EPA-R4-73-031
June 1973
Environmental Monitoring Series
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EPA-R4-73-031
EXISTING NEEDS
IN THE EXPERIMENTAL
AND OBSERVATIONAL STUDY
OF ATMOSPHERIC
CHEMICAL REACTIONS
by
John H. Seinfeld, Thomas A. Hecht, and Philip M. Roth
Systems Applications, Inc .
.9418 Wilshire Boulevard
Beverly Hills, California
Contract No. 68-02-0580
Program Element No. 1A1008
EPA Project Officer: Marcia C. Dodge
Chemistry and Physics Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
Prepared for
OFFICE OF RESEARCH AND MONITORING
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D . C. 20460
June 1973
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This report has been reviewed by the Environmental Protection Agency and
approved for publication. Approval does not signify that the contents
necessarily reflect the views and policies of the Agency, nor does
mention of trade names or commercial products constitute endorsement
or recommendation for use.
ii
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ACKNOWLEDGMENT
We wish to express our gratitude to Dr. Mei-Kao Liu
for his contributions to the discussions of solar radiation
and turbulence.
111
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TABLE OF CONTENTS
I. INTRODUCTION . 1
II. KINETIC MECHANISMS FOR ATMOSPHERIC
PHOTOCHEMICAL REACTIONS . . 5
A. The Nature of the Photochemical
Smog System 5
B. The Nature of Photochemical
Kinetic Mechanisms 9
1. Inorganic Reactions 17
2. Hydrocarbon Reactions 18
3. Free Radical Reactions ..... 24
C. Current Photochemical Kinetic
Mechanisms 26
D. The Evolution of a Lumped
Mechanism 32
1. Lumping of Hydrocarbons .... 33
2. Lumping of Radicals 41
3. Formulation of a Lumped
Mechanism 43
E. The Validation of Mechanisms With
Smog Chamber Data « 49
1. Estimation of Parameters in
Reaction Rate Equations from
Experimental Data 51
2. Analysis of the Accuracy of
Parameters Estimated in Rate
Equations Erom Experimental
Data 53
3. Extrapolation of the Model to
Data Other Than That Used to
Estimate Parameters 56
4. Sensitivity Analysis ...... 57
F. Adaptation of Kinetic Mechanisms for
Atmospheric Predictions 57
IV
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Page
III. URBAN AIRSHED MODELS 62
A. Fundamental Theory of Air Pollution
Modeling . 66
1. The Eulerian Approach 68
2. The Lagrangian Approach 73
3. Summary 74
B. Approaches to Obtaining Approximate
Models 76
1. Eulerian Approaches 76
2. Lagrangian Approaches 88
3. Summary of Approximate Urban
Airshed Models 89
C. Implementation of Urban Airshed
Models 90
1. Grid Models 92
2. Trajectory Models 100
3. Summary of Current Urban Airshed
Models for Photochemical Air
Pollution 109
D. Levels of Uncertainty in Input
Variables HI
1. Levels of Uncertainty in Source
Emissions HI
2. Level of Accuracy in Meteorological
Data , 122
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Page
3. Level of Accuracy in Reported
Airshed Data 124
4. The Problem of Disparate Scales 126
5. Other Sources of Inaccuracy . . 128
E. Relationship of Kinetic Mechanisms
to the Urban Airshed Model 129
F. Suggested Studies 134
1. The Effect of Concentration
Fluctuations on Turbulent
Chemistry 134
2. Parameterization of Sub-Grid
Scale Transport and Reaction
Effects in Grid Models 135
3. Sensitivity Studies with Airshed
Models ...... 135
4. Experimental Needs in Model
Development 136
IV. INVESTIGATION OF SPECIFIC ELEMENTARY
REACTIONS AND PARTICLE GROWTH PROCESSES
AFFECTING THE COURSE OF SMOG FORMATION . . . 138
A. Rate Constants and Elementary Reaction-
Mechanisms Requiring Further Study . . 139
1. Inorganic Reactions 140
2. Organic Reactions. 164
B. Investigation of Particle Growth
Processes and the Effect of Particles
on Smog Formation Kinetics. ...... 196
1. Particle Formation and
Growth 197
2. The Effect of Particles on
Smog Formation Kinetics 202
VI
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PAGE
V. CONTROLLED EXPERIMENTAL STUDIES IN
SM(
A.
B.
C.
D.
CHAMBERS
Chamber Effects
1.
2.
3.
4.
Stirring and Mixedness in the
Chamber .
Surface Effects. . .
Radiation Simulation
Summary
Analytical Procedures
1.
2.
3.
4.
5.
6.
Accuracy and Primary Standards .
Precision
Sampling Procedures
Response Time
Analytical Techniques
Available for Measuring
the Pollutants -*
Summary .
Recommended Smog Chamber Studies. . .
1.
2.
3.
4.
idix
Simple Hydrocarbon-NO Mixtures.
Jv
Controlled Irradiation of
Polluted Air Samples From
Urban Areas
Controlled Assessment of Natural
Scavenging Processes
Summary
: V.I: The Determination of k.
203
203
209
210
224
231
232
234
236
237
238
240
248
249
249
255
256
259
261
Vll
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Page
VI. FIELD MEASUREMENT PROGRAMS 270
A. Effects of Transport and Diffusion
on Species Distribution and Chemical
Rate Processes 278
1. Regional Scale Studies 285
2. Local Scale Studies 304
B. Heterogeneous Reaction Studies 309
1. Aerosols 310
2. Surface Sinks 320
C. Spatial and Temporal Variations
in Solar Radiation 323
D. Measurement and Identification of
Chemical Species 328
VII. REFERENCES 332
Vlll
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I. INTRODUCTION
A great many experimental and observational programs
have been carried out over the years in an effort to in-
crease our knowledge of atmospheric chemical reactions.
Carefully conceived laboratory experiments have provided
the basis for estimation of individual rate constants.
Smog chambers studies have served as an important aid in
establishing a qualitative understanding of the overall
smog formation process. Atmospheric observations have
also proven valuable in this respect, and in addition,
in the identification of pollutant species. Within the
last four years, however, advances in the development of
mathematical' descriptions of the photochemical reaction
process have created a need for refined experimental and
observational programs, programs geared to yielding in-
formation either of much greater accuracy than seemed
necessary five or ten years ago or of a type or kind that
has rarely been collected in the past.
Two major "breakthroughs" have spurred the interest in
increasingly complex and sophisticated experimentation in
the field of atmospheric chemistry--
the development of photochemical kinetics mechanisms
capable of describing the concentration-time behavior
of the major reactants and products, as monitored in
a smog chamber. While the comparisons between pre-
diction and observation have often been good for ex-
periments having a variety of initial conditions, the
hydrocarbon reactant has generally been a single
species or binary mixture.
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the development of mathematical models capable
of predicting the concentrations of photochemical
pollutants as a function of location and time over
a region of the order of two to five thousand .square
miles (i.e., a major metropolitan airshed). The
spatial resolution of such models is typically of
the order of one to two miles.
While development of both types of models has proceeded
rather smoothly and swiftly over the past three years, it
became apparent at an early stage that there presently exists
no data base of sufficient accuracy and detail to properly
support model validation studies. A major purpose of this
report is to specify in general terms experimental and ob-
servational programs that will meet this need.
But the collection of data for model validation pur-
poses alone suggests a rather narrow horizon. We see as
a primary value of model development the codification of
knowledge in the field of study, the "pulling together" of
the many bits and pieces in an attempt to gain an expanded
understanding of the whole. When viewed in this way, the
mounting of an experimental program with a model, models,
or modeling as the structural foundation for the pursuit
is a major step forward--from gaining knowledge in a piece-
meal fashion (and understanding often with long delays) to
gaining knowledge efficiently, in quantity, and in a coordin-
ated manner.* It is the purpose of this report to discuss
The notion of coordinating all elements of an experimental
and observational program is of great importance. For
example, if the concentration-time predictions of a vali-
dated kinetic mechanism are relatively insensitive to the
magnitude of a particular rate constant, there is little
point in expending effort to improve the accuracy of its
estimated value. Science is better served by concentrating
efforts in areas in which an increase in knowledge pays a
greater reward. The model serves admirably as a tool for
identifying such efforts.
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future needs in the measurement and observation of atmos-
pheric reaction processes with the broader perspective —
with the unifying element of the mathematical model, our
best descriptor of the dynamic processes that we are attempt-
ing to understand.
If we are to deal with the subject of atmospheric
reactions in a unified manner, it is necessary to discuss
mathematical modeling at an early stage. In Chapter II, we
examine the nature of the photochemical mechanism (i.e., its
mathematical structure, the degree of detail it incorporates,
etc.) and present a short history of model development. We
then discuss the need for lumping of hydrocarbon and radical
species and suggest a mechanism (not yet subjected to veri-
fication) that has strong potential for accurately describing
the concentration-time behavior of all measurable species
(except, of course, those that are lumped). Model assumptions
are carefully stated and the validation procedure is described.
Finally, we outline the alterations that must be made in any
kinetic mechanism if it is to be incorporated into an urban
airshed model.
In Chapter III, we present a full discussion of the two
major classes of urban airshed models — the Eulerian and the
Lagrangian. Fundamental equations are presented and applied
forms of the equations are derived so that the assumptions on
which the latter are based can be clearly discerned. The
two commonly applied types of models--the grid and the trajectory-
are detailed, and their advantages and shortcomings are dis-
cussed. Levels of uncertainty associated with input variables
to these models — emissions and meteorological — are presented.
The chapter concludes with a section summarizing possible
avenues of pursuit for improving the present generation of
models.
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The remaining three chapters, IV, V, and VI, are, in
many ways, the core of the report. They deal, respectively,
with laboratory studies concerned with the kinetics and
mechanisms of individual reactions, smog chamber studies, and
atmospheric observations. In each, we discuss existing def-
iciencies in knowledge, examine in detail the types of studies
needed, and recommend specific studies and/or general
programs. Thus, the three chapters, taken as a whole, con-
stitute a comprehensive review, analysis, and diagnosis of
needs in experimentation and observation of the atmospheric
chemistry of contaminants.
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II. KINETIC MECHANISMS FOR ATMOSPHERIC
PHOTOCHEMICAL REACTIONS
The formulation of a kinetic mechanism of general validity
for atmospheric photochemical reactions is an endeavor beset
by several inherent difficulties:
(1) There is a multiplicity of stable chemical species
present in the atmosphere. Most of these exist at
very low concentrations, thereby resulting in major
problems in detection and analysis. A number, in
fact, probably remain unidentified.
(2) There is a large variety of unstable species (highly
reactive, short-lived intermediates) in the atmos-
phere. These species cannot be measured because of
their extremely low concentrations and high reactivities.
(3) Among the stable and unstable species, there are
literally hundreds of potential chemical reactions
that may be occurring.
However, while we must admit to only a limited knowledge of
atmospheric reaction processes, it remains essential that we
attempt to formulate quantitative descriptions of these processes
which are suitable for inclusion in an overall simulation model.
The general considerations of, the progress toward, and the
remaining problems in the development and validation of a gen-
eralized mechanism for atmospheric photochemical reactions that
is to be included in an overall airshed model are the subjects
of this chapter.
A. The Nature of the Photochemical Smog System
The general features of the concentration-time behavior of
the photochemical smog system are shown in Figure 1. These
data were obtained by Altshuller et al. (1967). Although the
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experimental data in Figure 1 involve only the single hydro-
carbon propylene, propylene pkotoxidation in the presence of
NOX manifests the major characteristics of photochemical smog.
The rate of decrease of both propylene and NO does not reach a sub-
stantial value immediately after the lights are turned on, sug-
gesting an induction period. After the apparent induction
period NO is rapidly oxidized to N02« The concentration of
NO reaches a low value which persists throughout the latter
stages of the reaction. At about the time the N02 concentra-
tion reaches a maximum, measurable 0, formation begins to take
place. The subsequent loss of N09 is attributable to formation
Li
of organic pernitrates and nitric acid. Additional stable
organic products such as formaldehyde (HCHO) and acetaldehyde
(CH,CHO) also form in the propylene-NO system.
«j X
It has been observed that the peak amount of 0., produced
over a fixed time of irradiation increases rapidly, goes
through a maximum, and finally decreases as one performs a
series of controlled experiments in which the initial hydro-
carbon concentration is held constant and the total initial
concentration of NO is increased. We illustrate this phen-
Jn>
omenon qualitatively in Figure 2.
Although the data shown in Figure 1 are indicative of the
concentration behavior in atmospheric photochemical smog, a
number of factors may serve to make the chemical behavior in
a smog chamber differ from actual atmospheric chemistry:
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o
o
o
LO
o
ID
r-
cn
Q_
Q_
oc
o
_
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FIGURE 2. Effect of Initial Reactant Ratios On Ozone
Concentration in Smog Chamber Studies
[NO]
[HC1
[NO,].
[HC]
[HC1
[NO].
[N0x]o« [HC]o
0,
max
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(1) Wall effects which may be present in a chamber cannot
at this time be related to ground level surface
effects in the atmosphere,
(2) Most smog chamber experiments reported to date
have not included oxides of sulfur or aerosols
in the initial mixture. In most cases, these
two classes of species are present in the atmosphere,
(3) Concentration levels employed in smog chamber
experiments are often higher than atmospheric
levels, and
(4) The intensity and distribution of artificial
radiation employed in a chamber may not be rep-
resentative of solar radiation.
In spite of these potential problems, smog chamber studies
are a necessity in understanding tffe chemistry of the smog
system. This is so because it is virtually impossible to
isolate chemical reaction effects from those of transport
and diffusion in the atmosphere.
B. The Nature of Photochemical Kinetic Mechanisms
The object of developing a kinetic mechanism for photo-
chemical smog is to enable the prediction of both smog chamber
reaction phenomena, such as is illustrated in Figures 1 and 2,
and atmospheric reaction phenomena. There are some general
considerations which are important in developing such a
mechanism. First, the mathematical description of the mech-
anism (in terms of the number of species included) must not
be overly complex, as computation times for the overall air-
shed model within which the mechanism is to be imbedded are
likely to be excessive. On the other hand, an overly simplified
mechanism may omit important reaction steps, and thus be
inadequate to describe atmospheric reactions over a range of
conditions. A major requirement, then, is that the mechanism
predict the chemical behavior of a complex mixture of many
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hydrocarbons, yet that it include only a limited degree of
detail. Thus, the mechanism must strike a careful balance
between compactness of form and accuracy of prediction.
A kinetic mechanism, once developed, must be validated.
This procedure is commonly conceived as consisting of two
parts: validation in the absence of transport processes and
validation in their presence. In practical terms we are
speaking, respectively, of comparison of the model's predic-
tions with data collected in smog chamber experiments and
with data collected at contaminant monitoring stations in
an airshed. When we speak of validation of a kinetic mech-
anism in this section, we are referring to the comparison
between predictions and experiment based on smog chamber
studies. The second and more complex of the two parts,
validation of the kinetic mechanism in the presence of trans-
port processes (convection and turbulent diffusion) , will be
discussed in Chapter III.
To provide a. framework for the discussion of kinetic mech-
anisms, we will first consider the highly generalized kinetic
scheme given below.
N02 + hv -»- NO + 0
1
-»-
03 + NO -»- N02 + 0,
it
0_ + Hydrocarbons •* Stable Products + Radicals
Radicals* + Hydrocarbons •* Stable Products + Radicals
* "Radicals" include both 0-atoms and OH radicals, the
principal radical oxidizers of hydrocarbons.
10
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Radicals + NO -»• Radicals + NO-
Radicals + NO.
Stable Products
8
Radicals + Radicals ->• Stable Products
The reactions that take place in the generation of photo-
chemical smog, as exemplified by the above mechanism, can
be classified as follows (in the terminology of chain reactions):
i. Initiation reactions - those that provide free radicals
to induce chain reactions, e.g.,
N02 + hv ->• NO + 0*
2. Branching reactions - those in which there is a net
increase in radical species,
e.g. 0 + HC •»• Products + Radicals,
where more than one radical results.
3. Propagation reactions - those in which there is no net gain
or loss of radicals, but merely a
change in identity, e.g. Radical +
HC •*• Product + Radical.
4. Termination reactions - those that remove free radicals
through the formation of stable
end products, e.g. reactions 7 and 8.
This reaction is not the only initiation reaction that
occurs in the generation of smog. Photolysis of nitrous
acid, alkyl nitrites and aldehydes also provide free radi-
cals. For simplicity, and because NO^ photolysis is the
most important initiation reaction, we have omitted others
in this generalized mechanism.
11
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Let us now examine the behavior of this highly generalized
mechanism to see if it is capable of predicting the qualitative
features of the photochemical smog system, in particular, the
rapid rate of conversion of NO to NO- and the effect of varying
initial reactant concentrations on 0, formation. In the dis-
cussion that follows, we denote the total concentration of radi-
cals as [R] and that of hydrocarbons as [HC]. We can write a
material balance on the total concentration of free radicals
in the following manner:
a[NO-] + b[HC][R] - c[NO-][R] - d[ R]2
where the terms on the right hand side have the following significance:
a [NO-] = production of 0-atoms by reaction 1
b [HC ] [R] = the net rate of production of radicals from
reactions 4 and 5
c[N02][R] = the net depletion of radicals by reaction 7
d[R]2 = the net depletion of radicals by reaction 8
The symbols a,b,c,d represent the combination of appropriate
rate constants and stoichiometric coefficients.
We can identify two limiting cases of interest:
1. Near t = 0 when [R] = 0, i.e.
=a,N0]
12
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From this we can see that initially the concentration of free radicals
increases at a rate proportional to the N02 concentration. Presumably,
most of these radicals are oxygen atoms.
2. When the total radical population reaches a steady state (ss), dER]/dt
= 0 . At this point
0 = a[NOj + b[HC][R] - c[NOJ[R] - d[R]2
£ £
For case 2 we can examine the effect on [R]__ of the relative
O o
concentrations of N07 and HC. When [ N07] » [HC],
= o « a[N02] - c[N02][R]
ss
or [R] is a constant a/c, dependent only on the photolysis
5 d
rate of N02 and the rate of termination with N02. When the
rate of production by chain branching, b[HC] [R] equals the
termination rate with N02, clNO-JlK], the steady state radical
concentration is
1/2
[Rlss = I a[N02]/d]
Finally, when [HC] » [ N021 ,
0 « b[HC] [R] - d[R]2
so that [R]cc = b[HC]/d.
5 5
13
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Summarizing, at steady state the limits of total free
radical concentrations are
i < FR 1 < b[HC]
c - l Jss - 3
(high N02) (low N02)
Using these relationships, Johnston et al. (1970) have
estimated that actual concentrations may be:
c[N02]
b[HC]
[Rlss,ppm
10
l.lxlO"4
1
2xlO"3
0.1
3. 6x10 ~2
Leighton (1961) estimated that in photooxidation of an
olefin such as propylene, NO is converted to NO, at a rate
-1
of 0.04 ppm min by reactions of the type 6. This rate is
consistent with the steady state radical concentrations just
calculated. For example, using [R] = 10 ppm, [NO] = 0.1 ppm
-1 -1
and a rate constant for reaction 6 of 500 ppm min , the rate
of conversion of NO to N02 is 0.05 ppm min" .
Aside from predicting the rapid conversion of NO to N02,
a mechanism must also be capable of simulating the effect of
different initial reactant ratios on product formation in the
smog system, as illustrated in Figure 2. Let us consider the
two cases of low and high N07 concentrations. The photochemical
14
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smog process is initiated by N02 with the rate of increase
of the total radical population depending on the initial con-
centration of N02« The maximum concentration of N02 occurs
when the rate of conversion of NO to N02 just equals the rate
of termination of radicals by N02- If this maximum concentra-
tion of NO- is low (i.e. low total initial NO ), the concen-
£* X
tration of radicals reaches very high values. The radicals
rapidly convert NO to NO-, allowing ozone to form. As we in-
crease the total initial NO , and hence the NO- concentration
Jv £t
at its maximum, the amount of 03 formed should increase up to
a point. That point is the one at which radical removal by
N02 is at least as fast as chain branching, i.e. b[HC] * c [NO^ .
As we continue to increase the initial NOX, and hence the NO-,
the steady state radical concentration continues to decrease,
as we have seen. The result is that the rate of ozone forma-
tion slows down. Nevertheless, if we wait long enough there
will be a significant accumulation of 0,. Thus, if we consider
Oj formation only over a fixed time of irradiation, it will
seem that increasing initial NO is a beneficial policy with
respect to 0, formation, when, in fact, what has really happened
is that we have not waited long enough for the reaction to go
to completion.
We can also examine the effect of initial reactant ratios
on the maximum amount of 0, formed during an irradiation. Con-
sider first an experiment in which the concentration of initial
NOX (NO +N02) is large compared to initial HC. Note that the
relative amounts of NO and NO- will serve only to govern the
time needed to convert the NO to NO- and should not affect the
15
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ultimate maximum 0, concentration attained. Figure 2a
illustrates the type of concentration/time curves to be
expected when [NOx]Q » [HC]Q. We see that the hydrocarbon
is expended before all the NO is converted to NCU. Since
an appreciable amount of NO remains after the hydrocarbon
is depleted, no significant 0- concentration can be reached.
Consider next the opposite limit, namely [ NO ] « [HC] .
J\. Q O
In this case, the NO is rapidly converted to N09 with little
£t
expenditure of HC. As[NO] becomes small, 0, can accumulate.
However, because of the large concentration of HC, the
reaction of 0_ and HC will prevent [0,]from becoming too
large. This case is illustrated in Figure 2b. Finally, the
intermediate case of [HC] - [NO ] can be expected to yield
the largest 0, concentration. Thus, if one considers the
maximum 0., concentration achieved, regardless of the time of
irradiation, as a function of [HC] /[NO ] , one will get a
curve of the type shown in Figure 2c.
We have seen that the simplified mechanism presented early
in this section can account for several of the qualitative
features of the photochemical smog system. However, the mech-
anism is inadequate for quantitative predictions of concentration-
time behavior in smog chamber systems and the atmosphere for
two basic reasons:
1. Several important inorganic reactions involving NO, N02,
H20 and CO need to be included, and
2. The mechanism lacks detail in the treatment of hydro-
carbon and radical species.
In attempting to construct a mechanism capable of accurate
prediction, each of these points must be carefully considered.
16
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We now present a very brief survey of the important
inorganic and hydrocarbon reactions in the photochemical
smog system. Numerous reviews of these reactions are
available (Leighton, 1961 ; Altshuller and Bufalini,
1971; Johnston et al., 1970), so that we will consider here
only those elements of the chemistry important to the de-
velopment of a kinetic mechanism.
1. Inorganic Reactions
The reactions in the system of NO , air, H90 and CO
X £
have received much attention. A survey of rate constant
values reveals the following reactions to be of greatest
importance:
NO
0 + 02 + M
03 + NO
0 + NO + M
0 + N00
NO + 0
°3 + M
NOo + (
N0
M
NO + 0,
+ N02
0
3 +
+
M *
NO
N03 +
2
•
7
t-
NO *
NO
NO
3 + M
X
3 * °2
2N02
q
NO
r\
3 +
1
j_
NO
i **
L
tj
0
2
5
n
l
l
>•
0
>-
1
N2
NO
ou
°5
2 3
\ir\
2°5 +
i^w -*• £nnw.T
The N09-N0-Ot Cycle
tt 0
Important Reactions of
0 with Inorganic Species
The Chemistry of NO,,
N205, and HN03
17
-------
NO + HNO, -»• HNO,
3 2
13
HN02 + HN03 -»• H20
NO + N02 + H2Q *+ 2HNO
15
2HN02 •* NO +
16
HN02 + hv H- OH +
17
OH + N02 + M -»• HN03
18
OH + NO + M * HN02
+ NO
2
+ 2N02
2
NO, + H-0
*• L
NO
+ M
+ M
OH + CO + (02) -^ C02 + H02
20
HO, + NO -*• OH + NO,
H2°2
21
hv •»• 20H
Reactions of
with Inorganic Species
Chemistry of HN02
Important Reactions
of OH with Inorganic
Species
[Oxidation of NO by H02
[Photolysis of H,09
We shall discuss several of these reactions further in
Chapter IV, considering the degree of study they..have
received, the rates at which they proceed, and the un-
certainty associated with the individual reaction rate
constants.
2. Hydrocarbon Reactions
We first wish to make a fundamental distinction be-
tween types of mechanisms, based on the treatment of
hydrocarbon and free radical reactions. The first type
is that written for the photooxidation of a specific
hydrocarbon. This is the type we ordinarily envision, one
in which each species in each reaction represents a dis-
tinct chemical entity. The second type is the lumped
nechmiem, one which contains certain fictitious species
which represent entire classes of reactants.
18
-------
In many chemical systems the number of species is
often extremely large. In addition, there is usually
a significant range of reactivities of the species in
systems of this type. Certain species may not be present
in measurable concentrations and many rate constants
may not be known accurately. As a result, quantitative
predictions of reaction rates may be highly uncertain. In
such a case, one is unable to deal with each species sep-
arately; rather, one may partition the species into a
few classes (called lumped classes), and then consider
each class as an independent entity. This idea has
already been illustrated in the highly simplified general
mechanism cited earlier, in which all hydrocarbons and
free radicals were represented by HC and R, respectively.
General lumping theory in chemical kinetics has been
the subject of several recent investigations. Wei and
Kuo (1969a, 1969b) have presented a general lumping analysis
of monomolecular, first order reacting mixtures. Hutchinson and
Luss (1970), Luss and Hutchinson (1971), and Goli, Keri, and Luss
(1972) have studied the lumping of reaction mixtures consisting
of a large number of parallel, independent;, and irreversible nth
order reactions. In contrast to the work of Wei and Kuo, which
was directed toward the determination of conditions under which
exact lumping was possible, the studies of Luss have been con-
cerned with the problem of predicting a priori the maximum
error involved in lumping and with the type of species that
should be lumped together to ensure that the prediction error
is less than some given bound.
19
-------
No theory has yet been developed that is concerned
with the lumping of large sets of coupled, bimolecular
reactions, such as occur in the generation of photo-
chemical smog. We outline here some of the more important
questions that must be addressed if we are to effectively
model atmosphere photochemical reactions.
1. In the photochemical smog system the large number
of hydrocarbons and free radicals makes lumping
a necessity in developing a practical kinetic
mechanism. However, which hydrocarbons should be
lumped together and what criterion should be used to
establish groupings? For example, should the lump-
ing be carried out according to hydrocarbon class,
such as paraffins, aromatics, olefins, etc., with
respect to reactivity with 0, 0, and OH* regardless
of class, or with regard to the number of free radi-
cal products?
2. Which free radicals should be lumped together and
what criterion should be used to establish groupings?
For example, should the lumping be carried out with
respect to radical class such as alkyl, acyl, alkoxyl,
etc. , with respect to most probable chain length,
or with respect to reactivity?
3. How are the lumped rate constants and stoichiometric
coefficients to be determined?
4. Is the order of the reaction of the lumped hydro-
carbon species the same as the individual reaction
being represented?
20
-------
The one guideline that does generally apply is that
lumping should be carried out such that a balance is
achieved between accuracy of description of the under-
lying processes and compactness of the mechanism. Let
us now consider some of the alternatives for lumping
in photochemical smog systems.
Given a distribution of atmospheric hydrocarbons,
we must, first identify and tabulate the reactions in
which they may participate. Photochemical decomposition
of primary hydrocarbon pollutants is unimportant, except
perhaps for aldehydes; we must therefore focus our atten-
tion on thermal reactions.. Of the active species that we
have mentioned thus far, those capable of reacting with
hydrocarbons include 0, 03, and OH. In this discussion we
divide the primary hydrocarbons according to the classes--
olefins, paraffins, aromatics and aldehydes--and examine
the reactions of each with the three radical species.
While these groupings are certainly not inclusive of all
classes of hydrocarbons in the atmosphere, they comprise
the major portion. The two basic aspects of an individual
reaction that we will consider are: (1) the product dis-
tribution and (2) the rate constant.
a. Atomic Oxygen - Hydrocarbon Reactions
The principal products of 0 atom hydrocarbon reactions
are summarized below:
21
-------
blefin 0 +^7C =cC^ R- + RCO *
paraffin 0 + RH + R- + OH-
T>
aromatic 0 + {Qf -*• R- + OH-
aldehyde 0 + RCHO + RCO + OH-
b. Ozone-Hydrocarbon Reactions
Only olefins, among the four hydrocarbon group-
ings we are considering, are attacked readily by
ozone in the vapor phase. The so-called Criegie
mechanism for 03 addition to olefins can be summarized
as
0, +^TC=C^ -»- ^TC=0 + (gC-0-0 (Zwitterion)
The products are thus a carbonyl and an unstable
intermediate called a zwitterion, the subsequent
reactions of which are not very well known. Possible
decomposition reactions of the zwitterion are
HRCOO •*• ROH + CO
HRCOO •*• RO- + HCO
HRCOO -> RCO + OH-
In addition, the zwitterion may participate in reactions
with 02, NO or N02:
If one,of the carbons on the double bond is external,
both HCO and RCO can form.
22
-------
0-0 + A -OC—0 + AO (A = 02, NO or N02)
If this reaction predominated we would expect a
yield of two carbonyl compounds per olefin. Actually,
a yield between 1 and 1.4 is observed. In general,
then, a stable carbonyl and two free radicals are
formed through the 0,-olefin reaction. We might
note, however, that the dynamics of this class of
reactions are still not fully understood. We shall
return to 0,-olefin reactions in Chapter III where
we discuss reactions needing further experimental
investigation to elucidate product distributions.
c. Hydroxyl Radical - Hydrocarbon Reactions
Hydroxyl radicals react with hydrocarbons either
by abstracting a hydrogen atom or by addition. For
paraffins the reaction is known to be
RH + OH- -»- R- + H20
At this time there are no reported product data for
OH/olefin or OH/aromatic reactions, although it is
known that the propylene reaction proceeds via addi-
tion to the double bond to form a radical. If this is
the case with other olefins, we would expect one free
radical as a product,
^C = cC+ OH- -»• R-*
Aldehyde/OH reactions also yield one free radical,
HCHO + OH- •* H20 + HCO
I i
The actual structure of this radical would be HO-C-C'
23
-------
3. Free Radical Reactions
As we have just seen, the reactions of 0, 0,, and
OH- with hydrocarbons yield the following classes of
free radicals: R- , RCO, RO* , where R can be a hydrogen
atom, an alkyl group, or an alkyl group containing an
alcohol functional group. We must now trace the most
likely reactions of these species with the others in the
•
system. Consider R' , RCO and OH- as typical products.
• „,,
Both R- and RCO will most probably react with 02 by
ft
RCO + 02 -»• RCOO-
These peroxy radicals will undergo a variety of reactions,
the most important of which are with NO and N0~
ROO- + NO -> N02 + RO-
f fl
RCOO- + NO •*• N02 + RCO'
RCOO- + NO 2 -»• RCOON02
The two new radicals formed will then probably react in
the following manner:
24
-------
RO- + 0, -»- RCHO + HO.,'
o 2 Z
RCO' -»• R' + C02
R02-
The likely history of typical alkyl and acyl radicals
in chain propagation reactions can thus be depicted as
• 02 ff NO fl
RCO + RCOO- -> RCO
'2
NO
RO ' -v RO-
HC
NO
HO.' * OH-
We see that, during the lifetimes of R' and RCO, many
molecules of NO can be converted to N02 (of course, each
step in the sequence competes with other propagation and
termination reactions). When NO concentration becomes
sufficiently low, one possibility is that the peroxyacyl
radicals will react with N02 to give peroxy acyl nitrates.
The alkoxyl radicals may also react with NO- at this point
to yield alkyl nitrates.
Now the problem of representing hydrocarbon and free
radical reactions should be somewhat clearer. In a com-
plex mixture of hydrocarbons, such as is observed in the
atmosphere, we might divide the total hydrocarbon population
25
-------
into n lumped hydrocarbon species, HC,, HC^,..., HC .
Each of these may potentially react with 0, 0.,, and
OH, yielding varying numbers and types of free radicals
depending on the class of hydrocarbon participating in
the reaction. Thus, a careful analysis of lumping al-
ternatives is a necessary step in the development of a
generalized kinetic mechanism. In Section D we under-
take such an analysis. However, before going to this,
we present a brief synopsis of currently available kin-
etic mechanisms for photochemical smog reactions. This
review should be of aid to the reader in assessing the
extent to which current mechanisms adequately treat the
details of the inorganic and hydrocarbon chemistry.
With this background, it is relatively easy to identify
those areas in need of further development.
C. Current Photochemical Kinetic Mechanisms
It is only in the last ten years that general kinetic
mechanisms have been postulated to describe photochemical
smog chemistry. The mechanisms that have been proposed can
be classified as either specific (written for photooxidation
of a specific hydrocarbon) or lumped (written for one or more
species involving lumped reactants) and include the following:
Specific Mechanisms
Westberg and Cohen (1969) isobutylene
Behar (1970) propylene
Hecht and Seinfeld (1972) propylene
Niki et al. (1972) propylene
Demerjian et al. (1973) propylene
trans"2rbutene
isobutene
n^butane, and
formaldehyde
26
-------
Lumped Mechanisms*
Eschenroeder and Martinez (1972)
Wayne et al. (1971)
Hecht and Seinfeld (1972)
Specific mechanisms, while often quite complex (e.g.
the Hecht and Seinfeld propylene mechanism contains 81
reactions), can play an important role as an aid in under-
standing the fundamental chemistry of the photooxidation
process. However, for none of the specific mechanisms listed
above has there been reported a program of validation
over a range of initial reactant concentrations. Thus,
all five can only be considered at this point as .detailed
chemical speculations for the specific hydrocarbon system.
Assuming, however, that validated versions of specific
mechanisms are available, these mechanisms would still not
be suitable for inclusion in an urban airshed model. The
main reason for this centers on the philosophy underlying the
development of such mechanisms. The decision to develop and
implement a specific mechanism implies the desire to represent
reaction processes as accurately as is feasible. Thus, a
*Three lumped mechanisms, nearly identical in structure, were de-
veloped at an early stage by Eschenroeder (1969), Friedlander and
Seinfeld (1969) and Behar (1970). (Eschenroederfs mechanism,
slightly modified, is substantially the same as, or superior
to, those of Friedlander and Seinfeld and Behar). For the
obvious reasons of simplicity and convenience, it would be
desirable to adopt such mechanisms for general use. However
these mechanisms not only omit steps now known to be important,
but they were never successfully validated over a range of initial
conditions. All three have since been either abandoned or modified,
27
-------
relatively large number of reaction steps must be incorpora-
ted in a description of the dynamics of consumption of a
particular hydrocarbon, such as propylene. Reaction dynamics
will, however, vary for the many hydrocarbon species present
in the atmosphere. If, for example, thirty to forty steps are
required to describe propylene kinetics, and fifty hydrocarbon
species, each having unique dynamics, are believed to exert
a significant impact on atmospheric reaction processes, one
is faced with an intractable representation of the system.
Alternatively, adoption of a detailed representation of the
reactions of a single species (for example, propylene) which
may, upon development, be applied to a single, generalized
hydrocarbon is tantamount to constructing a mechanism having
many of the representational deficiencies of a lumped kinetic
scheme and, in addition, introduces a substantial parameter
estimation problem.
Each of the three lumped mechanisms listed above is
currently in use in programs of mathematical modeling of
photochemical smog in the Los Angeles basin. Detailed dis-
cussions of each are readily available in the original
references. We note, however, that the mechanisms of Eschen-
roder and Martinez and Hecht and Seinfeld are very similar.
Table I presents a comparison of the two mechanisms. The EM
differs from the HS mechanism in the treatment of HNOj and
HNCL, the inclusion of CO, and the treatment of HCL.
28
-------
TABLE 1. The Hecht-Seinfeld (HS) and Eschenroeder-Martinez
(EM) Mechanisms
HS EM
N02 + hv -»• NO + 0 N02 + hv -> NO + 0
2 2
0 + 02 + M-»-0- + M 0 + 02 + M-*-0- + M
03 + NO -»• N02 + 02 03 + NO -»• N02 + QZ
03 + N02 * N03 + 02 OH- + N02 + M •* HNOj + M
NO, + NO + 2ND, H20
L
3 2 $ 3
H20
NO + N02 -»- 2HN02
2HNO. + NO + NO. + H»0
HN02 +
CO +
L i. L
hv -*- OH + NO
02
OH -> C02 + H02
NO + NO, t- ZHNO,
2 5 2
7
OH- + NO + M -»• HN02 + M
0 + HC ^ b1(R02)
OH + HC + b2(R02)^
0
RO
R02
10
3 + HC * b3(R02)
ll
2 + NO ->- N02 + d(OH)
12
+ N02 -^ c(PAN)
H02 + NO -»• OH + N02
H02 + N02 -»• HN02 + 0
13
0 + HC •»• aR02
OH + HC -»•
Oj + HC -»•
R02 + NO -»• N02 + eOH
R02 + N02 -»• PAN
18
0 + HC2 •»• a2R02
OH + HC2 * B2R02
20
NO 2 •»• WALL OR PARTICLE
29
-------
lABLE 2. Wayne et al. Mechanism
N02 + hv •*• NO + 0
03 + NO I N02 + 02*
it
NO, + 0- -*• NO, + 0,
£t O O t*
N03 + NO •*• 2N02
C,H.O, + 0, J CH,CHO + 0-
242 2 3 3
NO + HO,-*- NO, + OH
2 2
H + 02 + M •»• H02 + M
DUMHC + 02* I CH3OOH
10
°2 n °2
CHjOOH + hv -»• CH30 + OH
N02 + OH -»• HN03
13
OH + 0, -*• H02 + 02
OH + CO -> H + C02
15
CH, + 0, + M -»• CH,09 + M
O £ «J £•
16
CH70, + NO •*• CH,0 + NO,
o ^ o ^
17
130 + 02 + NO -»• CH302 + N02
18
2H302 * NO.-*- C2H30 + N02
20
H402.+ NO •»• CH3CHO + N0
CH..O + 0, -»• HCHO + HO,
30
-------
TABLE 2. (Continued) Wayne et al. Mechanism
C,H, + 0 + CH, + C,H,0
3 0 5 L 3
C7H, + 0.. -»- HCHO + C-H.O.
6 O 3 L °i L
C..H, + 0 + 0, •*• HCHO + C9H.O_
36 Z Z 4 Z
C_H, + 0,* + CH,0 + C-H_0
5 0 L 5 L o
C,H, + H00 * CH_0 + CH7CHO
o O Z 3 3
C..H, + CH.O, -»- CH_ + CH-0 + C0H_0
3D 3Z 3 3 Z3
C2H30 + M ->• CH3 + CO + M
CH30 + N02 V CH3ON02
30 + 02 + N02 1° C2H303N02
DUMHC + 0 -*-1 CH3 + C2H30
HCHO + hv * H + H + CO
33
2 + N03 + H20 * 2HN03
31
-------
While the EH and HS mechanisms are quite similar, the
third in current use, that of Wayne et al., given in Table
2, adopts an inherently different approach. The mechanism
is based on the photooxidation of propylene, and its appli-
cation to atmospheric photochemistry is presumably based
on the assumption that the mixture of atmospheric hydrocar-
bons behaves as a binary mixture of propylene and a second,
relatively unreactive, hydrocarbon. This assumption is in
contrast to that inherent to the EM and HS mechanisms, i.e.
that the atmospheric hydrocarbon mixture can be represented
by two lumped hydrocarbon species, one more reactive than
the other, neither of which represents a specific hydrocarbon.
Because of the inclusion of detailed propylene chemistry in
the Wayne mechanism, many specific radical species have been
included, whereas only one lumped radical species (aside from
0 and OH-)* appears in the EM and HS mechanisms. In the vali-
dation exercises reported, the two lumped hydrocarbons in the
EM and HS mechanisms have been specified on the basis of
reactivity. As we shall see, when hydrocarbons are lumped
on this basis, it is difficult to ascribe precise values to
the generalized stoichiometric coefficients.
We now present a systematic analysis of hydrocarbon and
radical lumping in order to illustrate the various levels of
complexity that might be included in a mechanism and to iden-
tify the decisions which must be made in constructing a lumped
mechanism.
D. The Evolution of a Lumped Mechanism
As we have noted, the primary problem in the development of
a lumped mechanism is the representation of the hydrocarbon and
free radical reactions. In this section we shall give some in-
dication as to the options available in this representation.
If CO is present, HO"-' is retained as a separate species
in the HS mechanism.
32
-------
1. Lumping of Hydrocarbons
Consider first the question of the lumping of hydro-
carbons. Our objective is to form a small number of groups
of lumped hydrocarbon species which will represent the mix-
ture of hydrocarbons present in the atmosphere. Alternative
criteria are available by which to form the .hydrocarbon
groupings, for example:
1. Lump hydrocarbons based on class (olefins, aromatics,
paraffins, etc.).
2. Lump hydrocarbons based on reactivity with individual
oxidants, such as 0, 0, or OH'.
Let us discuss the implications of each of these two
lumping criteria. Consider criterion 1, the lumping of
hydrocarbons by class. For example, let
HC-L = olefins
HC, = aromatics
HC, = paraffins
HC. = aldehydes
Although the mechanisms for the oxidation of these four classes
of hydrocarbons by 0, OH,' and 03 have not yet been resolved
in detail, the likely product distributions are:
HC
1
R- + RCO
03 •» RCO + RO- + RCHO
OH- -*-1 R- *
*OH adds to the double bond of olefins forming an alcohol-like
free radical, RCHCH2, which we have assumed to react in the
OH
same fashion as an alkyl radical. This is not exactly true, as
this free radical decomposes in a different, manner than R' in
subsequent reactions. Specifically, RCHOHCH2 is thought to
react to form one additional aldehyde (Niki et al., 1972). We
have, therefore, included HC4 as a product of the OH-HCj ele-
mentary reaction in Table 4 to correct for this anomaly.
33
-------
0 + R- + OH-
0, •»• not important
•* ii
HC, +
OH- -
0
°3
OH"
H2°
R- + OH-
not important
HC4 +
k4
R- + H20
RCO + OH-
not important
'3
kl| .
OH- ->• RCO + H,0
kS •
hv -»-4 RCO* + H« + CO
Since the number of free radical products resulting
from 0, 0, and OH- attack on each lumped species is
essentially the same for all individual hydrocarbon mem-
bers of each lumped grouping, (i.e. OH- attack on all
paraffins is expected to yield one alkyl radical) the
number and type of free radical products in each step
shown above can be specified with some certainty. On
the other hand, within each lumped species there is a
distribution of rate constants for the reactions with
0, 0, and OH-. For example, within HC.. there is a wide
spectrum of rate constants for olefin-0 reactions. There-
fore, the rate constants for 0, 03 and OH- reactions with
each lumped species must be taken as average values which
reflect in some manner the relative amounts of different
individual species within each lumped species. Since
the differing reactivities of the1individual components
comprising a grouping will lead to their disappearance
at different rates throughout the course of photooxida-
tion, the effective rate constants for reaction of the
lumped species with 0, 0, and OH- must also vary during
the course of the reaction. In summary, then, lumping
If HC4 is HCHO, HCO (which decomposes to H-
rather than RCO, forms.
CO),
34
-------
of hydrocarbons by class will allow rather definite
assignment of stoichiometric coefficients but will
necessitate rate constants which reflect the average
reactivity of the individual species within each
lumped species as a function of time. .
We now consider criterion 2, the lumping of hydro-
carbons by reactivity. The first question we face
in this case is - reactivity with respect to what?
The three obvious choices are reactivity (rate constant)
with 0, 03 and OH-. Perhaps the most logical species
among the radicals 0, 0, and OH upon which to base the
reactivity grouping is that species which is most res-
ponsible for hydrocarbon disappearance in photooxidation
experiments. Computed rates of hydrocarbon disappearance
by 0, 0, and OH generally confirm that the OH-rate
is the most important of the three, except at the very
beginning of the photooxidation when the 0-atom rate is
predominant.
Table 3 presents rate constants relative to that of
propylene for the reactions of several hydrocarbons with
0, Oj and OH, together with the relative reactivities of
these hydrocarbons based on N0-N02 conversion rates ob-
served experimentally (Altshuller and Cohen, 1963; Glasson
and Tuesday, 1970). We see that the OH-hydrocarbon rate
constants .correlate quite well with reactivities for all
classes of hydrocarbons listed in the table. On the other
hand, 0-atom and 0, rates correlate with reactivities only
for the olefinic compounds. For the aromatics, aldehydes
and alkanes, the 0-atom and Oj rate constants are small
compared with the measured reactivies. Since the most
35
-------
important role played by OH is that of generating organic
free radicals for conversion of NO to N02, it would appear
that lumping of hydrocarbons with respect to their OH
reaction rate constant would be the most consistent with
measured hydrocarbon reactivities. Suppose, for example,
that we elect to divide the hydrocarbon mixture into three
classes based on their OH rate constant:
HC.
k < 1000 ppm" min"
1000 < k < 5000 ppm min"
k > 5000 ppm^min"1
HC!
1 " -1
IT s* ^ f\ f\ f\ - t _ . r» /\ r\ s\ __.__ _? J-
On this basis each group would contain all classes of hydro-
carbons, with the rate constants for reaction with OH
defined by the composition of the grouping. Rate constants
for reaction with 0 and Oj, however, would not necessarily
correlate with the grouping based on the OH rate and would
have to be determined in a manner similar to the case of
lumping with respect to hydrocarbon class. However, dur-
ing the main course of the reaction, the hydrocarbons within
each group would be consumed at roughly the same rate so that
the reactivity and stoichiometry of the group would not be
expected to change with time. In the late stages of the
photooxidation, 0,-hydrocarbon reactions become quite impor-
tant. This raises a potential problem for lumping on the
basis of the OH rate.
