United States
Environmental Protection
Agency
Environmental Monitoring and Support EPA-600/4-79-070
Laboratory October 1979
Research Triangle Park NC 27711
Research and Development
*>EPA
Statistical
Analysis of the
Los Angeles
Catalyst
Study Data
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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 nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are
1. Environmental Health Effects Research
2 Environmental Protection Technology
3 Ecological Research
4 Environmental Monitoring
5 Socioeconomic Environmental Studies
6 Scientific and Technical Assessment Reports (STAR)
7 Interagency Energy-Environment Research and Development
8 "Special" Reports
9. Miscellaneous Reports
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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STATISTICAL ANALYSIS OF THE
LOS ANGELES CATALYST STUDY DATA
by
Johannes Ledolter
George C. Tiao
Spencer B. Graves
Jian-tu Hsieh
Gregory B. Hudak
Department of Statistics
University of Wisconsin
Madison, Wisconsin 53706
Contract No. 68-02-2261
Harold B. Sauls
Project Officer
Analysis and Reports Branch
Environmental Monitoring Systems Laboratory
Environmental Protection Agency
Research Triangle Park, North Carolina 27711
This study was conducted
in cooperation with
The University Of Wisconsin
Madison, Wisconsin 53706
Environmental Monitoring Systems Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
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DISCLAIMER
This report has been reviewed by the Environmental Monitoring Systems
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 recommendation for use.
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FOREWORD
Measurement and monitoring research efforts are designed to anticipate
potential environmental problems, to support regulatory actions by developing
an in-depth understanding of the nature and processes that impact health and
the ecology, to provide innovative means of monitoring compliance with regu-
lations and to evaluate the effectiveness of health and environmental pro-
tection efforts through the monitoring of long-term trends. The Environmental
Monitoring Systems Laboratory, Research Triangle Park, North Carolina, has
the responsibility for: assessment of environmental monitoring technology and
systems; implementation of agency-wide quality assurance programs for air
pollution measurement systems; and supplying technical support to other
groups in the Agency including the Office of Air, Noise and Radiation, the
Office of Toxic Substances and the Office of Enforcement.
To assist in determining and evaluating effects of the catalytic
converter upon roadway pollutants, the University of Wisconsin Statistics
Department was contracted to conduct time-series analyses, develop appro-
priate models, and apply other statistical techniques to the data collected
in the Los Angeles Catalyst Study. This report documents their analyses
and findings.
Thomas R. Mauser, Ph.D.
Di rector
Environmental Monitoring Systems Laboratory
Research Triangle Park, North Carolina
i i i
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ABSTRACT
This research program was initiated for the purpose of performing
statistical analyses on the data from the Los Angeles Catalyst Study. The
objective of the program was to determine the effects of the introduction of
the catalytic converter on the atmospheric concentration levels of a number of
air pol1utants .
This report gives analyses of the CO, Pb, SOj, 0 , NO, and NO- data
covering the period from June 197^ to November 19/7- Models were designed
to evaluate the freeway contribution to CO and Pb as a function of traffic,
windspeed and wind direction. These models were used to assess both the time
trend in the pollutant measurements and the pollution concentrations at points
near the freeway. In addition, frequency distributions were determined for
ambient air quality data.
This report was submitted in fulfillment of Contract No. 68-02-2261 by
the University of Wisconsin under the sponsorship of the U. S. Environmental
Protection Agency. This report covers the period September 1977 to August 1978,
and work was completed as of September 1978.
IV
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CONTENTS
Disclaimer
Foreword
Abstract
Figures
Tables
1 . Introduction
2. Conclusions
3- Analysis of the CO Data
k. Analysis of the Pb Data
5. Analysis of SOg Data
6. Analysis of High Pollutant Concentrations
7- Frequency Distributions for Hourly and 4-Hourly Pollutant
Concentrations
8. Analysis of 0-, NO, and N02 Data ,
Appendix
References . ,
. . i i
. . i i i
. . iv
. . vi
. .VIM
. . 1
. . 3
. . 5
. . 16
. . 21
. . 2k
. 29
. . 37
. . 40
. . k2
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FIGURES
Number
1-1 Map of Los Angeles air monitoring stations at San Diego Freeway . 44
3~1a Monthly means of 4-hr afternoon (3 p.m. to 7 p.m.) CO
concentrations, Site A 45
3-lb Monthly 25th, 50th, 75th, and 90th percentiles of 4-hr
afternoon (3 p.m. to 7 p.m.) CO concentrations, Site A ... 45
3~2a Monthly means of 4-hr afternoon (3 p.m. to 7 p-m.) CO
concentrations, Site C 46
3-2b Monthly 25th, 50th, 75th, and 90th percentiles of 4-hr
afternoon (3 p.m. to 7 p.m.) CO concentrations, Site C . . . 46
3~3a Plot of 25th, 50th, and 75th percentiles of 4-hr afternoon
(3 p.m. to 7 p.m.) CO concentrations, Site A 47
3-3b Plot of 25th, 50th, and 75th percentiles of 4-hr afternoon
(3 p.m. to 7 p.m.) CO concentrations, Site C 48
3-4a Diurnal plots of CO at Site C; winter-summer comparison (weekday) 49
3~4b Diurnal plots of CO at Site C; winter-summer comparison (weekend) 49
3~5a Diurnal plots of CO at Site A; winter-summer comparison (weekday) 50
3~5b Diurnal plots of CO at Site A; winter-summer comparison (weekend) 50
3-6a Diurnal plot of traffic counts and traffic speed, weekday 1976 . 51
3-6b Diurnal plot of traffic counts and traffic speed, weekend 1976 . 51
3-6c Diurnal plot of traffic counts and traffic speed, weekday 1977 51
3-6d Diurnal plot of traffic counts and traffic speed, weekend 1977 51
3~7a Diurnal plot of traffic density (count/speed) weekday 52
3~7b Diurnal plot of traffic density (count/speed) weekend 52
3-8 Diurnal plots of WS_|_ 53
3-9 Diurnal plot of CO; Sites A, B, F, and C; summer weekday .... 54
3-10 Diurnal plot of CO; Sites A, B, F, and C; summer weekend .... 55
3-11 CO model 1977 summer weekday fit, Site C 56
3-12 Plot of the ratio CO/ (ct+kTD) versus WSi; Site F . . 57
3-13 CO model 1977 summer weekday fit, Site F (median strip) 58
3-l4a Joint CO model fit summer weekday, 1977, Site A 59
3-l4b Joint CO model fit summer weekday, 1977, Site B 59
3-l4c Joint CO model fit summer weekday, 1977, Site C 59
3-l4d Joint CO model fit summer weekday, 1977, Site F 59
4-la Monthly means of 4-hr afternoon Pb concentrations, Site A .... 60
4-lb Monthly means of 4-hr afternoon Pb concentrations, Site B . . . . 60
4-lc Monthly means of 4-hr afternoon Pb concentrations, Site C . . . . 61
4-ld Monthly means of 4~hr afternoon Pb concentrations, Site D . . . . 61
4-2a Monthly means of afternoon (3 p.m. to 7 p.m.) windspeed 62
4-2b Monthly frequencies of afternoon (3 p.m. to 7 p.m.) winds
from l45B-325° 62
v i
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Number Page
4~3a Monthly means of 24-hr Pb concentrations, Site C 63
4~3b Monthly means of 24-hr Pb concentrations, Site D 63
4-4a Monthly means of 4-hr (3 p.m. to 7 p.m.) Pb readings
weekday-weekend comparison, Site C 64
4-4b Monthly means of 4-hr (3 p.m. to 7 p.m.) Pb readings
weekday-weekend comparison, Site D 64
4-5a Plot of Pb/TC vs TS 65
4-5b Plot of Pb/TCxTS) vs WS| 65
5~la Monthly means of 4-hr hT-vol and membrane afternoon
readings of S0=,; Site A 66
5~lb Monthly means of 4-hr hi-vol afternoon readings of SO?; Site B . 66
5~lc Monthly means of 4-hr hi-vol and membrane readings of SO?;
Site C 7 .... 67
5~ld Monthly means of 4-hr hi-vol afternoon readings of SO?; Site D . 67
5~2a Plot of quarterly 25th, 50th, and 75th percent!les, minimum
and maximum of 4-hr hi-vol afternoon SO? concentrations
at Site C 7 68
5~2b Plot of quarterly 25th, 50th, and 75th percent!les, minimum
and maximum of 4-hr membrane afternoon SO? concentrations
68
69
69
70
70
71
71
71
72
72
72
73
73
73
8-4a Diurnal plots of 0 (Monday-Thursday) at Sites A and C 74
8-4b Diurnal plots of NO (Monday-Thursday) at Sites A and C 75
8-4c Diurnal plots of NO (Monday-Thursday) at Sites A and C 76
5~3a Monthly means of 4-hr hi-vol SO? (C-A) differences
5~3b Monthly means of 4-hr membrane SO? (C-A) differences
5-4a Plot of quarterly 25th, 50th, and 75th percent! les of
hi-vol afternoon SO? (C-A) differences
5-4b Plot of quarterly 25th, 50th, and 75th percent! les of
membrane afternoon SO? (C-A) differences . . . .
8-la Monthly means of 4-hr (3 p.m. to 7 p.m.) 0_ at Site A
8-lb Monthly means of 4-hr (3 p.m. to 7 p.m.) 0^ at Site C
8-lc Monthly means of 4-hr (3 p.m. to 7 p.m.) 0 (C-A) . .
8-2a Monthly means of 4-hr (3 p.m. to 7 p.m.) No at Site A
8-2b Monthly means of 4-hr (3 p.m. to 7 p.m.) NO at Site C
8-2c Monthly means of 4-hr (3 p.m. to 7 p.m.) NO (C-A) . .
8-3a Monthly means of 4-hr (3 p.m. to 7 p.m.) N02 at Site
8-3b Monthly means of 4-hr (3 p.m. to 7 p.m.) N02 at Site
8-^?c Monthlv means of 4-hr (3 D.m. tl 7 o.m.) N0» (C-a)
4-hr
4-hr
A
C
VI I
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TABLES
Number Page
3-1 Observed and Predicted CO Averages (Site C) 9
3-2 CO Trend Assessment at Site C 10
3~3 Observed and Predicted CO Averages (Site F) 13
3-4 Observed and Predicted CO Averages (Sites A, B, F, and C) . . . . 14
4-1 Observations for Summer 4-Hr Pb Data 18
4- la Observations for Summer 24-Hr Pb Data 18
5-1 Observations for Summer 4-Hr S0j= Hi Vol Data 23
5~la Observations for Summer 4-Hr S0=. Membrane 23
6-1 Description of Ancillary Data Accompanying the Upper Five
Percent of the CO Concentrations 26
6-2 Description of Ancillary Data Accompanying the Upper Five
Percent of the Pb Concentrations 27
6-3 Description of Ancillary Data Accompanying the Upper Five
Percent of the SOj (Hi-Vol) Concentrations 28
7-la Estimates of X, p, o? for Box-Cox Transformation: Los Angeles
Hourly CO Data, Site C 33
?-lb Estimates of u for Pareto Distribution with ZQ = 8.75: Los
Angeles Hourly CO Data, Site C 33
7-2a Estimates of A , p , a2 for Box-Cox Transformation: Los Angeles
4-Hr Afternoon S0j= Data (Hi-Vol), Site C 34
7-2b Estimates of a for Pareto Distribution with z as the 75th
Percent!le: Los Angeles 4-Hr Afternoon SO? Data
(Hi-Vol) Site C 7 34
7-3a Estimates of A, \i , a2 for Box-Cox Transformation: Los Angeles
4-Hr Afternoon S0j= Data (Membrane), Site C 35
7~3b Estimates of a for Pareto Distribution with z as the 75th
Percent! le: Los Angeles 4-Hr Afternoon 50-r Data (Hi-Vol),
Site C 7 35
7-4a Estimates of A , \i , a2 for Box-Cox Transformation: Los Angeles
4-Hr Afternoon Pb Data, S i te C 36
7-4b Estimates of n for Pareto Distribution with zn as the 75th
Overall Percent!le: Los Angeles 4-Hr Afternoon Pb Data
Site C 36
8-1 Observations for Summer Across-the-Freeway Differences
for Pollutants 38
VIII
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SECTION 1
INTRODUCTION
This report presents a statistical analysis of the Los Angeles Catalyst
Study (LACS) data collected between June 197^ and December 1977-
The primary objective of the study was to determine the impact of
catalyst equipped cars on the ambient air quality near freeways. The cataly-
tic converter was adopted by American automobile manufacturers in order to
meet federal and state emission standards. It has been used on new cars
since the 1975 model year. The converter was designed to reduce the emissions
of carbon monoxides (CO) and hydrocarbons (HC) . Since catalyst equipped
cars are required to use unleaded gasoline, the catalytic converter should
have lead to a reduction in lead (Pb) emissions. However, as pointed out by
Beltzer, Campion and Peterson (197*0 and Bockian, Tsou, Gibbons and Reynolds
(1977), the catalytic converter increased the emissions of sulfuric acid,
which is measured as sulfate ion (SO,).
