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OCR for page 161
Mathematical Modeling of
the Effect of Emission
Sources on Atmospheric
Pollutant Concentrations
ARMISTEAD G. RUSSELL
Carnegie Mellon University
Development of Air Quality Models / 162
Components of Exposure / 163 Source/Receptor
Relationships / 163 Historical Perspective / 165
Emission Source Characteristics / 165
Categories of Air Quality Models / 167
Empirical/Statistical Models / 167 Deterministic Models / 169
Temporal and Spatial Resolution of Empirical and Analytical
Models / 173
Modeling Approaches for Individual Processes / 174
Turbulent Transport and Diffusion / 174 Complex Terrain:
Street Canyons / 175 Removal Processes / 175
Representation of Atmospheric Chemistry Through Chemical
Mechanisms / 177 Aerosol Dynamics / 179
Model Evaluation / 181
Approaches for Testing Model Performance / 182 Data
Requirements / 182 Analysis of Model Performance / 184
Application of Air Quality Models / 187
Population Exposure Calculations / 187 Source Apportionment and
Control Strategies / 188 Future Uses / 192
Special Topics and Emerging Issues in Air Quality Modeling / 192
Modeling Large-Scale Processes / 192 Modeling Small-Scale
Processes / 193 Indoor/Outdoor Pollutant Relationships / 193
Conclusion / 195
Summary of Research Recommendations / 196
~ . ,
Air Pollution, the Automobile, and Public Health. @) 1988 by the Health Effects
Institute. National Academy Press, Washington, D.C.
161
OCR for page 162
162
Mathematical Modeling of Effect of Emission Sources
Development of Air knowledge of the chemical and physical
Quality Models
When air pollution began to have a signif
icant deleterious effect on human life, it
became necessary to discover and under
stand the links between emission sources
and the air quality deterioration and health
effects they cause. Only after the impacts of
sources have been assessed correctly will it
be possible to devise and implement ratio
nal, convincing, and effective policies to
improve air quality. Over $29 billion were
spent in the United States in 1983 on air
pollution abatement and control (Council
on Environmental Quality 1984~. If a frac
tion of that expense can be saved by better
understanding the relation of air quality
and health effects to emission sources, the
monetary benefits will be tremendous.
Knowledge of the relation between emis
sions by a source and pollutant concentra
tions in the air at later times and other
places (that is, the source/receptor relation
ship) is essential to calculating the exposure
of humans to these pollutants and hence to
predicting the health impacts resulting
from these source emissions. Mathematical
models have evolved as the most practical
means to relate source emissions to the
subsequent air pollution concentrations.
Mathematical models integrate our
Emissions
(Johnson)
~~
Atmospheric
chemistry
(Atkinson)
. ~
_ ~
1
=====
Mathematical .
air quality .
model(s)
(This chapter)
.
Transport
. (Samson)
_ =~ .
Indoor and outdoor
pollutant
concentrations
(Graedel)
Figure 1. Steps required to link source emissions to health effects.
processes ot pollutant dynamics Into a
structured framework that can be used to
explain the relationship between sources
such as motor vehicle exhaust and the
resulting impact on human health (figure
1~. The multistep process begins with char-
acterizing the emissions. The second step is
to accurately determine the effects that at-
mospheric transport and chemical reactions
have on pollutant concentrations. Mathe-
matical models are ideally suited to this
task. The next step is to correlate people's
activities with pollutant concentrations and
determine personal exposure. Exposure is
related, through deposition in and absorp-
tion by the respiratory tract tissues, to
dose. Finally, dose is related to health ef-
fects. Central to this process is the ability to
accurately calculate the air quality contri-
butions due to specific emission sources.
This chapter reviews the development
and current status of air quality models. It
differs from previous reviews in emphasiz-
ing the use of models in health-related
studies. It also assesses the current state of
air quality modeling technology. As a log-
ical outcome, gaps in our current under-
standing are highlighted and research op-
portunities identified. Chemically reacting
pollutant systems receive extra attention
for two reasons: first, many of the signifi
. .4, ~
,
,
Personal exposure
and dose
(*)
*Sexton and Ryan
Schlesinger
Sun, Bond and Dahl
Ultman
Overton and Miller
'L it'
1
_
Health
effects
Relevant chapters in this volume are given
in parentheses. Central to the process is a mathematical model to predict pollutant concentrations as a function of
emissions. Depending on the study, more than one model may be required, for example, to predict indoor
pollutant concentrations. Up to this point, mathematical modeling studies have been limited almost exclusively
to the steps within the boxed area.
OCR for page 163
Armistead G. Russell
163
cant components of automotive exhaust are
very reactive and contribute to the forma-
tion of secondary products that are of as
much, or more, concern as the original
components; and second, air quality mod-
els that include descriptions of atmospheric
chemistry are the most thorough and com-
plete and will be the basis for future ad-
vanced models. By comparing our present
knowledge with current needs, we can
identify what these advances are likely to
be. This chapter is intended for researchers
interested in relating automotive emissions
to the resulting health effects, not primarily
for specialists in air quality modeling, and
is organized to show how mathematical
models are useful for providing critical
information needed by the health effects
community.