36
-------
While rate constants can be determined relatively
accurately, the number and types of free radical products
within each lumped group would vary because each group
would contain hydrocarbons of all classes. This would
necessitate the adoption of stoichiometric coefficients
which reflect the individual makeup of each lumped group.
To illustrate the forms of lumped reactions following
the scheme based on OH-reactivity, let us assume we have
N groups, as, for example, the three defined above HC,,
HC2, HC3. The reactions with 0, 03 and OH can be written:
0 -»• U.-.R- + a.9RCO + a.^OH-
. 1J. 1 ^ 1 O
ki
Hci
°3 "*" &iiRCO + 6i2RO* + ^RCHO
OH -v Yi;LR' + Yi2RCO
i = 1,2,...,N
where aji» $11 an^ Yii are stoichiometric coefficients
which reflect the individual compositions of the HC^,
i = 1,2,...,N. For example, if HC, consisted entirely of
olefins we might expect a-, = a-7 = 1 and a-x = 0. Thus,
1 J. 1 Lt 1 O
the stoichiometric coefficients are not to be considered
as freely adjustable parameters, but rather as parameters
whose values are fixed because of the choice of hydro-
carbons comprising each lumped species HC-.
37
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TABLE 3.
Relative Rate Constants and "Smog Reactivity"*
Compound Relative Rate Constants Reactivity**
0 0, OH
Olefins —
Propylene 1.0 1.0 1.0 1.0
Ethylene 0.2 0.3 0.1 0.3
Isobutene 4.4 1.7 t, 2 2.5 1
Trans-2-Butene 4,9 2.8 * 36 4.2 4
2-Methyl-2-Butene 14 2.4 7.1 6
Tetramethylethylene 18 3.9 * 62 8.6 17
Aromatics
Benzene ,007 <_0.05 0.1
Xylene --- <0.2 1.1 1
Aldehydes
Formaldehyde 0.05 0.9 0.7
Acetaldehyde .15 — 0.9 0.7
Proprionaldehyde * .2 --- 1.8 2
.*
Alkanes
n-Butane .008 — 0.24 0.2
* Source of Table: Niki et al. (1972).
** Based on the rate of conversion of NO to NO-
38
-------
Let us summarize the advantages and disadvantages
of the two alternative hydrocarbon lumping crtieria.
For lumping by hydrocarbon class:
Advantages -
1. The definition of the lumped species depends only
on the type of hydrocarbon (i.e. olefin, aromatic,
alkane, etc.)•
2. Since the products of 0, 0, and OH reactions with
various hydrocarbon classes are essentially the
same within each class, the number and type of
free radical products would be well-defined for
each class (assuming tne products are indeed known).
Disadvantages -
1. The rate constants for reaction with 0, 0, and OH
vary for the individual components in each lumped
species necessitating the computation of "average"
rate constants.
2. The relative distribution of the hydrocarbons in
each lumped species will change throughout the
course of the photooxidation necessitating a change
in "average" rate constants with time.
For lumping by hydrocarbon reactivity (with OH):
Advantages -
1. The definition of the lumped species would correspond
closely to the role played by the individual hydro-
carbons comprising it in the conversion of NO to
39
-------
2. Since the reactivity of each lumped species is
roughly invariant in time, rate constants and
stoichiometric coefficients for the lumped OH-
HC reaction would not require adjustment during
the course of the reaction.
Disadvantages -
1. Each grouping would contain hydrocarbons of all
classes, making it difficult to account for the
distribution of free radicals produced as a re-
sult of reactions with 0, 0, and OH.
2. In the late stages of the photooxidation, ozonolysis
reactions assume a level of importance equal to or
greater than that of OH. A lumping on the basis
of OH reactivity may no longer reflect the reactivity
distribution of the total mixture at that stage.
Neither mode of hydrocarbon lumping appears overwhelmingly
superior to the other. Nevertheless, lumping by hydrocarbon
class seems to offer -several advantages over lumping by
reactivity. First, fewer stoichiometric coefficients need
be specified in the former method, thereby leading to fewer
unspecified parameters. Second, rate constant values for
hydrocarbon-OH reactions are in many cases not known precisely
enough to permit a clear distinction to be made among hydro-
carbons as to reactivity class. Third, atmospheric measure-
ments are made according to hydrocarbon class, and lumping
by class would enable direct comparisons of mechanism
predictions with atmospheric data. For these reasons, we
will subsequently employ hydrocarbon lumping by class in
our development of a general mechanism.
40
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2. Lumping of Radicals
The second aspect of the overall lumping problem is
the representation of free radicals. The two extremes
in the representation of radicals are the specific mech-
anisms in which no lumping is used (each radical species
is a distinct entity) and the qualitative mechanism em-
ployed earlier in which all free radicals were combined
into a single species R. The first limit is unrealistic
from a computational point of view and also in light of
our incomplete knowledge of free radical rate constants.
In contrast, the other limit does not afford us the ability
to distinguish the effect of different hydrocarbon mix-
tures on the concentration/time behavior of a specific
system. Therefore, we seek a basis for the lumping of
radicals that lies somewhere between these two extremes.
A detailed study of free radical reactions in photo-
chemical smog (Leighton, 1961) indicates that radicals
of similar structure usually undergo similar reactions
at roughly comparable rates. This suggests that the
most detailed representation of radicals would involve
having separate species for each radical class. The
classes of radicals involved have already been introduced.
They are
R- alkyl
•
RCO acyl
ROD' peroxyalkyl (including HO?')
RfOO' peroxyacyl
RCO- acylate
RO* alkoxyl (including OH-)
41
-------
In an earlier section we listed several of the most
probable reactions involving these radicals that would
take place in a hydrocarbon-NO.. -air system. We also
A
illustrated typical histories of acyl and alkyl radicals
in such a system. Based on these likely reactions, we
wish to propose a lumping scheme which is consistent
with the probable chain lengths of each radical (and thus
the conversion rate of NO to NC^).
i) Alkyl radicals - We assume that alkyl radicals quickly
add Oj to form peroxyalkyl radicals. Thus R00«, and
not R', need specifically enter into the mechanism.
ii) Acyl radicals - We assume that acyl radicals * like
alkyl radicals, quickly add 02 to form peroxyacyl
radicals. Thus, RCOO*, and not RCO, need specifically
enter into the mechanism.
iii) Peroxyalkyl radicals - These radicals undergo reaction
with NO to form NO^. Thus, they remain in the mechanism,
Because of the importance of H02f we remove it from
the class R00« and treat It as a separate species.
iv) Peroxyacyl radicals - Like ROD-, these can react with
both NO and N02* They are included in the mechanism.
v) Acylate radicals - These radicals result from reaction
of NO and peroxyacyl radicals. We assume that they
decompose quickly to form alkyl radicals (hence, peroxy-
alkyl radicals) and C02. Thus, they are not included
in the mechanism.
vi) Alkoxyl radicals - These radicals result from reaction of
peroxyalkyl radicals with NO and from ozonolysis of olefins
and enter into reactions with NO and N02 to form stable
products. The most important member of this class is the
hydroxyl radical. Because of the extreme importance of
OH, it seems desirable to remove OH from the RO class
and retain each in the mechanism.
42
-------
Summarizing, the radicals which appear to be of sufficient
importance to warrant separate treatment are:
RQO* (excluding HO,*)
RCOO*
RO- (excluding OH*)
OH*
H02-
3. Formulation of a Lumped Mechanism
The purpose of this section is to present the combined
conclusions of the previous two sections in a manner
illustrative of the development of a lumped mechanism.
In particular, we will employ the lumping scheme suggested
for hydrocarbon in section 1 and the categorization of
radicals described in section 2.
We first rewrite the hydrocarbon reactions so as to
correspond to the preferred lumping criterion, namely
by hydrocarbon class:
HC^ = olefins
HC2 = aromatics
HC, = paraffins
HC. = aldehydes
43
-------
HC-j^ + 0 -»• ROD- + aRCOO- + (1 - a) HO--
o
HC, + 0_ -»• RCOO- + RO- + HC,
13 4
HC1 + OH- + ROO-
HC2 + 0 -»- ROO- + OH-
HC2 + OH- -»- ROO- + H20
HC3 + 0 -»• ROO- + OH-
HC3 + OH- -^ ROO- + H20
Q
HC4 + 0 -»• RCOO- + OH-
o
HC4 + OH- -»• 6RCOO- + ( 1 - 6) H02- + H20
a is the fraction of carbon atoms attached to the double
bond in a mono-olefin which are not terminal atoms on
the chain; thus, this fraction can be specified a priori
B is the fraction of total aldehydes which are not
formaldehyde. Both parameters can be specified with a
high degree of confidence.
Consider the 0-HC., reaction for propylene and 2-
butene which, respectively, contain external and inter-
nal double bonds.
0 + CHCH=CH
CH3CH2- + CHO
44
-------
0 + CHCH=CHCH
3CH=CHCH3 - |CH3CCH2CI?3 - »• CHjC +
0 0
If we now assume that alkyl and acyl radicals react rapidly with
*
02 and that CHO decomposes into CO + H02 in the presence of 02,
these reactions can be rewritten in our generalized notation
as
and
CHCH=CH
RCOO-
0 + CH.CH=CHCH, •»• R00- + RCOO-
3 3 2 II
Now, if we further assume that 0 will react with equal proba-
bility with either carbon attached to the double bond, a = h
for propylene and o = 1 for 2-butene. By the same reason-
ing a can be shown to be zero for ethylene.
During smog chamber studies of the propylene-NO system,
A
equal quantities of formaldehyde and higher aldehydes are
observed to form. B is thus equal to h. In the case of
toluene, Altshuller et al. (1970)have observed that only 151
of the aldehydes are formaldehyde. In this case 8 is equal
to 0.85.
In Table 4, we summarize the full mechanism proposed, an
assemblage of all the inorganic, hydrocarbon, and free radical
reactions into a generalized lumped mechanism. Note that the
reactions of the inorganic species and the radical species,
n
ROO-, RCOO-, and RO' f have already been outlined in previous
sections.
45
-------
TABLE 4.
A Lumped Kinetic Mechanism for Photochemical Smog
0
0
0
NO 2
+ 02
°3
+ NO
0 +
+ N02
°3 +
N03
N03 +
+ hv
+ M
+ NO
+ M
NO 2
+ M
NO 2
+ NO
NO 2
N2°5
i
•i
3
•>
it
-*•
5
£
7
8
NO
°3
NO
NO
NO
NO
NO
+ 0
+ M
2 + °2
, + M
i.
+ °2
3 + M
\
3 2
•*• 2N02
9
10
N2
NO
°5 .
2 + N03
4,0, + H,0
£t D £*
NO + HNO,
11
12
2HN03
HN00 .+ NO,
HN02
HN0
-^ H,0 + 2NO,
NO
N02 + H20
2HN0
15
HN02 + hv
OH + N02
OH + NO + M
OH + CO + (02)
H02 + NO
16
NO + NO,
OH + NO
HNO,
H20
18
19
HNO.
COo
M
H0
20
OH + NO
The N02-NO-03 Cycle
Important Reactions
of 0 with Inorganic Species
The Chemistry of N03,
N205, and HN03
Reactions of HN03 with
Inorganic Species
Chemistry of HN02
Important Reactions of
OH with Inorganic Species
Oxidation of NO by H07
46
-------
TABLE 4. (Continued) A Lumped Kinetic'Mechanism for
Photochemical Smog
Pi
RCOO
«2°2
HCj
HCX
HC
HC2
HC
HC,
HC4
*T
HC4
ROO
T*
RCOO
RO
RO
RO
H02
H02
+ hv
, + 0
+ °3
+ OH
2 + 0
+ OH
3 + 0
+ OH
+ hv
+ OH
+ NO
(Q2)
+ NO,
L
* o2
+ N02
+ NO
+ H02
+ ROO
21
22
23
->•
2«t
-»•
25
-»•
26
27
28
29
30
31
-V
32
-»•
33
20H
ROO +
fl
RCOO
ROO +
ROO +
ROO +
ROO +
ROO +
BROO
ft
BRCOO
RO +
RgO +
II
aRCOO + (1 - cOHO^
i.
+ RO + HC4
HC4
OH
H2°
OH
H2°
+ (2 - B) HO,
+ (1 - B) HO, + H,0
/ / .
* M 4
NO, x
2
N02 + C02
•»• RCOONO.
-»•
35
-»•
36
•+•
37
•*•
38
•>•
39
H02 +
RON02
RONO
H2°2
ROOH
L
HC4
J
*'°2
+ °2
Photolysis of H,0,
Hydrocarbon
Oxidation
Reactions
Reactions of Organic
Free Radicals with
NO, N02, and 02
Peroxy Radical
Recombination
Reactions
2ROO •»• ROOR +
46 a
-------
Given the mechanism shown in Table 4, we can now examine
the assumptions inherent in the HS and EM mechanisms of Table 1,
Both the HS and EM mechanisms'have provisions for two
lumped hydrocarbon species, usually specified to be of
"high" and "low" reactivity. In each all the peroxy
radicals are combined into the single species R09.
t*
The main result of the reaction of atomic oxygen with
lumped species is the formation of peroxy radicals, rep-
resented by
HC + 0 -»• aR02-
Notice that production of hydroxyl radicals from 0 atom
reactions with paraffins and aromatics has been neglected
tyi this step,
The ozone-hydrocarbon reactions are assumed to yield
peroxy radicals and aldehydes,
03 + HC -*• YR02- + y'RCHO
In the new mechanism it is assumed that a peroxyacyl and an
alkoxyl radical, rather than the peroxyalkyl radical>form.
The OH-hydrocarbon reactions are assumed to yield pertfxy
radicals and a small quantity of aldehydes,
HC + OH- -> BR02- + B'RCHO
The remaining organic reactions are
47
-------
R02- + NO -»• N02 + eOH-
R02 + N02 -»• PAN
By comparison o£ the first reaction with the more correct
reactions,
ROO- + NO + N02 + eOH- + (1 - e) RO'
RCOO- + NO -f N02 + ROO-
we see that regeneration of ROO' has 'been neglected in the
conversion of NO to N02 by peroxyalkyl and peroxyacyl rad-
icals. Thus, the e in the HS and EM mechanisms cannot be
interpreted as the fraction of R02* that is H02« as it is
in the more correct reactions, but rather only as an empiri-
cal parameter. As a result, the original stoichiometric
coefficients o , 6 and y cannot be assigned the actual values
that would be expected from the chemistry of the individual
species. Rather, the a , B , Y and e become a set of
parameters governing the chain length (the average number
of free radical reactions, or propagation steps, that occur
as a result of each initiation reaction). This lack of
direct correspondence of the generalized stoichiometric
coefficients in the HS and EM mechanisms to actual stoichio-
metric coefficients is the chief weakness of the two mech-
anisms. .By virtue of its increased detail, the new lumped
mechanism of Table 4 circumvents this shortcoming, as the
stoichiometries are derivable directly from the underlying
chemistry of each elementary reaction.
48
-------
The generalized coefficients 6 and e in the HS
mechanism play a role in simulating the effect of CO.
It has been observed experimentally that CO concentra-
tions of the order of 100 ppm or more accelerate the
conversion of NO to NO, and the consumption of hydro-
carbons when compared to similar experiments carried out
in the absence of CO. Since OH' attacks both HC and CO
and since the products of both reactions are radical
species capable of oxidizing NO to N0£ (RC^' ^n tne f°rmer
case and HO-- in the latter), in order for the addition
of CO to a system to result in an increase in the rate of
conversion of NO to NO,, it is necessary that the number
of NO molecules oxidized as a result of the CO'-OH- reaction
(always equal to one) be greater than the number of NO
molecules oxidized as a result of the HC-OH- reaction.
If more than one NO molecule is oxidized (on the average)
to N02 as a result of chains initiated by the HC-OH- reaction,
then the addition of CO to the system would effectively re-
sult in CO inhibiting the rate of oxidation of NO to NO,.
This effect would be attributable to the scavenging of
OH- available for possible reaction with HC, an overall
reaction capable of oxidizing more NO molecules than the
single H02' produced in the CO-OH reaction. This is an
apparent inconsistency, since, as we have noted, experi-
mentally CO has been observed to accelerate the conversion
of NO to NO,- In Part III we propose a possible explana-
tion for this effect.
E. The Validation of Mechanisms With Smog Chamber Data
The validation of a mechanism using smog chamber data consists
of four basic steps:
1. Estimation of Parameters. Estimate all unspecified par-
ameters in the mechanism by comparison of the predicted
concentration-time profiles with experimental data.
49
-------
Estimation of lumped rate constants and stoichioraetric
coefficients can be carried out on a digital computer
using either automatic parameter estimation routines
or by trial and error. Of these two alternatives, by
far the automatic parameter estimation is clearly
preferable.
Determination of Confidence Regions. Using the pre-
dictions of the fitted model and the corresponding
experimental data, determine the confidence limits
associated with the estimated parameters. The level
of uncertainty is a function of the model as well as
of the data. A large confidence region indicates a
high level of uncertainty in the joint parameter
estimates, while an elongated region suggests that
variations in the magnitude of the parameters have
little effect on the model predictions.
Validation and Exercise of Mechanism. Employing
the parameter estimates determined above, compute
the predictions of the mechanism corresponding to
available experiments over a range of initial con-
ditions and, if possible, light intensities. Com-
pare predictions with experimental observation, the
experiments should clearly be different than those
used to determine the parameters, and,, if possible,
should include conditions extrapolated beyond those
of the experiments used to estimate the parameters.
Sensitivity Analysis. Perform a sensitivity analysis
of the mechanism for the conditions in step 3. Vary
each parameter over its expected range of values to
determine the effect of these variations on the pre-
dicted concentration-time profiles. Compare the range
of possible predictions with the data, taking careful
account of the level of accuracy of the data.
50
-------
In this section we shall consider briefly each of these
aspects of validation. The objective is to set forth a
consistent strategy for the validation of all present and
potential mechanisms using modern techniques of parameter
estimation and statistical analysis.
1. Estimation of Parameters in Reaction Rate Equations
From Experimental Data
During the past 10 years powerful algorithms for
estimating parameters in sets of coupled nonlinear ord-
inary differential equations have been developed (for
example, see Bard and Lapidus (1968)). In this section
we shall briefly review some of the key aspects of the
estimation of parameters in reaction rate equations.
The problem can essentially be defined as follows.
We have a set of N reaction rate equations of the form
* '' * *' ' 1 = ' ' * *
c-
which contain p unknown parameters k,,...,k . Those
parameters which are known are not explicitly indicated
in f- . In addition, we have a set of M experimental
concentration measurements y^ftj.), i = l,2,...,Mj
r = 1,2,...,R where M <_ N (not all dependent variables
need be measured) and R is the number of times at which
51
-------
data have been taken. These measurements are related
to the concentrations in the model by
y.(t ) = ci(tr) + (measurement errorsj
i * 1,2,...,M
where the first M concentrations are those that are
measured. The so-called output error methods are those
in which the k's are determined such that the sum of
squares of the errors between the data and the predictions
of the model,
R M 2
£ Z [yi(V - ci
-------
A general method which avoids the problems inherent
in the output error methods and has been successfully
applied to a variety of real data is the maximum likeli-
hood method (MLM). The MLM as developed by Mehra (1970)
is comprised of three parts: (1) correction of measured
concentrations for measurement error using Kalman filter-
ing, (2) estimation of parameters in the mechanism using
a modified Newton-Raphson optimization procedure (Lee,
1968), and (3) estimation of measures of model and
measurement error.
2. Analysis of the Accuracy of Parameters Estimated in
Rate Equations from Experimental Data
The second step in the validation of a kinetic mech-
anism is the analysis of the accuracy of the parameter
estimates obtained in the first step. We assume that
the model used,is adequate to represent the data. If it
is not, the parameter estimates will contain inaccuracies
due, not only to the errors in the data, but also to the'
errors in the model. Thus, the procedures involved in
this second step are designed to determine the inaccuracies
in parameter estimates due only to errors in the data
(under the assumption that the model is correct).
A measure of the precision of an estimated value is '.its
estimated standard deviation. The standard deviation .6,£.
a parameter estimate can be interpreted as follows. If
we perform a large number of replicate experiments, each
time estimating the same parameter, we can consider the
estimate as a random variable since the data from which
it has been estimated Contain random errors. The standard
deviation of the parameter estimate is a measure of its
53
-------
variation about the mean of the repeated determinations.
Based on the standard deviation we can specify the con-
fidence limits on the parameter estimate. For example,
the 95% confidence limits are those two values of the
parameter estimate between which we would expect the true
value to lie with 95% probability.
In most parameter estimation procedures an estimate
of the parameter standard deviation is obtained along
with the parameter estimates themselves. The estimates
of the standard deviations of individual parameters de-
pend on (1) the data, (2) the data record length, and
(3) the initial conditions. Analyses involving deter-
mination of standard deviations alone are concerned with
only one parameter. Joint measures of uncertainty (con-
fidence regions) are required in multi-parameter analyses.
An excellent discussion of the determination of confi-
dence intervals for parameters estimated in ordinary
differential equations is given by Rosenbrock and Storey
(1966).
The relationship between parameter estimation and
the specification of confidence regions may be illustrated
pictorally. Consider as an example the one-dimensional
parameter estimation problem shown in Figure 3, in which
the error criterion J is plotted against the value of
the parameter estimate for two cases: (1) curve A, a
"good" experiment, and (2) curve B, a "poor" experiment.*
"Good" is used in the sense of rich in information content,
"poor" in the sense of low in information content.
54
-------
The two curves shown might arise from choices of dif-
ferent initial conditions for the smog chamber reactants.
A A
The best estimates, kA and kg , are those at the res-
pective minima of the error criterion J . In a one-
dimensional example, the curvature of J in the vicinity
of the minimum is related to the confidence (or degree of
certainty) with which the parameter can be estimated.
Because of the larger curvature of curve A, the true
parameter value lies between points 1 and 2 with a higher
probability than for the case of the "poor" experiment.
This same notion of tighter confidence limits implying
better parameter estimates carries over to the multi-dimen-
sional parameter estimation problem. Illustrations of
this case are given by Rosenbrock and Storey (1966).
Curve B
(1)
Parameter
estimate
value
FIGURE 3. One-Dimensional Parameter Estimation Problem
55
-------
3. Extrapolation of the Model to Data Other Than That
Used to Estimate Parameters
A meaningful test of the accuracy of the parameter
estimates is prediction. This is typically carried out
by calculating concentration-time profiles from a set
of data for which estimation has not been performed
and comparing the predictions with the data. Thus, one
reserves a few sets of data (not using them for estima-
tion) for the purpose of verifying the accuracy of the
parameter estimates obtained from the main body of data.
The comparison between the predicted responses and the
measured data is carried out primarily by examining the
statistical properties of the residuals or fit errors.
The model fit is deemed acceptable when the residuals
are completely uncorrelated sample point to sample point.
If any systematic trends are left in the residuals, the
kinetic mechanism presumably is not fully adequate to
describe the observed data.
Various statistical tests are commonly used for model
verification. Principal among those that test ,the cor-
relation between the sample points are the whiteness test
(Mehra, 1971) and the X2--test (Box and Jenkins, 1970).
More recently Akaike (1970) has derived a goodness-of
fit-test based on the final prediction error (FPE) criterion,
This test computes the expected "one-step ahead" pre-
diction error of the fitted mechanism. If these statis-
tical tests, when applied, indicate that the assumed model
structure is inadequate to fit the observed data, modifi-
cations to the model must be made.
56
-------
^. Sensitivity Analysis
The final phase of the validation exercise is a
sensitivity analysis. After establishing estimates
for all parameters, the governing rate equations are
integrated to obtain concentration-time profiles cor-
responding to a particular set of conditions (initial
concentrations'and light intensity). These concentration-
time profiles constitute the so-called base case. Then,
each of the parameters, the initial conditions, and the
light intensity is systematically varied to ascertain
the effect on the computed concentration-time behavior.
The analog computer is particularly suitable for a sensi-
tivity analysis since parameter variations can be effected
by simply changing a potentiometer setting.
F. Adaptation of Kinetic Mechanisms for Atmospheric
Predictions
Up to this point we have confined our attention to the
development and validation of a kinetic mechanism capable of
simulating smog chamber reaction processes. The'ultimate
objective of developing such a mechanism is its use in at-
mospheric simulation studies. Therefore, once a mechanism
capable of describing smog chamber experiments becomes avail-
able, we must consider its adaptation for use in the prediction
of atmospheric reaction phenomena. In this section we shall
outline those elements of atmospheric processes which may
not receive recognition in a mechanism based solely on lab-
oratory studies.
57
-------
Kinetic mechanisms for photochemical smog previously
formulated have not included S02 as a primary reactant.
Both the lack of high SO, concentrations in the Los
Angeles basin and a lack of understanding of the processes
responsible for S02 oxidation in a photochemical oxi-
dizing environment are responsible for its omission.
However, there is clear evidence in Los Angeles, for
example, that areas of the basin with the highest SO-
concentrations frequently experience heavy haze forma-
tion. In addition, laboratory smog chamber experiments
in which S02 is present in many cases have exhibited
exceptionally high rates of aerosol formation. Clearly,
there is a great need to include SO- as a primary
reactant in photochemical kinetic mechanisms.
Somewhat related to the question of the role of S02 is
the general area of aerosol chemistry in photochemical
air pollution. Little is known at present about the
actual mechanisms of formation of photochemical aerosols,
although it is believed that aerosols may act primarily
as sinks for gas phase reaction products rather than
as catalysts for the gas phase reactions. No photo-
chemical kinetic mechanisms available at this time in-
clude aerosol formation. In order to account properly
for the effects of aerosols on observed gas phase con-
centrations and in order to predict rates of urban haze
formation, it will be necessary to include reactions
leading to aerosol formation in such kinetic mechanisms.
Many of the reported rate constants for atmospheric
reactions have only been measured at 298°K. In many
cases, such as for hydrocarbon oxidation reactions, there
58
-------
is little information on activation energies, and
thus on the temperature dependence of the rate constants.
Obviously, application of a kinetic mechanism to at-
mospheric reactions requires knowledge of the tempera-
ture dependence of rate constants. Such dependence
can easily be included in kinetic mechanisms; ithe
difficulties lie, however, in the experimental measure-
ment of values at different temperatures.
Most smog chamber experiments are conducted with a
constant value of the radiation intensity. Hence,
constant values for the first-order photodissociation
rate constants, such as for N02, HN02, H202 etc., pre-
vail. In the atmosphere, however, the radiation in-
tensity changes naturally throughout the course of
a day as well as when clouds appear and hazes are
present. As with the temperature dependence of rate
constants, changes in radiation intensity can be easily
accounted for in a mechanism as long as the effect of
the intensity changes on the dissociation rate constants
is known. The difficulty arises in relating the actual
radiation intensity at any time to the values of these
dissociation rate constants. In an actual atmosphere,
radiation intensity will vary with height above the
ground due to the presence of aerosols which may scatter
and absorb solar radiation. Ultimately, there must be
included in full scale urban models a submodel which
computes radiation intensity as a function of location
and time in the presence of cloud cover and atmospheric
aerosols.
59
-------
5. Smog chamber experiments are generally carried out
with well-defined initial hydrocarbon concentrations
and compositions (except in auto exhaust irradiation
experiments). In the atmosphere, however, the hydro-
garbon composition is a function of time and location.
Lumped reaction mechanisms, as we have seen, require
classification of hydrocarbons into groups depending
either on the hydrocarbon class or reactivity. Thus,
the application of these mechanisms to the atmosphere
will require knowledge of the spatial and temporal
distribution of- hydrocarbons, at least by class. The
mechanisms, of course, must have the ability to treat
such inhomogeneities. However, the key problem is
that source inventories for hydrocarbon emissions and
monitoring data generally report total hydrocarbons
rather than a breakdown by class. The current lack of
specific knowledge of atmospheric hydrocarbon distri-
butions will hinder the application of lumped mechan-
isms to the atmosphere. In view of this lack of knowledge,
the lumping employed in atmospheric studies may very well
be different than that used for smog chamber studies.
There are two other phenomena which may be important
in the atmosphere and not in a smog chamber. First, there
may exist sinks for gas phase species. Potential sinks in-
clude aerosol particles, vegetation^ and soil. Such sinks,
while not altering the fundamental kinetics of the system,
will have to be accounted for in an overall model. Second,
the presence of turbulent concentration fluctuations
60
-------
will tend in some cases to cause the actual reaction
rate to be different from the rate predicted on the
basis of the mean concentrations. In order to account
for the effect of turbulence on the observed reaction
rates, it may be necessary to modify the kinetic equations
so as to include the effect of turbulence within them.
This point will be discussed in more detail in Sections
III and VI.
Finally, we note that we have been discussing urban
scale reaction phenomena. On a somewhat smaller scale
there are two categories of source effluents that may
have associated reaction phenomena quite different from
that occurring on an urban scale:
1. Plumes - High local concentrations, temperatures
and relative humidities may result in different
reaction processes being important in plumes
than in the more dilute urban basin; and
2. Roadway Mixtures - High fluxes of NO, CO and hydro-
carbons, leading to elevated concentrations locally,
may result in much higher reaction rates in the
vicinity of the roadway than are normally expected
in the regions of the airshed removed from the
roadway. The extent to which these rapid reactions
influence overall conversion rates in the atmosphere
is not known.
61
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III. URBAN AIRSHED MODELS
Many difficult questions and complex issues arise
in planning for the abatement and control of air pollution
in an urban area. Certain key aspects of abatement plan-
ning are best addressed through the use of an urban air-
shed model; in some cases there are no alternative
means of examining the critical issues. Included among
those topics for which an airshed model may be particular-
ly useful as an analytical tool are:
the establishment of emissions control legislation,
the evaluation of proposed emission control
techniques and strategies,
the planning of locations of future sources of
air contaminants,
planning for the control of air pollution incidents,
the assessment of responsibility for existing
levels of air pollution.
An airshed model is an essential component of planning
studies in air pollution control because there commonly
exists a need to establish a quantitative relationship
between source emissions rates in an urban area and the
magnitude of ground level contaminant concentrations that
result from those emissions. Every urban locale has unique
climatological and meteorological conditions. The spatial
distribution of contaminant emissions, as well as the average
composition of these emissions, varies from city to city.
The concentration of secondary pollutants, formed in the
atmosphere through the chemical reaction of primary (or
emitted) pollutants, is influenced by local meteorology,
62
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emissions patterns, intensity of solar radiation, and
many other variables. Clearly, in order to predict the
spatial and temporal distributions of ground level con-
centrations of atmospheric contaminants, it is necessary
to account for these many complexities through the simul-
ation of the physical and chemical processes that actually
give rise to the air quality observed - in short, through
the use of an airshed model.
An airshed model may take many forms. It may be
based on the equation(s) of conservation of mass for
individual species, the equations of conservation of
momentum, the equations of conservation of energy, or
combinations of two or all three of these types of balances.
Most commonly, however, as we shall discuss in this chapter,
such models are based on the equations of conservation of
mass. Models may describe the behavior of reactive species,
or they may be'limited in application to inert species.
Furthermore, models may be formulated under the assumption
of steady state behavior, or they may be descriptors of
time-varying behavior. Temporal and spatial resolution
of models may vary widely. Models may be based on a fixed
grid, or they may be formulated so as to trace the variations
in concentration in an "air parcel" moving with the average
wind field.
Models based on the equations of continuity, of
course, cannot predict variations in the velocity field
(the momentum equations are needed) or the temperature
field (the energy equations are needed). Wind and temper-
ature information thus must be input as data. What such
63
-------
models can do, however, is relate in one equation (or
set of equations, for more than one species) the effects
of all the dynamic processes that influence the mass
balance on a parcel of air. These include the transport,
turbulent diffusion, and reaction of all pollutant species
of interest. Also treated in such models are the intro-
duction or removal of species.
A model based on the equations of conservation of
mass requires, as a part of its formulation or as data
input, information falling into the following categories:
emissions, atmospheric chemistry, and meteorology. Emissions
data includes information concerning emissions rates of
all pollutants of interest from both fixed and mobile
sources, often as a function of both location and time.
Meteorological information needed as input includes
wind speed, wind direction, mixing depth (or temperature
as a function of elevation),. and horizontal and verti-
cal turbulent diffusivities, again usually as^a function
of location and time. A kinetic mechanism for atmospheric
reactions is an essential component of a model that is
capable of predicting concentrations of chemically react-
ing species, as is knowledge of reaction rate constants
for the multiplicity of reactions that comprise the
mechanism.
Once the model is properly formulated, and informa-
tion concerning emissions, chemistry, and meteorology is
appropriately incorporated, the model may be solved to
obtain predicted concentrations of individual species
as a function of location and time. Air quality data
are normally required to assess the accuracy of the model,
by comparing predictions with observations. Methods of
solution may be simple or complex, involving small or
large amounts of time. In the case of steady state models
64
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based on the conservation of mass for a single species,
solutions may be read directly from charts or tables.
For more complex formulations, numerical integration of
the governing equations is usually necessary. Such
solution procedures are commonly computer-based, often
complex mathematically, and, in some cases, very time
consuming.
In this chapter, we present a detailed discussion
of urban airshed modeling. We first examine briefly the
fundamental basis for models, so that we can, in a method-
ical manner, present the assumptions upon which commonly
invoked approximations for the fundamental governing
equations are based, We then discuss some of the more
practical aspects of modeling, such as the implementation
of models and the levels of uncertainty in the input
variables. We then examine in some detail the relation-
ship of the kinetic mechanism to the urban airshed model.
Some specific questions that may be of interest to the
reader that we address include the following:
1. What are the inherent limitations imposed on the
spatial and temporal resolution employed in air-
shed models?
2, What levels of accuracy can be expected from air-
shed models in view of the uncertainties in input
variables and the inherent limitations of the models
themselves?
3. What fundamental restrictions, if any, are imposed
on kinetic models that are to be included in air-
shed models?
4. What theoretical problems require further study in
order to (a) better define the applicability and scope
of current airshed models and (b) develop improved
models?
65
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Before proceeding, we wish to point out that the
presentation which follows is a rather carefully con-
structed exposition of modeling. Our aim in writing
it in this way is to provide a rigorous, unambiguous,
concise development of the forms of airshed models that
are commonly in use. A major consequence of adopting
this approach, however, is that the presentation is
largely mathematical, often involving relationships
unfamiliar to the chemist. As a result, we make two
recommendations to the reader. First, we suggest that
on a first reading he not concern himself unduly with
the mathematical arguments presented. Skimming the chapter
should be sufficient. (We are aware, in fact, that many
readers may not wish to confront the mathematics directly
at any time, whether on a first or sixth reading.)
Second, we would urge any reader who is seriously
concerned with the role of chemical kinetics in airshed
modeling, or with airshed modeling in general, or who
will be working with such models, to carefully read the
chapter (after skimming it initially) to gain an under-
standing of the basis of such models and of their uses,
their shortcomings, and their limitations. It is to
provide such an understanding that this chapter was
included in this document.
A. Fundamental Theory of Air Pollution Modeling
An urban air pollution model is, in essence, a description
of the dynamic behavior of inert and reactive gaseous species
in a turbulent flow. In this introductory section we discuss
possible approaches to, and difficulties inherent in, properly
66
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describing the transport, turbulent diffusion, and reaction
of gases in the atmosphere. In the section following we
discuss the types of airshed models that have been developed
to date, together with the assumptions underlying each. We
include this and the following section because we believe that
it is vital that individuals who develop or apply airshed
models be clearly aware of the assumptions inherent in their
derivation, and thus of the restrictions that limit their
applicability.
In this section we shall develop the relationships for
certain statistical properties of the concentrations of species
in turbulence. These relationships will subsequently form
the basis for the governing equations on which urban airshed
models are based. The treatment in this section is divided
into two parts, corresponding to the two fundamental ways
of describing the behavior of species in turbulence. The
first is the so-called Eulerian approach, in which the be-
havior of species is described relative to fixed coordinates
(the most common way of describing concentration changes in
a flowing system). The second is the so-called Lagrangian
approach, in which concentration changes are described from
the viewpoint of one traveling with the fluid. The two
approaches yield different types of mathematical relationships
for the pollutant concentrations. Each type of relationship
is, of course, a valid description of turbulent diffusion;
however, each has shortcomings which limit its applicability
and which, of course, render exact description of the species
concentrations impossible.
67
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1. The Eulerian Approach
Consider N species in a fluid. The concentration of
each species must, at any instant in time, satisfy a material
balance taken over a volume element. Thus, any accumula-
tion of material over time, when added to the net amount
of material convected into the volume element, must be
balanced by an equivalent amount of material that is pro-
duced by chemical reaction in the "element", that is
emitted into it from sources, and that enters by molecular
diffusion. Expressed mathematically, the concentration
of each species c- must satisfy the continuity equation,
ic. 3 3 -2-
o = l a a
(1)
+ Si(x, t)*
where
u = a component of the wind velocity, a = 1,2,3
D^ = molecular diffusivity of species i in air, i = 1,2,...,N
R. = rate of generation of species i by chemical reaction
T = fluid temperature
S = rate of addition of species i from volumetric source
x represents the position vector in the system, (x^x^x-j) =
68
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In addition to the requirement that the c- satisfy
(1), the fluid velocities u and the temperature T must
satisfy the Navier-Stokes and energy equations, respectively,
which themselves are coupled through the u , c. and T
with the total continuity equation and the ideal gas law.
For many fluid systems it is necessary to carry out a sim-
ultaneous solution of the coupled equations of mass, mom-
entum and energy conservation to account properly for the
changes in T , ci and UQ and the effects of the changes
of each of these on each other. In considering the behavior
of contaminants in air, however, it is usually quite reason-
able to assume that, since pollutants are, in general,
present in the atmosphere at parts-per-million concentra-
tions, the presence of pollutants in the atmosphere does
not affect the meteorology to any detectable extent. Under
this assumption, the equations of continuity for contam-
inant species can be solved independently of the coupled
momentum and energy equations. Consequently, the fluid
velocities u can be considered to be independent of the
c^ . There is, however, perhaps one important exception,
one that is frequently observed in the Los Angeles area--
the attenuation of incoming radiation by atmospheric con-
taminants that are present in high concentration. The
temperature of the polluted layer may also be measurably
altered due to its absorption, reflection and scattering
of radiation. None of the models currently available in-
clude provisions for this coupling between pollutant con-
centrations, energy impact, and meteorology. Although in
most cases we would expect these effects to be negligible,
a lack of their consideration is a possible shortcoming
of current models.
69
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Since atmospheric flows are turbulent, it is conven-
tional to replace u by the sum of a deterministic
and a stochastic component, u. + u! . Replacing u by
u + .u1 in (1) gives*
a a ^ j e>
3
3Ci +V 3
a=l a a=l
(2)
+ Si(x,t)
Since the u1 are random variables, the c^ resulting
a i
from the solution of (2) must also be random variables.
Thus, the determination of the c^ , in the sense of
specifying a value of this variable at any time, is not
possible; rather, we can at best derive the probability
density functions satisfied by the c. . Unfortunately,
the complete specification of the probability density
function for a stochastic process as complex as atmos-
pheric diffusion is almost never possible. Instead, we
must be satisfied with the determination of the mean value,
t, of the random concentrations. This mean value
* We assume that the temperature is constant, and thus the
dependence of R^ on T need not be explicitly indicated.
It is not necessary to make this assumption; rather, it
simplifies the presentation.
t We denote the mean value of the concentration by brackets,
<>, and that of the velocities by overbars, since the process
by which the average velocities are determined is ordinarily
a time average rather than an ensemble average.
70
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is interpreted as the average value of c^(x,t) at
location, x , at time t over a very large number of
repetitions of the turbulent flow experiment. In the
terminology of probability theory, such a mean value
is called an ensemble mean. Clearly, an individual
measurement may differ considerably from the mean < c-> .
We represent the concentration c. as + cj ,
where the concentration fluctuation cj has by definition
a mean value of zero, = 0 .
Substituting c. = + cj into (2) and taking the
mean value of the resulting equation yields
3 - a
- and , o=l,2,3 . We
thus have four dependent variables and only one equation.
In order to provide a basis for solving this equation one
might attempt to generate equations for the new dependent
variables , a=l,2,3 . We can derive an equation for
the by subtracting (3) from (2), leaving an
equation for c' , and then multiplying the resulting
equation by u' and averaging over all terms. If this
is done, the constructed equations take the form
71
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(4)
ID 4- - ] a=l,2,3
While we have derived the desired equations, we have at the same
time introduced six new dependent variables ,
o, p
a,B = 1,2,3 . If we generate additional equations for these
variables, we find that still more dependent variables
appear in these equations. This problem, arising in the
Eulerian description of turbulent diffusion, is called
the closure problem, a problem for which no general solution
has yet been found.
The problem of closure becomes more severe if a nonlinear
chemical reaction is occurring. Consider, for example, the
decay of the single species by a second order reaction.
7 2
Then the term in (3) becomes -k2( + <.c' >) ,
7
where is a new dependent variable. If we were to
2
write an equation for , additional new dependent
2 3
variables, , and < (3c'/3x.)(3cf/9Xg)>
are introduced.
In summary, in order to use Eulerian equations of the
type (3) to compute mean concentrations of air pollutants,
we must overcome the closure problem by assuming some
relationship between the dependent variables of higher order
and those of lower order. Shortly we shall discuss con-
ventional means of closing equation (3).
72
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2. The Lagrangian Approach
The Lagrangian approach to studying the behavior of
species in turbulence is based on considering the sta-
tistics of a single representative fluid particle in
the flow. The fundamental quantity which embodies all
the information on the statistics of a fluid particle
is the transition probability density:
Q(x,t|x',t') = the probability that if a single "marked"
fluid particle is at x' at time t' ,
it will undergo a displacement to x at
time t .
Although Q refers to a single fluid particle, it can
also describe the displacements of a "swarm" of fluid
particles, or a continuous distribution of solute in a
turbulent fluid, since the statistical behavior of a
single particle is derived in principle from that of a
very large number of identical particles.
The mean concentration of a solute at any location x
and time t can be related to that at an earlier time to
by the following general relation (Monin and Yaglom, 1971)
/»
Q(x,t|xo,t0) dxQ (5)
- oo
If, in addition to the material present at t , there are
continuous sources of the species (solute) in the fluid
injected at the rate S(x,t) , (5) becomes
73
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=J Q(x,t|xo,t0) dx0
-00
(6)
/t /* ***
J Q(x,t|xf,t') S(x',t) dx'dt1
This is the fundamental relation for the mean concen-
tration of a species in a turbulent flow in which there
are sources. The determination of given the
initial concentration distribution t0)> an^ the
sources, S(x',t')' , rests on the evaluation of the
transition density Q(x,t|xf,t') . In contrast to the
Eulerian approach, no closure problem arises here.
Instead, we need to know the probability that a particle
released into the flow can be found at any particular
location at any designated subsequent time. Unfortunately,
such a thorough knowledge of the properties of a turbulent
field is unavailable except in the simplest of circum-
stances. Also, there is no convenient way to include
nonlinear chemical reactions in the Lagrangian formula-
tion, since one would have to keep track of all possible
particle "collisions". Nevertheless, under certain con-
ditions (to be specified later) it is possible to use a
modified form of (6) as the basis for a model in which
nonlinear chemical reactions are admissible.
3. Summary
The techniques for describing the statistical properties
of the concentrations of tagged particles, such as air
74
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pollutants, in a turbulent fluid can be divided into two
broad catagories--Eulerian and Lagrangian. The Eulerian
methods attempt to formulate the concentration statistics
in terms of the statistical properties of the Eulerian
fluid velocities, i.e. the velocities measured at fixed
points in the fluid. A formulation of this type is very
useful in air pollution modeling, not only because the
Eulerian statistics are readily measurable*, but also
because the mathematical expressions are directly appli-
cable in situations in which chemical reactions are taking
place. Unfortunately, the Eulerian approaches lead to
a serious mathematical obstacle known as the closure
problem, for which no generally valid solution has yet
been found. A number of approximate solutions have been
proposed (see Section B) but each leads to an equation
which gives accurate results for only a limited class of
problems.
By contrast, the Lagrangian techniques attempt to des-
cribe the concentration statistics in terms of the sta-
tistical properties of the displacements of groups of
particles released in the fluid. The mathematics of
this approach are more tractable than that of the Eulerian
method in that no closure problem is encountered, but
the applicability of the resulting equations is limited
due to the difficulty of accurately determining the re-
quired particle statistics. Moreover, the equations are
not directly applicable to problems involving nonlinear
chemical reactions.
As determined from continuous time recordings of the wind
velocities monitored by a fixed network of anenometers.
75
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In the preceding sections we demonstrated that exact
solution for the mean concentrations of
even an inert species in a turbulent fluid is not in
general, possible using either the Eulerian or Lagrangian
approaches. We must now consider what additional assump-
tions and approximations can be invoked to derive the
equations upon which practical urban airshed models may
be based. In the section to follow we will proceed from
the two basic equations for , namely (3) and
(6), to obtain mathematical formulations for the urban
airshed models that are currently in use. A particularly
important aspect of the next section will be delineation
of the assumptions and limitations inherent to each model.
B. Approaches to Obtaining Approximate Models
We have seen that both the Eulerian and Lagrangian approaches
to the prediction of the behavior of species in turbulence lead
to certain difficulties which render exact solution for the
mean concentrations impossible. In this section we shall out-
line some of the more common approximations which are made
in order to obtain useful models for the mean concentrations
of reactive species in turbulence.