DATA BASE
The San Diego Freeway in Los Angeles, California (Figure 1-1), was
selected as the location for studying the environmental impact of the cata-
lytic converter. Four air monitoring sites, two on each side of the freeway,
were established by the Environmental Protection Agency (EPA). The sites
were designated A, B, C, and D.
Data on a number of pollutants (including CO, Pb, S0j=, 0,, 0,, N0? , and
NO) and on meteorological variables (such as wind direction, windspeed,
temperature, and relative humidity) were collected from June 197^ to December
1977- Traffic counts and traffic speeds were measured on an hourly basis
beginning September 1976. In January 1977, a fifth measurement site (Site
F) was added for CO concentrations at the freeway median strip.
, The percentage of catalyst equipped cars passing the measurement sites
y_was a critical parameter and has been studied by Parry, Meyer, and Rodes
""'; (1977) and Rodes and Evans (1977)- It was found that starting in September
197^, the monthly increase rate for registration of catalyst equipped cars
was roughly .5 percent. After adjusting for actual miles driven, it was
estimated that the percentage of converter equipped cars passing the measure-
ment sites is approximately 30 percent in January 1977 and more than ^tO
' percent by the end of 1977-
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PROCEDURES
This report presents the findings of statistical analyses on (l) the
daily 4-hr SOr- readings from two types of sampling equipment; (2) the daily
4-hr afternoon and 24-hr Pb concentrations; (3) the hourly CO measurements,
and (4) the hourly NO, N0?, and 0, measurements. S0j= readings were collected
daily between 3 p.m. and / p.m. using a hi-vol (high volume) and a membrane
sampler. An hi-vol sampler was also used to collect samples for Pb concen-
trations.
An empirical mechanistic model was designed to relate the CO concentra-
tions at Sites A, B, C, and F to windspeed, wind direction, traffic count,
traffic speed, and the distance of the measurement site from the center of
the freeway. This model was used to extrapolate the CO concentrations to
other sites near the highway. We also designed an empirical mechanistic
model to relate the 4-hr afternoon Pb readings at Site C to windspeed, wind
direction, traffic count, and traffic speed. This model was used to assess
the trend in Pb emissions.
Frequency distributions for the ambient air quality data were interpreted
by an alternative approach. The distribution of pollutant measurements are
usually long-tailed and skewed to the right. It has been argued in the liter-
ature (Larsen [1969]) that the lognormal distribution provides a good approxi-
mation. In our analyses we used a more flexible class of distributions, which
are characterized by a power transformation of the observation. Specifically,
it transforms the pollutant concentrations to near normality and includes
the lognormal as a special case. We considered only high values of the pol-
lutants and used the Pareto distribution to represent the upper tail area of
the d i str i but ion.
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SECTION 2
CONCLUSIONS
PRINCIPAL FINDINGS
CO Findings
CO emissions decreased from 1975 to 1976, but a slight increase occurred
in 1977 (traffic also increased in 1977).
The joint model relating the CO concentrations at stations next to the
freeway was used to predict CO concentrations for given values of the input
variables wind direction, windspeed, traffic count, and traffic speed.
The proposed model was capable of predicting the CO concentrations for
downwind as well as upwind sites.
Pb Findings
Very little background Pb was present in the studied area; most of the
recorded Pb originated from automobile emissions on the freeway. Pb concen-
trations decreased until the end of 1976. In 1977, however, Pb concentrations
were substantially higher. This observed increase in Pb was caused by the
additional northbound traffic lane, which reduced afternoon traffic conges-
tions and increased the traffic speed.
Afternoon Pb concentrations are higher on weekends than on weekdays.
This weekday-weekend difference was attributed to afternoon weekend traffic
speed being higher, resulting in increased Pb emissions.
SOjF Findings
From June 197^ to May 1977 hi-vol and membrane SO? readings decreased
gradually at all four measurement stations.
The available hi-vol S0j= data for June to November 1977 showed a
considerable increase. On the other hand, membrane readings increased only
slightly during the same period. A comparison of membrane and hi-vol SOg
concentrations showed that while seasonal patterns are similar, the hi-vol
data were consistently higher.
From 1975 to 1977 the across-the-freeway differences (C-A) for the
^f-hr membrane SOf readings increased slightly. Hi-vol SQf (C-A) differences
behaved differently; from 1975 to the spring of 1977, a significant reduction
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was observed. In the summer and fall of 1977 the hi-vol SOg concentrations
were slightly higher than the averages of the previous year.
0 , NO, and NCL Findings
From 1976 to 1977, 0, concentrations decreased slightly at Sites A and C
From 1975 to 1977 significant increases in the NO and N0_ concentrations at
Site C and in the across-the-freeway difference (C-A) were noticed.
Analysis of High Pollutant Readings
High CO concentrations were usually recorded during traffic congestions
(low traffic speed), but high Pb and S0j= readings usually occurred at higher
than average traffic speeds.
High Pb readings are associated with high S0j= readings and vice versa.
Frequency Distributions for Pollutant Concentrations near the Freeway
The hourly CO and the 4-hr afternoon S0j= and Pb concentrations near the
freeway (Site C) did not follow a lognormal distribution. A square root
transformation of the CO concentrations and a cube root transformation of
the 4-hr afternoon SOg readings brought the distributions of the measure-
ments to near normality. For the 4-hr afternoon Pb concentrations, no
transformation appeared necessary, and the readings themselves appeared
to be distributed normally.
The Pareto distribution gave a good representation for the upper
tail area of the distribution of the pollutants studied.
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SECTION 3
ANALYSIS OF THE CO DATA
The CO data consisted of hourly observations at Sites A and C from
May 197A to November 1977, and at Sites B and F (median strip) from February
1977 to November 1977.
MONTHLY MEANS AND PERCENT!LES
As an initial step in the analysis of the CO data, the afternoon readings
(3 p.m. - 7 p.m.) were used to calculate monthly averages. Extreme observa-
tions in the data were eliminated according to the following procedure: Let
z. be an observation for a particular month, z the average, and s the estimated
standard deviation of the z.'s. If |z.-zl>3s, z. will be excluded and z
II
and s recalculated. The process was repeated until all observations fell
within z±3s.
The monthly means for Sites A and C are given in Figures 3~la and 3~2a.
To see how the observations are distributed within each month, various
percentiles of the empirical frequency distribution can be studied; in
particular, the 25th, 50th, 75th, and 90th percentiles can be plotted as
shown in Figures 3~lb and 3~2b for Sites A and C respectively. The distance
between the 25th percent!le and the 75th percent!le is called the midrange
and provides a robust measure for the variation in the data. The 50th
percent!le (or median) is a measure of the center of the distribution and
the 90th percentile describes the upper tail of the distribution.
From these figures we made the following observations:
The level of CO at Site C was considerably higher than the level at
Site A.
The behavior of CO was markedly seasonal; at both Site A and Site C the
CO concentrations were highest during the winter months.
During the summer months the CO level at Site A was very low since
afternoon winds blow predominantly across the freeway towards Site C.
In the winter the CO levels at Site A were higher. This may have
been caused by the changed meteorology; a larger percentage of
winds blew across the freeway towards Site A.
To discern the yearly trend movements more accurately, the strong seasonal
effects were blocked out by plotting the 25th, 50th, and 75th percentiles for
each month separately. The results are shown in Figures 3~3a and 3~3b.
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DIURNAL PLOTS OF CO
In Figures 3-^a and 3-kb diurnal plots of CO for the summer months
(May-October) and the winter months (November-April), weekdays (Monday-
Thursday) and weekends (Saturday, Sunday) are shown. Note that in all
diurnal plots the value for time (t) corresponds to the average of the hour
t to t+1, t = 0,1,...,23. From these four diurnal curves we observed that
the behavior of CO changed from weekday to weekend, and from summer to
winter. The summer weekday curve had two peaks which corresponded roughly
to the morning and afternoon rush hour traffic. The summer weekend curve
followed a different diurnal pattern, because of the changed weekend traffic
pattern. The weekday pattern in the winter did not show a peak during the
morning rush hours. This difference can be explained by the change
In windspeed and wind direction from summer to winter (Tiao and Hillmer
[1977]).
The diurnal plots for Site A are given in Figures 3~5a and 3~5b.
During most of the day Site A acted as a background station. In the morning,
however, part of the rush-hour contribution was recorded at this site because
the windspeed was lower and frequently in the direction of the ocean.
FACTORS INFLUENCING CO CONCENTRATIONS
Traffic and meteorological conditions, particularly windspeed and wind
direction, were the major factors which influenced CO concentrations. When
studying the effects of the catalytic converter, these variables must be
taken into account to properly assess the trend movements of CO. Hourly
observations on wind direction and windspeed were available for June 197^
and thereafter. Reliable traffic data were available from September 1976 to
December 1976, and September 1977 to November 1977-
TRAFFIC DATA
Hourly traffic counts and average traffic speeds were recorded for
every lane on the San Diego Freeway near the monitoring sites. From this
information we calculated hourly total traffic counts and average speeds
(weighted by the number of cars). Until January 1977 the freeway had four
lanes in each direction (northbound and southbound). The lanes were separated
by a concrete median strip. In February 1977 a fifth northbound lane was
added.
As shown in Figures 3~6a to 3~6d, hourly total traffic counts and
average traffic speeds were plotted for weekdays and weekends in 1976 and
1977. Comparing Figures 3~6a and 3~6b, we noticed a difference between week-
day and weekend traffic counts and traffic speeds. Weekday traffic counts
were characterized by two peaks which occurred during the morning and after-
noon rush hours; traffic speed was also considerably reduced during rush
hours. On weekends no morning peak was observed; traffic counts peaked
around noon and between 4 p.m. and 6 p.m. Two factors explained this
difference in peak times. Traffic during the night hours was heavier on
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weekends than on weekdays, and on weekends the freeway was less congested.
The average traffic speed rarely dipped below 50 mph.
A slight increase in traffic volume was noted from 1976 to 1977- A
comparison of the traffic data for the two years showed that the additional
northbound lane helped in reducing traffic congestion. The average weekday
traffic speed for the afternoon rush-hour period increased significantly from
1976 to 1977- However, the weekend traffic speed remained largely unaffected,
Comparing the diurnal pattern of summer weekday CO concentrations with
that of weekday traffic counts, Tiao and Hillmer (1977) observed that traffic
counts do not reflect the magnitude of CO during the afternoon rush hours.