Components of Exposure
Human exposure to a pollutant, and its
consequent impact on health, results from
the simultaneous occurrence of two
events a pollutant concentration c~x,tJ at
point x and time t, and the presence of
people:
Exposure = f[P(x, t), crux, t)]
where P(x,tJ represents the number of peo-
ple at point x and time t inhaling a pollutant
at concentration c~x,tJ. Sexton and Ryan
(this volume) explain in detail the three
components of personal exposure: magni-
tude of the concentration, duration, and (if
the exposure is a discrete event that recurs)
frequency; or, more generally, the magni-
tude c~x,tJ of the concentration as a func-
tion of the path of the subject characterized
by his or her position x at all times t for the
duration of the time interval in which ex-
posure takes place. This chapter discusses
how air quality models can be used to
determine how c~x,tJ depends on emission
sources.
Source/Receptor Relationships
The most direct method for observing the
effect of a single air pollution source is to
eliminate it completely, but complete elim-
ination is usually impractical or impossible.
A more feasible method is needed to pre-
dict the impacts of emission sources on air
quality. Two distinctly different methods
have been developed for making such pre-
dictions: mathematical models and physical
models. A mathematical air quality model
simulates pollutant evolution by interrelat-
ing symbolic descriptions of the important
physical and chemical processes occurring
in the atmosphere within a computational
framework. A physical model simulates
atmospheric processes with a scaled-down
representation of the atmosphere in a labo-
ratory setting. The most common example
of a physical model is a smog chamber used
to study atmospheric chemistry. Another
example is wind tunnel testing using scale
models of buildings to observe the trans-
port of pollutants in city street canyons.
Mathematical models have a number of
advantages over physical models when the
question is to find out how much of each
air pollutant at a given location is due to
each particular emission source a process
called source apportionment. For example,
smog chambers can only be used to study
atmospheric chemical reactions in a fixed
location and are not suited to simulate the
effects of diffusion, changing spatial and
temporal emission patterns, pollutant dep-
osition at the ground, and varying meteo-
rological conditions. On the other hand, by
accurately describing the dynamics of pol-
lutants as they travel from the many emis
. .
sion sites in a City to a samp ing, or recep-
tor, site, a mathematical model can keep
track of the separate contributions of the
sources of pollutants that influence air qual-
ity at a given location. The inputs to the
calculation are the pollutant emission rates,
and the output is the expected concentra-
tions of the several atmospheric pollutants
(figure 2~.
Mathematical models used in air pollu-
tion analysis fall into two types: empirical/
statistical and analytical/deterministic. In
the former, the model statistically relates
observed air quality data to the accompa-
nying emission patterns, whereas chemis-
try and meteorology are included only im-
plicitly (Seinfeld 19751. In the latter,
analytical expressions describe the complex
transport and chemical processes involving
air pollutants. The pollutant concentrations
OCR for page 164
164
Mathematical Modeling of Effect of Emission Sources
~,~j~ i, ~
INPUTS
Emissions
Land use
Topography
Initial concentrations
Background concentrations
Meteorology
Windfields
Turbulence
Temperature
Humidity
Mixing depth
Precipitation
Fog concentration
Mathematical
Model
MODEL TYPES
Empirical statistical
Rollback
Receptor models
Analytical deterministic
Transport
Gaussian plume
Lagrangian trajectory
Marked particle
Eulerian
Photochemical
Box model
Lagrangian trajectory
Eulerian grid
OUTPUTS
~ Pollutant concentrations
Source impacts
Figure 2. Inputs, outputs, and types of models commonly used in air quality
modeling studies.
are determined as explicit functions of the
meteorology, topography, chemical trans-
formation, and source characteristics,
which are inputs to the calculation.
The subject matter of this chapter neces-
sarily overlaps that of other chapters of this
book. To minimize duplication, this chap-
ter focuses on how mathematical models
are used to predict pollutant concentrations
as a function of emissions. Greatest atten-
tion is given to pollutants that are either
known to be or suspected of being harmful
to human health and to modeling on a scale
appropriate to urban areas where pollutant
concentrations and population densities are
highest.
Our discussion begins with a section
devoted to understanding the physical and
chemical nature of the emissions, for these,
in part, determine important characteristics
that should be described by a mathematical
model. Because of chemical reactions in the
atmosphere, the dynamics of some auto
. . . .
motive emissions anc . reaction proc ucts
depend on the presence of other anthrono-
genic and natural sources, and it Is often
insufficient to consider one without the
other. After the important emission source
types have been identified, it is necessary to
choose an appropriate model for each ap-
plication. The different types of air quality
models that are available are reviewed in
the next section along with possible ad
vances that could be made in their structure
and application.
The section on modeling approaches
presents our current understanding of the
various individual physical and chemical
processes (for example, transport, chemical
reaction, dry deposition) that affect pollut-
ant concentration in the atmosphere. A
model's capabilities are determined by the
level of detail at which each of the processes
is described within the modeling frame-
work. Many future advances in air quality
modeling will come from better quantita-
tive descriptions of individual processes, so
a number of topics for fruitful research
evolve from this section. The theoretical
basis and accuracy of the complete model,
each of its components, and the structure
interrelating the components must be eval-
uated, as described in the succeeding sec-
t~on.
After a model has been evaluated, it is
ready for use in conducting source appor-
tionment, population exposure, and con-
trol strategy studies, as discussed in the
next section. Studies of this type are of
great interest, but few comprehensive con-
trol strategy studies have been conducted
using state-of-the-art air quality models.
