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                                      A3 7

       To fix these ideas, consider two photographs of the same continuous
plume taken from above:  one is a snapshot and the other is a time exposure
(Figure A.I).  The plume in the snapshot is observed to follow a meandering path
called the streakline.  The width of the plume at any point is simply the actual
physical spread of material about the instantaneous position of the plume center-
line.  In the time exposure, however, the plume appears to follow a much straighter
path and is characterized by a much wider and more smoothly varying cross-section.
The longer the exposure, the wider the cross-section appears.  The time exposure
shows only the mean wind direction over the exposure time, and the observed dis-
persion about the apparent plume centerline represents not only the physical
spread but also the time-average effects of the meandering of the plume.  Thus,
meanders in the plume which take place over periods of time shorter than the
exposure, or averaging, time are considered part of the dispersion.  The snapshot
clearly exhiDi..^ the effects of the short-term wind fluctuations responsible for
meander i.ig.
       The practical consequence is that for the horizontal case the extent of
the dispersion about the mean plume centerline depends on the averaging time.
This effect dots not occur for vertical dispersion for averaging times longer
than about ten minutes due to absence of fluctuations in the vertical component
of the wind over these time scales.
       The example just given considered the case of a continuous release.  A
snapshot of the pollutant distribution following an instantaneous release during
non-calm conditions shows a cloud of material centered at some point downwind of
tha source, whereas a time exposure shows a meandering path originating at the
source.  In both pictures, the observed extent of the dispersion represents the
actual crosswimi spread of material in the cloud, although dispersion in the
downwind direction is not shown in the time exposure.  Meandering in the path
followed by the cloud should clearly not be treated as part of the dispersion
of the cloud.

       Based on this type of consideration, and assuming that only the mean
wind speed and direction are known over the averaging cim? o.t interest,
meandering should be considered part of the process of hori/;oncaj. dispersiou
from a point source when both the following conditions are met.

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                                     A38

          It'e duration of the release is greater than the
          averaging time, and
       *  The averaging time is greater than the source-
          ret, eptor travel time.
 If these conditions are not met, more information about the wind  field  is
 required so that a more realistic description of the actual trajectory
 followed by the pollutant emission may be obtained.  In particular,  variations
 in the wind which occur over times greater than the averaging  time but  less
 than  the travel time should be explicitly taken into account either  by  assump-
 tion  or by actual calculation of the trajectory.   (See Appendix A.3  for a  dis-
 cussion of treatments of the wind field.)
       The initial size of the emission determines the relative Importance
 of any further dispersion in either the horizontal or vertical direction.
 The larger a plume or cloud of pollutant, the slower is the relative rate
 of growth due to the action of atmospheric, turbulence because as  the plume
 grows an increasingly large part of the turbulence acts over too  small  a
 scale to be effective.  The effect on the horizontal dispersion estimates
 of changing the averaging time is also diminished for extended sources  such
 as lines and areas for the same reason.
       In order to quantitatively estimate the extent or rate of  dispersion
 under specified conditions,  the effect of those factors which detfrn'ir.e the
 intensity of atmospheric turbulence must be suitably parameter:! ".e.:i .  oecause
 dispersion is a direct result of the action of turbulence.  The must important
 factors governing the production of turbulence are:
       •   The wind speed,
          The roughness of the ground surface,  and
          The flux of heat being transferred between the
          ground surface and the air.
 The first two factors govern the mechanical generation of turbulence by friction
 due to the variation of wind speed with height (wind shear), itself caused by
 the frictional interaction between the general flow of the wind and the rough-
ness  of the surface.  The third governs the thermal generation of turbulence
due to surface heating.   The surface heat flux itself depends on:
          The solar angle (during the day),
          The extent of cloud cover (both day and night),

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                                     A39
       •  Thermal properties of the ground surface, and
       •  The extent of anthropogenic heat generation
          (in urban areas).
       In discussing atmospheric turbulence and dispersion, it is convenient
to introduce the concept of atmospheric stability.  At a given height, the
atmosphere may be classified as unstable^, neutral, or stable according to
whether the rate of decrease of temperature with height (the lapse rate) is
less than, equal to, or greater than a critical value called the dry adiabatic
lapse rate (equal to approximately 14C/100 meters), as shown in Table A.2.
The significance of this classification is that near the ground, high levels of
 turbulence  and high rates of  dispersion are  generally  associated with unstable
 conditions  and low  levels of  turbulence with stable conditions.   The terms
 used  in the classification are in  fact  descriptive of  the  effects of the
 different types  of  temperature gradient on vertical turbulent  motions,  vertical
 motion  being enhanced  under unstable conditions  and suppressed under stable
 conditions.   A temperature inversion is said to  exist  when the lapse rate is
 negative  (temperature  increasing with height).   The atmosphere is extremely
 stable  within an inversion and turbulence,is strongly  suppressed. As  a con-
 sequence  both the rate of vertical dispersion and  the  actual physical  spread
 of a  plume  in the horizontal  direction  are strongly suppressed,  although
 considerable meandering of  the plume can occur.

      Table  A.2.  General  Atmospheric Stability Classification  According
                  to  Temperature Lapse Rate3

 Relation  of  Actual  Lapse  Rate to the                Atmospheric  Stability
 Dry Adiabatic Lapse  Rate                             Classification
          Greater than                                    Unstable
          Equal  to                                        Neutral
          Less than                                       Stable
 o
 This classification is not the same as the  widely  used Pasquill  stability
 classification  scheme.

        The  temperature profile near  the ground  is  itself determined  by the
 same  factors listed  above as  being significant  determinants of atmospheric
 turbulence.   At any  given time, the  difference  between the actual lapse rate
 and the dry adiabatic  lapse rate is  determined  by  the  balance  between  two

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                                     A40
competing effects:  1) the addition to or removal from the air of heat energy
due to solar heating or radiational cooling of the ground surface, tending to
produce unstable or stable conditions respectively, and 2) the tendency of the
turbulence itself, whether mechanically or thermally generated* to smooth out
the temperature profile and produce neutral conditions.
       In order for an atmospheric dispersion model to be useful in a variety
of meteorological situations, some convenient measure of atmospheric stability
or  turbulence  intensity  is used  to determine  the appropriate values pf those
model parameters  (such as a  and a   in Gaussian plume models) which determine
the predicted  extent  or  rate of  dispersion,   A number of  different meteorolo-
gical parameters  or classification schemes have been used for this purpose and
an  increasing  number  of  models make  use of the more fundamental  measures of
turbulence  intensity.  Some of the more commonly used ones are given  in
Table A.3.   The user  should consult  a standard reference  (e.g.,  Slade, 1968)
or  an air pollution meteorologist  for the definitions of  the Richardson number
or  the Monin-Obukhov  length if the model being evaluated  makes use of one of
these parameters.  A  discussion  of the Pasquill-Gifford classification scheme
is  given by Turner (1969)  and the Brookhaven scheme is discussed by  Singer
and Smith (1966).  A  review of various systems for characterizing turbulence
is  given by Gifford (1976).
       The  basic  factors which determine atmospheric stability near the
ground have already been mentioned.  The dependence of these factors  on the
time of  day, the  nature  of the topography, and the nature  of the ground sur-
face gives  rise to certain characteristics of which the user should be aware.
       Atmospheric stability near the ground  undergoes very significant diurnal
variations  due to the  rising and setting of the sun.  On  sunny days,  the ground
is  warmed and  heat is  added to the air near the surface, causing  the air tempera-
ture to  rise and  producing unstable  conditions.  On clear nights, the ground cools
more rapidly than the  air, heat  is removed from the air near the ground, and a
ground-based "radiation  inversion" is produced.  At any time, cloud cover tends
to  balance  the exchange  of heat  and  produce neutral conditions.
        There  are important differences between urban and rural areas.  Urban
 areas are normally much rougher than the surrounding rural areas, and the heat
 produced by anthropogenie activity in the city is an important factor at
 night all year round as well as during the daytime in winter.   The combination
 of these factors results in substantially higher levels of turbulence,  and

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                                     A41
         Table A.3.  Commonly Used Measures of Atmospheric Stability
                     and Turbulence Intensity
       Continuous Measures
1.  Temperature gradient or, equivalently,  temperature difference between
    two reference heights.

»•  s-f  H                          -                       .       ..".
                                                                  •
        38 •                                                  •
        *— * (dry adiabatic lapse rate)-(ambient lapse rate)
        "z                                                    •
           = (l°C/100m + 3T/3z)
       g * acceleration due to gravity.
       T = ambient temperature.
       (S is negative in unstable conditions,  zero in neutral
        conditions and positive in stable conditions.)
3.  Standard deviation of the horizontal component of the wind direction
    (a,) or of the vertical component (0.).
4.  Richardson number.
5.  Monin-Obukhov length.
       Discrete Classification Schemes
1.  Pasquill-Gifford stability classification.
2.  Brookhaven gustiness classification.

correspondingly higher rates of dispersion,  over cities during both day and
night.  The frequency of surface inversions  is  much lower in cities than in
rural areas; when a surface inversion exists in the surrounding countryside,
the temperature profile within an urban area generally corresponds to neutral
or weakly stable conditions.
       Topography may significantly affect stability.  The nocturnal in-
version within a valley, for example, may be much deeper and longer lasting
in the morning than that over flat terrain.   This is caused by a combination
of uneven heating of the ground surface due  to  the variable angle with which
the sun's rays strike the ground and the tendency of cooler air to settle in
low places in the terrain.  The presence of  fog also delays the heating of
the ground and prolongs the existence of stable conditions.  Forested areas
and region- of complex terrain also have surface roughness comparable to those

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                                     A42

of urban areas, and rates of dispersion are correspondingly higher than over
gently rolling grassland, for example.
       The stability of the atmosphere at higher elevations is also an im-
portant factor for atmospheric dispersion.  At any given time the stability ,
of the atmosphere at heights above a few hundred meters is determined mainly
by the large scale features of the weather as well as by the general properties
of the atmosphere a* a whole.  Below 10*15 km, the atmosphere is on the average
slightly stable, so that turbulence generated at the surface can propagate up-
wards only so far before it is damped out.  This results in an upper limit,
called the mixing height, to the altitude to which pollutants will disperse
over a short period of time.  In the absence of an elevated inversion, this
mixing height is determined by the same variables that determine the stability.
An elevated inversion may exist, however, usually in association with a large
high pressure area.  Such inversions are called subsidence inversions and are
very effective in limiting vertical dispersion.  Subsidence inversions exist
at altitudes of the order of 1000 m and the maximum mixing height on any given
day is limited by the height of the base of these inversions.  Since relatively
low wind speeds are also associated with these large high pressure areas,
they cause some of the worst pollution episodes.
       An additional factor, relating primarily to vertical dispersion, :is the
fact that the earth's surface forms a barrier which limits not only the extent
of mixing in the vertical direction but also the physical size of the turbulent
fluctuations which cause the dispersion.  The first effect is normally handled
as a boundary condition, but the second implies that the higher the altitude
above ground, the greater the size of fluctuation that can exist.  In addition,
the relative importance of mechanically generated turbulence compared to ther-
mally generated turbulence decreases with altitude.  Thus, the rate of vertical
dispersion from elevated sources is somewhat different from that ground level
sources, at least until the emission from the elevated source reaches the ground.
       Since horizontal and vertical dispersion are considered to be separate
elements in this workbook, and in order to tie the previous discussions together,
it is useful to summarize here those factors which relate specifically to either
horizontal or vertical dispersion, or "both.  These summaries are given in
Tables A.4 and A.5.

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                                     A43
      Table A.4  Factors Affecting the Level of Atmospheric Turbulence
                 and the Rates of Horizontal and Vertical Dispersion
          Wind shear, itself dependent on
          - Wind speed,  and
          - SMrface roughness
          Surface heat flux, itself dependent on
          - Solar angle,
          - Cloud cover,
          - Surface thermal properties, and
          - Anthropogenic heat production.
          - Orography (ground slope relative to solar angle)
          Atmospheric stability, itself dependent on
          - The factors listed above,  and
          - Synoptic weather features  (particularly above
            a few hundred meters altitude)
            Table A.5.   Factors  Determining  Meandering  Contribution
                        to Horizontal  Dispersion
           Duration  of  pollutant  release
           Source-receptor  travel time
           Desired averaging  time for pollutant  concentrations
           Initial size of  the  emission
           Orographic barriers
           Street canyons
A.4.2  Treatment of Horizontal and Vertical Dispersion
       In order to evaluate the treatments of horizontal and vertical dis-
persion in a specific model, the user should know:
       •  The technical benefits and limitations of the
          different types of treatments and
       •  The various ways of parameterizing the effects of
          the important meteorological variables in each type.
The remainder of this section addresses these points.

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                                     A44

       A.4.2.1  Treatment Classification
       Treatments of dispersion may be usefully classified in the following
two ways:
       1)  According to the general modeling approach adopted:
              Numerical methods, which involve the numerical
              solution of equations describing the conservation
              of mass,
              Semiempirical methods, which assume a particular
              functional form for the pollutant distribution, and
              Methods which do not treat dispersion explicitly;
              and
       2)  According to the way the time dependence of the pollutant
           distribution is treated:
           •   Dynamic treatments, which predict the pollutant con-
              centration as a function of time as well as position,
              Steady state treatments, which predict the average
              pollutant concentration as a function of position only
              for short averaging times, and
              Climatological treatments, which predict the average
              pollutant concentration as a function of position only
              for long averaging times using a statistical distribution
              of meteorological conditions.
Methods which do not explicitly treat horizontal dispersion, vertical dispersion,
or both may still in some cases be simulation models arid examples will be
discussed below.  Empirical or statistical models, which also do not generally
contain explicit treatments of dispersion, are discussed in Section 7.

       Numerical Methods
       The most advanced and sophisticated models of atmospheric dispersion
fall into this category.  The current state of the art is represented by
"closure models" which consider both the concentration and the flax of pollutant
as well as most of the meteorological variables as unknown functions of position
and time to be determined by numerical solution of the relevant, equations.  The
flux obtained in this approach is directly related to the rate of dispersion.
This type of  treatment is still in its formulative stage and has not yet been
used in practical applications.  For this reason, closure models will not be
discussed further here.

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                                    A45
       The usual approach in numerical models is to describe the flux in
terms of the concentration distribution, so that the flux is no longer an
independent quantity.  This is done by rcaklrig the "gradient-transfer"
approximation, which assumes that the pollutant flux is proportional to the
concentration gradient.  The proportionality factor is called the eddy
diffusivity and is usually symbolized by the letter K, hence this approach
is often referred to as "K-theory."  The result of making this approximation
is an equation, called the adveo tion-diffus ion equation, which predicts the
pollutant concentration as a function of position and time.  Treatments of the
wind field are discussed in Section A.3.  The advection-diffusion equation
must usually be solved by any of a variety of numerical methods, including,
for example> finite-diTfecenne or particle-in-cell techniques, but the user
should no" be too concerned with the details of the numerical method used by a
model bei.'ig evaluated.  There are certainly advantages and disadvantages with
the varj.cs-3 approaches, but the focus here is more on the parameterization and
treatment of meteorological and other factors.
       Ths eddy diffusivities for dispersion in different directions are not
necessarily equal, but this discussion will be restricted to what is by far the
most common case, that in which only two eddy diffusivities are used, one for
vertical dispersion and one for horizontal dispersion.  The eddy diffusivity
values reflect the level of atmospheric turbulence and their parameterization
in terms of observable meteorological quantities should be considered by the
user in evaluating a numerical model.