. 1. Eulerian Approaches
The objective of this subsection is to describe means
for obtaining a closed form of (3). To do this we intro-
duce relationships between the mean concentrations and
the new dependent variables in (3), , a = 1,2,3 ,
as well as any that might arise from < R.> if chemical
76
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reactions are taking place. For the moment let us
consider only the case of chemically inert species,
so that R. = 0 .
The simplest means of relating the to the
is by the mixing length assumption, i.e. that the
turbulent mass flux is linearly related to the
gradients of < c-> ,
3 3< c. >
= -£ Kag -^- a =1,2,3 (7)
e=i e
where K 0 is the (a , $ ) element of a tensor K and
OP
is called an eddy diffusivity. Since (7) is essentially
only a definition of the K . , which are in general func-
Ctp
tions of location and time, we have, by means of (7),
replaced the unknowns with a new set of unknowns,
KQe , a , 8 = 1,2,3 .
In using (3) two other assumptions not related to the
closure problems are ordinarily invoked, namely (1) that
molecular diffusion is negligible when compared with tur-
bulent diffusion and (2) that the atmosphere is incom-
pressible. With reference to (3) this implies that
32
Di aFlT-". at-^i^
and _
3u
77
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With these assumptions and (7), (3), for inert pollutants,
becomes
3 ^ 3 ^v^ a 3
-re- *V« -I3T- -£E £- (Ka6 -,;*-> * si(x,t)
a=l a a=l3=l a g
where the K „ are a function of location and time. If
ag
the coordinate axes coincide with the principal axes of
the eddy diffusivity tensor K , only the three diagonal
components of K are non zero. Since there is no preferred
horizontal direction we let these three components be
{ KH , KH and KV } . Equation (8) then reduces to a form
reminiscent of the ordinary molecular diffusion equation,
3 __ 3 „ 3 3
- 1 _ 3 rv 1 •> 3 rv 1
t a 3x 3x H 3x 3y H 3y
a=l a
+ Jz (KV ^£> + SiCx,y,z,t) (9)
i = 1,2,...N
This equation has been called by Monin and Yaglom (1971)
the semi-empirical equation of atmospheric diffusion.
Let us now consider the case in which chemical reactions
are occurring. We again direct the reader's attention to
(3). In air pollution modeling studies involving chemical
reactions it has been customary not only to employ the
eddy diffusivity assumption as outlined above but also to
replace + c.^,..., < CN> + c^)> with R^(,...,
thereby neglecting the effect of concentration fluctua-
tions on the rate of reaction. The resulting equation is
78
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""i^u
3t -f a 3x 3X H 3 3y H 3y
_n a
a=l
(10)
3
Tz (KV —at-) * Ri(,...,) + S (x,t)
0 L i O L d. J- IN J. ~
Due to the assumptions:
(1) mixing length approximation to the turbulent
mass fluxes, (7)
(2) neglect of concentration fluctuations
(10) is not the fundamental equation governing the mean
concentrations of reactive substances in turbulence, but
rather is only an approximate equation which is consider-
ably limited in its applicability to reactive pollutants
in the atmosphere.
Lamb (1973) has derived mathematical statements for the
conditions under which (10) is a valid representation of
atmospheric transport and chemical reaction. In brief,
the conditions are:
(1) that the ratio of the Lagrangian time scale* of
the turbulence to the time scale for chemical
reactions be much less than one.
(2) that the ratio of the characteristic length scale
of the concentration field (i.e. the source
The Lagrangian time scale of turbulence may be visualized
as follows. Let us define a correlation coefficient between
the fluid velocities at a point at two times tp and t .
The Lagrangian time scale is given by (t^ - to), the largest
difference in times such that the correlation coefficient
is no less" than some preselected level.
79
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distribution) to that of the turbulence be
much greater than one, and
(3) that the ratio of the characteristic time scale
for changes in concentration field to that for
the turbulence be much greater than one.
In other words, (10) is a valid description of tur-
bulent diffusion and chemical reaction as long as the
reaction processes are slow compared to turbulent trans-
port and the characteristic length and time scales for
changes in the mean concentration field are large com-
pared to the corresponding scale for turbulent transport.
Because the Lagrangian time scale TT and length scale
2 %
^T are often quite large in the atmosphere, these
conditions are violated near strong isolated sources. For
example, for the lateral turbulent velocity component, TT
2
may be about 1 minute and - 1 meter/sec. Thus, to
satisfy condition (2) above, the spatial scale for varia-
tions in , and hence S , must be the order of 500
meters, which is not the case in the vicinity of point
and line sources. In addition, under these conditions
the time scale of the fastest reactions must be no smaller
than about 10 min. This condition is known to be violated
near sources of NO in the presence of 0,.
The conclusion we draw at this point is that (10) is
a valid model provided it is applied under conditions in
which chemical reactions are "stow" and the distribution
of sources is fairly uniform. These conditions can be
met by spatially averaging source emissions and considering
only the slower, rate-determining chemical reactions in
the function R- .
80
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We have noted that in the commonly used equation (10),
the contributions of concentration fluctuations c! to
the rate of reaction have been neglected. We have seen
that this omission can be justified only if the reactions
included take place on time scales much slower than the
turbulent dispersion. However, the question of how to
treat < R-> if these conditions are not met remains an
often issue. We shall now discuss this problem briefly,
as it is an important one for future study.
We would like to consider the possible role that con-
centration fluctuations may play in determining the rate
of chemical reactions. To do so we consider the reaction
A + B •»• C + D which proceeds at a rate kc.cfi . The
mean reaction rate in an infinitesimal volume of fluid is
given by
d< CA>
' ^AV = -^V'V + ]
where the temperature has been assumed constant. The
approximation of replacing by R^(< c->,...,< CN>)
would correspond in this case to letting
d
-^A-. -k (12)
Clearly, this approximation is valid only if <<
. From (11) we can see that if the correlation
A D
between CA and c£ is positive, i.e. > 0 , the
actual reaction rate will be faster than that predicted
by (12). On the other hand, if the reactants are random-
ly mixed or if positive fluctuations in one species are
associated with negative fluctuations in the other, the
81
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reaction rate would be suppressed relative to the
uniformly mixed case (12). Which of these two situations
would prevail in a particular situation depends on the rate
of mixing of the species by molecular and turbulent dif-
fusion as compared to the rate of reaction. Thus, in
order to assess the possible importance of terms of the
form it will be necessary to consider the other
processes responsible for formation and destruction of
the fluctuations, cl and cJL .
We can derive a general conservation equation for the
term in the following way. The continuity equations
for A and B are
3CA |n 9C. ^ 32C.
A ^ .. A _\ „ A . , (13)
at ^f "o ax
a=l a a=l 3x
a
'B ^V ""B x " 3 '
3 = 1 u a ct = l 3x
a
where we have assumed that D. = DB = D . Letting u = ua +
ll ' f* ~~ ^ ^* ^ «^ f* ' f* •"• ^ /"• S>
ua ' CA CA CA ' CB " < CB
values of each equation we obtain
C— < r* > *fr r*' r* sz^r* b- + r* ^ Jin/1 't'JiV'i'no' mAfln
A ^* A A 9 ^13 ^U ^"D cUltl LCLJS.XJIU JllCctll
A r\ xV D D o
- k( +) (15)
82
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A similar equation can be derived for . Subtracting
(15) and its counterpart for from (13) and (14) yields
equations for c and C , e.g.
3CA V> (-
TF +2J u
a=l *
3c! 3
—± - u' A-
3c!
3c!
a 3x a 3x a 3x a 3x
a a a a
3 32CA
(16)
3X
CB> -
CA> - kcACB * k<
a-j
Multiplying (16) by cfi and multiplying the corresponding
equation for c^ by cl , adding and taking mean values
yields the desired equation for
A J5
3
3t
a=-
3< CA> 3< CK:
'> A _ —
5 3X aCA 3X
a a
+ 3 rn _§_ f r' f '«
3x L 3X c ACB'
»«, ^ ACB;
0
a a
(17)
cn>) - k - k - k
o AD A JJ U A
83
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The terras in (17) have the following physical significance:
(^ = Convection of by the mean flow
(?) = Generation of < cAcfi> by the mean gradients
of A and B
® = Molecular diffusion of (nondissipative)
(4) = Transport of by turbulent velocity
fluctuations
(D = Dissipation of by molecular diffusion
(6) = Net destruction of by chemical reaction
In order to assess the relative importance of these
various processes we must examine the sizes of the
various terms in (17). However, (17) is quite complicated,
and, in any case, it is difficult to draw any general
conclusions from such an analysis as to the major processes
responsible for the dynamics of . Therefore, for
the purposes of illustration, let us consider only the
processes of molecular dissipation and chemical reaction,
thereby assuming that u = 0 and that gradients in the
mean concentrations are zero. Thus, in this case
3
-L < r'c'>
at A B
=i v o a a /
(18)
_ v (* t* ^ 4»^/* ^^ £ f* I f* ^ ** — V^ f*' f* l ^ — V^ f ' r* ' ^
K^ CA CR •* CACR K CACR K CA CR
*\ O t\ O f\ U f\ Ms
- k - k
84
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In a formulation such as this, it is customary to
represent the second term on the right hand side by
a concentration microscale, as follows (Hinze, 1959)
3c' 3c
*r i
a
2D
where X is a measure of the size of concentration
eddies. Donaldson and Hilst (1972a) have estimated
a typical value of X in the atmosphere to be 10 cm.
We would now like to compare the rate of dissipa-
tion of < clci> by molecular diffusion, i.e. (19),
to that by chemical reaction. From (19) we see that
a characteristic time for decay of < c^c^> by molecular
diffusion is
Tdiff = 2D
(20)
A characteristic time for decay of < cl ci> by chemical
reaction is estimated from the term -k(< c^> +< C>)<
and is taken to be
g
Let us now consider the relationship between the two
characteristic times, tdif£ and T
chem
If
Tdi££
«
tch » t*ie molecular dissipation of fluctuations will be
the dominant contribution to the change of < c^c^> in a
volume element. In that case, diffusion will tend to smear
85
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out the fluctuations such that < c!ci> is always close
to zero. Conversely, if T,j'ff >> T y,em » i-e. very fast
reactions, the decay of fluctuations due to the chemistry
will predominate and < c!ci> will always tend to be
approximately equal to - . In this case, A
and B will be poorly mixed because the molecular dissipa-
tion of fluctuations is too slow to eliminate inhomogeneities
Then, the rate of disappearance of A and B by chemical
reaction will be governed by the rate of molecular diffusion.
As a measure of the relative importance of diffusion and
reaction, Donaldson and Hilst (1972b) have proposed that
the ratio
be computed for typical atmospheric reactions. If:
r « 1 then < c^ci>/< CA>< cfi> = 0
or
r » 1 then < c!c,l>7< c^x cfi> = -1
Assuming X = 10 cm., Donaldson and Hilst (1972b) have
calculated the value of r for a number of individual
atmospheric chemical reactions. For many reactions they
2
found r to be the order of 10 , suggesting that the
fluctuating quantities might be important in determining
86
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the overall rate of such reactions. We can only view
these results as qualitative indications of possible
effects, because only individual isolated reactions
were considered, rather than coupled sets of reactions
such as actually occur in the atmosphere. In addition,
the effect of turbulent mixing was not included in the
above analysis.
Theoretical studies of closure methods for terms of
2
the form , , etc. have been the subject
of several papers by Corrsin (1958) and O'Brien (1966,
1968a, 1968b, 1969, 1970, 1971, 1972). Additional theor-
etical work on chemical reactions in turbulence has been
presented by Lee (1966) and Chung (1970). Experimental
measurements of second order reactions in turbulent have
been reported by Keeler et al. (1965) and Vassilatos and
Toor (1965). Those studies provide a strong foundation
for future work in analyzing the coupling of turbulence
and chemical reactions.
In summary, inhomogeneities in a reacting atmospheric
mixture are capable of exerting significant effects on
the overall reaction rate. These inhomogeneities are
currently not accounted for in large scale urban airshed
models in which the rates of chemical reactions are taken
to depend on the mean concentrations only. The effects
may be important in the vicinity of major sources where
high concentrations and inhomogeneous mixing may results
in reaction rates different than those predicted on the
basis of mean concentrations alone. This observation points
87
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to a need for studies of pollutant behavior in the
vicinity of major sources.
2. Lagrangian Approaches
As we have seen, the utility of (6) rests on one's
ability to evaluate the transition probability density
Q(x,t|x',t'). The question immediately arises: Are
there any circumstances under which the form of Q is
known? If the turbulence is stationary and homogeneous,
Q(x,t|x',t') = Q(x - x1; t - t') , i.e. the transition
density depends only on displacements in time and space
and not on where or when the particle was introduced
into the flow, and Q is Gaussian (Monin and Yaglom,
1971).
The Gaussian density, coupled with (6), gives the well-
known set of so-called Gaussian plume formulas (Slade,
1968; Turner, 1969) - normally applied with no decay of
pollutant. These formulas are the classical relations
for diffusion in stationary, homogeneous turbulence
and have been used extensively in predicting pollu-
tant dispersion from point and line sources. In
particular, a fair,degree of success has been achieved
in predicting long-time averages of concentrations near
the source (x^ - XiQ < 10 km.) under steady meteorological
conditions, when empirically determined values of the
variances of the distribution [such as the Pasquill curves
(Pasquill, 1962)] have been used. However, when so
applied, the plume formulas must be regarded as empirical
expressions capable of accurate prediction only for
88
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conditions that are reasonably similar to those
under which the empirical variances were determined.
However, due to the assumptions of stationary and
homogeneous turbulence, which almost never prevail
in atmospheric situations of interest, these equations
are now recognized to be an inadequate basis for a gen-
eral urban air pollution model.
Thus, we return to the problem of determining
Q(x,t|x',t) in the nonstationary, inhomogeneous turbu-
lence of the atmospheric surface layer. Perhaps the
only feasible way of doing this is by numerical simula-
tion of the turbulence, in a manner such as has been
reported by Lamb (1971a) who used the fluid simulation
model of Deardorff (1970). Because of the large computing
requirements of such a simulation model, this approach
does not appear to provide a practical basis for a full
urban airshed model. In addition, there is presently no
way in which nonlinear chemical reactions may be included
within the framework of (6). We therefore conclude that
(6) can be used as the basis of a general urban airshed
model only for inert pollutants (or those that decay by
a first-order reaction) and only when Q can be determined
from experimental data or numerical simulation. For an
illustration of the use of such a model for CO in Los
Angeles, we refer the reader to Lamb and Neiburger (1971).
3. Summary of Approximate Urban Airshed Models
In this section we have briefly discussed some con-
ventional approximate equations for the mean concentrations
89
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of species in turbulence. In order to summarize the
distinguishing features of the two general types of
models, we list in Table 5 the assumptions employed
in deriving their respective governing equations. Be-
cause there is no possibility of including in (6) non-
linear relationships expressing chemical kinetics, we
shall henceforth focus on (10) as the basis for a
generalized urban airshed model.
C. Implementation of Urban Airshed Models
We have thus far limited our discussion to an examina-
tion of equations which might provide a suitable basis for
a general urban airshed model. In this section we will
focus almost entirely on (10) as the fundamental equation
for such models. The remainder of Chapter III will be
devoted to the implementation of the various types of urban
airshed models which are more or less based on (10).
We divide the airshed models to be discussed into two
basic categories:
Grid Models
Trajectory Models
In the grid model the airshed is divided into a three-
dimensional grid, which can be envisioned as stacked layers
of cells, each cell being perhaps one to two miles on a
side and a few hundred feet high. The grid is then used
as a basis for the numerical integration of the N coupled
equations (10). In the trajectory approach a hypothetical
column of air, which may or may not be well mixed vertically,
90
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TABLE 5. Restrictions on the Applicability of Eulerian
and Lagrangian Equations as the Basis for a
General Urban Airshed Model
Parameter
Lagrangian Form
(6)
Eulerian Form
(10)
1. Coordinate system none
2. Source strength none
function
3. Initial condition none
distribution
4. Turbulence none
5. Mean velocity field none
6. Chemical reactions
first-
order
decay
only
Principal axes of K
op
Spatial and temporal
variations "smooth"
compared to resolution
of the equation
Spatial variation "smooth"
compared to resolution
of the equation
Turbulent velocity fluc-
tuations correlated on
length and time scales
much smaller than reso-
lution of the equation
Spatial and temporal
variations "smooth"
compared to resolution
of the equation
Time scales for the
reactions slow compared
to resolution of the
equation
91
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is followed through the airshed as it is advected by the
wind. Pollutants are emitted into the column, either at
its base or as volume sources, and chemical reactions
may take place within the column. Since these two classes
of airshed models involve significantly different concepts
in the implementation of (10) and therefore may have different
requirements in terms of the treatment of atmospheric chem-
istry, it is important that each be examined in some detail.
1. Grid Models
As we have just noted, grid models refer to those in
which (10) is solved numerically on a three-dimensional
(in some cases, two-dimensional) grid, the specific form
of the equation used being dependent on the simplifying
assumptions made.
We begin by restating the basic model. In this way
we can illustrate the means by which meteorological,
chemical and source information enter into the formula-
tion. The basic model consists of the N coupled (through
the chemical reaction term R^(< c^> ,...,< Cj.>)) partial
differential equations:
u
a< c.>
~ax
o=l
a<
ax
•• (K
ax
a< (
3z
3
si(x,t)
1,2,...N
(10)
92
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Meteorological information enters through:
1) the deterministic wind field, u (x,y,z,t) ,
assumed to satisfy the overall continuity equation
2) the eddy diffusivities, KH(x,y,z,t) and
Ky(x,y,z,t)
3) the dependence of R^ on light intensity
Chemical information enters through R^(< c, >,...,< CN>) ,
the rate of formation of species i in a chemical kinetic
mechanism for reactions among the N species. Volume
sources (those above ground) enter through S-(x,t) .
.L "*
The initial and boundary conditions associated with
(10) incorporate further meteorological and source in-
formation. The initial condition is that
is specified everywhere in the 'airshed- Vertical boundary
conditions are:
"Kv - a1;1"1 - Q, (x,y,t) z = 0 (ground)
V o Z 1
and
3< c. >
—-i— =0 z = H(x,y,t) (top of polluted layer)
o Z
where Qj(x,y,t) is the flux of species i from ground-
level sources at location (x,y) and time t , and H(x,y,t)
is the height of the base of an elevated inversion (or a
mixing height) at location (x,y) and time t . Horizontal
boundary conditions specify concentration levels at points
of flow into the airshed.
93
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Tn discussing grid models we will examine a number
of questions related to the practical implementation
of the basic equations (10). First, we briefly des-
cribe the types of numerical methods which may be used
for the solution of the N coupled partial differential
equations comprising the model. We then discuss the
effect of the spatial averaging inherent to carrying out
a solution on a finite difference grid on the accuracy
of prediction. This discussion will bring us to the
issue of the practical treatment of point and line sources,
and thus to the need for a "micro-scale model", that is,
a model capable of describing concentration behavior on
space and time scales smaller than those employed for
the basic model. Finally, we summarize both^the attractive
features and the shortcomings of the grid model approach
to urban airshed modeling.
a. Numerical Methods
We can classify numerical methods for solution of
the diffusion equations (10) in terms of:
Conventional finite difference methods
Particle in cell methods
Variational methods
We will discuss in this section finite difference
methods and particle in cell methods. Variational
methods involve assuming the form of the concentra-
tion distribution, usually in terms of an expansion
of known functions, and evaluating coefficients in
the expansion. There is currently very active
94
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interest in the application of these techniques
(Douglas and DuPont, 1970); however, they are
not yet sufficiently well developed that they
may be applied to the solution of three-dimensional,
time-dependent partial differential equations, such
as (10). For this reason we will not discuss these
methods here.
(1) Finite Difference Methods
The numerical analysis literature abounds with
finite-difference methods for the numerical solution
of partial differential equations. While these
methods have been successfully applied in the solution
of two-dimensional problems in fluid mechanics and
diffusion (Crowley, 1968; Fromm, 1969), there is a
dearth of reported experience in the solution of
three-dimensional, time-dependent, nonlinear prob =
lems. Application of these techniques, then, must
proceed by extending methods successfully applied
in two-dimensional formulations to the more complex
problem of solving (10). For general discussions
of the various types of finite-difference methods
applicable in the solution of partial differential
equations, and their advantages and disadvantages,
we refer the reader to the books by von Rosenberg
(1969), Forsythe and Wasow (1960), and Ames (1969).
The main advantage in using a finite-difference
method in the solution of (10), as compared with
other approaches, is that there has been extensive
95
-------
experience in applying these techniques to a
wide variety of partial differential equations.
Even though reported experience with three-dimen-
sional, time-dependent, nonlinear problems is
scanty, experience with simpler systems provides
a sound basis for the development of feasible
approaches. The disadvantages of finite difference
methods are well-known:
(a) Inaccuracies in approximating the first-
order advection terms in the continuity
equations give rise to second-order errors,
which have the mathematical characteristics
of diffusion processes. These inaccuracies,
often termed "numerical" or "artificial"
diffusion, can mask the representation of
true diffusion. Finite difference methods
based on approximations of higher than
second order are required to minimize this
difficulty; unfortunately, computational
times increase with increasing order of the
method used.
(b) Computing time and storage requirements
associated with accurate, stable methods
can be substantial for problems involving
several independent variables. When the
equations are nonlinear, time-consuming
iterations or matrix inversions are often
required in the solution.
96
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(2) Particle in Cell Methods
An alternative to the direct finite-difference
solution of (10) is the so-called particle in cell
(PIC) technique. The distinguishing feature of the
PIC technique is that the continuous concentration
field is treated as a collection of mass points,
each representing a given amount of pollutant and
each located at the center of mass of the volume
of material it represents. The mass points, or
particles, are moved by advection and diffusion.
It is convenient but not necessary, to have each
of the particles of a given contaminant represent
the same mass of material. The application of the
PIC technique in hydrodyriamic calculations is dis-
cussed by Harlow (1964). The PIC technique has
been adapted to air pollution modeling by Sklarew
et al. (1971),
The PIC technique has the following advantages:
(a) Artificial diffusion due to truncation
errors in the advection terms in (10) is
eliminated since these terms are not
approximated by finite-difference representations
(b) There are no stability restrictions on At
(although At should be small enough so that
the value of the particle velocity is rep-
resentative of the movement of fluid particles).
(c) Particles can be tagged as to their place of
origin, thus making it possible to identify
the sources of contaminants observed at any
location.
97
-------
and the following weaknesses:
(a) Computer storage requirements can become
excessive, as the coordinates of a large
number of particles must be kept in memory.
(b) If it is assumed that each particle of a
given contaminant represents the same mass
of material, then every cell will have a
residue that cannot be assigned to a particle.
On the average, this residual material will
equal one-half of a particle mass. If the
assumption that particles be of equal mass is
relaxed, the residue error can be eliminated,
but only at the cost of storing a large amount
of additional information--the masses of all
species in each cell.
b. The Practical Treatment of Point and Line Sources
Application of a grid model requires the numerical
solution of the atmospheric diffusion equations. Since
the solution is carried out on a digital computer, all
continuous variables must be converted to discrete
variables. This is accomplished by dividing the region
into a three-dimensional net, at each node of which the
variables are defined. As we have seen, this process
involves spatial averaging over the volume AxAyAz for each
grid square. Source emissions are likewise defined only
at the grid points, resulting in a similar averaging.
98
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Two of the most important types of sources are
point (stacks) and line (roadways). In developing
an airshed model, we must immediately deal with the
question, "What is the "proper" way of including
point and line sources in the source emission function?
The key problem arises with sources of reactive pol-
lutants, such as power plants and freeways. It is
improper to assume that emissions from these sources
are instantaneously and uniformly mixed in the grid
square in which they are emitted. This is because the
lower levels of concentrations resulting after averaging
may lead to reaction rates different than those actually
taking place in the more concentrated plume from the
source. Nevertheless, this assumption is currently
commonly made as a matter of convenience. A procedure
for allocating point source emissions in downwind cells
has been used by Roberts et-al. (1971), although to
date no account has been taken of the chemical reactions
which are taking place in the plume. Reactions are
allowed to occur only after the emissions have been
assigned to grid cells.
It is very clear that studies need to be conducted
to improve the practical treatment of point and line
sources in grid models. These studies can be divided
into two areas:
(1) Theoretical - Equations must be developed and
solved for a chemically reacting plume, par-
ticularly for a plume having high NO and H20
concentrations that is being emitted into an
99
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atmosphere of hydrocarbons and ozone. Both
the fluid mechanics of the plume and the
chemistry must be considered. The importance
of the effect of concentration fluctuations on
the turbulent chemistry should also be assessed.
(2) Experimental - Fundamental information is needed
concerning the degree of mixing and dispersion
that occurs in plumes from power plants and free-
ways. Tracer studies can play an important
role in elucidating these processes. An experi-
mental program of tracer measurements from
freeways in the Los Angeles basin is being con-
ducted by Professor F.H. Shair of the California
Institute of Technology. Preliminary results
from studies of this type should aid in carefully
defining a series of additional tracer studies.
These experiments are generally low in cost and
and would nicely complement theoretical studies.
2. Trajectory Models
As we have noted, the principal feature of trajectory
models is that concentration changes in a hypothetical
parcel of air are computed as the parcel traverses the
airshed. The parcel is visualized as a vertical column
of air of fixed area and variable height, with the top
of the column being defined by the base of an elevated
inversion or, in the absence of an inversion, by an
estimated maximum mixing height. The motion of the air
100
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column is assumed to correspond to the local instan-
taneous wind speed and direction, thereby tracing out
a particular surface trajectory in the airshed.
The following assumptions are inherent in the model:
(a) There is no horizontal transport of material across
the boundaries of the parcel. (There is, in fact,
no means of including horizontal diffusive trans-
port between the column and the environment.)
(b) There is no change in the horizontal wind velocity
with height.
(c) Vertical advection is neglected, i.e. the vertical
component of the wind does not exist.
The basic assumption underlying the approach is that
a parcel of air maintains its integrity while traversing
the airshed. It is unlikely that this is often the case
in the atmosphere over the time scales of interest.
Therefore, it is of prime importance to assess the validity
of this basic assumption before such a model is used for
practical computation. This point will be discussed more
fully in Chapter VI.
Referring to Figure 3, consider a volume which is moving
through an airshed in such a way that all points on the
boundary of the volume move with the mean wind ground-
level velocity u = (u^u^O) . The vertical movement
of the volume caused by vertical velocity components is
neglected. Note that the volume pictured in Figure 3
does not actually contain the same fluid particles at all
times; rather it is merely a hypothetical "cell" moving
along with the mean flow. Turbulent mixing across the
101
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walls of the cell insures that at each instant there
are fluid particles in the cell that were not there
previously. In order to assess the validity of assump-
tions a - c above, we now present an analysis of the
trajectory model depicted in Figure 3. In particular,
we wish to derive the equations satisfied by the mean
concentrations of pollutant species within the volume.
A material balance on species i within a cell of
arbitrary volume V(t) which is advected with the
mean fluid velocity u is given by:
Time rate of change of mass of species i in cell =
Rate of generation of i by chemical reaction +
Rate of introduction of i from sources +
Rate of introduction of i by turbulent mixing
with fluid not contained in the cell at time t
We make the following definitions:
= mean concentration of species i at
location (x,y,z) and time t in the
fluid
R.(c-,...,CN) = rate of generation of i by reaction
Q.(x,y,z,t) = rate of emission of i by sources
in the fluid
J.(x,y,z,t) = turbulent mass flux vector of species i
• 1
Employing these definitions, the material balance on species
i can be written explicitly as
Ztf dV = f RiCci»'"»cN} dV +f QidV ~f !?i " ?ds
v(t) v(t) v(t) set)"1
(22)
102
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SUNLIGHT IS GIVEN AS
A FUNCTION OF TIME
TIME-DEPENDENT MIXING
AND REACTION IS COMPUTED
FOR AIR PARCEL UP TO THE
MIXING HEIGHT h
SPA_CE/TIME TRACK
-THROUGH THE SOURCE
GRID IS DERIVED
FROM WIND DATA
•POLLUTANT INFLUXES AT ANY
ELEVATION (INCLUDING THE
GROUND) ARE IMPOSED BY THE
EMISSION SOURCE FUNCTIONS
FIGURE 3. A Volume Which Moves Through an Airshed in Such a
Way That All Points in the Volume Move With the
Mean Wind Velocity.
The drawing, in which the basic elements of a
trajectory model for photochemical smog are
illustrated, has been taken from Eschenroeder
and Martinez (1971).
103
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where S(t) is the surface area of the cell and n
is the outwardly-directed unit normal at each point
on the surface.
In line with our earlier treatment of grid models,
we now make two assumptions: (1) that the rate of
reaction R^ can be represented by the rate based on
the mean concentrations, R^ (< c,> ,...,< CN>) , and (2)
that the turbulent mass flux of species i can be
represented by
Ji = -K7 (23)
where K is the .eddy diffusivity tensor and where, for
conciseness, we have employed the gradient operator (V)
notation. We note that (22) does not contain an advective
transport term because the cell is assumed to move at the
mean velocity u . The turbulent transport arises, of
course, because of the fluctuations of velocity about the
mean.
Let us now define the volume-average concentration
of the cell at any time t as
Mt) - VTTT / dV . (24)
Differentiating c. with respect to time, we get
104
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(2S)
V(t)
Combining (22), (23) and (25), we obtain
V^'---'^ dv +
V(t) V(t)
nds -
Employing the divergence theorem to recast the third term
on the R.H.S. of (26) as an integral over the volume,
we get
- c.
i dt
105
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If it is now assumed that the volume- averaged rate of
reaction can be equated to the rate of reaction of the
volume- averaged concentrations, i.e.
Ri(,...,) dV = R^c^,...,^) (28)
which in general is unjustified because R. is nonlinear,
(28) becomes
V(t) V(t)
- dlnV(t)
ci dt (29)
We see that if the contribution of turbulent diffusive
mixing to the time rate of change of the volume average
concentration c~- in the cell is to be included, the
gradient of mean concentration, V , within the cell
must be known in order to evaluate the third term on the
R.H.S. of (29).
Two groups, Eschenroeder and Martinez (1971) and Wayne
et al. (1971), have reported results based on a trajectory
model. In each case the model involves a column of fixed
base area (say 1 m^) and variable height, depending on the
depth of the well mixed layer. Eschenroeder and Martinez
have allowed the volume-average concentration c~. to be
an average across a plane at constant z , i.e. c~. (z,t) ,
in order to include the vertical component of the turbulent
mass flux. The form of (38) employed their model' is
106
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3c.(z,t) , r • 3c.
—±-r = R. (c, ,... ,CM) + ^77^- / Q.dV + r^-(Kw -^)
3t l 1 N V(t) J i 3z V 3z
V(t)
(30)
where horizontal turbulent diffusion has been neglected.
The initial condition for (30) is that the concentration
within the column at the beginning of the traversal be
given, i.e.,
c.(z,0) = c.
1 1o
The boundary conditions on z at the ground,, z = 0 , and
the inversion base (on top of the column), z = H(t) , are
given by
3c.
-Kv(0) -r-=- = Q^(x,y,0,t) z = 0
V o Z 1
-KV(H) -^ = 0 z = H(t)
V O L
where H(t) is the height of the column as a function of
time. The movement of the column is reflected mathematically
only in Q- and H .
Wayne et al., in their formulation, have also neglected
horizontal turbulent diffusion and have, in addition, assumed
vertical homogeneity. Thus, their model is based on
inr =
v(t)
107
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where the column is simply a well-mixed cell of fixed
base area and variable height. The advantage of (31)
over (30) is purely computational, since (31) consists
of a set of ordinary differential equations rather than
a set of partial differential equations. Since (30)
does not involve an assumption of vertical homogeneity,
it is clearly more general than (31).
The essential virtue of the trajectory model is its
simplicity, since it is computationally advantageous to
avoid the integration of the diffusion equations in
three spatial dimensions and time. However, it is im-
portant to stress that the trajectory model is not a
full airshed model, nor is it intended as such. Rather,
it is a technique for computing concentration histories
along a given air trajectory. It is not feasible to use
this approach, even if its validity could be established
to predict concentrations as a function of time and location
throughout an airshed, since a very large number of tra-
jectory calculations would be required.
Let us conclude this discussion by summarizing the
main assumptions inherent in the trajectory models now
in use, e.g. that of Eschenroeder and Martinez (1971):
1. The contribution of horizontal turbulent diffusion
to the time rate of change of concentration in the
parcel is small relative to that of sources and
chemical reactions. In effect, this assumption
is tantamount to treating the parcel as an identi-
. fiable and integral parcel of air over the course
of a trajectory traversal.
108
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2. The parcel moves with the mean ground-level
horizontal wind velocities. Thus, vertical
components in the velocity field are neglected.
3. Changes in wind velocity and direction with
height are ignored. The parcel is assumed to
have a constant volume and shape over the course
of a trajectory.
4. The volume-averaged rate of chemical reaction
is based on the rate depending on the volume-
averaged concentrations.
While trajectory models have been employed in the
urban-scale modeling, their validity has yet to be
firmly demonstrated. The most serious deficiencies
are the neglect of horizontal diffusion in the model
and the inability to accommodate a truly three-dimen-
sional wind field. A theoretical evaluation of the
effect of these deficiencies on the predictions of the
model is needed before extensive studies are carried out
using these models.
3. Summary of Current Urban Airshed Models for Photo-
Chemical Air Pollution
We present in Table 6 a summary of urban airshed
models that may be used for predicting ground level
concentrations of reactive contaminants. Detailed des-
criptions of the models may be found in the references
cited.
109
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TABLE 5. Summary of Urban Airshed Models for Photochemical Air Pollution
Reference
Description of Model
Reported Results
Eschenroeder and
Martinez (1971)
Wayne et al. (1971)
Trajectory model. Model based on moving Applied to Los Angeles
column of air in which vertical diffusion for CO, NO, N02, HC, Oj.
and chemical reactions take place. Column Various wind trajectories
of air follows a surface trajectory inter- on six validation days.
polated from monitoring station wind readings.
EM kinetic mechanism used.
Trajectory model. Model based on moving
column of air which is well mixed and in
which chemical reactions take place.
Column of air follows a surface trajectory
interpolated from monitoring station wind
readings. Wayne kinetic mechanism used.
Applied to Los Angeles
for CO, NO, N02, HC, 03.
Various wind trajectories
on six validation days.
Roth et al. (1971)
Grid model. Model based on numerical.
solution of the three-dimensional, time-
dependent atmospheric diffusion equations.
Numerical solution based on the method of
fractional steps. HS kinetic mechanism
used. Three-dimensional wind field com-
puted from surface maps.
Applied to Los Angeles
for CO, NO, N92, HC, 03.
Complete spatial and tem-
poral distributions over
basin for six validation
days.
Sklarew et al.
(1971)
Grid model. Model based on numerical
solution of the three-dimensional, time-
dependent atmospheric diffusion equations.
Numerical solution based on particle-in-
cell method. EM kinetic mechanism used.
Three dimensional wind field computed from
surface maps.
Applied to Los Angeles
for CO, NO, N02, HC, 03.
Complete spatial and
temporal distribution
over basin for one vali-
dation day.
McCracken et al.
(1971)
Cell model. Model based on solution of
dynamic mass balance equations for an
interconnected array of well-mixed cells.
Gear's method used in numerical integration
of coupled, ordinary differential equations.
Two dimensional wind field and assumed ver-
tical velocity profile used.
Applied to San Francisco
Bay Area for CO. Complete
spatial and temporal dis-
tribution over Bay Area
for two consecutive days.
-------
D. Levels of Uncertainty in Input Variables
A necessary part of the development of any model is an
assessment of the levels of uncertainty in each of the in-
put variables and the effect of these uncertainties on the
predictions of the model. In this section it is our ob-
jective to enumerate those inputs to an urban airshed model
for which estimates of accuracy are particularly important.
In addition, we shall also consider the levels of uncertainty
in the concentration data reported at monitoring stations
against which the model is to be ultimately compared.
Certain input components can be estimated with consider-
ably greater accuracy than others. For example, an auto-
motive emissions inventory is, in general, based on a much
richer data base than are urban wind field maps. Because
of the large amount of data available for constructing an
inventory of automotive emissions and because of the impor-
tance of motor vehicle emissions relative to other sources
in areas plagued by photochemical smog, considerably greater
attention has been devoted to this source in the compilation
of inventories for use in urban airshed modeling. The rel-
ative paucity of data involving other source emissions in
particular and involving other model inputs in general is
a serious deficiency requiring future attention.
1. Levels of Uncertainty in Source Emissions
The first step in the validation of an urban air
pollution model is the compilation of a complete con-
taminant emissions inventory for the area of interest.
We can divide source emissions according to:
111
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a. Automotive Emissions
(1) Spatial distribution of traffic
(2) Temporal distribution of traffic
(3) Exhaust emissions
(1) Freeway traffic
(2) Non-freeway traffic
(4) Crankcase emissions
(5) Evaporative emissions
b. Fixed source emissions
(1) Power plants
(2) Refineries
(3) Other fixed sources
c. Aircraft emissions*
a. Automotive Emissions
Let us assume that the airshed has been divided
into a grid and that we desire to calculate the mass
of each contaminant emitted from motor vehicles into
each surface cell as a function of time. For each
cell this quantity can be computed, in principle, as
the product of M , the total vehicle miles traveled
J6
in the grid square in hour X- , and Q^ , the grams
of species k emitted per mile by an "average" vehicle
Actually, it is useful to differentiate between free-
way and non-freeway vehicle mileage because the driving
'We will not consider aircraft emissions here. While
these emissions may have a significant effect on the
atmosphere in the vicinity of an airport, contributions
from aircraft to the total emissions of an airshed are
generally no more than a few percent.
112
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characteristics, and hence, vehicle emission rates,
vary for each.
Both the spatial and temporal distribution of
traffic may be determined from traffic count data
taken as numbers of vehicles per hour passing a
specified location along the roadway. Using traffic
count data at a number of points along a given artery,
the number of vehicle miles per day traveled on the
artery can be determined. Such traffic count data
are readily available from the traffic department of
any large city.
The first issue to be faced in compiling an
"inventory" of traffic involves the level of detail
to incorporate. For example, should one include
traffic counts only for freeways and major and minor
arteries, ignoring residential and side streets, or
for all streets for which data are available. Since
this effort is undertaken only once, it is recommended
that the inventory be made as complete as possible.
Traffic flow can be estimated on small streets, for
which data are unavailable, from local traffic data
in the area, the type of neighborhood, and reference
to counts on similar types of streets.
For a given grid square the vehicle miles per
hour M (for the £th hour) traveled on all roads
in the cell can be computed from:
s*
M, » df E n t freeways
u=l
ss
M^ = d^ E nu^u surface streets
u=l
113
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where
n = vehicles per day (given as traffic counts
at a point, assignable to a segment of
road) , f = freeway, s = surface streets
t = miles of road segment to which the count
nu is assigned
fraction of th
count assignable to hourly period £
d. = fraction of the daily (24-hour) traffic
X
= number of road segments contained in the
f 5
grid square, s = freeway, s = surface
streets
A determination of M for week day traffic, compiled
JC
for a grid of 2 mi x 2 mi squares for Los Angeles, has
been reported by Roberts et al. (1971). They estimated
M for each grid square to be accurate to 5-10%. Thus,
a figure of 400,000 vehicle miles/day, for example,
should be interpreted as 400,000 +_ 40,000 if the
accuracy were +_ 10%.
It is commonly accepted that the hourly variation
in weekday traffic flow may be represented over a 24-
hour period by a bimodal distribution having peaks
at the morning and afternoon rush hours and a high
plateau between these peaks. However, the parameters
needed to describe this distribution--the height of
114
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each peak, the height of the plateau, the time
interval encompassing each peak--vary from street
to street. Shopping areas have a high frequency
of traffic between peak hours. Streets in lower
middle class neighborhoods experience earlier morn-
ing and afternoon peaks than do streets in upper
middle class neighborhoods. Downtown streets carry
light traffic following the afternoon peak, whereas
suburban and residential arterials have higher
traffic loads at this time.
Ideally we would like to compute a separate d
X*
and df for each grid square appropriate to the
X
traffic patterns in that square. Since the grid square,
the smallest spatial unit in the airshed model, usually
contains streets of many classifications, an average
of the temporal traffic distributions over all the
streets in the square would, in all likelihood, provide
a satisfactory estimate for d, and d? for that
square. A less time-consuming alternative, however,
is to determine airshed-wide "grand" distributions,
f s
d* and d^ , by averaging the hourly distributions
of traffic counts compiled for a sufficiently large
number of randomly selected city streets (the sample
being stratified according to the magnitude of the
daily traffic flow), the counts on individual streets
being weighted in proportion to the magnitude of
traffic flow on the street. While convenient, this
alternative is obviously less desirable than determining
square-by-square distributions, where the effect of
differences in traffic flows between central city.and
suburbs can be included.
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Roberts et al. (1971) have developed "grand"
temporal distributions, d* and df , for Los
Ai iL
Angeles. In order to judge the accuracy of the grand
distributions, the statistically derived distribution
was multiplied by the total daily vehicle mileage for
one chosen grid square. These calculated hourly vehicle
mileages were then compared with hourly vehicle mileages
for the same grid square, determined using actual
houly traffic counts. The calculated discrepancies
in surface street vehicle mileage for each time period
for the grid square in the Wilshire/LaBrea area were:
Approx. Percentage
Time Period Discrepancy of Daily Traffic Flow
6-7 a.m. -10.5% 3%
7-9 a.m. 0.3 13
9-11 a.m. -7.0 , 10
11 a.m.-4 p.m. 4.0 30
4-6 p.m. -6.0 16
6-8 p.m. -3.1 11
Based on the Los Angeles results, the estimated un-
certainties in the grand distributions are:
df: + 2-4% df: + 5-7%
I — A —
During the period when vehicular emissions were
uncontrolled, automobile exhaust emissions accounted
for approximately 65% of automotive hydrocarbon
116
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emissions and 100% of CO and NO emissions. As a
A.
result of vehicle modifications and changing legis-
lation through the 1960fs and 1970's, the magnitudes
and relative amounts of these three pollutants vary
with model year.
We turn now to consideration of exhaust emissions.
The basic premise underlying exhaust emission calcula-
tions is to determine for the airshed an "average" vehicle
and an "average" trip. The "average vehicle" is found
by averaging over the total vehicle population, taking
into account model year, manufacturer, weight and trans-
mission type (automatic or manual). The average trip
is chosen as being representative of the driving habits
of the airshed population. The trip, usually termed a
driving cycle, is composed of a series of driving modes
(idle, accelerate, cruise, and decelerate) in which a
pre-determined length of time is spent in each mode.
Such a cycle is formulated by "tagging" a large number
of vehicles on a particular day and analyzing their trips,
including the time spent in each mode. A recent study
of this type has been reported by Smith and Manos (1972).
The emissions from a large population of automobiles
are measured as the vehicles are run through the cycle
on a chassis dynamometer and the resulting average
yields a set of figures for each automobile type--the
grams of pollutant k emitted per mile. Averaging
over the total vehicle population yields Q^ , the
grams of species k/mile emitted by the "average"
vehicle when driven over the "average" cycle.
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Several test procedures for measuring exhaust
emissions have been proposed in recent years. These
procedures have as their common aim the simulation
of emissions in a stationary test of a vehicle being
operated in traffic. There is currently considerable
debate concerning the degree to which the various
test procedures are representative of actual vehicular
emissions, or, indeed, if it is possible to simulate
the emissions of a vehicle by any test procedure. A
choice must also be made between the use of a hot
start and a cold start procedure.
A method which has enjoyed widespread use in
recent years, including adoption as the Federal testing
procedure up to 1971, is the California Driving Cycle
(CDC). This is a seven-mode test procedure and is
based on a Los Angeles commuter run (see State of
California ARE (1968)). Recently, however, the rep-
resentativeness of the CDC has been questioned, and a new
method, the 1972 Federal test procedure, has been
proposed. This procedure employs a cold start and a
driving cycle (the LA-4 cycle) derived from a Los
Angeles driving route during heavy traffic periods.
Actual mass emissions are monitored over the entire
driving cycle, in contrast to the CDC, in which con-
centrations are measured. The differences between
the three procedures--hot start and cold start CDC
and 1972 Federal procedure — are illustrated by the
following figures (Sigworth (1971)):
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Approximate increase in
emissions rates when
measured by cold start
CDC, as compared with
hot start CDC (all
vehicles).
HC
CO
NO.
+ 30%
+ 0-10%
- 5%
Approximate increase in
emissions rates when
measured by 1972 Federal
procedure, as compared
with cold start CDC.
Pre-1966
vehicles
+ 401
+ 60%
+ 601
1966-1969
vehicles
+ 90%
+ 100%
+ 30%
It is apparent from these figures that measured emissions
rates are strongly dependent on the testing procedure
employed.
Values of Q^ for the 1969 Los Angeles vehicle
population have been computed by Roberts et al. (1971,
1973) using the CDC and the FDC. The results were:
Species
CO
HC (exhaust +
blowby)
NOY (as NO)
CDC
Hot Start
63.9 gm/mi
9.0
2.9
FDC
Hot Start
68.6 gm/mi,
10.8
2.7
Cold Start
91.0 gm/mi.
11.7
2.7
It is our belief that by far the greatest uncertainty
in the calculation of motor vehicle emissions is attrib-
utable to our inability to assess the representativeness
of a driving cycle in a particular locale. Recently,
119
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the FDC has replaced the CDC as the standard emissions
test procedure. Nevertheless, the representativeness
of the FDC or any other cycle has yet to be demonstrated.