Finally, a section addressing special topics
and emerging issues in air quality modeling
is followed by a summary of research rec-
ommendations.
OCR for page 165
Armistead G. Russell
165
Historical Perspective
The driving force behind the development
of mathematical air quality models has been
the Clean Air Act (American Meteorolog-
ical Society 1981~. Models have been used
to demonstrate compliance with regulatory
standards and to guide regulatory agencies
toward possible emission control strategies
for improving air quality. Air quality mod-
els motivated by the Clean Air Act are
designed primarily to predict the concen-
trations of pollutants such as carbon mon-
oxide (CO), nitrogen dioxide (NO2), and
ozone (03) that have been regulated by the
federal government for many years, but
not those of many trace toxic pollutants
that are already of growing interest to
health effects researchers and are likely to
be subject to regulation in the future.
By the early 1970s, analytical models had
been developed to the point that it was
possible to predict the concentrations of
pollutants such as CO that are largely de-
termined by transport but not by atmo-
spheric chemical reaction. The next step
was to incorporate atmospheric chemistry
into the model to describe the dynamics of
pollutants, such as O3 and NO2 that are
chemically active in the atmosphere (see,
for example, Transportation Research Board
1976~. By the early 1980s, photochemical
airshed models had been developed that
could accurately predict O3 and NO2 con-
centrations as a function of emissions. At
present, a limiting factor in our ability to
describe the dynamics of these two pollutants
in an urban area is the availability of high-
quality input data, not the model itself.
On the near horizon are models that
describe aerosol processes in the atmo-
sphere. So far, modeling studies have con-
centrated on specific aspects of the many
different processes that control the size and
composition of particulate matter in the
atmosphere. Advances in this area are vital
for providing better assessments of health
. ~ . .
Impacts ot emission sources.
The past decade has seen rapid develop-
ment of empirical/statistical air quality
models. Most models of the early 1970s
assumed that basinwide air quality changed
in direct proportion to total basinwide
emissions. These "rollback" models were
applied to basinwide emissions to predict
concentrations of chemically inert as well as
chemically reactive pollutants. Rollback
models are limited in application because
they ignore important effects due to the
spatial distribution of emission source
changes and atmospheric chemistry. Em-
pirical receptor-oriented models that use
the chemical composition of ambient pol-
lution samples as a tracer for pollutant ori-
gin were introduced in the 1970s, but were
initially applied in only a few cases. Because
they accurately resolve source contribu
. . . .
tons to particulate matter concentrations,
receptor models are now widely accepted
as a replacement for rollback models.
Although there are still critical aspects of
present models that could be improved, it
is clearly time for more extensive use of mo-
dels for explaining relationships between
sources and health effects. A particularly
pressing issue that can be studied using pres-
ent models is the relationship between the
nitrogen oxide emissions (NO and NO2 and
the sum is commonly symbolized schemat-
ically as NOX) and organic gas emissions in
the formation of O3 (the O3-precursor re-
lationship-see Pitts et al. 1976; Chock et
al. 1983; Pitts et al. 1983~. If resources are
provided, the next decade should see mod-
els that are able to describe the dynamics of
aerosols and currently unregulated toxic
gases and to resolve many current ques-
tions about sources and air quality.
An important but historically underused
facet of mathematical models is that they
collect and codify what is understood about
the constituent processes in a large system
such as the atmosphere. In cases where
models fail to perform well, they then
reveal what is not understood. In this way,
evaluation of model performance directs
our attention to fruitful problems and top-
ics for further research.
Emission Source
Characteristics
The composition of emissions from mobile
sources is discussed in detail by Johnson,
OCR for page 166
166
Mathematical Modeling of Effect of Emission Sources
and atmospheric chemical transformations
and transport are covered in chapters by
Atkinson and Samson, respectively (all in
this volume). It is important to realize that
if the air quality model is to be an effective
tool for predicting pollutant concentrations
and health effects and devising strategies for
controlling them, the essential characteris-
tics of the sources must be retained within
the model. For example, the dynamic be-
havior of power plant plumes is very dif-
ferent from that of automotive tail pipe
emissions in that plumes are not immedi-
ately dispersed by the motion of and tur-
bulence surrounding the source, but rise
hundreds of meters because of thermal
buoyancy. Likewise, the chemical compo
. . . . . . . .
SltlOn 01 automotive emlSSlOnS IS quite C .11
ferent from that of power plant emissions.
Consequently, it is useful to divide all
sources into two categories: mobile and
stationary. Most of the total mass of emis-
sions from mobile sources comes from
automobiles and trucks, but rail vehicles,
ships, aircraft, motorcycles and off-the-
road vehicles also make a contribution.
Stationary sources are divided further into
two classes: anthropogenic and natural
emitters.
It is imprudent to neglect stationary
sources when characterizing the impact of
mobile source emissions. Chemical com-
pounds emitted from stationary sources
react extensively with automotive emis-
sions to form various substances in the air.
A classic example is the formation of O3 in
urban areas. NOx emissions (primarily
from automobiles, trucks, and stationary
source combustion) react with hydrocar-
bons (HCs) from mobile and stationary
sources to form O3 and other photochem-
ical oxidants (Atkinson, this volume).
