INVESTIGATION OF CARBON MONOXIDE NATIONAL AMBIENT AIR
QUALITY STANDARDS BASED ON MULTIPLE EXPECTED EXCEEDANCES
SUMMARY AND CONCLUSIONS
Two statistical investigations have been made of the effects on
air quality of alternative multiple expected exceedance eight-hour
carbon monoxide (CO) national ambient air quality standards (NAAQS).
The studies made use of 1,199 site-years of CO concentration data
for the years 1979-1981 obtained from the Storage and Retrieval of
Aerometric Data (SAROAD) data base. The studies showed that, on
average, attaining a 7 ppm, 5 expected exceedances per year eight-
hour CO NAAQS gave comparable air quality to that obtained when a
site attained a 9 ppm, 1 expected exceedance per year standard.
Similarly a 9 ppm, 5 expected exceedance eight-hour CO NAAQS, gave,
on the average, air quality comparable to that which would be
expected with a 12 ppm, 1 expected exceedance per year standard. In
92% of the 1,199 site years of data both the 7 ppm, 5 expected
exceedances and 9 ppm, 1 expected exceedance standard gave the same
pass/fail results, (i.e., 62% of the site-years passed both
standards and 30% of the site years failed both standards). Similar
results were obtained when the 9 ppm, 5 expected exceedances and 12
ppm, 1 expected exceedance standards were compared.
When linear rollback procedures were used to estimate the
number of days with maximum eight-hour CO concentrations above 9 ppm
when sites not attaining the standard were rolled back to meet the
standard, there were 388 out of 335,826 had site-days above 9 ppm CO
when meeting the 9 ppm, 1 expected exceedance standard and 426 out
of 335,826 site-days above 9 ppm when sites were rolled back to meet
a 7 ppm, 5 expected exceedance standard. This result suggests that
the one expected exceedance standard is slightly more stringent than
the 5 expected exceedance standard. In the 9 ppm, 5 expected
exceedances and 12 ppm, 1 expected exceedance comparison there were
204 site-days above 12 ppm for the one expected exceedance standard
and 182 days above 12 ppm for the five expected exceedance standard.
t.S. Ihvlronmental Protection '&.£&
Region 5, Library (5PL-16)
1 230 S. Dearborn Street, Room 1670
Chicago, IL 60604
-------
In this case, the five expected exceedance standard appears to be
slightly more stringent than the one expected exceedance standard
considering the sites as a whole.
The investigation also demonstrated that tail-exponential
distributions fit the upper 5 and 10% of the daily maximum eight-
hour CO concentrations quite well. This finding permitted a more
general statistical treatment of the data base. The second
investigation showed that if all sites not attaining the eight-hour
CO standard could be brought just into attainment (a situation not
likely to be realized in practice) a 9 ppm, 1 expected exceedance
standard would give more uniform control among sites of the highest
eight-hour concentrations than a 7 ppm, 5 expected exceedance
standard. However, the difference would be small.
Under current practices (1), attaining the standard is based on
the second highest concentration observed in one year for a 9 ppm, 1
expected exceedance standard or a 12 ppm, 1 expected exceedance
standard and the sixth highest concentration in the case of a 7 ppm,
5 expected exceedance standard or a 9 ppm, 5 expected exceedance
standard. In this case the 5 expected exceedance standards gives
more uniform control among sites than the one expected exceedance
standards. When three years of data are available and the fourth
and sixteenth observed highest concentrations are used for one and
five expected exceedances standards, respectively, the differences
between the 9 ppm, one expected exceedance standard and 7 ppm, 5
expected exceedances standard become very small; but the 5 expected
exceedance standard continues to give slightly tighter control of
the highest concentrations among sites. Going to more years of data
or fitting distributions to the data is expected to result in the
one expected exceedance standards giving tighter control. However,
even in the limit when each site is brought into exact conformance
with an expected exceedance standard, which gives maximum advantage
to the one expected exceedance standard, the difference between the
one and five expected exceedance standards will be small. This
situation holds for both the 9 ppm, 1 expected exceedance compared
to the 7 ppm, 5 expected exceedances standard and the 12 ppm, 1
expected exceedance compared to the 9 ppm, 5 expected exceedances
-------
standard.
It was also shown that for the eight-hour CO NAAQS, expected
exceedance levels above five result in an increasing range of the
annual highest concentrations experienced at monitoring sites
subject to the standard.
INTRODUCTION
This report presents the results of two statistical
investigations of the effects of multiple expected exceedance eight-
hour carbon monoxide (CO) national ambient air quality standards
(NAAQS) on air quality in U.S. cities as monitored at established
ambient air monitoring sites.
Most primary NAAQS's specify 1. a pollutant concentration
averaging time appropriate to the health effects which the standard
is to protect against and 2. a concentration level, also based on
health considerations, above which, no more than a single measured
concentration is permitted to occur in a calendar year at a single
monitoring site in a given geographic area. Such standards have
been referred to as deterministic. The recently promulgated revised
NAAQS for ozone is statistically based. The expected annual
exceedance rate of the standard level is not permitted to be greater
than one at a single monitor. Standards expressed in either the
deterministic or the more recent statistical forms described above
focus attention on the behavior of the highest and second highest
time-averaged pollutant concentrations observed at a monitoring site
in a calendar year. While this is desirable from the point of view
of providing protection against unwanted health effects, concerns
have been expressed that such standards lead to practical problems
in determining attainment of the standard.
In particular, the concern is that an unusual meteorological
condition or the occurrence of some unusual event leading to short-
term high emissions of pollutant in the vicinity of a monitor can
cause the recording of concentrations which are atypically high for
the area. In the case of deterministically based standards, which
-------
make use of the second highest recorded value during the calendar
year, such occurrences could lead to the conclusion that an area is
in nonattainment even though pollutant levels in more typical years
would indicate attainment. Even in areas not in attainment,
atypically high concentrations could lead to an erroneously high
design value and, thereby, an incorrect judgment of the level of
control effort required to bring an area into attainment.
Statistically based standards should not have these problems if
adequate statistical methods are used to determine attainment and
design values. The reason is that a statistically valid measure
would make use of all the concentrations observed at a site over one
or several years or, minimally, a significant fraction of the high
concentrations. In current practice, however, attainment and design
values are determined, for the most part, by essentially
deterministic methods. For example, EPA guidelines permit the use
of the second highest value in one year and the fourth highest value
in three consecutive years of data to be used to determine
attainment and design values of the statistically based one expected
exceedance ozone NAAQS. These tests, because of their reliance on
the few highest observed concentrations, are therefore subject to
the above mentioned concerns. To reduce this dependence on the
highest observed concentrations it has been proposed that the
allowed maximum annual expected exceedance rate of the eight-hour CO
NAAQS concentration be set at five. Current EPA guidelines would
then permit the use the sixth highest eight-hour concentration in
one year or the sixteenth highest eight-hour concentration in three
years for attainment testing and determination of design values.
Such a multiple exceedance standard would be less sensitive to the
occurrence of unrepresentative or erroneous high concentrations than
one expected exceedance standards under present EPA guidelines.
The preceding argument for multiple expected exceedance
standards has also been stated in another way. It has been pointed
out that with one year of concentration data the value of the sixth
highest concentration is statistically more stable than the second
highest value. Likewise, with three years of data the measured
sixteenth highest value is more stable than the fourth highest
-------
value. Thus, not only are the sixth and sixteenth highest values
less sensitive to aberrant events and errors, they also provide, a
more accurate test of attainment and more accurate design values
than do the respective second and fourth highest values.
The concern with the use of multiple exceedance standards is
that they may tend to shift attention away from bringing under
control the highest concentrations which may occur in an area, and
therefore result in less protection for sensitive individuals. A
one expected exceedance standard is, in principle, exerting more
direct control on the behavior of the highest concentrations than a
multiple expected exceedance standard. A five expected exceedance
standard is exerting maximum control in the vicinity of the fifth
highest concentration and generally less control of the highest
concentrations.
The two investigations described in this report were undertaken
by EPA to obtain information on the effect on air quality of
multiple expected exceedance standards for CO. The first study was
undertaken by Dr. Thomas C. Curran of the Monitoring and Data
Analysis Division (MDAD) of EPA"*s Office of Air Quality Planning and
Standards (OAQPS) in Durham, North Carolina. It took as its data
base the air monitoring data in EPA's Storage and Retrieval of
Aerometric Data (SAROAD) data bank for CO concentrations obtained
during the period 1979-1981 and sought to draw conclusions based on
the actual data or, at the most, minimally adjusted data.
The second investigation was undertaken by the author of this
report for the Strategies and Air Standards Division (SDAD) of OAQPS
under Contract #68-02-3600. It was based on a subset of the MDAD
data base and tail-exponential distributions of the CO
concentrations which had been derived by Dr. Curran. The use of the
tail-exponential distributions provided the basis for a more general
statistical analysis of the application of multiple expected
exceedance standards to CO than is possible from manipulation of the
single-year data sets from which the distributions were derived.
Neither investigation undertook an investigation of the
possibility that multiple expected exceedance standards might have
some advantages over single expected exceedance standards when there
-------
is missing data.
The CO standards which are the subject of this report are based
on an eight-hour averaging time and apply to the observed daily
maximum eight-hour average concentration. Since eight-hour average
concentrations are calculated from successive one-hour average
concentrations, there are twenty-four possible running eight-hour
averages within a calendar day. A given eight-hour average is
identified as belonging to a given day if the beginning hour is
contained within the day. The highest of the observed twenty-four
running eight-hour average concentrations within a given calendar
day is the daily maximum for that day. In a typical year a CO air
monitoring site will have 365 daily maximum eight-hour CO
concentrations associated with it, if there are no missing data.
The only forms of the CO NAAQS that are considered in this
report are those which specify a level of the daily maximum eight-
hour CO concentration and the maximum allowable expected exceedances
of that level per year.
Principal attention is given to the following alternative
eight-hour CO standards: 9 ppm, 1 expected exceedance per year (9
ppm/1 xx); 7 ppm, 5 expected exceedances per year (7 ppm/5 xx); 9
ppm, 5 expected exceedances per year (9 ppm/5 xx); and 12 ppm, 1
expected exceedances per year (12 ppm/1 xx). The first standard is
at the same level as the current eight-hour CO standard and is
therefore a convenient reference point. It differs from the current
standard in that it is statistical in form rather than deterministic
and applies to the daily maximum eight-hour CO concentration. As
will be shown, the 7 ppm/5 xx standard, on the average, is expected
to provide about the same air quality as the 9 ppm/1 xx standard.
The two standards therefore provide a good basis for comparison of
multiple and single expected exceedance standards. The 12 ppm/1 xx
standard provides an alternate level of stringency for the analysis.
As will be shown, the 9 ppm/5 xx standard is expected to provide
about the same level of protection as the 12 ppm/1 xx standard, on
the average.
-------
ANALYSIS OF 1979-1981 SAROAD CARBON MONOXIDE CONCENTRATIONS
The analyses summarized in this section were performed by Dr.
Thomas C. Curran of the Monitoring and Data Analysis Division (MDAD)
of the EPA's OAQPS.
Data Base
The data base for the MDAD analyses was the CO data in SAROAD
for 1979-1981. The analyses performed by MDAD were obtained from
SAROAD on July 30, 1982. Only site-years with at least 90 days of
data were selected for analysis. This selection procedure resulted
in a data base containing 1,199 site-years of CO concentration data.
A data screening program and visual inspection identified some
suspect values but not in sufficient quantity to affect the
aggregate results. No data values were eliminated.
The 1979-1981 SAROAD data which were the basis for the
distributions used in the contractors's analysis were obtained by
MDAD in May, 1982. In this case only site-years with at least 189
days of data were selected. In addition, site-years in which the
highest daily maximum eight-hour concentration was below 9.5 ppm
were excluded. These constraints led to a data base of 449 site-
years.
