-------
is assumed not to exceed that given by Equation (1-42) with hH
replaced by 5 h^. The modified ay equation is given by:
oy' = 1.75hb + 0.067 (x-3hb) for 3hb*x<10hb
or (1-44)
= ay{x + Xy} for x;>10hb
The upper and lower bounds of the concentrations that can
be expected to occur near a building are determined
respectively using Equations (1-43) and (1-44). The user must
specify whether Equation (1-43) or Equation (1-44) is to be
used in the model calculations. In the absence of user
instructions, the ISC2 models use Equation (1-43) if the
building width to building height ratio h^/1^ exceeds 5.
Although Equation (1-43) provides the highest
concentration estimates for squat buildings with building width
to building height ratios (h^yi^) greater than 5, the equation
is applicable only to a stack located near the center of the
building when the wind direction is perpendicular to the long
side of the building (i.e., when the air flow over the portion
of the building containing the source is two dimensional).
Thusf Equation (1-44) generally is more appropriate then
Equation (1-43). It is believed that Equations (1-43) and
(1-44) provide reasonable limits on the extent of the lateral
enhancement of dispersion and that these equations are adequate
until additional data are available to evaluate the flow near
very wide buildings.
1-26
-------
The modified cry equation for a tall building is given by:
Oy' = 0.351^ + 0.067 (x-3hw) for 3hw^X<10hw
or (1-45)
= oy{x + Xy} for x^lOhw
The ISC2 models print a message and do not calculate
concentrations for any source-receptor combination where the
source-receptor separation is less than l meter, and also for
distances less than 3 hb for a squat building or 3 hH for a
tall building under building wake effects. It should be noted
that, for certain combinations of stability and building height
and/or width, the vertical and/or lateral plume dimensions
indicated for a point source by the dispersion curves at a
downwind distance of ten building heights or widths can exceed
the values given by Equation (1-37) or (1-38) and by Equation
(1-42) or (1-43). Consequently, the ISC2 models do not permit
the virtual distances xy and xz to be less than zero.
1.1.5.3.2 Schulman and Scire refined building downwash
procedures.
The revised procedures for treating building wake effects
include the use of the Schulman and Scire downwash method. The
revised procedures only use the Schulman and Scire method when
the physical stack height is less than hb + 0.5 Lg, where hb is
the building height and Lg is the lesser of the building height
or width. In regulatory applications, the maximum projected
width is used. The features of the Schulman and Scire method
are: (1) reduced plume rise due to initial plume dilution, (2)
enhanced vertical plume spread as a linear function of the
effective plume height, and (3) specification of building
dimensions as a function of wind direction. The reduced plume
rise equations were previously described in Section 1.1.4.11.
1-27
-------
When the Schulman and Scire method is used, the ISC2
dispersion models specify a linear decay factor, to be included
in the az's calculated using Equations (1-37) and (1-38), as
follows:
oz" - Aaz' (1-46)
where az' is from either Equation (1-37) or (1-38) and A is the
linear decay factor determined as follows:
A = 1 if he*hb
A = -^f^ + I if hb hb + 2LB
where the plume height, he/ is the height due to gradual
momentum rise at 2 1^ used to check for wake effects. The
effect of the linear decay factor is illustrated in Figure 1-1.
For Schulman-Scire downwash cases, the linear decay term is
also used in calculating the vertical virtual distances with
Equations (1-40) to (1-41).
When the Schulman and Scire building downwash method is
used the ISC2 models require direction specific building
heights and projected widths for the downwash calculations.
The ISC2 models also accept direction specific building
dimensions for Huber-Snyder downwash cases. The user inputs
the building height and projected widths of the building tier
associated with the greatest height of wake effects for each
ten degrees of wind direction. These building heights and
projected widths are the same as are used for good engineering
practice (GEP) stack height calculations. The user is referred
to EPA (1986) for calculating the appropriate building heights
and projected widths for each direction. Figure 1-2 shows an
example of a two tiered building with different tiers
controlling the height that is appropriate for use for
different wind directions. For an east or west wind the lower
tier defines the appropriate height and width, while for a
1-28
-------
north or south wind the upper tier defines the appropriate
values for height and width.
1.1.5.4 Procedures Used to Account for guovancy-Induced
Dispersion.
The method of Pasquill (1976) is used to account for the
initial dispersion of plumes caused by turbulent motion of the
plume and turbulent entrainment of ambient air. With this
method, the effective vertical dispersion aze is calculated as
follows:
'z
.... .J * d-48)
where az is the vertical dispersion due to ambient turbulence
and Ah is the plume rise due to momentum and/or buoyancy. The
lateral plume spread is parameterized using a similar
expression:
" '^/2 (1-49)
where a is the lateral dispersion due to ambient turbulence.
It should be noted that Ah is the distance-dependent plume rise
if the receptor is located between the source and the distance
to final rise, and final plume rise if the receptor is located
beyond the distance to final rise. Thus, if the user elects to
use final plume rise at all receptors the distance-dependent
plume rise is used in the calculation of buoyancy-induced
dispersion and the final plume rise is used in the
concentration equations. It should also be noted that
buoyancy-induced dispersion is not used when the Schulman-Scire
downwash option is in effect.
1-29
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1.1.6 The Vertical Term
1.1.6.1 The Vertical Term for Gases and Small
Particulates.
In general, the effects on ambient concentrations of
gravitational settling and dry deposition can be neglected for
gaseous pollutants and small particulates (diameters less than
about 20 micrometers). The Vertical Term is then given by:
V = exp
1=1
exp
-0.5 h^1
+ exp -0.5
(Si
+ exp
(1-50)
where:
H,
H, =
zi
hs + Ah
zr - (2iz. - h.)
zr + (2iz, - h.)
zr - (2iz. + he)
zr -i- (2iz. + he)
receptor height above ground (flagpole) (m)
mixing height (m)
The infinite series term in Equation (1-50) accounts for
the effects of the restriction on vertical plume growth at the
top of the mixing layer. As shown by Figure 1-3, the method of
image sources is used to account for multiple reflections of
the plume from the ground surface and at the top of the mixed
layer. It should be noted that, if the effective stack height,
he, exceeds the mixing height, z{, the plume is assumed to
1-30
-------
fully penetrate the elevated inversion and the ground-level
concentration is set equal to zero.
