United States
Environmental Protection
Agency
Atmospheric Sciences Research
Laboratory
Research Triangle Park NC 27711
Research and Development
EPA-600/S3-84-095 Jan. 1985
&EPA Project Summary
Continued Research in
Mesoscale Air Pollution
Simulation Modeling
J. P. Killus, J. P. Meyer, D. R. Durran, G. E. Anderson, T. N. Jerskey,
S. D. Reynolds, J. Ames, R. G. Lamb, W. R. Shu, J. H. Seinfeld, L. E. Reid, and
F. G. Gelbard
The work described in this Project
Summary is contained in three project
reports that comprise the completion of
a seven volume series. The first four
volumes covered evaluative and research
studies that were exploratory in nature
in an attempt to lay the groundwork for
various refinements to an Urban Airshed
Model developed under EPA sponsor-
ship. The final three volumes discuss
the completion of these studies and the
incorporation of several refinements to
the urban airshed model.
Specifically, the reports contain: (1)
details of model refinement activities
concerned with the improvement of
numerical integration techniques, the
incorporation of surface removal pro-
cesses, the development of automated,
objective procedures for preparing wind
inputs, the treatment of atmospheric
chemical reactions, and the estimation
of rate constants for photolysis reac-
tions; (2) discussion of microscale
modeling efforts aimed at the estimation
of eddy diffusivities and the improved
treatment of point and line sources; and
(3) progress in the development of
aerosol modeling capabilities.
This Project Summary was developed
by EPA's Atmospheric Sciences Re-
search Laboratory, Research Triangle
Park, NC, to announce key findings of
the research project that is fully docu-
mented in a separate report of the same
title (see Project Report ordering
information at back).
Introduction
Since the time of the original version of
the Urban Airshed Model developed in
1973, a number of modifications have
been implemented in the computer codes
to account more fully for the physical and
chemical phenomena believed to be
important in influencing urban air quality.
A synopsis of the current features of the
model is presented below.
Basically, the Urban Airshed Model
accepts emissions, meteorological chem-
ical, and air quality data as inputs and
produces predictions of pollutant concen-
trations during specified time intervals
within the cells of a three-dimensional
grid encompassing the region of interest.
Thirteen chemical species are considered:
ozone (Oa); nitrogen dioxide (N02>; nitric
oxide (NO); sulfur dioxide (SO2); carbon
monoxide (CO); peroxyacetylnitrate (PAN);
total aerosol; olefins(other than ethylene);
paraffins; aromatics and ethylene; alde-
hydes; nitrous acid (HNOz); and hydrogen
peroxide (H20z). The aerosol component
consists of primary particulate matter and
secondary nitrate, sulfate, and organic
aerosols.
The model simulates pollutant transport
through the action of advection and
turbulent dispersion. As mentioned above,
wind inputs are time-varying and fully
three-dimensional. Only horizontal wind
components are input; appropriate verti-
cal velocities are calculated using a mass
balance constraint. Thus, the influence of
convergence and divergence zones in the
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windfield can be handled properly. Eddy
diff usivity coefficients are estimated from
an algorithm that accounts for the effects
of atmospheric stability, surface rough-
ness, wind speed, and inversion height.
Chemical transformations are repre-
sented by the 42-step chemical mecha-
nism mentioned above. Organics are
segmented into four classes that are
based primarily on carbon bond charac-
teristics and to a lesser extent on reactivity
and reaction products. The mechanism
can account for the effects of hourly
temperature variations on reaction rate
constants through the use of the Arrheni us
relationship. Photolysis rate constants
are allowed to vary in time as well as in
space. Aerosol predictions in a column of
grid cells are used to estimate the effect
of light scattering on the photolysis rate
constants in each grid cell of that column.
Removal of pollutants by surface sinks
is treated by means of the deposition
velocity concept. The effects of both
atmospheric turbulence and surface
uptake characteristics are considered.
