United States
         Environmental Protection
         Agency
          Office of Air Quality
          Planning and Standards
          Research Triangle Park, NC 27711
EPA-450/4-92-008b
March 1992
         Air
xvEPA
USER'S GUIDE FOR THE
INDUSTRIAL SOURCE COMPLEX
(ISC2) DISPERSION MODELS
         VOLUME II - DESCRIPTION OF
                     MODEL ALGORITHMS

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                              EPA-450/4-92-008b
    USER'S GUIDE FOR THE
INDUSTRIAL SOURCE COMPLEX
  (ISC2) DISPERSION MODELS

 VOLUME II - DESCRIPTION OF
      MODEL ALGORITHMS
                            ction Agency
                      ,
                  77 Vi!ci"<'>. . •
                  Chicago, I
     U.S. ENVIRONMENTAL PROTECTION AGENCY
      Office of Air Quality Planning and Standards
          Technical Support Division
      Research Triangle Park, North Carolina 27711

              March 1992

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                            NOTICE
     The information in this document has been reviewed in its
entirety by the U.S. Environmental Protection Agency (EPA), and
approved for publication as an EPA document.  Mention of trade
names, products, or services does not convey, and should not be
interpreted as conveying official EPA endorsement, or
recommendation.
                              11

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                            PREFACE
     This volume of the User's Guide for the Industrial Source
Complex (ISC2) Dispersion Models (Version 2) describes the
dispersion algorithms utilized in the IS2C 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 ISC models, and to improve the
"end-user" documentation for the models.  Volume I of the ISC2
User's Guide provides user instructions for setting up and
running 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.
                              iii

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                        ACKNOWLEDGEMENTS
     The User's Guide for the original version of the ISC
Dispersion Models was written by J.F. Bowers, J.R. Bjorklund,
and C.S. Cheney (1979) of the H.E. Cramer Company, Inc., Salt
Lake City, Utah.  That work was funded by the Environmental
Protection Agency under Contract No. 68-02-3323, with George
Schewe as the Project Officer.  The second edition of the
User's Guide for the original models was prepared by David J.
Wackter and John A. Foster, TRC Environmental Consultants,
Inc., East Hartford, Connecticut.  That effort was funded by
the Environmental Protection Agency under Contract No.
68-02-3886 with Russell F. Lee as Project Officer.  The User's
Guide for the ISC2 Models has been prepared by Roger W. Erode
and JieFu Wang of Pacific Environmental Services, Inc., Durham,
North Carolina.  This effort has also been funded by the
Environmental Protection Agency under Contract No. 68D00124,
with Russell F. Lee as Work Assignment Manager.
                              IV

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                            CONTENTS

PREFACE	

ACKNOWLEDGEMENTS   	  iv

FIGURES	vi

TABLES	vii

SYMBOLS	Viii

1.0 THE  ISC2 SHORT-TERM DISPERSION MODEL EQUATIONS   .... 1-1
     1.1 POINT SOURCE EMISSIONS 	 1-2
          1.1.1 The Gaussian Equation	1-2
          1.1.2 Downwind and Crosswind Distances  	 1-3
          1.1.3 Wind Speed Profile	1-4
          1.1.4 Plume Rise Formulas	1-5
          1.1.5 The Dispersion Parameters	1-14
          1.1.6 The Vertical Term	1-30
          1.1.7 The Decay Term	1-37
     1.2 VOLUME AND AREA SOURCE EMISSIONS	1-38
          1.2.1 General	1-38
          1.2.2 The Short-Term Volume Source Model   . .  .  1-38
          1.2.3 The Short-Term Area Source Model  ....  1-40
     1.3 THE ISC2 SHORT-TERM DRY DEPOSITION MODEL ....  1-42
          1.3.1 General	1-42
          1.3.2 Point and Volume Source Emissions ....  1-43
          1.3.3 Area Source Emissions	1-44

2.0 THE ISC2 LONG-TERM DISPERSION MODEL EQUATIONS 	 2-1
     2.1 POINT SOURCE EMISSIONS 	 2-1
          2.1.1 The Gaussian Sector Average Equation  .  .  . 2-1
          2.1.2 Downwind and Crosswind Distances  	 2-3
          2.1.3 Wind Speed Profile	2-3
          2.1.4 Plume Rise Formulas	2-3
          2.1.5 The Dispersion Parameters	2-4
          2.1.6 The Vertical Term	2-5
          2.1.7 The Decay Term	2-6
          2.1.8 The Smoothing Function	2-6
     2.2 VOLUME AND AREA SOURCE EMISSIONS	2-7
          2.2.1 General	2-7
          2.2.2 The Long-Term Volume Source Model 	 2-7
          2.2.3 The Long-Term Area Source Model	2-7
     2.3 THE ISC2 LONG-TERM DRY DEPOSITION MODEL	2-8
          2.3.1 General	2-8
          2.3.2 Point and Volume Source Emissions 	 2-9
          2.3.3 Area Source Emissions	2-9

