DRAFT
WORKBOOK FOR THE COMPARISON
OF AIR QUALITY MODELS
- APPENDICES -
(After public review and comment this document
will become part of the OAQPS Guideline Series)
November 1977
Monitoring and Data Analysis Division
Office of Air Quality Planning and Standards
U. S. Environmental Protection Agency
Research Triangle Park, North Carolina
DRAFT
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DRAFT
Workbook for the Comparison
of Air Quality Models
Appendices
by
Albert E. Smith, Kenneth L. Brubaker,
Richard R. Cirillo, and Donald M. Rote
Energy and Environmental Systems Division
Argonne National Laboratory
Argonne, Illinois 60439
November 1977
Interagency Agreement No. EPA-IAG-D6-0013
EPA Project Officer: Joseph A. Tikvart
Prepared for
ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Waste Management
Office of Air Quality Planning and Standards
Monitoring and Data Analysis Division
Research Triangle Park, North Carolina 27711
DRAFT
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TABLE OF CONTENTS
Page
APPENDIX A A 7
A.1 EMISSION CHARACTERISTICS A 7
A.1.1 GENERAL A 7
A. 1.2 TREATMENT OF SOURCE-RECEPTOR RELATIONSHIP A 8
A.1.3 TREATMENT OF EMISSION RATE A13
A.1.4 TREATMENT OF COMPOSITION OF EMISSIONS
CHEMICAL COMPOSITION A18
A.2 PLUME BEHAVIOR A2O
A.2.1 GENERAL A20
A.2.2 TREATMENT OF PLUME BEHAVIOR A23
A. 3 HORIZONTAL AND VERTICAL WIND FIELDS A27
A.3.1 GENERAL A27
A. 3.2 TREATMENT OF HORIZONTAL AND VERTICAL WIND FIELDS A3O
A.4 HORIZONTAL AND VERTICAL DISPERSION A34
A.4.1 GENERAL A34
A.4.2 TREATMENT OF HORIZONTAL AND VERTICAL DISPERSION A43
A.4.2.1 Treatment Classification A44
A.4.2.2 Benefits and Limitations A48
A. 4.2. 3 Parameterization A54
A.5 QIENISTRYANDREACTIONMECHANISM . A56
A.5.l GENERAl..... A56
A.5.2 TREATMENT OF CHEMISTRY AND REACTION MECHANISM A61
A.6 PHYSICALREMOVALPROCESSES ................... A66
A.6.1 GENERAL A66
A.6.2 TREATMENT OF DRY DEPOSITION A68
A.6.3 TREATMENT OF PRECIPITATION SCAVENGING A71
A.7 BACKGROUND, BOUNDARY AND INITIAL CONDITIONS A73
A.7.1 GENERAL A73
A. 7.2 TREATMENT OF BACKGROUND, BOUNDARY AND INITIAL
CONDITIONS A77
A. 8 TEMPORAL CORRELATIONS A8O
A.8.1 GENER.A.IJ A8O
A. 8.2 TREATMENT OF TEMPORAL CORRELATIONS A82
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TABLE OF CONTENTS (Cont’d)
Page
A. 9 IMPORTANCE RATINGS FOR APPLICATION ELEMENTS A83
APPENDIX B B 1
B. 1 REFERENCE )DEL TREATMENTS OF APPLICATION ELEMENTS B 7
B. 2 REFERENCE MODEL ABSTRACTS AND EQUATIONS B 35
B.2.1 CDM B37
8.2.2 pjj B38
B.2.3 SINGLE SOURCE (CRSTER) B41
B.2.4 VALLEY B44
8.2.5 ATM B46
B.2.6 STRAN B47
B.2.7 APRAC—1A B48
B.2.8 HIWAY B50
B.2.9 DIFKIN B51
B.2.1O SAl 852
GLOSSARY OF SYMBOLS B55
APPENDIX C C 1
C.1 EXAMPLE 1: SCIM/1243 C 7
C.2 EXAMPLE 2: AQDM/1143 C23
C.3 EXAMPLE 3: PTDIS/1213 C37
C.4 EXAMPLE 4: PTMAX/1213 C49
C.5 EXAMPLE 5: PTMTP/1213 C61
C.6 EXAMPLE 6: HANNA—GIFFORD/1243 C73
C.7 EXAMPLE 7: HANNA—GIFFORD/1143 C87
C.8 EXAMPLE 8: APPENDIX J/6243 ClOl
APPENDIX D D 1
REFERENCES
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LIST OF TABLES
Number Page
A.l Comparison of Widely Used Plume Rise Formulae A 25
A.2 General Atmospheric Stability Classification According
toTemperatureLapseRate
A.3 Commonly Used Measures of Atmospheric Stability and
and Turbulence Intensity A 41
A.4 Factors Affecting the Level of Atmospheric Turbulence
and the Rates of Horizontal and Vertical Dispersion A 43
A.5 Factors Determining Meandering Contribution to Horizontal
Dispersion A 43
B.l Reference Model Classification B 9
B.2 Treatment of Source—Receptor Relationship by Reference
Models B 10
B.3 Treatment of Emission Rate by Reference Models B 14
B.4 Treatment of Composition of Emissions by Reference Models . B 16
B.5 Treatment of Plume Behavior by Reference Models B 18
B.6 Treatment of Horizontal Wind Field by Reference Models B 19
B.7 Treatment of Vertical Wind Field by Reference Models B 21
B.8 Treatment of Horizontal Dispersion by Reference Models B 22
B.9 Treatment of Vertical Dispersion by Reference Models B 24
B.lO Treatment of Chemistry and Reaction Mechanism by
Reference Models B 26
B.ll Treatment of Physical Removal Processes by Reference Models.... B 27
B.l2 Treatment of Background, Boundary and Initial Conditions
byReferenceModels B29
B.13 Treatment of Temporal Correlations by Reference Models B 34
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LIST OF FIGURES
Number Page
A.l Dependence of Crosswind Pollutant Distribution from a
Continuous Point Source on Averaging Time A 36
B.l Mixing Height Algorithm Used in RAN B 40
B.2 Mixing Height Algorithm Used in CRSTER. B 43
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APPENDIX A
TECHNICAL SUPPORT MATERIAL
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CONTENTS OF APPENDIX A
Page
A.1 EMISSION CHARACTERISTICS A 7
A.1.1 GENERAL
A.1.2 TREATMENT OF SOURCE-RECEPTOR RELATIONSHIP
A.1.3 TREATMENT OF EMISSION RATE
A.1.4 TREATMENT OF COMPOSITON OF EMISSIONS
A. 2 PLUME BEHAVIOR
A 7
.A 8
•A13
.A 18
.A2 0
A.2.1 GENERAL A 20
A.2.2 TREATMENT OF PLUME BEHAVIOR A 23
A.3 HORIZONTAL AND VERTICAL WINDFIELDS
A .3.1 GENE RAL
A.3.2 TREATMENT OF HORIZONTAL AND VERTICAL WINDFIELDS
A27
•A27
•A30
A. 4 HORIZONTAL AND VERTICAL DISPERSION
A.4.1 GENERAL
A.4.2 TREATMENT OF HORIZONTAL AND VERTICAL DISPERSION
•A34
A.51 GENERAL A 56
A.5.2 TREATMENT OF CHEMISTRY AND REACTION MECHANISM A 61
A.6 PHYSICAL REMOVAL PROCESSES
A.6.1 GENERAL
A.6.2 TREATMENT OF DRY DEPOSITION
A.6.3 TREATMENT OF PRECIPITATION SCAVENGING
A.7 BACKGROUND, BOUNDARY AND INITIAL CONDITIONS
A.7.1 GENERAL
A.7. 2 TREATMENT OF BACKGROUND, BOUNDARY AND INITIAL
CONDITIONS
•A66
A66
A68
‘A 7].
.A73
.A73
A.4.2.l Treatment Classification
A.4.2.2 Benefits and Limitations
A.4.2.3 Parameterization
•A34
A 43
•A44
‘A48
‘A54
A.5 CHEMISTRY AND REACTION MECHANISM A 56
‘ ‘ ‘ •A77
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CONTENTS OF APPENDIX A (Cout’d)
Page
A.8 TEMPORAL CORRELATIONS A 80
A.8.1 GENERAL A 80
A.8. 2 TREATMENT OF TEMPORAL CORRELATIONS A 82
A.9 IMPORTANCE RATINGS FOR APPLICATION ELEMENTS A 83
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Appendix A: TECHNICAL SUPPORT MATERIAL
Sections A.1—A.8 of this Appendix contain technical discussions of
the application elements and describe methods of treating them in models.
Brief discussions of the rationale for the importance ratings are given in
Section A.9.
A.l EMISSION CHARACTERISTICS
A.l.l General
To predict the concentration of a pollutant, a model must treat the
emissions of that pollutant and its precursors, if any, as well as the
emissions of those substances which react with the pollutant or its precursors.
The emissions and their distribution can be characterized by specifying the:
• Source—receptor relationships,
• Emission rates, and
• Composition of the emissions.
These three application elements are discussed together here but the user
should make separate comparisons of their treatments.
The source—receptor relationship includes:
• Source location,
• Height at which emissions are released into the
atmosphere,
• Receptor location,
• Receptor height,
• For line and area sources, the orientation of the
source to a fixed direction, and
• Downwind and crosswind distances between source—receptor
pairs.
Thus defined, source—receptor relationship comprises the positional factors
which determine the extent to which dispersive, chemical, and removal pro-
cesses affect pollutant concentrations. Once released at a particular loca-
tion and height, pollutants travel downwind and are dispersed, ultimately to
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be detected at the receptors of interei t. It is during this time of flight
that dispersion, secondary generation, and removal processes are active in
altering the concentrations of the pollutant of interest.
Emission rates are clearly important because they determine the total
quantities of materials emitted into the atmosphere during the time of in-
terest. A source’s emission rate generally varies with time. For example,
emission rates from a stack generally vary over time scales ranging from
minutes to years. For line and area sources, spatial variation within a
single source may also be important. The treatment of these temporal and
spatial variations must be considered when two models are compared and are
discussed in Appendix A.l.3 dealing with the treatment of emission rates.
Finally, Uie composition of emissions must be considered in some
applications. Chomical composition is important for secondary or reactive
pollutants and in some situations where several species of particulate
matter are of interest. The size distribution of particulate emissions is
also important when fallout, deposition, or precipitation scavenging must
be considered. It should be noted that the identification of possible sinks
and secondary production mechanisms can depend upon knowing the composition
of emissions other than those with which the user is mainly concerned.
The following three subsections describe the treatments of these
application elements.
A.l.2 Treatment of Source—Receptor Relationship
In this discussion, location means a specification of the source’s
horizontal position. The release height specifies the vertical position of
the release of emissions to the atmosphere, and does not include a specific
discussion of treatments of plume rise, which are discussed as a separate
element, plume behavior, in Appendix A.2.
For point sources, there are basically two levels of detail with which
horizontal location can be treated. The first allows each source to be
accurately located at its true position with respect to some horizontal grid
system, thus allowing a maximum degree of spatial resolution. The second and
less detailed approach locates each point source only to the extent of identi-
fying a grid cell containing the source, thus sacrificing some degree of spa-
tial resolution. This latter treatment is used by numerical models that treat
all point sources lying within a given basic grid cell without regard to their
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precise location but that do distinguish between sources located in different
cells. The loss of resolution between the first and second levels is essen-
tially the same as that incurred in developing an emissions inventory when
small point sources are aggregated to area sources. For the purpose of this
workbook, however, the inventory is assumed to be given and the less detailed
treatment then involves the assignment of the point sources to grid cells
despite the availability of more precise information. If the aggregation to
area sources is part of the inventory, it should not be considered when coin—
paring models. The comparison should be based on the treatments of the point,
area, and line sources given in the inventory.
The location of point sources by grid cell can, of course, be treated
at various levels of detail, the most detailed treatments preserving signif 1—
cant spatial resolution on a relatively fine grid and the least detailed
sacrificing all spatial resolution and not distinguishing between sources
regardless of their location within the region of interest. Models using the
least detailed treatment cannot adequately treat situations involving alt era—
tions in the spatial distribution of emissions. Detailed treatments also
frequently permit a finer grid to be used in areas where the user desires a
high degree of spatial resolution. This treatment is somewhat more detailed
than one using a fixed grid size, if the block size is smaller while allowing
the user the added flexibility of matching the degree of resolution to the
needs of the specific application.
Occasionally, a model may aggregate sources on a basis not directly
related to location. This occurs when sources are aggregated, for example,
by industrial category. Unless this type of treatment is used in conjunction
with one of the locational treatments described above, it provides no infor-
mation on the location of sources and is equivalent to the least detailed
treatment of horizontal location.
The release height of point sources is treated in its most detailed
form when both the physical stack height (without plume rise) and the elevation
of the base of the stack above some reference elevation can be specified for
each source. A less detailed treatment assumes flat terrain and considers only
the physical stack height or release height above grade. These treatments can
be used even when the horizontal locations of the sources are tgriddedlt by the
model onto subareas of the region of interest. Less detailed treatments are
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frequently used when the model grids the point sources. These involve
specifying one or several representative release heights, which may include
an elevation correction, for each subarea of the grid. Less detail is
available when the same release heights are applied to all the subareas.
(When representative release heights must be assigned, the user frequently
calculates a representative plume rise and adds it to the physical release
height, since models using such treatments generally make no provision for
the internal calculation of a typical plume rise.) At the least detailed
level release height is not treated explicitly; all emissions are treated as
if they are released at the same height. This non—explicit treatment is used
in numerical models in which all emissions are treated as part of the boundary
condition at ground level.
Before proceeding, it is convenient to discuss receptor location
br cause receptors are usually taken as points. As is the case with point
sources, the horizontal locations of receptors can be specified as precise
points or as locations in some grid block. When the receptors are located
precisely two methods or a combination of the two are generally used. The
first allows the user to locate the receptors arbitrarily. The second places
the receptors at the intersections of a grid network, the spacing or scale
of which may be fixed or under the user’s control. Both methods may provide
equivalent levels of detail and the user must decide which is better suited
to the particular application. It may also be, of course, that specifying
receptor locations by subarea only is sufficient to the user’s purpose, but
here such treatments will be rated as less detailed than treatments that
locate receptors precisely in the horizontal. The level of detail of receptor
locations also depends upon whether the elevation of the receptor can be spe-
cified. Given comparable specification of horizontal receptor locations, a
treatment which allows the user to specify arbitrary receptor heights is more
detailed than one which assumes that all receptors are at the same height
(usually ground level).
in the context of source and receptor locations, it must be stressed
that the user should not always rate one treatment against another solely
on the level of detail. Consideration should also be given to whether the
level of detail provided is necessary in the particular application. For
instance, if the application involves the impact of a single source at a
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specific location, the ability to locate numerous sources and receptors
precisely is irrelevant as long as the pair to be studied can be located
as desired. Thus, the comparisons made by use of the tables in the workbook
should be modified to reflect the specific requirements of the application of
interest. The table assumes that it is desired to locate a number of sources
and receptors at arbitrary locations. Since all required cases could not be
foreseen, the user must modify this general list to reflect the application of
interest.
For area sources, the treatments of source location and release height
follow the same general progression as for point sources, that is, a full
specification in three dimensions (both horizontal location and release
height) at the most detailed level and a complete lack of explicit recognition
of different source locations and heights at the least detailed level. Two
additional considerations must be given to area sources, however, because of
their two dimensional nature. First, a model which accepts area sources at
arbitrary locations provides more detail than one which places all area
sources on a fixed grid even if the size of the grid can be changed by the
user. In the latter case, the user’s area sources must be mapped onto the
model’s gridded areas and hence the differences between areas tend to be
averaged out. Such a loss of detail may be unimportant when the difference
in emission rates in adjacent areas is small. The user must decide this
based on his knowledge of the situation of interest. Second, models which
treat arbitrarily sized area sources generally allow greater flexibility
than those which limit area sources to one or several set sizes. This can be
particularly important when dealing with “true” area sources such as open pit
mines or dusty fields. Again the user must decide when comparing models
whether this consideration is important in the particular application of
interest.
Another difference between point and area sources arises because an
area can have an arbitrary orientation with respect to the wind direction.
Most models treat area sources on some type of grid system that is fixed in
space and hence the orientation of an area cannot be adjusted even when the
real physical source is tilted with respect to the model grid. For computa-
tional purposes, some models assume a specific orientation which may be
unrelated to the actual orientation of the source. This assumption is
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frequently reasonable when the area sources are aggregates of many small
point or line sources. A somewhat more detailed treatment permits the area
sources to assume an arbitrary orientation; such treatments may be useful
when dealing with true area sources where the orientation of the actual
sources can be arbitrary.
The most detailed treatment of line sources specifies the precise
location and orientation of the line by, for example, using its endpoints
and provides for some width and height for the line (thus really treating
it as an elongated volume source). For infinite lines, only the orientation
of the line is specified. Curved lines are usually approximated as series
of straight line segments and for highways some width can be provided by
allowing the number of lanes, medial strip width, and roadway width to be
specified. Less detailed treatments specify only the horizontal location
and fail to allow for width; a release height may be specified. Care must be
taken with line source models to ascertain whether they allow the line to
assume an arbitrary orientation with respect to the receptor. Some models,
for example, require that the receptor be located near the perpendicular
bisector of the line and will not properly treat a receptor lying near the
axis of the line source. As with point and area sources, increasing degrees
of aggregation within the model produce less detailed treatments.
En applications involving a combination of source types, the degree
of detail of the treatment can be different for different source types.
However, an overall evaluation can still be made by comparing the reference
model treatment with the study model treatment for each source category and
making some assessment of the importance of each category to the particular
application.
Some modeling parameters determined by the source—receptor relation-
ship may depend explicitly on the downwind or crosswind distances between
source—receptor pairs. For instance, in Gaussian plume models the dispersion
parameters are normally functions of the downwind distance. When this is the
case, these distances must be calculated. It should be noted, however, that
a model may not ever need to calculate the downwind or crosswind distance
explicitly. For example, a numerical dynamic model may move an air parcel
along a trajectory but never use the distance along the trajectory. In such
cases, the downwind/crosswind distances are not calculated and their treatment
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can be ignored. When required by the model these distances are usually assumed
to be determined by the horizontal separation between pairs and hence do not
depend upon release height or receptor height. When point sources are involved
and both the sources and receptors are located as points, the capability exists
to calculate a unique downwind and crosswind distance for each source—receptor
pair either along a curved trajectory or assuming a steady—state wind in a
single direction. When a model grids either sources or receptors, less detail
is available, since only average or representative separations can be determined.
This is also the case for area and line sources. Finally, no downwind or cross-
wind distances can be determined if no distinctions between sources and recep-
tors are made on the basis of location. This is the case, for instance, when a
box model includes an entire region in a single box.
These treatments of source—receptor relationship are listed by their
level of detail in Table 5.1. Treatments by the reference models are given in
Table B.2.
A.l.3 Treatment of Emission Rate
Once the positional relationships between sources and receptors have
been determined, the emission rate of each source must be specified. Two aspects
of the element emission rate are important:
— Spatial distribution of emissions and
— Temporal variation of emissions.
The treatment of the spatial distribution of emissions is closely related
to the treatment of horizontal location discussed in Appendix A.l.2, since the
degree of spatial resolution available depends upon how close to their real
positions the model locates sources. For point sources, no additional infor-
mation is required to describe the spatial distribution beyond what is already
given in the treatment of source—receptor relationship. In the case of line or
area sources, however, the manner in which the distributed nature of the source
is taken into account requires consideration and is discussed in this section.
Two points of view exist regarding the treatment of distributed sources. In
determining the treatment of distributed sources by a model it is useful to
identify which point of view is adopted simply in order to clarify the treatment.
In many cases, there is no intrinsic difference in the level of detail associated
with the two possibilities.
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From the first point of view, the total contribution of the entire
emission distribution is estimated by adding up estimates of the contributions
from many individual parts, each consisting of a uniformly emitting area or
line segment. For example, sulfur dioxide emissions from residential space
heating in an urban area are most commonly represented as a rectangular array
of square area sources, each characterized by a given emission rate per unit
area. Another example is the representation of automotive emissions as a set
of finite line sources, each of which is characterized by a given emission
rate per unit length. Each part is considered to be a separate source, and
the contribution from each of these parts to the pollutant concentration is
estimated. The total contribution from the entire distribution is then esti-
mated by summing all these individual contributions.
From the other point of view, the overall distribution is regarded as a
single entity in which, however, the local emission rate may vary from point to
point. A single estimate of the total contribution from the given emission
distribution is made without explicitly estimating the contribution from each
of the individual parts comprising the source inventory, even though the source
inventory may have exactly the same form as before. This point of view may be
adopted for an array of square area sources as in the first example above, as
well as in cases in which only one line or area source is of interest. In the
latter situation, the emission rate per unit length or per unit area may be
allowed to vary within the source itself.
There is no intrinsic difference in the levels of detail associated with
these two points of view if only the total contribution to the estimated pollu-
tant concentration is of interest. If the individual contributions are desired,
a treatment which adopts the first point of view is likely to be superior to one
which adopts the second, although much depends upon the level of detail of the
methods used to make the individual estimates in the two treatments. In order
to estimate individual contributions within a model adopting the second approach,
an algorithm for allocating the total calculated contribution among the indivi-
dual parts must be incorporated, whereas in the first approach the individual
contributions are independently estimated.
Whatever point of view is adopted, some technique must be used to esti-
mate the contribution of either the overall distribution or of each of its
component parts. The rest of the discussion addresses methods of making these
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estimates. The various possible methods fall into two general categories:
— Analytic or numerical integration, and
— Source substitution — the replacement of a line or area
source with a small number of point sources.
In principle, the most detailed treatment of the spatial distribution
of emissions involves the integration over the given distribution of the con-
tribution from an infinitesimal area or line segment, assumed to contribute as
a point source. If the spatial distribution and the infinitesimal contribution
have a sufficiently simple form, the integral may be evaluated analytically.
Thus, for example, the pollutant concentration downwind of a uniform horizontal
line source of specified length oriented perpendicular to the wind may be esti-
mated by means of a formula obtained by integrating the Gaussian plume expression
for the contribution from each infinitesimal segment of the line. In general,
however, the spatial distribution and the point source concentration estimates
are sufficiently complicated that such an analytic expression cannot be derived.
En such cases, alternative methods must be used.
One alternative is to evaluate the integral by some appropriate numerical
procedure. If the numerical procedure is sufficiently detailed that the spatial
variation present in both the emissions and the point source formula is taken
into account, the result may be equivalent to that which would be obtained by an
analytic integration. The level of detail of the treatment is directly related
to the distance between sampling points at which the emission rate and point
source estimate are evaluated; the smaller the distance, the higher the level
of detail. Since for a given receptor the nearby emissions are expected to
contribute n re heavily than those father away, treatments which incorporate
high resolution near the receptor and progressively lower resolution at greater
distances involve a relatively high level of detail.
Another alternative is to simplify the integration by introducing
additional approximations so that either an analytic expression may be derived
or the numerical integration is made significantly easier. For example, a
common approximation used in dealing with an array of area sources is to assume
that emissions are uniformly distributed in the crosswind direction. In most
urban areas, this may be a reasonable assumption; in general, the level of
the treatment depends upon the appropriateness of the assumptions in the user’s
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specific application. The example just given corresponds to what is often
called the narrow plume approximation. In this approximation, only the
emissions from those area sources which are directly upwind of the receptor,
or in general those which are intersected by a trajectory which subsequently
passes through the receptor location, have an effect on the estimated pollu-
tant concentration. Further discussion may be found in Appendix A.4.2.
The least detailed treatments involve the replacement of a line or
area source by a small number of point sources having a combined emission
rate equal to that of the source they are replacing. The smaller the number
of effective point sources is, the less detailed is the treatment; a treatment
involving the use of a large number of points amounts to the use of a numeri-
cal integration procedure. The position of the effective points may be chosen
to approximate the spread of emissions within the source being replaced, and
the strength of each may depend upon their position.
There are two components to the treatment of temporal variation of
emission rates:
— The degree of temporal resolution which the model allows
and
— The suitability of the technique for treating the variations
to the particular application.
The degree of temporal resolution is determined by the interval at which
emission rates can be changed in the model. Even the most detailed treatments
can usually handle properly at most hourly variations in emission rates. The
overall temporal resolution of a model is often limited by the temporal reso-
lution of the meteorological data. The emission data should reflect a similar
resolution at the most detailed level. If a large number of time intervals
must be treated, say all 8760 hours in a year, some models take a sample of all
the hours and thus treat only a subset of all available time intervals. This
approach provides somewhat less detail than accounting for all time intervals
but may give results which are equivalent to those obtained from a fully de-
tailed treatment particularly when the accuracy of the model is considered.
Less detail is offered by treatments which allow no temporal variation, per—
mitting only constant emission rates to be specified. Within these limits, the
shorter the interval over which changes in emission rates can be specified, the
more detailed the treatment.
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For those models which allow some temporal variation in emission
rates, the suitability of the technique of handling the variations must also
be considered. One technique is commonly used in dynamic models. The total
time period of interest is divided into intervals. Each time interval is
modeled in succession, the pollutant distribution at the end of one interval
serving as the initial distribution for the next. This type of detailed
approach is necessary when significant variations in emission rates occur
over the averaging time of interest. In simpler situations, a second tech-
nique treating the situation as a set of steady states is applicable; the
steady—state approach is generally simpler to implement. This approach looks
at each time period separately. it can account for the time sequence, but it
ignores the pollutant distribution remaining at the end of each interval when
a new interval is considered. The steady state treatment is the more common.
Some models allow the entire set of steady—state situations to be treated.
Others simulate only a single situation at a time and must be applied repeti-
tively when longer time periods are of interest.
The repititious application of a model allows temporal variations in
emission rates to be treated using only constant rates. For example, if it
is desired to use a climatological model designed to estimate annual averages
from average emissions rates and the sources have significant monthly varia-
tions, the model could be run twelve times with emission rates appropriate for
each month and the twelve individual results averaged. It would, of course,
also be necessary to use meteorological data appropriate to each month in
the individual runs.
As was the case with spatial variation, a model that aggregates sources
is inherently less detailed than one which treats each source individually.
In aggregating, each source’s emission pattern is masked in an average value
and some details of the situation are lost.
One further aspect of emission rate must be discussed: the treatment
of the amount of emissions based on other input parameters such as VMT,
vehicle mix, or population. When actual emission rates (or a sequence of rates)
are supplied to the model, the degree of detail depends upon the degree of
detail used in generating these numbers and is not limited by the model itself.
When the model itself calculates the emission rates, a model requiring more de-
tailed input generally provides a more detailed treatment. For example, a model
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which estimates vehicular emissions based on VMT, average speed, and vehicle
mix is less detailed than one which uses VMT, vehicle mix, and allows a
different average speed to be assigned to each class of vehicles. Since the
number of possibilities is large, no attempt to rank treatments will be made
here. As a general guideline, the user should compare the levels of detail
required in the inputs of the models being evaluated. It should also be
noted that evaluating this aspect of emission rate may be impossible as, for
example, when the one model requires specific emission rates to be input and
a second calculates emission rates from other information.
Table 5.2 gives the general treatments of emission rates in order of
decreasing level of detail; the specific treatments used by the reference
model are given in Table B.3.
A.l.4 Treatment of Composition of Emissions
Chemical Composition
In applications involving chemical reactions (secondary generation or
reactive pollutants), the chemical composition of emissions is important. At
the most detailed level, the emissions of all relevant individual compounds
are treated. Somewhat less detail is obtained when several or many related
compounds are “lumped” together into a single class and only the total
emissions of all members of the class are treated. Two things must be con-
sidered when a model treats the emissions of at least some of the relevant
compounds in terms of lumped classes. First, the criterion for determining
in which class a particular compound belongs must be appropriate for the
chemistry to be modeled. Second, the compound chosen to represent the class
must also be chosen appropriately; in some cases, it may not be an actual
compound but a hypothetical representative compound. For example, in the
case of photochemical oxidants, it would be impractical to use full detail and
treat the emission of every possible organic compound individually. Con-
sequently, they may be lumped into classes depending upon their degree of
photochemical reactivity. Thus, if five reactivity classes were used, each
source could have associated with it up to five different emission rates for
organic compounds, one emission rate for each reactivity class. This classi-
fication would also be appropriate to the oxidant problem whereas classifica-
tion by, for instance, molecular weight may not be. In general, the greater
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A19
degree of classification into appropriate, distinct classes, the greater the
level of detail of the treatment. Less detail is available when assumptions
regarding the composition of emissions are built into the model, such as when
a phoiochemical oxidant model assumes a certain percentage of the organic
emissions to be reactive regardless of the actual nature of the sources in—
volved. Still less detailed treatments describe the emissions of only one of
several compounds known to interact.
Model treatments must also be checked to ascertain whether all relevant
emissions have been treated. For example, models for photocheinica]. oxidants
that treat reactive organic compounds but not NO and NO emissions are inher-
ently less detailed than those which treat NO and/or NO, because NO can act
as an ozone scavenger and the NO/organics ratio is important in determining
the extent of ozone formation. Expert advice may be needed in making these
determinations. With regard to this last point, care must be exercised to
consider here only compounds which are actually “emitted tt by the sources.
These may only be a subset of the total number of compounds which are in-
volved in the chemical kinetics and may not even include the pollutant of
interest. For example, ozone “emissions” are negligible or zero but the
emissions of the organic precursors must be treated in models for photochemical
oxidant. The user would not deem a photochemical model inappropriate because
ozone emissions are not treated.
Size Distribution of Particulate Matter
The most detailed treatment of the size distribution of emitted partic-
ulate matter would take into account a continuum of particle sizes by allowing
the functional form of the particle size distribution to be specified. In
somewhat less detail an appropriate distribution is assumed and the parameters
necessary to describe that distribution are input. Less detail is available
in treatments which treat all particles within a given range of sizes as if
they had the same representative size. This treatment is analogous to the
lumping of various chemical species described above. Similarly, a treatment
using smaller size intervals offers more detail (generally, more size intervals)
than a treatment that divides the total range of sizes into fewer, wider inter-
vals. Even less detail is contained in treatments that assume that some
fraction of the particulates are affected by the mechanism of interest. This
is really a two—class treatment: a fraction of the particulates, for example
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A2 0
might be assumed large enough to fall out of a plume, while the remaindeç
are assumed to behave like a gas. The least detail, of course, is offered
by treatments which fail to treat the size distribution explicitly in
situations in which it may be important. Such is the case when all particulate
emissions are treated as a gas, including that fraction which is sufficiently
large to be subject to significant gravitational settling.
It should be noted that a complete characterization of the composition
of emissions may require a joint treatment of chemical composition and the
size distribution. In such cases, the appropriate size distribution may not
only vary from source to source but may also vary from chemical compound to
chemical compound. Such detail is beyond the level at which models presently
operate but the user should be aware of the complexity of a complete specifica-
tion of the application.
Tables 5.3 and B.4 give the treatments of the composition of emission
in general and by the reference models, respectively.
A.2 PLUME BEHAVIOR
A.2.l General
Upon release, an effluent generally has some upward momentum and buoy-
ancy. Mixing with the ambient air begins immediately and continues as the
effluent travels downwind and disperses. In the initial phases of this travel,
the plume centerline is determined simultaneously by the rise due to the
initial momentum and buoyancy and the downwind advection. As mixing continues,
the plume centerline is determined by the initial conditions to progressively
lesser degrees until it is determined predominantly by the downwind advection.
The height to which the initial momentum and buoyancy carry the effluent is
called the “plume rise” and this height plus the physical release height is termed
the “effective stack height.”
As these definitions indicate, some models treat plume rise only for
point sources. When area and line sources are aggregates of small point
sources, the plume rise associated with each individual area or line source is
an average or representative value. This discussion focuses on plume rise
from point sources and certain other types of plume behavior. The user should
be aware, however, that the same factors as discussed herein must be considered
if a model explicitly treats plume rise from area or line sources.
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Many interacting factors affect plume behavior. When the stack exit
velocity is small compared to the wind speed, the plume may bend over immediately
after release and downwash may occur behind the stack. This is one of several
special situations to be considered when plume behavior is treated. If the
stack exit velocity is large, mixing of the effluent and ambient air will be
increased, rapidly dissipating the plume’s buoyancy and momentum and causing
a low plume rise. The same effect also occurs with increasing atmospheric
turbulence and may be represented as a dependence of plume rise on stability,
atmospheric temperature gradient, or wind speed. The buoyancy of a hot plume
is determined by the heat release rate ; hotter plumes rise higher than colder
plumes, other conditions being the same. The heat release rate depends on the
stack exit velocity, the effluent’s temperature, molecular weight, and specific
heat, on the stack diameter, and on the atmospheric temperature and pressure.
A formula relating these variables may be found in Moses and Kraimer (1972).
In addition, the relative humidity and moisture content of the plume may be
important. Many plumes contain some water and after release the condensation
of gaseous water or vaporization of liquid water adds or removes heat from the
plume and hence affects buoyancy. The condensation of water vapor can be large
enough to cause a very low plume rise, as can be the case with cooling tower
plumes.
The momentum of the plume depends upon the mass of the effluent and the
stack exit velocity. The density of the plume is thus important and the product
of velocity and stack diameter is a measure of the square root of the momentum
release rate. For stacks with very high exit velocities, the momentum term may
be much larger than the buoyancy term. This “momentum only” case is not en-
countered in most common applications, in which the principal interest is in
buoyancy effects.
There are other factors which also affect plume rise:
• Terrain and nearby buildings,
• Number of nearby stacks and local heat sources,
• Shape of the stack opening,
• Wind direction in directionally inhomogenous situations,
• Wind shear, and
• Precipitation.
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A22
No single treatment of plume rise deals with all these factors and there
is no generally accepted treatment; over twenty separate formulae are available
and new ones continue to appear. Most analytical formulations make the plume
rise directly proportional to the reciprocal of the wind speed at the top of
the stack. Two terms, one proportional to the square root of momentum and the
other to some power of the heat release rate, are also included but the momentum
term Ls frequently omitted, its effect being negligible in many common situations.
When plume rise is treated as a function of distance, data for power plant plumes
indicates that the plume rise varies as the 2/3 power of the downwind distance.
There may be separate formulae for different sized stacks and different stabi-
lities but the treatment of special plume behavior is generally not included in
the treatment of plume rise.
The special plume behaviors usually considered include:
• Dowawash
• Plume trapping, and
• Inversion breakup fumigation.