They argued that traffic congestion during the afternoon rush hour period
could be a possible reason. Thus, instead of using traffic counts they
considered traffic density (TD), which is defined as the ratio of traffic
count to average speed. The diurnal curves for the weekday and weekend
traffic density in 1976 and 1977 are given in Figures 3~7a and 3'7b. Whereas
the weekend traffic density was largely unaffected by the additional north-
bound lane, a rather substantial decrease in traffic density was recognized
during the weekday afternoon rush hours.
When weekday and weekend traffic densitites were compared with the
corresponding summer CO concentrations at Site C, the diurnal patterns looked
very similar. CO concentration appeared almost linearly related to the
traffic density.
In the winter, the weekday CO averages did not exhibit a peak during the
morning rush hours. The meteorological variables, wind direction and wind-
speed, must be taken into account in order to explain this absence of a
morning peak because they are important factors for diffusion and transport
of the freeway CO contribution.
METEOROLOGICAL VARIABLES
Data on windspeed and wind direction were collected on an hourly basis,
Wind direction (WD) was an important factor since it controlled the trans-
port of CO. The freeway is situated 145°, therefore winds coming
from l45°-325e transported the freeway contribution towards Site C, while
Site A acted as a background station. When winds were from 325°-l45° the
freeway contribution was recorded at Site A.
Windspeed (WS) is also an important variable since it controls the
diffusion of CO as well as its transport. The higher the windspeed, the
more CO will be diffused.
Following Phadke, Tiao and Hillmer (1977) and Tiao and Hillmer (1977),
the hourly wind vector was divided into two components, one of which was
perpendicular (WS ) and the other parallel (WS. .) to the freeway:
-------
WS, = WS cos(WD-2359)
WS ( = WS sin(WD-235°)
Positive directions of these two components of the wind vector are shown
in Figure 1-1.
The diurnal patterns of WSj_ for the winter of 1975/76 and the summer of
1976 are given in Figure 3-8. Notice that in the summer the perpendicular
wind component was higher than in the winter. Also notice that in the morn-
ing during the winter months (including rush hours) winds blew away from Site
C towards Site A. This change in WSj_ could explain the absence of the CO
morning peak at Site C during the morning rush hours in the winter.
EMPIRICAL MODELS FOR CO CONCENTRATIONS AT SITES A, B, C, AND F
A new site, F, was added in February 1977 at the median of the freeway.
Since that time, hourly data were collected on CO concentrations at the four
locations, A, B, C, and F- The diurnal curves of CO for the summer (May-
October) weekdays and weekends of 1977 are given in Figures 3~9 and 3-10.
Empirical mechanistic models were used to relate CO concentrations to
traffic and meteorological variables. First, models for CO at Sites C and
F were considered individually. Then a joint model was proposed which re-
lated CO concentrations at all four stations.
A MODEL FOR CO AT SITE C
Tiao and Hillmer (1977) derived a model relating the diurnal behavior of
CO at Site C to traffic density and the perpendicular wind component. Their
model is given by:
-b(WS. -co)2
C0t = a + kTDte -1- + a^ (3.1)
where CO , TD , and WS. are the observed CO concentration, traffic density,
and perpendicular windcomponent at hour t respectively; a is the error
term; a is a parameter measuring the background CO; k is a parameter propor-
tional to emissions and
-b(WS t-co)2
e *-
is a diffusion factor involving the perpendicular wind component and two
parameters b and to.
This simple model, which requires only four parameters (a, k, b, co) to
be estimated from the data, was extensively verified on summer and winter,
8
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weekday and weekend CO averages from the LACS data base (Tiao and Hillmer
[1977]). The validity of this model may be illustrated by using the most
recent data on CO, traffic, and WS . Employing 1977 weekday summer CO
averages at Site C and the corresponding TD and WD values, the parameters
the model were estimated as:
WD values,
n
May 1977-October 1977 Weekdays (M-R)
Parameter Est imate Standard Error
a
k
b
1.27
0.023
0.019
3-51
0.20
0.0014
0.0080
The actual CO readings and the initially predicted values for CO are
plotted in Figure 3-11 and listed in Table 3-1. Apart from an apparent
underpred ict ion during the period from the 8th to the 15th hours, the model
(3.1) produced a close agreement between actual and predicted values.
CO trend analysis at Site C
The primary objective of this study was to assess the effect of the
catalytic converter on the CO concentrations. An analysis on the CO data
was done in terms of Model 3.1. We first investigated whether k, the para-
meter proportional to the emissions, changed over time.
TABLE 3-1. OBSERVED AND PREDICTED CO AVERAGES
Hour
0
1
2
3
k
S
6
7
8
9
10
11
Observed
CO Average
2.36
1.67
1.38
1.18
1.24
1.97
3-43
5.82
6.80
6.63
6.56
6.26
Pred icted
CO Average
2.16
1.74
1.55
1.45
1.49
2.01
4.04
6.12
6.47
6.13
5.70
5.49
Hour
12
13
14
15
16
17
18
19
20
21
22
23
Observed
CO Average
5-79
5-47
5-91
6.76
7.00
7-36
6.36
5-03
3-85
3-51
3-27
3.06
Predicted
CO Average
5.23
5-05
5.42
6.65
7.29
8.01
7-33
5-51
3-89
3.61
3.46
2.85
*Averages for Site C; 1977 Summer Weekdays (Model 3-0
The entire time span was divided into the following seven periods:
(1) June 1974 through October 1974; (2) November 1974 through April 1975;
(3) May 1975 through October 1975; (4) November 1975 through April 1976;
-------
(5) May 1976 through October 1976; (6) November 1976 through April 1977; and
(7) May 1977 through October 1977- This division corresponded roughly to
the "summer" and "winter" periods. To test for possible emission changes, a
different emission parameter k was allowed for each period. However, the
remaining parameters a, b, and co were constrained to be the same for all
seven periods. Within each 6-month period the 24-hourly averages for weekday
CO and WS were calculated for each of the three consecutive 2-month segments
This division was chosen to allow for possible changes in the meteorology
within each season. Since continuous reliable traffic data for the entire
period under study were not available, the following procedure was adopted:
(l) for all the 2-month periods prior to January 1977, the same average
weekday traffic density figures calculated from the available traffic data
for the period September 1976 through December 1976 were employed: and (2)
from January/February 1977 onwards, traffic data from the period September
1977 through November 1977 were used.
The CO, WS and TD were then employed to calculate estimates of the
parameters a, b, to, k,, ..., k?. A weighted least squares procedure was
used, which allowed for the possibility of variances differing from one
period to another. The parameter estimates are given in Table 3~2:
TABLE 3-2. CO TREND ASSESSMENT AT SITE C
Period Parameter Estimate Std. Error
Summer
Winter
Summer
Wi nter
Summer
Wi nter
Summer
7<»
7V75
75
75/76
76
76/77
77
a
b
0)
k
k
k
k
k
k
k
i
1
0
L.
4
T
6
\J
1
1
0
2
0
0
0
0
0
0
0
.69
.018
.80
.0175
.0209
.0228
.0200
.0197
.0222
.0209
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
069
0021
13
00065
00070
00066
00082
00051
00091
00066
The estimates of k to kr were comparable to those obtained by Tiao and
Hillmer (1977)- Table 3-2 shows that the estimate of k decreased between
winter 1974/75 and winter 1975/76, and also between summer 1975 and summer
1976. This decrease can be associated with the increase in the number of
catalyst equipped cars. The increase in k from summer 1974 to summer 1975
was at first surprising, but may have been caused by the same TD data (de-
rived from the September-December 1976 period) having been used. Specifi-
cally, a major change in the speed limit (from 70 mph to 55 mph) occurred in
January 1975- Since TD is the ratio of traffic counts to average speed, the
density figures used for summer 1974 were inflated and could account for the
increase in k from summer 1974 to summer 1975- Comparing the estimates
between 1976 and 1977, a slight increase was observed from summer 1976 to
10
-------
summer 1977 and from winter 1975/76 to winter 1976/77-, The evidence,
however, was not very strong (increase not significant at .05 level).
A MODEL FOR CO CONCENTRATIONS AT SITE F
Summer weekday data for 1977 were used to design a CO model for the
median strip. As a first approximation one might expect that the CO concen-
trations were linearly related to the traffic densities; CO = a + kTD. Wind,
however, acts to diffuse CO emissions from automobiles. A plot of the ratio
COt/(a+KTD ) versus WSj_t is given in Figure 3-12. CO TD , and WSj_t
(t=0, 1, ..., 23) are hourly summer weekday CO averages at Site F, TD, and
the perpendicular component of the wind vector, respectively. The least
squares estimates of CO = a + kTD + a were a and k.
Figure 3"12 shows that apart from three points (which corresponded to
the early morning period 2 a.m. to 5 a.m. and which are most likely influ-
enced by additional meteorological variables) the ratio decreased slowly
with increasing WS.|. Such a relationship can be approximated by the
diffusion factor
-Y|WS |6
e
where 5 is chosen to be .5, and y is a parameter.
These components led to the following model:
-Y|WS. I'5
C0t = (a+kTDt)e ^ +at (3-2)
Summer (May-October 1977) weekday CO averages at Site F and corresponding
weekday averages of WS| and TD were used to estimate the parameters. The
results are given below":
May 1977-October 1977 Weekdays (M-R)
Parameter Estimate Standard Error
a 2.17 0.30
k 0.047 0.0025
Y 0.16 0.021
The actual CO readings and the predicted values are plotted in Figure 3~13
and listed in Table 3~3- It can be concluded that Model 3-2 produces an
excel lent fit.
A JOINT MODEL FOR CO CONCENTRATIONS AT SITES A, B, C, AND F
A joint model covering all four stations was designed in addition to
the univariate models built for Sites C and F.
11
-------
As shown in Figure 1-1, Site A was 150 feet and Sites B and C were both
75 feet from the median strip F. Any joint model covering different sites must
include the distance from the center of the freeway as an explanatory variable.
Since the wind vector controls the transport of the freeway contribution,
our model had to reflect that Sites A and B were on opposite sides of the
freeway from Site C. Thus, d was chosen to be an indicator variable for the
distance such that d = 2; d = 1; d = 0; d = -1, where one unit corre-
sponded to 75 feet. h
The proposed joint model took the form:
A
- ylliK I ' ^
'it'
CO. = ( ct+kTD e -1- +a.
Jt / t /TTflU I , Jt
e J J
/1+Bldjl I
(3.3)
where
CO. = the observed CO concentration for Site j(A,B,F or C) at hour t
« TD = the traffic density at hour t.
« d. = the distance of each location from the median strip as defined
J above.
WS = the perpendicular component of the wind vector at hour t.
sgn = sign function; sgn(x) =j_, .,
a. = error terms, and
1 if x>0
x<0
a,k,n,3,w and Y are unknown parameters to be estimated from the data.
12
-------
TABLE 3-3. OBSERVED AND PREDICTED CO AVERAGES-
Hour
0
1
2
3
4
5
6
7
8
9
10
11
Observed
CO Average
4.88
3-19
2.k]
1.87
2.20
4.68
10.36
14.50
13-73
11.58
9.80
8.46
Pred icted
CO Average
4.26
3-30
2.87
2.57
2.63
3-95
9.04
14.32
14.49
11.67
9.20
8.07
Hour
12
13
14
15
16
17
18
19
20
21
22
23
Observed
CO Average
7-56
7-25
8.06
10.38
11 .61
12.34
9-19
7.44
6.65
6.91
6.96
6.41
Predicted
CO Average
7.57
7-36
8.04
10.01
10.91
11 .82
10.91
8.71
6.72
6.93
7-00
6.04
Averages for Site F; 1977 summer weekdays (Model 3.2)
Model 3-3 was fitted using the 1977 summer weekday CO averages for the
four sites and the corresponding WS. and TD values. The parameter estimates
are given below:
Joint CO model - Summer weekday 1977
Parameter Estimate Standard Error
a
k
n
3
03
Y
1.58
0.051
0.088
1.29
-4.12
0.17
0.11
0.0015
0.014
0.19
0.32
0.016
by:
The correlation matrix between errors at Sites A, B, F, and C is given
P=
1.00 .53 .28
1.00 .58
1.00
34
32
25
1 .00
Actual CO averages and predicted values are plotted in Figures 3-l4a through
3-l4d and listed in Table 3-4. Model 3-3 is quite parsimonious in the para-
meters; apart from the covariances for the errors only six parameters have
to be estimated from the data. It produced a satisfactory overall fit at
all four locations.
