-------
TABLE 5-2. Number of sites classified as low, medium, or high probability
of nonattainment of three one-year 24-hour PM10 standards using a national
cumulative distribution function of PM15/TSP ratios compared with
probability classifications from climate and region distributions.
Standard
Climate cdfs
Low Med High
Low
75 yg/m3 Med
High
46
9
0
1
74
3
0
6
31
55 78 37
47
89
34
170
EPA Region cdfs
Low Med High
41
8
0
6
77
9
0
4
25
49 92 29
47
89
34
170
Low
100 yg/m3 Med
High
86
6
0
6
59
5
0
1
5
94 70 6
94
66
10
170
79
7
0
15
58
5
0
1
5
86 78 6
94
66
10
170
150 yg/nr
Low
Med
High
150
6
0
1
13
0
0
0
0
156 14 0
151
19
0
170
145
3
0
6
16
0
0
0
0
86 78 6
151
19
0
170
8506** 2
65
-------
ratio and a PM10 concentration were available. At all three standards,
there are no sites for which the use of the national distribution results
in a high probability of nonattainment and use of one of the geographical
distributions results in a low probability of nonattainment, or vice-
o
vera. For the 75 and 100 ug/m standards, use of the national and geo-
graphic distributions results in different probability classifications for
about 11 to 16 percent of the site-years; in these cases more monitoring
is dictated by the use of one distribution than the other. For the 150
yg/m standard, which is in the range of the standards being considered,
classification differences occur in only about 5 percent of the site-
years. At even higher standards it seems likely that the percentage of
sites with different classifications would be even smaller because the
vast majority of the sites will be classified as having a low probability
of nonattainment.
One notable difference between Tables 5-1 and 5-2 is that, for any stan-
dard, the percentage of sites classified as having a high probability of
nonattainment is greater when using the PM10/TSP distribution (Table 5-1)
than when using the PM15/TSP distribution (Table 5-2). In fact, in Table
5-2 no sites are classified as having a high probability of nonattainment
o
of the 150 ug/nr 24-hour standard, while in Table 5-1 about 4 percent of
the sites are so classified. This discrepancy is due to the difference in
the sites used to construct the two ratio distributions. Those sites with
both PM10 and TSP data have significantly higher TSP concentrations than
those sites with both PM15 and TSP data. In addition, ratios correspond-
ing to the lower percentage points (i.e., below the median) of the
PM10/TSP distribution are lower than the corresponding ratios from the
PM15/TSP distribution multiplied by 0.85, so that a given TSP concentra-
tion results in a higher probability of exceedance using the PM10/TSP
We considered multiplying the PM15 concentrations by 0.85 to estimate
PM10 concentrations and then determine attainment status. However,
because of the variability in PM10/PM15 ratios, we considered this
procedure invalid in this context.
85061+p 6
66
-------
distribution than with the PM15/TSP distribution. This topic will be
discussed further in Section 7.
CROSS-VALIDATION APPLIED TO ANNUAL AVERAGE RATIO DISTRIBUTIONS
The range of concentrations proposed for the annual average primary PM10
standard is 50 to 65 yg/m . Because so few of the site-years in the IP
network data base exceed even 50 yg/m , we have chosen to perform the
cross-validation analysis assuming annual average PM10 standards of 30,
•3
35, and 50 yg/m , a range that is wide enough 1
results depend upon the level of the standard.
•3
35, and 50 yg/m , a range that is wide enough to determine whether the
Figures 5-5 and 5-6 show P-P plots of nonattainment probabilities for an
annual average 35 yg/irr standard derived from a national distribution and
from climatic distributions of PM10/TSP and PM15/TSP, respectively. As in
the 24-hour P-P plots, each plotted point represents one site-year. In
both plots we see that sites in the West Coast and arid climates have a
lower probability of nonattainment under the climate-specific distribu-
tions than under the national distribution, while the converse is true for
sites in the third climatic region; this is the same pattern as in Figures
5-1 and 5-2 for the 24-hour standard of 100 yg/m. This is because the
percentiles of the West Coast and arid distributions are always less than
those of the national and the third climatic distribution; this can be
seen in the cdf comparison plots of Figures 4-3 and 4-6 for the 24-hour
and annual average ratios, respectively.