The conditions leading to downwash were noted above. A rule—of—thumb says that
downwash should be considered whenever the physical stack height is less than
about 2 1/2 times the height of the building it is on or the height of nearby
obstacles to airflow or whenever the stack exit velocity is less than about
1 1/2 times the windspeed at the top of the stack. This rule—of—thumb is only
a rough guide and in many situations, for instance, with a cold plume having
little buoyancy, downwash may need to be considered even for stacks whose
heights exceed those indicated. Plume trapping occurs when a stable layer
exists above a neutral or unstable layer. A plume emitted into the lower neutral
or unstable layer will rise until it reaches the base of the stable layer where
it becomes trapped between the stable layer and the ground. Very hot or fast
plumes may be able to “punch through” the stable layer and thus may not be
trapped. Fumigation occurs when a stable surface—based inversion is broken up
by heating from the ground. Pollutants that were emitted into the stable layer
are then thermally mixed in the vertical and relatively high ground level con-
centrations can result, as discussed in Appendix A.4.
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A23
A.2.2 Treatment of Plume Behavior
As noted previously, there is no generally accepted method of treating
plume rise. Several types of treatments of various degrees of detail exist.
Within each type, the appropriateness of a given treatment depends upon whether
the method has been verified in the field for the application of interest. In
fact, the best comparison of two plume rise formulae is obtained by comparing
their predictions with observed plume rise values under the conditions of in-
terest. If such data are available they should be used in preference to the
method described below. In general, a formula validated for the application of
interest and producing gpod agreement with observed values is to be preferred
to one for which no validatic i data is available or ft r which validation data
show poor agreement with observations. It would not be proper to rank treat-
ments simply by counting the number of parameters they handle, because some
simple formulae perform better than more complex ones using many parameters.
The most detailed level of treatment would account for the simultaneous
rising and dispersing of the plume. This problem is extremely complex and has
been treated only in very specialized applications such as self—contamination of
buildings where the behavior of the plume immediately after release is of pri-
mary concern.
Most andels are unable to handle dispersion during the initial rising
phase of plume travel and usually treat the situation by separating the rising
plume from the dispersing plume and considering two distinct steps:
First, the plume rise is determined based on stack and
meteorological parameters. This plume rise may be a function
of the downwind distance.
Second, dispersion is treated by assuming a virtual source
emitting at an effective stack height equal to the physical
release height plus the plume rise.
This is the type of treatment found in most dispersion models for primary
pollutants. However, many formulae are used to estimate the plume rise. As
noted above, comparison to a reference model’s treatment should be based upon
which treatment gives better agreement with observed plume rises for the
application under consideration. Such comparative results are scanty and
another method must normally be used if a comparison is to be made.
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A24
Without prejudice to other treatments, models using the following
plume rise formulae can be considered applicable in many situations, unless
comparative field studies indicate otherwise for the case at hand:
• Briggs’ 2/3 power law or a later modification,
• Holland,
• cONCAWE or WNCAWE simplified, and
• ASME.
The Briggs’ and Holland formulae have been “verified’ t for power plants.
Only Holland has a separate immentum term and correction factors have been
suggested to account for stability. Briggs uses separate formulae for
different stability classes and is the only one which treats plume rise as a.
function of downwind distance. The ONCAWE formulations consist of single
formulae and are the only ones in which plume rise is inversely proportional
to a fractional power of the wind speed. It must be stressed that this list
does not mean that other formulae should not be used. These four are widely
used and do a fairly good job of prediction in many cases. Other formulae may
be better in specific applications, but the only valid evidence of this is
direct comparison with observations.
If the user has an unverified formula in a study model, the following
general guidelines, valid for hot, buoyant plumes only, may be helpful:
• Plume rise should be proportional to the reciprocal
of wind speed to some power between 1.0 and 0.70,
• A buoyancy term must be included (heat release rate
should be raised to a power between 1/3 and 1),
• Other things being equal, a formula with an additional
nxmentum term would be preferred,
• Other things being equal, a formula giving plume rise as
as function of downwind distance would be preferred.
(This consideration is n re important for low level sources
than for elevated sources.)
It must again be stressed that verification in the field for the application
of interest is the preferred decision parameter, followed by use of one of
the four widely used formulations. Use of the guidelines is recommended only
as a last resort. For ease in comparison, the widely used formulae are corn—
pQred under these guidelines in Table A.1.
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Table A.l. Comparison of Widely Used Plume Rise Formulaea
1.. ,
Formula
Wind Speed
Proportionality
Buoyancy
Proportionality
Momentum
Term Included?
Function of
Stability?
Function of
Downwind
Distance?
Briggs
(lf )” stable
1/u neutral, unstable
Q 1 ’ 4 stable ’
neutral, unstable
no
yes
yes
Holland
if u
q
yes
yesC
vu
CONCAWE
(1/u) °’ 7 °
Q 0 ’ 58
no
no
no
CONCAWE
simplified
(ifu) ° 75
q” 2
no
no
no
ASNE
(1/u)1 ’3 stable
1/ u neutral, unstable
stable
neutral, unstable
no
yes
!
no
an = wind speed at top of stack
Q = heat release rate
bA momentum term is included in the
formulations used in models.
literature but is omitted in the most co non
en recommended correction factors are used.
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A2 6
The next lower level in detail still uses the two—step procedure but
does not attempt to estimate a specific plume rise based on stack parameters.
Instead, the user specifies a value for the product of some power of the wind
speed and plume rise. The model then calculates a plume rise for each wind
speed. This method usually assumes that plume rise is inversely proportional
to the wind speed but does not allow differences between sources or other
meteorological parameters to affect the plume rise.
A still less detailed treatment allows plume rise to be considered
but only permits a small number of specific values. This treatment is used
frequently for aggregate sources and hence is common in the treatment of area
sources in urban models. The values of plume rise chosen are average or re—
piesentative values and are often included in the release height (see
Appendix A.l.2).
The least detailed treatment does not deal with plume rise explicitly.
This is the case, for example, in proportional models and models which treat
vertical dispersion by assuming uniform mixing.
There are only a limited number of treatments of the special plume
behavior. Downwash is typically not treated explicitly. Treatments of down—
wash are normally developed expressly for that problem alone. Halitsky (1965,
1968) and Turner (1969) discuss downwash in general and should be consulted if
downwash is expected to be significant.
Plume trapping can be accommodated in two—step models by assuming that
the plume is reflected from the base of the stable layer aloft and from the
ground. Repeated reflections lead to uniform mixing. The plume is assumed to
be unaffected by the inversion lid until its vertical spread reaches the stable
layer and to be uniformly mixed after some suitable downwind distance there-
after. Between these two distances, interpolation of concentrations is used.
(See the discussion of boundary conditions in Appendix A.7.) Carpenter et al.
(1971), Pooler (1965), and Turner (1969) give treatments that can be used for
trapping and Turner’s treatment frequently is used in Gaussian plume models.
Inversion breakup is generally not treated by models. Carpenter et al.
(1971), Turner (1969), and Pooler (1965) give formulas which can be used to
estimate ground level concentrations during inversion breakup if the user must
consider this condition. (See the discussion in Appendix A.4.)
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A27
One further treatment of plume behavior used to treat the deposition
of particulate matter for which gravitational settling is important should be
noted. This is called the “tilted plume” approximation and is discussed in
Appendix A.6.2.
The various general treatments of plume rise are given in Table 5.4.
Treatments of special plume behavior are n:.jL rated. The user should note how
the study model compares to the reference model in the number of special cases
of plume behavior each treats and compare these treatments to those given in
the references cited above. Treatments by the reference models are described
in Table B.5.
A.3 HORIZONTAL AND VERTICAL WIND FIELDS
A.3.l General
The primary mechanism for the transport of pollution in the atmosphere
is advection, the horizontal motion of air which carries pollutants along from
one place to another. This transport of pollution by the wind must be accounted
for by any deterministic model which attempts to predict the spatial distribution
of some material being emitted from a set of known sources. In certain circum-
stance, there may also be a significant vertical component to the mean atmos-
pheric motion and in these cases pollutants may be transported in the vertical
direction as well. This appendix describes the general features of and methods
for treatment of the horizontal and vertical transport of pollution by the wind.
Horizontal Wind Field
This term refers to the magnitude and direction of the horizontal compo-
nent of the wind velocity as functions of horizontal position, height above
ground, and time. Hereafter, when the terms wind speed and direction are used
they will refer to the horizontal component, in accord with common usage.
The general properties of the wind speed and direction most relevant
for pollutant transport are:
• A systematic increase in speed and shift in direction with
height above ground which
— Is very pronounced within an inversion,
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A28
— Becomes less and less pronounced as the atmosphere
ranges from stable through neutral to unstable con-
ditions, and
— Is significantly affected by variations in surface
properties upwind and possibly downwind of the location
in question;
• A sensitivity to the presence of topographic features such
as
— Hills or mountains
— River valleys, and
— Large bodies of water;
• A significant diurnal variation, reflecting the diurnal
variation of atmospheric stability; and
• Significant seasonal variations, reflecting seasonal
changes in the weather.
The variation with altitude is due to the frictional interaction between
wind and the surface of the earth. Its effects are most pronounced near the
surface and becomes less evident at higher elevations until at some altitude
the surface effects become negligible. The effects of variations in atmos-
pheric stability on the rate at which wind speed and direction change with
altitude simply reflect variations in the extent to which the air at different
levels is being mixed by turbulence. Enchariced vertical mixing such as exists
under unstable conditions tends to smooth out and decrease the dependence of
wind speed and direction on height. In stable conditions, vertical mixing and
with it the influence of one layer of air on another is decreased. As a
result, both wind speed and direction can have a significant dependence on
height in stable, and especially inversion, conditions.
The gross effect of hills, mountains, or river valleys on wind speed
and direction is to channel the airflow and to promote the formation of local,
organized circulation patterns. More subtle effects can occur as well, such
as mountain and valley breezes and drainage flows, and the possibilities are
numerous and varied. A useful summary and discussion is given by Slade (1968).
The principal effect of large bodies of water is similar to certain topographic
effects in the sense that it is due to differences in air temperature above ad-
joining land and water surfaces. A breeze, called a lake or sea breeze depending
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A29
on the body of water involved, tends to blow from the water toward the land
during the day. This breeze may blow in a direction opposite to the prevailing
wind and may extend a considerable distance inland. En situations in which the
lake or sea breeze acts against the prevailing wind, a convergence zone in
which there are significant upward vertical motions is formed and pollutants
may be blown inland near the surface, rise in the convergence zone, and be
blown back out over the water at heights of several hundred meters. Situations
in which the lake or sea breeze acts in the same direction as the prevailing
wind are less complex and “circulation cells” such as were just described do
not form, although the movement of cooler air onto an adjacent land surface
can result in a temperature inversion extending some distance inland, often
terminating in a zone in which there is an essentially continuous fumigation
situation.
It should also be pointed out that urban areas themselves have a sig-
nificant effect on the wind field, ranging from modification of the flow when
regional wind speeds are high to the establishment of local circulation patterns
due to the urban heat island effect when regional winds are weak. Systematic
changes in wind direction and speed occur over urban areas and even in strong
regional flows there is a systematic tendency of the air to rise over cities,
accompanied by a net m l low at low levels.
Both seasonal and diurnal variations in the mean wind speed and direc-
tion occur. We will not discuss seasonal variations except to point out that
they depend on the location of the region of interest and can be significant.
Dramatic variations may also occur during frontal passages or other weather
changes. Diurnal variations are related to the diurnal variation of stability
and the effect of stability on the variations of the wind field with altitude.
Diurnal variations are most important during periods of cloudless weather, in
which there are strong diurnal variations in stability and correspondingly large
variations in the extent of atmospheric mixing. In stable conditions at night,
the wind speed near the ground may be very low while at the same time at heights
of a few tens of meters it is often quite high. In unstable conditions the wind
speed, although usually rather low, is not strongly dependent on altitude. Both
high and low wind speeds may occur under neutral conditions, although high wind
speeds tend to produce neutral conditions even on clear days and nights, as
discussed in Appendix A.4.
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MO
The horizontal wind speed and direction are in fact randomly fluctuating
quantities with fluctuations occurring over time scales from much less than a
second up to years and beyond. Qualitatively, short—term fluctuations are
perceived as turbulence while long—term fluctuations are perceived as part of
the day—to—day changes in the weather. For the purposes of describing the
transport of pollution, the interest is normally in the mean wind speed and
direction over some specific time interval, or over each of a sequence of
time intervals. The transport of pollutants by the mean wind is the opera-
tional definition of advection, and the transport of pollutants by the fluc-
tuations about this mean is the operational definition of dispersion. In any
given situation, the averaging time for which mean wind measurements are
available determines the distinction between ad.vection and dispersion. Typical
averaging times in practice range from about 10 minutes up to about 3 hours.
Vertical Wind Field
The vertical component of the wind velocity is in many cases much less
important than the horizontal components, for the simple reason that in many
cases it is zero over the averaging time of interest. In some situations,
however, primarily those in which there are significant topographic features
in the region of interest, significant vertical wind components may be pre-
sent. When they are, they provide an effective mechanism for vertical trans-
port of pollution and should be taken into account.
A.3.2 Treatment of Horizontal and Vertical Wind Fields
The treatment of the wind field by an air quality model depends on the
type of model according to the classification scheme introduced in Appendix A.4.
For example, dynamic models treat the time dependence of the wind field in
addition to its spatial dependence, numerical models can generally handle more
complex spatial variations than semiempirical models, and so on. Thus, treat-
ments of wind field may be classified by the way both spatial and temporal
variations are handled.
Spatial. variation in either horizontal or vertical directions is
usually handled in numerical models by specifying the wind velocity components
at discrete points defined by a suitable grid, the grid spacing being chosen
to reflect the actual spatial resolution available in the data from which the
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A3 1
model wind field is calculated. This grid spacing then determines the spatial
resolution of the model as a whole. The grid may be one, two or three—dimen-
sional depending on the model. Similarly, in dynamic models the temporal
variation in wind speed and direction at a given point is usually handled by
specifying a sequence of mean values representing averages over some basic
time step, typically one hour.
An alternative to the use of measured wind speeds and direction in
combination with an interpolation procedure is to model the wind flow within
the region of interest in a separate calculation using fluid flow modeling
techniques and to thereby determine the wind field in a manner suitable for
use in the air quality simulation model. This approach is often used with
dispersion models for complex terrain, and in principle allows great flexibility
in the spatial and temporal variations in the wind field that can be described
by the model. The user should be aware, however, that not only are simplifying
assumptions generally introduced in practice, but also that the manner in which
the basic equations are implemented in a computer code must be carefully con-
sidered in order to minimize numerical errors. Expert advice may be necessary
to properly take these considerations into account.
Treatments at lower levels of detail involve progressively larger numbers
of simplifying assumptions regarding both spatial and temporal variations. Most
semiempirical models incorporate such assumption in their formulation and, if
sufficient information is available, the user should consider whether they are
appropriate or acceptable for the specific application of interest. Expert
advice may be necessary in these considerations. Often the utility of a
semiempirical model designed for use in a limited set of circumstances is ex-
tended by making additional assumptions. An example illustrating this practice
will be given below.
The nature of the desired results may affect the amount of detail
necessary in the treatment of the wind field, particularly in regard to the
size of the region of interest and whether or not the entire spatial and tem-
poral distribution of pollutant is desired. It is more important, for example,
to be able to describe the spatial variations in the wind field over a large
area than over a smaller one simply because the variations are expected to be
more significant in the former case. Another example is the situation in which
the maximum concentration for a given averaging time is to be estimated, rather
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A3 2
than the expected mean concentration value. In this case, assumptions or
information on wind persistence may be required.
Another major factor which determines the required level of detail in
treating the wind field is the extent to which it is necessary to describe the
vertical component. As mentioned above, it is often a reasonably good approxi-
mation to assume that the mean vertical component of the wind velocity is zero
over the averaging time of interest. If this assumption is made, the practical
treatment of the wind field is very much simplified; only the horizontal wind
need be treated. The horizontal variation of the wind speed and direction is
constrained by the physical requirement that air cannot accumulate anywhere,
and normally the simplest possible approximation is made, i.e., that the wind
speed and direction are independent of horizontal position over the region of
interest and depend only on the height above ground. In practice, the depen-
dence of wind direction on height is often ignored as well. The dependence of
wind speed on height is usually given by an assumed functional form which may
depend on the surface roughness and atmospheric stability. The most common form
is a simple power law dependence with different exponents for different stabi-
lities although a logarithmic form may be used near the ground under neutral
conditions. Finally, the simplest treatment in the zero vertical component
case is to assume that the wind speed and direction are uniform within the
mixing layer over the region of interest. This treatment is often adopted in
semiempirical models. The wind speed is normally chosen to be that which would
be observ2d at a height equal to the emission height and this value is often
estimated using a measured or assumed value at some lower reference height,
usually 10 meters, in combination with an assumed wind profile. This proce-
dure results In a different effective wind speed for each different emission
height and potentially each different source as well. Alternatively, a single
effective wind speed can be used for all sources regardless of individual
differences in emission height.
If the vertical component of the wind cannot be assumed to be zero,
the treatment of the entire wind field is complicated again by the requirement
that air cannot locally accumulate, except that now there is no constraint on
the vertical component. In practice, this requirement provides a relationship
between the horizontal and vertical components which Is used to calculate the
vertical wind speed, given measurements of the horizon components at several
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A33
locations within the region of interest. Wind fields which satisfy this non—
accumulation requirement are often called 1t mass consistent’ wind fields because
the requirement is derived from the concept of the conservation of mass. Any
wind field used in a dispersion model should be mass—consistent; otherwise,
errors in the estimated concentration will result. Wind fields determined by
fluid—flow models are generally designed to satisfy the mass—consistency require-
ment.
It is relatively easy to satisfy the mass consistency requirement if the
vertical wind component may be assumed to be zero. In this case, for example,
if the wind speed and direction do not depend on the horizontal position coordi-
nates x and y, the mass consistency requirement is automatically satisfied
regardless of the dependence of either speed or direction on height above ground.
An air quality model designed for use in complex situations may either
require the wind field to be input and therefore place the burden of determining
the proper wind field on the user or require the necessary measurements so that
the wind field may be calculated internally. In the latter case, the wind field
may be determined prior to or concurrently with the actual dispersion calcula-
tions. As indicated above, simplifying assumptions are often incorporated.
For example, a model designed for use in flat terrain may be combined with
assumptions regarding the flow of air over topographic features to produce a
new model which may give results of sufficient validity for the user’s purpose.
Often such treatments of the vertical component are implicit , being incorporated,
for example, in the form of assumptions about the height of the plume centerline
above the terrain without an explicit determination of the vertical component
that would result in such behavior. For the purpose of this workbook, such
assumptions represent an implicit treatment of the vertical wind speed and
should be evaluated as such.
The situations in which treatment of the vertical component is desirable
are those in which the region of interest contains significant geographic
complexities such as mountains or hills, river valleys, large bodies of water,
and so on. In the first two cases, the usual problem is to describe the chan-
neling and vertical displacement effects of the terrain on the general wind
flow. Models which are capable of doing this have been developed and are in
current use. Near large bodies of water, the problem is to describe the effect
of a temperature difference between adjacent surfaces. Although models of this
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A34
situation have been developed, they are primarily of a research nature and
have not been incorporated into a dispersion model.
In applications involving averaging times of a month or more, a
climatological approach is often used. The entire range of possible wind
directions is divided into several (usually 16 or 36) sectors, and the entire
range of possible wind speeds is divided Into several (typically six) discrete
classes. At the same time, the possible range of atmospheric stabilities is
also divided into some number (usually six) of discrete classes. The proba-
bility of observing simultaneously the wind direction in a given sector, the
wind speed within a given class, and the stability within a given class is
determined from local observations for each possible combination of wind
direction, wind speed, and stability class. The resulting joint frequency
distribution is called a stability wind rose. Each combination of the three
elements defines a particular meteorological situation for which dispersion
calculations are done, normally using a semiempirical model. The long—term
average pollutant distribution is obtained by multiplying the results for
each meteorological situation by the probability of observing that particular
situation and summing over all possible cases. Thus, more information about
the wind field than just the mean wind speed and direction over the averaging
time of interest is used, although in each meteorological situation the
assumption is commonly made that the wind is uniform and constant. The
climatological approach is not necessarily restricted to semiempirical models;
in principle, any type of model could be used to do the basic dispersion cal-
culations as long as discrete wind field “classes” could be suitably defined
and the probability of observing each determined.
The various treatments of the horizontal wind field are listed in
Table 5.5 and the treatments of the vertical wind field are given in Table 5.6.
Treatments used by the reference models can be found in Tables B.6 and B.7
for horizontal wind field and vertical wind field, respectively.
A.4 HORIZONTAL AND VERTICAL DISPERSION
A.4.l General
One of the most important elements in assessing the impact of emissions
on air quality is the estimation of the extent to which the effluent
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A35
from sources is dispersed by the atmosphere. In comparing the treatments of
dispersion by two different models, the user should keep the following three
factors in mind:
• The operational definition of dispersion,
• The duration and size of the emission and the
source—receptor distance or travel time, and
• The connection between the extent or rate of
dispersion and the level of atmospheric turbulence.
These factors determine the applicability of the various treatments of
dispersion and the physical features of the problem which need to be taken
into account.
The term “dif fusionit is used by some authors in exactly the same sense
that the term “dispersion” is used throughout this workbook. The term dis-
persion is used here to avoid any confusion with the process of molecular
diffusion, in which the spread of one substance in another is the result of
entirely different phenomena than those responsible for atmospheric dispersion.
The operational definition of dispersion is interrelated with that
of advection and depends upon the averaging time of interest. The wind speed
and direction at a point are randomly fluctuating quantities; rapid fluctua-
tions are perceived as turbulence and very slow fluctuations as part of the
day—to—day variations in the weather. The operational definition of advection
is the transport of pollutant by the mean wind as measured over some specified
averaging time. The operational definition of dispersion is the transport of
pollutant by fluctuations about this mean which occur over times less than the
averaging time. In other words, advection is the overall downwind movement
of the emission as a whole and dispersion is the spreading of the pollutant
about this overall motion.
To fix these ideas, consider two photographs of the same continuous
lume taken from above: one is a snapshot and the other is a time exposure
(Figure A.l). The plume in the snapshot is observed to follow a meandering
path and the width at any point is simply the actual physical spread of
material about the instantaneous position of the plume centerline. In the
time exposure, however, the plume follows 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
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2 HOUR AVERAGE PLUME
Figure Al,
Dependence of Crosswind Pollutant Distribution
from a Continuous Point Source on Averaging Time .
I
RELATIVE CONCENTRATION
LA )
0 ’
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A3 7
shows only the mean wind speed and direction over the exposure time, and the
observed dispersion about the apparent plume centerline represents not only
the physical spread but also the time—averaged 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 exhibits the effects of the short—term
wind fluctuations responsible for meandering.
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 does 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
shows a cloud of material at some point generally downwind of the source, and
a time exposure shows a meandering path originating at the source. In both
pictures, the observed extent of the dispersion represents the actual crosswind
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 time of interest,
meandering should be considered part of the process of horizontal dispersion
from a point source when both the following conditions are met
• The duration of the release is greater than the
averaging time, and
• The averaging time is greater than the source—
receptor 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.)
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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 determine the
intensity of atmospheric urbulence must be suitab...y parameterized, because
dispersion is a direct result of the action of turbulence. The most 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),
• 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 l°C/lOO meters), as shown in Table A.2.
The significance of this classification is that near the ground, high levels of
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Table A.2. General Atmospheric Stability Classification According
to Temperature Lapse Ratea
Relation of Actual Lapse Rate to the
Dry Adiabatic Lapse Rate
Atmospheric Stability
Classification
Greater than
Unstable
Equal to
Neutral
Less than
Stable
aTh S classification is not the same as the widely used Pasquill stability
classification scheme.
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
notion 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.
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
competing effects: 1) the addition or removal of heat energy from the air
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
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A4 0
or turbulence intensity is used to determine the appropriate values of 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 mt Leorolo—
gical parameters or classification schemes have been used for this purpose and
an increasing number of models make use of the more fundamental r’easures 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 tor L1 1e definitions of the Richardson number
or the Monin -Obukhov length if the model being evaluat d makes use of one of
these parameters. A discussion of the Pasquill—Gifford cl3ssification 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 temperature 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. The phenomenon of fumigation is due to the morning breakup
from the ground of pollutants emitted into and trapped within the inversion
during the night.
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 anthropogenic 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
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,
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Table A.3. Commonly Used Measures of Atmospheric Stability
and Turbulence Intensity
Continuous Measures
1. Te 1 aperature gradient or, equivalently, temperature difference between
two reference heights.
2
T az
= (dry adiabatic lapse rate)—(ambient lapse rate)
= (1°C/lOOm + T/ z)
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
(os) or of the vertical component (ci ).
4. Richardson number.
5. Monin—Obukhov length.
Discrete Classification Schemes
1. Pasquill—Gif ford stability classification.
2. Brookhaven gustiness classification.
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 regions of complex terrain also have surface roughness comparable to those
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A4 2
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 as 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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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
— Surface roughness
• Surface heat flux, itself dependent on
— Solar angle,
— Cloud cover,
— Surface thermal properties, and
— Anthropogenic heat prcduction.
• Atmospheric stability, itself dependent on
— The factors listed above, and
— Synoptic weather feati.res (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
f Dr pollutant
concentrations
.
Initial size of the e nission
A.4.2 Treatment of Horizontal and Vertical Dispersion
In order to evaluate the tr atments 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 pararneterizing the effects of
the important meteorological variables in each type.
The remainder of this section addresses these points.
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A4 4
A.4.2.l 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 and 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 t which consider both the concentration and the flux 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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A4 5
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 making 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.’ t The result of making this approximation
is an equation, called the advection—diffusion 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—difference or particle—in—cell techniques, but the user
should not be too concerned with the details of the numerical method used by a
model being evaluated. There are certainly advantages and disadvantages with
the various approaches, but the focus here is more on the parameterization and
treatment of meteorological and other factors.
The 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 iiiterest in the process of running the model Itself.
The most common example of a semiempirical method is the Gaussian
plume treatment of dispersion from a continuous source as described by
Turner (1969). This particular approach involves the assumption that the
horizontal crosswind pollutant distribution from such a source may be
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A4 6
described, on average, by a Gaussian function and that, except for the effects
of the ground, so can the vertical distribution. The only parameters beside
the wind speed 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 connection 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 that 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 which one or more
trajectories of pollutant releases are calculated from wind field data, or
are simply assumed on any reasonable basis, are also included under the
definition of dynamic models followed in this workbook. Dynamic treatments
may be either numerical or semiempirical in nature.
Dynamic models must be able to properly handle situations 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 generalization 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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A4 7
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—
dif fusion 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—
lectory 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
semiempirical/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.
Climatological Treatments
This category includes methods which predict the average pollutant
distribution for long averaging times, typically a month, season, or year,
using a joint 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. Climatological
models may in principle use either a numerical or semiempirical approach for
the individual calculations, although in practice semiempirical/steady—state
treatments are almost always used.
A.4.2.2 Benefits and Limitations
Numerical Methods
The nh .1fl benefit to be gained by using a numerical approach is
flexibility in the specification of the wic d 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 within
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 grid spacing
and is therefore partially determined by that spacing; and
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A4 9
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 any turbulent eddies contributing significantly to the dispersion.
As a result, the eddy diffusivity approach is not fundamentally suitable for
describing horizontal dispersion, and in particular the meandering contribution,
but because of constraints on the size of vertical fluctuations due to the
presence of 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 sources 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 phenotnenological 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 sometimes possible to describe the pollutant distribution on a
scale smaller than the grid spacing in an empirical or theoretical way, and
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 which to base the prediction of eddy
diffusivity values, particularly at heights above 100 meters or so. This
means that further assumptions must be made regarding the appropriate values to
use in a model.
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Aso
Semiempirical Methods
The principal technical benefit gained in this type of approach is
that the assumed 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 be appropriate
for the real situation.
As indicated above, the most coimnon example of this type of approach
is the Gaussian plume treatment of continuous emissions. En their basic form,
Gaussian—plume based methods are inherently restricted to:
• Flat or gently rolling terrain 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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AS 1
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 distri-
bution, it is difficult, if not impossible, to assess its validity.
It should be pointed 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 constant. 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—conser-
vative 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. 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 some 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 trajectory
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 treat—
ment of vertical dispersion may be either semiempirical or numerical.
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A5 2
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 ahove.
Time dependence is more commonly treated .y dividing the 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 well 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 pointed 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 ave aging 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.
Climatologic al Treatments
This type of approach is used in practice only for the calculation oi
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—state calculations.
A calculation is done for each set of meteorological conditions which
is represented in the joint distribution being used, and the average pollutant
distribution is obtained with the contribution from each set of conditions
being weighted by its probability of occurrance.
Limitations of the method may be divided into two categories:
• Limitations of the nodel 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 that 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-
ditions 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 such as precipitation and mixing height from the joint
frequency function.
Regarding treatments of dispersion at least one of the parameters
defining the frequency function should be some measure of the level of at-
mospheric turbulence. The measure of turbulence most commonly used in
climatological models is the Pasquill stability classification, although
others could be used. It is also common to use the narrow plume approximation
for point sources, which amounts to the assumption that the crosswind or
angular distribution of pollutant from a point source over a sufficiently long
period of time is given simply by the frequency distribution of the wind
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direction, or in other words by the wind rose. This assumption is reasonable
if the variation in the wind direction frequency function is negligible over
an angular interval corresponding to the angular width of the plume. Since
the wind 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 u’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 be 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 use 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 model by using different numerical
values for the relevant model parameters such as eddy diffusivities or Gaussian
standard deviations. The determination of the appropriate values from meteoro-
logical and other data is an important part of the total procedure by which
predictions of pollutant concentrations 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, particularly if they clearly 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 ncdify. The determination
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AS 5
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 used in 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 the horizontal diffusivity, to force a numerical model to
reproduce approximately the results of a more sophisticated calculation, or of
a semlempirical 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 diffusivity near the ground may be reasonably estimated
in terms of the wind speed, surface roughness (given in terms of a parameter
called the ‘ t roughness length”, see Slade (1968) or Pasquill (1974) for the
definition and estimates for different situations), and parameters which
determine the 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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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.
Seniiempirlcal Models
Since the Gaussian plume model is by Ear the most common example,
the discussion will be restricted to t1 is 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 sta il,ity 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 c .ass 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 treatuients of atmospheric stability
and surface roughness, respectively. Tables B.8 and B.9 list treatments
of horizontal and vertical dispersion, respectively, used by the reference
models.
A.5 CELEMISTRY AND REACTION MECBANIS)
A.5.l General
There are two common situations in which chemistry plays a role in
determining atmospheric pollution levels. On one hand, the pollutant of
interest may undergo chemical reaction with some other atmospheric 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 band, the pollutant 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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i 57
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 (03). If the pollutant of interest is both primary and
inert, the element of atmospheric chemistry is irrelevant and does not need to
be considered.
As pointed Out lfl Section 3.3, the decision to regard a pollutant as
being either reactive or inert depends upon the effective rate of reaction
compared to the length of time that the pollutant spends within the region
of interest. 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
In 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 of 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 components is not at present
well understood but if this possibility exists, the advice of an expert should
again be sought. However, many of the same considerations apply as in the
completely gaseous case.
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A5 8
The basic problem in modeling the dispersion of reactive systems is
to describe the rates of production and removal of various pollutants and,
equally as important, the interaction between the chemical reaction processes
and the dispersion process. En 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 inhomogeneity
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 reaction 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 written reflects
the true sequence of events on the molecular level. For example, an important
reaction in photochemical smog is that between ozone and nitric oxide (NO).
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 molecule each of
NO and oxygen (0 ). The most important property of elementary reactions is
2
that the rate of such a reaction is a predictab ç, 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 the ozone and nitric oxide
concentrations. On the other hand, a “complex reaction” is essentially a state-
ment of the net effect of some (possibly large) number of elementary reactions
operating simultaneously, with only the initial reactants and final products
being explicitly written. In general, the rate at which the initial reactants
disappear is not equal to the rate at which the final products appear, and
neither rate is a predictable function of 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 of what is known about the reaction mechanism. It should be
pointed out that the mechanism of a complex reaction usually involves the
existence of other chemical species in addition to the main reactants and
products of interest and that, in general, these need to be treated also.
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 ,react ions.
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 whereas 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
reactants)
concentrations of two
Second
(constant)
x
(the product of the
reactants)
concentrations of three
Third
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A6 0
En order to describe the evolution of a complex reacting system, it is
normally necessary to know the reaction mechanism, which consists of a set of
(elementary) reactions whose rates are known functions of the pollutant con-
centrations. If the initial pollutants are uniformly mixed within some closed
volume, their concentrations as functions of time may be predicted by numerical
solution of a set of coupled ordinary, non—linear differential equations, which
may be 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 or in which the net effect of many has been expressed in terms of just
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 values 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, but there is
often considerable uncertainty in the experimental measurement of rate constants
and the values of ones 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
and in some cases it may be important to use values appropriate for the ambient
temperature 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 local phenomena in
the sense that the rate of an elementary reaction at some point in space depends
upon the reactant concentration(s) at that point . Thus, the rate of a given
reaction is in general a function of position and time, reflecting the spatial
and temporal variation in reactant concentrations. For most reactions of in-
terest, the rate expression is a nonlinear function of pollutant concentrations,
because most reactions of interest happen to be second—order. This implies that
in most cases of interest the average rate of a given reaction within some finite
volume of interest cannot be obtained from the rate expression simply by in-
serting the average reactant concentrations, unless all reactants are uniformly
mixed within this volume. En this case, there is no spatial variation in the
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reactant concentrations and hence no spatial dependence of the reaction rate.
The only other situation in which the average reaction rate is given by the
rate expression using the average pollutant concentration is that of a first—
order reaction, in which case this is always correct no matter what the
spatial distribution. In most cases of interest, spatial inhomogeneity in
the reactant concentrations causes the chemical and dispersion processes to
be coupled in a very complicated way.
The nature of turbulent dispersion and the small size of most real
emission sources guarantee that in applications of practical interest there
are significant variations in the concentrations of reactive pollutants over
distances much smaller than the spatial resolution of most current models.
The degree of inhomogeneity depends on the level of atmospheric turbulence
and on the spatial distribution of the sources. In principle, the effect
on the average reaction rate of this inevitable inhomogeneity at distance
scales below the resolution of the model should be taken into account. In
practice, however, 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 with some empirically derived effective
rate constant.
A first—order process has the property that the rate of that process
is a linear function of the concentration of the reactant involved. As a
result, it turns out that the effect of one or more first—order processes on
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the reactant and product concentrations may be determined independently from
the effect of dispersion; in other words, first—order transformation processes
and the dispersion process are completely separable and any of the many treat-
ments of dispersion may be used. Furthermore, in cases where more than one
source is involved, the contribution from each may be evaluated and the total
predicted concentration obtained by simply adding the individual source con-
tributions.
The simplest case arises with a primary pollutant subject to some
first—order removal process. In 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 from 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, although statis-
tical models have been developed for some limited applications.
Two aspects of the treatment by a given model should in principle be
evaluated:
• The level of detail used in the reaction mechanism, and
• The treatment of the effect of inhomogeneous mixing on
average reaction rates.
With regard to the treatment of reaction mechanism, little can be said in
general, because so much depends on the specific details of the chemistry.
