TECHNICAL MEMORANDUM 1516
                                             JUNE 1971
CONCEPTS AND APPLICATIONS OF
PHOTOCHEMICAL SMOG MODELS
                                        A. Q. Eschenroeder
                                        J. R. Martinez
           GENERAL
           RESEARCH mw CORPORATION
           P.O. BOX 3587, SANTA BARBARA, CALIFORNIA 93105

-------
~ i
Portions of this work were performed pursuant to Contracts
CPA 22-69-127, National Air Pollution Control Administration,
Dept. of Health, Education, and Welfare, CRC-APRAC Project
No. CAPA-7-68, Coordinating Research Council, and EHSD 71-22,
Air Pollution Control Office, Environmental. Protection Agency.

-------
ABSTRACT
Following an overview of mathematical methods of analyzing air
pollution, detailed developments of inputs, techniques, and validations
are presented for photochemical smog modeling.
,
Finite difference formu-
lations are employed to comp~te concentration histories.
The chemical
kinetics are expressed as lumped parameter reaction mechanisms derived
from laboratory data in the literature.
Turbulent diffusion coefficients,
which depend on height and time, come from atmospheric measurements. .
Inputs consist of source inventories for the Los Angeles basin and solar
irradiation curves for the appropriate days.
Predicted time histories
of reactive hydrocarbons, oxides of nitrogen, and. ozone are consistent
with the variations observed at air monitoring stations.
With refined
descriptions of advection, the mathematical model will serve as a tool
in planning legislation and guiding urban planning in the future.

-------
SECTION
I
II
III
IV
V
CONTENTS
ABSTRACT
INTRODUCTION
A.
B.
Background Discussion
Dispersion Models Based on Inert Pollutants
C.
D.
Related Work on Photochemical Smog Modeling

Overview of the Combined Photochemical/Diffu-
sion Model
SOME SIMPLIFIED KINETIC MECHAN~SMS
A.
B.
The Original Scheme
Addition of More Realistic Oxidation Chaiqs
Influence of Initial Composition
C.
D.
Atmospheric Adaptation Based on Reactivity
Data Analysis
THE ATMOSPHERIC MODEL AND ITS NUMERICAL SOLUTION
A.
B.
The Governing Equations

Application of Pade Approximants to Smog
Chamber Calculations
c.
Application of Pade Approximants to the
Atmospheric Model Equation

Meteorological Reformulation of Model
D.
THE EXERCISE AND VALIDATION OF THE MODEL
A.
B.
Objectives of the Tests
Sources of Dat;:i
C.
D.
Validation Tests of An Early Version of the Model

Sensitivity Studies on 1969 Trajectories with
the Expanded Model

History Analysis of the 1030 El Monte Trajectory
E.
CONCLUDING REMARKS
LITERATURE CITED
'~1--
PAGE
....,
i
+
1
4
8
10
14
14
23
31
39
49
49
52
57
/)2
65
65
6?
82
97
101
110
116
ig

-------
NO.
11
ILLUSTRATIONS
1

2
Schematic of Diffusion Model for Air Pollution Simulation
Original Reaction Mechanism
3
Computed and Observed Reactant Histories for the Trans-2-
Butene/Nitric Oxide System

Computed and Observed Product Histories for the Ttans-2~
Butene/Nitric Oxide System
4
5
6
Expanded Kinetic Mechanism

Computed Curves Compared with Experimental Points fot
the Propylene/Nitrogen Oxides System
7
8

9
Hydrocarbon Decay with Two Reactivities

Ozone Buildup with Two Reactivities

Influence of NO: HC-Ratio on Oxidant Production
x
Average Reactivity History for Commerce, 1969: Hydrocarbon
Consumption Scale from Altshuller
10
12
Average Reactivity History for El Monte, 1969:
Consumption Scale from Altshuller

Average Reactivity History for Commerce, 1969: Biological
Effects and Product Formation Scale from Altshuller
Hydrocarbon
13
Average Reactivity History for El Monte; 1969: Biological
Effects and Product Formation Scale from Altshuller

Variations of Diffusivity with Height for Different
Average Wind Speeds
14
15
Estimated Trajectory of Air Mass Arriving at El Monte,
1030 hours, 29 Sept. 1969

Estimated Trajectory of Air Mass Arriving at El Monte,
1130 hours, 29 Sept. 1969
16
17
Estimated Trajectory of Air Mass Arriving at El Monte,
1230 hours, 29 Sept. 1969

Estimated Trajectory of Air Mass Arriving at El Monte,
1330 hours, 29 Sept. 1969
18
19
Geographical Traffic Distribution in Los Angeles County,
ca. 1951

Los Angeles Traffic/Time Distributions ca. 1951
20
PAGE
12
15
16
17
26
29
32
34
36
43
44
46
47
67
70
71
72
73
77
78
v

-------
ILLUSTRATIONS (cont'd)
NO.
21
Geographical Distribution of Freeway Traffic in
Angeles Basin Area ca. 1970

Los Angeles Traffic/Time Distributions ca. 1970

Carbon Monoxide Concentration at Huntington Park on
Type 3 Day

C2H2/NOx Ratios for High Oxidant Days

CO/NO Ratios for Huntington Park 1968
x
CO/NO Ratios for Commerce 1969
x
(NO + N02) - Concentration Ground Level Huntington Park

on Type 3 Day
the Los
22

23
24

25
26

27
28
High-Reactivity Hydrocarbons Concentration on the
Type 3 Day

'Ozone Concentration at Huntington Park on Type 3 Day

Nitric Oxide Concentration at Huntington Park on Type 2
Day 1968. f = 1/4; r = 1/2
29
30
31
High Reactivity Hydrocarbon Concentration at Huntington
Park on Type 2 Days 1968. f = 1/4; r = 1/2

Ozone Concentration at Huntington Park on Type 2. Days 1968.
f = 1/4; r = 1/2
32
33
Reactive Hydrocarbon History Along the 1030 Trajectory.
f = 1/4; r = 1/2
34
Nitric Oxide History Along the 1030 Trajectory.
r = 1/2
f = 1/4;
35
Nitrogen Dioxide History Along the 1030 Trajectory.
f = 1/4; r = 1/2

Oxides of Nitrogen (NO + N02) History Along the 1030

Trajectory. f = 1/4; r = 1/2
36
37
Ozone History Along the 1030 Trajectory.
f = 1/4; r = 1/2
vi
PAGE
79
80
84
86
87
88
90
91
92
94
95
96
103
104
105
107
108

-------
NO.
'tABLES
1
Rate Coefficients for Trans-2-Butene/Nitttc Oxide System
2
Rate Coefficients for Expanded Model of the Hydrocarbon/
Nitric Oxide Mechanism
3
Influence
in Fig. 6
(OH + CO)
Minutes
of ioo ppm Carbori Monoxide
with Various Values of the
Reaction Rate Coefficients
on the System ShoWn
Ratio of (OH + HC)/
ReaCtion Time in
4
Hydrocarbon Reactivity Scales
5
Cbc 6400 Central Prdcessor Time to Run C3H6 + NO + hv
Chamber Experiment Simulation
6
Contaminants in Tons Per,bay from Major Sdurces Within
Los Angeles County in 1968
7
Results of Model Sensitivity Study Using 1969 El Monte Data
PAGE
20
30
39
4i
56
75
100
vii

-------
I.
INTRODUCTION
A.
BACKGROUND DISCUSSION
Atmospheric simulation models will playa central role in our
efforts to improve the quality of the urban air environment because
decision-makers must anticipate the outcomes of available courses of
action.
Although air pollution models are still under development,
their validation will provide the link needed to establish the source
emission limits required to achieve desired air quality standards.
This approach can be broadened to answer questions of social and economic
significance for different ameliorative strategies.
The anticipated evolution of modeling methods leads ever closer
to a direct contact with our immediate problems.
Whereas we are pre-
sently seeking a technical understanding of chemical interactions with
transport processes, the next step is integration of this understanding
in cost-benefit analyses.
(In view of the difficulties arising, probably
a more realistic goal is a cost-of-restoration study.)
Successive im~
provement and confirmation of m0deling techniques will offer quantitative
criteria for Fede'ral and State legislation to improve air quality by
controlling mobile sources of emissions.
Addressing more specific prob-
lems, local government needs criteria for urban planning to prescribe
population patterns and industrial land uses that tend to preserve air
~
quality.
Hence the local application of predictive modeling influences
the dispositions of both' fixed and mobile emitters.
At the finest level
of detail, a predictive ,model could provide the logic for the data
I

-------
processor in a real-time tactical system to guide decisions 'for temporary
source shutdowns that would avoid calling alerts after dangerous pollu-
tant buildups.
Although we would hope that preventive policies would preclude the
need for this kind of alarm system, it is possible that some communities
may be moving toward unacceptable limits faster than controls can be
imposed.
Implementation plans for abating air pollution problems require a
quantitative cause-and-effect relationship to estimate future air quality
in terms of source controls proposed for the region.
Mathematical models,
which are most likely to provide this needed connection, must ultimately
describe chemical transformations as well as meteorological transport.
Air quality criteria documents now exist for particulate matter, sulfur
oxides, carbon monoxide, photochemical oxidants, and hydrocarbons.
Each
of these materials is involved in chemical changes in urban atmospheres.
All except possibly CO (carbon monoxide) and some particulates are either
transformed or decay within a short enough time scale so that their
concentrations in the urban domain are substantially affected by chemical
reactions.
(Even both CO and particulates are now suspected of direct
involvement in the chemistry.)
Although our understanding of the de-
tailed mechanisms is far from complete, we do possess at this time a
workable mathematical framework for modeling atmospheric dispersion of
multi component pollutant systems undergoing coupled chemical reactions.
2

-------
Having recognized these modeling requirements imposed by imple-
mentation planning, how best can we exploit our available methods to
meet the immediate needs?
For a limited number of regions, we can test
some of the simplistic linear relationships connecting pollution with
emissions (1, 2).
For those areas that have had many sensors in the
field measuring air contaminants over the years, the relationships are
assumed to be derivable from piots of pollution levels versus emission
tonnages.
Global background concentration has been suggested as an
initial intercept point for the straight-line formulas.
For most regions, however, not even a simple quantitative rationale
can be used for implementation planning because neither time nor money
is available for deploying a network of sensors and collecting a signi-
ficant sample of monitoring data.
This dilemma suggests another approach:
the requirements that have been imposed can be met by instituting a
deliberate effort to adapt second-generation mathematical models to the
implementation-planning problem.
Admittedly, unresolved conflicts in
present experimental results may seem to indicate that this approach is
premature, but the urgency of the situation likely justifies parallel
activities.
The adaptation of the mathematical framework can proceed
simultaneously with laboratory investigations and field programs.
As
fundamental knowledge expands, the blanks in the framework can be filled.
In the meantime, thepie1iminary ftamework will already be in operation
examining atmospheric pollution relationships.
In addition, early
attempts to solve planning problems .with models will highlight specific
deficiencies and will provide valuable feedback to the research community.
3

-------
The two-way interaction between modeling and data-gathering can
be considered as mutual support between research activities and enforce-
ment activities.
The efforts put forth in abatement are thereby more
directly related to research efforts put forth on meteorology, chemistry,
and physics.
With the emerging complexities of economic factors, the
decision-maker must employ techniques more subtle than massive rollback.
The legislative approach based on flat prohibitions can be pressed to
some extent, but it ultimately meets some very stout barriers in the
real world.
A powerful combination of quantitative justification and
technological innovation will be needed to penetrate these ba~riers.
Optimization will be the key word; concern for computer expenditures.
will wane as the dollar costs of damage caused by air pollution and of
resources needed to control it are generally realized.
B.
DISPERSION MODELS BASED ON INERT POLLUTANTS
Atmospheric spreading of inert gaseous contaminant that is not
absorbed at the ground has been described by the various Gaussian plume
formulas.
Many of the equations for .concentration estimates originated
with the work of Sutton (3).
Subsequent applications of the formulas
for point and line sources state the Gaussian plume as an assumption,
but it has indeed been rigorously shown to be an approximate solution
to the transport equation with a constant diffusion coefficient and with
certain boundary conditions (4).
The restrictive conditions just recited
occur only for certain special situations in the atmosphere.
Hence,
these approximate solutions must be applied with great care.
4

-------
Prior to extensive application of these piume models~ Frerikiel
employed a puff model to study photochemical smog in Los Angeles (5).
A point source was assumed to he cehtered withiri each four-miie~square
in the grid pattern extending over the basin.
Nashville~ Tennessee was
the subject of some later papers by Pooler and Turner; who used Gaussian
formulations (6, 7).
Point sources were assumed in Ref; 6, but cross-
wind line sources were assumed in Ref. 7 to approximate the emission
emanating from each area element.
Checks against field measurements of
SOz
were made in each case.
Turner ailowed for a first-order reaction
in the gas phase to remove
SOz
from the air.
Extending the work to include
NO
x
(oxides of nitrogen)~ Clarke
divided Cincinnati into sixteen angular sectors, each having four radial
zones (8).
This grid was centered on a monitoring station.
Reacd6ris
were allowed to deplete
SOz ' but not
NO
x
Koogler later added
allowance for changing wind direction by periodically treating old
plumes as new line sources (9).
Also, the vertical confinement of an
elevated inversion layer was approximated along with height variation
of wind speed.
Evidentiy the
SOz
was not allowed to react.
Miiier
and Holzworth also considered a limited mixing layer by assuming a uni-
form vertical profile when the "effluent reaches the top cif the mixing
layer" (10).
The method was applied to Los Angeles, Washirigton; and
Nashville for
SOz
and
NO
x
A seasonal or monthly average model
was reported by Martin and Tikvart; to be applied to
CO
arid
SOz
5

-------
concentrations (11).
Following Turner's equations (7), a program was
developed for the IBM 1130 computer.
Analysis and tabulations of data to be used in Gaussian plume
formulas are also available.
The report for the St. Louis Dispersion
Study (12) gives further insights into tracer-spreading over urban areas
in contradistinction to open areas where many measurements have been
made.
Detailed working charts and numerous examples in Turner's work-
bQok (13) offer a real aid for practical estimation of atmospheric dis-
persions under the conditions outlined above.
For very approximate calculations of either peak or average pollu-
tant levels, a simple slab model can be employed for the air overlying
the urban area.
The ground is the lower boundary and the uppermost
extent of mixing (e.g., an elevated inversion base) is the upper boundary
of the slab.
Uniform vertical profiles are assumed, and horizontal flow
carries the polluted air away.
This concept was suggested by Smith for
order-of-magnitude estimates (14).
It was also discussed in Wanta's
review article (15) along with most of the Gaussian plume models referred
'to above.
In an effort to overcome the limitations of th'e Gaussian plume
assumptions, Lamb presented a Green's function approach to the solution
of the transport equation, with both area sources at the ground and
volumetric sources due to reactions (16).
Two further features included
in the model were time dependence and absorption at the ground.
(The
latter generalization of boundary conditions might be especially
6

-------
important for pollutants such as
NOx ' S02 ' and
03 ' which combine
with surfaces or with moisture on surfaces.)
Recent work at Stanford Research Institute has been directed to-
ward a simple and practical urban diffusion model for carbon monoxide (17).
Its objectives include not only hour~to-hour predictions, but also long-
term climatological effects.
Traffic distributions in time and space
are inputs to the mod~l and concentration history at some receptor point
is an output.
This approach is still in the developmental stage and
will be improved with the aid of validation tests against field data to
account for peculiarities of sampling sites and their microclimates.
Combination of the philosophy of this approach with our methods of treat-
ing photochemical reactions may provide an urban modeling technique that
could be used for planning and abatement.
Puff models such as that in Ref. 5 employ Gaussian spread para-
meters, but by subdividing the effluent into discrete contributions,
they avoid the restrictions of steady-state assumptions that limit the
plume models just described.
A recently documented application of a
puff model for urban diffusion is that of Roberts, et. a1. (18).
It is
capable of accounting for transient conditions in wind, stability, and
mixing height.
Continuous emissions are approximated by a series of
instantaneous releases to form the puffs.
The model, which has the
capability of describing multiple area sources, has been validated for
the City of Chicago by comparison with over 10,000 hourly averages of
sulfur dioxide concentration.
7

-------
I
C.
RELATED WORK ON PHOTOCHEMICAL SMOG MODELING
Models for photochemical air pollution require extensions of ear-
lier methods.
Coupled chemical reactions and radiation attenuation in
the ultraviolet introduce nonlinearities into the analysis.
As a conse-
quence, the superposition of linear solutions from collections of point,
line, or finite-area sources may inaccurately describe the chemical
interactions with meteorological conditions in the air basin.
Chemical
evolution of pollutants, therefore, demands a step-by-step description
to reflect the cumulative effects of the processes occurring.
Efforts aimed at overcoming the limitations have resulted in methods
that range from modified classical treatments to entirely new formulations.
,
Because detailed chemical descriptions were not yet available, the pre-
viously referenced work of Frenkiel (5) on the Los Angeles basin stresses
diffusive aspects of the problem by treating plume trajectories from a
collection of puff sources.
Other early work (i9) made use of simplified
chemistry in an analogue computer solution for composition histories in
a network of homogeneously mixed cells.
The horizontal faces of each
cell were assumed to be the inversion base and the ground respectively. .
This approach somewhat resembles that of Ref. 14.
Suggestions have been'
made that chemical changes be superimposed on a dispersion model like
that of Frenkiel's (5), but only inert gases have been treated.
Friedlander and Seinfeld, recognizing that the generality needed
could be provided by finite difference numerical solutions to the diffu- ,
sion equations, developed their dynamic model of photochemical smog (20).
8