Relationship Between Standards with Different Expected Exceedances
In general it is expected that if an area is just in attainment
of a standard based on one expected exceedance a year, it would also
be just in attainment of a standard at some appropriately lower
level which specified a multiple number of expected exceedances. To
determine what this relationship is for a daily maximum eight-hour
CO NAAQS based on expected exceedances, it is necessary to know the
underlying distribution of the CO concentrations over a period of
one year or more when the one expected exceedance standard is just
being attained. The reason is that the concentration which has N
expected exceedances is strictly determined by the distribution. It
is that concentration which has an expected frequency of exceedance
of N/365.
-------
Tail-exponential distributions, discussed in a later section of
this report were fit to each site-year data set in the 449 site-year
data base. The concentrations corresponding to one through ten
expected exceedances per year were calculated from the parameters of
each distribution. Each concentration for a given site-year was
ratioed to the concentration corresponding to one expected
exceedance.
The average values of the ratios over all sites is shown in
Table 1. The right-most column shows the resulting concentration
level if the concentration corresponding to one expected exceedance
per year is equal to 9 ppm. It is seen that if NAAQS concentration
levels are restricted to whole numbers for a given unit, then, on
the average, 9 ppm/1 xx, 8 ppm/2 xx, 7 ppm/5 xx, and 6 ppm/11 xx are
all about the same stringency. The table further suggests that the
7 ppm/5 xx standard, on the average, is slightly less stringent than
the 9 ppm/1 xx standard.
The ratios in the the middle column can also be used with other
standard levels. For example, a 9.2 ppm/5 xx standard is, on
average, about as stringent as a 12 ppm/ Ixx standard. That is, a 9
ppm/5 xx standard is, on average, slightly more stringent than a 12
ppm/ 1 xx standard.
Table 1 represents average behavior. Individual sites will
differ. For example, the base data from which Table 1 was derived
show that at the five expected exceedance level 50% of the sites
will fall between 6.7 ppm and 7.2 ppm, and 90% will fall between 6.2
ppm and 7.7 ppm when the concentration with one expected exceedance
is 9.0.
Number of Site-years in which Standard is Exceeded
One possible measure of the relative stringency of two
standards with different permitted expected exceedance rates is to
compare the number of site-years that would fail to meet either
alternative. Table 2 compares the two standard pairs 9 ppm/1 xx vs.
7 ppm/5 xx and 12 ppm/1 xx vs 9 ppm/5 xx.
A site year was considered to exceed the 9 ppm/1 xx standard if
the second highest daily maximum eight-hour value was 9.5 ppm or
8
-------
Table 1 Estimated Average Equivalence of Eight-Hour Carbon Monoxide
Ambient Air Quality Standard Levels for Different Expected
Exceedances, Based on 1979-1981 SAROAD Data.
Expected Ratio3 Average Equivalent
Exceedances Standard Levelb
(ppm)
1
2
3
4
5
6
7
8
9
10
1.00
0.90
0.85
0.81
0.77
0.75
0.73
0.71
0.69
0.68
9.0
8.1
7.7
7.3
6.9
6.8
6.6
6.4
6.2
6.1
aRatio of concentration corresponding to Nth expected exceedance
level and concentration corresponding to one expected exceedance
bAssumes standard level at one expected exceedance is 9.0 ppm.
However, ratios in column 2 can be applied to other levels.
-------
Table 2 Comparison of Alternative Eight-Hour Carbon Monoxide
Ambient Air Quality Standards Based on 1,199 Site-Years
of Data from SAROAD for 1979-1981.
7ppm/5 xx Std.
PASS
FAIL
9 ppm/1 xx Std. PASS 748
FAIL 44
47
360
795 (66%)
404 (34%)
792
(66%)
407
(34%)
9ppm/5 xx Std.
PASS
FAIL
12ppm/l xx Std. PASS 961
FAIL 24
70 1031 (86%)
144 168 (14%)
985
(82%)
214
(18%)
10
-------
higher. A site-year with a sixth highest value of 7.5 ppm or higher
was considered to exceed the 7 ppm/5 xx standard. Similar rules
were used with the 12 ppm/1 xx and 9 ppm/5 xx standards. These
rounding procedures are consistent with EPA guidance for the ozone
NAAQS (1).
Table 1 indicates that by this test the two 5 expected
exceedances standards are about as stringent as the two respective
one exceedance standards with which they were compared. For the 9
ppm/1 xx - 7 ppm/5 xx comparison, the data in the middle square show
that on an individual site-year basis both alternatives give the
same result 92% of the time (i.e. 62% of the site-years pass both
and 30% of the site-years fail both). For the 12 ppm/1 xx - 9 ppm/5
xx comparison both alternatives also give the same result 92% of the
time with 80% of the site-years passing both and 12% of the site-
years failing both standards. The higher pass rate with the latter
pair of standards is a result of reduced stringency compared to the
9 ppm/1 xx and 7 ppm/5 xx standards.
The data also suggest that the 9 ppm/5 xx standard is slightly
more stringent than the 12 ppm/ Ixx standard since a slightly
greater percentage of site-years fail the 9 ppm/5 xx standard.
No adjustment was made in this comparison for missing data.
When an adjustment is made, as described in Appendix A, the 9 ppm/1
xx and 7 ppm/ 5 xx standards give the same result 90% of the time
with 56% of the site-years passing both standards and 34% of the
site-years failing both standards. With the 12 ppm/1 xx and 9 ppm/5
xx standards, both gave the same result 90% of the time. In this
case 76% of the site-years passed both and 14% of the site-years
failed both.
Number of Days Above a Given Concentration Level
Another way to compare a multiple expected exceedance level
standard with a corresponding one expected exceedance standard is to
estimate how many site-days above the concentration level of the one
expected exceedance standard would occur if every site was first
made to meet the one expected exceedance standard and then the
multiple expected exceedance standard. In the case of the 9 ppm/1
11
-------
xx standard if the second highest value for a given site-year data
set is greater than 9.5 ppm, the data set is rescaled in a
proportional manner so the the second high value is made equal to
9.0 ppm. For site-years in which the second highest value was less
than 9.5 no scaling of the data is done. A similar procedure is
followed with the 7 ppm/5 xx standard. This procedure is
essentially that of linear rollback.
Under the above described comparison there were 388 site-days
above 9 ppm with the 9 ppm/1 xx standard and 426 days above the
standard with the 7 ppm/5 xx standard. In both cases there was a
total of 335,826 site-days. After adjusting for missing data
(Appendix A) the site-days above 9 ppm were 291 and 384 respectively
for the 9 ppm/1 xx and 7 ppm/5 xx standards. These data suggest
that the 9 ppm/lxx standard is somewhat more stringent than the 7
ppm/5 xx standard.
The data base before application of the rollback procedures had
5,405 days above 9 ppm or 1.6% of the site-days.
When the procedure was applied to the 12 ppm/1 xx and 9 ppm/1
xx standards, 204 days were above 12 ppm for the 12 ppm/1 xx
standard while 182 days were above 12 ppm for the 9 ppm/ 5 xx
standard, which suggest that the 9 ppm/ 5 xx standard is slightly
more stringent than its corresponding one expected exceedance
standard.
PPM-Days Above a Given Concentration Level
This measure weights each site-day above a given level by the
CO concentration in order to give increasing weight with increasing
concentration above that level. For this computation each
concentration is rounded to the nearest whole number in ppm and the
number of site-days at each ppm above the level are multiplied by
the ppm level. The resulting products are summed to give total ppm-
days above the concentration level.
For the 9 ppm/1 xx and 7 ppm/5 xx standards the appropriate
level was 9.0 ppm. This procedure yielded 4,123 ppm-days in the
case of the 9 ppm/1 xx standard and 4,692 ppm-days in the case of
the 7 ppm/5 xx standard. The missing data adjustment altered these
12
-------
values to 3,112 and 4,189 ppm-days, respectively.
For the 12 ppm/1 xx standard there were 2,846 ppm-days above 12
ppm, while the 9 ppm/5 xx standard gave 2,642 ppm-days above 12 ppm.
In the original data base there were 64,682 ppm-days above 9
ppm and 23,100 ppm-days above 12 ppm.
Percent of Days Above a Given Concentration Level
Table 3 shows the distribution of site-days over daily maximum
eight-hour concentrations above 9 ppm for the current data base and
for the 9 ppm/1 xx and 7 ppm/5 xx standards and over 12 ppm for the
12 ppm/1 xx and 9 ppm/5 xx standards. The distribution values are
percent of total site-days. No adjustment for missing data has been
made. The data continue to show the same comparability of the 9
ppm/1 xx with the 7 ppm/5 xx standard and the 12 ppm/1 xx with the 9
ppm/5 xx standard. As before, the 9 ppm/1 xx standard is slightly
more stringent than the 7 ppm/5 xx standard, while the 12 ppm/1 xx
standard is slightly less stringent than the 9 ppm/5 xx standard.
Representation of CO Data by Tail-Exponential Distributions
It is well established that the time averaged concentrations
that will be observed within a calendar year at a monitoring site
can be represented statistically by a cumulative distribution
function which indicates the expected frequency with which
concentrations above any given level will occur. This distribution
can be approximated by suitably plotting time-averaged concentration
data obtained over one or more years. Often the distribution can be
accurately represented by mathematical functions such as lognormal,
Weibull, or exponential distributions (2,3,4). Recent
investigations have suggested that the upper portions of
distributions may be accurately represented by tail-exponential
distributions (5). The MDAD investigation demonstrated that both 5%
and 10% tail-exponential distributions fit daily maximum eight-hour
CO data quite well. Using a probability level of 0.05 as the
acceptable cut-off for a goodness of fit test, 98% of the site years
had adequate fits of the 10% tail and 96% had adequate fits for the
5% tail-exponential distribution.
13
-------
Table 3 Percent of Total Site-Days At Given Concentration Level For Current
Data Base and Alternative Eight-Hour Carbon Monoxide Ambient Air
Quality Standards.
Cone.
(ppn)
10
11
12
13
14
15
16
17
18
19
20
>20
Actual
1978-81
0.57
0.35
0.23
0.15
0.10
0.07
0.036
0.030
0.016
0.015
0.012
0.027
9ppm/lxx
0.073
0.027
0.0080
0.0039
0.0024
0.0012
0.0000
0.0003
0.0000
0.0000
0.0000
0.0000
7ppm/5xx 12ppm/lxx
0.063
0.034
0.015
0.0063
0.0021
0.0015
0.0030
0.0003
0.0009
0.0000
0.0003
0.0000
_
-
-
0.031
0.016
0.0080
0.0027
0.0012
0.0009
0.0006
0.0003
0.0003
9ppm/5xx
_
-
0.026
0.0095
0.0068
0.0030
0.0036
0.0009
0.0021
0.0012
0.0012
14
-------
Since the concentration which has N expected exceedances per
year is, by definition, the concentration on the cumulative
distribution which has an associated frequency of N/365, the tail-
exponential distributions derived in the MDAD study can be used to
investigate the effect of standards with multiple exceedances on air
quality. Such an investigation is the subject of the next section.
ANALYSIS BASED ON BEHAVIOR OF DISTRIBUTIONS OF EIGHT-HOUR CARBON
MONOXIDE CONCENTRATIONS
The investigation summarized in this section was undertaken by
the contractor for the Strategies and Air Standards Division (SASD)
of. EPA's OAQPS. It is based on the work of Dr. Thomas C. Curran,
reported in the previous section, and, in particular, makes
extensive use of the tail-exponential distributions he fit to
individual site-year data sets from the SAROAD CO concentrations for
the years 1979-1981.