In Table 5-3 the probability of nonattainment (low, medium, and high, as
described above) resulting from the use of a national PM10/TSP distribu-
tion and climatic distributions are compared to the actual attainment
status of a site-year for each of the three standards considered. Actual
attainment status was determined by using the sample annual average PM10
concentration for the site-year as an estimate for the true annual aver-
age; only site-years with at least 10 days of sampling both PM10 and TSP
are considered. For the most severe misclassifications—nonattainment
8506<+r 6
67
-------
uoiq.nqijjs.ia dSl/OIWd IBUOLJBN B
(juaDwtad) ^{.
68
-------
< < _ —X
Linquis.LQ dSl/9IWd
69
-------
TABLE 5-3. Number of sites classified as low, medium, or high probability
of nonattainment of three annual PM10 standards compared with actual
attainment status (pass. * attainment, fail = nonattainment): comparison
between national and climate PM10/TSP cumulative distribution functions.
Standard
30 yg/nr
National cdf
Low Med High
Pass
Fail
3
1
8
18
0
9
4 26 9
11
28
39
Climate cdf's
Low Med High
6
1
5
19
0
8
7 24 8
11
28
39
35 yg/nr
Pass
Fail
8
1
8
16
1
5
9 24 6
17
22
39
10
1
6
16
1
5
11 22 6
17
22
39
50 ug/nr
Pass
Fail
26
0
7
5
0
1
26 12 1
33
6
39
27
1
6
2
0
3
28 8 3
33
6
39
65064 2
70
-------
sites classified as having a low probability of nonattainment or attain-
ment sites classified as having a high probability of nonattainment--there
is almost no difference between using the national and the climatic
PM10/TSP distributions. The only difference is at the 50 ug/nr* standard,
where the national distribution performs slightly better. In comparing
site-years in which the standard was not attained but the probability of
nonattainment was declared not to be high (so that not enough monitoring
would be required), there is almost no difference between the misclassi-
cation rates based on the national and the climatic distributions. The
climatic distributions perform slightly better, however, in avoiding the
misclassification of attainment sites deemed medium or high probability of
nonattainment.
The probabilities of nonattainment based on a national and separate cli-
matic PM15/TSP distributions are compared in Table 5-4. There is no evi-
dence that the use of climatic distributions improves the classification
of sites. As with the 24-hour standard, there is no site-year for which
the national distribution predicts a high nonattainment probability while
the climatic distribution predicts a low probability of nonattainment, or
vice versa. The percentage of site-years in which the probability classi-
fications are different is only about 5 percent for all three standards.
In most of these cases the nonattainment probability classification
predicted by the national distribution is higher than that predicted by
the climatic distributions, i.e., the national distribution dictates more
monitoring for these sites than does the climatic distribution.
8506HT 6
71
-------
TABLE 5-4. Number of sites classified as low, medium, or high
probability of nonattainment of three annual PM10 standards using a
national cumulative distribution function of PM15/TSP ratios versus
probability classifications from climate distributions.
Standard
30 yg/nr
Low
Med
High
Climate cdfs
Low Med High
29
1
0
0
78
4
0
2
19
30 82 21
29
81
23
133
35 ug/m3
Low
Med
High
49
6
0
0
70
1
0
0
7
55 71 7
49
76
8
133
50 ug/rrr
Low
Med
High
115
5
0
0
13
0
0
0
0
120 13 0
155
18
0
133
72
85061+ 2
-------
6 ESTIMATING DESIGN VALUES USING PM10/TSP RATIOS
Annual and 24-hour PM10 design values can be predicted by using the
observed PM10/TSP ratio distributions. Annual average design values are
simple to predict, but 24-hour design value estimates require repeated
calculations. The methods for predicting design values will be summarized
below, but for a more complete explanation and examples the reader is
referred to Appendix B of the PM10 SIP Development Guideline (EPA, 1984).