3.0 REFERENCES	3-1

INDEX

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                            FIGURES

Figure                                                     Page

1-1  LINEAR DECAY FACTOR, A AS A FUNCTION OF EFFECTIVE
     STACK HEIGHT, He.   A SQUAT BUILDING IS ASSUMED FOR
     SIMPLICITY	    1-45

1-2  ILLUSTRATION OF TWO TIERED BUILDING WITH DIFFERENT
     TIERS DOMINATING DIFFERENT WIND DIRECTIONS ....    1-46

1-3  THE METHOD OF MULTIPLE PLUME IMAGES USED TO SIMULATE
     PLUME REFLECTION IN THE ISC2 MODEL	    1-47

1-4  SCHEMATIC ILLUSTRATION OF MIXING HEIGHT INTERPOLATION
     PROCEDURES	    1-48

1-6  ILLUSTRATION OF PLUME BEHAVIOR IN COMPLEX TERRAIN
     ASSUMED BY THE ISC2 MODEL	    1-49

1-7  ILLUSTRATION OF VERTICAL CONCENTRATION PROFILES FOR
     REFLECTION COEFFICIENTS OF 0., 0.5, AND 1.0.  . . .    1-50

1-8  RELATIONSHIP BETWEEN THE GRAVITATIONAL SETTLING
     VELOCITY, V  AND THE REFLECTION COEFFICIENT, yN,
     SUGGESTED BY DUMBAULD, et al. (1976)	    1-51

1-8  EXACT AND APPROXIMATE REPRESENTATION OF LINE SOURCE BY
     MULTIPLE VOLUME SOURCES  	  1-52

1-9  REPRESENTATION OF AN IRREGULARLY SHAPED AREA SOURCE
     BY 11 SQUARE AREA SOURCES	1-53
                              vi

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                             TABLES

Table                                                      Page

1-1  PARAMETERS USED TO CALCULATE PASQUILL-GIFFORD ay  .  .  1-15

1-2  PARAMETERS USED TO CALCULATE PASQUILL-GIFFORD 
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                            SYMBOLS
Symbol                        Definition

  A    Linear decay term for vertical dispersion  in
       Schulman-Scire downwash
  D    Exponential decay term for Gaussian plume  equation
  ds    Stack inside diameter (m)
  Fb    Buoyancy flux parameter  (m4/s3)
  F,,,    Momentum flux parameter  (m4/s2)
  f    Frequency of occurrence of a wind speed and stability
       category combination
  g    Acceleration due to gravity (9.80616 m/s2)
  hb    Building height (m)
  he    Plume (or effective stack) height (m)
  hs    Physical stack height (m)
 nter   Height of terrain above stack base (m)
 hs'   Release height modified for stack-tip downwash  (m)
  h^    Crosswind projected width of building adjacent  to  a
       stack (m)
  Ly    Initial plume length for Schulman-Scire downwash
       sources with enhanced lateral plume spread
  1^    Lesser of the building height and crosswind projected
       building width (m)
  p    Wind speed power law profile exponent
  QA    Area Source pollutant emission rate (g/s)
  Qs    Pollutant emission rate (g/s)
  QT    Total amount of pollutant emitted during time period  T
  R0    Initial plume radius for Schulman-Scire downwash
       sources
  r    Radial distance range in a polar receptor  network
                             viii

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 s    Stability  parameter  =
                               ••»

 S    Smoothing  term for smoothing across adjacent sectors in
      the  Long Term model

 Ta    Ambient  temperature  (K)

 Ts    Stack gas  exit temperature (K)

uref   Wind speed measured  at reference anemometer height
      (m/s)

 us    wind speed adjusted  to release  height (m/s)

 V    Vertical term of  the Gaussian plume equation

 vs    Stack gas  exit velocity  (m/s)

 X    X-coordinate  in a Cartesian  grid receptor network

 x0    Length of  side of square area source (m)

 Y    Y-coordinate  in a Cartesian  grid receptor network

 0    Direction  in  a polar receptor network

 x    Downwind distance from source to receptor (m)

 Xy    Lateral  virtual point source distance (m)

 xz    Vertical virtual  point source distance (m)

 xf    Downwind distance to final plume rise (m)

 x*    Downwind distance at which turbulence dominates
      entrainment  (m)

 y    Crosswind  distance from  source  to receptor (m)

 zr    Receptor height above ground (i.e.  flagpole)  (m)

 z{    Mixing height (m)