13
-------
TABLE 3-4. OBSERVED AND PREDICTED CO AVERAGES'
Hour
0
1
2
3
it
5
6
7
8
9
10
1 1
12
13
14
15
16
17
18
19
20
21
22
23
Si te A
Averages
Obs. Pred.
2.01
1.73
1.50
1.33
1.34
2.00
2.3k
3-43
3-25
2.68
1.97
1.33
1 .01
0.86
0.76
0.73
0.59
0.49
0.64
0.97
1.52
1=91
2.31
2.43
1.73
1.66
1.63
1.57
1.57
1.72
2.30
2.92
2.66
1 .90
1.38
1.16
1 . 10
1.06
1 .04
1 .04
1.05
1 .10
1.19
1-33
1.49
1-74
1 .86
1 .92
Site B
Averages
Obs. Pred.
2.53
1 .94
1 .66
1.41
1.47
2.51
4.81
6.12
5.05
3-99
2.63
1.43
1.13
0.92
0.83
0.74
0.62
0.54
0.64
0.68
2.21
2.71
3-09
3.08
2.34
1.97
1 .82
1.70
1-71
2.22
4.20
6.27
5.82
3-89
2.31
1.52
1.31
1.18
1.14
1.16
1.21
1.39
1.73
2.11
2.35
2.87
3.08
2.95
Site F
Averages
Obs. Pred.
4.88
3-19
2.41
1.87
2.20
4.68
10.36
14.50
13-73
11 .58
9.80
8.46
7.56
7-25
8.06
10.38
11.61
12.34
9-19
7.44
6.65
6.91
6.96
6.41
3.87
2.83
2.35
2.03
2.11
3.54
9.04
14.73
14.92
11 .83
9-17
7.96
7-43
7.20
7.91
9-97
10.92
11.89
10.96
8.65
6.53
6.76
6.83
5-79
Site C
Averages
Obs. Pred,
2.36
1.67
1.39
1.18
1.24
1.97
3.43
5.82
6.80
6.63
6.56
6.26
5.79
5.47
5-91
6.76
7.00
7.36
6.36
5.03
3.85
3.51
3.27
3.06
2.25
1.98
1 .82
1.70
1.72
2.19
3-97
5.81
6.39
6.08
5.83
5.63
5.23
4.86
5-07
6.24
7.01
8.05
7-59
5.66
3-91
3.61
3-50
3.02
"Averages for Sites A, B, F, and C; 1977 summer weekdays (Model 3.3)
14
-------
Interpretation of the joint model
* If d=0 (median) Model 3.3 reduces to Model 3.2, (the univariate model
for CO concentrations at Site F) .
For any fixed d^O, the first factor in Model 3-3 corresponds to the
univariate model for CO concentrations at Site C (Model 3-0- Moreover,
in the joint model the background concentration a and the free-
way contribution were diffused by the factor
-Y | WS '5
e
For fixed WS , CO concentrations decreased with increasing distance from
the freeway. This decrease was less for the downwind sites.
One advantage of the joint model (3.3) was it could be used to predict
CO concentrations at any given distance from the freeway median.
It is worth noting that this model was different from other models considered
in the literature, notably the HIWAY model (Zimmerman and Thompson [1975])-
The HIWAY model can be used only to predict pollutant concentrations in the
downwind direction from the source. In future research it would be worth-
while to compare the predictive accuracies of those models using the LACS
data and data from other regions.
15
-------
SECTION 4
ANALYSIS OF THE Pb DATA
Since catalyst equipped cars are required to use unleaded gasoline, the
catalytic converter should lead to a reduction in Pb emissions. A statistical
analysis of ambient Pb concentrations was conducted in order to test this
assumption. The Pb data used consisted of 4-hr afternoon (3 p.m. to 7 p.m.)
and 24-hr hi-vol Pb concentrations at Sites A, B, C, and D.
ANALYSIS OF MONTHLY MEANS
Figures 4~la through 4~ld show the monthly averages of the 4-hr afternoon
readings, for Sites A, B, C, and D respectively. Monthly averages of the
afternoon (3 p.m.-7 p.m.) windspeed are shown in Figure 4-2a. Figure 4-2b
shows the monthly relative frequency of the afternoon wind from the direction
(l45°-325°), i.e., when the wind was blowing across the freeway towards Site
C. The following observations were recorded:
The levels of Pb at downwind Sites C and D were substantially higher
than those at upwind Sites A and B.
In the summer months when the afternoon winds were blowing predominantly
across the freeway towards Site C (Figure 4-2a and 4~2b), very little Pb
was seen at Sites A and B. This absence of Pb indicated there was
almost no background Pb in this area, and that most of the recorded Pb
came from automobile emissions on the freeway. In the winter months
when the proportion of.winds from l45°-325° was smaller, some of the
freeway contribution was noted at Sites A and B.
The 4-hr Pb concentrations at Sites C and D decreased gradually until
the end of 1976- The summer (May-October) means of the 4-hr afternoon
readings are given in Table 4-1. At Site C the decrease from summer
1975 to summer 1976 was approximately 17 percent; at Site D the average
annual decrease from 1975 to 1976 was 11 percent.
Starting in February 1977, Pb concentrations increased sharply, especi-
ally at Site C, which was closest to the freeway on the downwind side.
Table 4-1 shows that from summer 1976 to summer 1977 Pb concentrations
increased 70 percent. The increase at Site D was approximately 40
percent (less data were available for Site D since hi-vol sampling for
Pb at this station was discontinued in June 1977)- The addition of a
fifth lane (northbound) to the freeway explained this sudden increase.
The opening of the extra lane increased afternoon traffic speed on lanes
16
-------
closest to Sites C and D (Figure 1-1). Laboratory studies (Hirschler,
et al. [1957]) have shown that Pb emissions increase with traffic speed.
The increase in Pb at Site D was smaller than the increase at Site C.
This discrepancy may have occurred because most of the larger sized Pb
particles, which are emitted at higher speeds, settled near the freeway.
2^-hr Pb averages
The monthly means of the 24-hr Pb data at Sites C and D are plotted in
Figures 4~3a and 4-3b. The summer (May-October) averages for these data are
listed in Table 4-la. Notice at both sites the 24-hr Pb concentrations
decreased gradually until 1976. From 1976 to 1977, because of the change in
traffic speed, the 24-hr Pb readings increased at both locations. The
increase observed in the 24-hr Pb averages, however, was small compared to
the increase seen in the 4-hr afternoon data, because the additional north-
bound lane affected the northbound traffic speed mainly in the afternoon.
Comparison of weekday and weekend afternoon Pb
To further explore the argument that higher speeds cause higher Pb
emissions, weekday and weekend Pb readings were compared. Phadke, Tiao and
Hillmer (1977) and Tiao and Hillmer (1977) reported that the afternoon Pb
readings were about 60 percent higher on weekends than on weekdays, even
though on weekends fewer cars passed the measurement stations.
This difference between weekday and weekend Pb readings was attributed
to the afternoon traffic speed being higher on weekends than on weekdays,
resulting in increased weekend Pb emissions. A comparison of the traffic
data for 1976 and 1977 shows the average afternoon traffic speed on weekdays
increased from 37 mph in 1976 to 47 mph in 1977- The speed of northbound
traffic closest to Site C increased even more; from 27 mph in 1976 to 47 mph
in 1977. At the same time there was very little change in the weekend speed
between 1976 and 1977- Therefore, the speed difference between weekdays and
weekends decreased in 1977 and thus the difference between weekday and
weekend afternoon Pb should have been less prominent. This prominent reduc-
tion was confirmed by Figure 4-4a (Site C) and Figure 4-4b (Site D).
A simple model for the 4-hr afternoon Pb data at Site C
Daily afternoon (3 p.m. to 7 p.m.) averages of traffic count, traffic
speed, WS., and Pb from the periods August 27-December 27, 1976, and September
l4-Novembe~r 30, 1977, were used to build an empirical model for the concentra-
tions. Since reliable data on both traffic count and traffic speed were
available for these two periods, there was no need to distinguish between
weekdays and weekends.
The average of the 4-hr afternoon Pb readings for the 1976 period was
7-91 yg/m3. For the 1977 data (after the additional northbound lane was
opened) the average rose to 10.87 yg/m3. The proposed model helped to
determine whether this increase could be explained by changed meteorological
and/or traffic conditions.
17
-------
TABLE 4.1. OBSERVATIONS FOR SUMMER 4-HR Pb DATA
4-Hr Pb Concentrations (3 p.m. to 7 p.m.)
Site Year(s)
1975
C 1976
1977
1974
n 1975
1976
1977
r 1976-1975
1977-1976
1975-1974
D 1976-1975
1977-1976
Mean
8.16
6.77
5.64
4.90
4.40
6.18
N/A
N/A
N/A
N/A
N/A
Standard
Devi at ion
2.78
2.25
2.14
1.29
1 .00
0.96
1.18
N/A
N/A
N/A
N/A
N/A
Number of
Observat ions
174
166
92
151
176
166
20
N/A
N/A
N/A
N/A
N/A
t-stat i st ic
N/A*
N/A
N/A
N/A
N/A
N/A
N/A
-5.05
16.14
-5.83
-4.71
7-63
Not Applicable
TABLE 4.la. OBSERVATIONS FOR SUMMER 24-Hr Pb DATA
24-Hr Pb Concentrations
Site Year(s)
1974
1975
C 1976
1977
1974
n 1975
° 1976
1977
1975-1974
C 1976-1975
1977-1976
. 1975-1974
u 1976-1975
1977-1976
Mean
8.19
7-98
7.00
7.43
5.00
4.19
3.75
4.16
N/A
N/A
N/A
N/A
N/A
N/A
Standard
Devi at ion
1.83
1.48
1.60
1.19
1.02
1.01
0.73
0.70
N/A
N/A
N/A
N/A
N/A
N/A
Number of
Observations
143
173
166
74
46
57
57
63
N/A
N/A
N/A
N/A
N/A
N/A
t-stat ist ic
N/A*
N/A
N/A
N/A
N/A
N/A
N/A
-1.13
-5.86
2.07
-4.03
-2.67
3-14
'Not Applicable
18
-------
As noted earlier (Hirshler, et al, [1957]), an increase in traffic speed
produces an increase in Pb emissions. This relationship is illustrated in
Figure 4~5a, where the ratio of afternoon Pb to the total afternoon traffic
count (TC) is plotted against the average afternoon traffic speed. Averages
of Pb/TC for successive traffic speed intervals were plotted instead of
individual observations. This plot shows that the ratio (Pb/TC) increases
proportional to traffic speed, implying a relationship of the form:
Pb/TC = kTS or Pb = kTCxTS. (4.1)
The wind affects Pb concentrations by means of transport and diffusion.
These influences are shown in Figure 4-5b, where we plotted Pb/(TCxTS)
against WS which is to take Pb/(TCxTS) proportional to the dispersion
factor
-b(WS,-u>)
e
2
1 (4.2)
where b and w are appropriate constants.
Combining 4.1 and 4.2 the relationship can be written as
-b(WS -u)2
Pb = kTCxTSe ^ (4.3)
The parameters k = k. , for 1976 and k = k« for 1977 were introduced to
test whether a change occurred in the Pb emissions from 1976 to 1977- After
having modeled the dependence of Pb on traffic and meteorological variables,
it was possible to test whether the parameter k, which was proportional to
the Pb emissions, changed over time.