Model inputs include a spatial array of
surface types corresponding to the land
use in each grid cell.
Several microscale features are incor-
porated in the model. Subgrid-scale
concentration variations arising from the
spatial characteristics of point and line
sources can affect the spatially averaged
predictions obtained from a grid model.
However, these effects are only important
when a contaminant emitted from a point
or line source reacts rapidly with another
pollutant. One such example is the
reaction of NO with Oa to form N02 and
02.
To account for the subgrid-scale influ-
ences of line sources, the model treats
the lowest layer of grid cells in a special
manner. First, this layer is considered to
have a depth of only about 20 m. Second,
NO emissions from motor vehicles are
allowed to react immediately with only
the Oa in close proximity to the roadway.
This treatment of the lowest layer also
considers ground-level emissions from
areal sources and surface removal pro-
cesses. In addition to predicting "ground-
level" concentrations, the algorithm
developed for the lowest layer also pre-
dicts the net flux of each pollutant into the
second layer of grid cells.
Emissions from large point sources are
distributed in grid cells aloft through the
use of a plume rise algorithm. Consider-
ation is given to whether a plume
penetrates an elevated inversion layer,
and, if so, whether it ultimately breaks
through the layer.
The governing equations of the model
are solved through the use of finite
difference relationships. The three-
dimensional equation is split into the
following four fractional steps:
• Advection and diffusion in the x-
direction.
• Advection and diffusion in the y-
direction.
• Advection and diffusion in the z-
direction.
• Chemistry.
Emissions, removal, and microscale
considerations are included in the third
step. The SHASTA algorithm is employed
to calculate pollutant transport, and the
trapezoidal rule is used in the chemistry
step.
Results and Discussion
In project report V, two numerical
integration methods identified as having
features that provided significant im-
provements over the technique originally
embedded in the Airshed model have
been evaluated. Of particular concern
was the treatment of horizontal transport.
The methods examined were the SHASTA
and Egan-Mahoney methods. In several
numerical experiments involving the
transport of an inert pollutant in both one
and two dimensions, we found that the
SHASTA method seems to possess the
best blend of computational speed coupled
with minimum error propagation. Further
tests with a problem involving both
transport and chemical transformations
confirmed the enhanced reliability of this
method over that used previously. In a
final set of experiments, the SHASTA
method was employed in an actual air-
shed simulation of the Los Angeles Basin.
The resulting predictions differed no more
than about 20 percent from those gener-
ated using the original method.
Uptake by the ocean, ground, and biota
is generally acknowledged to be of
considerable importance for some air
pollutants, especially when they are
transported over long distances. The
possible importance of including these
processes in an urban-scale air quality
model has been reviewed, but very little
information exists regarding the rates of
uptake of photochemical pollutants by
characteristic urban materials. The up-
take rates are parameterized through use
of the deposition velocity concept, in
which the rate of uptake is assumed to be
proportional to the pollutant concentra-
tion just above the surface. The propor-
tionality constant (i.e., the deposition
velocity) is influenced by the stability of
the atmosphere and the type of surface,
An algorithm that relates the overall
effective deposition velocity to these two
influences has been implemented. Sensi-
tivity studies using best estimates of the
deposition velocities indicate that surface
removal processes may significantly
affect the concentrations of O3, N02, and
S02 in the Los Angeles Basin. The
specification of uptake para meters for the
Los Angeles Basin is discussed in detail
to aid model users in estimating these
inputs for other urban areas.
Theoretical assessments and model
sensitivity studies indicated the impor-
tance of treating the full three-dimensional
nature of the windfield. As a result, the
model was modified to accept time-
varying, fully three-dimensional wind
mputs(namely, a one-hour-average wind
speed and direction for each grid cell). An
objective analysis technique to prepare
such a windfield using available measure-
ments both at the surface and aloft has
been developed. This technique also
attempts to account for urban heat island
effects. It should be directly applicable to
relatively flat areas, such as St. Louis.
