ALTERNATE FORMS
OF THE
AMBIENT AIR QUALITY STANDARD
FOR PHOTOCHEMICAL OXIDANTS
May 1978
Staff Summary Paper
Strategies and Air Standards Division
Office of Air Quality Planning and Standards
U.S. Environmental Protection Agency
Research Triangle Park. North Carolina 27711
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ALTERNATE FORMS OF THE AMBIENT AIR QUALITY STANDARD FOR PHOTOCHEMJ^^DANTS
Summary
The present review of the primary and secondary ambient air quality
standard for photochemical oxidants includes an examination of the overall
form of the standard as well as a consideration of the appropriateness of
the concentration level and averaging time. The present form appears to
be simple and readily understood. By using the annual second highest
hourly average, an apparently simple means is available for determining
compliance. However, analysis shows that there are problems of sufficient
importance that alternate forms must be given serious consideration.
Because the annual second highest concentration is a single measurement
a large measurement error may occur and missing monitoring data may cause
the true second highest value to be missed. Further analysis reveals a
more fundamental difficulty which has not been as generally recognized.
Photochemical oxidant concentrations are subject to random changes in weather
and in daily precursor emission levels. Therefore, the average concentration
observed in any hour has a random aspect not recognized in the present form.
The standard concentration of 0.08 ppm is allowed to be exceeded once annually
but never more than once. However, if at a given level of precursor emissions
a certain meteorological condition can occur which will lead to oxidant
concentrations above the standard once in a year, then there is a definite
probability that these same conditions can occur two or more times in a year
and, therefore, lead to multiple violations in some years. The only way to
assure compliance with the present standard over all years in a given area
is to control precursor emission levels to the point that 0.08 ppm is never
exceeded, which is not a feasible expectation.
Thus, the current standard is more severe than apparent from first
inspection. As discussed in the report its seeming simplicity can lead to
inconsistent treatment from one AQCR to the next in deciding both compliance
and degree of emission control required. The report recommends that the
following form be adopted:
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X^ yg/m3 hourly average concentration with expected (average)
number of exceedances per year less than or equal to one. •
*"v
This form represents the least possible departure from the present form
while fully taking into account the random statistical nature of factors
influencing oxidant concentrations. The recommended form allows for the
occasional occurrence in some years when more than one hourly average con-
centration will be above the standard (the number of such years is set by
the choice of the expected number of exceedances per year); it also provides
the basis for a consistent approach to decisions on compliance and degree of
emission control required. Use of the recommended statistical form requires
the use of a substantial portion of the air monitoring data collected in
a given year. Thus the statistical estimates that are needed to determine
compliance and degree of control are much less subject to measurement error
and statistical variation than the annual second highest concentration now
used.
Introduction
The present primary and secondary ambient air quality standards for
photochemical oxidants are both the same and may be stated as follows:
160 pg/cu. meter (0.08 ppm) maximum hourly average con-
centration not to be exceeded more than once per year.
The review of the oxidant standard now under way will not only include
an examination of the appropriateness of the concentration level and averaging
time based on our present knowledge of health and welfare effects but will
also consider the appropriateness of the overall form (expression) of the
standard. The form of the standard could be expressed in many ways, examples
of which are: the mean (geometric and arithmetic); expected value; percentile;
and some level never to be exceeded. However, since health effects are of
primary importance, the form must be compatible with current medical opinion
that adverse health effects occur when oxidant levels exceed certain levels
for short periods of time. Thus, any form of the standard selected must be
directed at minimizing excursions above the designated standard level.
While health and welfare effects are the primary considerations in
choosing the most appropriate form of the standard it is also important that
the form provide an adequate and clear basis for defining the overall quality
of ambient air it is desired to achieve. We, therefore, would want the form
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to be such that it: 1. adequately defines what must be measured to determine
compliance and measurements which can be made with the needed accuracy; 2.
provides clear, unambiguous criteria for determining whether an area is or
is not in compliance; and 3. provides a clear, unambiguous definition of
the air quality it is desired to achieve to serve as a target for the develop-
ment and verification of control strategies. This report examines the form
of the standard from this point of view and will provide a proper basis for
examining the impact of health and welfare effects on the form.