Since a larger contribution was expected from the northbound traffic
lane (because it was closest to the receptor at Site C) , the effects of
the northbound and the southbound traffic were separated. The next step
was to design the model:
where: Pb = the observed 4-hr afternoon Pb reading at Site C for day t,
TC ,TC = total afternoon northbound (southbound) traffic count for
day t,
N S
TS ,TS = average afternoon northbound or southbound traffic speed
for day t,
WS average afternoon perpendicular component of the wind vector,
a = error term,
k,,k9 = parameters proportional to the Pb emissions; k = k, for the
1976 period and k = k2 for the 1977 period,
19
-------
a = parameters measuring the relative contribution of the north-
bound and southbound lane,
b,w = parameters in the dispersion factor involving the perpendi-
cular wind component.
Using the set of data on Pb, traffic, and WS described above, the parameters
in Model b.k were estimated by nonlinear lea's! squares. The parameter
estimates and their standard errors are given below:
Parameter Estimate Standard Error
(1976)
(1977)
a
b
to
8.77
8.75
0.75
0.011
2.19
0.39
0.52
0.10
0.0035
0.56
Various diagnostic checks such as residual plots failed to reveal any apparent
inadequacy in the model. In particular, a plot of residuals against traffic
speed showed no apparent relationship, thus indicating that the model ade-
quately described the relationship between Pb and traffic speed.
Two important observations were made from the parameter estimates:
The estimate for a (.75) showed that the northbound lane, which is
closest to the receptor Site C, had a much larger contribution to the
Pb concentrations at this site than the southbound traffic lane. That
the heavier Pb particles settle fairly quickly explained the larger
contribution of the northbound lane.
The estimated emission constants kj and k£ for 1976 and 1977 did not
differ significantly, indicating that the 37 percent increase in the
means from 1976 to 1977 was caused by the change in traffic speed.
20
-------
SECTION 5
ANALYSIS OF SO^ DATA
The catalytic converter was designed to reduce the levels of
hydrocarbon and carbon monoxide emissions. Although, it successfully
reduces the emissions, the catalyst also converts the sulfur in gasoline
to sulfate ion (SO-r). This feature of the converter caused alarm since
an increase in ambient sulfate concentrations from catalyst equipped
automobiles could have harmful health effects.
The SO? data analyzed consisted of daily 4-hr afternoon (3 p.m. to
7 p.m.) concentrations from both the hi-vol and membrane sampler. The
difference in the 4-hr concentrations between Sites C and A reflected
the contribution from the freeway, since in the afternoon the wind blew
predominantly in a direction perpendicular to the freeway (Evans and
Rodes [1977]).
In analyzing the SO? data daily afternoon readings were used to calculate
monthly averages at the different sites.
MONTHLY SOjj AVERAGES FROM HI-VOL SAMPLERS
The monthly SO? averages from the hi-vol sampler at Sites A, B, C, and
D are given by the solid lines in Figures 5~la through 5~ld. It was noticed
that SO? decreased gradually at all four stations until May 1977
Available data for June 1977 to November 1977 at Sites A and C showed a
considerable increase in SO?. No data were available to confirm this increase
for Sites B and D.
Monthly means at Sites C and D downwind from the freeway were slightly
higher than those for the background Sites A and B, indicating a contribution
to SO? from the freeway. The contribution, however, was very small.
MONTHLY S0jj AVERAGES FROM MEMBRANE SAMPLERS
The broken lines in Figures 5~la and 5~lc show the monthly membrane
sampler SO? averages from June 1974 to November 1977- A slight reduction
in membrane SO? was noticed at both Sites A and C until May 1977- As on the
hi-vol readings a slight increase occurred for the last part of the data
(June-November 1977)-
21
-------
A comparison of membrane and hi-vol SO? concentrations, showed that
although seasonal patterns were similar, the hi-vol data were consistently
higher than the membrane readings.
AN ADDITIONAL GRAPHICAL REPRESENTATION OF THE SO? DATA
In Figures 5~la through 5~ld the monthly averages of the hi-vol and
membrane SO? are plotted. These were useful for a preliminary trend
assessment. The minimum, the 25th, 50th, and 75th percentiles, and the
maximum were also plotted to describe the variations of the SO? samples.
Since every month (or quarter) did not have the same number of data points
box plots (Tukey [1977], McGill, Tukey, and Larsen [1978]) were used to
incorporate this information into the plots. The box plots are illustrated
in Figures 5~2a and 5~2b for both the hi-vol and membrane SO? readings at
Site C. The data are grouped into 3-month periods corresponding to the
seasons: winter (December, January, February); spring (March, April May);
summer (June, July, August), and fall (September, October, November). The
lower line in each box corresponds to the 25th percentile (lower quartile);
the broken line gives the median and the upper line gives the 75th percentile
(upper quartile) of all observations for each season. The length of the
box measures the interquartile range and the width of the box indicates the
group size. It is chosen proportional to the square root of the number of
observations in each group. This choice was made because most measures of
variation (e.g. the sample standard deviation) are proportional to the
square root of the group size. Figures 5~2a and 5~2b show the maximum and
the minimum SO? readings within each season.
ACROSS-THE-FREEWAY DIFFERENCES
It was pointed out earlier that the difference between the 4-hr afternoon
readings at Sites C and A can be represented as the contribution from the
freeway. Monthly means and quarterly box plots for the (C-A)SO? differences
between these sites are given in Figures 5~3a through 5~4b. A slight increase
was observed in both monthly means and quarterly medians of the membrane SO?
differences. These observations were confirmed by the means of the summer
differences shown in Tables 5~1 and 5~'a. The increase in the summer differ-
ences, however, was not statistically significant. Figure 5~4b indicates
that for the first year of the study little data on membrane SO? were
ava ilable.
Hi-vol SO? (C-A) differences behaved quite differently from the corre-
sponding membrane readings. From 1975 to the spring of 1977 a significant
reduction in the hi-vol SO? differences was observed. At the same time the
membrane differences increased slightly. The hi-vol SO? differences for the
summer and fall of 1977 were slightly higher than the averages for the
previous year, but were still significantly smaller than those in 1975
(Table 5~1). The discrepancy between the hi-vol and membrane readings raised
an important question: Which, if either, of the two measurement methods was
giving the correct pollutant reading? One possible conjecture was put
forward by Tiao and Hillmer (1977)- They argued (l) that the 4-hr hi-vol
difference was caused by SO reacting on the filter to form SO?, and (2) that
22
-------
this artifact formation also occurred on the membrane filter, but to a lesser
extent. Although this theory explained the observed discrepancies fairly
well, further research is necessary to determine the precise nature of these
two fi1ters.
TABLE 5-1
OBSERVATIONS FOR SUMMER 4-HR SO^ HI VOL DATA
Year(s)
1975
1976
1977
1976-1975
1977-1976
1977-1975
'V
Not Appl i cable
TABLE 5-la.
Mean
4.87
2.53
3-29
N/A
N/A
N/A
OBSERVATI
Standard
Deviat ion
3-98
3.86
5-49
N/A
N/A
N/A
ONS FOR SLIMMER
Number of t-statistic
Observat ions
164
156
87
N/A
N/A
N/A
4-HR SOjj MEMBRANE
N/A*
N/A
N/A
-5.34
1.26
-2.61
Year(s)
1975
1976
1977
1976-1975
1977-1976
1977-1975
Mean
.14
.67
.99
N/A
N/A
N/A
Standard
Deviat ion
4.53
2.04
2.15
N/A
N/A
N/A
Number of t-
Observat ions
46
150
134
N/A
N/A
N/A
stat istic
N/A
N/A
N/A
1 .12
1 .29
1.69
Not Applicable
23
-------
SECTION 6
ANALYSIS OF HIGH POLLUTANT CONCENTRATIONS
Ancillary variables such as traffic, meteorology, and the concentrations
of other pollutants which accompanied high concentrations of CO, Pb, and
SOj (hi-vol) at Site C were investigated. The upper five percent of each of
the above three pollutants were identified. They were augmented by the
corresponding concentrations of the remaining two pollutants, by meteoro-
logical variables (wind direction, windspeed, relative humidity and temper-
ature), and by traffic count and traffic speed. Earlier studies of this
kind using aerometric data from other regions can be found in Cleveland,
Kleiner, and Warner (1976) and Tiao, Box, and Hamming (1974).
Since the Pb and SOg data considered were daily 4-hr afternoon readings,
the accompanying meteorological and traffic variables were averaged over the
3 p.m. to 7 p.m. period. For the hourly CO data the daily maxima were
cons idered.
Several tables which present data for the upper five percent of the
highest daily CO readings are given. Table 6-1 shows a dot diagram indicating
in which months the high values occurred. Dot diagrams of the corresponding
Pb and SO? 4-hr afternoon readings in terms of their percentiles and the
proportion of corresponding winds from the direction l45°-325° (blowing
across the freeway towards Site C) are given in Table 6-2. Table 6-3 displays
the proportions of the corresponding measurements on windspeed, relative
humidity, temperature, traffic count and traffic speed which are above/below
their overall average for that particular hour of the day.
CO FINDINGS
High concentrations of CO usually occurred during the fall and winter
period (September-March)- When traffic speed was low and winds blew across
the freeway towards Site C with below average windspeeds, high concentrations
of CO were also recorded.
Pb FINDINGS
High Pb readings were recorded in the summer of 1975 and in 1977 when
fifth lane was added in the northbound direction. The new lane reduced
24
-------
traffic congestion and increased traffic speed. High Pb readings also
occur when traffic speed was above average and when winds blew perpendicular
to the freeway at lower than average speed. Furthermore, high Pb readings
were recorded when both relative humidity and temperature rose above average
High S0|= readings were associated with the upper five percent of the Pb
read ings.
SOjj FINDINGS
High SQ=r readings occurred throughout the year, with most of the high
SO^ concentrations recorded in 1975- On days of high traffic speed and
across-the-freeway winds blowing towards Site C, high S0> readings were
observed. Furthermore, high S0> values usually occurred on days with high
relative humidity. A very large proportion of high S0j= readings was accom-
panied by high Pb concentrations.
25
-------
time of occurrence
J ftA
I . 8.1
1/75
A«ft_
:
1/76
1/77
11/77
correspond ing
4-hour afternoon J*-<^L*-±SUif i ti »t+i»i«i ti ti ^i*!*!i_ftL
Pb 0% 25% 50%. 75% 100%
! I ! I I* I « I [[[|«I»1«I»I>|8|
correspond ing
4-hour afterffoon
0%
25%
i i ii »i Si
50
75%
100%
wi nd
d i rect ion
wi ndspeed
l45°-325°
77-6%
below average
85.4%
3250-145'
22.4%
above average
14.6%
relat ive
humid i ty
temperature
traffic
count
traffic
speed
56.8%
48.8%
79-2%
95-8%
43.2%
51.2%
20.8%
4.2%
TABLE 6-1. DESCRIPTION OF ANCILLARY DATA ACCOMPANYING THE UPPER
FIVE PERCENT OF THE CO CONCENTRATIONS.
26
-------
time of occurrence
1/75
1/76
i
1/77 H/77
correspond ing
daily max.
CO
0%
251
50%
100%
correspond ing
4-hour afternoon
SO,
I*II 1*1
25%
50%
75%
100%
wi nd
d i rect ion
windspeed
l45°-325°
92.9%
below average
67-4%
7-1%
above average
32.6%
relat i ve
humid i ty
temperature
traffic
count
traffic
speed
22.
30.
50.