Equation (1-50) assumes that the mixing height in rural
and urban areas is known for all stability categories. As
explained below, the meteorological preprocessor program uses
mixing heights derived from twice-daily mixing heights
calculated using the Holzworth (1972) procedures. These mixing
heights are believed to be representative, at least on the
average, of mixing heights in urban areas under all stabilities
and of mixing heights in rural areas during periods of
instability or neutral stability. However, because the
Holzworth minimum mixing heights are intended to include the
heat island effect for urban areas, their applicability to
rural areas during periods of stable meteorological conditions
(E or F stability) is questionable. Consequently, the ISC2
models in the Rural Mode currently delete the infinite series
term in Equation (1-50) for the E and F stability categories.
The Vertical Term defined by Equation (1-50) changes the
form of the vertical concentration distribution from Gaussian
to rectangular (uniform concentration within the surface mixing
layer) at long downwind distances. Consequently, in order to
reduce computational time without a loss of accuracy, Equation
(1-50) is changed to the form:
v . z (1-51)
Zi
at downwind distances where the az/z. ratio is greater than or
equal to 1.6.
The meteorological preprocessor program, RAMMET, used by
the ISC2 Short Term model uses an interpolation scheme to
assign hourly rural and urban mixing heights in the basis of
the early morning and afternoon mixing heights calculated using
the Holzworth (1972) procedures. The procedures used to
interpolate hourly mixing heights in urban and rural areas are
illustrated in Figure 1-4, where:
1-31
-------
= maximum mixing height on a given day
H|>{min} = minimum mixing height on a given day
MN = midnight
SR = sunrise
SS = sunset
The interpolation procedures are functions of the stability
category for the hour before sunrise. If the hour before
sunrise is neutral, the mixing heights that apply are indicated
by the dashed lines labeled neutral in Figure 1-4. If the hour
before sunrise is stable, the mixing heights that apply are
indicated by the dashed lines labeled stable. It should be
pointed out that there is a discontinuity in the rural mixing
height at sunrise if the preceding hour is stable. As
explained above, because of uncertainties about the
applicability of Holzworth mixing heights during periods of E
and F stability, the ISC2 models ignore the interpolated mixing
heights for E and F stability, and treat such cases as having
unlimited vertical mixing.
1.1.6.2 The Vertical Term in Elevated Terrain.
The ISC2 models make the following assumption about plume
behavior in elevated terrain:
The plume axis remains at the plume stabilization
height above mean sea level as it passes over elevated
or depressed terrain.
The mixing height is terrain following.
The wind speed is a function of height above the
surface (see Equation (1-6)).
Thus, a modified plume stabilization height he" is
substituted for the effective stack height he in the Vertical
1-32
-------
Term given by Equation (1-50). For example, the effective
plume stabilization height at the point x, y is given by:
d-52)
where :
zs = height above mean sea level of the base of the
stack
z I (x y> ~ nei9nt above mean sea level of terrain at the
receptor location (x,y)
It should also be noted that, as recommended by EPA, the ISC2
models now ."truncate" terrain at stack height as follows: if
the terrain height z - zs exceeds the source release height,
hs, the elevation of the receptor is automatically "chopped
off" at the physical release height. The user is cautioned
that concentrations at these complex terrain receptors are
subject to considerable uncertainty. Figure 1-5 illustrates
the terrain-adjustment procedures used by the ISC2 models.
1.1.6.3 The Vertical Term for Large Particulates.
The dispersion of particulates or droplets with
significant gravitational settling velocities differs from that
of gaseous pollutants and small particulates in that the larger
particulates are brought to the surface by the combined
processes of atmospheric turbulence and gravitational settling.
Additionally, gaseous pollutants and small particulates tend to
be reflected from the surface, while larger particulates that
come in contact with the surface may be completely or partially
retained at the surface. The ISC2 Vertical Term for large
particulates includes the effects of both gravitational
settling and removal by dry deposition. Gravitational settling
is assumed to result in a tilted plume with the plume axis
inclined to the horizontal at an angle given by arctan(Vs/us)
where Vg is the gravitational settling velocity. A
1-33
-------
user-specified fraction (y) of the material that reaches the
ground surface by the combined processes of gravitational
settling and atmospheric turbulence is assumed to be reflected
from the surface. Figure 1-6 illustrates the vertical
concentration profiles for complete reflection from the surface
(Y equal to unity), 50-percent reflection from the surface (y
equal to 0.5) and complete retention at the surface (y equal to
zero).
For a given particulate source, the user must subdivide
the total particulate emissions into N settling-velocity
categories (the maximum value of N is 20). The ground-level
concentration of particulates with settling velocity Vsn is
given by Equation (1-1) with the Vertical Term defined as
(Dumbauld and Bjorklund, 1975):
V = <|>n \ exp
-0.5 •=£•
yn exp
n exp
+ Yn exp
-0.5 —i
-
(1-53)
where:
mass fraction of particulates for nth settling category
zr - [2iz. - (he - hv)]
zr + [2iz, - (h. - hv)]
zr - [2izf 4- (he - hv)]
zr + [2iz, + (he - \)}
reflection coefficient for particulates in the nth
settling velocity category (set equal to unity for
complete reflection)
1-34
-------
hy = Vsn x/us = plume height correction for plume tilt
V _ = settling velocity of particulates in the nth settling
sn
velocity category.
The total concentration is computed by the program by summing
over the N settling-velocity categories. The optional
algorithm used to calculate dry deposition is discussed in
Section 1.3.
Use of Equation (1-53) requires a knowledge of both the
particulate size distribution and the density of the
particulates emitted by each source. The total particulate
emissions for each source are subdivided by the user into a
maximum of 20 categories and the gravitational settling
velocity is calculated for the mass-mean diameter of each
category. The mass-mean diameter is given by:
+d|)]1/3 (1-54)
where d1 and d2 are the lower and upper bounds of the
particle-size category. McDonald (1960) gives simple
techniques for calculating the gravitational settling velocity
for all sizes of particulates. For particulates with a density
on the order of 1 gram per cubic centimeter and diameters less
than about 80 micrometers, the settling velocity is given by:
v
,
where :
Vs = settling velocity (cm/s)
p = particulate density (gm/cm3)
g = acceleration due to gravity (980.6 cm/s2)
r = particle radius (cm)
H = absolute viscosity of air (JLI- 1.83 x 10"4
gm/cm/s)
1-35
-------
It should be noted that the settling velocity calculated
using Equation (1-55) must be converted by the user from
centimeters per second to meters per second for use in the
model calculations.