Most mobile source emissions are gener-
ated by combustion, but other noncom-
bustion releases occur. Significant quanti-
ties of HCs come from fuel evaporation,
and particulate matter originates from tire
wear, brake wear, and road dust. Auto
exhaust contains NO, NO2, CO, organics
(commonly referred to as HCs), NH3, and
a variety of particulate species such as aero-
sol carbon, lead (especially in older vehi
cles), and bromine. Near the source, the
pollutants are rapidly mixed by turbulence
generated mechanically from the move-
ment of the automobiles. After initial mix-
ing, the pollutants move away from the
road by convection, and are further dis-
persed by atmospheric turbulence and
transport.
Stationary sources, such as power plants
and industrial complexes, and natural
sources such as forest canopies, emit HCs,
NOx, sulfur oxides (SO2 and SO3, com-
monly called SOx), NH3, particulate mat-
ter, and CO. Large point sources often
emit from tall stacks, and the momentum
and buoyancy of the emitted gas can carry
the pollutants above the mixed layer, re-
ducing their local impact, but increasing
their persistence in the atmosphere over
long distances.
Organic compounds and NOx emissions
are both involved in reactions leading to
the formation of 03, NO2, nitric aclct
(HNO3), particulate nitrate (NOT ), peroxy-
acetyl nitrate (PAN), and other oxidized
and nitrated organic compounds, and can
increase the oxidation rate of sulfur dioxide
(SOT. Some of the compounds formed in
the atmosphere by gas-phase reactions in-
volving automotive exhaust compounds
are mutagenic and potentially carcinogenic,
for example nitroarenes (Pitts and Winer
1984), nitro-polycyclic aromatic hydrocar-
bons (nitro-PAHs) (Grosjean et al. 1983),
and nitroxyperoxyalkyl nitrates and dini-
trates (Bandow et al. 1980; Atkinson et al.
1984~. Less effort has been devoted to de-
veloping mathematical models that will
. . .
estimate concentrations anc . source contrl-
butions to the formation of these toxic trace
species for a number of reasons: these spe-
cies are not regulated, few data exist to
quantify their ambient concentrations, and
the chemistry leading to their formation is
not completely understood. The necessary
data are beginning to be assembled, and the
use of mathematical models to study the
formation and transport of trace, muta
. . . .
genlc, anc . caranogenlc organic com-
pounds will become an important activity
in the future.
Primary organic particulates, soot (also
_ _ 7
OCR for page 167
Armistead G. Russell
167
called elemental carbon or graphitic car-
bon), lead, and bromine compounds do not
participate extensively in the photochemi-
cal reactions but can be affected by gas-
phase pollutants. Studies are beginning to
elucidate the extent of formation of second-
ary atmospheric organic particulates and
the conversion of compounds from one
type to another while in the aerosol phase.
For modeling purposes, there are two
distinct types of emissions: unreactive and
reactive. Unreactive emissions include CO,
lead, soot, and some fraction of the organic
particulates. (CO participates in photo-
chemical reactions, but its concentration is
determined predominantly by direct CO
emissions. Pollutants are referred to as un-
reactive if reactions do not appreciably af-
fect their concentrations over the time
scales being modeled.) Reactive pollutants
include HCs, NOX, and SO2, which can
react to form secondary pollutants such as
03, PAN, and aerosol sulfates. As will be
discussed in the next section, it is often
more efficient and sometimes necessary to
use different types of mathematical models
to describe the dynamics of these two cat-
egories of pollutants.
Categories of Air Quality
Models
Health effects can arise from exposure to a
single pollutant species or from combined
actions and interactions of a mixture of
compounds the subject is exposed to. The
health effects of short-term exposure to
high concentrations may not be equivalent
to those from longer contact with moderate
levels of the pollutant of interest. These
alternatives must be reflected in the choice
of models used to establish connections
between sources and ultimate health effects.
First, the pollutants and the time and spatial
scales of interest are defined, and then an
appropriate Codeless is chosen. Models
have been formulated in a number of ways.
Each formulation involves certain approx-
imations and has certain strengths and lim-
itations. This chapter shows how models
can be used for relating health effects to
sources. Consequently, limitations and
strengths are stressed to assist in choosing
the most effective models to best utilize the
available resources.
If care is not exercised In Choosing a
model, one of two undesirable outcomes
may ensue: a model may be chosen that by
its formulation is incapable of doing the job
(such as using a nonchemically reactive
model to estimate the concentrations of 03,
PAN, and even NO2), or a model is chosen
that is more complex and time-consuming
than is necessary (such as a photochemical
airshed model to estimate elemental carbon
or CO levels in an area heavily impacted by
mobile source emissions).