The Present Form of the Oxidant Standard
The current form of the oxidant standard has several advantageous features:
1. It seems to be simple and readily understood. 2. It reflects medical
opinion that protection should be provided against the highest levels likely
to be encountered in an area when brought under control. 3. It provides in
the annual second highest hourly average concentration, a simple, clear indi-
cation of the measurement to be made and a clear criterion for determining
compliance. However, as the analysis in this section will show, there are
problems with the current form which are of sufficient magnitude that alter-
native forms should be given serious consideration.
Two aspects of the present form of the standard have been criticized by
workers in the field and are brought out in the recent petition of the
American Petroleum Institute (API) for review and revision by EPA of the
oxidant standard. The two concerns stem primarily from the fact that the
standard focuses on a single measurement for determining compliance, the
annual second highest hourly average concentration. The petition points
out that Air Quality Control Regions (AQCR) differ widely in the completeness
of their monitoring data over a given year. Because of missing data the
probability of capturing the actual second highest concentration can vary
from as little as 1% to as high as 99% from one AQCR to the next, depending
upon the data retrieval rate. This can result in underestimation of control
levels needed on man-made emissions. In some areas a more serious result
would be the erroneous judgment that the areas are in compliance with the
standard when, in fact, they are not.
The second concern is that the second high is a single measurement and,
therefore, bears the full brunt of experimental error. The petition suggests
this error may be almost equal in magnitude to the second high itself at the
0.08 ppm level.
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The effects of these problems can be reduced by improved monitoring
equipment and procedures. They can also be reduced substantially by changing
to a form which requires the use of more of the available data to develop a
more "robust" statistic, that is, a statistic whose estimates have lower
variance or are less subject to random error. Examples might be: the expected
(or average) value of the second high, the expected (or average) number of
exceedances of the standard, the arithmetic mean of the hourly averages, or
the geometric mean.
Further consideration of the form of the present standard, however,
shows that it has a more fundamental problem than those discussed in the
proceeding paragraphs and one which has not been generally recognized. The
present form does not provide a clear, unambiguous definition of the air
quality it is desired to achieve, and, therefore, does not provide a clear
target for the development of control strategies and their verification.
The present standard appears to establish as a target a quality of ambient
air over an AQCR such that one hourly average concentration in a given year
may exceed 0.08 ppm but never more than one. This is a situation, however,
which does not appear to be feasible. There is no level of control of oxidant
precursor emissions which will yield a situation in which the standard can
be exceeded once in some years but never more than once. Hourly average
oxidant concentrations are subject to the random changes in weather and
in emission levels. If at a given level of precursor emission control a
certain meteorological condition can occur which will lead to oxidant con-
centrations above the standard once in a year, then there is a finite
probability that these same conditions can occur two or more times in a
year and, therefore, lead to multiple violations in some years. In this
situation the area will comply with the standard some years and be out of
compliance in other years.
For example, if under a given level of emissions the probability any
given hourly average oxidant concentration will exceed 0.08 ppm is 1 in
8760 (the number of hours in one year), the percentage of years 0.08 ppm
would be exceeded a given number of times is shown in Table 1. In 74 years
out of 100, the AQCR in question would be in compliance with the standard
(either one or zero exceedances), whereas in 26 years out of 100 it would
not be. On the average, the AQCR would violate the standard about once every
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TABLE 1
VIOLATIONS PER YEAR WHEN STANDARD EXCEEDED AN AVERAGE OF ONCE PER YEAR
NUMBER OF TIMES
STANDARD EXCEEDED
IN A GIVEN YEAR
0
1
2
3
>4
PERCENT OF YEARS
OCCURRING*
37
37
18
6
2
CUMULATIVE
PERCENT
OCCURRENCE
37
74
92
98
100
*ASSUMES INDEPENDENCE OF HOURLY AVERAGES AND UNIFORM PROBABILITY OVER
ALL HOURS
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four years. The average number of exceedances per year over a number of
years is one in this example (see Note #1). Although the above numbers
are not fully applicable to real situations, owing to seasonal and diurnal
variations and interdependence of hourly averages, they do illustrate the
principle involved.
The only way to assure compliance with the present standard over all
years in a given area is to control emission levels to the point that
0.08 ppm is never exceeded. Thus, both from the point of view of compliance
and emission control, the present standard is fully equivalent to a standard
in which the hourly average concentration 0.08 ppm is never to be exceeded.
