EPA-600/4-76-029C
June 1976
Environmental Monitoring Series
IIPIRICAL TECHNIQUES FOR ANALYZING
QUALITY AND METEOROLOGICAL DATA
Part III. Short-Term Changes in
Ground-Level Ozone Concentrations:
An Empirical Analysis
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into five series. These five broad
categories were established to facilitate further development and application of
environmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the ENVIRONMENTAL MONITORING series.
This series describes research conducted to develop new or improved methods
and instrumentation for the identification and quantification of environmental
pollutants at the lowest conceivably significant concentrations. It also includes
studies to determine the ambient concentrations of pollutants in the environment
and/or the variance of pollutants as a function of time or meteorological factors.
This document is available to the public through the National Technical Informa-
tion Service. Springfield, Virginia 22161.
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EPA-600/4-76-029C
June 1976
EMPIRICAL TECHNIQUES FOR ANALYZING AIR QUALITY
AND METEOROLOGICAL DATA
Part III: Short Term Changes in Ground-Level
Ozone Concentrations: An Empirical Analysis
by
Leo Breiman and W. S. Meisel
Technology Service Corporation
2811 Wilshire Boulevard
Santa Monica, California 90403
Contract No. 68-02-1704
Project Officer
Kenneth L. Calder
Meteorology and Assessment Division
Environmental Sciences Research Laboratory
Research Triangle Park, North Carolina 27711
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF RESEARCH AND DEVELOPMENT
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
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DISCLAIMER
This report has been reviewed by the Environmental Sciences
Research Laboratory, U.S. Environmental Protection Agency, and
approved for publication. Approval does not signify that the
contents necessarily reflect the views and policies of the
U.S. Environmental Protection Agency, nor does mention of trade
names or commercial products constitute endorsement or recommen-
dation for use.
n
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PREFACE
This is the third of a trilogy reporting work performed under EPA
contract no. 68-02-1704 examining the potential role of state-of-the-art
empirical techniques in analyzing air quality and meteorological data.
The three companion reports are entitled as follows:
I. The Role of Empirical Methods in Air Quality and Meteorological
Analyses
II. A Feasibility Study of a Source-Oriented Empirical Air Quality
Simulation Model
III. Short-Term Changes in Ground-Level Ozone Concentrations:
An Empirical Analysis
m
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ABSTRACT
This volume reports the results of a preliminary exploratory analysis
of ozone and ozone precursor data. Parcels of air were tracked mathe-
matically as they traveled over a region of the Los Angeles basin. The
one- and two-hour changes in ozone levels in a parcel were related to
previous hourly readings in that parcel of reactive hydrocarbons, methane,
nitrous oxide, nitrogen dioxide, ozone, solar radiation, and temperature
data. The data were formed by spatial interpolation of the hourly pollu-
tant and wind field measurements taken during the summer of 1973 at seven
stations scattered over the Los Angeles basin.
Through a nonlinear, nonparametric regression technique, we found
that virtually all of the predictive capability was contained in three
variables:
(1) the current ozone level,
(2) the current solar radiation reading (Langleys per hour), and
(3) the current nitrogen dioxide level.
These three variables explained 71% of the variance in the next two-hour
change in ozone and 60% of the variance of the noisier one-hour ozone
change data.
A continuous piecewise linear multivariate approximation to the two-
hour change data was used to explore and model the relationship between
the ozone change and the current ozone, nitrogen dioxide, and solar radiation
values, explaining 61% of the variance. The qualitative conclusions are
that there are basically two regimes:
IV
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(1) Below the average of one-hour ozone levels, the ozone change is
determined largely by the solar radiation and nitrogen dioxide
levels, with larger values of these latter two related to larger
values of the ozone change. The largest positive changes in
ozone occur in this regime.
(2) At above-average one-hour ozone levels, the ozone level has
a strong negative association with ozone change, and moderate
to high levels of nitrogen dioxide and solar radiation are asso-
ciated with low to moderately above-average changes in
ozone.
The specific equations of the empirical model provide a quantitative
statement of the relationship which produces a correlation between pre-
dicted and actual values of 0.78 over 1800 samples. This approach can
be extended to the derivation of a full set of empirical difference equa-
tions for the main chemical species, incorporating emissions.
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CONTENTS
PREFACE iii
ABSTRACT iv
FIGURES viii
TABLES ix
ACKNOWLEDGMENTS x
1. INTRODUCTION 1
1.1 MOTIVATION 1
1.2 TECHNICAL APPROACH 5
Empirical Difference Equations 5
Estimating Transport and Dispersion Effects 8
1.3 SUMMARY OF THE STUDY 11
2. PROJECT PURPOSE AND DESIGN 15
3. THE TRAJECTORY INTERPOLATION PROGRAM 19
4. THE EXPLORATORY PHASE 25
5. THE RELATIONSHIP OF A03 TO 03, N02, AND SR 37
6. CONCLUSIONS 51
REFERENCES 52
CONCLUDING REMARKS OF PROJECT OFFICER 57
APPENDIX 62
vn
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FIGURES
Number Page
1 Estimated trajectory of air arriving at
Pasadena, El Monte, Long Beach, and
Santa Ana at 0400 September 29, 1969 9
2 Estimated trajectory of air arriving at
Pasadena, El Monte, Long Beach, Santa Ana,
and Pomona at 1600 September 29, 1969 10
3 An illustration of the basis of a
statistical interpretation of the
trajectory estimation procedure 12
4 The study region 20
5 Interpolating pollutant levels over
a triangular region 22
6 Temperature vs. solar radiation 29
7 03 vs A03 (every 4th point sampled) ....... 33
8 SR vs A03 (every 4th point sampled) 39
9 N0? vs A03 (every 4th point sampled) 40
10 Graph of EFAP regression surface, SR = 100 ... 47
11 Graph of EFAP regression surface, N0? = 9.0 ... 48
12 Graph of EFAP regression surface, 0, = 6.1 ... 49
vm
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TABLES
Number Page
Frequency Breakdown of One-Hour Changes
in A03 26
2 Frequency Breakdown of Two-Hour Changes
in ACL 26
3 Percent of Variance Explained (Single Variables) ... 28
4 Percent of Variance Explained (Pairs of Variables) . . 28
5 Percent of Variance Explained (Triplets of
Variables) 28
6 Frequency of HC Levels (ppm) by Hour
For All Stations 31
7 Relation of 03 Levels at Pomona to HC Levels at
Los Angeles Civic Center 31
8 PVEs Computed for the Four New Data Bases 33
9 Results of Linear Stepwise Regression of the
Dependent Variable LogUCU) 34
10 Two-Hour A03 Averages Stratified by SR and 03 41
11 Means of Variables by Region 42
12 Mean Value Characteristics 42
13 Standard Deviations of Variables by Region 43
14 EFAP Equations for A03 44
15 Normalized Equations for AO-, 44
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ACKNOWLEDGMENTS
The suggestions of EPA reviewers, particularly the project monitor,
Kenneth L. Calder, have led to significant improvements in the clarity
of this report.
Without the able aid of Saul Miller, William Liles, and Mike Teener
of Technology Service Corporation in programming and data base prepara-
tion, this report literally could not have been completed.
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1. INTRODUCTION
The intent of this study was to examine the possibility of deriving
empirical difference equations that would describe the production of
ozone (03) in the urban environment. One- and two-hour changes in ozone
concentration were related to the concentrations of certain precursor pol-
lutants and meteorological variables. As part of a three-part study of
the role of empirical approaches in air quality and meteorological appli-
cations, the present study was limited in scope to an exploratory analysis
of this concept. Accordingly, a difference equation for ozone alone was
examined. Further, limitations on the scope of the study and the data
available prevented consideration of a number of meteorological variables
that could potentially be important. Emissions measurements were not
available in the data base constructed for this exploratory analysis
and were not used. Hence, the objective of this study was to obtain an
indication of the degree to which the observed data could be explained
despite the limitations indicated.
In the remainder of this introduction, the ozone problem is reviewed
and the study summarized.
1.1 MOTIVATION
Ozone and its precursors have been investigated, studied, and analyzed
extensively in the past five years. Since A. J. Haagen-Smit revealed his
findings on ozone formation in photochemical oxidation of organic sub-
stances some twenty years ago, the subject of oxidant pollution has evolved
from a local phenomenon in the Los Angeles area to a problem of national
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importance. The air pollution literature abounds with articles by chem-
ists, meteorologists, mathematical modelers, statisticians, and research
scientists that discuss the chemical formation, transport, and destruction
of oxidants in the troposphere and the stratosphere on spatial scales
ranging from micro to synoptic.