-------
This mpdel allowed for nonlinear chemi~ali~teractions"but the Lagrangian
profile similarity required by the diffu~ion scheme ~till m~y be too re~
strictive to allow full freedom in$pe<::ifying grpund bO!-lndary conditio~s.
Tests of the technique for photoche~ical smog with actual emission ipven~
tory data (in the form of distributed gro~nd boundary condttiom;) have
not been reported.
The models developed by Calvert (2+) and by WaYPe, et al. (2~)
stress chemical kinetic mechanism.
In the former, the photochemical
smog mechanism is reduced to 17 ste?S and in the latter to 31 steps.
In the larger mechanism, care is t~~en to describe pl~u~ible rea,ctiQ~s
for the C3H6/NOx/ air system, but it is ultimately applied to the atmos-
pheric case where dozens of smog-forming hydrocarbon~ are invQlved.
To
preserve a consistent level of detail, the number of reactions m4st be
increased by a large factor; however, this is avoided by adj~sting the
rate constants to obtain observed results.
Homogeneously stirred air
parcels following wind trajectorie~ ar~ assumed in order to retain first-
order, ordinary differential equations.
Chemical kinetic studies have
been carried out by numerical integrations of the coupled rate equations
for conditions appropriate to laboratory chamber experiments in the
absence of diffusion.
Other computer investigations of this genera+
nature include the work of the ~roup headed by Dr. Bernard Weinstock of
Ford Motor Company, and of Dr. Karl Westberg at the Aerospace Corpor-
ation
(23) .
These approaches follow the philosoPhY of studying a pro-
posed chemical scheme by modeling laboratory data.
Modifications are
usually necessary for applications to the atmosphere.
9

-------
Three-dimensional, time-dependent methods (24, 25) have been pro-
posed recently, but results , for reactive atmospheres have not been re-
ported at this writing.
Simplified chemistry must be employed in each
of these approaches because of the emphasis on details of advection and
diffusion.
Unfortunately, the body of data for most air basins falls
short of the input requirements for any transport formulation of this
complexity.
In some cases, it maybe difficult to avoid the problem of
allowing too many unspecified parameters to obscure the physically based
portions of the calculation.
*
coordinate frame
One of the new methods employs an Eulerian
which introduces the chronic problem of artificial
(or numerical) diffusion.
Small time and space steps are the only means
suggested heretofore to remedy this problem.
The other method uses a
discretized representation of species concentrations in a Lagrangian

*
frame.
For multicomponent systems, the latter type of approach has
previously been limited because of the large quantity of rapid access
memory storage needed for each species.
Both of these problems have
been recognized for some time with three-dimensional, time-dependent
calculations.
More powerful computers and novel algorithms may well
be required for their solutions.
D.
OVERVIEW OF THE COMBINED PHOTOCHEMICAL/DIFFUSION MODEL
Following a desire to incorporate the best aspects of some pre-
vious work, we have endeavored to balance the detail between the chemical
*
Lagrangian coordinates refer to a fiuid mass
and space in contrast with an Eulerian frame
relative to a fixed coordinate system.
which is followed in time
which has fluid moving
10

-------
and meteorological formulations in our model.
The development method-
ology begins with pure chemical kinetics validations using laboratory
data from irradiation chamber experiments.
This development has evolved
through two stages--one involving only seven reactions and another em-
p10ying twelve reactions.
Both are based on a lumped-parameter approach
that includes groups of parallel reactions that perform a common function
into a single effective kinetic step.
Another aspect of the lumping is
the collapse of a reaction chain into a rate-controlling step.
Non-
stoichiometric product yields sometimes occur with these simplifications.
The application of the chemical schemes to atmospheric phenomena
requires a diffusion formulation that reflects time-dependence and spa-
tia1 variability of meteorological conditions.
An attempt has been made
to keep the mathematical description near the level of detail and preci-
sion of the observational data.
This has resulted in a Lagrangian air
parcel formulation with finite-rate vertical diffusion.
The approach
avoids the artificial numerical diffusion because it uses natural (or
so-called "intrinsic") coordinates that are aligned with fluid motion.
This permits us to include upward dispersion and chemical change simu1-
taneously.
Figure 1 schematically illustrates the main features of the
formulation.
High-speed memory requirements are limited by allowing
sequential point-by-point output of the history of the air parcel.
Some insights into model requirements are gained by examining some
length and time scales characteristic of the Los Angeles basin, the region
chosen as a prototype for validation.
The horizontal scale of the air
region is tens of kilometers, but the distance from ground to inversion
11

-------
--POLLUTANT INFLUXES AT ANY
E L EV A TlON (INCLUDING TH E ~"
GROUND) ARE IMPOSED BY THE "-'-
, ,
EMISSION SOURCE FUNCTIONS '~,
i
",\1//
~D~-

...... .......

/ I , \ ""

----

--------
SUNLIGHT IS GIVEN AS
A FUNCTION OF TIME
/
c:::.
It;)
co
C'..
C\J
I
~
u
Figure 1. Schematic of Diffusion Model for Air Pollution Simulation
12

-------
base is usually less than one-half kilometer during smog episodes.
Dur-
ing late morning buildup of secondary pollutants, winds are only three or
four kilometers per hour and the vertical diffusion coefficient averages
-2 2
approximately 10 km /hr or less.
High reactivity hydrocarbons are
halfway photo-oxidized about two or three hours after their appearance in
the morning.
If vertical diffusion approximates a random walk, the charac-
teristic diffusion time from the ground to the inversion base can be one
to four hours.
A ten-kilometer downwind drift also occurs within this
interval.
Consequently, we conclude that a smog event must be modeled by
treating simultaneously the processes of vertical diffusion, horizontal
advection, and finite rate photochemistry.
This paper describes the evolution and validation of our mathe-
matica1 model for photochemical smog.
The methodology stresses f1exi-
bi1ity of input specifications, efficiency in computation, and conformity
with observable phenomena.
The central sections of the paper deal suc-
cessive1y with simplified chemical kinetic schemes, finite-difference
formulation, and atmospheric validation tests.
In the chemical kinetic
discussions, the two versions of mechanisms are developed.
Novel app1i-
cations of Pade approximants are covered in the mathematical section in
some detail.
1968 and 1969 Los Angeles basin data form the bases of
numerical tests described in the validation section.
Tests are out-
lined using a simple slab model for stagnant conditions and the moving
parcel model for wind conditions.
The concluding section establishes
some future directions of research and application that are suggested
by the previous course of development.
13

-------
.
II.
SOME SIMPLIFIED KINETIC MECHANISMS
A.
THE ORIGINAL SCHEME
The photochemical reactions lead to most of the uniquely new require-
ments placed on this model.
Before treating atmospheric studies, we must
understand the action of the chemistry and describe it simply enough to
keep the ultimate computer requirements within reasonable bounds.
Fi rs t ,
an extremely simple version of a kinetic mechanism (26) will be explained
aI1.d examined.
Experimental chamber results have been computer analyzed to pro-
vide a kinetic model for the Los Angeles basin studies.
In developing
the model scheme, we began by trying combinations of elementary reaction
steps that have been suggested previously (27-32).
After many successive
simplifications, we obtained the seven species by seven reaction model
mechanism which is the version to be discussed first.
Simultaneous solu-
tions of the coupled rate equations guided the evolution of the repre-
sentation.
We retained only those classes of rate-controlling steps
needed to replicate observed concentration histories.
On the other hand,
enough generality is included to validate the assumptions over a range
of composition and light intensity conditions representative of photo-
chemical air pollution.
Hence, no claim is made that the scheme is a
complete, mechanistic embodiment of the available chemical kinetic hypo-
theses.
Figure 2 illustrates the lumped-parameter kinetics by means of a
block diagram and Figs. 3 and 4 show concentration histories in a trans-
2-Butene/nitric oxide system which illustrate the action.
Symbolically,
14

-------
  r    """"    """" CO
       E    t
   h.,     .... RO  I
         I
   l t        I
          I
 NO    N02  ~~  R02
     l  
     ,.      
         +2 
S ~          
           
U    +02+M 3    PAN  
R    l      
C           
E ~          
     \...   E   
 HC l  \... l      ~
          \ 
          I 
L = RATE CONSTANT FROM LITERATURE
E = RATE CONSTANT ESTIMATED
Figure 2.
*
Original Reaction Mechanism
*
""
"-
..,.
<6
......
I
:c:
~
~
ALDEHYDE
Stoichiometry imbalances may occur because of lumped parameter
assumptions in the schematic diagram.
15

-------
10 ppm -MODEL t'i;)
  EXPERIMENT (33) 0')
  t'i;)
  0')
W   N
~ 8 0 TRANS-2-BUTENE I
:<::
  "<:
....  6. NITROGEN DIOXIDE 
Z  0 NITRIC OXIDE 
0   
....   
~   
a:: 4  
....  
Z   
w   
U   
Z 2  
0   
u   
o
o
2
4
6
8
TIME
10
12
14
16 m in
Figure 3.
Computed and Observed Reactant Histories for the Trans-2-
Butene/Nitric Oxide System (Rate Coefficients in Table 1)
16

-------
3 ppm
z
o
.....
<
at:
.....
Z
w
u
Z
o
u
2
o
o
Figure 4.
o
o c:::,
~
t<:J
~
,...,
~~
~
o
MODEL
EXPERIMENT (33)
o
OBSERVED OZONE
o FIN Ale 0 NeE N T RAT I 0 N--
6
o
8
10
1 2
TIME
14
16
18
20 m in
Computed and Observed Product Histories for the Trans-2-
Butene/Nitric Oxide System (Same Conditions as Those for
Figure 3)
17

-------
the diagram shows species as boxes and reactions as path intersections.
In Fig. Z, the emitter is labeled "SOURCE" and sunlight is denoted by
"hv."
The experiment (33) illustrated in Figs. 3 and 4 replaces the
source with a premixed charge of
HC
and
NO
and employs simulated
sunlight.
Examination of Fig. Z shows that the
NOZ
photodissociates to
contribute O-atoms and
NO .
The O-atoms attack the hydrocarbon and
produce free radicals represented here by
ROZ .
In turn, the
to
ROZ
This path
provides an oxygen source for reconversion of
NO
NOZ .
augments the already rapid reaction of ozone with
NO
to form
N02 .
with
contributes most of the ozone;
Three-body association of
o
02
2
with
R02
also provides
however, an abstraction reaction of

*
ozone.
Nitrate formation removes
N02
in chain termination reactions.
One minor branch of the chain is included in Fig. 2 as the production
of peroxyacetyl nitrate (PAN).
This is included in the model because
PAN has been established to be a phytotoxicant.
Following the concentration histories in Figs. 3 and 4, we note
that the hydrocarbon disappearance contributes
R02
which oxidizes
NO
up to
N02 .
When this induction phase is complete, ozone concentration
rises because there is no longer any
NO
to compete for the ozone.
Nitrate formation and photodissociation then take over to reverse the
*
In the more advanced version of the model, this abstraction reaction
is dropped because it is energetically unfavorable. It is needed
here to provide ozone buildup at late time.
18

-------
rising trend in
NOZ .
In the later stages, ozone becomes a serious
competitor with oxygen atoms in the attack on hydrocarbons.
Before we assess the validity of the calculations, we shall enumer-
ate some of the processes which are absorbed in certain overall steps so
that the simplicity of the scheme is preserved for ultimate economy in
computation.
First, free radicals like
ROZ
or
OH
also attack hydro-
carbons so that the
 + HC
and
03 + HC
rates must be artificially
elevated.
Second, aldehyde photolysis (34) is an additional branch of
the mechanism that must be absorbed in the rates and stoichiometry of a
lumped parameter scheme.
Third, inorganic particulate nitrate products
would be added if it were necessary to complete the material balance to
account for nitrogen (35).
Fourth, radical regeneration involving
CO
may be implicitly absorbed in the chain branching factor applied to
ROZ (36).
*
Curves in Figs. 3 and 4 illustrate calculated results
for the
conditions of one of Tuesday's experiments.
Table 1 details the reac-
tion stoichiometry and rate constants for the calculation.
The calculated
photo-oxidation rates for the main reactants are somewhat slow around 8
minutes time and the appearance rate of PAN is too fast between lZ and
16 minutes time.
This results from a compromise needed because of a
certain inflexibility in the schematic kinetics.
The calculation employs
*
Quasi-stationarity is assumed for O-atom and ROZ-radicals to facili-

tate calculations. Numerical tests confirm the validity of these
approximations.
19

-------
Reaction
TABLE 1

RATE COEFFICIENTS FOR TRANS-2-BUTENEjNITRIC OXIDE SYSTEM

(Stoichiometry imbalances occur in some reaction steps
because of lumped parameter kinetic assumptions.)

Nominal Va1ues*
**
Validation Values
N
o
hv + N02 + NO + 0
o + 02 + M + 03 + M
0.072 to 0.55
. -1
m1.n
0.072 to 0.55
. -1
m1.n
03 + NO + N02 + 02
o + C4HS + 2.5 R02 + 0.12 Ald.
-5 -2 -1
1.32 x 10 ppm min
-1 -1
21. S ppm min
-5 -2 -1
1.32 x 10 ppm min
-1 -1
21. S ppm min
03 + C4HS + 2.5 R02 + 0.12 Ald.
4 -1 -1
3.34 x 10 ppm min

4.2 x 10-2 to
-1 -1.-1
6.4 x 10 ppm m1.n
5 -1 -1
1.11 x 10 ppm min
-1 -1 -1
6 x 10 ppm min
RO 2 + NO + NO 2 + RO
R02 + 02 + 0.5 03
-1 -1
.::. 50 ppm min
-1 -1
.::. 50 ppm min
-1 -1
50 ppm min
-5 -1 -1
3 x 10 ppm min
R02 + N02 + 0.67 PAN
-1 -1
.::. 50 ppm min
-1 . -1
1 ppm m1.n
*
**
See Sec. II for sources.
Values consistent with experimental measurement (33).

-------
established values of rates from the literature for the three inorganic
reactions. The NOZ photolysis was calibrated (33) according to the

light intensity at 0.37 min-l and the other two reaction rate constants
were obtained from Ref. 37, assuming an ambient temperature of Z7C.
In order to obtain observed oxidation rates, the O-atom plus
C4HS
rate
was increased nearly fourfold to absorb the competing radical reactions
and the ozone on
C4HS
rate fell near the upper end of measured range.
Nominal values for these reactions are obtained from the literature (30).
Collision theory estimates yield upper limit nominal values for the last
three reactions listed in Table 1.
The discussion has centered on a single experiment to illustrate
the validation of the simple scheme.
Other experiments bring out special
features.
For example, the ozone reaction with a hydrocarbon is actually
far more complex than a single step because somewhat lower rate values
for
03 + C4HS
(still in the nominal range shown in Table 1) are ob-
served in experiments involving
C4HS/NOZ
systems under irradiation.
Apart from this complication, the set of rates in Table 1 exhibit good
modeling results near the value of initial C4HS/NO-ratio employed in
the prototype experiment.
These rates also give excellent agreement
for experimental light intensities both below and above that used for
Fig. 3 (see Table 1 for range).
Several features of this particular system, however, are atypical
of photochemical air pollution.
Such features include the reactivity,
the concentration levels, the time scales, and the organic nitrate
Zl

-------
production.
Trans-2-Butene is far more reactive than the average of
atmospheric hydrocarbons.
Even omitting low reactivity components
(methane, ethane, and acetylene) from automotive exhaust compositions,
we find that the remaining fraction of hydrocarbons has a weighted
average reactivity index (38) many times less than that of the butenes.
Regarding concentration levels, the experiment (33) cited begins with
10 ppm reactive hydrocarbon whereas atmospheric values are ten times
less.
As a result of these two differences, smog reaction times are
close to 20 times longer than those of the experiment.
Finally the PAN
yields from butene oxidation exceed those of the atmospheric reactants.
Despite these limitations, Ref. 33 covers a broader scope of parametric
variables than most experiments reported in the literature.
Therefore,
it gives many validation benchmarks for various compositions and light
intensities.
Since the propylene-nitric oxide system is more nearly
like reactive systems in air pollution, validation tests were conducted
on that system also.
Again, measured composition behavior from chamber
irradiation tests (39, 40) serves as a basis for modifying some of the
rate constants to absorb the additional effects.
Lower oxidation rates
and lower PAN yields occur with propylene compared with trans-2-butene.
Lumped rate constants for 0 + C3H6 and
4 -1 -1 -1
4.97 x 10 and 1.8 x 10 ppm min
03 + C3H6
were found to be
respectively, for use with this
simple mechanism.
In the more complex mechanism to follow the liter-
ature values are adhered to.
In viewing the transition from the simple to the complex mecha-
nisms, one should realize what the limitations and objectives are for
22

-------
the simple mechanism.
It provides a description of pure hydrocarbon
photooxidation with nitric oxide within a rather restricted range of
initial mixtures typical of polluted air; however, it describes well
the overall rate dependence on light intensity.
The rate constants
for organic reaction steps must be changed for different hydrocarbons
as evidenced by the changes cited above needed to fit the propylene
results.
Major objectives of the more complex treatment discussed in
the following sections are to relax the restrictions on initial mixture
composition and to describe the chain initiating steps individually
(instead of lumping them in the 0 + HC-rate) .
B.
ADDITION OF MORE REALISTIC OXIDATION CHAINS
As alluded to above, it has been known for some time that hydro-
carbon consumption rates observed in chamber experiments cannot be ex-
p1ained by ozone and oxygen atom attack alone.
This is discussed in
the review by Altshu11er and Bufa1ini (30) where it is noted that Schuck
and Doyle (41) termed the disparity an "excess rate."
Our previous mode1-
ing work treated this by increasing both the
03
and O-atom rates of
reaction with hydrocarbon.
To use known rate constants to a maximum extent in the present
work, we have added a hydrocarbon oxidation chain to reflect the attack
of
RO
upon the hydrocarbon.
Because of its suspected dominance (42, 43),
hydroxyl radical (OH) was assumed to be the only
RO
reacting with the
hydrocarbon.
23

-------
Following the inorganic cycle formed by
hv + NOZ ~ NO +  . 1


 + 0z + M ~ 03 + M
*
(1)
NO + 03 ~ NOZ + 0z
( Z)
we have allowed each hydrocarbon oxidation to generate multiple
ROZ
radicals as expressed by the b-factors in the steps
 + HC ~ bl (ROZ)
(3)
OH + HC ~ bZ (ROZ)
(4)
03 + HC ~ b3(ROZ)
(5)
Subsequent conversion of
NO
to
NOZ
was assumed to occur via
ROZ + NO ~ NOZ + d(OH)
(6)
where
d
expresses that fraction of the conversion responsible for
returning hydroxyl to the system.
Note that reactions (4) and (6) form something of a closed loop
and that a stability requirement like
bZd < 1
may be needed to prevent
ROZ-runaway.
This is not a precise requirement because of the variety
of external factors that influence the flow rate of free radicals around
*
The two reaction steps bracketed by (1) are combined by assuming O-atom
stationarity internal to the logic of the computer program. Hence
reaction (1) nets the system hv + 0z + NOZ ~ NO + 03 .
Z4