The present standard requires, therefore, a greater level of control than is
apparent from superficial inspection of its form. It seems unlikely that
this situation was intended by its formulators. This is the reason for saying
the current form seems to be simple and easily understood when its advantages
were listed at the beginning of this section. The statement of the standard
is straightforward, but its true meaning is understood only when the stochastic
or random aspect of oxidant concentrations is appreciated.
From the preceeding arguments it is clear that the present form has
difficulties of a fundamental nature. The end state of overall air quality
the standard appears to define is not realizable. In fact, the standard can
only be satisfied by an end state in which exceedances never occur.
This latter point has not been fully recognized in establishing guide-
lines for developing emission control strategies for meeting the standard.
For example, if, for the purposes of this discussion, it is assumed the
current Part 51 Guidelines for calculating control levels needed for com-
pliance give correct results, the level of overall air quality that would
be attained in a given area is such that the area could be in violation
(more than one exceedance per year) 50% of the succeeding years. The present
practice is to apply Appendix J (or Proportional Rollback) to the second
highest hourly average observed in a base year to calculate the degree of
control needed to make 0.08 ppm the second highest value. However, because
the hourly oxidant values are subject to the random behavior in weather patterns
and daily emissions, the observed second highest values will tend to vary
from one year to the next. The potential impact of this variation on the
calculation of required control levels is shown in Figure 1.
Here it is assumed that the AQCR under consideration has an air quality
such that the most probable value of the second highest concentration is 0.18
ppm. The observed second highs in any year around this most probable value
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FIGURE 1
EFFECT OF STOCHASTIC BEHAVIOR OF SECOND HIGH CONCENTRATION ON APPARENT
AMOUNT OF CONTROL NEEDED AND VIOLATIONS OF STANDARD AT CONTROL LEVEL
I
Amount Control for No Violations '
Distribution '
of second high
concentrations
0.08
0.18
0.08
0.18
note: Shaded area represents fraction of years standard violated
whpn tarnof rontrol 1
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are represented by the probability density function centered about 0.18 ppm.
The distribution functions shown are purely hypothetical and only serve
to illustrate the stochastic (random) behavior of the annual second high.
The top illustration in the figure shows the situation in which data for
only one year are available and the most probable value of the second
high was observed in this base year. The line marked "apparent control
needed" divided by 0.18 ppm (the observed second high) gives the amount of
control required by the proportional rollback method. If it is assumed that
this level of control shifts the distribution in a manner such that the
most probable second high would be at 0.08 ppm, then it is seen that in half
the years the second high will be above 0.08 ppm and the standard will be
violated half the years. This would be approximately the situation for
most AQCR's having this distribution of second high values.
The middle illustration shows the outcome if the observed second high
was on the high side of the distribution. In this case a higher
level of control would be calculated. But there still would be some years
in which the standard is violated. In the bottom illustration the observed
second high is below the most probable value. A lower level of control is
calculated and the resulting air quality will lead to violations in excess
of 50% of the years. Thus, the current form, by focusing on the second
high hourly average, has led to recommended procedures that are not likely
to lead to compliance and, furthermore, can give rise to unequal treatment
of AQCR's having the same air quality.
The top illustration in Figure 1 also shows the degree of control that
would be required to bring the AQCR into full compliance, that is the over-
all air quality in which no exceedances of 0.08 ppm occur. This is, as seen,
a higher level of control than would be required through use of the observed
second high in any one year.
The situation depicted in Figure 1 is most directly applicable to the
situation in the early 1970's when implementation plans were first being
formulated. At this time the base year was given as 1971 and, generally,
there was little data from other years to modify the second highest value.
The most recent guidelines (Guideline Series, OAQPS NO 1.2-047, January 1977)
allow the use of the second high concentration from one year if data from
other years is not available, but recommends using the highest of the second
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high values from three ormone years when available. When applied, this
procedure tends to favor the case shown in the middle illustration of
Figure 1. Even in this case there will tend to be some years in violation
and, overall, the effect on different AQCR's will be uneven. Differences
will be greatest when AQCR's use different numbers of years to determine
the second high. Those which use the smallest numbers of years will tend
to have relatively more lenient control requirements.