Currently, the motor vehicle is the principal source of oxidant pre-
cursors in urban atmospheres. The emissions of hydrocarbons and oxides
of nitrogen from motor vehicles augmented by industrial sources and fos-
sil fuel power plants in our metropolitan complexes appear to be the
source of oxidant concentrations some 50 to 100 miles away.
In recent years, several field studies of ozone and/or its precursors
have been conducted in nonurban areas. Although these areas are remote
from large population centers, ozone concentration levels exceed the na-
tional ambient standard of 160 yg/m (0.08 ppm). At such times, it appears
that meteorological factors such as fronts, low-level stability, mixing
height, and high-pressure systems are directly related to observed ozone
concentrations.
Excessive photochemical air pollution, characterized by ozone, is
the source of eye irritation, headaches, and chest discomfort. Consequently,
well founded oxidant control strategies are necessary to minimize the im-
pact of ozone and its precursors. Such strategies cannot be developed
without a clear understanding of the causes of high ozone concentration
in rural and urban atmospheres.
There has been a great deal of research on the oxidant problem. The
bibliography of this volume was limited to articles published after 1969.
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There are more than fifty of them. Our review does not include photochem-
ical models since a very thorough discussion of such work was recently
published by Roth [45].
Many of the characteristics of ozone formation and transport are
controversial. Some conclusions and claims reported in the literature
follow:
(1) Oxidant air pollution may be characterized as the result of
a complex series of photochemical reactions stemming from reactive hydro-
carbon (RHC) and nitrogen oxide (NO ) emissions. The rate and extent
rt
of the photochemical reactions are affected by precursor concentrations,
solar radiation (SR), residence time in the air and current oxidant con-
centration [9,10,11,18,22,40,42].
(2) Several meteorological factors have been related to the spatial
and temporal changes in observed oxidant concentrations. The important
meteorological parameters are (a) temperature at the top of the inversion,
(b) surface wind speed, (c) the intensity of solar radiation, (d) maximum
surface temperature, (e) depth of the mixing layer, and (f) the water
vapor mixing ratio [1,2,10,19,27,31,35,48].
(3) During weather periods that are conducive to air quality stag-
nation and thus to the onset of episode-conditions, the buildup of oxidant
concentrations aloft in the inversion layer is suspected of contributing
substantially to the observed increases in surface concentrations. Topo-
graphical features such as land-sea contrasts and mountain-valley altitude
differences play a fundamental role in these situations [3,5,6,25,26].
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(4) Urban oxidant pollution is transported by the wind field
over distances as great as 100 miles and adds to the pollution of rural
communities [7,8., 12,13,14,16,17,33,43,46,50,52].
(5) Results of field studies across the country have shown that
local ozone control strategies are unlikely to succeed. In general,
broad-scale regional oxidant control measures are required to meet NAAQS
levels [18,19,30,33,50,52]. There are indications that ozone and/or its
precursors can be transported over 1000 km to give readings in excess
of 0.1 ppm.
(6) The chemistry of oxidant formation in the atmosphere is more
complex than that suggested in the smog chamber. Some researchers claim
that ozone formation is significantly influenced by aerosol-radical inter-
actions and thus that photochemical models that omit heterogeneous chem-
istry cannot accurately represent the chemistry of the urban atmosphere
[18,20,33,29,41].
(7) Sulfur compounds, CO and CH^, are unimportant species in urban
photochemistry [18].
(8) Even though there is a distinct reduction in the emission of
primary pollutants between the hours of 5 a.m. and 1 p.m. on weekends as
compared to weekdays, there is no corresponding reduction in 0- concen-
trations. This is known as the "weekend effect." It is supportive evi-
dence that the proportional mix, and not only absolute amounts of primary
pollutants, is of importance in oxidant formation [15,44,53].
(9) In the Los Angeles area, the reduction in hydrocarbon emissions,
due to automotive controls, in combination with the increase in NO emis-
/\
sions has contributed to the decrease in oxidant concentration [24,34].
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It is obvious that the oxidant formation and transport process is
quite complex. Unraveling the sometimes contradictory conclusions of re-
searchers to obtain a clear insight into the effect of controls will not
be simple to do. The present study uses available data to perform an ex-
ploratory analysis of the amount of information required to explain ob-
served data. In the following subsection, that research is summarized.
1.2 TECHNICAL APPROACH
The intent of the present study is not to obtain definitive results
on the process of ozone formation but to test a technical approach that
has the potential of clarifying some of the issues and providing a rela-
tively simple empirical model for estimating the impact of control meas-
ures. There are two key components of the technical approach.
(1) The development of empirical difference equations for one-
and two-hour changes in a pollutant as functions of the
last measured values of the pollutant, meteorological fac-
tors, and emissions. This approach is used to model the
chemistry of the process.
(2) An interpolation approach to estimating the effect of
transport and dispersion. An approximate trajectory is
used to estimate the precursor concentrations.
It is beyond the scope of the present study to formulate these ap-
proaches in a full theoretical framework. We will, however, attempt to
provide an intuitive framework.
Empirical Difference Equations
Suppose a set of differential equations describing a physical pro-
cess was given by Equation 1:
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dC1
2
eft -- F2^1* ^2' '"' ^R' Ul ' U2* "'* US
dCR
d~t FR^CT C2* " CR; UT U2 ..... US^ '
where
C-, , Cyi , CR are state variables and
u-j , u2, .... us are input variables.
(In the present context, C.. could be regarded as a concentration of a par-
ticular pollutant and u. as an external influence such as a meteorological
variable or an emission.)
In implementing such equations on the computer, one usually uses a
numerical integration technique. One such technique is Euler integra-
tion, where the derivative is in essence approximated as a difference over
a small time interval At:
dCi C.(t + At) - C
Bl~~ - Al
Replacing the derivatives in Eq. (1) with an approximation such as in
Eq. (2) results in a set of difference equations, for example,
CR(t); Ul(t) ..... us(t)] , (3)
where
AC.(t) = C.(t + At) - C.(t) .
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Since the values of the state variables and the external variables are
calculated only at discrete intervals, the result of the difference equa-
tions is only an approximation to the result given by the differential
equations. In this context, the smaller At, the more accurate the ap-
proximation to the differential equation.
However, if one begins with the point of view that the intent is to
obtain an empirical difference equation of the form of Eq. (3), the focus
of the problem shifts. In the empirical case, the difference AC as well
as values of C.. and u.. are obtained from measurements. This encourages
use of a considerably larger interval At for the following reasons:
(1) Data is measured at discrete time intervals, and most his-
torical data is available for large time increments such
as one hour.
(2) Measuring short-term changes is similar to measuring deri-
vatives of a continuous signal. The shorter the interval,
the more susceptible the measurement is to "noise." (A brief
discussion of this question is given in more formal terms in
the Appendix.)
(3) It may require a much larger set of state variables and ex-
ternal variables to describe very short-term changes, even
if the data were available. If the empirical model is to be
used in a context where longer-term changes are of most in-
terest, then attempting to explain those changes alone (rather
than as a sequence of smaller changes) can potentially allow
the use of fewer state variables at the expense of a less com-
plete explanation of the process.
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To implement this approach in full, difference equations for all the
major pollutants and precursors on which measurements were available would
be derived empirically. In the present exploratory analysis, we have
simply chosen one of these equations (for ozone) and studied the degree
to which we can relate the one-hour and two-hour changes in this species
to precursor pollutants and to some meteorological variables. Emissions
measurement were not easily available and could not be included within
the scope of this study, nor could all potentially important meteorologi-
cal variables be considered. The context in which the reader should then
interpret the results is as the degree to which the change in ozone can
be explained despite these limitations. Whatever degree of explanation
of the variance in one- or two-hour changes in ozone we can achieve within
these limitations can be improved when more of the omitted factors are
taken into account. This analysis will thus provide a pessimistic esti-
mate of the degree of success that can be expected in a full-scale imple-
mentation of the approach.