DESIGN VALUES ESTIMATED FROM TSP DATA AND RATIO DISTRIBUTIONS
Annual average PM10 design values can be estimated by multiplying the
observed annual average TSP concentrations by a factor which represents
the distribution of the PM10/TSP ratios of annual averages. The factor
can be either the mean of the distribution or the median; we prefer the
latter because it is less influenced by outliers. As can be seen in
Tables 3-2 and 3-4, the medians of the annual average PM10/TSP distribu-
tions are 0.49 and 0.47 for all annual ratios and for those based on high
annual average TSP concentrations, respectively.
The 24-hour design value is that PM10 concentration which has an expected
exceedance rate of once per year. This value can be estimated from the
distribution of 24-hour PM10/TSP values by following these steps:
(1) Assume a design value, e.g., the level of the standard
(2) Using the 24-hour PM10/TSP ratio distribution, calculate the
probability of exceedance for each day for which there is a
valid TSP concentration.
73
-------
(3) Calculate the expected number of eXceedances by summing the
exceedance probabilities calculated in Step 2. Adjust for miss-
ing sampling days by multiplying by the ratio of the number of
days in the year divided by the number of sampling days with
valid TSP concentrations (this assumes that the exceedance rate
in the unsampled days is the same as the exceedance rate in the
sampled days).
(4) If the expected number of exceedances calculated in Step 3 is
equal to one, then the design value is found. If it is less
than one, then go back to Step 2 with a lower design value. If
it is greater than one, then go back to Step 2 with a higher
design value.
A computer program which performs the required iterative calculations is
available from EPA (Freas, 1984); this program was modified for the pre-
sent study to consider a one-year attainment period for the 24-hour stan-
dard rather than a three-year period.
COMPARISON WITH DESIGN VALUES ESTIMATED FROM PM10 DATA
Annual and 24-hour PM10 design values were calculated for 24 site-years
for which 35 or more PM10/TSP ratios were available. The PM10 design
values estimated from the TSP data for these site-years are listed in
Table 6-1 along with design values calculated from the PM10 data for these
site years. Annual design values were calculated from the PM10 data
simply as the observed annual average.
We also looked at linear and loglinear regressions of annual PM10
average on annual TSP average. The intercepts in the regression were
insignificant, and the slopes were approximately the same as the 0.47
and 0.49 factors from the median of the distribution of annual
average PM10/TSP.
74
-------
TABLE 6-1. Estimation of PM10 design values from PM10 data and
from PM10/TSP ratio distributions.
SITECODE
2
11
27
27
46
60
88
93
94
95
96
98
1 17
118
123
128
128
129
129
144
149
150
156
158
YEAR
83
82
82
83
83
83
83
83
83
82
83
83
83
83
83
82
83
82
83
83
83
83
83
83
NSAMP DV24TAIL DV24ALL DV24HIGH
50
43
41
38
38
50
45
45
52
35
49
49
38
53
51
43
46
36
47
46
46
47
36
49
140
138
214
257
102
146
107
72
139
123
104
117
213
128
113
134
217
98
112
160
122
124
117
102
157
151
212
247
129
159
111
144
259
136
97
100
198
154
102
121
131
88
96
145
100
116
75
137
143
137
189
226
120
146
100
132
238
125
91
93
181
143
92
113
119
84
90
133
90
109
68
124
PM10AVG
47.5
38.6
73.6
77.9
27.1
35.5
27.5
26.3
33.8
35.3
2S.1
34.1
46.6
40.9
25.7
37.6
47.5
34.8
30.5
58.1
25.0
29.1
28.1
31 .0
TSPAVG
87.2
95.8
126.1
133.2
60. 1
77.3
59. 1
81 .8
120.6
64.9
47.0
50.3
83.2
83.4
55.9
60.2
71 .8
62.3
59.8
89.0
50.6
61 .4
41 .0
75.1
ANNDVALL
42.7
46.9
61 .8
65.3
29.4
37.9
29.0
40. 1
59. 1
31 .8
23.0
24.6
40.8
40.9
27.4
29.5
35.2
30.5
29.3
43.6
24.8
30. 1
20. 1
36.8
75
-------
Twenty-four-hour PM10 de-sign values were estimated by fitting a tail expo-
nential model to the highest 20 percent of the PM10 concentrations. This
model assumes that, no matter what the underlying distribution, the upper
20 percent of the values drop off exponentially; for a variety of under-
lying distributions such a model fits well. Complete details of the
model, its derivation, and its application to estimating design values can
be found in Breiman et al. (1978). After obtaining the parameters of a
tail exponential distribution for a given site-year, the design value is
found by calculating the 364/365 percentile of the distribution, i.e.,
that value which is exceeded only once per year.