Background
A term that is used frequently in the following discussion is
characteristic highest value. If the concentrations of a pollutant
observed at a monitoring site in a calendar year are realizations of
some underlying frequency distribution, the annual characteristic
highest concentration is that concentration which has an expected
exceedance of once per year. It is the point on the cumulative
distribution curve of daily maximum time-averaged concentrations
which corresponds to a frequency of 1/365 (the concentration which
is expected to be exceeded on an average of once in 365 days).
The Nth characteristic highest concentration is the
concentration which is expected to be exceeded N times in a year.
Its associated frequency on the cumulative distribution is N/365.
Thus, the most precise meaning of a daily maximum eight-hour CO
NAAQS of 9 ppm/1 xx is that the characteristic highest value of the
daily maximum eight-hour CO concentration is 9 ppm or less at any
monitoring site which attains the standard. For a 7 ppm/ 5 xx
15
-------
standard the characteristic fifth highest value would not be greater
than 7 ppm.
The demonstration by MDAD that the highest 5 to 10% of the
daily maximum eight-hour CO concentrations observed at a site in a
calendar year can be represented in over 95% of the cases by a tail-
exponential distribution (see previous section) greatly facilitates
further analysis of the 1979-1981 CO concentration data base. The
reason for this is that the concentrations corresponding to one
expected exceedance per year or higher expected exceedances (the
characteristic Nth highest values) can be directly determined, given
the parameters of the distribution curve (Appendix B).
Under present EPA guidelines, with a one expected exceedance
standard, the second highest concentration observed at a site in a
calendar year can used as a measure of the characteristic highest
concentration. In statistics it would be considered an estimator of
the underlying characteristic highest value. The observed second
highest value will normally change from one year to the next at a
given monitoring site due to random changes in weather and/or
pollutant emission levels. But, so long as there is no overall
trend in weather or pollutant emissions in the broad area around the
site, the underlying frequency distribution, and therefore the
characteristic Nth highest values will not change. These parameters
are statistical properties of the underlying distribution whereas
the observed Nth highest concentrations are random variables.
Also, under present EPA guidelines, if three years of data are
available at a monitoring site, the observed fourth highest
concentration would generally be used as the estimator for the
characteristic highest value. If the standard is based on five
expected exceedances per year, then, following the above mentioned
practices, the observed sixth highest concentration in one year or
the sixteenth highest in three years would be used as estimators for
the characteristic fifth highest concentration.
Figure 1 is a frequency plot for the observed ten highest daily
maximum eight-hour CO concentrations observed in 1980 at Site #
20040021101. The line shown is the tail-exponential distribution
function which has been fitted to the highest 10% of the
16
-------
Figure 1 -Distribution of Ten Highest Daily Maximum Eight-Hour
Carbon Monoxide Concentrations Observed at a Monitor
and Tail-Exponential Distribution Fitted to Highest
Ten Percent of Concentrations.
8
9 10 11
CONCENTRATION
12
(PPM)
14
15
16
17
-------
concentrations for the year. The vertical axis is the frequency
scale. For present purposes, it is convenient to show the scale in
terms of the characteristic Nth highest value (each of these values
is associated with a frequency equal to N divided by the total
observations in the time period under consideration.)
It is seen from Figure 1, that the characteristic highest value
estimated by the tail-exponential is 15.4 ppm and the characteristic
fifth highest value is estimated to be 10.6. These values would
have to be 9 ppm or lower and 7 ppm or lower for this site to be in
conformance with the 9 ppm/1 xx or 7 ppm/5 xx standards,
respectively. It is also seen that the second highest concentration
is 14.0 ppm or 1.4 ppm below the characteristic highest value
estimated from the distribution. The sixth highest value is 9.7 ppm
or 0.9 ppm below the characteristic fifth highest value estimated
from the distribution.
As indicated above, if there were no trends in weather or
overall emission levels in the neighborhood of the site, it would be
expected that subsequent years of data would yield much the same
tail-exponential distribution. Therefore, estimates of the
characteristic first and fifth highest values wou,ld change
relatively little, whereas the observed second and sixth highest
values would vary over a relatively wider range.
The analyses discussed in the following sections are based on
the properties of the tail-exponential distributions fitted to all
site-years in the 1979-1981 SAROAD CO data base in which the highest
observed daily maximum eight-hour CO concentration was greater than
9.5 ppm. There were 449 such sites. Of these, 436 site-years were
successfully fit by the tail-exponential at p=0.05. An important
characteristic of these distributions was that the slope of the
upper tail of the distributions varied from site to site. This is
apparent in the variation among sites in the ratio of the
characteristic fifth highest value to the characteristic highest
value discussed in the preceding section. From the data base it was
possible to characterize the distribution of this slope (or ratio).
Also, by comparing the observed Nth highest concentrations with the
corresponding calculated tail-exponential frequency distributions
18
-------
it was possible to characterize the frequency distribution of the
first through tenth highest values about the respective
characteristic Nth highest values. Under appropriate conditions,
the characteristic Nth highest concentration is the most probable
value of the observed Nth highest value. However, the characteristic
Nth highest value is somewhat lower than the mean and median values
of the observed Nth highest concentration. This is the basis for
the choice of the observed YN+1 highest concentration (where Y is
the number of years of data) as the estimator for the characteristic
Nth highest concentration in the EPA guidelines.
By using the empirically determined distribution of the upper-
tail slopes among site and the distributions of the highest values,
and representing the air quality by the tail-exponential
distributions it is possible to investigate the effects of multiple
exceedance standards without further recourse to the data base of
observed CO concentrations. A detailed description of how the base
distributions were derived and how the analyses were performed is
given in Appendix B. The observed ten highest concentrations and
parameters of the 10% tail-exponential distribution fit to each
site-year are given in Appendix C. These are the base data for the
analysis.
All Sites Just in Attainment.
Given that a primary concern in setting an air quality standard
is limiting the highest concentrations to which sensitive
individuals will be exposed, then one method of comparing standards
is to compare their effects on the distributions of annual highest
concentrations among sites just meeting the standards. As indicated
in the previous section, this would mean for a 9 ppm/1 xx standard
that the characteristic highest concentration for a calendar year is
exactly 9.0 ppm for each of the sites under consideration. This is,
of course, a hypothetical or idealized situation that is very
unlikely to be realized in practice, because the underlying
characteristic highest concentration at a site is unlikely to be
known precisely. Nor is it likely to remain constant over a
substantial time period since there will be inevitable trends in
19
-------
pollutant emissions and long term weather patterns. Furthermore, the
application of emission control measures is not likely to bring all
sites to the point of just meeting a NAAQS. However, for the
purposes of analysis this situation provides a useful, well-defined
end state for the investigation and comparison of alternative
standards.
Table 4 shows estimated distributions for the annual highest
eight-hour CO concentration among sites for a range of one expected
exceedance standards with concentration levels varying from 7 ppm to
12 ppm. The distributions are given in terms of percentiles. For
example, 75 percent of the sites in a given year would experience a
highest concentration equal to or less than the concentration given
for the 75th percentile. It is seen that even though the
characteristic highest concentration at each site is, by definition,
exactly at the standard level, there is a significant variation in
the annual highest concentration. For a 12 ppm/1 xx standard one
percent of the sites would experience a concentration of about 19
ppm or higher in a given year. For a 9 ppm/1 xx standard one
percent would experience about 14 ppm or higher. Relatively high or
low levels of the observed highest concentration could occur at any
of the sites in a given year. This variation comes about from the
random nature of weather and hour by hour emission levels. It is,
in a sense, a given. Any variation among sites in attaining a
standard will result in a wider distribution of the highest
concentrations than shown in the top half of Table 4.
Table 4 also shows the distribution of highest concentrations
for three different five expected exceedance standards with
concentration levels of 7, 8, and 9 ppm. In the Table each of these
distributions has been placed under the distribution of the one
expected exceedance standard it most closely approximates. It is
seen that the 7 ppm/5 xx standard is most like the 9 ppm/1 xx
standard. The 9 ppm/5 xx standard is most like the 12 ppm/1 xx
standard. The 8 ppm/5 xx standard falls between the 10 ppm/1 xx and
the 11 ppm/1 xx standards.
Since there will always be a distribution among sites of the
observed annual highest concentrations it is useful to have another
20
-------
Table 4 Distribution of Annual Highest Eight-Hour Carbon Monoxide
Concentrations for Alternative Ambient Air Standards under
Conditions in Which All Sites Just Attain Standard.
Mean (ppm)
Std. Dev.
7ppm/lxx
7.6
1.0
Distribution Among
1%
5%
10%
25%
50%
75%
90%
95%
99%
Mean (ppm)
Std. Dev.
5.8
6.3
6.5
6.9
7.4 - -
8.2
8.9
9.5
11.0
(ppm)
Distribution Among
1%
5%
10%
25%
75%
90%
95%
99%
8ppm/lxx
8.7
1.2
Sites (ppm) :
6.7
7.2
7.4
7.9
- 8.5 - -
9.3
10.2
10.8
12.6
Sites (ppm) :
9ppm/lxx
9.8
1.3
i
7.5
8.1
8.4
8.9
- 9.6 - -
10.5
11.5
12.2
14.2
7ppm/5xx
9.9
1.6
7.6
8.0
8.3
8.8
10.7
12.0
12.9
15.0
IQppm/lxx
10.9
1.5
8.3
9.0
9.3
9.8
- - 10.6 -
11.7
12.8
13.5
15.8
llppm/lxx
12.0
1.6
9.2
9.8
10.2
10.8
- - 11.7 - -
12.8
14.0
14.9
17.4
8ppm/5xx
11.1
1.6
8.7
9.1
9.4
10.1
12.2
13.7
14.8
17.1
12ppm/lxx
13.0
1.8
10.0
10.7
11.2
11.8
- - 12.7
14.0
15.3
16.2
18.9
9ppm/5xx
12.8
2.0
9.7
10.3
10.6
11.4
13.8.
15.4
16.6
19.3
21
-------
means of comparison which will be the same for all sites when two
standards yield the same air quality in terms of the behavior of the
peak concentrations at a site. The distribution among sites of the
characteristic highest value is a useful measure serving this
purpose. Under the conditions specified in Table 4 each of the one
expected exceedance standards has a single value of the
characteristic value at all sites. The five expected exceedance
standards do not. This difference is illustrated in Figures 2 and
3.
Figure 2 shows the situation that would occur if all sites not
in attainment were just brought into attainment with a 9 ppm/1 xx
eight-hour CO NAAQS. To be just in attainment means, in this case,
that the characteristic highest concentration for each site is
exactly equal to 9 ppm. The figure shows three tail-exponential
distributions plotted on the same basis as Figure 1. The three
distributions represent the range of distributions which will result
from the site-to-site variation in the slope of the upper tail of
the distribution. The middle line is the median distribution. That
is, half the distributions will fall to the left of the median and
half will fall to the right. All distributions, however, will pass
through 9 ppm at the expected exceedance level of one, since, by
definition, all have a characteristic highest value of 9 ppm.
The left-most line is the one-percentile line. That is, one
percent of the distributions will fall to the left of this line.
They will of course, continue to pass through the 9 ppm, 1 expected
exceedance point. Likewise, one percent of the distributions will
fall to the right of the 99-percentile line.
The median line passes through 6.9 ppm at the five expected
exceedance level, indicating that a 7 ppm/5 xx standard is slightly
less stringent than the 9 ppm/1 xx standard at the median site. In
agreement with the MDAD analysis, 98% of the sites will have
characteristic fifth highest values from 5.9 to 8.1 when they all
just meet the 9 ppm/1 xx standard.