       Semiempirical Methods
       This category includes all treatments in which an explicit functional
form is assumed for the concentration distribution.  The assumed form may be
based on observation, theoretical considerations, numerical ^simulation, or a
combination of these.  It may be a function determined elsewhere and assumed
appropriate for the given application or it may be determined specifically
for the application of interest in the process of running the model itself.
       The most common example of a semiempiricaJ raethod LP th_ 'Jaussian
plume treatment of dispersion from a continuous source as desc> ibt-i bv
Turner (1969) .  This particular approach involves the assumption tho.t tne
horizontal crosswind pollutant distribution from such a sourer may be

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                                    A46
described, on average,  by a Gaussian function and that,  except ior the effects
jf the ground, so can the vertical distribution.   The only parameters beside
die wind speec1 which Appear explicitly in these functions and which reflect
the prevailing meteorological conditions are the  horizontal and vertical
standard deviations, or dispersion coefficients,  corresponding to the assumed
horizontal and vertical Gaussian distributions.
       Another example  of a semiempirical model is the simple box model,
which assumes a spatially uniform pollutant distribution within some
region.  Dispersion is  not explicitly treated in  such a model, but additional
assumptions are implicitly being made.  If the pollutant distribution is taken
to be uniform in the vertical direction up to some specified height, the
process of vertical dispersion is implicitly being assumed fast enough to
justify that treatment  over the time scale of the problem.  The assumption
of uniformity in the horizontal crosswind direction is often used and is
justified if the distribution of emissions is relatively uniform; this
approximation, when used in conjunction with the  determination of pollutant
levels due to area source emissions, is called the narrow-plume approximation.
A type of narrow-plume  approximation may also be  used for treating point
sources in climatological models and will be discussed in chat context later
in this section.

       Dynamic Treatments
       This category includes all methods in which the concentration is pre-
dicted explicitly as a  function of time.  Treatments in whicn one or more
trajectories of pollutant releases are calculated from wind £ Laid data, or
are simply assumed on any reasonable basis, are also included under the
definition of dynamic models followed in this vorkbook.   Dynamic treatments
may be either numerical or semiempirical in nature.
       Dynamic models must be able to properly handle sit aations involving
changing meteorological conditions and the resulting changes in the rate of
dispersion.  There is usually no difficulty in doing this in numerical models,
but if a time-dependent generalisation of a semiempirical steady-state method
is used, problems can arise in making sure that the model parameters which
describe the extent of  dispersion at any given time are continuous functions
of time.  For example,  if the horizontal crosswind pollutant distribution

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                                     A47

about some trajectory is assumed to be Gaussian, the horizontal standard
deviation should be a. continuous function of time.  Most commonly used
formulae or graphs give the standard deviation as a function of downwind
distance or travel time only for the case in which the meteorological con-
ditions are constant, and are not directly applicable under changing conditions.
A treatment which uses a description of the rate of change of the standard
deviation as a function of meteorological conditions is usually preferable
for dynamic models.
       Examples of numerical/dynamic treatments are 1) those using the
numerical solution to the full time-dependent three-dimensional advection-
diffusion equation and 2) those using the narrow-plume approximation for a
grid of area sources over which a trajectory is calculated and treating
vertical dispersion by numerically solving the one-dimensional (vertical)
time-dependent diffusion equation.  An example of a semiempirical/dynamic
treatment would be one in which a trajectory originating at the location of
a point source is calculated and the pollutant distribution about the tra-
iectory is assumed to be Gaussian.  Gaussian puff models, in which a plume is
treated as a series of puffs which follow their own trajectories, are also
s emi emp ir ic al/dynamic models.

       Steady-State Treatments
       This category includes all methods in which temporal variations of all
relevant quantities are ignored and in which the treatment of advection uses
only the mean wind speed and direction for the averaging time of interest.
This type of treatment predicts the average concentration as a function of
position only.  Steady-state methods may be either numerical or semiempirical
in nature.  The most familiar example of a semiempirical/steady-state treatment
is the basic Gaussian plume model and an example of a numerical/steady-state
treatment is one in which the time-independent version of the advection-diffusion
equation is solved numerically.

       Climate-logical Treatments
       This category includes methods which predict the average pollutant
distribntion for long averaging times, typically a month, season, or year,
using 6 j^J-ut frequency distribution which gives the probability of simulta-
neously observing specified wind speed, wind direction, and other meteorological

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                                    A48

variables.  In this approach, more information about the wind field than just
the mean wind speed and direction over the desired averaging time is used in
order to avoid treating variations which occur over time scales less than the
averaging time as part of the horizontal dispersion process.  Clinatological
models may in principle use either a numerical or senrLempirical approach for
the individual calculations, although in practice sendempirical/steady-state
treatments are almost always used.

       A.4.2.2  Benefits and Limitations

       Numerical Methods
       The main benefit to be gained by using a numerical approach is
flexibility in the specification of the wind field and the meteorological
variables determining atmospheric turbulence levels as functions of position
and time and in the specification of boundary conditions.  In principle,
numerical methods allow the description of dispersion for a realistic wind
field in complex situations.  They are also, in principle, capable of treating
the spatial distribution and temporal behavior of chemically reactive pollu-
tants .
       The main technical limitation is one of spatial resolution.  Numerical
methods calculate concentration values at only a finite number of points in
space, normally corresponding to some conveniently defined grid, and the
resolution which can be achieved is fixed by the grid spacing.  In addition,
the grid spacing should not be considered arbitrary, since it, may be determined
to a large extent by the way the wind field is determined (see Appendix A.3).
Variations in the concentration distribution, in the wind speed and direction,
and in the emissions themselves which occur over distances smaller than the
grid spacing cannot be resolved.  This lack of resolution has several conse-
quences :
          Emissions from point or line sources into a specific
          grid cell are in effect dispersed instantaneously v,ithin
          the cell, rather than described in terms of a sub-grid
          scale distribution;
          The value of the eddy diffusivity must reflect the intensity
          of turbulent fluctuations up to the size of the «ria spacing
          and is therefore partially determined by that spacing; and

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                                     A4S

       •   Pollutant concentrations cannot be predicted at arbitrary
          receptor locations, except by interpolation from concen-
          tration values at grid points.
The seriousness of these consequences depends on the specific application,  and
on the existance of practical limits to the amount of computational effort
required and to the computer storage requirements.  In general, however,  the
numerical approach is inappropriate for the treatment of dispersion when  the
size of the emission being dispersed is smaller than the grid spacing.
       Another way of stating this conclusion is that the numerical approach
using the eddy diffusivity concept is inappropriate when the size of  the
pollutant distribution being dispersed is smaller than or comparable  to the
size of ai.y tu>"balent eddies contributing significantly to the dispersion.
As _• resvLe, i he eddy diiA'sivity approach is not fundamentally suitable  for
dec;*'- cibii-;" Horizontal dispersion, and in particular the meandering contribution,
but bec-"u':.t: ol constraints on the size of vertical fluctuations due to the
^rt: vance  .r boundaries at the ground and at the mixing height, can be justified
for the treatment of vertical dispersion from ground level sources or from
elevated "oarc».s after the plume has reached the ground.  Treatments  of hori-
zontal dispersion using the eddy diffusivity approach do exist, however,  in
spite of the physical fact that dispersion by meandering cannot be considered
a gradient-transfer process.  Such treatments describe horizontal dispersion in
a. phenomenological way, rather than in a manner which reflects the basic
physical processes, and the selection of an appropriate value for the horizontal
eddy diffusivity must be based on more empirical grounds than is the  case for
the vertical diffusivity.  (See the discussion of parameterization in numerical
models later in this appendix.)
       It is cometimes possible to describe the pollutant distribution on a
scale smaller than the grid spacing in an empirical or theoretical way, arid
use the numerical approach to describe the large scale distribution.  This  is
in fact desirable in the case of point sources in order to minimize the numer-
ical errors resulting from the poor resolution near the source.
       Another limitation in most cases is the lack of fundamental knowledge
and appropriate meteorological data upon whi::h to base the prediction of  eddy
diffusivity values, particularly at heights above 100 meter;-; or so    Ti:i.-;
means that further assumptions must be made r^g^rdiiig the appr<">pr~'c:i--' values <~o
use in a model.

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                                    A50

                     Methods
       The principal technical benefit gained in this type of approach is
that the adsuraed shape of the pollutant distribution may be based upon actual
observational data.  Furthermore, the distribution observed experimentally
may be assumed to be the same under similar meteorological and topographical
conditions, thus eliminating the need for new observations for each new
application.  In some cases, the assumed distribution may be derived on the
basis of theoretical considerations.
       The semiempirical approach has two advantages over the numerical
approach from a technical point of view:
          Better spatial resolution can often be achieved in
          practice and
       •  The effect of meandering may be treated in a more
          appropriate way.
       The general limitation on this type of approach is that it should not
be used in situations in which there is insufficient observational data or
theoretical results from which to determine the proper functional form.  If
the assumed shape is derived theoretically, its suitability depends on the
nature of the assumptions made in the derivation.  These may not l.e appropriate
for the real situation.
       As indicated above, the most common example of this type of approach
is the Gaussian plume treatment of continuous emissions.  In tbeir basic form,.
Gaussian-plume based methods are inherently restricted to:
          Flat or gently rolling uerrain for a considerable
          distance upwind and downwind of the source,
          Primary pollutants, and
          Conservative pollutants, i.e., no significant physical
          or chemical sinks.
It is possible to extend the utility of Gaussian models to applications in-
volving complex terrain by making various assumptions regarding the extent
to which the plume follows the terrain and by making modifications to the basic
formulae.  These models all fall within the category of semiempirical models
and in view of the wide range of possible modifications and interpretations
expert advice may be required in making a comparison.  The only general guide-
line that can be given is that the basis or justification for the assumed

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                                     A51
pollutant distribution should be scientifically sound.  Ideally, modifications
to the basic Gaussian distribution should be based on appropriate observational
data, often in combination with theoretical considerations.  If no information
is available regarding the basis for any particular assumed pollutant distribution,
it is impossible to accurately assess its validity except through an appropriate
field measurement program.
       It should be point out that, given certain approximations, the standard
Gaussian plume formula represents the steady-state solution to the advection-
diffusion equation for a single point source.  The conditions which have to be
met are that 1) the wind field must be uniform, constant, and have no vertical
component, 2) the rate of pollutant dispersion along the direction of the wind  •
must be negligible compared to the rate of pollutant transport by advection, and
3) the horizontal and vertical eddy diffusivities must also be uniform and con-
stant.  The extent to which the application of interest deviates from these
assumptions determines the need for modifications to the formula or for a different
modeling approach, e.g., a numerical model.
       It is also possible to extend the basic Gaussian model to non-conservative
pollutants.  (See Appendices A.5 and A.6 for discussions of possible treatments.)
       Limitations to the basic Gaussian plume model also exist because of the
steady-state nature of the model.  These are discussed in the subsection on
dynamic treatments,
       The narrow plume approximation mentioned earlier deserves further comment
at this point.  This approximation can be used for either point or area sources,
although its use for point sources is restricted to climatological models except
for the short-term mode of the Valley Model.  For area sources, the narrow plume
approximation amounts to the assumption that emission rates from nearby sources
are sufficiently similar that the pollutant distribution may be assumed to be
horizontally uniform.  In the narrow plume approximation, pollutant concentrations
along soiue well-defined trajectory are functions of height above ground and
possibly travel time but not of horizontal crosswind position.  The narrow plume
approximation may be used in either a steady-state or a dynamic approach and the
; raje-..'.orv may be a straight line, a constant path determined, for example, by
topography, or it may be determined from actual wind field data.  The accompanying
treatment of vertical dispersion may be either semiempirical or numerical.

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                                    A52

       Dynamic Treatments
       The main benefits are:
       •  The ability to describe the temporal variation of
          the pollutant concentration and
       •  The ability to treat the effects of time variations
          in and correlations between emissions, meteorological
          parameters, and removal processes.
       Technical limitations depend upon how the time dependence is handled.
Time dependence may be incorporated in an empirical or ad hoc way, in which
case the suitability of the treatment in a given application depends on the
observational or theoretical basis for that particular treatment, as with the
empirical methods discussed above.
       Time dependence is more commonly treated by dividing th« total period
of interest into a number of sequential time steps.  The variation of some
quantity such as an emission rate is then simulated by prescribing a sequence
of values, one for each time step.  Such an approach predicts the concentration
at a finite number of points in time and the temporal resolution of the method
is determined by the size of the time step.  Time variations more rapid than
the time step cannot be resolved.

       Steady State Treatments
       No significant technical benefits are gained by using a steady-state
model in preference to a dynamic approach.  Steady-state models are generally
simpler and easier to use,  however, and the decision to use such an approach
is based on these considerations as x^ell as on the fact that the most widely
used semiempirical approach, the Gaussian plume method, is a steady-state
method.
       Limitations include the assumptions of a constant emission rate and
a constant level of atmospheric turbulence.  The specified averaging time
should be greater than the source-receptor travel time, as iv;i:itcu out in the
general discussion, so that the effect of meandering is properly treated.  The
assumption of constant emission rate guarantees that the duration of the re-
lease is longer than the averaging time, and the steady-state approach is
clearly limited to the treatment of those sources which satisfy this require-
ment.  Instantaneous or very short releases must be treated using dynamic

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                                     A53

methods.  Within its limitations, the steady-state  approach  is just  as
applicable as the dynamic approach for the calculation of average  concen-
tration values.

       Climatological Treatments^
       This type of approach is used in practice only for the calculation  of
long-term average concentrations, the principal benefit being one  of con-
venience compared with the alternatives of using a  dynamic model or  a sequence
of a large number of steady-sfite calculations.
       A calculation is done for each set of meteorological  conditions  which
is represented in the joint distribution being used, and the average pollutant
d Istrj.but3 on is  obtu^ned v-ith the contribution from each set of conditions
c-siug w -.1 M*ted by it3 t-tobability of occurrance.
       Limitations of the method may be divided into two categories:
          Limitations of the model used to do each  separate
          calculation, and
          Limitations of the climatological approach, per se.
The former are described in other parts of this section and  the only additional
remark chat: needs to be made here is that the model used must be of  sufficiently
general applicability to be able to handle the variety of meteorological con-
ditions represented in the climatological frequency distribution.  The  latter
include the approximations incurred by representing the wide range of con-
di t-ions that occurs in nature by a finite number of specific situations, by
the. suitability of those situations which are used, and by the omission of
meteorological variables sach as precipitation and  mixing height from the  joint
frequency function.
       In the treatment ->f dispersion, at least one of the paiameters defining
the frequency function should be a measure of the level of atmospheric  tur-
bulence.  The measure of turbulence most commonly used in cJi;>iai.ological models
is the Fasquill stability clarification, although  others ruui.I bf  used,   It
-1,6 al^o comrnoi  tc ^.-e tbc narrow plume approxi.tratJun f.jr pom  ::• .-ci con,  This
approxinv'tion requires an assumption that the ci'jcswlnd or aumilar distributic,:;
of pollucauL f, on: a puint source over a sufficiently long period of  time is
given simply b>  the frequency distribution of tht wind direct'-on.   this

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                                     A54
assumption is reasonable if the variation in the wind direction frequency func-
tion is negligible over an angular interval corresponding to the angular width
of the plLiine,  Since the uirid direction frequency function takes the form of
probabilities of observing wind from within well defined sectors (commonly 10°
or 22.5° wide), this approach is also referred to as "sector averaging."

        A summary  of the different  general  types  of  treatment is given in
 Table 5,7.   It should  be pointed  out  that  in  any given  model,  horizontal
 and vertical dispersion may  be treated in  completely different ways (although
 both will he either dynamic  or steady-state)  and the treatments in any case
 should be evaluated separately.   In Table  5 ,,7,  the  treatments  are  ranked in
 order of decreasing level of detail,  but  the  user is cautioned that _in_ the
 cases of horizontal and vertical  dispersion the  relative level of  detail of
 two treatments is not  by itself a  reliable indication of their relative tech-
 nical performance.   As discussed  above,  there are limitations  on the applica-
 bility of certain approaches,  and  the user must  determine for  his  specific
 application if these are violated.   If they are, those  approaches  should not
 be used.   If the  two models  being  compared use the  same, or two equally
 applicable approaches,  the relative level  of  detail may be used as a valid
 indicator.