Estimating Transport and Dispersion Effects
Because of transport and dispersion, the concentration of ozone at a
given location may result from concentrations of precursor pollutants oc-
curring earlier in the day at other locations. We thus include in the anal
ysis consideration of the transport and dispersion mechanism. For this
exploratory analysis, we have adopted a rather simple model. The model es-
timates the trajectory of a "parcel" of air from ground-level measurements
of the wind field. As illustrated in Figures 1 and 2, a parcel arriving
at a given location at a given time (e.g., Pasadena at 1600 hours) is es-
timated, from the current wind direction, to have been at another location
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Hoooo
\OIOO
/,
BURBANK
O
0200
0300
X.0400
O
PASADENA
EL MONTE
O
AZUSA
O
POMONA
0300
0400
\o
n ^
ฐ100
0 2
8 10
An irregular early morning meandering
pattern exists at Long Beach, Santa Ana,
and El Monte. Pasadena, on the other
hand, shows a northerly flow pattern
due to nocturnal air drainage down the
mountains combined with an offshore
wind flow. The lengths of the arrows
give an indication of how much the air
has moved during an hour interval.
None of the stations show more than
4 mph air movement for the early morning
hours.
Figure 1. Estimated trajectory of air arriving at Pasadena,
El Monte, Long Beach, and Santa Ana at 0400
September 29, 1969.
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10
BURBANK
o
PASADENA
O
1600
I600Q
EL MONTE
1600 LONG
O BEACH
O
AZUSA
1500
I600O
POMONA
SANTA
ANA
MILES
0246 8 10
All of the stations show the dominance of onshore
sea breezes with a tendency of higher velocities
later in the afternoon. The more regular air
trajectories of afternoon also show a greater air
movement than early in the morning as shown by
the greater lengths of the arrows. The deflecting
influence of the Santa Monica mountains causes the
air trajectory to curve northward as it approaches
Pasadena.
Figure 2. Estimated trajectory of air arriving at Pasadena,
El Monte, Long Beach, Santa Ana, and Pomona at
1600 September 29, 1969.
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11
one hour earlier. The distance traveled from that direction is given by
the current wind speed. The trajectory is tracked backwards to give a
sequence of hourly locations. The values of pollutant levels at these
points at the given times are obtained by an interpolation procedure
described in the body of the report.
Figure 3 illustrates the basis for interpreting the trajectory esti-
mation procedure statistically. It is important to emphasize that we are
not assuming that this trajectory represents physical fact or that only
ground-level wind measurements are important; we are simply taking an ap-
proximate approach to the dispersion/transport problem and attempting to
determine how far this simple approach will carry us. To the degree that
this approach is a reasonable average approximation to the effects of trans-
port, it will suffice. This certainly does not imply that a more elaborate
approach might not produce better results.
1.3 SUMMARY OF THE STUDY
We "tracked" parcels of air as they traveled over a region of the Los
Angeles basin. We then related the one- and two-hour changes in 03 levels
in a parcel to previous hourly readings in that parcel of reactive hydro-
carbons, methane, nitric oxide, nitrogen dioxide, ozone, solar radiation,
and temperature data. The data were formed by interpolating the hourly
pollutant and meteorological measurements taken during the summer of 1973 at
seven stations scattered over the Los Angeles basin. However, the hourly
solar radiation data were available only at Los Angeles Civic Center, and
hourly temperature was available at only three locations in the region.
Emission data were not used, so the emissions into a parcel of air during
the change period produce part of the unexplained variance in the data.
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12
REGION OF
UNCERTAINTY
PASADENA
Figure 3. An illustration of the basis of a
statistical interpretation of the
trajectory estimation procedure.
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13
The project was carried out in two phases: First, we attempted to
discover which of the variables were most significantly related to the
03 changes, and how strong the relationship was. Secondly, we proceeded
to model and explore the functional relationship between the 03 changes
and the variables giving the best predictive capability.
Through extensive use of a nonlinear, nonparametric, exploratory
regression technique developed by TSC [8], we found that virtually all
of the predictive capability was contained in three variables,
the current 03 level
the current solar radiation reading
the current NO^ level.
These three variables explained 71% of the variance in the next two-hour
change in 0-, and 60% of the variance of the noisier one-hour 03 change
data. Adding other variablessuch as current NO; current temperature;
reactive hydrocarbons, current and three, four, and five hours earlier;
and current methaneproduced little additional increase in percent of
variance explained.
We believe these results are quite gratifying; particularly since
(1) we had to use the same current one-hour solar radiation data for all
parcels of air over a region about 30 miles long by 10 miles wide and
stretching from near the Pacific Ocean to hot, dry, and clear areas,
and (2) for the interpolation over this region, data were available from
only seven stations.
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14
A TSC technique of fitting a continuous piecewise linear approxima-
tion to the data was used to both explore and model the relationship be-
tween the 03 change and the current 03, N02, and SR values. The qualita-
tive conclusions are that there are basically two regimes:
At below average 03 levels, the 03 change is determined largely
by the SR and N02 levels, with larger values of these latter
two related to larger values of the 03 change. The largest
positive changes in 03 occur in this regime.
At above average CU levels, the CU has a strong negative asso-
ciation with 03 change, and moderate to high levels of NO^ and
SR are associated with low to moderately above-average
changes in 03>
The continuous function prediction F(03, N02, SR) produced in this latter
part of the study is fairly simple, consisting of eight hyperplane seg-
ments patched together in a continuous way. As a predictor of the two-
hour 03 change, it explains 61% of the variance. In view of its simpli-
city, we regard this as a promising approach to the data-analytic modeling
of ozone production. A fuller account of the study follows.
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15
2. PROJECT PURPOSE AND DESIGN
The purpose of this study was to perform a data analysis of the
formation of ozone from its precursors, and to determine the effects of
solar radiation (SR) and temperature (T) on the formation process.
To do this, we interpolated the wind field in a region of the Los
Angeles basin so that we were able to track parcels of air as they moved
through the basin. The pollutant readings at seven APCD stations were
also interpolated so that we could keep hourly records of non-methane
hydrocarbons (HC), methane (CH4), ozone (03), and the nitrous oxides
(NO, N02) along the trajectory of the parcel. We also had the hourly
solar radiation readings at the Los Angeles Civic Center location of the
APCD, hourly temperature readings at three representative locations in
the basin, and the mixing height estimated for the Civic Center location.
This data base was created largely from APCD data and reformatted for this
study.
Our study was carried out over the five summer months, June through
October 1973, About 7000 trajectories were formed and placed in the pri-
mary data base.
At each hour along each trajectory, we then extracted the following
data:
03 for that hour (pphm)
NO (pphm)
N02 (pphm)
HC (Dpm)
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16
CH4 for that hour (PPM)
SR (gm. cal./cm2/hr)
T (ฐF)
and A03, the change in 03 over the next hour. Basically, we wanted to
find a function F-j such that the equation
A03 - F1(03, NO, N02, HC, CH4, SR, T) (4)
is a nearly "best" fit to the data.
Although mixing height was available in our data base, we did not
use it as one of the independent variables since we did not have reliable
estimates of its rate of change. Wind speed and direction were implicit
variables since we were tracking the parcel of air. Furthermore, emissions
data were not available.
Because we suspected that the hourly changes in (k might be subject
to considerable noise, we also used a data base with A03 equal to the two-
hour change in ozone and the other variables as above, except that SR is
replaced by a two-hour SR total. (See Appendix for a discussion of this
point.) We planned to use this two-hour data base to express the two-hour
change in ozone level as
A03 = F2(03, NO, N02, HC, CH4, SR, T) (5)
Perhaps even more important, we wanted to determine which of the
variables were most significantly related to the change in ozone. There-
fore, we really had two objectives in this study:
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17
(1) To find those subgroups of the variables most significantly
related to the ozone change.
(2) To find the form of the function F providing the best fit
to the data.
The remainder of the report will cover:
(1) A description of the interpolation program which produced the
trajectories and pollutant values along the trajectories.
(2) The exploratory phase and the winnowing out of the signifi-
cant variables.
(3) The relationship of A03 to the three variables 03, N02 and SR
which was found to be significant.
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19
3. THE TRAJECTORY INTERPOLATION PROGRAM
In 1972, nine air quality monitoring stations in the greater Los
Angeles Basin started to make hourly measurements of HC (hydrocarbons
minus methane), CH4 (methane), NO, and N02, along with the usual hourly
pollutant measurements. Only seven of the nine stations are in the wind
funnel of the basin. These are located at:
Pomona
Azusa
Pasadena
Burbank
Lennox
Whittier
Los Angeles Civic Center
These locations are shown in Figure 4. When connected by lines, they
form a convex polygon with only the Los Angeles Civic Center location in
the interior. All of these stations are also wind measurement stations,
but the wind data at Lennox was not available. We assigned to Lennox
wind data at Los Angeles County APCD sampling station #76, less than three-
quarters of a mile away over flat terrain.
The area included in the polygon formed the area under study in this
project. It was triangulated as shown in Figure 4 with an extra point added
near Pomona that formed an additional triangle. The reason for adding this
extra point will be explained below. This point was assigned pollutant
levels and wind data identical to that at Pomona.