However, it should also be possible to
extend the technique for application to
areas with greater relief.
A chemical kinetic mechanism is one of
the most important components of any
model capable of predicting the concen-
trations of secondary air contaminants. A
42-step mechanism suitable for describ-
ing the chemical transformations of
organics, nitrogen oxides (NOX), Oa, and
SOa and the production of sulfate, nitrate,
and organic aerosols is presented The
organic/NOx/O3 mechanism consists of
32 steps. A unique feature of this mecha-
nism is the explicit consideration given to
the carbon bonds making up each organic
molecule. In simulations of smog chamber
experiments, this mechanism overcomes
some deficiencies exhibited by reaction
schemes previously employed in the
Urban Airshed Model. For the addition of
SO2 and sulfate aerosol prediction capa-
bilities to the model, a seven-step
mechanism describing the conversion of
SOz to sulfate aerosol has been assem-
bled. Three reaction steps were postulated
to describe the formation of organic and
nitrate aerosols.
A discussion of the treatment of rate
constantsfor photolysis reactions used in
the chemical mechanism is also provided,
and through the use of our Multi-Layer
Light-Scattering Model, the influence of
aerosols on the attenuation of sunlight
within a column of polluted air is exam-
ined. The results led to the formulation of
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a linear relationship with height above
the terrain for the photolysis rate con-
stants In effect, the total integrated
aerosol mass in a column of grid cells is
used in conjunction with nominal esti-
mates of the clean air values of the
photolysis rate constants to calculate
values of the rate constants for each grid
cell in that column
In project report VI, techniques for
modeling the microscale phenomena
associated with urban air pollution were
developed. In this context, the term
"microscale" refers to all phenomena
that have characteristics temporal or
spatial scales that are too small to be
resolvable in an explicit, deterministic
manner in urban-scale air pollution
models. Examples of microscale phenom-
ena include turbulent diffusion, turbulent
concentration fluctuations, and subgrid-
scale variations in the time-averaged
concentration field.
In this work the so-called optimal eddy
diffusivities were reexamined to deter-
mine whether (1) the diffusivities are
unique, (2) they have a universal form
when properly scaled, and (3) they are
dependent on source height. Optimal
diffusivities are designed to make the
predictions of the diffusion equation agree
as closely as possible with the mean
concentration distributions derived from
a sophisticated numerical model of turbu-
lence in the planetary boundary layer.
Using a test case for which the analytic
solution of the diffusion equation is
available, it can be shown that the method
used to derive the optimal diffusivity
produces unique results that agree very
closely with the true value. Using concen-
tration data for two different unstable
cases, namely, z,/L = -4.5 and z,/L =
-1100, for all stabilities in the range z,/L
<4.5, it can be shown that the optimal
vertical diffusivity Kz(z) appears to have a
universal form when z is normalized by z,,
the depth of the mixed layer, and when Kz
is scaled with w*z,, where w* is the
convective velocity scale. The universal
form of Kz for a source near ground level
has also been determined. Finally, using
concentration data for sources of different
heights in the same flow, it was found
that the optimal diffusivity depends quite
strongly on the source elevation.
A model for describing the effects of
turbulent concentration fluctuations on
second-order chemical reactions has also
been developed, implemented, and tested.
The model equation contains a reaction
parameter, whose value can be approxi-
mated by unity in most problems of air
pollution, and two mixing parameters.
whose functional forms are determined
solely by the nature of the turbulence and
the configuration of reactant sources. For
given source characteristics, the mixing
parameters can be expressed as universal
functions of the flow conditions. Approx-
imate expressions for the mixing param-
eters applicable to the case where one
reactant is emitted from a point source
into an atmosphere containing a uniform
concentration of a co-reactant have been
derived. Using these expressions, we
applied the model to the case of NO
emanating from a point source into an Os
laden atmosphere and found that the rate
of conversion of NO to N02 is greatly
inhibited by turbulent concentration fluc-
tuations, even under stable conditions.