        A.4 .2.3 Parameterization
        Atmospheric dispersion models  are generally  designed for as-.-, in a
 variety of conditions,  each  characterized  by  a different level of  atmospheric
 turbulence and consequently  different rates of dispersion.  Various meteorolo-
 gical conditions  are handled within a given modfl fc>y using different numerical
 values for the relevant model parameters sui.l1 as e<'dy aiffusivities or Gaussian
 standard deviations.  The determination of thr- appropriate values  from meteoro-
 logical and other data is an important part of the  total procedure by which
 predictions of pollutant concaulratien-  are made.  In an evaluation, the user
 should take into  account any constraints on these parameters that  are inherent
 in or built into  the model,  particuJL'irly If they cleanly preclude  the use of
 the correct values. An example of such a  constraint is a built-in eddy
 diffusivity or standard deviation value which is not appropriate for the user's
 application and which  the user cannot conveniently  modify.  The determination

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                                    A55
of the appropriateness or correctness of any such specific parameter value
may require expert assistance but a general guideline is that the value in
question should be obtained from observations or theoretical analysis as
closely associated as practicable with the specific location and meteorological
conditions of interest.  If sufficient information about the source of the
values usea bi a given model is available, the appropriateness of those speci-
fic parameter values should be considered in making the evaluation.  Table 5.10
provides a list of some of the possibilities for both numerical and semiempi-
rical models.
       Some general remarks regarding the way in which atmospheric stability
and surface roughness are treated by various types of models are in order
here.

       Numerical Models
       Confining our attention to gradient-transfer models only, the horizontal
and vertical eddy diffusivities are the parameters through which the influences
of stability and surface roughness on dispersion are manifested.
       As indicated above, the eddy diffusivity approach is not in general
appropriate for the treatment of horizontal dispersion.   For this reason, the
basis for choosing a specific value of the horizontal diffusivity needs to be
considered further.  It is possible, by appropriate selection of the time or
space dependence of che horizontal diffusivity, to force a numerical model to
reproduce approximately the results of a more sophisticated calculation, or of
a i-emiempirical model.  If this is the case, the parameterization of the
horizontal diffusivity needs to be judged on the basis of the treatment being
reproduced.
       In general, the horizontal diffusivity may be expected to be roughly
independent of horizontal position except when significant terrain features
are present.
       The vertical diffnsivity near the ground may be reasonably estimated
in terms of the wind speed,  surface roughness (given in  terms of a parameter
called the "roughness length",  see Slade (1968) or Pasquill (1974)  for the
definition and estimates for different situations),  and  parameters which
determine Use rate of heat-exchange between the earth's  surface and the air.
An expert should be consulted for the details of the formulation.

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                                     A56

       At higher altitudes, there is very limited data and the exact para-
meterization of the vertical diffusivity is a subject of current research.
Consequently, any parameterization must be based on further assumptions and
it is not uncommon to simply use a convenient functional form having the
desired qualitative behavior and having the correct behavior near the ground.

       Semiempirical Models
       Since the Gaussian plume model is by far the most common example,
the discussion will be restricted to this case.  The user should be able to
follow a similar line of thought for other treatments.  In the Gaussian plume
approach as described by Turner (1969), the horizontal and vertical standard
deviations need to be parameterized.  Atmospheric stability is divided into
several discrete classes and the stability class to be used in a given
situation is determined from the wind speed, solar angle, and the extent
of cloud cover.  The horizontal and vertical standard deviations are then
prescribed functions of the stability class and downwind distance from the
source.  The effects of surface roughness may be accounted for in the nature
of the prescribed functions or by additional modification of the basic stan-
dard deviation or may not be treated explicitly.
       Tables 5.8 and 5.9 list various treatments of atmospheric stability
and surface roughness, respectively.  Tables B.8 and B.9 list treatments
of horizontal and vertical dispersion, respectively, used by suggested
reference models.

A.5  CHEMISTRY AND REACTION MECHANISM

A.5.1  General
       There are two common situations in which chemistry plays a role in
determining atmospheric pollution levels,  On one hand,, f.".e polJutant of
interest may undergo chemical reaction with some other ae-iOfphPri:. component:',
that is, a chemical sink exists for that pollutant and it is referred to as
being reactive.  (If the pollutant undergoes no reaction, it is called inert..!
On the other hand, the oollutant of interest may be produced in the atmosphere
by chemical reactions involving other pollutants (precursors); such a substance
is called a secondary pollutant.  (If the pollutant is directly emitted by

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                                    A57

sources, it is called primary.)  Clearly, in each case the chemical reactions
involved affect the concentration of the pollutant of interest.  In the first
case they provide a process for the removal of that pollutant and serve to
decrease its ambient concentration, while in the second case they serve to
generate the pollutant and increase its concentration.  Examples of primary
reactive pollutants are the hydrocarbon precursors of photochemical smog.
Examples of secondary, relatively inert materials are sulfate and photochemical
aerosol.  A pollutant may be both secondary and reactive; examples are nitrogen
dioxide (NO ) and ozone (0 ).  If the pollutant of interest is both primary and
           2              3
inert, the element of atmospheric chemistry is irrelevant and does not need to
be considered.
       As pointed out in Section 3.3, the decision to regard a pollutant as
being e;ther reactive or inert depends upon the effective rate of reaction
rornpar--' \ to the length of time that the pollutant spends within the region
of ir.. f-i-est.  If the user is interested in a short-range application involving
a slowly reacting material, that pollutant may be regarded as effectively inert
for the application even though over a longer range this would be a poor approx-
imation,  An example of such a pollutant is sulfur dioxide (SO ).
                                                              2
       lu the case of a secondary pollutant, some treatment of the chemical
reactions which produce that pollutant will be required.  Otherwise, the
connection between precursor emissions and the concentration of the pollutant
of interest is completely lost.
       The subject of atmospheric chemistry encompasses an extremely wide range
of topics and only those very basic or general aspects that are directly rele-
vant can be described in this workbook.  If atmospheric reactions play a signi-
ficant role in the user's application, the advice of an expert should be sought
regarding the. level of detail with which the particular set rf chemical reactions
used by the model represents the system to be simulated.
       This discussion will refer primarily to reactions between gaseous
materials.  The extent to which atmospheric particulate matter actually
participates in chemical reactions with gaseous component^ is not at, present
well understood but if this possibility exists, the advice cr ao expert should
again be sought.  However,  many of thp same •uonr-ideration? apply as in the
completely gaseous case.

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                                    A 58

       The basic problem in modeling the dispersion of reactive systems is
to describe the rates of production and removal of various pollutants.
Equally as important is the interaction between the chemical reaction processes
and the dispersion process.  In order to assess the treatment of chemical
reactions by a model, the user must consider two different aspects of that
treatment:
          The level of detail with which the chemical reaction
          mechanism is described, and
       •   The manner in which the effects of spatial inhomogeneit}'
          on the average rates of change of the pollutant concen-
          trations are treated.
       It will be useful for the user to understand a few basic facts re-
garding the general nature of chemical reaction rates.  The rate of a chemical
reaction may be defined with sufficient precision for the purpose of this
workbook as the magnitude of the time rate of change of the concentration of
a reactant or product of the reaction in question.  (The reactants are the
chemical species actually undergoing reaction.)  The reac:ion rate depends on
the concentrations of all of the atmospheric components participating in the
reaction.
       Reactions can be classified as either elementary or complex,  An
"elementary reaction" is one in which the chemical reaction as wrl* ;; -n reflects
the true sequence of events on the molecular level.  For example, i>.r, important
reaction in photochemical smog is that between ozone and nitrJr c;. •-.'-J- (110; .
This reaction involves the collision of a molecule of NO with a molecule of 0  ,
                                                                             3
followed by a reaction and the separation of the products, one IPO" ecule each of
NO  and oxygen (0 ).  The most important property of elementary reactions is
  2              Z,
that the race of such a reaction is a predictable, simple function of the reactant
concentrations.  In the example above, the rate of the reaction is simply equal
to a constant (the rate constant) times the product, of tha ozone and nitric oxide
concentrations.  On the ot ler Ivncl, a "complex reaction" is essentially a state-
ment of the net effect of some (possibly Lar^el number of elementary reactions
operating simultaneously, with only the- iuit-.al reactauts and final products
being explicitly written.  In general, the rute at which the initial reactants
disappear is not equal to the rate at which the final products appear.
Neither rate is a predictable function ot the concentrations of only the initial
and final chemical species.  The sequence of elementary reactions whose net

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                                     A59

effect is of interest forms what is called the "reaction mechanism" and the
description of the pollutant concentrations as functions of time must usually
be made In terms cf what is known about the reaction mechanism.  It should be
pointed out that, in addition to the main reactants and products of interest,
che machciaisai oi <•• complex reaction usually involves the existence of other
chemical species tnai, should also be treated.
       An extreme example of a complex reaction is the generation of photo-
chemical smog from nitric oxide and hydrocarbons under the action of sunlight.
In this case the reaction mechanism involves literally hundreds or even thou-
sands of reactions.
       As mentioned above, the expression for the rate of an elementary
reaction can be predicted in an a priori way.  In practice only three cases
need to be considered; these three cases are outlined in Table A.6, in which
the "order" of each type of reaction is also defined.  The constant appearing in
the rate expression for a given reaction is called the rate constant for that
reaction.
       The most important feature in Table A.6 of which the user should be
aware is that the rate of a first-order reaction is a linear function of the
pollutant concentration.   The rates of second and third-order reactions
are nonlinear functions of the pollutant concentrations.  This fact has signi-
ficant consequences when the spatial distribution of reactive pollutants is of
interest.
              Table A.6.  Elementary Reaction Rate Expressions
Rate Expression                                          Reaction Order
(constant) x (the concentration of one single reactant)      First
(constant) x (the product of the concentrations of two
              reactants)                                     Second
(constant) x {the product of the concentrations of three
              reactants)                                     Third

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                                     A60
       In order to describe the evolution of a  complex  reacting  sy&tem,  it is
normally necessary to know the reaction mechanism.   This mechanism  consists of
a set of (elementary) reactions whose rates are known functions  of  the pollutant
concentrations.  If the initial pollutants are  uniformly mixed within some
closed volume, their concentrations as functions of  time :nay be  predicted  by
numerical solution of a set of coupled ordinary, non-linear differential equa-
tions derived from the reaction mechanism.  In  practice, a simplified mechanism
may be used in which many of the reactions of lesser importance  have  been
omitted.  Also the net effect of many reactions may  have been expressed  in
terms of a few characteristic reactions using some kind of average  or composite
rate constant.  The level of detail with which  the reaction mechanism is treated
affects the accuracy of the results and the mechanism being used should  be
justified by comparison with experimental studies.
       Knowledge of the reaction mechanism includes  not only knowledge of  the
reactions which can occur but also knowledge of the  valves of the rate con-
stants of these reactions.  The appropriate values are normally  supplied with
the model so that the user generally does not need to supply them.  However,
there is often considerable uncertainty in the experimental measurement  of
rate constants and the values of constants important in atmospheric chemistry
are continually being redetermined.  Obviously, in a practical application the
values used should be as up-to-date as possible.  In addition, rate constants
depend on temperature.  In some cases it may be important to use values  appro-
priate for the ambient tenperature in the user's specific application.

       Further complications arise when dispersion is considered,  It is impor-
tant to emphasize at this point that chemical  reactions are _lpcal_ phenomena in
the sense that the rate of an elementary  reaction  at so013  point   in space depends
upon the reactant concent ration(s) at_jtha_t__p_£int.  Thus,  the  rate or  a given
reaction is in general a  function  of po&ir.ion  anc;  tiire,  reJ laetlag tre spatial
and temporal variation  in reactant concent rations,   ior r-^f.;;  Tea<.fi-.v,s ,A   in-
terest, the rate expression is a nonlinear  function  of  p ill uL.-uL ,  r-> -. era,. .1. - nc.
because most  reactions  of interest happen, to  be seconu-orde-r.   Th".-: i^rles that
in most cases of interest the average  rate  of  a given  reaction  wi :Mr. some finlLf
volume of interest c.annpt be obtained  from  the rate  expression s imply by  in-
serting the average  reactant concentrations,,  unless  all reactanc.> are unifo/inly
mixed within  this volume. In  this case,  there is  no spatial  variiticn in  the

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                                     A 61
reactant concentrations and hence no spatial dependence of  the  reaction  late.
The only other situation in which the average reaction rate  is  give:i  by  the
rate expression using the avera^,? peilutai.t concentration is  that  of  a first-
order reaction.  In mo3i cases of .interest  sratial  inhomogeneiUy  in  the
reactant concentrations causes the chemical ana dispersion  processes  to  be
coupled in a very complicated w.-iy.

       The nature of  turbulent  Dispersion  and the  small  size of most  real
emission sources c;.u -.rant ^  J-uit  Li applications of practical interest there
are signnficari.  •.•ariatJcns  in t";e concentrations of reactive pollutants  Ov'er
distances r, -c!i s.nsll er  than che  spatial  resolution of roost  current models,
Thr ciegrc-- of  ? ahomo£er,':it> depend*; on the level of atmospheric turbulence
and JTL t >••_ snaLi.al distribution  of the sources.  In principle,  the effect
jn the a vr...go reaction rate of  this inevitable inhomogeneity at distance
scales r- i ,,'>•? the resolution of the model should be taken  into account.   In
practice, i..-.wevf-r, this has proved to be a difficult problem and is still
fundamentally unsolved.