Other approaches have been suggested which may provide more uniform
treatment. R. Larsen has suggested the (average) annual maximum hourly
average could be used for calculating the required degree of control. But
this measure does not flow as naturally from the standard as does the
second high, and there will be some years in which the-standard will be
violated. Larsen estimates 1 in 8 years will exceed the standard more than once
if the annual expected maximum is used as a "design value" to calculate required
control. The method, therefore, does not lead to an overall air quality which
will fully meet the implicit requirements of the standard.
Alternative Forms of the Oxidant Standard
From the previous discussion it is clearly worthwhile, in reviewing
the potential impact of the current understanding of health and welfare
effects on the form of the standard, to consider alternatives which avoid
the problems inherent in the current form. To provide a clear, unambiguous
definition of the air quality which will provide the desired protection of
the public health and welfare it will be necessary that the form take into
account the stochastic nature of ambient concentrations of oxidant. Forms
meeting this requirement will generally define a statistic that is estimated
from a significant-fraction of the total data base. The measured statistic
will be more robust than the second high and, therefore, not as sensitive to
missing data and measurement error.
An exception is the nonstochastic form: 0.08 ppm hourly average never
to be exceeded. This form provides a well defined end state and a simple
test of compliance and is, therefore, acceptable in these respects. However,
the maximum possible ozone level in an AQCR is infrequently observed (the
maximum value observed in a given year would typically be below this value),
and would need to be estimated in some way in order to use currently available
methods for calculating degree of control needed. . •
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Table 2 lists several alternate statistical forms each of which
unambiguously defines a desired end state of overall air quality. The
forms shown were chosen to parallel the present standard in limiting
exposure to extremal values of the hourly average oxidant concentration.
The first five forms do this directly, the last two indirectly. There
should be no difficulty in defining the appropriate statistical forms
should medical opinion change concerning the type of protection needed.
The first alternative departs least from the present form. By
placing the number of exceedances on an expected or average value basis
it avoids the pitfalls of the present standard. Under the statistical form,
years in which the 0.08 ppm hourly average was exceeded more than once
would not be considered in violation of the standard unless the estimate
of the expected number of exceedances was greater than one. Setting the
expected exceedances at one is roughly equivalent to the situation depicted
in Table 1 (see Note #1). We would, therefore, expect violations of the
present form (more than one exceedance per year) to occur on the average of
approximately once in four years if the alternate were adopted. Note also
from Table 1 that three or more violations in a year would occur an average
of approximately only once in every 12 years.
If it is considered that the excursions above 0.08 ppm would be too
frequent with the expected number of exceedances set at once per year, the
number can be set at a more stringent value such as 1 in 5 years. Thus
EPA has two parameters, the concentration level and expected number of exceedances,
which can be adjusted to obtain whatever level of protection is needed.
At the present time this general form is recommended over the others
in the table because it represents the least departure from the present form,
is easy to understand, and the expected number of exceedances can be readily
estimated from the distribution of hourly averages over one or more years
(see Note #2).
An example of how health considerations enter into the form of the
standard is seen in the following variation of the recommended form:
0.08 ppm daily maximum hourly average with expected exceedances per year
less than or equal to one. This form would be preferred if medical opinion
shifted from the current emphasis on hourly average concentrations to
concern about maximum daily hourly average concentrations.
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TABLE 2
ALTERNATE STATISTICAL FORMS OF OXIDANT STANDARD
NI
• 0.08 ppm HOURLY AVERAGE WITH EXPECTED NUMBER OF EXCEEDANCES PER
YEAR LESS THAN OR EQUAL TO ONE.
• 0.08 ppm HOURLY AVERAGE WITH 90% PROBABILITY (CONFIDENCE) THAT THIS
CONCENTRATION WILL NOT BE EXCEEDED IN ONE YEAR.
e 0.08 ppm HOURLY AVERAGE NOT TO BE EXCEEDED ON THE AVERAGE BY MORE
THAN 0.01% OF THE HOURS IN ONE YEAR.
• 0.08 ppm ANNUAL EXPECTED MAXIMUM HOURLY AVERAGE.
• 0.08 ppm ANNUAL EXPECTED SECOND HIGHEST HOURLY AVERAGE
t 0.0125 ppm ANNUAL AVERAGE.
0 0.0100 ppm ANNUAL GEOMETRIC MEAN.
