National  Oceanic  and Atmospheric  Administration
Research  Triangle Park,  NC  27711
                                                                  10.PROGRAM ELEMENT NO.
                               11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS

National  Exposure  Research  Laboratory
Office of research and  Development
U.S.  Environmental Protection Agency
Research  Triangle  Park,  NC  27711
                                                                  13.TYPE  OF REPORT AND PERIOD COVERED
                               14.  SPONSORING  AGENCY CODE
15. SUPPLEMENTARY NOTES
16.  ABSTRACT
The increasing environmental concern over hazardous emissions from landfills, landfills, settling ponds, agricultural
fields, surface mines, and surface impoundments has renewed interest in improving concentration estimates downwind
from area sources.  Simplistic and numerically efficient methods (for estimating area source impacts) are the virtual point
source approach (Turner, 1970) as used in the models LONGZ (Bjorklund and Bowers,  1979) and VALLEY (Burt,
1977), and the finite line source approach as used in ISCST (Bowers et al., 1979). The virtual point source and finite
line segment algorithms are most appropriate for estimating concentrations at downwind distances significantly larger
than the side width of the area source (Hwang,  1986 and Weber,  1982).  However, these constructs fail for
concentration estimates within or near the area source. Thistle and Londergan (1989) showed that these algorithms
behaved in a manner inconsistent with mathematical and physical principles.

Shortly after the Thistle and Londergan study, the Office of Air Quality Planning and Standards in the U.S.
Environmental Protection Agency (EPA) decided to update the area source algorithm in ISC2 (U.S. EPA, 1992) using
the approach contained in PAL.  At about the same time the Office of Research and Development in EPA was involved
in a project to improve the computational efficiency of the area source algorithm in PAL. It is more efficient version of
the PAL area source algorithm that has been implemented in  ISC2 and will be described in this paper.  In addition, the
improved area source algorithm is utilized in a new approach to modeling open-pit sources.
17.
KEY WORDS AND DOCUMENT ANALYSIS
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                  b. IDENTIFIERS/ OPEN ENDED
                  TERMS
c.COSATI
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