33-
6%
0%
0%
3%
77.4%
70.0%
50.0%
66.7%
TABLE 6-2. DESCRIPTION OF ANCILLARY DATA ACCOMPANYING THE UPPER
FIVE PERCENT OF THE Pb CONCENTRATIONS
27
-------
time of occurrence
* i
*i i *
I I ! & |
1/75 1/76 1/77 11/77
corresponding « I
1,
daily max. ,« , . S.M I 1,
C° 0? 25% 50% 75% 100?
corresponding
4-hour afternoon
SO
0% 25^ 50^ 75? 100?
wind l45°-325° 325°-l45°
direction 9^.7? 5-3?
below average above average
windspeed 45-9? 54.U
relative 13-5? 86.5?
humid i ty
temperature 41.7? 58.3?
traffic 71-4? 28.6?
count
traffic 28.6? 71.4?
speed
TABLE 6-3- DESCRIPTION OF ANCILLARY DATA ACCOMPANYING THE UPPER
FIVE PERCENT OF THE SO^ (HI-VOL) CONCENTRATIONS
28
-------
SECTION 7
FREQUENCY DISTRIBUTIONS FO*R HOURLY AND 4-HOURLY POLLUTANT CONCENTRATIONS
CLASS OF POWER TRANSFORMATIONS (MODEL 7.1)
In Section 3 the monthly 25th, 50th, 75th, and 90th percentiles of the
hourly CO measurements were plotted. Quarterly percentiles of the 4-hr
afternoon SO? concentrations were presented in Section 5. The distributions
of the pollutant measurements appear to be long tailed and skewed to the
right. Various models for such distributions have been put forward in the
literature, in particular the lognormal distribution, Aitchinson and Brown
(1957).
There is substantial literature, Zimmer and Larsen (1965), Larsen
(1969, 1973), Michels (1971), and Kornreich (197*0, which indicates that the
lognormal distribution is generally useful in representing ambient air
quality data. Theoretical reasons for believing so have been put forward by
Singpurwalla (1972), and Kahn (1973). However, cases have been reported in
the literature, for example, by Kalpasanov and Kurchatova (1976), DeNevers
and Lee (1977), in which the data deviate significantly from the lognormal
hypothesis.
In this section a more general class of distributions, which includes
the lognormal distribution as a special case, is considered. This particular
class of distributions (which are sometimes called Box-Cox transformations,
due to the work by Box and Cox [1964]) arises from power transformations.
Specifically, letting z. be the original observation, it is assumed that the
transformed variable x.,
1 _ \ _ i
(7-1)
x. =
is normally distributed with mean y and variance a2.
In Model 7-1, X is the transformation parameter. I f A = 1> the original z.
z.A-1 '
is normally distributed; if A +0, 1im ^ = log z. is normally distributed,
i.e., z. follows a lognormal distribution; if A = 1/2, the square root of
the original observation is normally distributed.
The introduction of the additional parameter A makes it possible to
check whether the lognormal distribution provides a good overall representa-
tion of the frequency distribution or whether other power transformations
29
-------
(such as square root or cube root) are more suitable. The distribution of
the z. can be written as:
f(z.|X,y,a2) =
r
1
/27TCT
or
1
/2-rra
X ] ]
20 ^
1 s 1
2i 2a2
z.X-l
[' , , 1 2 i JT_ ,- -\ _L n
X
-Finn -7 -U 1 T for X D
(7.2)
Maximum likelihood estimates for the parameters X, y, and a2 can be derived
and the interested reader is referred to the appendix for technical details.
CO Analysis
This approach is illustrated for the hourly CO measurements in Table 7~la,
for the 4-hr afternoon SO? (hi-vol and membrane) measurements and for
the Pb data shown in Tables 7~2a through 7~4a (all for Site C) .
The hourly CO concentrations were divided into consecutive 3~month
periods to block out possible seasonal and/or trend effects. The estimates
for X are given in the first column of Table 7-la. Notice that X varied
closely around .50, indicating that the square roots of the hourly CO concen-
trations followed a normal distribution. In columns 2 and 3 of Table 7-la.
estimates for y and a2 are given for the various seasons by constraining X
to be the same over the entire time span. In this case the maximum likeli-
hood estimate of X was .50, further supporting that the square root was the
appropriate transformation to consider, and that the hourly CO data at Site
C did not follow a lognormal distribution.
SO, Analysis
In column 1 of Tables 7-2a and 7-3a estimates are given of X for
consecutive 6-month periods of the daily 4-hr afternoon hi-vol and membrane
readings. Compared with the values of X for CO in Table 7;-la the variability
of X across the periods was considerably greater for the SO? readings.
Columns 2 and 3 present estimates of y and a2 for the various periods by
constraining X to be the same for all seasons. The estimates were .40 and
.35 for SO? hi-vol and SO? membrane readings respectively. These estimate
indicated the cube root transformed the observations to near normality.
Pb Analysis
The same analysis is given for the Pb data at Site C. No transformation
was necessary for the daily 4-hr afternoon Pb readings (overall estimate of X
was .85). The readings themselves appeared to be distributed normally.
30
-------
DISTRIBUTIONS FOR THE UPPER TAIL
In studying air pollutant data, interest often centers on high readings.
Although the class of power transformations may provide a good oveA&tt
description of the frequency distribution, this class of distributions
does not necessarily always give a good fit. The upper tail of the
distribution is of the main interest.
Thus focus was placed on the high values of the ambient air quality
data and a distribution was proposed which provided an adequate description
of the upper tail probabilities. In particular, the observations exceeding
some threshold value z were assumed to follow a Pareto distribution
rZ0 > ° (7'3)
and a > 1
Given z~, maximum likelihood estimates of the parameter a were easily derived
(details are given in the appendix).
In deciding on the threshold value z , excessive values were avoided
since a sufficient number of observations have to be available for an effi-
cient estimation of the parameter a.
For the hourly CO data at Site C, 8.75 ppm was chosen as the value of
ZQ. This value was approximately the 95th percent! le of all hourly CO
measurements. Again the parameter a was estimated separately for consecutive
3-month periods to block out possible seasonal and/or trend variation.
The estimates of a are given in the first column of Table 7-lb. The
second column compares the empirical frequency distribution with the theo-
retical Pareto distribution with parameter a. Using the null hypothesis
which states that data are from a Pareto distribution, the statistic in
column 2 follows approximately a Chi-square distribution with eight degrees
of freedom (nine separate intervals were considered). Comparing these
entries with the tabulated values from a Chi-square distribution with eight
degrees of freedom (xi(-05) = 15-5; x§(-°') = 20.1) only one was particularly
large (for September T975 through November 1975.)
In Tables 7~2b through l~kb estimates of ex and Chi-square goodness-of-
fit statistics are given for k-hr afternoon hi-vol and membrane SO? and Pb.
In order to obtain enough observations for estimation, the cutoff point z~ in
the Pareto distribution was chosen as the 75th percent! le of all 4-hr after-
noon data. The agreement with the Pareto distribution was excellent in most
cases.
AN APPLICATION OF THE PARETO DISTRIBUTION TO DETERMINE TAIL PROBABILITIES
The Pareto distribution was used to assess the probability of exceeding
a certain standard.
31
-------
The first step was to let z be the air quality standard for hourly
CO concentration, and the assumption that z > z~ be the threshold value
of the Pareto distribution. The probability that z > z then becomes:
P(z > zs) = P(z > z0)P(z > zjz > ZQ) (7.It)
The first factor in Model 1.k was determined by the choice of the threshold
value z_; the second term depended on the parameter in the Pareto
d i str i but ion.
Specifically,
z 1-a
P(z > zs[z > ZQ) = ^ (7-5)
As an illustration we considered July, August, and September 1977- The
estimate of a was a = 8.30 for this period. Furthermore, P(z > 8,75 ppm)
was equal to .0509.
Twenty ppm was assumed an important standard for hourly CO concentra-
tions. The probability of exceeding 20 ppm was then
P(z > 20 ppm) = P(x > 8.75 ppm)P(z > 20 ppm|z > 8.75 ppm) = .0001219.
We let x be the number of times 20 ppm was exceeded. For the roughly
2000 hourly CO measurements which were collected over a period of three
months, the model shows:
P(x = 0) = 0.7837
P(x = 1) = 0.1910
P(x = 2) = 0.0233
P(x > 3) = 0.0020
The expected number of exceedances was E(x) = .2^37-
These calculations are for illustration only. However, studies of
this kind can be useful in the formulation and assessment of air quality
standards.
32
-------
TABLE 7-la. ESTIMATES OF A, y, a2 FOR BOX-COX TRANSFORMATION:
LOS ANGELES HOURLY CO DATA, SITE C
Time Period
June, July, August (197*0
September, October, November (197*0
December, January, February (1975)
March, April, May (1975)
June, July, August (1974)
September, October, November (1975)
December, January, February (1976)
March, April, May (1976)
June, July, August (1976)
September, October, November (1976)
December, January, February (1977)
March, April , May (1977)
June, July, August (1977)
^
X
0.65
0.50
0.35
0.55
0.60
0.45
0.45
0.55
0.45
0.50
0.55
0.55
0.60
X = .50
y
1 .86
2.09
1.70
1.94
2.22
2.57
2.06
1.71
2.07
2.13
2.03
1.73
2.18
a2
1.56
1.85
3-70
1.36
1.23
1 .82
2.30
1.51
1.15
2.36
2.33
1.53
1 .42
TABLE 7-lb.
ESTIMATES OF a FOR PARETO DISTRIBUTION WITH
LOS ANGELES HOURLY CO DATA, SITE C
ZQ= 8.75:
Time Period
June, July, August (1974)
September, October, November (1974)
December, January, February (1975)
March, April, May (1975)
June, July, August (1974)
September, October, November (1975)
December, January, February (1976)
March, April , May (1976)
June, July, August (1976)
September, October, November (1976)
December, January, February (1977)
March, April , May (1977)
June, July, August (1977)
a
10.33
6.29
4.84
8.69
10.18
5-53
6.16
7-35
10.77
5.23
5-84
8-35
8.30
2
*8
2.04
20.06
16.42
17-31
9-15
29.83
19-31
9.26
1-34
17-28
8.14
9.64
2.43
33
-------
TABLE 7-2a. ESTIMATES OF X, y, o2 FOR BOX-COX TRANSFORMATION:
LOS ANGELES 4-HR AFTERNOON SO^ DATA (HI-VOL),
SITE C
Time Period
November 1974 - April 1975
May 1975 October 1975
November 1975 - April 1976
May 1976 October 1976
November 1976 April 1977
May 1977 - September 1977
X
0.75
0.15
-0.10
-0.10
0.45
0.75
A = .40
y
4.81
6.21
5.04
5.19
3.83
5.41
S2
1.76
1.52
1.73
1-27
2.44
1.67
TABLE 7-2b. ESTIMATES OF a FOR PARETO DISTRIBUTION WITH z AS THE
75th PERCENT! LE: LOS ANGELES 4-HR AFTERNOON S0j= DATA
(HI-VOL), SITE C
Time Period
November 1974 - April 1975
May 1975 - October 1975
November 1975 - April 1976
May 1976 - October 1976
November 1976 - April 1977
May 1977 - September 1977
a
7.40
4.54
4.78
4.54
4.84
6.41
4
13.20
7.07
8.82
16.64
9-89
6.31
34
-------
TABLE 7-3a. ESTIMATES OF X, y, a2 FOR BOX-COX TRANSFORMATION:
LOS ANGELES 4-HR AFTERNOON SOg DATA (MEMBRANE) ,
SITE C. 4
Time Period
November
May 1975
November
May 1976
November
May 1977
197^ - April 1975
- October 1975
1975 - April 1976
- October 1976
1976 - April 1977
- September 1977
A
-0.
-0.
0.
0.
0.
0.
70
15
25
35
30
55
X = .35
y
3
4
2
3
2
3
-94
.58
-49
.55
-52
.52
a
2.
1 .
1 .
2.
2.
2.
2
41
75
58
48
56
01
TABLE 7-3b. ESTIMATES OF a FOR PARETO DISTRIBUTION WITH z AS
75th PERCENT! LE: LOS ANGELES 4-HR AFTERNOON SO?