-------
the loop.
Some of the
R02
is formed by the other two reactions, and
there are radical removal processes in the chain termination steps we
discuss in the following paragraph.
Both
R02
and
OR
are held in check by removal steps that ter-
minate the chains.
We continue to use some lumped parameter reactions
such as
R02 + N02 -+- c(PAN)
(7)
and some elementary reactions like
OR + NO + M -+- RONO + M
(8)
OR + NO 2 + M -+- RNO 3 + M
(9)
This rounds out the expanded mechanism.
Figure 5 shows it in the form
of a schematic diagram.
In summary, the main changes from the scheme described in Sec. II A
are:
addition of radical species
RO
(treated as OR), the provision
for a multiplicity of hydrocarbons (not shown in equations), and the
elimination of ozone production from an
R02
reaction.
The multiplicity
of hydrocarbons is done by adding parallel reactions to (3), (4), and (5).
The omission of the ozone production reaction is justified on the basis
of its suspected endothermicity (23).
For our initial validation tests, we tried the rate constants cdm-
piled and estimated by Westberg and Cohen (23).
Stoichiometric coeffi-
cients
b l' b 2' b 3' and
d
were determined by hand-calculation analysis
25

-------
r-----------~-_!_-I
I I I
: r- - -... - -, I
I h &I
I
"
I
::
NO
N02
RO
(OH)
R02
(H02)

+02+M
3
PAN
HC
I I I t
I I I
I I I
r--~-, I I I
: HC/ L--_i_---_.t_-______l_____J
I I
L - - _J
Figure 5. Expanded Kinetic Mechanism
26

-------
of some of the propylene data represented by Ref. 39.
We found that
bd ~ I , where
b
is a composite branching factor, and
b ~ 2 in order
to explain the decay rate of
NO
compared with that of propylene.
Explosions of R02-concentration characterized some early choices
of bd-combinations because of the positive feedback loop involving rad-
ical reactions shown in Fig. 5.
Since these occurred in the first few
seconds of real time, they were difficult to detect.
This is unexpected
because of the longer time scales usually associated with the system.
Sudden drops of
NO
and
HC
(to some nonzero levels) occurred during
the first minute followed by the dynamic equilibrium between
and
3
with a slow decay of hydrocarbon.
NO, N02'
The underlying pathology was
discovered by rerunning with special diagnostic outputs.
Nominal rate constants were adjusted to reconcile computed results
with measured values.
For example, the (OH + HC)-rate was cut to about
one-third the estimated value and the (NO + R02)-rate was increased
eightfold.
Reaction rates which have been reported individually in the
literature were held at their nominal values including the (0 + HC)-rate
which we had to increase many-fold in Sec. II A.
Also, the retention
of reaction (5) was still necessary to describe the continued C3H6-decay
after the near disappearance of
NO .
In order to reproduce the late-time behavior of
N02
and propylene,
we included chain termination reactions in addition to those indicated
in Fig. 5.
In their more recent review (44), Altshuller and Bufalini
27

-------
point out that
HONO
might be formed by the reaction with water vapor
NO + NOZ + HZO + ZHONO
(10)
which is likely to proceed in the two steps
NO + NOZ + NZ03
(11)
NZ03 + HZO + ZHONO
(12)
A possible source of OH-radical (4Z, 43) is the photodissociation of
HONO
hv + HONO + OH + NO
(13)
Figure 6 shows the computed concentration history using this
scheme to describe the experimental observations of Altshuller, et al.
(39) and Table 2 summarizes the reaction rate constants that were used.
The column in Table 2 labeled "nominal" gives the values we started from
on the basis of tabulations in Ref. 23.
Following an empirical proce-
dure, our calculations effectively combined HZO-concentrations with the

rate constant for reaction (iO) as indicated; therefore no comparable
nominal value is shown.
Higher levels of precision than that shown in
Fig. 6 were not among our objectives, since a detailed investigation
of propylene is not justified for describing the potpourri of hydro-
carbons in the urban atmosphere.
Orders of magnitude for conversion
times and levels are sufficiently good to proceed from here.
The objec-
tive that we have fulfilled is to represent the so-called "excess rate"
Z8

-------
N
\.0
2.5 p p m
z
o
.....
<
~
.....
Z
w
u
Z
o
u
2.0
.. PROPYLENE
. NITRIC OXIDE
. NITROGEN DIOXIDE
T OZONE
I ~
~
EXPERIMENTAL ~
POINTS OF ~
ALTSHULLER, et 011391 "'<:
1.5
160 min
03
1.0
T
0.5
.
o
o
.
.
.
120
100
140
20
40
60
80
TIME
Figure 6.
Computed Curves Compared With Experimental Points for
the Propylene/Nitrogen Oxides System

-------
lJ.J
o
TABLE 2
"
RATE COEFFICIENTS FOR EXPANDED MODEL OF THE HYDROCARBON/NITRIC OXIDE MECHANISM
Reaction
(Stoichiometry imbalances may occur because of lumped parameter assumptions.)

Nominal Values for
Propylene System (23)
Model Values from Validation
hv + N02 + NO + 0
o (+ 02) + M + 03 + M
-1
0.4 min
-1
0.4 min
-5
1. 32 x 10
-2 . -1
ppm m1n
-5 -2.-1
1.32 x 10 ppm m1n
-1 -1
22-44 ppm min
-1 -1
6100 ppm min
-1 -1
244 ppm min
R02 + N02 + PAN
*
OH + NO + HN02
-1 -1
40 ppm min
-1 -1
6100 ppm min
-1 -1
80 ppm min
-1 -1
1500 ppm min
-1 . -1
6 ppm m1n
-1 -1
10 ppm min
-1 -1
30 ppm min
-1 -1
122 ppm min
-1 -1
122 ppm min
03 + NO + N02 (+ 02)
o + HC + 2R02
OH + HC + 2R02
R02 + NO + N02 + 0.5 OH
*
OH + N02 + HN03
03 + HC + R02
-1 -1
99 ppm min
-1 -1
300 ppm min
**
(H20 +) NO + N02 + 2HN02
hv + HN02 + NO + OH
-1 -1
0.0125 ppm min
-1 -1
0.01 ppm min

0.001 min-1
-1 . -1
0.00927 - 0.0125 ppm m1n
*
Rate constant lumps third body concentration
** .
Water vapor lumped into rate coefficient

-------
of hydrocarbon oxidation with added reactions instead of artificially
increasing the O-atom rate with hydrocarbon.
C.
INFLUENCE OF INITIAL COMPOSITION
1.
Synergism Between Hydrocarbons
The fact that free radicals produced in the photooxidation of one
hydrocarbon can accelerate the attack on a coexistent hydrocarbon has
been illustrated with experimental findings by Altshuller and Bufalini
(44) .
Because of the limited understanding of detailed interactive
mechanisms, we limited our multiple hydrocarbon investigation to a
simple parametric study.
Using a truncated version of the mechanism
in Table 1, we added a parallel series of oxidation steps.
This scheme
is shown in the flow chart of Fig. 5 with dashed lines along the bottom
portion of the diagram.
In the parametric study, the same initial values of total hydro-
carbon and nitric oxide as those in Fig. 6 were employed.
The hydro-
carbon, however, was partitioned into two hypothetical compounds, one
having triple the (OH + HC) rate constant and the other having one-third
the (OH + HC) rate constant as propylene.
The compound with the tripled
rate is called species "B" and the one with the decreased rate is called
species "A."
All other reactions in the scheme are the same in all
respects as their counterparts in the (C3H6 + NOx)-system.
Figure 7 shows the hydrocarbon decay curves from the parametric
study.
On the same coordinates, we plot curves for model calculations
31

-------
SPECIES 'A' HAS AN (OH+HCI-RATE ONE-THIRD THAT OF C3H6
SPECIES '8' HAS AN (OH+HC)-RATE THREE TIMES THAT OF C3H6
ppm
32
2.0
~
......
.......
""
,
"
k ,C'
~. ~L
-1, '\ .,
xk ~.p
~ <9, , {;,.-v

,
,
,
"
"
z
o
.....
<
IX
.....
Z
w
U
Z
o
u
,
U
::I:
1.5
1.0
0.5
o
o
---.J
100 120
20
40
60
80
TIME
I
140
Figure 7. Hydrocarbon Decay With Two Reactivities
.-,
"-
"-
lr,)
q
I
<:
"'t
160 m in

-------
of pure hydrocarbon "A", pure hydrocarbon "B", and pure propylene for
comparative purposes with the half-and-half mixture of hypothetical
compounds.
The most interesting aspect of Fig. 7 is that the mixture
decays faster than propylene even though it contains equal quantities
of "A" and "B" which bracket propylene sYIml1.etrically.
The coupling
between the two hydrocarbons occurs via the
ROZ
conversion of
NO
to
NOZ
and the production of
OH .
Evidently the combination of the
rapid incubation (afforded by the reactive hydrocarbon) with the twofold
chain-branching is sufficient to increase the decay rate over that of
pure propylene.
Figure 8 shows corresponding curves for ozone buildups predicted
in the computer experiment.
Again the combination seems to exceed the
pure propylene in its rapidity to produce ozone.
This occurs because
of the enhanced conversion rate of nitric oxide to nitrogen dioxide
stimulated by the early abundance of
ROZ
generated by the high-
reactivity fraction.
These findings illustrate a plausible mechanism for the interaction
of multiple hydrocarbons.
In future applications of our photochemical/
diffusion model, this type of representation is likely to be more real-
is tic than a super-detailed single hydrocarbon mechanism with many
adjustable constants.
Also, other radical interactions like
RO Z + HC
and
RC03 + HC
might provide plausible coupling paths (44) in addition
to the hydroxyl attack on the hydrocarbon.
Indeed, other forms of cou-
pIing may favor the slower reacting hydrocarbon in a similar numerical
experiment with a half-and-half mixture.
33

-------
HYDROCARBON 'A' HAS AN (OH+HC)-RATE ONE-THIRD
THAT OF C3H6

HYDROCARBON 'B' HAS AN (OH+HC)-RATE THREE TIMES
THAT OF C3H6

ppm
1.0
z
o
~
<
CI:
~
Z
w 0.5
u
Z
o
u
,
M
o
o
o
34
.".,~
","
./
~~ ,;I"
~ ./
~b/
G'" /
/
/
/
/
/
/
./
./
PURE 'A'
20
40
60
80
TIME
100
140
160min
120
Figure 8.
Ozone Buildup With Two Reactivities
C\)
('...
('...
I.t;)
C\)
I
::z::
"I;
I

-------
'2.
Modeling the Influence of NO IRC-ratio on Oxidant Production
x
Our main purpose in including the chain termination results for
nitrogen oxides in the previous subsection was to improve the modeling
of initial mixture effects.
It will be recalled that in Sec. II A we
issued a caveat restricting the seven-step mechanism to a narrow range
of
NO IRC
x
ratios.
Seinfeld (45) pointed out that the slope of the
curve of peak oxidant versus
NO IRC-ratio did not even have the correct
x
sign.
If modeling is to be used to evaluate hypothetical abatement
strategies, it is clear that this deficiency must be remedied.
*
Figure 9 shows the results from the twelve-step
mechanism given
in Table 2.
Experimental results for pure and mixed hydrocarbons are
shown on this plot of peak oxidant versus NO IRC-ratio.
x
The model
mechanism displays a monotonically declining trend of oxidant production
as the oxides of nitrogen increase.
Both of the pure hydrocarbons
measured by Altshuller, et al., show peaks at widely separated values
of the mixture ratio.
It seems plausible then that the typical mixture
of atmospheric pollutant hydrocarbons should show a decrease of oxidant
with increasing NO IRC-ratio.
x
This is supported by the fact that the
relative abundance of hydrocarbon species decreases with increasing
reactivity.
Now since the low reactivity species peak at lower NO IRc-
x
ratios the combined effect should give a negative slope.
The two plots on Fig. 9 of oxidant production from diluted and
irradiated automobile exhaust (47, 48) both have negative slopes com-
parable to that of the model.
As stated earlier, our purpose in using
*
Stationary state treatment of O-atoms reduces this to eleven.
35

-------
36
z
o
~
-<
a::
~
Z
o
u
~
z
-<
o
><
o
ppm
1.2
3 ppm n-C4Hl0
(461
1 TO 2 ppm NMHC.
.', AUTO/EXHAUST (471

'~

."
,
, LOS ANGELES
, INVENTORY
, RATIO
AUTO EXHAUST' .
2 ppm NMHC. ,
w-. (481 ,
~!.I . '
"
.
0.5
1.0
0.8
0.6
0.4
0.2
o
o
,
,
,
I',

2 ppm HC ~"
MODel
RESULTS..
1.0
""
cv
cv
C:>
C\J
I
:e:
"'>:
,
,
,
~
1.5
MOLE RATIO NOX TO HYDROCARBON

NMHC:NON-METHANE HYDROCARBON
..THIS CURVE IS LOWERED CONSIDERABLY BY OUR
SUBSEQUENT ADOPTION OF ONE-HALF THE
PROPYLENE RATES FOR ATMOSPHERIC CALCULATIONS
Figure 9.
Influence of NO :HC-Ratio on Oxidant Production
x

-------
chamber data for propylene to validate the mechanism is to capture the
main features of the experiments that apply to the atmosphere.
1ft on
the other handt propylene were the subject of our studYt we would pro-
ceed to expand on the mechanism to get the proper curve shape shown in
Fig. 9.
Having subjected the lZ-step mechanism to these laboratory testst
we use it in its present form for atmospheric validation studies des-
cribed in a later section.
3.
Examination of Carbon Monoxide Effects
Recent work (43t 49t 50) of photochemistry of smog has suggested
that carbon monoxide may playa role in accelerating the photooxidation
of hydrocarbon/nitric oxide mixtures.
The mechanism suggested is
OH + CO -r CO Z + H
(14)
H + 0z + M -r HOZ + M
(15)
HOZ + NO -r OH + NOZ
(16)
(HZO +) HOZ + NOZ -r ZHNOZ
(17)
Reaction (15) is postulated to contribute
HOZ
rapidly as it responds
to the presence of H-atomt and reaction (16) enhances the NO-to-NOZ
conversion already occurring in reaction (6).
Likewiset the hydroxyl
radical supplied by reaction (16) goes on to react with the hydrocarbon
in reaction (4) t producing ROZ-radicals in a branched chain already des-
cribed.
Reaction (17) is a chain termination step suggested for
HOZ .
37

-------
The key feature we wish to examine in this alternate path is the
competition of
co
with hydrocarbon for the hydroxyl radicals.
The
rate constant for
OH + C3H6
suggested in Ref. 23 is approximately
equal to that suggested in Ref. 49 for
00+00.
We tried a wide range
of (OH + CO)-rates holding the basic system at the values in Table 1.
Since reaction (15) is fast, reactions (14) and (15) were added to give
the overall reaction
02 + OH + co ~ C02 + H02
(18)
The rate constant for reaction (16) was taken to be the same as its
R02-analogue, reaction (6), and the rate constant for reaction (17) was
-1 -1
assigned the value of 1.2 ppm min based on the estimate in Ref. 23.
The species
02
is carried implicitly in the calculation, and the rate
constant for reaction (18) is varied parametrically for this study.
Beginning with (CO + OH)-values at the level suggested in Ref. 49,
-1 -1
(k18 ~ 200 ppm min ) we found very rapid NO-to-N02 conversion and
HC
disappearance with 100 ppm added
CO .
Only when
k18 was lowered to
-1 , -1 d'd b. 1
1 or 2 ppm m1n 1 we 0 ta1n on y small effects.
Since much experi-
mental verification is yet to be done, only a limited effort was devoted
to this aspect of the study.
Table 3 summarizes the main findings.
It
indicates that the half disappearance time of
NO
is the strongest
effect of
k18
on the system, and the half-disappearance time of hydro-
carbon is least affected.
Both the peaking time for
N02
and the half-
rise time of ozone are moderately sensitive to the rate constant.
38

-------
TABLE 3
INFLUENCE OF 100 ppm CARBON MONOXIDE ON THE SYSTEM
SHOWN IN FIG. 6 WITH VARIOUS VALUES OF THE RATIO
OF (OH + HC) / (OH + CO) REACTION RATE COEFFICIENTS
REACTION TIME IN MINUTES
k4/k18    tl/2 - NO tpk - N02 tl/2 - HC tl/2 - 03
*       
0.4    <1 4 40 10
4    6 13 48 22
40    25 43 73 62
80    29 52 81 73
System in Fig. 6    
(No CO)   36 66 92 83
*       
This is with k18 set at the estimated value from Ref. 49.
In any event, whether we use the estimated rate of (OH + CO)-
reaction or even only preserve its ratio to that of the (OH + HC)-
reaction suggested in Ref. 23, we get very large effects.
Other work
(42) suggests a much larger (OH + HC)-rate constant for propylene.
In
view of our findings and of the wide disagreements on some of the rates,
a very real need exists for definitive experimentation to achieve a
deeper understanding of the kinetics.
D.
ATMOSPHERIC ADAPTATION BASED ON REACTIVITY DATA ANALYSIS
In order to apply the reaction mechanisms developed above to cases
of realistic photochemical air pollution, some means must be devised to
39

-------
convert the laboratory-derived rate constants to those suitable for
atmospheric processes.
Although the atmosphere over a city contains a
wide variety of hydrocarbon species, we will attempt to characterize it
by a single "averaged" species.
The averaging will be in the sense of
reactivity; that is, the hydrocarbon's susceptibility to oxidative attack,
its ability to produce oxidants, or its likelihood to lead to undesirable
biological effects.
To do this we will relate the reactivity of po11u-
tant species to the pure species observed in the laboratory.
When a deeper understanding of hydrocarbon synergism is attained,
we can model the interactions by including the key reactions; however,
an interim approach has been adopted for scaling hydrocarbon rate con-
stants according to observed reactivities.
Gas chromatographic measure-
ments made by Scott Research Laboratories (51, 52) provide the input
information employed in the analysis.
Air samples were analyzed at a
central basin station and at a northeastern basin station for two smog
seasons.
Prior to interpreting the results of the analysis it is useful to
examine the reactivity scales and their application.
For some time
reactivity ratings have been assigned to the individual hydrocarbon
compounds occurring in photochemical air pollution (38, 53, 54, 55).
Various classification criteria have evolved on the basis of different
observable effects.
Reactivity response numbers represent the relative
extent to which each effect occurs.
Some of the effects are hydrocarbon
consumption rate, nitric oxide consumption rate, nitrogen dioxide peaking
40