The distribution of the highest concentration is shown along
the concentration axis of Figure 2. It is seen that although the
characteristic highest value has been brought to 9 ppm at all the
22
-------
Figure 2 Ranges of Distributions and Observed Highest
Concentrations Over Monitor Sites When All Sites
Just Attain a 9 PPM, 1 Expected Exceedance, Daily
Maximum, Eight-Hour Carbon-Monoxide Ambient Air
Standard.
CO
u
w
o
§
Cj
b
cu
>x.
1
13
14
15
CONCENTRATION (PPM)
23
-------
Figure 3 Ranges of Distributions and Observed Highest
Concentrations Over Monitor Sites When All Sites
Just Attain a 7 PPM, 5 Expected Exceedances,
Daily Maximum, Eight-Hour Carbon Monoxide Ambient
Air Standard.
10
9
8
u
U
w
eu
r
1L
i r
l r
!
99%
1%\5 2
75
95
99%
am
8
10
11 12 13
14
15
CONCENTRATION (PPM)
24
-------
sites, there is still a wide variation in the observed highest
concentration. Ninety-eight percent of the sites just in attainment
of the 9 ppra/1 xx standard will observe highest annual daily maximum
concentrations in a given year which fall in the range 7.5 - 14.2
ppm. The highest concentrations at half the sites will fall in the
range 8.9 - 10.5 ppm. As discussed above, this variation does not
indicate any change in the overall air quality from one site to
another. It is primarily due to random fluctuations in hourly
weather and pollutant emission levels.
Figure 3 shows the situation in which all sites not in
attainment are just brought into attainment with a 7 ppm/5 xx eight-
hour CO NAAQS. Now all the distributions pass through the common
point 7 ppm, 5 expected exceedances. All of their characteristic
fifth highest concentrations are 7 ppm. But, because of the
differences among sites in the slope of the tail of the
distribution, the characteristic highest values show a range of
values. The median site has a characteristic highest concentration
of 9.1. Ninety-eight percent of the characteristic highest values
fall between 8.1 and 10.6 ppm. Thus, if the optimum value of the
characteristic highest concentration is 9 ppm, somewhat less than
half the sites would be over controlled, while somewhat more than
half the sites would be under controlled. However, the range of 8.1
to 10.6 represents a relatively small spread of about 1 ppm on
either side of a 9 ppm standard.
A further comparison is obtained from the distribution over
sites of the observed highest concentration. It is seen that the
spread in characteristic highest values has resulted in only a small
increase in the spread of the observed highest concentrations when
the two standards are compared. For the 7 ppm/5 xx standard 98% of
the observed highest concentrations fall between 7.6 and 15.0 ppm.
It is clear from Figures 2 and 3 that in the hypothetical
situation illustrated, the one expected exceedance standard would
provide more uniform protection among sites than the five expected
exceedance standard. However, the actual differences in the case of
the CO NAAQS appear to be relatively small.
Table 5 displays the data from which Figures 2 and 3 were
25
-------
Table 5 Comparison of Alternative Eight-Hour Carbon Monoxide Ambient Air
Standards Under Conditions in which All Sites Just Attain Standard.
Character ist ic
Highest Value
(ppm)
Mean
Std. Dev.
Distribution
1%
5%
10%
25%
Cnjl
OUT*
75%
90%
95%
99%
Mean
Std. Dev.
Distribution
1%
5%
10%
25%
50%
75%
90%
95%
99%
9ppm/lxx
9.0
0.0
Among Sites:
9.0
9.0
9.0
9.0
9n
9.0
9.0
9.0
9.0
7ppm/5xx
9.1
0.6
Among Sites:
8.1
8.3
8.4
8.7
- - 9.1
9.5
9.8
10.1
10.6
Highest
Value
(ppm)
_ _ _ _
9.8
1.3
7.5
8.1
8.4
8.9
- Q fi _
10.5
11.5
12.2
14.2
^ ._rr ! m
9.9
1.6
7.6
8.0
8.3
8.8
- 9.6 -
10.7
12.0
12.9
15.0
Characteristic Highest
Highest Value Value
(ppm) (ppm)
_ _ _ _
12.0
0.0
12.0
12.0
12.0
12.0
19 n
±.*L U
12.0
12.0
12.0
12.0
« ^ .» «
11.7
0.7
10.4
10.6
10.9
11.2
117
J L. /
12.2
12.7
12.9
13.7
12ppm/lxx
13.0
1.8
10.0
10.7
11.2
11.8
197
14.0
15.3
16.2
18.9
9ppm/5xxx
12.8
2.0
9.7
10.3
10.6
11.4
19 A
j-£ 4z
13.8
15.4
16.6
19.3
26
-------
constructed and provides additional data for the 12 ppm/1 xx and 9
ppm/5 xx alternatives.
Attainment Based on Observed N+l Highest Value in One Year
In practice, the characteristic Nth highest concentration at a
site is never known precisely and this uncertainty will effect how
closely the idealized situation discussed in the preceding section
can be realized. Thus the methods used to determine attainment and
to arrive at design values are an important factor in comparing the
relative abilities of multiple exceedance standards in controlling
the highest concentrations to which sensitive individuals are
exposed.
To investigate these effects, a 9 ppm/1 xx and 7 ppm/5 xx
standard were compared in terms of their ability to control both the
characteristic highest value and the observed highest value at
monitor sites when the observed second highest and sixth highest
concentrations were used as estimators for the characteristic first
and fifth highest concentration, respectively. While practical and
easy to use, the observed N+l highest concentration in one calendar
year is only a fair estimator of the characteristic Nth highest
concentration. As discussed, and illustrated in Figure 1, the
observed Nth highest value will fluctuate even when the overall air
quality at a site is stable from year to year and will tend to be
somewhat off the underlying frequency distribution. It is also the
case, however, that the larger the value of N the more accurate and
stable the observed N+l highest concentration becomes as an
estimator of the characteristic Nth highest value. Thus, use of the
observed sixth highest concentration as a measure of attainment and
design values for a five expected exceedance standard, on this
basis, would provide more uniformity among sites than the use of the
observed second highest concentration with a one expected exceedance
standard.
The fluctuations in the observed N+l highest concentration, in
general, will lead to an erroneous estimate in the design value and
therefore an erroneous estimate of the emission reductions required
to just attain the standard. The end result will be that some sites
27
-------
will be over controlled and some under controlled. This situation
was simulated on a computer using the distribution of the upper-tail
slopes, the distributions of observed Nth highest concentrations,
and the assumption that the distribution of daily maximum eight-hour
CO concentrations was tail-exponential (Appendix B). The results
for a 9 ppm/1 xx are shown in Figure 4 and those for a 7 ppm/5 xx
standard are shown in Figure 5.
The three lines shown in each of the Figures 4 and 5 have a
different meaning from their counterparts in Figures 2 and 3. The
lines represent the distribution among sites of the characteristic
Nth highest concentrations. For example, referring to Figure 4, one
percent of the sites will have characteristic third highest values
which are at or below 6 ppm. Fifty percent will be at or below 8.1
ppm, and 99% will be at or below 9.5 ppm. Thus, the 1-percentile
and 99-percentile lines bound about 98% of the distributions. The
50-percentile line is a good representation of the middle
distribution. The simple interpretation possible in Figures 2 and 3
cannot be applied because in the present case the distributions do
not pass through a common point.
The spreading of the distributions in Figures 4 and 5 is
directly due to the variability of the observed second and sixth
highest concentrations. The 7 ppm/5 xx standard clearly has a
somewhat tighter distribution of both the characteristic highest and
first highest concentrations. This comes about from the lower
variability of the observed sixth highest concentration compared to
the variability of the observed second highest value. The effect
would be larger were it not for variation in slopes of the upper-
tails of the distributions among sites. This effect is greater for
the five expected exceedance standard than for the one expected
exceedance standard.
It is also seen that the variation in the characteristic
highest and observed highest concentrations is greater in Figures 4
and 5 than in Figures 2 and 3. This is again due to variability of
the observed second and sixth highest concentrations. In Figures 2
and 3 it was assumed the characteristic highest and fifth highest
concentrations, respectively, were exactly known.
28
-------
Figure 4 Ranges of Distributions and Observed Highest Concentrations
Over Monitor Sites When Attainment of a 9 PPM, 1 Expected
Exceedance Carbon Monoxide Standard is Based on the
Observed Second Highest Daily Maximum Eight-Hour Concentration
in One Year.
en
w
u
23
o
8
Q
63
EH
a
w
a,
9
8
7
6
5
4 r-
3 ;-
8 9 10 11 12
CONCENTRATION (PPM)
13 14 15
29
-------
Figure 5 Ranges of Distributions and Observed Highest
Concentrations Over Monitor Sites When Attainment
of a 7 PPM, 5 Expected Exceedance Carbon Monoxide
Standard is Based on the Observed Sixth Highest
Maximum Eight-Hour Concentration, in One Year.
en
u
I
o
Q
H
s
W
0,
X
.. 1%, 5 2^ 50 75\
10 11 12
13 14 15
CONCENTRATION (PPM)
30
-------
It is concluded from Figures 4 and 5, that in cases where
attainment of the standard and design values are to be judged from
the observed N+l highest value in a single year of data, a 7 ppm/1
xx standard gives somewhat better control of characteristic highest
and observed highest concentrations than does a 9 ppm/1 xx standard.
Figures 2 and 3 suggest that if the accuracy of the estimators could
be significantly increased then the situation would be reversed.
The 9 ppm/1 xx standard would give somewhat better control of the
characteristic and observed highest concentrations. The use of
several years of data, in cases where there was no trend in emission
levels, would increase the accuracy of the observed YN+1 highest
concentrations as extimators of the Nth characteristic highest
value. Fitting distributions to one or more years of data would
further improve accuracy by making more complete use of the
available concentration data.
Table 6 gives the distribution data for the 9 ppm/1 xx and 7
ppm/5 xx alternative standards as well as for the 12 ppm/1 xx and 9
ppm/5 xx alternatives.
Attainment Based on 3N+1 Highest Concentration in Three Years
For cases in which there are three consecutive years of CO
concentration data which exhibit no pronounced trends the 3N+1
observed highest concentration would be used as an estimator of the
Nth characteristic highest concentration under present EPA
guidelines. Thus with three years of data the observed fourth
highest concentration would be used with a one expected exceedance
standard while the observed sixteenth highest concentration would be
used with a five expected exceedance standard. These observed 3N+1
highest concentrations will exhibit less variation from year to year
than the corresponding observed N+l highest concentrations in one
year of data and therefore will be more accurate estimators of the
Nth characteristic highest concentrations.
To investigate the effect of using three years of CO
concentration data on the comparison of alternative multiple
expected exceedance standards, it was necessary to develop within-
site distributions for the observed Nth highest concentration in
31
-------
Table 6 Comparison of Alternative Eight-Hour Carbon Monoxide Ambient Air
Standards Under Conditions in which the Observed N+l Highest
Concentration in One Year is Used in Attaining an N Expected
Exceedance Standard.
c
F
Mean
Std. Dev.
Distribution
1%
5%
10%
25%
cna _ _
75%
90%
95%
99%
Mean
Std. Dev.