 6    Entrainment coefficient  used in buoyant rise for
      Schulman-Scire downwash  sources =0.6

 6    Jet  entrainment coefficient  used in gradual momentum
plume rise calculations
*                          3
                                -+— -
                             IX

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  Ah    Plume rise (m)

dQ/dz  Potential temperature gradient with height (K/m)

  Y    Reflection coefficient for large particulates

  rr    pi  = 3.14159

  t    Decay coefficient - 0.693/T1/2 (s'1)

  0    Fraction of mass in a particular settling velocity
       category for  large particulates

  a    Horizontal (lateral)  dispersion parameter (m)

  a^    Initial  horizontal dispersion parameter for virtual
       point source  (m)

  
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       1.0 THE ISC2 SHORT-TERM DISPERSION MODEL EQUATIONS
     The Industrial Source Complex  (ISC2) dispersion models
described in this  document refer to restructured and
reprogrammed versions of the original ISC models described in
the ISC Dispersion Model User's Guide - Second Edition
(Revised) (EPA,1987).  The models were reprogrammed in order to
improve the quality of the computer code, to improve the user
interface, and to  improve the end user documentation of the
models.
     The Industrial Source Complex  (ISC2) Short Term dispersion
model provides options to model emissions from a wide range of
sources that might be present at a typical industrial source
complex.  The basis of the model is the straight-line,
steady-state Gaussian plume equation, which is used with some
modifications to model simple point source emissions from
stacks, emissions  from stacks that experience the effects of
aerodynamic downwash due to nearby buildings, isolated vents,
multiple vents, storage piles, conveyor belts, and the like.
Emission sources are categorized into three basic types of
sources, i.e., point sources, volume sources, and area sources.
The volume source  option may also be used to simulate line
sources.  The algorithms used to model each of these source
types are described in detail in the following sections.  The
point source algorithms are described in Section 1.1.  The
volume and area source model algorithms are described in
Section 1.2.  Section 1.3 gives the optional algorithms for
calculating dry deposition for point, volume and area sources.
     The ISC2 Short Term model accepts hourly meteorological
data records to define the conditions for plume rise, transport
and diffusion.  The model estimates the concentration or
deposition value for each source and receptor combination for
each hour of input meteorology, and calculates user-selected
short-term averages.  The user also has the option of selecting
averages for the entire period of input meteorology.
                              1-1

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1.1 POINT SOURCE EMISSIONS
     The ISC2 Short Term dispersion model uses a steady-state
Gaussian plume equation to model emissions from point sources,
such as stacks, isolated vents, and the like.  This section
describes the Gaussian point source model, including the basic
Gaussian equation, the plume rise formulas, and the formulas
used for determining dispersion parameters.

1.1.1 The Gaussian Equation
     The ISC2 short term concentration model for stacks uses
the steady-state Gaussian plume equation for a continuous
elevated source.  For each source and each hour, the origin of
the source's coordinate system is placed at the ground surface
at the base of the stack.  The x axis is positive in the
downwind direction, the y axis is crosswind (normal) to the x
axis and the z axis extends vertically.  The fixed receptor
locations are converted to each source's coordinate system for
each hourly concentration calculation.  The hourly
concentrations calculated for each source at each receptor are
summed to obtain the total concentration produced at each
receptor by the combined source emissions.
     The hourly concentration at downwind distance x (meters)
and crosswind distance y (meters) is given by:
                               exp
                       27CUaOy02

where:
       Q  =  pollutant emission rate (mass per unit time)
       K  =  a scaling coefficient to convert calculated
             concentrations to desired units (default value of
             1 x 106 for Q in g/s and concentration in /ig/m3)
       V  =  vertical term (See Section 1.1.6)
       D  =  decay term (See Section 1.1.7)
                              1-2

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If the X and Y coordinates of the source are X(S)  and Y(S),  the
downwind distance x to the receptor, along the direction of
plume travel, is given by:
          x = -(X(R) -X(S))sin(WD) - (Y(R) - Y(S)) cos (WD)     (1-4)

where WD is the direction from which the wind is  blowing.  If
any receptor is located within 1 meter of a source,  a warning
message is printed and no concentrations are calculated  for  the
source-receptor combination.  The crosswind distance y to the
receptor from the plume centerline is given by:
          y = (X(R) -X(S) )COS(WD) - (Y(R) -Y(S) )sin(WD)      (1-5)
1.1.3 Wind Speed Profile
     The wind power law is used to adjust the observed wind
speed, uref, from a reference measurement height, zpef, to the
stack or release height, hs.   The equation is of the form:
                                                           d-6)
where p is the wind profile exponent.  Values of p may be
  •
provided by the user as a function of stability category and
wind speed class.  Default values are as follows:


  Stability Category	Rural Exponent	Urban Exponent
A
B
C
D
E
F
0.07
0.07
0.10
0.15
0.35
0.55
0.15
0.15
0.20
0.25
0.30
0.30
     The stack height wind speed, ug,  is not allowed to be less
than 1.0 m/s.
                              1-4

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1.1.4 Plume Rise Formulas
     The Briggs plume rise equations are discussed  below.   The
description follows Appendix B of the Addendum to the MPTER
User's Guide  (Chico and Catalano, 1986) for plumes  unaffected
by building wakes.  The distance dependent momentum plume  rise
equations, as described in (Bowers, et al., 1979),  are used to
determine if the plume is affected by the wake region for
building downwash calculations.  These plume rise calculations
for wake determination are made assuming no stack-tip downwash
for both the Huber-Snyder and the Schulman-Scire methods.   When
the model executes the building downwash methods of Schulman
and Scire, the reduced plume rise suggestions of Schulman  and
Scire (1980) are used.

     1.1.4.1 Stack-tip Downwash.
     In order to consider stack-tip downwash, modification of
the physical stack height is performed following Briggs (1974,
p. 4).  The modified physical stack height hs'  is found from:

        ha'  =hs + 2d8|li-1.5J    for  va<1.5ug

                                                           (1-7)
 or

        hs'  = hs                for  v8£l.5uB

where hs  is  physical  stack height (m) ,  vs is stack gas exit
velocity (m/s), and ds is  inside  stack  top  diameter  (m) .  This
hs'  is used  throughout the remainder of the plume height
computation.  If stack tip downwash is not considered,  hs'  = hs
in the following equations.
                              1-5

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     1.1.4.2 Buoyancy and Momentum Fluxes.
     For most plume rise situations, the value of  the Briggs
buoyancy flux parameter, Fb (m4/s3) , is needed.  The following
equation is equivalent to Equation (12), (Briggs,  1975,  p.  63):

                                                           d-8)
where AT = Ts - Ta, T8 is stack gas temperature  (K) , and Ta is
ambient air temperature (K) .
     For determining plume rise due to the momentum of the
plume, the momentum flux parameter, Fm (m4/s2) ,  is calculated
based on the following formula:
                                                           (1-9)
     1.1.4.3 Unstable or Neutral - Crossover Between Momentum
     and Buoyancy .
     For cases with stack gas temperature greater than or equal
to ambient temperature, it must be determined whether  the plume
rise is dominated by momentum or buoyancy.  The crossover
temperature difference, (AT)C,  is determined by setting Briggs1
(1969, p. 59) Equation 5.2 equal to the combination of Briggs1
(1971, p. 1031) Equations 6 and 7, and solving for AT,  as
follows:
for Fb <  55,

                      (AT)C = 0.0297TS^7-                 (1-10)
                                      vfl1/3
and for Fb > 55,
                      (AT)C = 0.00575Ta^|7I                (1-H)


If the difference between  stack gas and ambient temperature,
AT, exceeds or equals  (AT)C,  plume rise is assumed to be •
                              1-6

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buoyancy dominated,  otherwise  plume rise is assumed to be
momentum dominated.

     1.1.4.4 Unstable  or Neutral  - Buoyancy Rise.
     For situations  where  AT exceeds (AT)C as determined  above,
buoyancy is assumed  to dominate.   The distance  to  final rise,
xf, is determined from the equivalent of Equation  (7),  (Briggs,
1971, p. 1031), and  the distance  to final rise  is  assumed to be
3.5x*,  where x* is the  distance at which atmospheric turbulence
begins to dominate entrainment.   The value of xf is calculated
as follows:
for Fb < 55:
and for Fb £ 55:
                                                          (1-12)
                           x = 119F£/5                     (1-13)
     The final effective plume height, he (m) , is determined
from the equivalent of the combination of Equations  (6)  and (7)
(Briggs, 1971, p. 1031) :
for Fb < 55:
                       he = h/ + 21.425^-                 (1-14)
                                      ua
and for Fb > 55:
                       he = h/ + 38.71-^—                  (1-15)


     1.1.4.5 Unstable or. Neutral ^ Momentum Rise.
     For situations where the  stack gas temperature  is  less
than or equal to the ambient air temperature, the assumption is
made that the plume rise is dominated by momentum.   If  AT is
less than (AT)C from Equation (1-10)  or (1-11),  the assumption
is also made that the plume rise is dominated by momentum.   The
                              1-7

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plume height is calculated from Equation  (5.2)  (Briggs,  1969,
p. 59):
                        h.- V +3ds
Briggs (1969, p. 59) suggests that this equation is most
applicable when vs/us is greater than 4.