Given that a point was in any triangle, the pollutant levels were in-
terpolated to that point from the measurements at the three vertices in a
straightforward way: using the three values of the variable being inter-
polated at the vertices as heights, a plane was passed through the three
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BURBANK
PASADENA
I /
/ \
if'LOS ANGELES
PLAYA DEL REY
AZUSA
.^POMONA
N
SCALE IN MILES
ro
o
JHUNT1NGTON BEACH
Figure 4. The study region.
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21
points and the value of the variable at the interior point was the height
of the plane above the point in question. (See Figure 5.)
At each station the wind speed and direction were combined to find
the components of the wind WN, WE in the north direction and the east di-
rection. Then WN was interpolated over the region in exactly the same
way as the pollutant interpolation. The same was true for Wr.
Using this interpolation scheme, we could start with any point x^ in
the polygon, get pollutant levels and wind speeds at x, for any given hour,
and then use the wind speed at x.i to find the location of the air mass the
hour before. Calling this prior location Xo, we repeated the procedure,
finding pollutant values and wind speeds at Xo.
In this way we built up a trajectory
X-i ซ- *ฃ ซ- x.3 < x^ + . . .
that terminated when we found a prior point outside of the polygon.
The prevailing wind pattern for these five summer months is southerly
near the coast, is southwesterly near downtown Los Angeles, and curves to
westerly near Pomona.
We used trajectories ending at Burbank, Los Angeles, Pasadena, Azusa,
and Pomona. The prevailing winds were such that the trajectories tended
to stay in the polygon until they exited by crossing over the line between
Lennox and Whittier. The extra triangle was added near Pomona so that
the first point prior to Pomona would not be out of the polygon.
We had additional meteorological data:
hourly temperature measured at Lockheed Airport--Burbank, L.A.
Civic Center, and Ontario Airport
hourly solar radiation measured at L.A. Civic Center
daily mixing height computed for the L.A. Civic Center location
-------
22
reading at
station #1
reading at station #3
this height is the
interpolated reading
at the interior point
below
reading at station #2
interior point
of triangular region
Figure 5. Interpolating pollutant levels over
a triangular region.
-------
23
The last two variables were used for all locations in the polygon, but
the temperature assigned to a triangle was that measured at whichever
one of the three temperature-measurement stations was closest to the
triangle.
A master file of trajectories was constructed as follows:
t Starting with a given location xj and time, find the corresponding
values of the pollutants, wind speeds,and meteorological variables,
Use the wind speeds to find the predecessor point x? and repeat
the first step.
Keep going until the point passes out of the polygon.
We use the five stations listed above as starting points and traced tra-
jectories backwards from 8 a.m. through 5 p.m. at hourly intervals. We
did not compute trajectory values prior to 5 a.m. This gave us ten tra-
jectories per day for each station.
-------
25
4. THE EXPLORATORY PHASE
From the bank of 7000 trajectories, we extracted over 12,000 data
vectors of the form
(A03, 03, NO, N02, HC, CH4, SR, T) ,
where A03 was a one-hour change and over 8000 vectors where A03 was a two-
hour change. However, a large majority of these vectors had small, usually
positive A03 readings, as shown in Tables 1 and 2.
For our purposes, the data vectors with small values of A03 are largely
uninformative, and keeping all of them in the working data base would swamp
it with largely irrelevant information. For that reason, we sampled from
the two histogram bins containing most of the A03 values to reduce the
total number of data vectors in those bins to about 50% of the total. For
instance, in the two-hour data, we selected the first 400 entries in the
range 1.9 +_ 2.8 and the first 500 in the range 7.5 +_ 2.8 and rejected the
remainder from our working data base.
For the variable selection and exploratory phase, we used INVAR, a
general method for estimating efficiently how much of the variability in
the dependent variable can be explained by a subgroup of the independent
variables [8]. This technique estimates the limiting value of percent of
*
variance explained (PVE) by a "smooth" nonlinear model. We first tested
Percent of variance explained equals
100 x
variance of error in prediction
1 " variance of dependent variable]
-------
26
Table 1. Frequency Breakdown of One-Hour
Changes in ACU
ARange
(pphm)
-21.4 + 2.7
-16.0 + 2.7
-10.7 + 2.7
-5.3 +_ 2.7
0.0 +_ 2.7
5.3 +_ 2.7
11.7 + 2.7
16.0 +. 2.7
21.3 + 2.7
26.7 +. 2.7
Frequency
(original )
2
5
22
222
8426 } 94%
3391 )
407
51
21
6
Frequency
(after sampling)
2
5
22
222
400 I 52%
400 i
407
407
21
6
actual class interval length is 5.34
Table 2. Frequency Breakdown of Two-Hour
Changes in ACL
ARange
(pphm)a
-20.7 +_ 2.8
-15.0 + 2.8
- 9.4 ^ 2.8
- 3.7 + 2.8
1.9 i 2.8
7.5 ^ 2.8
13.2 i 2.8
18.8 ^ 2.8
24.4 + 2.8
30.1 +_ 2.8
Frequency
(original )
2
7
22
181
5171 I 89%
1985 )
550
100
32
8
Frequency
(after sampling)
2
7
22
181
400 I 50%
500 )
550
100
32
8
actual class interval length is 5.64
-------
27
all independent variables as individual predictors, then pairs of var-
iables, and then added variables to find the best three, etc. Some re-
sults for single variables are tabulated in Table 3. The most significant
individual variables (in approximate order of importance) are SR, N02ป T,
and 03.
Exploring pairs of variables, we found the results shown in Table 4.
Other pairs were run that resulted in lower percent of variance explained
than those in the table.
Triplets of variables were then explored with one really significant
improvement showing. Some results are shown in Table 5.
The final significant increase occurred when we added temperatures
to 03> N02, SR. But, somewhat strangely, the increase was significant only
for the data base of one hour AOo. Here we obtained
Variables One-Hour PVE
03, N02, SR, T 65.9
Our original thinking was that SR and T might be highly dependent. How-
ever, as the scatter plot (Figure 6) of 300 hourly readings of SR and T
shows, the two are not closely related, particularly at high levels of SR.
Still, the evidence is that temperature is much less strongly associated
with A03 than is SR. In all of the INVAR runs using HC and CH4, neither of
them significantly increased the PVE. For instance, when HC and CH4 were
individually added to the variables N02, NO, 03, and SR, the maximum in-
crease in PVE was 2.1%.
-------
28
Table 3. Percent of Variance Explained
(Single Variables)
Variable
ฐ3
NO
N02
HC
CH4
SR
T
One hour A03
15.8
13.4
25.7
19.2
16.6
30.3
17.1
Two hour AO-,
24.1
12.9
41.7
15.6
19.3
36.7
35.8
Table 4. Percent of Variance Explained
(Pairs of Variables)
Variables
N02, 03
N02, SR
N02, T
N02, NO
03, SR
SR, T
ฐ3' T
One hour AO-,
40.8
42.3
38.7
34.8
53.0
43.6
33.2
Two hour AOo
55.0
49.6
52.9
50.1
58.8
52.1
46.7
Table 5. Percent of Variance Explained
(Triplets of Variables)
Variables One-hours AO^ Two-hour AO^
03, N02, SR
N02, NO, SR
03, N02, T
60.2
46.7
46.7
71.1
53.8
64.9
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Figure 6. Temperature vs. solar radiation.
-------
30
Similarly, the effect of NO was small. When NO was added to the
three variables CU, NO^, and SR, there was no increase in PVE.
We considered these results to be highly promising in view of the ap-
proximations involved in the interpolation program used to determine the
trajectories and pollutant values. In fact, we had not expected to be
able to do this well.
Puzzles that remained were the small effect of the HC and the fairly
large effect of the 0,. The 03, by itself, is not particularly signifi-
cant in relation to A03, but 03 combined with SR has the highest PVE in
the one-hour A03 case. On the other hand, HC, which contains the reactive
hydrocarbons, is surprisingly insignificant in its effect on 03 production.
Examining the HC records, we found that the maximum HC levels occurred
early in the morning. Table 6 classifies the HC readings by hour and by
level for all seven stations over the five-month period. The peak HC
levels occur mainly at the 6 a.m., 7 a.m., and 8 a.m. readings. This
might indicate rapid removal of HC in the presence of solar radiation and
other reactive pollutants.
Table 7 gives the frequency breakdown of maximum daily 03 at Pomona
versus maximum daily HC at the Los Angeles Civic Center. It does indicate
that there is some association between HC levels and later 03 levels.