The reflection coefficient yn can be estimated for each
particle-size category using Figure 1-7 and the settling
velocity calculated for the mass-mean diameter. If it is
desired to include the effects of gravitational settling in
calculating ambient particulate concentrations while at the
same time excluding the effects of deposition, yn should be set
equal to unity for all settling velocities. On the other hand,
if it is desired to calculate maximum possible deposition, yn
should be set equal to zero for all settling velocities. The
effects of dry deposition for gaseous pollutants may be
estimated by setting the settling velocity Vsn equal to zero
and the reflection coefficient yn equal to the amount of
material assumed to be reflected from the surface. For
example, if 20 percent of a gaseous pollutant that reaches the
surface is assumed to be retained at the surface by vegetation
uptake or other mechanisms, yn is equal to 0.8.
The derivation of Equation (1-53) assumes that the terrain
is flat or gently rolling. Consequently, the gravitational
settling and dry deposition options cannot be used for sources
located in complex terrain without violating mass continuity.
However, the effects of gravitational settling alone can be
estimated for sources located in complex terrain by setting yn
equal to unity for each settling velocity category. This
procedure will tend to overestimate concentrations, especially
at the longer downwind distances, because it neglects the
effects of dry deposition.
It should be noted that Equation (1-53) assumes that az is
a continuous function of downwind distance. Also, Equation
(1-53) does not simplify for oz/z. greater than 1.6 as does
Equation (1-50). As shown by Table 1-2, crz for the very
unstable A stability category attains a maximum value of 5,000
1-36
-------
meters at 3.11 kilometers. Because Equation (1-53) requires
that a2 be a continuous function of distance, the coefficients
a and b given in Table 1-2 for A stability and the 0.51 to 3.11
kilometer range are used by the ISC2 models in calculations
beyond 3.11 kilometers. Consequently, this introduces
uncertainties in the results of the calculations beyond 3.11
kilometers for A stability.
1.1.7 The Decay Term
The Decay Term, which is a simple method of accounting for
pollutant removal by physical or chemical processes, is of the
form:
D = exp I -i|r— I for i|r > 0
(1-56)
or
= 1 f or i|r = 0
where:
if = the decay coefficient (s~1) (a value of zero means
decay is not considered)
x = downwind distance (m)
For example, if T1/2 is the pollutant half life in seconds, the
user can obtain if from the relationship:
l/2
The default value for if is zero. That is, decay is not
considered in the model calculations unless if is specified.
However, a decay half life of 4 hours (if = 0.0000481 s"1) is
automatically assigned for SO2 when modeled in the urban mode
1-37
-------
1.2 VOLUME AMD AREA SOURCE EMISSIONS
1.2.1 General
The volume and area sources options of the ISC2 models are
used to simulate the effects of emissions from a wide variety
of industrial sources. In general, the ISC2 volume source
model is used to simulate the effects of emissions from sources
such as building roof monitors and line sources (for example,
conveyor belts and rail lines). The ISC2 area source model is
used to simulate the effects of fugitive emissions from sources
such as storage piles and slag dumps.
1.2.2 The Short-Term Volume Source Model
The ISC2 models use a virtual point source algorithm to
model the effects of volume sources. Therefore, Equation (1-1)
is also used to calculate concentrations produced by volume
source emissions. If the volume source is elevated, the user
assigns the effective emission height he. The user also
assigns initial lateral (ayo) and vertical (azo) dimensions for
the volume source. Lateral (Xy) and vertical (xz) virtual
distances are added to the actual downwind distance x for the
ay and az calculations. The virtual distances are calculated
from solutions to the sigma equations as is done for point
sources with building downwash.
The volume source model is used to simulate the effects of
emissions from sources such as building roof monitors and for
line sources (for example, conveyor belts and rail lines). The
north-south and east-west dimensions of each volume source used
in the model must be the same. Table 1-6 summarizes the
general procedures suggested for estimating initial lateral
(ayo) and vertical (azo) dimensions for single volume sources
and for multiple volume sources used to represent a line
source. In the case of a long and narrow line source such as a
rail line, it may not be practical to divide the source into N
volume sources, where N is given by the length of the line
1-38
-------
source divided by its width. The user can obtain an
approximate representation of the line source by placing a
smaller number of volume sources at equal intervals along the
line source. In general, the spacing between individual volume
sources should not be greater than twice the width of the line
source. However, a larger spacing can be used if the ratio of
the minimum source-receptor separation and the spacing between
individual volume sources is greater than about 3. In these
cases, concentrations calculated using fewer than N volume
sources to represent the line source converge to the
concentrations calculated using N volume sources to represent
the line source as long as sufficient volume sources are used
to preserve the horizontal geometry of the line source.
Figure 1-8 illustrates representations of a curved line
source by multiple volume sources. Emissions from a line
source or narrow volume source represented by multiple volume
sources are divided equally among the individual sources unless
there is a known spatial variation in emissions. Setting the
initial lateral dimension ayo equal to W/2.15 in Figure 1-8(a)
or 2W/2.15 in Figure 1-8(b) results in overlapping Gaussian
distributions for the individual sources. If the wind
direction is normal to a straight line source that is
represented by multiple volume sources, the initial crosswind
concentration distribution is uniform except at the edges of
the line source. The doubling of a by the user in the
approximate line-source representation in Figure 1-8(b) is
offset by the fact that the emission rates for the individual
volume sources are also doubled by the user.
There are two types of volume sources: surface-based
sources, which may also be modeled as area sources, and
elevated sources. An example of a surface-based source is a
surface rail line. The effective emission height he for a
surface-based source is usually set equal to zero. An example
of an elevated source is an elevated rail line with an
1-39
-------
effective emission height he set equal to the height of the
rail line.
TABLE 1-6
SUMMARY OF SUGGESTED PROCEDURES FOR ESTIMATING
INITIAL LATERAL DIMENSIONS a^ AND
yo
INITIAL VERTICAL DIMENSIONS 0) on or azo = building height
Adjacent to a Building divided by 2.15
Elevated Source (he > 0) not azo = vertical dimension of
on or Adjacent to a Building source divided by 4.3
1.2.3 The Short-Term Area Source Model
The ISC2 area source model is based on the equation for
a finite crosswind line source. Individual area sources are
required to have the same north-south and east-west dimensions.