     1.1.4.6 Stability Parameter .
     For stable situations, the stability parameter, s, is
calculated from the Equation (Briggs, 1971, p. 1031) :
                                                          d-i7)
                                 Aa

As a default approximation, for stability class E  (or 5)  dQ/dz
is taken as 0.020 K/m, and for class F (or 6), dQ/dz is taken
as 0.035 K/m.

     1.1.4.7 Stable - Crossover Between Momentum and Buovancv .
     For cases with stack gas temperature greater than or equal
to ambient temperature, it must be determined whether the plume
rise is dominated by momentum or buoyancy.  The crossover
temperature difference, (AT)C ,  is  determined by setting
Briggs1 (1975, p. 96) Equation 59 equal to Briggs1  (1969, p.
59) Equation 4.28, and solving for AT, as follows:

                     (AT) c =  0.019582 Tsva^/S                (1-18)

If the difference between stack gas and ambient temperature,
AT, exceeds or equals (AT)C,  plume  rise is assumed to be
buoyancy dominated, otherwise plume rise is assumed to be
momentum dominated.
                              1-8

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     1.1.4.8 Stable - Buoyancy Rise.
     For situations where AT exceeds  (AT)C as determined above,
buoyancy is assumed to dominate.  The distance to  final rise,
xf,  is determined by the equivalent of a combination of
Equations  (48) and  (59) in Briggs,  (1975), p. 96:

                        xf = 2.0715 -^                   (1-19)
                                     v/s

     The plume height, he,  is determined by the equivalent of
Equation (59) (Briggs, 1975, p. 96):
                                   ( P  X1/3
                      he »V + 2.6  -1M                   d-20)
                                   (uB3)

     1.1.4.9 Stable - Momentum Rise.
     Where the stack gas temperature is less than  or equal to
the ambient air temperature, the assumption is made that the
plume rise is dominated by momentum.  If AT is less than  (AT)C
as determined by Equation (1-18), the assumption is also made
that the plume rise is dominated by momentum.  The plume height
is calculated from Equation 4.28 of Briggs ((1969), p. 59):
                      he = h/ + i.s|-l=-|                  (1-21)
The equation for unstable-neutral momentum rise  (1-16) is also
evaluated.  The lower result of these two equations is used as
the resulting plume height.

     1.1.4.10 All Conditions - Distance Less Than Distance to
     Final Rise.
     Where gradual rise is to be estimated for unstable,
neutral, or stable conditions, if the distance downwind from
source to receptor, x, is less than the distance to final rise,
                              1-9

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the equivalent of Equation 2 of Briggs  ((1972), p.  1030)  is
used to determine plume height:

                                                          d-22)

This height will be used only for buoyancy dominated
conditions; should it exceed the final rise for the  appropriate
condition, the final rise is substituted instead.
     For momentum dominated conditions, the following equations
(Bowers, et al, 1979) are used to calculate a distance
dependent momentum plume rise:
  a) unstable conditions;

where x is the downwind distance  (meters) , with  a maximum value
defined by x^ as follows:

                  4ds(vs + 3us)2
= 49F|/8
= 119Fb/5
  b) stable conditions :
                  he = V
             3F,
                                    _
                                    f OI  Fb -
                                   for 0 < Fb i 55m4/s3
                                   for Fb > 55m4/s3

(1-25)
where x is the downwind distance  (meters) , with  a maximum value
defined by x^ as follows:
                                                          (1-26)
                              1-10

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The jet entrainment coefficient, &.}, is given by,

                          P  . 1 + ±L                     (1-27)
                           j   3   V8

As with the buoyant gradual rise, if the distance-dependent
momentum rise exceeds the final rise for the appropriate
condition, then the final rise is substituted instead.

     1.1.4.10.1 Calculating the plume height for wake effects
     determination.
     The building downwash algorithms in the ISC2 models always
require the calculation of a distance dependent momentum plume
rise.  When building downwash is being simulated, the equations
described above are used to calculate a distance dependent
momentum plume rise at a distance of two building heights
downwind from the leeward edge of the building.  However,
stack-tip downwash is not used when performing this calculation
(i.e. hs'  = hg).  This wake plume height is compared to the
wake height based on the GEP formula to determine whether the
building wake effects apply to the plume for that hour.
     The procedures used to account for the effects of building
downwash are discussed more fully in Section 1.1.5.3.  The
plume rise calculations used with the Schulman-Scire algorithm
are discussed in Section 1.1.4.11.