The simplest case is that in which either the disappearance of a particular
pollutant, or the appearance of its reaction products, or both are of in-
terest. En this case, if the reaction time scale is rather long compared
to the dispersion time scale and if the reaction products are relatively inert
so that, for example, the original pollutant is not regenerated by further
reaction, it may be sufficient to approximate the reaction by a first—order
process using an effective rate constant determined empirically. In this
approximation, all details of the actual reaction mechanism are ignored. The
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conversion of sulfur dioxide to sulfate aerosol over long distances is
commonly treated in this manner.
In more complex cases, such as that of photochemical smog, the
mechanism should be treated at some more appropriate level of detail. The
required level of detail depends on the nature of the reactions being des-
cribed and the number of different chemical species involved. The user should
seek expert advice in evaluating a model with respect to the mechanism being
used. In any case, the assumed mechanism should be sufficiently valid so as
to give reasonable agreement with 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 or stationary—state approximation, should be tested for validity
in any specific case and there are indications [ Farrow and Edelson (l974)J that
it is 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 consisting of only two reactions: 1) the photolysis (absorption of
light, followed by chemical reaction) of NO to produce NO and 03 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 just 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 equilibrium approximation may be used in steady—state as well as
dynamic models and allows the prediction of the chemical composition of the
pollutant mixture at a given point given the composition of the original pollu-
tant emission, the composition of the surrounding air into which that emission
is being dispersed, and the concentrations predicted on the basis of the dis-
persion 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 (unless it can be shown
explicitly that the error introduced thereby is truly negligible) and that the
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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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 Is desired.
The other aspect that needs to be evaluated is the way in which the
rates of change of the average pollutant concentrations are evaluated. Dis-
persion models for reactive pollutants generally attempt to predict the
average concentrations of all relevant pollutants within some suitably defined
volumes or cells as functions of time and need to be able to evaluate the time
rates of change of these quantities. As discussed earlier, if the pollutants
are uniformly distributed within a given cell the appropriate rates of change
may be calculated from the elementary reaction rate expressions, using the
average concentrations appropriate to the given cell. Errors will be intro-
duced if this procedure is used In cases In which spatial Inhomogeneities
exist in the pollutant concentrations over distances smaller than the cell
size. At present, this effect is generally not treated at all. This is not
to imply that modelers are unaware of the effect, but the problem of providing
an adequate general treatment is still essentially unsolved.
En 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 but In general any reasonable treatment
would be better than none 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 rate of change of average pollutant
concentrations is provided, since at this writing no practical general treatments
exist except In models developed solely for the purpose of doing basic research.
Table B.lO gives the treatments of chemistry and reaction mechanism used by the
reference models.
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A.6 PHYSICAL REMOVAL PROCESSES
A.6.i. General
The two major physical removal processes which affect ambient at-
mospheric pollution levels are dry deposition and precipitation scavenging.
In identifying them as physical processes, the intention is to distinguish
them from the chemical processes discussed in Appendix A.5, even though on a
fundamental level there are chemical aspects to each. After 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 well as the proceedings
of the symposia on precipitation scavenging [ Engelmann and Slinn (1970)] and
on atmosphere—surface exchange of particulate and gaseous pollutants [ Engelmann
and Sehinel (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 particulate
pollutant at the earth’s surface by any of the several processes, including
impaction, absorption, and chemical reaction. The important point is that
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 distinction has been
made between the absorption or other collection of pollution by cloud droplets
before precipitation actually occurred (denoted by the term “rainout”) and
the scavenging of pollutant by the precipitation itself as it falls through
the polluted air (denoted by the term “washout”). For purposes of this work-
book, this distinction will not be emphasized but the user should be aware of
its existence.
Dry Deposition
The rate of removal of an atmospheric pollutant per unit area of ground
surface is called the deposition rate (dimenflons: mass/time/area). It
depends upon
• The nature of the mechanism by which the pollutant, once
transported to the ground, interacts with and is removed
at the ground surface and
• The rate of vertical transport of that pollutant.
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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 smooth out this gradient by transporting pollutant downwards,
thereby providing nvre for possible removal. The ambient pollutant concen-
tration near the ground is lower than it would be otherwise, with the magnitude
of the depletion depending on the relative rate of removal at the surface, -“d
a corresponding net decrease per unit time in the total amount of pollutant
being advected by the wind is also observed.
The deposition 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 and if the pollutant of interest is found
predominantly within a certain size range, this fact 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
ref er 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 may be removed before it is transported out of the region of in-
terest and ambient atmospheric concentrations can be significantly affected.
In some application, the deposition rate or the total deposition within a
given area over some specified period of time may be of interest, in addition
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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 droplc s 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 gaseo is pollutant, the
solubility in water is the most important factor and this often depends to a
sign Lficant 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 D!position
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—uniform
vertical distribution.
All treatments of dry deposition that are used in practice describe 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 concentration at ground
level, the proportionality constant actually being dependent on a variety of
factors such as:
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• The nature of the pollutant,
• The nature of the ground surface, and
• The prevailing meteorological conditions, particularly
the atmospheric stability near the ground.
The proportionality constant is called the “deposition velocity” and its
value in any given situation determines the significance of the effect of dry
deposition on pollutant concentration. Theoretical procedures exist whereby
appropriate values may be estimated for a specific application but their
accuracy is uncertain and values derived from field observations are nearly
always used in practice.
Assuming that the downwind flux of pollutant nay be parameterized in
this way, the problem of treating dry deposition becomes one of describing
its effect on atmospheric pollutant concentrations and of calculating the
amount of pollutant deposited in the area of interest. Different types of
models treat these effects in different ways, depending specifically on the
way vertical dispersion is treated and on the way the dependence of the
pollutant 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 then 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 semiempirical method do not
necessarily handle dry deposition in a less appropriate way than do numerical
models. If, for example, the assumed form for the vertical concentration
distribution is based on suitable analytic solutions of the vertical diffusion
equation obtained using the correct boundary conditions, the treatment may be
as appropriate as any other. Normally, however, semiempirical models incorporate
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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 and has the additional
result that the pollutant concentration is nearly independent of height near
the ground. It 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 dry deposition on the iertical 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 removal 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 is the use of an
exponential decay factor in several currently available models. By appropriate
choice of the value of the decay constant, it is possible to simulate crudely
the effect of the removal of pollutant. An implicit assumption in this treat-
ment is that the shape of the vertical concentration distribution is unaffected
by the removal process; this assumption Is valid only if the rate of vertical
mixing is large compared to the rate of pollutant removal.
A somewhat more detailed treatment, described in Slade (1968), involves
the assumption that the pollutant is removed at a rate proportional to the
ground level concentration but that this concentration is given by, say, the
Gaussian plume formula with perfect reflection, modified by a factor to account
for that mass of pollutant already lost. The effective source strength as a
function of downwind distance must be determined 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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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 time or downwind distance using whatever model is appropriate and
a downward motion with a velocity equal to the appropriate settling velocity
is added to whatever other motion has been predicted for the distribution.
For steady—state models, the effect is to tilt the plume centerline downwards
with a slope determined by the ratio of the settling velocity to the horizon-
tal wind speed. One should in principle use a different settling velocity,
and hence a different 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 the 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, and we will be concerned here only with this type of
approach.
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 502 by cloud
droplets is not really an exponential process because of chemical reactions
which occur in the droplets themselves. 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 and if removal by falling precipi-
tation is treated as an exponential process, the decay constant is called the
washout coefficient. These coefficients in principle depend on a wide variety
of drop and pollutant characteristics. Empirical values are often used and it
is often assumed that the relationship between the washout coefficient and the
total rainfall rate may be expressed by a power law. The washout coefficient
is a function of drop size, and a more detailed treatment would take this into
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account and determine the total rate of pollutant removal by integrating over
an assumed drop size distribution function, but this is rarely done in practice.
If the rainfall rate is variable, so is the washout coefficient and
the pollutant concentration decreases in a manner reflecting this variability;
the decrease is not represented by simple exponential decay. For the purpose
of describing the effect of rainfall on pollutant concentrations, the washout
coefficient must be known or assumed, including any time variation due to
variations in the rainfall rate.
If the application involves an averaging time sufficiently long that
more than one rainfall occurrence needs to be treated, even simpler methods
are often used. For example, the assumption may be made that every time it
rains the ambient pollutant level is decreased by some constant factor which
may be empirically derived or estimated from the average duration of rain-
fall in the area. If a climatological model Is being used, the correlation
between frequency of rainfall and other meteorological parameters, particularly
wind direction, should be taken into account. Ignoring this correlation
represents an even less detailed treatment and correspunds to simply super-
imposing total rainfall contours on calculated concentration contours to
estimate the effect on long—term average concentration values. This correlation
Is most simply handled in climatological models by including precipitation in
the set of meteorological variables for which the joint frequency function is
used. In this case, exponential decay may be an appropriate treatment of the
effects of precipitation. Many climatological models now available provide the
option of specifying an exponential decay rate but do not specifically treat
precipitation conditions separately. These models apply the exponential decay
factor in every distinct meteorological condition modeled; this is not an
appropriate treatment of precipitation scavenging due to the intermittancy of
rainfall.
Table 5.13 lists the possible treatments of precipitation scavenging
which are within the scope of this discussion and Table B.ll lists the
treatments used by the reference models.
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A. 7 BACKGROUND, BOUNDARY MID INITIAL CONDITIONS
A.7.l General
An air pollution model describes the pollutant distribution within
a limted volume of space for a limited period of time. This volume is
bounded on the bottom by the earth’s surface, on the sides by the perimeter
of the region of interest, and on the top by the upper limit to vertical
dispersion. Even for models which calculate only ground level concentrations
explicitly, the three dimensional nature of dispersion is accounted for
through inclusion of such parameters as stack height, plume rise, or mixing
height. In any case, treatments of the following four aspects of the given
application are required:
• Effects due to the existence of a finite upper limit
to dispersion,
• The 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 semiempirical models, because they relate to effects at well
defined physical boundaries. The upper limit to dispersion is commonly treated
as an absolute barrier which keeps pollutants above it from entering 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 of pollutant
through the boundary. This condition is called the perfect reflection boundary
condition and is a common assumption used for the upper boundary; other
assumptions regarding the upper boundary condition are less common. However,
there are circumstances in which pollutants may enter the modeled region through
the upper boundary. For example, pollutants lying above the mixing layer can be
entrained within the modeled volume as the mixing height increases in the morning
as a result of solar heating. In practice, only numerical/dynamic models treat
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such situations in detail. A great deal of imprecision exists in specifying
the flux (or flow) of pollutant across the upper boundary due to the lack
of reliable estimates of such transfer in real situations. Even when
perfect reflection is assumed, the exact value of the mixing height is
generally subject to error, being based on extrapolations from measurements
made at different locations or times than those being modeled.
Two effects determine the nature of the lower boundary condition:
• The behavior of the earth’s surface as a barrier to
downward dispersion, and
• The rate of removal of the pollutant at that surface.
These two effects are usually assumed to be related, because the rate of re-
moval is proportional to the ground—level concentration. Various processes
determine the degree of absorption and which are most important depends upon
the particular situation. For example, large particulates can settle out
(be perfectly absorbed) under the influence of gravity. Sulfur dioxide can
be absorbed by vegetation and ozone can react chemically with various mate—
rials on the earth’s surface. The ground can also serve as a source of
pollutants as, for example, when settled particulates are reentrained in
sufficiently strong winds or when some pollutant is being emitted by vegetation.
It would be exceedingly complex to attempt to treat any of these processes in
detail and models must rely on approximate treatments of the most important
processes. When removal at the surface can be ignored, there is no net flux
of pollutant through the lower boundary and the perfect reflection boundary
condition is appropriate. When the removal rate is very large the situation
approaches the condition which would be called “perfect absorption.” Between
these two extremes both effects must be treated. Their relative importance is
determined by the rate of removal compared to the rate of vertical transport.
It is thus important that applications involving physical sinks at the earth’s
surface handle vertical transport in an adequate manner. The removal of
pollutants at the earth’s surface is termed “dry deposition” and is discussed
in more detail in Appendix A.6.
It should also be noted that numerical models generally treat at least
some fraction of the emissions of pollutants by specifying the appropriate
flux through the lower boundary as part of the lower “boundary condition.”
In this discussion, the “boundary condition” refers to what happens to pollutants
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already emitted; emissions treated as occurring at the boundary should
be considered as aspects of source location and emission rate (Appendix Al).
The third aspcct, advection of pollutants into the volume of interest,
is related to the concept of a background level. Such concentrations are due
to natural and man—made sources not being modeled, because they are outside
the modeled region. This definition of background differs from another
sometimes sometimes used in which the background 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 the 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.
Ozone, which is both reactive and secondary, illustrates the situation
well. “Background” ozone concentrations measured just upwind of urban areas
are frequently reduced within these areas due to the initial scavenging of
ozone 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 tern but is a function of
position and time within the region of interest. A single, additive background
number can be defined only for primary conservative pollutants. Otherwise, the
flux of pollutant and/or precursors into the study region at the vertical
boundaries must be known. Even for primary conservative pollutants, the in-
coming flux must be known as a function of position and time if significant
variations occur over time or distance scales small compared with the averaging
time and the size of the region of interest. Rural SO or sulfate levels pro—
2
vide examples of situations in which a single, additive background level is
likely to be appropriate.
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It has been assumed in this discussion of background and the side
boundary conditions that the study region has been chosen carefully to
include all important sources. It would be improper, for 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 th’ 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 beginning 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 time—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 important for such
pollutants and a dynamic approach is better suited to their treatment. This
is particularly true when short—term concentrations are desired as is the case,
for example, with ozone.
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A.7.2 Treatment of Background, Boundary and Initial Conditiohs
Since numerical and semiempirical models treat dispersion from different
poiutb of view, they employ different methods for handling background and
boundary conditions. Initial conditions are treated differently by dynamic
and steady—state models. The user should be aware that both “boundary
conditions” and “initial conditions” signify two related but not entirely
equivalent concepts. First, they mean a set of mathematical expressions
req’iired to solve the partial differential equations used in numerical models
add second, the physical conditions being modeled. The mathematical expressions
are the representations of the physical conditions in a form suitable for
numerical models. Saniempirical models must treat the same physical conditions,
still often referred to as the boundary conditions, using different methods.
The discussion is conveniently divided by considering first the treatments of
background and boundary conditions by numerical and semiempirical models and
then the treatments of initial conditions by dynamic and steady—state models.
Background and Boundary Conditions
Part of the difference between the treatments of background and boundary
conditions by numerical and semiempirical models is simply a difference in the
methodologies used to express the same physical condition. As will be seen,
however, the numerical approach generally provides a more detailed and flexible
treatment of these conditions. At this point, the user should keep in mind
that applicability of both approaches to the application as discussed in
Appendix A.4.
As noted above, many processes can take place when a pollutant contacts
the earth’s surface. Perfect reflection or absorption are generally approx-
imations to the real situation. The appropriateness of the approximation being
used must be assessed by the user when comparing models. Numerical models
treat perfect reflection mathematically by requiring that the vertical gradient
of pollutant concentration be zero at the surface, that is, what comes down
must go back up. Perfect absorption corresponds to the requirement that the
concentration be zero at the boundary. Perfect reflection is normally assumed,
because it is usually a much better approximation to the physical situation
than is perfect absorption. Both of these situations may also be handled
easily by semieinpirical models. Semiempirical models treat perfect reflection
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at the lower boundary by including an “image source” equivalent to the
real source but located like its mirror image with the earth’s surface as
the mirror. The “method of Images” Is the technique employed in the most
widely used forms of the Gaussian plume model and can only be used to handle
perfect reflection or absorption.
Partial reflection at the earth’s surface is treated in numerical
models by using the concept of a “dry deposition velocity.” This parameter is
a measure of the rate of pollutant removal at the earth’s surface. In essence,
the mathematical formulation allows part of the incoming pollutant to be ab-
sorbed so that the total amount being dispersed is depleted after reflection.
Most semietnpirical model? developed to date cannot treat partial reflection as
a boundary condition. An approximate treatment of dry deposition as a pollu-
tant removal process by assuming an exponential decay of the pollutant is fre-
quently used. This is discussed in more detail in Appendix A.6. 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 boundary
condition. Numerical models can also change the amount of absorption to
represent different conditions throughout the study region; semiempirical
models can usually only deal with one overall average dry deposition rate
throughout the region of interest.
At the mixing height, perfect reflection is generally assumed.
Numerical models use the same form of mathematical boundary condition as at
the surface but apply it at the height corresponding to the top of the mixing
layer, which can vary with location and time. These models could also be
used in principle to cover the case of partial penetration 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 account for the transfer
of pollutants into the region of interest by suitable modifications of the
upper boundary conditions and thus treat fumigation or entrainment. It should
also be noted that numerical models require a finite 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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for the reflections from that barrier, which is generally assumed to have a
constant elevation. It turns out that an infinite number of images are required
to account for the multiple reflections from the ground and the mixing height
[ see Turner (1969)] and the result is expressed as an infinite sum. In most
cases only the first few tens of the sum contribute significantly and the sum
may be evaluated easily to sufficient accuracy. A more common treatment relies
upon the observation that near the source the plume is not affected by condi-
tions at the 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 remain constant
after the vertical spread of the plume (o ) exceeds some fraction of the mixing
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 will generally give more accurate results than interpolation.
The gain in accuracy is slight considering the magnitude of other inaccuracies
in modeling treatments and interpolation is used more frequently. Semiempirical
models can also, in essence, ignore the upper boundary condition by using a
functional form for the vertical concentration profile that places no limits on
the height to 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. Sanienpirical models can be modified to account for fumigations
by using equations (functional forms) for predicting concentrations during the
time of the fumigation. (See, for example, the equations in the appropriate
references cited in Appendix A.2.)
Numerical models treat the conditions at the sides of the region as
mathematical specifications of the pollutant flux into the region. As noted
above, this is the most fundamental way of treating background levels. Semi—
empirical models cannot treat these as boundary conditions and “background”
can only be treated as a general additive term. This term may be a function
of location within the region but is generally treated as a single constant
value thus ignoring directional dependence and spatial variations. Any temporal
variation is also generally ignored.
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Initial Conditions
As pointed out previously, initial conditions are treated explicitly
only by dynamic models. Any contributions to the concentrations due to
pollutants initially present would be handled as part of the 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 clinatological 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 clinatological models will depend upon the nature of the model used for
the dispersion calculations. Both dynamic and sequential steady—state models
can, of course, account for temporal variations in background and boundary
conditions. Dynamic models usually allow important parameters to change re-
latively snoothly over time; sequential steady—state 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.l2 lists the treatments of back-
ground, boundary and initial conditions used by the reference models.
AM TE} ORAL CORRELATIONS
A.8.l 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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MU
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 diurnal variations in atmospheric stability described in
Appendix A.4. When such correlations occur it is usually important that the
model correlate the tine—dependent quantities, that is, treat them in such a
way that concentration estimates are made on the basis of values which do
occur together in the application of interest.
Implicit in the last statement is a realization that the treatment of
correlations is closely related to the degree of temporal resolution obtainable
in the model. In particular, the resolution time for the correlated quantities
must be less than the tine over which the variations can occur. For example,
if two correlated quantities vary hourly, the model must treat each of them
with a tine resolution of one hour or less for the treatment of correlations
to be possible.
As pointed out previously, there is a limit, frequently based on practical
considerations or data availability, to the resolution tine and hence to times
over which correlations can be considered. The limiting factor is that element
or quantity with the minimum degree of tine resolution among those elements which
are important to the particular application and which exhibit sufficiently
large temporal variability to affect the model results. The primary interest
is generally in correlating emission rates, meteorological parameters, and rates
of removal and transformation processes. of course, in applications where
emission rates are almost constant, correlations involving them are small and
may be ignored. Generally speaking, the correlations between the various
meteorological parameters also need to be treated.
Dynamic and sequential models handle temporal correlations automatically
within the tine resolution used by the model. These models generally allow
the values of most important parameters to be changed at each time step and
since the data for each step are generally input as a unit by the user, they are
automatically correlated. Steady—state models which treat one or several
specific sets of emission and meteorological data treat correlations which
occur on a tine scale longer than the averaging tine of the data automatically
and ignore those which occur over shorter tines. The correlations are implicit
in the structure of the input data as in the dynamic case. This type of treatment
is frequently encountered in models which estimate short—term concentrations.
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On the other hand, cllinatological models use statistical wind roses
and hence the only correlations inherent in this approach are between those
parameters upon which the wind rose is based, typically atmospheric stability,
wind speed, and wind direction. A three—hour resolution is typical of wind
roses. All other correlations, particularly those involving emissions, must
be treated separately.
Two factors should be considered when evaluating the treatment of
correlations:
• The magnitude of the variations in the given application
over time scales less 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 that
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 three levels
at which temporal correlations can be treated:
• Sequential and fully 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 automatically. The second type
of treatment is exemplified by cliinatological models. Although some statistical
models may implicitly treat correlations by their 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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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 the 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
importance 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—term concentrations are more sensitive to this relationship
than long—term concentrations, since changing meteorological conditions tend
to average differences in concentrations from point to point. The concentra-
tion distribution in situations involving limited numbers of sources depends
heavily on the source—receptor relationship. In situations invo1vin multiple
sources where small inaccuracies in one relationship are likely to be balanced
by inaccuracies in another, this relationship is less important. Area source
applications require a little less detail than point or line applications,
because the spatial extent of an area source makes an error in the source—
receptor relationship less significant 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.
At long distances emissions have usually become relatively uniformly mixed and
a change in separation or orientation that would be critical at short range
produces only a negligible effect. The importance of the source—receptor
relationship to each of the applications is given in Table 4.2.
Emission Rate
Other things being equal, concentrations of primary pollutants are
proportional to emission rates. For secondary pollutants, the relative
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A84
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 when 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 such
as changing meteorology and removal processes normally can assume greater fin—
portance for determining concentrations. Emission rates are rated as somewhat
more important in situations involving a limited number of sources, because of
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 given 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 an
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. No
difference in importance between long-term and short—term applications is assumed.
A slight extra importance is assigned to applications involving multiple sources
or long—range transport, because of the increased possibility for chemical re-
actions when many different emissions are mixed or a long time is allowed 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 more important in cases where physical sinks
are present than when chemical or no sinks are present. This is because the
plume behavior determines how easily the plume contacts the ground, allowing
the physical removal process to operate. Chemical removal can occur through-
out the entire volume of mixing. Plume behavior is also rated more important
in short—term than in long—term averages, because over short—time spans small
variations, masked by averaging over long time spans, may be significant.
The greater spatial inh mogeneities associated wth point sources make plume
behavior more important for point sources than for line sources. Similarly,
it is somewhat more important for line than for area sources. In complex
geographic situations, plume behavior is important in determining whether the
plume will be affected by the complex situation or rise above its influence.
Over a long range, vertical mixing tends to become uniform and hence plume
behavior is relatively unimportant.
Horizontal Wind Field
The horizontal wind field is generally an important element in any
application, because advection is the principal process for pollutant
transport. It is considered somewhat more important when chemical reactions
are important and when short—term rather than long—term averages are desired,
because of the need to know the wind field more precisely. The determination
of the horizontal wind field is more important in complex terrain due to the
channeling of the wind and other effects. The horizontal wind field is some-
what more important in limited point or line source cases than area or multiple
source cases. Finally, the horizontal wind field is considered to be very
important in those situations in which the actual trajectory of a parcel of
air must be determined, because the temporal and spatial variation must be
reproduced. This is the case for long range transport and for very short re-
lease times (puffs). Table 4.6 gives the importance rating of horizontal wind
field for each application.
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A86
Vertical Wind Field
The vertical wind field is considered generally unimportant in many
cases of interest, because it is nearly zero on average. Vertical wind field
is important in situations requiring the estimation of concentrations at
moderately short ranges in regions containing complex terrain due to the effect
of the terrain on the (three—dimensional) wind field. Vertical wind field is
considered slightly more important in applications involving chemistry than
those in which chemistry is unimportant due to the need for a more accurate
description of the wind field. Vertical wind field is also considered more
important in estimating short—term rather than long—term estimates. No dis-
tinction was made for different source geometries or numbers. Table 4.7 gives
the importance ratings of vertical wind field for the indexed applications.
Horizontal Dispersion
Table 4.8 gives the importance rating of horizontal dispersion for each
of the indexed applications. Horizontal dispersion is considered to be of at
least medium Importance in every application. Horizontal dispersion is more
important at short range than at long range, because the dispersion process
is the most rapid and produces the greatest changes in concentration estimates
at short ranges. Horizontal dispersion is considered less important for area
sources than for line sources, and less for line than for point sources due to
the emission size effect. In the case of secondary pollutants and/or the case
of chemically reactive pollutants, it is very important to be able to describe
the mixing of emissions with the ambient air, since chemical reaction rates are
sensitive to local concentrations; therefore horizontal dispersion is considered
quite important in these cases. Similarly, if physical sinks are present, it
is generally more important to handle horizontal dispersion properly, depending
on the nature of the removal process. The importance of horizontal dispersion
is considered to be higher for short—term averages than for long—term, because
the averaging which can occur over long times generally 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 time, and approximately independent of the type of terrain. Vertical
dispersion is considered much more important at short range than at long range,
and more important for secondary and/or chemically reactive pollutants or if
physical renvval processes, particularly dry deposition, are operative. Finally,
the importance of vertical dispersion is considered independent of source type
or number.
Chemistry and Reaction Mechanism
The importance of chemistry and its treatment is determined primarily
by the chemical nature of the pollutants involved and to some extent by the
travel distance; no other characteristics 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 f or 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, Boundary and Initial Conditions
The importance rat ngs of background, bound.ry 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
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A89
associated with temporal correlations in complex geographic situations. Here
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.
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A90
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Bi
APPENDIX B
BAQ(GROUND MATERIAL ON REFERENCE } )DELS
-------
B2
-------
B3
Appendi’z B. BACKGROUI4ID MATERIAL ON REFERENCE MODELS
Apper d1.x B is divided into two parts. The first, Appendix B.l, consists
of Table B.l giving the classification of each reference model, and Tables
B.2—B.13 giving the treatment of each of the twelve application elements used
by the reference models. The second part, Appendix B.2, provides abstracts
of and the working equations used by the reference models. A glossary of
symbols is provided at the end of Appendix B.2.
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B4
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B5
CONTENTS OF APPENDIX B
Page
B .1 REFERENCE MODEL TREATMENTS OF APPLICATION ELEMENTS B 7
B.2 REFERENCE MODEL ABSTRACTS AND EQUATIONS B35
B .2.1
DM
B37
B .2.2
RAIl . . .
. . . . . . . . . . . . B38
B.2.3
Single Source
(CRSTER) B4l
B.2.4
Valley
B44
B .2.5
AT?.!
B46
B .2.6
STRAI}1
. . . B47
B.2.7APRAC—1A
. B48
B .2.8
HIWAY
B50
B .2.9
DIFKIN
B5l
B .2.10
SA l
B52
Glossary of
Symbols . . . . . . . . . . . . . . . . . . B55
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B6
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U
B.1. REFERENCE MODEL TREATMENTS OF APPLICATION ELEMENTS
This appendix provides the classification of each reference model in
Table B.l and the treatment used by each reference model of each of the twelve
application elements in Tables B.2-B.13.
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B8
-------
B9
Table B.1. Reference Model Classification
Reference
Model Classification
APRAC—lA Semiempirical/Sequential (steady—state)
ATM Semiempirical/Climatological (steady—state)
CDM Semiempirical/Cllaatological (steady—state)
Single Source (CRSTER) Semieznpirical/Sequential (steady—state)
DIFKIN Numerical (vertical)/Seiniempirical (horizontal) /
Dynamic
HIWAY Semiempirical/ Steady—state
RAM Semiempirical/Sequential (steady—state)
SAl Numerical/Dynamic
STRAM S emiemp ir ical/Dynamic
Valley (short—term) Semiempirical/Steady—state
(long—term) Semiempirical/Climatological (steady—state)
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B 10
Table B.2. Treatment of Source—Receptor Relationship
by Reference ide1s
a. Horizontal Source and Receptor Location
Reference Source
Model Geoe’etfl Method of Treatment
APRAC—1A Line and area User specifies line sourcee (traffic links) with arbitrary locations and lengths.
Area sourcee (off link traffic) allocated to 2 ci x 2 mi grid.
For each receptor both are aggregated onto wedge—ehaped areas of a polsr grid
centered on a receptor (a different grid is used for each receptor) such that:
1) Radii of circular boundaries increase in geoaetric progression.
2) Radial boundaries art 22.50 beyond 3.000 a and 450 under 1000 a from receptor.
(3,3 for ares, line)a
Up to 10 arbitrarily Located receptors.
Street canyon eubmodel: Four interna 1y located receptors on each user
designated street. (2 for line)a (lI)
ATM Point, area, Arbitrary location for all souccea. (1 for all source types)a
and tine
Areas should be roughly square or circular.
Arbitrary receptor location. (l)b
Assumes flat terrain; elevation not treated.
Treats multiple point, area, and line sources.
Treste up to ten receptors.
6DM Point and area Arbitrary location for point sources. (1 for point)a
Area sources are a uarea of uniform size in user—defined grid, user nay specify
sources which are integer multiples of the grid size, but these must be auper-
isposable directly on the grid. (2 for area)
Receptors located arbitrarily.
Single Source 8 Point Up to 19 sources aLl assumed to be located at same user—specified, arbitrary
(CRSTER) position. ( 1 .. 2 )a
Receptor locations restricted to 36 azimutha (every 3. 0) and five user—specified
radial distances. ( 3 )b
DIFKIN Point and area All aourcas aggregated to square 2 m i x 2 ci grid cells in an array
25 cells x 25 cells. (2,2 for point. area) 3
Sources classified as points (power plants, refineries), distributed stationary,
and mobile.
Receptors located arbitrarily within boundaries of emission grid. ( 2 )b
HIWAY tine Straight finite line segments (will treat up to 24 parallel segments), srbitrarily
located. (2)
Arbitrarily located receptors.
Cut aection node:
Emissions treated as coming f ton 10 lines at top of cut. (2—3)
Receptors cannot be i tt cut.
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Bll
Table B.2 (Cont’d)
a. (Cont’d)
Raference Source
Model Geometry Method of Treatment
RAM Point end area Arbitrary location for point sourcea. (1 for POiflt)a
Receptora may be:
1) Located arbitrarily, ( 1 )b
2) Located internally near individual source maxima, (4Y’
3) Located on internally generated hexagonal grid to give good coverage in user—
defined portion of region of interest. (4)0
Area aources are multiples of unit equarea on a grid; uaer controls ecele of
Rrid. (2 for aree)a
SAX Point end area All sources aggregated to square grid of arbitrary spacing and up to 25 x 25 cells.
(2,2 for point, area)a
Sources classified as points (power plants), distributed stationary and mobile.
Multiple receptors located arbitrarily within boundaries of emission grid. ( 2 )b
Concentrations alao calculated in each grid cell (up to 25 x 25 x 5 estimates)
STRAN Point Arbitrary location for each source.
Up to 10 arbitrarily located receptors plus receptors at intersections of a grid
of up to 13 a 13 equally spaced boundaries. ( 1 , 3 )b
Valley Point and area Arbitrery location and elevation for each point source. (1 for point)a
Arbitrary location, elevation, end size for square area sources. (1 for aree)a
Must be lees then 51 sources.
Receptors (112) on 16 direction radial grid; relative radial distances fixed
internally, scale and origin of grid defined by user. ( 3 )b
b. Release end Receptor Heights
Reference Source
Model Geometry Method of Treatment
APRAC—lA Line end area Sources assumed at ground level. (3,5 for line, aree)c
Receptors assumed at ground level.
ATM Point, area Arbitrary release height for each source. (2,3,2 for point, line, area)c
and line
Receptors at ground level. ())d
0DM Point and area Assumes flat terrain; arbitrary stack height for each aource. (2,3 for point,
area) c
Chooses larger of input stack height or 1 a.
Receptors at ground level.
Single Sourceg Point Arbitrary stack height for each source.
(CRSTER)
Unique topographic elevation for each receptor: must be lees then each stack
height.
Receptors must be at ground level. (combination of 2 , 7 )d
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312
Table 3.2 (Cont’d)
b. (Cont’d)
Reference Source
Model Geometry Method of Treatment
DIPEDI Point and area Emissions treated aa upward pollutant fluxes at ground surface. (5,5 for point.
area) C
Receptors at equally spaced hetghts from the ground to the mixing height. ( 4 yi
HIWAY Line Arbitrary release heights. ( 2 )t
Arbitrary receptor heights.
RAM Point and area Arbitrary release height for each point source. (2 for
Up to three effective release heights (appropriate for Sm/sec winds) may he
specified for area sources. (2 for area)t
Value for a particular ares must be one of these three.
Receptors all of same height at or above groLnd level; flat terrain assumed. (fit
S U Point and area Arbitrary release height for point sources (power plants). (1 for point)c
Point source emissions assumed untformly mixed throughout vertical column in
which emission takes place.
Other emissions treated as upward fluxes at ground surface; arbitrery topographic
elevatLon. (Combinstion of 1,3 for area)c
Receptors at ground level.
STRAtI Point Arbitrsry telease height for each source. ( 2 )c
Roceptors at ground levei; flat terrain assumed. (flu
Valley Point arid area Arbitrary release height for each source. (1, combination of 1, 3 for point,
ares)
RecePaore at ground level with s unique topographic elevation. (Combinstion of
2, 7)
c. Downwind/Crosswind Distancese
Reference Source
Model Geometry Method of Treatment
APR.AC—lA Line and ares Uses exact downwind distances to the two radial boundaries of each gridded
area source. (1 for area)
ATM Point, ares Uniqus downwind and crosswind distances for each point source—receptor pair,
for three points within each area source, and for nine points slong each
line source. (1 for all source types)
CDM Point and area Calculates unique downwind distance for each point source—receptor pair.
Cslculates representative distances for ares source—receptor pairs. (1, 2 for
point, eras)
Single Sour e Point Calculated fron source to each receptor locstion. (1)
(CRSTRR)
DIFEIN Point snd ares Not applicable. Distance traveled along computed trsjectory not used explicitly.
HIWAY Line Precise downwind end croqswind distsncea for each point aloeg line. (1)
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B 13
Table B.2 (Cont’d)
c. (Cont’d)
Reference Source
Model Geometry Method of Treatment
RAN Point and aree Unique downwind and croaewind dietences for eech point source—receptor peir.
(1 for point)
Downwind distance calculated for points along rays which intereect area sourcee.
(1 for area)
SA l Point and area Not applicable.
STRAN Point Not applicable, concentration calculated et each receptor based upon distance
along and distance from trajectory centerline.
Valley 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
Ref erence Source
Model 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 snd ares Sides of areas must lie along grid directions.
Single Point Not applicable.