Distribution
1%
5%
10%
25%
cria _
75%
90%
95%
99%
:haracter istic
lighest Value
(ppm)
- - 9ppm/lxx
9.6
0.9
Among Sites:
7.2
8.0
8.5
9.0
9P,
10.2
10.7
11.1
11.7
7ppm/5xx
9.2
0.7
Among Sites:
7.9
8.2
8.4
8.7
91
9.6
10.1
10.6
11.4
: Highest
Value
(ppm)
(2nd Hi) - -
10.4
1.8
7.1
8.1
8.5
9.2
in o _ _
11.4
12.7
13.8
15.8
(6th Hi) - -
10.0
1.7
7.5
8.0
8.3
8.9
97
10.8
12.2
13.4
15.2
Character istic
Highest Value
(ppm)
12ppm/lxx (2nd
12.8
1.2
9.6
10.7
11.3
12.1
- 1 "? Q
13.6
14.3
14.7
15.6
9ppm/5xx (6th
11.9
0.9
10.2
10.5
10.8
11.2
UQ _
. O
12.4
13.0
13.6
14.6
Highest
Value
(ppm)
Hi) - -
13.9
2.3
9.4
10.7
11.3
12.3
_ -I 0 C
XJ.D
15.2
16.9
18.4
21.0
Hi) - -
12.9
2.1
9.7
10.3
10.6
11.4
IOC
13.9
15.7
17.2
19.5
32
-------
and observed highest concentrations among sites.
The one year data in Table 7 continue to show that the 7 ppm/5
xx standard gives somewhat tighter control of the both the
characteristic highest concentration and the observed highest
concentration among sites than does the 9 ppm/1 xx standard when the
observed sixth and second highest concentration are used as
estimators, respectively. There seems to be no heightening or
diminishing of the relative effectiveness of the two standards. On
this basis, it is concluded that the data in Table 7 give a reliable
indicator of the relative effect of using three years of data.
Comparing the one year and three year results in Table 7f it is
seen that going to three years results in a lowering of the mean and
median values of both the characteristic highest and the observed
highest concentrations among sites and in a narrowing of the
respective distributions among sites. However, the effect is
greater for the 9 ppm/1 xx standard than for the 7 ppm/5 xx
standard. The result is that the differences between the two
standards which are quite apparent in the one year case are markedly
narrowed in the three year case. Nevertheless, when three years of
data are used there is still a sight advantage for the 7 ppm/5 xx
standard over the 9 ppm/1 xx standard in terms of greater control
over peak CO concentrations.
The greater effect on the 9 ppm/1 xx standard when going to
three years of data is explained by two factors: 1. going to three
years improves the accuracy of the estimator of the characteristic
highest value to a greater extent than it does the accuracy of the
estimator of the characteristic fifth highest value, and 2. as the
accuracy of the estimator is increased the relative effect of the
upper-tail slope, which favors the lower expected exceedance
standards, increases. If enough years of valid data were available,
at some point the one expected exceedance standard would give
tighter control among sites, using the observed YN+1 highest
concentration as the estimator. The results shown in Figures 2 and
3 and Tables 4 and 5 represent the limiting case since the
underlying assumption is that the characteristic Nth highest
concentration is known precisely and each site is brought to that
35
-------
value. It is noted, however, that even in the limiting case for the
eight-hour CO NAAQS, the difference between a one and five expected
exceedances standard is still relatively small.
Another way in which the -accuracy of estimator can be
increased, whatever number of years of data is available, is to make
greater use of the data. That is, fit a distribution to all of the
data or to the upper tail and estimate the characteristic values
directly from the distribution.
Finding the Optimum Expected Exceedance Level
The optimum expected exceedance level can be defined as
follows. Consider a series of alternative eight-hour CO standards
with expected exceedances 1, 2, 3,...,N. For each alternative
adjust the standard concentration level so that the median
characteristic highest concentration among sites just meeting the
standard is the same value for each of the standards. Assume the
sites are just brought into attainment by application of an
estimator for the Nth characteristic highest concentration. The
standard which results in the least variation among sites in the
characteristic highest concentration can reasonably be considered
the optimum standard of the group.
What this optimum expected exceedance level is will depend
strongly on the accuracy of estimator. If, for example, the
estimator gave the exact value of the characteristic highest
concentration at a site, then the one expected exceedance standard
would be optimum since, at attainment, all sites would have a
characteristic highest concentration equal to the standard level.
This is the situation illustrated in Figure 2. For standards with
higher expected exceedance levels the variation among sites in the
slopes of the upper tails of the CO distributions will cause
variation among sites in the characteristic highest concentration,
even though the characteristic Nth highest concentration is brought
to the same value at each site. This is the situation shown in
Figure 2.
The situation in which the observed YN+1 highest concentration
in Y years is used as the estimator for an N expected exceedance
36
-------
standard is more complex. The effect of the upper tail slope will
be counterbalanced by the increasing accuracy of the estimator as N
increases. As indicated in the previous section, as the number of
years (Y) increases the accuracy of the estimator increases for any
particular N. This increase is most rapid for small values of N.
The limiting case is when the estimator is exact, as discussed in
the previous paragraph. In this case the optimum is the one
expected exceedance standard.
Table 8 shows the trade-off between the effects of the upper
tail slope and the accuracy of the estimator when the observed N+l
highest concentration in one year is used as an estimator. For each
observed N+l highest concentration, a standard level was chosen
(line 2 of Table 8) which gave a median value among sites of 9.0 ppm
for the characteristic highest concentration. The distributions of
the characteristic highest values shown in Table 8 are plotted as
contours of equal percentile in Figure 6. Figure 7 uses the
standard deviations of the distributions divided by the mean of the
distributions as a measure of variation among sites. Dividing by
the mean corrects for variation in the standard deviation due to
changes in the overall level of the concentrations (in this case, a
small effect).
Inspection of Table 8 and Figures 6 and 7 shows that the
optimum level occurs at the observed fourth highest concentration in
one year. It is seen that there is a sharp drop in variation among
sites of the slope of characteristic highest value proceeding from
use of the first to fourth observed highest concentration as
estimators. The rise after the minimum is reached is slower. The
observed third through sixth highest concentrations are all within
the vicinity of the minimum. It is also seen, in agreement with
Figures 4 and 5 and Table 6, that the observed sixth highest value
is clearly superior to the second highest value as an estimator.
The presence of the observed highest concentration in Table 8
and Figures 6 and 7 needs to be explained. Although the treatment
up to this point has associated the observed N+l highest
concentration with an N expected exceedance standard, the
association is, to some extent, arbitrary. The Nth highest
37
-------
u
D
§
4J 03
£ -H
Q"i
H rH
W
^
C m
(d .a
C i_i
'd jg
t- rn
H £
ij "^
< W
d)
*-* J2
03 4J
D
^1
Jj
CO 01
^ vJ
8*8
o o
5 M
C CD
O u
H OS
" ^f
4J
03 01
vj CD
-P 0
c e
CD oJ
"^ *^^
8 "8
Q CD
o o
P W
03
.C CD
FT\ i j w
ffi &j rH
o S*>
H pa -
-p ~ S
M TS 2
H a) -H
* * 7i
0) 0 ,2
4J iH S
O rj
03 C o3
c: a; -p
u JS 2
5 c
M-l P
O TJ O
^i
C 03 KJ
0*0^
-H C C
4J 03 -H
i»s
H Q 03
c J5 a
03 w -n
XI 03 T!
a o <
CO
%
03
^T
^
S g
CD
CD o
« 1
Vj ^Q
03 -H
t3 M
C -P
3 03
4J -H
CT Q
VO
rH cn
cn o
o
en o
m
rH 00
cn o
r^»
H r^
t
cn o
CN
o r-
o\ o
o
o r^
t
ON o
VX>
O V£>
en o
rH f>-
*
en o
'sD
O CO
OS O
10
Cn rH
CO rH
-H
-U
03
-H
s
(Q 'O
23
C CD
-H >
0) 0
H CD S
03 03 >
_ o ^
^* 00 O ^* O *sO rO 00 O O^ <^ 0-)
» C 5 c/)
r^r^ooooo>CNOoc^ *H x3
fH rH rH ^ r^ O
i j ^^^ ^^^
^^^^ ^^^ **^
i -ri § o
Cg -H
mooo^ovocNr^co QS -P
64j 03
r^r>-cococncnoorH rn H
'H rH H 03 -P
n) £
I 1 W /|\
4*1 /- UJ
i m 5 y
*- ^
vo^iHinovocNr^r^ Sn> Q
2c u
r^r*-cococncnoorH TJ-H
! ^^ s-S «
i -P fj -S
S -P cn
r^ocNinomomrn gaj -H
r>-COCOoOC»CTiOOrH Sp
rH rH rH OS O
i o y -H
u jj
1 T?! W
.53 ^
V ^
t^OOCOCOC^CTi^O'H ^rt, -P
rH rH -S it U
fl -1 -.J M^
1 -^ w 03
UJ -, XI
r^iHC^^O^ON^frH 2m O
»** *^ lir
r^cocooo-cocococnencnoo "^ X3*
rH rH ^ jJ P
^^^ ^^ *^ ^^ *
1 § £ "03
rocncNvcomoroo r^Si, -P *
********* 5 .ST en
r^r^cococncnoorH ^ Q
rH rH rH . t 2> * 03 CD
I -P *^> CD J3
S 0 ^ 'P
I JB 2 -Q _g ^
coincnmovorH^ro 51 --P cn-i-i
'Hrp 3S
^r-r^oocrtcytoorH ^$CD -n
rHrHrH rt. JQ J= r^r^
* n ^^^ ^** ^^
1 2 3 JJ 03 S-i
fi ^, 03
| -*-1 r>'^:J' X 03
» fft>oocT*aNOOrH ..SC 0303
^^^ aJo'J S m
l 1 1 ^^^J ^*^ *!_
t ^M r^ r^
1 m _LJ . **
UJ ^*^ i 1 r^ t 1
t f*4 ^"* Jt^ +T*+
i u 2 x o
P^. ri CD o3 CTI
i ^ £ C a) fi
° m -H
I Vj ^ rti <* r*
1 r^ 22 t-! *-«
« § 5 -1 -3
H U rH 4J
i .c u c CD -P
i <»"H m *
S S c ^-^
! 'H _g CD 03
^^^^^ ^^*fc l^a^i ^^^1
5rf '& dPdPdPc»PdP<*Pc*Pc*P C >jrH 03 03
rHinoinoinoincn CD
rHcNinr^encncn CDO)> a)rH
^! C 0) ^ rH
PH O rH P-* 03
I fQ O
CO
-------
Figure 6
Change in Distribution of Characteristic Highest
Concentration Among Sites Just Attaining a Carbon
Monoxide Standard Based on the Observed Nth Highest
Concentration in One Year When Allowed Expected
Exceedances are Increased While the Standard Level
is Adjusted to Maintain a Constant Median Characteristic
Highest Concentration Over Sites.
13
12
11
CL
Q_
10
o
CC
8
O
o
99%
75
50%-
5 ;
I
I
I
I
2 3* 56789 10
ORDER STATISTIC OF OBSERVED CONCENTRATION
39
-------
Figure 7
Change in Variation of Characteristic Highest
Concentration Among Sites Just Attaining a
Carbon Monoxide Standard Based on the Observed
Nth Highest Concentration in One Year When
Allowed Expected Exceedances are Increased.
o
o
H
X
u
&
o
Cfl
M
O
H
B
a
H
CO
H
U
p
Q
14
13
12
11
10
8
i ! !
1 2
[
3
f
4
1
5
1
6
1
7
1
8
1 1
S 10
ORDER STATISTIC OF OBSERVED CONCENTRATION
40
-------
concentration can also be used, with some justification. This is
seen in line 2 of Table 8 which shows the levels to which the
standard concentration must be adjusted in each case in order to
attain a median value of 9.0 ppm among the sites. The observed
fifth highest concentration required an adjustment to 7.1 ppm while
the observed sixth highest concentration required an adjustment to
6.9. Thus the observed fifth and sixth highest values are about
equivalent in representing a 7 ppm/5 xx standard which yields a 9.0
median characteristic highest concentration among sites. Using the
fifth highest concentration would make the 7 ppm/5 xx standard
slightly more stringent.