The predictions of the model compare
well with empirical data from both
atmospheric and laboratory studies.
A method of parameterizing the effects
of chemical reaction rates of both
subgrid-scale concentration variations
arising from ground-level sources and
turbulence-induced concentration fluctu-
ations has also been developed In
essence, the parameterization scheme is
simply a modified lower boundary condi-
tion on the concentration field that takes
into account the effect of subgrid-scale
concentration variations. This scheme
has been implemented in the Airshed
Model and is currently undergoing tests.
The resolution of point source plumes
in grid models of urban air pollution has
been studied and a sub-model capable of
restoring point spatial resolution to any
grid model was developed, but is applica-
ble only to inert and first-order reactants.
Finally, theoretical frameworks for two
models of pollutant levels around road-
ways have been developed. The more
general of the two models can treat
photochemical pollutants; the effects of
turbulent concentration fluctuations pro-
duced by vehicle wake and ambient
turbulence; calm winds or winds parallel
to the roadway; exhaust buoyancy effects;
elevated, depressed, or at-grade high-
ways; pollutant deposition; and other
phenomena normally included in air
pollution models.
In project report VII, a simplified model
of the dynamics of photochemical aero-
sols has been developed, and initial
applications of it have been presented.
The model, which can be incorporated in
or coupled to a photochemical air quality
simulation model, takes into considera-
tion the emissions of particles with
diameters of 0.01 fim to 1.0 fjm and their
growth in this size range by the formation
of secondary aerosol. The formation of
very small particles by homogeneous
nucleation and their subsequent growth
is treated as a boundary condition on the
particle size distribution function at a
diameter of 0.01 /urn. Although coagula-
tion is not included in the model, methods
were studied for obtaining solutions to
the coagulation equation with computa-
tional efficiency.
In the aerosol model, the formation of
paniculate matter is assumed to occur in
two stages—condensable material first
forms in the gas phase and then diffuses
to the particles. A pseudo-steady-state is
assumed in which the rate of formation of
condensable material in the gas phase is
set equal to the rate at which condensa-
tion occurs on particles. Calculations are
presented that justify this assumption for
secondary aerosol production rates and
particle concentrations typical of moder-
ate smog conditions in the Los Angeles
Basin. Estimates are made of the rate of
formation of sulfunc acid droplets by
homogeneous nucleation as a function of
the aerosol number density, the rate of
production of condensable material, and
the relative humidity.
Model simulations are presented for a
batch system (with constant rates of
aerosol production) both with and without
sources of primary aerosol and for a
trajectory system. Model simulations and
smog chamber experiments are in quali-
tative agreement.
Conclusions and
Recommendations
Investigation of numerical methods
appropriate for the solution of the species
transport equation have identified the
SHASTA and Egan-Mahoney algorithms
as numerical integration methods offering
greater accuracy than the existing Price
algorithm currently used in the Urban
Airshed Model. In addition, both the
SHASTA and Egan-Mahoney techniques
have shown promise of being as compu-
tationally efficient as the Price method.
The following conclusions can be drawn
on the basis of the examination of the
SHASTA and Egan-Mahoney algorithms;
• Of all the variants of the SHASTA
technique, the non-flux-limited, non-
mass-conservative formulation appears
to be the most accurate, as well as the
most computationally efficient.
• The non-flux-limited, non-mass-
conservative SHASTA algorithm is
substantially more accurate than the
Price integration method. In the two-
dimensional reactive and nonreactive
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analyses, the predictions of the
SHASTA algorithm were superior to
those of the Price algorithm.
• The SHASTA algorithm, unlike the
Price method, is stable for all values of
the parameter e less than 1 /2. Hence,
simulations over long time intervals do
not exhibit the instability observed
when the Price algorithm is used.