(CRSTER)
DIFKIN Point and area Areas oriented by fixed grid boundaries. (2)
HIWAY Line Line assumed horizontal with arbitrary orientation. (2)
RAN Point and area Sides of areas must lie along grid directions. (2)
SAX Point and area Areas oriented by fixed grid boundaries. (2)
STRAN Point Not applicable.
Valley Point and area Area sources assumed oriented with one side parallel to wind direction.
(Somewhat less detailed than 2)
aNumbars in parentheses refer to treatments of horizontal source location for the appropriate source type as given in
Table 5.1 a.
bNu ers in parentheses refer to treatments of receptor location as given in Tsble 5.1 a.
cNumbars in parentheses refer to treatments of release height for the appropriate source typa as given in Table 5.1 b.
Sumbers in parentheses refer to treatments of receptor height as given in Table 5.1 f.
5 Numbers in parentheses refer to treatments of downwindfcroaswind 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.
¼RSTER ahould be used only when the receptor is below stack height.
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B 14
Table B.3. Treatment of Emission Rate by Reference Models
Arbitrary line aource amiaaions aggregated onto grid
deacribed 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
formulas; contributions calculated from sll upwind
sources located within the wedge—shaped grid.
(2 for gridded sres sources)
Ares sources transformed into polar sress each of
which is represented by three effective point sources;
shape of ares depends upon angle subtended by ares at
each receptor.
Totsl 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, ares, line)
Trests “windblown” source as an ares source of TSP
with emission rate determined by user input values of
type of mstarial, density, saltation diameter. snd
suspension diameter appropriate to each source snd
the wind speed. (“Windblown” source: modified 4)
Point and Arbitrary emission rate for each point and ares
ares source.
Ares sources assumed uniform.
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 rats for link of interest
is input by user. (5)
Day/night vsriations in emissions;
same vsristion for all sources. (2b)
c
Single Source
(CRSTER)
DIFKIN
Point
Point end
ares
Area source contributions integrated numaricelly
one 22.50 sector at a time, based on ssmpling
points located at specific angular and radial
intervals on a polar grid centered st receptor
(1, 3 for point, ares)
Arbitrary emission rate for each source. (1)
Emissions treated as upward pollutant fluxes at
ground surface.
Monthly variation in emission rats
sllowed. (3)
Sequence of hourly average rates
for mobile sources.
Individual rats for esch 2 mi x 2 mi grid square:
Rates for mobile sources determined from ussr—
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, ares)
Program option allows user to input drcctly ar-
bitrary surface pollutant fluxes for up to three
pollutants (not necssssrily photochemically re-
active).
Stationary source rates assumed
constant. (1,3)
APRAC—lA Line and
Raference
Model
Method of Treatment
Source b
Geometry Spatial Varistiona Temporal Variation
Point,
area, and
line
Arbitrary rate for each point, line and ares source. Constant emission rates. (5)
ATM
CDM
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815
Table 8.3 (Cont’d)
Reference
I lodel
Source
Geometry
Method of Treatment
Spatial Variationa
b
Temporal Variation
HIWAY
Line
Uniform emiesion rate for each traffic lane.
Constant emission
rates. (5)
Each lane integrated cLacilcally to obtain con-
tribution. (3)
RAM
Point and
area
Arbitrary emission rate for each point and area
source.
Constant emission
rates. (5)
Area source contributions obtained by numerical inte-
gration along upwind distance of narrow—plume approxi-
mation formulae for eras source with given effective
releas,. height.
Includes only those areas intersected by the upwind
ray. (1 for point; 4,5 for area)
SAt
Point and
area
Point source emiasions distributed homogeneously
throughout entire vertical column above grid
square containing the source; emission rates
supplied by user.
Other emissions treated as upward pollutant fluxes
at ground surface.
Sequence of hourly
for mobile sources
Stationary source
constant (1,3)
average rates
rates assumed
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)
STRA t I
Point
Arbitrary emission rate for each sourcs. (1)
Constant emission
rstes. (5)
Valley
Point and
area
Arbitrary rate for each point and area source.
Area sources treated as single effective point
sources.
Constant emission
rates. (5)
Total sres source contribution estimated as a sum of
individual contributions. (1,4 for point, area)
umbers in
parentheses refer
to treatments of spatial variation as given in Table 5.2.
bNumbers in
psrentheses refer
to tTestments of temporal variation as given in Table 5.2.
cC 5TER should be used only when the receptor is below stsck height.
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Table B.4. Treatment of Composition of Emissions
by Reference Models
Nethod of Treatment
Reference
)bdel Chemical Composition Size Distribution
APRAC—1A Not applicable; model designed for primary, unreactive Not applicable; model designed for gase,us pollutants.
pollutant.
ATM Not applicable; model designed for primary, unreactive User inputs single particle size (and density) for use
pollutant. in calculating terminal velocity for particulates.
Treats three types of sand (uniform, naturally graded,
wide size range) and single saltation and suspension
diameters (and single density) for windblown sources. ( 4 )b
CDM Not applicable; model designed for primary pollutants. Not treated explicitly. (7)1
Sin 1e Sourcec Not applicable; model designed for primary, unreactive Not treated explicitly. (7)1)
(CRSTER) pollutant.
0 ’
DIFKINd Treats emissions of CO. NO, and reactive hydrocarbons. Not applicable; model designed for gaseous pollutants.
Emissions of NO in inventory assumed to be entirely
NO 2 ; converted internally entirely into NO.
Hydrocarbons in inventory assumed to be total hydro-
carbons; reactive fraction of mobile source hydrocarbon
emissions assumed to be 70.4% by weight.
Stationary source hydrocarbons assumed to be 100%
reactive. ( 4 , 5 )a
Program option: User directly input fJ.uxes up to three
arbitrary pollutants (for applications not involving
photochemical smog). (Not applicable: chemical reaction
not treated.)
HIWAY Not applicable; model designed to treat primary, unre— Not applicable; model designed for gaseous pollutants.
active pollutant.
RAM Not applicable; model designed to treat primary, unre— Not treated explicitly. ( 7 )b
active pollutant.
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Table B.4 (Cont’d)
aNumbers in parentheses refer to treatments of chemical composition in Table 5.3.
bNumbers in parentheses refer to treatments of size distribution in Table 5.3.
ccRSTER should be used only when receptor height is below stack height.
dDesigned specifically to treat photochemical oxidants.
Reference
Method of Treatment
Model
Chemical Composition
Size Distribution
1 d
Treats emissions of reactive hydrocarbons, unreactive
Not
applicable; model designed for
gaseous
pollutants.
hydrocarbons, NO, 1402, and CO.
User imputs mobile source emissions of hydrocarbons,
NOR, and CO.
Mobile source hydrocarbon emissions split internally
into 67.4% (mole fraction) reactiwe fraction and 32.6%
unreactive fraction.
Mobile source NOx emissions assumed to be 99% NO 2 ;
converted internally to NO.
User inputs stationary source (both point and area)
emissions of reactive hydrocarbons, unreactive hydro-
carbons, NO, 1402 and CO. ( 4 , 5 )a
STRM4
Treats two compounds; one is assumed to be 502 the other,
sulfate (504). ( 4 )a
Not
treated explicitly. (7)1
Valley
Treats only one compound.
Not
treated explicitly. ( 7 )b
Capable of treating at most one compound or a single
representative compound in cases where chemical reactions
occur. ( 6 )a
I - .
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B18
Table B.. . Ireatm nt of Plume Rise by Reference Modt.ls
Reference
Treatment
of
Model
Treatment of Plume Risea
Downwash/Fumigation
APRAC—lA
Not treated explicitly. (5)
Does
not treat
either.
For each point source, user inputs a value representing Does not treat either.
the product of plume rise with 1) wind speed end 2) the
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).
CDM Briggs’ 2/3 (1971) neutral/unstable formula used for Does not treat either.
point sources.
If (stsck height) + (plume rise) exceeds mixing height,
ground level concentrations are assumed equal to zero.
(Modified 4a)
Aa an alternative to Brigge’, 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)
Single sourceb Rriggs’ (1971, 1972) final plume rise formulas; plume rise Does not treat either.
(C aSTER) not treated as a function of downwind distance.
If plume height exceeds mixing height, concentrations
further downwind assumed equal to zero. (4a)
DIFKIN Not treated explicitly. (5) Does not treat either.
HIWAT Not treated explicitly but could be included in release Does not treat either.
height. (4e,5)
RAN Uses Briggs’ (1971, 1972) downwind distance dependent Does not treat either.
plume rise formulse for point sources.
If plume height exceeds mixing height, ground level
concentrations assumed zero. (Modified 4s)
No plume rise calculated for sres sources; could be
included in release height. (4e,5)
SkI Uses Briggs’ formulae (1971) for point sources (power Does not treat either.
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)
STRA t I Not treated explicitly; could be included in release Does not treat either.
height for each source. (4e,5)
Valley Uses Briggs’ (1971, 1972) plume rise formulae for Does not treat eithsr.
both point end eres sources.
Option: A single constant plume rise value may be
input for any or all sources. (OptionS 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 llzsited to the mixing height.
(Modified 4a)
aNumbers in parentheses refer to treatments as given in Table 5.4.
bCRSTER should be used only if receptor height is below stack height.
-------
Table B.6. Treatment of Horizontal Wind Field by Reference Models
Reference
Model Method of Treatmenta
APRAC— 1A Constant, uniform wind speed and direction assumed for each of a sequence of hours.
Wind speed, direction values input by user. (4,7,2)
Street canyon sub—model: specific positional and height dependence built in; constant
in time. (3,5,4)
ATM Constant, uniform wind speed and direction.
Climatological treatment with sixteen wind sectors, S wind speed classes used. (4,7,3)
CDM Constant, uniform wind speed and direction.
Wind speed is estimated value at release height, correction from value at reference
height (1Gm) dependent only on stability class.
Climatological treatment with sixteen wind sectors, 6 wind speed classes used. (4,6,3)
Single sourceb Constant, uniform wind speed and direction assumed for each of a sequence of hours.
(CRSTER) Wind speed, direction values input by user;c speed corrected for release height depend—
ing on stability class. (4,7,2b)
DIFKIN Trajectory model.
Wind speed and direction specified for each of a sequence of time steps at point on a
horizontal grid, interpolated from nearest 1, 2, or 3 surface measurements.
Discrete user—specified number (n) of wind directions allowed, 4< n <99
Arbitrary wind speed values allowed.
Wind speed, direction independent of height. (2,7,2b)
Program option allows direct user input of trajectory.
HIWAY Constant, uniform wind speed and direction.
Wind speed, direction values input by user for the hour of interest. (4,7,4)
RAM Constant, uniform wind speed and direction assumed for each of a sequence of hours.
Wind speed, direction values input by user.c
Wind speed is modified to correspond to value at release height, modification
dependent only on stability class. (4, modified 6,2b)
SA l Fixed grid model.
Wind speed and direction specified for each of a sequence of hours at point on a
horizontal grid, interpolated from surface measurements.
Arbitrary wind speed, direction values allowed.
Wind speed, direction independent of height. (2,7,2b)
-------
Table B.6 (Cont’d)
Reference
Model Method of Treatmenta
STRM4 Trajectory model.
Wind speed and direction specified at 12—hour intervals on a horizontal grid, inter-
polated from radiosonde measurements.
Wind speed and direction interpolated in time between measurements.
Arbitrary wind speed, direction values allowed.
Wind speed, direction independent of height. (2,7,2a)
Valley 1. Long—term calculations:
Constant, uniform wind speed and direction.
Climatological treatment with sixteen wind sectors, 6 wind speed classes.
Wind speed class values input by user, used without correction for height. (4,7,3) C ’
2. Short term calculations (24—hour maximum only):
User—defined direction used.
Wind speed assumed 2.5 rn/sec . with persistence of 6 hours out of 24.
Stable conditions in complex terrain with receptors at or above plume centerline:
Implicit treatment of locational and height dependences — effect of plume
deflection by terrain accounted for by linear interpolation of centerline
concentration values between the lOm value at point of impingement and zero
at 400m above point of impingement. (6,8,5)
Stable conditions with receptor below plume centerline:
Uniform wind direction assumed. (4,7,5)
Does not treat neutral or unstable conditions.
aNumbers in parentheses refer to the dependence on horizontal location, height above ground, and tine as
given in Table 5.5.
bCRSTER should be used only if the receptor height is less than the stack height.
cAssumes wind directions given to nearest 10°, randomizes wind direction by addition of the amount (n—4) 0
where n is a random number between 0 and 9.
-------
Table B.7. Treatment of Vertical Wind Field by Reference Models
Reference a
Model Method of Treatment
APRAC—lA Assumed equal to zero. (4b,4b,3)
Street canyon sub-model: specific positional and height dependence built in,
assumed constant in time. (3,3,3)
ATM Assumed equal to zero. (4b,4b,3)
CDM Assumed equal to zero. (4b,4b,3)
Single sourceb Assumed equal to zero. (4b,4b,3)
(CRSTER)
DIFKIN Assumed equal to zero. (4b,4b,3)
HIWAY Assumed equal to zero. (4b,4b,3)
I . ’ ,
RAM Assumed equal to zero. (4b,4b,3)
SAT Vertical wind speed specified for each of a sequence of hours at points on a
three—dimensional grid.
Values assumed linearly increasing functions of height, values near surface
determined from horizontal wind speed and directions using mass consistency
requirements. (2 ,3,2b)
STRA]4 Assumed equal to zero. (4b,4b,3)
Valley 1. Long—term calculations:
Assumed equal to zero for stable atmospheric conditions. (4b,4b,3)
Implicit treatment for neutral and unstable conditions: plume assumed
to remain at a constant height above terrain. No time dependence. (4a,4a,3)
2. Short—term calculations (24—hour maximum only): as in long—term calcula-
tions for stable conditions. (4b,4b,3)
Does not treat neutral or unstable conditions.
awumbers in parentheses refer to the dependence on horizontal location, height above ground, and time
as given in Table 5.6.
bCRSTER should be used only if the receptor is Less than the stack height.
-------
B 22
Table B.8. Treatment of Horizontal Dispersion
by Reference Models
Reference
Model classification Method of Treatment
APRAC— 1A Semiempirical /sequentisi Sector averaging (narrow plume approximation)
(steady—state) 45.00 less than 1 km.
22.5° beyond 1 km.
Atmospheric stability not treated explicitly.
Surface roughness not treated explicitly. (4b,3,3 ,na)a
ATM Semiempirical/climatological Uniform horizontal distribution assumed within each of 16
(steady—state) 22.50 sectors (sector avereging).
Atmospheric stability not treated explicitly.
Surface roughness not treated explicitly.
Averaging time assumed long enough for sector averaging to
be valid. (Sc,3,2a,na)a
CDM Semiempirical/climatologicel Uniform horizontal distribution assumed within eech of 16
(steady—state) 22.5° sectors (sactor averaging).
Atmospheric stability not treated explicitly.
Surface roughness not treated explicitly.
Averaging time assumed long enough for sector averaging to
be valid. (Sc,3,3,ns) 5
Single Sourcet Semiempirical/sequential Gaussian plume function assumed.
CCRSTER) (steady—state)
Atmospheric stability divided into seven classes.
Surface roughness not explicitly treated.
One hour averaging tine used. (4a, 2 b, 3 ,3)a
DIPKIN Numerical Cvertical)/ Narrow plume approximation about calculated trajectory.
Semiempirical (3c ,3,3 ,na)a
(horizontal) /dynami c
HIWAY Semiempirica1/ ’ r .cady—state Gaussian plume function assumed for each point along line;
numerical integration along line.
Atmospheric stability divided into six (Paaquill—Gif ford)
classes.
Dispersion coefficients from Zimmerman and Thompson (1975)
less than lOOm, from Turner (1969) beyond lOOm.
Level grade mode — initial value of dispersion coefficient
set at 3.0 m.
Cut section mode — initial value of dispersion coefficient
an empirical function of wind speed.
Surface roughness not treated explicitly.
One hour averaging time used. (4a,2b.3,3) 5
RA I l Semiempirical/sequentisi Gaussian plume function assumed.
(steady—state)
Atmospheric stability divided into six (Pasquill—Gif ford)
classea.
Dispersion coefficients from Turner (1969) or McElroy and
Pooler (1968) at user option.
Surface roughness not treated explicitly.
One hour averaging time used.
Point sources: (4a,2b ,3,3) 5 ; Area sources: (4b,3,3,ne) 5
-------
B23
Table B.8 (Conttd)
Reference
Model Classification Method of Treatment
SA l Numerical/dynaaic Numerical solution of advection—diffusion equation in three
dimensions.
Horizontal eddy diffusivity value assumed uniform and
constant and is fixed in the code. (lb,3,3,3)a.(4.4,3)b
STR.AM Semiempirical/dynamic Crosswind distribution about calculated trajectory assumed
Gaussian.
Atmospheric stability divided into six (Paaquill—Gifford)
classes.
Same atability claaa assuned to hold over entire region of
interest.
Surface roughness not treated explicitly.
Diapersion coefficianta determined by integration of expres—
eiona for ratee of change; based on Turner (1969) up to bObs,
Heffter and Ferber (1975) beyond 100 km.
Averaging time specified by user. (3b,2b,3,3 and S)
Valley Semiempirical/climatological Long—term calculations:
(steady—state) Uniform horizontal diatribution assumed within each of
16 22.50 sectors (sector averaging).
Atmospheric stability not treated explicitly.
Surface roughness not treated explicitly.
Averaging time assumsd long enough for sector averaging
to be valid. (5c,3,3,na)a
Semiempirical/steady—state Short—term calculations (24—hour maximum only):
Uniform horizontal distribution assumed within each of
16 22.5° sectors (sector averaging).
Atmospheric stability not treated explicitly.
Surface roughness not treated explicitly.
Averaging time: 24 hours.
(Sc,3 ,3,na)a
LiNumbars in parentheses refer to treatments listed in Tables 5.7, 5.8, 5.9 and 5.10 respectively. The user should
refer to the appropriate aection (numerical or samiempirical) of Table 5.10 according to the modal classification.
bNumbera in parentheses refer to the dependence of the horizontal eddy diffusivity on horizontal location, height
above ground. and time as given in Table 5.11.
c
CRZTER should be used only when the receptor is below stack height.
-------
B24
Table B 9. TrcaL ,iient of Vertical Dis’ rsion by Reference Mo’kls
ReferenLe
Model Clasalfication Method of Treatment
APRAC— 1A Semiempirical /sequential Gaussian plume function assumed.
(steady—state) Atmospheric stability divided into six (modified
Pasquill—Gifford) classes.
Dispersion coefficient modif ted from McElroy and
Pooler (1968).
Surface roughness not treated explicitly.
Downwind distance dependence of dispersion coefficient
assumed axb for purposes of doing analytic integration.
In street—canyon submodel, semiempirical function of
wind speed, street width, and direction is used.
(4a, Zb,3,3) 5
ATM Semiempirical/climatological Gaussian plume function assumed.
(steady—state) Atnoapheric stability divided into six (Pasquill—
Gifford) classes.
Dispersion coefficients from Turner (1969) or Hosker
(1973). (user option).
Surface roughness characterized by a user—specified
roughness parameter (Hosker dispersion coefficients
only)
(4a,2b,2a,3)a
CDM Semiempirical/climatological Gaussian plume function assumed.
(steady—state) Atmospheric stability divided into six (Pasquill—
Gifford) classes, with neutral stability divided into
day and night cases.
Stability class decreased by one class (more
unstable) for area sources.
Surface roughness not treated explicitly.
Dispersion coefficients from Turner (1969).
(4a,2a,3,3) 5
Single Sourcec Semiempirical/sequentisl Gaussian plume function assumed.
(cRSTER) (steady—state) Atmospheric stability divided into seven (P—G) classes.
Surface roughness not treated explicitly.
Dispersion coefficients from Turner (1969).
(4a,2b,3,3)a
DIFKIN Numericai (verticsl)f Numerical integration of diffusion equation in
Seniempirical (horizontal)f vertical direction.
drtamic Vertical eddy diffusivity values specified hourly by
user at user—defined discrete heights above ground.
(lb,Za,3,2)a, (4,3,2b)b
RIVA l Semiempirical/steady—state Gaussian plume func ion assumed.
Atmospheric stability divided into six (Pasquill—
Gifford) classes.
Dispersion coefficient from Zimmerman and Thompson
(1975) less than lOOm, from Turner (1969) beyond lOOm.
Level grade mode — initial dispersion coefficient set
at l.5m.
Cut section mode — initial dispersion coefficient an
empirical function of wind speed.
(4a,2b,3,3)a
-------
F2
Table 1’. J (Coot’d.)
Reference
Model Classification Method of Treatment
RAN Semiempirical/sequential Gaussian plume function assumed.
(steady—state) Atmospheric stability divided into six (Pasquill—
Gifford) classes.
Dispersion coefficients from Turner (1969) or McElroy
and Pooler (1968) at user’s option.
Surface roujhnssa not treated explicitly.
(4a.ab,3.3Ya
SAl Numerical/dynamic Numerical solution of advection—diffusion equation in
three dimensions.
Vertical eddy diffusivity an empirical function of
wind speed and height above ground.
(lb,3,3.2) 5 , ( 4 ,S, 2 b)b
STRAM Semiempirical/dyneetic Two options are available to the user:
1) Gaussian plume function assumed.
Atmospheric stsbility divided into six (Pasquill—
Gifford) classes.
Same stability class assumed to hold over entire
region of interest.
Surface roughness not treated explicitly.
Dispersion coefficients determined by integration
of expressions for rates of change; based on
Turner (1969) up to 100 kit, Beffter and Ferber
(1975) beyond 100 km.
2) Uniform vertical distribution up to mixing height
assumed.
(3b or 3d,2b,3,3)a
Vslleye Semiempiricel/climetological Long—term calculations:
(steady—state) Gaussian plume function assumed.
Atmospheric stability divided into six (Pasquill—
Gif ford) classes.
Surface roughness not treated explicitly.
Dispersion coefficients fron turner (1969).
(4a,2b, 33 )S
Semiempirical/steady—atste Short—term calculations (24—hour maximum only):
Gaussian plume function assumed.
One stability class (stable Pasquill—Gif ford
“F”) used.
Surface roughness not treated explicitly.
Dispersion coefficients from Turner (1969).
(4a,2c,3,3)a
aNumbers in parentheses refer to treatments listed in Tables 5.7, 5.8, 5.9 and 5.10, respectively, The user
should refer to the appropriate section (Numerical or Semiempirical) of Table 5.10 according to the model
classification.
bNnmbers in parentheses refer to the dependence of the vertical eddy diffusivity on horizontal location,
height above ground and time is given in Table 5.11.
CCRSTER should be used only when the receptor is below stack height.
-------
B2’
rable B.1() Treatment of Chemistry and Reaction Mechanism by Refsrcnce Models
Reference
a
Models Method of Treatment
APRAC—lA Not treated explicitly. (7)
ATM Not treated explicitly. (7)
CDM Treats only first—order removal processes: exponential decay.
Single, constant user—supplied halflife used. (6)
Single Source 1 ’ Not treated explicitly. (7)
(CRSTER)
DIFRIN Photochemical smog system: (4)
Sixteen reactions involving 10 chemical species (NO, Hc, NO 2
03, HNO 2 , NO 3 , N20 5 , OH, R02, CO).
Lumping approximation for 2 species (Hc, R0 2 ).
Steady—state approximation for 4 species (NO 3 , N 2 0 5 , OH, R0 2 ).
User specifies NO 2 photolysis rate constant as function of
time (up to 300 sequential values).
No adjustment made for effects of imconplete turbulent mixing
below the resolution of the grid.
Program option allows user to prescribe arbitrary chemical
reaction mechanism (up to 20 chemical species, up to 20
reactions).
HIWAY Not treated explicitly. (7)
R AN Treats only first—order removal process: exponential decay.
Single, constant user—supplied half life used. (6)
SA l Photochemical smog system: (4)
Fifteen reactions involving 10 species (NO, NO 2 , Oj, Mc, 0,
OH, 1102, R0 2 , NO 3 , 1*102).
Lumping approximation for 2 species ( Mc, RO 2 ).
Steady—state approximation for 6 species (NO 3 , 0, RO , OH,
HO 2 , HNO 2 ).
NO 2 photolysis rate calculated internally as a function of
time.
No adjustments made for the effects of incomplete turbulent
mixing below the resolution of the grid.
STRAM 5O 2 —sulfate aerosol system:
SO 2 to sulfate conversion approximated by a first—order
process with internally defined value of the rate constant. (6)
Valley Treats only first—order removal processes: exponential decay.
Single, constant user—supplied halflife used. (6)
a Numbers in parentheses refer to treatment numbers in Table 5.12.
1’ CRESTER should be used only if receptor height is less than stack height.
-------
‘r?tbis li i. ‘ircatmiant f Ph’si al Itemoval Processes t’, kefetence Models
Reference
Model Method of Treatment
APRAC—]A Not treated explicitly. (415)
ATM Dry deposition : (2a)b
Pollutant removal simulated by effective source treatment.
Multiplicative factor determined by downwind integration of removal rate.
Rate of removal determined from ground—level pollutant concentration and a constant deposition velocity.
Deposition velocity (gases) adjusted within internally defined range of values by user—supplied measure of surface
roughness, related to extent and type of vegetation cover.
Effect of atmospheric stability not treated explicitly. ( . 1
Deposition velocity (particulate matter) is the greater of the gravitational settling velocity or 0.01 rn/sec.
Tilted plume approximation used for particulate matter if gravitational settling velocity is greater than 0.01 rn/sec.
(3)b
Effect on vertical concentration profile not treated explicitly except in tilted plume case.
Precipitation scavenging : ( 2 )c
Exponential decay with constant washout coefficient.
Removal occurs only for fraction of time equal to frequency of occurrence of rainfall (input by user); not correlated
with any other meteorological variables.
Washout coefficient calculated imtermally from user supplied mean rainfall rate.
CDM Treats only first—order removal processes; exponential decay.
Single, constant user—supplied halflife used. (2b,5)a
Single Source ’ Not treated explicitly. (4, 5 )a
(CRSTER)
D IPKIN Not treated explicitly. ( 4 ,s)a
-------
1MI1L 5.11 (Cont’d)
Reference
Model Method of Treatment
RIWAY Not treated explicitly. ( 4 , 5 )a
RAM Treats only first—order removal processes: exponential decay.
Single, constant user—supplied halflife used. (2b .5)a
SA l Not treated explicitly. (4,s)a
STRAM Dry deposition : (2a)b
Pollutant removal simulated by effective source treatment.
Multiplicative factor determined by downwind integration of removal rate.
Rate of removal determined from ground—level pollutant concentration and constant deposition velocity.
Deposition velocities for SO 2 , sulfate aerosol are fixed in the program at 1.0 and 0.1 cm/sec., respectively.
Effects of surface roughness or atmospheric stability not treated explicitly.
Effects on vertical concentration profile not treated explicitly.
Precipitation scavenging : (S)
Not treated explicitly.
Valley Treats only first—order removal processes: exponential decay.
Single, constant user—supplied halflife used. (2b,5)a
aFirst number refers to treatments of dry deposition in Table 5.13, second number refers to treatments of precipitation scavenging
in Table 5.13.
bNumbers refers to treatments of dry deposition in Table 5.13.
cNumbers refers to treatments, of precipitation scavenging in Table 5.13.
dCRSTER should be used only if receptor height is less than stack height.
-------
Table B 0 i2, raatment of Lackgrouitd, P.jund r’ nd Initial Conditions by Reference Models
a. Backgrounda
Reference
Model Classification Method of Treatment
APRAC—1A Semiempirical/sequential Value calculated for each receptor; box model used to estimate contributions from upwind
(steady—state) sources beyond 32 km based on wind speed, mixing height and annual fuel consumption. (2)
in street csnyon sub—model, contribution from other streets is included in the back-
ground. (2)
Semiempiricel/climatological Not treated explicitly. (3)
(steady—state)
CDM Semiempirical/climatological Single constant input values for each pollutant. (2)
(steady—state)
Single Source g Semiempirical/sequential Not treated explicitly. (3)
(CKSTER) (steady—state)
DIFKIN Numerical (vertical)/ Not applicable.
Semiempirical
(horizontal) /dvnamic
RIWAY Semieepirical/ateady—state Not treated explicitly. (3)
0
RAM Semiempirical/sequential Not treated explicitly. (3)
(steady—state)
SA l Numerical/dynamic (Treated as a boundary condition on flux at vertical boundanea.)
STRA It Seieiempirical/dynasaic Not treated explicitly. (4)
Valley Semiempirical/climatological Long—ten calculations. Not treated explicitly. (3)
(steady—state)
Semiempirical/steady—state Short—term calculations (24—hour maximum only). Not treated explicitly. (3)
b. Upper Boundary Condition (at Mixing Height)b
APRAC—lA Semiempirical/sequential Perfect reflection: ignores effect until concentration equals that calculated using box
(steady—state) model; usea box model (uniform vertical distribution) thereafter. (intermediate between 2—3)
Mixing height determined from morning radiosonde data and during day, surface temperature
variations
Midnight to dawn: constant at ore—dawn value obtained uaine minimum urban temperature;
Dawn to sunset: afternoon maximum temperature used to obtain maximum height; hourly values
obtained from surface temperature variations;
Sunaet to midnight: linear interpolatinn over time.
-------
Table B.lz (C.nt’d)
b. (Cont’d)
Reference
Model Classifications Method of Treatment
ATh Semiempirical/cllmatological Treated implicitly by limiting vertical disperaion coefficient to be no larger than
(steady—atate) mixing height. (4)
CON Semiempirical/climatological Perfect reflection: no effect until vertical disperaion coefficient equala 0.8 of
(ateady—atate) the mixing height, uniform vertical mixing assumed thereafter. (2)
Single Semiempirical/aequential Perfect reflectionS method of multiple images trested by summation of aeriea until
(CRSmR) (steady—state) vertical dispersion coefficient = l. 6 x (mixing height), uniforn vertical mixing
thereafter. (1)
Mixing height for a given hour obtained by interpolation of radiosonde data (see Appendir
8.4 for algorithm).
DIFICIN Numerical (vercical)/ Perfect reflectionS flux required to be equal to zero at boundary. (3)
Seniempirical Mixing height can change at hourly intervals.
(horizontal) /dynamic
HIWAY Semiempirical/steady—state Perfect reflection:
1) Stable conditions or mixing height greater than 500Dm. assume no effect (treats only
reflection from ground); (3)
2) Neutral or unstable conditions with mixing height less than 500Dm: method of multiple
imagee treated by aununation of infinite aeriea until vertical dispersion coefficient >
1.6 x (mixing height), uniform vertical distribution thereafter (1)
RAM Semiempirical/sequential Perfect reflectionS
(steady—state) 1) Neutral and unstable conditions method of multinle images treated by summation of
infinite series until l.6x (mixing height); uniform mixing assumed thereafter; (1)
2) Stable conditions: mixing height sasumed to have no effect. (3)
Mixing height for a given hour obtained interpolation of radiosonde data (see Appendix 8.8
for algorithm).
SA l Numerical/dynamic Perfect reflection for pollutants within region of interest (turbulent diffusive flux = 0).
Allows for entrainment of pollutants from above mixing layer (1)
STRAM Semiempirical/dynam]c Two options.
1) Uniform mixing (perfect reflection) (4) or
2) Mixing height assumed to have no effect. (3)
Valley Semiempirical/climatological Perfect reflection:
(eteady—state) and 1) Neutral and unstable conditions perfect reflection; method of multiple images
Semiempiricsl/steady—state treated by summation of infinite series; (1)
2) Stsble conditions: ignores effect of upper boundary. (3)
-------
Table L.12 (Cont’d)
c. Lower Boundary Condition (at Earth’s Surface)c
Reference
Model Classification Method of Treatti ent
APRAC— 1A Semiempirical/sequentitl Perfect reflection; single image source. (Intermediate between 3—4).
(steady—state)
ATM Semienpirical/climatological Perfect reflection; single image source. (4)
(steady—state)
ON Semiempirical/climatological Perfect reflection; single image sourcei (3)
(steady—state)
Single sourceg Semiempirical/sequential Perfect reflection in plane at same height as receptor; multiple Image sources. (2)
(CRSTER) (steady—state)
DIflIN Numerical/ (vertical) I Emissions treated as upward fluxes at the ground.
(horizontal)/ Implicit perfect reflection; no adjustment made to fluxes to account for removal. (3)
HIWAT Semiempirical/steady—state Perfect reflection by method of multiple images. (2)
RAM Semiempirical/sequential Perfect reflection by method of multiple images. (2)
(steady—state) F-’
SA l Numerical/dynamic All non—point source (power plant) emissions treated at upward fluxes at ground.
Implicit perfect reflection; no adjustment made to fluxes to account for removal. (3)
STR.AM Semiempirical/dynamic Perfect reflection by method of single image source. (4)
Valley Semiempirical/climatological Perfect reflection by method of multiple images in stable cases and single image source
(steady—state) and in neutral and unstable casesJ (stable: 4; other: 2).
Semiempiricalf steady—state
d. Boundary Condition at Vertical Sidesd
APRAC—lA Semienpirical/sequential Not applicable; treated as background.
(steady—state)
A T M Semiempirical/climatological Not applicable; treated as background.
(steady—state)
CM Semiempirical/climatological Not applicable; treated as background.
(steady—state)
Single gour Semiempirical/sequential Not applicable; treated as background.
(CRSTER) (steady—state)
-------
1.? (Je_Lt ‘‘
d (Cont’d)
Reference
Model Classification Method of Treatment
DIFKIN Numerical (vertical)! Not treated explicitly, horizontal uniformity assumed (5)
Semiempirical (horizontal)!
dynamic
HIWAY Sesiempirical/ateady—atate Not applicable, treated aa background.
RAM Semiempirical/sequential Not applicable, treated as background.
(steady—state)
SA l Numerical/dynamic Treated as a function of position and elevation, total flux normal to aide of region
required to be continuoua across boundary at each point. (1)
STRA}1 Semiempirical /dynamic Not applicable, treated as background
Valley Semiempirical/climatological Not applicable, treated as background.
(steady—state) and
Semiempirical/steady _stete
e. Initial Conditionee
APRAC-lA Semiempirical/sequential Not applicable
(steady-state)
ATM Semiempirical/climatological Not applicable.
(steady—state)
COP ! Semiempirical/clinatologicsl Nor applicable.
(steady—state)
Single Sourceg Semiempirical/sequential Not applicable
(CRSTER) (steady—state)
DIFKIN Numerical (vertjcal)/ User specifies arbitrary initial concentrations for all specios not treated by steady—state
Semiempirical (horizontal)/ assumption (all but NO 3 , N 2 0 5 , R0 2 , OH st each discrete height above ground (1)
dynamic
HIWAY Semiempiricsl/stesdy—stste Not applicable.