-------
time, product yields, and biological responses.
Also, a number of experi-
mental studies on distributions of specific hydrocarbons in polluted
atmospheres are reported in the literature (e.g., Refs. 56 through 60).
Each of these studies analyzed data that are limited either in number of
samples or number of compounds when compared with the body of data pre-
sented for analysis in the present program.
Consequently our data base
permits us to go further in drawing general conclusions.
Table 4 shows
the two reactivity scales used for this analysis.
Group No.
TABLE 4
HYDROCARBON REACTIVITY SCALES (54)
1
Class of Compounds
Reactivity Response

Product Formation
and Biological
Effects
2
3
4
5
6
7
Hydrocarbon
Consumption
Cl-C5 paraffins, acetylene,  
benzene   0 0
C6 + paraffins  1 1
Toluene and other   
monoalkylbenzenes  3 3
Ethylene   4 4
Dialkyl- and trialkyl-  
benzenes, diolefins 8 6
l-alkenes   17 7
Internally doub Ie-bonded  
olefins   100 8
41

-------
We use the reactivity groupings as a method of classifying com-
pounds to provide some insights into the processes occurring.
Means and
standard deviations for the values at each time of day are derived using
the whole sample of days available.
For the level of detail in the pre-
sent work, this approach gives more breadth to the results than one of
focusing attention on a limited number of compounds or on a limited
number of days.
Figures 10 and 11 show reactivity histories averaged over all 1969
data days in the Scott program (52) using the hydrocarbon consumption
scale (54).
Our interest in this scale is directed mainly to the model-
ing problem.
In these graphs, and in succeeding ones, we have aggregated
the hydrocarbons of non-zero reactivity response and have determined the
mole fraction within each group number.
The reactivity for any particular
time is found by summing the products of the reactivity response of each
group and the mole fraction in the group.
Although summation of these
products may not be a precise way of characterizing the mixture, we
have used it for our analysis because generalized algorithms are not yet
available for computing overall reactivity.
Examining the results in Figs. 10 and 11, we note that the reac-
tivity at Commerce picks up in the hours following the morning traffic
but decreases in the early afternoon hours as the photochemical fraction-
ation overtakes the input of new hydrocarbons.
All changes are small
with a mean reactivity value of about 6.
Because of its remoteness from
42

-------
~ 10

>-en
I- Z
- 0
~u
GZ
-
J:
~
\..oJ
~
It)
12
{GROUP 5, TABLE 4
DIALKYL -
AND TRIALKYL -
BENZENES,
DIOLEFINS
8
6
4
0/

(GROUP 4,
. TABLE 4/
\ ETHYLENE
2
o
0600
Figure 10.
2.. ONE STANDARD DEVIATION
0800
1000
TIME, PST
1200
Average Reactivity History for Commerce, 1969:
Consumption Scale from Altshuller (54)
Hydrocarbon
t'r;)
t'..
co
~
C\J
I
:<::;
"C
1400 hr

-------
.p.  12
.p. 
 ~ 
 Il') 
 W 
 ~ 10
 < 
 u 
 en 
 Wz 
 enO 8
 z -
 0'- 
 ~~ 
 en~ 
 w::::> 
 ~en 
 >z 6
 ~O 
 >u 
 .-z 
 uO 
  
 ::L 
~"~
"-
OJ
'"
C\]
I
<:
~
{GROUP 5, TABLE 4
DIALKYL - AND
TRIALKYL -
BENZENES,
DIOLEFINS
4
{GROUP 4,
TABLE 4
ETHYLENE
2
o
0600
Figure 11.
MEAN
i.. ONE STANDARD DEVIATION
1200
1400 hr
0800
1000
TIME, PST
Average Reactivity History for El Monte, 1969:
Consumption Scale from Altshuller (54)
Hydrocarbon

-------
the strong sources, El Monte has a lower and flatter reactivity mean of
about 5.
The scatter at El Monte is far less than that at Commerce.
From the standpoint of adapting a simple kinetic model to the atmos-
phere, the behavior of the average reactivity is indeed fortuitous.
The
flatness of the histories and the modest scatters about the mean suggest
that our propylene validation cases be scaled down by factors of two or
three in the hydrocarbon rate constants.
This adjustment arises because
propylene is in Group No.6 on Table 4 showing a hydrocarbon consumption
response of 17.
Beside kinetic parameters, we should check the influences of various
hydrocarbons on receptors to see if they display the same type of aver-
aged behavior.
Indeed, more significant from an abatement point of view
are reactivity scales based on biological effects and on product formation;
Figs. 12 and 13 show reactivity histories using such scales due to
Altshuller (54); the reactivity responses of exhaust hydrocarbons and
evaporative gasoline emissions are indicated in the figures for purposes
of comparison.
Only slight variations are noted throughout the daytime
hours.
Commerce begins at its highest point at 0600 hours PST and de-
creases only slightly thereafter.
As might be expected from windborne
transport from the west, El Monte experiences its peak at about 0900 hours
PST after which time it decreases slightly to approximately the same
values as those at Commerce in the early afternoon.
Both curves move
only narrowly between reactivity responses of 3.4 and 3.9.
Slightly
higher peak reactivities are observed at El Monte than at Commerce
45

-------
  6   
~     If;)
0\   EXHAUST HYDROCARBON l'..
   0:>
   (38,47,55)  ""
    C\J
    I
     <:
  5   "'C
   MEAN 
 w    
 CI)    
 Z 4   
 0    
 D..    
 CI)    
 W    
 IX    
 > 3   
 .....    
 >  + ONE STANDARD DEVIATION 
 .....    
 u 2   
 <   
 W    
 IX  EVAPORATIVE GASOLINE 
   EMISSIONS (38,57) 
SEE TABLE 4 FOR REACTIVITY RESPONSES
OF COMPOUND GROUPS
o
0600
0800
1000
TIME, PST
1200
1400 hr
Figure 12.
Average Reactivity History for Commerce, 1969: Biological
Effects and Product Formation Scale from Altshuller (54)
-

-------
w
V).
z
o
~ 3
w
CI::
>-
~
> 2
~
u
<
w
~
.!:"-
.......
5
4
EXHAUST
HYDROCARBON
138,47,55)
EVAPORATIVE
GASOLINE
EMISSIONS
138,57)
o
0600
MEAN
~ ONE STANDARD DEVIATION
SEE TAB lE 4 FOR REA C T I V IT Y RES P 0 N S E S
OF COMPOUND GROUPS
0800
1000
TIME, PST
1200
Figu re 13.
Average Reactivity History for El Monte, 1969: Biological
Effects and Product Formation Scale from Altshuller (54)

-------
(in contrast with the hydrocarbon consumption scale results); however,
the relative flatness in the average curves and the tightly grouped data
that generate the curves still prevail.
Consequently, both on the basis
of hydrocarbon consumption and of biological effects, we can begin to
approach the atmospheric kinetics problem with a single lumped hydro-
carbon.
Prior to incorporating this in the diffusion model, the properties
of the governing equations will be examined and an efficient numerical
solution method will be described in the next section.
48

-------
III.
THE ATMOSPHERIC MODEL AND ITS NUMERICAL SOLUTION
A.
THE GOVERNING EQUATIONS
Having a simplified chemical scheme, we now turn our attention to
incorporating it in an atmospheric transport model.
We have sought
approximations appropriate to air basins subject to photochemical pollu-
tion.
Because of the severity of the problem and the availability of
data, the Los Angeles basin area serves as the object of validation studies.
Probably the most characteristic causative factor in Los Angeles
smog is the lid created by the stagnation of warm air subsiding on the
cool marine layer.
Late in the summer, air flows from an anticyclone
over the Pacific Ocean and compresses as it loses altitude in its outward
course.
Onshore movement of marine air under this outflow maintains a
buoyantly stable interface at the base of the elevated inversion which
is marked by a temperature increase with height.
Sometimes this inversion
base starts out at ground level in the morning.
This condition, which is
chronic and of large scale, should not be confused with the transient
inversions due to nocturnal radiative cooling.
The regularity exhibited by this phenomenon holds the key to exten-
sive reduction in atmospheric model detail.
As mentioned in the intro-
duction, the relatively thin (marine) layer between the ground and the
inversion base contains the bulk of the pollutants.
The diurnal horizon-
tal flow patterns within the marine layer are almost reproducible from
day to day of the smog season.
Periodic variations in height (above
land) are experienced by the elevated inversion base over any given day.
49

-------
Some of the best detailed data illustrating these points are found in a
report by Neiburger and Edinger (61).
A subsequent report (62) in the same
series has some graphs which associate smog events with the meteorological
conditions.
The entire picture described above strongly suggests that we make
a marine layer model with a prescribed internal flow field.
The top of
the layer is nearly as wall-like as the bottom because vertical distur-
bances are strongly resisted by buoyant forces.
Therefore, very little
Reynolds stress momentum transfer occurs across the interface just as
there is almost no normal transport of species (a property with which
Angelenos are very familiar).
For the species budget along a streamtube in the marine layer, we
assume a channel-like flow with zero flux through the top "wall" and some
specified flux from the ground.
In choosing boundary conditions for the
balance equations governing free radicals, we are confronted with the
usual uncertainties regarding wall catalycity.
Computational tests rang-
ing from infinite to zero catalytic efficiency for removal of oxygen
atoms and
R02
result in unimportant differences at instrument eleva-
tions of several meters because the radicals achieve steady state much
faster than they diffuse over several meters.
The governing species equation is taken to be
l + u . = .L (D .) + R
at dX dZ dZ
(19)
so

-------
where
c = mass concentration
t = time
u = wind speed
x = downwind distance
z = height above ground
D = vertical turbulent diffusion coefficient
R = production rate
Mean vertical advection is suppressed by the channel-like character of
the marine layer and horizontal diffusion is relatively unimportant
because of a nearly uniform distribution of emission sources.
Hence
these terms do not appear in Eq. 19.
The chemical source term is
calculated from the usual rate expressions.
Since a significant period following sunrise on a high smog day
has little wind. much is to be learned by omitting the. second term and
studying slab solutions of the heat-equation-with-sources form.
As will
be summarized in a later section. this was the first approach that we
followed (63) to extend laboratory data on kinetics to the atmosphere.
The problem without advection (second term. Eq. 19) was solved using the
Crank-Nicolson technique (64). To test advection and diffusion without
chemistry. we modeled carbon monoxide only using Eq. 19 with
R = 0 .
Using Eulerian (ground-fixed) coordinates. the complete equation with
the simple chemistry ran a minute of CDC 6400 time for each minute of
real time that was simulated.
*
This was considered to be unacceptable.
*
Slow computation resulted for the ten-cell test case because of the
chemistry. It also had artificial diffusion which is an error from
numerical differencing of the equation. It produces effects that
resemble physical diffusion in the x-direction.
51

-------
We also use a restricted form of Eq. 19 for the kinetics studies
described in the previous section.
Smog chamber analyses use just the
first and last terms so that they depend on ordinary differential equa-
tions.
These are solutions which describe the time-dependent behavior
of a homogeneous gas mixture.
We used standard Runge-Kutta techniques to
solve them at the outset of the work, but as will be shown here, adapta-
tions of Pade approximants have been employed to improve computational
efficiency.
The combined needs for computing efficiency and meteorological
realism have been met by improvements described in this section.
The
first two subsections describe the incorporation of a classical approxi-
mation method into our numerical integration.
The implementation of these
computing techniques strengthen the study by allowing numerous modeling
trials on both laboratory and atmospheric cases.
The final subsection
outlines the change from Eulerian to semi-Lagrangian coordinates in the
meteorological formulation.
By following air masses, we use a natural
coordinate system thereby eliminating the artificial diffusion errors.
B.
~
APPLICATION OF PADE APPROXIMANTS TO SMOG CHAMBER CALCULATIONS
The chemical model previously described is implemented in rate
equations which must be integrated numerically.
Because of the widely
varying reaction rates, the equations possess a characteristic known as
"stiffness" which makes their integration difficult.
In the interest of
economy and accuracy, special techniques must be employed in obtaining
52

-------
a solution.
Below we describe a method which utilizes Pade approxi-
mants (65, 66).
For these ordinary differential equations, the procedure
has yielded significant speed improvements over the Runge-Kutta method
previously used.
For this class of problem, the implicit approach is the basic
advantage of the new method, thus guaranteeing stability.
Consequently,
accuracy controls step size.
This provides the principal gain in
computing time.
The rudiments of the integration method are twofold.
One involves
a linearization of the nonlinear chemical term at every step; the other
an approximation of the exponential term that appears as a result of the
linearization operation.
Thus, consider the following system of equations
that describe the changes in species concentration due to chemical reaction:
dc
- = R(c)
dt
(20)
where
c = vector of species concentrations
R(c) = vector of chemical reaction rate functions
cl
Rl(c)
R2(c)
c2
c =
R(c) =
c
s
R (c)
s
s = number of chemical species
53

-------
To linearize the rate vector
R(c) , we expand it about
c
o
in a Taylor
series.
The subscript "0" denotes evaluation at some time
t = t
o
. Thus
R(c) = R(CO) + J(c - co) + 0(~c)2
(21)
where
J = [C3Ri]
de.
J
i,j = 1, 2, . . . , s
is the matrix of order (s x s) of first derivatives (the Jacobian matrix)
of the rate function.
Substituting Eq. 21 into Eq. 20 yields
dc = Jc + B
dt
(22)
where
B = R(c ) - Jc .
o 0
It should be noted that at time
t = t ,the
o
quantities
c , R(c ) , and
o 0
J
are known.
Hence, the matrix differential
equation (Eq. 22) is a linear equation with constant coefficients and a
constant forcing function.
Its formal solution is, therefore,
c(t) = eJM [co + J-1B )- J-1B
(23)
where
-1
J
denotes the inverse (or reciprocal) of the matrix
J.
An approximate solution of Eq. 22 is obtained from Eq. 23 by
suitably approximating the matrix exponential
JM
e
This is accom-
plished by means of the Pade approximants of the exponential function.
These Pade approximants are rational function of the form
J~t - P(J~t) = Q-lp
e - Q(JM)
(24)
54

-------
where P(JL\t) and Q(JL\t) are matrix polynomials of degree p and q,
respectively. They are defined by    
  p      
 P = 2: (p + q - k)! p! (JL\t)k   (25a)
 (p + q)!k!(p - k)!  
  k=O      
  q      
 Q = 2: (p + q - k)! q! k   (25b)
 (p + q)!k!(q - k)! (-J L\t)  
  k=O      
Thus, substituting Eq. 24 into Eq. 23, we obtain
c(t) = Q-1p [ Co + J-1B] - J-1B
(26)
The choices
p= q = 1
and
p = q = 2
are especially useful.
The
former yields a third-order integration formula, the latter a fifth-order
formula.
As an example, for
p = q = 1
we obtain from Eq. 25:
P = I + 1/2 JL\t
and
Q = I - 1/2 JL\t
(27)
where
I
is the identify matrix.
Substituting Eq. 27 into Eq. 26 yields,
after the appropriate manipulations,
c(t) = c + [I - 1/2 JL\t]-lL\tR(c )
o 0
(28)
Equation 28 has a form that is especially well-suited for digital compu-
tation.
Note that the process requires at every time step:
(1) the
evaluation of
R(c)
and
J , and (2) the inversion of the matrix Q .
55

-------
The latter is by far the more computationa11y costly of the two require-
ments.
In our case~ the number of species determines the size of the
matrix to be inverted.
Since this number is not large in our mode1~ the
matrix inversion poses no special problems.
Fortunate1y~ the number of
species is usually smaller than the number of reactions.
Table 5 shows examples of the gains obtained using the new compu-
tationa1 scheme.
The typical rea1-time/computer-time ratio was increased
from 36/1 to 180/1.
Perhaps more significant is the fact that the Pade
method has allowed us to obtain acceptable solutions in situations where
Runge-Kutta either failed to converge or produced spurious solutions.
One such instance is the integration of full differential equations for
the free-radical species:
the Pade method successfully computed solu-
tions without algebraic substitution of stationary-state assumptions~
whereas Runge-Kutta failed to produce any solution.
TABLE 5
CDC 6400 CENTRAL PROCESSOR TIMES TO RUN
C3H6 + NO + hv CHAMBER EXPERIMENT SIMULATION
Type of Run
Runge-Kutta
Pade Approximant
Rapidly changing free radical
concentration
2400 seconds
122 seconds
Typical run for 150 minutes
real time
250 seconds
50 seconds
Run which diverged for
Runge-Kutta
267 seconds
(diverged at)
80 minutes~
real time
50 seconds
(ran to comp1etion~)
150 minutes real
time
56

-------
As mentioned previously, the step size must still be controlled in
order to preserve accuracy.
Referring to Eq. 21 we can see that the
difference
6.c = c - c
o
determines the order of the truncation error of
the linearization operation.
The step size must be constrained so that
6.c
will remain within some bound specified by the user.
Our codes con-
tain a variable-step-size feature which ensures that
6.c
will stay
within the prescribed bounds.
It should also be noted that the nature of our chemical model is
such that it leads to a very good first-order approximation as indicated
in Eq. 21.
This occurs because the full expansion of our particular rate
function,
R(c) , contains only three terms.
Hence in the first-order
approximation only one term has been dropped from the expansion.
C.
APPLICATION OF PADE APPROXIMANTS TO THE ATMOSPHERIC MODEL EQUATION
We now describe the use of Pade techniques to solve the diffusion
equation with chemical reactions.
The equation in question is referred
to a moving air mass.
*
Use of the Lagrangian approach
eliminates the
second term in Eq. 19 which is reduced to
1 =..L (D 1)+ R(c)
at az az
(29)
where
D
is the vertical diffusion coefficient and
c
and
R(c)
have
been defined previously.
Applying the "method of lines" to Eq. 29, the
*
The Lagrangian approach we use is a moving air parcel with vertical
nonuniformity due to finite rate diffusion. It is introduced by
schematic description in Sec. I D.
57

-------
I
partial differential equation is transformed into an ordinary differ-
entia1 equation for a line describes the concentration changes for a
fluid mass moving along the line.
The equation for the ith
line is
derived from Eq. 29 to give
dc.
1
-=
dt
D