Figure 6-1 compares 24-hour PM10 design values estimated from the national
24-hour PM10/TSP distribution and from the PM10 tail exponential model.
For many site-years the differences between the TSP-based estimate and the
PMlO-based estimate is small. Nevertheless, there are some very large
differences, as high as 119 yg/m ; the average absolute difference is 25.5
pg/m. A similar plot for design values estimated from high TSP data
(i.e., those ratios with TSP greater than or equal to 100 ug/m ) is not
provided because it appears almost the same as Figure 6-1, since these
design values are all between 5 and 10 percent less than the design values
estimated from the ratio distribution undifferentiated by TSP concentration,
A comparison of PM10 annual design values estimated from TSP data (by
multiplying by 0.49, the median of the complete annual average PM10/TSP
distribution) and from the annual PM10 average is shown in Figure 6-2.
Here too there is much scatter in the plot, and some large discrepancies
between the two estimates can be seen. The largest difference between the
•D
PMlO-based and the TSP-based annual design value estimates is 25 pg/md;
•3
the mean absolute difference is approximately 7 yg/m . The observed
differences are approximately the same for TSP-based design values
estimated from the median of the annual average PM10/TSP distribution for
high TSP concentration (i.e., ratios for which the annual average TSP is
at least 55 pg/m3); since the multiplier is 0.47 instead of 0.49, there is
very little difference between the resulting annual design value esti-
mates.
76
-------
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DISCUSSION AND RECOMMENDATIONS
In this section we summarize the results of our analyses and recommend
which ratio distributions to use to determine the probability of attain-
ment of 24-hour and annual PM10 standards. Our results are based on the
PM10 and PM15 data from the IP netowrk for 1982-1983, and on TSP data from
collocated monitors, as described in Section 1.
SITES SELECTED TO MONITOR PM10 AND PM15
Analyses of the IP network data are complicated by the way in which sites
were selected to measure PM10 and PM15. The IP network sites were selec-
ted to represent larger urban areas. After the initial selection of
sites, a few more sites were added in smaller rural locations in the
West. State and regional EPA offices then requested additional sites.
Since the sites were not selected randomly and are not geographically
representative, inferences to the larger population of monitors across the
country must be made carefully.
Initially, all IP network sites monitored PM15; however, they did not all
use the same kind of sampler. Those sites that did not have dichotomous
samplers had problems and did not record valid data. Those sites selected
to monitor PM10 were sites where the highest TSP concentrations were
observed, i.e., the sites where the highest PM10 concentrations were
expected. Initially it was thought that the proposed particulate matter
standard would be based on PM15 concentrations. However, when it was
decided that the standard would be based on PM10 instead, the inlet on the
8506<+r e
79
-------
PM15 dichotomous sampler was changed to sample PM10 (Pace, personal com-
munication). Thus there are very few monitors which sample both PM10 and
PM15, and the monitors that sample PM10 are at sites where high concentra-
tions occur.
NATIONAL VERSUS LOCAL DISTRIBUTIONS OF RATIOS
One of the main issues that this report addresses is whether the likeli-
hood of attainment for a site should be based on a single national distri-
bution of particulate matter ratios or on a more local distribution.
Analyses of variance were performed to see if there are differences in the
means of ratios grouped geographically (see Section 4). For both 24-hour
and annual average ratios, statistically significant differences in ratio
distributions were observed among climatic regions, EPA regions, states,
cities, and sites, for all three kinds of ratios examined (PM10/TSP,
PM15/TSP, and PM10/PM15). The results did not change when the ratios were
limited to a subset with high TSP concentrations. Statistical issues in
the interpretation of ANOVA results were provided in that section, and the
cumulative distribution functions for geographical groupings permit one to
see the practical differences.