RAN Semieepiricsl/sequentssl Not applicable
(steady—state)
SAl Nusericsl/dynamic Mean initial concentrations of 6 species (reactive HC, NO, 03, NO 2 , CO, unresctive He)
specific for each grid cell. (1)
STRAP! Semiempirical/dynsmic Not applicable
Valley Semiempirical/climatological Not applicable
(steady—state) and
Semiesipirical/steady state
-------
Table B.l2 (Cont’d)
aNumbers in parentheses refer to treatments of background given in Table 5.l4a for models having the same
classification as the reference model.
bNumbers in parentheses refer to treatments of the upper boundary condition (at the mixing height) given in
Table 5.l4b for models having the same classification as the reference model.
cNumbers in parentheses refer to treatments of the lower boundary condition (at the earth’s surface) given
in Table 5.l4c for models having the same classification as the reference model.
dNumbers in parentheses refer to treatments of the boundary condition at vertical sides given in Table 5.l4d
for models having the same classification as the reference model.
eNumbers in parentheses refer to treatments of initial conditions given in Table 5.l4e for models having
the same classification as the reference model.
see also the description of the treatment of the upper boundary condition.
CRSTER should be used only when the receptor height is below the stack height.
-------
B 34
Table B.l3 Treatment of Temporal Correlations
by Reference Models
DIBRIN Sequentia] treatment up to 24
hours; correlations
automatic.
RIWAY Not appliceble.
S A l Sequential treatnept up to 24
hours; correlations
automatic.
ST RM I Sequential treetment; cor-
relations automatic for
meteorological variables.
Emissions a function of hour of the day snd day of the week.
Wind speed, direction, stability and mixing height are func-
tions of hour of the day. (la)
Wind speed, wind direction, stability correlated via atabili—
ity wind rose.
Emiaeion rates constant, not corralated with other parameters.
Mixing height correlated with atabilit ). class through limits
on 0 m. different limit for each cleas. (2b)
Wind speed, wind direction, atabit3ty correlated via
stability wind rose.
Mixing height adjusted according to stability class:
Class A——l.5 x (afternoon climatoLogical value).
Cleaa 0 (ni ht)-—average of morning and afternoon ciinato—
logical values.
Class B——Morning clliaatological value.
Class B, c, D (day)——Appropriate climatological value.
Emiaaion rater day—night veriationa allowed; all sources
vary by same factor. (2b)
User supplies hourly values of wind speed, wind direction,
mixing height, and other meteorological variables required
for determining stability class and plume rise.
Monthly emiasion variation allows limited emission—meteorology
correlations. (lc)
Parameters updated each hour: mobile estisaiona from each
grid square, wind speed and direction (trajectory); vertical
diffusivity values at each height, mixing height, NO 2 phota—
lyaie rate constant.
Update based on user input values. (lb)
Not applicable; user inputs specific parameter valuea for
the hour of interest.
User supplies hourly values of wind speed, wind direction,
mixing height, and other meteorological variables required
for determination of stability class and plume rise.
Emission ratea constant, not correlated with other parameters.
( Ic )
Parameters updstei every hour: mobile aource emission for
each ground—level grid square, point source (power plant)
emissions, wind speed end direction, mixing height at every
vertical column of grids, varrical eddy diffumivity at every
vertical interface of grid cella, incoming fluxes at bound—
ariea, 502 photalysie rate constant.
Update based on user input values. (la)
Stability class end mixing height changed each hour based on
user—input values.
Horizontal components of windfield updated at 12 hour inter-
vals based om radioaonde date; changed eech hour by inter-
polation between updates.
Emission rates conatant; not correlated with other parameters.
( Ic)
APRAC— 1A
geference Degree
Model Type of Treatment and
of Temporal Resolution
Quantitiea Correlatede
Sequential; correlations
automatic.
ATM Non—sequential (clinatolog—
icel) ; limited correlation
between some meteorological
parameters.
CDM Non- equential (clinatolog—
icai). limited correlation
between total emission rate
and meteorological parameters.
Single Source ’ Sequential, correlations
(CRSTER) automatic for meteorological
parameters.
RAM Sequential treatment; cor-
relations automatic for
meteorological parameters.
Valley Non—aequential (climatolog—
icel); limited correlation for
meteorological variables.
Wind speed, direction, atability correlated vie stability
wind rose.
Emisafon rates constant; not correlated with other parameters.
Mixing height adjusted according to stability class (2b)
thong—term mode
Class D (night)——0.5 x (afternoon climatological
value).
Stnble classes—-Mixing height not cotaidared.
Class A, B, C—Appropriate cliisatological value;
•Short—ten mode—input value ignored, only F atability
considered.
5 Nuzabera in parentheses refer to treatment numbers in Table 5.15.
should be used only when receptor height is below stack height.
-------
B35
B.2. REFERENCE MODEL ABSTRACTS AND EQUATIONS
This appendix provides abstracts and working equations for each of the
reference models used in this workbook. A glossary of symbols is given at
the end of this appendix.
-------
B36
-------
837
8.2.1 CD ) !
Reference : Busse and Zimmerman (1973), Brubaker, et. al. (1977).
Abstract : The Climatological Dispersion Model (CDM) is a clitnatological steady—
state Gaussian plume model for determining long—term (seasonal or annual)
arithmetic average pollutant concentrations at any ground level receptor in an
urban area.
A statistical model based on Larsen (1968) is used to transform the
average concentration data from a limited number of receptors into expected
geometric mean and maximum concentration values for several different averaging
times.
Equations :
N 6 6
= 2 L l m ]. ‘ ¼&m S jp)/P
Xarea = tl 2l ltPin S (ø)] dp
with = JQ( p ,e)de
Sector k
exp [ -4 (f) 2 ]ex [ _o.692o] for a 0.8L
P .m utL L uzTi, 2 j z
= ap ’; a, b = functions of stability class (m) and downwind distance (p) —
three ranges of distance used: 100 — 500, 500 — 5000,
5000 — 50000 m
Calibration: x +A+BTX
calibrated background tnca librated
with V V
A u ncalibrated ftp 0 mt area
Statistical transformation of averaging times for 1—24 hour averages.
-------
B 38
B.2.2 R.A}1
Reference : Hrenko and Turner (1975).
Abstract : RAM is a steady state Gaussian plume model for estimating concen-
trations of relatively stable pollutants for averaging times from an hour to
a day in urban areas from point and area sourc9s. Level or gently rolling
terrain is assumed. Calculations are performe for each hour.
Equations :
Contribution from single upwind area source
x
XA 2 f dx, integral evaluated numerically
xl
x 1 , x 2 = points of intersection of ray from receptor through area
source in question.
Stable conditions: f =
— ___
— 2rrua a g 1 g 2
yz
Neutral or stable conditions with a < l.6L
z —
=
= 2rruaa g 1 g 3
Neutral or unstable conditions with a > l.6L
z
1
L
— ____
- 12 uLa
y
In which 2
Fly
= exp L
y
-------
B39
2. 2
I 1 z—H I I 1 z+H
+ exP [ - -
z z
2 2
° r 1 z-H+2nL I 1 z+H+2nL
g 3 = te L_ + exP [
z z
Mixing Height Algorithm :
Two different mixing heights can be calculated. One is for basically
rural surroundings; the other is for urban locations. The user is given the
option to specify which he wants to use. The way in which hourly mixing
heights are determined from maximum mixing heights (MXDP) for yesterday
(i—i), today (i) and tomorrow (i+1) and minimum mixing height (MNDP) for
today (i) and tomorrow (i+l) is depicted in Figure B.l.
For urban mixing height, between midnight and sunrise; if the
stability is neutral interpolate between NXDP 1 _ 1 and MXDP. (i’), if
stability is stable use MNDP. (s). For hours between sunrise and 1400,
if the hour before sunrise was neutral, interpolate between MXDP _ 1 and
MXDP. For sunrise to 1400, if the hour before sunrise was stable,
interpolate between MNDP. and MXDP. (i). For 1400 to sunset, use MXDPj
For hours between sunset and midnight; if stability is neutral interpolate
between MXDP and DP + 1 ( , if stability is stable interpolate between
MXDP. and MNDP 7
1 1+1
For rural mixing height between midnight and sunrise, interpolate
between MXDP 11 and MXDP . For hours between sunrise and 1400, if
the hour before sunrise was neutral interpolate between MXDP 1 _ 1 and MXDP ( .
For sunrise to 1400, if the hour before sunrise was stable, interpolate
between 0 and MXDP. . For 1400 to sunset, use MXDP. . For sunset
to midnight, interpolate between MXDP. and MXDP.+i
-------
(a) URBAN
TODAY
I 0 MXDP 1
-
I
(b) RURAL
I
I
®
I
I
/
I v _1 -
MIDNIGHT
S U FIR IS E
I 400
TIME
TOMORROW
I
I
S... 5 S.... • • •• •• • SI SI ••s
‘ ‘ NEUTRAL
—— STABLE
I — BOTH
MXDP I+ I
I
SUNSET MIDNIGHT
YESTERDAY
MXDP ... 1
Li.I
x
F-
I -,
U i
=
MXDP _
C,
‘C
C
Figure B.1. Mixing Height Algorithm Used in RAM
-------
B43
B.2.3 Single Source (CRSTER)
Reference : EPA (1977).
Abstract : S ngJe Sourc : (CRSTER) is a sce—-ly state Gaussian plume technique
applicable where terrain elevation does not exceed physic i stack h ht. The
purposes of the technique are: 1) to determine the maximum 24—hout concen-
tration from a single point source of up to 19 stacks for one year, 2) to de-
termine the meteorological conditions which cause the maximum concentrations,
and 3) to store concentration information useful in calculating frequency
distributions for various averaging times. The concentration for each hour
of the year is calculated and midnight—to—midnight averages are determined
for each 24—hour period.
Equations :
X = 2irucjcy g 1 g 3 for y < l.6L
x g fora >l.6L
2iruLG 1 z
x 0 (stability class 7)
L constant, independent of downwind distance
D = (stack height + plume rise) — (difference in elevation between receptc r
and base of stack)
ex [ _ 4 2]
g3 exp (2nL D)2] + exp [ (2nL÷D)2]}
Mixing Height Algorithm :
Two different mixing heights can be calc.lated. One is for basically
rural surroundings, the other is for urban locations. The user is given
the option to specify which he wants to use. The way in which hourly
mixing heights are determined from maximum mixing heights (MXI)P) for
yesterday (i-i), today Ci) and tomorrow (i+l) and mimimum mixing height
(MNDP) for today (i) and tomorrow (1+1) is depicted in Figure B.2.
-------
B42
For urban mixing height between midnight and sunrise; if the
stability is neutral interpolate between MXDP. and MXDP.(?J, if
stability is stable use MNDP 1 For hours between sunrise and 1400,
if the hour before sunrise was neutral, interpolate between MXDP _ 1 and
MXDP ( . For sunrise to 1400, if the hour before sunrise was stable,
interpolate between MNDP. and MXDP. 4 . For 1400 to sunset, use MXDP 5
1 1 1
For hours between sunset and midnight; if stability is neutral interpolate
between MXDP. and NXDPI+i ( , if stability is stable interpolate between
MXDP. and MNDP 7
1 1+1
For rural mixing height between midnight and sunrise, interpolate
between MXDP 1 1 and NXDP 1 (j. For hours between sunrise and 1400,
if the hour before sunrise was neutral interpolate between MXDP 1 _ 1 and
NXDP For sunrise to 1400, if the hour before sunrise was stable,
interpolate between 0 and MXDP 1 . For 1400 to sunset, use MXDP 1 ©
For sunset to midnight, interpolate between MXDP 1 and MXDPi+l
-------
(a) URBAN
YESTERDAY
MXDP 1 ..., 1
MXDP _ 1
TODAY
I ..... MXDP
—Q- ®
—-.
MNDP
_________________ I
I
(b) RURAL
1
®
I
I
/
I I,
MIDNIGHT
SUIRISE 1400
TIME
TOMORROW
I
•. •.
MXDP 1 ÷i
•••‘• ••‘ NEUTRAL
—— STABLE
— BOTH
MXDP 1 +,
SUNSET MIDNIGHT
w
I —
=
I .,
x
Figure B..2, MLxi.; g Heigh Algorithm Used in CRSTER
-------
B44
B.2.4. Valley
Reference : Burt (1977),
Abstract : Valley is a climatological, Gaussian model whose primary intended
use is the estimation of the maximum 24—hour SO 2 and TSP concentrations from
single facilities in complex terrain, although annual average SO 2 and TSP con-
centrations may also be estimated in flat terrain applications.
Equations :
Long—term calculations:
N 6
= I ,m with as follows:
n=l m1 n
Neutral or unstable conditions —
16 1 °. 693 P
X —g expi— fl
n m 2irp u
L u T½
1 [ 1 1 2iL—H 1 1 1 2iL+H
g 3 = i i [ exp [ j + exp [ - a
for . 2L
g forcr >2L
L z
X =OifH>L.
nR,m
Stable conditions —
16 Q 1 r 1 H 21 1 °1 693 1)n
Xn m = 2 n i exp L - exp [ u T½
Define D = (stack height + plume rise) — (receptor elevation)
if 0 > 10 meters, set H D
if D < 10 meters, set H = 10 meters and Interpolate concentration linearly to
zero at a height of 400 meters above (stack height + plume rise).
o Short—term calculations:
(Maximum 24—hour concentration for a single elevated point source.)
X = 24
-------
B45
with given by the stable conditions formula on the preceding page,
and with
n = 1 (single point source),
9. = wind speed class index corresponding to u 9. = 2.5 meter/sec, and
in = 6 (Pasquill—Gifford “F” stability class).
-------
B46
B.25. ATM
Reference : Culkowski and Patterson (1976).
Abstract : The Atmospheric Transport Model (ATM) is a climatological steady—
state Gaussian plume model for use in mesoscale range (up to 50 1cm) modeling.
This model includes the effect of surface roughness on dispersion coefficients,
treats dry deposition and precipitation scavenging, and treats gravitational
settling of heavy particulates using a tilted plume approximation. The model
is primarily intended for calculating monthly averages but averages for other
time periods can be estimated by the use of appropriate climatological data.
Equations :
= r 1 £ m l nim kZm S (p)/p
with Qn tmthn) = n [ w exi (_APn/ul) + exp [ _(vg/u 1 ) m(Pn)]]
= effective source strength
= true source strength modified by depletion of pollution due to
deposition and washout at distances less than
A = washout coefficient
= 5.55 [ Rainfall rate (mm/hr)]0 6
vg = dry deposition velocity (meter/sec)
= 2/ir exp (_H 2 I2c1 2 )dx
f = fraction of the time washout occurs
w
2.032 2 2
= a u exp (-H /2a
zZ
o = vertical dispersion coefficient, a function of stability class (m)
Z and downwind distance
The equations for the emission rate from a windblown source are quite
complex and will not be given here.
-------
B47
B.2.6. STRAM
Reference : Hales, et. al. (1977).
Abstract : STRAM (Source—Transport—Receptor Analysis Model) is a trajectory
model using a Gaussian crosswind pollutant distribution designed to
estimate ground—level concentrations of pollutants over source—receptor
distances of up to approximately 1000 km. STRAN is designed to treat
SO 2 emissions from several elevated point sources and the conversion of
SO 2 to sulfate aerosol.
Equations :
(1) Unlimited mixing height case:
C = exp (....Y2/2 2){exP [ _ (z;h) 2 ]÷ exp [ — ( z+h) 2 ]}
= R 1 — — if 7 ( i ’di ) exp (—h 2 /2cj 2 )
= Q = the emission rate of the ith source at x = 0.
(2) For a limited mixing height (L):
c. = , exp (—y 2 12a 2 )
dQ 1 — R ____ jVdi
dx 1 u uL
= Q 01 at x 0.
Where C 1 = ground level concentration of species i.
= total mass of species i in the plume passing a downwind plane
per unit time
R 1 = ffr.(x .Y z)dYdz
r 1 rate of gain (or loss) of species I by chemical reaction
A. = washout coefficient for species i
Vdi dry deposition velocity for species i.
-------
B48
B.2.7. APRAC—IA
Reference : Ludwig and Mancuso (1972) and Ludwig and Dabbert (1972).
Abstract : APRAC is a model which computes hourly average carbon monoxide
concentrations for any urban location. The model calculates contributions
from dispersion on various scales: extraurban, mainly from sources upwind
of the city of interest; intraurban, from freeway, arterial, and feeder
street sources; and local, from dispersion within a street canyons APRAC
requires an extensive traffic inventory for the city of interest.
Equations :
—11
Extraurban — x = 5.15 x 10 F F = annual fuel consumption within 22.5°
U sector extending from 32 km to 1000 km
upwind of receptor.
1—b.. 1—b
0.8Q. x. 13 —x.
Intraurban — x.. = 1 i+1 1 until this expression equals
13 ua,. 1—b..
13 13
the “box model value” — X 4 X.
uL
Thereafter the box model formula is used.
i = upwind area segment label
j = stability class label b
a.. and b.. from (c i ).. = a.. x 13 for x within segment i
1 ] 13 Z1J 13
KQ
Street Canyon — Lee side XL = L
(u+0.5) [ (x 2 + z 2 ) + L]
KQ (B—z)
Windward side ½ = ( u+o 5) SB
Intermediate wind direction = 4 (XL + (less than ±30° from Street
direction).
-------
B49
In which
x = horizontal distance from traffic lane
z height above pavement
K constant 7
a vehicle size 2 meters
u = rooftop wind speed
Q a CO emission rate/meter
S street width
B = average building height 38.8 meters
-------
B 50
B.2.8. IIIWAY
Reference : Zimmerman and Thompson (1975).
Abstract : HIWAY is a Gaussian plume model that computes the hourly
concentrations of non—reactive pollutants downwind of roadways. It is
applicable for uniform wind conditions and level terrain. Although
best suited for at—grade highways, it can also be applied to depressed
highways (cut sections).
Equations :
x = fd2, integral along length of line segment, evaluated
J° using trapezoidal rule.
q = CO emission rate/unit length
for stable conditions or if mixing height L > 5000 m
1
2ira g 1 g 2 ,
yz
for neutral or unstable conditions, with a < 1.6 L
z—
1
— 2iTcy a g 1 g 3
yz
for neutral or unstable conditions, with a > l.6L
z
1
— y i a L
y
with 2
= ex [ _4( _) ]
g 2 2
+00 2
1 2nL
g3=2 ex [ _. (. _) ]
-------
B 51
B.2.9. DIFKIN
Reference : Martinez. et.al. (1973).
Abstract : The DIFKIN (Diffusion/Kinetics) model is a numerical/dynamic
(trajectory) model for photochemical smog simulation. It determines the
trajectory of an air parcel across an emission grid network and calculates
pollutant concertrations as functions of time. The model obtains con-
centrations and fluxes at up to ten mesh points between ground level and
the top of the mixing layer.
Equations:
DIFKIN numerically solves the vertical diffusion equation
= L( c j 1&) + for Q. = 1, 2, . . ., p
Along a trajectory determined from surface wind measurements, subject to the
following initial and boundary conditions;
A. Initial Conditions
CQ (z, tiiii) = f (z = initial concentration distribution for
Species j ,,
B. Boundary Conditions
(1) z = 0 (at ground level)
ac
— = (t) (perfect reflection plus addition of emissions
from ground level flux)
(2) z = L(t) (at mixing height)
ac,
— K. = 0 (perfect reflection)
where = mean concentration of species t
= rate of production ( r depletion) of species Q. through
chemical reaction
vertical eddy diffusivity, a function of height z.
q (t) = ground—level flux of species Z
-------
B52
B.2.lO. SAt
Reference : Reynolds (1973).
Abstract : The SA l model is a numerical/dynamic model for studying the
dispersion of photochemical pollutants, employing a fixed grid coordinate
system and a finite difference solution of the atmospheric diffusion
equation. The model calculates an emission inventory based on extensive
traffic input data as well as stationary source emissions. It requires
extensive meteorological data including both spatial and temporal variations
and uses a kinetic mechanism for photochemical smog involving fifteen
chemical reactions and ten chemical species.
Equations :
SAl numerically solves the advection—diffusion equation:
h ( J1c ) + F (uMlcz) + i — (vAHc ,) + f- (Wc )
= ( + $&)
+ h ( i&) + R àH ÷ SLd H £ = 1, 2,
where All = R(x,y,t) — h(x,y) = elevation difference between the mixing
height and ground level,
3WO
W = w — p 3t , and
— z — h(x,y )
— H(x,y,t) — h(x,y)
subject to the following:
A. Initial Conditions
= f (x,y,p) = initial concentration distribution for
species £,
-------
B53
B. Boundary Conditions
(1) p = 0 (at ground level)
Ky ac 2
— = q ,(x,y,t) (perfect reflection plus addition of
emissions from ground level flux)
(2) p = 1 (at mixing height)
x a
Wc 2 — Wg if W < 0 (material from outside of region
entrained if mixing height is
increasing)
Ky
— - — = 0 if W > 0 (perfect reflection with no entrainment
p otherwise)
(3) x = XE or x. (along the east or west vertical boundaries)
. -
uc 2 — K - -- = ua 2 if U • n < 0 (transport wind into region;
material advected in from
outside)
ac - -
— K.d 2 = 0 if U • n > 0 (transport wind out of region)
ax
(4) ‘ = or (along the north or south vertical boundaries)
Similar to (3), except involving v, the y— component of the wind.
where
U = horizontal wind vector
= outwardly directed unit vector perpendicular to the vertical
boundary
C 2 , = mean concentration of species 2.
p = number of species
u,v,w = components of wind in x, y, z directions
= horizontal and vertical eddy diffusivities
-------
B54
S 2 , = emission rate of species 2. from elevated source
= production rate of species 2 , by chemical reaction
= ground—level flux of species £
g 2 , = concentration of species 2. above region
2. = concentration of species 2. outside region
XNIXS XE X.W = northern, southern, eastern, western boundaries of region
h(x,y) = terrain elevation
H(x,y,t) = elevation of inversion base.
-------
B55
GLOSSARY OF SYMBOLS
A, B Regression coefficients used in calibration procedures.
h Stack height
H Effective stack height = (stack height) + (plume rise)
k Wind sector index
Wind sector index corresponding to the sector containing
the n—th point source
2 Wind speed class index
L Mixing height
m Stability class index
n Point source index
N Total number of point sources
Q Emission rate
Emission rate for the n—th point source
T½ Pollutant half—life
uZ Representative horizontal wind speed for the l—th wind speed
class
u, v Components of horizontal wind speed
w Vertical wind speed
x Downwind distance or distance In x—direction
y Crosswind distance or distance in y—direction
z Vertical distance
p Do wind distance
Crosswind, vertical dispersion coefficients
P ‘ 1 m Meterological joint frequency function for wind in sub—
n m cardinal direction k , k
n
) Pollutant concentration
-------
B56
-------
Cl
APPEI 1DIX C
APPLICATIONS TO SPECIFIC MODELS
-------
C2
-------
C3
APPENDIX C APPLICATIONS TO SPECIFIC MODELS
This appendix contains examples of the application of the methodology
presented in this workbook to several specific atmospheric dispersion models.
Each subsection deals with a different study model and illustrates the nature
of the information required ‘about a study model, the factors involved in making
individual element—by—element comparisons with a reference model, and the pro-
cess of arriving at a final technical evalt;ation. Each subsection consists of
a body of text in which the reasons for obtaining the various element—by—element
comparisons and the final technical evaluation are explained. In the first
example, the entire procedure is illustrated. In subsequent examples, it is
assumed that the first five steps in the comparison need little additional ex-
planation and that the Application Classification Form and the Evaluation Form —
Part A have been completed. In each example, the application for which the
study model is considered has been chosen so that the study model is in fact
applicable in order to illustrate the methodology. A complete set of forms
for each example, filled out in accordance with the discussion presented in the
text, is located at the end of each subsection. The user should refer to these
completed forms while reading the text.
-------
C4
-------
C5
CONTENTS OF APPENDIX C
Page
C7
C23
C37
C4 9
C61
C73
C8 7
Clol
C.1
EXMIPLE1:
SCIM/1243.
C.2
EXAMPLE
2:
AQDM/1143 . . . . . . . . .
C.3
EXAMPLE3:
PTDIS/1213
C .4
EXAMPLE
4:
PTMAX/1213. . . .
C.5
EXAMPLE
5:
PTMTP/1213. . . .
C.6
EXAMPLE
6:
HANNA—GIFFORD/1243
.
C.7
EXAMFLE7:
}IANNA—GIFFORD/1143.
C,8
EXAMPLE
8:
APPENDIX J/6243 . .
-------
C6
-------
C7
C.l EXAMPLE 1: SCIM/l243
In this example, the application of interest involves estimating the
maximum expected one—hour sulfur dioxide concentration in Sample City, a moder-
ately sized urban area located in gently rolling terrain far from any large
bodies of water • Each step in the entire methodology is illustrated. While
reading the text, the user should refer to the completed forms at the end of
the section.
The first step involves the classification of the application as ex-
plained in Section 3. with regard to pollutant characteristics, sulfur dioxide
is a primary pollutant not subject to significant removal processes within the
time scale of the application. The size of the region of interest is of the
order of 50 km or less, and the residence time of a pollutant emitted within
this region is less than 5—8 hours for typical wind speeds. As indicated in
Table 3.1, the appropriate pollutant characteristics index number under these
circumstances is one.
The averaging time is short (under 24 hours); the appropriate averaging
time index number is two, as discussed in Section 3.4.
The Sample City emission inventory is assumed to contain both point and
area sources and the appropriate source characteristics index number is there-
fore four, as explained in Section 3.5.
Finally, since the terrain in which Sample City is located is simple and
the size of the region of interest is lass than 100 lan, the appropriate trans-
port characteristics index number is three, as explained in Section 3.6.
The completed Application Classification Form for this example can be
found at the end of this section. As indicated, the appropriate application
index is 1243.
At this time, the basic information sections of the Evaluation Form —
Part A are also completed by listing the reference documentation and preparing
a short abstract describing SCTh’s mode of operation.
This completes step 1.
The next step in the comparison involves the documentation of the study
model equations. The references listed on the front of the Evaluation Form —
Part A are used to determine the working equations shown on the reverse side
of the form to complete step 2.
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C8
These references also indicate that SC m ! selects a sample of one—hour
periods from the total number in some period of record, typically one year.
The sample is obtained by taking every n—th hour where n is an integer speci-
fied by the user. Having selected the sample, SC m ! applies a steady—state
Gaussian model separately to each hour in the sample and estimates from these
results both the long term average concentration and the frequency distri-
bution of one—hour concentrations. With this information, SCIM may be classi-
fied and its compatibility with the application of real interest checked (steps
3 and 4 in the comparison).
It is assumed, in this example, that the Sample City emission inventory
is structured in a manner compatible with SCIM input requiretnertts, specifically
that all required source information is available, that area sources are de-
fined in a suitable manner, that the number of point and area sources is within
SC m ! limitations, and so on. It is also assumed that the necessary meteoro-
logical and other data are available in the appropriate format.
The user has already classified the application and in the process has
determined that sulfur dioxide transformation and removal are not important
enough to select any other pollutant characteristics branch than number one.
As a consequence, no check need be made at this point to determine whether or
not SCIM incorporates treatments of these elements. Had the application index
begun with number three, for example, indicating that some physical removal
process is important, the user would have been required at this point to de-
termine whether SC m ! incorporates a treatment, however simplified, of that
process. SCIM provides estimates of various percentile one—hour concentra-
tions at each receptor, including the maximum expected value, and therefore
does estimate precisely the quantity of interest. If the application had in-
volved the estimation of the maximum 24—hour SO 2 concentration, SCIM would
not have been found applicable, because it does not estimate this quantity
directly, even though the necessary program modifications to do this calcu-
lation may be straightforward or even though the necessary calculations could
easily be done by hand.
As a result of these checks and determinations, SCIM is found to be
applicable to the application of interest. The “Applicable” hox on Part A is
checked to indicate this determination.
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C9
The description above also implies that SCIM is a simulation model and,
in view of the guidelines for model classification in Section 4.3, the appro-
priate classification is:
semiempirical/Sequential (Steady—State).
Step 5 simply involves referring to Table 4.1 to identify RAM as the
reference model for application 1243.
The next step (step 6) is to review the importance ratings of the appli-
cation elements for application index number 1243 and to determine if modif i—
cations to these ratings are necessary to more accurately define the relative
importance of the elements in the situation of real interest. Expert advice
may be necessary in this step. It is assumed here that the importance ratings
as given in Tables 4.2 — 4.13 are appropriate with the exception of those for
composition of emissions and chemistry and reaction mechanism, which are modi-
fied from LOW to IRRELEVANT for purposes of this example. Notice that the
rating for physical removal has not been changed from LOW to IRRELEVANT even
though no physical removal process Is considered important enough to affect the
application classification. The distinction between LOW and IRRELEVANT is that,
as explained In Section 4.4, the treatments of IRRELEVANT elements are not taken
into account at all in the evaluation, while the treatments of LOW elements may
be considered In certain cases. It is assumed for this example that the involve—
taent of sulfur dioxide in atmospheric chemical reactions in and around Sample
City is considered so unimportant that it should play no role at all in evalu-
ating simulation models. Therefore, the elements compo5jtjon of emissions”
and “chemistry and reaction mechanism” are in fact irrelevant. In contrast, it
is assumed that dry deposition of sulfur dioxide, while not important enough to
affect the application classification, nevertheless does occur and is not in-
significant enough to be totally irrelevant. Thus, the importance rating of
physical removal is kept at LOW. Both initial and modified importance ratings
for each element are inserted in Part B of the Evaluation Form.
The next step (step 7) is the deterriination of the treatment by SCIM of
all application elements not rated IRRELEVANT. Operating equations used by
SCIM are reproduced on the reverse side of Part A of the evaluation form. Using
these equations and the material in the references as sources, descriptions of
the treatments by SCIM, together with the corresponding reference model treat-
ments obtained from Tables B .2— B.l3 and the importance ratings for each ele-
ment, are entered on Part C of the evaluation form. The treatments by SCIM
-------
do
were determined in accordance with. the guidelines given in Section 5, supple-
mented by the discussions presented in Appendix A.
After both the study model and reference model treatments of a given
element have been entered on the Evaluation Form — Part C, the comparison of
these two treatments may be made using the guidelines in Section 6.2.1. The level
of detail involved in each treatment is examined with reference to the relative
ranking of treatments in Tables 5.1—5.15. The result of each comparison con-
sists of the single adjective from the set BETTER, COMPARABLE, WORSE which most
accurately describes the treatment used by the study model in comparison with
that used by the reference model. This result is then entered in the place
provided in each section of Part C.
The various treatments by SCIM and RAM of most application elements are
clearly COMPARABLE, and are virtually identical in several cases. The ex-
ceptions are the elements horizontal wind field and background, boundary and
initial conditions. The two treatments of horizontal wind field are basically
COMPARABLE. However, SCThI does not employ a randomization procedure for wind
direction and RAN does, with the result that SCM only allows 36 different wind
directions while RAM allows 360. Thus, SCIM be somewhat WORSE in its treat-
ment of the horizontal wind field. In cases of doubt, both results are indi-
cated on the form; the primary evaluation as usual, followed by a secondary
evaluation in parentheses (see the entries on Part C). The same situation
arises for background, boundary and initial conditions. The two treatments
are basically COMPARABLE, but 5dB ’ ! may be a little WORSE because of its less
detailed treatment of the upper boundary condition. On the other hand, SCIM
allows a background value to be input. Both comparisons are indicated on Part
C of the Evaluation Form.
In the cases of emission rate and temporal correlations, it is necessary
to judge the importance of area source emissions in Sample City before making
the comparisons because SCIM and RAN differ in the level of detail with which
the temporal variation of area source emissions are described. The comparisons
actually made in the example assume that area source contributions are not sig-
nificant enough to justify rating the SC 1M treatment BETTER. If these contri-
butions were more Important in the application, the additional detail in the
SCIM treatment might justify a BETTER rating.
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Cl i
The synthesis of these individual comparisons into a final technical
evaluation (step 9) is documented on the Evaluation Ton — Part D. The guide-
lines in Section 6.2.2 are used to arrive at this final evaluation. In the
example, there are no CRITICAL elements. Therefore, the initial evaluation is
based on the comparisons for the three HIGH—rated elements. All of these com-
parisons are COMPARABLE, resulting in an initial comparative rating of COMPAR-
ABLE. Of the elements rated MEDIUM, all five have COMPARABLE treatments; there-
fore no change in the initial rating is indicated. Even if the secondary evalu-
ations for horizontal wind field and background, boundary and initial con-
ditions were used, they would not carry sufficient weight to alter the evalu-
ation. Thus, the technical evaluation of SCIM for Application 1243 is that
SCIM is COMPARABLE to the reference model, RAN. This evaluation is further
supported by the distribution of comparisons for the LOW elements, although
these would not be considered here, because the rating based upon HIGH and
MEDIUM elements is unambiguous.
-------
Cl 2
APPLICATION CLASSIFICATION FORM
0
A.
POLLUTANT /
C HA R ACT E R ISTICS \
\ SECONDARY
CHEMICAL
PHYSICAL
CHEMICAL &
N ON E
7’ CHEMICAL
SIC AL
\ CHEMICAL &
INDEX
NUMBERS
INSERT APPROPRIATE
NUMBERS IN THE
BOXES PROVIDED:
2
3
PHYSICAL..
-v
-5
-6
7
PHYSICAL 8
B. AVERAGING
TIME
C. SOURCE
C HA RA CT ER IS TIC S <
LONG—TERM
-TERM
LIMITED
POINT
7
AREA
LINE
PLE/CO TIO
COMPLEX
D. TRANSPORT
K CTERISTIC4 PLE
SHORT — RANGE
LONG—RANGE
RA E
Form the application index by transferring the four index
the corresponding boxes below:
\.,.,. APPLICATION
IN DEX
j
I
J
112
J
1
2J
1413
numbers into
2
2
3
4
2
3
4
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C 13
EVALUATION FORM
Part A: Abstract and References
Study Model : Sampled Chronological Input Model (5Cr!)
References : Koch, R.C. and GH. tadsklev, A User’s Manual for the
Sampled Chronological Input Model (3dM), GEOMET Report
No. E—261, prepared for U.S. EPA under Contract No.
68—02—0281. (December 1974).
Koch, R.C. and S.D. Thayer, Validation and Sensitivity
Analysis of the Gaussian Plwne Multiple - Source Urban
Diffusion Model, NTIS PB 206951, National Technical
Information Service, Springfield, Va. 22151.
(November 1971).
Abstract : The Sampled Chronological Input Model (5Cr!) is a Gaussian
plume—based model designed to estimate mean long—ten pollu-
tant concentrations and the frequency distribution and maxi-
mum of one—hour pollutant concentrations in an urban area.
Classification : Semiempirical/Sequential (Steady—State)
4pplication Index : 1243 Reference Model : RAN
Application Description : )là.x$jnun 1 —hour SO 2 concentration in an urban area.