A.5.2  Treatment of Chemistry and Reaction Mechanism
       It is convenient to divide the discussion of treatments  into two  separate
parts, the first dealing with the special  case in  which  all relevant  reactions
are first-order reactions,  the second with the more general situation.
       As pointed out in the general discussion, most chemical  reactions of
importance in air pollution are  second-order reactions.   This being the  case,
it may seem unrealistic to  consider an application in which all  the reactions
of interest are first-order.  There are  two situations, however,  in which only
first-order reactions need be considered.   The first involves the  treatment
of radioactive rather than chemical transformations; radioactive decay is
rigorously a first-order process.  The second arises as a result of approx-
imating the disappearance of one pollutant and the appearance of its  reaction
products as a first-order process v/ith some empirically  derived effective
rate constant.
       A first-order process has the property thrt the rate- of  that process
is a linear function of the coucentration  cf the reactant involved.  As  a
result, it turns out that the effect of  one or more first-order ric-n^ses on

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                                     A62
v he recc7. arr  nud  prnruct con<".:>i. traMons may be determined .independently from
• lio P.fTe-t  jf JlspeTcio-;:  ii. c'jher words,  fi i ot-uj:d<-,i  cray be used,   Furthermore, in  cases  why .re more the:- one
source  11 involved, the contribution from  ^a; h may be  evaluated and the total
predicted concentration obtained by siriplv adding  the  individual source con-
tributions .
        The  simplest case arises with a primary pollutant subject to some
first-order removal process,  Tn this case, the  effect of the process is
simply  to cause  the pollutant concentrations to  decay  exponentially with  a
half-life which may be  easily determined frori the  rate constant for the process
Many dispersion models  now in use have the capability  of simulating this
situation.
        More often,  however,  the user's application involves a system of
chemical reactions, most of which are second—order;  the  most common example
is photochemical  smog.   In general, a numerical/dynamic  model is required,
since the chemical  mix  evolves in time in  a nonlinear  way.  The. observational
basis for a semiempirical  approach is not  usually  available, -u.though statis-
tical models  have been  developed for some  limited  applications.
        Two  aspects  of the  treatment by a given model should in pritir.inle  ' *:•
evaluated:
          The level of  detail used in the  reaction mechanism, mid
        •  The treatment of the effect of inhomogeneous riixirg un
          average reaction rates.
Witli regard t.o the  treatment oi rec.-' rion mec .am <=>•..>  ii it „•-.'. -, t..r> bs- ssld in
genera], because  so much depends on v.he s^o"  . 1.-   ^tnLl.  ~  ..  f n>; cticn?,i;;try,
The iimpxest  case is that  Jn whic.n ^itnc-r  ul,-- -i^ .-•..^pef-r.." ;•  ct ?•• ;-arfLcular
pollutant,  or the appearance -,f it.- -eact.;''., prod.. •• i s, ; ; -/ot^ ''"•"t- of in-
tC--:-yt.  In this  ras-,  i2  t ne  • jc-.:.^1 t.'ro  .r - 1'..  i,- ra-.  ;ev Jouf; compared
to the  dispersion ti.-r.e  sci.lu ar.a ;t L!I,  11 -ic  L-J)' prud-:>t3 vr,-. relatively  inert
sc that, for  example.,  the  original pul .utant is  not  regenerated by further
reaction, it  may  be ;5ui f icier, t *.o appro^iiu-i.i? the  reaction by a first-order
process  using an  effective rate con.staric detBrmined  empirically.  In this
approximation, all  details cf the actual reaction  mechanism are ignored.  The

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                                     A 63

conversion of sulfur dioxide to sulfate aerosol over long distances is
commonly treated in this manner.
       In moia complex cases, such as that of photochemical smog, the
mechanism should be treated at some more appropriate level of detail.  The
require.-' lf-vej 01 detail depends on the nature of the reactions being des-
cribed u;-d fit. ;iamber of different chemical species involved.  The user should
c-eek experi. advice  Ln evaluating a model with respect to the mechanism being
used.  'n any case, the assumed mechanism should be sufficiently valid so as
to give reasonable agreement wJth experimental observations.
       In the photochemical smog case, three approximations are commonly used
and will be discussed briefly as examples of the possibilities that can arise.
       The first deals with the treatment of highly reactive intermediates
which are present in photochemical smog.  These intermediate species can be
treated just like any other pollutant in that their concentrations may be des-
cribed explicitly as functions of time.  Due to their high reactivity, how-
ever, the approximation is usually made that they exist in a steady or stationary
state such that for each the rate of removal equals the rate of production.
Making this approximation allows their concentrations to be expressed mathema-
tically in terms of those of measurable pollutants and thus eliminated from
the rate expressions altogether.  By eliminating these species from the
equations, considerable simplification occurs.  This approximation, called the
steady-state o~ stationary-state approximation, should be tested for validity
ir any specific case and there are indications [Farrow and Edelson (1974)] that
It ir. not necessarily valid for the photochemical smog case even though it is
commonly used,  This approximation is not restricted to applications involving
photochemical smog but may be used in describing any reactive system in which
highly reactive intermediate species are present.
       A second and less detailed treatment is sometimes used when the reaction
mechanism may be approximated by a small number of fast reactions such that each
one in the set is accompanied by its reverse reaction.  For example,  over a
short period of time the photochemical smog system may be approximated by a
mechanism i.onsisting of only two reactions: 1) the photolysis (absorption of
light, followed by chemical reaction)  of NO  to produce NO and 0  and 2)  the
reverse reaction of NO and 0  to produce NO .   If each reaction in the set is
                            3              2
fast enough, the entire system responds very rapidly to changes in composition

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brought about by dispersion, and the chemical composition of the pollutant
mixture at any point may be predicted by assuming the system of chemical
reactions to be in equilibrium.   This approximation,  called the equilibrium
approximation, is equivalent to  the assumption that the rate of removal equals
the rate of production for every chemical species present,  not jast the re-
active intermediates.  The equilibrium approximation is; valid when the reaction
time for each reaction in the system is much shorter than the time required for
significant concentration changes resulting from dispersion processes
       The equilibrim approximation may be used in steady-state as well as
dynamic models.  It allows the prediction of the chemical composition of the
pollutant mixture at a given point given (1) the composition of the original
pollutant emission,  (2) the composition of the surrounding air into whici.
that emission is being dispersed, and (3) the concentrations predicted on the
basis of the dispersion model alone.
       The third approximation deals with the very large number of hydrocarbons
which are actually present in the polluted atmosphere, all  of which participate
in the formation of photochemical smog.  As a practical matter it is impossible
to model the concentration of each even if their emission rates were known,
which they are not in general.  The approximation is made that classes of hydro-
carbon may be defined such that  all members of a given class share some de-
sirable property, such as having similar reaction rates or reaction products.
The total concentration of all members of each class is then modeled using a
simplified reaction mechanism involving the use of average class rate constants,
This technique is termed "lumping" of hydrocarbons.  The validity of the pro-
cedure should be determined by comparison of predictions with observations from
experiments.
       For the purpose of comparing two models it should be assumed that, all
other things being equal, it is  better to treat reactive intermediates ex-
plicitly than to employ the steady-state approximation,  lha more accurate
the reaction mechanism being used the better.

       If the detailed spatial and temporal evolution of a  dispersing reactive
system is to be described, the system of chemical reactions should be treated
in some detail.  For other purposes, particularly involving secondary pollutants,
experimental and/or observational data may be used to provide the necessary link

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                                     A65

between  the  concentration  of  the  pollutant  of interest and the precursor levels
at an earlier  time.   This  may be  especially useful for cases in which not
enough is  known  about the  reaction  mechanism or in which only a maximum con-
centration regardless of  location i.--. Desired.
       The other aspect  mat  -iceds  to he evaluated is the way in which the
rates of change  o+  tne average pollutant c'f ir^ntrations are evaluated.  Dis-
persion  models fo •-  react >ve pollutant-"  generally attempt to predict the
average  concentrations of  ^1!  relevant  pollutants within some suitably defined
volumes or c'LJs a;~ fut.it. I.jus  ui  Line.   Thus  these  models  should  be  able  to
evaluate ";u- "'hut i^ter CL' cha-.ige of  these  quantities.   As  discussed earlier,
if thn volli-Lc?r ts are  ua.^formiv distributed within  a  given  cell,  the appropriate
rr*>-g ot c:hin>',!? mav be calculated from  the  elementary reaction  rate  expressions
uo.i"^ 1 -~u average concent cations  appropriate  to  the given  cell.   Errors will be
inttoai   ••' i.-  this procedure  is used  in  cases in which  spatial  inhomogeneities
drl.-.T   .. the pollutant concentrations over  distances  smaller than the cell
KLze.  At  present,  this  effect is generally not treated at all.  This is not
to Jmpiy that  modelers are unaware  of the effect,  but the problem of providing
an adequate  general  treatment is  still  essentially unsolved.
       In  summary, most  dispersion  models for reactive pollutants use elementary
reaction rate  expressions  which are truly valid only  in homogeneous regions
and  make no  attempt  to account for  imperfect mixing at sub-grid distances.  If
the  user is  confronted with a model which does  in fact treat the effect of
inhomogeneities  in  some  fashion,  expert advice  should be sought on the manner
of treatment before making an evaluation.  However, in general, any reasonable
treatment  would  be  better  than rone at  all.   Table 5.12 gives the treatments
of chemistry and reaction  mechanism that have been discussed.  No table of
treatments of  the effect of spatial inhomogeneities on the race of change of
average  pollutant concentrations  is provided.  At this writing no practical
general  treatments  exist except in  models developed solely for the purpose of
doing basic  research.  Table  B.10 gives the treatments of chemistry and reac-
tion mechanism used  by suggested  reference  models.

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                                     A66
A. 6  PHYSICAL REMOVAL PROCESSES
A . 6 . 1
       The two Lia j or physical removal processes which affect ambient  at-
mospheric pollution levels are dry deposit. for and precipitation  scavenging.
In identifying them c s physical processes, tie intention  is  to distinguish
them from "he chemical processes discussed ir Appendix A ,. 5 ,  even though on a
fundamental level there are chemical aspects to each.  Afcer defining these
elements, each will be discussed in turn.  For a more technical  discussion the
user is referred to the article by Hidy  (1973) as ^el] as  the proceedings
of the symposia on precipitation scavenging  [Engelniann and  Slim (1970)]  and
on atmosphere-surface exchange of particulate and Caseous  pollutants  [Engelmann
and Sehmel (1976)].  Technical but still  introductory discussions are also
given by Van der Hoven and Engelmann in  Slade  (1968) .
       Dry deposition is defined as the  removal of  a gaseous or  particulars
pollutant at the  earth's surface by any  of the several processes, including
impaction, absorption, and chemical reaction.  The  important point is thai;
this process occurs only at the surface,
       Precipitation scavenging is defined as  the .removal of a  gaseous or
particulate pollutant by precipitation.   In  the past,  the distinct n"*n ha< hsen
made between the  absorption or other collection of  pollution by  ?iov JronJPts
before precipitation actually occurred  (denoted '\y  ::he  term "r/, t-\rur ' '. and
the scavenging of pollutar.t by the precipitation  i'^eif  ?u; ir  titSc thr^r-i
the polluted air  (denoted by the term  "washout") ,   For purposes   ;f tq G vork-
book, this distinction. will not bo. eriphas Jze.d  but  ib?.  ,jper s -utl be aware of
its existence.

       Dry j)epos it ion
       The rat3  of  removal of o.n atmoRpheric >:ol3.ncant per unit  area of ground.
surface  is called the deposition raf.e  (dimc-us ;.or:s :   mass/ time/area) .   It
depends  upon
          The nature .if the mechdnisr,:  by which the  pollutant,  once
          transported to the ground,  interact;; with and  is removed
          at the ground surface and
          The rate  of vertical transport of  that  pollutant.

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                                     A 67
The pollutant is removed from the air near  the ground,  thereby creating a
non-zero vertical concentration gradient near that surface.  Vertical dispersion
processes tend to snoota out this gradient by transporting pollutants down-
wards, thereoy providing more for possible removal.  The ambient pollutant
concent,-ado/; near the giound is lower than it would be otherwise, with the
magnitude of the depletion depending on the relative rate of removal at the
surface.   A corresponding net decrease per unit downwind distance in the total
amount of pollutant being advected by the wind is also observed.
       The  depositior.  rate depends  on the nature of  the interaction between
pollutant and ground  surface and as  such depends on  a wide variety of pollutant
and surface characteristics.  Although these are highly dependent on the
specific, application  of interest, a few general statements can be made.  The
deposition  of gaseous  pollutants, for example, increases as  the  solubility or
reactivity  of the gas  increases.  The deposition of  airborn  particulate matter
is highly dependent on particle size.  If the pollutant of interest is found
predominantly greater  than a certain size range, this added  factor should be
taken  into  account in  the treatment, as discussed  below.
       The  deposition  rate also depends strongly on  the rate of  vertical
transport and therefore on the same  factors as does  vertical dispersion.
(See Appendix A 4 for  a discussion  of these factors.)
       With regard to  the deposition of particulate  matter,  these remarks
on deposition refer primarily to particles smaller than approximately 10 microns
in size,   Particles larger than this are sufficiently massive that gravitational
settling becomes significant and these particles simply drift downward at a
rate dependent on their size and weight.  This deposition mechanism is very
different from that described so far and in general  must be  treated differently;
see for example the discussion in Slade (1968) .  Particulate matter smaller
than 10 microns behaves much like a  gas in  many respects and gravitational
settling is usually negligible.
       If the removal  is efficient  enough,  a significant fraction of the
pollutant raay be removed before it  is t-ransported  out of the region of in-
terest and  arobiont atmospheric concentrations can  be significantly affected.
In some application,  the deposition  rate or the total deposition within a
Siveii  area  over some  specified period of time may  be of interest, in addition

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                                    A 68
to or instead of the actual ambient concentration.   In either case,  dry
deposition is an important phenomenon.

       Precipitation Scavenging
       This term includes processes which take place within clouds,  such as
the formation of cloud droplets about pollutant particles which serve as
condensation nuclei and the absorption of pollutants into existing droplets,
as well as the scavenging action of precipitation falling through polluted
air.  The importance of each of these processes depends strongly on the
characteristics of the pollutant, as in the case of dry deposition,  and
again only very general comments can be made.   For gaseous pollutant, the
solubility in water is the most important factor and this o?ten depends to a
significant extent on the presence of other dissolved material in the precipi-
tation.  The solubility of sulfur dioxide, for example, decreases as the
acidity of the precipitation increases.  The particle size is again the most
important factor for the scavenging of aerosols.  The rate of pollutant re-
moval by falling precipitation is also determined to a significant extent by
the size of the falling drops and the rainfall rate.

A.6.2  Treatment of Dry Deposition
       As indicated above, the removal of pollutant at the ground surface has
two major effects on ambient pollutant concentrations:
       •  A depletion of the mass of pollutant being advected by
          the wind, resulting in lower concentrations than would
          otherwise be expected, and
       *  A reduction of ground level concentrations compared to
          those at higher elevations, resulting in a non-undiorro
          vertical distribution.
All treatments of dry deposition that are used in practice coscrij.  the first
effect but not all describe the second.
       The net downward pollutant flux resulting from removal at ground level
is commonly assumed proportional to the pollutant concentratJon at ground
level, the proportionality constant actually being depandent on a variety of
factors such as:

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                                     A69

          The nature of the pollutant,
          The nature of the ground surface, and
          The prevailing meteorological conditions, particularly
          the atmospheric stability nen-r 1 he ground.
The proportionality constant is ca^lc.l  • h<-:  "Deposit ion velocity"  and  its
value in any given sltar-tion ^star-mine" tne significance  of  the effect cf  dry
deposition on poli^tan1: •, .-mcenf ratir-n .  Theoretical procedures exist  whereby
appropriate v-luep rv.y  be esLi •.".". e-J  tor a specific  application but  their
accuracy i , ur certain an" '.'ain<-s derive.)  from  field observations  are  nearly
always u.~Pd in. practice.
       AbC'iming that tV a downwind. flux  of pollutant may be parameterized in
this; w? - r t ifc problem of treating dry deposition  becomes  one of describing
its efl-' •. ... on atmospheric pollutant  concentrations  and of calculating the
amour'   :  pollutant deposited  in the area of interest.  Different types of
models  r. ,eit these effects in  different ways,  depending  specifically  on the
way vc-ri. iral dispersion is treated and  on the  way the dependence  of the
        '**- concentration on height above ground is predicted.
       Since pollutant removal occurs  at  the  ground surface,  the best
treatment of dry deposition  is to mathematically specify the  appropriate
boundary condition at the  earth's surface and to determine or describe the
corresponding effects numerically or analytically.   The mathematical statement
of the boundary condition, which is used  in models  which treat vertical dis-
persion by a numerical method,, involves both  the vertical eddy diffusivity
and the deposition velocity  and defines the relationship between the pollutant
concentration and the concentration gradient  at  the ground,   Numerical solu-
tion of the diffusion equation in the  vertical direction ther determines the
predicted pollutant concentration as a function  of  height as  well as the pre-
dicted rate of pollutant deposition on the ground.   This procedure may be used
in either dynamic or steady -state models.
       Models which treat  vertical dispersion by a  semiempiiical method do not
necessarily bandit- dry deposition in a less appropriate  ;ay '',•.•'•, do r.uiierical
models.  If, for example,  the. assumed  fora for the  verticil . oncers IrjLjf a
distribution is based z,\ suitable analytic ^lurions of the \/-e.t i_ ;rql diffu^jou
equation obtained using the  correct boundary  condition.? s tne  trertiest nviy bt~
as appropriate as any other. Normally, howevei , semie^ipiri' vtl av d :^> s ineorpoivte

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                                     A70
certain assumptions which are to some extent invalid for the treatment of
dry deposition.
       Most semiempirical models incorporate the perfect reflection boundary
condition, as discussed in Appendix A.7.  Mathematically, this corresponds
to the assumption that there is no net vertical pollutant flux and no net
removal of pollutant from the atmosphere at the ground.  An additional result
is that the pollutant concentration is nearly  independent of height near  the
ground.  This also corresponds to the special case of a zero value for the
deposition velocity.  A model incorporating the perfect reflection boundary
condition cannot treat the effect of diy deposition on the vertical concen-
tration profile.  If this approximation is used in a model, as it is in most
Gaussian plume models, but it is still desirable or necessary to allow for
the depletion of the plume as it is advected along, a time or downwind distance-
dependent factor may be applied to the concentration value calculated by  the
basic semiempirical formula.  This factor serves to simulate a reduction  in
the total mass of pollutant  In the plume and to model pollutant temovaJ by dry
deposition.  In essence, this type of treatment involves the determination of
an effective source strength which is a decreasing function of travel time or
downwind distance.  The simplest example of this treatment Ls the us*j   .  an
exponential decay factor in  several currently available models.  By cp;roprLjte
choice of the value of the decay constant,  it  is possible to siru-lut <: ' rudely
the effect of the removal of pollutant.  An implicit  isi-airptiou in rhlr. treat-
ment is that the shape of the vertical concentration distribution 15; uiia^ftcted
DV the removal process.  This assumption is valid onlv  If  r.he r^fr- -it vertical
mi sing is large compared tc  the rate  cf ;;oili.ir? ed  in Sl-r^e (1953), involves
the assumption that the pollutant is  re^o/ed af ~. ratr proportional to the
ground level concentration.  However, ;hi.- cone, ntration is ^i-./es. by the
Gaussian plume formula .*: ui perfect reflection, modified hv a factor to account
for that mass of pollutant already lest .  The  effective .source strength as a
function of downwind distance must be determine! by quadrature for the specific
parameter values involved and presented for use in graphical or tabular form.
As in the simpler and less detailed exponential decay treatment, the implicit
assumption is made  that the  shape of  the vertical pollutant distribution  is
unaffected.