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The second form in Table 2 also has two adjustable parameters and
has the desirable feature of directly displaying the level of confidence
that the given concentration level will not be exceeded in a given year.
However, the confidence level is not readily deduced from ambient air
data. At the present time, it would be necessary to use existing equations
developed from extreme value and order statistics which assume no inter-
dependence of the hourly averages. Since these assumptions are not correct
for hourly average oxidant concentrations the use of this form, or any
form requiring these assumptions, is not recommended at the present time.
If independence of hourly averages is assumed, a confidence level of about
37% would provide the same air quality as the first alternate form (see
Note #3).
The third form is essentially equivalent to the first but refers
directly to the distribution of hourly averages. Notice that in order
to avoid the problem of the present form it is necessary to talk about
average (or expected) percentage of exceedances. This form is considered
less desirable than the first alternate because using a percentage figure
forces the use of a very small number, such as the 0.01% in the illustration.
There will be less intuitive grasp of the effect of this number of years
(the first form). The third and the first forms, as stated in the table,
give roughly equivalent protection (see Note #4).
The next two forms each involve a single parameter and thus provide
less flexibility than the preceeding forms. As in the case of the second
form in the table, they also require the assumption of independence of hourly
average concentrations if their values are to be estimated from hourly
average ambient air data. The use of an expected or average value results
in two distinct air quality end states for these two forms. Based on the
discussion in the last section, an AQCR meeting the expected maximum value
standard would (assuming independence of hourly averages) violate the
present standard an average of 1 in 8 years, while an AQCR meeting the
expected second high form would violate the present standard an average
of every other year. If the two forms were based on observed maximum
or second high values in a given year, the only way either standard could
be met consistently year after year would be to achieve an air quality where
0.08 ppm would never be exceeded. This is, of course, the problem with the
present standard. In fact, the form 0.08 ppm not to be exceeded by the
second highest hourly average in a given year is equivalent to the present
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form of the standard.
The final two forms are included to bring attention to the suggestion
which has been made occasionally that mean values be used in the oxidant
standard in place of extremal values because the former use all the avail-
able hourly average data. They are, therefore, much more robust than
forms based on extremal values. The presumption is that there exists a
correlation between the extremal values and mean values of hourly averages.
Supporting data has been advanced to show this to be the case. While good
correlations may exist, it would be preferable that the standard reflect
the type of protection desired from health and welfare effects. Present
medical opinion is that protection should be directed against the excur-
sions in oxidant concentrations rather than at maintaining average levels
below some value. Thus the standard should be based on minimizing excur-
sions of the highest ozone concentrations above certain levels. The use
of standards based on extremal values would not prevent the use of cor-
relations between average values and extremal values as a means of developing
control strategies or confirming compliance with a standard based on extremal
values.
Application of Statistical Forms
An understanding of how alternate statistical forms such as the first
form in Table 1 might be used in practice can be obtained from examining
three potential problems with their use which have been suggested. The
first is that year to year variations in weather and emission levels will
make it difficult to obtain a stable estimate of the statistic. This
difficulty applies to any statistic whose yearly value must be estimated.
The second highest oxidant value observed in a given year is, in fact,
more subject to this source of variance than the alternate statistical
measures given in Table 2. For example, even if general weather patterns
and emission levels did not shift from year to year, the observed second
high would change from year to year due to fluctuations in weather and
emissions within the year to year patterns. There would be an additional
source of variation arising from lack of a complete data set and the effect
of random experimental error on a single observation.
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In contrast, if the first form in Table 2 were adopted, the overall
air quality for a given AQCR could be characterized by that hourly average
concentration level for which the expected number of exceedances was one.
It would not be correct to estimate this statistic by finding the second
highest oxidant value for that year. Ambient air data would be plotted on
a suitable probability paper and a "best line" fitted to the data (see
Note #2). The concentration above which 1/8760 of the data for one year
lie is read from the line. The expected exceedance of this concentration
is once per year. The concentration corresponding to an expected exceedance
of one determined by the above procedure would be expected to show relatively
small changes from year to year unless there were significant shifts in
overall weather and emission patterns.