The adjusted standard levels for the observed highest and
second highest concentrations fall about equally above and below the
9.0 ppm level and therefore both estimators have about equal claim
to representing the 9 ppm/1 xx standard. However, use of the
observed highest concentration would lead to a significant increase
in variability of the characteristic highest concentration among
sites.
Figure 8 compares the one year and three year cases using
theoretical distributions for the observed Nth highest
concentration. To put the two curves on the same basis, the value
of N (labeled order statistic in the figure) is divided by the
number of years. Thus, the order statistic 5 corresponds to the
fifth highest concentration in one year and the 15th highest
concentration in three years. The observed fourth and 16th highest
concentrations used in Table 7 occur at 1.33 and 15.33,
respectively, on the three year curve.
Comparing the one year curves in Figures 7 and 8, it is seen
that at all values of the order statistic the variation among sites
is greater when the theoretical distributions are used. There is
also a broader minimum and there is a slower rise after the minimum
with the theoretical curves. However, the minimum occurs at about
four in both cases.
Comparing the one year and three year curves in Figure 8, it is
seen that there is a significant reduction in variation among sites
at all values of the order statistic, but the reduction is sharper
41
-------
Figure 8
Change in Variation of Characteristic Highest
Concentration Among Sites Just Attaining a Carbon
Monoxide Standard Based on the Observed Nth Highest
Concentration in One and in Three Years When Allowed
Expected Exceedances are Increased.
(Uses Theoretical Distributions of Nth Highest Concentration.)
16
o
0 15
o
o
u
CO
W
ffi
H
a
o
H
EH
CO
H
H
O
Q
Q
CO
X
iz 14
13
12
11
10
8
3 Years
8
ORDER STATISTIC OF OBSERVED CONCENTRATION/YEARS
10
42
-------
for lower values of the order statistic. This effect causes the
minimum to shift to lower values. The minimum now appears to occur
in the vicinity of the observed sixth to ninth highest concentration
in three years. Increasing the number of years would move the curve
further downward, i.e., the minimum would shift toward 1.
Thus, it is concluded that with one year of data a three
expected exceedance standard using the fourth highest value is
optimum. However, to employ this standard to achieve a
characteristic highest value of about 9 at the median site would
require the use of a fractional standard level of 7.4 or 7.5 ppm.
five expected exceedance allows use of an integral value for the
standard level (expressed in ppm). In this case either the observed
fifth highest or sixth highest concentration would give close to the
minimum variation of the characteristic highest concentration among
sites. Use of the observed sixth highest concentration is in
conformance with present EPA guidelines.
It is also concluded that neither the observed highest or
second highest concentration are quite satisfactory for a 9 ppm/1 xx
standard. The use of the second highest observed value is more
appropriate to an 8.4 or 8.5 standard under an objective to achieve
a characteristic highest value close to 9 ppm at the median site.
In the three year case the sixth to ninth observed highest
value would be optimum but these would require a fractional value of
about 7.5 ppm for the standard. Again the use of the fifteenth or
sixteenth highest value associated with a 7 ppm/5 xx standard gives
close to the minimum variance. The use of the sixteenth highest
value conforms to present guidelines.
The use of the observed fourth highest value in three years
conforms to about an 8.7 ppm standard. This is an improvement over
the use of the second highest value in the one year case. The use
of the observed third highest value in three years conforms to a 9.2
ppm standard which is better. However, the variation of the
characteristic highest value among sites is now significantly higher
than it would be for a 7 ppm/5 xx standard using the observed
sixteenth highest concentration.
It appears that in cases where the estimator is to be the
43
-------
observed N+l highest concentration, the 7 ppm/5 xx standard
represents a practical optimum exceedance level when the objectives
are: 1. minimum variability of the characteristic highest
concentration among sites, 2. a median value among sites of 9 ppm
for the characteristic highest concentration, and 3. the use of an
integral value for the standard level. As the expected exceedances
increase above five there is a continuing increase in the range of
the characteristic highest concentrations and, therefore, the
observed highest concentrations among sites.
If the desired median value is 12 ppm then repeating the above
analysis would yield 9 ppm/5 xx as a practical optimum.
44
-------
REFERENCES
1. "Guideline for the Interpretation of Ozone Air Quality
Standards", EPA-450/4-79-003, Office of Air Quality Planning
and Standards, EPA, Research Triangle Park, NC 27711, January,
1979.
2. R. I. Larsen, "A Mathematical Model for Relating Air Quality
Measurements to Air Quality Standards", Office of Air Programs
Publication No. AP-89, EPA, Research Triangle Park, NC 27711,
1971.
3. "The Validity of the Weibull Distribution as a Model for the
Analysis of Ambient Ozone Data", Draft Report to EPA by PEDCo
Environmental, November 17, 1977.
4. T. C. Curran and N. H. Frank, "Assessing the Validity of the
Lognormal Model When Predicting Maximum Air Pollution
Concentrations", Presented at the 68th Annual Meeting of the
Air Pollution Control Association, Boston, June 15-20, 1975.
5. L. Breiman, J. Gins, C. Stone, "Statistical Analysis and
Interpretation of Peak Air Pollution Measurements", Final Report
to EPA by Technology Service Corporation, Contract No. 68-02-
2857, Report No. TSC-PD-A190-10, November, 1978.
45
-------
APPENDIX A
ADJUSTMENT FOR SAMPLE SIZE
In some analyses, a simplified adjustment was incorporated to
partially account for the effect of missing data. The purpose was
to introduce an allowance for missing data without predicting new
values or extrapolating beyond the existing data. It uses the
intuitive idea that if data are missing a higher observed value
should be used to determine status. A convenient way to implement
this idea for a data base of this size was to multiply the allowable
exceedance rate plus one by the fraction of days with data, round to
the nearest integer and use this result to choose which value should
be used to determine status. This approach can be illustrated by
considering the following equation and examples:
INDEX=GREATEST INTEGER - (ALLOWABLE RATE + l)x (FRACTION OF DATA)+0.5
For example, if a site has complete data and the allowable
exceedance rate is one then the above equation indicates that the
second highest value should be used. However, if the site had only
50% complete data then the above equation would indicate that the
maximum observed value should be used. In addition, when the sample
size adjustment was used in an analysis, the number of days above 12
ppm was determined by weighting each day by the inverse of the
fraction of days of data. In other words, if a site-year was 50%
comlete, each day above 12 ppm would be counted twice (i.e.
multiplied by I/.5) to compensate for missing data. Therefore, the
missing value adjustment may be viewed as having two opposing
effects. On the one hand, it may mean that a higher value is used
to estimate the rollback factor so that the high values are reduced
more; on the other hand, those values remaining above the level of
interest are weighted more heavily.
46
-------
APPENDIX B
MATHEMATICAL DESCRIPTION OF METHODOLOGY
The computations in- this report make extensive use of
computations made by Dr. T. Curran of MDAD/OAQPS who fit tail-
exponential distributions to 430 sets of 8-hour CO concentrations
The tail-exponential distribution may be written as follows:
(1) G(C) = GQexp(-(C - CQ)/k)
where: C = time-averaged concentration.
G(C) = fraction of concentrations above C.
CQ = minimum concentration for which the tail-
exponential distribution is valid.
GO = G(CQ), the frequency corresponding to CQ
k = constant.
For convenience, the distribution G(C) has been defined as the
compliment of the more usual cumulative distribution F(C) where F is
the fraction of concentrations less than or equal to C. That is,
G(C)=1-F(C). Thus, if the tail-exponential distribution applies to
the highest ten percent of the concentrations, then GQ=O.!.
In setting statistically based standards the interest is in
establishing a standard concentration level at which the expected
exceedances in one year cannot be greater than a specified value.
In the statistical theory of extreme values this is a point on the
distribution curve and is called the characteristic mth highest
value. By definition
(2) G(Cm) = m/n
where: n = number of concentrations in a data set.
= the characteristic mth highest concentration.
By substituting (2) into (1) and solving for k, it can be shown
that:
47
-------
(3) 1/k = log(G0n/m)/(Cm - CQ)
If all concentrations are expressed as fractions of C-i, the
characteristic highest concentration, a quantity Z can be defined
such that:
(4) z = (x - x0)/(l - xQ)
where: x = CC- : XQ =
Note that: z = 0 at x = XQ or C = CQ and
z = 1 at x = 1 or C = -]
x is the concentration in units of the characteristic highest
concentration, z has a similar interpretation but with XQ as the
origin.
Substituting into Equation (1):
(5) G(z) = GQ exp (-z log GQ n)
Written this way, the tail-exponential becomes a universal curve.
The quantity XQ is a measure of the slope of the upper tail of
the distribution and consequently was used to express the variation
in slope among sites.
Appendix C contains a listing of the observed ten highest
concentrations for 436 site-years and the computed parameters of the
tail-exponential distribution CQ and k (Equation 1) for GQ=O.!.
Given CQ and k for a site, Equation (3) can be solved for C-^ and the
quantity XQ calculated.
When more than one year of data was available for a
given site the XQ values were averaged. This procedure yielded XQ
values for 251 sites. These values were rank ordered. A frequency
48
-------
R/(N + 1) was assigned to each of the ordered values where R is the
rank and N the total number of values. This distribution, referred
to as FQ(XQ), was used in the computations.
It was also necessary to obtain distributions of the observed
Nth highest concentrations. This was done for the ten highest
concentrations at each site (listed in Appendix C). As above,
Equation (3) was used to calculate C^ and XQ given k and Cg for a
site. Given the mth highest concentration it was possible to
calculate x/m) = c(m)/cl an(^' therefore:
(6) z(m) = (x(m) - xQ)/(l - xQ) m = 1,2,....,10
The z/mx for a given m were rank ordered and a separate distribution
developed for each value of m. These distributions were labeled
F(m) (z(m) )
The reason for developing distributions of z/m\ rather than
/-x is that the z/m\ are independent of the level of the
concentrations and independent of XQ. The distribution of z is not
independent of the number of observations, however, and,
consequently, missing values will cause some distortion in the
distributions. Since the data sets were reasonably complete, it is
not believed that missing data caused sufficient error to cast doubt
on the results of the study.
Table 6 of the report presents distributions among sites of the
characteristic highest and observed highest concentrations for N
expected exceedance standards. The observed N+l highest
concentration in one year is used as an estimator for the Nth
characteristic highest concentration. The distributions are
obtained as follows:
1. A number is chosen randomly from a uniform distribution of
numbers between 0 and 1. This number is used as the cumulative
frequency in the empirically determined distribution F,QX(XO) to
find the corresponding XQ value.
2. For an N expected exceedance standard the same process is used
49
-------
with the distribution F(N+I) (Z(N+1) ^ to 9enerate a value
3. The process is repeated with the distribution Fm(zm) to
generate a value z /-x.
4. From Equation (6) it follows that:
o
and
(8)
where the z/jj+]\, Zm/ an^ XQ have been determined in Steps 1, 2,
and 3.
The observed N+l highest concentration is by definition x
/N+-j_\
5. With this concentration as a design value/ the perceived needed
adjustment to the original distribution to bring it into conformance
with the standard is:
u - C
std/x(N+l)Cl
This perceived adjustment isf of course, generally in error because
the correct adjustment is cstd/xNCl
(Note: X(N+1) ^s a randomly generated, observed N+l highest
concentration whereas XN is the characteristic Nth highest
concentration of the original distribution.)
Thus, the new characteristic highest concentration is calculated
from:
Cl ~ (Cstd/x(N+l)Cl)Cl ~Cstd/x(N+l)
6. The corresponding observed highest concentration is then:
50
-------
(11)
7. Steps 1 through 5 are repeated a large number of times. The
result is to produce a population of characteristic highest values,
C]_, and highest values, C/-^. These distributions are representative
of the distributions of the annual characteristic highest values and
highest values of daily maximum eight-hour CO concentrations of a
large number of sites all brought to conformance with an N expected
exceedance standard. The standard, in turn, is based on an estimate
of the characteristic Nth highest concentration and is subject to
error .