Model Applicability : Applicable Not Applicable
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C 14
EVALUATION FORM
Part A (reverse): Ej tions
Study Model : SCfl4
Equations :
Point sources:
[ 2
qn
Jex (... )
Xn=2 aa gexp 2Ia
yz ‘ yg
2 2’
1 I H—z
u+z I I
with g(x,z;H) = exp [ ] + exp [ — 4 [ j ,
ZI J
Area sources:
Xd
1 1 (x )
_ _ _ _ - — dx
;ll) exp ( i c c
uçy g(x,z
uJ
0 Z
with (x) q(x,o), q(r,9) = emission rate per unit area at
position (r,9) from receptor
(Narrow plume approximation)
Integral evaluated using trapezoidal rule.
N
Total estimated concentration = +
n=l
N = number of point sources
Vertical dispersion coefficient:
b
a =ax xx
‘x+x -2x
a L( 1
z i i x—x ) x
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C15
EVALUATION FORM
Part B: Importance Ratings
Application Index: 1243
Application Importance Rating
Element Initial Modifieda
Source—Receptor Relationship N N
Emission Rate N N
Composition of Emissions L I I
Plume Behavior H H
Horizontal Wind Field M N
Vertical Wind Field L L
Horizontal Dispersion H H
Vertical Dispersion H H
Chemistry and Reaction Mechanism L I I
Physical Removal Processes L L
Background, Boundary, Initial Conditions N N
Temporal Correlations N H
aW1 h the exception of the designation of IRRELEVANT elements, it is expected
that at most one CRITICAL designation and possibly one ot her modification
may be made.
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EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1243
Application Element: Source _ Receptor Relationship Application Element: Emission Rate
Reference Model: R Reference Model:
Treatment: Arbitrary location and release height Treatment: Arbitrary constant emission rate for
for each point source. Flat terrain, each point and area source.
Area sources defined as square cells (or multiples) Area source contributions obtained by numerical
in a rectangular array; up to three effective re— integration along upwind distance of narrow—
lease heights (for u5m/sec) user—specified. plume approximation formulae for area source
with given effective release height.
Arbitrary receptor locations — all at the same
height above (or at) ground. Includes only those areas intersected by the
upwind ray.
Precise downwind, crosswind distances for each
source—receptor pair. c
I - a
Sides of area sources must lie along grid boundary a’
directions,
Study Model; SCIM Study Model: SCD 1
Importance Rating: MEDIUM Importance Rating: MEDIUM
Comparative Evaluation: COMPARABLE Comparative Evaluation: COMPARABLE
Treatment: Arbitrary location and emission Treatment: Arbitrary constant emission rate for each
point source.
height for point sources. Flat terrain.
Arbitrary average emission rate for each area source;
Arbitrary location and height for receptors. area source emissions assumed functions of average
Area sources defined as square cells in up to emission rate, temperature and time of day.
three concentric arrays with user—defined grid Area source contributions obtained by numerical inf-e—
sizes.
gration along upwind distance of narrow—plume approx—
Up to five user—defined release heights for area tmation formulae for area source with given effec—
sources. tive release height; includes only those areas
intersected by the upwind ray.
Precise downwind and crosswind distance for each
source—receptor pair.
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EVALUATION FORM
Part C: Treatment of Elements
Application Index :_j
Reference Model: RAN
Treatment:
Uses Briggs’ (1971, 1972), downwind distance de-
pendent plume rise for point sources.
If plume height exceeds mixing height, ground
level concentrations assumed zero.
No plume rise calculated for area sources;
assumed to be included in release height.
Fumigation, downwash not treated.
Study Model:
Importance Rating:
Comparative Evaluation:
Treatment:
Two step procedure using Briggs’(1969) for
point sources.
Not treated explicitly for area sources—
assumed included in input release heights.
If stack height +50% of plume rise exceeds
mixing height, source is excluded.
Fumigation, dowawash not treated.
Application Element: Horizontal Wind Field
Reference Model:
Treatment: Semiempirical/Sequentia]. (Steady—state)
Constant, uniform wind speed and direction assumed
for each of a sequence of hours.
Arbitrary wind speeds and direction values to 1O
lnput 0 by user; directions randomized by addition of
(ri—4) with n = random integer from zero to nine.
Wind speed is modified to correspond to valtie at
release height, modification dependent only on
stability class.
Study Model: 6dM
Importance Rating: MEDIUM
Comparative Evaluation: COMPARABLE (WORSE)
Treatment: Semiempirical/Sequential (Steady—State).
Constant, uniform wind speed within each of sequence
of one—hour periods.
Arbitrary wind speeds and directions to 100 input
by user.
Wind speed modified (power law) to correspond to
value at release height, modification procedure
depends only on stability (unstable, neutral,
stable).
Application Element: Plume Behavior
SC IN
HIGH
COMPARABLE
H
-------
Study Model: SCIM
Importance Rating: LOW
Comparative Evaluation: COMPARABLE
Treatment: Semiempirical/Sequentlal (Steady—
State).
Assumed equal to zero (implicit).
Application Element: Horizontal Dispersion
Reference Model: RAM
Treatment: Semiempirical/Sequential (Steady—State).
Gaussian plume function assumed for point sources.
Atmospheric stability divided into six (Pasquill—
Gif ford) classes, determined hourly.
Dispersion coefficients from Turner (1969) or McElroy
and Pooler (1968) at user option.
Surface roughness not treated explicitly
One hour averaging time used.
Area sources: Narrow plume approximation.
Study Model: SCIM
Importance Rating: HIGH
Comparative Evaluation: COMPARABLE
Treatment: Semiempirical/Sequential (Steady—State),
Gaussian plume function for point sources.
Atmospheric stability divided into four classes
or five classes (rural), determined hourly.
Dispersion coefficients: NcElroy—Pooler (1968) for
urban area, Pasquill—Gifford (Turner, 1969) for
rural areas.
Surface roughness not treated explicitly.
One—hour averaging time.
Area Sources: Narrow plume approximations
EVALUATION FORM
Part C : Treatment of Elements
Application Index: 1243
Application Element: Vertical Wind Field
Reference Model: R AN
Treatment: Semiempirical/Sequential (Steady—
State).
Assumed equal to zero (Implicit).
H
(urban)
-------
Reference Model: RAN
Treatment: Semiempirical/Sequential (Steady—
State).
Gaussian plume function assumed.
Atmospheric stability divided into six (Pasquill—
Gif ford) classes, determined hourly.
Dispersion coefficients from Turner (1969) or
McElroy and Pooler (1968) at user’s option.
Surface roughness not treated explicitly.
Study Model: scn
Importance Rating: HIGH
Comparative Evaluation: COMPARABLE
Treatment: Semiempirical/Sequential (Steady—
State).
Gaussian plume function.
Atmospheric stability divided into four classes
(urban) or five classes (rural), determined
tiourly.
Dispersion coefficients: McElroy—Pooler (1968)
(urban), or Pasquill—Gifford (Turner, 1969)
(rural).
Surface roughness not treated explicitly.
lApplication Element: Physical Removal
Reference Model: RAN
Treatment: Semlempirical/Sequential (Steady—State).
Exponential decay — first order (linear).
Single, constant user—specified decay constant.
Study Model: sci
Importance Rating: LOW
Comparative Evaluation: COMPARABLE
Treatment:
Exponential decay.
Single, constant user—supplied decay constant.
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1243
Application Element: Vertical Dispersion
‘ .0
-------
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1243
Emission rates constant,
parameters.
Application Element: Background, Boundary, initia1
Reference Model: RAM Conditions
Treatment: Background not treated explicitly.
Both upper and lower boundaries — perfect
reflection.
1) Meutral and unstable conditions: method of
multiple images treated by summation of
infinite series until a = l.6x(mixirtg
height); uniform mixing assumed thereafter;
2) Stable conditions: mixing height assumed to
have no effect.
Mixing height for a given hour obtained inter-
polation of radiosonde data.
Application Element: Tei poral Correlations
Reference Model:
Treatment: Sequential.
User supplies hourly values of wind speed, wind
direction, mixing height, and other meteorological
variables required for determination of stability
class and plume rise. (Correlations automatic.)
not correlated with other
Study Model: scmt
Importance Rating: MEDIUM
Comparative Evaluation: COMPARABLE (WORSE)
Treatment: Background — Single Constant Value
Lower boundary — perfect reflection.
Upper boundary — implicit treatment; no effect
until O.5 (mixing height), maximum :lz value =
mixing height, linear interpolation on a in
transition region , transition distances deter—
mined using a =ax
z
Mixing height interpolated from radiosonde data.
0
Study Model: SCIM
Importance Rating: MEDIUM
Comparative Evaluation: COMPARABLE
Treatment: Sequential.
User supplies hourly values of wind speed, direc-
tion, mixing height and other variables required
for stability determination. (Correlations automatic.)
Point source emissions constant, not correlated
with other parameters.
Area source emissions an empirical function of
ambient temperature and hour of the day.
(Correlations automatic.)
-------
tVALUATION FORM
Part C: Treatment of Elements
Application index: 1243
Application Element: Application Element :
Reference Model: Reference Model:
Treatment: Treatment:
Two IRRELEVANT elements:
• Composition of Emissions
• Chemistry and Reaction Mechanism
I. - ’
Study Model: Study Model:
Importance Rating: Importanca Rating:
Comparative Evaluation: Cow arative Evaluation:
Treatment: Treatment:
-------
EVALUATION FORM
Part D: Technical Comparison
Application Index: 1243 Reference Model: RAM Study Model SCIM
Importance Rating Comparative Rating
of Application Number of Treatments of
— Elements Total BETTER COMPARABLE WORSE Study Model
CRITICAL 0 — — — —
RIGH 3 0 3 0 COMPARABLE
MEDI.m4 5 0 5 (3) 0 (2) COMPARABLE
LOWa 2 0 2 0
IRBELEVAI T 2 m
Total 12 (Should equal 12)
TECHNICAL EVALUATION COMPARABLE
aUsed only fn ambiguous cases.
-------
C23
C.2 EX PLE 2: AQDN/1143
The application of Interest involves the estimation of long—term sulfur
dioxide concentrations in Sample City, a moderately sized urban area located in
gently rolling terraia, the same urban area used in Example 1, Appendix C.1.
The appropriate application index is 1143 and the corresponding reference model
is CDL The completed Application Classification Form and Evaluation Form for
this example may be found at the end of this section.
It Is assumed that the user can classify AQDN, determine that AQDM is
applicable, review and modify the importance ratings, determine the equations
used by AQDM, and determine the treatments of the application elements by both
AQDM and CDL The classification and applicability checks are straightforward.
The importance rating modifications are the same as in Example 1, specifically,
that the elements composition of emissions and chemistry and reaction mechanism
are rated IRRELEVMT due to the non—involvement of sulfur dioxide in atmospheric
chemistry over the distances and times of interest. The determination of the
equations and of the treatments are straightforward. The results are presented
on the Evaluation Form—Part A(reverse) and C, respectively.
AQDM and CDM are similar In most respects and most comparisons result
En COMPARABLE ratings. The two exceptions are emission rate and horizontal
wind field, for both of which AQDM is rated WORSE. The AQDM treatment of
emission rate is rated WORSE primarily because of the use of a single effective
point source approximation for area sources instead of the more detailed
numerical integration used by CDM, and secondarily because CDM allows a day!
night variation in emission rates whereas AQDM allows no variation. The AQDM
treatment of the horizontal wind field is rated WORSE, because CDM uses a
wind speed which is corrected for emission height while AQDM does not incorpo-
rate any such variation.
With only one element rated of HIGH importance, the initial rating is
the same as the rating for that element; in this case, the initial rating is
COMPARABLE. The MEDIUM—rated elements, however, definitely show a bias toward
a rating of WORSE. In this case, taking Into account the relatively low number
of HIGH—rated elements, the relatively high proportion of MEDIUM—rated elements
for which AQDM uses a WORSE treatment, and the absence of any elements that are
treated BETTER by AQDM, a change In the comparative rating of AQDM from COMPAR-
ABLE to WORSE is justified. Furthermore, the distribution of comparisons for
-------
C24
the LOW—rated elements supports this conclusion, although little weight should
be given to the LOW—rated elements. Therefore, the appropriate technical
evaluation for AQDM in application 1143 is WORSE.
-------
C2 5
APPLICATION CLASSIFICATION FORM
0
A. POLLUTANT
C 1M
CHARACTER IST1CS\
\ SECONDARY
B. AVERAGING
TINE
C. SOURCE
CHARACTERISTICS
C TERM
‘ zI SHORT—TERM
/ CHEMI L
Y SIC AL
\ CHEMICAL &
NONE
/ jc H EM IC AL
PHYSICAL
\ CHEMICAL 8
INDEX
NUMBERS
INSERT APPROPRIATE
NUMBERS IN THE
— I BOXES PROVIDED:
—2
—3
PHYSI CAL
5
6
7
PHYSICAL 8
POINT
LIMITED
K PLE,COMBIL 1 )
NATION
2
2
3
4
COMPLEX
SPORT
SHORT—RANGE
LONG—RANGE
SHORT-RANGE
LONG—RANGE
Form the application index by transferring the four index
the corresponding boxes below:
_________ APPLICATION
IN DEX
j
Li
J
1
j
ii
J
I3
numbers into
2
3
4
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C26
EVALUATION FORM
Part A: Abstract and References
Study Model : Air Quality Display Model (AQDM)
References : TRW Systems Group. “Air Quality Display Model.” Prepared for
National Air Pollution Control Administration under Contract
No. P11—22—68—60 (NTIs PB 189194), DHEW, U.S. Public Health
Service, Washington, D.C., November 1969.
Abstract : The Air Quality Display Model (.AQDM) is a cliinatological steady
state Gaussian plume model that estimates annual arithmetic
average sulfur dioxide and part icu.1.ate concentrations at ground
level. A statistical modal based on Larsen (1969) is used to
transform the average concentration data from a limited number
of receptors into expected geometric mean and maximum concen-
tration values for several different averaging times.
Classification : Semieiupirtcal/C limatologtca l (Steady—State)
pplication Index : 1143 Reference Model : CDM
Application Description : Urban, Long—term, conservative pollutants,
simple terraim.
Model Applicability : Applicable Not Applicable LI
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C2 7
EVALUATION FORM
Part A(reverse): Equations
Study Model : AQDM
Equations :
Point sources only.
X = - N = Number of sources
n1 L1 m1
with
Xn m — 2Q 1 ( ) exp [ — • (. _) 2] for x < XL
2iruci z
XnLm — ( ) for x 2 XL
linear interpolation for XL < x <
XL is defined by a(xL) = O.47L
y = crosswind distance between receptor and sector k centerline
C = sector width at receptor location
Cx) = axb + c; a, b, c = functions of stability class (m)
Z a, b, c for neutral conditions split into
x > bOOm case and x . lOOQn case.
Calibration: Xcalibrated = A + B (Xbackgroufld + Xuncalibrated)
with Xuncalibrated given by the first equation above.
Larsen (1971) statistical transformation of averaging times used for
1 — 24 hour averages.
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C28
EVALUATION FORM
Part B: Importance Ratings
Application Index: 1143
Application Importance Rating
Element Initial Modifieda
Source—Receptor Relationship M M
Emission Rate M M
Composition of Emissions L I /
Plume Behavior N M
Horizontal Wind Field M N
Vertical Wind Field L L
Horizontal Dispersion M M
Vertical Dispersion H H
Chemistry and Reaction Mechanism L I !
Physical Removal Processes L L
Background, Boundary, Initial Conditions N M
Temporal Correlations L L
8 With the exception of the designation of IRRELEVANT elements, It is expected
that at most one CRITICAL designation and possibly one other modification
may be made.
-------
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1143
Application Element: Source—Receptor Relationshi Application Element: Emission Rate
Reference Model: CDN Reference Model: CDM
Treatment: Treatment:
Arbitrary location for each point source.
Area sources specified as integral multiples Single arbitrary emission rate for each point and
of basic grid cell size, located on user— area source.
defined grid; sides lie along grid boundary Area integrations are done numerically one 22.50
directions. sector at a time; sampling at discrete inter—
Receptor location arbitrary. vals on a polar grid centered on the receptor.
Arbitrary release heights for point and area
sources. Dayfnight variations in emissions, same
Precise separation for each source—receptor variation assumed for all sources.
pair.
Receptors are at ground level.
No terrain differences between source/receptor . _________________________________________________
Study Model: AQDM Study Model: AQDI
Importance Rating: MEDIUM Importance Rating: MEDIUM
Comparative Evaluation: COMPARABLE Comparative Evaluation: WORSE
Treatment: Treatment:
Arbitrary location for each point source. Point sources: single rate for each source.
Arbitrary location and size for each area sourc
Area sources: single rate for each source.
Up to 225 receptors located on uniform
rectangular grid. Each source treated by effective single source
Up to 12 user—specified receptor locations, approximation.
Arbitrary release height for each point, No temporal variation allowed.
area source. -
Precise downwind and crosswind distance for eaci
source—receptor pair.
Receptors at ground level.
No terrain differences between source and
receptor.
-------
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1143
Application Element: Plume Behavior
Reference Model:
Treatment:
CDM
Briggs’ 2/3 (1971) neutral/unstable formula used.
If stack height + plume rise is greater than
mixing height, ground level concentrations
assumed equal to zero.
Alternative to Briggs — input value of plume rise
times wind speed for each point source.
No plume rise calculated for area sources.
Does not treat fumigation or downwash.
Study Model:
Importance Rating:
AQDM
MEDIUM
Comparative Evaluation: COMPARABLE
Treatment:
Holland (1953) formula, with adjustment for
stability.
No plume rise calculated for area sources.
Does not treat fumigation or downwash.
If stack height plus plume rise is greater than
mixing height, ground level concentration
assumed equal to zero.
Application Element: Horizontal Wind Field
Reference Model:
Treatment:
CDM
Climato logical approach.
16 wind directions.
6 wind speed classes.
Jind speed corrected for release height based on
power law variation, exponents from DeMarrais (1959).
Constant, uniform (steady—state) wind assumed.
Study Model:
Importance Rating:
AQDM
MEDIUM
Comparative Evaluation: WORSE
Treatment:
l1matological approach.
16 wind directions.
6 wind speed classes.
Jo variation in windspeed with height.
Constant, uniform (steady—state) wind assumed.
C)
0
-------
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1143
Application Element: Vertical Wind Field Application Element: Horizontal Dispersion
Reference Model: CDM Reference Model: CDM
Treatment: Treatment:
Assumed equal to zero. Semiempirical/Climatologlcal (Steady—State).
Uniform distribution within each of 16 sectors
(narrow—plume approximation).
Averaging time = 1 month to 1 year.
Surface roughness not treated explicitly.
Study Model: AQDM Study Model: AQDM
Importance Rating: LOW Importance Rating: MEDIUM
Comparative Evaluation: COMPARABLE Comparative Evaluation: COMPARABLE
Treatment: Treatment:
Assumed equal to zero. Climatological approach.
Linear interpolation between 22.5° sector center-
lines; center value calculated by sector averaging
procedure (narrow plume approximation).
Averaging time = 1 month — 1 year.
Surface roughness not treated explicitly.
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EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1143
Application Element: Vertical Dispersion pplication Element: Physical Removal
Reference Model: CDM eference Model: CDM
Treatment: ‘reatment:
Seiniempirical/climatological (Steady—State)
Dry deposition only.
Gaussian plume function assumed.
5 stability classes as defined by Turner (1964). Effective source treatment using exponential decay
Neutral stability split into day/night cases, (First—order process).
giving six classes in all. Single constant user—supplied half life used.
Dispersion coefficients taken from Turner (1970).
Area sources — stability class is decreased by 1
category from input values to account for urban
effects.
Neutral dispersion coefficients are used for all
neutral and stable classes.
No provision for variations in surface roughness . ________________________________________________
Study Model: AQDM Study Model: AQDM
Importance Rating: RICH Importance Rating: LOW
Comparative Evaluation: COMPARABLE Comparative Evaluation: WORSE
Treatment: Treatment:
Semi—empirical/Gaussian plume. Not treated explicitly.
5 stability classes (Turner, 1964).
Neutral stability split internally into 60% day,
40% night.
Dispersion coefficients .from Pasquill (1961) and
Gifford (1961).
Neutral dispersion coefficients used for all
neutral and stable classes.
No provision for variations in surface roughness.
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EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1143
Treatment:
Input single constant background value for each
pollutant.
Lower boundary (ground): assumes perfect
reflection; uses single image source,
Upper boundary (mixing height): no effect until
vertical dispersion coefficient equals 0.8 of
mixing height, uniform vertical mixing assumed
beyond this point.
Study Model: AQDM
Importance Rating: MEDIUM
Comparative Evaluation: COMPARABLE
Treatment:
Input single constant background value for each
pollutant.
Lower boundary (ground): perfect reflection;
single image source.
Upper boundary (mixing ht): no effect until
a >.47H (occurs at XXL) for x> 2xL uniform
mixing; in between, linear interpolation
transition region used.
Application Element: Temporal Correlations
Reference Model: CDM
Treatment:
Wind speed, direction, stability correlated via
wind rose.
Mixing height is adjusted according to stability
class:
Class A — 1.5 x afternoon climatological value,
Class D (night) — average of morning and after—
noon climatological values,
Class E — morning cliniatological value.
Emission rates: day—night variation allowed; all
sources assumed to vary by same factor.
Non—sequential (climatological) limited correlation.
Study Model: AQDM
Importance Rating: LOW
Comparative Evaluation: COMPARABLE
Treatment:
Wind speed, direction, stability correlated via
wind rose.
Emission rate — not correlated with any other factor.
Non—sequential (cllmatological) limited correlation.
Mixing height adjusted according to stability class:
Class A — 1.5 x afternoon climatological value,
Class D (night, internally divided) average of
100 meters and afternoon climatological value,
Class E — assumes 100 meters.
Reference Model:
Application Element: Background, Boundary , Initial
CDM Conditions
L)
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EVALUATION FORM
Part C : Treatment of Elements
Application Index:__1143
Application Element: Application Element :
Reference Model: Reference Model:
Treatment: Treatment:
Two IRRELEVANT elements:
• Composition of Emissions
• Chemistry and Reaction Mechanism
Study Model: Study Model:
Importance Rating: Importance Rating:
Comparative Evaluation: Comparative Evaluation:
Treatment: Treatment:
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EVALUATION FORM
Part D: Technical Comparison
Application Index: 1143 Reference Model: N - Study Model AQD 1
Importance Rating Comparative Rating
of Application Number of Treatments of
— Elements Total BETTER COMPARABLE WORSE Study Model
CRITICAL 0 —— — —— ——
HIGH 1 0 1 0 COMPARABLE
MEDIUM 6 0 4 2 WORSE
LOWa 3 0 2 1
IRRELEVANT 2 xxx xxx
Total 12 (Should equal 12)
TECHNICAL EVALUATION WORSE
aused only in ambiguous cases.
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C36
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C37
C.3. EXAMPLE 3: PTDIS/1213
The application of interest involves the estimation of ground level
centerline sulfur dioxide concentrations at various distances downwind of a
power plant located in relatively flat terrain. The appropriate application
index is 1213 and the appropriate reference model is CRSTER (Single Source).
Both CRSTER and B.A24 are given as reference models for application 1213 in
Table 4.1. In accordance with footnote j of that table, CRSTER has been
chosen, since the application of interest involves only a single power plant.
PTDIS is classified as a Semiempirical/Steady—State model and is determined to
be applicable. Part A of the Evaluation Form summarizes the general informa-
tion regarding this example.
The importance ratings are given on Part B of the Evaluation Form; in
this example three modifications have been made. Due to the physical and
chemical characteristics of sulfur dioxide and the short range of the applica-
tion the elements physical removal processes, chemistry and reaction mechan-
ism, and composition of emissions have been rated IRRELEVANT.
The reverse side of Part A of the Evaluation Form gives the equations used
used by PTDIS and Part C gives the treatments, importance ratings, and compari-
son results for all elements not rated IRRELEVANT. As can be seen, the treat-
ments are very similar in all cases and in all cases a comparative rating of
COMPARABLE is appropriate. For source—receptor relationship and horizontal
wind field, some confusion may arise regarding the appropriate rating, the
possible source of confusion being the specification in the application des-
cription on Part A that centerline ground level concentrations are desired.
PTDIS is designed specifically for this application, whereas CRSTER (Single—
Source) is designed to estimate concentrations at receptors on a polar grid
with a 100 increment between successive radial directions. In addition, CRSTER
accepts real meteorological data in which the wind direction is assumed given
to the nearest 10° and randomizes this direction by the addition of an integer
chosen from the values —4° to +5°. Thus CRSTER, may not provide centerline
concentration estimates; it was never intended to do so explicitly. CRSTER
would in fact be found not applicable in this case were it the study model and
PTDIS the reference model. This difference in objectives does not invalidate
the use of CRSTER as a basis for comparison but implies that those aspects of
source—receptor relationship and horizontal wind field which have treatments
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C38
which differ simply because of the different objectives of the two models
should not be considered in making the comparisons.
The Evaluation Form — Part D suimnarizes the individual comparison re—
suits and shows that the technical evaluation of PTDIS for application 1213
is obviously COMPARABLE.
-------
CHARACTER ISTICS
C39
APPLICATION CLASSIFICATION FORM
the four index numbers into
j
I
j
112
j
I
J
113
INDEX
NUMBERS
INSERT APPROPRIATE
NUMBERS IN THE
I BOXES PROVIDED:
LUTANT
CHARACTER ISTICS
2
3
6
B. AVERAGING
7
2
2
3
D. TRANSPORT
4
2
3
Form the application index by transferring
the corresponding boxes below:
4
APPLICATION
IN DEX
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C4 0
EVALUATION FORM
Part A: Abstract and References
Study Model : PTDIS
References : Environmental Protection Agency, User’s Network for Applied
Modeling of Air Pollution (UIVAMAP), NTIS PB 229771, National
Technical Information Service, Springfield, Va. (1974).
Turner, D.B., Workbook of Atmospheric Dispersion Estimates,
NTIS PB 191482, National Technical Information Service,
Springfield, Va.
Abstract : PTDIS is a steady—state Gaussian plume model that estimates
short—term center—line concentrations directly downwind of a
point source at distances specified by the user for a single
user—specified set of meteorological conditions. The effect
of limiting vertical dispersion by a mixing height can be
included and gradual plume rise to the point of final rise is
also considered. An option allows the calculation of isopleth
half—widths for specific concentrations at each downwind
distance.
Classification : SemempiricalfSteady—State
Application Index : 1213 Reference Model : Single Source
(CRSTER)
Application Description : Single elevated point source, flat terrain, sulfur
dioxide, downwind centerline ground level concen-
trations only.
Model Applicability : Applicable Not Applicable
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C41
EVALUATION FORM
Part A(reverse): Equations
Study Model : PTDIS
Equations :
X(x;O,O;H) = 2rrua g 1 g 3
yz
with g=1
+a r
1 1 1 2nL—H 2 1 2nL-1-H
and g f exp I — ) J + exp [ — - a ] ]
L z t zJ
X 0 Lf H > L
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C42
EVALUATION FORI!
Part B: Importance Ratings
Application Index: 1213
Application Importance Rating
a
Element Initial Modified
Source—Receptor Relationship H H
Emission Rate H H
Composition of Emissions L I I
Plume Behavior H H
Horizontal Wind Field H H
Vertical Wind Field L L
Horizontal Dispersion H H
Vertical Dispersion H H
Chemistry and Reaction Mechanism L I I
Physical Removal Processes L I I
Background, Boundary, Initial Conditions M M
Temporal Correlations M M
aWi h the exception of the designation of IRRELEVANT elements, it Is expected
that at most one CRITICAL designation and possibly one other modification
may be made.
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EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1213
Application Element: Source—Receptor Relationship Application Element: Emission Rate
Reference Model: Single Source (CRSTER) Reference Model: Single Source (CRSTER)
Treatment: Treatment:
Up to 19 sources all assumed to be located at
Single arbitrary value for each source.
same position.
Receptor locations restricted to 36 azimuths 4onthly variation allowed.
(every 100) and five user—specified radial
distances.
Arbitrary stack height for each source.
Unique stack height for each source.
Unique topographic elevation for each receptor:
must be less than each stack height.
Receptors must be at ground level.
Precise downwind/crosswind distance for each sourc
receptor pair. ________________________________
Study Model: PTDIS Study Model: PTDIS
Importance Rating: HIGH Importance Rating: HIGH
Comparative Evaluation: COMPARABLE Comparative Evaluation: COMPARABLE
Treatment: Treatment:
Single stack of arbitrary height. Single arbitrary constant value.
Up to 50 receptors, all at ground level, directly
underneath plume centerline, at arbitrary user—
specified downwind distances.
Flat terrain assumed.
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EVALUATION FORN
Part C: Treatment of Elements
Application Index: 1213
pplication Element: Plume Behavior
Reference Model: Single Source (CRSTER)
Treatment:
Briggs’ (1971, 1972) final plume rise formulas;
plume rise not treated as a function of down-
wind distance.
If plume height exceeds mixing height, concen-
trations further downwind assumed equal to zero.
Does not treat either fumigation or downwash.
Application Element: Horizontal Wind Field
Reference Model: Single Source (CRSTER)
Treatment:
Seiniempirical/Sequential (Steady—state)
Constant, uniform wind speed and direction assumed
for each of a sequence of hours.
Wind speeds (arbitrary) and directions (nearest 100)
input by user; directions rar.domized by addition
of (n—4)° with n = random integer from 0 to 9.
Wind speed corrected for release height with correc-
tions dependent only on stdbilitv class,
Study Model: PTDIS
Importance Rating: HIGH
Comparative Evaluation: COMPARABLE
Treatment:
Briggs (1971, 1972) plume rise formulae.
Alternatively, one user-supplied plume rise value
can be used.
Does not treat fumigation or downwash.b
If plume height exceeds mixing height, ground
level concentration assumed equal to zero.
Study Model: PTDIS
Importance Rating: HIGH
Comparative Evaluation: COMPARABLE
Treatment:
Semiempirical/Steady—state)
Wind directions implicit along source—receptor
direction.
Uses user—defined wind speed.
No variation in wind speed with height.
Constant, uniform (steady—state) wind assumed.
-------
Application Element: Vertical Wind Field
Reference Model: Single Source (CRSTER)
Treatment:
Assumed equal to zero (implicit).
Study Model: PTDIS
Importance Rating: LOW
Comparative Evaluation: COMPARABLE
Treatment:
Assumed equal to zero (implicit).
Application Element: Horizontal DisperaEcin
Reference Model: Single Source (CRSTER)
Treatment:
Semiempirical/Sequential (Steady—State) -
Gaussian plume function assumed.
Atmospheric stability divided into seven classes
(Pasquill—Gifford); class 7 — extremely stab e —
elevated plume assumed not to touch ground.
Dispersion coefficients from Turner (1969).
Surface roughness not treated explicitly.
1—hour averaging time.
Study Model: PTDIS
Importance Rating: HIGH
Comparative Evaluation: COMPARABLE
Treatment:
Semiempirical/ Steady—State.
Gaussian plume function assumed.
Calculations for a single user—specified (Pasquill—
Gif ford) stability class.
Dispersion coefficients from Turner (1969); no
adjustments made for variations in surface rough-
ness, averaging tiuLe or travel time.
Averaging time unknown, approximately 10 — 60 minutes.
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1213
C
U I
-------
Application Element: Background, Boundary, Initial
Conditions
Reference Model: Single Source (CRSTER)
Treatment:
Background not treated explicitly.
Lower boundary: perfert reflection in horizontal
plane at receptor height.
Upper boundary: perfect reflection; method of
multiple images treated by summation of series
until vertical dispersion coefficient = l.6x
(mixing height); uniform vertical mixing thereafter.
Mixing height for a given hour obtained by inter-
polation of radiosonde date.
Study Model: PTDIS
Importance Rating: MEDI uM
Comparative Evaluation: COMPARABLE
Treatment:
Background not treated explicitly.
Lower boundary: perfect reflection.
Upper boundary: (neutral and unstable conditions)
user—input mixing height used; perfect ref lec—
tion assumed.
Upper boundary: (stable conditions) — concept of
mixing height not employed; no upper boundary
considered — given meteorological conditions
implicitly assumed to extend higher than plume
at all distances.
Multiple reflections numerically accounted for by
summation of series.
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1213
Application Element: Vertical Dispersion
Reference Model: Single Source (CRSTER)
Treatment:
Semiempiricalf Sequential (Steady—State).
Gaussian plume function assumed.
Atmospheric stability divided into seven (Pas—
quill—Gif ford) classes; class 7 — extremely
stable — elevated plume does not touch ground.
Dispersion coefficients from Turner (1969).
Surface roughness not treated explicitly.
Study Model: PTDIS
Importance Rating: HIGH
Comparative Evaluation: COMPARABLE
Treatment:
Semiempirical/ Steady—State.
Gaussian plume function assumed.
Calculations done for user—specified (Pasquill—
Gif ford) stability class.
Dispersion coefficients from Turner (1969).
Surface roughness not treated explicitly.
C )
C ’
-------
Application Element: Temporal Correlations
Reference Model: Single Source (CRSTER)
Treatment:
Sequential; correlations automatic for meteorolog-
ical parameters.
User supplies hourly values of wind speed, wind
direction, mixing height, and other meteorolog-
ical variables required for determining sta-
bility class and plume rise.
Monthly emission variation allows limited eints—
sion/meteorology correlations.
Study Model: PTDIS
Importance Rating: MEDIUM
Comparative Evaluation: COMPARABLE
Treatment:
User supplies appropriate values of all input
variables for the hour in question; correlations
automatic.
Study Model:
Importance Rating:
Comparative Evaluation:
Treatment:
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1213
pplication Element:
Reference Model:
Treatment:
3 IRRELEVANT Elements:
Composition of Emissions
• Chemistry and Reaction Mechanism
• Physical Removal
0
a-
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EVALUATION FORM
Part D: Technical Comparison
Application Index: 1213 Reference Model:Single Source (CRSTER)Study Model__PTDIS
Importance Rating Comparative Rating
of Application Number of Treatments of
Elentents Total BETTER COMPARABLE WORSE Study Model
CRITICAL 0 — — — —
HIGH 6 0 6 0 COMPARABLE
MEDIUM 2 0 2 0 COMPARABLE
LOWa 1 0 1 0
IRRELEVANT 3 xxx xxx xxx
Total 12 (Should equal 12)
TECHNICAL EVALUATION COMPARABLE
aused only in ambiguous cases.
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C49
C.4. EXAMPLE 4: PTMAX /1213
The application of interest involves the estimation of maximum ground
level concentrations of sulfur dioxide downwind of a single power plant lo-
cated in relatively flat terrain, as well as the downwind distance to the
maximum, for a variety of conditions. The appropriate application index is
1213 and the appropriate reference model is Single Source (CRSTER). CRSTER
is used instead of RAM because the application involves a single point source,
as explained in footnote j to Table 4.1. PTMAX Is classified as a SemiempirIcal/
Steady—State model and is determined to be applicable. Part A of the Evalua-
tion Form summarizes the general Information for this example.