Empirical/Statistical Models
Mathematical air quality models are of one
of two types: empirical/statistical or deter-
ministic (figure 2~. Empirical/statistical
models, such as receptor-oriented and roll-
back models, are based on establishing a
relationship between historically observed
air quality and the corresponding emis-
sions. The linear rollback model is simple
to use and requires few data, and for those
reasons has been widely used (see, for
example, Barth 1970; South Coast Air
Quality Management District and South-
ern California Association of Governments
1982~. Linear rollback models assume that
the highest measured pollutant concentra-
tion is proportional to the basinwide emis-
sion rate, plus the background value; that
Is,
Cmax = aE + Cb (1)
where cmax is the maximum measured pol-
lutant concentration, E is the emission rate,
cb is the background concentration due to
sources outside the modeling region, and a
is the constant of proportionality. The con-
stant a accounts for the dispersion, trans-
port, deposition, and chemical reactions of
the pollutant. Thus, the allowable emission
rate, Ea' necessary to reach a desired ambi-
ent air quality goal, c,t, using the linear
rollback model can be calculated from
OCR for page 168
168
Mathematical Modeling of Effect of Emission Sources
Ea ca,- Cb
_= (2)
Eo CmaX - Cb
where Eo is the emission rate that prevailed
at the time that cmax was observed. Presum-
ably, pollutant concentrations at other
times would also decrease toward back-
ground levels as emissions are reduced, and
similar expressions can be written for relat-
ing annual mean concentrations to emission
rates. Obviously this is a very simplified
approach, and its application is limited.
Nonlinear processes such as chemical reac-
tions and spatial or temporal changes in the
emission patterns are not accounted for
explicitly in the rollback model formula-
tion.
A second class of empirical/statistical
models of continuing interest is the recep-
tor-oriented model, used extensively for
estimating source contributions to particu-
late matter concentrations in a number of
geographic areas (Friedlander 1973; Heis-
ler et al. 1973; Gartrell and Friedlander
1975; Gatz 1975, 1978; Gordon 1980; Wat-
son et al. 1981; Cass and McRae 1983;
Watson 1984; Hopke 1985~. Nonreacting
gases have also been tracked by receptor
modeling methods (Yamartino 1983~. Re-
ceptor models compare the measured
chemical composition of particulate mat-
ter concentrations at a receptor site with
the chemical composition of emissions
from the major sources to identify the
source contributions at ambient monitor
. .
ng sites.
There are three major categories of re-
ceptor models: chemical mass balance,
multivariate, and microscopic. Hybrid an-
alytical and receptor (or combined source/
receptor) models have been proposed and
used, but further investigation into their
capabilities is required.
~. .
.
Receptor models are powerful tools for
source apportionment because of the vast
amount of particulate species characteriza-
tion data routinely collected at many sam-
pling sites within the United States. Most
of the information available is for elemental
concentrations (for example, lead, nickel,
aluminum) although recent measurements
are leading to increased data on concentra
tions of compounds such as ionic species
and carbon compounds. At a sampling (or
receptor) site, the aerosol mass concentra-
tion of each species i is
n
~ aijS; i= 1, 2, . . . m (3)
j=1
where ci is the mass concentration of species
i at the receptor site; Sj is the total mass
concentration of all species emitted by
source category j as found at the receptor
site; aij is the fraction of the total mass from
source j emitted as species i arriving at the
sampling site; m is the total number of
species measured; and n is the total number
of sources. The mass concentration ci mea-
sured at the receptor site of interest and
the coefficients aij that describe the chemical
composition for the major sources are the
inputs from which Sj, the mass apportioned
to sourcej, is determined. Because aid char-
acterizes the source, it is referred to as the
source fingerprint and should be unique to
the source. When the chemical composition
of the emissions from two source catego-
ries are similar, it is extremely difficult for
receptor models to distinguish between the
sources. The categories of receptor models
are differentiated by the techniques used to
determine Sj.
Chemical Mass Balance Methods. Given
that the source fingerprints aid for each of n
sources are known, and that the number of
sources is less than or equal to the number
of measured species (n ' m), an estimate for
the solution to the system of equations in
equation 3 can be obtained. If m > n, then
the set of equations is overdetermined, and
least-squares or linear programming tech-
niques are used to solve for Sj. This is
the basis of the chemical mass balance
(CMB) method (Miller et al. 1972; Cooper
and Watson 1980~. If each source emits a
particular species unique to it (commonly
called a tracer species), then a very simple
tracer technique can be used (Friedlander
1977~. Examples of tracers commonly used
are lead and bromine from mobile sources,
nickel from fuel oil, and sodium from sea
OCR for page 169
Armistead G. Russell
169
salt. Often the necessary condition to use
the latter method that each source have a
tracer species unique to itself-is not met in
practice.
Microscopic identification models are
similar to the CMB methods except that
more information is included that distin-
guishes the source of the aerosol. Such
chemical or morphological data include
particle size and individual particle compo-
sition and are often obtained by electron or
optical microscopy.
Multivariate Models. Multivariate mod-
els, including factor analysis models
(Henry and Hidy 1979, 1982; Hopke 1981,
1985), rely on finding the underlying struc-
ture of large sets of particulate air quality
data in order to determine the sources of
the aerosol. Models based on factor analysis
are the most widely used. Multivariate
models operate by identifying bundles of
elements whose concentrations fluctuate
together from day to day, implying that
these bundles come from a single "source."
When the composition of the hypothetical
source is compared to the known compo-
sition of specific sources, it often becomes
obvious what the group of cofluctuating
chemical elements stand for. For example,
lead and bromine concentrations are usu-
ally highly correlated because they are
emitted primarily by the same sources (au-
tomobiles burning leaded gasoline). Thus,
multivariate techniques identify groups of
pollutants whose concentrations are corre-
lated, and thus suggest the nature of the
source. They do not rely on a detailed
knowledge of the source fingerprint, aid,
and can be used to refine estimates of the
fingerprint.