We recommend that studies such as those reported by
Smith and Manos (1972) be undertaken for cities for
which urban airshed models are to be developed.
b. Fixed Source Emissions - Power Plants and Refineries
The principal problem associated with fixed source
emissions is a lack of data. Few measurements of effluent
concentrations are made, and there are virtually no data
available that reflect the effect of process variations
on emissions rates. In addition, temporal variations,
particularly in the operation of power plants, are often
considerable, yet unpredictable, since they frequently
depend on such unreliable and capricious factors as
the weather.
Generally, highly simplified assumptions are made in
estimating emissions rates from large "point sources" in
an urban area. For example, emissions rates from refineries
are usually assumed to be directly proportional to the
crude throughput rate. This rate is not only assumed
uniform over a day (uniform temporal distribution), but
usually represents an average taken over a period of one
month to a year. Data related to emissions from power
plants is generally easier to obtain, and often is fairly
complete (see, for example, that computed for Los Angeles
by Roberts et al. (1971,1973)). However, measurements made
for one day are generally assumed to apply for all days,
120
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corrected for daily temporal distribution and season
(summer vs. winter); the validity of this assumption
remains in question.
The following types of data are needed to estimate
emissi-ons rates from power plants :
1) electric capacity of plant (megawatts)
2) mass flow of flue gas (pounds/hr)
3) volume flow of flue gas (cubic ft./min.)
4) effluent temperature
5) volume concentration of NOX and S02 (ppm)
6) likely 'temporal distribution of operation
Similar data are needed to estimate emissions from
refinery process units, although temporal variations
(on a daily basis) are likely to be unimportant. In
addition, emissions and evaporative losses of both
reactive and unreactive organic gases must be estimated,
the latter being particularly difficult to determine.
In general, then, emissions data from power plants,
while of variable quality (from quite good to rather
poor), are generally available. Refinery emissions
data are usually unavailable, and thus estimates of
emissions from this class of sources are highly uncer-
tain (perhaps up to +_ 100% or more). Inaccuracies in
emissions rates from large, concentrated or point sources
can have a noticeable impact in model prediction, par-
ticularly in the case of NOX . In Los Angeles, for
example, over 25% of NOX emissions emanate from power
plants and refineries. See Roberts et al. (1971, 1973)
for an example of a fixed source emissions model and inventory,
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2. Level of Accuracy of Meteorological Data
Meteorological data needed in model validation
can be classified as follows:
1) Vertical variation of temperature as a
function of time and location
2) Three-dimensional wind field as a function
of time.
The vertical variation of temperature must be
known to determine the height of an inversion layer,
as well as to establish the importance of buoyancy-
generated turbulence relative to mechanically generated
turbulence. The temperature profile is of interest in
the latter instance because it is related, to a degree,
to the magnitude of the vertical eddy diffusivity Ky .
In most urban areas there is virtually a total lack of
vertical temperature profile data. Thus, the upper limit
for mixing must be estimated, at best on the basis of one
or two soundings taken during the day at one location
(often at the airport, which is generally not centrally
located relative to the urban area). For an inland city,
these few soundings may be sufficient to permit specifica-
tion of the mixing depth, since the temperature profile
aloft at any given time should not vary substantially with
location. However, for a coastal area, such as Los Angeles,
there are significant spatial, as well as temporal, varia-
tions in the mixing depth. For example, at 1 PM on a given
day, the mixing depth at Santa Monica can be one-fourth
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that at El Monte, 25 miles east. Thus, in such areas,
soundings at one location are not sufficient to specify
the inversion behavior.
In the Los Angeles area soundings are currently made
at two locations in the Basin, Los Angeles International
Airport and El Monte, twice a day--at approximately 6 AM
and 11 AM. Using these data, fairly accurate estimates
of mixing depth may be made during the morning hours for
the greater part of the Los Angeles Basin. But the height
of the inversion base is not known in the afternoon, nor
is it known over certain highly populated areas, such as
the San Fernando Valley and Orange County. Hence, it can
be estimated only with great uncertainty at these times
and over these areas. As a second example, rawinsonde
measurements have traditionally been made no closer than
100 miles to St. Louis, at Columbia,-Missouri. The degree
to which these measurements represent the actual profiles
over St. Louis clearly must be established. (With the
advent of the RAPS program, vertical temperature profiles
will be measured over the city on a routine basis.)
We now turn our attention to wind data. The wind field
is determined by interpolation of wind station readings.
The density of stations needed for adequate interpolation
depends on the terrain of the airshed; a denser net of
stations is required when the terrain is hilly or moun-
tainous. Most urban areas do not have a wind monitoring
system adequate for preparing a ground-level wind field
having spatial, resolution comparable to that of a model.
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The greatest errors in wind speed measurement
occur at low speeds; in this range errors of 1001 are
not uncommon. Wind direction, usually measured accurately
at moderate speeds, can also be a problem at low speeds.
The largest uncertainty arises in estimating winds aloft,
both in speed and direction, as such data are generally
unavailable. In fact, the specification of winds aloft
probably represents at this time the largest source of
error in an urban airshed model.
3. Level of Accuracy of Reported Airshed Data
As part of its current Los Angeles modeling program,
SAI has reviewed the concentration measurement techniques
employed by the Los Angeles APCD in terms of accuracy,
specificity, and reliability. In general, accuracies in
determination of the concentration of any pollutant are no
better than +_ 101. Degree of specificity and reliability
varies greatly, depending upon the measurement. The follow-
ing tentative conclusions have been drawn with regard to
the use and interpretation of the APCD data:
CO no correction needed
NO the oxidation of NO to N02 and ..subsequent
colorimetric measurement of the product
NC-2 is 70-851 efficient. Thus, reported
NO concentrations must be increased by
about 20% for use in validation.
NO- PAN interferes with measurement of N02-
Accuracy of measurements is +_ 10-201.
No correction is recommended due to lack
of information-- knowledge of PAN concen-
tration and other sources of error.*
*A1though not presently in routine use, chemiluminescence
techniques, which are more specific than methods currently
employed by control agencies, are now available.
124
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Oxidant Methods in use are not specific for
ozone; contributions of NO,, PAN,
and other specific oxidants
must be subtracted from the total
reading. Presence of NO- increases
oxidant readings by 10-20% of the N02
concentration; SO- decreases readings
by an amount approximately equal to
S02 concentration.*
Total Flame ionization is specific for
Hydrocarbons carbon, recording oxygenated hydrocarbons
as well as hydrocarbons. Readings are
difficult to interpret because: i) cali-
bration is carried out using a specific
hydrocarbon (APCD uses methane), whereas
the hydrocarbons measured are a complex
mixture. While it is assumed that
response is proportional to number of
carbon atoms, significant deviations
from this assumption have been observed.
ii) methane is by far the dominant con-
stituent, making determination of non-
methane constituents by difference an
uncertain matter, iii) variation in
reactivity with type of HC affects measure-
ment. At this time, total hydrocarbon
measurements are probably too uncertain
to be useful in model validation.
In addition to these problems of measurement, there
exist two fundamental problems related to sampling:
1) Unless a sample is taken instantaneously, it
will generally contain a mixture of contaminants
that is not necessarily representative of the
pollutant concentrations at the monitoring site
at the reported time of sampling.
2) If the time lag associated with collection and
and analysis is long, then the possibility that
further chemical reaction has taken place in the
sample gases must be considered. Thus, time lags
must be taken into account in analysis of data.
We will return to questions of instrumentation and measure-
ment in Chapter V when we discuss smog chamber experiments.
* See footnote on preceding page.
125
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4. The Problem of Disparate Scales
Clearly, uncertainties in emissions and meteor-
ological data can only serve to degrade the quality of
predictions provided by an urban airshed model. And
uncertainties in air quality data can only enhance dis-
crepancies between prediction and measurement in model
validation. However, an additional factor contributes
to the difficulties that inhere to validation, the
inappropriateness of comparing "point" measurements
with spatially averaged predictions.
Consider, as an example, the validation of an urban .air-
shed model, where carbon monoxide is the pollutant of concern.
Suppose that the model is based on the assumption that emissions
are uniformly distributed in space and time (over an hourly
interval) over cells of appropriate horizontal dimension
(say 2 miles x 2 miles), and that meteorological conditions
are also invariant over this scale. The direct result of
these assumptions is that the predicted pollutant concentra-
tions are uniform within each grid square (or cell). The
observed values of CO, however, typically are represen-
tative only of the CO concentrations in the immediate
vicinity of the sampling site (perhaps, a range of 20 to
200 feet). Of the ten monitoring stations operated by the
Los Angeles County APCD, seven are located within 100 feet
of a roadway having a daily traffic count in excess of
15,000 vehicles. Ott (1971) has shown that CO concentra-
tions measured at a monitoring station situated along a busy
city street are approximately twice the background level
126
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(400 feet or more away from the street) and slightly
more than half that measured at the sidewalk located
between the street and the station. While we may ex-
pect that a properly formulated urban scale model will
predict background levels with reasonable accuracy
over the scale selected, there is no justification for
comparing these predictions with local point observations.
We refer to the inappropriateness of comparing predicted
and measured concentrations as "the problem of disparate
scales".
Some basis for comparison is required, however,
if the validity of the model is to be established. Either
background observations may be made, or a model may be
developed that is capable of predicting concentrations
at a nearby point that are due to local emissions. As
it is currently virtually impossible to make area-wide
(2 mile x 2 mile or similar) measurements,* it is necessary
to develop models of subgrid scale phenomena to resolve
the problem. Such models may be incorporated in an
urban scale model, or exercised independently.
Remote measurement from satellites may provide a means
for making area-wide measurements. However, the equipment,
techniques, and systems required are not yet well enough
developed to be implemented.
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5. Other Sources of Inaccuracy
Three sources of inaccuracy, other than those
discussed thus far, plague modeling -- establishment
of initial conditions, specification of boundary con-
ditions, and estimation of hydrocarbon reactivity.
We discuss each briefly.
Initial conditions at the ground may be established
by interpolating measured concentrations made at the time
of interest. Inaccuracies may be great in certain areas,
however, depending upon the location and spacing of the
monitoring stations. In general, no measurements are
available for establishing initial conditions aloft;
these can only be guessed. A common practice is to assume
that initial conditions at any point (x,y,z) are equal to
those directly below, i.e., at the surface at location
(x,y,0). While this assumption may be satisfactory (though
not necessarily accurate) during the day when the atmos-
phere is often reasonably well mixed, it is probably not
valid during the early morning hours (a time when most
model solutions are initialized) due to the lack of vertical
mixing.
The only information generally available for specifying
boundary conditions, both at the ground and aloft, are those
concentrations Measured at sites near the boundaries. By
chance, the location of sites might, on occasion, be suitable;
however, such occurrences are fortuitous.' Thus, unless
boundaries are selected so as to pass through regions where
conditions may be estimated with some ease (such as over a
large body of water), the specifications of concentrations
at the boundary is a highly uncertain undertaking. (See,
for example, Chapter II of Reynolds et al. (1973).)
128
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Hydrocarbon reactivity may be established if the
composition of hydrocarbons in the atmosphere, for any
specific mode of grouping, is measured. Gas chromatographic
analysis provides the means for obtaining the required data.
However, such analyses are never performed routinely be-
cause they are involved and complex and require a large
manpower commitment. While Eschenroeder and Martinez (1970)
have found that the average hydrocarbon reactivity (excluding
methane) of the atmosphere is approximately constant over a day
in the Los Angeles area, it remains important to determine the at-
mospheric hydrocarbon reactivity by groups (such as for the
groupings suggested in Chapter II) if mechanisms of the
sophistication of that shown in Table 4 are to be included
in airshed models.
E. Relationship of Kinetic Mechanisms to the Urban
Airshed Model
In order to use (10) as the basis of an urban airshed
model, one must be aware of the restrictions that exist on
the time scale of the chemical reaction processes described
by R^ (see Table 5). In particular, the time scale for
the reactions should be large compared to the temporal reso-
lution of (10). We have already presented in Chapter II a
detailed discussion of photochemical kinetic models. The
criteria which guided the development of the generalized
mechanisms discussed in Chapter II dealt primarily with
measures of accuracy in prediction of observed chemical be-
havior and of parsimony with respect to the number of indi-
vidual species included in the mechanism. Given the res-
trictions on R- and the kinetic mechanisms developed or
referred to in Chapter II, a basic question must be faced.
Are the lumped kinetic mechanisms in common use compatible
with the time-scale requirements on R- that must be satis-
fied if (10) is used as an urban airshed model?
129
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The purpose of this section is to explore the issue
of the time scales associated with various kinetic mech-
anisms for photochemical smog in order to assess the appro-
priateness of their inclusion in an overall airshed model based
on (10). In other words, we wish to examine whether the
degree of detail incorporated in the kinetic portion of
the overall model is consistent with the degree of detail
in the remainder of the model. The kinetic mechanism en-
ters the overall model (10) through the specification of
the functional form of R-(c,,...,CN). Thus, we shall be
specifically interested in how the restrictions on R- are
related to restrictions on the structure of the underlying
kinetic mechanism from which the R. are derived.
In Table 5 we indicated that in order to use (10) as
an urban airshed model the time scale of the chemical reaction
processes should be long compared to the temporal resolu-
tion of the model. Let us now quantify this condition.
Given values of the mean concentrations, we can represent
R. (< c, >,...,< CN>) as R. (x,t) , a "generation" or "source"
term analogous to S^(x,t) , in (10). Let the time incre-
ment for numerical solution of (10) be fit . It can be
shown (Lamb and Seinfeld, 1973) that At must satisfy the
conditions:
T. « At « T_ •
L L
where T. is the Lagrangian time scale of the turbulence
and T/-. is a characteristic time for changes in the concen-
tration field. Typical values of these three times might be
TL - 1 min.
At ~ 10 min.
Tc - l hr.
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The condition stated at the beginning of this paragraph
can be quantitatively written as
, 3R. ,
R Cx tl TT<
Since R- is not an explicit function of time, it is
difficult to verify this condition directly or to determine
how such a restriction might influence the form relation of
R^ . For this reason, we must resort to an alternative means
of judging whether or not a particular R- satisfies (32).
To do this, let us consider the batch chemical reaction system
dc-
= Ri(c1,...,cN) i = 1,2,...,N (33)
and attempt to obtain a measure of the time scale associated
with such a system. By a time scale we specifically mean a
characteristic time interval over which concentration changes
might occur in a chemical system governed by (33). The con-
cept of a characteristic time scale can be seen by consider-
ing the decay of a single species by a first order reaction.
In this case
at'-"'
and
c(t) = c(0)e-kt
131
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Thus, c(t) decays exponentially, a measure of the time
scale of which is k~l (e.g. c(t) decays to 1/e of its
initial value in a time equal to k~* ). For coupled sets
of first order reactions, the solutions for concentrations
take the general form
N
1.2,. ...N
The parameters X,,...,XN are called the eigenvalues of
the system of linear reaction rate equations. When written
in the condensed form,
dc
the eigenvalues X,,...,XM are merely the eigenvalues of A .
-1 -1 ~
The time scales for the reactions are given by X, , ...,XN .
By analogy to the example of sets of linear reactions, the
time scales for nonlinear reactions can be given by the eigen-
values of the nonlinear differential equations. The eigen-
values, X,,...,XN of a set of nonlinear ordinary, differential
equations are those of the N x N Jacobian matrix J , the
i , jth element of which is 3R-/8c- , and are the N
solutions of the equation, det (J - XI) = 0 .
Table 7 presents the eigenvalues of the reaction rate
equations corresponding to the HS mechanism in Table 1 (diff-
erential equations for HC, NO, N0£ and 0^). In spite of the
132
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TABLE 7. Eigenvalues of the HS Mechanism (Lamb and Seinfeld, 1973)
t,min A,
1.3
60.3
119
-33.1
-21.2
-21.5
4.63xlO"2
3.51xlO"2
-8.98xlO"3
1.24xlO"4 1.28xlO"7
4.83xlO"4-6.59xlO"4i 4. 83xlO~4+6. 59xlO~4i
-2. 04x10" 2-l. 71x10 "2i -2. 04x10 ~2+l. 71x10 ~2i
NOTE: Initial conditions used were C
C03(0) = 0, CHC(0) =3.0.
NO,
(0) = 0.04, CNQ(0) = 1.5,
fact that the pseudo-steady state approximation has been employed
for the free radical species, there is still a broad range in
the magnitudes of the eigenvalues. After one minute the com-
ponent of the linearized solution corresponding to A, will
have a magnitude the order of e"30 and will be negligible.
Thus, the important rate determining eigenvalue is
is of the order of 10" 2 min. .
which
The condition that A^ >> At implies that At <_ 10 min.
Fortunately, this estimate is consistent with the estimate
for the probable magnitude of At given earlier. Therefore,
we can conclude that the HS (and EM) mechanism is compatible
with the time scale requirements of (10) . Proposed kinetic
mechanisms should be evaluated using requirements of the type
A? » At , where A- is the rate-determining eigenvalue of
the system. Such evaluations may indeed indicate that a
kinetic mechanism that adequately matches smog chamber data
may be inappropriate for use in conjunction with an airshed
133
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model. (For example, the specific mechanisms noted in
Chapter II would undoubtedly contain more detail than is
compatible with the other portions of the airshed model.)
F. Suggested Studies
As a result of this discussion of urban airshed models,
a number of important "unsolved" problems have emerged as be-
ing central to the continuing development of a consistent
theory of urban airshed modeling.
1. The Effect of Concentration Fluctuations on
Turbulent Chemistry
We noted earlier that turbulent fluctuations can lead
to a mean rate of reaction different than a rate based on
the mean concentrations. There exists in the literature
a number of theoretical studies of closure methods for
^
terms of the form and as arise in the
second-order decay of a single reactant or the second-
order reaction of two species. However, no one has yet
been able to determine whether turbulent concentration
fluctuations have a significant effect on atmospheric
reactions in situations of practical interest. We
recommend that:
a. Theoretical studies of Eulerian closure methods
for simple reactions (e.g. A + A •*• products or
A + B -»• products) be carried out for situations
in which there exists advection, turbulent diffu-
sion and molecular dissipation, for example, a
continuous source in a uniform wind. Such studies
may serve to identify regimes in which each of
the processes will predominate.
134
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b. Experimental studies of chemical reactions in
wind tunnels with well-defined turbulence be
carried out to determine profiles of mean and
fluctuating concentrations which can be com-
pared with theoretical predictions.
2. Parameterization of Sub-Grid Scale Transport and
Reaction Effects in Grid Models
In Section B we noted that at the present time
there does not exist a consistent means of including
point and line sources of reacting contaminants in grid
models. What is required is a means of having the source
emission input into the overall airshed model reflect
the transport and reaction phenomena that have taken
place in the plume in the vicinity of the source. (For
example, the emissions need not necessarily be allocated
entirely to the grid square in which the source is lo-
cated nor need the chemical composition of the source
emissions function be that which was observed (or pre-
dicted) at the source.) We recommend that modeling
studies be carried out on scales smaller than the urban
scale, in particular, for plumes emitted from strong point
and line sources. These models would then serve as "sub-
models" to properly introduce emissions from concentrated
sources into the overall airshed model.
3. Sensitivity Studies with Airshed Models
In Section 4 we examined the methods of computing and
and levels of uncertainty in the emissions and meteorological
135
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inputs to an airshed model. A study such as presented
in Section 4 is helpful in identifying those parameters
which are poorly determined and at the same time can
have a significant effect on the predictions of the model.
However, validation results for any urban airshed model
must be accompanied by a thorough series of sensitivity
runs in which each important parameter is varied over
its limits and the effect on the model output is computed.
At this time there do not exist any consistent sets of
sensitivity runs for photochemical air pollution models.
As a result, there is uncertainty as to which inputs and
parameters most affect the predictions of models. There
is an urgent need for such sensitivity runs, and we
recommend these be carried out as soon as possible.
4. Experimental Needs in Model Development
We have presented in Chapters II and III an assessment
of the current state of the mathematical modeling of both
atmospheric photochemistry and transport and dispersion.
Clearly, the development of validated models in both areas
will provide valuable tools for prediction and planning.
In the course of this validation several types of experi-
mental programs will be necessary. We discuss here some
of the principal experimental needs for future model
development.
Kinetic mechanisms must be tested using both laboratory
and actual atmospheric data. Since chemical changes in
the atmosphere cannot be divorced completely from transport
136
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and diffusion effects, laboratory studies are a necessary
prerequisite to validation with actual atmospheric data.
Thus, Chapters IV and V are devoted to needs in relation
to laboratory studies, both in smog chambers, where
atmospheric processes are simulated, and in more well-
defined chemical systems, in which important individual
reactions are studies to determine specific rate constants
and/or product distributions.
After a kinetic mechanism has been validated by
comparison of its predictions with smog chamber data for
a variety of conditions, then the mechanism is integrated
into an airshed model that is capable of describing the
dynamic transport and diffusion of pollutants in the at-
mosphere. As we have seen, there are several different
types of airshed models, each with different restrictions,
ranges of applicability and requirements imposed on a
reaction kinetics model that is to be included in it.
The validation of a full airshed model is clearly a more
difficult undertaking than the validation of a kinetic
mechanism using data from a controlled laboratory ex-
periment. Measurements must include not only chemical
compositions but also the wind flow and temperature
structure of the atmosphere. And this information is, of
course, needed at a substantial number of locations.
Chapter VI is devoted to an examination of needs, as re-
gards an atmospheric measurement program that will serve
as the basis for model validation.
137
-------
IV. INVESTIGATION OF SPECIFIC ELEMENTARY REACTIONS AND
PARTICLE GROWTH PROCESSES AFFECTING THE COURSE OF
SMOG FORMATION
As we have noted in Chapter II, atmospheric contaminants
participate in a large number of elementary reactions. At this
time it appears that most of the important reactions that con-
tribute to the pollutant formation in the atmosphere have been
identified. Yet, our complete understanding of the mechanism
of smog formation depends upon our ability to measure rate
constants and to determine the mechanisms and products of
several elementary reactions presently thought to be significant,
In this chapter we have attempted to gather and discuss what
we feel are the most important problems remaining to be solved
that involve fundamental chemical kinetics.
Although our primary objective in this discussion is to
identify those areas of pursuit that are -most important to
achieving an understanding of the pollutant-generating gas
phase reactions in the atmosphere, we also examine briefly
the phenomenology of gas to particle conversion, that is, the
"mechanism of aerosol growth. As this is a large and complex
topic, one which is not well understood, we have limited the dis-
cussion to a coverage of only the key issues that require
further study. We have included this cursory examination
primarily to emphasize that gas phase reactions of pollutants
and the formation of light-scattering aerosols are coupled
processes, and thus should be investigated in a related
fashion.
138
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A. Rate Constants and Elementary Reaction Mechanisms
Requiring Further Study
The formulation of a descriptive and predictive chemical
mechanism of smog formation requires identification of all
the important reactions contributing to the chemical dynamics.
Similarly, thorough investigation of a specific reaction is
achieved only when the reaction rate constant has been care-
fully determined and the reaction mechanism properly specified.
Due to the large number of important reactions that take place
in the atmosphere, the rapid rates of many of them, and the
low concentrations of most reactants (e.g. free radicals),
the experimental investigation of photochemical smog forma-
tion is an enormously large and difficult task. Much has
been accomplished, however, in recent years. Excellent com-
pilations and discussions of kinetic and mechanistic studies
which have been carried out can be found in Leighton (1961),
Johnston et al. (1970), Altshuller and Bufalini (1971), and
Demerjianet al.(1973). In this section we limit ourselves to a
consideration only of those inorganic and organic reactions
whose rate constants or mechanisms require further investiga-
tion in order to assess their importance with regard to the
dynamics of pollutant transformations.
As will be seen in the following section the important
inorganic reactions that occur in the atmosphere are reasonably
well known. Approximately 15 species, mostly nitrogen-containing,
participate in about 20 elementary reactions. Most of the
reaction mechanisms are well understood, and the remaining
problems of interest concern mainly the determination of the
reaction rate constants. The set of reactions involving
139
-------
organic constituents, on the other hand, is extremely com-
plex, involving hundreds of reactants. Simplified descrip-
tions of these processes can be achieved only in that the
organics can be divided into fi.ye general classes^ the con-
stituents of each class having a tendency to react similarly
with a particular reactant (such as 0, OH, and 0.,. See
Chapter II). Also of interest is the identification and
determination of products of hydrocarbon-oxidant reactions
and the measurement of rates of free radical reactions.
1. Inorganic Reactions
In this section we focus our attention on both the
direct photolysis and thermal reactions of importance
that occur in the atmosphere and that involve inorganic
species. [Included among the inorganics are free radical
species (e.g. 0, OH, HO-, NO, N02, NO-), inorganic acids
and acid anhydrides (e.g. HN02, HNO-, N20r), peroxides
(e.g. H202), and other simple oxides (e.g. CO, S02) . ]
Photodissociation reactions result in the generation
of free radical species which initiate the photochemical
smog process. The thermal reactions important in smog,
on the other hand, are mainly chain continuing or chain
terminating processes which result in the oxidation of
NO, the accumulation of Oj, and the formation of stable
products such as HNOj and CC^.
a. Direct Photolysis Reactions
The rate constant for photodissociation of a
species is normally expressed as the product of the
140
-------
specific absorption rate, k0 , and the quantum
cl
yield, <|> . The specific absorption rate is a
function of the intensity and spectral distribu-
tion of the incident radiation. Rates of photo-
disscciation reactions are usually .known only
with uncertainty because of the difficulty in
measuring the spectral distribution of sunlight
and artificial radiation sources. We defer the
discussion of light intensity measurements un-
til Chapter V.
At least three inorganic species, NO^, HNC^,
and H-O-, will photolyze when exposed to incoming
solar radiation of spectral composition typically
observed at the earth's surface. Of these N07
It
dissociation is clearly the most important. At
this point the significance of HN02 decomposition
and the effect of this reaction on smog dynamics has
not been clearly established, largely because HNC^
is rarely, if ever, measured either in the atmos-
phere or in smog chambers. Probably the least im-
portant contributor to smog formation of the three
reactions mentioned above is the photolysis of H-O-.
^02 does not photolyze readily and, because
it is produced late in the smog formation cycle,
has little effect on the overall chemical dynamics.
(Ozone will also photolyze slowly. Because 03 does
not accumulate until the N02 maximum has been reached,
this reaction would not be important until late
afternoon, if at all.)
141
-------
(1) N02
NO- is the primary energy absorber of
those pollutants present in the atmosphere.
The photodissociation of N09,
Lt
N02 + hv •»• NO + 0
has long been recognized as the most important
chain initiation reaction in smog formation.
We shall discuss the experimental measurement
of the photolysis rate constant for this
reaction in Chapter V.A.
(2) HNO_2
A second energy-absorbing species thought
to be present in polluted air and in smog chambers
is nitrous acid. (In Chapter IV. A.I.b. (3). We discuss
the chemistry of nitrous acid formation.) At
o
wavelengths greater than 3000 A two primary
photodissociation reactions are possible (Leighton,
1961):
HONO + hv -»• OH + NO - (~60kcal)
MONO + hv -»• H + N02 - (~80kcal)
The rate of photolysis of HN02 is about 1/10
that of NO-. (Johnston et al., 1970.)
142
-------
The importance of HNO- in initiating smog
formation is a consequence of the high
reactivity of the OH radical with hydrocarbons.*
In the case of the second reaction the H atom
combines rapidly with 02 to form an HO- radical.
The H02 radicals may then react with NO or
another H02 radical, thereby initiating reactions
which ultimately lead to the formation of OH radicals.
H07 + NO -»• OH + NO.
£*
H02 + H02 -»• H202 +
H202 + hv •»• 20H
Although measurements of atmospheric HN07 con-
£
centrations have not been reported, we can
estimate roughly the equilibrium concentration
of HN07 that would be established under typical
Lt
atmospheric conditions. Using equilibrium
constants determined by Wayne and Yost (1951)
and concentrations of NO (0.2.ppm), N02 (0.1
ppm) and humidity (63% at 25°C) which are
typically observed in Los Angeles just before
sunrise, we estimate the equilibrium concentra-
tion of HN02 to be about 0.026 ppm or about 1/4
Hydroxyl radicals react about fifty times more-rapidly with
alkanes, and about 10 times more rapidly with olefins, than
do oxygen atoms.
143
-------
of the NO- concentration. At these low
concentrations HN02 will form at a rate of
about 0.10 ppm/hour. (If the concentration
of NO were 0.40 ppm and NO- were 0.20 ppm,
the rate of nitrous acid production would
rise to about 0.40 ppm/hour, and the equi-
librium concentration would be about 0.05
ppm). Thus, nitrous acid may well be an
important source of free radicals early in
the morning in a polluted atmosphere.
(3) H202
Recent evidence suggests that hydrogen
peroxide may exist in significant concentra-
tions in polluted air. Bufalini et al. (1972)
measured 0.18 ppm of H20- under severe smog
conditions in Riverside, California and they
suggested that H20~ forms primarily as a re-
sult of H02~H02 recombination. However, hydrogen
peroxide is probably not a major factor in
hydrocarbon oxidation ( by production of OH
radicals) for the following reasons:
1. Under equivalent irradiation condi-
tions, its photodissociation ratt,
is only 1/250 that of NO.. (Leighton,
1961.)
2. Maximum concentrations of H202 observed
in the laboratory and the atmosphere
are much less than the corresponding
maximum concentrations of N09 (Bufalini
L
et al., 1972).
144
-------
3. H2^2 forms at tjie fastest rate
after the NO- peak, coincident
with the onset of oxidant forma-
tion and after much of the hydro-
carbon has been oxidized.
4. H2°2 actuaHy serves as a sink
for HC>2 radicals, since the sub-
sequent production of OH radicals
from photolysis is slow.
For these reasons it is probably important
to measure the concentration of ^02 only for
the purposes of modeling the post-N02-peak
smog formation behavior.
b. Thermal Reactions
When a mixture of N02, NO, CO, S02, and H20
is irradiated in air, a large number of "secondary"
reactions can occur subsequent to NO? photolysis.
These "secondary" reactions are thermal rather than
photolytic in nature, since the energy contained in
the reactants and that produced by their collision,
rather than light energy, drives the reaction. In
this section we discuss the important inorganic
reactions that occur in the atmosphere, examining
in particular the formation of the inorganic acids,
HN03 and HN02, and the oxidation of NO, CO, and S02>
Before doing this, however, we briefly discuss the
effect of temperature on the rate of the homogeneous
reactions contributing to smog formation.
145
-------
It has been observed by several investigators
that increasing the operating temperature of a smog
chamber results in an increase in the photooxidation
rates of hydrocarbons and in the ozone levels attained.
(Early literature on this subject has been reviewed
by Altshuller and Bufalini (1965).) This is the
effect one would expect of reactions having substan-
tial activation energies. However, most of the
inorganic and organic reactions contributing to smog
formation for which activation energies (E.) have
been determined have values of E. less than 5 kcal.
(See Johnston et al. (1970).) For instance, the NO-
0-z reaction (IV.A.l .b. (1)) , which contributes sub-
stantially to NO and 0, loss rates and the N09 forma-
•3 £*
tion rate, has an activation energy of 2.5kcal. In-
creasing the temperature from 77°F to 95°F (25°C to
35°C) increases the rate constant from 29.4 ppm" min
to 33.8 ppm min , (a 151 change, which by itself
should have little effect on the time to the N02 peak
or the ozone level attained). The activation energy
of the N02-03 reaction (IV .A.l.b.(l)), on the other
hand, is 7.0 kcal, and a 10°C increase in temperature
results in a 46% increase in the rate constant. The
only reaction of those listed in Johnston et al. (1970)
having a high activation energy is the reaction
N2°5 "" N02 + N03
which has an activation energy of 21 kcal.
146
-------
To determine the effect of temperature on the
rate of smog formation it will be necessary to in-
corporate the thermal; dependence of the various
rate constants into kinetic mechanisms. However,
activation energies have not yet been determined
for all the reactions thought to be important in
smog formation (for example, the HN02 formation
and H02~NO reactions). Thus, we recommend that
an effort be made to obtain the data needed to
establish k versus T relationships.
(1) Reactions of 03 With NO and N02
Ozone, which forms as a product of N02
photolysis by the reactions,
N02 + hv -»• NO + 0
k2
0 + 09 + M-»-0, + M M= third body
£ O
is destroyed rapidly in the presence of NO
by the reaction
k3
0, + NO -»• NOo + 0-
As the overall smog formation process proceeds,
NO is depleted and N02 and 0, accumulate. When
N02 and 0., reach sufficiently high concentration
levels, the reaction
147
-------
k4
°3 * N02 * N03 + °2
becomes more important than the O-j-NO reaction.
Two determinations have been made of the
rate constant for the 0,-N09 reaction, k,, :
_ i _ i ° *• ^
0.106 ppm min by Johnston and Yost (1949)
and 0.0485 ppnf^-min"1 by Ford et al. (1957).
The earlier measurement was made at partial
pressures of N09 between 0.001 and 0.01 atmos-
• Li
pheres--pressures that are much higher than
those typically observed. The latter deter-
mination was made at concentrations of NO- and
03 below 1 ppm. In that study Oj and NO-
entered a flow reactor at known concentrations.
The effluent stream was analyzed continuously
for N09 using a wet method similar to the
Saltzman method (SBB Chapter V), while ozone
was determined in situ by ultraviolet photometry.
The accuracy of the rate constant determined
by Ford et al. is affected by several factors,
including the constancy of the inlet reactant
concentrations, the completeness of mixing,
and the accuracy of the N09 and 0^ measurements.
L O
Because of the possible sources of error and
the lack of agreement between the two experimental
148
-------
determinations of k,, it would be worth-
while to re-evaluate this rate constant.*
(2) The Chemistry of NO^, N2°5 > and HN03
Any NO, formed by reaction 4 before
the N02 peak will react rapidly with NO
to regenerate N02 by the reaction,
k5
N03 + NO -*• 2N02
After the N02 peak, a time after which NO
has reached low levels, N03 will react
primarily with N0?, presumably leading to
Lt
an equilibrium concentration of N0r.
NO. + NO. * N-0C
J * v ^ b
Eschenroeder (1972) found it necessary, in validating
a photochemical mechanism proposed by Him to use a
value of k4 = 0.005 ppm "J-min"1, while Hecht and Seinfeld
(1972) used a value of 0.006 ppm'^min"!. Employing
values closer to the lowest experimental value of £4
resulted in a reduced maximum N02 concentration, in
much more rapid disappearance of N02, and in greatly
(601) reduced ozone levels. Because both mechanisms
are subject to a large amount of uncertainty, there
is no assurance that values of k4 necessary to sim-
ulate smog chamber data are, indeed, closer to reality.
Nonetheless, the modeling results serve to raise questions
about validity of k4 determinations carried out to date.
149
-------
In the presence of water, however,
can hydrolyze to form nitric acid.
N205 + H20 5 2HN03
Smith (1947) has observed that HN03
reacts with NO by a process having the
following overall stoichiometry :
2HN03 + NO + 3N02 + H20
A reaction sequence that may possibly
account for this (Johnston et al. , 1955;
Gray et al. , 1972) is
HNO- + NO + HN0 + NO
L,
HNO, + HN09 ->- 2NO, + H,0
3 Li Li Lt
The magnitudes of the rate constants and the
effect of surfaces on the rates of these two
elementary reactions have not yet been estab-
lished quantitatively. But, in view of the
large amount of HNO, which forms in smog,
such an investigation would be valuable.
Beyond those two reactions, HNO, is not
thought to enter into any reactions of impor-
tance with the other pollutants present in a
smog chamber. And, while the acid will photo-
dissociate at shorter wavelengths, the photol-
ysis does not proceed at wavelengths present
in smog chambers (Berces and Forgeteg, 1970a,
1970b). (In the atmosphere, however, HN03
can read rapidly with NH, to form NH^NO,, a
constituent of atmospheric aerosols.)
Although nitric acid has been found on
the walls of smog chambers (Gay and Bufalini,
150
-------
1971), the rate of hydrolysis of N205 has
not been established, and it is not yet cer-
tain that reaction 8 is the primary source of
HNO,. (An alternate source of HNOj is the
reaction of OH and N02 .) Wilson (1972) has
charged a humidified reactor with N205 and
observed that the oxide disappears very slowly.
This behavior suggests that gas phase hydrolysis
of N205 is similarly very slow. Thus, the presence
of a third body covered with at least a mono-
layer of water may be required to promote
the hydrolysis reaction.
If the hydrolysis of N-Or is slow,
one could reasonably expect a large steady
state concentration of NUOr to be present
in smog chambers. Wilson (1972) carried
out an experiment in which he irradiated
a hydrocarbon-NO mixture until the NO had been
A.
oxidized and the 0^ maximum reached. He then
extinguished the lights and injected NO into
the system in an amount in excess of that
needed to destroy all ozone present. Subsequent-
ly, he observed that the remaining NO was
slowly oxidized to N02. A possible explanation
for this observed behavior is that N20r had
accumulated during the HC-NO irradiation and
Jv
then reacted with the excess NO via reactions
5 and 7. Were this the case, one would expect
to observe three parts of N07 formed for each
151
-------
part of NO consumed. Note that this is the
same stoichiometry as that observed for the
HNO,-NO oxidation process just described.
In summary, the atmospheric chemistry
of N-Or requires further investigation.
In particular, it will be important to
measure the gas phase rate constant for the
N2°5~H2° reaction> tne rate of the HN03-
NO reaction, and the steady state concentra-
tion of NpOr in a dry system.
(3) The Chemistry of HN02
The photolysis and estimated equilibrium
concentration of nitrous acid in the atmos-
phere have been discussed earlier in this
chapter. We briefly examine here the re-
actions which produce HN02. Nitrous acid is
known to form in aqueous solution by the
reactions
*H?
NO + NO, vi N,0-
^1 f\ it «J
fc
N90, + H90 i12HN09
£* j £ t*
GrUtzel et al. C1970) have studied this
system and have determined the pseudo-first
order rate constant for the hydrolysis of
152
-------
of N203 to be 3.18 x 104min"1. Nitrous acid
is presumed to form in the atmosphere by the
same mechanism, although the homogeneous gas
phase hydrolysis of N90_ may be very slow, as
w O
is the case for N-0,.. Wayne and Yost (1951)
£ 3
studied the third order gas phase reaction,
NO + N02 + H20 -»• 2HN02 ,
- f\ — "7
obtaining a rate constant of 4.3 x 10 ppm
rnin" for the reaction. Westberg (1972)
has questioned the accuracy of this deter-
mination, based on thermodynamic consider-
ations.
In the ambient system nitrous acid can
form at night through the hydrolysis of
N20_, so that an equilibrium concentration
of N90~ may be reached by sunrise. Hydrolysis
£* O
of N70_ is probably also a favored reaction
£ «J
on wet surfaces, such as on particles or walls
^As such, it very likely occurs on surfaces
in smog chambers. Because of the potentially
important role of HN02 in atmospheric photo-
oxidation reactions, we recommend that the
rate of formation of this species in the gas
phase be carefully assessed.
153
-------
(4) Reactions of OH with NQ and NO.,
From our discussion in Chapter II, it
should be clear that OH is the most important
oxidizer of hydrocarbons in smog. Thus,
any reactions which affect the concentration
of OH can result in a pronounced change in
the rate at which smog is observed to form.
Two such reactions are the termination re-
actions of OH with N02 and NO.
OH + N00 i2 HNO,
'2
OH + NO + M * HN02 + M
Morley and Smith (1972) have determined k,2
for conditions between 20 and 300 torr,
conditions which they have shown exhibit a
transition between third and second order
kinetics. Based on their data they have
- 1 - 1 '
estimated 15000 ppm min to be the lower
limit of the rate constant at 300°K and
atmospheric pressure. Using a separate tech-
nique Simonaitis and Heicklen (1972) have
determined k12 to be 13,000 ppm" min" at
300°K and atmospheric pressure. There have
been no determinations of k13 at pressures
greater than 30 torr (Morley and Smith, 1972).
However, Demerjian et al. (1973) have estimated
154
-------
k13 to be equal to 0.8(k12) at atmospheric
pressure. Because of the importance of OH
in the smog formation process, an effort
should be made to confirm this estimate ex-
perimentally.
(5) Oxidation of NO by H02
Until recently there has been little
direct evidence to substantiate the hypothesis
that H02 is an important oxidizer of NO in the
smog formation process. Wilson and Ward (1970)
have observed that irradiation of NO (~1 ppm)
in the presence of large amounts of CO (-500 ppm)
in air results in the complete oxidation of
NO to N02 and the formation of Oj. The mech-
anism generally assumed to explain this obser-
vation is as follows. Water in the air
reacts with NO and traces of N02 to form nitrous
acid, which subsequently photolyzes to form
OH radicals. The following reactions then
occur:
k,.
H
OH
+ 0
HO
H
2
2
* CO
V
J\.
+ M
V
f*.
+ NO
-* CO
15
-» HO
16
2 +
2 +
+ OH +
H
M
NO
2
155
-------
The rate constant for reaction 14 is now
well established (see the next section),
and the combination of H with 02 is very
fast. Apparently the first reported value
for k,fi was that determined by Johnston
-1 -1
et al. (1970), 3 ppm min . Recently,
however, Davis et al. (1972) have experimen-
tally established lc, . as being 700 ppm min
The earlier low value is probably incorrect,
since with such a value the oxidation of
NO in the presence of CO and light cannot be
satisfactorily explained. We recommend
that the value determined by Davis be used
in subsequent calculations.
(6) Oxidation of CO
Carbon monoxide has been shown to accel-
erate the oxidation of NO to N09 when present
it
in concentrations of 100 ppm or more (Westberg
et al., 1971). The effect of CO is explained
by reactions 14-16; accordingly, the first
step in the chain, the oxidation of CO by OH
(reaction 14), has received a great deal of
attention. Demerjian et al. (1973) have
averaged the experimental determinations of
k,.. made by several investigators and have
-1 -1
obtained a value of 250 ppm min . Because
ambient concentrations of CO are well below
100 ppm, often on the order of 5-30 ppm, CO
probably has little effect on smog formation
(Dodge and Bufalini,1972).
156
-------
A simplified example may be used to
illustrate the acceleration in the rate of
oxidation of NO in the presence of CO due
to an increase in the ratio of the rate of
radical formation to the rate of radical
termination. The four most important react-
ions in smog involving OH are
OH + N02 + HN03 k = 15,000 ppm^min"1
OH + NO -»• HN02 k = 12,000 ppm^min"1
°2
OH + HC -> 1R02 k = 25,000 ppnT1min"1
for propylene
°2
OH + CO -»- 1H02 k = 250 ppm^min"1
If propylene, N0j and N02 are all present at a
concentration of 1 ppm,
n _ The rate of radical formation
The rate of radical termination
25000 ~ n 4R
' 15000+12000+25000 "
If 100 ppm CO are added to the system,
25000+25000
15000+12000+25000+25000
n ,,-
"
Thus, the addition of 100 ppm of CO to this
system results in a 35% increase in the
157
-------
ratio of the rate of radical formation to the
rate of radical termination.
The effect of CO is even more striking
in a system containing a hydrocarbon of lower
reactivity, such as n-butane, for which the
OH-n-butane rate constant is 3800 ppm'^min"1.
In this case, if (n-butane) = (NO) = (N02) - Ippm,
3800
_______
~ 15000+12000+3800 ' >
Upon addition of 100 ppm CO, R increases to
n- ,„„„ » n v
K~ 15000+12000+3800+25000 u' ^
The ratio of the rate of radical formation to
the rate of termination has, therefore, in-
creased fourfold upon addition of the CO.
Thus, the effect of high concentration of CO
on the rate of smog formation may be expected
to be proportionately greater for systems
containing hydrocarbons of low reactivity than
for those containing hydrocarbons of high reactivity,
Recently, there has been some interest in
the possible oxidation of CO by H02,
k!7
H02 + CO * OH + C02
Westenberg (1972) has determined experimentally
the ratio of the rate of this reaction to that
158
-------
of H02 and H. In particular, he estimated
that the HC^-CO reaction is probably very
fast, with a rate constant on the order of
8.8x10 ppm min . If this is the case,
the H02-C0 reaction has the effect of raising
the OH concentration predicted by kinetic
mechanisms. Consequently, the rate of loss
of hydrocarbon through reaction with OH and
the rate of generation of NO-oxidizing free
radicals is also increased. The value Westen-
berg obtained for the HO^-CO rate constant,
however, depends crucially on the kinetic
mechanism upon which the data analysis was
based. In his analysis he omitted from the
mechanism the reaction between OH and H09,
OH + H02
a reaction which must be of some importance.
This omission resulted in the overestimation
of the H02-C0 rate constant (Dodge, 1973).
Davis et al. (1972), too, have recently com-
pleted a study of the HO^-CO reaction and have
obtained a value for the rate constant of less
than 8 x 10 ppm min . Thus,it now appears
that reaction 17 is too slow to be of import-
ance in smog formation.
159
-------
(7) Oxidation of S02
The oxidation of S02 in an atmosphere
containing oxides of nitrogen and hydrocarbons
and in the presence of sunlight is an extremely
complicated process, one which is not fully
understood. The following reactions have been
studied thus far:
1) the direct photolysis and
quenching of S02
2) the reaction of S02 in its
excited states with 02 and
3) the oxidation of S02 by 0
and 0,
If these were the only S02 oxidation reactions
occurring, we would expect a maximum rate of
disappearance of S02 in the atmosphere of about
2% per hour, a value which is considerably lower
than that observed in an atmosphere containing
NO and hydrocarbons. We shall not endeavor
^^
to examine photochemical oxidation reactions
involving S02 in detail here, as a thorough
review of these reactions has recently been
presented by Bufalini (1971). Rather, we will
restrict ourselves to a discussion of reactions
which have recently been postulated to explain
the atmospheric photochemistry of S02.