The present guidelines use year to year data to define a highest
second high for a period of several years. This highest second high is
also subject to statistical variance as well as trends over time in weather
and emission levels. It would be possible to apply this same procedure to
the forms in Table 2. For example, the highest concentration corresponding
to an expected exceedance of 1 could be determined from such concentrations
for several consecutive years. In reducing the effects of weather and emissions
variations within any given year by using more of the available data, the
estimated oxidant concentration (expressed in any of the forms in Table 2)
would be more reliable and statistically valid because within year variations
would be adjusted out. Subsequently, longer-term (year to year) changes in
weather and emissions levels also could be separated out of the statistic.
The improved statistical forms would therefore allow more accurate tracking of
progress in improving air quality.
The second potential problem suggested is that the statistical forms in
Table 2 do not provide a positive indicator that an AQCR is out of compliance.
This consideration is only potentially applicable to situations in which an
AQCR is close to compliance since the statistical forms would easily detect
regions significantly out of compliance. Before considering the statistical
forms it will be worthwhile to examine the limitations of the trigger provided
by the second high concentration. First, the absence of an incomplete data
base and experimental error may cause the second high value to indicate
compliance when an AQCR is not in compliance. Second, experimental error
can also lead to a false indication that the AQCR is in compliance. These
problems are reduced with the more robust measures provided by the statistical
forms.
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Probably more important is the year to year variation in the second
high due to "within year" and "year to year" variations in weather and
emissions. As discussed in earlier sections, even after emission levels
have been brought to the levels indicated necessary by the second high
value in a base year or over several years, the AQCR will continue to
violate the standard in some years. If further control action is initiated
after each violation (two exceedances in a year), violations will continue
to occur after each new control action until finally a level of control is
reached in which the 0.08 ppm level is never exceeded. This would be overkill
in terms of the air quality which was desired but would be the inevitable
consequence of triggering control action every time the 0.08 ppm was exceeded
twice in one year.
In actual practice this is not likely to happen. If the control levels
which have been calculated from the base year(s) have been reached and a
given year is mildly in violation (say three exceedances), control officials
recognizing the variability of oxidant concentrations likely will wait to
view the number of violations occurringnext year or over several years
before requiring further control. If these years also show violations
they would probably impose further controls. If violations occurred rela-
tively infrequently in succeeding years the officials would probably be
disinclined to act further since a substantial amount of additional control
might be required to totally eliminate violations. Thus, the positive
trigger provided by the present form would probably not be fully acted on
by knowledgeable control officials. Such discretion on the part of control
officials would not be required with the new form of the standard which would
correctly allow for occasional excursion above the standard.
With regard to the alternative statistical forms, it is possible to
make these into as positive triggers as desired. The statistic in each
of these forms can be estimated solely from the hourly average data within
a given year using the approaches discussed in preceeding paragraphs. If
the estimate indicates a violation,that year could be established as a new
base year and further controls imposed.
However, even though these estimates are less subject to variation
than the observed second high it would still be unwise to use the yearly
'estimates of these statistics alone as positive triggers. Since the yearly
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estimates are only estimates of the real statistic corresponding to the
overall air quality for a given level of control, it would be better to
establish confidence intervals around these estimates. If a predetermined
confidence level is exceeded, further control action could be taken.
These procedures would only be needed when the region was close to com-
pliance. At this point, each year of additional data would build increased
confidence in the estimate of the compliance statistic and provide a more
reliable test of departure from compliance. There is, therefore, no
inherent problem with the alternate statistical forms as triggering mechan-
isms for control action.
The third potential problem area is concerned with how to handle an
AQCR with multiple sampling sites. The most stringent method would be to
pool all hourly averages from all sites in determining compliance by whatever
form chosen. In this case an area with several monitors experiencing an
oxidant episode spread relatively uniform over the region would almost
certainly be in violation. Since it is the same episode over the area this
procedure seems rather strict. In the case of the third, fourth, and fifth
forms in Table 2 there would be no convenient way to apply this procedure.
With these forms, data from the different monitoring sites would in effect
be simply averaged.
The second alternate would be to pool all the data from all sites
in determining the probability distribution but calculate the statistics
on the basis of 8760 observations (the hours in one year). This would put
all the forms in the table on the same footing. But it would also dilute
the effect of the sites experiencing the highest ozone levels during an
episode.
A third alternate would be to apply the standard to each site separately.