(l1z)2
[ci-1 - 2ci + ci+1] + Ri
(30)
where
R. = R(c.), i = 1, 2,
1 1
. .. , M,
where
M
is the number of mesh
points from the ground up to the mixing depth.
The symbol
C.
1
defines
a vector of
s
species at the ~th point in space.
Similarly,
Ri
defines a vector of
s
rate functions at the ith mesh point.
Thus,
c2i
Rli
R2i
cli
c. =
1
R =
i
c .
S1
R .
S1
In order to solve Eq. 30 by the Pade method,
R.
1
is linearized as
in Eq. 21 to yield
R. = R. + J.(c. - c. ) + 0(l1c.)2
1 10 1 1 10 1
(31)
58

-------
where the zero subscript again denotes evaluation at time
t = t , and
o
J.
1
is the Jacobian matrix of the rate function at the ith spatial mesh
point.
Substituting Eq. 31 into Eq. 30 yields
dc.
---1:. =
dt
A[C. 1 - 2c. + c'+l] + J.(c. - Ci ) + R.
1- 1 1 1 1 0 10
(32)
where A = D/(~z)2 .
Writing Eq. 32 more compactly we obtain, after
collecting terms,
ddC=(AA+J)C+R -JC
too .
dC = HC + B
dt
(33)
where H = AA + J, B = R - JC , and
o 0
cl -21 I 0 
c2 I -21 I 
 0 I -21 I
C = A =   
o
o
o
~    I -21
Jl 0  RIo 
J2  R20 
J =   R =  
  0  
0 JM  ~o 
    59

-------
Equation 33 now has the same form as Eq. 22 and its formal solution is
thus analogous to Eq. 23.
Hence
C(t) = eH6t [ Co + H-1B] - H-1B
(34)
Approximating the exponential by
H6t
e
'"
I + 1/2 H6t P -1
I - 1/2 H6t = Q = Q P
and substituting in Eq. 34 and simplifying we obtain
C = C + Q-1C 6t
o 0
(35)
where
C
o
= 'AAC + R
o 0
It should be noted that any boundary conditions are implicitly contained
in Eq. 35.
Equation 35, which is the analog of Eq. 28, may appear to be simple,
but the inversion of
Q
poses some problems arising from its dimensions.
H
is an (M x M) matrix each one of whose entries is an (s x s) matrix.
Hence
Q
is an (sM x sM) matrix, and its storage as well as its inver-
sion may be difficult.
For example, if we have 10 species (s = 10) and
10 space grid points (M = 10) then
Q
is (100 x 100) and requires rather
long computing times as well as large amounts of core storage.
However,
60

-------
we take advantage of the structure of
Q
to develop an algorithm that
reduces the problem to the inversion of
M matrices of size (s x s).
It is noted that since
J
is a diagonal matrix and
A
is tri-
diagonal, then
H
is tridiagonal.
Moreover, the off-diagonal entries
of
H
are identity matrices.
Forming
Q
we have
Q = I - 1/2 H~t
and it is apparent that
Q
is tridiagonal, its off-diagonal entries
being identity matrices also.
Thus only the
M
diagonal entries of
Q
need be stored, thereby reducing memory requirements to
2
Ms cells com-
pared to the maximum of
M2s2 .
Writing Eq. 35 in the form,
QC = QC = G ~t
o 0
we note that the tridiagonal property of
Q
allows us to solve for
C
without explicitly inverting
Q .
This simplification is afforded by an
extended form of Gaussian elimination (64) which requires the inversion
of
M
matrices of size (s x s).
This is preferable to inverting the
full (sM x sM) matrix.
Note that we can also take advantage of the fact that the off-
diagonal elements of
Q
are identity matrices to reduce the amount of
computation.
Because series are truncated in these approximations, some
remarks about the resultant errors are necessary.
The order of the
61

-------
truncation error of the solution is
0(~t)3 .
This occurs because the
approximation of the exponential is
H~t
e
~
I + 1/2 H~t
I - 1/2 H~t
Also, as in the solution of the chemical rate equations, a linearization
error of order
0(~C)2
appears in the approximate solution.
Thus, the
same precautions that were taken to preserve accuracy in solving the
ordinary chemical rate equations are required in the solution of the
atmospheric model equation.
The new scheme has yielded a better than fourfold increase in the
rea1-time/computer-time ratio, i.e., from 7/1 to 30/1.
A more detailed
description is given in a separate report by Martinez (67).
D.
METEOROLOGICAL REFORMULATION OF MODEL
Long computer runs and unacceptable error propagation hampered the
operation of the earlier time-dependent advection and kinetics (TADKIN)
code (63).
Its application was limited to an analysis of carbon monoxide
to examine the influence of advection added to that of vertical diffusion.
At the inception of the present work, these severe limitations dictated
a reformulation of the advective description before any atmospheric runs
were attempted.
Combined with the mathematical advances just described,
the semi-Lagrangian embodiment of the diffusion with kinetics (DIFKIN)
code, extends the application of photochemical diffusion modeling to a
great many more cases than previously thought practicable.
62

-------
Following a center-of-mass fixed coordinate system tied to an air
mass, we make use of intrinsic coordinates to avoid artificial diffusion
in the horizontal direction.
Physical diffusion, therefore, is distinct
and identifiable because the moving control volume can be allowed to
undergo mass exchange with a neighboring air mass in a prescribed fashion.
The question of horizontal spatial resolution is answered by a selection
of source grid size and the vertical resolution is set by the choice of
the interval size in the z-direction.
Mixing depth or vertical extent of the pollution layer can be
handled in one of two ways.
In the first, the vertical diffusion coeffi-
cient is assigned spatially and temporally dependent values according to
the combined effects of shear and buoyancy as turbulent energy sources.
The vertical extent of the grid is chosen far above the conventional
mixing depth so that the pollutants are automatically confined vertically
to a degree which depends on the diffusion coefficient profile.
In the
second way of specifying the vertical behavior, however, the vertical
grid either continuously adjusts to the input values of mixing depth or
assumes an average value for the inversion base altitude.
We have favored
the use of this second approach because it limits the field of computa-
tion to the polluted region and thereby conserves computer time.
A zero-
flux boundary condition is imposed at the top of the net.
The next section summaries both the early validations and the
results in testing the improvements we attempted in the chemical, mathe-
matical, and meteorological aspects of the problem.
Indeed, many times
63

-------
it appeared that the earlier simple concepts gave better results, but
working with better data and more demanding theoretical descriptions
than before, we uncovered some significant areas for further investiga-
tions.
64

-------
IV.
THE EXERCISE AND VALIDATION OF THE MODEL
A.
OBJECTIVES OF THE TESTS
With the development of a more complete chemical model than the
previous one, the mathematical and meteorological improvements offset
the potential computing slowdowns due to added reactions.
Having de-
scribed these advances in technique, we turn now to the task of subjecting
the model to validation tests.
Huntington Park is the site of the ear-
lier validation, but El Monte is the station of interest in the recent
work.
El Monte is closer to the edge of the urbanized areas than
Huntington Park or Commerce, and is, therefore, likely to show larger
random fluctuations of pollutant concentrations.
In view of the vari-
ability of wind directions, this is expected because the air over El Monte
may have originated from either high or low pollution areas (see Figs.
15-18).
Hence the accuracy of the initial conditions for the test cal-
culation may be as important as the accuracy of the flux boundary condi-
tions.
In this section we will examine sources of data, validation tests
with simple chemistry and stagnant conditions, and validation tests with
complex chemistry and advection from one station to another.
B.
SOURCES OF DATA
1.
Input Information
Except for initial profiles, the input data for the model are the
meteorological conditions and the source emission conditions.
Wind speed
and diffusion coefficients depend on both position and time.
Source
65

-------
inventories include the flux of each primary pollutant as it depends upon
location in the basin and time of day.
Empirical parameters governing atmospheric dispersal pervade the
literature on this subject.
Like most cases of turbulent transport,
elimination of a disposable coefficient in one place leads to a reappear-
ance of one somewhere else.
The present work uses an experimentally
determined turbulent diffusion coefficient,
D , in Eq. 19.
Near the
ground and near the inversion base we must assign a height
( z)
depen-
dence to the diffusion coefficient.
Going up from the ground, the functional dependence assumed for
D
upon
z
allows a linear increase to some constant value.
At intermediate
levels,
D
is held constant, but approaching the inversion base a linear
decrease with height is assumed.
A variation on the lower part of the
profile has been to maintain the ground value up to some point prior to
initiating the linear increase.
This variation causes little change from
the original trapezoidal profile.
The elevation where constancy is
achieved varies from 40 to 100 meters depending upon meteorological con-
ditions.
Figure 14 shows typical values of the turbulent diffusion coeffi-
cient we assumed for our model compared with the values either derived
or observed by other investigators.
At a wind speed of
1 m/s , a surface
2/" " h" h
value of 30 m m1n 1S 19 compared with Pasqui11's (68) values at 200
centimeters elevation, but we use it because effective roughness in an
66

-------
200 m
 150
.... 
, 
I- 
~ 
C> 100
w 
~ 
'"
-..J
50
IV ANOV (73) T LETTAU (72) t V)
u - 6 mj s I u - 15 mj s I ~

~ ~I ~

I I
I I
I I
\ /'
\ /
y/
e/\
I
~

I ROSSBY AND
MONTGOMERY (69)
(residual turbulence
oJ free air)
ASSUMPTION FOR
ALEKSANDROV A (711 SAMPLE MODEL OF
(stable, sublayerl l.A. BASIN (180 m
u = 1 mjs inversion base,
~ u = 1 mI'


~ASQUILL (200 cm values for
/": different roughnesses)(68)
Note: Ivanov and Lettau data used
to determine velocity dependence
900m2jmin
o
100
200
300 400 500 600
TURBULENT DIFFUSION COEFFICIENT
Figure 14.
Variations of Diffusivity with Height for Different
Average Wind Speeds

-------
urban area far exceed those of "mud flats" or "high grass."
The assigned
plateau value is slightly higher than that for the residual turbulence
of free air attributed to Rossby and Montgomery (69) in Priestley's mono-
graph (70).
The decrease approaching the inversion base is introduced
to reflect the wall-like inhibition of vertical turbulent motion by
buoyant stability.
Note on Fig. 14 that the sub layer region corresponds closely to the
values deduced from Aleksandrova's formulas and mast measurements for the
precipitation of a puff released from a point source (71).
The values
reported by Lettau (72) (as "Austausch" coefficients) were obtained from
Leipzig wind profile measurements.
The data of Ivanov (73) for mean
square velocity and dissipation rate were used in Hanna's (74) empirical
formula to obtain the 6 m/s values.
Neither the Ivanov nor the Lettau
results were obtained for stable lapse conditions.
The assumed values
for the coefficient correspond closely to the turbulent transport ob-
served by Craig (75), who measured water vapor profiles 30 miles off-
shore as warm air moved seaward across Massachusetts Bay.
For light
winds, values of 6 to 12 m2/min were observed at elevations of 1 to 2
meters.
At 60 to 80 meters elevation, diffusion coefficients up to
300 m2/min were found with 6-m/s wind speeds with reduced stability.
The plateau value in our profile, therefore, may be expected to vary

50(u+5) m2/min
where
u
is in
m/s .
with wind speed approximately like
This simple relationship has been employed based on the cited findings.
Other sources of diffusion coefficient data (76, 77, 78) that are not
plotted on Fig. 14 give values which are consistent with those shown.
68

-------
Wind speed, wind direction and inversion base height are the prin-
cipal meteorological inputs.
Wind data are obtained from Scott Research
Laboratories (SRL) measurements (51, 52) and from other observation sta-
tions in the area.
Inversion data are deduced from airborne temperature
measurements (51, 52) where possible and from morning soundings reported
(79) by the Los Angeles County Air Pollution Control District (LAAPCD).
Some wind data from the district's files have also been employed.
As an example of the preparation of windfield inputs from the
station data, let us examine the results for one morning in the Los
Angeles basin.
The advection patterns are obtained by taking a weighted
average of wind-station readings surrounding the point in question.
This is truly a receptor-oriented modeling approach, since the trajec-
tories are constructed in hourly upwind segments from the measuring sta-
tion.
Reciprocal distance weighting is employed because of the dominant
plane flow pattern which is governed by combinations of sources, sinks,

*
or vortices.
In most cases the three nearest neighbor stations are
included in the stepwise upwind tracing or air movement, but occasionally
conditions of proximity suggest including only the nearest one or two
stations where coastal crossings are involved in the analysis.
Figures 15, 16, 17 and 18 show examples of the paths of air masses
estimated in the manner just described.
The times of arrival in El Monte
are used to identify each trajectory in any subsequent references in this
report.
The date of September 29, 1969, is chosen because of the rich
*
See Sec. I D for a discussion of characteristic scale sizes.
69

-------
it
;1,
o
2
4
6
8
10 mi
METROPOLIT AN
LOS ANGelES
.~
Figure 15.
Estimated Trajectory of Air Mass Arriving at E1 Monte,
1030 hours, 29 Sept. 1969
70

-------
.
r;il~.
----......
'"
~,
:'.
..:
N~
o
4
8
10 mi
2
METROPOLIT AN
LOS ANGelES
.~
Figure 16.
Estimated Trajectory of Air Mass Arriving at E1 Monte,
1130 hours, 29 Sept. 1969
6
71

-------
I
.
I
,.
rt
~~
------
N~
o
2
.4
6
8
10 mi
METROPO LIT AN
LOS ANGELES
.~
Figure 17.
Estimated Trajectory of Air Mass Arriving at E1 Monte,
1230 hours, 29 Sept. 1969
72

-------
-\(1,
"
~------."'
-------
N~
o
2
4
6
8
10 mi
METROPOLITAN
LOS ANGELES
.~
Figure 18.
Estimated Trajectory of Air Mass Arriving at El Monte,
1330 hours, 29 Sept. 1969
73

-------
variety of data that we have available for that day.
Note that the
earlier morning meandering patterns give way to the dominant onshore flows
for all trajectories after 0800 to 0900 hours Pacific Standard Time.
The
meteorological formulation that we have adopted takes the time and loca-
tion information from these trajectories to establish the initial condi-
tions and the boundary conditions.
Initial conditions are specified as
vertical profiles of concentration and boundary conditions as time his-
tories of surface-based pollutant emissions.
Of courset these trajec-
tories are not used in the validation tests of the slab model.
They are
employed to test the moving air parcel model.
Using this approach with data from the two monitoring sitest we are
able to match the computing requirements to the data base.
Little justi-
fication exists at this time to apply complicated grid methods to these
validation studies because we only have measurements in great detail from
Commerce and EI Monte.
Just as overly-elaborate chemical models cannot
be adequately tested in the atmospheret neither can highly complex dif-
fusional and atmospheric formulations be checked out with our present
store of field observations.
CertainlYt the day will come when frequent
high-resolution readings are made and some of the more detailed theories
can be tested.
Even more difficult than the meteorological inputs are those for
surface emission fluxes of hydrocarbont nitric oxide and carbon monoxide
species.
Originally we did a simple statistical estimate on moving
sources based on the California Driving Cycle for a velocity distribution
74

-------
function and a packing density based on a car length spacing for every
ten miles per hour speed for all the arterials and freeways in the basin.
Although we arrived at surprisingly realistic values for tonnages of
emission and total cars on the road, we switched to LAAPCD inventory
estimates (80) when they became available.
Table 6 summarizes some of
the totals from this official publication.
Since tons per day are given,
one can compute average surface fluxes, knowing that the basin comprises

some 1250 mi2 according to the same publication.
TABLE 6
CONTAMINANTS IN TONS PER DAY

FROM MAJOR SOURCES WITHIN LOS ANGELES COUNTY IN 1968 (80)
 Organic Gases     
Maj or  Reactivity  Particulates NO S02 CO Total
Source High Low Total  x  
Motor        
Vehicle 1255 475 1730 45 645 30 9470 11,920
Non-Motor        
Vehicle 200 620 820 55 305 195 225 1,610
Total 1455 1095 2550 110 950 225 9695 13,530
Additional adjustments must be made for the fact that the source
emission strengths are not uniformly distributed in either time or space.
75

-------
To approximate the automotive sources we used the data reported for the
geographical (see Fig. 19) and the temporal (see Fig. 20) distributions.
For nonautomotive sources, averages were employed as constant background
emissions.
The tonnage partitioning between high-reactivity and low-
reactivity hydrocarbons from automotive sources roughly represents the
ratio of compounds having nonzero reactivity index to those having a
zero value in automotive emissions.
Although the source distribution data in Figs. 19 and 20 are nearly
twenty years old, they were the best available at the time of the early
validation studies.
Of course, the tonnages used were from 1968 and they
were distributed according to Figs. 19 and 20.
For the more recent vali-
dation runs involving air trajectories, we used the source distributions
developed by the group at Systems Applications, Inc. under the direction
of Dr. P. M. Roth.
Figures 21 and 22 were adapted from their report (82).
Maps for surface street traffic and for stationary sources were also
given, but Fig. 21 (for freeways) typifies the data as displayed on a
two-mile grid.
To get emissions from mileages, we used emission factors
based on weighted averages of various model years according to the method
of Ref. 83.
The weighting factors corne from vehicle age distributions.
2.
Validation Information
With the atmospheric and emission source inputs, we test the model
by predicting time histories of the concentration field in the marine
layer.
The predictions are then evaluated against a background of val i-
dation data.
The primary sources of these data are the SRL reports
(51, 52) for the 1968-1969 smog seasons.
76

-------
,
/
.......
.......
---
,
\
\
\ 0.90
\
0.30
0.40
0.610.760.42
1 .060.61
00
N
00 0
M N
. .
o 0
o 0
1.34
0.39
0.54 ,
Figure 19.
Geographical Traffic Distribution in Los Angeles County,
ca. 1951. Numbers Shown Represent Percentage of County's
Daily Traffic, in car miles, Occurring in Area (81)
\

I "<11

\ ~
j~


,

/
<:T
N

-------
......
CX)
~
::>
o
~
~
W
Q.
HOLLYWOOD FREEWAY - CAHUENGA PASS ON A WEEKDAY
LOS ANGELES BASIN AVERAGES
10
8
---
u
LL
LL
<
~
to-
6
>
~
<
o
4
LL
o
2
--------
to-
Z
w
U
~
W
Q.
o
2400
0800
1200
TIME OF DAY
1600
2000
0400
Figure 20.
Los Angeles Traffic/Time Distributions ca. 1951 (81)
C}
......
......
C}
......
2400