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                                     A71

       The special case of particulate matter for which gravitation settling
is important is generally treated by what has come to be known as the tilted
plume approximation.  The vertical pollutant distribution is determined as a
function of tine or downwind distance using whatever model is appropriate.
A downva-'d "lOtlon with a velocity equal to the appropriate settling velocity
is addei >:•<  Y. :-=ver other notion hap been predicted for the distribution.
FOJ  Jcaady-Ktei e models,, ch<=> effect iri to tilt the plume centerline downwards
vjLth a slope determined by the r.3t.:.o of the settling velocity to the horizon-
tal wir.d speed.  One should in principle use a different settling velocity,
and hence a Jifcerent slope, for particulate matter in different size ranges.
       Table 5.13 lists possible treatments of dry deposition.  Table B.ll
lists the treatments used by suggested reference models.

       A.6.3  Treatment of Precipitation Scavenging
       The various processes whose net effect is called precipitation
scavenging are not usually modeled individually except perhaps in specialized
research-level models.  Instead, the total effect is generally treated  in an
approximate way.

       Both the removal of pollutants in clouds and the scavenging by falling
precipitation are usually considered to be exponential processes.  This may
not be strictly true in all cases.   For example, the uptake of SO  by cloud
droplets is not really an exponential process because of chemical reactions
which occur in the droplets t-hemselves.  Precipitation falling through a
polluted layer may take up a soluble gas at one height and release  it at a
lower height because of evaporation of the drops exposed to a clean at-
mosphere.  These effects must be modeled on an individual case-by-case basis.
       If removal in clouds is treated as an exponential process, the decay
constant is called the rainout coefficient.  If removal by falling precipi-
tation is treated as an exponential process, the decay constant is called the
vajhout co-ffi'-ient.  These coefficients in principle depend on a wide variety
•>r urop and pollutart characteristics.  Empirical values are often used and it
is often - ^.-,ua;ed that trie relationship between the washout coefficient and the
total raiiuall rate may be expressed by a power law.  The washout coefficient
is 3 f- a^txou of drop size.  A moie detailed treatment would take this into

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                                       A72
account and  determine the total  rate of pollutant  removal by integrating ever
an assumed drop size distribution  function.   iiiis.  is rare-. Ly .to'ie  i_u  practj^.r.
       If the rainfall rate  is variable, so  ii'  the washon1; co?.f i" ic lc it,
Ihe pollutant  concentration  then decreases- in a n^.-iner rcJlec-.in-j ;;n is v~.? iain.1. i
the decrease is not represented  by simple expo^c-ci i,il. de.ay.  "or the -r^r^nse
of describing the effect of  rainfall on pol'lataal,  cone etit <"at ions, Liu-, vasho1-..?
coefficient  must be known or assumed, including any time variation due to
variations in the rainfall rate,
       II" the application involves an averaging time sufficiently long that
more than one rainfall occurrence  needs to be treated, even sjvplcr  methods
are often used.  For example, the  assumption may be made that every  time  it
rains the ambient pollutant  level  is decreased  ty  some cc-;,.start,  factor wnl^h
may be empirically derived or estimated from the average -.:ura :.:;-.on of rain-
fall in the  area.  If a climatologic.al model  is be-ing u?eci,  .ht;  correlation
between frequency of rainfall and  othi;r rrieteor<>lcgle£l paramt.' '  "s, particular] y
wind direction, should be taken  into -••.ccouiii. ,   ;_n,aing (.Ms < orrftjar ion
represents an even less detailed treatit.er-c c-nd
imposing total rainiall -o^touT.s :»;. ct jf.'.j a ted
cst.iir:ot'- the effect oa  ..--'j  -".. •:>„ .-JYC,--J;J;<.   .•-.••:•
Is nirf-i. Dimply handled .ir :J ••r.-.t'olov-1'  a"1
Ci<3 sf^' ',-t" ;,   'c;._-" ,_A: ..   ..••• i^D'  •    ,   •
.;sC'-'! ,       • .'    "•.-;'-   .- 1    -". • --i' • -.'
 • jf oo. '. .1 '  ~:'< •     •'.   .'•    '   '     ' '

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                                      A73
A.7  BACKGROUND,  BOUNDARY AND INITIAL CONDITIONS

A.7.1  General
       An air pollution model describe • * he  po'lutanL distribution within
a liiated volume  of  snare for a limit'.'d reriod  of  time.   This volume is
bounced on  the bolt-ij'> by chf c 'trh'"- °<;rfa.j •   on  the sides by the perimeter
of the refill of r-tcrest. and ...ri the -->p b}  the  upper  limit LO vertical
dispers Lor*.   rven < c ~ me a c-"is v- leh ca1 crj.it^  oi.ly  ground level concentrations
explicitJ.y,  ;!.;{.•  toiee ci'\v:isi,  'H' nature -.'t  dispersion  is accounted Tor
through  ;-i:'.-J-.'.si ...1 o c  sucb o-aiatne^ers as stack  height, plume rise, or mixing
height,   n  ru:v  case, tre.-n tmen.:,-'. of the  i'olj owing  four  aspects of the given
app : ic at ion  t. ra  required:
       *  Effects due to the existence of a  finite upper limit
           ;o  dispersion,
           "he effect  of the earth's surface  as a  barrier to dis-
          persion and as a potential sink for  atmospheric pollutants,
          The contribution to pollutant levels within the volume
          of  interest from upwind sources not  included  in the
          model,  and
       *  The initial concentrations throughout the volume of
          interest  at the beginning of the time period  of interest.
Numerical and semiempirical models treat the  first three aspects in different
ways; dynamic and steady-state models treat  the last aspect in different ways.
       The  first two  aspects are generally called  boundary conditions in both
numerical and semiempiriraL models, because-  they  relate to effects at well
defined physical boundaries.  The upper lirult  to  dispersion is commonly treated
as an absolute barrier which keeps pollutants  above jt  from er" ering the modeled
volume and which prevents pollutants dispersing upward  within the modeled volume
from going  any higher.  In such cases, there  is no net  flux o >: pollutant
through the  boundarv.  This condition is called the perfect reflection boundary
condition and is a  common assumption used lor  the  upper bouprl;-ivy; other
assumptions  regarding the upper boundary <.'r>i>'l ; t ion are  iet\~ - "imion,  However,
t^ere are c:rcurns- -.ncec in winch noJ J i.rant;.  ', c-r7 -.ritcr  he :rc   r,<] re c,ii.-r. ;ii»o-.gh
the upper bound, rrv.   For examule, pollutants  .;yJn^, :iho-/e ci'e ^jxiti.L, L,-.% •  c-.;1 be
entrained within the  modeled iToiune as the n.;y:.ng  height i^cr-ar-'^; in the ^''Tnin
as a reS'Jt  of scl;;r  heating.  In prarti--e,  oniy  i :i'nr j.U.-;l'\l- • -.iai i  "'ojeis t r«  •

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                                         A74
£uc.h  .'iltu-'iLiariG  in def.aii .   A ,i,rei t deal  of imprecision exists  in specifying
...he fl;;;-,  ',.->»  /. .-,./)  of poll' '.;.,  t  ^.ivs'  th"' upper boundary -:<-;e  :_o the  ujck
of ri-1 i-'b"1 e estrniatfs of  such tr?iif , •;.-  in re,0! situations.   Even when
perfo  *•  r-:.f - er-1J ;;n is ?CJSLTU€-,"!,  f,hi  •.„».,-,.•::  u_?.j:if .if  the m.j.yln^  height is
g^Tieially -ubj--':t  to f-rrot ,  he I - j, b. ';-., i ui  ;--,t,'V:jol.H,:_,on£ L'roru  'aeasurcnents
I'ad."1  a*  'iTf?r(-:s'  3.'j_c,: Loi .-•  cc  v l^c./ ;:T-.on ' '. i/i~-- htn'.i,' ncdalac.
        Two effeci £ -i^carrnln;  L:!C -^i UTP of t!'.<"• 1 owf-.r bourdary  com.ditioii:
        *   The ""ehavior of the earth's  surface at- a barrier  to
           downward d tsoersior., and
           The rate of removal of the pollutant at  t at s-jr^.'-ce.
These  two effects  are usually assumed  to  be related, becaus.? the rate  of  re-
moval  is  proportional tc  tho ground-ievkj concentre:ion.  YJIJOUS processes
detexialne the degree cf nbscrptlou cii-j  whi.;'h arc me «•' lr-"O:"-«r:r dp.pends up?:'
the particular situation,  for cxain ^': e 3  iarg'.1 parti.vi.e3 ca'-  Pej;tl-. cat:
fbe perfectly absorbed) under the  irfluer::;e •>!" gravity.   S'-lfur
be absorbed by vegetation ;-ind o^or. • v:.i~  r27,r '- '-!\:,i1'; c -ts ly  ,-'i';< "
rlalr. on the earth's1 •5-Jri:v;e,  ~"l^~ <:t:' ii-.-;   :•  -:• .^s.,  .•..•/-.--  ; •-  ,-
                 "Ollg •/!--
                 -.-. ^ in,;f v
        It  --hould also he  .lote.n thjL  ,varerl,':aJ TV ode? ^ e.eiH'rallv treat  at least
 some fraction  oi the e.ni&sionh' or  pollutants  jv  specifying  the appropriate
 flux through the lower  bcu-idary 3.3  part of ,':1;-  lower "boundary condition."
 In  this discussion, the  "boundary  condition"  refers to what happens to pollutants

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                                     A75
already emitted; emissions treated as occurring at the boundary should
be considered as aspects of source location and emission rate  (Appendix A.I).
       The '"bird aspect, advection of pollutants into the volume of  interest,
is relci'od *:o <;he concept of a background level.  Such concentrations are due
*:o na^.rti .ivi r^n-maoa sources not being modeled, because they are  outside
the KoJeled refM.ir.  Tnis def'iuLtion of background differs from another
sometimes used in which the jaukgro^nJ level is taken as the concentration
which would exist if all sources in the modeled inventory ceased to  emit.  The
latter definition would include contributions from sources within  the modeled
region but not included in tae inventory.  In the sense used here, background
might be defined operationally as the pollutant concentration  measured just
outside the upwind boundary of the region of interest.  Such a concentration
would frequently depend on the direction of the wind, the location of the
measurement, or the time when the measurement was made.  For non-conservative
pollutants, this concentration would be expected to change as  the  air is
advected through the study region due to the operation of various  removal
mechanisms.  For secondary pollutants, the incoming fluxes of  precursors must
also be taken into account, because they will generally interact significantly
with emissions within the region and greatly affect the predicted  levels of  the
pollutant of interest.
       Ozona, which is both reactive and secondary, illustrates the  situation
well.  "Barkp;round" ozone concentrations measured just upwind  of urban areas
TO. frequently reduced within these areas due to the initial scavenging of
•j*:one by precursor nitric oxide emissions.  Downwind of the urban  area, the
precursors react and ozone concentrations rise again to high levels.  Back-
ground is thus usually not a simple additive term but is a function  of
position ar.d time within the region of interest.  A single, additive background
number" orn be defined only for primary conservative pollutants.  Otherwise,  the
flux <. f pollutant and/or precursors into the study region at the vertical
boundaries inusr be known   Even for primary conservative pollutants, the in-
v. 'ping fl'i>. ".use be known as a function of position and time if significant
 •'Tia'. ;• /•-  <--!ir ovc " M-ie or distance sen •-.-.s small compared with  the averaging
"TC ar.J _•«  rlre of the: L'cgiC!  of interest.  Rural SO  or culface levels pro-
                                                      9
vide examples of situation9 in which a single, additive background level is
iikeiv to ".„•• appropriate.

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                                     A76
       It has been assumed in this discussion of background and the. side
boundary conditions that the study region has been chosem carefully to
include all important sources.  It would be improper,  ior example, to estimate
the total 24-hour maximum SO  concentration in the vicinity of a power plant
                            2
while treating the contribution of a nearby plant as a background value.  Both
plants would need to be included in the study region and modeled.  The second
plant could be excluded only if the contribution of the first plant alone.
rather than the total concentration, were desired.
       One other point needs to be made about background.  Circumstances may
arise in which background is negligible, any background  concentration being
small in comparison to the concentration of interest.   For example, In cases
where the maximum short-term concentrations near a large, relatively isolated
source are being estimated, background can usually be ignored.  In such cases,
models ignoring background are applicable.  The user must consider the appli-
cation carefully when making such a. determination.
       The last aspect covers the initial conditions,  those concentrations
existing throughout the study region at the beginring of the time period of
interest.  These concentrations are not treated explicitly in steady-state
models but must be specified in order to solve the equations used in dynamic
models.  Initial concentrations may be included implicitly in steady-state
models when background levels are estimated.  They are likely to be most
important for short-term averages for which the initial concentrations can
constitute a substantial part of the final Lime-averaged concentration.  This
situation would occur most frequently when the initial concentrations are
large and travel time across the region of  Interest is equal to or greater
than the averaging time of interest.  As noted in Appendix A, 4, this type of
situation calls for a dynamic, rather than a steady-state,, treatment,.  The
concentrations of secondary and reactive pollutants are particularly sensitive
to the initial concentrations and distributions of precursors and potential
reactants, respectively.  Initial conditions are  thus irnportar t tor such
pollutants and a dynamic approach is better suited to their treatment..  This
is particularly true when short-term concentrations are desirec as is the case--,
for example, with ozone.