Cox and Penkett (1971) have reported that
S09 is oxidized by a product of the CU-olefin
160
-------
reaction, presumably the so-called
"zwitterion".
RCHOO9 + S02 -»- S03 + RCHO
Since the disappearance rate of S02 in a
smog chamber experiment increases during
the period of ozone accumulation (Wilson
and Levy (1970), this reaction is plausible.
The zwitterion, a peroxide characterized
by strong charge separation, should be an
effective oxidizing agent. Wilson et al.
(1972) have suggested that • S0'2may be oxidized
by either NOj or N205, or both:
N03 + S02 -»• S03 + N02
0 + S0 ->- S0 + 2N0
2
3 2
This hypothesis is of interest in that it
implies that only 03 and N02, the precursors
of NO, and N90r, are 'needed to oxidize S09.
O £» 0 £
While Wilson et al. (1972) made their observa-
tions for a system also containing hydrocarbons,
it would be interesting to perform a "dark"
reaction for a system of N02, 03, and S02 in
air. Carrying out the reaction in the dark
would prevent the formation of 0 atoms, which
are known to oxidize SO-.
161
-------
0 + S02 + M •* S03 + M
It has long been speculated that peroxy
radicals (H07, RO-, etc.) might be important
£* Lt
in the photochemical oxidation of S02. How-
ever, this now seems to be unlikely. Recent
preliminary results obtained by Davis et al.
(1972) indicate that the H02-S02 reaction is
very slow, having a rate constant of only about
0.8 ppm" min" .
c. Summary
In the foregoing presentation we have discussed
several inorganic reactions of importance, or possible
importance, in smog formation which require further
investigations and understanding. Many of these
reactions have already been studied in detail; how-
ever, some may require a careful re-determination
of the rate constants. Specifically, we recommend
that:
1) The rates of photodissociation of N02,
HN02, and H202 be measured carefully
in both smog chambers and the atmosphere.
Additionally, the concentrations of HN02
and H202 should be monitored continuously,
as is now done for N02, so that their
importance as free radical initiators
in the smog system can be evaluated.
162
-------
2) The OT^NO? rate constant be re-determined.
The magnitude of this rate constant strongly
affects the N02 disappearance rate and peak
ozone levels predicted by smog mechanisms.
3) The rate of reaction of N205 and H20
in the gas phase be measured. Nitrogen
3-
balances in snrog chambers have been
notoriously po©r, a difficulty that is
attributable to the formation of HNCU.
A point of interest in the development
and validation of kinetic mechanisms is
to establish whether HNO, forms in the
gas phase and is transported to surfaces,
or whether the hydrolysis takes place
predominantly on walls and particles.
4) The rate of formation of HN02 by the
hydrolysis of N20., be re-determined in
the gas phase. Again, HN02 should be
measured routinely in smog chambers and
the atmosphere if its formation rate is
significant.
5) The rate of reaction of OH and NO be
determined. Such knowledge is needed
if we are to predict accurately the rate
of hydrocarbon oxidation by OH up to the
time of the N09 peak.
163
-------
6) The rates at which NO,, N^Or, zwitterions,
and free radicals react with S02 be de-
termined. This information will aid in
explaining the observed rates of SO-
oxidation in photochemical smog formation.
2. Organic Reactions
Although the irradiation of a system containing NO,
CO, H20, and air will result in the oxidation of NO and
production of ozone, the addition of any of several organic
species to the system substantially accelerates the photo-
oxidation process. Organics that will enhance the oxidation
rate include olefins, aldehydes, ketones, most paraffins
and aromatics, and the longer chain acetylenes. These
species enter the atmosphere in several ways. .
1) Auto exhaust contains large amounts of
unburned and partially burned gasoline.
2) The filling of gas tanks displaces air
saturated with gasoline into the atmosphere.
3) Organic solvents used in metal working
plants, dry cleaning, and as carriers for
paints evaporate into the air.
4) Organic products escape to the atmosphere
from chemical manufacturing plants such as
petroleum refineries.
The -contribution from motor vehicles is the highest,
however, being about 66$ of the total organics and 861
of the reactive organics found in the Los Angeles
atmosphere.
164
-------
In a study of the effect of varying engine
operating conditions on exhaust composition, Jackson
(1966) found that ethylene, propylene, and butenes
constituted approximately 34% of the hydrocarbons
found in exhaust, toluene and xylenes about 10%, and un-
reactive hydrocarbons (methane, ethane, propane, acetylene,
and benzene) about 241. Eccleston and Hum (1970) have
measured the composition of exhaust emissions from eight
automobiles in an effort to determine the effect of
switching from leaded to unleaded gasolines. The average
emissions from cars using regular leaded gasoline were:
38.34% paraffins
36.45% olefins
13.34% aromatics
1.41% oxygenates
10.61% acetylenes
i
Running the cars on a regular, low olefin fuel resulted
in a large increase in the aromatic content and a moderate
decrease in the olefinic content:
34.02% paraffins
28.75% olefins
25.95% aromatics
1.66% oxygenates
9.63% acetylenes
165
-------
Exhaust analysis of the cars run on an unleaded, high
olefin fuel showed a moderate increase in aromatic
emissions and an almost equal decrease in olefinic
emissions, when compared with emissions measured using
regular leaded fuel:
35.92% paraffins
31.34% olefins
21.06% aromatics
1.86% oxygenates
10.13% acetylenes
Thus, switching from leaded to unleaded gasoline re-
sulted in an increase in combined olefinic and aromatic
emissions and reduced paraffinic emissions. Because
olefins and aromatics are, as a class, more reactive
than are paraffins with respect to the oxidation of NO,
removal of lead from gasoline will probably result in
an atmospheric hydrocarbon mix of increased photo-
chemical reactivity. .
In 1967 Altshuller et al. (1971) measured the
hydrocarbon composition of the atmosphere at two lo-
cations in the Los Angeles Basin. They found that
atmospheric organics consist of about:
53% paraffins (excluding methane)
16% olefins
20% alkyl benzenes
11% acetylene
166
-------
Considerable effort has been expended in the past
to study the reactions of paraffins and olefins with
oxidants. Yet, Altshuller's study shows that aromatics
constitute a significant percentage of the total hydro-
carbon in the Los Angeles Basin. Altshuller et al.
(1971) found that toluene and m-xylene are two of the
ten individual hydrocarbons present in the greatest
concentrations and that these two hydrocarbons con-
stitute about half of the alkylbenzene fraction. As
will become apparent in the discussion that follows,
the elementary reaction mechanism for the oxidation
of aromatics in the atmosphere is poorly understood.
In view of the high aromatic content of the atmosphere
and of auto exhaust, this lack of understanding stands
as an impediment to progress in the kinetic modeling
of photochemical smog.
In this section we begin by examining the mech-
anism and products of the oxidation of each class of
hydrocarbons (paraffins, olefins, aromatics, and
acetylenes) by 0, OH, Oj, and 02. We then discuss
the reactions of aldehydes and ketones that can occur
in the atmosphere. Finally, we describe the reactions
of free radicals, the products of hydrocarbon oxidation
reactions. Some of this material to be presented has
been discussed previously (in Chapter II) in explicating
the development of generalized kinetic mechanisms. How-
ever, particular attention will be given here to those
elementary reactions whose mechanisms require further
investigation.
167
-------
a. The Mechanisms of Oxidation of Hydrocarbons
in Smog"
Elucidation of the mechanisms of hydrocarbon-
oxidant reactions that contribute to smog formation
has proven to be an arduous task. The low concentra-
tions of the reactants, the typically rapid rates of
reaction, and the short life-times and low concentrations
of the products of the primary oxidation have, in general,
precluded definitive experimental investigations. In this
section we discuss the reactions of the four most
common classes of hydrocarbons (paraffins, olefins,
aromatics, and acetylenes) with 0, OH, and 0^, the
oxidants thought to be the most important in smog
formation. We also briefly examine the role of
singlet oxygen in hydrocarbon oxidations. We will
not tabulate the rate constants of the hydrocarbon-
oxidant reactions here, since this has been done
recently by Johnston et al. (1970) and Demerjian
et al. (1973). However, where omissions have been
made in their tabulations, or where new data have
become available, we will so note.
(1) 0 Atom Oxidation Reactions
Oxygen atoms form as a result of N02
photolysis and are generally thought to be
the species that initiate the reactions
leading to pollutant formation in smog
chambers. However, while 0 atoms react
rapidly with olefins, reactions of aromatics
and acetylenes with 0 atoms proceed slowly,
at rates about one to two orders of magni-
tude slower than for olefins.
168
-------
(a) Reactions with Paraffins
The reaction of 0 with paraffins
probably results in the abstraction of
a H atom (Leighton, 1961 )
RH + 0 -»• R- + OH
The result of the reaction then is free
radical branching to an alkyl radical
and an OH radical.
(b) Reactions with Olefins
Oxygen atoms generally add to olefins
forming an excited epoxide, which then
decomposes to an alkyl and an acyl radical.
(Leighton, 1961)
/ \
3 + [RI^C - < 3 I
R4 \R2^ V ^R4/
, — C- + R.C
1 I 4II
R3 0
or
R,C- + R0 — C- , etc.
Xll Z I
0 R.
4
This reaction, thus, results in the formation
of two free radicals.
169
-------
(c) Reactions with Aromatics
The mechanism for 0 atom attack on
aromatics is not yet known. Among the
products that have been observed from
the reaction chain initiated by 0 attack
on aromatics are peroxides, acids, and
alcohols (Eventova and Pryktova, 1960).
The reaction of 0 with benzene is very
slow. With mono-substituted aromatics
0 might attack either the alkyl side
chain (as it would a paraffin) or the
ring. There is little evidence to in-
dicate which of the two mechanisms
predominates,.but studies of toluene and
NO in smog chambers have led to the
J\.
observation of benzaldehyde and peroxy-
benzoylnitrate as products (Heuss and
Glasson, 1968). The fact that these
products are formed suggests that at
least some oxidants react with toluene
in such a way that chain opening does
not directly result. Since 0 attack on
an alkyl side chain of a substituted
aromatic is such a reaction, we speculate
about the reaction in some detail.
In the case of a mono-substituted
aromatic, 0 attack on the side chain
would probably occur at the carbon atom
170
-------
in the alpha position relative to
the ring location. The carbon-hydrogen
bond at that position has an unusually
low bond dissociation energy, as the
aromatic ring stabilizes alpha free
radicals. Four canonical structures
can be drawn to demonstrate the delocal-
ization of the free electron over the
aromatic ring.
Among the dialkyl substituted
aromatics one might expect the meta-
substituted isomers to be the most
reactive with respect to smog forma-
tion. Consider the reactions of ortho,
meta, and para xylene. The initial
hydrogen abstraction is identical in
171
-------
each case, a radical forming for which
four delocalization structures can be
written:
CH
para Q)
CH,
0 , OH
+ 0 -»• OH +
CH.
CH
CH2
CH.
CH2
&
°3
CH0
H,
meta
+ 0 * OH + (
•CH2
-CH,
CH:
U
M,
CH.
Thus, the initial product is a very stable
free radical. The addition of molecular
oxygen to the ortho or para free radicals
at any of the four positions, or to the
172
-------
meta free radical in positions M^ or M~ ,
results in a loss of free radical delocali-
zation, that is, only one canonical structure
can be written. Thus, the peroxy radical
is less stable than the alkyl radical, and
there is a tendency for the radical to split
off the 62 again. Positions Mj and M^
of the meta free radical are special cases,
however, with the addition of molecular oxygen
favored at these sites. Upon addition of
oxygen the radical takes the form,
173
-------
with the free electron localizing on
the outer oxygen. Note that in each
case the two oxygens, two carbons on
the ring, and the carbon and a hydrogen
of the methyl group form a six-membered
ring. Given the proximity of these
various groups and atoms to each other,
transfer of an H atom from the methyl
group to the peroxy radical is highly
likely. Thus we would expect the following
reaction to occur:
hydrogen
shift OQH
hydrogen
shift
M4 M4
174
-------
In each case radicals form (M'^ and M^)
which create the opportunity for an
additional degree of delocalization to
occur. Thus, reactions involving the
meta radical differ from these involving
the ortho and para radicals in that oxi-
dation is energetically favorable at
more than one position on the ring. In
the presence of sunlight and photochemical
oxidants the oxidation will probably
result in complete fragmentation of the
radicals M'j and MV. However, it is not
possible at this time to specify the mode
or degree of branching.
From the foregoing discussion it is
apparent that little is known about the
mechanism of 0 atom oxidation of aromatics.
In addition, we should note that rate
constants for 0 attack on aromatics in the
gas phase have been measured only for
benzene and toluene. Thus, as a serious
gap exists in our understanding and knowledge
of the 0 aromatic reaction system, we
strongly recommend that
(1) rate constants for 0 attack on
important aromatics other than
benzene and toluene (such as o,
m, and p xylene, ethylbenzene,
1,2,4-trimethylbenzene) be
measured
175
-------
and (2) the mechanism of the 0-
aromatic reaction and the
radicals formed either
directly as products or as
the result of fragmentation
of the initial products in the
reaction be determined.
(d) Reactions with Acetylene
The reactions of 0 with acetylene
have been studied in flames (Fenimore
and Jones, 1963) over a temperature range
of 970° to 1660°K and in shock tubes
(Glass et al., 1965), also at very high
temperatures. Possible products of the
reaction suggested by these investigators
include
H + HC20 Fenimore and Jones
0 + C2H2 •> CH2 + CO Fenimore and Jones
^*
C2H + OH Glass et al.
Fenimore and Jones have determined the
rate constant to be between 2.45 x 10 and
4.90 x 104 ppm^min"1, with little tempera-
ture dependence over the range 970-1660 K.
At room temperature the rate constant may
176
-------
be slower than that for the 0-olefin
reactions and faster than that for the
0-paraffin reactions (Leightonf 1961) ,
but apparently it has not been conclusively
measured. It is desirable that the mech-
anism and rate of 0 attack on acetylene
be determined, since acetylenes constitute
a significant portion of atmospheric
hydrocarbons.
(2) OH Radical Oxidation Reactions
Hydroxyl radicals enter the photochemical
smog system as a result of HNO^ photolysis
and as products of the degradation reactions of
free radicals such as those that follow the 0-
hydrocarbon reactions.
HN02 + hv + OH + NO
NO
CH3 + 02 + CHjOO -»- CH-jO + N02
L*
HO- + HCHO
NO
U OH + NO.,
Reactions of OH with hydrocarbons are very
similar to those of 0, with two exceptions:
177
-------
(1) the reactions of OH with a given
hydrocarbon are generally very much
faster than those of 0; and
(2) hydrogen abstraction reactions do not
result in chain branching since the
•OH becomes HoO, whereas -0 becomes
•OH
(a) Reactions with Paraffins
The paraffin-OH reaction results in
hydrogen abstraction, an alkyl radical
and water being formed.
RH + OH -»• R- + H20
Note that this is a chain transfer rather
than a chain branching reaction. The rate
of reaction of an individual hydrocarbon
with OH generally increases with the number
of H atoms on the molecule, especially
secondary and tertiary hydrogens. Rate
constants for these reactions are compiled
in Johnston et al. (1970).
(b) Reaction with Olefins
Hydroxyl radicals react with olefins
by addition at the double bond. Morris
et al. (1971) have observed OH adducts
directly in the reactions of OH with C-H4
and CH.
178
-------
OH + CH,CH=CH7 + CH7CHCH0OH or CH,CHCH<,
•J * 32 31 2
OH
Recently, the rate constants for OH attack
on several olefins have been measured by
Morris and Niki (1971). Their results in-
dicate that, for a given olefin, the rate
constant for the OH-olefin reaction is about
ten times .greater than for the corres-
ponding 0-olefin reaction. Less is known
about the reactions of the OH adduct radi-
cal that take place subsequent to the initial
addition, although possible reaction mech-
anisms have been proposed by Westberg and
Cohen (1969), Niki et al. Q.972 ) and
Hecht and Seinfeld (1972). As such, it is
important to establish the reactivity of
this adduct with respect to NO oxidation
and to identify its decomposition products.
With this information the role of the OH-
olefin reaction in smog formation can be
firmly established.
(c) Reactions with Aromatics
It is current speculation that hydroxyl
radicals abstract alpha hydrogen atoms
from branched aromatics in the same manner
as we have assumed occurs in the case of 0.
179
-------
+ OH -»•<§> + H20
If the reaction does, indeed, proceed
as indicated, it would once again be
a chain transfer rather than a branching
step. The arguments presented earlier
concerning the delocalization stabiliza-
tion of free radicals formed by H abstrac-
tion from alkyl and dialkyl aromatics
also hold in this case. It is also pos-
sible that OH adds to the ring. At this
time, however, the experimental evidence
is insufficient to permit specification of
the exact mechanism of the reaction.
(d) Reactions with Acetylene
The OH radical is generally thought
to react with acetylene by abstracting a
hydrogen atom.
OH + HC=CH •*• HCEC- + H20
*
The acetyl radical thus formed may react
in air as follows (Stevenson and Tipper,
1967)
CO + HC'
+ °2 * -g-ffH r s
°2
r
H02 + CO
00 o- C09 + HCO
Z 2 „
0
b
H02
180
-------
The overall result of the indicated
reaction sequence, then, is a chain
transfer, with H02 replacing OH as
the active species. Semi-quantitative
measurements of the OH-acetylene reaction
reported in Johnston et al. (1970) in-
dicate that at,ambient temperatures the
reaction is quite slow, being about as
fast as the OH-ethane reaction. We
recommend that a quantitative value of
OH-acetylene rate constant be obtained.
If, indeed, it is a slow reaction, then
the photochemical oxidation of acetylene
will not contribute appreciably to smog
formation.
(3) 0^ Oxidation Reactions
Ozone begins to form in significant amounts
when the N0£ concentration reaches a level about
twenty five times that of the NO concentration.
Ozone is not nearly as strong an oxidizing agent
as 0 or OH. However, concentrations of ozone
of about .25 ppm or greater are not uncommon
in polluted atmospheres; at these concentrations
ozone and olefins will react at appreciable
rates
(a) Reactions with Paraffins and Aromatics
Ozone does not react at a significant
rate with either paraffins or aromatics.
Several paraffin-ozone rate constants have
181
-------
been determined, and these have been
summarized by Peters and Wingard (1970).
(b) Reactions with Olefins
The reactions of ozone with olefins
in the gas phase have been studied ex-
tensively during the past two decades,
and rate constants for the ozonolysis
reaction are available for a large number
of olefins (see Johnston et al., 1970 ).
However, the mechanism of olefin-ozone
reaction in the gas phase has not yet been
established, and the 'initial decomposition
products have not yet been conclusively
identified. Although the exact mechanism
is still unresolved, ozone is thought to
add to the olefin double bond in the liquid
phase to form a molozonide intermediate,
the molozonide then decomposing into an
aldehyde and a diradical (or "zwitterion").
C,H, + 0, + CH,CH - CH7 * HCHO + CH.CH
3 0 3 31 | L 31
No
0\ 00.
f \
CH-CHO + H9COO-
o ^
Ozonolysis in the gas phase may proceed
by this same mechanism or by allylic oxida-
tion, which would lead to the same decom-
position products.
182
-------
C,H, + 0, -*• CH,CH - CH9 ->• HCHO + C9H,.0
5 o J J . i / 4
'0 — 0 — 0 CH-CHO + CH70-
J £i £t
e e
We recommend that the mechanism of the
reaction in the gas phase be firmly est-
ablished. In particular, it will be im-
portant to identify the transient inter-
mediates such as diradicals, and to establish
subsequent reactions of these species in
polluted air.
(c) Reactions with Acetylenes
Rate constants for reactions of ozone
with acetylene and higher alkynes have
been determined by DeMore (1971). The low
values for the rate constants Indicate that
these reactions have little, if any, in-
fluence on the smog formation process.
(Typically the rate constants for ozonolysis
of acetylenes are about 10~ ppm min .)
(4) Singlet Oxygen
There have been numerous recent publications
concerning the possible role of singlet molecular
oxygen in smog formation. (For a review see
Pitts et al., 1969 and Johnston et al., 1970.)
183
-------
Singlet oxygen can be produced in the air
by such processes as the photolysis of ozone,
the oxidation of NO by ozone, and energy
transfer through collision with excited
molecules. The concentration of singlet oxygen
has not been determined in the atmosphere, but
Frankiewicz and Berry (1972) have estimated
that it is only about two orders of magnitude
greater than that of 0. In view of those low
concentrations and the low rate constants for
lOo - olefin reactions summarized by Herron
and Huie (1970) we may assume that singlet
oxygen is probably not a major hydrocarbon
oxidant.
b. The Mechanisms of Oxidation of Oxygenated
Hydrocarbons
Seizinger and Dimitriades (1972) have shown
that aldehydes and ketones are present in the ex-
haust of automobile engines fueled by simple hydro-
carbons. As indicated earlier, oxygenates constitute
only about 1.5% of the hydrocarbons found in auto
exhaust. Thus, the most important source of atmos-
pheric oxygenates may be the oxidation of hydro-
carbons and the decomposition of free radicals. Of
the oxygenates produced in this manner, aldehydes
seem to form more readily than ketones, for ketones
are produced only when reaction occurs at a carbon
atom bonded to at least two other carbons atoms
in the molecule being oxidized, e.g.
184
-------
n T iv^v
T 2 1 || 2 2 l|f 2
Leighton (1961) has supported this view, concluding
that the atmospheric processes that result in the
formation of aldehydes apparently do not generate
ketones in comparable amounts. In this section,
therefore, we focus our attention on the reactions
of aldehydes.
Aldehydes will photodissociate in sunlight
and react with 0 atoms, forming alkyl radicals (and,
thus, peroxyalkyl radicals), formyl radicals (and,
thus, hydroperoxy radicals), and hydroxyl radicals.
Therefore, the reactions of aldehydes can contribute
significantly to the initial accumulation of RCU,
H02, and OH.
(1) Photolysis
Aldehydes photodissociate in sunlight at
wavelengths greater than 3000 X in chain initiating
reactions.
185
-------
RCHO + hv -> R- + -CHO
Leighton (1961) has estimated that the rate
of this photolysis reaction is about one-
hundredth the rate of N02 photodissociation.
In the case of formaldehyde, a second primary
photodissociation is possible (Calvert et al.,
1972).
HCHO + hv -»• H2 + CO
This reaction pathway, which does not directly
result in the formation of free radicals, has
a probability of occurrence about equal to
that for the chain initiating reaction.
(2) 0 Atom Oxidation Reactions
The typical rate constant for the 0-
aldehyde reaction falls between those of the
0-olefin and 0-paraffin reactions. The reaction
is one of chain branching
0 + RCHO -> RC-+ HO-
0
resulting in the formation of an acyl radical.
(3) OH Oxidation Reactions
Hydroxyl radicals abstract a hydrogen atom
from aldehydes forming an acyl radical and water.
186
-------
OH + RCHO -* RC' + H00
II 2
0
The chain transfer reaction takes place about
as rapidly as the reaction of OH with propylene.
The rate constants for the reaction of OH with
formaldehyde and acetaldehyde have been deter-
mined by Morris and Niki (1971). They are
both about 22,500 ppm" min" as compared with
25,000 ppm^min"1 for the propylene-OH reaction.
Thus, the reactions of OH radicals with aldehydes
may serve as an important mechanism for removal
of aldehydes from the atmosphere and as a sig-
nificant source of free radicals capable of
oxidizing NO,
(4) 03 Oxidation Reactions
The kinetics of the ozone-aldehyde reactions
apparently have not been studied in detail.
Leighton (1961) has estimated that the reaction
is probably slower than the ozone-olefin reaction
by about two orders of magnitude. As a result,
this reaction probably does not contribute
significantly to the overall smog formation
process. However, organic acids, constituents
of atmospheric aerosols, might form as a result
of the ozonolysis of aldehydes. Consequently,
it would be worthwhile to determine the rate
constant, mechanism, and products of the ozon-
olysis reaction for several different aldehydes.
187
-------
c. Free Radical Reactions
The reaction between a single hydrocarbon
species and a particular oxidant (say, 0, OH, or
ozone) often yields more than one set of products.
For instance, in the case of the OH-propylene
reaction, OH can add to either side of the double
bond.
CH3CH=CH2 + OH •»• CH3CHCH2OH or CH3CHCH2
OH
Adding to the difficulty of identifying or specifying
the products of initial reaction steps involving
free radicals is the fact that the fate of the
radicals in subsequent reactions is often unknown.
For example, it has not yet been determined if the
products of the propylene-OH reaction are stable entities
or if they decompose rapidly as a result of the excess
heat supplied by the formation reaction. Because of
uncertainties such as this, it is extremely difficult
to estimate the overall chain length and number of
NO molecules oxidized per OH-propylene reaction.
Difficulties in specifying products and estimating
chain lengths are, of course, enhanced as the com-
plexity and size of the hydrocarbon species involved
in the reaction increases.
In considering the reactions of highly sub-
stituted molecules, the number of NO molecules
oxidized per hydrocarbon molecule consumed will
depend strongly upon the degree of fragmentation (i.e.
188
-------
the degree of branching) taking place, as well
as upon the rate of the initial hydrocarbon oxi-
dation reaction. In particular, high molecular
weight hydrocarbons are often considerably more
reactive with respect to NO oxidation than are
smaller, straight-chain hydrocarbons. For a classi-
fication of NO oxidation rates by hydrocarbon
type the reader is referred to the summary in
Johnston et al. (1970).
As noted in Chapter II, the oxidation of the
various classes of hydrocarbons by 0, OH, and ozone
results in the formation of several different types
of free radical products. Some of these radicals,
notably alkyl and acyl, are extremely reactive,
combining immediately with molecular oxygen to form
peroxyradicals.* In this discussion we give our
attention only to the more slowly reacting radicals,
If the alkyl radical is a product of highly exothermic reaction,
it is possible that the 02 might abstract a hydrogen at a
position alpha to the free radical, forming an olefin rather
than adding at the site, e.g.
CH3CH2CHCH3 + 02 -»• CH3CH2CH=CH2 + H02 or
CH3CH=CHCH3 + H02
This reaction is observed in high temperature flames (i.e. 425 C)
(Benson, 1968). At ambient temperatures, however, probably no
more than II of the R--02 reactions proceed in the manner, the
remaining 991 resulting in the formation of the conventional
peroxyalkyl radicals. Even so, this type of reaction may be a
source of olefins in the oxidation of paraffinic systems and,
as a consequence, merits further experimental investigation.
189
-------
RO- alkylperoxy
RCO- acylperoxy
RO alkoxy
those that substantively influence the photochemical
reaction process. We note that the H02 radical,
closely related to RCU, has been discussed earlier,
in the section dealing with inorganic reactions.
Peroxyradicals enter into reactions of interest
with three species: NO, N02, and ROO. Unfortunately,
the rate constants for each class of reactions is
presently unknown. The primary mechanism by which
NO is thought to be oxidized to N02 without the con-
sumption of ozone is through reaction with peroxy
radicals.
R02 + NO -»• N02 + RO
The rate of this type of reaction probably decreases
as the size of the R group increases, because large
R groups have a greater number of vibrational degrees
of freedom over which to distribute the energy of
the free radical. Denier jian et al. (1973) have estimated
that the rate constants for the CH,09--NO and CH,C07'-NO
i A
reactions are 910 and 470 ppm"imin"J- respectively?.
Spicer et al. (1971), however, have found the CH302-NO
reaction to be quite slow. As the time to the N02
peak predicted by kinetic mechanisms currently in use
is quite sensitive to the magnitude of this rate
constant, it is of interest to establish its value
190
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for the reaction of NO with each of several
different peroxy radicals.
As NO is oxidized and N02 accumulates during
smog formation, the reaction of peroxy radicals with
N02 becomes increasingly important. If the peroxy
radical is an acyl peroxy radical, stable products,
peroxyacylnitrates (PAN), will form.
RCOO + NO, -f RCOONO,
IT ^11 ^
0 0
Formylperoxynitrates, however, are thought to be
extremely unstable, if, indeed, they do form at
all; they have never been observed in smog chamber
studies. Similarly, alkylperoxynitrates and aryl-
peroxynitrates have yet to be observed in smog
chambers, and it is not known whether or not these species
are stable. Rather, the reaction of peroxyalkyl-
radicals with N0£ might go through a peroxynitrate
transition state, resulting in the formation of N03-
ROO + N02 -»• [ROON02] •*• RO + NOj
This reaction is, however, endothermic and thus has
a low probability of occurrence.
Given these gaps in knowledge, it is clearly
of interest to determine the mechanism of the RO--
N02 reactions and to estimate the associated
rate constants. This information will be partic-
ularly useful in the validation of kinetic mech-
anisms, as the magnitudes of the reaction para-
meters strongly affect the predicted asymptotic
level of ozone, the height of the N02 peak, and
the rate of decay of N02 after the peak.
191
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The population of peroxy radicals in the
smog system is limited by radical-radical recom-
bination reactions. These reactions may be direct
recombinations to form a peroxide and 02
R02 + R02 -»• ROOR + 02
or disproportionations to form an aldehyde (or
ketone), an alcohol, and 02.
R02 + R02 •»• R'CH + R'CH2OH + 02
0
Because the rate of radical-radical recombination in-
fluences the radical population and the time scale
of NO oxidation, the rate constants for this class
of reactions must also be determined.
It had been thought that, because of the
high rates of the OH-olefin reaction, peroxyradicals
might also react rapidly with hydrocarbons. However,
Hendry (1973) recently studied the reaction of H02
with olefins and of 01^2 with tetramethylethylene
and butadiene in the liquid phase and reached a
different conclusion. He found that the rate con-
stants for the reactions are quite small, on the
order of 10" ppm min . It is likely that this
reaction is also slow in the gas phase and can be
ignored in accounting for the consumption of
hydrocarbons.
192
-------
Alkoxy radicals are formed as a product of
the R07-N0 reaction and some R09-N0, reactions
ROo + NO + RO + N00
2
(Peroxyacyl radicals react with IvO to form acylate
radicals and N02; the acylate radical, however,
is very unstable and loses C02, forming an alkyl
radical.)
RCOO + NO + RCO- + NO,
II II 2
0 0
R- + CO
I
2
Alkoxy radicals react predominantly with 02 to
form an aldehyde and H02;
RO + 02 •*• RCHO + H02
the rate constant for the pseudo-first order
reaction has been determined by Heicklen (1968)
to be about 4.4 x 103 ppm" min" , when R is CH3
or C-Hr. The only competing reactions might be
those of ]
nitrates,
RO + NO -f RONO
RO+ N00 -v RONO,
those of RO with NO and N02 to form nitrites and
193
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However, the low concentrations of nitrites and
nitrates observed in smog chamber product analyses
suggest that these reactions are not sufficiently rapid
to be important.
We recommend that an effort be made to
establish the mechanism and determine the rate
constants for the reactions of several organic
peroxy radicals with NO, NCU, and R09. Also of
It Lt
interest, but of lesser importance at this time,
is the study of rate constants for the reactions
of oxy radicals with Oj, NO, and N02> and the
investigation of alternative mechanisms for the
R. - C>2 reactions.
d. Summary
In this section we have examined the reactions
of paraffins, olefins, aromatics,- acetylenes, and
aldehydes with the most important oxidants found
in the atmosphere. We have also discussed the
possible subsequent reactions of the free radical
products of these oxidation reactions. During the
course of the discussion we have identified a
number of reactions that require investigation. In
summarizing our findings, we recommend that the
following studies merit immediate attention.
(1) Branched aromatics constitute approximately
201 of the hydrocarbon mix in polluted
atmospheres such as that of Los Angeles.
194
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Thus, the rate of reaction of branched
aromatics with both 0 and OH should be
measured. The products of these
oxidation reactions should also be
determined.
(2) The rate of oxidation of NO predicted
by kinetic mechanisms depends strongly
upon the products assumed to form in
the OH-olefin reactions. Thus, sub-
sequent decomposition reactions of the
OH-olefin adducts should be identified.
(3) Although the 0_-olefin reaction does
not appear to consume a significant
portion of the total olefin, the suggested
intermediates of the reaction, so-called
zwitterions, may be powerful oxidants.
Thus, the mechanism and products of
the Oj-olefin reaction require further
study. It is also of interest to in-
vestigate the reactions of zwitterions
with atmospheric pollutants.
(4) Peroxy radicals are thought to be im-
portant oxidizers of NO. It is believed
that they also react with NO- to form
stable products. The importance of these
processes cannot be fully assessed, however,
until the rate constants for these reactions
have been determined.
195
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(5) The population of free radicals in
photochemical smog may possibly be
limited by the rates of radical-
radical recombinations. Thus, the
rates of these termination reactions
should be measured.
B. Investigation of Particle Growth Processes and the
Effect of Particles on Smog Formation Kinetics
It has long been recognized that atmospheric photo-
oxidation processes are frequently accompanied by aerosol*
formation. Despite this early recognition, the available
smog chamber data and the existing atmospheric data have
been neither sufficient nor adequate to characterize fully
either the physical or chemical mechanisms which govern
photochemical aerosol formation in the atmosphere or the
interaction of aerosols with the homogeneous gas-phase
formation of photochemical smog. This deficiency in under-
standing is due to the experimental difficulties associated
with (1) measuring the distributional properties of aerosols
and (2) generating a representative aerosol distribution.
Ultimately, it will be useful to formulate a model for
the combined gaseous and particulate components of an urban
atmosphere. The success of such an endeavor depends upon
our degree of understanding of aerosol
* suspended liquid droplets and solid particles
196
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(1) sources
(2) growth kinetics , and
(3) interactions with the gas phase constituents.
The first of these topics must necessarily be investigated
primarily in the atmosphere; discussion of it is thus deferred
until Chapter VI. The second and third topics, however, can
be investigated meaningfully in the laboratory and will be
discussed here.
1. Particle Formation and Growth
Aerosols can be classified into two distinct
groupings--the larger, so-called "primary" aerosols
which consist of particulates introduced into the
atmosphere from sources (e.g. dust, smoke) and the
smaller, sub-micron size, "secondary" aerosols which
are produced in the atmosphere by condensation and
chemical reaction. We consider the secondary aerosols
here specifically because they are
(1) responsible for the reduction in visibility
associcated with smog
(2) implicated in aggravating respiratory
ailments , and
(3) products of photochemical smog.
Both chemical and physical mechanisms play important
roles in aerosol formation and growth. Chemical reactions
provide species convertible from the gas to the particulate
(liquid or solid) phase and may take place in the particles
themselves. Physical processes such as nucleation,
197
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condensation, absorption, adsorption and coagulation
are primarily responsible for determining physical
properties; i.e., number concentration, size distribu-
tion, optical properties, settling properties, etc. of
the formed aerosols. Based on the results of the 1969
Pasadena Smog Experiment (Chapter VI), Husar and Whitby
(1973) have proposed the following mechanism for photo-
chemical aerosol formation: "The driving force for the
gas-particle conversion is provided by a gaseous photo-
chemical reaction or chain of reactions. The gaseous
reaction(s) produces a supply of molecular species (or
radicals) which, upon collision with each other, agglomer-
ate and form molecular clusters; i.e., homogeneously
nucleate. If suitable aerosol particles or ions are
present, the monomers or radicals deposit preferentially
on the existing surfaces and thus the nucleation is
heterogeneous. The growth rate of the newly formed
particles is controlled by the diffusion rate, i.e.,
the collision rate of the condensable species. The
condensation* itself may be physical (governed by
supersaturation) or chemical (if the condensable species
react with each other upon collision). If the concentra-
tion of the droplets is sufficiently high, they may
interact by coagulation.11
In this context, the term "condensation" is used to designate
a diffusion controlled growth process, regardless of the
nature of the accommodation process; i.e., physical or
chemical.
198
-------
In an initially particle-free chamber, Husar and
Whitby found that the chronological evolution of a photo-
chemical aerosol may be characterized by:
1. Initial rapid increase in total number concen-
tration by nucleation.
2. Coagulation when the aerosol concentration
reaches a sufficiently high level (maximum
concentration when production rate equals
coagulation rate).
3. The attainment of a steady-state surface
area sufficient to accommodate all the vapor
(the nucleation rate then diminishes). Decay
of number concentration by coagulation. Gas-
particle conversion rate associated with the
steady-state surface areas.
Although particle-free systems have been the subject
of most smog chamber studies, it is well-recognized
that the study of the growth of atmospheric aerosols
must include consideration of the presence of foreign
nuclei and therefore of heterogeneous nucleation. Hetero-
geneous nucleation is extremely complex, depending on
the size distribution and surface properties of the
foreign nuclei, as well as on the concentration and
chemical composition of the vapor. There is consider-
able evidence that in Los Angeles the mode of nucleation
of photochemical aerosols is primarily heterogeneous.
Thus, the total nuclei count is governed by ground sources
and not by self-nucleation (Husar and Whitby, 1973).
199
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In order to investigate the physical and chemical
behavior constituents of photochemical smog in the
formation and growth mechanisms of aerosols, we rec-
ommend that the following studies be undertaken:
(1) A complete chemical identification of the
individual constituents of secondary aerosols
should be made. Combined gas chromatography-
mass spectrometry systems offer promise in this
regard. Organic species represent a significant por-
tion of the atmospheric photochemical aerosol
on a weight basis (Friedlander, 1973). Only
after the relative abundance of individual
species (e.g. organic acids and diacids,
aldehydes, paraffins, polynuclear aromatics,
organic and inorganic nitrates, sulfates,
1^0, etc.) in the aerosol is assessed will
it be possible to postulate a chemical mech-
anism for the growth of particles. With
such information, however, it will also be
possible to assess the importance of aerosols
as a sink for gas-phase pollutants.
(2) The threshold levels of specific hydrocarbons
and S02 should be established for a polluted
atomosphere in which aerosol is formed.
Hydrocarbons selected for investigation should
be those which participate in reactions leading
to the formation of oxidation products observed
in the atmospheric aerosol (Task 1). For
200
-------
instance, if adipic acid (C, diacid) were
observed during the first task, it would be
necessary to determine threshold levels of
cyclohexene and 1,7-octadiene necessary for
the formation of aerosol. Further, threshold
levels of hydrocarbon mixtures must be estab-
lished. In so doing, it will be possible to
judge the importance of preferentially con-
tolling the emissions of individual hydro-
carbons in an effort to meet a given visibility
standard.
(3) The rate of chemical oxidation of SCK and
N02 at the surfaces of aerosols should be
determined. Although sulfates in particles
can result from the photochemical oxidation
of 862 in the gas phase, followed by condensa-
tion, it is also possible that (1) S02 is
oxidized in liquid droplets through reaction
with CU or metal ions or (2) SO^ is catalytically
oxidized on the surfaces of solid particles.
Similarly, nitrate formation results from the
reaction of N07 with NaCl, a pathway for nitrate
L*
production additional to that provided by the gas
phase NOj reaction.
(4) The effects of changes in factors such as temp-
erature, humidity, stirring intensity, and
turbulence level, all of which are known to
affect the growth rates and size distributions
of particles, must be quantitatively assessed.
201
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2. The Effect of Particles on Smog Formation Kinetics
We have thus far examined the ways in which photo-
chemical smog can contribute to aerosol formation and
growth. Because of the high surface area that aerosols
present to the gas phase, it is also possible that their
presence affects the rate of formation of smog. Before
meaningful studies can be carried out, however, we
must be able to reconstruct experimentally the measured
atmospheric spectrum of aerosol properties, notably
with, respect to size and chemical composition. If this
effort is successful, it will then be possible to deter-
mine if the kinetics of the overall formation process
of smog is affected by the presence of particles. For
example, particles may quench free radical chains or
adsorb free radical initiators such as NC^ or HNC^,
thereby slowing the oxidation of NO, or they may oxidize
NO at the surfaces if they are catalytically active or
if they contain strong oxidants, thereby accelerating
smog formation. If aerosols are shown to affect the rate
of smog formation, it would then be useful to alter the
characteristics of the simulated aerosol in the chamber
to investigate the effects of changes in (1) chemical
composition and (2) number and size distribution on the
resultant smog kinetics. Only upon completion of such
studies can validation of kinetic mechanisms be meaning-
fully undertaken using data collected in smog chambers in
which particles were present initially.
202
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V, CONTROLLED EXPERIMENTAL STUDIES IN SMOG CHAMBERS
The formation of photochemical smog occurs in an
extremely complicated system, one in which meteorology,
continuous emissions of pollutants, and photochemistry
all play important roles. In order to isolate the effects
of photochemistry from other variables present in an at-
mospheric environment, investigators have simulated the
chemical reaction process by irradiating the primary
pollutants in static reactors, so-called smog chambers,
some of the results of which are described briefly in
this chapter. The observed results must be interpreted
with great care, however, for even in a smog chamber
factors other than the photochemistry can still influence
the course of the overall smog formation process. We
therefore devote much of this chapter to procedural con-
siderations such as wall effects, radiation simulation,
analytical procedures, and reproducibility of experiments.
In short, we point out the necessity of completely char-
acterizing the smog chamber before experimental studies
are conducted. Finally, we discuss ways in which an
operating system can be used to generate data for the
validation of kinetic mechanisms, to demonstrate inter-
actions between specific pollutants and typical urban air
pollution samples, and to investigate scavenging processes
that occur in the natural environment.
A. Chamber Effects
A very important question to examine at the outset
of experimental smog chamber studies is how and to what
203
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degree the design, construction, and operation of the
chamber affect the observed results. Similar smog chamber
experiments performed in different chambers, but with the
same hydrocarbons, have not all exhibited the same con-
centration-time behavior. Because initial concentrations
are similar, it appears that effects characteristic of the
chambers themselves are influencing the courses of the
experiments. Possible explanations for the disparate
behavior include differing degrees of mixedness, surface
effects, and irradiation intensity between chambers. In-
deed, experiments performed in a single chamber are not
always reproducible in the same chamber a month later
(Westberg, 1972). The problem of non-reproducibility is
quite possibly serious enough to render much of the exis.ting
smog chamber data unsuitable for the purposes of model val-
idation. If smog chamber experiments .are to be used as
a tool for broadening our understanding of smog formation,
individual chamber effects must be minimized or eliminated.
At the very least they must be understood quantitatively.
In this section, therefore, we undertake to point out what
we consider to be the most critical of chamber effects.
So that the examination of chamber effects can be compre-
hended in the perspective of current experimental methods,
however, we begin our discussion by surveying the various
types of smog chambers in common use.
Smog chambers can be classified into three general
categories. The earliest and most popular were the large
environmental chambers having volumes from fifty to five
hundred cubic feet. The large volume is appealing because
of the "wall-less" nature of the atmosphere being simulated.
204
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Due to their size, these chambers have traditionally been
constructed of the most convenient materials, e.g. plate
glass, aluminum, or Teflon-lined materials. Although the
size has as an advantage reduced surface to volume ratios,
there are several inherent shortcomings in this type of
chamber:
1. Due to. the large surface areas involved,
cleaning of surfaces can be a long and
tedious task, one which is often neglected.
2. Direct measurement of light intensity in
these chambers by the conventional procedure
(see part 3 of this section) requires that
all of the Q£ in the chamber be displaced
by an inert gas such as nitrogen. This is
both difficult and expensive. (Alternately,
k-, , the photolysis rate -of N09, can be deter-
J. &
mined in a smaller bag inside the chamber,
but this procedure requires proper and accurate
compensation for the absorption of light by
the bag.)
3. Unless the chamber is carefully designed and
stirred, a significant percentage of the chamber
contents may not be well-mixed.
4. A large bank of analytical instruments must be
available to monitor the chemistry, and each
of these instruments must be recalibrated
regularly to insure its accuracy. (A notable
exception to the former problem is use of long
path infrared systems (to be discussed shortly),
205
-------
in that the single spectrometer is capable
of monitoring all of the major contaminants.)
A second type of smog chamber is simply a plastic
or Teflon bag. The chief advantage of bags is that con-
stant pressure is maintained during sampling without the
necessity of dilution due to collapse of the enclosing
surface. Because of their reduced volume, bags are
convenient to work with and have the advantage of allow-
ing easier measurement of the light intensity. Bags,
however, suffer the disadvantages cited above, as well
as having
1. a high surface to volume ratio
2. no facilities for mechanical stirring, and
3. pollutant absorption on, or reaction with,
the surface material.
The third popular type of smog chamber is the long
path infrared spectrometer (LPIR) with a small (^100 liters)
reactor enclosing the optics. LPIR's have as an advantage
the fact that all the pollutants are monitored using a
single instrument, the spectrometer, so that only the
optics require adjustment to assure accurate monitoring.
The reactors, however, have less favorable surface to
volume ratios than do environmental chambers, and they are
very difficult to clean by wet methods. Removal of the
reactor for cleaning is a delicate and time consuming task,
and care must be taken not to misalign the optics. Finally,
mechanical stirring devices cannot be introduced into such
a system.
In the past considerable effort has been expended in
simply identifying the precursors of atmospheric reaction
206
-------
products and in obtaining general information about the
importance of such factors as the influence of hydrocarbon
to NO ratios on the level of oxidant formed. Each of the
^^
three systems described above can be used in performing this
task. However, the general aspects of 5
-------
In our estimation, those factors causing similar
smog simulation experiments to differ from chamber to
chamber (and, for that matter, from chamber to atmosphere)
fall into three broad classes:
(1) degree of stirring and mixedness in the
chamber
(2) surface effects, and
(3) radiation simulation.