-------
166    94 119                   
    155 68 144                  
    242  156 158 109                
    222  126 17 104 150    37           
169 271 311 383 890 456 426 494 178 395 190 51             
    352   140 275  423  13 90 28   41 74 66 65 43 11 0 
    356    215 194 290 335 193 109           
    242 137    205 436 620 257 257 297 306 311 254 362 291 214 203 170 173 159
     473 141 333 426 466 795 452 585 518 224 79 234 285 147      16
   " 101 295 511 51   531 449 623 576   205 263 156 70    32 15
    '\  295 160   391   283 332  265   12 59 42 21 3 
     ,  404   366   281 129 444 33        
     \  348   305   302  527 30        
      ~ 351 32  257  159 131  314 289 104       
      \  391 326 217  241  56 383 102 243 253   15   16
      ,    625  236   278  59 83 330 251 138 108 207 85
          131 343 545 340 323 195     145 68  137 
      V    143 45 107   529 349 213 144  25 398 156 161 
      1\     I"l..oo.' - ...........           
         ~ ,,/ )j ~   181 112 183 150  257 131 
      ....... """'-   II'" '"    "         
      r---....        153 78   67 169 77
         ""'"       '\   115 160 163 148  91
                 I"    97 95 61 59
                  f'  80 6   
                   " ~18    
                    ......;; t--.   
                     '-  
""
CO
0',)
0',)
""
I
~
<:::t:
Figure 21.
Geographical Distribution of Freeway Traffic in the Los
Angeles Basin Area ca. 1970 (thousand vehicle miles per
day) (Adapated from Robertst Roth and Nelsont Ref. 82)
79

-------
 10 FREEWAYS    r<:>
     Q:)
      0'>
  --- NON.FREEWAYS    0'>
     C\:)
      I
      ~
a::      "I;
~      
0 8  r--'  
x   I I  
  I  
a::      
w   I   
~   I   
u   I   
LL 6  ~   
LL   I  
<  I   
a::  I  L -1 
~  I   I 
>-  I   I 
.....    
<  I   I
e 4 I   I
LL  I   I 
0  I    
~  ~    
Z      
w      
u 2     
at:      
W      
~      
o
2400
0400
0800
1200
1600
2000
2400
TIME OF DAY
Figure 22.
Los Angeles Traffic/Time Distributions ca. 1970 (Adapted
from Roberts, Roth, and Nelson, Ref. 82)
80

-------
Because Volume I of Ref. 51 contains detailed descriptions of the mea-
surements program, it will be reviewed here only briefly.
Two fixed
sites, Huntington Park and El Monte, California had instrumented trailers
which monitored pollutant concentrations, meteorological data and ultra-
violet radiation.
The sites are 12.7 miles apart and lie along a prevail-
ing air trajectory.
The great step forward in this program was the reso-
lution of hydrocarbon concentrations into more than 100 individual species
up to
CIO
with a sensitivity to levels below one part per billion using
highly refined gas chromatography techniques.
Reference 52 gives descriptions and reports data for a similar
program conducted in the 1969 season.
The central basin station was
located at Commerce and the northeastern basin station remained at El
Monte.
These sites are separated by 10 miles.
Great improvements in
data frequency and reliability were made in the 1969 measurement program.
Limited use of other data has been made to supplement the SRL mea-
surements.
In 1967 a joint study was made by the National Center for Air
Pollution Control, the California Air Resources Board Laboratory, and
the Los Angeles County Air Pollution Control District.
The objective of
the study was directed toward improvement in detailed chemical measure-
ment.
It involved air sampling at two sites, Downtown Los Angeles and
Azusa.
Some of the reduced data (84) have been used in the validation
studies.
The LAAPCD monitors concentrations over a nine-station network.
We have used some of this information from 1968 to augment the SRL data.
81

-------
The large volume of field data must be assimilated by some form of
preprocessing before it is useful for validation tests.
Two states of
reduction which we have employed are sorting days by type characterized
*
by peak oxidant
and then averaging data over all days of each given type.
Consistent with the lumped parameter approach, we reduce the hydrocarbon
ensemble by grouping compounds into brackets on a reactivity scale.
For
a beginning, only two reactivity classes have been employed in accordance
with the source inventories shown in Table 6.
Low reactivity hydrocarbons
include methane, ethane, propane, acetylene, methylacetylene, and benzene.
All others are considered to be high reactivity.
C.
VALIDATION TESTS OF AN EARLY VERSION OF THE MODEL
In addition to studying the chemistry using chamber data, we studied
atmospheric transport of inert and low reactivity species to concentrate
on diffusion effects.
For initial validation tests, Huntington Park is
superior to El Monte because of the symmetry in surrounding source dis-
tribution, the remoteness from any mountain interferences, and the regu-
larity in the data.
Our search for type 3 days turned up October 23,
1968 as the only one with sufficient data for validation.
This was used
for the initial DIFKIN tests because the low wind speeds minimize the
error in omitting the horizontal advection term.
The simplest form of
the chemical model (the one diagrammed in Fig. 2) was used in these
validation tests.
*
Days are typed by peak oxidant as follows: type 0, both stations
< 20 pphm; type 1, either station 20-30 pphm; type 2, either station
> 30 pphm; type 3, either station> 30 pphm and western station peak
> eastern station peak (pphm = parts per hundred million). Western
and eastern stations are taken to be Huntington Park and El Monte for
SRL data, or Downtown Los Angeles and Azusa for LAAPCD data.
82

-------
Figure 23 shows results for ground level carbon monoxide concen-
trations at Huntington Park.
This species is practically inert so that
the results are a test of the transport formulation and the chemical
source term for carbon monoxide is neglected.
Using measured values to
*
start at 0600,
we computed the solid curve from DIFKIN (no advection)
and the dashed curve from TADKIN (input wind observations).
Comparison
of SRL data with output from the models shows that advection only becomes
significant after the first three hours.
Good agreement is exhibited by
the models (using input data described above) with the validation data.
The ventilation behavior is consistent with the local wind speeds dis-
played on an auxiliary graph on Fig. 23.
This approach has been applied
on a small-scale grid to study the carbon monoxide pollution in the
nearby vicinity of a freeway (85).
Test results with photochemistry have been obtained for type 2 and
3 days using the DIFKIN code.
Prior to discussing these results, it is
necessary to digress briefly and examine some special features of the
data.
First, consider the ratio of acetylene
(C2H 2)
to total oxides
of nitrogen
(NO) .
x
In morning samples,
C2H2
is essentially unreacted
and the
NO
x
has not been depleted much by the chain breaking reactions.
Hence we should expect a plateau of the
C2H2/NOx
ratio characteristic
of motor vehicle exhaust.
Previous investigators (84) have shown this
*
Using
days,
by an
airborne sample measurements with ground measurements for type 2
we determined the early morning profiles to be well approximated
exponential decrease with height using a ISO-meter scale height.
83

-------
100 P P m
Z 10
o
~
~
~
~
Z
w
U
Z
o
U
Figure 23.
84
0.1
--- SRL DATA
DIFFUSION MODEL (DIFKIN)
-- DIFFUSION/HORIZ.
ADVECTION (TADKIN)
-
DIFKIN
, .....
-- .....
.............'
,',

CONCENTRATIONS '\. "
'\\ /
T ADKIN\'--/

HALF HOURLY

LOCAL WINDS-mph
10 mph
1
1
14
NO WIND
1 m ph
0.1
1300 PST
0700
0900
1100
TIME OF DAY
Carbon Monoxide Concentration at Huntington Park on
Type 3 Day
0')
C)
0')
C)
C\J
I
:<:::
"<:
~
Z
o

-------
ratio to be about four times that typifying automobile exhaust from the
*
California Driving Cycle.
These results are displayed on Fig. 24 sug-
gesting that the estimates from Table 6 may need modification.
If we
assume that nitric oxide, the emitted pollutant, is depleted in prefer-
ence to
C2H2 (say by heterogeneous reactions), then we should lower the
NO
x
estimates.
This hypothesis is tested below by reducing the source
strengths for
NO
in the calculation.
Another bit of evidence leading
to suspicions of the nitrogen balance is found in the ratios of
CO
to
NO (86).
x
Carbon monoxide has long atmospheric reaction times, and since
it is nearly exclusively of vehicular origin, it too can be considered
as a tracer.
Figures 25 and 26 are plots of the
CO/NO
x
ratios as they vary
throughout an average day of each type.
Figure 25 shows the anomaly
occurring on high oxidant days in 1968.
Morning peaks of
CO/NO
x
ratio
appear to follow traffic curves.
They exceed the vehicular ratio of 24
and the all-sources ratio of 16 by large amounts.
At its extremum, the
average for high-oxidant days exceeds the all-sources value by a factor
of four.
This is the basis of the inconsistency between air levels and
source inventories discovered in the modeling study.
The physical ex-
planation for this inconsistency is not yet available.
Further diagnostic
measurements will be needed to isolate the phenomenology.
Even the low-
oxidant curve exceeds the source ratios in the morning.
It seems to
follow the high-oxidant curve at a fixed interval below it until mid-
morning.
Then both curves begin to merge.
*
This is observed for high-oxidant days in 1967.
85

-------
86
o
1.2
LOCATION YEAR SOURCE c:>
N
0:>
o DOWNTOWN L.A. 1967 (84) ~
D.. AZUSA 1967 (84) ~
o HUNTINGTON PARK 1968 (51)
D..
to-
< 1.0
aI:
><
o 0.8
z
.........
w
z 0.6
w
.....
~ 0.4
w
u
<
   o 
  t:J  0
 t:;  ~
D..   
  0  
 0 0 
0    
   0 0 0 0 
   0 
0.2
AUTOMOBILE EXHAUST VALUE (84)

o
0400
0800
1200
1600 PST
TIME OF DAY
Figure 24. C2H2/NOx Ratios for High Oxidant Days

-------
70
(CURVES FAIRED THROUGH DATA POINTS)
60
AVERAGE OF TYPE '1,2 AND 3' DAYS
 sO    
0   ~  
~     
< 40    
~    
)(     
0   ~ 
Z   
......... 30  AVERAGE OF TYPE '0' DAY ~ 0
o     
u     
  --   
 20    
  ALL SOURCES   
 10    
o
0600
0800
ex>
--.J
o
o
-----------
IV;)
C)
C\1
lr,)
C\1
I
:<::
~
1000
TIME OF DAY
. 1200
1400 PST
Figure 25.
CO/NO Ratios for Huntington Park 1968
x

-------
ex>
ex>
50
.40
o
~
 30
~
)(
o
z 20
........
o
u
10
(CU'RVES FAIRED THROUGH DATA POINTS)
AVERAGE OF TYPES '1,2 AND 3' DAYS
1::.
1::.
--
o
"11
C)
C\J
l.Q
C\J
I
~
~
1::.
1::.
o
- -1::.VEHICLES
1::.
-----
--
o
---0----
ALL SOURCES
o
0600
0800
1000
TIME, PST
1200
Figure 26.
CO/NO RaLios for Commerce 1969
x
1.400 h r

-------
It seems plausible to suspect that there are lower morning
NO
x
levels some days and that this raises peak oxidant.
We will see from
the model studies that the morning buildups of hydrocarbon and carbon
monoxide agreed well with predictions derived directly from inventory
statistics.
Hence, higher
HC/NO
x
ratios are associated with higher
peak oxidant as shown by the chamber experiments reported in Ref. 47.
The 1969
CO/NO
x
ratios do not show the strong association with
peak oxidant that the 1968 data exhibit.
Figure 26 for Commerce indi-
cates that both high- and low-oxidant days have ratios only slightly
higher than the emission source values.
The high-oxidant days are
likely to have an
NO
x
deficit rather than a superabundance of
CO .
The lack of similarity between 1968 and 1969 nitrogen oxide ba1-
ances underscores the need to select a wide sample of days for model
validation.
Conclusions drawn from a single smog episode cannot be
relied upon for establishing a general abatement strategy.
One suspects
that sampling for a particulate nitrate may be a significant step toward
resolving the problems of nitrogen-oxide balances.
Nitrogen dioxide
oxidation processes and interaction with water vapor may form nitric acid
which then leads to nitrates in solution or other condensed phases.
The initial tests of the model (DIFKIN) combining diffusion with
kinetics were conducted for the type 3 day.
Both the rate ratio and
NO
x
source strength ratio hypotheses were tested, as shown in Figs. 27, 28,
and 29.
The first set of graphs illustrates most clearly the need for a
89

-------
160 pphm CURVE PARAMETERS  C\J
  ,....,
     0')
 CURVE r f  c:::.
  C\J
140     I
A 1/2 1 r = RATE RATIO. :<;:
 "'t:
 B 1/3 1 / ~ f = NO FLUX RATIO 
120 C 1/2 1 / ~ 
Z D 1 1/4  
0 100     
.... 
~ 
a&:: 
.... 80
Z 
w 
u 60
Z
o 
u 
 40
 20
 o
 0600
SRL DATA (51)
0800
1000
1200
1400 PST
TIME OF DAY
Figure 27.
(NO + N02) - Concentration Ground Level Huntington Park
on Type 3 Day
90

-------
I
1000 pphm
z
o
....
~
CI=:
.... 100
Z
w
u
Z
o
u
CURVE PARAMETERS
CURVE r f
A 1/2 1
B 1/3 1/4
C 1/2 1/4
D 1 1/4
r = RATE RATIO
f = NO FLUX RATIO
t<;)
1"-i
0)
C)
C\J
I
~
~
0800
1000
TIME OF DAY
1200
1400 PST
Figure 28. High-Reactivity Hydrocarbons Concentration on the Type 3 Day
SRl DATA (51)
10
0600
91

-------
100 pphm
Figure 29.
92
Z 10
o
.....
~
a!::
.....
Z
w
U
Z
o
U
0.1
0600
1
r = RATE RATIO
f = NO FLUX RATIO
CURVE PARAMETERS
CURVE r f
A 1/2 1
B 1/3 1/4
C 1/2 1/4
D 1 1/4
"'"
1"'-;
0}
c::.
C\J
I
~
~
0800
1000
1200
1400 PST
TIME OF DAY
Ozone Concentration at Huntington Park on Type 3 Day

-------
downward adjustment in the nitric oxide source strength (or flux).
Con-
sistent with the results of Refs. 84 and 86, Figs. 24, 25, and 26 suggest
a reduction.
Using
f = 1/4
(a fourfold strength reduction), we see a
great improvement in the model predictions in the
NO
x
curves in Fig. 27.
Because of our present inability to represent the gas-liquid or gas-solid
reactions mentioned above, this flux reduction is not merely a curve
fitting, but is likely to reflect real physical processes.
For these
reasons, the f = 1/4 adjustment must be regarded as a tentative correc-
tion pending the availability of further research data on removal processes
for oxides of nitrogen.
The ratio of rates is examined in these three
figures by comparing curves B, C, and D.
Evidently something between 1/2
and 1/3 the propylene oxidation rate constants gives the best agreement
with the observed values (51).
This tends to support the hypothesis that
the reactivity index goes like the oxidation rate constants in the results
shown in Fig. 10 and 11.
Expanding the validation data to a larger sample, we selected type
2 days for which data were available during the 1968 smog season.
The
statistical preprocessing program derived half-hourly means and standard
deviations for this sample of days.
Hatched areas on Figs. 30, 31, and 32
show the mean values plus or minus one standard deviation.
Again, the
DIFKIN modeling was tested using five mesh stations including the ground
and the inversion base.
Moreover, a homogeneous mixing model was demon-
strated.
This model assumes that anything entering the marine layer from
the ground is vertically mixed instantaneously.
Reactions proceed accord-
ing to the kinetic model derived in Sec. II.
For all of the results in
93

-------
100 pphm
Figure 30.
94
//// MEAN OF OBSERVED DATA (51)
//// .!. STANDARD DEVIATION

- FIVE STATION DIFFUSION MODEL
~
---0900 HOMOGENEOUS MIXING MODEL ~
-- 0600 WITH INITIAL CONDITIONS ~
AT TWO DIFFERENT TIMES ~
~
-<
ex
~
Z
w
U
Z
o
u
1
r = 1 / 2
f=l/.4
0.1
0600
0800
1000
1200
1.400 PST
TIME OF DAY
Nitric Oxide Concentration at Huntington Park on Type 2
Day 1968. f = 1/4; r = 1/2

-------
pphm
100
z
o
~
~
01:
Z 10
w
u
z.
o
u
1
0600
\.0
VI
Y&@~~
~,..-/~
~////
\,\ '
',\
\
\
\
//// MEAN OF OBSERVED DATA (51)
//// .:!:..STANDARD DEVIATION

FIVE STATION DIFFUSION MODEL
HOMOGENEOUS MIXING MODEL
--- 0900 I WITH INITIAL CONDITIONS AT
-- 0600 TWO DIFFERENT TIMES
r-..
1"-1
0")
C:>
"J
:<::
~
0800
1000
TIME OF DAY
1200
1.400 PST
Figure 31.
High Reactivity Hydrocarbon Concentration at Huntington Park
on Type 2 Days 1968. f = 1/4; r = 1/2

-------
\0
(j\
pphm
100
z
o
.....