(HI-VOL) , SITE C
THE
DATA
Time Period
November 1974 - April 1975
May 1975 - October 1975
November 1975 - April 1976
May 1976 - October 1976
November 1976 - April 1977
May 1977 - September 1977
a
3.06
3-19
*§
1.73
5.88
too few data points
above overal 1 75th
percent i le
3.61
4.16
4.47
5.80
16.45
12.44
35
-------
TABLE 7-4a. ESTIMATES OF X, y, a2 FOR BOX-COX TRANSFORMATION:
LOS ANGELES 4-HR AFTERNOON Pb DATA, SITE C
Time Period
November 1975 April 1975
May 1975 - October 1975
November 1975 - April 1976
May 1976 - October 1976
November 1976 April 1977
May 1977 - September 1977
X
1 .00
0.50
1.15
0.00
0.85
1 .00
A = .85
y
5.00
5-78
4.30
4.76
6.21
7-90
. 52
4.50
4.04
2.81
2.78
6.31
2.84
TABLE 7-4b. ESTIMATES OF a FOR PARETO DISTRIBUTION WITH z AS THE
75th OVERALL PERCENTILE: LOS ANGELES 4-HR AFTERNOON
Pb DATA, SITE C.
Time Period
November
May 1975
November
May 1976
November
May 1977
1974 - April 1975
- October 1975
1975 April 1976
- October 1976
1976 - April 1977
- September 1977
a
8.81
5.85
11 .00
10.88
8.41
6.04
2
X8
7.31
14.29
1.75
10.82
15.98
24.07
36
-------
SECTION 8
ANALYSIS OF 0 NO, AND N02 DATA
In the LACS program, chemi1uminescence instruments for monitoring
nitric oxide (NO) and nitrogen dioxide (NO ) were added in January 1975 and
instruments for measuring ozone (0 ) were added in January 1976. Hourly
observations for these three pollutants were made at Sites A and C.
A preliminary analysis of the 4-hr afternoon (3 p.m. to 7 p.m.) 0 , NO,
and N0_ measurements was conducted. The afternoon period was of particular
interest for trend assessment since during the afternoon hours the wind
usually blew roughly perpendicular to the freeway. Thus the difference in
the readings at Sites C and A should have reflected the contribution from
the freeway traffic.
MONTHLY MEANS OF 4-HR AFTERNOON 0 NO, AND NO
The monthly averages of the 4-hr afternoon readings of 0.,, NO, and N0~
at Sites A and C as well as their across-the-freeway difference (C-A) are
plotted in Figures 8-la through 8-3c. From these plots we made the following
observat ions:
3: The level of 0-a_tjt he background site (A) was considerably
Jljjjher than 0, at Sfte C. Since the NO emitted from the automobiles
reacted very rapidly with the available 0, to form N0_, the background
0, was essentially consumed before it reached Site C.
0, was highly seasonal. High concentrations occurred in the summer
months because of increased solar radiation and strong and persisent
night and daytime inversions (Tiao, Box, and Hamming [1975]), and Tiao,
Phadke, and Box [1976]).
At both Sites A and C, the concentrations of 0_ decreased from
1976 to 1977; a slight reduction also occurred in tne across-the-
freeway difference. This observation was confirmed by the sample means
and standard deviations of (C-A) for the periods May-October 197& and
May-October 1977 (Table 8-la).
NO: The NO concentration at Site A practically vanished during the
s~ummer months when winds blew from the ocean towards Site C, indicating
there was very low NO background in this area. During the winter
months we observed some NO at Site A since in the winter period winds
occasionally blew towards the sea.
37
-------
While Figure 8-2a through 8-2c exhibits very little change in the
background level, it does show a significant increase from 1975 to 1977
in the NO concentrations at Site C and in the across-the-freeway differ-
ence (C-A). Means and standard deviations for May-October 1975, 1976,
and 1977 are given in Table 8-1.
NO
2_: The monthly means at Site C were considerably higher than
those at Site A, indicating a substantial contribution to NO from
the freeway. Although NO is not considered a primary pollutant
from the automobile, it quickly formed between Sites A and C through
the reaction of NO with the available 0 .
As in the NO data, very few yearly changes were noticed in NO,., at
the background station. On the other hand, a significant increase from
1975 to 1977 in the concentrations at Site C and in the across-the-
freeway differences was observed. The averages and standard deviations
of (C-A) for the period May-October are given in Table 8-1.
TABLE 8-1. OBSERVATIONS FOR SUMMER ACROSS-THE-FREEWAY DIFFERENCES
FOR POLLUTANTS -\
Pol lutant
°3
Year(s)
1976
1977
Mean
-5-39
-6.29
Standard
Deviat ion
3.43
3.07
Number of
Observat ions
^93
676
t-stati
N/A
N/A
stic
NO
NO,
1977-1976
N/A
N/A
1975
1976
1977
1976-1975
1977-1976
1977-1975
1975
1976
1977
1976-1975
1977-1976
1977-1975
0.273
0.314
0.435
N/A
N/A
N/A
0.0530
0.0623
0.0728
N/A
N/A
N/A
0.192
0.109
0.102
N/A
N/A
N/A
0.0241
0.0358
0.0308
N/A
N/A
N/A
N/A
560
576
668
N/A
N/A
N/A
596
556
688
N/A
N/A
N/A
-4.71
N/A
N/A
N/A
4.44
20.21
18.86
N/A
N/A
N/A
5.20
5.60
12.69
38
-------
DIURNAL DIAGRAMS FOR 0 , NO, and NO
Monthly means of the afternoon (3 p.m. to 7 p.m.) period (Figures 8-1 a
through 8-3c) were used to assess the overall trend in 0_, NO, and N0?.
Summer (May-October), weekday (Monday-Thursday) 1977 diurnal plots of these
three pollutants at Sites A and C are given in Figures 8-ka through 8-kc.
From these plots the following observations were made:
Ozone at the background station peaks around 2 p.m. in the afternoon.
As the wind transports ozone across the freeway it is consumed by NO
to form NO This reaction is very fast and, thus, only low 0 concen-
trations are recorded at Site C.
NO concentrations at Site A are essentially zero from 10 a.m. through
8 p.m. since the wind is transporting the NO emissions from the auto-
mobiles away from Site A towards Site C. Since part of NO reacts with
0 , NO at Site C peaks after the ozone is depleted. There is appar-
ently not enough 0, at the freeway to convert all of the NO automobile
emissions to N0?.
N0« concentrations at Site C follow a pattern similar to that of
ozone at Site A. The formation of N0« at Site C reaches its peak at
the same time when 0, peaks at Site A and gradually diminishes with the
depletion of ozone.
39
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APPENDIX A
MAXIMUM LIKELIHOOD ESTIMATES OF X, y, AND a2 FOR THE DISTRIBUTIONS
INVOLVING POWER TRANSFORMATIONS
z.A-l
It is assumed that the transformed variables x. = r - (l^i
-------
MAXIMUM LIKELIHOOD ESTIMATE OF THE PARAMETER a IN THE PARETO DISTRIBUTION
Suppose we have n independent observations z.,...,z
from the Pareto distribution with density
f(z.|a) = -^z.-, z. >z >0 (A.6)
Z0
The joint probability density of z},...,z is
- 1 n n
f(zrz2,...,zja) = hy^pl n z.~a, z.>z0 for all l
-------
REFERENCES
Aitchison, J., and J.S.C. Brown. 1957- The Lognormal Distribution. Cambridge
University Press, New York, New York.
Beltzer, M., R. J. Campion, and W. L. Peterson. 1974. Measurement of Vehicle
Particulate Emissions. Society of Automotive Engineers Paper 740286,
February 1974.
Bockian, A. H., G. Tsou, D. Gibbons, and R. Reynolds. 1977- Sulfate Concen-
trations at Two Los Angeles Freeways. The Los Angeles Catalyst Study
Symposium. EPA-600/4-77-034, U.S. Environmental Protection Agency,
Washington, D. C., p. 281.
Box, G.E.P., and D. R. Cox. 1964. An Analysis of Transformations. J. Royal
Stat. Soc., Series B, 26: 211.
Cleveland, W. S., B. Kleiner, and J. L. Warner. 1976. Robust Statistical
Methods and Photochemical Air Pollution Data. J. Air Pollut. Control
Assoc., 26:36.
DeNevers, N., and K. W. Lee. 1977. Extreme Values in TSP Distribution
Functions. J. Air Pollut. Control Assoc., 27:995.
Hirschler, D. A., L. F. Gilbert, F. W. Lamb, and L. M. Niebylski. 1957.
Particulate Lead Compounds in Automobile Exhaust Gas. Ind. Eng.
Chem., 49:1131
Kahn, H. 1973- Distribution of Air Pollutants. J. Air Pollut. Control
Assoc., 23:973.
Kalpasanov, Y., and G. Kurchatova. 1976. A Study of the Statistical
Distribution of Chemical Pollutants in Air. J. Air Pollut. Control
Assoc., 26:981
Kornreich, L. D. ed. 1974. Proceedings of the Symposium on Statistical
Aspects of Air Quality Data. EPA-650/4-74-038, U.S. Environmental
Protection Agency, Washington, D.C.
Larsen, R. I. 1969- A New Mathematical Model of Air Pollutant Concentration
Averaging Time and Frequency. J. Air Pollut. Control Assoc., 19:24.
Larsen, R. I. 1973- An Air Quality Data Analysis System for Interrelating
Effects, Standards and Needed Source Reductions. J. Air Pollut. Control
Assoc., 23:993-
42
-------
Michels, D. E. 1971- Lognormal Distribution for Plutonium in the Outdoors.
In: Proceedings of Environmental Plutonium Symposium. E. B. Fowler,
R. W. Henderson, and M. F. Milligan, eds., Kept. LA-4756, Los Alamos
Scientific Laboratory.
McGill, R., J. W. Tukey, and W. A. Larson. 1978. Variations of Box Plots.
The Am. Statist. 32:12.
Parry, E. P., R. A. Meyer, and C. E. Rodes. 1977- Determination of Percen-
tage of Diesel Trucks and Catalyst Equipped Cars. In: The Los Angeles
Catalyst Study Symposium, EPA-600/4-77-034, U.S. Environmental Protection
Agency, Washington, D. C., p. 147.
Phadke, M. S., G. C. Tiao, and S. C. Hillmer. 1977- Statistical Evaluation
of the Environmental Impact of the Catalytic Converter. Paper presented
at the 1977 Annual Meeting of the Air Pollution Control Association,
Toronto, Canada, June 1977-
Rodes, C. E., and G. F- Evans. 1977- Summary of LACS Integrated Pollutant
Data. In: The Los Angeles Catalyst Study Symposium, EPA-600/4-77-034,
U. S. Environmental Protection Agency, Washington, D. C., p.301.
Singpurwalla, N. D. 1972. Extreme Values from a Lognormal Law with Appli-
cations to Air Pollution Problems. Technometrics, 14:703.
Tiao, G. C., G.E.P. Box, and W. J. Hamming. 1974. A Statistical Analysis of
the Los Angeles Ambient Carbon Monoxide Data. Technical Report No. 265
Department of Statistics, University of Wisconsin, Madison, Wisconsin.
Tiao, G. C., G.E.P. Box, and W. J. Hamming. 1975- Analysis of the Los Angeles
Photochemical Smog Data: A Statistical Overview. J. Air Pollut. Control
Assoc., 25:260.
Tiao, G. C., and S. C. Hillmer. 1977- Statistical Analysis of the Los Angeles
Catalyst Study Data - Rationale and Findings. In: The Los Angeles
Catalyst Study Symposium. EPA-600/4-77-034, U.S. Environmental Protec-
tion Agency, Washington, D. C. p. 415. Also in Environ. Science and
Technol., 12:820, July 1978.
Tiao, G. C., M. S. Phadke, and G.E.P. Box. 1976. Some Empirical Models for
the Los Angeles Photochemical Smog Data. J. Air Pollut. Control Assoc.