Research intended to extend the power
of receptor models for source apportion-
ment is continuing, including development
of methods to integrate measurement un-
certainties into the analysis, incorporation
of aerosol properties other than elemental
composition, and inclusion of the effect of
chemical reactions on secondary aerosol
formation. Friedlander (1981) has proposed
a method that includes a decay factor in the
formulation of equation 3 to take into
account the chemical transformation of
aerosols such as PAHs. This method is
limited to first-order decay and assumes a
knowledge of the average pollutant resi-
dence time in the atmosphere. A more
general technique that can be used to esti-
mate the source contributions to secondary
aerosol mass loadings using receptor mod-
eling techniques would be of use.
Attempts to circumvent some of the
limitations of receptor models include hy-
bridization with source-oriented models
that rely on mass emission rate data from
the pollutant sources. Applications of this
sort have met with varying success (Gar-
trell and Friedlander 1975; Pace 1979; Ya-
martino and Lamich 1979~. Yamartino and
Lamich used a hybrid model to identify
areas with noninventoried emissions of
CO. In theory, the source strengths of
noninventoried or unknown emitters could
be estimated using a hybrid technique, al-
though uncertainty and sensitivity analyses
need to be conducted on this type of model.
Pace used a microinventory approach, as-
suming that most of the aerosol mass at a
receptor is derived from nearby emitters,
and was able to account for total suspended
particulate concentrations (TSP) with a
standard error of 17 percent. Note that
hybrid models require additional data (that
is, source strengths and meteorological
data), but the prospects of added accuracy
can justify the added effort. Hybrid models
potentially could account for the secondary
aerosols present in source apportionment
studies. Further development and use of
hybrid models is clearly warranted, since
they potentially retain the strength of re-
ceptor-oriented as well as source-oriented
(analytical) models.
· Recommendation 1. Research should
continue on the development of receptor
models, especially on the hybridization of
these models with other types of models.
The inclusion of aerosol properties and
formation should also be pursued.
Deterministic Models
Deterministic air quality models describe in
a fundamental manner the individual pro-
cesses that affect the evolution of pollutant
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Representative terms from entire chapter:
emission sources
170
concentrations. These models are based on
solving the atmospheric diŁusion/reaction
equation, which is in essence the conserva-
tion-of-mass principle for each pollutant
species (Lamb and Seinfeld 19731:
dci
-+ U Vci = V D`Vc
at
+ Ri(Cl, C2, C3, · · · en)
+ Si(x, t) i= 1, 2, 3, . . ., n (4)
where ci is the concentration of species i; U
is the wind velocity vector; Di is the mo-
lecular diŁusivity of species i; Ri is the net
production (depletion if negative) of species
i by chemical reaction; Si is the emission
rate of i from sources; and n is the number
of species. R can also be a function of the
meteorological variables. In essence, this
equation states that the time rate of change
of a pollutant (term 1) depends on convec-
tive transport (2), diffusion (3), chemical
reactions (4), and emissions (5). As dis-
cussed in the chapter on pollutant transport
(Samson, this volume), the closure prob-
lem makes it necessary to approximate this
equation, usually by K-theory (Lamb 1973):
foci) + (O . V
Armistead G. Russell
A
Air parcel moving t , 4( x t) Lagrangian
along trajectory_ ~ = - (( x t) coordinates
A< T
Column i ,~ -~
height , it(c) "`
z H t) ,' l i ~
' , LED '71 z(t) Mixing height
ANY ~__ ~ . variation along
~x ~ JO ~ . trajectory path
Euterian ~1
coordinates / V9C - K d
Trajectory path do
B
2 ~deli+ 2
zj R(c,)-i
T i-2
zz~l. 1
Liz 1 2
Figure 3. Schematic diagram of a Lagrangian trajec-
tory model: (A) The column of air being modeled is
adverted at the local wind velocity along a trajectory
path across the modeling region. Within the moving
air parcel, the model describes the important processes
affecting the pollutant (i) evolution and concentration
(c) such as chemical reactions (R), deposition (VR)'
emissions (E), and vertical diffusion (Knot). (B) Verti-
cal resolution is gained by dividing the column into a
number of cells in the vertical direction.
height fields, deposition parameters, and
data on the spatial distribution of emis-
sions. Lagrangian trajectory models assume
that vertical wind shear and horizontal dif-
fusion are negligible. Other limitations of
trajectory and Eulerian models are dis-
cussed by Liu and Seinfeld (1975~.
Gaussian Plume Model. One of the basic
and more widely used transport models
based on equation 5 is the Gaussian plume
model (figure 4~. Gaussian plume models
for continuous sources can be obtained
from statistical arguments or can be derived
by solving:
- Bc 62c 62c
U ~ = Kyy ~ 2 + Kzz ,~z2 (7)
where U is the temporally and vertically
averaged wind velocity; x, y, and z are the
171
distances in the downwind, crosswind, and
vertical directions, respectively; and Ky
and Kzz are the horizontal and vertical
turbulent difFusivities, respectively. For a
source with an effective height H. with
emission rate Q. and a reflecting (nonab-
sorbing) boundary at the ground, the solu-
tion is:
Y ~27,U(,y~x~az~x) P fx1
o
~ 2trzZ~x) xp 2(1i~:X' 1 (8)
LIZ' This solution describes a plume with a
Gaussian distribution of pollutant concen
trations, where tTy(X) and Mix) are the
standard deviations of the mean concentra
tion in the y and z directions (figure 3~. The
standard deviations are the directional dif
fusion parameters, and are assumed to be
related simply to the turbulent diffusivities,
Kyy and K=z. In practice, crux) and a=(x)
are functions of x, U. and the atmospheric
stability as discussed by Samson (this vol
ume), Gifford (1961), and Turner (1964,
1967~.