• Although more accurate, the Egan-
Mahoney method requires consider-
ably more computational time and
substantially more computer storage
than the SHASTA method. For a non-
reactive species, such as CO alone,
this technique could most probably be
optimized to produce superior results
at reasonable computing costs for a
three-dimensional problem. In cases
involving many species, however, the
computational costs and storage re-
quirements for the necessary genera-
ting moments would be exorbitant.
• In the future, efforts should be devoted
to optimizing the computer codes and
simulation scheme so as to increase
program efficiency and to reduce exe-
cution time. Searching for an optimal
time step, putting the kinetic mecha-
nism into an individual step, and
computing the reaction rates of every
other time interval are some of the
possible ways in which this objective
could be achieved. In addition, efforts
should be made to keep abreast of the
latest developments in the literature
concerning integration of partial dif-
ferential equations and changes in
computer technology to permit imple-
mentation of methods that are cur-
rently unattractive with the existing
technology.
A simple model for the removal of
gaseous pollutants by surface sinks has
been incorporated into the Urban Airshed
Model. The surface sink model considers
surface removal to occur in two phases—
transport to the surface followed by
adsorption on the surface. The resistance
to surface uptake (the reciprocal of the
deposition velocity) was determined from
deposition velocities measured under
atmospheric conditions that lead to rapid
transport to the surface (that is, so that
surface removal was limited by the sur-
face uptake rate).
Deposition rates have been measured
under the widest range of conditions for
SOz, but even for this pollutant, few
surface types have been studied. Because
of this lack of data, it is necessaryto make
crude estimates for deposition rates over
4
surfaces found in the urban environment.
The improvement of these estimates for
the Los Angeles Basin awaits additional
measurements of deposition velocities
under a variety of meteorological condi-
tions over surfaces common to the Basin.
Sensitivity studies performed with our
estimated deposition rates indicate that
surface uptake of SC>2, NO2, and Oa in the
Basin can have a significant effect on the
concentration of these pollutants.
A new objective-analysis wind field
algorithm has been evaluated and im-
plemented in the Urban Airshed Model on
the basis of general principles and prior
experience. This algorithm will miss some
significant wind-field features, such as
the bending of the thermal cell in the
boundary layer shear zone and effect of
surface friction variations. However, it is
also anticipated that the analysis will
reproduce the most important phenomena
known to influence the urban boundary
layer and will, in particular, avoid intro-
ducing the large spurious features that
might be expected from any algorithm
that depends on influence factors or other
unconstrained interpolation techniques.
The computed horizontal velocity is not
irrotational unless soundings show it to
be so. The total velocity vector is irrota-
tional about a vertical axis. This is, of
course, not perfectly true in nature, but in
most cases the dominant perturbations to
the mean flow are irrotational. In this
case, the only perturbance addressed is
the heat island effect, which is a potential
flow disturbance except to the extent that
it couples to the mean shear profile. Since
the momentum and energy equations
were not used, these second-order effects
could not be addressed.
It is recommended that subgnd-scale
bias be investigated for a typical St. Louis
site by collecting and statistically ana-
lyzing wind records from several (say 5 to
10) surface anemometers placed within
the same grid cell.
Since gas-to-particle conversion is an
important factor in aerosol behavior, one
must understand to a large extent the
gaseous processes as a prerequisite to
understanding aerosol processes. Aero-
sols are influenced not only by the same
advection-diffusion processes that influ-
ence gases, but also by such complex
processes as diffusion of gaseous species
to surfaces, chemical reactions within
particles, and coagulation. Modeling aero-
sols is thus more complicated than
modeling gaseous pollutants. Character-
izing an aerosol requires, in principle, the
distribution of particles by size, compo-
sition, location, and time, which is indi-
cative of the complexity of aerosol model-
ing.