However, as shown by Figure 1-9, the effects of an area source
with an irregular shape can be simulated by dividing the area
source into multiple squares that approximate the geometry of
the area source. Note that the size of the individual area
sources in Figure 1-9 varies; the only requirement is that each
area source must be square. The ground-level concentration at
1-40
-------
downwind distance x (measured from the downwind edge of the
area source) and crosswind distance y is given by:
X - (1-58,
where :
QA = area source emission rate (mass per unit area per
unit time)
K » units scaling coefficient (Equation (1-1))
V » vertical term (see Section 1.1.6)
D = decay term (see Section 1.1.7)
E = error function term = erf I r° +Y I +erf r° ~Y
XQ = length of the side of the area source (m)
0~ = effective radius of area source = x0/^n (m)
and the Vertical Term is given by Equation (1-50) or Equation
(1-53) with the effective emission height he assigned by the
user. In general, he should be set equal to the physical
height of the source of fugitive emissions. For example, the
emission height he of a slag dump is the physical height of the
slag dump. A vertical virtual distance, equal to xo, is added
to the actual downwind distance x for the az calculations. If
a receptor is located within r0" plus 1 meter of the center of
an area source, a warning message is printed and no
concentrations are calculated for the source-receptor
combination. However, program execution is not terminated.
It is recommended that, if the separation between an area
source and a receptor is less than the length of the side of
the area source x0, then the area source should be subdivided
into smaller area sources. If the source-receptor separation
is less than x0, the finite line segment algorithm does not
adequately represent the source-receptor geometry.
1-41
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1.3 THE Z8C2 SHORT-TERM DRY DEPOSITION MODEL
1.3.1 General
The Industrial Source Complex short-term dry deposition
model is based on the Dumbauld, et al (1976) deposition model.
This model, which is an advanced version of the Cramer, et al
(1972) deposition model, assumes that a user-specified fraction
Yn of the material that comes into contact with the ground
surface by the combined processes of atmospheric turbulence and
gravitational settling is reflected from the surface (see
Section 1.1.6.3). The reflection coefficient yn, which is a
function of settling velocity and the ground surface for
particulates and of the ground surface for gaseous pollutants,
is analogous in purpose to the deposition velocity used in
other deposition models. The Cramer, et al (1972) deposition
model has closely matched ground-level deposition patterns for
droplets with diameters above about 30 micrometers, while the
more generalized Dumbauld, et al (1976) deposition model has
closely matched observed deposition patterns for both large and
small droplets.
Section 1.1.6.3 discusses the selection of the reflection
coefficient yn as well as the computation of the gravitational
settling velocity Vsn. The ISC2 dry deposition model should
not be applied to sources located in elevated terrain or for
receptors above local terrain. Also, as noted in Section
1.1.6.3, uncertainties in the deposition calculations are
likely for the A stability category if deposition calculations
are made at downwind distances greater than 3.11 kilometers.
Deposition and ambient concentration calculations cannot be
made in a single program execution. In an individual computer
run, the ISC2 models calculate either concentration (including
the effects of gravitational settling and dry deposition) or
dry deposition.
1-42
-------
1.3.2 Point and Volume Source Emissions
Deposition for particulates in the nth settling-velocity
category or a gaseous pollutant with zero settling velocity Vsn
and a reflection coefficient yn is given by:
DEP.
QTK(1 -
2«oyazx
exp
h- (til
(1-59)
where the Vertical Term is defined as follows:
vd = [btt^-hj +hj exp
-0.5
.i-l riT
Yn
[b (2iz± - (h. -hj ) -hj exp
(b,-!^) ) +hv] exp
-0.5
/2izi-(h.-hv)
(1-60)
K, D, and hy were defined previously (Equations (1-1), (1-53),
and (1-56)). The parameter Qr is the total amount of material
emitted during the time period T for which the deposition
calculation is made. For example, QT is the total amount of
material emitted during a 1-hour period if an hourly deposition
is calculated. To simplify the user input, and to keep the
maximum compatibility between input files for concentration and
deposition runs, the model takes emission inputs in grams per
second (g/s), and converts to grams per hour for deposition
calculations. For time periods longer than an hour, the
program sums the deposition calculated for each hour to obtain
the total deposition. The coefficient b is the average value
of the exponent b for the interval between the source and the
downwind distance x (see Tables 1-1 to 1-4). Values of b exist
for both the Pasquill-Gifford dispersion parameters and
Briggs-McElroy-Pooler curves. In the case of a volume source,
the user must specify the effective emission height he and the
1-43
-------
initial source dimensions cr^ and azo. It should be noted that
for computational purposes, the model calculates the quantity,
NVS
S(l-Yn)nVd, as the "vertical term.
1.3.3 Area Source
For area source emissions Equation (1-59) is changed to
the form:
K, D, Vd are defined in Equations (1-1), (1-56), and (1-60),
respectively. The parameter QAT is the total mass per unit
area emitted over the time period r for which deposition is
calculated and E is the error function term defined in Equation
(1-56).
1-44
-------
w
/
1U
FIGURE 1-1.
LINEAR DECAY FACTOR, A AS A FUNCTION OF
EFFECTIVE STACK HEIGHT, He. A SQUAT BUILDING IS
ASSUMED FOR SIMPLICITY.
1-45
-------
100
90
H-«0
•utWtnf Tier «t
TO
•2 H-M
T
North and South wind:
HW1
H
W2
60 +
W + 1^(70)
150
185
Therefore, the upper building tier
width and height
(II = 80, W = 70) are used
tier 2 dosriMtM
Height of wake effects is Hw - H + 1.5 LB
where LB is the lesser of the height of the
width.
East and west wind:
*~~ ew » « + 1.5(50) a 135
Hjjj • » + 1-5(10) = 9s
Therefore, the lower building tier #1 width and
height
(H » 60, W - 50) are used
tl«r 1
-------
\ y / /
\ / \ / '
ZH..+H V V /
L^xy/
v w
/ /
/
FIGURE 1-3.
THE METHOD OF MULTIPLE PLUME IMAGES USED TO
SIMULATE PLUME REFLECTION IN THE ISC2 MODEL
1-47
-------
o
u
X
i
X
2
(Neutrol) „+
*** f
+' 1
,~" I
(StaMe)
/
/
t
**fJM 1 ^Hlvff f
i . ,
DAY,.,
• ^^^
^
(Stable)
^
max} \
\
\
N
i i
(Neutral) DAY,
""~*"""-^
"*"*••»•»
i
/
(Stable)
/
i3u
I"!
r™™ ^~^
\ ^"
(Stable)
\
\
,
DAYj^i
•-^J Neutral)
•**^^ (Neutral!
">n
/
— y Mm
(Stable)
,
r~x
(Stable)
' 1
maxf
, J
' i
MN SR 1400 SS MN SR 1400 SS MN SR
TIME (LST)
(a) Urban Mixing Heights
I4OO SS
MN
H
X
O
UJ
X
z
X
2
M
DAY,.,
(NeutroO^-i
^^ 1
^^ 1
1
j
1
1 Mm
/
j
(Stable)
/
/ i
\ ^
maij
1 t
DAY,
^-^^(Nwtral)
rn
/
h"'
i
i
i
i
i
(Stable)
/
/ i
r^**^
^^«
max}
i .