The first of these, the effect of gas-phase heterogeneities
on the rate of the overall photochemical reactions, has
been discussed extensively in Chapter III. It is a problem
that, once recognized, can be solved by careful chamber
design. The key point is that the experimenter must insure
that the contents of his chamber are well-mixed so that the
chamber is in practice an ideally-mixed vessel. Only then
can the concentration changes be represented by the usual
ordinary differential reaction rate equations.
The complete elimination of surface effects is
probably an impossible goal. Rather, we must be satis-
fied with controlling and, at the very least, under-
standing the influence of the surfaces on the photo-
»
chemistry. The extent of surface-gas phase interactions
can be determined by measuring the rates at which known
concentrations of pollutants adsorb or decompose on the
walls, and those values should complement the gas phase
material balance to account for the entire initial
reactant charge (less that lost by sampling and dilution).
208
-------
The problems associated with radiation simulation are
two-fold: (1) the achievement of a uniform light intensity
distribution throughout the chamber and (2) the careful
measurement of light intensity. Solution to the former
problem can be achieved by careful placement of the lamps.
Light intensity measurement techniques are presently avail-
able; however, they are cumbersome, particularly those which
require the complete displacement of 02 from the reactor.
Convenient methods must be developed to encourage the
routine monitoring of light intensity. These three
factors, then, represent the most serious influences
of smog chambers on the homogeneous gas phase chemistry.
Given a quantitative assessment of each of these operating
parameters, however, it will become possible to extract
meaningful kinetic data from smog chamber experiments.
1. Stirring and Mixedness in the Chamber
Although smog chambers are often thought of as
atmospheric or environmental simulation chambers, one
of their primary functions is to permit the study of
the macroscopic smog kinetics in an uncomplicated and
controlled system. Variables that the experimenter
may wish to control are the concentrations of the
reactants, the temperature and humidity of the cham-
ber, and the radiation intensity. Another variable
of interest, one that is more difficult to define
precisely, is the degree of mixing in the chamber.
We have already seen in Chapter III that hetero-
geneities in the reactant-gas mixture will lead to the
209
-------
observation of "apparent" kinetics, that is reaction
rates that differ from those occurring in a well-
mixed, homogeneous system. Certainly, the atmosphere
is not a homogeneous reactor; however, if smog
chambers are to be used as a tool for studying chem-
istry solely, they must, ideally, be well-mixed.
The achievement of a homogeneous system is primarily
a matter of careful design.
The flow patterns observed in a smog chamber
depend critically on two factors, the geometry of the
chamber and the stirring apparatus employed. In
some conventional smog chambers equipped with mixing
devices, it has been estimated that a poorly mixed
region characterized by laminar (versus turbulent)
flow develops at the walls or boundary of the cham-
bers and can encompass upwards of 25% of the total
volume of the chamber (Liu, 1972). The judicious
placement of mechanical stirrers can reduce that
problem substantially.
2. Surface Effects
Ideally, the presence of surfaces in the reactor
should not affect the results of a smog chamber ex-
periment. In practice, however, there is little
reason to believe that is the case. Carbon and nitrogen
material balances for the gas phase materials over
the course of an irradiation have often been poor.
For example, Altshuller et al. (1970) reported that
they were able to account for only 3% of the initial
carbon and 10-20% of the initial nitrogen after a
210
-------
6 hour irradiation of toluene in NO . Part of the
^^
difficulty may be explained by the failure of many
investigators to measure all of the products of the
photochemical reactions. In the irradiation of
ethylene-NOv mixtures, CO and C09 are important
J\. ' if
carbon-containing products which are not always
monitored (Gay and Bufalini, 1971). The irradia-
tion of aromatic-NO mixtures results in the forma-
J\.
tion of acetylene as a major carbon-containing
product; failure to measure that'species probably
accounts for the poor carbon balance reported by
Altshuller et al. (1970) for toluene and m-xylene.
Another reason for poor carbon balances is that
free radicals and polar species such as aldehydes
and organic acids are adsorbed on the walls. The
relative contributions of these two effects in
accounting for the initial carbon charge has yet
to be assessed in quantitative terms.*
Other possible reasons for poor material balances are
(1) that strongly polar products such as organic
acids may be lost to the sides of sampling tubes lead-
ing to the monitoring instrument and (2) that the
analytical instruments may be improperly calibrated.
211
-------
The major reason for poor nitrogen balances
is definitely attributable to surface effects.*
The work of Gay and Bufalini (1971) supports this
hypothesis, in that they were able to obtain a con-
sistent nitrogen balance when they included the
nitrate and nitrite washed from the walls of their
irradiation vessel. Their results suggest that the
presence of surfaces affects both the observed rates
and the product distributions.
The necessity of achieving and maintaining a
mass balance for carbon and nitrogen over the entire
course of a photochemical smog experiment cannot be
overemphasized. Without a mass balance there is no
assurance that all the important products in the
system are being detected. Nor can one be sure that
the products have been measured accurately. Certainly,
the problems associated with achieving a consistent
material balance are great, but a 100% balance should
be the goal.
It had been thought that molecular nitrogen might be
a product of the ethylene-NOx reactant system (Bufalini
and Purcell, 1965), but Gay and Bufalini (1971) have
since disproved this hypothesis.
212
-------
While it seems unlikely that surface effects can
ever be completely eliminated, it is possible to iden-
tify, quantify, and minimize the various types of sur-
face-gas interactions. Topics to be discussed in this
section include studies of the rates at which various
chamber surface materials adsorb constituents of smog,
the effect of surface to volume ratios on the rate of
wall adsorption, the cleaning and preparation of the
surfaces, and the effects of wall temperature and the
amount of water adsorbed on the walls on the rates of
wall reactions.
a. Surface Materials and Wall Adsorption Studies
Recently, several groups have begun to explore
the influence of various surface materials on the
loss rate of pollutants in chambers. At Lockheed
Missiles and Space Company, Jaffee (1972) is in-
vestigating the effect of four surface materials
on the results observed in his chamber during hy-
drocarbon-NO irradiations. They include Pyrex,
A.
stainless steel, aluminum, and Teflon. In work
recently completed, Sabersky et al. (1973) have
determined the loss rate of ozone in a small cham-
ber containing large sheets of several different
materials. They .found that the decomposition rate
of ozone was the least for aluminum and plate
glass, was 6 times greater for Lucite, 24 times
greater for polyethylene, and almost 100 times
greater for neoprene. In their experiments the
213
-------
temperature of the system was maintained at 72°F
±1°F and the relative humidity at 50% ±5%. Mixing
was accomplished through the use of several large
fans. These investigators are presently carrying
out a similar set of experiments using nitric oxide.
Tentative results for the effects of Teflon
on reaction dynamics are available from two sources.
Holmes (1973) of the California Air Resources Board
has postulated that ozone is absorbed by the Teflon
surface of the ARE chamber during cleaning opera-
tions, at which time the walls are exposed to 20
to 40 ppm of ozone for 24 hours. His conjecture
is based upon the fact that ozone continues to
appear in his nitrogen-filled chamber for several
days after the original ozone has been flushed
from the system, the ozone presumably being re-
emitted by the Teflon. It is important to inves-
tigate this phenomenon in some depth, since Teflon
FEP bags are widely used as reactors, and the up-
take of 0, by the bag could alter the course of
the reaction. Also, several experimenters have
reported the use of Teflon sampling tubes (Gay and
Bufalini (1971). Gay and Bufalini (1971), however,
have found 93% of the initial nitrogen charge pre-
sent (in the form of nitrogen-containing compounds)
in the gas phase in a trans-2-butene-NO experiment
J\.
carried out in a Teflon FEP reactor. They suspect
that Teflon might have a lower adsorption rate for
oxides of nitrogen than does glass, but this obser-
vation is based on a single run.
214
-------
Clearly, an optimal surface material must be
identified before further expensive smog chamber
studies are carried out. The best material will
be the one showing the lowest loss rate for each
pollutant individually (i.e., NO, N02, 0,, various
hydrocarbons, aldehydes) and collectively (i.e.,
under irradiated smog chamber conditions). Further-
more, it will be necessary to determine quantita-
tively the loss rate for each pollutant once a
material has been selected.
bo Surface to Volume Ratios
The effect of surface to volume ratio on smog
chamber experiments has been largely ignored in
the past. In a recent study, however, Sabersky
et al. (1973) found that the ozone decay rate in
their chamber was directly related to the surface
to volume (S/V) ratio. Certainly, increasing the
S/V will in turn increase the probability of a
given molecule striking the surfaces. Thus, other
factors being equal (e.g., concentrations, wall
conditions, mixing rate, etc.), a reduction in the
ratio will lessen surface effects.
Ideally, the S/V ratio should be as close to
zero as possible. Unfortunately, problems other
than those associated with surface effects arise
in using large chambers. Thus, we must set as a
goal the understanding of the effects of S/V
ratio on smog chamber experiments, so that we can
215
-------
correct or otherwise compensate for them (rather
than eliminate them). In his current study, Jaffe
(1972) plans to compare chamber results using two
different S/V ratios for the same initial condi-
tions. In principle, identical chamber runs
should be performed at four or five S/V ratios.
Also, baffling or other packing (e.g., turnings)
of the same composition as the walls can be added
to the chamber to evaluate the effect of increased
surface area.
c. Cleaning and Preparation of the Surfaces
In order to obtain reproducible results from
a chamber, the chamber surfaces must, among other
things, be brought to a known initial condition.
Several techniques have been -used with varying
degrees of success. The most common technique of
cleaning a chamber between runs, especially a
large environmental chamber, is simply to force
filtered laboratory air through the chamber with
lights on and fans running either overnight or
until no more pollutants are detected by the moni-
toring equipment.. Unfortunately, this technique
does little to remove the adsorbed materials from
the walls of the chamber.
A second technique is to evacuate the chamber
using a vacuum system. This is an efficient way
of removing the bulk gas, especially for small
chambers. Removal of material from the walls
216
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would require several days of pumping unless the
walls were heated to drive off the water and other
species. Under these conditions, pumping would
only require several hours. The cleaning efficien-
cy of this technique, however, remains to be
assessed.
A method used by some experimenters for clean-
ing the surfaces involves allowing high levels of
ozone, for example, 20 to 40 ppm, to react with
materials on the walls of the chamber for several
hours. This procedure results in complete oxida-
tion of all substances which will react readily
with ozone, but it does not remove any of the oxi-
dation products from the walls.
A technique reported by Gay and Bufalini
(1971) £p,r cleaning of the walls of a small (72
liter) boro-silicate glass reactor involves
washing the surfaces before each irradiation with
aqueous cleaning solution, acetone, and finally
with distilled water (the latter, several times).
This is the surest way of removing material from
the surfaces, but it is a time-consuming, manual
task that is unsuitable for larger environ-
mental chambers. Whatever surface material is
chosen for future chambers, it will be necessary
to evaluate the various methods of cleaning the
surfaces. At this time it appears that the three-
stage washing technique of Gay and Bufalini is pre-
ferable to other suggested procedures.
217
-------
Independent of the relative degree of suc-
cess or failure of each of these cleansing techni-
ques, there remains some question as to whether
"the cleanest surface is the best." Sabersky
et al. (1973) found that the decomposition rate
constant of ozone on Lucite decreased by 501 over
the first eight hours of the material's exposure
and then continued to decrease slowly as the cham-
ber "aged". The same general trend was observed
for neoprene (701 decrease in the rate constant
in the first 100 minutes of exposure). These
results suggest that clean walls can be partially
deactivated by intentionally exposing them to
ozone. Surfaces of metal-walled chambers become
deactivated as an oxide layer forms at the air-
wall interface. If the oxide layer remains
intact after cleansing, the cleansing procedure
might well result in a stable and reproducible
surface condition.
d. Effect of Adsorbed Water on Wall Reactions
Even in so-called dry systems it is reasonable
to assume that an adsorbed layer of water will be
found on the walls of the chamber. This would cer-
tainly be the case in experiments run under ambient
conditions with 25-751 relative humidity. Although
little attention has apparently been paid in the
past to carefully controlling the relative humidity
in smog chambers, there is reason to believe that the
218
-------
amount of water in a chamber markedly affects the
rate of loss of pollutants to the surfaces.
In one set of experiments Cox and Penkett
(1972) found that a three-fold increase in the
relative humidity (from 30% to 861) resulted in
a 35-fold increase in the first order decomposition
rate constant (from 0.00425 min to 0.139 min )
of S02 on a gloss paint surface. In examining the
decomposition of ozone on aluminum surfaces they
found that increasing the relative humidity from
321 to 83% resulted in a three-fold increase in
the first order loss constant, from 0.0038 to
0.0112 min" . They accounted for the degree of
mixedness of the system in their calculations,
but because of their experimental method, they were
forced to add NO to the ozone system prior to the
experiment to prevent aerosol formation from oc-
curring. Since NO reacts rapidly with ozone and
since experimental data collected are based
upon a single determination, the 0, loss data should
be scrutinized carefully. Nevertheless, the sub-
stantive effect of variations in relative humidity
on the loss rate of S02 and 0_ seems to be clearly
established in this work. In related work Mueller
et al. (1973) has found that the decomposition rate con-
stant of ozone on aluminum is greatly influenced
by the relative humidity. Sabersky et al. (1973),
however, found the rate constant for ozone loss
on Lucite to be little affected by humidity over
a range of 15% - 90% RH. This effect is, as of
219
-------
yet, unexplained, although it may be a function
of surface material, the temperature of the sur-
face, and consequently, the amount of water on
the surface.
The most direct way in which water can serve
as a scavenging agent for the chamber pollutants
is through the dissolution of the gr.-es in the
adsorbed water layer on the wall' l.i examining
vegetation as a sink for atmospheric pollutants,
Hill (1971) demonstrated a relationship between
the absorption rate and the solubility in water
of each pollutant he studied. In particular, SO-
is very soluable in water (39.4 cc/cc H20 at 20°C),
0- is slightly soluble (0.26 cc/cc H70), and NO
o *•
(.05 cc/ccH20) and CO (.02 cc/cc. H20 are much less
soluble. The loss rate data for SO- and 0, col-
£• «j
lected by Cox and Penkett (1972) confirm this
general trend. Although Gay and Bufalini (1971)
did not investigate the problem of N02 adsorption
in detail, they found that when they irradiated
6 ppm of N02 for four hours in air about 10% of
the initial N02 was adsorbed on the walls, hydro-
lyzing to equal amounts of nitrate and nitrite,
6N02 + 3H20 * 3HN03 + 3HN02
3HN02 t HNOj + 2NO + H20
We have not found chamber adsorption data for NO
or CO.
220
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One pollutant not included in the solubility
table found in Hill (1971), but which forms in
significant quantities after the N02 peak, is
N20r, the acid anhydride of nitric acid.
This species hydrolyzes readily by the reac-
tion
N205 + H20 •* 2HN03
Gay and Bufalini (1971) have suggested that this
is the major source of nitrate on the walls. To
test the hypothesis they performed two experiments
Knowing that N70c forms by the reactions:
N02
they first introduced 6 ppm of N02 and 1.6 ppm of
03 into a 72 liter glass reactor and allowed them
to react for four to six hours. Gas phase analy-
sis did not indicate the formation of nitrate, but
washing the walls with a basic solution yielded
3.1 ppm of nitrate and 0.1 ppm of nitrite. (The
stoichiometry of the above reactions suggests that
a maximum of 3.2 ppm of nitrate would form if all
the 0- reacted with N02) . In the second experiment
they introduced vaporized nitric acid into their
reactor. After three hours nearly all of the nitric
acid was still confined to the gas phase. These
experiments strongly suggest that N20r is adsorbed
and hydrolyzed on the walls of the reactor rather
221
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than hydrolyzing in the gas phase and then
diffusing to the surfaces as nitric acid.
The literature concerning the effect of
water on the photo-oxidation rate of hydrocarbons
has been reviewed recently by Altshuller and
Bufalini (1971). Although various investigators
have seen some increase in reactivity when water~
was added to an experimental system, Altshuller
and Bufalini attributed these observations to
changes in the reactivity of walls. Presumably,
water can deactivate surface sites on a wall with
the consequence that free radicals are longer
lived. This hypothesis is worthy of further in-
quiry.
In the future investigators should attempt
to estimate the amount of water on the surfaces
of smog chambers. One should expect that the
quantity of water will depend both upon the rela-
tive humidity in the system and the temperature
of the walls. Wall uptake studies should also be
performed for individual gaseous pollutants to
assess the rate of loss of these species to the
walls under various typical experimental condi-
tions. It now appears that N2°5 and S02 are
strongly affected by the amount of water on the
walls, 0, and N09 are affected to a moderate
O £
degree, and based solely on solubility data, NO
and CO may be affected the least. Data for the
222
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interaction of aldehydes and the various class of
hydrocarbons with water-covered surfaces remain
to be determined.
e. Effect of Temperature
In chapter IV we noted that several investi-
gators have observed the rate of smog formation
to accelerate when the operating temperature of a
chamber is raised. We presented as one possible
explanation the fact that the majority of reactions
contributing to smog are thermal, and for the most
part, will proceed somewhat faster at higher tem-
peratures. It is not presently known, however,
if this effect is sufficient to explain completely
the effect of changes in temperature on the rate
of smog formation. Dimitriades (1967) has suggested
that surface effects might change with the tempera-
ture of the walls. For example, water evaporates
from the surfaces as their temperature increases,
potentially exposing more reactive sites and de-
creasing the probability of pollutant loss by dis-
solution in the water layer and by heterogeneous
hydrolysis. The effect of temperature on surface
effects might be determined by repeating an iden-
tical smog chamber experiment at a constant air
temperature but with heated and/or cooled walls.
If no change in the rate of smog formation were
observed, the effect of temperature could be at-
tributed entirely to changes in the rates of the
223
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thermally-induced elementary reactions. Other-
wise, surface effects must be determined as a
function of temperature, so that proper compen-
sation can be made when interpreting the data.
3. Radiation Simulation
The principal driving force in the smog reaction
system is the photolysis of N09:
£
ki
N02 + hv -* NO + 0.
Although there are other absorbing species present in
the atmosphere (e.g., peroxides, aldehydes), these are
not considered "driving forces" as either they are
found at low concentrations relative to N02 or their
photolysis rates are low. As a result, the rate of
photolysis of NO^, k-,, can serve as a useful measure-
ment of the ultraviolet light intensity. Because of
the importance of this photo-initiation reaction to
the overall smog kinetics,* the measurement of the
spectral distribution, spatial intensity distribution,
spatial intensity distribution, and absolute intensity
of the radiation are extremely important. If they are
not determined with care, one can neither meaningfully
The sensitivity of the smog formation rate to ki is
demonstrated in a computer simulation of the n-butane/
toluene/NO system (Hecht, 1972). Using a base value
of k, = 0.266 min'l, the N02 peak occurred at 112 min-
utes. Decreasi n a Vi tn O.lfifi min"! rp«ii11^ in a timp
utes. Decreasing ki to 0.166 min"1 resulted in a time
-- -*-- "~ ---'- -" *"* ' ' • to 0.366
minutes.
to the N02 peak of 169 minutes; increasing ki to 0.366
min'1 resulted in a time to the N02 peak of 84 minu
224
-------
compare experiments performed in different chambers,
nor extract quantitative information from an indivi-
dual experiment.
a. Artificial Irradiation
Tuesday (1961) has shown that the spectral
distribution of fluorescent lamps centered at
3550A is somewhat different than that of the
ultraviolet spectrum of the sun. A question then
arises as to whether these differences signifi-
cantly affect the course of photochemical smog
formation. Laity (1971) studied this problem by
comparing product concentrations observed after
irradiation of several synthetic smog mixtures
by blacklight fluorescent lamps with concentrations
observed when identical mixtures were irradiated
using natural sunlight. (In this study it was
not necessary for the output of the lamps to re-
main constant in intensity, for the results were
compared with those obtained for irradiation by
sunlight, which varied in intensity over the course
of the experiment. In chamber kinetic studies,
however, it is important that the intensity be
constant or, at least, well defined). He found
no significant discrepancies between comparable
mixtures over the period of the irradiations,
thereby justifying the use of blacklight fluores-
cent lighting in smog chamber studies.
225
-------
While the output of lamps undergoes a natural
deterioration with age, a process accelerated by
operating the lamps at an overvoltage, a critical
factor in stabilizing the UV output of the black-
light fluorescent lamps is that the operating
temperature of the lamps be kept constant
(Dimitriades,. 1972). Holmes et al. (1973) report
that a rise of 30°F in the temperature of the air
surrounding the lamps results in a 40% decrease
in the UV output. Because temperature increases
of this magnitude are not uncommon in smog cham-
bers, these results highlight the importance of
placing the lamps outside the chamber where they
can be maintained at a constant temperature by
forced air cooling. Outside installation of the
lamps, however, introduces the additional con-
straint that at least portions of the chamber
walls be transparent to UV radiation, thereby
restricting the choice of surface materials.
b. Distribution of Light Intensity
Since variations in light intensity at vari-
ous locations within the chamber result in differ-
ing rates of N02 photolysis, hence, of smog forma-
tion, it is vital that the radiation be uniform
throughout the chamber. Often, lamps are located on
one or two sides of cylindrical or box-shaped cham-
bers. Because intensity is inversely proportional to
the distance from long cylindrical lamps, such a con-
figuration can lead to intensity gradients in the
226
-------
chamber. It should be noted that Niki (1973)
has built a cylindrical chamber of glass with
lamps placed in a geometric configuration about.
the reactor such that the maximum variation in
intensity in the chamber is no more than 5-101.
Thus, the existence of intensity gradients in
chambers need not be accepted as an inevitable
consequence of a particular geometric configur-
ation.
c. Measurement of Light Intensity
Although it would be desirable to determine
the radiation within a chamber by measuring the
intensity as a function of wavelength, such an
approach requires equipment which is both com-
plex and expensive. Thus, it has become custom-
ary in photochemical smog studies to calibrate
UV sources by measuring a manifestation charac-
teristic of the light source, namely, the photo-
sis rate of N02. The rationale for this method
is that the fundamental photochemical process in
smog formation is the photolysis of N09
£»
kl
N02 + hv -*• NO + 0
and that the rate of this reaction determines,
to a large extent, the rate of the overall pro-
cess. The method, first suggested by Tuesday
(1961), consists of photolyzing an initial charge
of N02 in an inert atmosphere (e.g., N2) ,and in
227
-------
some manner determining the first order rate
constant for N02 decay, k^, from the N02-time
data.
Originally, a pseudo first-order decay
parameter, k-,, was taken as a measure of the
light intensity. But because the decay of N02 in
N2 is not a first-order process, k, reflects the
combined result of a large number of reactions
(see Table 8) rather than the result of just
the single reaction 1 . Therefore, k, is not
a fundamental rate constant of the system.
When smog chamber data are used for the purpose
of validating chemical mechanisms, k^, not k^,
must be specified.
Holmes et al. (1973) have shown that k^ can
be determined directly from the N02~time data
obtained by irradiating N02 in dry, oxygen-free
nitrogen. One simply notes the initial ([N02]Q)
and final ([N02D concentrations of N02 and the
length of photolysis (At) , k^ is then determined
from the following equation;
C1
ln
CN°2]° - It
[N02] Z
[N02]0
_[N02]
- 1
0.27
0.16
(34)
228
-------
TABLE 8. Reactions and Rate Constants for the
Photolysis of Nitrogen Dioxide in N2 and 0^
No.
1.
2.
3.
to
S 5.
6.
7.
8.
9.
10.
llo
N02
0 +
°3 +
0 +
0 +
N03
0 +
2 NO
N03
N2°5
NO,
Reaction
+ hv -»• NO + 0
0- + M -»• 03 +
NO * N02 + 02
NO, f NO + 0,
£• Lt
N02 + M + N03
+ NO * 2 N02
NO + M •»• N02 +
+ 02 -»• 2 N02
* N02 * N205
•*• N03 + N02
+ 0, * NO- + 0
M
+ 1
M
t
Rate Constant
To be Estimated
2.33 x 10"S ppm"2 min"1
2.95 x 101 ppm" min"
1.38 x 104 ppm"1 min"1
-3 -2 -1
4.50 x 10 ppm min
4 -1 -1
1.48 x 10 ppm min
_ T _ 2 - 1
2.34 x 10. ppm min
7.62 x 10"10 ppm "2 min"1
4.43 x 103 ppm"1 min"1
1.38 x 101 min ~l
1.06 x 10"1 ppm"1 min"1
Reference
Johnston C1968)
Johnston arid Crosby (1954)
Schuck et al. (1966)
Schuck et al. (1966)
Schott and Davidson (1958)
Kaufman (1958)
Glasson and Tuesday (1963)
Schott and Davidson (1958)
Mills and Johnston (1951)
Johnston and Yost (1949)
-------
The validity of this equation was established
both through experiments in a long path infra-
red spectrometer cell and through computer si-
mulation of the "Ford-Endow" mechanism (Ford
and Endow, 1957) for the reactions taking place
in the N02-N2-light system (see Table 8). Since
one can obtain k, directly via this procedure,
we suggest that future investigators use k,
rather than the pseudo-first order decay con-
stant for N09, k,, to characterize UV intensity
£* Q
in photochemical smog experiments.
It is impractical or impossible to purge
and fill large environmental chambers with a
/N2 mixture. Rather, one can formulate the
/N2 mixture in a semi-transparent Tedlar bag
and irradiate it for a short period, determining
both the initial and final NCU concentrations.
£
Equation (34) can then be used to calculate k
although a correction must be made for transmis-
sion by the Tedlar. Such a technique is used
by California Air Resources Board investigators
in establishing k. for experiments carried out
T1
in their 1100 ft chamber (Holmes et al., 1973).
Determination of the light intensity in an
outdoor chamber is a more difficult problem, as
it is impossible to control the intensity of the
230
-------
sunlight. (In his study Laity (1971) found that
"k^" outdoors varied between 0.15-0.30 min de-
pending on the day and time.) Consequently, it
is necessary to determine k, several times during
the course of a run, and particularly, to note
any abrupt changes in the light intensity. In
view of Laity's results showing that fluorescent
lamps produce the same results as sunlight for
comparable experiments and the fact that it is
impossible to control the intensity of natural
sunlight, there does not appear to be any advan-
tage in performing outdoor smog chamber studies
if kinetic information is being sought.
Because it is difficult to remove all the
&2 from the system, as is required in determining
k^ by the procedure just described, it would be
useful to develop a means for determining k, in
air. We devote Appendix A to a discussion of a
general method by which k, can, in principle, be
determined directly and accurately from the NO-
concentration-time data observed when an arbitrary
mixture of NO^ and NO (if any) is photplyzed in
air. The essential feature of the method is that
a computer estimation algorithm (presented in the
appendix), rather than a simple expression such as
(34), is required to determine the value of k,.
4. Summary
While it would be desirable to develop and design
an entirely new smog chamber after techniques have been
231
-------
developed for reducing chamber effects, consideration
of such an approach must be tempered by an evaluation
of costs and development time involved. Failing the
development of a new chamber, it is necessary to es-
tablish quantitatively in an existing chamber:
the completeness of mixing
the interactions between the surfaces and
the gas phase chemistry, and
the uniformity and intensity of the arti-
ficial irradiation.
Furthermore, particular effort must be made to estab-
lish material balances during smog chamber irradiations,
If smog chamber data are to be used for validating kinet-
ic mechanisms, no variable associated with the smog
chamber system that can potentially affect the outcome
of the photochemical process should be ignored or over-
looked. All such variations must be monitored and
reported.
B. Analytical Procedures
The usefulness of reproducible smog chamber data ulti-
mately depends to a large degree on the reliability and com-
pleteness of the chemical measurements. Five species, namely
N02, NO, 0_, hydrocarbons, and aldehydes, are the most impor-
tant reactants in smog and, with the exception of aldehydes,
have generally been measured in chamber experiments. In this
section we examine alternative analytical techniques that may
be used in determining the concentrations of these five spe-
cies. There are, however, many other species present in
232
-------
smog (such as peroxides and nitric acid) which one might
wish to monitor, both to elucidate the mechanism of smog
formation and to validate kinetic mechanisms. These spe-
cies are discussed in part c of this section.
Analytical instruments fall into two classes. The
first class includes instruments which may be used to make
a direct measurement for some physical property of the
species under observation. An example of such an instru-
ment is the infrared spectrometer, which detects the amount
of infrared radiation absorbed by specific pollutants. The
second class of instruments, and by far the most common, is
the chemicophysical. In this case the pollutant being mea-
sured first undergoes chemical transformation; the product
of the reaction is then measured using an appropriate analy-
tical technique. As an example, the classical "wet" chemi-
cal techniques are all chemicophysical. In these, a sample
of the pollutant is collected for a period of time in a
liquid absorber. The sample is then reacted with another
reagent, resulting in a change in color or in the formation
of another product. The intensity of the color-or the con-
centration of the products are related to the concentration
of the original pollutant. Many newer types of instrumenta-
tion, such as chemiluminescent devices (which are based on
measuring the light emitted when the pollutant being moni-
tored reacts with another reagent), are also chemicophysical
A number of criteria may be specified for evaluating
the appropriateness and utility of an analytical technique
for a particular application. These include:
233
-------
1. the accuracy, specificity, and ease of calibra-
tion of the instrument
2. the precision or reproducibility of the measure-
ments
3. the volume of gas required to make a determination
4. the response time of the instrument.
In the discussion that follows, we first examine these cri-
teria individually. We then use them in evaluating the qual-
ity of measurements to be expected from analytical instru-
ments which either have been employed extensively in the past,
or have recently been developed, to measure NO^, NO, Oj, hy-
drocarbonr, and aldehydes.
1. Accuracy and Primary Standards
The accuracy of a method, that is, the extent to
which the observed or measured value and the "true"
value agree, depends on both the specificity of the
technique and the accuracy of calibration. Lack of
specificity, or the presence of interferences due to
species other than the one desired, is the greatest
shortcoming of all wet methods. For example, in the
measurement of ozone by the potassium iodide (KI)
method (see part 5 of this section), peroxides, N07,
£*
and peroxyacylnitrates, in addition to ozone, will all
give a positive response, while SO- and dust give a
negative response relative to the value observed with-
out the interference. Thus, the accuracy of the indi-
cated 0, concentration is, at best, questionable when
these other species are present.
234
-------
The accuracy of calibration procedures depends
upon the availability of primary standards. The well-
established wet chemical techniques fare very well in
this regard (Katz, 1968), while suitable primary stan-
dards are still being sought for many of the gas phase
monitoring techniques. For instance, as of yet no
primary standard for Oj has been developed, and ozone
sources such as air ozonizers must be calibrated by
potassium iodide titration or other techniques before
each use as an ozone source. Nitric oxide and many
hydrocarbons, on the other hand, can be obtained
in prepurified gas cylinders and can thus serve as
precision gas standards for those species.
Recently, O'Keefe and Ortman (1966") developed
permeation tubes as calibration standards. They found
that liquified gases, such as S02, N02, and hydrocarbons,
sealed in Teflon tubing, would permeate through the walls
of the tubing at a constant rate which is dependent
upon the surface area of the tubing and the temperature
of the surroundings. The success of this technique
depends on the fact that the equilibrium vapor pressure
of a liquid is a constant when temperature is held
constant. Under these conditions, the permeation rate
of the gas through the tube is constant, and the
absolute amount of gas released by the tube over a
period of time can be calculated from the change in
weight of the tube. Permeation tubes have been used
successfully for SO.,, H^S, many hydrocarbons, anhydrous
£» £*
NHj, anhydrous HF, COC^ (phosgene), and organic mercury
compounds (c.f. Saltzman et al.,1971). Unfortunately,
235
-------
it has been found that NO- permeation tubes are
seriously affected by relative humidity and the
past history of exposure (Saltzman et al., 1971).
Thus, permeation tubes for N02 are not suitable
as a primary standard unless they have been recent-
ly calibrated.
The frequency of recalibfation must be established
for each instrument in the laboratory. Loss of
calibration can occur as a result of aging and decom-
position of chemical reagents or because of changes in
ambient operating conditions (i.e. temperature,
relative humidity, pressure). The need for recalibration
will also depend on the sensitivity of the plumbing,
the stability of the electronic components, and the
conditions under which the instrument is used.
Recalibration should be performed sufficiently often
to assure the accuracy of the results. Any observed
drift between calibrations should, of course, be noted.
Finally, the calibration experiments should be performed
over the full concentration ranges of the species
observed during an experiment (e.g., for NC^, concentrations
vary from 0.005 ppm to 2 ppm).
2. Precision
Precision refers to the extent to which a given
set of measurements agrees with the mean of the
observations. Although, the precision of each instrument
must be determined individually, it has been found, in
general, that both wet chemical techniques and instrument-
based techniques such as chemiluminescence produce highly
reproducible results (Maugh, 1972). It is, of course, im-
portant that the precision of the measurements be reported
with the results. Care should be taken to establish the
236.
-------
precision as a function of concentration. Photo-
chemical simulation studies have shown that the
predicted time to the NC^ peak can be shifted by
15 minutes or more because of uncertainties of
+_.02 ppm in an initial NC^ concentration of .04 ppm
(Hecht, 1972). Thus it is particularly important to
know precision bounds at low NC^ concentrations if
the predictions of kinetic mechanisms are to be
correctly evaluated.
3. Sampling Procedures
The reliability of a measurement depends to a
large degree on the technique used to sample the
bulk gas. Presumably, a representative sample can
be drawn from any location within a well mixed reactor.
The sampling tube material should be selected to
minimize the heterogeneous loss of pollutants during
sampling. Further, the residence time in the
sampling line should be as short as possible to
minimize the possibility of chemical reaction along
the path. The overall accuracy of a measurement
will depend upon careful calibration of the air flow
rate into the monitoring equipment, for the signal
output of the instrument must be corrected for the
total volume of gas being determined. Calibrated low
capacity rotameters can be used to measure low air
sampling rates, while very high volumetric flow rates
can be calibrated more accurately with such devices
as Venturi meters or Pitot-static tubes.
One final consideration related to sampling is
that it is desirable to minimize the total volume of air
237
-------
required for the analytical instruments so as to
minimize the loss of reactants from the smog chamber.
It is not uncommon for up to 25% of the initial
reactants to be removed from a moderate sized chamber
(10,000 liters) through sampling over a six hour ir-
radiation . Such removal can be reduced substantially
by using newer measurement techniques, such as
chemiluminescence, which requires samples no larger
than a few cubic centimeters. (Older wet methods
often require that many liters of gas be bubbled
through a concentrating solution before a reading
can be made). In any case it is important to report
the dilution rate in the experiments so t.hat corrections
for losses can be made.
4. Response Time
In smog chambers in which the concentrations of
pollutants are changing continuously, knowledge of the
response time of the measuring systems is necessary
for interpreting the data relative to real time.
Response time is the time from the moment the
pollutant enters the sampling instrument to the moment
that the measured value is obtained. The measured
value, in turn, is taken to be a specified percentage
of the final or true value, such a^ 901. Thus, if it
requires two minutes to achieve 90% of full response,
two minutes is the response time. For systems in which
the sample lag time is great Mage (1972) and Schnelle
and Neely(1972) have shown that the transient and
frequency response of the instruments can be accounted
for by use of a transfer function.
238
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Measurements carried out using instrumentation
employed in chamber work are generally made either on
~a continuous, discrete, or averaged time basis. The
first and most desirable type of measurement is
continuous and is carried out using instruments
with very fast response times, such as infrared
spectrometers. A second class of measurements,
discrete, includes those analyses in which a sample
is injected into the instrument. Gas chromatographic
analysis is an example of a discrete procedure.
The sensitivity of discrete measuring instruments to
short-term fluctuations and sharp peak concentrations
will depend upon the rapidity with which determinations
can be made. In the limit, as the time between
measurements goes to zero, discrete measurements,
of course, become the same as continuous measurements.
Monitoring devices which require a pollutant to be
collected over a finite period of time in order to obtain
measureable concentrations yield integrated or averaged
results. Most wet techniques operate on this principle.
Such methods, of course, suffer from the obvious
disadvantage that they are insensitive to short-term
variations in concentration. Thus, wet chemical
techniques, which require a ten minute or longer
sampling time, will represent a sharp NO^ peak as a
lower and broadened peak because of their slow response
times (and, thus, low time resolution).
239
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5. Analytical Techniques Available for Measuring
The Pollutants
Because of the wide variety of analytical
instruments presently available for monitoring the
constituents of smog, there is often uncertainty
concerning which procedures are "best". Although
recommended procedures are published regularly by the
U.S. government in The Federal Register, review
articles on current trends in instrumentation suggest
that techniques now in use will soon be replaced by
more rapid, more reliable,. more efficient and
certainly more expensive techniques (Maugh, 1972).
A logical goal in upgrading analytical devices would
be to develop a single instrument capable of measuring
many or all of the pollutants simultaneously. Micro-
wave spectrometers, which measure the rotational energy
of polar molecules at discrete frequencies, appear
promising in this regard, but commercial availability
is at least two years away (Maugh, 1972). Because
of the uncertainties concerning analytical procedures,
it is worthwhile to examine briefly the techniques
most often used to measure the standard pollutants
(N02, NO, 03, HC's, aldehydes) and to discuss the
advantages and disadvantages of techniques now becoming
available.
a. NO 2
Nitrogen dioxide has generally been deter-
mined by the Saltzman method (Saltzman, 1954).
240
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In this technique the sample is bubbled through
an absorbing reagent at a rate of about 0.4 liter/
minute for 10 minutes in order to concentrate
the N02. Reaction of NO- with the absorbing solution
results in a color change which can be related to
the N02 concentration. The technique is quite
reproducible but suffers interferences from
ozone and PAN (Leithe, 1970). The primary sources
of error in this method are chemical interferences,
inefficiency of collection, and the aging of
reagents.
No substantial improvement over the Saltzman
method has, as yet, been made for determining
N02. Hodgeson et al. (1972) have suggested
reducing the N02 to NO using "carbonized sugar"
or glass wool as a catalyst and measuring the
resulting NO by chemiluminescence (see paragraph
Sb). The problem with this approach is that the
catalyst will reduce all the higher oxides of
nitrogen (i.e. nitrates, PAN, nitrite, N02) to
NO, so the technique lacks specificity. One
promising approach for measuring N02 which is
currently being developed involves exciting N02
to a higher energy state with a tunable dye laser.
The N02 concentration can then be determined by
measuring the fluorescence of the excited molecules
(Nader, 1972).
b. NO
Until recently, there was no available
technique for determining nitric oxide concentrations
241
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directly. The pollutant gas was passed
over an oxidizing agent such as dichromate
which oxidizes NO to N02. Total oxides
of nitrogen were then determined as N02 by
the Saltzman method, and NO was calculated
by subtracting the N02 re.ading made at the
same time from total NO . In addition to
^v
all the difficulties involved with the Saltzman
method, the technique depends on the efficiency
of oxidation of NO. Efficiencies of only 70 -
85% were not uncommon, and thus measurements
of NO made by this method were unreliable
(Tokiwa and Mueller, 1971).
Recently Stedman et al. (1972) and
Hodgeson et al. (1972) have shown that NO can
be determined very accurately by chemiluminescence
In this technique the pollutant sample is exposed
to a large excess of ozone. The ozone reacts
rapidly with the NO to form N02 in an excited
state.
NO + 03 -*• NO* + 02
Collapse of the excited N02 to the ground state
is accompanied by the emission of light, which
is then measured and related to the initial NO.
NOS
* -^ NCfc + light
242
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This technique is sensitive to 10 ppm of NO,
has an overall response time of ten seconds,
and requires a flow rate from the chamber of
only 20 cc/minute. Interferences can be caused
by collisional deactivation of the excited
NO- (this problem is reduced by operating the
system at low pressures) and by the reaction
of other species present with 03, the product
of which will also chemiluminesce. Stedman et al.
investigated the possibility of interferences
from S02, N02, C12, H20, CH4, C2H2, C2H4, and
CjHg at a concentration of 100 ppm in air, but
found that these species did not emit a detect-
able amount of light in the region of the NO 5
luminescence. An interesting feature of this
instrument is that it can be used as an ozone
detector as well by subjecting an air sample to
an excess of NO. In view of its accuracy, re-
sponse time, sensitivity, stability, and versa- .
tility,this instrument shows great promise for
the future.
c. 03
Traditionally, ozone determination has been
based on reaction of the species with potassium
iodide (KI)
2 KI + 03 + H20 -»• I2 + 02 + 2 KOH
243
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and measurement of the amount of iodine which
is liberated by the reaction. Under well con-
trolled laboratory conditions, this method can
be quite accurate, and the technique remains as
one important method for calibrating ozone
sources. However, automatic monitors for ozone
based on the KI reaction suffer from numerous
difficulties. Several species, including N02,
peroxides, and PAN, give a positive response
for Oj in varying degrees, while the presence
of S02 and reducing dusts result in a serious
negative interference (Katz, 1968). Although
some of the interfering species such as S07
Li
can be removed by chemical.scrubbing before
the pollutant gases reach the ozone monitor and
others can be corrected for mathematically
(e.g., NO^), the KI method must be regarded, at
best, as a method for determining the total
oxidant concentration in a smog chamber. An
additional difficulty with the method is that
the oxidant must be collected in a concentrating
solution by bubbling gas from the chamber at the
rate of 1-2 liters per minute for 15 minutes;
full development of the color requires an addi-
tional 30-60 minutes. Thus, in summary, the KI
method provides a non-specific, averaged oxidant
concentration with poor response time.
Two techniques have recently been developed
as commercial products for determining ozone. The
first method is based on the chemiluminescence of
244
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the ozone-ethylene reaction (Warren and Babcock,
1970). An air sample containing ozone is exposed
to a large excess of ethylene in a reaction ves-
sel. The light released during the reaction is
then measured using a photomultiplier tube and
related to the ozone concentration.
Ozone can be determined by its chemilumin-
escent reaction with many species besides ethylene.
We have already mentioned that the reaction of 0-
with NO has been used successfully by Stedman et
al. (1971). Recently, Kummer et al. (1971) have
pointed out that ozone will undergo chemilumines-
cent reactions with many olefins and sulfides in-
cluding tetramethylethylene and dimethylsulfide, and
that these reactions result in a much greater intensity
of emitted light than the ozone-ethylene reaction.
Chemiluminescent methods for ozone appear to
be free of interferences from other species present
in smog, and they are sensitive and fast. However,
they suffer the disadvantage of having to be oper-
ated at very low pressures in the reaction vessel
(0.5-5 Torr). Tanks of gaseous reagents must also
be used in operating the equipment.
The second technique marketed recently
measures the ultraviolet absorption of ozone in a
sample of polluted air (Bowman and Herak, 1972).
The air is divided into two portions in the instru-
ment. One portion passes over a catalyst which
245
-------
converts the ozone to oxygen and becomes the
reference gas, while the other portion is un-
treated. Ozone concentration is then calcu-
lated from the difference in UV absorption of the
two samples. The referencing technique has the
advantage of minimizing interference from mois-
ture and other pollutants, since they are pre-
sent in equal amounts in each sample, and the
differencing method ideally produces a net
signal of zero. Because the source of the UV
light is a mercury vapor lamp, mercury contami-
nation in the air can provide a serious inter-
ference. The mercury can be eliminated, however,
with a gold surface absorber placed at the sam-
ple inlet. Another potential source of inter-
ference is the presence of any molecules which
absorb ultraviolet radiation, such as S02 and
aromatics. However, tests conducted at concen-
tration levels of 0.2 ppm of SC^ and 1.00 ppm
of benzene showed no detectable response. The
instrument is sensitive to 0.001 ppm, has an
accuracy of ±3%, precision of ±1%, and has a
response time of 30 seconds (90%)• One negative
feature of the instrument, when it is to be used
for chamber studies, is that it requires a flow
rate of 3 liters/minute; thus, it is not suitable
for continuous monitoring in small chambers.
246
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d. Hydrocarbons
Measurement of the concentrations of indivi-
dual hydrocarbons cannot be made until the hydro-
carbons are separated from the other pollutant
gases and from each other. This is in contrast
to the requirements placed on analytical proce-
dures employed in the measurement of N02, NO, and
0-, which involve the use of an unrefined sample
of bulk gas. Gas chromatography has been applied
very successfully for separating hydrocarbons.
With appropriate choice of columns (see Altshuller,
1968) and a flame ionization detector, paraffins
having carbon content of up to at least Cfi, olefins
up to at least C6, aromatics in the Cg-C,, range,
and acetylenes can be resolved and measured accu-
rately. The principal drawbacks of GC analyses
are the time required to separate a sample and the
complexity and maintenance requirements of the
measurement. Although discrete samples are analy-
zed, the cycling time is much too large to approxi-
mate continuous monitoring. Unfortunately, no
significantly better techniques for measuring in-
dividual hydrocarbons than gas chromatography have
yet been suggested.*
Total hydrocarbon analyses of samples from the bulk gas
can be made directly using a flame ionization detector;
total non-methane hydrocarbons can also be determined by
difference if the methane.is separated from the gas with
an activated charcoal column and determined individually.
Because of the complexity of the hydrocarbon mixture and
the fact that all carbon-containing molecules give a re-
sponse, these measurements contribute little to elucidat-
ing the state of the system.
247
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e. Aldehydes
No satisfactory method exists at this time
for measuring individual aldehydes. Total
aldehydes have been determined in chambers
using both infrared spectrometry and
wet chemical techniques. Wet chemical techniques
based on the use of chromotropic acid or other
reagents have been employed to measure formalde-
hyde, but these methods suffer from several types
of interferences (e.g., olefins and aromatics)
(Altshuller, 1968). Some progress has been made
by Seizinger and Dimitriades (1972) in separating
and identifying aldehydes by gas chromatography,
but the technique is still cumbersome and time
consuming. Again, we are not aware of any cur-
rent improvements being made for the rapid mea-
surement of individual aldehydes.