The chemical and physical data neces-
sary for detailed modeling of the size and
composition of an urban aerosol do nol
exist at present. Nevertheless, it is im-
portant that modeling be considered now
so that the types of data needed for
modeling can be elucidated. This report
represents the first phase of an effort to
develop mathematical models for urban
aerosols. We developed much of the
theoretical basis that will ultimately be
required for aerosol modeling. However,
we adopted a somewhat limited objective—
to develop a model capable of predicting
the overall submicron aerosol size dis-
tribution (and therefore the total aerosol
volume and surface area). The model was
formulated in such a way that it could be
included within a gas-phase model.
Although the chemical composition of
a particle influences its rate of growth by
vapor condensation, and the chemical
composition changes with time, explicitly
including particle chemical composition
in a model cannot be justified at this time.
As first approximation, it has been
assumed that the transfer of vapor species
to the aerosol occurs independently of the
particle composition. In spite of the
neglect of particle composition, the inte-
gration of the aerosol model into the
airshed models gas-phase module will
not be a straightforward task because of
the new independent variable, particle
diameter. With only 10 particle diameters
characterizing the aerosol size distribu-
tion, which spans two orders of magni-
tude, an additional 6.25K of storage would
be required to include the aerosol model
into the gas-phase module with a 25x25
grid and no vertical resolution. Further-
more, in a simulation of a seven-hour
period, the current aerosol model would
add roughly 10 minutes of CPU time (CDC
7600 computer) to the computing time,
which represents approximately a 100
percent increase over the current execu-
tion time for the gas-phase module alone.
The aerosol model developed in this
study is capable of predicting the dy-
namics of the size distribution, and its
inclusion in the gas-phase module would
represent a justifiable effort. The portion
of the aerosol model that predicts the rate
of secondary aerosol formation has been
incorporated into the Airshed Model to
predict the total aerosol mass concentra-
tion as a function of location and time.
The major question to be considered at
this point is the direction of further
research. We could add complexity to the
aerosol model by explicitly including
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particle chemical composition and by
developing microscale source-oriented
models that consider coagulation. Another
path would be to integrate the current
model into the gas-phase module and
thoroughly test it with pertinent available
data. Thus, the second path would not
center on further model development but
would focus on application and use of the
current aerosol model. It is recommended
that future work follow the second path.
It is recommended that the following
studies be carried out in conjunction with
the continued development of an urban
aerosol model:
1. The total mass concentration aero-
sol model, currently integrated into
the Airshed Model, should be tested
on available data for Los Angeles
and St. Louis. Sensitivity studies
should be carried out with respect
to gas-to-particle conversion rates.
2. The aerosol model developed in this
study should be integrated into the
Airshed Model. The model should
then be tested on available data for
Los Angeles and St. Louis. Sensi-
tivity studies should be carried out
with respect to primary source
emission rates and particle size
distributions, background aerosol,
and gas-to-particle conversion
rates.
This approach will serve the purpose of
providing a usable urban aerosol model in
the minimum period of time.
J. P. Killus, J. P. Meyer, D. R. Durran, G. E. Anderson, T. N. Jerskey, S. D. Reynolds,
J. Ames, R. G. Lamb, and L E. Reid are with Systems Applications. Inc., San
Rafael, CA 94903; W. R. Shu, J. H. Seinfeld, and F. Gelbard are with the
California Institute of Technology, Pasadena, CA 91109.
Kenneth L. Demerjian is the EPA Project Officer (see below).
The complete report consists of three volumes, entitled "Continued Research in
Mesoscale Air Pollution Simulation Modeling:"
"Volume V. Refinements in Numerical Analysis. Transport, Chemistry, and
Pollutant Removal," (Order No. PB 85-137 362; Cost: $20.50)
"Volume VI. Further Studies in the Modeling of Microscale Phenomena,"
(Order No. PB 85-137 370; Cost: $23.50)
"Volume VII. Mathematical Modeling of Urban A erosol Dynamics," (Order No.
PB 85-137 388; Cost: $19.00)
The above reports will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Atmospheric Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
. S. GOVERNMENT PRINTING OFFICE-. 1985/559-111/10769
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