For Tables 4 and 5 in which all sites were brought exactly into
attainment with the standard, the distribution of z/N\ was set to a
fixed value so that z/N% = ZN for all percentiles. The value of
was computed from Equation (5) by setting G(z) = N/n and GQ = 0.1
(since the tail-exponential fits in Appendix C were for the upper
10% of the data). Thus, for this case, the random procedure in Step
2 always generates the same value, ZN.
In Table 7 theoretical distributions of z/nj are used. If it is
assumed that the daily maximum 8-hour CO concentrations are
independently and identically distributed over the days of the year,
it is possible to show that
m-1
F(m) =
v=0
n-v
where G, in the present application, is the tail-exponential
distribution of daily maximum 8-hr CO concentrations. (See W. F.
Biller, "Studies in the Review of the Photochemical Oxidant
Standard" Report prepared for the EPA Office of Air Quality Planning
and Standards under Contract No. 68 02 2589, January, 1979.)
Performing the three year computations is straightforward. For
example, where the 16th highest concentration in three years is used
as an estimator, the theoretical distribution for z/i g\ in three
years, computed from (12), is used in Step 4 to determine an xm. In
51
-------
the remaining steps the computation is transformed to the one year
case by setting m equal to 5.333. For the 4th highest value m is
set equal to 1.333.
52
-------
APPENDIX C
DATA BASE USED IN INVESTIGATION OF MULTIPLE EXPECTED EXCEEDANCES
AMBIENT AIR STANDARDS EMPLOYING TAIL-EXPONENTIAL DISTRIBUTIONS
The data base for the investigation of multiple expected
exceedances standardards employing tail-exponential distributions
was obtained by MDAD from the 1979-1981 eight-hour CO concentration
in the SAROAD data bank. Site-years with less than 189 days of data
were excluded as were site-years whose observed highest eight-hour
concentration was less than 9.5 ppm. This selection procedure gave
a data base of 449 site-years. A statistically acceptable tail-
exponential fit (p = 0.05) could not be made to 13 of the site
years. Consequently the working data base consisted of 436 site-
years.
For each site-year the following table lists:
1. Site identification.
2. Calendar year.
3. Concentration CQ corresponding to G = 0.1 (See Equation
(1)/ Appendix B).
4. Tail-exponential distribution parameter k (See Equation
(1), Appendix B).
5. Number of eight-hour CO concentrations in the site-year
6. Observed ten-highest daily maximum, eight-hour CO
concentrations in ppm.
53
-------
CO
c
o
>H
CO
H
Q
rH
-H
C
c
I
M
H
E-t
C
H
^
§
-H
4J
05
-H
-U
CO
0)
c
H
CO
(U
O
*v
8
Q)
Q
'S
JJ
r T
w
(1)
rH
ex
-H
i
OJ
CO
05
CQ
05
o
1
CO
C
O
H
05
u
| CO
8
8
u
Tvo
CO
H
a
0)
-H
ffi
C
(U
EH CN
8
0)
§
f
r-|!H!H.-t
,-HrHiHrHHfH.H
O O CO O CO
vr> co
iHr-HrHi-liHi-l-H
co
t
co r* rH
*
»*»»*
**
§*
**
*
HrHrHrHr-t
,-Hr-lrHiHiHrHrH rHiH
iHrHrH
ON
CN
iH rH
fH CM rH
A
oJ r*** oo f*H r*** ty\ &\ G^ co vo c^ ^o
fH rH rH ^ rH rH
rHCNrHrHiHiHrHrHr-liHrHrHrHrH iHfH
*§
*
iHrH
CN
rHrH.HfH rH H
rHrHrHiHrH
ft
CD CD c^ vo c^ ^D r^ r**11* t**** oj ^j* ^j co LO ^D vo LO K>O
rHrHrHfHHOJCNrHHiHfHiHrHiHCNrHrHrHrH
»«
*
rHCMiHrH
rHrHr-fCNrH
cx)r^iHvoc^rHv£>cNiiHrHroiH
onHa^c»cocNcoc^
««fffttt«*9»9««
rH fH
Q)
ooooooooooooooooooooooooooooooooooo
-------
CO
m
ro
CM
CO
03
O
u
03
0)
H
03
O
55
en
ro in
rH rH
Cn
in v0 v0 r^ m en
cocov0v0ooocMcnv0cnocnr^^i'co^'ocncococno
rHrH rH rHrHrHrH rH
rH CM ro in in en m
rH rH rH rH rH rH rH
O rH
ro ^0 in
H rH H
rH in v0
* co co
co co ro
*
co rH CM en v0 o
rH rH
ocnr^tnootnocncocooorHrorotnincntno
' ' ' ' rHHrHrHrHrHrHrHiHrH
oinv0cMCMinr^OrHcn
*
m
rH
CO CO
co rH CM en P*- o rH
rH rH rH rH
r^mcoinocncocooorHro^voincTtinrH
rHrHrHrH rHrHrHrHrHrHrHrHrHiH
CM m en rH H o
ftftftftftftftftftft
O O rH
p* ^o r- p* en co P-
en CM
rHrHrHrHrHrHrHiHrHrH
iH rH ro r^
vo
rH H
o en
H
H O O
ft ft ft
p* cn ro
rH rH rH
ft*ftftftft*
ftftftftftft*
HrHrH
rHCMrHiH
rHrHrHrHrHHrHCMiHrH
cMromv0p-v0cnrHorH
p-vocop-ocnp-p-cnro
rH rH rH rH
*
*
.HCMrHrHrH
rHrHrHiHrHrHrHCMrHrH
mp*^0rHOOrHr^rH
I
r^-voencOrHocop^enroroooOrH
rHrHrH rHrH rHrHrH rH
»
*
ococnocorHrHcncnrH
rH rH CM rH rH rH rH
rHCMrof>r^r^ocoH
rHrHrHrHrHiHCMrHrH
O ^ rH
m
V0 CO ^ CM
o co co cn ^* ^*
cnrHrorHcncnrHcorH
rH rH rH rH CM rH rH
CO rH
ro cn rH p- v0 co co
incMcncncorHooococn'oincMrHCMrocMoorHcnrHrH
H CN rH rHrH rHrHrHrHrHrHiHrHCMCMrHrHrH
OCnCMCMCM^P-Cnp^OCOCM
rH rHrHrHrHrHrHrHCMrHrH
ocncMCMCMinr^cno^to^o
rH rHrHrHrHiHrHCMCMCMrH
rHCMocnp-rHCMr^cn
ftftftftftftftftftftft
ftft
ftft
ft«ftftftftftftftftft
in^rrHoororHOrHenrH
HCMCMrHrHrHrHrHrH CMrHH
HrHHHrHCMCMrHrHHrHrHrHrHrHrHrHCMCMCMCMrH
OrHcnr^inrocOrHo
roinv0vom^ov0oocninin
cororororocNrOiHCMrorororornrocMrocMrorororororocMrn
r^OV0rHV0COrHCM^0rHO
rorHvo^'oocMrH^^'inp*
COOOrHCnorOV0rH
rHCMCMCMrHCMrHrHiHororOCM
rH CM H rH
*§*
»*
rHCMrOCMrHHrHrHrHCMCMCNnrOCM^rOCM
m ro co in cn
ro cn ^* cn ^0
*
rH o ro m
CMininineninr^roroincoroooincOrHcoorHinco^0ininro^oo
inrHov0rHOincNien^o^J*rHv0cncM>cocor^cocor^cocococor*»copi-cocop*
cncnoScncncncncncncncncncncnc^cTtcncjNcncncncncncncj>c^c^
H rH rH rH
O O O O
CM CM
O O
O O
o o
o o
cn cn
o o
tn m
o o
CM ro
o o
o o
o o
O V0
cn CM
O rH
in m
o o
o
M
rH
O
O
O
O
O O
M M
CM CM
O O
o o
o o
in
o
m m
o o
o o o
M M M
CM CM H
000
o o o
000
CO
10
CM
in
o o o
CM CM
in in
o o
% %
in in
o o
o o
o o
o o
CO CO
CM CM
m m
o o
o o
Cn M
in cn
o ro
O CM
O O
o o
CO CO
o o o
M M M
rH H rH
O O O
o o o
o o o
CM CN CM
VO V0 ^0
o o
M M
rH rH
O O
O O
O O
CM O
^0 cn
rHrHHrHrHrHrHrH
oooooooo
rHrHMMrHMMM
rHHCNCNCNCMrOrO
OOOOOOOO
OOOOOOHH
OOOOOOOO
oooooococo
CncnrHrHrHrHrHrH
rH rH
o o
M M
V0 rH
O O
rH O
O O
CO O
H CM
O O
M M
H H H
O O O
O O O
O O O
O O V0
CM CM CM
O O O
M M M
rH H rH
O O O
O O O
O O O
VO \£> V0
CM CM CM
m m m in m
o o o o o
inininininminininininininminininin
oooooooooooooooooo
p* co cn o H CM ro
ro ro ro ro
m
55
-------
00
un
03
I
*
*«»
H rH
rH rH
rH rH rH rH rH
CM
in vo o o o o
rH rH rH rH
rH rH
«*i*i
tt
rH rH
O in o CN
+ *
rHrHrHrHrH
****
rHrHrHrHfHrHrH rH
I****
^^ ^ft CO 0^ lO ^3 ^5 iH ^^ ON ^H CO L^ ^3 ^^ ^3 ^* ^* ^0 00 rH
rH rHrHrHrHrH rH rHiH iHrHrHrHrHrH
r- r* ro
*
HrHrHrHrHrHrHrH
rHfHrH
rHrHnHrH^HrHrHH
rHrHrHrHrHrHrHiH
O
*»**«**
rH rH rH rH
rHrHrOOOOrH
CN
O O O O
o o o o
o o o o
o o o m
CN CN ^ CO
m m in in m m
o o o o o o
o o
o o
o o
CO CO
OS OS
o
ro
00
o
ro
CO
o
ro
CO
o o
rH fH rH rH rH rH
o o o o o o
M M H M &4 fe
^ rH rH rH CN CN
o o o o o o