6. Summary
The shortcomings of analytical techniques based
on wet chemical methods are very serious, notably a
general lack of specificity and poor response time.
Newer techniques, based upon chemiluminescence and
determination of the spectral properties of various
molecules, have already been shown to provide rapid,
accurate, and continuous measurements of NO and 0, at
low concentrations. In the future these techniques
should be used for monitoring smog chamber experiments.
There is still a need, however, to develop rapid and
accurate analyzers for NO-, hydrocarbons, and aldehydes
248
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Even with the appearance of the newer instruments,
the quality of the data will depend upon the extent to
which the instrumentation is properly calibrated and
maintained. The experimenter must recalibrate each in-
strument sufficiently often to guarantee the accuracy
of the observed data; the degree of maintenance required
will depend on the stability of the components of each
instrument and the conditions of use.
Permeation tubes and standard precision gases can
be used as primary standards for many gases, but a pri-
mary standard for ozone is still not available.
C. Recommended Smog Chamber Studies
Our discussion thus far has been limited to an exam-
ination of the operational aspects of a smog chamber. Once
a system is operating reliably and reproducibly, it is pos-
sible to perform a large number of simple experiments use-
ful in model verification and mechanism elucidation. In
this section we discuss some chemical systems, including
both artificial smog mixtures and polluted urban air samples,
that might be examined profitably, as well as ways in which
•$
smog chambers can be used to assess various atmospheric
scavenging processes.
1. Simple Hydrocarbon-NO Systems
•^^
Although hundreds of individual hydrocarbons are
present in polluted atmospheres, the majority of the
reactive hydrocarbons can be classified as paraffins,
olefins, and aromatics. Because each member of a
class (e.g., paraffins) tends to react with a given
249
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oxidant in a manner and at a rate similar to that of
other members of the class, it is possible to approxi-
mate crudely the atmospheric hydrocarbon mixture using
a simple mixture of a single paraffin, olefin, and
aromatic. By further implementing the principles of
design in the choice of the initial reactant concen-
trations for a program of experiments and by measuring
the concentration of some of the secondary products
with time, it is possible to obtain data that should
prove to be very valuable for validating chemical
mechanisms.
a. Hydrocarbons to be Studied
As a prelude to atmospheric validation, it
is desirable to demonstrate the validity of a
chemical mechanism using smog- chamber data based
on the reactions of relatively simple hydrocarbon
mixtures. Such mixtures, if properly formulated,
will simulate actual atmospheric mixtures in
terms of the range in reactivity of the individual
components and the composition by hydrocarbon
grouping. For example, an appropriately chosen
mixture of n-butane, pvopylene, and toluene,
which are assumed to typify paraffins, olefins,
and aromatics, respectively, may well be a suita-
ble surrogate. Note that each individual species
1. Constitutes a significant percentage of
its class of compounds in polluted
atmospheres.
250
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2. Reacts with 0, OH, and 03 at rates typi-
cal of its respective class.
3. Has been thoroughly studied, both with
respect to its elementary reactions with
oxidants* of interest and in the more
complex reaction environment of the smog
chamber.
Any chemical mechanism valid for atmospheric
reaction systems must certainly be capable of
describing the dynamics of systems composed of
species mentioned, individually and in combination.
Thus, we recommend a three-stage experimental pro-
gram. In the first phase each individual hydrocar-
bon would be studied in a smog chamber over a wide
range of HC/NO ratios; in the next stage the hydro-
A
carbons would be investigated in pairs; finally,
the full three hydrocarbon system would be examined.
b. Statistical Considerations in Formulating the
Initial Conditions
Selection of the initial conditions should be
based upon levels of hydrocarbons and NO presently
A
observed in the atmosphere and those expected as a
consequence of current and future emission abate-
ment programs. Statistical planning of experiments
An exception is the OH-toluene reaction, for which neither
the rate constant nor the mechanism of reaction have yet
been determined.
2S1
-------
should prove of value in selecting sets of ini-
tial conditions that provide the most useful
data base, in terms of both information content
and ease of analysis. Randomization, factorial
and fractional factorial designs, replication of
runs, and augmentation of designs should all be
considered at the planning stage. See Hunter
(1960) and Davies (I960) for further information
regarding the statistical design of experiments.
c. Additional Species Identification and
Measurement in the Smog Chamber Useful for
Model Validation
As model validation is essentially the pro-
cess of comparing concentration-time profiles for
primary and secondary products predicted by the
chemical mechanism with those observed experimen-
tally, the "quality" of a validation effort in-
creases with the number of species monitored.
Usually, concentration-time profiles are reported
only for hydrocarbon, NO, NO-, and 0.,. Other spe-
cies have generally not been followed because spe-
cific and accurate analytical methods have not
been available for them. While we are aware of
the experimental difficulties that such measurements
involve, we still believe it is of importance to
enumerate species that must eventually be measured
if real progress is to be made in model validation.
We recommend that the following species be monitored
in future chamber studies:
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Aldehydee: Aldehydes are formed as direct
products of some hydrocarbon oxidation re-
actions and also as products of alkoxy ra-
dical decomposition. They begin to appear
as soon as the hydrocarbon is oxidized and
can accumulate to significant (ppm) levels
during smog chamber experiments. Because
aldehydes are one of the most important
classes of secondary products in smog, the
confirmation of kinetics mechanisms* pre-
dictions for this species provides an ex-
cellent additional check on the accuracy of
the mechanisms. For generalized models,
the measurement of total aldehydes would be
sufficient; for more detailed mechanisms it
would be desirable to have separate measure-
ments of at least formaldehyde and acetaldehyde,
Hydrogen Peroxide: Hydrogen peroxide has been
observed in smog chamber studies and in the
atmosphere by Bufalini et el. (1972). It is
formed by the recombination of hydroperoxyl
H02 + H02 -»• H202 + 02
radicals, and knowledge of its concentration,
along with the rate constant for the recombi-
nation reaction (about 5300 ppm" min
(Johnston et al., 1970)> provides one gauge
for estimating the concentration of H02
253
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radicals. ^2^2 can» °^ course, photo-
dissociate to form OH radicals, but this
reaction is slow, being less than 0.5% of
the rate of photolysis of NO- (Leighton,
1961).
P emit rate e : Nitrogen containing species
such as PAN represent an important class
of secondary products. Measurements of PAN
are presently carried out on occasion. We
recommend that pernitrates be measured rou-
tinely in future chamber experiments.
Nitric Acid: Nitric acid currently .appears to
be the principal sink for nitrogen in the
smog system. Little of the HNO, seems to be
present in the gas phase; it forms mainly on
the walls and on particles. Thus, continuous
measurement of HNO, is very difficult. These
difficulties not withstanding, accurate, con-
tinuous analysis of HNO, would be most
valuable.
Nitrous Acid: As indicated in Chapter IV,
nitrous acid may be present in significant
quantities in the atmosphere at sunrise,
and also in smog chambers prior to irradia-
tion. Thus, the photolysis of HNO- may
strongly affect the early oxidation rate of
hydrocarbons and NO. We recommend that HN02
be monitored in order to establish the
254
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possible importance of this effect as well
as to confirm the levels of HN02 predicted
by kinetic mechanisms.
2. Controlled Irradiation of Polluted Air Samples
from Urban Areas
Because of the number, diversity and complexity
of species present in urban atmospheres, the irradi-
ation of simple mixtures may not always be sufficient-
ly representative of pollutant chemistry. It is thus
of interest to examine the chemistry of more complex
contaminant mixtures. One means for doing this is to
charge or "dope" a sample of urban air with a known
amount of pollutant and irradiate the mixture in a
controlled system. During the 1975 RAPS program in
St. Louis some studies of this type are apparently
being planned. We recommend that at least four spe-
cific doping studies be carried out. For each study an
"undoped" or control sample must also be irradiated
f
simultaneously. The experiments recommended are:
1. Raise the CO level in one bag to 25 ppm and
irradiate for 8 hours or until sundown, if
outdoors. The goal is to assess the effect of
low levels of CO on the rate of oxidation
of NO and 0- formation in the atmosphere.
2. Add .25 ppm of toluene to one bag. Increased
usage of unleaded gasolines in the future will
result in greater emissions of aromatics.
This experiment is designed to examine that
effect.
255
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Add .25 ppm of SC^ to one bag. Measurement
of the effect of S02 on 0, levels and on the
time to the NO^ peak, as compared with the
magnitude of these quantities measured for
an undoped sample, is the primary objective.
4. Dilute one bag 251 with clean air. This
experiment is designed to study the effect
on smog levels of a uniform reduction in all
pollutants.
These are a few examples of the kinds of doping
experiments that can be performed. Others may also be
of interest, such as adding water vapor to one bag, ir-
radiating bags of varying surface roughness, and add-
ing various types of particulates to the bags. The in-
tent of each experiment is to reveal the effect of vary-
ing a single parameter on the observed concentration
dynamics.
3. Controlled Assessment of Natural Scavenging
Processes
Surface sinks are one of two broad categories of
"ultimate pollutant receptors", aerosols being the other.
A number of recent studies indicate that both soils and
vegetation take up several of the major pollutants at
significant rates. Levy (1970) and Inman et al. (1971)
have observed in laboratory studies that nonsterile
soils take up carbon monoxide at very rapid rates. Fungi
appear to be the organisms involved in the biochemical
256
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reactions. Abeles et al. (1971) have reported that
hydrocarbons, sulfur dioxide, and nitrogen dioxide
react with soil through microbial or chemical means.
Vegetation has also been observed to react with at-
mospheric pollutants. Katz and Ledingham (1939)
measured absorption rates of S02 by alfalfa, and
Tingey (1968) has estimated rate of uptake of N02
by alfalfa and oats. Hill (1971), in a rather ex-
tensive study, has rank-ordered major pollutants ac-
cording to the rate at which they absorb into alfalfa.
He observed that S02, NO-, and ozone were absorbed
most rapidly, NO quite slowly and CO not at all.
Finally, the more reactive pollutants undergo trans-
formation in contact with materials. Sabersby et al.
(1973), for example, have measured relatively rapid
ozone decomposition rates on surfaces such as rubber,
fabrics, and plastic. The importance of determining
rates of losses of pollutants to atmospheric sinks is
twofold:
1. It is essential to establishing quantitative
methods for estimating losses as a function
of a number of variables that influence loss
rates.
2. It is essential to completion of material
balances over a control volume in the atmos-
phere.
In general, loss rate for a particular pollutant is re-
lated to specific rate of absorption by soil, vegetation,
257
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or material, the surface properties of the absorbing
substance, concentration of the pollutant in the gas
phase, humidity, surface area, surface roughness, and
turbulent eddy diffusivity. Also, radiation intensity
can influence the rate of absorption by vegetation.
To our knowledge, there has been only one attempt to
correlate loss rates with these variables through
atmospheric observation. Hill (1971) has observed
that light intensity, windspeed, height of the vege-
tative canopy (surface^roughness), and pollutant con-
centration all affect pollutant uptake rates. He has
estimated the degree to which changes in a variable
influence uptake for particular species--increase in
windspeed from one to two mph increases 0- uptake by
50%, increase in height of canopy increases uptake
rates about linearly, and increase in 862 concentra-
tion results in a proportionate increase in uptake
rates.
The effects of certain influencing variables are
best determined in the chamber. For example, specific
absorption rates as a function of concentration, tem-
perature, relative humidity, light intensity, and wind
speed have been studied under controlled conditions
(see Hill, 1971) . Effects of surface properties can
also be examined in this way. Eventually, effects of
levels of turbulence and degree of surface roughness
must be simulated in the laboratory. Studies of this
nature, however, are likely to be rather involved and
complex.
258
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To summarize, in order to .better understand the
nature of surface scavenging processes, we recommend
that the effects of variables having a significant
influence (as delineated in preceding paragraphs) on
the specific absorption rates of the major individual
constituents of smog by soil, vegetation, and materials
(e.g., cement, asphalt, paint, etc.) be quantitatively
determined.
D. Summary
Before smog chamber data can be used to validate photo-
chemical simulation models, the reproducibility and reliabil-
ity of the data must be established. Thus, successful vali-
dation will depend upon the quantitative assessment of all
the heterogeneous effects in the chamber, careful measure-
ment of the light intensity over the course of the irradia-
tion, and knowledge of any shortcomings in the analytical
measurements.
Reproducibility is a measure of the overall precision
in smog chamber experiments. Given identical initial condi-
tions (e.g., concentrations, temperatures, humidity, stirring
rates, etc.) the concentration-time profiles of the individ-
ual pollutant species should be coincident for runs perform-
ed on different days or weeks. Lack of reproducibility may
be due to one or more of several possible causes, as discus-
sed earlier in this chapter. First, the activity of the walls
may change with time, illustrating the necessity of insuring
that the walls are at a known, standard, initial condition
before each run. Second, the light sources in the chamber
259
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may deteriorate with time. The possibility of this occur-
ring can be examined by measuring k,. Third, the analyti-
cal instruments may be out of calibration.
As a good test of repeatability, we suggest carrying
out, as often as is necessary, to guarantee the accuracy
and stability of the experimental technique and the repro-
ducibility of the results, a control experiment with ini-
tial conditions .such as the following: 3 ppm toluene,
1.25 ppm NO, 0.05 ppm N02. Kopczynski (1972) has shown
that about half of the hydrocarbon will be lost, the NC^
peak will be reached in about two hours, and about 0.5 ppm
of ozone will form. Tests such as these are admittedly
time consuming, for they require an entire day, but they are
absolutely necessary if the chamber data are to be used for
mechanism validation purposes.
It is also necessary for the investigator to character-
ize his chamber quantitatively. Some considerations include
knowledge of the rate of loss of the individual pollutants
to the walls under standard operating conditions, the effect
of relative humidity and mixing on the observed photochem-
istry, the shortcomings, inaccuracies, and imprecisions of
the analytical instruments, and the rate of dilution of the
reactants due to sampling. The necessary procedures must,
of course, be carefully defined and meticulously planned.
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APPENDIX A. THE DETERMINATION OF k1 IN AIR
In part A of this chapter we described a method for
determining k, in an inert atmosphere. However, there is
a great need for a general method of computing k, from the
N©2 concentration vs. time data collected during the photo-
lysis of a given mixture of N02, N2 and 0- (such as N02 in
air). This need arises for two reasons. First, it is
often difficult to purge all the 02 from a system of N02
and N2, and thus it is of interest to know at what level
of 02 impurity deviations from the behavior of a pure
N02-N2 system begin to appear. Second, with the advent of
large outdoor irradiation chambers, it will be impractical
to determine k, in an N02~N2 system; rather, one must be
able to estimate kj from an N02-air system. We present in
the appendix a general method for directly and accurately
determining k, from the N02 concentration-time data gathered
during the photolysis of a mixture of N02, NO, N2 and 02
of any initial concentration.*
The method is the following. One irradiates N02 or
N02 and NO in N2 and 02 (e.g. dry air), noting the initial
concentrations and thereafter recording the N02 concentration
in the system at several times over the course of the
irradiation, for example, every minute or so for a period
of ten minutes. The experimental data obtained can be denoted
by N0|xp(ti), i = 1,2,...,R, where R is the number of data
points. Since the reaction mechanism of a system consisting
of N02, NO, 02 and is known, and all the rate constants except
* It is important to point out that the validity of this
approach is subject to experimental confirmation under a
range of conditions. Such verification is necessary to
guarantee that the mechanism in Table 8 completely
describes the chemistry of NOX in the presence of 02«
261
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k, are known (see Table 8), one can numerically integrate
the differential rate equations governing the system, given
any assumed value of k., . Let us denote the result of this
calc
integration by N02 (t) . The objective, then, is to determine
that value of k, which produces the closest match between
calc
the calculated N09 concentrations, NO., (t.), and the
pvn
experimental concentrations, N02 p(t.)«
A useful way to quantify the stated problem is as follows:
Find that value of k, which minimizes the unweighted least
squares objective function
(35)
(If we suspected that some data points were subject to more
experimental error than others, we might weight the residuals
so as to reflect these differences.) We thus wish simply to
estimate a set of constant parameters (in this case, only
one) in a system of ordinary differential equations, given
a set of experimental data, a problem that has received an
enormous amount of attention in the literature, particularly
with regard to chemical kinetics (for example, see Bard and
Lapidus , 1968) . A particularly efficient technique for
carrying out the minimization of S is called quasilinearization,
a procedure which essentially involves an extension of the
Newton-Raphson method to systems governed by ordinary
differential equations. For details of the method we refer
the reader to Lee (1968) and Seinfeld (1970).
262
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In order to estimate k, using this technique we need
first to formulate the differential equations for the spe-
cies in the mechanism in Table 8. A differential equation
is not needed for oxygen atoms, as the concentration of
this species is at steady state. Let [N02] = z^t [NO] =
z2, [03> z3, [N03] - *4, [02] = z5, [N205] = z6 and the
desired parameter k = Z. Using the steady state relation,
[03= Zlz7/(k2z5 [M] + k4zx + ksZl [M3+ k?z2 [M]) (36)
in the rate equations for z, to z,, we can write the rate
equations in the form
dz.
In addition, since k, is constant,
dz7
The g. are obtained directly from Table 8. The differential
equations (37) can be integrated easily on a digital computer.
263
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We now summarize the digital computer algorithm for
estimating k, (the derivation of the algorithm may be found
in Lee (1968)):
1. Make an initial guess for k^(z-) and integrate
Equations 37 from t = 0 to t = tR. Denote this
solution by z^0)(t) = [z^0)(t),... ,z^(t)] .
2. Solve the six homogeneous equations
d- v-* / 3S- \
^F= Zllfz^) V *i C0) = °
3 = 1 N '>)
i = 1,2,...,6 (39)
from t = 0 to t = tR with *7 = k, the initial
guess.
3. Solve the six inhomogeneous equations
(40)
j-1 X°^'/
PjCO) = zA(0) i = 1,2, ...6
from t = 0 to t = tR. Note that p?(t) = 0.
264
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4. Compute an improved estimate of k.. from
R
-)
-------
Although we have not obtained experimental data with
which to test the algorithm, we have been able to assess
theoretically the effect of 02 on the decay rate of N02
in sunlight. Figure 4 shows the effect of the level of 02
on the N02 behavior during irradiation, based on the mech-
anism shown in Table 8. We note that, as the amount of
oxygen present increases, the initial rapidity of disap-
pearance of N02 increases, but the total amount of N02
lost over a fixed time of irradiation decreases. Thus,
two potential measurement problems exist in such an experi-
ment. First, small changes in N09 concentration must be
L*
detected. For example, upon irradiation of 1 ppm of N02
in air, only 101 of the initial charge is lost over a five-
minute interval. Second, since the greatest change in N09
L*
concentration occurs in the first minute, measurements
must be carried out rapidly. Instrument response time is
important in this regard. Both problems might be circum-
vented by measuring the accumulation of NO instead of the
depletion of NO-, since NO can be measured more accurately
and quickly than N09 (e.g., by chemiluminescence). The al-
£
gorithm presented requires only minor modification if NO,
rather than N02, is to be.measured.
We have tested the algorithm for estimating kj for the
NO--N9-00 system by generating N09 vs. time data for [N07] -
L L L - 1 £ O
1 and 10 ppm and k, = 0.4 min through numerical integra-
tion of the mechanism in Table 8. Five data points, collected
over a period of 1.5 minutes, were selected as "experimental
data" with which to estimate k, using the algorithm. The
results of the computer experiments are summarized in Table
9. The algorithm rapidly converged to the "true" value of
266
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o.o
Figure 4. Predicted Decay of NO, Photolyzed in N2 with Varying
Added Amounts of 0,.
02 B 210,000 ppm
°2~= 1000 ppm
1.0
2.0 3.0
TIME (MINUTES)
-------
k^, and, as can be seen in Figure 5, the final predicted
decay of NO^ in air (solid line) agrees very well with the
data used for the estimation (triangles).
It is important to emphasize again that, although we
have demonstrated the applicability of the algorithm for
estimating ^ using the mechanism shown in Table 8, the
validity of this mechanism has yet to be established
experimentally.
Table 9. Estimation of k, from N02 Photolysis in Air
N02 Q(ppm) kj^Onin"1) Iterations kj£inal) (min"1)
1.0 0.2 13 .400
1.0 0.35 10 .400
10.0 0.35 12 .399
268
-------
o
o
Figure 5. Predicted Decay of NO, (Solid Line) Using Value of k.
Estimated by Algorithm from Data Points (Triangles)
C(N02)(
1 ppm; (02)0 = 210,000 ppm]
en
•
o
0.2 min\ initial guess
0.4 min", estimated value
0.4 min" true value
CL.
Q-
O
i—i
CE en
UJ
LJ
Z
O
CM
O
Z LO
CO
•
o
<0
O
CO
0.0
0.3
0.6
TIME
0.9
(MINUTES)
1.2
1.5
-------
VI. FIELD MEASUREMENT PROGRAMS
The planning, organization, and execution of a useful
and successful field measurement program is a particularly
difficult undertaking, regardless of the modestness of its
scope. Many of the difficulties are attributable to the
fact that there are a multiplicity of physical and chemical
processes occurring simultaneously in the atmosphere. Many
of the processes are complex in nature, and most are variable
in space and time. Since we cannot exercise control over
these processes as we do in varying degree in the laboratory,
we can only passively observe, hoping to filter some signal
associated with the phenomenon of interest out of the substan-
tial level of noise* that is likely to be present. If obser-
vational programs are not undertaken with great care - that
is, with clearly defined objectives, carefully conceived
measurements, and highly specific methods of data analysis -
the information sought may well be inaccessible due to the
dominance of other signals. Most of the remaining difficulties
in atmospheric observation are associated with instrument
limitations - lack of accuracy or specificity, incapability
of making a particular measurement**, or incapability of
measuring with requisite resolution or frequency.
**
Not really "noise" but rather the complex aggregate of
all other signals that are not of interest during the
particular observation.
For example, identifying the presence of an atmospheric
contaminant at very low concentrations or measuring the
composition of an aerosol sampled from a restricted
spatial volume over a short time period.
270
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If measurement in the atmosphere and observation of at-
mospheric phenomena are such difficult and potentially un-
rewarding undertakings, why should attempts at carrying out
such programs be considered at this time? There seem to be
two major reasons:
1. Certain atmospheric phenomena cannot, for one reason
or another, be simulated in the laboratory. For
example, we cannot yet simulate the range of atmos-
pheric turbulence in a controlled manner, so as to
establish the possible effects of transport limit-
ing processes on observed rates of chemical reaction.
2. The existence or occurrence of certain phenomena
must be identified, and this identification must
be made in the atmosphere. For example, we may
wish to detect HNO^ in the atmosphere before we
undertake laboratory studies to simulate its behav-
jor and to assess its importance in the produc-
tion of smog.
If, in the second case, we can learn enough about a phenomenon
to adequately characterize it, it may then be possible to simu-
late the phenomenon in a controlled environment, thereby per-
mitting more desirable conditions of observation. However,
some phenomena, even if properly characterized, may be so
difficult to simulate that our inability to create controlled
conditions for their observation and analysis may prove to be
the critical obstacle to achieving a full understanding of
atmospheric processes. The coupling of turbulent transport
and chemical reactions may well be such a phenomenon.
271
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In this planning document, we are to focus primarily on
those phenomena that are predominantly "chemical" in nature.
However, in considering atmospheric observations one is
always faced with the fact that fluid dynamical processes--
advection and turbulent diffusion--are always in evidence
and are often dominating in their influence on observables.
It is thus quite impossible to study chemical dynamics,
per se, in the atmosphere. We are, in fact, really quite
limited in what we can accomplish in carrying out "chemical
observations". The nature of observational programs to be
proposed reflects these rather severe limitations inherent
to atmospheric studies.
A number of efforts have been mounted over the last
few years to assess the status of our knowledge of atmos-
pheric chemistry and to make recommendations as to the
directions that future efforts might take. In 1969, the
American Chemical Society (reference cited) prepared a
report that had a two-fold purpose--assessment "of the
current status of the science and technology of environmen-
tal improvement" and presentation of recommendations "of
measures that, if adopted, should help to accelerate the
sound development and improvement of that science and tech-
nology". While the focus of the study was on chemistry and
chemical engineering, the scope was broad--air, water,
solid wastes, and pesticides. As a result, recommendations
tended to be encompassing rather than specific. Shortly
thereafter, in 1970, MIT sponsored a series of far-reaching
environmental panel studies, one of which, "Man's Impact
on the Global Environment: Assessment and Recommendations
for Action", touched on problems in atmospheric pollution.
272
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But, as the title implies, the study's focus was global
rather than regional, its concern more with climate and
longer term phenomena than mesoscale processes and short-
time periodicities.
Two more recent publications, the results of studies
undertaken by the TR-1 Research Committee of APCA (1971)
and the Chemist-Meteorologist Workshop (1972), deal more
specifically with regional air pollution problems and
related areas of research and study. The TR-1 Committee
conducted a survey of APCA members to determine principal
areas of research need. Their report provides a very com-
plete compilation of problems in seven principal areas--
sources, sampling and analysis, control technology, atmos-
pheric phenomena, effects, control agencies and related
topics, and system definition and optimization. The
Chemist-Meteorologist Workshop was composed of four panels,
one of which was concerned with "Regional Studies of
Atmospheric Pollution from Near-Surface Sources". The
panel dealt directly with problem areas of concern—transport
and dispersion, atmospheric transformations, removal pro-
cesses, effects of air pollutants, sources, and aerometric
measurements. They presented descriptions of past, current,
and planned field studies (including RAPS), and they set
forth a series of general and specific recommendations. In
both of these studies, most important problem areas were
identified and research needs pinpointed. However, in
neither study was there an attempt made to delineate an
experimental and observational program geared to carrying
out recommendations made.
273
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the most ambitious effort that has been made to date
in planning a field study for enhancing knowledge in air
pollution is that mounted by the Stanford Research Insti-
tute (1972). In Part II of their four-part report dealing
with the proposed Regional Air Pollution Study (RAPS) to
be carried out by EPA in St. Louis over the period 1973
to 1978, they present a very detailed research plan. Three
research areas comprise the plan—meteorological processes,
atmospheric chemistry and transformation processes, and
emissions estimates. The report, in dealing with chemical
phenomena, focuses on the SO- cycle, the photochemical
cycle, the particulate cycle, rainfall measurements and
collection, and the CO cycle. Sources, important reactions,
and removal processes for each pollutant, or class of pol-
lutants, are reviewed. Each review and discussion is follow-
ed by a series of recommended measurements and observations
to be carried out for that class of pollutants. In general,
the report gives recognition to known species of importance
and specifies measurements that will be of value in the
validation of regional airshed models. Attention is given
primarily to routine measurements and monitoring, although
it is recommended that a number of "special" measurement
programs be carried out on a limited basis. The report is
quite thorough and provides a valuable contribution to the
planning of an integrated and comprehensive interdisciplinary
field program.
We make no attempt to assess, codify, or critically re-
view the SRI recommendations here. Rather, we have sought
274
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to identify specific areas of inquiry*
1. for which atmospheric observations are necessary,
areas in which laboratory and/or chamber studies
will not suffice
2. in which knowledge gained will be of substantial
value in the development of simulation models of
transport, diffusion, and chemical reaction pro-
cesses in the atmosphere
3. concerned with phenomena primarily of "chemical"
content, as distinguished from transport, emissions,
etc. However, to the extent that transport and/or
diffusion mask the chemical processes of interest,
we have also given attention to these "interfering"
phenomena.
Specifically, we will consider four general areas of study.
These center on carrying out observations for the purpose
of elucidating:
The coupling of transport and chemical processes
in the atmosphere. Included are observations sup-
portive of validation of both Lagrangian and Ruler*-
ian simulation models of regional scale. Major
areas of inquiry include assessment of validity of
the parcel concept, quantification of the effect
of turbulent diffusion on "apparent" reaction rate
constants, and identification of atmospheric pollu-
tant sinks through observation of critical ratios
275
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(C0/N0x, C2H2/NOx) as a function of location,
elevation, and time. Data collection programs
to be carried out in the vicinity of plumes and
roadways are also considered; these data are of
use in the validation and improvement of "local"
simulation models.
The nature of heterogeneous reactions affecting
the distribution of atmospheric pollutant concen-
trations. We consider two distinct classes of
observations--those concerned with reactions involv-
ing solid or liquid materials suspended in the at-
mosphere (aerosols and particulates) and those in-
volving reactions, largely biochemical, which take
place at the "walls of the atmospheric reactor";
i.e., reactions with soils, vegetation, and the
like. With regard to suspended materials, it is
of primary interest to characterize them with re-
spect to size and number distribution, concentration,
and composition. If this can be successfully accom-
*
plished, we can then address the problem of genera-
ting aerosols in the laboratory that have physical
and chemical properties similar to those of the
atmospheric aerosol. If such aerosols can indeed
be generated in the laboratory, investigation of
this class of heterogeneous atmospheric reactions
can "move indoors" and be carried out under controlled
conditions.
276
-------
The effect of radiation on important photolysis
reactions -that occur in the atmosphere. Reactions
of primary concern include the photolytic decom-
position of N02 and HN02. Of interest is observa-
tion of variations in intensity with location (in-
cluding elevation) and time in an urban area to
gain an understanding of the influence of water,
aerosol, and particulates on attenuation of the
incoming direct and scattered spectral distribution.
The chemical composition of the atmosphere. The
focus here is the identification and measurement of
intermediates and products occurring at low concen-
trations. Included are PAN and other peroxynitrates,
nitrogen compounds (N^Or, HNO,, ^0.,, HNO-) , alde-
hydes , organic acids, and peroxides. Also of inte-
rest, but extremely difficult to measure, are the
multiplicity of free radical species present in the
atmosphere.
A fifth area of inquiry that merits attention is the
development and testing of instruments that will enable in-
vestigators to carry out measurements in situ and at concen-
trations one to two orders of magnitude less than can current-
ly be accomplished. Such instrumentation is needed if measure-
ment programs in the four areas outlined are to be carried out
successfully. However, we will not attempt here to suggest
research programs in expanding instrument capabilities and
developing new tools; delineation of such programs is beyond
the scope of this effort. Rather, we mention it to indicate
277
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that pursuits in all areas of atmospheric observation are
critically dependent on the range, accuracy, and selectiv-
ity^ of instruments, that the ambitiousness of the effort
mounted must, in the end, be determined by the quality of mea-
surements that can be carried out, and, as a result, that
instrument development merits as great a degree of atten-
tion as the field measurement effort itself.
In the sections that follow, we examine each of the
four areas of inquiry in greater detail. In discussing
them we address the following questions:
What is the specific objective envisioned?
What type OP types of measurements (or observa-
tions) are needed to meet these objectives?
What method or methods will be applied in the
analysis of the data collected?
' What is the nature of the expected result (util-
ity t accuracy, applicability3 etc)?
A. Effects of Transport and Diffusion on Species Distribu-
tion and Chemical Rate Processes
As we have emphasized, atmospheric phenomena are charac-
terized by strong coupling between physical (transport and
turbulent diffusion) and chemical rate processes. The na-
ture of this coupling has been examined rather fully in
Chapter III. Chapter V is devoted specifically to topics
involving the study of chemical rate processes in the absence
of transport limitations. In this section we address the
extremely difficult problem of carrying out investigations
of atmospheric chemical processes in the presence of trans-
port and diffusion limiting rate processes. But first we
278
-------
review that body of previous work which has served to de-
fine the role of turbulent transport processes in deter-
mining chemical rates.
The importance of the effect of turbulent fluctuations
and degree of mixing on chemical reactions has long been
recognized. In his classical treatise on the interactions
of dynamics and chemical kinetics of reacting systems,
.Frank-Kamenetskii (1947) discussed a particular case of
turbulent combustion in which, the fuel is fragmented into
small discrete parcels distributed in the airstream. The
rate of combustion was found to be controlled not by the
chemical reaction rate but by the turbulent mixing of fuel
and air. The implication is that, for sufficiently fast
reactions, the reaction rate is governed not only by the
magnitude of the rate constants but also by the rapidity
with which turbulence can bring the reacting species into
contact. In a similar context, von Karman (1953) empha-
sized the desirability of developing statistical theories
for reacting flows. More recently, Corrsin (1961, 1964)
considered the interaction of first- and second-order iso-
thermal reactions and stationary, isotropic turbulence and
found that the spectrum of turbulent concentrations is sig-
nificantly affected by the existence of chemical reactions,
O'Brien (1968a, 1971, 1972) has also considered the in-
teraction of turbulence and chemical reactions. For very
rapid reactions, he found that the random concentration
field consists of two distinct phases: a first stage in
which the reactions proceed in tiny fluid fragments before
279
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turbulent mixing begins and a second stage in which the
fluid fragments, having reacted to completion individually,
are folded together and mixed by the turbulence. The most
significant result of this analysis is that, even if at the
beginning of the first stage the mixture is fairly uniform,
at the end of that stage there may exist strong concentra-
tion inequalities as a result of the very rapid reaction in
localized fluid particles.
As mentioned in Chapter III, Donaldson and Hilst (1972)
have shown in a recently completed study that chemical re-
actions may be slowed considerably by concentration fluctu-
ations. The magnitude of this effect is determined by the
intensity of the fluctuations. In the limiting case of no
molecular diffusion, no apparent chemical reaction occurs
at the end of the first stage of the reaction even though
considerable amounts of both react ants are still present.
However, there is some doubt as to whether the results of
this simple model apply in a real situation, as the valid-
ity of the assumptions imposed come into question. The im-
portance of two factors, in particular, must be examined--
the effect of higher order correlations and the counteract-
ing effect of both turbulent and molecular diffusion.
Experimental tests have confirmed various aspects of the
theoretical results that we have discussed. For very fast
reactions in a turbulent field, the asymptotic reaction
rate is governed by the rate of .turbulent mixing, and not
by the absolute chemical rate of the homogeneous reaction.
However, it must still be demonstrated by measurements that
the amplitudes and intermittencies of the concentration
280
-------
fluctuations in the atmosphere are such that the turbulence-
chemistry interaction cannot be neglected (Vassilatos and
Toor (1965) and Keeler, et al. (1965)). Previous experiments
of this kind have been plagued by poor accuracy or slow re-
sponse of conventional instruments. However, a breakthrough
in measuring ozone and nitric oxide has been recently re-
ported (Stedman et al. (1972)). A chemiluminescent technique
with an accuracy in the ppb range and a time response of
less than 10 seconds was used to monitor the ambient air
downwind of roadways in Detroit, New York, and Boston.
Stedman etal. reported that rapid fluctuations of nitric
oxide and ozone were observed and, more significantly, that
the measured NO and 0, concentration/time profiles were
found to be 180° out of phase with each other.
Since one would expect that emissions, immediately after
their release from sources, should be uncorrelated or posi-
tively correlated, it is our opinion that the strongly nega-
tively correlated concentrations that were observed provide
substantive evidence that the interaction of chemistry and
turbulence does take place in the atmosphere. Eschenroeder et.
al.(1972) have analyzed some of these data and found that
the correlation coefficient is as high as -0.742. We have
further studied these same data and found that
= 0.0978 and °3
281
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Based on these results, the theory developed by Donaldson
and Hilst would imply that the apparent 0,-NO reaction rate
will decrease and approach zero asymptotically even when
about 20% of the original reactants remain. These estimates
are only approximate because, as we have mentioned earlier,
the effects of higher order correlations and diffusion have
not been considered in the model. In particular, diffusion
tends to smooth the concentration gradients and oppose the
fluctuations created by the interactions between chemistry
and turbulence.
In conclusion, both the theoretical and experimental
studies carried out thus far clearly indicate that the
effect of coupling between chemical reactions and turbulent
fluctuations is important in determining the reaction rates
of photochemical reactions in the atmosphere.
In the introduction to this chapter we have alluded to
the difficulties inherent to atmospheric observational stud-
ies. It is clear that laboratory simulation of atmospheric
phenomena is preferable when feasible, as we can exercise
control over the experiment. However, it is quite difficult
to simulate certain aspects of atmospheric processes, parti-
cularly those involving the interaction of turbulence and
chemistry. Also, we are unable in many instances to suppress
or eliminate those phenomena that occur in the laboratory
but not in the atmosphere. More specifically, chamber stud-
ies are characterized by a high degree of mixedness, re-
stricted size of the experimental system, artificial light
sources, and the absence of aerosol or lack of controllabil-
ity of aerosol properties. In addition, the turbulence level
282
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in an unstirred smog chamber will typically be low compared
with levels existing in the free atmosphere. Thus, in ex-
trapolating the results of such studies for application in
the analysis of atmospheric observations, we find that we
are incapable of properly dealing with spatial nonuniformi-
ties, turbulent fluctuations, and the effects of aerosols,
Furthermore, we do not yet know how to assess and thus pro-
perly compensate for certain "chamber effects", such as re-
action at the walls. Finally, the degree to which the at-
mospheric spectral distribution of radiation has been pro-
perly simulated in the chamber is uncertain. Thus, despite
the difficulties that inhere to an observational program,
we must still undertake such programs to obtain information
fundamental to gaining an understanding of the effect of
turbulence on chemical rate processes.
Having discussed the importance of the coupling of
chemistry and transport and the need for an observational
program, we must now consider how best to structure such a
program. It is important to state at the outset that any
*
division of effort will, of necessity, be somewhat arbitrary.
However, we herein present our thoughts on the matter. One
useful means for segmenting an observational program focuses
on validation of models, in the hope that discrepancies be-
tween observation and prediction will indicate in what re-
spects and to what extent our knowledge is deficient.
283
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Analysis of the data collected will perhaps suggest
further studies to be carried out in the laboratory or
in the smog chamber that will be useful in clarifying
dilemmas. Another method of grouping involves the iden-
tification of specific gaps in our knowledge and the design
of an experimental program with these in mind. As a
matter of convenience, we have elected to segment this
discussion according to the modeling framework, as follows:
Regional Scale Studies
Lagrangian Program
Eulerian Program
Local Scale Studies
Plumes
Roadways
We find this division useful because, by examining the model,
it is an easy matter to identify the questions that might be
raised, the quantities that must be measured, the effects of
284
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uncertainty in the various parameters of interest, and the
like. The model is in effect a tool useful in organizing
thought. However, within each section we will also address
issues that do not arise solely because of modeling consi-
derations; each will be included in the section that seems
most appropriate. For example, material balances will be
discussed as a part of regional fixed grid studies, whereas
the investigation of "apparent" kinetics will be a part of
regional Lagrangian studies.
1. Regional Scale Studies
Topics of discussion in this subsection are restric-
ted to measurements and observations to be made in a pro-
gram of regional scale--of the order of 10 to 50 miles.
Not all topics, however, must be included in a program
of this scale. Some observations should also be made
(and perhaps are better placed) in programs of more
limited spatial extent (for example, the study of the
effects of turbulent fluctuations on chemistry); others
are included as a matter of convenience in classification,
However, all will be of value in providing information
useful in the modeling and analysis of phenomena that
are of interest on a regional scale.
a. A Lagrangian Program
In many ways the parcel concept is the natural
framework for studying atmospheric chemistry. As a
285
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parcel of air is advected through an urban area,
it accepts pollutants emitted both at the ground
and aloft. Chemical reactions take place within
the parcel, and secondary pollutants are formed.
However, it is generally assumed that the parcel
does not exchange material with its surroundings
(except for direct emissions), nor does it res-
pond to vertical movements of air. We thus may
view the parcel quite simply as a horizontally
transported chemical reactor with variable rates
of reactant input and removal.
Unfortunately, serious questions arise as to
the validity of the parcel concept, questions
which we have discussed rather fully in Chapter III.
The major issues center on the following arguments:
At low wind speeds, turbulent diffusion con-
tributes heavily to net transport. "Parcels"
tend to "disintegrate" under these conditions
and cannot be clearly defined.
Under conditions of intense incoming radia-
tion and thus strong ground heating, or when
transport takes place over terrain of rapidly
varying elevation, vertical movements can be
important. These tend to destroy "parcels".
Wind speed and direction can vary with height.
Under such conditions, parcels are subjected
to shear, are distorted and fragmented, and
are ultimately destroyed,
286
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The first two conditions described tend to be
prevalent on "high pollution" days in the Los
Angeles area, days for which the use of such a
model would be of particular interest.
One can view the question of parcel inte-
grity in another way. Consider at one extreme
a parcel having small dimensions--say ten meters
in diameter. A parcel of this size is subject
to the effects of shear, of turbulence, and of
exchange with its surroundings (having a rela-
tively large surface-to-volume ratio) during
its traverse across an urban area. It would be
surprising if a parcel of this size would re-
main an identifiable entity over, for example,
a 1,000 meter traverse. In contrast, consider
a parcel of 2,000 meter diameter. This parcel
would be virtually unaffected by local fluctua-
tions and variations and would exchange little
mass with its surroundings. But within the par-
cel there are likely to be large variations in
concentration at any one time. A great deal of,
chemical detail is thus unresolved. A parcel of
interest, then, lies somewhere between these two
extremes in size--between 200 and 1000 meters in
diameter. To what extent does a parcel of this
size maintain its integrity over time periods of
interest on an urban scale—periods of two to eight
hours in duration? To what extent do turbulence,
buoyancy, and shear alter the size, shape, and
287
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structure of the "parcel"? How is the degree
of mixedness affected by these processes? To
what extent do "high-concentration" packets of
air, heated at the ground, rise and penetrate
the parcel -- thereby introducing "new air" and
fresh pollutants?
Two observational programs having the par-
cel concept as their core are now in the planning
stages. One, being planned at Stanford Research
Institute, involves monitoring parcel movements
along the centerline of San Francisco Bay, fol-
lowing the parcel southeastward to the San Jose
area from the point at which it leaves land at
the eastern side of San Francisco. Air quality
and meteorological measurements will be made
from a houseboat that will follow a tetroon
along its trajectory. A major consideration in
mounting this study is that it has been observed
that air movements consistently follow the Bay
centerline toward the southeast during periods of
high oxidant formation (Robbins and Cavanagh (1972))
As the parcel passes over water during the period
of observation, the only pollutant sources along
its path are the two bridges crossing the central
and southern portions of the Bay. Thus, the parcel
approximates a moving, unbounded chemical reactor
with virtually no sources and only minor sinks.
The second program, currently being planned
by W. A. Perkins of Metronics Associates, consists
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of a very comprehensive monitoring study in the
Los Angeles Basin. Parcels will be identified and
tracked through use of tetroons and radar. Heli-
copters will measure air quality in the vicinity
of the tetroon, and both laterally and vertically.
Aircraft will be employed in measuring winds aloft.
A mobile van will follow the tetroon, obtaining
air quality data while in motion. Tracer materials
(either fluorescent particles or SFg) will be re-
leased with the tetroon and will be collected both
at the ground and aloft. Multiple tetroon launches
will be made to assess the validity of the parcel
concept.
Both programs are currently being planned,
and, as a result, no formal documents are yet avail-
able which describe the projects. However, perti-
nent reports of a preliminary nature are available--
Robbins and Cavanagh C.1972) and Perkins C1972) . We
refer the reader to these to gain a better under-
standing of the planned program; we will not attempt
to describe them here. Rather, the reader should
assume that the commonly made and more obvious
measurements will be carried out. We will consider
here only measurements or observations of a more
specific nature--either those useful in exploring
the effects of transport and diffusion on chemical
rate processes or those that are a logical adjunct
to a Lagrangian field study. The entire data base,
of course, will be used in the validation of
Lagrangian models.
289
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The major issues with which we will concern
ourselves here are:
Investigation of the validity of the parcel
concept. Over what range of conditions--wind
speed, wind shear, level of turbulence, nature
of terrain, intensity of radiation (surface
adsorption and convective heating)--does a
parcel maintain its integrity for time periods
commonly of interest? Over what spatial scale?
To what extent do turbulent processes induce
lateral and vertical diffusion?
Characterization of the degree of mixedness
of a parcel. To the extent that reactants in
a parcel are not intimately mixed, their
access to each other is limited. Apparent re-
action rates under these conditions can be sub-
stantially less than absolute reaction rates.
Characterization of turbulence to aid in deter-
mining the effects of these processes on ob-
served reaction rates, as well as on the chemi-
cal mechanism assumed. High levels of turbu-
lence will encourage mixing and lessen the
effect of transport limitations on apparent
kinetics.
The measurements that we recommend be carried out are
as follows:
Integrity of parceZ—multiple, simultaneous
tetroon launches to assess magnitude of
290
-------
diffusion within, and in the vicinity of, a
parcel; collection aloft of tracer released
at surface at time of tetroon launch; varia-
tions in wind speed and direction with height;
concentration of CO, NO, NO-, 0-, and possibly
hydrocarbons as a function of distance, both
horizontally and vertically, in the vicinity
of the tetroon. These measurements have
already been recommended by W. A. Perkins
(1972) for the proposed Los Angeles study
and will very likely be incorporated into it.
Mixedness--high frequency measurements of pol-
lutant concentrations aloft (NO, N02» 0~,
' other) as a function of time (measurement inter-
vals of the order of 10" to 10 seconds) to
permit determination of the correlation in
fluctuations between pairs of reacting pollu-
tants; measurement of CO and C2H2 concentra-
tions in the vicinity ,of the parcel to aid in
estimating the rate at which material is intro-
duced to or lost from the parcel.
Turbulence intensity--intensity of turbulent
fluctuations in the vicinity of the tetroon,
employing an instrument such as the MRI tur-
bulence meter (UITS 1120).