The importance ratings are given on the Evaluation Form — Part B; In
this example four modifications have been made. Due to the physical and chem-
ical characteristics of sulfur dioxide and the short range of the application
the elements physical removal processes, chemistry and reaction mechansim, and
composition of emissions have been rated IRRELEVANT. In addition, due to the
desire on the part of the user to estimate maximum downwind concentrations under
a variety of conditions, the importance rating of background, boundary and
initial conditions has been modified from MEDIUM to HIGH. This modification
reflects the need for treating the effects of limited mixing due to a low—lying
inversion, a situation which may result in relatively high ground level concen-
trations.
The reverse side of Part A of the Evaluation Form gives the equations
used by PTMA.X and Part C gives the treatments, importance ratings, and com-
parison results for all elements not rated IRRELEVANT. As can be seen, the
treatments are very similar In all cases and in all but one case a rating of
COMPARABLE is appropriate. The one element which PTMAX does not treat in a
manner comparable to that used by CRSTER is background, boundary and Initial
conditions, for which the treatment by PTMAX is rated WORSE. As in the pre-
vious example, PTMAX is rated COMPARABLE to CRSTER for source—receptor rela-
tionship and horizontal wind field in spite of obvious differences in the
treatments of these elements, because the differences relate to aspects of
each element which are not relevant to the real application of Interest.
Part D of the Evaluation Form summarizes the individual comparison re-
sults. The initial technical evaluation for PTMAX is WORSE due to the worse
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C50
treatment of background, boundary and initial conditions, Specifically, the
treatment used by PTNAX of the effects of the upper boundary is worse than that
used by CRSTER. Since the user is particularly interested in maximum concen-
trations, which may result in part f rain a low—lying upper boundary, this single
RSE comparison is considered sufficient justification for a WORSE initial
comparison. Furthermore, due to the small number of ) IUM— and LOW—rated ele—
ments, there is no justification for modifying this initial rating. Thus, the
appropriate technical evaluation for PThAX in application 1213 is 1K RSE.
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APPLICATION CLASSIFICATION FORM
INDEX
NUMBERS
INSERT APPROPRIATE
NUMBERS IN THE
BOXES PROVIDED:
2
3
SECONDARY
NONE
5
/ CHEMICAL
. PHYSICAL
6
B. AVERAGING
7
TIME
CHEMICAL a PHYSICAL 8
LONG—TERM I
2
2
3
0. TRANSPORT
4
CHARACTERISTICS
2
3
Form the application index by transferring
the corresponding boxes below:
4
the four index numbers into
APPLICATION
I N DEX
L ii 211 13
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C52
EVALUATION FORM
Part A: Abstract and References
Study Model : PTMAX
References : Environmental Protection Agency, user’s Network for
Applied Modeling of Air Pollution (UNAi’14P), NTIS PB
229771, National Technical Information Service,
Springfield, Va. (1974).
Turner, D . B., Workbook of Atmospheric Dispersion Esti—
nates, NTIS PB 191482, National Technical Information
Service, Springfield, Va. (1969).
Abstract: PTMAX is a steady—state Gaussian plume model that per-
forms an analysis of the maximum short—term concentrations
from a single point source as a function of stability and
wind speed. The final plume height is used for each com-
putation. A separate analysis must be made for each
individual stack; the model cannot give the maximum
concentrations from a combination of stacks.
Class if icat ion : Semiempirical/Steady—State
4pplication
Index : 1213 Reference Model : Single Source
(CR5 TER)
Application Description : Maximum ground level sulfur dioxide concentrations
from a single power plant in relatively flat terrain.
Model Applicability : Applicable 1jJ Not Applicable [ IJ
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C5 3
EVALUATION FORN
Part A(reverse): Equations
Study Model : PThAX
Equations;
Q I1H 2
X(x,O,O;H) = exp L
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C54
EVALUATION FORM
Part B: Importance Ratipgs
Application Index: 1213
Application Importance Rating
Element Initial Mod if ieda
Source—Receptor Relationship H H
Emission Rate H H
Composition of Emissions I I 9’
Plume Behavior 1 1 H
Horizontal Wind Field H H
Vertical Wind Field L L
Horizontal Dispersion 11 B
Vertical Dispersion H H
Chemistry and Reaction Mechanism L I I
Physical Removal Processes L I I
Background, Boundary, Initial Conditions M H I
Temporal Correlations 24 M
aW h the exception of the designation of IRRELEVANT elements, it is expected
that at most one CRITICAL designation and possibly one other modification
may be made.
-------
Study Model:
Importance Rating:
Comparative Evaluation:
Treatment:
Single stack of arbitrary height.
Determines downwjnd distance of maximum
ground level concentration.
Flat terrain assumed.
Application Element: Emission Rate
Reference Model: Single Source (CRSTER)
Treatment:
Single arbitrary value for each source.
Monthly variation allowed.
Study Model:
Importance Rating: HIGH
Comparative Evaluation: COMPARABLE
Treatment:
Single arbitrary constant value.
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1213
Application Element: Source—Receptor Relationship
Reference Model: Single Source (CRSTER)
Treatment: Up to 19 sources all assumed to be
located at same position.
Receptor locations restricted to 36 azimuths
(Every 100) and five user—specified radial
distances.
Arbitrary stack height for each source.
Unique topographic elevation for each receptor:
must be less than stack heights.
Receptors n’ust be at ground level.
Precise downwind/crosswind distance for each
source receptor pair.
PTNAX
HIGH
COMPARABLE
‘ -I,
U i
-------
EVALUATION FORM
Study Model: PTMAX
Importance Rating: HIGH
Comparative Evaluation: COMPARABLE
Treatment: Two step procedure using Briggs’
(1971, 1972) final plume rise formulae.
Does not treat fumigation or downwash.
Study Model: PTMAX
Importance Rating: HIGH
Comparative Evaluation: COMPARABLE
Treatment: Semiempiricaif Steady—State.
Wind directions implicit along source—receptor
direction.
No variation in wind speed with height.
Constant, uniform (steady—state) wind assumed.
Uses fixed, internally defined set of wind speed
values ranging from 0.5 to 20 rn/sec.
Part C: Treatment of Elements
Application Index: 1213
Application Element: Hori onta1 Wind Ff 1d
Application Element: Plume Behavior
Reference Model: Single Source (CRSTER)
Treatment: Briggs’ (1971, 1972) final plume rise;
not treated as a function of downwind dis-
tance.
If plume height exceeds mixing height, con-
centrations further downwind assumed equal
to zero.
Does not treat either fumigation or downwash.
Reference Model: Single Source (CRSTER)
Treatment: Semiempirical/Sequential (Steady—State).
Constant, uniform wind speed and direction assumed
for each of a sequence of hours.
Wind speeds (arbitrary) and directions (nearest
10°) input by user; directions randomized by
addition of (n—4.° with n=random integer from zero
to nine.
Wind speed corrected for release height, correction
using power law variation with exponents depen-
dent on stability class.
U i
-------
Study Model:
Importance Rating:
Comparative Evaluation:
Treatment:
Assumed equal to zero
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1213
Application Element: Horizontal Dispersion
Reference Model: Single Source (CRSTER)
Treatment: Semiempirical/Sequential (Steady—State).
Gaussian plume function assumed.
Atmospheric stability divided into seven classes
(Pasquill—Gif ford); Class 7 — extremely stable —
elevated plume assumed not to touch ground.
Dispersion coefficients from Turner (1969).
Surface roughness not treated explicitly.
One—hour averaging time.
Study Model: PThAX
Importance Rating: LOW
Comparative Evaluation: COMPARABLE
Treatment: Semiempirical/Steady—State.
Gaussian plume function assumed.
Calculations for each of six Pasquill—Gifford
stability classes.
Dispersion coefficients from Turner (1969); no adjust-
ments made for variations in surface roughness,
averaging time or travel time.
Averaging time unknown, approximately 10—60 minutes.
Application Element: Verti eat t4-tnd Field
Reference Model: Single Source (CRSTER)
Treatment:
Assumed equal to zero (implicit).
PIMAX
LOW
COMPARABLE
(implicit).
0
L i,
‘ -4
-------
Application Element: Vertical Dispersion
Reference Model: Single Source (CRSTER)
Treatment: Semiempirical/Sequential (Steady—
State).
Gaussian plume function assumed.
Atmospheric stability divided into seven
(Pasquill—Gif ford) classes; Class 7 — extremely
stable — elevated plume does not touch ground.
Dispersion coefficients from Turner (1969).
Surface roughness not treated explicitly.
Study Model: PTMAX
Importance Rating: HIGH
Comparative Evaluation: COMPARABLE
Treatment: Semiempirical/Steady—State
Gaussian plume function assumed.
Calculations done for six Pasquill—Gif ford
stability classes.
Dispersion coefficients from Turner (1969).
Surface roughness not treated explicitly.
Application Element: Background, Boundary, Initial
Reference Model: Single Source (CRSTER) Conditions
Treatment: Background not treated explicitly..
Lower boundary: perfect reflection in horizontal
plane at receptor height.
Upper boundary: Perfect reflection: method of
multiple images treated by summation of series
until vertical dispersion coefficient = l.6x
(mixing height); uniform vertical mixing there-
after.
Mixing height for a given hOUL obtained by inter-
polation of radiosonde data.
Study Model: TMAX
Importance Rating: HIGH
Comparative Evaluation: WORSE
Treatment:
Background not treated explicitly.
Lower boundary: perfect reflection at ground level.
Upper boundary: mixing height assumed high enough
to have no effect.
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1213
“I
00
-------
Application Element: Temporal Correlations
Reference Model: Single Source (CRSTER)
Treatment: seqnential; correlations automatic
for meteorological parameters.
User supplies hourly values of wind speed, wind
direction, mixing height, and other meteoro-
logical variables required for determining
stability class and plume rise.
Monthly emission variation allows limited
emission—meteorology correlations.
Study Model:
Importance Rating:
Comparative Evaluation:
Treatment:
Correlations automatic — user supplies appro-
priate data for situation of interest.
Application Element :
Reference Model:
Treatment:
Three IRRELEVANT Elements:
Composition of emissions
Chemistry and Reaction Mechanism
Physical. Removal
Study Model:
Importance Rating:
Comparative Evaluation:
Treatment:
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 121
PT AX
MED IUN
COM1’ARABLE
U ’
-------
EVALUATION FORM
Part D: Technical Comparison
Application Index: 1213 Reference Model:Siflgle Source (CRSTER)Study Model PTMAX
Importance Rating Comparative Rating
of Application Number of Treatments of
Elements Total BETTER COMPARABLE WORSE Study Model
CRITICAL 0 — — — —
HIGH 7 0 6 1 WORSE
MEDIUM 1 0 1 0 — WORSE
LOWa 0 1 0
IRRELEVAMT 3 xxx
Total 12 (Should equal 12)
TECHNICAL EVALUATION — WORSE
aUsed only in ambiguous cases.
-------
C61
C.5. EXAMPLE 5: FDCPfI213
The application of interest involves the estimation of total one and
24—hour ground level sulfur dioxide concentrations from a few (less than 10—
20) nearby power plants located in gently rolling rural terrain. The applica-
tion index is 1213 and in this example the appropriate reference model is RAN,
since the application involves several sources at different locations. PTMTP
is classified as a Semiempirical/Sequential (Steady—State) model and is deter-
mined to be applicable.
The importance ratings, shown on Part B of the Evaluation Form, incor-
porate the modification of composition of emissions, chemistry and reaction
mechansim, and physical removal processes from LOW to IRRELEVANT. No other
modifications are made.
The reverse side of Part A of the Evaluation Form gives the equations
used by PTMTP and Part C gives the treatments, importance ratings, and compari-
sons results. As can be seen, the treatments by PTMT? are all quite similar
to those used by RAN and are rated COMPARABLE in all cases. The treatments by
RAN of those a 7ects of source—receptor relationship, emission rate, and other
el?men!s that xnvolve consideration of area sources are not given in Part D
in this example, because area sources are not involved in this application.
These tz’ ctments by RAN are irrelevant and are not considered in making the
comparisons. A question may arise with regard to horizontal wind field, be-
cause PTMTP does not adjust the input wind speed for the source release heights
in estimating the contribution of each as does RAM. However, PTMTP does not
require that the. wind speed near the surface be input, and the user is free to
input values appropriate for an average release height for the sources involved.
PTMTP does not distinguish between different heights and uses the input wind
speed for all sources. This difference between RAN and PTMTP is not considered
significant enough to rate PTMTP worse.
The results of the element—by—element comparisons are summarized in
Part D of the Evaluation Form and clearly indicate that PT ffP should be rated
COMPARABLE to RAM for this application.
-------
C62
APPLICATION CLAcSIFICATION FORM
BEGIN
— A. POLLUTANT
/
CHARAdE RISTICS\\
c Th
/ CHEM ICAL
PHYSICAL
CHEMICAL a
CHEMICAL
SECONDARY
NONE
PHYSICAL
INDEX
NUMBERS
INSERT APPROPRIATE
NUMBERS IN THE
I BOXES PROVIDED:
2
3
PHYSICAL
5
6
.7
CHEMICAL a PHYSICAL 8
B. AVERAGING
TIME
C. SOURCE
CHARACTERISTICS
LONG—TERM
ERTh
/ AREA
\ LINE
MULTIPLE/COMBINATION
TRANSPORT /
COMPLEX
iA ERisT Ics
SHORT—RANGE
LONG—RANGE
I,Ø .RANGE
LO N G — RAN G
Form the application index by transferring the four Index
the corresponding boxes below:
APPLICATION
INDEX
L J
L
‘
I
2
1
3
2
2
D.
4
2
3
4
numbers into
-------
C6 3
EVALUATION FORH
Part A: Abstract and References
Study Model : PTMTP
References : Environmental Protection Agency. User’s Ne1 ork for Applied
Modeling of Air Pollution (UNA 4P) NTIS PB 229771, Na-
tional Technical Information Service, Springfield, Va. (1974).
Turner, D .B., Workbook of Atmospheric Dispersion Estimates
NTIS PB 191482, National Tech tLcal Information Service,
Springfield, Va. (1969).
Abstract : PTMTP is a steady—state, Gaussian plume model that estimates
for a number of arbitrarily located receptor points at or
above ground—level, the concentration from a number of point
sources. Plume rise is determined for each source. Down-
wind and crosswind distances are determined for each source—
receptor pair. Concentrations at a receptor from various
sources are assumed additive. Hour by hour calculations
are made based on hourly meteorological data; both hourly
concentrations and averages over any averaging time from
one to 24 hours can be obtained.
Classification : SemiempiricalfSequential (Steady—State)
Application Index : 1213 Reference Model : p ,
Application Description : Short term (one and 24 hour) ground level’ con-
centrations of sulfur dioxide from several power plants, relatively flat
terrain, short range, rural area.
Model Applicability : Applicable Not Applicable L II
-------
C64
EVALUATION 1’ORM
Part A(teyerse); Equations
Study Model : PTMTP
Equations :
N
X(x,y,z) = Lx (x y,z;H )
Ti
n =1
with
Q g 1 g 9
27rua a
yz
[ ... AIz.J 21
g=exp 2Ia I
I yI j
2 2
—— n
= II (exp r i z—H + 2kL 1 + exp [ ( z + H + 2kL
L 1 (
2 a jJ a
k z z
x = 0 if H > L.
11 fl
-------
C65
EVALUATION FORM
Part B: Importance Ratings
Application Index: 1213
Application Importance Rating
Element Initial Modif leda
Source—Receptor Relationship H
Emission Rate H H
Composition of Emissions L I I
Plume Behavior I I H
Horizontal Wind Field H a
Vertical Wind Field L L
Horizontal Dispersion H
Vertical Dispersion H H
Chemistry and Reaction Mechanism L I I
Physical Removal Processes L I I
Background, Boundary, Initial Conditions H M
Temporal Correlations N N
aWl h the exception of the designation of IBRELEVABT elements, it is expected
that at most one CRITICAL designation and possibly one other modification
may be made.
-------
Application Element: Source—Receptor Relationship
Reference Model: p j
Treatment: Arbitrary location and release height
for each point source. Fin terrain.
Arbitrary receptor locations — all at the same
height above (or at) ground.
Precise downwind, crosswind distances for each
source—receptor pair.
Study Model: mrr
Importance Rating: HIGH
Comparative Evaluation: COMPARABLE
Treatment: Point sources only.
Arbitrary location and release height for each of
up to 25 point sources.
Flat terrain assumed.
Arbitrary location and height for each of up to
30 receptors.
Precise downwind, crosswind distances evaluated
for each source, receptor pair.
Study Model:
Importance Rating: HIGH
Comparative Evaluation: COMPARABLE
Treatment:
Single constant emission rate for each point
source.
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1213
pplication Element: Emission Rate
Reference Model:
rreatment:
Arbitrary constant emission rate for each point
source.
C
a . ’
-------
Application Element: Plume Behavior
Reference Model: RAN
Treatment: Two step procedure.
Uses Briggs’ (1971, 1972) downwind distance
dependent plume rise formulae for point
sources.
If plume height exceeds mixing height, ground
level concentrations assumed zero.
Fumigation, downwash not treated.
Study Model:
Importance Rating: HIGH
Comparative Evaluation: COMPARABLE
Treatment: Two step procedure.
Uses Briggs’ 2/3 (1971, 1972) downwind distance
dependent plume rise formulae.
Does not treat fumigation or downwash.
If plume height exceeds .mixing height, concen-
tration further downwind assumed zero.
Application Element:Horizontal Wind Field
Reference Model: RAM
Treatment: Semiempirical/Sequential (Steady—State).
Constant, uniform wind speed and direction assumed
for each of a sequence of hours.
Arbitrary wind speeds and direction values to 100
input by user; directions randomized by addition
of (n—4)° with n=random integer from zero to
nine.
Wind speed is modified to correspond to value at
release height, modification dependent only on
stability class.
Study Model: PTMTP
Importance Rating: HIGH
Comparative Evaluation: COMPARABLE (WORSE)
Treatment: Semiempirical/Sequential (Steady—State)
Uses sequence of up to 24 user—supplied hourly values
of wind speed (arbitrary) and direction (nearest
degree).
Constant, uniform wind speed and direction for each
hour; no variation of wind speed, direction with
height; no correction made for release height.
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1213
C’
-------
Application Element: Vertical Wind Field
Reference !tdel: RAM
Treatment: Semiempiricaif Sequential (Steady—
State),
Assumed equal to zero (implicit).
Study Model:
Importance Rating:
Comparative Evaluation:
Treatment: Semiempirical/Sequential (Steady—
State),
Assumed equal to zero (implicit).
Application Element: Horizontal Dispersion
Reference Model: RAM
Treatment: Semiempirical/Sequential (Steady—State),
Gaussian plume function assumed.
Atmospheric stability divided into six (Pasquill—
Gifford) classes, determined hourly.
Dispersion coefficients from Turner (1969) or McElroy
and Pooler (1968) at option.
Surface roughness not treated explicitly.
One hour averaging time used.
Study Model: PTMTP
Importance Rating: HIGH
Comparative Evaluation: COMPARABLE
Treatment: Semiempirical/Sequential (Steady—State),.
Gaussian plume function assumed.
Atmospheric stability divided into six (Pasquill—
Gifford) classes, supplied hourly.
Dispersion coefficients from Turner (1969).
Surface roughness not treated explicitly.
One hour averaging time.
EVALUATION FORM
Part C: Treatment of Elements
Application Index: l213
PTMTP
COMPARABLE
-------
Application Element: Vertical Dispersion
Reference Model: RAN
Treatment: Seiniempirical/Sequential (Steady—
State).
Gaussian plume function assumed.
Atmospheric stability divided into six ( asquill—
Gif ford) classes, determined hourly.
Dispersion coefficients from Turner (1969) or
McElroy and Pooler (1968) at user s option.
Surface roughness not treated explicitly.
Study Model: PTMTP
Importance Rating: HIGH
Comparative Evaluation: COMPARABLE
Treatment: Semiempirical/Sequential (Steady—
State).
Gaussian plume function assumed.
Atmosperic stability divided into six (Pasquill—
Gif ford) classes, supplied hourly.
Dispersion coefficients from Turner (1969).
Surface roughness not treated explicitly.
One hour averaging time.
pplication Element: Background, Boundary. Initial
Conditions
eference Model: RAN
Creatment: Background not treated explicitly.
Both upper and lower boundaries — perfect reflection.
1) Neutral and unstable conditions: method of mul-
tiple images Lreated by summation of infinite
series until = l.6x (mixing height); uniform
mixing assumedZthereafter;
2) Stable conditions: mixing height assumed to
have no effect.
Mixing height for a given hour obtained by interpola-
tion of radiosonde data.
Study Model:
Importance Rating:
Comparative Evaluation:
rreatment: Background not treated explicitly.
Both upper and lower boundaries — perfect reflection
assumed.
Multiple reflections treated by summation of series.
Uses user—supplied hourly mixing height.
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1213
0 ’
PTMTP
MEDIUM
COMPARABLE
-------
Application Element: Temporal Correlations
Reference tibdel: R A N
Treatment: Sequential
User supplies hourly values of wind speed, wind
direction, mixing height, and other meteoro-
logical variables required for determination of
stability class and plume rise. (Correlations
automatic,)
Emission rates constant, not correlated with other
parameters.
Study Model: Study Model:
Importance Rating: Importance Rating:
Comparative Evaluation: Comparative Evaluation:
Treatment: Sequential, treatment:
User supplies hourly values of wind speed, wind
direction, stability class, mixing height.
Correlations among these parameters are auto-
matically treated.
Emission rates constant.
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1213
pplication Element:
teference Model:
E reatment:
Three IRRELEVANT elements:
Composition of Emissions
Chemistry and Reaction Mechanism
Physical Removal Processes
PTMTP
MED IUM
COMPARABLE
0
-4
0
-------
EVALUATION FORM
Part B: Technical Comparison
Application Index:
1213
Reference Model: RAM
Study Model PTMTP
0
-J
I - I
Importance Rating
of Application
Elements
Number
of
Treatments
Comparative Rating
of
Study Model
Total
BETTER
COMPARABLE
WORSE
CRITICAL
HIGH
MEDIUM
LOWa
0
6
2
1
—
0
0
—
6(5)
2
1
—
0(1)
0
0
—
COMPARABLE
COMPARABLE
IRRELEVANT
3
XXX
XXX
XXX
Total
12
(Should
equal
12)
TECHNICAL
EVALUATION
COMPARABLE
aU sed only in ambiguous cases.
-------
C72
-------
C73
C.6 EXAMPLE 6: HANNA—GIFFORJ)/l243
In this example, the application of interest involves the estimation of
one and twenty—four hour total suspended particulate concentrations from near
ground—level area sources within an urban area located in relatively flat ter-
rain. The application index is 1243 and the appropriate reference model is
RAM.
There are two forms of the Hanna—Gifford model which have been discussed
in the modeling literature. One form is that used in this example, and the
other form is used in Example 7, Appendix C.7. The user may examine the equa-
tions presented on the reverse side of Part A of the Evaluation Form in these
two examples to see the differences between the two versions of the model.
The Hanna—Gif ford model is not available as a computer program accom-
panied by a comprehensive user’s manual. Rather, the model has been presented
and discussed in a series of literature publications, three of which are cited
on Part A of the Evaluation Form. Consequently, different users may implement
the methods of Manna and Gif ford in different ways and the results obtained
may not be strictly said to have arisen from the same algorithm. In this ex-
ample it is assumed that the equations are applied separately to each of a
sequence of twenty—four hours. The reference model, RAM, works in the same
manner.
The Manna—C U ford model is classified Semiempiricalf Sequential (Steady—
State) and is determined to be applicable to the situation to be modeled.
The importance ratings shown on Part B incorporate three modifications.
Chemistry and reaction mechanism has been designated as IRRELEVANT. The im-
portance of plume behavior has been changed from MEDIUM to LOW on the assump-
tion that the particular area sources in question do not give rise to signif i—
cant plume rise. Also, since the sources are neat ground—level, there is no
need to consider downwash and fumigation. Finally, the importance rating of
horizontal dispersion has been changed from HIGH to MEDIUM due to the fact that
only area sources are of interest in this case. The modified rating corresponds
to the rating for horizontal dispersion in application number 1223, which in-
volves area sources only.
-------
C74
Part C gives the treatments, importance ratings, and comparison results.
It should be noted that the treatmenis by RAN, the reference model, of the
various aspects of each element that deal with point sources have been omitted.
These treatments are irrelevant in this particular application and are not con-
sidered in making the evaluation.
Both RAN and the Hanna—Gif ford model make use of similar methods for
estimating total area source contributions and this similarity is reflected
in the treatments of many of the application elements. Significant differences
in the two models occur, however, as a result of differences in the implementa-
tion of these similar methods. Nevertheless, the initial comparative evalua-
tion cf the Hanna—Gifford model is COMPARABLE, based on comparable treatments
of the three HIGH—rated elements. It should be noted that for one of the high
elements, source—receptor relationship, the Hanna—Gif ford model was rated CON—
PARABLE even though It assumes ground level emissions while RAN allows the user
to specify non—zero effective emission heights. En the application of interest
this difference is unimportant, because the emissions are known to be released
near the ground. In other applications, In which it is known that some or all
such emissions effectively occur above ground level, this difference may be
significant enough to justify a WORSE rating. This type of decision can only
be made by a person familiar with the actual situation of interest.
The two MEDIUM—rated elements whose treatments by the Hanna—Gifford
model are rated WORSE are horizontal wind field and background, boundary and
initial conditions. The treatment of horizontal wind field by the Hanna—
Gil ford model Is rated WORSE, because oniy sixteen possible wind directions
are used whereas RAN accepts wind directions to the nearest 100 and randomizes
these so that the wind direction may correspond to any of 360 different values.
The Lreatment of background, boundary and initial conditions is rated WORSE,
because the Hanna—Gif ford model does not treat the effects of the upper boun-
dary. A secondary comparison of COIIU)ARABLE is indicated, because for ground
level sources the effects of the upper boundary may not be felt for a substan-
tial distance downwind, depending on the depth of the mixed layer and the wind
speed.
The substantial number of MEDIUM—rated elements that are treated WORSE
by Hanna—Gifford together with the relatively small number of HIGH—rated ele-
ments and the absence of any HIGH or MEDIUM—rated elements that are treated
-------
C75
BETTER provides adequate justification for modifying the comparative evalua-
tion from COMPARABLE to WORSE in this application. The treatments of the LOW—
rated elements support this modification although little weight is attached to
them. The appropriate technical evaluation of the Ilanna—Gifford model in appli—
cation 1243 is therefore WORSE.
-------
76
APPLI CATION CLASS IF ICATION FORM
8
A. POLLUTANT
t
\
CHEMICAL
2
3
SICAL
PHYSICAL
CHEMICAL a PHY
NONE
CHEMICAL
PHYSICAL
CHEMICAL 8
-u
5
6
1
PHYSICAL 8
INDEX
NUMBERS
INSERT APPROPRIATE
NUMBERS IN THE
— I BOXES PROVIDED:
B. AVERAGING
TIME
C. SOURCE
C HA RA CT ERIS TIC S (
LONG—TERM
-TERM
--
LIMITED
POINT
AREA
C E/COMBINATION)
SHORT—RANGE
N S P0 RI
AC S IM P L
RANGE
s LONG—RANG
Form the application index by transferring the four index
the corresponding boxes below:
APPLICATION
IN DEX
J
I
J
‘I
J
2J Lj
L i
3
numbers into
C TMAi
CHARACTERISTICS\
\ SECONDARY
2
2
3
4
2
3
4
-------
C77
EVALUATION FORM
Part A: Abstract and References
Study Model : Hanna—Gifford
References : Manna, S.R., “A Simple Method of Calculating Dispersion from
Urban Area Sources.” J. Air Pollution Control Assn., Vol. 21,
No . 12, pp. 774—777, December 1971.
Gifford, l.A., and S.R. Manna, “Modeling Urban Air Pollution.”
Atmospheric Environment, Vol. 7, pp. 131—136, 1973.
Gif ford, PA. and S.R. Manna, “Urban Air Pollution Modeling.”
Paper No. ME—320, Proc. 2nd International Clean Air Congress,
Washington, D.C., pp. 1146—1151 (December 1970).
Abstract : The Hanna—Gif ford model is an area source model based upon
the assumption of a Gaussian pollutant distribution in the
vertical and using the narrose-plume approximation (homo-
geneous emissions in the crosswind direction) in the
horizontal direction.
Classification : Semiempirical/Sequential (Steady—State)
Application Index : 1243 Reference Model : R AM
Application Description : One and twenty—four hour concentrations of total
suspended particulate matter from area sources in an urban area for a
given period, flat terrain.
Model Applicability : Applicable f J Not Applicable
-------
C78
EVALUATION FORM
Part A(reverse): Equations
Study Model : Hanna—Gif ford
Equations :
x = -/ ‘ - fq( dx Narrow plume approximation, ground
z level sources.
= 1 ( i x/2) [ Q 0 + Q. [ 2 i+l 1b 1 b]]
b
y(x) = ax
N = number of upwind grid squares.
= width of a grid square.
-------
C79
EVALUATION FORM
Part B: Importance Ratings
Application Ind ex: 1243
Application Importance Rating
a
Element Initial Modified
Source—Receptor Relationship M M
Emission Rate M M
Composition of Emissions L L
Plume Behavior H L. I
Horizontal Wind Field M M
Vertical Wind Field L L
Horizontal Dispersion H M /
Vertical Dispersion H H
Chemistry and Reaction Mechanism L I I
Physical Removal Processes L L
Background, Boundary, Initial Conditions M N
Temporal Correlations M N
aW1 h the exception of the designation of IRRELEVANT elements, it is expected
that at most one CRITICAL designation and possibly one other modification
may be made.
-------
Application Element: Source—Receptor Relationship
Reference Model: RAN
Treatment:
Area sources defined as square cells (or multi-
ples) in a rectangular array; up to three effec-
tive release heights (for u = 5m/sec) user—
specified; sides lie along grid boundary direc-
tions.
Arbitrary receptor locations — all at the same
height above (or at) ground.
Flat terrain assumed.
Downwind distance calculated for points along rays
which intersect area sources.
Study Model: Hanna—Gifford
Importance Rating: MEDIUM
Comparative Evaluation: COMPARABLE
Treatment:
Area sources only, square cells in a rectangular
array.
Receptors and sources both at ground level.
Each receptor assumed located at center of a grid
square.
Flat terrain assumed.
Application Element: Emission Rate
Reference Model: RAN
rreatment:
Arbitrary constant emission rate for each area source.
Area source contributions obtained by numerical . rr —
gration along upwind distance of narrow—plume
approximation formulae for area source with given
effective release height.
Includes only those areas intersected by the upwind
ray.
Study Model:
Importance Rating:
Comparative Evaluation:
Treatment:
Arbitrary constant emission rate for each area source,
Area source contributions obtained by analytic inte-
gration along upwind distance of narrow—plume
approximation formulae for area source at ground
level oriented perpendicular to upwind direction.
Includes only grid squares directly upwind of
receptor.
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1243
0
0
Hanna—Gifford
MEDIUM
COMPARABLE
-------
EVALUATION FORN
Part C: Treatment of Elements
Application Index: 1243
Application Element: Composition of Emissions Application Element: Plume Behavior
Reference ? bde1: RAN Reference Model: RAM
Treatment: Treatment:
Single representative pollutant only; no treat— No plume rise calculated for area sources; assumed to
ment of size distribution, be included in release height.
Fumigation, downwash not treated.
Co
I-I
Study Model: Hanna—Gif ford Study Model: Hanna—Gif ford
Importance Rating: LOW Importance Rating: LOW
Comparative Evaluation: COMPARABLE Comparative Evaluation: WORSE
Treatment: Treatment:
Single representative pollutant only. Not treated explicitly; effective release height
assumed zero.
No treatment o size distribution.
Fumigation, downwash not treated.
-------
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1243
Application Element: Horizontal Wind Field
Reference Model: R
Treatment: Semiempirical /Sequential (Steady—
State)
Constant, uniform wind speed and direction assumed
for each of a sequence of hours.
Arbitrary wind speeds and direction values to 100
input by user; directions randomized by addi-
tion of (n — 4)0 with n = random integer from
zero to nine.
Wind speed is modified to correspond to value at
release height, modification dependent only on
stability class.
Study Model: Hanna—Gifford
Importance Rating: MEDIUM
Comparative Evaluation: WORSE
Treatment: Semiempirical/Sequential (Steady—
State).
Constant, uniform wind speed, direction assumed
for each of a sequence of hours.
Wind speed arbitrary; wind direction restricted
to one of 16 equally spaced directions.
pplication Element:Vertical Wind Field
Reference Model: RAM
Treatment: Semiempirical/Sequential (Steady—State)
Assumed equal to zero (implicit).
n
F ’ )
Study Model: Hanna—Gjf ford
Importance Rating: LOW
Comparative Evaluation: COMPARABLE
Treatment: Semiempiricalf Sequential (Steady—State),
Assumed equal to zero (implicit).
-------
Application Element: Horizontal Dispersion
Reference Model: RAN
Treatment: Semiempiricalf Sequential (Steady—
State)
Narrow plume approximation for area sources;
horizontal dispersion not treated explicitly.
Study Model: Hanna—Gif ford
Importance Rating: MEDIUM
Comparative Evaluation: COMPARABLE
Treatment: Semiempirical/Sequential (Steady—State),
Narrow plume approximation; horizontal dispersion
not treated explicitly.
Application Element: Vertical Dispersion
Reference Model: RAN
Treatment: Semiempirical/Sequential (Steady—State),
Gaussian plume function assumed.
Atmospheric stability divided into six (Pasquill—
Gifford) classes, determined hourly.
Dispersion coefficients from Turner (1969) or McElroy
and Pooler (1968) at user’s option.
Surface roughness not treated explicitly.
Study Model: Ranna—Gifford
Importance Rating: HIGH
Comparative Evaluation: COMPARABLE
Treatment: Semiempirical/Sequential (Steady—State).
Gaussian plume function assumed.
Atmospheric stability divided into classes (Smith
1968).
Dispersion coefficient = axb with a,b from Smith
(1968) or Briggs (1973 .
Surface roughness not treated explicitly.
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1243
Co
-------
Application Element: Physical Removal
Reference Model: p aj,.j
Treatment:
Exponential decay — first order (linear)
processes.
Single, constant user — specified decay constant.
Application Elen’ent: Backgrounds Boundary. Initial
Reference Model: R.A 1 Conditions
Treatment: Background not treated explicitly.
Both upper and lower boundaries perfect reflection.
1) Neutral and unstable conditions: method of mul-
tiple images treated by summation of Infinite
series until a = l.6X (mixing height); uniform
mixing assumedZthereafter;
2) Stable conditions: mixing height assumed to have
no effect.
Mixing height for given hour obtaIned by interpola-
tion of radiosonde data.