The analyses show that ratio distributions by site are significantly dif-
ferent. It is our judgment that geographic differences, e.g., among EPA
regions, may be statistically significant not because of actual regional
differences but because each geographical region comprises only a few
sites--in many cases, only one or two sites, especially in smaller geo-
graphical groupings, such as state and city—and there are major differ-
ences between sites. A larger data base is required to be able to detect
actual regional differences, if they exist.
Observed differences by year (and quarter) may also be attributed to site-
to-site differences: Not all of the monitors were placed in service at
8506V 8
80
-------
the same time and many monitors did not operate for long periods. Thus
the ratios are rarely derived from the same set of sites over a given
period.
The practical implications of using a single national ratio distribution
instead of climate or EPA regional distributions were also examined (see
Section 5). The results must be viewed in the light of the large differ-
ences in ratio distributions across sites. Using the "leave-out-one"
cross-validation approach, nonattainment probabilities were calculated for
each site using a ratio distribution that did not include ratios from that
site. The observed differences in nonattainment probability for a site
between one calculated from a national distribution and from a climatic or
regional distribution may only be an artifact of the large site-to-site
differences.
We recommend the use of a single national distribution except when suf-
ficient data at a site permit the site-specific distribution to be
reliably estimated. The two major reasons for this recommendation are (1)
site-to-site differences are so much larger than geographic differences,
and (2) attainment classifications based on a one-year test do not appear
to be improved by the adoption of climatic or regional distributions.
There are other statistical considerations favoring this recommendation.
First, because sites have not been chosen randomly within geographical
regions, the observed regional distributions cannot necessarily be con-
sidered representative of regions in which they are located. Second,
geographical distributions are based on much smaller sample sizes than the
national distribution and are thus less reliable.
At the same time the nonrandom location of sites could also be used as an
argument against the use of a single national distribution. However,
since the national distribution is based primarily on ratios observed at
8506^ 8
81
-------
urban sites with high concentrations, and since the probability of non-
attainment is zero unless the TSP concentration is above the PM10 stan-
dard, the Pace and Frank methodology will only be used by similar, high-
concentration sites. In addition, given the large site-to-site differ-
ences, the national distribution represents a greater range of sites than
any one geographic distribution.
RATIOS DIFFERENTIATED BY TSP CONCENTRATION
A second major issue is whether the probability of nonattainment should be
estimated from distributions differentiated by TSP concentration. We saw
significant differences in particulate matter ratios corresponding to high
or low TSP concentration (see Sections 2 and 3). Ratios at lower TSP
concentrations are more variable than ratios at higher TSP concentra-
tions. We recommend a national ratio distribution based on high TSP con-
centrations (above 100 pg/irr for 24-hour concentrations and 55 yg/nr for
annual average concentrations) for two reasons. First, the distribution
based on high TSP concentrations is less prone to measurement error than
the undifferentiated distribution. Second, the ratio distributions will
only be applied to site-years and site-days with high TSP concentrations,
i.e., higher than the level of the standard, because otherwise the exceed-
ance probability is nil (since PK10 is assumed to be less than TSP). It
is logical, then, to have a ratio distribution based on high TSP concen-
trations only.
It should be noted here that in cross-validation analyses (see Section 6),
complete national distributions were used rather than the high-TSP distri-
butions. This was done because the sample sizes for the high-TSP distri-
butions for specific geographical units were too small to perform the
cross-validation analyses. We assume that the results using the high-TSP
distribution, if enough data were available, would be similar. In fact,
it is likely that differences in nonattainment probabilities observed
82
-------
between national and geographic distributions (see Section 5) would be
even smaller if high-TSP distributions were used, because of the reduced
variability in the ratio distributions.
Estimation of design values using the Pace and Frank methodology was per-
formed for a small subset of sites (see Section 6). In the analysis both
the complete and the high-TSP national distributions were used, and there
was little difference in the resulting design value estimates. These
estimates did not agree well in some cases with design values estimated
from actual PM10 data, but this may be because very little PM10 data was
available for each site-year (at most 53 samples out of a possible 365).
Further analyses are recommended when more PM10 data are available.