DAYU,
*«^^^
"*T^
/
/
§
(SMM«)
/ H"
/ ,
^ —
:—}
i ,
IN SR I40O SS MN SR I40O SS MN SR I4OO SS M
TIME (LST)
(b) Rural Mixing Heights
FIGURE 1-4
SCHEMATIC ILLUSTRATION OF (a) URBAN AND (b)
RURAL MIXING HEIGHT INTERPOLATION PROCEDURES
1-48
-------
FIGURE 1-5.
ILLUSTRATION OF PLUME BEHAVIOR IN COMPLEX
TERRAIN ASSUMED BY THE ISC2 MODEL
1-49
-------
I
FIGURE 1-6.
ILLUSTRATION OF VERTICAL CONCENTRATION PROFILES
FOR REFLECTION COEFFICIENTS OF 0., 0.5, AND 1.0
1-50
-------
0.30
rn—i i i i i i
0.2 0.4 Od6 0.8
REFLECTION COEFFICIENT rn
1.0
FIGURE.1-7,
RELATIONSHIP BETWEEN THE GRAVITATIONAL SETTLING
VELOCITY, Vsn AND THE REFLECTION COEFFICIENT,
SUGGESTED BY DUMBAULD, et al. (1976)
1-51
-------
2.15
w
10
(a) EXACT REPRESENTATION
2W
W
2W-
(b) APPROXIMATE REPRESENTATION
FIGURE 1-8.
EXACT AND APPROXIMATE REPRESENTATIONS OF A LINE
SOURCE BY MULTIPLE VOLUME SOURCES
1-52
-------
• I
'10
• 9
'II
FIGURE 1-9.
REPRESENTATION OF AN IRREGULARLY SHAPED AREA
SOURCE BY 11 SQUARE AREA SOURCES
1-53
-------
2.0 THE I8C2 LONG-TERM DISPERSION MODEL EQUATIONS
This section describes the ISC2 Long-Term dispersion model
equations. Where the technical information is the same, this
section refers to the ISC2 Short-Term model description in
Section 1 for details. The long-term model provides options
for modeling the same types of sources as provided by the
short-term model. The information provided below follows the
same order as used for the short-term model equations.
The ISC2 long-term model uses input meteorological data
that have been summarized into joint frequencies of occurrence
for particular wind speed classes, wind direction sectors, and
stability categories. These summaries, called STAR summaries
for STability ARray, may include frequency distributions over a
monthly, seasonal or annual basis. The long term model has the
option of calculating concentration or deposition values for
each separate STAR summary input and/or for the combined period
covered by all available STAR summaries. Since the wind
direction input is the frequency of occurrence over a sector,
with no information on the distribution of winds within the
sector, the ISC2 long-term model uses a Gaussian sector-average
plume equation as the basis for modeling pollutant emissions on
a long-term basis.
2.1 POINT SOURCE EMISSIONS
2.1.1 The Gaussian Sector Average Equation
The ISC2 long-term concentration model makes the same
basic assumption as the short-term model. In the long-term
model, the area surrounding a continuous source of pollutants
is divided into sectors of equal angular width corresponding to
the sectors of the seasonal and annual frequency distributions
of wind direction, wind speed, and stability. Seasonal or
annual emissions from the source are partitioned among the
sectors according to the frequencies of wind blowing toward the
sectors. The concentration fields calculated for each source
2-1
-------
are translated to a common coordinate system (either polar or
Cartesian as specified by the user) and summed to obtain the
total due to all sources.
For a single stack, the mean seasonal concentration at a
point (r > 1m, 6) with respect to the stack is given by:
QfSVD (2_i}
where :
K = units scaling coefficient (see Equation 1-1)
Q = pollutant emission rate (mass per unit time) ,
for the ith wind-speed category, the kth
stability category and the 1th season
f = frequency of occurrence of the ith wind-speed
category, the jth wind-direction category and
the kth stability category for the 1th season
A0' = the sector width in radians
R = radial distance from lateral virtual point
source (for building down wash) to the receptor =
+ y2]1'2
x = downwind distance from source center to
receptor, measured along the plume axis
y = lateral distance from the plume axis to the
receptor
x = lateral virtual distance (see Equation (1-33)),
equals zero for point sources without building
downwash, and for downwash sources that do not
experience lateral dispersion enhancement
S = a smoothing function similar to that of the AQDM
(see Section 2.1.8)
us = mean wind speed (m/sec) at stack height for the
ith wind-speed category and kth stability
category
crz = standard deviation of the vertical concentration
distribution (m) for the kth stability category
2-2
-------
V = the Vertical Term for the ith wind-speed
category, kth stability category and 1th season
D = the Decay Term for the ith wind speed category
and kth stability category
The mean annual concentration at the point (r,6) is
calculated from the seasonal concentrations using the
expression:
Xa = 0.25 £ Xi (2-2
l-i
The terms in Equation (2-1) correspond to the terms
discussed in Section 1.1 for the short-term model except that
the parameters are defined for discrete categories of
wind-speed, wind-direction, stability and season. The various
terms are briefly discussed in the following subsections. In
addition to point source emissions, the ISC2 long-term
concentration model considers emissions from volume and area
sources. These model options are discussed in Section 2.2.
The optional algorithms for calculating dry deposition are
discussed in Section 2.3.
2.1.2 Downwind and Crosswind Distances
See the discussion given in Section 1.1.2.
2.1.3 Wind Speed Profile
See the discussion given in Section 1.1.3.
2.1.4 Plume Rise Formulas
See the discussion given in Section 1.1.4.
2-3
-------
2.1.5 The Dispersion Parameters
2.1.5.1 Point Source Dispersion Parameters.
See Section 1.1.5.1 for a discussion of the procedures use
to calculate the standard deviation of the vertical
concentration distribution az for point sources (sources
without initial dimensions). Since the long term model assumes
a uniform lateral distribution across the sector width, the
model does not use the standard deviation of the lateral
dispersion,
-------
ay* is held constant at the value of ay' calculated at a
downwind distance of 10 building widths.
2.1.5.3 Procedures Used to Account for the Effects of
Building Wakes on Effluent Dispersion.