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                                       A//
A . 7 . 2  Treatment of BackgroundJ,_ Boundary and^nitj.al^ Conditions
       Since numerical and  sera temp ir Leal models  treat  dispersion from different
points of  view,  th^v employ different  ioeUK--j s for  handling background and
boundary  rendition^.  Initial  conai Lions ar-s treated dif f eir.'intl y by dynamic
and steady-state r.v-deis.  The  v.ser :hou3a be. aware -:hat  ooch "boundary
conditions '  and   'initial coKdi Lions'" sign.i.iv two related but nut entirely
equiva ..ara  concur; s.  !<;~si",  ''bey m^-en a set ot  mathematical expressions
required  to solve the partial  differential  equations used in numerical model ••>
and >r.rond, tbo  Dhysir =] corv! ir Lous  beirif modeled.   The  n&t hcmatical expressions
are u-v repre^enir !.lon^ of  L;.£  physical <_onditions in a  form suitable for
  ,'.r?>- -.:. c. .-  Tno'!el&.  Sei ieinpii ical models inust treat the same: physical conditions,
s?'.i". ]  .fit--1 lefene.-4 '.o as  the boundary coud Lti^ns ,  using different methods.
1 ae i1-'-. _ :sr-xo.o IF  •oTvo'i'' enf ly divided by considering first the treatment.? of
bickf  Jru' .;nd boundary conditions by numerical  and  semiempirical models  ar.c
. i. -    :,c  ", rcatme:i.-b of initial  conditions by dynamic and steady-state models.

          '-^ ami ft.'-und.xi   Condj tins
        ' '„-!.  of the difference between the treatments of background  and  boundary
condit :.,-n<;  by numerical and  semiempirical models  is simply a difference in the
methodologies used to express the same physical condition.  As will be  seen,
howevei ,  the a-mierical approach generally provides a more detailed  and  flexible
treatment  of these conditions.   Al  this point, the user should keep Ln  mint!
that .Applicability of both approaches to the application as discussed in
Append, tx  A ,4 .
        As noted above, ii£.nv  processes can take place when a pcliu^.ant contacts
the earth 'i>  surface.  Perfect reflection or absorption ;n e generally approx-
imations  to  the real situation.   The apptovriatepec-s - " tli'- approximatior  being
used must be ass-oseci ;:>y  th'  user wner "omp.jring  DKV'I.LJ,  .'."v-ier im.l models
treat perfect reflection  mat. hei,,;:" ically ''y requiring t!:at. ;. re vertical  f.:rt su- -'ion i jf vesponris  to i '-•• ; .- : tt^E^iit   .r. i i;^
cc.rv.en' I'cii "km H-. f.-.-io ,-.r  the '(:-. 'uii^a ,:v   l._-,-i^  • r1 r I '•*.<"•.   ~ <\ :in,j  v  assT'^ed
because  i"  is i!,;u-?Llv .- muci. beti..-r ar yj ^.7-; ';7.j !zion to rh.. "... 1.,  -j. t Lr
than  LCJ perfect db^orpLjion.   Both of these situations iia? a1.--"- '>- . b^nci.1 -..'
easily  by semi8>;:plL ica : models.   Semicnip'Jrirs.L u'O'Jei;; tre ; r-'.t'"^ t re"'1^

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                                     A7S
c* the lover br^j^.dary by  indud it-g an  "linage  .source" equivalent to the
leal ;,-Mirce but locsteJ like  its mirror  image with  the earth'a surface as
the tr.ii-i.-o-'.,  T, •> 'Wt'rod  or images"  is the  . echnique employe ,1 in the most
widely used forr,--1--  jf th°  Gauss I; r pjuKC.  moaei and  can only be used to handle
perfect •. of le.ct.ica or absorption.
       Partial ref^eccion at  tie earth's surface  is treated in numerical
models by using Lhe concept of  a "dry  deposition  velocity."  This parameter is
a measure of tho rate of  pollutant removal  at the earth's surface.  In essence,
the mathe.tnai-.ica: f .-rnrnlatiori  alj ows  part of the incoming polluta.it to be ab-
sorbed sc that the. total  amount being  dispersed is depleted after reflection.
Most semiempirical models developed  t.o date cannot ; r-^t partial reflection ar
s. boundary condition.  An approximate  treatment of dry deposition 33 a pollu-
tant removal process by assuming an  exponential decay of the pollutant is  fre-
quently used.  Tfiis is discussed xn  pore de.i ail In Append";'-, ",,o.  Dry deposition
could also be  treated as  a boundary  condition by semiempirical models if the
assumed functional form of the  pollutant distribution were based upon analytical
solutions of the diffusion equations subject  to the appropriate •;•: .;.d,-'ry
condition.  Numerical models  can also  change  the amount cf abyorjt i.->it L?
represent different conditions  throughout" U>e study region; seaii-m:: jx lc.^1
models can usually only deal  with one  ove*-nll average cry d-.pjsJclc^   . ->•
throughout the region of  interest,
       At the  mixing height,  perfect reflection is geaerally 'i«sii;,,er\
Numerical models use tne  same form of  mathematical boundary c'-'.tl'.t ion ^.o at
the surface but apply  it  at the height, corresponding to the t::»p •->: the mining
layer, which can vary with location  ,-,ad  time.  Theso model?. crniM  also be
used in principle  to cover the  case  of partial nent't lation of-' the mixing layer
(.partial reflection) simply by  altering  the boundary condition as is done  to
treat dry deposition at the surface.  They can also accoui.it. for the  transfer
of pollutants  into the regicr of  interest by  B 'icanlp modilications  ot the
upper boundary conditions and t fius  treat fumig itLon o: ontrairmenl:.  It should
also be noted  that numerical  models  require a Linite upper limit to  dispersion
in order to  solve  the  relevant  equations.
       As at the ground,  semiempirical models generally treat only the case of
perfect reflection.  Two  methods  are commonly used.  The  first is the method
of images in which image  sources  are added above the mixing height to account

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                                    A79

for the reflections from that barrier, which  is generally  assumed  to  have  a
cur.stant el ov;_t ioi,.  It turns out that an  infinite number  of  images are  required
T.O accc:T. L •"-. r the multiple reflections from  the ground  and  the mixing height
[?:*e Turnei  (1969)] and the result is expressed as an  infinite sum.   In  most
cases cnlv  he first rev; terras of the sura  contribute significantly and the sum
iaay be evf'i-^aLod easily to sufficient accuracy.  A more  common treatment relies
upon the o";s^rva'-ion that near the source  the plume is not affected by condi-
tions at t'-e top of the mixing layer and that far enough downwind, the pollutant
is uniformly mixed within the entire mixing layer.  Between  the distance at which
the plume first feels the effects of the finite mixing height and  the distance
at which the vertical profile becomes uniform, the concentration  is obtained by
interpolation  [see Turner (1969)].  A variation of this  treatment  used  in  some
Gaussian plume models treats the effect of the mixing  height  implicitly  by
limiting the vertical spread of the plume  by  requiring that  a remain constant
after the vertical spread of the plume  (a  ) exceeds some fraction of  the mixing
                                         z
height.  Pasquill  (1976) discusses the limitations of  the  undisturbed and
uniform mixing approximations and has presented a table  for  use  in interpolating
results in cases where the sum must be evaluated.   [See  also  Yamartino  (1977)].
Evaluating the sum w\~. 1 generally give more accurate results  than  interpolation.
The gain in ac-'t-racy is slight considering the magnitude of  other  inaccuracies
in modeling treatments and interpolation is used more  frequently.  Semiempirical
modal s can al-30, i... essence, ignore the upper boundary condition  by using  a
functional * ortn for the vertical concentration profile that  places no limits on
the height ;  • which pollutants can disperse.   This may be  an  appropriate repre-
sentation of the real situation of the large  mixing heights  at short  distances
from the source.  Semiempirical models can be modified to  account  for fumigations
by using equations (functional forms) for  predicting concentrations during the
rime ol tho fumigation,  (See, for example, the equations  in  the appropriate
references cited in Appendix A.2.)
       iv'umprical models treat the conditions  at the sides  of  the region  as
matnanatical specifications of the pollutant  flux into the region. As noted
-_,;-,,,V6; thi.-  is the mc-.it fundamental way of treating background levels.   Semi-
emjiti lea! rr.olels camut treat these as boundary conditions and "background"
C.-XP 3i;ly  -  :.r---,ated j • a general additive  term.  This  term may be  a function
cf 1.3,.atic:i within the region but is generally treated as  a  single constant
vsii-e ii,^ ig'.or Lng directional dependence and spatial variations. Any  temporal
-ar/at ion  •-, « 1 bO generally ignored.

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                                     A80
       Initial Conditions
       As pointed out previously,  initial  conditions are  treated  explicitly
only by dynamic models.   Any contributions tc  the  concentrations  duu  to
pollutants initially present would be handled  as part  of  t.he additive back-
ground level by steady-state models.   As such  they would  be indistinguishable
from the concentrations  assumed  to be advected into the region  as "true"
background.  In dynamic  treatments, more detail is available when the initial
conditions can be arbitrary functions of location  than when single uniform
values must be assumed throughout  the region of interest.
       A final word is in order  about climatological models and temporal
variations.  As noted in Appendix  A-4,  this; approach can  make use of  any  of
the basic types of models discussed although a steady-state method is most
often used.  Thus, the treatment of background, boundary  and initial  conditions
by climatological models will depend  upon the  nature of tba model used for
the dispersion calculations.  Both dynamic and sequential  sf"eady-state models
can, of course, account  for temporal  variations in background and boundary
conditions.  Dynamic models usually allow important parameters  to change  re-
latively smoothly over time; sequential steady-stite models allow parameters
to assume new values at  the beginning of each  new  time interval over  which a
steady-state is assumed  to hold.  Dynamic models most  frequently  treat the
amount of material advected or entrained into  the  region  of interest  or the
mixing height as time dependent; sequential steady-state  models most  frequently
treat only temporal variations in the mixing  height.
       The ranking of treatments of background, boundary,  and  initial condi-
tions is given in Table 5.14.  In treating these elements, almost any combination
of types of treatments at the various boundaries can occur.  In rating a  model,
the user should rate the model's treatment of  each element separately and combine
them to arrive at an overall rating.   Table B.12 lists the treatments of  back-
ground, boundary and initial conditions used  by suggested reference  models.

A.8  TEMPORAL CORRELATIONS

A.8.1  General
       As noted in previous subsections, many  of the  elements  or  quantities
used to parameterize an element treated by a model can vary with  time. The

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variations of  these  quantities about their mean values  are  frequently
correlated in  the  situation being modeled.  For example,  the application may
involve a source with a diurnally varying emission  rate and meteorology with
the typical  diurna"!  variation", in atmospheric  stability described in
Appendix A.4.  Wher  such correlafi'^v. trcur ;t is usually important that the
model correlate  the  niira-dependenr quantities, that is. treat them in such a
way that con Cent car. ion estiira^fc;- arc made ur the basin  of values which do
occur together ir  the application of interest.
       Implicit  ir* the last s-'atement is A realization  that the treatment of
correiauioas is  d .>-~aly ,-.;-] acod to thu degree  of temporal resolution obtainable
in the ii-o»!el.   I.n  particular, the resolution time  for  the correlated quantities
ir, b~-  U-'-st, '_har>  the tine o^/er which the variations can  occur.  For example,
I: tvc  o.T^l;-,ted  q\;ar" •• : cs v.ar; hourly, the  model must  treat each of them
vlth  - " >•-  r, t.yli ^i-.iii oi  one hour or less for the treatment of correlations
tc te   'jpsii'Le.
       ,i; j.'Oii.red  out previously, there is i limit, frequently based on practical
co-is \d-. ;•-•1 ioris or  >utta Availability, to the resolution  time and hence to times
over w  :. ". '.CLTelat '-ons can be ccn.&ideted.  The limiting  factor is that element
t,r .-juautity  vit;h the minimum degree of time resolution  among those elements which
are iEp.-r^arit  to  thf. particular application and which exhibit sufficiently
large ter.pnraJ -.•ariabll I ty to affect f.h". model results.  The primary interest
is generally i::  correlating emission rates, meteorological  parameters, and rates
of removal -met '' r^nsformation processes.  Of course, in applications where
emission  rates are almost constant, correlations  involving  them are small and
may be ignored,   f eneraliy speaking, the oortelauions between the various
meteorological parasr.ettrs also need uc be treated.
       Dynamic and sequential models handle temporal correlations automatically
within the time resolution used by the model.  These models generally allow
the values of  mopt imporrant parameter,-- to be  changed  at  aach time step arid
since the data for each step art-, ^enerall-"  input as a unit  py the user,, they ax e
automatically  correlated.  Steady--state models which treat  one or poi't-ral
specific  sets  of  emission and -n;-^eoroi ou l-.al cl^ta  trea*- ..or.- oL, t f --c Ai.,->o
ccci-.r on  a time  vale  longer thai the avera^ji^;  uim-^  ." "-i-.-  ^'  : a^. .?-,-.*..ica i " v
anct  ignore those vi^'eh occur over snorter tfr.in'..   Tl\:- f,-vi    f-:c/;i a.-,/  U*M,' " it
in che structure of  the input data as in  tne  iynamir rase   m1-.:   ' -T: -  ,•. • : p = L:r,--.t
is frequently  er. "'.ntored  in models whLch e.-jt uriatt- s^:i ,-t..n jr.,  it/;ir. Lor

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                                    A82
       On the other hand, c.Iiaiatologica]  mode.1 s use r.tatistical wind rcses
°-nd hfnce the only correlations inherent  in t';.i<= approach art- between those
parameters u.pon vhich the t^ini. rose is base-1,  typicaJly a mo spheric stability,
wind speeUi and vind direction.  A ':*.ree-hour  resolution is typical of wind
roses.  A.H other correlations, particularly tnose involving emissions, must
be treated separately,
       Two tactors should be considered when evaluating the treatment of
correlations:
          The magnitude of the variations in the given application
          over time scales Hess than the averaging time, and
       •  The importance to the application of the quantities involved.
The first factor has been discussed above.  As for the second, simply
correlating many time-dependent quantities may be less important than
correlating a few critical quantities, e.g., wind direction and emission
rate when the effect of a peaking power plant  at a specific location is
desired.

A.8.2  Treatment of Temporal Correlations
       Beginning with the most detailed,  there are basically thrse It vels
at which temporal correlations can be treated:
       •  Sequential and full}?- correlated,
          Non-sequential with limited correlation, and
          Not treated explicitly.
The first type of treatment is found in dynamic models or in sequential models.
In these models, the correlations are treated -mtomatically.  The  second type
of treatment is exemplified by climatological uodels.  Although some statistical
models may implicitly treat correlations by th.3.ir choice of variables, they are
classified here as using the  third type of treatment and are discussed in
Section 7 .
       Within the first: two treatments there is a variation in the level of
detail depending on:
          The degree of temporal resolution and
       •  The quantities allowed to vary.

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                                    A 83

The determinants and importance of these aspects have been discussed in the
general discussion in Appendix A.8.1.
       Table 5.15 lists the treatments of temporal correlations and the
treatments by suggested reference models are given in Table B.13.

A.9  IMPORTANCE RATINGS FOR APPLICATION ELEMENTS

       Source - Receptor Relationship
       The source-receptor relationship is assumed to be of at least medium
imporLance in all applications.  Many factors influencing transport and
dispersion depend on the source-receptor separation and orientation.  The
relationship is somewhat more important for secondary pollutants,  because of
the need for a detailed description of the mixing of various precursors.  For
similar reasons, it is also somewhat more Important when chemical sinks are
involved,  Short-team concentrations are more sensitive to this relationship
than long-term concentrations, since changing meteorological conditions tend
to average differences in  -.oncentrations from point to point.  The concentra-
tion distribution in situations  involving limited numbers of sources depends
heavily on th- source-receptor relationship.  In situations involving multiple
sources whera sir"II inaccuracies in one relationship are likely to be balanced
by inaccuracies ia another, this relationship is less important.  Area source
applications require a. little less detail than point or line applications,
because tK ^patial extent of an area source makes an error in the source-
rr-ceptor relationship Less cigrr.f leant in affecting concentration estimates.
The importance of this element is somewhat enhanced in complex geographic
situations which place considerable importance on the precise relationship
between source, receptor, and geography.  Short-range applications are more
sensitive to the source-receptor relationship than long-range applications.
AC leap; distances emissions have iisually become relatively uniformly mixed and
a change in separation cr orientation that would be critical at short range
produces only a negligible effect.  The importance of the source-receptor
relationship tc each of trie applications is given in Table 4.2.