Analytical studies of three types are needed
to treat the data collected. The first type involves
direct data reduction, correlation, and analysis,
29.1
-------
employing appropriate statistical techniques, in
order to identify and quantify the effects under
investigation. The second entails theoretical
studies, the aim of which is to establish cause-
effect relationships based on phenomenological
analyses. Finally, we wish to evolve methods for
incorporating into urban airshed models the ob-
served effects of transport-limiting processes on
reaction rates.*
Specifically, we have in mind here the need for estab-
lishing relationships of the following type:
Effective = ^absolute' *• c'i • c'icf j • other Parameters)
where ^ ff ti e = Pseuc^° reaction rate constant for the
atmospheric reaction of interest
k , , = absolute rate constant for the homo-
geneous reaction, as measured in the
laboratory
K = turbulent diffusivity
Such expressions have been derived for simple heterogeneous
systems, an example being a first-order reaction at a sur-
face. If the reactant species diffuses through a boundary
layer of thickness x , then
Effective k absolute
Note that, when K is large, kef£ective s ^absolute' and
the dynamics are reaction rate-limited. When 1C is small,
the dynamics are diffusion- limited.
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Each category of analysis merits attention as an
area worthy of immediate support if the suggested
observational program is to be carried out. More-
over, methods of data reduction and analysis should
be carefully defined prior to finalization of the
plans for the observational programt so that needed
measurements will be made, so that measurements
have the resolution, specificity, and accuracy re-
quired, and so that they are carried out with suf-
ficient frequency. Specifically, as a part of
planning the observational program, the following
questions must be answered:
1. Exactly which parameters should be measured?
2. What specifications (or constraints) should
be placed on each type of measurement (i.e.,
in terms of specificity, accuracy, frequency,
etc. 1?
3. What instrument (or type of instrument) should
be used for the measurement?
In concluding this discussion, we will comment
briefly on the planning aspects, without attempting
to deal with questions of post-observational analysis.
We have suggested in our recommendations what
parameters might be measured. However, we have not
been sufficiently specific in some areas. For ex-
ample, Donaldson and Hilst have found that, for a
reaction involving only two species and under spe-
cial conditions, the assessment of inhomogeneities
293
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in concentration of the participating species and
their cross-correlation, as measured by cf , c' ,
ct p
c'c' , respectively, are of primary importance in
estimating the magnitude of departures in concen-
tration from those expected in a homogeneous sys-
tem. However, it may well be that higher order
fluctuations are also determining factors, in which
case the fluctuations of a third species should
perhaps also be follpwed, Furthermore, to the extent
that molecular diffusion influences the intensity
of fluctuations, key parameters that reflect the
magnitudes of these coefficients should also be
monitored. Theoretical studies, however, do not
constitute the only means for identifying these
parameters; identification may be achieved by
adopting novel investigatory approaches, For exr
ample, Eschenroeder et al. (1972) have proposed
that deviations from quasi-equilibrium [for the
reactant system, NO, N02, Oj] can be used to indi-
cate the magnitude of the effect of turbulence on
chemistry. Despite the fact that quasi-equilibrium
may never be realized, even in a perfectly homogen-
eous atmosphere, because of the effects of compet-
ing reactions, this type of analysis, nevertheless,
deserves further investigation.
With regard to specifications that might be
placed on a particular type of measurement, we re-
fer primarily to questions of accuracy, specificity,
frequency and/or duration of measurement, etc. For
294
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example, the frequency with which concentrations
are measured for the purpose of correlational
analysis to assess the degree of mixedness must
be determined prior to the beginning of the ob-
servational program. If measurements are made,
say, at 1-second intervals, but theoretical
analysis suggests that measurements of 100 sec
frequency or greater are needed to support mean-
ingful analysis of the concentrations fluctuations
of two reacting species, then observations taken
at one-second intervals will be of little use. To
present this in more precise terms, consider the
cross correlations c'c' , where
o p
where is the co-spectrum and v is the frequency,
Although concentration fluctuations of all frequen-
cies may appear, contributions from only a finite
range are dominant in computing this double cor-
relation. It is therefore important to decide in
advance how to choose the upper and lower cut-off
frequencies, v.. , v, , respectively, so that
we may adequately approximate the above integral by
/U rlnvU
CiC8 "J VB'(v)dv = J v*o,6,(v)dv
VL lnvL
295
-------
The choice will, of course, depend upon the parti-
cular situation, but, in any case, will be the major
determinant in properly specifying the frequency of
observation, and thus the resolution of the moni-
toring apparatus. In general, then, questions con-
cerning accuracy, specificity, and frequency of ob-
servation must be raised, carefully stated, and an-
swered prior to planning the actual measurements if
truly useful data are to be collected.
The need for judicious selection of instrumen-
tation seems self-evident. Data collected will be
of little or no use if they do not satisfy the re-
quirements discussed above. For example, experimen-
tal evidence of the interaction between turbulence
and chemical kinetics can be obtained only if a
highly stable, highly sensitive (capable of measur-
ing in the parts per billion range), and short
time response ( 1 sec) measuring device, such as the
chemiluminescence method, is available. Clearly,
careful studies must be carried out to determine the
capabilities of the existing instruments.
One final comment seems appropriate regarding
planning of the measurement program and analysis of
the results. Angell and his co-workers have for
several years carried out observational programs in
the lower troposphere involving the use of tetroons
and have established a substantial level of exper-
tise (Pack et al. 1970; Angell et al. 1971a,b,c,d; 1972a,
b). Their studies have provided a rich collection of
296
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data involving such diverse phenomena as horizontal
and vertical movements of air parcels, rates of dis-
persion, helical circulations, and urban heat island
effects. Of particular interest is the study by
Angell et al. (1971b) involving the nearly simultan-
eous release of tetroons, thereby providing a basis
for estimating turbulent diffusivities. Angell et
al. (1972b)have also carried out a comprehensive
program of tetroon .tracking in Los Angeles. In
that program they found that, on occasion, signifi-
cant variations in horizontal wind direction with
elevation occur in the area. Thus, given the ex-
pertise and experience of this group, we strongly
recommend that they be asked to participate in the
planning of atmospheric experiments of the type we
are suggesting here.
In summary, a Lagrangian regional study will
provide the following:
Means for assessing the validity of the parcel
concept — if valid, its range of validity, spa-
tially and temporally.
Data useful in validating "moving parcel"
models.
Information useful in assessing the degree of
mixedness aloft of major reactive and unreac-
tive pollutants.
Data useful in attempting to develop a means
for incorporating diffusion-limiting effects
in the kinetics portion of airshed simulation
models.
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b. An Eulerian Program
While the Eulerian, or fixed coordinate,
framework is a natural coordinate system for char-
acterizing meteorology and emissions, it is in
some ways a less desirable reference system than
the Lagrangian for investigating questions per-
taining primarily to chemistry. For this reason, we
have included in the preceding discussion of obser-
vations to be carried out in the Lagrangian reference
tern a number of questions in critical need of study
However, there are several classes of observations
that would be of considerable value in elucidating
chemistry insofar as kinetic mechanisms are an in-
tegral part of an airshed model. These measure-
ments, in all cases, should be carried out so as
to establish variations in the quantity measured
as a function of location and time--hence, their
inclusion in this section.
In general, on the basis of what has been
said thus far, one might include in this discussion
observation of any variable that could be of use
in modeling. In an integrated and coordinated ob-
servational program, however, many measurements
are commonly made, and on a routine basis. Ground
level concentrations of CO, NO, NO-, oxidants and wind
speed and direction are examples. We will thus dis-
cuss only those measurements that are not routinely
carried out, and that are in fact rarely made. In
298
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selecting these classes of observations or mea-
surements, we have the following objectives in
mind:
Acquisition of pollutant concentration data
aloft; also improved characterization of
nighttime pollutant concentration distribu-
tions aloft. The former objective is based
on the utility of such data in model veri-
fication, an exercise which has been restrict-
ed to date to evaluations at ground level.
Nighttime observations are of value in es-
tablishing initial conditions and boundary
conditions in models. Knowledge of variations
in ozone levels aloft in the absence of radi-
ation may shed some light on the atmospheric
chemistry of this species. We may also be
able to gain insight as to why multiple
layers of high concentration material form
aloft. (While the formation of multiple in-
version layers is, of course, heavily depen-
dent on transport considerations, the chemis-
try of such layers may be of considerable in-
terest.) Finally, our knowledge and under-
standing of variations in concentrations aloft
is poor; such information is badly needed.
Establishment of a data base sufficient to
permit a mass balance to be made for nitrogen
and sulfur.
299
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Determination of variations in reactivity of
the atmospheric hydrocarbon mixture with lo-
cation and time.
Each objective, if satisfied, would improve our
ability to model the atmosphere. Improved models
would make more meaningful the results of sensi-
tivity studies. These results, in turn, will
better illuminate areas in which acquisition of
knowledge is vital.
There are six categories of observations
which we recommend be carried out to satisfy the
stated objectives and which are not commonly made.*
They are:
Vertical soundings of concentration. Included
are measurements of some or all of the follow-
ing- -CO, NO, N02, 0-, non-methane hydrocarbon
(NMHC), S02--from the ground to 200 to 500 feet
above the base of the elevated inversion. (We
assume here that measurements of this kind will
be made during a high pollution period, and
that in such circumstances an elevated inver-
sion will be present.) Measurements are to be
While we do not include a discussion of purely meteoro-
logical measurements, even though they may be of im-
portance, we do wish to mention one "non-routine" class
of observations — the monitoring of winds aloft. Usually,
only surface wind data are available; fox; a comprehensive
study such as we are discussing, measurement of the ele-
vated wind field is also needed.
300
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made two or three times during the day (or
more frequently if warranted) above two to
four strategically selected ground locations
in an urban area.
Mapping of concentrations aloft at night.
Measurement of some or all of the following--
CO, NO, N02, 03> S02--as a function of loca-
tion (i.e., the x-y coordinate position) and
height. Measurements to be carried out from
one to three times daily during the dark hours.
Temperature soundings, more frequently than is
common. We suggest at least three soundings
during the day and two or three at night, per-
haps at four-hour intervals. (We note, however,
that, if temperature is found to have a signi-
ficant effect on the overall rate of chemical
transformations in the atmosphere, then the
suggested frequency of measurement will very
likely be inadequate.) In an area over which
«
the height of the inversion base varies only
slightly with location at a given time, a
sounding at one location will suffice. In an
area such as Los Angeles, over which there is
considerable spatial variation in the height
of the inversion base, soundings at a number
of locations are recommended. (For Los Angeles,
we suggest five to six sites.)
301
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Measurement of the distribution of indivi-
dual hydrocarbon and oxygenated hydrocarbon
species as a function of location and time.
This suggests gas chromatographic measure-
ments at a number of locations spread through-
out the urban area. While measurement in the
vertical would be highly desirable, it is not
feasible at this time. However, if the aging
of bag samples can be shown to have a negli-
gible effect on the determination of hydro-
carbon distribution, delayed analysis, at
ground stations, of samples collected aloft
is quite acceptable.
Execution of a "sink" inventory. This involves
estimation of the available sink surface, both
for aerosols and ground sinks. We discuss this
more fully in Section B, Heterogeneous Reaction
Studies.
Measurement of the variations in radiation in-
tensity as a function of ground location, ele-
vation, and time. We wish here to establish a
relationship between aerosol concentration (and
other aerosol characteristics), cloud cover,
and intensity. We discuss this topic in Section
C, Spatial and Temporal Variations in Solar
Radiation.
Because of the very comprehensive nature of this
program, the measurements will involve careful plan-
ning and substantial costs. They also should be
302
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coordinated so that a full set of measurements is
acquired for specific periods of observation. We
thus do not view this program as being routinely,
or even frequently, undertaken. Rather, we expect
that, in a study such as RAPS, such observations
would be made on perhaps a half dozen to a dozen
occasions, with at least two or three of the days
being consecutive. Clearly, it is preferred that
"measurement days" be days of high pollution levels.
Analysis of data will, of course, involve the
use of Eulerian airshed simulation models. In fact,
the measurements suggested are, to a large extent,
those that are presently needed, but unavailable,
for validation purposes. However, these data,
along with more routinely collected data, will
also permit:
An attempt to establish a mass balance for
nitrogen and sulfur. If measurements of
vertical variation of wind velocity with
height are made and the concentrations of
appropriate pollutants are monitored at the
boundaries, incoming and outgoing mass fluxes
can be estimated. With chemical reactions in-
cluded in the model and an appropriate emissions
inventory available, net loss to sinks can be estimated.
This estimate can be compared with an inde-
pendent estimate of losses to sinks, as dis-
cussed in Section B.
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Calculation of ratios of reactive species to
inert (or nearly inert) species as a function
of location and time. Examples: NO /CO,
Jv
NO /^^ ^^ acetylene is monitored) , olefins/
olefitics
r •
data may provide a basis for estimating rates
of appearance and disappearance of reactive
species. They may also be of value in estimat-
ing rates of loss to aerosols, particularly if
gaseous chemistry can be clearly established.
Estimation of the extent to which equilibrium
between NO, N02, and 0., is approached. Equili-
brium is unlikely to be established near the
ground due to sources, but it may be achieved
rapidly aloft. With chemiluminescent analyses,
averaging times will be sufficiently short to
make such computations meaningful.
Computations and analyses involving sinks and radia-
tion will be discussed in subsequent sections.
2. Local Scale Studies
We have thus far given attention to observational
needs that are to be met as part of a regional or urban
scale monitoring program, with the focus on enhancement
of knowledge in atmospheric chemistry. A similar need
exists at the local scale, a need for observational
studies to elucidate the nature of chemical reaction pro-
cesses that occur in plumes and in the vicinity of
roadways.
304
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a. Plumes
Transport and dispersion of pollutants emit-
ted from stacks has been a subject of investiga-
tion for many years. However, chemical reactions
that take place within plumes have received rela-
tively little attention. Nitrogen oxides and sul-
fur oxides are the reactive species of greatest
interest in plumes, due to the high rate of emis-
sions of these pollutants from fixed sources. The
.need for study of their reactions in plumes rests,
not on the fact that reactions of the species
have not been heavily investigated, but on the
knowledge that the conditions existing in a plume
(e.g., temperature, humidity, concentration):
1. May be quite different than the condi-
tions under which reactions of SQ
^
NO are carried out in the laboratory,
X
and
2. Are often inaccurately known,, if at all
Combustion products normally leave a furnace
chamber at 1500-2000°F, whereupon they enter a
vertical stack. As the primary function of the
stack is to ensure that the product stream is dis-
persed well aloft in the atmosphere, safely away
from people and their structures , stacks are de-
signed to impart maximum buoyancy and high-exit
velocity to the plume. Stacks are thus well in-
sulated, thereby maintaining the vented stream at
305
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high temperature until its exit. Cooling of the
stream then occurs rapidly due to the entrainment
of air as the plume rises, loses buoyancy, and
comes under the influence of the prevailing winds.
The exiting stream, then, consisting primarily of
nitrogen, CO-, water, carbon monoxide, and other
combustion products, and carrying NO and S07 at
X £
temperatures of the order of 400 to 800 F as it
leaves the stack, enters the atmosphere at condi-
tions far different than ambient.
The high temperature of the plume will, of
course, considerably influence rates of reaction.
High temperatures also suggest the possibility of
thermal reactions occurring at significant rates
that are unimportant at ambient temperature. More-
over, high concentrations may favor reactions not
ordinarily of interest, such as 2ND + 0- •*• 2NC>2.
The high water content of a plume suggests that
rapid adsorption and dissolution of N02 takes
place upon condensation of the vapor. Should con-
ditions in the plume favor conversion of SCU to SO,
sulfate-containing aerosol will immediately be
formed. Finally, the high NO content of the plume
implies that ozone concentrations will be low in
its vicinity, due to the reaction of NO and 0^.
The importance of these reactions and others in
determining the composition of plume as it assumes
ambient flow conditions is largely unknown. We
thus recommend that a measurement program be under-
taken to provide the data needed to investigate
these questions.
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A suitable measurement program would consist
of monitoring stack conditions — temperature, flow
rate, and composition of the exit stream—and mak-
ing traverses of the plume at two to four downwind
positions to measure the cross-sectional concentra-
tion distribution of-NO, N07, SO-, CO, ozone, and
Li Lf
aerosol (if possible). We also suggest measuring
temperature and water concentrations at each tran-
section location. Finally, ambient temperature
and pollutant concentrations, along with local
meteorological parameters, should be monitored
continuously in the vicinity of the plume, as
should radiation intensity. The development of
suitable models of reactive plumes, in conjunction
with the analysis of such data, will provide valu-
able insight into the transformation processes that
occur within these important sources of atmospheric
pollutants, and we will finally gain some knowledge
as to the contribution of fixed sources to air
pollution on the regional scale.
b. Roadways
While automobiles emit "plumes" at high temper-
atures that contain combustion products such as H20,
C09, CO, NO , and partially burned hydrocarbons, our
£* J\.
interest in studying atmospheric chemistry in the
vicinity of these emissions sources stems from con-
siderations quite different than those which are sup-
portive of studying the chemistry of plumes emitted from
307
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large fixed sources. The exhaust stream that is
emitted from the vehicle cools very rapidly, rul-
ing out an interest in high temperature reactions
It also mixes with its surroundings very rapidly
under most conditions, due to the stirring induced
by the movement of the vehicles. The conditions
of interest, then, are local high concentrations
of NO, N02, hydrocarbons, and CO at ambient, or
near ambient, temperatures.
Of primary importance is our obtaining an
understanding of the influence that the enhanced
production of N02 through the NO-0^ reaction has
on photochemical kinetics at the local scale. Be-
cause of the steady input of NO in the immediate
X
vicinity of a heavily used roadway, the equilibrium
between 0,, NO, and N02 that may exist aloft due
to the reactions
hv
N09 -»• NO + 0
M
NO + N02
does not hold near such sources. Ozone levels are
very low, whereas NO and hydrocarbon concentrations are
A.
elevated. It would thus be of considerable value to deter-
mine if"chemical mechanisms are capable of describing
the concentration behavior of these species on the
308
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local level, and to better assess how to include
the observed pollutant mix as input, via an emis-
sions inventory, in models of regional scale.
We envision an appropriate measurement pro-
gram to include the simultaneous monitoring of
pollutant concentrations upwind, alongside, and
downwind of a major artery. NO, NO-, 0~, NMHC,
Lt O
H^O, and CO should be measured, along with temper-
atures and radiation intensity. Local meteorolo-
gical conditions, including level of turbulent
fluctuations, and vehicular flow rates should also
be monitored throughout the period of observation.
Such data will provide a basis for validating
"reactive roadway models" and thus for studying
the kinetics of reactions at high NO and HC
X
concentrations.
One final note is appropriate. In a monitor-
ing program to be carried out in the vicinity of
roadways, it would be of considerable value to
collect data useful in assessing the effects of
turbulent fluctuations and lack of mixedness on
reaction rates. We thus recommend the use of
apparatus for measuring NO, N02, and 0, concentra-
tions that are capable of high frequency determina-
tion of concentrations.
B. Heterogeneous Reaction Studies
While the reactions of gaseous species have been thor-
oughly studied in the investigation of transformations of
atmospheric pollutants, gas-liquid and gas-solid interactions
309
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also constitute important transformation mechanisms.
Largely, these involve adsorption of pollutant species
on and often diffusion into liquid droplets, suspended
solid particles, and solid surfaces, whereupon reactions
may take place. However, whether or not chemical reactions
occur, aerosols (suspended liquids and solid particles) and
surface materials do constitute sinks for pollutants. In
previous chapters we have discussed the role of each in
pollutant removal from the atmosphere. In particular, we
refer the reader to Chapter IV for a discussion of labora-
tory studies of aerosol formation and to Chapter V for a
discussion of the role of smog chambers in investigating
natural scavenging processes. In this chapter we explore
the types of atmospheric observations that might be of
value in enhancing our knowledge of contaminant removal
mechanisms.
1. Aerosols
Apparently, the first large-scale program aimed
at understanding the behavior and properties of photo-
chemical aerosols was the 1969 Pasadena Smog Experiment.
During the experimental period of about three weeks
(August and September 1969), aerosol size distribution,
along with other physical, chemical, and meteorological
parameters, were measured in six intensive experimental
periods of about one day each. The experimental data
and analysis are reported in Aerosol Measurements in
Los Angeles Smog (1971) and by Whitby et al. (1972a,
1972b) , Husar et al. (1972), Ensor et al. (1972), Thielke
et al. (1972) and Miller et al. (1972).
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A second major photochemical aerosol characteriza-
tion study is now in progress. The study, aimed at the
Los Angeles aerosol, is sponsored by the State of Cali-
fornia Air Resources Board and is being conducted by
North American Rockwell with the participation of a
number of universities and laboratories.
Viewed from the standpoint of air pollution control,
the objective of aerosol measurements is to relate both
gaseous and particulate source emissions to urban aero-
sols .which are responsible for visibility impairment
and possible health effects. The goal, then, is to ac-
count in as much detail as possible for the origin, at-
mospheric concentration» and fate of atmospheric particles.
Knowledge of the following elements are required to
achieve this goal:
1. Aerosol sources: automobile and industrial
emissions, natural aerosol production, etc.
2o Meteorological parameters: inversion height,
wind speed and direction, relative humidity,
temperature, solar radiation intensity, etc.
3. Chemical and physical rate processes: gas-gas
reactions, gas-particle reactions, nucleation,
condensation, coagulation, growth by absorp-
tion, adsorption, etc.
4. Removal mechanisms: settling, washout, etc.
At this time the full modeling of combined gas and particle
behavior in an urban atmosphere is beyond our capabilities.
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This is primarily due to our lack of understanding of
aerosol sources, growth kinetics, and interactions with
the gas phase constituents. The principal focus of an
experimental program, then, is to obtain the data neces-
sary to understand these aspects and eventually enable
mathematical modeling of urban aerosol dynamics.
We consider first the question of an aerosol
"source inventory" for an urban area. The compilation
of an aerosol source inventory is more difficult than
the compilation of a gaseous emission inventory because:
1. Primary sources can be either anthropogenic
or natural.
2. Of the aerosols of anthropogenic origin, a
significant quantity are formed in the atmos-
phere (secondary) and cannot be accounted for
in a primary emissions inventory.
3. Aerosols are distributed not only with respect
to chemical composition but also with respect
to size.
Hidy and Friedlander (1970) have estimated the relative
importance of major natural and anthropogenic sources
of the Los Angeles aerosol from limited data on their
chemical composition. The fractional contribution of
each source was estimated from data on emissions of gases
and particles, in combination with the use of tracer ele-
ments from some sources. Their results suggest that
about two-thirds of the Los Angeles aerosol is anthropo-
genic. Of this, as much as one-third is secondary in
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origin, coming from chemical reactions or condensation
of vapors in the atmosphere.
In subsequent studies, Friedlander and his col-
leagues (Miller et al, 1972, Friedlander, 1972) have
developed a novel means for estimating the contribution
of various sources to the atmospheric aerosol measured
at any point in an airshed. The method is essentially
based on a mass balance for various individual elements
which are known to come primarily from certain well-
defined sources such as:
Sodium - sea salt
Aluminum - soil dust
Lead - automobile exhaust
Vanadium - fuel oil flyash
Using the data from the 1969 Pasadena Smog Experiment,
Friedlander estimated that 15% of the particulate matter
resulted from primary natural sources and 25% from pri-
mary anthropogenic sources. About a third of the total
was estimated to result from atmospheric reactions.
About 701 of the total particulate burden was accounted
for, with water probably making up a significant portion
of the remaining 30%.
It is important to stress that an ordinary source
inventory based merely on estimates of emission rates
from various sources is inadequate for aerosols because
it is uncertain how much material is emitted from sources
such as the soil and the sea. In addition, the fraction
which remains airborne is often unknown. The mass bal-
ance method circumvents these difficulties by essentially
313
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employing certain characteristic elements, such as the
four listed above, as fingerprints for specific types of
sources. In some cases, particularly for the elements
carbon, sulfur, and nitrogen,it is necessary to have
some information on the combined state in order to know
whether an element is present in the gas or particulate
phase. In the first two studies (Miller et al. 1972,
Friedlander, 1972) the chemical composition has been
averaged over the size spectrum. A recent study (Heisler
et al. 1972) included the effect of a size distribution.
From the contributions of the separate sources and mea-
sured size distributions and chemical compositions from
the literature, Heisler et al. estimated the size and
chemical element distributions of the atmospheric aerosol.
The second area requiring study involves formation
mechanisms and rates of particle growth. The two basic
questions of interest are (Husar and Whitby, 1972) :
1. What is the primary mode of gas to particle
conversion: homogeneous or heterogeneous
nucleation?*
In homogeneous nucleation particles are formed in the
vapor phase by molecular clustering without the aid or
intervention of foreign nuclei. In heterogeneous nucle-
ation foreign particles are present in the vapor and act
as nuclei for the growing particles.
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2. Is the particle growth rate controlled by a
surface catalyzed reaction which proceeds at
the particle-gas interface, or is the diffu-
sion rate of the vapor phase toward the par-
ticle surface the rate-controlling step?
Husar and Whitby have attempted to answer these questions
in a series of laboratory studies, the results and conclu-
sions of which are summarized in Chapter IV.B.I.
However, much remains to be done. In particular, in
order to meet the objectives of understanding the for-
mation, growth, and removal mechanisms of photochemical
aerosols, attention must be given to the following needs:
1. Development of analytical apparatus for measuring
aerosol composition. The development of a source
inventory will depend on the accurate measurement
of the elemental composition of the aerosol.
There is a need for an instrument capable of
continuous, real-time measurements of the key
inorganic components of particulate matter, in-
cluding Pb, Na, V, Zn and Ba. There is no com-
mercially-proven device currently available for
the continuous monitoring of the elemental
components of particulate matter, although
X^ray fluorescence techniques are promising
(Friedlander, 1972) . For example, neutron acti-
vation analysis sensitivites for V and Pb are
approximately 0.002 and 0.5 micrograms, respec-
tively, corresponding to the total particulate
matter in about 100 liters of Los Angeles air.
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To obtain enough aerosol for a measurement,
air must be withdrawn over a period, leading
to a time-averaged reading.
Knowledge of the conversion rates from gas
to particles for key species such as carbont
sulfur,and nitrogen. Most of the carbon-
containing compounds in photochemical smog
are present in the gas phase. The carbon-
containing portion of the aerosol, however,
represents a significant fraction of the
particulate phase, about 201 in reported
measurements (Miller et al. 1972). With
associated hydrogen, oxygen, and nitrogen,
the organic constituents represent a major
portion of photochemical aerosol on a weight
basis. Details of the hydrocarbon conversion
processes from gas to particle phase are not
well understood. It has been found that
cyclic olefins are particularly susceptible
to aerosol formation in photo-oxidation sys-
tems. The opening of the rin.g and formation
of polar groups, such as the carboxylic acid
group, lead to non-volatile products. (Glu-
taric acid has a melting point of 97.5 C,
while the corresponding cyclic olefin, cyclo-
pentene, has a boiling point of 44°C.) Sev-
eral possible mechanisms may control the con-
version of carbon from gas to particulate
phase: (a) reaction in the gas phase, followed
by homogeneous nucleation, (b) condensation on
foreign nuclei, and (c) diffusion to existing
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particles, followed by surface reaction.
A very important need is the development
of an accurate means for measuring the
concentration of not just total carbon, but
of individual organic compounds in the aero-
sol. The complexity of current wet-chemical
methods is evident in the recent study of
Cukor et al. (1972), who measured organic
fractions in New York City aerosol. Gas
ch.romatography and mass spectrometry offer
promise in this regard. Sulfates in aero-
sols result from:
a.' Photochemical oxidation of So *n t>ie
gas phase? followed by condensation
b. Oxidation of SO- in liquid drops with
metal ions , and
c. Catalytic oxidation of SO^ on solid
particles.
Nitrate formation results from:
a. Reaction between NCU and NaCl and
b. Photochemical oxidation followed by
condensation.
Determination of the particular types of sul-
fate and nitrate compounds formed is needed.
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3. Ability to reconstruct the measured atmos-
pheric spectrum of aerosol properties, notably
with respect to size and chemical composition,
given the characteristics of the "known sources
and conversion mechanisms. This will require
accurate measurement of:
a. Size distribution for particles of di-
ameter >_ O.Oly
b. Chemical composition as a function of par-
ticle size
c. Total particle mass concentration
d. Total number concentration.
"At present it is possible to collect data on
a routine basis for (a) the size distribution
of atmospheric aerosols in the range above 0.2y
in diameter, and (b) the chemical element com-
positions for many species integrated over all
sizes. For research purposes it is possible to
measure size spectra for particles larger than
O.Oly and to fractionate chemical element com-
position rather coarsely with respect to par-
ticle size" (Heisler et al. 1972).
4. Understanding of the fate of elements, such as
Pb, Znt V, Ba. It is not known what fraction
of the total mass of these elements that is
.found in the atmosphere leaves an airshed to
be removed ultimately by washout, and what
fraction is actually deposited within the
318
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airshed as a result of various scavenging
and removal processes.
A measurement program should be planned so as to
meet as many of the stated objectives as possible.
Therefore, at each measuring station, it is recommended
that the following measurements be made:
Size distribution of particles >_ O.Olp
Chemical composition as a function of parti-
cle size
Elemental (Pb, Na, V, Zn, Al, etc.)
Organic compounds
Gas phase concentrations (NO,'N02, 0-, 802)
Relative humidity and temperature
Total mass concentration
Total number concentration.
Since these measurements will necessarily involve expen-
sive equipment, they can only be made at a few selected
locations at the same time. A feasible program, there-
fore, is to measure the properties listed at two (or
more) points along a common air trajectory. The data
analysis could include consideration of sources between
the two points and atmospheric conversion mechanisms oc-
curring during the aging and traversal of the aerosol.
Such a procedure is currently being employed in the
California Air Resources Board aerosol characterization
study.
319
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It should be emphasized, in closing, that the main
purpose of the atmospheric study of aerosols is their
characterization. More ambitious goals would appear to
be illusory, as the phenomena of interest are extremely
complex and the atmosphere is a poor laboratory. Rather,
if characterization can be successfully accomplished
with respect to both physical and chemical parameters,
and if we can devise suitable means for generating aero-
sols having the same properties as those found in the
atmosphere, then the chamber will be the proper labora-
tory for the study of aerosols.
2. Surface Sinks
In Chapter V (pp. 248-251) we reviewed the labora-
tory and outdoor canopy studies that have been carried
out to investigate the nature of surface scavenging pro-
cesses. We also recommended experimental studies that
may be pursued in a controlled environment which might
shed further light on the dynamics of surface removal
mechanisms. In this section, we consider, as a natural
extension of the earlier discussion, observation programs
that might provide further information of value.
As very little has been done to date to formulate
a basis for estimating losses to surface sinks, establish-
ment of relatively simple correlations should prove to be
an important step forward. We thus view data collection
with regard to surface sinks at two levels of effort — one
quite unsophisticated, the second with some degree of
concern for the effects of various parameters on
320
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adsorption rates. The decision to mount either effort,
however, must await the results of chamber studies
recommended in Chapter V. These must indicate that
specific adsorption rates are sufficiently high that
vegetation can and does constitute an important sink.
In order to arrive at simple correlational relation-
ships, we recommend that a survey of unpaved land area
be carried out in order to estimate surface area per
unit land area of different classes of vegetation and
of soil. This should be carried out on a subdivided
grid, so that spatial distribution of sink materials
is accounted for. Assuming that pollutant concentra-
tions and wind parameters will be measured in any case,
and that specific adsorption rates have been estimated
as a function of temperature, humidity, and radiation
intensity for different pollutants, we will then have
a basis for estimating the total mass adsorption per
unit time. The estimate would, of course, be crude,
within a factor of two or three, assuming that aerosol
uptake rates are known to within +_ 50 to 1001 at the
time.
In order to try to estimate the effects of trans-
port on loss rate to surface sinks, surface roughness
and turbulence intensity levels must also be determined,
preferably taking into account spatial variations.
Lettau (1970) has summarized means for estimating sur-
face roughness. Turbulent intensity can be measured
as suggested in Chapter III, However, to properly
treat this aspect of surface adsorption, a turbulence
model for the surface layer is needed.
321
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A more rigorous approach to the treatment of surface
sinks may be provided by the mathematical modeling of pollu-
tant removal mechanisms, the equation for the conservation
of mass serving as the basic relationship. For conditions
of high pollutant concentrations, the dominant terms in the
equation will be the time-dependent term and the diffusive
and chemical reaction terms. The rate of absorption at the
surface will enter as a boundary condition. Successful imple-
mentation of this approach will yield analytic relationships
between the various physical parameters , such as the diffusion
coefficient, the gas phase reaction rate, the surface proper-
ties, etc. However, before such rigorous modeling can be
meaningfully undertaken, a great deal more must be learned
about surface absorption, hence the need for both the chamber
and field studies recommended in this report.
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C. Spatial and Temporal Variations in Solar Radiation
Solar radiation in the lower atmosphere both initiates
and sustains the photochemical reaction process. In partic-
ular, the photolysis of nitrogen dioxide and nitrous acid
are initiated by absorption of radiation in the ultraviolet
region of the solar spectrum. In Chapter V, we discussed
the importance of simulating the intensity, as well as spec-
tral distribution, of irradiation in smog chamber experiments,
The eventual goal is to establish a firm relationship between
the rates of photolytic dissociation reactions and the inten-
sity of radiation with given spectral composition. Unfortu-
nately, the relationships obtained from chamber tests alone
are not sufficient for either modeling the photochemical
reaction processes in an urban airshed or interpreting the
data collected in an atmospheric experiment involving chemi-
cal reactions. Chamber results must be augmented by tropo-
spheric measurements of the radiation intensity and its spec-
tral composition. Such observations are necessary because
it is unlikely that radiative transfer processes will be
amenable to theoretical description in the near future. We
note, however, that present techniques for measuring solar
radiation are subject to some controversy, as will become
apparent in the subsequent discussion.
In this section, it is our purpose to suggest the need
for measurements of solar radiation that are of considerably
broader scope than are normally carried out. We envision
three objectives in mounting this effort:
To provide information needed in atmospheric
modeling studies and in the refinement of models
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To provide a basis for establishing correlations
between radiation intensity both at the earth's
surface and aloft as a function of the size dis-
tribution and concentration of aerosols (haze)
and of cloud cover.
To provide data for other air pollution studies,
such as fundamental studies in atmospheric chem-
istry, correlation studies to establish oxidant
levels as a function of various parameters, and
the like.
We first present a discussion of the spatial and temporal
variability of solar radiation intensity in the lower tropos-
phere. We then briefly discuss various techniques for mea-
suring ultraviolet radiation. We conclude with recommenda-
tions for an observational program.
Solar radiation entering the uppermost layers of the
planetary atmosphere can essentially be considered to be
black body radiation at about 6000°K. Only minor variations
from this distribution, consisting of many absorption lines
(the Fraunhofer lines) of the component elements of the solar
atmosphere (hydrogen, sodium, etc.), are present in the solar
spectrum. As the solar radiation reaches the stratosphere,
most of the electromagnetic energy below 3000 A is absorbed
by ozone, which has a peak concentration at an altitude of
about 25 km. The irregularities appearing in the solar spec-
trum at the earth's surface are caused by the absorption and
scattering of the radiation by natural constituents in the
atmosphere and by man-made air pollutants in the lower tropos-
phere. The causes of these irregularities may be conveniently
classified as the following:
324
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1. Rayleigh scattering due to the gaseous components
of a clean atmosphere (i.e., blue sky scattering).
2. Absorption due to the gaseous components of a
clean atmosphere (notably water vapor and carbon dioxide.
3. Scattering and absorption by water droplets (clouds).
4. Scattering and absorption due to aerosols.
5. Absorption due to man-made gaseous pollutants
(notably nitrogen dioxide and nitrous acid).
As the first two effects occur in clean as well as in polluted
atmospheres, as they are virtually invariant with location and
time, and as they are in any event relatively well understood,
we will be concerned here only with the last three types of
effects,
The temporal variation of the solar "radiation, as affected
by the solar zenith angle, is well known. At a particular
location on the earth's surface, the solar zenith angle depends
upon the:
1. Latitude of the location
2. time of the day
3. Day of the year
The solar zenith angle for any locality can be obtained from
accurate astronomical calculations.
Although the change with solar zenith angle is primarily
responsible for the temporal variation of solar radiation,
significant variations in intensity and in spectral content
is also caused by the diurnal appearance of haze in the urban
atmosphere. While solar radiation can accelerate the formation
325
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of smog, gaseous contaminants and aerosols can also alter the
incoming or outgoing radiation by absorption and scattering.
Measurements made by Scott Research Laboratories at Commerce
and El Monte in 1969 have clearly demonstrated the effect.
Deviations of the observed intensity-time relationship from
a near parabola, as expected from solar zenith angle change,
ranged from 20% to more than 50% during mid-day or afternoon,
when smog formation is intense. Supportive of these observa-
tions, Randerson (1970) has reported a 231 loss in the radia-
tion intensity due to the presence of atmospheric pollutants.
As we have stated earlier, cloud cover, aerosol content,
and gaseous pollutant concentrations can greatly change with
the intensity and the spectral distribution of the incoming
solar radiation. Since these variables may be expected to
exhibit spatial variations, solar radiation intensity, as
experienced by an air mass in the atmosphere, may similarly
be expected to vary from place to place. Bach (1971) has
studied the vertical attenuation of solar radiation over an
urban area. He found that the extinction due to air molecules
is dominant in the higher and relatively cleaner'portions of
the atmosphere. Within the shallow layer of the atmosphere
directly above the ground (about 50 meters thick) , however,
anthropogenic pollutants, particularly aerosols, are primarily
responsible for radiation attenuation. In particular, Bach
observed a difference of 35% in total solar attenuation be-
tween "clean" and "polluted" atmospheres.
Horizontal variations are more difficult to characterize.
Idso (1972) has recently published solar radiation measure-
ments made in metropolitan Phoenix area over a period of
several years. The results, in terms of both long-term trends
326
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and diurnal variations, are considered in light of concurrent
meteorological conditions, as well as with regard to the spa-
tial and temporal variations of airborne particulates.
Difficulties in characterizing solar radiation in an
urban airshed have compelled the investigator to resort to
real-time measurements. Hopefully, continuous radiation data,
collected at a sufficient number of locations in an airshed,
will, through extrapolation, provide a complete picture of
the temporal and spatial distribution of radiation within the
airshed.
In the past, there have been a.number of techniques used
to measure ultraviolet radiation. Among them are:
1. Filter-Photocell sensor (Eppley sensor).
2. Filter-Phototube sensor.
3. Photochromic glass sensor.
4. Photosensitive plastic sensor.
5. Photochemically-treated filter paper.
6. Photochemical reaction cell.
The most widely used are the filter-photocell sensors for
general UV measurements and the photochemical reaction cell
for air pollution studies. The latter technique, first pro-
posed by Tuesday (1961) , permits the determination of radia-
tion intensity by observing the apparent decomposition rate
of nitrogen dioxide. As discussed in Chapter V, the photo-
chemical reaction cell can be used to measure k1 accurately
and quickly.
327
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From the preceding discussion it is clear that radiation
intensity not only varies with ground location (x, y), eleva-
tion (z), and time (t), but that its variation with x, y, z,
and t is, or can be, sufficiently strong that it must be
accounted for if accurate modeling of the atmosphere is
desired. As a result we recommend that, as a part of a com-
prehensive monitoring program, radiation intensity be mea-
sured at a number of locations throughout the urban area,
that it be measured as a function of time, and that it be
measured on an airborne platform above the ground monitoring
sites (aircraft, helicopter, etc.) as frequently as the
monitoring program permits. While it may not be possible to
make airborne measurements on a routine basis, they should
be made with sufficient frequency that a variety of aerosol
size distributions and concentrations and levels of cloud
cover are concurrently observed. It is, of course^ essential
that the physical properties of the atmospheric aerosol are
properly characterized if correlational relationships are to
be derived. To this end, we recommend that the size distri-
bution and the concentration of the aerosol be measured in
conjunction with solar intensity observations. (See Whitby
et al. (1972) for a discussion of measurement procedures.)
D. Measurement and Identification of Chemical Species
Concern has been expressed from time to time that
chemical mechanisms, when applied in the simulation of atmos-
pheric reactions, are oversimplified. While this claim is
clearly a valid one, it should be pointed out that the simpli-
fied structure of currently used mechanisms is a reflection of
Our level of understanding of the important
reactions contributing to atmospheric photo-
oxidation processes
328
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and
The limited number of species for which
concentration-time profiles are available.
The application of more detailed mechanisms in atmospheric
modeling is justifiable only if they can be validated; thus,
a broader and more complete data base, in terms of number
and type of species monitored, is presently needed. In this
section, we consider, albeit briefly, both the monitoring and
the identification of pollutant species in the atmosphere.
At the present time four individual chemical species
and two classes of species that are found in the atmosphere
are monitored on a routine bas£s--NO, N09, S07, CO, hydrocar-
i* £*
bons and oxidants. Measurements of the two classes of
species are of little value from the viewpoint of developing
and applying chemical mechanisms. In particular, .total
carbon analysis does not reflect the "reactivity" of the
atmospheric hydrocarbon mix, and ozone, not total oxidants,
is the species included in all photochemical kinetics mecha-
nisms. We thus recommend that
More detailed analysis of hydrocarbons becomes
a routine feature of atmospheric monitoring. At
present it would be useful to measure the concen-
trations of the following groupings*:
Unfortunately, no simple technique has yet been
devised to measure these groupings in the atmosphere.
Infrared analysis, however, does hold some promise
in this regard. For instance, terminal olefins
absorb at frequencies between 905-910 cm'1, aromatics
(including benzene) at frequencies of 690 and 760 cm"1,
and aldehydes, acids, and ketones in the region of
about 1735 cm"1. Until techniques for infrared
analysis become sufficiently well refined, however,
more complete measurements of the hydrocarbon mix
using computerized gas chromatographic methods must
329
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C^ paraffins
olefins, excluding ethylene
aromatics, excluding benzene
aldehydes
ethylene
Ozone be monitored on a routine basis.
In Chapter V we discussed the need for measuring alde-
hydes, peroxides, and peroxyacetylnitrate (PAN) in smog
chambers, both as an aid in model validation and to provide
important information concerning the smog formation process.
Aldehydes are major products of the oxidation of hydrocarbons,
being found in the atmosphere at concentrations of the order
of 10 to 20 pphm. Peroxides have been identified as inter-
mediates in the smog formation process and have been measured
at concentrations of up to 18 pphm (Bufalini et al., 1972).
PAN, also a product of atmospheric reactions, additionally
serves as a scavenger for free radicals and N02» and conse-
quently affects the late time behavior of the chemical dynam-
ics. Because of the important role that each of these species
(or class of species) plays, we believe that it would be highly
desirable if each were measured on a regular basis in the
oe performed^Unfortunately, as the individual
species concentrations are then grouped together,
a great deal of information is discarded. (The
relative concentrations of the individual hydro-
carbons which comprise these groupings change
not only from day to day, but continuously through-
out the course of the day. Therefore, it does
not appear possible to characterize the "reactivity"
of the atmosphere by the measurement of three or
four key species such as hexane, propylene,
toluene, and formaldehyde.)
330
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atmosphere. Unfortunately, monitoring techniques for these
species are very poor. Aldehydes and peroxides require wet
chemical methods, while measurement of PAN involves long path
infrared spectrometry, a procedure not suitable for routine
measurement outdoors. Thus, measurement of these species
presupposes the development of appropriate analytical proce-
dures .
We believe that it would be worthwhile to attempt to
identify two additional species that are believed to be impor-
tant participants (or products) in atmospheric reactions--
nitric and nitrous acid. The roles that these species play
in the chemical dynamics have been discussed in Chapters II
and IV. If these species are found in significant amounts
in the atmosphere, it will be necessary to develop analytical
instrumentation that will permit their monitoring on a rou-
tine basis.
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BIBLIOGRAPHIC DATA
SHEET
1. Report No.
EPA-R4-73-031
3. Recipient's Accession No.
4. Title and Subtitle
Existing Needs in the Experimental and Observational Study
of Atmospheric Chemical Reactions
5' Report Date
me. 1975
June, 19
(.Date of
6. (Date of Preparation;
7. Author(s)
John H. Seinfeld. Thomas A. Hecht. and Philip M. Roth
8- Performing Organization Kept.
N°- R73-21
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Systems Applications, Inc.
9418 Wilshire Boulevard
Beverly Hills, California
10. Project/Task/Work Unit No.
ROAP 26AAD/Task 10
11. Contract/Grant No.
68-02-0580
12. Sponsoring Organization Name and Address
Environmental Protection Agency
Office of Research and Monitoring
National Environmental Research Center
Research Triangle Park. N. C. 27711
13. Type of Report & Period
Covered
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14.
15. Supplementary Notes
16. Abstracts This report contains recommendations to aid those concerned with photochemica
nodeling in planning studies. The suggested programs are designed to provide informa-
tion needed to develop kinetic models to describe the chemical transformations of atmos-
pheric pollutants. The core of this report focuses on kinetic and mechanistic studies
Df individual reactions, smog chamber studies, and atmospheric measurement programs that
:he authors feel should be undertaken to provide the necessary data for model developmen
Existing deficiencies in knowledge in each of these areas are discussed and the types
programs needed to provide the missing information are examined in detail. The
report also includes a short history of model development, describing the various
)hotochemical mechanisms developed to date.
17. Key Words and Document Analysis. 17o. Descriptors
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chemical kinetics
photochemistry
atmospheric chemistry
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