     1.1.4.11 Plume Rise When Schulman and Scire Building
     Downwash is Selected.
     The Schulman-Scire downwash algorithms are used by the
ISC2 models when the stack height is less than the building
height plus one half of the lesser of the building height or
width.  When these criteria are met, the ISC2 models estimate
plume rise during building downwash conditions following the
suggestion of Scire and Schulman (1980).  The plume rise during
building downwash conditions is reduced due to the initial
dilution of the plume with ambient air.
                              1-11

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     The plume rise is estimated as follows.  The initial
dimensions of the downwashed plume are approximated by a line
source of length 1^ and depth 2R0 where:
    R0 = V2A02         x = 3LB

    Ly = V2*(oy-oz)     x = 3LB,  ay*oz                      (l-29a)

    Ly = 0             x = 3LB,   the  initial  plume
would be represented by a circle of radius R0.  The 
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The stable distance-dependent rise  is calculated by:
             p;     i «P2   P2 J     2p2ua3
with a maximum stable buoyant rise given by:
                                                      s
                                                      s
   73 + ifia + ±±2  72 +  OKoH + ^K°  z .   orb             (i-3ib)
       UP    P J     I np2     P2 J     P2u8s
where:
    Fb  = buoyancy flux term  (Equation 1-8)  (m4/s3)
    FM  = momentum flux term  (Equation 1-9)  (m4/s2)
    x  = downwind distance  (m)
    us  = wind speed  at release height (m/s)
    vs  = stack exit  velocity  (m/s)
    ds  = stack diameter (m)
    8  = entrainment coefficient  (=0.6)
    g.  = jet entrainment coefficient   = — +—-

   s   = stability parameter  =

The larger of momentum and buoyant rise,  determined  separately
by alternately setting Fb or Fm =  0 and solving for Z,  is
selected for plume height calculations for  Schulman-Scire
downwash.  In the ISC2 models, Z  is determined by  solving  the
cubic equation using Newton's method.
                              1-13

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1.1.5 The Dispersion Parameters

     1.1.5.1 Point Source Dispersion Parameters .
     Equations that approximately fit the Pasquill-Gifford
curves (Turner, 1970) are used to calculate a  and az (in
meters) for the rural mode.  The equations used to calculate  cry
are of the form:
                    oy = 465. 11628 (x) tan (TH)               (1-32)

where :
                  TH = 0.017453293 [C -din (x)l              (1-33)

In Equations (1-32) and (1-33) the downwind distance x  is in
kilometers, and the coefficients c and d are listed  in  Table
1-1.  The equation used to calculate az is of  the form:
                            a  = axb                       (1-34)
where the downwind distance x is in kilometers and CTZ is in
meters.  The coefficients a and b are given in Table 1-2.
     Tables 1-3 and 1-4 show the equations used to determine  ay
and CTZ for the urban option.   These expressions were determined
by Briggs as reported by Gifford (1976) and represent a best
fit to urban vertical diffusion data reported by McElroy and
Pooler (1968) .  The Briggs functions are assumed to be valid
for downwind distances less than 100m.  However, the user  is
cautioned that concentrations at receptors less than 100m  from
a source may be suspect.
                              1-14

-------
                           TABLE 1-1
        PARAMETERS USED TO CALCULATE PASQUILL-GIFFORD ay
                                      CT -  465.11628  (x)tan(TH)
                                TH -  0.017453293  [c  -  d ln(x)]
       Pasguill
      Stability
       Category
          A
          B
          C
          D
          E
          F
24.1670
18.3330
12.5000
 8.3330
 6.2500
 4.1667
2.5334
1.8096
1.0857
0.72382
0.54287
0.36191
where CT  is in meters and x is in kilometers
                             1-15

-------
                      TABLE 1-2

  PARAMETERS USED TO CALCULATE PASQUILL-GIFFORD  Oz
Pasquill
Stability
Category
A*








B*


C'
D





x (km)
<.10
0.10 - 0.15
0.16 - 0.20
0.21 - 0.25
0.26 - 0.30
0.31 - 0.40
0.41 - 0.50
0.51 - 3.11
>3.11
<.20
0.21 - 0.40
>0.40
All
<.30
0.31 - 1.00
1.01 - 3.00
3.01 - 10.00
10.01 - 30.00
>30.00
az (meters) = ax1*
a
122.800
158.080
170.220
179.520
217.410
258.890
346.750
453.850
**
90.673
98.483
109.300
61.141
34.459
32.093
32.093
33.504
36.650
44.053
(x in km)
b
0.94470
1.05420
1.09320
1.12620
1.26440
1.40940
1.72830
2.11660
**
0.93198
0.98332
1.09710
0.91465
0.86974
0.81066
0.64403
0.60486
0.56589
0.51179
If the calculated value of az exceed 5000 m,  az  is  set to
5000 m.