The 03 effect may be due partly to its being scavenged to produce a
negative change in 03 levels. We also considered it possible that the 03
variable is a surrogate that reads the progress and strength of a slow re-
action that started hours earlier with the take-up of the HC.
-------
Table 6. Frequency of HC Levels (ppm)
by Hour For All Stations
Hour
5 a.m.
6
7
8
9
10
11
12 noon
1 p.m.
2
3
4
5 p.m.
599
519
470
496
538
567
593
615
661
676
680
690
688
359
407
412
423
416
406
388
380
343
330
329
318
319
41
71
92
79
47
37
26
17
8
8
2
3
6
12
14
13
12
11
3
5
1
0
0
2
2
0
2
1
6
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
Table 7. Relation of 03 Levels at Pomona to
HC Levels at Los Angeles Civic Center
Max HC
(Civic Center, ppm)
Max 03 (Pomona, pphm)
0-10
11-20
21-30
31-40
0
1
2
3
4
9
17
5
1
0
16
48
11
1
0
4
17
10
1
1
2
1
0
0
0
-------
32
To see if this was consistent with the data, we constructed new data
bases in which the HC was replaced by:
1. The HC on the trajectory three hours earlier.
2. The average HC over three, four, and five hours earlier, if
the trajectory stayed in the region that long, otherwise, the
average over the period three and four hours earlier.
The data bases constructed this way still had a dominant number of AOo
values close to zero and these were reduced by sampling until the new data
bases contained 1000-1500 points each. Using both one- and two-hour
changes yielded four new bases. The new bases were different than the
old because data was taken from a point on a trajectory only if the tra-
jectory had been in the region for three or four hours already.
The INVAR runs on this new data did not reveal a significant con-
tribution from the earlier HC concentration, as can be seen in Table 8.
There is, in the last two entries of the second column of Table 8, some
possible evidence of increase in PVE with addition of HC. But the 64.0
PVE may be an unstable high value due to over-fitting. (Although the INVAR
program contains a test to prevent over-fitting, the random character of
the procedure infrequently produces too much splitting and a slight over-
fitting. )
These results concluded, in the main, the exploratory phase of our
study. The variables found most significantly related to ACL were CL,
3 O
N02ป and SR. A puzzling result was the failure to find any significant
relationship with HC or NO.
-------
33
Table 8. PVEs Computed for the Four New Data Bases
Variables
HC
HC4
NO
N02
ฐ3
SR
T
03,SR
HC.SR
HC,N02,SR
HC,03,SR
03,N02,SR
HC,N02,03,SR
One-Hour
HC(-3)
6.6
7.1
4.9
19.7
14.4
23.6
19.7
35.5
34.9
40.1
43.1
49.8
52.9
A03 Data Bases
HC(-3.-4.-5)
5.7
5.7
4.4
22.0
19.2
24.4
23.8
42.7
33.1
42.4
47.8
57.7
64.0(60.8)
Two-Hour
HC(-3)
9.5
9.4
7.0
33.6
26.0
27.1
23.1
44.6
36.2
48.1
52.1
62.2
61.4
A03 Data Bases
HC(-3,-4,-5)
7.5
15.5
4.0
35.5
23.9
34.2
25.9
54.4
39.5
54.5
55.4
62.4
62.7
-------
34
Another exploratory task undertaken was to study the effects of
solar radiation, temperature, and mixing heights alone--the key meteoro-
logical variableson ozone production. We looked at trajectories that
ended at one of the five "entry" stations at the time of maximum 03 reading
for that day at that station. We found the 03 reading at the time the par-
cel of air entered the study region and formed the variable
log(A03) = log[03(end) - O^enter)]
We deleted all trajectories such that 0-Jend) - (Menter) < 0. This depen-
dent variable measures the change over the whole trajectory and essentially
measures the final ozone level achieved at the end of the trajectory, since
the ozone level at the beginning of the trajectory will generally be small.
This variable is hence of a different character than the shorter changes.
Along each such trajectory we computed the sum of the solar radiation
(SSR) for all the hours the trajectory took until it left the region, the
average temperature (AVT) over the trajectory, and the mixing height (MH)
for the day. We then did a linear stepwise regression with log(A03) as
the dependent variable and
log SSR, log AVT, log MH
as the independent variables. The results are shown in Table 9.
Table 9. Results of Linear Stepwise
Regression of the Dependent
Variable Log (A0?)
VariablePVE
log SSR 42.3
log SSR, log MH 45.7
log SSR, log MH, log AVT 45.8
-------
35
That log SSR had a PVE as high as 42% by itself with the form of the
equation restricted to be loq linear is a bit surprising. Even more sur-
prising is the conclusion that adding log MH and log AVT made very little
difference in the PVE. This analysis supports the dominance of solar radia-
tion observed in the short-term ozone changes. We did not run INVAR on
this data as previous work with similar variables [10] had indicated a good
fit with a log-linear model. However, we feel that this should be checked
in future work.
-------
37
5. THE RELATIONSHIP OF A03 TO 03, N02> AND SR
In this part of the study, we focus on the nature of the functional
relationship between the two-hour change in 03 and the (L, N02, SR var-
iables. Throughout this analysis, we used the 1800 data points in the
reduced data base except in the plots, where every sixth point was used.
Although it is generally difficult to understand a multidimensional re-
lationship from single variable regression, we plotted 0.,, N02, and SR
individually vs A03 (Figures 7, 8, and 9) to see what could be under-
stood on this level. The scatter is immediately apparent, and the
only apparent systematic relationship is positive correlation between
N02 and A03.
The next step in the analysis was to stratify the A03 by the 03, SR
levels and take the average A03 in each bin. The results are shown in
Table 10. Here, an underlying pattern emerges.
High SR is associated with high A03
t High 0., is associated with low A03
However, to get a continuous functional form for the relationship of
A03 to 03, N02, and SR, we used EFAP, a program developed by TSC [32, 37],
that fits a piecewise linear continuous regression surface to the data.
Since the surface generated by EFAP is smoother and less general than
that used in INVAR estimates, EFAP generally does not achieve the level
of PVE obtained by INVAR. Conversely, because INVAR usually splits the re-
gion into many subregions and fits a discontinuous surface, the resulting
fit is difficult to interpret physically. The continuous piecewise linear
-------
t-l_l-_L_L-J_L i_L_L_L_L_J_J_Lj.__l_J_.L L L.I _L_l_l_J__l.L L 1 L.Li L..1 1
I
H
I
-I
i
i
H
-10
co
co
Figure 7. 03 vs A03 (every 4th point sampled).
-------
Ci
o
CM
SR
O
G O
O
Q
o
11
n# r-
o
CEP
0ฐ,-
IoJ
(Q)
3 ฎ\ 3 Q
3K ~ ,T
xD n o
QU
Q
U
O Q
(U 3
oo
10
3D
o
r
r
AO-
Figure 8. SR vs A03 (every 4th point sampled).
-------
J !_
DJ
CV1 _
N02 ฃ
o
LO
^ I I I ! I
-20
AO
3
h
I
r_
F
i
r
o
i _
F
1
Figure 9. NO^ vs A03 (every 4th point sampled)
-------
41
Table 10.
Two-Hour A03 Averages Stratified by SR and 03.
Entries in table are A03- (SR in Langleys
averaged over two-hour periods; 03, A03 in pphm.)
ฐ3
0-5
5-10
10-15
15-20
20-25
25-30
30-35
35-40
40-45
SR
0-40
.3
-2.1
a
a
a
a
a
a
a
40-80
3.9
.1
7.0
a
a
a
a
a
a
80-120
9.3
8.8
.0
-1.2
-4.8
-3.4b
-13. lb
-10. Ob
a
120-160
12.2
11.5
10.1
6.3
.2
-1.9
2.0b
-12. 2b
-11. 6b
160-200
12.3
9.8
8.3
7.7
3.4b
5.8b
a
a
a
aNo samples in bin
bAverage is based on six or fewer samples
-------
42
surface generated by EFAP gave a PVE of 60.7%. The final fitted surface
is fairly simple, consisting of a continuous patching together of eight
hyperplane segments. The equations for five of these are tabulated later.
Three-dimensional slices of this surface are graphed in Figs. 10, IT, and 12,
Of the eight regions, there are three together that contain only 1.0% of
the total number of points. We will ignore these and restrict our analysis
to the relevant information contained in the functional fit to AO^ in the
five other regions.
As a quick preliminary summary, in Table 11 we give the means of all
variables corresponding to the points in each region.