With the exception of the equations used to calculate the
lateral virtual distance, the procedures used to account for
the effects of building wake effects on effluent dispersion are
the same as those outlined in Section 1.1.5.3 for the
short-term model. The calculation of lateral virtual distances
by the long-term model is discussed in Section 2.1.5.2 above.
2.1.5.4 Procedures Used to Account for Buoyancy- I nduced
Dispersion.
See the discussion given in Section 1.1.5.4.
2.1.6 The Vertical Term
2.1.6.1 The Vertical Term for Gases and Small
Particulates .
Except for the use of seasons and discrete categories of
wind-speed and stability, the Vertical Term for gases and small
particulates corresponds to the short term version discussed in
Section 1.1.6. The user may assign a separate mixing height z.
to each combination of wind-speed and stability category for
each season.
As with the short-term model, the Vertical Term is changed
to the form:
(2-4)
zi
at downwind distances where the az/z,. ratio is greater than or
equal to 1.6. Additionally, the ground-level concentration is
set equal to zero if the effective stack height he exceeds the
mixing height z, . As explained in Section 1.1.6.1, the ISC2
2-5
-------
model currently assumes unlimited mixing for the E and F
stability categories.
2.1.6.2 The Vertical Term in Elevated Terrain.
See the discussion given in Section 1.1.6.2.
2.1.6.3 The Vertical Term for Large Particulates.
Section 1.1.6.3 discusses the differences in the
dispersion of large particulates and the dispersion of gases
and small particulates and provides the guidance on the use of
this option. The Vertical Term for large particulates is given
by Equation (1-53).
2.1.7 The Decay Term
See the discussion given in Section 1.1.7.
2.1.8 The Smoothing Function
As shown by Equation (2-1), the rectangular concentration
distribution within a given angular sector is modified by the
function S{6} which smooths discontinuities in the
concentration at the boundaries of adjacent sectors. The
centerline concentration in each sector is unaffected by
contribution from adjacent sectors. At points off the sector
centerline, the concentration is a weighted function of the
concentration at the centerline and the concentration at the
centerline of the nearest adjoining sector. The smoothing
function is given by:
-lV-»-|) for IV-6'I «A8'
(2-5)
or
= 0 for |0j' -8'| > A0'
where:
2-6
-------
9-' = the angle measured in radians from north to the
J centerline of the jth wind-direction sector
6' = the angle measured in radians from north to the
receptor point (R, 6) where R, defined above for
equation 2-1, is measured from the lateral virtual
source.
2.2 VOLUME AMD AREA SOURCE EMISSIONS
2.2.1 General
As explained in Section 1.2.1, the 1SC2 volume and area
sources are used to simulate the effects of emissions from a
wide variety of industrial sources. Section 1.2.2 provides
guidance on the use of the volume source model and Section
1.2.3 provides guidance on the use of the area source model.
The volume source model may also be used to simulate line
sources. The following subsections give the volume and area
source equations used by the long-term model.
2.2.2 The Long-Term Volume Source Model
The ISC2 Long Term Model uses a virtual point source
algorithm to model the effects of volume sources. Therefore,
Equation (2-1) is also used to calculate seasonal average
ground-level concentrations for volume source emissions. The
user must assign initial lateral (ayo) and vertical (azo)
dimensions and the effective emission height he. A discussion
of the application of the volume source model is given in
Section 1.2.2.
2.2.3 The Long-Term Area Source Model
The 1SC2 Long Term Model also uses a virtual point source
algorithm to model the effects of area sources, however the
form of the equation is slightly different since the area
source emissions, Q., are in emissions per unit area. The
2-7
-------
seasonal average concentration at the point (r, 6) with respect
to the center of an area source is given by the expression:
Xl = y * (2-6)
'
where :
K - units scaling coefficient (see Equation (1-1))
radial distance from the lateral virtual point source
to the receptor = [ (x + x^2 + y2]1'2
decay term = exp -i|r
(x-r0)l
x - downwind distance from source center to receptor,
measured along the plume axis
y = lateral distance from the plume axis to the receptor
ro = effective source radius = x0/v'«
xo = length of the side of the area source (m)
Xy = lateral virtual distance (see Equation (2-3))
S = smoothing function (see Equation (2-5))
A vertical virtual distance, equal to x0, is added to the
actual downwind distance x for the az calculations. The
vertical terms V for gaseous pollutants and small particulates,
and for cases with settling and dry deposition, are given in
Section 1.1.6 with the emission height he defined by the user.
2.3 THE I8C2 LONG-TERM DRY DEPOSITION MODEL
2.3.1 General
The concepts upon which the ISC2 long-term dry deposition
model are based are discussed in Sections 1.1.6.3 and 1.3.
2-8
-------
2.3.2 Point and Volume Source Emissions
The seasonal deposition at the point (r, 9) with respect
to the base of a stack or the center of a volume source for
particulates in the nth settling-velocity category or a gaseous
pollutant with zero settling velocity Vsn and a reflection
coefficient Yn is given by:
DEP, . = "^ I*'** £ W^;Vd" (2-7)
i"k az
where the vertical term for deposition, Vd, was defined in
Section 1.3.2. K and D are described in Equations (1-1) and
(1-56), respectively. Q,. is the product of the total time
during the 1th season, of the seasonal emission rate Q for the
ith wind-speed category, kth stability category. For example,
if the emission rate is in grams per second and there are 92
days in the summer season (June, July, and August) , QT t_3 is
given by 7.95 x 106 Qt_3. It should be noted that the user need
not vary the emission rate by season or by wind speed and
stability. If an annual average emission rate is assumed, Qr
is equal to 3.15 x 107 Q for a 365-day year. For a plume
comprised of N settling velocity categories, the total seasonal
deposition is obtained by summing Equation (2-7) over the N
sett ling- velocity categories. The program also sums the
seasonal deposition values to obtain the annual deposition.
2.3.3 Area Source Emissions
With slight modifications, Equation (2-7) is applied to
area source emissions. The user assigns the effective emission
height he and Equation (2-7) is changed to:
, ,
where
DEP, , = nno Y itd (2-8)
K = units scaling coefficient (Equation (1-1))
2-9
-------
QAT = the product of the total time during the 1th season
and the emission rate per unit area for the ith
wind-speed category and kth stability category
Vd = vertical term for dry deposition (Equation (1-60)
D = decay term (see Equation (2-6))
2-10
-------
3.0 REFERENCES
Bowers, J.F., J.R. Bjorklund and C.S. Cheney, 1979: Industrial
Source Complex (ISC) Dispersion Model User's Guide. Volume
I, EPA-450/4-79-030, U.S. Environmental Protection Agency,
Research Triangle Park, North Carolina 27711.