-------
Figs. 30-32, the curve parameters are
f = 1/4
and
r = 1/2.
The symbol
r
refers to the ratio of the atmospheric-hydrocarbon oxidation rate con-
stants to those of propylene.
Average profile values at 0600 PST and at
0900 PST are used to initiate homogeneous mixing runs.
Some of the pre-
cision of detail is lost in this approximation.
Considering that homo-
geneous mixing calculations only require 5 to 10 percent of the central
proces~or time needed by the five-station diffusion runs, they may well
be useful for cases where parametric effects are studied for many dif-
ferent conditions.
D.
SENSITIVITY STUDIES ON 1969 TRAJECTORIES WITH THE EXPANDED MODEL
Based on the semi-Lagrangian formulation of the photochemica1/
diffusion model, the computed end-point composition of the air masses
depends on initial conditions, flux from the ground along the trajectories,
and on reaction rates.
For our tests, we concentrate on E1 Monte data
because much of the polluted air there comes from somewhere else.
This
is believed to be a more severe test of the model than that at Huntington
Park.
The initial conditions are based on measurements insofar as pos-
sible.
The principal initial values for the 1030 trajectory are as
follows for 0730 hours (PST).
*
~C = 51 pphm
(6 ppm C total HC)
cNO = 24.5 pphm
2

cNO = 3.5 pphm
*
pphm = parts per hundred million.
97

-------
These were interpolated from the Azusa station data (87) from the Los
Angeles County Air Pollution Control District.
Reference to Fig. 15 shows
the basis of this choice.
The reactive hydrocarbon value is derived from
the assumptions of 34 percent reactive fraction and an average carbon
number of 4 for the reactive family of compounds.
These are seasonal
averages over the 1969 measurement months (52) at E1 Monte.
The analysis
that generated the values from gas chromatographic data is discussed
elsewhere (86).
Similarly the 0730 initial values for the 1130 trajec-
tory are obtained from the Commerce data log (52).
They are:
~C = 94.5 pphm (9.7 ppm C)
~O = 43.9 pphm
cNO = 17.4 pphm
2
The hydrocarbon conversion factors here are 41 percent reactive fraction
and an average carbon number of 4.2.
Since the 1230 trajectory begins near the coast, we employ station
76 (La Cienega Boulevard) measurements for 0630 hours (PST) initial
values of nitrogen oxides.
No hydrocarbon data are available from that
station and an
HC/NO -ratio
x
of 2 was chosen.
Although this is not
representative of the inventory ratio, it is representative of many morn-
ing air samples.
Such an observation further reinforces the suspicion
of an NO -deficiency on high oxidant days (86).
x
Thus, the values are:
~C = 54 pphm
~O = 18 pphm
cNO = 9 pphm
2
98

-------
The location of the 1330 trajectory origin is near no station and the
data indicate that the initial pollution cannot be neglected.
Conse-
quently, results were not obtained for the 1330 trajectory.
Ultraviolet data from Ref. 52 were employed to get photodissoci-
ation rates for
N02
by means of calibration functions developed in the
data analysis study (86).
Inversion base altitudes were averaged from
the airborne temperature measurements provided by Scott Research Labor-
atories (52).
To examine parametrically the influence of inventory levels, we
altered the rate. of emission for ground level.
Halving the nominal NO-
fluxes is suggested by the departures of the CO/NOx-ratios and the C2H2/
NO -ratios obtained for high oxidant days (86).
x .
Subsequent halving of
both reactive hydrocarbon and nitric oxide fluxes brings us down to the
adjustment represented by
f = 1/4
in Figs. 30, 31, and 32 but preserves
the HC/NO -ratio.
x
In both cases, the full propylene oxidation rates
were employed.
Table 7 summarizes the results for trajectory end points.
Advancing
down the table we note an ever-growing sensitivity of the results to the
flux adjustments.
This occurs because the increasing wind speed lengthens
the trajectories and there is larger relative exposure of the air mass to
high pollutant fluxes.
In the 1030 case, both hydrocarbon and nitric oxide are low, but
N02
and ozone are high.
Changes in the fluxes have marked effects on
99

-------
TABLE 7
RESULTS OF MODEL SENSITIVITY STUDY
USING 1969 EL MONTE DATA
Concentrations at E1 Monte in pphm
  NO   HC   N02   03 
El Honte          
Trajectory  (1/2HNO (l/4HNO  (l/2HNO (l/4)~NO  (l/2HNO (l/4HNO  (l/2HNO (l/4HNO
Arrival Measured Full ~HC (1/2HHC Measured Full ~HC (l/2HHC Measured Full ~HC (l/2)~HC Measured Full ~HC (l/2HHC
Time (PST) Values Values Values Values
1030 3.4 0.5 0.3 43 34.3 24 16.4 20.5 14.5 13.4 32.6 35.3
1130 3.2 1.5 1.5 64 87.4 70.1 21. 3 58.5 48.6 23.6 28.4 24.2
1230 1.5 1.1 1.0 38 67.5 48.1 10.3 49.2 34.6 24.5 30.9 24.8
NOTE: Nominal values of emission fluxes are denoted by
halved the fluxes derived from inventories.
41. Hence. (l/2)~ means that we
everything but the ozone.
Comparing these end-point compositions with
the initial values cited above, we note a strong dependence on initial
conditions accuracy for this short time scale.
Fortunately, the Azusa
data are available as an aid in this respect.
For the 1130 results, the ozone and nitric oxide come in closer
to the data, but
N02
is extremely high.
This is symptomatic of the
large departures from the radiation-supported quasi-equilibrium that we
noted in analyzing the E1 Monte data (86).
Although the model does not
assume quasi-equilibrium among the three reactions
hv + N02 ~ NO + 
 + 02 + M ~ 03 + M
03 + NO ~ N02 + 02
100

-------
the differential equation solutions nearly always approximate it rather
well.
Again, with the 1230 trajectory, the ozone and nitric oxide levels
match observations reasonably well, but hydrocarbon and
N02
are both
high.
Despite the passage of this air from the seashore and then over
extensive regions of the central basin, we note that the initial values
of the primary pollutants still influence the final concentrations in
a dominant manner.
E.
HISTORY ANALYSIS OF THE 1030 EL MONTE TRAJECTORY
Because of the relative completeness of initial conditions that
we can relate to the Azusa station, we have chosen the 1030 trajectory
to discuss in some detail.
Examining Table 7, we note an overabundance
of ozone at 1030 and a correspondingly rapid completion of
NO ~ N02
conversion.
Reactivity analyses (Sec. II D) and our early modeling
studies suggest reduction of the oxidation rate constants.
To achieve
some level of comparative assessment with the previous work, we assign
one-fourth the nominal
NO
flux and one-half the oxidation rate; hence
f = 1/4
and
r = 1/2
describe the conditions as before.
This time,
however, we preserve the HC/NO -ratio as in the entries in Table 7 and
x
reduce hydrocarbon fluxes by a factor of two.
This means that the dif-
ference in end-point concentrations between this case and the
1/4~NO '
1/2~HC
entries is solely due to the rate constant reduction.
This
differs from the earlier work in which hydrocarbon fluxes were not
reduced.
101

-------
Figure 33 shows the reactive hydrocarbon history starting at Azusa
at 0730 and ending at E1 Monte at 1030 on September 29, 1969.
Despite
the sharp reduction in hydrocarbon fluxes, the calculated curve stays
above the Azusa levels until 1000 hours when it begins to slope-off in
the observed manner.
The model output clearly bears a closer re1ation-
ship to the Azusa measurements than it does to the E1 Monte observations.
This problem is typical of the difficulties we encountered in attempting
to model conditions at the eastern portion of the basin at E1 Monte.
On Fig. 34 we note a sharp drop from the interpolated NO-level
between 0730 and 0740 hours.
This is reflective of the previously noted
failure of the data to approach quasi-equilibrium between
NO, N02' 03'
and sunlight intensity under high-oxidant conditions.
The NO-conversion
seems to proceed at roughly the observed rate after the transient is
absorbed in the system; however, the level ends up closer to Azusa values
than to El Monte values.
Note that if we were to employ 0830 E1 Monte
concentrations as initial values, we would have a lower HC/NO-ratio and
could expect still slower nitric oxide conversion rates.
Thus, both
nitric oxide and hydrocarbon decay more like the Azusa data than the
E1 Monte data.
The N02 behavior on Fig. 35 exhibits more nearly what one would
expect than do either the reactive
HC
or the
NO .
Proceeding from
the end of its transient adjustment to observed sunlight intensity,
the air mass gradually undergoes N02-transition from Azusa levels to

E1 Monte levels as it meanders about in the northeastern area of the
102

-------
60 pphm
z
o
I-
~
~
I-
Z
w
U
Z
o
u
50
40
30
7
Figure 33.
El MONTE
.......-,MODEl
....... ,
- --- AZUSA --
8
12 PST
9 10

TIME OF DAY
11
Reactive Hydrocarbon History Along the 1030 Trajectory.
f = 1/4; r = 1/2 (Ground level concentrations)
t<;)
Q')
<:0
co
C'\]
I
~
~
103

-------
10 pphm
z
o
.-
<
0::
.-
Z
w
u
z
o
u
Figure 34.
104
8
6
4
2
, -.
CD
~:~:
:"-
"
....... MODEL'
----
---
AZUSA
7
8
11
12PST
9 10
TIME OF DAY
Nitric Oxide History Along the 1030 Trajectory.
r = 1/2 (Ground level concentrations)
f = 1/4;

-------
40 pphm
Z 10
o
~ 8
4:
a: 
~ 
Z 6
w 
u 
z 
0 4
u 
El MONTE
20
MODEL ---
--
r
2
1
7
9 10
TlMEOFDAY
11
8
Figure 35.
Nitrogen Dioxide History Along the 1030 Trajectory.
f = 1/4; r = 1/2 (Ground level concentrations)
'-I:;;
~.~.)
'"J'.
:~~
12PST
105

-------
basin.
Nitric oxide conversion supported by increasing sunlight inten-
sities drives the
NOZ
upward.
The ground-based sources continue to
feed in
NO
as it reacts and diffuses upward.
Summing over
NO
and NOZ ' we get excellent total balance behavior
for these oxides of nitrogen.
Figure 36 indicates that not only slopes,
but also magnitudes are represented rather well in the gradual change of
composition moving from initial to final conditions over the three-hour
period.
Apparently the dominant effect of the good behavior of the
NOZ
brings the balance into favorable agreement with the data.
It will be
recalled that this was a key test in the choice of
f = 1/4
after con-
ducting our original modeling study.
Finally, the history of ozone concentration may be seen on Fig. 37.
The measurements of both Azusa and E1 Monte show a remarkable degree of
smoothness and regularity compared with the jagged curves of the species
displayed in the previous figures.
Again, due to the rapid transient
response of the 03/NO/NOz-system to the sunlight ultraviolet intensity,
there is a sharp change in the first ten minutes of the model curve.
As in the case of
NOZ ' however, the ozone undergoes a smooth transition
from its origin to its destination.
Considering the usual sensitivity
of ozone to competing rate determining factors, this degree of realism
is gratifying.
If we applied this same set of assumptions to the other trajec-
tories, we would get too little ozone at the end points.
Table 7 indi-
cates fair agreement with
f = 1/4 and
r = 1
as shown in one of the
106

-------
40 pph m
20
Z 10
o 
.... 8
< 
CI:: 
.... 6
z
w 
U 
Z 
0 4
U 
Figure 36.
.,
.;~
'<-
(()
q
I
~. :
,
2
1
7
9 10
TIME OF DAY
11
12PST
8
Oxides of Nitrogen (NO + NOZ) History Along the 1030
Trajectory. f = 1/4; r - l/Z (Ground level concentrations)
107

-------
.40pphm
z
o
.....
-<
~
.....
Z
w
u
Z
o
u
Figure 37.
108
/
/
"
"
"
MODEL.......""'"
"
.......
.......
"
/
/
/
\ /
v
20
10
8
6
.4
2
1
7
8
11
9 10
TIME OF DAY
Ozone History Along the 1030 Trajectory.
(Ground level concentrations)
f = 1/4; r = 1/2
r-...
0>
'.Q
co
C\;
I
~
<:t
12PST

-------
columns.
The hydrocarbon agreement for these other cases would be even
worse than it stands if
r
were decreased to 1/2.
Because of low con-
fidence in the initial values that apparently dominate, the other trajec-
tories would likely be less than satisfactory as tests of the model.
109

-------
v.
CONCLUDING REMARKS
An overview of these further developments of the GRC photochemical/
diffusion model holds answers to many questions and points the way to
future research needs.
Before detailing the accomplishments and recom-
mending new directions, we might make the general observation that apply-
ing and adapting the modeling tools that we possess now appears preferable
to initiating effort on far more detailed chemical dispersion formulations.
We have maintained a balanced posture in which the model advances and the
improvements in measurements have kept pace with one another.
The chemical descriptions offered here hold the main features of
the NO -chain termination that controls composition effects on secondary
x
pollutant production.
In concert with this, the addition of hydroxyl
radical chemistry is a first step in explaining the "excess rate" of
hydrocarbon oxidation (over that attributable to O-atom attack).
Probably
one of the most uncertain aspects of the system is our inclusion of
HONO
formation (from NO + NOZ) and opposed by photodissociation.
If this is
an important feature of the free radical balance, we really need to know
the photodissociation absorption coefficients for
HONO
as well as some
of the radical-molecule collisional reaction rates.
In his task force
report (88) for Project Clean Air, H. S. Johnston stresses the need to
consider nitrous and nitric acids in the photochemical mechanism.
This
suggests a very real need to monitor these compounds in the laboratory
experiments and in the atmosphere.
Their involvement in aerosols and
surface reactions may well hold the key to the apparent anomalies in
110

-------
the nitrogen balance.
The identification of chemo-mutagenic effects of
ROOO
is yet another reason that it should be investigated.
The brief
examination of hydrocarbon synergism shows at least one way that the
radical chains are cross-linked to influence combined reaction rates.
Experimental data on mixed hydrocarbons will help sort out the most
likely mechanisms.
Likewise, our small study on possible CO interactions
indicates that suggested values of these rate constants indicate a very
strong influence on the propylene/nitric oxide system at concentration
levels as high as 100 ppm.
It may be that atmospheric hydrocarbons that
are not involved in the OR-cycle are far less affected.
In any event,
atmospheric levels of
CO
are much lower than 100 ppm except in the
vicinity of traffic arteries.
Reacting to the need for extended chemical representations, we have
applied Pade approximant techniques to the numerical integration algo-
rithms.
Speed increases of at least four or fivefold are obtained in
the computation comparing the Pade method for the more complex chemical
system with previous methods for the simpler system.
For equal-sized
chemical matrices, the improvements would most likely be even better.
In the interest of making these advances available to the community at
large, we show the mathematical steps in some detail.
Besides the mathematical improvements, the atmospheric model has
been adapted to a semi-Lagrangian formulation.
By following selected
air masses, we avoid commitments of large quantities of memory and the
incursions of artificial diffusion errors.
Most important, we do not
III

-------
end up with stacks of computer printout that relate to regions where
there are no measurements.
It should be added that predictive ca1cu1a-
tions will become ever more useful, but our present levels of resources
and sophistication demand that effort be concentrated on validation.
Only in this way can the confidence be built that is needed for applying
modeling techniques- to implementation planning.
Validation tests of the model for 1969 Los Angeles basin data
turned up several useful findings.
For time intervals within a diurnal
scale, we must use extreme care in selecting initial conditions.
A way
to overcome this need is to compute for several days of real time on a
continuous basis.
Increasing the time scale makes sense because episodes:
tend to cycle through several days.
The cost in computing will go up
more than proportionately, however, because as time scales increase so
must the spatial domain.
Perhaps 100 kilometers of urban/rural influence
zone might be needed in lateral expansion.
Correspondingly, a larger
vertical field will have to be included to account for slow transport
within the inversion layer, if there is one.
Models that require arti-
ficia1 image flows above the marine layer or that assume artificially
inflated "background" levels at the edge of the net will no longer be
useful.
What used to be boundaries will now be included in the compu-
tational field.
The sensitivity tests in the validation studies confirmed some of
the suspicions that we expressed earlier (86), namely, that the quasi-
equilibrium relationship between ozone and the oxides of nitrogen does
112

-------
not seem to be recovered in the data.
The largest departures are for
the highest ozone levels.
Attempting to represent the physical setting
in a consistent manner, we find it difficult to use the measured ultra-
violet intensity to account for the observed ozone buildup and NO-conver-
sion simultaneously.
The inconsistency even appears in the initial
behavior of a modeling run as a transient "induction" process that
rapidly adjusts concentrations to satisfy the rate equations.
Unlike
some models, ours does not impose the quasi-equilibrium, but rather
solves for time history of species with O-atom, ROZ-radicals, and
OH
in the stationary state.
Because of the extreme dependence on initial conditions, our his-
tory analysis concentrates on an air mass with relatively well-defined
concentrations at the beginning and the end of its travel.
Giving it
the initial values, we see the concentrations unfold as the air parcel
moves through the computed simulation procedure.
In view of the sensi-
tivities discovered, the transition of oxidant species
3
and
NOZ
proceeds better than one might expect.
The previously adopted biases
on the NO-flux and the propylene oxidation rates were confirmed. in this
run having very different conditions than those in Huntington Park
represented by 1968 data.
Much more work remains to be done.
We have so many uncertainties
in both the data and the model assumptions, that systematic tests must
be devised to isolate the individual influences of the various parameters.
Our very limited sensitivity study illuminates some of these very serious
113

-------
questions that need to be answered.
The anomalous pattern of NO-flux
followed from our original work, through the data analysis project, and
into this work.
Either some very serious deficiency exists in the trans-
port formulation, or there are some rapid loss mechanisms for oxides of
nitrogen that reduce the apparent emission strengths.
In view of the
extensive efforts directed toward NO -controls, high priority must be
x
given to measuring the terms of the nitrogen balance equation in an urban
area.
Nitric acid vapor, nitrous acid vapors, and particulate nitrates
could hold the key to this question.
The modeling is not precise enough
to pin down the deficit, but the CO/NOx and CZHZ/NOx analyses of the

Los Angeles data (86) showed significant deviations on high-oxidant days.
Since the same types of questions have appeared in laboratory experiments,
it seems that a greater latitude of nitrogen-bearing compounds should be
sought in future atmospheric studies.
The plans announced for a regional air pollution study should hold
many of the solutions to the problems identified here.
Conversely, appli-
cation of the model should provide valuable feedback to such programs.
Clarifications in the chemical mechanism should take the form of better
values of rate constants for the controlling reactions.
Perhaps the very
selection of which reactions to include might be altered for the air con-
. taminant hydrocarbon mix.
Mathematical techniques seem well enough ad-
vanced to match the simpler formulations of photochemical modeling schemes
to the computing machinery available.
The more complex schemes proposed
recently will continue to shed light on questions of dispersion parameters
and inventory accuracy.
114

-------
The future of the mathematical modeling techniques is linked to
cooperative activity between the theoretical and experimental arts in
the field of air pollution.
Phenomena of importance are yet to be added
to any of the mathematical schemes.
The formation of aerosol and its
extinction of ultraviolet radiation has not been explicitly treated in
the computations.
Moreover, the whole area of heterogeneous reactions
on either particulate surfaces or urban surfaces remains obscure.
The
reacting flow problem of mixedness and its influence on kinetics has
not been reduced to an engin~ering procedure for calculational purposes.
Urgent needs for improved air quality management demand renewed
vigor in our attack on many of the fluid dynamic and chemical kinetic
areas plagued by chronic difficulties.
Turbulent mixing and free radical
processes play significant roles here as in many previous technical prob-
1ems.
Pragmatic perspective must guide us, however, in the development
of mathematical modeling lest it become a prophecy which fulfills itself
in totally abstract research activity.
115