Table 11. Means of Variables by Region
Percent of Points
Overall (100)
Region 1 (46)
Region 2 (33)
Region 3 (8)
Region 4 (7)
Region 5 (5)
A03
7.1
3.7
11.0
1.2
14.7
8.7
ฐ3
6.1
3.6
4.6
20.4
5.4
16.7
NO 2
9.0
4.9
11.9
7.3
20.3
12.8
SR
100
73
118
139
119
149
In Table 12 the mean values are characterized by region.
Table 12. Mean Value Characteristics
Region 1
Region 2
Reqion 3
Region 4
Region 5
A03
very low
high
very low
high
above average
ฐ3
very low
low
high
below average
high
N02
very low
above average
below average
high
above average
SR
very low
above average
high
above average
high
-------
43
This layout of mean values is itself interesting. Region 1, con-
taining almost half of the sample points, is representative of low pollu-
tion levels, low 03 production, and low solar radiation. Region 2, with
33% of the points, contains data with above average mean N02 and solar
radiation levels, below average 03 levels, and high positive changes in
03. The other three regions, with a total of 20% of the sample points,
represent more extreme conditions.
As can be seen in Table 13, the standard deviations of the variables
in these regions give more information.
Table 13. Standard Deviations of
Variables by Region
Overall
Region 1
Region 2
Region 3
Region 4
Region 5
A03
7.0
5.2
4.4
8.8
5.7
7.9
ฐ3
6.2
3.1
3.4
6.1
2.5
4.2
N02
5.2
1.9
2.5
2.1
3.1
2.1
SR
52.8
59.9
32.1
18.5
19.3
11.0
Region 1, which contains the low mean values, has low standard devia-
tions in all variables except for SR, which fluctuates over a wide range.
Region 2 is similar. Regions 3, 4, and 5 have, generally, moderate stan-
dard deviations in the independent variables and larger deviations in the
A03.
The equations of the EFAP hyperplanes in each region are given in
Table 14.
-------
44
Table 14. EFAP Equations for A03
Region
1
2
3
4
5
-.14 (03)
-.097 (03)
-.87 (03)
-.092 (03)
-.82 (03)
+.87 (N02)
+.52 (N02)
+.86 (N02)
+.28 (N02)
+.26 (N02)
+.054 (SR)
+.056 (SR)
+.029 (SR)
+.059 (SR)
+.034 (SR)
-3.9
-1.4
+9.0
+2.3
+15.1
Before discussing these results, since the size of the above coefficients
depend on the scaling of the variables, we introduce normalized variables
by dividing the original variables by their overall standard deviations,
i.e., denoting normalized variables by super asterisks,
03* = 03/6.2, N02* = N02/5.2, SR8 = SR/52.8
The equations are given in terms of the normalized variables, in Table 15.
Table 15. Normalized Equations for AOo
(AO^ not normalized)
Region
1
2
3
4
5
-0
-0
-5
-0
-5
.9
.6
.4
.57
.1
(03*)
*
<03)
(03)
-------
45
From the table, then in Region 1 the predicted value of A03 would
be -0.9(03*) + 4.5(N02*) + 2.8(SR*) - 3.9.
The most drastic change between the five equations is in the coeffi-
*
cient of 03> The implication is that when there are generally low pollu-
tant and SR values, the dominant factors are the N02 concentration and SR
intensity. But,in the region where the values are generally above average,
the 03 concentration has a strong inhibiting effect on the change in 03>
Further, the role of SR is substantially diminished.
The equations in Regions 2, 3, 4, and 5 should be cautiously evaluated
since the PVEs are 28.8, 26.1, 17.5, and 8.4, respectively. This implies
that in these regions the mean value of ACL is almost as good a predictor
as the given equations. The table of mean values is equally informative
in these regions. Looking at the mean values in Regions 2, 3, 4, and 5,
it is clear that
High A03 values are associated with low CU and high or above
average values of N02 and SR
t Low to moderately above average AO- values are associated with
high 03, even in the presence of above average or high N02 and
SR.
The negative values of A03 largely correspond to points in Region 2
with some in Region 5. These are also the two regions with above average
to high 03>
We can split the qualitative conclusions above into two regimes:
t At below average 03 levels, 03 has little to do with the
resulting A03. The dominant variables are N02 and SR. The
-------
46
relationship is monotonic in the sense that increasing
N0~ or SR leads, on the average, to higher AO., values.
At above average or high CL levels, CU has a strong negative
effect on AO-. Increasing NCL and SR values are offset by
increasing 03 values, and the associated A03 levels are
only moderately above average. This apparent self-limiting
effect of oxidant has been noted by others [18,19].
This behavior can be seen graphically in Figures 10, 11, and 12.
Figure 10 is a plot of the EFAP regression surface with SR fixed at its
mean value of 100; Figure 11 is a plot of the surface with NOp fixed at
its average of 9.0, and Figure 12 uses 0^ set at its average value of
6.1.
As the final output of this study, we have not only arrived at some
understanding of the association between change in 0^ levels and its pre-
cursors; but we also have constructed a simple model which predicts changes
in 03 level as a function of current 0.,, NO^, and SR measurements with a
correlation between predicted and actual values of .8. Equation (6) for
this preliminary empirical model is given below; the form of the equation
is a characteristic of the methodology [37].
For the continuous piecewise-linear model for two-hour ozone concen-
tration changes, the change in 0, over the next two hours is computed by
calculating the linear equations A, B, C, D, E, F below with current
values of the variables; taking the maximum of A, B, and C and multiplying
that by -5.125; adding the result to the product of -1.167 and the maximum
of D, E, and F; and finally, adding that result to 10.48. We have
-------
Figure 10. Graph of EFAP regression surface, with SR = 100.
-------
AO
2CM
co
45
Figure 11. Graph of EFAP regression surfaces, NCL = 9.0.
-------
2CM
(0,0)
NO
30
Figure 12. Graph of EFAP regression surface, 03 = 6.1
-------
50
A03 - -5.125 max(A,B,C) -1.167 max(D,E,F) + 10.48 (6)
where:
and
A
B
C
D
=-0.2146
= .0211
= .1638
ซ
4
X
X
= .02709
1
xl
1
Xi
-.0701
-.101
* A i
i
3 ;
-.09855 3
-.301
5 ;
? - .002268 X
<2 -.01075 X3
<2 -.005938 X
<0 + .001298
3 +
+ 2
3 -
A *} '
.9376
.275
2263
2.304
E = -.009565 X1 + .0005252 X2 -.001079 X3 + .2306
F = -.0144 X] + .2066 X2 -.003171 X3 -2.943
X1 = 03 concentration (PPHM)
X2 = N02 concentration (PPHM)
X = solar radiation (gm. cal./cm /hr. )
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51
6. CONCLUSIONS
The intent of the present study was to explore the possibility of
developing empirical difference equations describing the production of
ozone in the atmosphere. We examined the degree of predictability of
one- and two-hour changes of ozone under very limiting conditions (no
emissions data, a restricted set of meteorological variables, and only
ground-level measurements). Only the change in ozone and not the other
chemical species was modeled in the present analysis.
The results obtained were of two sorts:
(1) Three variables seem to produce the main effect in the
change in ozone levels:
the current 0, level;
the current solar radiation reading; and
the current NOp level.
(2) A model relating the two-hour change in ozone to these variables
was derived, and an attempt was made to extract the qualitative
implications of the quantitative model. The predictions of this
final empirical model were correlated with actual measurements
with a correlation coefficient of .78 over 1800 samples. (This
corresponds to explaining 61% of the variance.)
These results were quite encouraging. They suggest that a more com-
plete implementation of the concepts suggested in the introduction of this
report could result in a useful empirical model and some qualitative in-
sights into aspects of the photochemical pollution problem.
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52
REFERENCES
1. Air Pollution in California, Annual Report 1974. Air Resources Board
State of California. March 1975.
2. Altshuller, A. P. Evaluation of Oxidant Results at Camp Sites in the
United States. JAPCA. 25_, January 1975.
3. Angel!, J. K., et al. Three-Dimensional Air Trajectories Determined
from Tetroon Flights in the Planetary Boundary Layer of the Los Angeles
Basin, JAM. IJk 451-471, April 1972.
4. Baboolal, L. B., I. H. Tombach, and M. I. Smith. Mesoscale Flows and
Ozone Levels in a Rural California Coastal Valley. First Conference
on Regional and Mesoscale Modeling, Analysis, and Prediction of the
AMS. Las Vegas. May 6-9, 1975.