PM10/TSP VERSUS PM15/TSP DISTRIBUTIONS
The third and final issue is which ratio distribution to use for calcula-
ting probabilities of attainment. With only TSP monitoring data avail-
able, there are two choices. One may use either the PM10/TSP ratio dis-
tribution or the PM15/TSP ratio distribution multiplied by 0.85. In pre-
vious studies the PM10/TSP distribution was recommended for the 24-hour
standard and the PM15/TSP distribution (multiplied by an appropriate fac-
tor) was recommended for the annual standard (Pace and Frank, 1982; Thrall
and Hudischewskyj, 1984). In these studies only 1982 Network PM10 data
were available, and annual average PM10/TSP distributions were based on
too few samples to be considered reliable.
With the 1983 IP Network PM10 data, however, there is a much larger sample
size for the annual average PM10/TSP distribution, and we recommend its
use as well as the 24-hour distribution. Although the annual average
PM15/TSP distribution is based on a substantially larger number of site
years, multiplying by 0.85 or any other factor assumes that PM10/PM15 is
relatively constant, which has been shown not to be the case.
85061*1- g
83
-------
ATTAINMENT PROBABILITIES WHEN ONLY PM15 DATA ARE AVAILABLE
There may be some sites for which the only particulate matter monitored
is PM15. Until actual PM10 data become available for these sites,
attainment/nonattainment classification may be made either by using a PM15
to PM10 conversion factor or by using a PM10/PM15 distribution. Because
of the variation in the distribution of PM10/PM15 ratios, we recommend
against the use of a single factor. We recommend that a single national
distribution based on days with high TSP be used for the reasons listed
above. The percentiles of these 24-hour and annual distributions may be
found in the first column of Tables 3-3 and 3-4, respectively.
CONCLUSION
In summary, we recommend the use of PM10/TSP distributions based on high
TSP concentrations. Unless enough data are available to develop a site-
specific PM10/TSP distribution, we recommend that a national distribution
of annual average and 24-hour ratios be used to estimate nonattainment
probabilities for the respective standards. The percentage points and
summary statistics of the recommended distributions may be found in the
middle column of Tables 3-3 and 3-4.
8506»+r 8 34
-------
REFERENCES
Breiman, L., J. Gins, and C. Stone. 1978. "Statistical Analysis and
Interpretation of Peak Air Pollution Measurements." Technology
Service Corporation, Santa Monica, CA (TSC-PD-A190-10).
Dixon, W. J., ed. 1983. BMDP Statistical Software. University of
California Press.
EPA. 1984. PM10 SIP Development Guideline. U.S. Environmental
Protection Agency, Research Triangle Park, NC.
Federal Register. 1984. Proposed Revisions to the National Ambient Air
Quality Standards for Particulate Matter, 49(55):10408.
Frank, N. H. 1984. "Nationwide Trends in Total Suspended Particulate
Matter and Associated Changes in the Measurement Process." Air
Pollution Control Association/American Society for Quality Control
Specialty Conference on Quality Assurance in Air Pollution
Measurements. Boulder, CO (14-18 October).
Freas, W. P. 1984. User's Guide for PM10 Probability Guideline
Software. U.S. Environmental Protection Agency, Research Triangle
Park, NC.
Hosteller, F., and J. W. Tukey. 1968. "Data Analysis Including
Statistics." In Handbook of Social Psychology, Vol. 1, G. Lindsey
and E. Aronson, eds., Addeson-Wesley, Reading, MA.
Pace, T. G., and N. H. Frank. 1984. Procedures for Estimating
Probability of Nonattainment of a PM10 NAAQS Using Total Suspended
Particulate or Inhalable Particulate Data. U.S. Environmental
Protection Agency, Research Triangle Park, NC.
Thrall, A. D., and C. S. Burton. 1983. "Characterizing Ratios of
Particulate Concentrations: A Preliminary Step in Assessing Likely
Attainment Status Under a PM10 National Ambient Air Quality
Standard." Systems Applications, Inc., San Rafael, CA (SYSAPP-
83/078).
8506^ 9 85
-------
Thrall, A. D., and A. B. Hudischewskyj. 1984. "An Update on the Use of
Participate Ratios to Assess Likely PM10 Attainment Status." Systems
Applications, Inc., San Rafael, CA (SYSAPP-84/100).