Bowers, J.R., J.R. Bjorklund and C.S. Cheney, 1979: Industrial
Source Complex (ISC) Dispersion Model User's Guide. Volume
II, EPA-450/4-79-031, U.S. Environmental Protection
Agency, Research Triangle Park, North Carolina 27711.
Briggs, G.A., 1969, Plume Rise, USAEC Critical Review Series,
TID-25075, National Technical Information Service,
Springfield, Virginia 22161.
Briggs, G.A., 1979: Some Recent Analyses of Plume Rise
Observations, In Proceedings of the Second International
Clean Air Congress. Academic Press, New York.
Briggs, G.A., 1972: Discussion on Chimney Plumes in Neutral
and Stable Surroundings. Atmos. Environ. 6:507-510.
Briggs, G.A., 1974: Diffusion Estimation for Small Emissions.
In ERL, ARL USAEC Report ATDL-106. U.S. Atomic Energy
Commission, Oak Ridge, Tennessee.
Briggs, G.A., 1975: Plume Rise Predications. In Lectures on
Air Pollution and Environmenta1 Impact Analysisf American
Meteorological Society, Boston, Massachusetts.
Chico, T. and J.A. Catalano, 1986: Addendum to the User's
Guide for MPTER. Contract No. EPA 68-02-4106, U.S.
Environmental Protection Agency, Research Triangle Park,
North Carolina 27711.
Cramer, H.E., et al., 1972: Development of Dosage Models and
Concepts. Final Report Under Contract DAAD09-67-C-0020(R)
with the U.S. Army, Desert Test Center Report DTC-TR-609,
Fort Douglas, Utah.
Dumbauld, R.K. and J.R. Bjorklund, 1975: NASA/MSFC Multilayer
Diffusion Models and Computer Programs — Version 5. NASA
Contractor Report No. NASA CR-2631, National Aeronautics
and Space Administration, George C. Marshall Space Center,
Alabama.
Environmental Protection Agency, 1986: Guideline for
Determination of Good Engineering Practice Stack Height
(Technical Support Document for the Stack Height
Regulations) - Revised EPA-450/4-80-023R, U.S.
Environmental Protection Agency, Research Triangle Park,
North Carolina 27711.
3-1
-------
Gifford, F.A., Jr. 1976: Turbulent Diffusion - Typing Schemes:
A Review. Nucl. Saf.. 17. 68-86.
HoIzworth, 6.C., 1972: Mixing Heights, Wind Speeds and
Potential for Urban Air Pollution Throughout the
Contiguous United States. Publication No. AP-101, U.S.
Environmental Protection Agency, Research Triangle Park,
North Carolina 27711.
Huber, A.H. and W.H. Snyder, 1976: Building Wake Effects on
Short Stack Effluents. Preprint Volume for the Third
Symposium on Atmospheric Diffusion and Air Quality.
American Meteorological Society, Boston, Massachusetts.
Huber, A.H. and W.H. Snyder, 1982. Wind tunnel investigation
of the effects of a rectangular-shaped building on
dispersion of effluents from short adjacent stacks. Atmos.
Environ. 176. 2837-2848.
Huber, A.H., 1977: Incorporating Building/Terrain Wake Effects
on Stack Effluents. Preprint Volume for the Joint
Conference on Applications of Air Pollution Meteorology.
American Meteorological Society, Boston, Massachusetts.
McDonald, J.E., 1960: An Aid to Computation of Terminal Fall
Velocities of Spheres. J. Met.. 17. 463.
McElroy, J.L. and F. Pooler, 1968: The St. Louis Dispersion
Study. U.S. Public Health Service, National Air Pollution
Control Administration, Report AP-53.
National Climatic Center, 1970: Card Deck 144 WBAN Hourly
Surface Observations Reference Manual 1970. Available from
the National Climatic Data Center, Asheville, North
Carolina 28801.
Pasquill, F., 1976: Atmospheric Dispersion Parameters in
Gaussian Plume Modeling. Part II. Possible Requirements
for Change in the Turner Workbook Values.
EPA-600/4-76-030b, U.S. Environmental Protection Agency,
Research Triangle Park, North Carolina 27711.
Schulman, L.L. and S.R. Hanna, 1986: Evaluation of Downwash
Modifications to the Industrial Source Complex Model. J.
Air Poll. Control Assoc. 36. (3) , 258-264.
Schulman, L.L. and J.S. Scire, 1980: Buoyant Line and Point
Source (BLP) Dispersion Model User's Guide. Document
P-7304B, Environmental Research and Technology, Inc.,
Concord, MA.
3-2
-------
Scire, J.S. and L.L. Schulman, 1980: Modeling Plume Rise from
Low-Level Buoyant Line and Point Sources. Proceedings
Second Joint Conference on Applications of Air Pollution
Meteorology, 24-28 March, New Orleans, LA. 133-139.
Turner, D.B., 1970: Workbook of Atmospheric Dispersion
Estimates. PHS Publication No. 999-AP-26. U.S.
Department of Health, Education and Welfare, National Air
Pollution Control Administration, Cincinnati, Ohio.