-------
10.
11.
LITERATURE CITED
1.
Barth, D. S., "Federal Motor Vehicle Emission Goals for CO, HC,
and NOx Based on Desired Air Quality Levels," Journal of the Air
Pollution Control Association, August 1970, Vol. 20, No.8,
pp. 519-523.
2.
Callaghan, D. J. and M. Feldstein, Meeting Air Quality Standards.
The Pragmatic Approach, Second International Clean Air Congress
Paper AD-36H, Washington, D.C., December 6-11, 1970.
3.
Sutton, 0. G., "A Theory of Eddy Diffusion in the Atmosphere,"
Proc. Roy. Soc., 1932, Vol. A135, pp. 143-165.
4.
Sutton, O. G., Micrometeorology, McGraw Hill, New York, 1953,
p. 34 et seq.
5.
Frenkiel, F. N., "Atmospheric Pollution in Growing Communities,"
Smithsonian Institute Annual Report, 1956, pp. 269-299.
6.
Pooler, F. Jr., "A Prediction Model of
Use with Standard Wind Roses," Into J.
Vol. 4, Nos. 2/4, pp. 199-211.
Mean Urban Pollution for
Air and Water Poll., 1961,
7.
Turner, D. B., "A Diffusion Model for an Urban Area," J. of App1.
Met., February 1964, Vol. 3, pp. 83-91.
8.
"A Simple Diffusion Model for Calculating Point
for Multiple Sources," J. of the Air Pollution
Sept. 1964, Vol. 14, No.9, pp. 347-352.
Clarke, J. F.,
Concentrations
Control Assn.,
9.
Koogler, J. B., R. S. Sholtes, A. L. Danis, and C. I. Harding,
"A Multivariable Model for Atmospheric Dispersion Predictions,"
J. of the Air Pollution Control Assn., 1967, Vol. 17, pp. 211-214.
Miller, M. E. and George C. Holzworth, "An Atmospheric
Model for Metropolitan Areas," J. of the Air Pollution
January 1967, Vol. 17, No.1, pp. 46-50.
Diffusion
Control Assn.,
Martin, D. O. and J. A. Tikvart, A General Atmospheric Diffusion
Model for Estimating the Effects of One or More Sources on Air
Quality, US DHEW Public Health Service, National Air Pollution
Control Administration, 1968.
12.
McElroy, J. L. and F. Pooler, Jr., St. Louis Dispersion Study,
Volume II-Analysis, USDHEW Public Health Service, National Air
Pollution Control Administration, December 1968.
116

-------
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
Turner, D. B., Workbook of Atmospheric Dispersion Estimates, US
DHEW Public Health Service, National Center for Air Pollution Con-
trol, 1967.
Smith,
in the
phere,
M. E., "The Concentrations and Residence Times of Pollutants
Atmosphere," Chemical Reactions in the Lower and Upper Atmos-
Stanford Research Institute, April 1961, pp. 273-286.
Wanta, R. C., "Meteorology and Air Pollution," Air Pollution, 1968,
Vol. 1 2d ed, A. C. Stern Ed., Academic Press, New York, Ch. 7.
Lamb, R. G., An Air Pollution Model of Los Angeles, University of
California Los Angeles, M. S. Thesis, 1968.
Ludwig, F. L., W. B. Johnson, A. E. Moon, and R. L. Mancuso, !
Practical. Multipurpose Urban Diffusion Model for Carbon Monoxide,
Stanford Research Institute Report, September 1970.
Roberts, J. J., E. J. Croke, A. S. Kennedy, J. E. Norco, and L. A.
Conley, A Multiple-Source Urban Atmospheric Dispersion Model,
Argonne National Laboratory Report ANL/ES-CC-007, May 1970.
Karplus, W. J., G. A. Bekey, P. J. Pekrul, "Atmospheric Diffusion
of Air Pollutants," Ind. and Eng. Chern., 1958, Vol. 50, pp. 1657-
1660.
Friedlander, S.
chemical Smog,"
Vol. 3, No. 11,
K. and J. H. Seinfeld, "A
Environmental Science and
pp. 1175-1182.
Dynamic Model of Photo-
Technology, November 1969,
Calvert, S., "A Simulation Model for Photochemical Smog," California
Air Environment, July-September 1969, Vol. 1, No.3, p. 1.
Wayne, L., R. Danchick, M. Weisburd, A. Kokin, and A. Stein, Model-
ing Photochemical Smog on a Computer for Decision-Making, Paper
#7-018 at the 63rd Annual Meeting of the Air Pollution Control
Association, S to Louis, Mo., June 14-18, 1970.
Westburg, K. and N. Cohen, The Chemical Kinetics of Photochemical
Smog as Analyzed by Computer, Paper No. 70-753, American Institute
of Aeronautics and Astronautics 3rd Fluid and Plasma Dynamics Con-
ference, Los Angeles, California, June 29-July 1, 1970.
Sklarew, R. C., A New Approach: The Grid Model of Urban Air Pollu-
tion, Air Pollution Control Association Paper 70-79, 63rd Annual
Meeting, St. Louis, Missouri, June 14-18, 1970.
25.
Seinfe1d, J. H., P. Roth, S. D. Raynolds, and T. A. Hecht, Simula-
tion of the Los Angeles Basin, 161st National Meeting of the American
Chemical Society, Los Angeles, California, March 28-April 2, 1971.
117

-------
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
Eschenroeder, A. Q., Validation of Simplified Kinetics for Photo-
chemical Smog Modeling, General Research Corporation IMR-1096,
September 1969.
Leighton, P. A., Photochemistry of Air Pollution, Academic Press,
New York, 1961.
Saltzman, B. E., "Kinetic Studies of Formation of Atmospheric Oxi-
dants," Industrial and Engineering Chemistry, April 1958, Vol. 50,
No.4, pp. 677-682.
Wayne, 1. G., "On the Mechanism of Photo-Oxidation in Smog,"
Archives of Environmental Health, August 1963, Vol. 7, No.8,
pp. 113-123.
Altshuller, A. P., and J. J. Bufalini, "Photochemical Aspects of
Air Pollution: A Review," Photochemistry and Photobiology, 1965,
Vol. 4, pp. 97-146.
Haagen-Smit, A. J., and 1. G. Wayne, "Atmospheric Reactions and
Scavenging," Air Pollution, Vol. I, ed. A. C. Stern, Academic Press,
New York, 2nd ed., 1968, pp. 149-186.
Stephens, E. R., "Chemistry of Atmospheric Oxidants," J. Air Poll.
Control Assn., March 1969, Vol. 19, pp. 181-185.
Tuesday, C. S., The Atmospheric Photo-oxidation of Trans-Butene-2
and Nitric Oxide, General Motors Research Laboratories GMR-332,
1961.
Bufalini, J. J. and K. L. Brubaker, Photo-oxidation of Formaldehyde
at Low Partial Pressures, Symposium for Chemical Reactions in Urban
Atmospheres, GM Research Laboratories, Warren, Michigan, October
6-7, 1969.
Altshuller, A. P., DHEW, private communication, September 1969.
Westberg, K., Aerospace Corporation, private communication.
37.
DASA Reaction Rate Handbook, DASA 1948, October 1967.
38.
Caplan, J. D., "Smog Chemistry Points the Way
Emission Control," Vehicle Emissions II: SAE
1966, Vol. 12, New York, pp. 20~3l.
to Rational Vehicle
Progress in Technology,
39.
Altshuller, A. P., S. L. Kopczynski, W. A. Lonneman, F.
and R. Slater, "Chemical Aspects of the Photo-oxidation
Propylene-Nitrogen Oxide System," Environmental Science
~, November 1967, Vol. 1, pp. 899-914.
L. Becker,
of the
and Techno-
118

-------
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
Kopczynski, S. L., unpublished data, transmitted October 1969.
Schuck, E. A. and G. J. Doyle, Photooxidation of Hydrocarbons in
Mixtures Containing Oxides of Nitrogen and Sulfur Dioxide, Air
Pollution Foundation Report No. 29, San Marino, California, October
1959.
Stedman, D. H., E. D. Morris, Jr.,
Weinstock, The Role of OH Radicals
Chemical Society Division of Water
Illinois, September 13-18, 1970.
E. E. Daby, H. Niki, and B.
in Photochemical Smog, American
Air and Waste Chemistry, Chicago,
Holmes, J. R., A. D. Sanchez, and A. H. Bockian, Atmospheric Photo-
chemistry: Some Factors Affecting the Conversion of NO to N02,
Pacific Conference on Chemistry and Spectroscopy, San Francisco,
October 6-9, 1970.
Altshuller, A. P. and J. J. Bufalini, "Photochemical
Air Pollution: A Review," Environmental Science and
January 1971, Vol. 5, No.5, pp. 39-64.
Aspects of
Technology,
Seinfeld, J. H., private communication, letter dated June 2, 1970.
Altshuller, A. P., S. L. Kopczynski, D. Wilson, W. Lonneman, and
F. D. Sutterfield, "Photochemical Reactivities of n-Butane and
Other Paraffinic Hydrocarbons," Journal of the Air Pollution Control
Assn., October 1969, Vol. 19, No. 10, pp. 787-790.
Korth, M. W., A. H.
carbon to Oxides of
Part 1," Journal of
Vol. 14, No.5, pp.
Rose, Jr., and R. C. Stahman, "Effects of Hydro-
Nitrogen Ratios on Irradiated Auto Exhaust,
the Air Pollution Control Assn., May 1964,
168-175.
Agnew, W. G., "Automotive Air
1968, Series A, Vol. 307, pp.
paper by C. S. Tuesday, B. A.
Nebel, June 1967).
Pollut ion Research," Proc. Roy. Soc.,
153-181. (Data reproduced from APCA
D'Alleva, J. M. Heuss, and G. J.
Heicklen, J., K~ Westberg, and N. Cohen, The Conversion of NO to N02
in Polluted Atmospheres, Pennsylvania State University Center for
Air Environment Studies Publication 115-69, July 1969.
Westberg, K., N. Cohen, and K. W. Wilson, "Carbon Monoxide: Its
Role in Photochemical Smog Formation," Science, March 12, 1971,
Vol. 171, pp. 1013-1015.
Final Report on Phase I. Atmospheric Reaction Studies in the Los
Angeles Basin, Vols. I and II, Scott Research Laboratories, June
30, 1969.
119

-------
52.
53.
54.
55.
56.
57.
58.
Final Report. 1969 Atmospheric Reaction Studies in the Los Angeles
Basin, Vo1s. I-IV, Scott Research Laboratories, February 1970.
Stephens, E. R., and W. E. Scott, "Relative Reactivity of
Hydrocarbons in Polluted Atmospheres," Proceedings of the
Petroleum Institute, 1962, Vol. 42 (III), p. 665.
Various
American
A1tshu11er, A. P., "An Evaluation of Techniques
tion of the Photochemical Reactivity of Organic
May 1966, Vol. 16, No.5, pp. 257-260.
for the Determina-
Emissions," J. APCA,
Bonamassa, F. and H. Wong-Woo, "Composition and Reactivity of Ex-
haust Hydrocarbons from 1966 California Cars," Division of Water
Air and Waste Chemistry 152nd National Meeting American Chemical
. Society, New York, N. Y., September 11-16,1966.
Ne1igan, R. E., "Hydrocarbons in the Los Angeles
Archives of Environmental Health, December 1962,
pp. 581-591.
Atmosphere,"
Vol. 5, No. 12,
Stephens, E. R., and Frank R. Burleson, "Analysis of the Atmosphere
for Light Hydrocarbons," Journal of the Air Pollution Control Assn.,
March 1967, Vol. 17, No.3, pp. 147-153.
Gordon, R., H. Mayrsohn, R. Ingels, "C2-C5
Angeles Atmosphere," Environmental Science
1968, Vol. 2, pp. 1117-1120.
Hydrocarbons in the Los
and Techno10~y, Decembe~
59.
A1tshu11er, A. P., S. L. Kopczynski, W. A. Lonneman, and F. D.
Sutterfield, "A Technique for Measuring Photochemical Reactions in
Atmospheric Samples," Environmental Science and Technology, June 1970,
Vol. 4, No.6, pp. 503-506.
60.
Stephens, E. R., and F. R. Burleson, "Distribution of Light
carbons in Ambient Air," Paper 69-122 Air Pollution Control
ciation 62nd Annual Meeting, 1969.
Hydro-
As s 0-
61.
Neiberger, N. and J. Edinger, Meteorology of the Los Angeles Basin
with Particular Respect to the "Smog" Problem, Air Pollution Founda-
tion Report No.1, April 1954.
62.
Renzetti, N. (ed.), An Aerometric Survey of the Los Angeles Basin
August November 1954, Air Pollution Foundation Report No.9, July
1955.
63.
Eschenroeder, A. Q., and J. R. Martinez, Mathematical Modeling of
Photochemical Smog, General Research Corporation IMR-1210, December
1969 (Also AlAA paper 70-116 presented at the 8th Aerospace Sciences
Meeting, New York, N. Y., January 19-21, 1970).
120

-------
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
Ames, W. F., Nonlinear Partial Differential Equations in Engineer-
ing, N. Y. Academic Press, 1965, pp. 341-342.
Varga, R. S., "On Higher Order Stable Implicit Methods for Solving
Parabolic Partial Differential Equations," J. Math and Physics,
1961, Vol. 40, pp. 220-231.
Magnus, D. and H. Schecter, Analysis and Application of the Pade
Approximation for the Integration of Chemical Kinetic Equations,
Technical Report 642, General Applied Science Laboratories, Inc.,
1967.
Martinez, J. R., Improving the Efficiency in Atmospheric Reaction
Modeling Calculations, General Research Corporation IMR-1291,
April 1971. (Also Air Pollution Control Association Paper 71-138
at the 64th National Meeting, Atlantic City, New Jersey, June 27-
July 1, 1971.)
Pasqui11, F., Atmospheric Diffusion, Van Nostrand and Co., London,
1962, p. 72.
Rossby, C. G., and R. B. Montgomery, "The Layer of Frictional In-
fluence in Wind and Ocean Currents," Physical Oceanography and
Meteorology, M.I.T. and Woods Hole Oceanographic Institution, 1935,
Vol. 3, No.3.
Priestly, C. H. B., Turbulent Transfer in the Lower Atmosphere,
University of Chicago Press, 1969, pp. 33-38.
Aleks, androva A. K., N. L. Byzova, and G. B. Mashkova, "Experiments
on the Spreading of Precipitating Admixture from a Point Source in
the Bottom Layer of the Atmosphere," Investigation of the Bottom
300-Meter Layer of the Atmosphere, ed. N. L. Byzova, (translated
from the Russian by Israel Program for Scientific Translation),
Jerusalem, 1965, pp. 1-12.
Lettau, H., "A Reexamination of the 'Leipzig Wind
ing Some Relations Between Wind and Turbulence in
Layer," Te11us, 1950, Vol. 2, pp. 189-200.
Profile' Consider-
the Frictional
Ivanov, V. N., "Statistical Characteristics of Turbulent Diffusion
and Their Estimation in the Bottom Layer of the Atmosphere,"
Investigation of the Bottom 300-Meter Layer of the Atmosphere,
ed. N. L. Byzova (translated from the Russian by Israel Program for
Scientific Translation), Jerusalem, 1965, pp. 36-42.
74.
Hanna, S. R., "A Method for Estimating Vertical Eddy Transport in
the Planetary Boundary Layer Using Characteristics of the Vertical
Velocity Spectrum," J. of Atmospheric Sciences, November 1968,
Vol. 25, No.6, pp. 1026-1033.
121

-------
75.
76.
77.
78.
79.
80.
81.
82.
Craig, R. A., "Vertical Eddy Transfer of Heat and Water Vapour in
Stable Air," J. of Meteorology, 1949, Vol. 6, pp. 122-133.
Wu, S. S., "A Study of Heat Transfer Coefficients in the Lowest
400 Meters of the Atmosphere," Journal of Geophysical Research,
April 15, 1965, Vol. 70, No.8, pp. 1801-1807.
Hosler, C. R., "Vertical Diffusivity from Radon Profiles," Journal
of Geophysical Research, December 20, 1969, Vol. 74, No. 28, pp.
7018-7026.
De Zorzo, G., "App1icazione della Equazione di Diffusione a110
Studio del1a Bassa Atmosfera," Rivista di Meteoro1ogica Aeronautica.
March 1970, Vol. 30, No.1, pp. 3-28.
Monthly Reports of Meteorology, Air Pollution Effects and Contami-
nant Maxima, Air Pollution Control District, County of Los Angeles.
Lemke, E. E., G. Thomas, W. E. Zwiacher (eds.), "Profile of
Pollution Control in Los Angeles County," APCS, Los Angeles
January 1969, p. 3.
Air
County,
Larson, G. P., J. C. Chipman, and E. K. Kauper, "Distribution and
Effects of Automotive Exhaust Gases in Los Angeles," Vehicle Emis-
sions I. SAE Progress in Technology Series, 1964, Vol. 6, pp. 7-16.
Roberts, P. J. W., P. M. Roth, and C. L. Nelson, Contaminant Emis-
sions in the Los Angeles Basin--Their Sources Rates and Distribution,
Systems Applications, Inc. Report 71SAI-6, March 1971.
83.
Eschenroeder, A. Q., Some Preliminary Air Pollution Estimates for
the Santa Barbara Region. 1970-1990, General Research Corporation
IMR-1278, March 1970.
84.
Gordon, R. J., H. Mayrsohn, and R. M. Ingels, "C2-C5 Hydrocarbons
in the Los Angeles Atmosphere," Environmental Science and Technology,
December 1968, Vol. 2, pp. 1117-1120.
85.
Eschenroeder, A. Q., An Approach for Modeling the Effects of Carbon
Monoxide on the Urban Freeway User, General Research Corporation
IMR-1259, January 1970.
86.
Eschenroeder, A. Q., and J. R. Martinez, Analysis of Los Angeles
Atmospheric Reaction Data from 1968 and 1969, General Research
Corporation CR-1-170, July 1970.
87.
Monitoring Data Sheets from Los Angeles County Air Pollution Control
District, 1969.
122

-------
88.
Johnston, H., "Reactions in the Atmosphere," Project Clean Air Task
Force Assessments, September 1, 1970, Vol. 4, Task Force No.7,
Section 3, University of California, p. 3-1.
123

-------