CTZ is equal  to 5000 m.
                         1-16

-------
                   TABLE  1-2
                   (CONTINUED)

PARAMETERS USED TO CALCULATE PASQUILL-GIFFORD ffz
Pasquill
Stability
Category x
E <
0.10
0.31
1.01
2.01
4.01
10.01
20.01
(km)
.10
- 0.30
- 1.00
- 2.00
- 4,00
- 10.00
- 20.00
- 40.00
>40.00
F <
0.21
0.71
1.01
2.01
3.01
7.01
15.01
30.01
.20
- 0.70
- 1.00
-2.00
- 3.00
- 7.00
- 15.00
- 30.00
- 60.00
>60.00
ff2( meters) = axb
a
24.260
23.331
21.628
21.628
22.534
24.703
26.970
35.420
47.618
15.209
14.457
13.953
13.953
14.823
16.187
17.836
22.651
27.074
34.219
(x in km)
b
0.83660
0.81956
0.75660
0.63077
0.57154
0.50527
0.46713
0.37615
0.29592
0.81558
0.78407
0.68465
0.63227
0.54503
0.46490
0.41507
0.32681
0.27436
0.21716
                      1-17

-------
                       TABLE 1-3
 BRIGGS  FORMULAS USED TO CALCULATE MCELROY-POOLER ff..
       Pasguill
      Stability
       Category
          a (meters)'
          A
          B
          C
          D
          E
          F
0.32 X  (1.0 +  0.0004 x)'1/2
0.32 X  (1.0 +  0.0004 X)'1/2
0.22 X  (1.0 +  0.0004 X)'1/2
0.16 X  (1.0 +  0.0004 X)'1/2
0.11 X  (1.0 +  0.0004 X)'1/2
0.11 X  (1.0 +  0.0004 X)"1/2
Where x is  in meters

                       TABLE 1-4
 BRIGGS FORMULAS USED TO CALCULATE MCELROY-POOLER a.
       Pasguill
      Stability
       Category
          az (meters)'
          A
          B
          C
          D
          E
          F
0.24 x (1.0 + 0.001  x)1/2
0.24 x (1.0 + 0.001  x)1/2
0.20
0.14 X (1.0 + 0.0003 X)"1/2
0.08 x (1.0 + 0.0015 X)"1/2
0.08 X (1.0 + 0.0015 X)"1/2
Where x is  in meters.
                         1-18

-------
     1.1.5.2 Lateral and Vertical Virtual Distances.
     The equations in Tables 1-1 through 1-4 define the
dispersion parameters for an ideal point source.  However,
volume sources have initial lateral and vertical dimensions.
Also, as discussed below, building wake effects, can enhance the
initial growth of stack plumes.  In these cases, lateral  (Xy)
and vertical (xz)  virtual distances are added by the ISC2
models to the actual downwind distance x for the ay and az
calculations.  The lateral virtual distance in kilometers for
the rural mode is given by:
                          ^-l-"]                       f1-35'
                               \ p /
where the stability-dependent coefficients p and q are given in
Table 1-5 and a^n  is the standard deviation in meters of the
               yo
lateral concentration distribution at the source.  Similarly,
the vertical virtual distance in kilometers for the rural mode
is given by:
*b!30Wt
-------
stability classes D, E, and F.  The cubic equations are solved
using Newton's method.

                           TABLE 1-5
    COEFFICIENTS  USED  TO CALCULATE LATERAL VIRTUAL  DISTANCES
             FOR PASQUILL-GIFFORD DISPERSION RATES
f „ \ 1/1
«.-(*)
Pasquill
Stability
Category
A
B
C
D
E
F
P
209.14
154.46
103.26
68.26
51.06
33.92
q
0.890
0.902
0.917
0.919
0.921
0.919
     1.1.5.3 Procedures Used to Account for the Effects of
     Building Wakes on Effluent Dispersion.
     The procedures used by the ISC2 models to account for the
effects of the aerodynamic wakes and eddies produced by plant
buildings and structures on plume dispersion originally
followed the suggestions of Huber (1977) and Snyder (1976).
Their suggestions are principally based on the results of
wind-tunnel experiments using a model building with a crosswind
dimension double that of the building height.  The atmospheric
turbulence simulated in the wind-tunnel experiments was
intermediate between the turbulence intensity associated with
the slightly unstable Pasquill C category and the turbulence
intensity associated with the neutral D category.  Thus, the
data reported by Huber and Snyder reflect a specific stability,
building shape and building orientation with respect to the
mean wind direction.  It follows that the ISC2 wake-effects
evaluation procedures may not be strictly applicable to all
                              1-20