o o o o o o
o o o o o o
^T CO CN CN CN CN CN
m
o
m
o
m
o
O
co
in
o
CO CO CO CO CO O O
m in m m m
56
-------
o
H
00
*
rHrHrHrHrHrH
rH rH
*** * *
rHrHrHrHrHrH
CSrHrH
rH H rH rH rH rH ,H (N rH
rH rH
**»***»*
ooJCSrHfHiHrHrHrH rH rH
CN
«
OJCNrHrHrH
Lnino4^
***§*
*
rH rH
HHHrHHrHrHrHrHHHHrHHfHHrHHrHrHrHHHrHHrHrHrHHrHHHrHHH
rHU^iHrHrHrHiHrHrHrHrHiHrHrHrHiHrHrHrHrHrHrHiHrHrHrHiHrHrHiHM
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOrHrHrHOOOOOOOOrHOOOOCNCNCNrHrH
ooooooooooooooooooooooooooooooooooo
ooooooooooooooooooooooooooooooooooo
OOOOOOOOOOOOOOOOOOOrHrHrHCNCNOOOOOOrHfHrH
vDvovD^^vovovovo^KOv^vovovovovovovovo^ovovovor^r^r^r^r^r^r^r^r^
ooooooooooooooooooooooooooooooooooo
oo
o o o o
H rH H rH
HrHrHHrHrHrHrHrHrHHrHrHrHrHrHHrHrHrHrHrHrHrHrHrHrHrHrHrH
57
-------
**»*
rH rH
rH rH
00
rH rH
rH rH
***
* *
CNj
rH
*»»* ****
rH rH rH rH
»»* *
cNiHaN^r^
rH rH
in
ft
oor**LncN«*mr^^^0
»*»*
«*»*§
iHrHrHrHrH
rHrH
»** !*
rHrHiHrHrHrH
rHrH
| fH rH rH
rHrHrHrHrHrHrHrHrHrH
rHrH
iHrHrHrHrHrHiHrHrHrHrHrHrHiHrHrHrHrHrHrHrHrHrH
CO
I
rHrH rH
ocNr^ro
0)
4J
-H
*
CNrHrHrHrH
«*
iHrHrHfHC\IrHiHiHrHrHrHCNliHiHC\JiHrHHrHHOrHrHrHOrHrHrHrHrH
rHHrH^rHrHrHHrHHrHHrHiHrHrHHHrHHHHHrHHHHHrHHrHrHrHrHrH
iHrHCN
CM
O
rH
O
O O O O O O O
M
ro
CN
O O O O
H
O
rH
o
rH
O
rH
O
rH
O
rH
O
H
O
H
O
H
O
rH
O
rH
O
OJ
O
rH
O
O
CN
O
fa
CO
o
rH
O
fa
00
H
O
O
CN
o
O
fci
O
rH rH rH rH
O O O O
fVi fr.t ^rt rv*
^^^^ ^^^1 ^^^^ ^^^^
o o F
o
O
CN
O
O
(Tt
o
o
-------
o
r-i
00
ro
CM
CO
I
O
H
cn
O CT» 00
*********** + *********»*
rH H fH rH
ro
4**«*****«
*
*
t *
rH VO
*
rH rH
CO O
*
o
ft*
+ **«*
rH r-f
rH rH
Lnr^ovoinmo^cn
H
o oo vo
rHrH
rHrH
rHrH
«**
*
**
O CN 00 iH
rH fH
rH ^f in m
* * *
rHrH
rHrH
rHrH
rHiHrHrH
ro
-------
CO
ro
CM
03
I
**
****»*»»
rH
rH
««***ft*«t**f
ft
rH
OrHrHrHrHfOCMP^r^OO
I
co
rH rH rH rH rH
O CN
O CO O CO O> CN
H rH
**
*»**
ft*
r-irHrHrHrHrHrHrHrHrH
rH rH rH
O CO LH
rH rH
rHfHrHrHrHrHrHrHrHrHrHrH
O
,_| ,_] H rH rH
rHrHCNrHrH rHrHrH
HHrHrHHHHiHrH^rHHrHHrHrHrHiHrHH
HrHHrHHrHrHrHrHrHrHrH
CM
o
in
o
cn
CM
CN
CM
vo
rH
O
ro
CM
co
rH
ro
CN
oo
rH
rH
ro
CM
HHrHrHrHrHfHrHrHrHrHrHrHrHrHrHrHrHrHrHrHHrHrHrHrHrHrH
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
a^M _ F f\ F f\ F ^1 F ^1 ^w _ ^M _ RM « r ^1 r ^1 ^1 ^T^' ^₯^ "T^ ^T^" ^T^^ PP a ^^ 4 ^1 P^ ^^^ ^^^^ MP * I ^1 ^1 f ^1 ^^1^" ^^^^ ^^^"
^^^J V. J V. J t. J fc. J ^^^J ^^^J ^^^J V. J V^_J *^ - ^^^d ^^^J ^^^d ^^^J ^^^d HVl ^J^B V J ^^^J ^^^J ^^^J ^^4 V_ J ^ _J V _J ^^^J ^^^rf ^^^J
rHCMrncoc5cx>r^r^^coooo5inLnij^rHrH^cjNrHr^c^Fc^
CMOOrHrHrH^r^^rHrHrHCNCMCMrorororOOOOCNCNOOOO^OVO
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
OOVOVO^rr^VOVOVX>CMCNCMCMCNCMOOOO^OOOOOOOOCMCMCMOOOOCO
rHr^CNOOOCMCMCMHrHrHCMCMCMrOrOrOrOOrHrOrOrOHrHrHCMCNCM
iH^LnrHrHrHCNCMCMrorororororororororOiHCNCMCNCN^^f^1^*^^
CMCMCNCNCMCNCMCMCMCMCNCMCMCNCNCNCNCMCMCMCMCMCMCMCNCMCMCMCMC^
CN
O
O
\0
^D
VO
rHiHrHrHHHHrHrHCNCMCNCMCNCNCMCMCMCNrorororororororororo^^^^
CNCMC^CMCNCMCMCMCMCMCMCNCMCMCMCMCMCNCMCMCMCMCMCMCMCNCNCMCMCNCMC^
60
-------
I + + **** + **** +
*»»»
oo
H rH rH
ft
iH
rH
iHrHrHrHiH
» * *
CNJ o vo
***»*******
CM O CO
HrHrHrHrHrHiHrH rH rHrH
oo r^ CM CM
*
*
rHrHrHrHrH rH rH rH
rHrH
ft****!****
co oo oo 0*1 vo ^JF r*^ rH o^ r*1* i-n ^T ^3 rH CD ro
,H ,H rH rH .HrHrHrHrHiHiH
en
CN rH ^* ro
* 4
ro co
rH
**»****»*
n*^ ro &\ oo vo ^i* CD ^H ^D ro ^^ o^ oo
rHiHrH rH rHrHrHrHiHrHrH rH
*
o\ o^ oo ^^ oo c^i ^iD
rH rH rH
rH O 00 O
O O CN rH
rH rH rH rH
I
! CM p* ID LO
O> 00
rH rH rH
rH CMrHrHrHrH
HrHrH rH rHrHrHrH
03
H rH
o o in
rH rH CM rH CN
A
rH rH VO rH ^* rH in rH CN O 00 CD rH CD in ^* P* rH CM O rH rH CO CM
rHHrHCNCMrHrHrHrHrHrHrHrHrHrHrHrHrHrHiHrHrHrHrHrHrHrH
00 CO 00 O
H ro o in
ro CM ro ro
rH rH
0)
HrHrHrHHiHtHHrHrHrHrHiHrHHrHHHrHrHrHrHHHrHHfHHr^
rHrHrHrHrHHHrHrHiHrHrHiHrHHrHiHininininrHrHrHrHrHrHrHrHrHiHr^
^r
ft
H
CO
oooooooooooinmmooooooooooooooooooooo
ooooooooooooooooooooooooooooooooooo
CD ^ID lO if) if) LO LO 00 00 00 CO CO CO CO ^* ^J* in CO ^3* ^* ^^* ^3 rH rH VO P1** CO CO VO VO CO 00 CO CO CO
rHrHrHrHiHrHrHrHrHrHOOOOOOOOOOOOOOOOrHrHrHiHiHHCMCNCM
rHHiHrHrHiHrHrHrHrHrHrH
cococococococococococoro
CNCMCMCNC^CMCMCMCMCMCNCMCMCMCMCMCNCMCMCMCMCMCMCNCMCMC
61
-------
rH rH
^rLnorn^*<^LncriOcovovoc CO CNl
*
00
I rH
HHiHHrHHrHHrHH
-------
CO
in rH ro
*
CO O CO rH rH
CM rH rH iH
ft
rH rH rH rH
*
rH rH rH rH
rH rH
rH rH rH rH rH rH
iHrHr-HrHrHf-lrH
c^ <^ ^D f^ c^ c? F"** r^ ro r*H r^1* C3 o^ o^ co oo oo &\ r^* ^* c^j I~H ^D c? ^D cj ^^
^H ^H ^^ ^^ ^t r^ ^^ ^^ ^^ r^H ^^ r^ r1^ ^M r1^ ^^ ^^
rH rH H rH H rH
*
rH rH rH rH
1 CM
ft
rHrHrHrHrH rHrH rHrHrH rH rHrHrHrHrHrHrH
O O CO
CMrHrHrHrHrH rH rH rHrHrHrHrHrHrHrHrHrH
**
rHrHrHHrHrHrH
i cn
rH CM O O rH
rHCMCMrHrHrHrHCMiHrHrHrHrHrHrHrHrH
rHrHrHCMrHrHrHrHrHrHrHrHrHrHrHrH
OrHCMCMCNrHrH
ft
COCNrHHrHrHrHHrHOHCNJHrHrHrHHHHrHrHHH
03
rHHrHrHHrHHrHrHiHrHHrHHrHrHiH
HrHrHrHrHrHrHHrHrHrHr^
ooooooooooooooooooooooooooooooooooo
OrHOOOOOOO
CO
0
12
63
-------
00
03
I
** ***«****»
CM «a* m oj in
**»»*
*«
*
rH rH
ONCMVOONP^OOO
*t**t****««««ft»«*
* t
pHr-(rHr-lrHiH
******
rH .-I rH rH rH CM rHrH
ft* »****
r-l rH .H rH CM rHrH .HrHrH rH rH rHrHrH
oo in CM rH CM in CM
rHHrHrHrHrHrHrHrHrHCNrHrHrHrH
rHrHrHrH
rH rHrHrHrHrHrHrHrH
r^cM^1
rHrHrHrHHHrHOCNr^HCNCNlrHrHrHrHHHrHrHHrHfHiHHOrHC^CNIrHrHrHrHrH
rH rH
HrHiHrHHHrHHiHrHrHHrHrHrHrHfHHrHiHrHHHfHrHfHrHrHrHrHrHrHrHrHrH
5
CO
rHrHrHHrHrH
in
oooooooooooo
O
O
O
O
O
00
in
O
O
O
CN
O
O
O
O
CM
O
O
rH
o
85
CM
O
O
O
00
rH rH rH rH H H rH
r-
ON
ro
CM
r-
O
O
O
vo
CM
O
O
O
CM
O
O
rH
O
CM
O
O
rH
O
O O
rH iH rH rH
o o o o
rHrHrHrHrHrHrHrHrHrHrHrHrHfHrH
CM
O
O
CM CM CM CM
ON
O O
ro
o
co ro
ON
ro
O
CO
O
rH
ON ro CM CM r^ P- rn
OOOOCNCMrHCM
oooooooo
oooooooo
O O CM CM 00 CO
CO ON ON ON CO CO
O rH rH rH O O
rH CM CM CM
O
^T
CM
rH
CM
CM
O
O
_
CO
O
O
ro
CM
ro
CM
in
CM
m
CM
CM
O
o
o
CM
O
o
o
CM
o
ro
o
o
o
in
CM
m
rH
in
m
CM
m
m
^
m
o
O
o
o
o
VD
O
o
vo
ro ro ro
64
-------
00
«**
rHCOr^VOOOOVOrHO
H H rH rH
H rH
»
o o r- vo
rH rH
rH rH
rH rH rH
vo
tn
I
0)
4J
H
cn
rHrHrHiH
iH r-H
HrH
iHrH
rHrH
rHrHrHrH
iHr-lrH
ro
CT\ CT> ON ON ON
65
-------
00
CN
tn
i
***
DATE DUE
*
*
vo
*
ooHOrHGor^oop-r^^H
rH rH H r-( rH rH .H
rH rH rH rH rH rH
***
cNi
rH
rH rH rH rH rH rH
§
rOrHiHin
rHrHrHHiH
!
HrHrHrHrHrHrHrHrHrH HrH
u
rHrHrHrHCNrHCSrHiHrHrHrHOCNrHrH
rHrHrHHHrHfHrHrHrHrHHrHrHrHrH
rHrHrHrHrH
rHrHrHrHrHrHfHCNrHrH
OOOOOOOOOO
(U
-U
H
cn
oooooooooooooooo
oooooooooooooooo
OOOOrHrHrHCNCN^T^^rrHCNCNCN
CNCNCNCNCNCNCNCNCNCNCNCNCNCNCNCN
i O
I 25
66
------- |