Gaussian plume models are easy to use,
//
no''\ ~
\
X
Figure 4. Diffusion of pollutants from a point
source. Pollutant concentrations have separate Gaus-
sian distributions in both the horizontal (y) and verti-
cal (z) directions. The spread is parameterized by the
standard deviations (a) which are related to the diffu-
sivity (K).
196
Mathematical Modeling of Effect of Emission Sources
actual physical phenomena involved. Dep-
osition processes and some aspects of aero-
sol dynamics fall in this category. On the
other hand, development of advanced
chemical mechanisms is quite possible us-
ing our present knowledge of atmospheric
chemistry.
Inclusion of aerosol processes within fu-
ture air quality models was identified as a
key area for future research, particularly
because of the suspected health effects of
small particles. The ability to relate particle
size and composition to the original
sources will be critical in future exposure
and impact studies. By advancing air qual-
ity modeling methods now, we will be able
to answer questions that now face us and be
situated to address, in a timely manner,
questions that arise in the future.
It is clear that models now can predict the
dynamics of the regulated pollutants such
as CO, NO2, 03, and some components
of particulate matter directly from data
on emissions and thus are well suited for
defining source-air quality relationships
for those pollutants. However, it is also
clear that this capability has been extended
to only a few of the many nonreguiateu
pollutants that may be of interest to the
health effects research community in the
future. Inasmuch as regulation has been the
principal driving force for model develop-
ment, this is understandable. However,
progress in expanding model capabilities
could be encouraged if toxicologists and
epidemiologists collaborated with physical
scientists to specify the additional pollu
. . .
tents, concentrations, anc . averaging times
of interest, so that air quality scientists
could develop or modify models to suit the
specific needs of the health effects research
community and anticipate the demands
likely to arise from future regulation.
Clearly the research proposed here would
involve a variety of disciplines. This coop-
eration would lead to a better understand-
ing of the sources of the pollutants that
impact human health.
~.
Summary of Research Recommendations
Evaluating the present state of mathematical modeling as a
means to relate emissions to air quality and consequently health
effects points to a number of areas for promising research. How-
ever, advances in mathematical air quality models are ultimately
limited by our understanding of the basic physics and chemistry
being described within the model. In this regard, Samson and
Atkinson (both this volume) have identified research that would
enhance mathematical modeling of air quality by improving the
understanding of the underlying physical and chemical processes
on which such models are based.
We are currently able to describe mathematically the dynamics of
unreactive pollutants in urban areas with a great deal of confidence.
In addition, our ability to model NO2 and O3 is well advanced,
though the issues that surround the effect of NOx controls on O3
air quality still should be resolved. Recommendations 5 and 7
(detailed below) would result in greatly increased confidence in
model predictions and lead to answering major questions. Much of
the limitation to developing a greater capability for defining
source/air quality relationships is not due to the model itself, but
rather to a lack of accurate data for use in the models.
Processes affecting the formation and growth of aerosols are not
nearly as well understood as processes involving the gas-phase
alone. The ability to model aerosol dynamics is, likewise, relatively
undeveloped. This is understandable. It was necessary to develop
Armistead G. Russell
197
gas-phase models before attempting a complete description of
aerosol processes, because the formation and growth of aerosols is
directly affected by gas-phase compounds, whereas the gas-phase is
only slightly affected by aerosols. Presently, photochemical air
quality models are able to provide the basis for an aerosol processes
model. Because of the importance of inhalation of aerosols to
human health, an aerosol process model is essential in determining
source/health effects relationships. Recommendation 6, below,
would lead to rapid development of a comprehensive aerosol
process air quality model.
The final step in constructing a system for determining source/
air quality relationships for use in exposure studies involves devel-
oping a comprehensive indoor air quality model, as described by
Recommendation 9. The model envisioned would include gas-
phase chemistry as well as aerosol dynamics, and hence relies on
completing the first three projects.
Completion of the four high-priority research recommendations
listed below is essential to an improved understanding of relation-
ships between sources and health effects. A number of moderate-
and lower-priority research recommendations arising from consid-
erations in the text are listed next. Undoubtedly there are others
whose urgency and importance will command attention as the
field evolves. The following recommendations emphasize research
efforts that will rapidly increase the capability to apply air qua-
lity models to describe the dynamics of air pollutants believed
to be harmful to health, and to identify the sources of those
pollutants.