In this way if the data from any one site in the area is in violation the
whole AQCR would be considered in violation. This alternate is intermediate
in effect between the two above methods. It appears to combine the positive
features of each and, therefore, seems the most reasonable. This alternate
is recommended for use with the present standard in the most recent air
quality standards guideline. (Guidelines for the Interpretation of Air
Quality Standards, EPA-OAQPS-HDAD, February, 1977).
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Other concerns with statistical forms which have been expressed are
that they lack the simplicity and directness of the present form and, there-
fore, may not be as readily understood by the public and may present problems
in legal proceedings. However, it is clear that the form of the present
standard is flawed. If the present standard is applied as stated, an AQCR
will only attain full compliance when conditions are such that the standard
concentration will never be exceeded. This, as was shown, is a direct
consequence of the variable or random aspect of hourly average oxidant con-
centrations. This stochastic feature of oxidant concentrations can only be
taken into account by statistical forms such as those shown in Table 2.
These forms are also based on more robust statistics than the second high
and provide clear, unambiguous targets for compliance and the development
and verification of control strategies.
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Notes
1. Probability theory shows that if the probability that a certain
event will occur in a given trial is p then the probability, Pm,
that the event will occur m times in n repeated independent trials
is:
_ n« m /, \n-rn
This equation is knov/n as the binomial distribution. If it is assumed
that p(C) is the probability that the average concentration for any
hour of the year is greater than or equal the hourly average concen-
tration C (assumption of independence of hours), the probabilities
of 0, 1, 2, 3 exceedances of a given concentration in the 8760 hour
in a year can be calculated.
For example:
For no exceedances per year:
8760 i 0 1 8760
p = _ / _ !_wi __ —\
0 0! 8760! 18760M 8760;
8760
J
8760
For one exceedance per year:
P = . ,_[_U1 1 .8759
1 1! (8760 - I)! 18760M' " 8760;
1 ,8759
8760) = °'3679-
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For two exceedances per year:
8760' 1 2 1 8758
_ _ O/OU. / I \ /-I _J \
2 r. (8760-2)1 V8760; V " 8760;
8759 1 8758
(1 - ^TTT) = 0.1840.
2 x 8760
The expected or average number of exceedances per year is obtained
by sunning each number of exceedances per year weighted by its
probability of occurance. Referring to Table 1,
Expected exceedances per year = 0.37 x 0 + 0.37 x 1 + 0.18 x 2
+ 0.06 x 3 + 0.02 x 4 + etc.
Thus the concentration which corresponds to p(C) = 1/8760 is also
the concentration with an expected exceedances/year of one.
2. The cummulative distribution of hourly averages over one or more years
is defined as a function f(C) where f(C) is the fraction of hourly
averages which exceeds the concentration C. This function can be
estimated from a collection of one or more years of hourly average
concentration data by standard plotting techniques.
If the standard concentration level is 0.08 ppm then the relative
frequency f(0.08) multiplied by 8760 is the average or expected
number of exceedances per year of the standard concentration. This
follows directly from the definition of f(C). This frequency, f(C),
is read from the "best fit" line drawn through a plot of hourly
average concentration vs. frequency data.
Another useful statistic is the concentration which corresponds
to exceedances/year of one. In this case the concentration corres-
ponding to f(C) = 1/8760 is read from the best fit line.
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Recent studies suggest that the log normal distribution function
does not give a good fit to the distribution of hourly average oxidant
concentrations, but the Weibull distribution does. In any case, if a
statistical form of the standard is adopted, detailed guidance will
need to be given on how to treat the air monitoring data to obtain
the needed statistics.
3. The probability that a given concentration level will not be exceeded
in a given year corresponds to PQ of the binomial distribution given
under Note 1. As shown, for p(C) = 1/8760 the expected exceedances/
year is one (corresponding to the first alternate form of the standard
in Table 1), and for p(C) = 1/8760, PQ = 0.37 (corresponding to the
second form of the standard in Table 1).
Note that calculation of P assumes independence of hourly average
concentrations. At the present time there are no formulas for exactly
calculating Pfi for the nonindependence case,
4. By the definitions in Note #2, 100 x f(C) is the per cent frequency
to be used in the third alternate form. f(C) = 1/8760 for the concen-
tration with an expected exceedances/year of one, and, therefore,
1/8760 = 0.0114% = approx. 0.01%.
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