5. Blumenthal, D. L., et al. Three Dimensional Pollutant Gradient Study--
1972 Program. Meteorology Research, Inc., Altadena. May 18, 1973.
6. Blumenthal, D. L., et al. Determination of the Feasibility of Long-
Range Transport of Ozone or Ozone Precursors, Final Report. MRI to
RPA. Contract No. 68-03-1462. November 1974.
7. Blumenthal, D. L., and W. H. White. The Stability and Long Range
Transport of Ozone or Ozone Precursors. Meteorology Research, Inc.
(68th Annual APCA Meeting. Boston. June 1975.)
8. Breiman, L., and W. S. Meisel. General Estimates of the Intrinsic
Variability of the Data in Nonlinear Regression Models. Research for
the U.S. Air Force Office of Scientific Research under Contract
#F44620-71-C-0093, March 19, 1975, submitted to JASA.
9. Bruntz, S. M. Ozone Concentrations in New Jersey and New York:
Statistical Association with Related Variables. Bell Laboratories.
May 1974.
10. Bruntz, S. M., et al. The Dependence of Ambient Ozone on Solar
Radiation, Wind, Temperature, and Mixing Height. (Symposium on
Atmospheric Diffusion and Air Pollution. Santa Barbara. September
9-13, 1974.) Published by Amer. Meteor. Society, Boston, Mass.
11. Buffington, P. D., and E. A. Bartczak. Ozone: Chemical Action and
Reaction in the Lower-Level Transport Winds. Regional Air Pollution
Control Agency. Dayton, Ohio. (68th Annual APCA meeting. Boston.
June 1975.)
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53
REFERENCES (Cont.)
12. California Air Resources Board Bulletin, February 1975.
13. Cavanaugh, L. A. Atmospheric Photochemical Smog Measurements over
San Francisco Bay. Progress Report No. 4. Stanford Research Institute
Project 2092, March 15, 1973.
14. Chock, David P., and Susanna B. Levitt. A Space-Time Correlation Study
of Oxidant and Carbon Monoxide in the Los Angeles Basin, General
Motors Research Laboratories. Warren, Michigan. (68th Annual APCA
Meeting. Boston. June 1975.)
15. Cleveland, William, S. Sunday and Workday Behavior of Photochemical
Air Pollutants in New Jersey and New York. No date.
16. Cleveland, William S., et al. Using Robust Statistical Methods in
Analyzing Air Pollution Data with Applications to New York - New Jersey
Photochemistry. (APCA Annual Meeting. Denver. June 1974.)
APCA No. 74-76.
17. Cleveland, William S., and Bert Kleiner. The Transport of Photochemical
Air Pollution from the Camden-Philadelphia Urban Complex. Bell Lab-
oratories, 1974.
18. Cleveland, William S., et al. Chemical Kinetic and Data Analytic
Studies of the Photochemistry of the Troposphere. Bell Laboratories.
(EPA Symposium on the Atmospheric Chemistry of NO . Washington, D.C..
February 1975.)
19. Cleveland, William S., et al. The Analysis of Ground-Level Ozone Data
from New Jersey, New York, Connecticut, and Massachusetts: Data Quality
Assessment and Temporal and Geographical Properties. (68th National
APCA Meeting. Boston. June 1975.)
20. Corn, Morton, et al. Photochemical Oxidants: Sources, Sinks, and
Strategies. J. APCA. 25_, January 1975.
21. Dabberdt, Walter F., et al. Studies of Air Quality On and Near Highways,
First Interim Report. Prepared for Dept. of Transportation, FHWA,
July 1974.
22. Demerjian, Kenneth L., et al. The Mechanism of Photochemical Smog
Formation. In: Advances in Environmental Science and Technology,
James N. Pitts, Jr., and Robert L. Metcalf, editors, Volume 4, 1974.
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54
REFERENCES (Cont.)
23. Development of an Air Pollution Model for the San Francisco Bay Area,
Second Semiannual Report to NSF by Lawrence Livermore Laboratory.
February 1974.
24. Duckworth, Spencer, and Robert W. McMullen. Can We Ever Meet the
Oxidant Standard? California Air Resources Board. (68th Annual APCA
Meeting, Boston, Mass. June 1975.)
25. Edinger, James, G., et al. Penetration and Duration of Oxidant Air
Pollution in the South Coast Air Basin of California. JAPCA, 22_,
November 1972.
26. Edinger, James G. Vertical Distribution of Photochemical Smog in
Los Angeles Basin. Environmental Science & Technology. 7_, March 1973.
27. Environmental Quality--1974, The Fifth Annual Report of the Council
on Environmental Quality, U.S. Gov't. Printing Office. December 1974.
28. Episode Contingency Plan Development for the Metropolitan Los Angeles
Air Quality Control Region. Final Report. Prepared by TRW for EPA,
Region IX, December 1973.
29. Eschenroeder, Alan Q., et al. Evaluation of Transportation Plan
Impacts on Photochemical Smog. Environmental Research & Technology,
Inc.. (68th Annual APCA Meeting. Boston. June 1975.)
30. Gloria, H. R., et al. Airborne Survey of Major Air Basins in California.
JAPCA. 24-: 645-652, 1974.
31. Holmes, J. R., and F. Bonamassa. Application of the Results of Recent
Chamber Studies to the Control of Photochemical Oxidant. Proceedings
of the NERC-RTP Conference on Smog-Chamber Experimentation.
October 24-25, 1974.
32. Horowitz, Alan, W. S. Meisel, and D. C. Collins. The Application of
Repro-Modeling to the Analysis of a Photochemical Air Pollution Model.
Prepared for EPA under contract #68-02-1207. December 31, 1973.
33. Investigation of Ozone and Ozone Precursor Concentrations at Nonurban
Locations in the Eastern United States. Contract No. 68-02-1077.
Prepared by Research Triangle Institute for EPA, May 1974.
34. Leonard, M. J., et al. Effects of the Motor Vehicle Control Program
on Hydrocarbon Concentrations in the Central Los Angeles Atmosphere.
Los Angeles County APCD. (68th Annual APCA Meeting. Boston. June 1975.)
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55
REFERENCES (Cont.)
35. Martinez, E. L. Temporal-Spatial Variations of Nonurban Ozone Con-
centrations and Related Meteorological Factors. (Conference on Air
Quality Measurements. Austin. March 10-11, 1975.)
36. McCollister, George M., and Kent R. Wilson. Linear Stochastic Models
for Forecasting Daily Maxima and Hourly Concentrations of Air Pollutants.
Atmospheric Environment. 9.: 417-423, March 1975.
37. Meisel, W. S., and D. C. Collins. Repro-Modeling: An Approach to
Efficient Model Utilization and Interpretation. IEEE Trans, on Systems,
Man, and Cybernetics. SMC-3. (4): 349-359, July 1973.
38. Meisel, W. S., The Role of Empirical Methods in Air Quality and
Meteorological Analyses. Interim Report to Office of Research and
Development, EPA, Contract No. 68-02-1704, December 1974.
39. Meisel, W. S., and D. C. Collins. Continuous Piecewise Linear Regression,
In preparation.
40. Paskind, Jack, and John R. Kinosian. Hydrocarbon, Oxides of Nitrogen
and Oxidant Pollutant Relationships in the Atmosphere over California
Cities. (Annual APCA Meeting. Denver. June 9-13, 1974.)
41. Perkins, William A., Jr. The Los Angeles Reactive Pollutant Program.
(LARPP Symposium. Santa Barbara, California. November 12-14, 1974.)
42. Photochemical Smog and Ozone Reactions. In: Advances in Chemistry
Series, Robert F. Gould, editor. American Chemical Society. 1972.
43. Price, J. H., et al. Estimation of Minimum Achievable Oxidant Levels
by Trajectory Analysis: Implications for Oxidant Control. Texas Air
Control Board. (68th Annual APCA Meeting. Boston. June 1975.)
44. Relationship of Oxidant Peak, High-Hour and Slope Values as a Guide
in Forecasting Health-Effect Days. Final Report to State of
California Air Resources Board, by Bay Area APCD Technical Services
Division, February 1973.
45. Roth, P. M. Photochemical Air Pollution Simulation Models: An Over-
view and Appraisal. In: Proceedings of the Symposium on Chemical
Aspects of Air Quality Modeling. Lawrence D. Kornreich, editor.
Sponsored by TUCAP and EPA. April 17-19, 1974.
46. Rubino, R. A., et al. Ozone Transport. Connecticut Dept. of Environ-
mental Protection. (68th Annual APCA Meeting. Boston. June 1975.)