       Er.-_A3sion Rate
       Other things being equal, concentrations of primary pollutants are
proportional to emission races.  For secondary pollutants, the relative

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                                    A 84

concentrations of the precursors are very important  factors  in  determining
concentrations.  Emission rates were thus always  rated  as  of  at least  medium,
importance to all applications, and as  somewhat more important  for  secondary
than for primary pollutants.  The same  consideration applies  to reactive pollu-
tants, making emission rate slightly more important  xvhen chemical  sinks  are  in-
volved than when only physical sinks or inert  pollutants are  modeled.   Emission
rates must generally receive more attention in short-term  or  short-range appli-
cations than in long-term or long-range applications where other factors su~h
as changing meteorology and removal processes  normally  can assume greater im-
portance for determining concentrations.   Emission rates are  rated  as  somewhat
more important in situations involving  a limited  number of sources, because  oi
the likelihood of compensating errors  in the multiple source  case.   No distinction
is made between different source geometries nor  between the  importance of
emission rates in simple and complex geographic  situations.   Ratings of  the
importance of emission rates to the various applications are ^iven in Table  4.3,

       Composition of Emissions
       This discussion deals only with the chemical  composition of  emissions.
If the user's application requires the specification of a  size  distribution  for
particulate matter, the importance ratings in  Table  4.4 should  be reconsidered.
No general statements can be made in this case,  and  the, user  should consult  ar.
expert to determine importance ratings appropriate to the  application of interest.
       Chemical composition of emissions is critically important when secondary
pollutants or chemical sinks are involved and  of  little importance  when dealing
with primary pollutants and either no  sinks, or  physical sinks  only.  Sfo
difference in importance between long-term and short-term  applications is assumed.
A slight extra importance is assigned  to applications involving multiple source"
or long-range transport, because of the increased possibility for chemical re-
actions when many different emissions  are mixed  or a long  timt  f.c, .41'1."wed for
reactions to occur.  The importance in simple and complex  geographic situations
is the same.  The importance ratings for the chemical composition of emissions
are given in Table 4.4.

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                                     A85
       Plume  Behavior
       Table  4.5  gives the importance of plume  behavior to each of the  indexed
applications.   Plume behavior is equally Important for both primary and
secondary  pollutants but is rated rio^e important  in cases where physical  sinks
are present than  when chemic-il or ;io sinks are  present.  This is because  the
plume behavior  determines how easily the plume  contacts the ground, allowing
the physical,  removal process to operoL'e,  Chemical removal can occur through-
out the  entire  volume oC mixing.  Plume behavior  is also rated more important
in short-term t'"a \  in loag-t^nr averages, because over short-time spans small
variat i.O£>.s ma:>ku,:d  by av^rag^'no ovei long time  spans, may be significant.
The £i -c.'---. spatial Infiomogeneities associated  with point sources make  plume
bchavi"- ;ar cf> important for point sources than  for line sources.  Similarly,
• :. is   - *  •' -i r  wore-- important 1 ">r line than  for area sources.  in complex
t'.aOf.i  ."  '   -• !•' '-ia:. Jons . fl-.int behavior is important in determining whether the
•'-'"! i  •     1 •  ->e affe.cced by the complex situation or rise above its influence.
 •"«'-' " i-, :-'-.;; range,  ver>. icdl mixing,  tends to  become uniform and hence plume
^c-f-MV ' c .'5 relatively ^nim
                        Field
       '!.'ha horizontal wind field is generally  an importar. c element in any
    ic.) rJon,  because advection is the principal piocess for pollutant
         f" .   It  is  considered somevhaf ^iore  important when chemical reactions
-ire important and  when short-term rather than  long-term averages are desired,
because  ot the  need L-  Know the v iricl tieli  more precisely.  The determination
ct the horizontal  wjnj ."ielJ it, tac. r;- l-iprrt.nr.'r ir, complex terra''-1 due ro the
channeling ,>f thf  wind a:v, other' effe'cts.   The horiicnta: ,'i: 3 tl^lfj is some-
what more important in limited point s.r  i. 're source ca::-';° r! ,n urea or multiple
source cases.   Finally, the horizontal wind field is considered i.c be very
important in  those siu>;;; ious in x/nl.c^ the  actual trajectory of n parcel of
air must be determined, co.vvise •.''•'- t^mi/'n c-.l aad spatial variation must be
reproduced.   This  is the cas'3 ,'._. • long •'•ciigc transport, arid '.^r very short re-
lease times  (puff';1*.  Ti.-Me>.  .6 g'.viS r"ie iTr.r or lance rating of horj.^oiiu.-i.l wind
fielc for each  :<;.•  licatiori,

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                                    A86
       The virtues'* WLU.! field is considered  generally unimportant in many
c^ses of  m:. cro.st, because it is vitjriy  aero  on average.   Vertical wind i ieid
is import"n;: in ,?j ._Ud"ions requiring  cMe est iiiia-.J-on of concentrations at
srcderateLy ;;hjrt janges iu regions  contaxniri^ coxplcx terrain due to the effect
of the terrain on  the (i hree-diorarisional} wiad Jieid.   Vertical wind field is
considered slightly more important  in applications  involving chemistry than
tnose in which c^c.TT.tt ry is unimportant  due  to the  need for a more accurate
description of tne wind field.  Vertical wind field is also r,onsi:'ered more
important in estimating short-term  racher than ? ong-term estimate: .   No dis-
tinction was made  for different source geometries or numbers.  Table 4.7 give*
the importance ratings of vertical  wind  field for the indexed applications.

       Horizontal  Dispersion
       Table 4.8 gives the importance rating  of horizontal dispersior for each
of the indexed applications.  Horizontal dispersion is considered to be of ai;
least medium importance in every application.  Horizontal dispersion i^ more
important at short range than at long range,  because the disper^vor process
is the most rapid  and produces the  greatest  changes ip concentrate or estimates
at short ranges.   Horizontal dispersion  is> considered Jess impc-rc: i-f i  - ;• ra£
sources than for line sources, and  less  for  line than for potrt :?o-i-- «•- due to
the emission size  effect.  In the case of secondary poL.lutfocs .inc. •'(>>. u'.ie Cctir-e
of chemically reactive pollutant 3,  it is very iiiiportaru  to be "L, <  i;o aesc,- xbe
the mixing of emissions with the ambient air, since chemical reaction ratet.- are
sensitive to local concentrations,  chereiore  ao., i^oat. ax C.P s.'er-; loo 's considered
quite important in these caseis .  Similarly,  if ;.hvstcc..i  sin,<,.; sr'j. present, it
is generally more  important to handle horizoiitaj disnersion properly, depending
on the nature of the removal  process .  "'he importance cf hot Lzontrl dispersion
is considered to be higher LOT s^rt-Lorio averaj-.es  than for ic[3g-ierms because
the averaging which can occur ovar  long  time,, gfuerailv allows simpler treat-
ments to be adequate.  Finally, horizontal dispersion is considered to be equally
important in either simple or complex terrain,

       Vertical Dispersion
       Table 4.9 gives the importance rating of vertical dispersion for each
of the indexed applications.  Vertical dispersion  is given at least a medium

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                                       A87

rating for every application.   Its  importance is considered independent of
averaging tine, and apprr -. - <••?.l>. "I;  Ar.-.Ierer.Jant .">  -V- type - c terrain.  v?rti
      sic-, :.,= consic'ei: e<'  >- r*-.  >•_•- ~  A-I-JOI~  it ,s : -.  -•   -^ >;- ,:han at !,>-;;.;  o?r.
      •/.- -r;r ;•",-.11  ;•'.-,  ;.-.   ' •, - _.  =.r;.'.-:  -j  ...,.-...         : v- prllut- v.';., ,
       The iinuoirtaviL-e  ol  caen.1 -:~•"•' i-cJ i<:t. treatav.   if. determined  primarily
by  ^-he chemical  nature o^" '^.<-  ,.,-^ I'' -.'tants involved and to  some extent  by  the
travel distance; no  other charge c.«r is tics of the application need be  considered..
Chemistry is  irrelevant for primary inert pollutants, is  of importance for
primary reactive or  secondary  inert pollutants, and is of even more importance
for secondary reactive pollutants.  The importance of chemistry is  rated lower
for primary reactive and  secondary inert pollutants than  for secondary reactive
pollutants.   If  chemical  reactions provide both a source  and a sink for  a given
pollutant, chemistry is more important than if they provide either  source or  sink,
but not both.  This  is a  somewhat  arbitrary ranking; the  real importance of a
detailed treatment of  chemistry depends on the complexity of the system  of  re-
actions and the  number of pollutants involved.   Chemistry is considered
slightly more important for long-range than for short-range applications due
to the longer travel time and  greater opportunity for reactions to  occur.
Table 4.10 gives the list of importance ratings of chemistry and reaction
mechanism for each of  the indexed  applications.

       Physical  Removal Processes
       We consider two processes in this category:  dry deposition  and pre-
cipitation scavenging.  Physical removal is important, by definition, in those
applications  for which the user has taken the physical or chemical/physical
sink branch on the Application  Tree.   Physical removal is also slightly  more
important for pollutants  with  chemical sinks than conservative ones.  Physical
removal is more  important for  long-range than for short-range applications,
because of the cumulative effects  of the process.   Its importance is considered
roughly independent  of source  type and averaging time.  Physical removal  is

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                                      A88

considered slightly more important in complex rather than simple terrain, due
to the increased surface roughness.  It should be pointed out that the importance
of precipitation scavenging, as a removal process, depends primarily on the
fraction of the time during which precipitation occurs in the application of
interest.  Thus, for short-term applications precipitation scavenging may
usually be neglected, while for long-term, or possibly long-range, applications
a convenient measure of its importance is the rainfall probability.  Table 4.11
lists the importance ratings of physical removal for the indexed applications.

       Background, jtoundary and Initial Conditions
       The importance ratings of background, boundary and initial conditions
to the indexed applications are given in Table 4.12.  These conditions were
rated as highly important for secondary pollutants where precursor background
levels can significantly influence the pollutant concentrations in the region
of interest and for applications involving sinks where the advected concentra-
tions might be significantly depleted during transit.  These elements are
crucial for applications involving reactive pollutants where the details of the
pollutant mix must be known.  These elements are equally important for short
and long-term averaging times and for short and long-range transport.  They
are independent of the specific source characteristics and geography and are
assumed to be of at least medium importance to all applications.

       Temporal Correlations
       Temporal correlations relate the time variations of the other application
elements in their proper sequence.  The importance of temporal correlations to
the indexed applications is given in Table 4.13.  They are rated more important
for secondary than for primary pollutants, because the exact sequence and
correlation of emissions and meteorology determine whether the pollutants are
brought into contact so that reactions can occur.  The ambient concentration is
less sensitive to correlations for primary pollutants.  Similarly, when physical
and chemical sinks are involved, it is important to treat correlations.  When
treating short-term averages, it is generally important to know the detailed
short-term fluctuations in the relevant factors and to correlate them properly;
such detail is usually unnecessary when treating long-term averages.  Thus,
correlations are more important in short-term than in long-term applications.
No distinctions are made between the various source types.  More importance is

-------
     iutcc wicr. ie:-pcra_  correxf.L. •:;<=  _;.  c.~"'f  t.^ geograpaxc situations.  her^
correlations between emissions and dispersion  factors can determine whether a
particular emission passes within the  perturbing influence of the complex
geography.  Short-range applications usually require more attention to temporal
correlations.  At short range, rapid changes normally occur in plumes whereas
at long range these changes are  slower and require less' detail to treat
adequately.

-------
                        Bl
                    APPENDIX B
BACKGROUND MATERIAL ON SUGGESTED REFERENCE MODELS

-------
                                B3

  Appendix B.  BACKGROUND MATERIAL ON SUGGESTED REFERENCE MODELS
        Appendix B is divided into two parts.  The first, Appendix B.I,
consists of Table B.I which provides the classification of each suggested
reference model, and Tables B.2-B.13 which provide the treatment of each
of the twelve application elements used by these models.  The second part,
Appendix B.2, provides abstracts of and the working equations used by the
suggested reference models.  A glossary of symbols is provided at the end
of Appendix B.2.

-------
                                    B5


                           CONTENTS OF APPENDIX B
                                                                       Page

B.I  REFERENCE MODEL TREATMENTS  OF APPLICATION ELEMENTS  ........ B 7


B.2  REFERENCE MODEL ABSTRACTS AND EQUATIONS .............. B35
     B.2.1  COM
     B.2. 2  RAM ............................ B38
     B.2. 3  Single Source (CRSTER) ................... B41
     B.2. 4  Valley ........................... B44
     B.2. 5  ATM ............................ B46
     B.2. 6  STRAM ........................... 347
     B.2. 7  APRAC-1A .......................... B48
     B.2. 8  HIWAY ........................... B50
     B.2. 9  DIFKIN ........................... B51
     B.2.10 SAI ............................ B52
            Glossary of Symbols .................... B55

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                                B7
     B.I.  REFERENCE MODEL TREATMENTS OF APPLICATION ELEMENTS
        This appendix provides the classification of each suggested
reference model in Table B.I and the treatment used by each model of
the twelve application elements in Tables B.2-B.13.

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                                        B9

                   Table B.I.  Reference Model Classification
 Suggested

 Reference                               Classification
   Model	

APRAC-1A                        Semiempirical/Sequential (steady-state)


ATM                             Semiempirical/Climatological (steady-state)


CDM                             Semiempirical/Climatological (steady-state)


Single Source  (CRSTER)          Semiempirical/Sequential (steady-state)


DIFKIN                          Numerical (vertical)/Semiempirical (horizontal)/
                                Dynamic


HIWAY                           Semiempirical/Steady-state


RAM                             Semiempirical/Sequential (steady-state)


SAI                             Numerical/Dynamic


STRAM                           Semiempirical/Dynamic


Valley (short-term)             Semiempirical/Steady-state


       (long-term)              Semiempirical/Climatological (steady-state)

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                                                       BIO
                Table  B.2.    Treatment  of Source-Receptor  Relationship
                                  by Reference Models
                                    a.  Horizontal Source and Receptor Location
  Reference
    Model
APRAC-1A
ATM
Single Source^
(CRSTER)
DIFKIN
HIWAY
                   Point, area,
                   and  line
  Geometry                                     Method of Treatment

Line and area     User specifies line sources  (traffic links) with arbitrary locations  and lengths.

                 Area sources (off link traffic) allocated to 2 mi x 2 mi grid.

                 For each receptor both are aggregated onto wedge-shaped areas of  a polar grid
                 centered on a receptor (a different grid is used for each receptor) such that:

                 1)  Radii of circular boundaries increase in geometric progression.

                 2)  Radial boundaries are 22.5° beyond 1000 m and 45° under 1000  m  from receptor.
                 (3,3 for area, line)3

                 Up to 10 arbitrarily located receptors. (1)

                 Street canyon submodel:  Four internally located receptors on each  user-
                 designated street.  (2 for line)3  (4)b

                 Arbitrary location for all sources.  (1 for all source types)3

                 Areas should be roughly square or  circular.

                 Arbitrary receptor location. (1)

                 Assumes flat terrain; elevation not treated.

                 Treats multiple point, area, and line  sources.

                 Treats up to ten receptors.

Point and area   Arbitrary location for point sources.  (1 for point)3

                 Area sources are squares of  uniform size in user-defined grid;  user may specify
                 sources which are integer multiples of the grid size, but these must  be super-
                 imposable directly on the grid.  (2 for area)

                 Receptors located arbitrarily.   (1)

Point            Up to 19 sources all assumed to be located at same user-specified,  arbitrary
                 position.  (l-2)a

                 Receptor locations restricted to 36 azimuths  (every 10°) and five user-specified
                 radial distances.  (3)b

Point and area   All sources aggregated to square 2 mi x 2 mi grid cells in an array
                 25 cells x 25 cells.  (2,2  for point, area)a

                 Sources classified as points (power plants, refineries), distributed  stationary,
                 and mobile.