Study Model:
Importance Rating:
Comparative Evaluation:
Treatment:
Background: single additive constant.
Lower boundary: perfect reflection.
Upper boundary: assumed high enough to have no effect;
atmospheric stability assumed constant to above the
the plume height.
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1243
Study Model:
Importance Rating:
Comparative Evaluation:
Treatment:
Not treated explicitly.
Hanna—Gif ford
LOW
WORSE
Hanna—Gif ford
MEDIUM
WORSE (COMPARABLE)
-------
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1243
Application Element: Temporal Correlations
Reference Model: RAN
Treatment: Sequential.
User supplies hourly values of wind speed, wind
direction, mixing height, and other meteor-
ological variables required for determination
of stabilit.’ class and plume rise. (Correla-
tions automatic,)
Emission rates constant, not correlated with
other parameters.
Study Model: Hanna—Gifford
Importance Rating: MEDIUM
Comparative Evaluation: COMPARABLE
Treatment: Sequential.
Hourly values of wind speed, direction, stability
supplied by user. (Correlations automatic.)
Emission rates constant; not correlated with other
parameters.
Application Element:
Reference Model:
Treatment:
One IRRELEVANT element:
‘Chemistry and Reaction Mechanism
Study Model:
Importance Rating:
Comparative Evaluation:
Treatment:
‘ -Il
-------
EVALUATION FORM
Part D: Technical ComDarison
Application Index:
1243
Reference Model:
RAI4
Study Model Hanna—Gifford
C)
03
a’
Importance Rating
of Application
Elements
Number
of
Treatments
Comparative Rating
of
Study Model
Total
BETTER
COMPARABLE
WORSE
CRITICAL
HIGH
MEDIUM
LOW
0
1
6
4
—
0
0
0
—
1
4 (5)
2
—
0
2 (1)
2
—
COMPARABLE
WORSE
IRRELEVANT
1
Q(X
XXX
XXX
Total
12
(Should equal
12)
TECHNICAL
EVALUATION
WORSE
-------
CS 7
C.7 EXAt ’Lg 7; HA}ThIA—GIflQRD/1143
The application of interest involves the estimation of long—term ground—
level total suspended particulate concentrations arising from near ground—level
area sources in an urban area located in relatively flat terrain. The applica-
tion index is 1143 and the appropriate reference model is CD ) !.
As explained in Example 6, Appendix C.6, two forms of the Hanna—Gif ford
model have been discussed in the references given on Part A of the Evaluation
Form. One was used in Example 6 and the other is used in this example. Also,
as pointed out in Example 6, the Hanna—Gifford model has been presented in a
series of literature publications rather than in a user’s manual accompanied
by a computer code. As a result, the implementation of the ilanna—Gifford model
in a specific application may depend to some extent on the user. In this ex-
ample the procedure used by Hanna (1971) is considered.
The Hanna—Gifford model is classified Semiempirical/Climatological
(Steady—State). The climatologlcal classification seems most appropriate,
since a climatological average wind speed is used in the equation, even though
this form of the model does not appear to exactly correspond to the definiticn
of a climatological model used in this workbook. In fact however, the equation
used in this example may be derived from a climatological version of the other
form of the model given certain assumptions regarding the nature of the sta-
bility—wind rose used. The Hanna—Gif ford model is determined to be applicable
to the situation to be modeled.
Two modifications have been made in the importance ratings. Chemistry
and reaction mechanism has been rated IRRELEVANT, and the importanct rating
of plume behavior has been changed from MEDIUM to LOW due to the assumed nature
of the area sources in question, as in the previous example.
The working equations are given on the reverse side of Part A and the
treatments, importance ratings, and comparisons are given on Part C of the
Evaluation Form. The treatments by the reference model (CDM) of point—source
related aspects of each element have been omitted as they are irrelevant in
this application.
Only one element, vertical dispersion, is rated as being of HIGH im--
portance in this application and the treatment by this form of the Hanna—
-------
C88
Gif ford model is considered WORSE than that used by CDM, because only one
stability class (neutral) is considered. Had the model been implemented in
a slightly different way, this particular aspect of the treatment could have
easily been modified. A secondary comparison of COMPARABLE is indicated,
because neutral stability is indeed expected to occur more frequently than
any other in an urban area. A user familiar with the specific area to be
modeled is in the best position to judge the adequacy of this treatment in
that area. Other aspects of the two treatments of vertical dispersion are
comparable.
The treatments of the MEDIUM—rated elements show a definite bias toward
a WORSE rating. The treatments of emission rate and horizontal dispersion are
rated definitely COMPARABLE, and the treati ient of source—receptor relationship
is rated COMPARABLE although with a secondary rating of WORSE due to the treat-
ment of only the one grid square containing the receptor. The validity of
this procedure is related to the spatial variability of the emission rates for
nearby grid squares, which in turn depends in part on the size of the grid
square used. The treatment of horizontal wind field is rated WORSE, as is the
treatment of background, boundary and initial conditions although for this
element on a secondary rating of COMPARABLE is indicated. The uncertainty in
the comparison for background, boundary and initial conditions arises because,
although the Hanna—Gifford model does not treat effects due to the upper boun-
dary, these effects may not be important for ground level sources at short to
moderate range, depending on the depth of the mixing layer. Of the two uncer-
tain ratings, the one for background, boundary and initial conditions is con-
sidered the greater, and the distributions of treatments for MEDIUM—rated ele-
ments which deserve the most consideration are 0,3,2 and 0,2,3.
The results for the MEDIUM—rated elements clearly support the initial
rating of WORSE and the LOW—rated elements also support this rating. The
appropriate technical evaluation for this form of the Hanna—Gif ford model
is therefore WORSE in this application.
-------
C89
APPLICATION CLASSIFICATION FORM
A. POLLUTANT
c-i
C I RY ,‘ CHEMICAL
PHYSICAL
CHAR ACT E R 1ST I CS \
\ SECONDARY
B. AVERAGING
TIME
C. SOURCE
CHARACTER IS TIC S
TERM
3
L 4
5
6
CHEMICAL a PHYSICA
NONE
CHEMICAL
PHYSICAL
7
SHORT—TERM
—
LIMITED
POINT
,‘ REA
INDEX
NUMBERS
INSERT APPROPRIATE
NUMBERS IN THE
— I BOXES pROvIDED:
—2
D. TRANSPORT
CHARACTERISTICS
SHORT—RANGE
COMPLEX
,, RAE3E
LONG—RANG
APPLICATION
IN DEX
Form the application index by transferring the four index numbers into
the corresponding boxes below:
J
I’
I
ii
13
CHEMICAL 8
PHYSICAL 8
2
2
3
4
\ LINE
( 1 PL E /COM O
2
3
4
-------
C90
EVALUATION FORM
Part A: Abstract and References
Study Model : ilanna—Gifford
References : Hanna, S 0 R., “A Simple Method of Calculating Dispersion from
Urban Area Sources.” T. Air Pollution Control Asan., Vol.
21, No. 12, pp. 774—777, December 1971.
Gifford, F.A., and S.R. Manna, “Modeling Urban Air Pollu-
tion.’ t Atnospheric Environment, Vol. 7, pp. 131—136, 1973.
Gif ford, F.A., and S.R. Hanna, “Urban Air Pollution Model-
ing.” Paper No. ME—32O, Proc. 2nd International Clean Air
Congress, Washington, D 0 C., pp. 1146—1151 (December, 1970).
Abstract : The Hanna—Gifford model is an area source model based upon
the assumption of a Gaussian pollutant distribution in the
vertical and using the narrow—plume approximation (homo-
geneous emissions in the crosswind direction) in the hori-
zontal direction.
Classification : Semiempirical/Climatological (Steady—State)
Application Index : 1143 Reference Model : CDM
Application Description : Long—term ground—level total suspended particulate
concentrations from near ground—level area sources in an urban area.
Model Applicabi]4fl : Applicable Not Applicable
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C9 1
EVALUATION FORM
Part A(reverse): Equations
Study Model: Ranna—Gif ford
Equations :
Q
x c— 2 .
with
X = ground level concentration in a given grid square.
emission rate per unit area in the same square.
u = average wind speed over the period of interest.
1—b
[ 52 214 -I -i 1
C = Yrr 2 Ax a(i—b)
with
14=4
tat = grid spacing (meters)
i—b
a = 0.15 meters
b = 0.75
(a and b correspond to parameters in the representation of the
vertical dispersion coefficient:
b
a = ax
2
The values are those recommended by M.E. Smith (1968) for neutral
stability.)
-------
C92
EVALUATION FORM
Part B: Importance Ratings
Application Index: 1143
Application Importance Rating
Element Initial Modifieda
Source—Receptor Relationship M
Emission Rate M M
Composition of Emissions L L
Plume Behavior N L I
Horizontal Wind Field N
Vertical Wind Field L L
Horizontal Dispersion N N
Vertical Dispersion H H
Chemistry and Peaction Mechanism L I I
Physical Removal Processes L L
background, Boundary, Initial Conditions M N
Temporal Correlations L L
aW h the exception of the designation of IRRELEVANT elements, it Is expected
that at most one CRITICAL designation and possibly one ot h er modification
may be made.
-------
Application Element: Source—Receptor Relationship
Reference Model: CDM
Treatment:
Area sources integral multiples of basic grid
square.
Receptor location arbitrary.
Arbitrary release heights for area sources.
Precise separation for each source—receptor pair.
Receptors are at ground level.
No terrain differences between source/receptor.
Sides of area sources lie along grid boundary
directions 0
Study Model: Hanna—Gif ford
Importance Rating: MEDIUM
Comparative Evaluation: COMPARABLE (WORSE)
Treatment:
Single square, ground—level area source over which,
emissions are approximately uniform, considered
for each receptor.
Arbitrary grid size, user—specified.
Ground—level receptors, located arbitrarily within
source area.
Flat terrain assumed.
Area sources square cells in user—specified grid.
Application Element: Emission Rate
Reference Model: CDM
Treatment:
Arbitrary emission rate for each area source.
Area integrations are done numerically one 22.5°
sector at a t:ne; sampling at discrete points
defined by specific radial and angular Intervals
on a polar grid centered on the receptor.
Day/night variations in emissions, same variation
assumed for all sources; no other temporal varia-
tion.
Study Model:
Importance Rating:
Comparative Evaluation:
Treatment:
Single constant emission rate for the source area.
Area source contribution obtained by analytic
integration along upwind direction of narrow—
plume approximation formulae for ground—level
source.
EVALUATION FORM
Part C: Treatmont of Elements
Application Index: 1143
Hanna—Gifford
NED IUN
COMPARABLE
-------
EVALUATION FORM
Part C: Treatment of Elements
Application Index: ll4
Application Element: Composition of Emissions Application Element: Plume Behavior
Reference Model: CDM Reference ! bdel: CDM
Treatment: Treatment:
Treats up to two independent pollutants. No plume rise calculated for area sources. Does not
treat fumigation or downwash.
C)
Study Model: Hanna—Gifford Study Model: Banna—Gifford
Importance Rating: LOW Importance Rating: LOW
Comparative Evaluation: COMPARABLE Comparative Evaluation: COMPARABLE
Treatment: Treatment:
Independent pollutants, treated one at a time. Not treated explicitly; effective release height
assumed zero.
Does not treat downwash or fumigation.
-------
EVALU&TION FORM
Part C: Treatment of Eleiments
Application Index: 1143
Application Element: Horizontal Wind Field pp1ication Element: Vertical Wind Field
Reference }bdel: Reference de1: CDM
Treatment: Climatological. Treatment:
16 wind directions. Assumed equal to zero (implicit).
6 wind speed classes.
Wind speed corrected for release height based on
power law variation; exponents from DeMarrais
(1959). Stability class dependent.
Constant, uniform (steady—state) wind assumed.
U I
Study Wdel: Hanna—Gif ford Study Wdel: Hanna—Gjf ford
Importance Rating: MEDI JM Importance Rating: LOW
Comparative Evaluation: WORSE Comparative Evaluation: COMPARABLE
Treatment: Climatological Treatment:
Only average wind speed in area of interest is Assumed equal to zero (implicit).
considered.
No variation of wind speed with height.
-------
Application Element: Horizontal Dispersion
Reference Model: CDN
Treatment: Semieinpirical/Climatological (Steady—
State) 1
Uniform distribution within each of 16 sectors
(sector averaging).
Averaging time = one month to one year.
Atmospheric stability and surface roughness not
treated explicitly.
Study Model: Hanna—Gif ford
Importance Rating: MEDIUM
Comparative Evaluation: COMPARABLE
Treatment: Semiempirical/Climatologlcal (Steady—
State).
Narrow—plume approximation; horizontal dispersion
not treated explicitly.
Application Element: Vertical Dispersion
Reference Model: CDM
Treatment: Semiempirical/Cliinatological (Steady—State).
Gaussi fl plume function assumed.
Five stability classes as defined by Turner (1964),
neutral stability split into day/night cases.
Dispersion coefficients taken from Turner (1970).
Area sources — stability class is decreased by one
category from input values to account for urban
effects.
Neutral dispersion coefficients are used for all
neutral and stable classes.
Surface ro g hness not treated explicitly .
Study Model: Hanna—Gif ford
Importance Rating: HIGH
Comparative Evaluation: WORSE (COMPARABLE)
Treatment: Semiempirical/Climatological (Steady—State)
Gaussian plume function assumed.
Single atmospheric stability (neutral) considered.
Dispersion coefficient a axb ; a, b from Smith
(1968). z
Surface roughness not treated explicitly.
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1143
-------
Application Element: Physical Removal
Reference Model: CDN
Treatment:
Treats only first—order (linear) processes.
Single, constant user—supplied haiflife used —
exponential decay.
Application Element: Background, Boundary, Initial
Reference Model; cn Conditions
Treatment:
Input single constant background value for each
pollutant.
Lower boundary (ground): Perfect reflection.
Upper boundary (mixing height): Perfect ref lec—
tion.
No effect until vertical dispersion coefficient
equals 0.8 of mixing height, uniform vertical
mixing assumed beyond this point.
Study Model: Nanna—Gjfford
Importance Rating: MEDIUM
Comparative Evaluation: WORSE (COMPARABLE)
Treatment:
Background: single additive constant.
Lower boundary: perfect reflection.
Upper boundary: Assumed high enough to have no
effect; atmospheric stability assumed constant to
above the plume height.
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1143
Study Model:
Importance Rating:
Comparative Evaluation:
Treatment:
Not treated explicitly.
Hanna-.Gjf ford
LOW
WORSE
-------
4pplication Element: Temporal Correlations
Reference Model: CDM
Treatment: Wind speed, direction, stability
correlated via wind rose; mixing neight is ad’-
justed according to stability class:
Class A — 1.5 x afternoon climatological value;
Class D (night) — average of morning and after
noon climatological values; Class E — morning
climatological value.
Emission rates: daysnight variation allowed; all
sources assumed to vary by same factor.
Mon_sequential (clinatological) llnited corre—
lat ion.
Study Model: Hanna ’ -Gif ford
Importance Rating:
Comparative Evaluation:
Treatment:
Correlations not treated explicitly.
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 1143
Application Element:
Reference Model:
Treatment:
One IRRELEVANT element:
• Chemistry and reaction mechanism.
LOW
WORSE
Study Model:
Importance Rating:
Comparative Evaluation:
Treatment:
0
\0
-------
EVALUATION FORM
Part D: Technical Comparison
Application Index: 1143
Reference Model:
CDM
Study Model Hanna—Gif ford
0
‘0
‘ .0
Importance Rating
of Application
Elements
Number
of
Treatments
Comparative Rating
of
Study Model
Total
BETTER
COMPARABLE
WORSE
CRITICAL
HIGH
MEDIUM
LOW
0
1
5
5
—
0
0
0
—
0 (1)
3 (4—2)
3
—
1 (0)
2 (1—3)
2
—
WORSE
WORSE
IRRELEVANT
1
)(JOC
XXX
XXX
Total
12
(Should
equal
12)
TECHNICAL
EVALUATION
WORSE
-------
c:Loo
-------
C i a ’
C.8. EXAMPLE 8: APPENDIX 3/6243
In this example, the application involves the estimation of the percent
reduction of hydrocarbon emissions required in order to achieve the National
Ambient Air Quality Standard for photochenical oxidant in Sample City, a
moderately sized urban area located in gently rolling terrain. The appropriate
Application Index is 6243 and the associated reference model is the SAl urban
photochemical model.
The study model in this example is Appendix 3. Appendix 3 consists of
a single graph of percent hydrocarbon reduction against maximum measured one—
hour photochemical oxidant concentration. Given the appropriate oxidant mea-
surement from Sample City, the required percent reduction may be read directly
from the graph. The curve is based on a simple rollback model in combination
with an empirical “upper limit curve,” which represents the upper envelope of a
plot of maximum daily one—hour oxidant levels against 6—9 AN non—methane hydro-
carbon levels, the data being accumulated from several U.S. cities. The upper
limit curve provides an approximate relationship between oxidant levels and
precursor (hydrocarbon) levels under worst case conditions. The appropriate
classification of Appendix 3 is therefore Rollback/Statistical.
The equations are documented and Appendix 3 is determined to be appli-
cable and the “applicable t ’ box of Fart A of the Evaluation Form is checked.
Then, in accordance with the instructions in Section 2, the guidelines in Sec-
tion 7 are consulted immediately following Step 4 of the procedure, the classi-
fication of the study model as a Rollback/Statistical model. It is assumed
that an element—by—element examination of the approximations inherent in Appendix
3 compared to the SA l model is desired. Therefore, Parts B, C, and D of the
Evaluation Form are filled out in the same manner as if two simulation models
were being compared. -
With only one exception, the element—by—element comparisons of Appendix
3 with the SAl model indicate that Appendix 3 is WORSE. The single element in
which they are rated COMPARABLE is physical removal, which is not treated by
the version of the SAt model used as a reference model in this workbook. The
technical evaluation of Appendix 3 is clearly WORSE. This should be interpreted
as meaning that the approximations that must be made to reduce the SA l working
equations to the Appendix 3 curve are determined to be not justified in this
application.
-------
C102
APPLICATION CLASSIFICATION FORM
0
A. POLLUTANT
I
PRIMARY
NONE
MICAL
\
PHYSICAL
CHEMICAL 8
INDEX
NUMBERS
3
PHYSICAL
NONE
5
6
CHARACTE RISTICS\
CHEMICAL
PHYSICAL
CHEMICAL & PIIYSICA
INSERT APPROPRIATE
NUMBERS IN THE
I BOXES PROVIDED:
2
B. AVERAGING
TIME
C. SOURCE
CHARACTERISTICS
LONG—TERM
T-T M
LIMITED
POINT
AREA
7 LINE
\ (1 ZPL CO M BINA T ION
D. TRANSPORT
CHARACTER ISTICS
/
COMPLEX
SHORT—RANGE
LONG—RANGE
SHORT—RANGE
LONG—RANGE
Form the application index by transferring the four index
the corresponding boxes below:
APPLICATION
IN DEX
j
6 J
2 J
L;
numbers into
2
2
3
4
2
3
4
-------
C 103
EVALUATION FORM
Part A: Abstract and References
Study Model : Appendix J
References : Federal Register 36 No. 158, August 14, 1971.
Air Qual ity Criteria for Nitrogen Oxides, AP—84, En-
vironmental Protection Agency, Washington, (January 1971).
AbstrLct : Appendix J is a method for estimating the percent reduc-
tion of hydrocarbon emissions within an urban area required
in order to achieve the National Ambient Air Quality Stan-
dard for photochemica]. oxidant in that area. The method
is based on the use of simple rollback together with an
empirical —elationship between the maximum observed oxidant
concentration and measured non—methane hydrocarbon concert—
tract ions
Classification : Rollback/Statistical
Affiplication Index : 6243 Reference Model : SAL
Application Dascription : Estimate percent reduction in hydrocarbon emis-
sions in given urban area required to meet photocheinical oxidant standard.
Model Applicability : Applicable Not Applicable EIIIJ
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C104
EVALUATION FORM
Part A (reverse): Equations
Study Model :
Appendix J
Equations:
- X 5
Percent hydrocarbon emission reduction = x 100
Xmax
(Assumes zero background hydrocarbon concentration).
= nonmethane hydrocarbon concentration associated with the
ax observed maximum oxidant level.
Xstd = noninethane hydrocarbon concentration (0.24 ppmC)
associated with the photochemical oxidant national
ambient air quality standard (0.08 ppm over a 1—hour
period).
The hydrocarbon concentration for a given oxidant concentration is
determined using the empirical “upper limit curve,” the upper envelope
curve of a plot of maximum daily oxidant level against observed 6—9 AN
hydrocarbon level, the data being accumulated from several U.S. cities.
The result is the Appendix J curve:
MAXIMUM MEASURED I-HOUR PHOTOCHEMICAL OXIDANT CONCENTRATION, ppm
a . j
I-
uJ
‘U
a
uJ
C ,, =
z a.
0
C,, —
— IC.
a
‘ U
a
-
o a
o ,<
_ , a
o
100
40
20
600
80
60
MAXIMUM MEASURED I-HOUR PHOTOCHEMICAL OXIDANT CONCENTRATION, pg/rn 3
-------
C105
EVALUATION FORM
Pai B: Importance Ratings
Application Index: 6243
Application Importance Rating
Element Initial Modifieda
Source—Receptor Relationship H H
Emission Rate H H
Composition of Emissions H H
Plume Behavior H M f
Horizontal Wind Field H H
Vertical Wind Field L L
Horizontal Dispersion H H
Vertical Dispersion H H
Chemistry and Reaction Mechanism H H
Physical Removal Processes L L
Background, Boundary, Initial Conditions H H
Temporal Correlations H H
aW h the exception of the designation of IRRELEVANT elements, it is expected
that at most one CRITICAL designation and possibly one other modification
may be made.
-------
Application Element: Source—Receptor Relationship
Reference Model: SAl
Treatment: All sources except power plants aggre-
gated to square grid cells in 25 x 25 array;
location of power plant specified only by grid
cell; grid cell size arbitrary.
Arbitrary release height for power plant; other
emissions treated as upward fluxes at ground
level; topographic elevation arbitrary.
Receptors at ground level and in each of up to
five vertical cells; horizontal location
arbitrary.
Ar as oriented by fixed grid boundaries.
Study bdel: Appendix J
Importance Rating: HIGH
Comparative Evaluation: WORSE
Treatment:
Receptors at ground level.
Other aspects not treated explicitly.
pplication Element: Emission Rate
Reference bdel: SAl
reatment: Point source (power plant) emissions dis-
tributed homogeneously throughout entire vertical
column above grid square contain 1g the source;
emission rates sup 4ied by user.
Other emissions treated as upward pollutant fluxes at
ground surface.
Sequence of hourly average rates for mobile sources.
Stationary source rates assumed constant.
Rates for mobile sources determined from user—supplied
emission factors and traffic data.
Rates for stationary sources inDut by user .
Study Model: Appendix J
Importance Rating:
Comparative Evaluation:
Treatment:
Does not treat variations within study area explicitly.
Accounts for change in total emissions in region of
interest between baseline and prediction periods.
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 6243
0
HIGH
WORSE
-------
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 6243
Application Element: cnmpositinn f pplication Element: Composition of Emissions — (Contd. )
Reference I’ bdel: SA l eference Model: SAl
Treatment: Treats emissions of reactive hydro— Creatment:
carbons, unreactive hydrocarbons, NO, NO 2 , and
CO. User inputs stationary source (both point and
area) emissions of reactive hydrocarbons, un—
User inputs mobile source emissions of hydro— reactive hydrocarbons, NO, NO 2 , and CO.
carbons, NO , and CO.
x
Mobile source NO emissions assumed to be 99%
NO 2 ; convertedXinternally to NO.
Mobile source hydrocarbon emissions split inter-
nally into 67.4% (mole fraction) reactive frac-
tion and 32.6% unreactive fraction.
0
Study Model: Appendix J Study Model:
Importance Rating: hIGH Importance Rating:
Comparative Evaluation: WORSE Comparative Evaluation:
Treatment: Treatmeat:
Non—methane hydrocarbon emissions only.
-------
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 6243
Application Element: Plume Behavior
Reference Model: SAl
Treatment:
Uses Briggs’ formulae (1971) for point sources
only to determine if plume from a power plant
penetrates inversion.
If plume height exceeds mixing height, emissions
from source are not treated.
Does not treat either fumigation or downwash.
Plume rise not treated explicitly for sources
other than power plants.
Study Model:
Importance Rating:
Comparative Evaluation:
Treatment:
pp1ication Element: Horizontal Wind Field
eference Model: SAl
L reatment: Numerical/Dynamic
Fixed grid model.
Wind speed and direction specified f or each of a
sequence of hours ac points on a horizontal
grid, interpolated from surface measurements.
Arbitrary wind speed, direction values allowed.
Wind speed, direction independent- of height.
Study Model: Appendix J
Importance Rating: HIGH
Comparative Evaluation: WORSE
Treatment: Rollback/Statistical.
I—i
0
Appendix J
MEDIUM
WORSE
Not treated explicitly.
Not treated explicitly.
-------
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 6243
Application Element: Vertical Wind Field
Reference Model: SA l
Treatment: Numerical/Dynamic.
Vertical wind speed specified for each of a
sequence of hours at points on a three—dJinen—
sional grid.
Values assumed linearly increasing functions of
height, values near surface determined from
horizontal wind speed, directions using mass
consistency requirement.
Study Model: Appendix J
Importance Rating: LOW
Comparative Evaluation: WORSE
Treatment: r ollback/Statistica1.
Nnt treated explicitly.
Application Element: Horizontal Dispersion
Reference Model: SAl
Treatment: Numerical/Dynamic.
Numerical solution of advection—diffusion equation
in three dimensions.
Horizontal eddy diffusivity value assumed uniform
and constant and is fixed in the computer code.
Study Model: Appendix J
Importance Rating: HIGH
Comparative Evaluation: WORSE
Treatment: Rollback/Statistical.
Not treated explicitly.
I-
C
-------
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 6243
Study Model: Appendix 3
Importance Rating: HIGH
Comparative Evaluation: WORSE
Treatment: Rollback/Statistical.
Not treated explicitly.
Application Element: Chemistry and Reaction
Reference Model: SAl Mechanism
Treatment: Photochemical Smog System.
Fifteen reactions involving 10 species (NO, NO 2 ,
O3 Hc, 0, OH, HO 2 , R0 2 , NO 3 , HNO 2 ).
Lumping approximation for 2 species (Mc, R0 2 ).
Steady—state approximation for 6 species (NO 3 , 0,
R0 2 , OH, HO 2 , HNO 2 ).
NO 2 photolysis rate calculated internally as a
function of time.
No adjustments made for the effects of incomplete
turbulent mixing below the resolution of the grid.
Study Model: Appendix 3
Importance Rating: HIGH
Comparative Evaluation: WORSE
Treatment: Photochemical oxidant estimation only.
Two species only: non—methane hydrocarbon and
photochemical oxidant.
Empirical relation (the “upper limit curve”) used
to describe relation between hydrocarbon con-
centrations under worst case conditions.
Application Element: Vertical Dispersion
Reference Model: SAl
Treatment: Numerical/Dynamic,
Numerical solution of advection—diffusion equation
in three dimensions.
Vertical eddy diffusivity an empirical function of
wind speed and height above ground.
C)
I - .
0
-------
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 6243
Application Element: Physical Removal ipplication Element: Background, Boundary ,
Reference Model: SAl Reference Model: SAl Initial Conditions
Treatment: Treatment: Numerical/Dynamic.
Not treated explicitly.
Background (see treatment of fluxes at vertical
sides)
Upper: Perfect reflection for pollutants within
region of interest (turbulent diffusive flux =
0).
Allows for entrainment of pollutants from above
mixing layer.
Lower: Implicit perfect reflection; no adjustment
made to emission fluxes to account for removal .
Study Model: Appendix J Study Model: Appendix J
Importance Rating: LOW Importance Rating: HIGH
Comparative Evaluation: COMPARABLE Comparative Evaluation: WORSE
Treatment: Treatment: Rollback/Statistical.
Not treated explicitly. Background levels of non—methane hydrocarbon and
photochemical oxidant both assumed zero.
Boundary, initial conditions not treated
explicitly.
-------
EVALUATION FORM
Part C: Treatment of Elements
Application Index: 6243
Application Element: Background Boundary Initial
Reference Model: SAl Conditions (Contd.)
Treatment: Numerical/Dynamic 4
Vertical: Treated as a function of position and
elevation; total flux normal to side of region
required to be continuous across boundary.
Initial: Mean initial concentrations of six
species (reactive HC, NO, O3 NO 2 , CO, Un—
reactive HC) specified for each grid cell.
pplication Element: Temporal Correlations
teference Model: SAl
reatment: Sequential up to 24 hours.
Correlations automatic.
Parameters updated every hour: mobile source emission
for each ground—level grid square, point source
(power plant) emissions, wind speed and direction,
mixing height at every vertical column of grids,
vertical eddy diffusivity at every vertical inter-
face of grid cells, incoming fluxes at boundaries,
NO 2 photolysis rate constant.
Update based on user input values.
Study Model:
Importance Rating:
Comparative Evaluation:
Treatment:
I-I
I —
Study Model: Appendix J
Importance Rating: HIGH
Comparative Evaluation; WORSE
Treatment:
Not treated explicitly.
Total emissions allowed to change between baseline
and forecast periods.
m
-------
EVALUATION FORM
Part D: Technical Comparison
Application Index: 6243 Reference Model: SA l — Study Model Appendix 3
Importance Rating Comparative Rating
of Application Number of Treatments of
Elements Total BETTER COMPARABLE WORSE Study Model
CRITICAL 0 — — — —
HIGH 9 0 0 9 WORSE
MEDIUM 1 0 0 1 WORSE
LOW 2 0 1 1
IRRELEVANT 0 XXX XXX XXX
Total 12 (Should equal 12)
TECHNICAL EVALUATION WORSE
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C114
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D l
APPENDIX D
APPLICATION CLASSIFICATION AND
MODELS EVALUATION FORMS
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D2
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D3
APPENDIX D. APPLICATION CLASSIFICATION AND MODEL
EVALUATION FORMS
Included in this appendix is an outline of the steps in the mode]. eval-
uation methodology presented in this workbook together with a copy of each form
required by the procedure.
The following page, entitled, WORKBOOK SECTION AND FORM FOR EACH STEP
IN COMPARISON, lists the nine steps in the comparison procedure. It refers the
reader to the workbook section containing instructions for each step and identi—
fies which form to use for documenting the results.
Thc first step classifies the application and the results are recorded
on the APPLICATION CLASSIFICATION FORM. Some basic information about the study
model is also recorded on the EVALUATION FORM — Part A.
The results of steps 2 — 5 are also documented on the EVALUATION FORM —
Part A. These steps involve documenting the study model equations (reverse
side of form), checking the study model compatibility, classifying the study
model, and identifying the reference model.
In step 6, the importance rating of the application elements are re-
viewed and modified if necessary. The EVALUATION FORM — Part B is used to
record both the initial and modified importance ratings.
The treatment of the application elements by both models are described
on the EVALUATION FORM — Part C and then compared. Results of the element—by—
element comparisons are recorded on the form to complete steps 7 and 8.
Combining the comparisons of individual elements with the importance
ratings to arrive at a technical evaluation of the study model is the last
step in the procedure. EVALUATION FORM — Part D provides a convenient frame-
work for making this overall comparison.
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D4
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APPLICATION CLASSIFICATION FORM
PRIMARY
A. POLLUTANT
CHAR ACT E R 1ST I Cs
SECONDARY
B. AVERAGING
TiME
C. SOURCE
CHAj ACTERISTICS
D. TRANSPORT
/
CHARACTERISTICS \
LONG—TERM
#._.._ SHORT—TERM
INDEX
NUMBERS
NONE
/ CHEMICAL 2
P lYSICAL 3
\ CHEMICAL & PHYSICAL 4
NONE 5
CHEMICAL - 6
PHYSICAL
CHEMICAL 8 PHYSICAL 8
POINT
LIMITED 1 /’ REA
\ LINE
MULTIPLE/COMBINATION
LONG—RANGE
SIMPLE
SHORT—RANGE
SHORT-RANGE
2
2
3
4
2
3
LONG—RANGE 4
r’orm the application index ly transferring the four index
he corresponding boxes below:
APPLICATION
INDEX
1 Jit9J aJ j
numbers into
INSERT APPROPRIATE
NUMBERS IN THE
BOXES PROVIDED:
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WORKBOOK SECTION AND FORM FOR EACH STEP IN COMPARISON
Step
Workbook Form in
Number Action Sections Appendix D
1 Classify application 3 Application Classi-
fication Form
Record study model information 2.3 Evaluation Form A
2 Document study model equations 2.3 Reverse side of
Evaluation Form A
3 Check study model compatibility 4.2 Evaluation Form A
4 Classify study model typea 4.3 Evaluation Form A
5 Identify reference model 4.4 Evaluation Form A
6 Review importance ratings 4.5 Evaluation Form B
7 Determine treatments of elements 5 Evaluation Form C
8 Compare treatments on element—by—
element basis 6.2.1 Evaluation Form C
9 Synthesize individual comparisons
into overall comparison 6.2.2 Evaluation Form D
a 1 f the study model has been classified as a rollback/statistical model, the
user should proceed directly to Section 7 wherein such models are discussed.
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EVALUATION FORM
Part A: Abstract and References
Study Model:
References:
Abstract:
Classification:
Application Index: Reference Model:
Application Descr p ion:
Model Applicability : Applicable Not Applicable
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Study Model:
EQuations :
EVALUATION FORM
Part A (reverse): Equations
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EVALUATION FORM
Part B: Importance Ratings
Application Index:
Application — Impprtance Rating -
Element Initial Modifieda
Source —Recepto Relationship
Emission Rate
Compo..ition of Emissions
Plume Behavior
Horizontal Wind Field
Vertical Wind Field
Horizontal Dispersion
Vertical Dispersion
Chemistry and Reaction Mechanism
Physical Removal Processes
Background, Boundary, Initial Conditions
Temporal Correlations
aW h the exception of the designation of IRRELEVANT elements, it is expected
that at most one CRITICAL designation and possibly one other modification
may be made.
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EVALIJAT ION FORM
Part C: Treattnent of Elements
Application Index:__________
Application Element: Application Element :
Reference Model: Reference Model:
Treatment: Treatment:
Study Model: Study Model:
Importance Rating: Importance Rating:
Comparativc Evaluation: Comparative Evaluation:
Treatment: Treatment:
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EVALUATION FORM
Part D: Technical Comparison
Application Index:___________________ Reference Model:___________________ Study Model:
Importance Rating
of Application
Elements
Number
of
Treatments
Comparative Rating
of
Study Model
Total
BETTER
COMPARABLE
WORSE
CRITICAL
HIGH
MEDIUM
LOW
IRRELEVANT
m
XXX
XXX
Total
(Should
equal
12)
TECHNICAL
EVALUATION
-------
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