-------
situations.  The ISC2 models also provide for the revised
treatment of building wake effects for certain sources, which
uses modified plume rise algorithms, following the suggestions
of Schulman and Hanna (1986).  This treatment is largely based
on the work of Scire and Schulman (1980).  When the stack
height is less than the building height plus half the lesser of
the building height or width, the methods of Schulman and Scire
are followed.  Otherwise, the methods of Huber and Snyder are
followed.  In the ISC2 models, direction-specific building
dimensions may be used with either the Huber-Snyder or
Schulman-Scire downwash algorithms.
     The wake-effects evaluation procedures may be applied by
the user to any stack on or adjacent to a building.  For
regulatory application,  a building is considered sufficiently
close to a stack to cause wake effects when the distance
between the stack and the nearest part of the building is less
than or equal to five times the lesser of the height or the
projected width of the building.  For downwash analyses with
direction-specific building dimensions, wake effects are
assumed to occur if the stack is within a rectangle composed of
two lines perpendicular to the wind direction, one at 5L,,
downwind of the building and the other at 21^ upwind of the
building, and by two lines parallel to the wind direction, each
at 0.5L,, away from each  side  of  the  building,  as  shown below:
              Wind direction
                Building
                                                       1/2
                                                       1/2
                                   -5V
                              1-21

-------
1^ is the lesser of the height and projected width of the
building for the particular direction sector.  For additional
guidance on determining whether a more complex building
configuration is likely to cause wake effects, the reader is
referred to the Guideline for Determination of Good Engineering
Practice Stack Height  (Technical Support Document for the Stack
Height Regulations) - Revised (EPA, 1986).  In the following
sections, the Huber and Snyder building downwash method, as
used in all versions of ISC, are described followed by a
description of the Schulman and Scire building downwash method.

     1.1.5.3.1 Huber and Snyder building downwash procedures.
     The first step in the wake-effects evaluation procedures
used by the ISC2 model programs is to calculate the gradual
plume rise due to momentum alone at a distance of two building
heights using Equation (1-23) or Equation (1-25).  If the plume
height, he,  given by the sum of  the stack height (no stack-tip
downwash adjustment) and the momentum rise is greater than
either 2.5 building heights (2.5 \)  or  the  sum of the building
height and 1.5 times the building width (\  + 1.5  hj , the
plume is assumed to be unaffected by the building wake.
Otherwise the plume is assumed to be affected by the building
wake.
     The ISC2 model programs account for the effects of
building wakes by modifying both a  and  az for plumes with
plume height to building height ratios less than or equal to
1.2 and by modifying only az for plumes  from stacks with plume
height to building height ratios greater than 1.2 (but less
than 2.5).  The plume height used in the plume height to stack
height ratios is the same plume height used to determine if the
plume is affected by the building wake.   The ISC2 models
defines buildings as squat (h^ > hb) or tall  (hw < hb) .   The
ISC2 models includes a general procedure for modifying az and
cry at distances  greater than or  equal to 3hb for squat

                              1-22

-------
buildings or 3hw for tall buildings.  The air flow in the
building cavity region  is both highly turbulent and  generally
recirculating.  The  ISC2 models  are not  appropriate  for
estimating concentrations within such regions.   The  ISC2
assumption that this recirculating  cavity region extends to a
downwind distance of 31^ for a squat building or 3hu  for a tall
building is most appropriate  for a  building whose width is not
much greater than its height.  The  ISC2  user is cautioned that,
for other types of buildings, receptors  located at downwind
distances of 3hb (squat buildings) or 3hu (tall  buildings) may
be within the recirculating region.
     The modified az equation for a squat building is given by:

    oz' = 0.7hb + 0.067 (x-3hb)    for  3hb<;x
-------
account for the enhanced initial plume growth caused by the
building wake.  The virtual distance is calculated  from
solutions to the equations for rural or urban sigmas provided
earlier.
     As an example for the rural options, Equations (1-34)  and
(1-37) can be combined to derive the vertical virtual distance
xz for a squat building.   First,  it follows from Equation
(1-37) that the enhanced az is equal to 1.2hb at a downwind
distance of 101^ in meters or O.Olh^ in kilometers.   Thus,  xz
for a squat building is obtained from Equation  (1-34)  as
follows:

               oz  {0.01hb} = 1.2hb = a(0.01hb  + xz)b         (1-39)

                         (•\ ?h Wb
                     xz = I 1'2h*>    - o.01hb                U

where the stability-dependent constants a and b are given  in
Table 1-2.  Similarly, the vertical virtual distance for tall
buildings is given by:
                     x, =
For the urban option, xz is calculated from solutions to the
equations in Table 1-4 for az = 1.21^  or CTZ = 1.2 hy for tall or
squat buildings, respectively.
                              1-24

-------
     For a squat building with  a  building width to building
height ratio \/\  less than or  equal to 5, the modified ay
equation is given  by:

    oy'  = O.ash,, + 0.067(x-3hb)    for  3hbsx
-------
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

-------
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

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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

-------
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

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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

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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

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                         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

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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

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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

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                             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

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     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

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     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

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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

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                                     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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