                 Receptors located arbitrarily within boundaries of emission grid.  (2)b

                 Straight finite line segments (will treat up to 24 parallel segments), arbitrarily
                 located.  (2)a

                 Arbitrarily located receptors.   (1)

                 Cut section mode:
                     Emissions treated as coming from 10 lines at top of cut.  (2-3)3

                     Receptors cannot be in cut.  (2)

-------
                                                         Bll
                                           Table B.2   (Cont'd)
                                                     a.  (Cont'd)
  Reference
    Model
RAM
SAI
STRAM
Valley
  Geometry                                      Method  of Treatment

Point and area    Arbitrary location for point  sources.   (1  for  point)a

                  Receptors may be:

                  1)  Located arbitrarily,  (1)
                                                                           b
                  2)  Located internally near individual  source  maxima,   (4)

                  3)  Located on internally generated hexagonal  grid  to  give good coverage  in user-
                      defined portion of region of  interest.   (4)

                  Area sources are multiples of unit squares  on  a  grid;  user controls scale of
                  grid.   (2 for area)3

Point and area    All sources aggregated to square  grid of arbitrary  spacing and up to 25 x 25 cells.
                  (2,2 for point, area)2

                  Sources classified as points  (power plants), distributed stationary and mobile.

                  Multiple receptors located arbitrarily within  boundaries of emission grid. (2)

                  Concentrations also calculated in each  grid cell  (up to 25 x 25 x 5 estimates).

Point             Arbitrary location for each source.   (1)

                  Up to  10 arbitrarily located  receptors plus receptors  at intersections of a grid
                  of up  to 13 x 13 equally  spaced boundaries.  (1,3)

Point and area    Arbitrary location and elevation  for each point  source.  (1 for point)

                  Arbitrary location, elevation, and size for square  area sources.  (1 for area)3

                  Must be less than 51 sources.

                  Receptors (112) on 16 direction radial grid; relative  radial distances fixed
                  internally;  scale and origin  of grid defined by user.  (3)
                                           b.   Release and Receptor  Heights
  Reference
    Model
APRAC-1A
ATM
CDM
Single SourceS
(CRSTER)
                   Line and area
                   Point, area
                   and line
                   Point and area
                   Point
                                               Method of Treatment
                  Sources  assumed  at  ground  level.   (3,5 for line, area)c

                  Receptors  assumed at  ground  level.   (7)

                  Arbitrary  release height  for each  source.  (2,3,2 for point, line, area)c

                  Receptors  at  ground level.   (7)<*

                  Assumes  flat  terrain;  arbitrary stack height for each source.  (2,3 for point,
                  area)c

                  Chooses  larger of input stack height or 1 m.

                  Receptors  at  ground level.   (7)

                  Arbitrary  stack  height for each source.  (l)c

                  Unique topographic  elevation for each receptor:  must be less than each stack
                  height.

                  Receptors  must be at  ground  level.  (combination of 2,7)^

-------
                                                        B12
                                            Table  B.2    (Cont'd)
                                                    b.  (Cont'd)
  Reference
    Model
DIFKIN
HIWAY
RAM
SAI
STRAM
Valley
  Geometry                                     Method of Treatment
Point and area    Emissions  treated  as upward pollutant fluxes at ground surface.   (5,5 for point,
                  area)c

                  Receptors  at  equally spaced heights from the ground to the mixing height. (4)

Cine              Arbitrary  release  heights.  (2)C

                  Arbitrary  receptor heights.   (1)

Point and area    Arbitrary  release  height  for  each point source.  (2 for point)

                  Up to three effective  release heights (appropriate for 5m/sec winds)  may be
                  specified  for area sources.   (2 for area)c

                  Value for  a particular area must be one of these three.

                  Receptors  all of same  height  at or above ground level; flat terrain assumed.   (7)c

Point and area    Arbitrary  release  height  for  point sources (power plants).  (1 for point)0

                  Point source  emissions assumed uniformly mixed throughout vertical column in
                  which emission takes place.

                  Other emissions treated as upward fluxes at ground surface; arbitrary topographic
                  elevation.   (Combination  of 1,3 for area)c

                  Receptors  at  ground  level.  (7)

Point             Arbitrary  release  height  for  each source.  (2)

                  Receptors  at  ground  level; flat terrain assumed.  (7)

Point and area    Arbitrary  release  height  for  each source.  (1, combination of 1, 3 for point,
                  area)c

                  Receptors at  ground level  at any  elevation on  existing
                  topographic  features.   (combination of  7)
                                           c.  Downwind/Crosswind Distances6
  Reference
    Model

APRAC-1A
ATM
CDM
Single Source8
(CRSTER)

DIFKIN

HIWAY
  Geometry^                                     Method of Treatment

Line and area     Uses exact downwind  distances to the two radial boundaries of each gridded
                  area source.   (1 for area)

Point, area       Unique downwind and  crosswind distances for each point source-receptor pair,
                  for three points within  each area source, and for nine points along each
                  line source.   (1 for all source types)

Point and area    Calculates unique downwind distance for each point source-receptor pair.
                  Calculates representative distances for area source-receptor pairs.  (1, 2 for
                  point, area)

Point             Calculated from source to each receptor location.  (1)


Point and area    Not applicable.  Distance traveled along computed trajectory not used explicitly.

Line              Precise downwind and crosswind distances for each point along line.  (1)

-------
                                                        B13
                                            Table  B.2    (Cont'd)
                                                     c.   (Cont'd)
  Reference
    Model
RAM
SA.I

STRAM


Valley
                                                                   Method of  Treatment
Point and area    Unique downwind and crosswind  distances  for each point source-receptor pair.
                  (1 for point)

                  Downwind distance calculated for points  along rays which intersect area sources.
                  (1 for area)

Point and area    Not applicable.

Point             Sot applicable; concentration  calculated  at each receptor based upon distance
                  along and distance from trajectory  centerline.

Point and area    Exact downwind distance calculated  for each point-source receptor pair,
                  (1 for point)

                  Single representative downwind distance  used for area sources.  (2 for area)
d . Orientation
Reference
Model
Source
Geometry
Method of Treatment
APRAC-1A           Line and area     Traffic links (lines)  may have  arbitrary horizontal orientation but this detail is
                                     lost when links are gridded onto  the  receptor-centered polar grid.  (2,2 for area,
                                     line)

ATM                Point, area       Orientation of areas not  treated  explicitly.   (3  for area)
                   and line          Lines horizontal,  arbitrary orientation.   (2 for  lines)

CDM                Point and area    Sides of areas must lie along grid  directions.

Single Source      Point             Not applicable.
(CRSTER)

DIFKIN             Point and area    Areas oriented by  fixed grid boundaries.   (2)

HIWAY              Line              Line assumed horizontal with arbitrary  orientation.  (2)

RAM                Point and area    Sides of areas must lie along grid  directions.  (2)

SAI                Point and area    Areas oriented by  fixed grid boundaries.   (2)

STRAM              Point             Not applicable.

Valley             Point and area    Area sources assumed oriented with  one  side parallel to wind difection.
                                     (Somewhat less detailed than 2)


 Numbers in parentheses refer to treatments of horizontal source location  for the appropriate source type as given in
 Table 5.1 a.

 Numbers in parentheses refer to treatments of receptor location as  given  in Table  5.1 e.

lumbers in parentheses refer to treatments of release  height  for the  appropriate source type as given in Table 5.1 b.

Tlumbers in parentheses refer to treatments of receptor height as given  in Table 5.1 f.

 Numbers in parentheses refer to treatments of downwind/crosswind distances  for the appropriate source type as given
 in Table  5.1 c.

 Numbers in parentheses refer to treatments of source orientation for  the  appropriate source type as given in
 Table 5.1 d.

gCRSTER should be used only when the receptor is below  stack height.

-------
                                                         B14
              Table  B.3.    Treatment of  Emission  Rate by  Reference  Models
  Reference
    Model
                                                                  Method of Treatment
 Source
Geometry
Spatial Variation3
                                                                                             Temporal Variation
APRAC-1A
ATM
COM
                   Line  and
                   Point,
                   area, and
                   line
                  Point  and
                  area
                                                                                      Daily trafic volume for each link
                                                                                      and off-link grid square is input
                                                                                      and modified to produce hour-by-
                                                                                      hour emissions.  (Equivalent to 2b)

                                                                                      Street canyon submodel:  Hourly
                                                                                      emission rate for link of interest
                                                                                      is input by user.  (5)
             Arbitrary  line source emissions aggregated onto  grid
             described  under source-receptor relationship (Table
             B.2).

             Arbitrary  off-link grid squares assumed uniform  and
             aggregated to same grid.

             Area source  contributions from grid obtained by
             numerical  integration of narrow plume approximation
             formulae;  contributions calculated from all upwind
             sources  located within the wedge-shaped grid.
             (2 for gridded area sources)

             Arbitrary  rate for each point, line and area source.     Constant emission rates. (5)

             Area sources transformed into polar areas each of
             which  is represented by three effective point sources;
             shape  of area depends upon angle subtended by area at
             each receptor.

             Total  area source contribution estimated as a sum  of
             individual contributions.

             Line sources treated as ten effective points.

             Areas  and  lines assumed uniform. (1,  modified 4,4  for
             point, area, line)

             Treats "windblown" source as an area source of TSP
             with emission rate determined by user input values of
             type of  material, density, saltation diameter, and
             suspension diameter appropriate to each source and
             the wind speed.  ("Windblown" source: modified 4)
             Arbitrary emission rate for each point and area
             source.
                                       Day/night variations in emissions;
                                       same variation for all sources.  (2b)
                               Area sources assumed uniform.
Single Source
(CRSTER)

DIFK1N
                               Area source contributions integrated  numerically
                               one 22.5° sector at a time,  based  on  sampling
                               points located at specific angular and  radial
                               intervals on a polar grid centered at receptor.
                               (1, 3 for point, area)

                   Point        Arbitrary emission rate for each source.   (1)
                   Point  and    Emissions treated as upward pollutant  fluxes  at
                   area         ground surf.ace.

                               Individual rate for each 2 mi x 2  mi grid  square:
                                  Rates for mobile sources determined from user-
                                  supplied emission, factors and traffic data.
                                  Rates for stationary sources input  by user.

                               Calculates contributions from grid squares along
                               trajectory.  (1, modified 3 for point,  area)

                               Program option allows user to input Jii-ectly  ar-
                               bitrary surface pollutant fluxes for up to three
                               pollutants (not necessarily photochemically re-
                               active) .
                                                                    Monthly  variation,  in  emission rate
                                                                    allowed.   (3)

                                                                    Sequence of  hourly average  rates
                                                                    for mobile sources.

                                                                    Stationary source  rates  assumed
                                                                    constant.  (1,3)

-------
                                                          B15
                                             Table  B.3    (Cont'd)
                                                                   Method of Treatment
  Reference         Source	•	•	—	-—	
    Model          Geometry                     Spatial Variation                              Temporal Variation

HIWAY              Line         Uniform emission rate  for  each  traffic lane.            Constant emission rates.  (5)

                                Each lane integrated numerically to obtain con-
                                tribution.   (3)

RAM                Point and    Arbitrary emission  rate for  each point and area         Constant emission rates.  (5)
                   area         source.

                                Area source contributions  obtained by numerical inte-
                                gration along  upwind distance of narrow-plume approxi-
                                mation formulae  for area source with given effective
                                release height.

                                Includes only  those areas  intersected by the upwind
                                ray.   (1 for point; 4,5 for  area)

SAI                Point and    Point source emissions distributed homogeneously        Sequence of hourly average rates
                   area         throughout  entire vertical column above grid            for mobile sources,
                                square containing the  source; emission rates
                                supplied by user.                                       Stationary source rates assumed
                                                                                       constant.   (1,3)
                                Other emissions  treated as upward pollutant fluxes
                                at  ground surface.

                                Rates for mobile sources determined from user-
                                supplied emission factors  and traffic data.

                                Rates for stationary sources input by user.  (Mod-
                                ified 1,3 for  point, area)

STRAM              Point       Arbitrary emission  rate for  each source.  (1)           Constant emission rates.  (5)

Valley             Point and   Arbitrary rate for  each point and area source.          Constant emission rates.  (5)
                   area
                               Area sources treated as single  effective point
                                sources.

                                Total area  source contribution  estimated as a sum of
                                individual  contributions.  (1,4 for point, area)
 Numbers in parentheses  refer  to  treatments of spatial variation as given in Table 5.2.

 Numbers in parentheses  refer  to  treatments of temporal variation as given in Table 5.2.

CCRSTER should be used only when  the  receptor is below stack height.

-------
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                                                     B18
                                  Treatment  of Plume  Rise  by  Reference  Models
Reference
  Model
                     Treatment of Plume Rise3
      Treatment of
   Downwash/Tumigation
APRAC-1A

ATM
CDM
Single Sourceb
(CRSTER)
DIFKIN

HIWAY


RAM
SAI
STEAM
Valley
     Not treated  explicitly.  (5)

     For each point  source, user inputs a value representing
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     cube root of the wind speed for neutral and stable cond-
     itions,  respectively.

     Maximum  effective stack  height limited to 1500 m.
     (Modified 4b)

     No plume rise  for area and line sources; a constant value
     could be included in  user-supplied release height. (4e,5)
     Uses "tilted plume" approximation to treat deposition of
     particulates (see Table  5.13).

     Briggs'  2/3  (1971) neutral/unstable formula used for
     point sources.
     If (stack height) +  (plume rise) exceeds mixing height,
     ground level concentrations are assumed equal to zero.
     (Modified 4a)
     As an alternative to  Briggs1, the user may input a value
     of the product  of plume  rise and wind speed for each point
     source.  (Alternative  : 4e)
     No plume rise  calculated for area sources; a constant value
     could be included in  user-supplied release height. (4e,5)

     Briggs'  (1971,  1972)  final plume rise formulas; plume rise
     not treated  as  a function of downwind distance.

     If plume height exceeds  mixing height, concentrations
     further  downwind assumed equal to zero. (4a)

     Not treated  explicitly.  (5)

     Not treated  explicitly but could be included in release
     height.  (4e,5)

     Uses Briggs'  (1971, 1972) downwind distance dependent
     plume rise formulae for  point sources.
     If plume height exceeds  mixing height, ground level
     concentrations  assumed zero. (Modified 4a)

     No plume rise  calculated for area sources; could be
     included in  release height. (4e,5)

     Uses Briggs'  formulae (1971) for point sources (power
     plants only)  to determine if plume penetrates inversion.
     If plume height exceeds  mixing height, emissions from
     source are not  treated.  Other power plant emissions
     included in  ground level flux. (4a)
     Treats emissions as ground level fluxes; plume rise not
     treated  explicitly.  (5)

     Not treated  explicitly;  could be included in release
     height for each source.  (4e,5)

     Uses Briggs'  (1971, 1972) plume rise formulae for
     both point and  area sources.
     Option:   A single constant plume rise value may be
     input for any  or all  sources. (Option: 4e)
     If plume height exceeds  mixing height:
     A.  For  long-term calculations, ground level concentra-
         tions assumed equal  to zero.
     B.  For  short-term calculations, maximum plume height
         is limited  to the mixing height.
         (Modified  4a)
Does not treat either.

Does not treat either.
                                                                                  Does not treat either.
Does not treat either.
Does not treat either.

Does not treat either.


E'oes not treat either.
                                                                                  Does not treat either.
                                                                                  Does not treat either.
                                                                                  Does not treat either.
 aNumbers  in parentheses refer to treatments as given in Table 5.4.
 bcRSTER should be used only if receptor height is below stack height.

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