HIGH PRIORITY
Recommendations Development of an accurate, condensed chemical mechanism
Construction of an would increase the confidence in using models to assess source
Advanced Chemical impacts on air quality and could be used to examine the dynamics
Mechanism of compounds suspected of causing health problems. The mecha
nism should accurately reproduce smog chamber experiments
, , ~ ,
when the expected wall radical source is included and agree with a
large explicit "master" mechanism that includes a detailed descrip
tion of atmospheric chemistry as it is now understood. As discussed
by Leone and Seinfeld (1985), the concentration predictions from
that condensed mechanism (including trace radical species) as well
as the relative production routes of various species such as O3
should be close to the predictions of an explicit mechanism over a
variety of initial conditions and emission rates during the simula
tion. The condensed mechanism must be small enough to be used
in an urban air quality model. The mechanism should then be
incorporated into one of the advanced air quality models, and
research Recommendation 7 then should be pursued.
Recommendation 7 The most advanced air quality models should be compared
Model Comparison against each other and against field experimental observations,
and Evaluation using a detailed and accurate set of input and verification data.
Collection of the needed data is vital to air quality model develop
ment. Reasons for any discrepancies should be identified. Input
198
Mathematical Modeling of Effect of Emission Sources
data preparation would need to be well documented and open to
review. A major issue to be addressed as part of this study concerns
the effect of NOx emissions on the formation of O3 (Pitts et al.
1983~. Previous modeling studies of the problem have been con-
ducted with differing conclusions. It is very important to reconcile
these conflicting findings, and this type of project is the most direct
method to do so.
Recommendations The scientific knowledge currently exists that would permit
Aerosol Process development of models for basic atmospheric aerosol processes,
Model Development but the atmospheric data needed to conduct preliminary tests of
such a model are not available. What is required are size-resolved
and chemically resolved aerosol measurements collected in a man
ner that can be fully utilized for model development. A three-step
procedure is suggested:
a. Preliminary model calculations should be made using the
limited data currently available to identify specific parameters that
need to be well characterized during a large-scale aerosol measure
ment experiment.
b. A measurement program should be designed and conducted
to obtain the data identified in step (a).
c. The results of steps (a) and (b) could then be used for more
detailed model development and more thorough model testing.
The model should include reactions leading to highly toxic com
pounds, such as PAH reactions with NOx.
Recommendation 9 Indoor air quality models complementary to outdoor air quality
Indoor Air Quality models are needed to relate indoor air quality and exposure to
Modeling sources. Mathematical models are currently under development,
along with characterization of important input parameters. Further
work is needed, especially to advance model descriptions of
gas-phase chemistry, deposition, and aerosol dynamics indoors.
Receptor-oriented models have received less attention for indoor
applications, although they could be a powerful tool for use in
_ . ~
source apportionment studies. Results from indoor air quality
studies that relate indoor pollutant concentrations to those out
doors can be combined with similar studies on outdoor air to help
develop air quality standards and conduct source-related health
impact studies.
MODERATE PRIORITY
Recommendation 3 Dry deposition of chemically reactive air pollutants and aerosols
Pollutant Deposition is an area of current research interest. Given the importance to the
Modeling fate and impact of pollutants, and as a vital part of any modeling
studies, better characterization of the process leading to deposition
~ ~ .
would be valuable. This problem should be attacked using field
experiments as well as laboratory analyses, complemented by
derivation of new computer-based algorithms to be used for
describing dry deposition processes based on fundamental physical
principles. Laboratory analyses should focus on the mechanics of
particle transport through boundary layers by making detailed
Armistead G. Russell
199
particle velocity measurements near surfaces. Outdoor deposition
measurements would benefit from improved instrumentation.
Recommendation 1 Receptor models such as those using chemical mass balance
Receptor Modeling techniques have proven to be very convenient tools for apportion
ing the contributions of sources to atmospheric particulate matter
concentrations. Combining receptor and source models appears to
have great potential. Further studies using hybrid or combined
models will benefit from the strengths of both types of models.
Also, it may be possible to add the ability to identify the sources of
secondary aerosols when using receptor models.
Recommendation 2 Studies to date have concentrated on pollutant transport but not
Pollutant Dynamics chemical interactions. Inclusion of chemical reactions within a
in Street Canyons street canyon model is important to determine near-source effects
on the concentrations of pollutants such as NO2 and O3. A field
study in which reactive pollutants such as O3, NO, and NO2 and
a tracer are closely monitored in and above a street canyon would
provide the data required for testing a chemically reactive street
canyon air quality model.
LOWER PRIORITY
Recommendation 4 Interactions between smog and fog droplets are known to
Fog Chemistry increase fog acidity and acid deposition, although direct health
effects are not well known. Smog/fog interactions will also affect
the evolution of gas-phase pollutants. We should combine our
knowledge of gas-phase and fog droplet chemistry into a single
model to investigate how the interaction affects pollutant evolution
in an urban atmosphere.
Recommendation 8 Plumes may dominate pollutant concentrations in the near field,
Reactive Plume and such as near a power plant or highway. Much of the work to date
Subgrid Scale has considered chemically inert plumes, and the few reacting plume
Modeling models have adopted extensive approximations. Given the reactiv
ity of vehicular exhaust and the amount of time people spend on the
road, it is important to gain a better understanding of the near
source dispersion and reaction of pollutants.
Acknowledgments
I thank Drs. Glen Cass and Ken Sexton
for their comments during the preparation
of this manuscript and am grateful for
the many helpful comments of the review-
ers.
Correspondence should be addressed to Armistead G.
Russell, Department of Mechanical Engineering, Car
negie Mellon University, Pittsburgh, PA 15213.
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