26:485-
Tukey, J. W. 1977. Exploratory Data Analysis. Addison-Wesley, Reading,
Massachusetts.
Zimmer, C. E., and R. I. Larsen. 1965- Calculating Air Quality and its
Control. J. Air Pollut. Control Assoc., 15:565-
Zimmerman, J. R., and R. S. Thompson. 1975. Users Guide for HIWAY, a Highway
Pollution Model. USEPA, February 1975.
43
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N
SiteD
Figure 1-1. Map of Los Angeles air monitoring stations at San Diego Freeway.
-------
1/75
1/76
Figure 3-1a. Monthly means of 4-hour afternoon (3 p.m. to 7 p.m.) CO concentrations. Site A.
15 r
1/75
1/76
Figure 3-1 b. Monthly 25th, 50th, 75th, and 90th percentiles of 4-hour afternoon (3 p.m.
to 7 p.m.) CO concentrations. Site A.
-------
Figure 3-2a. Monthly means of 4-hour afternoon (3 p.m. to 7 p.m.) CO concentrations, Site C.
Figure 3-2b. Monthly 25th, 50th, 75th, and 90th percentiles of 4-hour afternoon (3 p.m.
to 7 p.m.) CO concentrations, Site C.
-------
7.5
5.0
2.5
JAN
I
FEB
I I I
MAR
2.5
I y I
APR
MAY
I
JUN
2.5
7.5
5.0
2.5
JUL
Jl
OCT
74 75 76 77
AUG
NOV
74 75 76 77
f
SEP
DEC
74 75 76 77
Figure 3-3a. Plot of 25th, 50th, and 75th percentiles of 4-hour afternoon (3 p.m. to 7 p m.
CO concentrations. Site A.
-------
12
JAN
FEB
MAR
12
APR
I I
MAY
JUN
12
JUL
AUG
SEP
12
OCT
74 75 76 77
NOV
74 75 76 77
DEC
74 75 76 77
Figure 3-3b. Plot of 25th, 50th, and 75th percentiles of 4-hour afternoon (3 p.m. to 7 p.m.)
CO concentrations, Site C.
-------
SUMMER 76
WINTER 75/76
12 15
HOURS
18 21 24
Figure 3-4a. Diurnal plots of CO at Site C;
winter - summer comparison (weekday).
SUMMER 76
- WINTER 75/76
0369
12 15
HOURS
21 24
Figure 3-4b. Diurnal plots of CO at Site C;
winter - summer comparison (weekend).
-------
- SUMMER 76
- WINTER 75/76
SUMMER 76
WINTER 75/76
0 3 6 9 12 15 18 21 24
0369
Figure 3-5a. Diurnal plots of CO at Site A;
winter - summer comparison (weekday).
Figure 3-5b. Diurnal plots of CO at Site A;
winter summer comparison (weekend).
50
-------
Figure 3-6a. Diurnal plot of traffic counts
and traffic speed, weekday 1976.
Figure 3-6b. Diurnal plot of traffic counts
and traffic speed, weekend 1976.
COUNT
SPEED
12 16 20 21
Figure 3-6c. Diurnal plot of traffic counts
and traffic speed, weekday 1977.
Figure 3-6d. Diurnal plot of traffic counts
and traffic speed, weekend 1977.
51
-------
1976
1977
12 16 20 24
12 16 20 24
Figure 3-7a. Diurnal plot of traffic density
(count/speed) weekday.
Figure 3-7b. Diurnal plot of traffic density
(count/speed) weekend.
-------
\
SUMMER 1976
WINTER 1975/76
0.
0 3 6 9 12 15 18 21
Figure 3-8. Diurnal plots of WS..
_L
53
-------
16
12
I 8
12 15 18 21 24
Figure 3-9. Diurnal plot of CO; Sites A, B, F, and C; summer weekday.
-------
16 r
12
t
12
15 18 21 24
Figure 3-10. Diurnal plot of CO; Sites A, B, F, and C; summer weekend.
55
-------
10
X PREDICTED
OBSERVED
Q.
Q.
12
15
18
21
24
Figure 3-11. CO model 1977 summer weekday fit. Site C.
-------
1.5
1.0
o
h-
+
O
o
0.5
ws.
Figure 3-12. Plot of the ratio CO/ («+ kTD) versus WS, ; Site F.
-------
16
14
10
0
X PREDICTED
OBSERVED
0 36 9 12 15 18 21 24
gure 3-13. CO model 1977 summer weekday fit, Site F (median strip),
53
-------
X PREDICTED
OBSERVED
X PREDICTED
OBSERVED
XX*-*
Figure 3-14a. Joint CO model fit summer
weekday, 1977, Site A.
Figure 3-14b. Joint CO model fit summer
weekday, 1977, Site B.
X PREDICTED
_ OBSERVED
X PREDICTED
OBSERVED
0 3 6 9 12 15
Figure 3-14c. Joint CO model fit summer Figure 3-14d Joint CO model fit summer
weekday, 1977, Site C. weekday, 1977, Site F.
59
-------
Figure 4-1a. Monthly means of 4-hour afternoon Pb concentrations. Site A.
Figure 4-1b. Monthly means of 4-hour afternoon Pb concentrations. Site B.
60
-------
Figure 4-1c. Monthly means of 4-hour afternoon Pb concentrations. Site C.
Figure 4-1d. Monthly means of 4-hour afternoon Pb concentrations. Site D.
61
-------
Figure 4-2a. Monthly means of afternoon (3 p.m. to 7 p.m.) windspeed.
Figure 4-2b. Monthly means of afternoon (3 p.m. to 7 p.m.) winds from 145° 325°
62
-------
Figure 4-3a. Monthly means of 24-hour Pb concentrations. Site C.
I
1/76
Figure 4-3b. Monthly means of 24-hour Pb concentrations, Site D.
63
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WEEKEND
WEEKDAY
Figure 4-4a. Monthly means of 4-hour (3 p.m. to 7 p.m.) Pb readings weekday weekend
comparison. Site C.
WEEKDAY
Figure 4-4b. Monthly means of 4-hour (3 p.m. to 7 p.m.) Pb readings weekday - weekend
comparison. Site D.
-------
* 2
u
o
H
i
20 40 60
TRAFFIC SPEED TS, mph
Figure 4-5a. Plot of Pb/TC vs TS.
4-202
WS^.mph
Figure 4-5b. Plot of Pb/TC x TS vs
65
-------
E
a
MEMBRANE
Figure 5-1a. Monthly means of 4»hour hi-vol and membrane afternoon readings of SOg; Site A.
MEMBRANE
Figure 5-1b. Monthly means of 4-hour hi-vol afternoon readings of SOg; Site B.
66
-------
MEMBRANE
1/75
1/76
Figure 5-1c. Monthly means of 4-hour hi-vol and membrane readings of SOg; Site C
I
MEMBRANE
1/75
1/76
Figure 5-1d. Monthly means of 4-hour hi-vol afternoon readings of SO^; Site D.
67
-------
T
SU FA VUl SP SU FA Wi SP SU FA
1976 1977
Figure 5-2a. Plot of quarterly 25th, 50th, and 75th percentiles, minimum and maximum of 4-hour
hi-vol afternoon SO5 concentrations at Site C.
T
WI SP SU FA WI SP SU FA WI SP SU FA
'975 1976 1977
Figure 5-2b. Plot of quarterly 25th, 50th, and 75th percentiles, minimum and maximum of 4-hour
membrane afternoon SO| concentrations at Site C.
68
-------
1
1/75
1/76
I
Figure 5-3a. Monthly means of 4-hour hi-vol SCN (C - A) differences.
1/75
1/76
Figure 5-3b. Monthly means of 4-hour membrane S0| (C - A) differences.
-------
SP SU FA Wl SP SU FA Wl SF SL F,
197C 1976 197"
Figure 5-4a. Plot of quarterly 25th, 50th, and 75th percentiles of 4-hour hi-vol afternoon
SO (C - A) differences.
Wl SP SU FA Wl SP SU FA Wl SP SU FA
1975 1976 1977
Figure 5-4b. Plot of quarterly 25th, 50th, and 75th percentiles of 4-hour membrane
afternoon S0| (C - A) differences.
70
-------
Figure 8-1a. Monthly means of 4-hour (3 p.m. to 7 p.m.) 63 at Site A.
Figure 8-1b. Monthly means of 4-hour (3 p.m to 7 p.m.) 03 at Site C.
Figure 8-1 c. Monthly means of 4-hour (3 p.m. to 7 p.m.) 63 (C A).
71
-------
Figure 8-2a. Monthly means of 4-hour (3 p.m. to 7 p.m.) NO at Site A.
Figure 8-2b. Monthly means of 4-hour (3 p.m. to 7 p m.) NO at Site C.
Figure 8-2c. Monthly means of 4-hour (3 p.m. to 7 p.m.) NO (C - A).
72
-------
A
Figure 8-3a. Monthly means of 4-hour (3 p.m. to 7 p.m.) NO2 at Site A.
Figure 8-3b. Monthly means of 4-hour (3 p.m. to 7 p.m.) NO2 at Site C.
Figure 8-3c. Monthly means of 4-hour (3 p.m. to 7 p.m.) ISIO2 (C A).
73
-------
0 36 9 12 15 18 21 24
0 3 6 9 12 15 18 21 24
Figure 8-4a. Diurnal plots of 03 (Monday - Thursday) at Sites A and C.
74
-------
0 3 6 9 12 15 18 21 24
0 3 6 9 12 15 18 21 24
Figure 8-4b. Diurnal plots of NO (Monday - Thursday) at Sites A and C.
75
-------
0 3 6 9 12 15 18 21 24
0 3 6 9 12 15 18 21 24
Figure 8-4c. Diurnal plots of N0£ (Monday - Thursday) at Sites A and C.
76
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA 600/4-79-070
3. RECIPIENT'S ACCESSI Of* NO.
4. TITLE AND SUBTITLE
STATISTICAL ANALYSIS OF THE LOS ANGELES CATALYST
STUDY DATA
5. REPORT DATE
1979
6. PERFORMING ORGANIZATION CODE
7.AUTHOR(s) Johannes Ledolter, George C. Tiao, Spencer B.
Graves, Jian-tu Hsieh, Gregory B. Hudak (U. of Wi.sc)
R Sai.U. FPA/FMSI, RTF, N,
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Department of Statistics
University of Wisconsin
Madison, Wisconsin 53706
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
68-02-2261
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Monitoring and Support Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, N.C. 27711
13. TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
EPA-600/08
15. SUPPLEMENTARY NOTES
16. ABSTRACT ~~
This research was initiated to perform statistical analyses of the
data from the Los Angeles Catalyst Study. The objective is to determine
the effects of the introduction of the catalytic converter upon the
atmospheric concentration levels of a number of air pollutants.
This report gives an analysis of the CO, Pb, SO,, 0_, NO and HO^
data covering the period from June 197^ to November T977- Models are
built to evaluate the freeway contribution to CO and Pb as a function of
traffic, windspeed and wind direction. These models are used to assess
both the time trend in the pollutant measurements and the pollution con-
centrations at points near the freeway. Furthermore frequency distributions
for ambient air quality data near freeways are discussed.
This report was submitted in fulfillment of U.S. E.P.A. Contract
No. 68-02-2261 with the University of Wisconsin. It covers work done
during the period September 1977 through August 1978.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDEDTERMS
c. COSATI Field/Group
mobile source pollution
freeway pollution
mobile pollution modeling
CO model ing
mobile source monitoring
freeway monitoring
catalyst effects
Los Angeles
catalytic converter
ozone
lead
sulfate
carbon monoxide
43F
68A
3. DISTRIBUTION STATEMENT
Release to public
19. SECURITY CLASS (This Report)
Unclass if ied
21. NO. OF PAGES
77
20. SECURITY CLASS (This pagej
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
77
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