3-3
-------
INDEX
Area source
deposition algorithm 1-44, 2-9
for the Long Term model 2-7
for the Short Term model 1-38, 1-40
Briggs plume rise formulas
buoyant plume rise 1-7, 1-9
momentum plume rise 1-7, 1-9
stack tip downwash 1-5
Building downwash procedures 1-22, 2-4
and buoyancy-induced dispersion 1-29
effects on dispersion parameters 1-20
for the Long Term model 2-2, 2-4, 2-5
general 1-5, 1-21
Huber and Snyder 1-22
Schulman and Scire 1-5, 1-11, 1-27, 1-28
Schulman-Scire plume rise . 1-11, 1-13
virtual distances 1-19
wake plume height 1-11
Building wake effects
see Building downwash procedures
Buoyancy flux 1-5, 1-13
Buoyancy-induced dispersion 1-29, 2-5
Buoyant plume rise
stable 1-9
unstable and neutral 1-7
Cartesian receptor network 1-3
Crossover temperature difference 1-6
Crosswind distance 1-2, 1-3, 1-4, 2-3
Decay coefficient 1-37
Decay term 1-3, 1-37
for the Long Term model 2-3, 2-6
for the Short Term model 1-37
Direction-specific building dimensions 1-21, 1-28
with Huber-Snyder downwash 1-28
Dispersion coefficients
see Dispersion parameters
Dispersion parameters
for the Long Term model 2-4
McElroy-Pooler 1-14, 1-18
Pasquill-Gifford 1-14, 1-15, 1-16, 1-17
Distance-dependent plume rise
see Gradual plume rise
Downwind distance 1-2, 1-3, 1-4, 2-3
and virtual distance : . 1-19
for area sources 1-41
for building wake dispersion 1-23
for dispersion coefficients 1-14
Dry deposition 1-3, 1-33, 1-35, 1-36, 2-8
INDEX-1
-------
for the Long Term model 2-8
for the Short Term model 1-42
in elevated terrain 1-42
Elevated terrain 1-32, 2-6
and deposition calculations 1-42
truncation above stack height 1-33
Entrainment coefficient 1-13
see also Jet entrainment coefficient
Error function term
Area sources 1-41, 1-44
Final plume rise 1-29
distance to 1-7
stable 1-9
unstable or neutral 1-7
Flagpole receptor 1-30
Gaussian plume model 1-2
sector averages for Long Term 2-1
GEP stack height 1-11, 1-28
Gradual plume rise 1-9
for buoyant plumes 1-10
for Schulman-Scire downwash 1-12, 1-13
stable momentum 1-10
unstable and neutral momentum 1-10
used for wake plume height 1-11
Gravitational settling categories . . . 1-33, 1-34, 1-35, 1-36,
1-42, 1-43, 2-9
Half life 1-37, 1-38
Huber-Snyder downwash algorithm
see Building downwash procedures
Initial lateral dimension
for the Long Term model 2-4
for volume sources 1-39, 1-40
Initial plume length
Schulman-Scire downwash 1-12
Initial plume radius
Schulman-Scire downwash 1-12
Initial vertical dimension
for volume sources 1-40
Jet entrainment coefficient 1-11, 1-13
Lateral dispersion parameters 1-15, 1-18, 1-29
for the Long Term model ............... 2-4
Lateral virtual distance
for the Long Term model 2-2, 2-4
Lateral virtual distances
for building downwash 1-25
Line source
INDEX-2
-------
approximation for Schulman-Scire sources 1-12
Line source treatment of area sources 1-40
Line sources, modeled as volumes .... 1-38, 1-39, 1-40, 2-7
Linear decay factor
Schulman-Scire downwash 1-12, 1-28
Long-term dispersion model 2-1
Mass fraction 1-34
McElroy-Pooler dispersion parameters
see Dispersion parameters 1-18
Mixing heights 1-31
Momentum flux 1-5, 1-6, 1-13
Momentum plume rise 1-11, 1-22, 1-28
stable ,1-9
unstable and neutral 1-7
Pasquill-Gifford dispersion parameters
see Dispersion parameters 1-15
Plume rise
for Schulman-Scire downwash 1-11
for the Long Term model 2-3
for the Short Term model 1-5
Point source
deposition algorithm 1-43, 2-9
dispersion parameters 1-14, 2-4
for the Long Term model 2-1
for the Short Term model 1-2
Polar receptor network 1-3
Receptors
calculation of source-receptor distances .... 1-3, 1-4
Reflection coefficient 1-35, 1-36, 1-42, 1-43, 2-9
Rural
dispersion parameters 1-14
mixing height treatment 1-31
virtual distances 1-19, 1-24
Schulman-Scire downwash algorithm 1-5
Short-term dispersion model 1-1
Sigma-y
see Lateral dispersion parameters
Sigma-z
see Vertical dispersion parameters
Smoothing function
for the Long Term model 2-2, 2-6, 2-8
Smoothing term
see Smoothing function
Stability parameter 1-8, 1-13
Stack-tip downwash 1-5
for wake plume height 1-11
Tilted plume axis 1-33
INDEX-3
-------
Uniform vertical mixing 1-31
Urban
decay term for SO2 1-38
dispersion parameters 1-14
mixing height treatment . . . . 1-31
virtual distances ..... 1-19, 1-24
Vertical dispersion parameters 1-16, 1-17, 1-18
Vertical term ..... 1-3, 1-34, 1-41, 2-5
for gases and small particulates 1-30
for large particulates 1-33, 2-6
for the deposition algorithm 1-43
for the Long Term model 2-3, 2-5
for the Short Term model 1-30
for uniform vertical mixing 1-31
in elevated terrain 1-32, 2-6
Vertical virtual distances
for building downwash 1-23, 1-24
Virtual distances . . . 1-19, 1-20, 1-27, 1-28, 1-38, 1-41, 2-8
for the Long Term model 2-4, 2-5
for volume sources 1-38
Virtual point source 1-38, 2-2, 2-7, 2-8
Volume source 1-40
deposition algorithm ... 1-43, 2-9
for the Long Term model 2-7
for the Short Term model 1-38
Wind speed
minimum wind speed for modeling 1-4
Wind speed profile 1-4, 2-3
INDEX-4
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
2.
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
User's Guide for the Industrial Source Complex (ISC2)
Dispersion Models, Volume II - Description of Model
Algorithms
5. REPORT DATE
Marrh 1QQ?
6. PERFORMING ORGANIZATION COOE
7. AUTHOR(S)
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Pacific Environmental Services, Inc.
3708 Mayfair Street, Suite 202
Durham, NC 27707
1O. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
Source Receptor Analysis Branch
Technical Support Division
U.S. Environmental Protection Agency
13. TYPE Of REPORT AND PERIOD COVERED
. SPONSORING AGENCY CODE
QQC__^_L. Tyi^nnJo
Mr 9T711
1S. SUPPLEMENTARY WOTES
16. ABSTRACT
This volume of the User's Guide for the Industrial Source Complex (ISC2) Dispersion
Models (Version 2) describes the dispersion algorithms utilized in the ISC2 models.
Much of the discussion in this document is based on Section 2.0 of the Industrial
Source Complex (ISC) Dispersion Model User's Guide - Second Edition (Revised), EPA-
450/4-88-002a (EPA, 1987). The ISC2 User's Guide has been developed as part of a
larger effort to restructure and reprogram the original ISC models, and to improve the
"end-user" documentation for the models. Volume II of the ISC2 User's Guide provides a
technical description of the dispersion algorithms utilized in the ISC2 models.
Volume III provides a guide to programmers, including a description of the structure of
the computer code and information about installing and maintaining the code on various
computer systems.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COSATI Fiekl.Group
Air Pollution
Turbulent Diffusion
Meteorology
Mathematical models
Computer model
Industrial Sources
Deposition
Downwash
Dispersion
18. DISTRIBUTION STATEMENT
Release Unlimited
19. SECURITY CLASS iTJiu Report/
Ilnr1a
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