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56
REFERENCES (Cont.)
47. Severs, R. K. Simultaneous Total Oxidant and Chemiluminescent Ozone
Measurements in Ambient Air. JAPCA. 25_, April 1975.
48. Stephens, E. R. Chemistry and Meteorology in an Air Pollution Episode.
JAPCA. 25_, May 1975.
49. Sticksel, P. R. The Stratosphere as a Source of Ozone. Battelle-Columbus
Laboratories. (68th Annual APCA Meeting. Boston. June 1975.)
50. Stoswik, Jr., William N., and Peter E. Coffey. Rival and Urban Ozone
Relationships in New York State. JAPCA. 24_: 564-568, 1974.
51. Trijonis, John C. Economic Air Pollution Control Model for Los Angeles
County in 1975. Environmental Science and Technology. 8_, September 1974.
52. Vaughan, Leland M., and Alexander R. Stankunas. Field Study of Air
Pollution Transport in the South Coast Air Basin. Final Report to
State of California Air Resources Board. July 1974.
53. White, Warren H., and Paul T. Roberts. The Nature and Origin of
Visibility-Reducing Aerosols in Los Angeles. Meteorology Research, Inc.
(68th Annual APCA Meeting. Boston. June 1975.)
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57
CONCLUDING REMARKS OF PROJECT OFFICER
In discussing a first draft of this report, some insights were de-
veloped that appeared to provide an even stronger motivation than was
originally in mind for the exploratory research that is described. Al-
though some attempt has been made to reflect this in the final account,
this is only done briefly. These concluding remarks represent the pro-
ject officer's proposal of a context for the research; they will hope-
fully be useful in further development of the idea of an empirically-based,
emissions-oriented photochemical pollution model.
For simplicity we consider a two-dimensional horizontal atmospheric
mean motion V_(r.ปt), and assume that turbulent mixing in the vertical is
sufficient to produce a uniform distribution of all pollutants from the
ground surface up to the mixing height H(r_,t). The effects of horizontal
turbulent dispersion on the concentration field will be disregarded. This
is the somewhat idealized photochemical model situation first proposed by
Wayne, Kokin and Weisburd and extensively developed under earlier EPA con-
tracts [See "Controlled Evaluation of Reactive Environmental Simulation
Model (REM)," Vols. I & II, NTIS PB 220 456/8 and PB 220 457/6, Feb. 1973].
It simulates the photochemical reactions that occur in a parcel or vertical
column of air of variable height moving along a wind trajectory. The time-
rate of change of concentration of the i pollutant, following the motion
of the parcel, is given by the conservation equation
D[HC.]
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58
where R. = rate of generation of i species by chemical reaction
Q. = rate of source emissions of species i,
and
D_Ei_+V
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59
constitute the set of functions R. were based on ad hoc photochemical
chamber experiments. However, the approach of the present report may, in
principle, be regarded as an initial step in the direction of empirical
determination of these functions from actual observations of the species
concentrations in the ambient atmosphere. More specifically, the analysis
attempts to develop an equation, by multivariate regression techniques, for
the Lagrangian-trajectory time-rate of change of concentration of just the
single pollutant ozone (03) in terms of the estimated concentrations of
ozone, hydrocarbons not including methane (HC), methane (CH^) and the
nitrous oxides (NO, N02) together with the solar radiation intensity (SR)
and air temperature (T). In this initial feasibility analysis this is done
without regard to the variations in the atmospheric mixing depth, i.e., as-
suming that H = constant so that DH/Dt = 0; also since ozone is a secondary
pollutant, the emissions strength Q^ = 0 (for i = 03). In order to develop
a complete prediction model along the lines suggested, it would, of course,
be necessary to develop in some optimal fashion the full set of coupled
equations for the chemical reaction functions R.. (i = 1, 2....N). Possibly,
however, some of these functions might be developed empirically from atmos-
pheric air quality data and some from chamber tests. Since the set would
have to include emissions of primary pollutants (Q.. j4 0), they might then
(like the conventional type photochemical model as suggested, for example,
by Wayne, et al) hopefully be used to study various control strategies as
applied to these primary species.
It should be emphasized that the air quality and wind data available
for an analysis of the type being suggested, will be Eulerian data com-
prising the
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60
(i) Species concentration field C^ (r., t), i = 1, 2, ...N
(ii) Wind velocity field V_(r.,t)
In terms of these (and with H = constant) the governing equation above
would become
V(r,t) . srad C.(r,t) = R.(Cr C2, ...CN) + Q.
For i = 1, 2, ...N, this is now a set of partial differential equations,
and analysis (or interpretation) of the relationship between the local time-
rate of species concentration (as provided at the fixed observing stations)
and the other variables would now be much more complicated, because of the
dependence on the wind velocity field V_. By adopting a Lagrangian analysis
following the air motion, the changes in concentration due to advection are
effectively decoupled from the central problem. However, the Lagrangian
trajectory must, of course, be estimated from the Eulerian wind field, as
is done in the report.
The preceding suggestions only relate to the empirical determination
of the chemical kinetics module of an overall emission-oriented photochemical
pollution model. The meteorological module that is implied by the Lagrangian
trajectory concept is very simplistic and much simpler, of course, than those
under consideration by some air quality modelers at the present time, and
which involve the use of sophisticated atmospheric transport and turbulent
diffusion equations. However, in another volume of this trilogy on empirical
techniques, an analysis is developed for the feasibility of determining at-
mospheric transport and dispersion functions by appropriate empirical
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61
analysis of air quality data, and in this case for an inert pollutant, un-
complicated by any effects of chemical reactions. This suggests the possi-
bility of eventually developing an emission-oriented approach that might
combine, with realistic complexity, both the meteorological and chemical
aspects of the problem in an empirical fashion.
Research Triangle Park, N.C. Kenneth L. Calder
October 1975
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62
APPENDIX
Statistical Noise in One-Hour and Two-Hour Changes
One-hour chanaes are usually more difficult to predict than two-hour
changes because two-hour changes are usually less susceptible to measure-
ment and interpolation error. This can be illustrated by the following
simplified model: Suppose the error in estimating the change in 0^ due to
all sources (e.g., wind field interpolation and pollutant interpolation)
during the first hour is e, and during the second hour is e^. Suppose
there is a true change during both hours of amount 6. Defining the error
ratio as the ratio of standard deviation of the error in measuring the
change to the change itself, then the error ratio for the one-hour change
is a/6 where a is the standard deviation of e-, . Assuming that e? has the
same standard deviation as e-| and that they are uncorrelated, the standard
deviation of e-| + e~ is aSz. Hence the error ratio for the two-hour change
is
/? _ J_
"
about 2/3 as large as the one-hour error rate.
Many other models of the process will illustrate the same character-
istic.
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63
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
i. REPORT NO.
EPA-600/4-76-029C
3. RECIPIENT'S ACCESSION-NO.
TLE EMPIRICAL TECHNIQUES FOR ANALYZING AIR
QUALITY AND METEOROLOGICAL DATA.
Part III. Short-Term Changes in Ground-Level Ozone
Concentrations: An Empirical Analysis
5. REPORT DATE
June 1976
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Leo Breiman
William S. Meisel
8. PERFORMING ORGANIZATION REPORT NO.
TSC-PD-132-1
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Technology Service Corporation
2811 Wilshire Boulevard
Santa Monica, California 90403
10. PROGRAM ELEMENT NO.
1AA009
11. CONTRACT/GRANT NO.
EPA 68-02-1704
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final May 74-Oct 75
14. SPONSORING AGENCY CODE
EPA-ORD
15. SUPPLEMENTARY NOTES
This is the last of three reports examining the potential role of state-of-the-
art empirical techniques in analyzing air quality and meteorological data.
16. ABSTRACT
An empirical analysis of ambient air quality data for the Los Angeles Basin
is used to relate the one- and two-hour changes in oxidant levels in the urban
environment to the preceding levels of precursor pollutants and to meteorological
variables. The intent was to demonstrate the feasibility of developing a set of
empirical difference equations for the production of oxidant over time. The
main variables determining one- and two-hour oxidant changes were identified
using nonparametric regression techniques. A model for the oxidant changes was
developed using nonlinear regression techniques. The implications of the model are
discussed.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS C. COS AT I Field/Group
* Air pollution
* Ozone
* Meteorological data
* Regression analysis
Empirical equations
* Mathematical models
13B
07B
04B
12A
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (This Report}
CLASSIFIED
21. NO. OF PAGES
73
20. SECURITY CLASS (Thispage)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
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