Weiner, B. J. 1971. Statistical Principles in Experimental Design, 2nd
edition. McGraw-Hill, New York.
86
-------
Appendix A
MONITORING SITES USED IN THE ANALYSIS
8506^ 10
-------
Appendix A
MONITORING SITES USED IN THE ANALYSIS
On the following pages is a complete list of the monitoring stations used
in our analyses. PM10 and PM15 data were taken from IP network monitoring
records; TSP data were taken from monitoring records of collocated SAROAD
TSP monitors. For this project we assigned to each collocated pair of IP
network and SAROAD TSP monitors a unique three-digit site number.
Additionally, the EPA assigns to each monitoring site a unique 12-digit
ID for entry in the SAROAD system. The first nine characters uniquely
identify the physical location of a monitor; these appear in the column
labeled SAROAD. The remaining three characters indicate controlling
agency (one letter) and project classification (two digits). The column
labeled IP contains the agency and project codes for the IP Network
monitor; the corresponding codes for the colocated TSP monitor are in the
column labeled TSP. State and city names were extracted from the AEROS
Manual of codes (EPA, 1983) for the SAROAD system, which also contains a
map of EPA regions. Climate classifications were provided by the project
officer.
Reference
EPA. 1983. AEROS Manual Series Volume V: AEROS Manual of Codes. U.S.
Environmental Protection Agency, Research Triangle Park, NC (EPA-
450/2-76-005a).
85064 10 88
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Appendix B
LISTING OF SITE-DAYS ON WHICH AT LEAST
ONE 24-HOUR RATIO EXCEEDS 1.0
8506H 10
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Appendix C
DETERMINATION OF CRITERIA FOR A VALID ANNUAL MEAN
85061+ 10
-------
Appendix C
DETERMINATION OF CRITERIA FOR A VALID ANNUAL MEAN
The variability of an annual ratio depends on the number of sample days
used to calculate the ratio. An annual ratio calculated from only a few
sample days is much more variable than an annual ratio calculated from 20
or 30 sample days. We decided to include annual ratios, i.e., consider
them valid, only if at least 10 sample days contributed to the annual
average ratio. Justification of 10 days as the cutoff point is described
here.
The annual average is calculated by dividing an annual average numerator
by the annual average demoninator (not by calculating the average across
the individual ratios). Suppose the annual averages are composed of n 24-
hour measurements and denote the annual average numerator by x"
and the annual average demoninator by y". Then the variance of the annual
average ratio can be approximated as
2 2
where S , S , and S are, respectively, the sample variance of x and y
x y x y
and their sample covariance. The approximation is valid provided n is
large enough for "x" and y to have an approximate joint normal distribution
(Ku, 1979). The approximation ignores any autocorrelation in the 24-hour
measurements, but this is probably not large, particularly for a once-per-
six-day monitoring scheduling, which is common.
10 fOi
-------
If we have K annual average ratios Rp ..., RK, from K site-years, with
n^, ..., nK sample days in the respective numerators and denominators,
then the variance of the average of these annual ratios is
Var(Tf) = Var[i(R1 + ... 4 RK)J
••^ Var(R1 + ... + RK)
Var(RK)]
if we make the reasonable assumption that the K ratios are uncorrelated
(any actual correlation is probably quite small). If we make the further
simplifying assumption that the variance and covariance of 24-hour
collocated measurements are approximately the same for all sites, then the
variance of the average across the annual average ratios is
We estimated the mean and variance of the average ratio for each of the
ratios PM10/PM15, PM10/TSP, and PM15/TSP, for all possible cutoff values
of the numbers of sample days required, and then examined ,the results to
find the most reasonable cutoff value. There are trade-offs to be made in
the choice of a cutoff value, for as we require more 24-hour measurements
per site, the site-specific ratios included in our analysis become more
reliable, but the analysis rests on those few sites having a large number
of measurements.
The complete calculations for the PM10/TSP annual average ratio are given
in Table C-l. There are 53 annual average PM10/TSP ratios from the
8506^ 10 102
-------
1982-1983 IP Network and SAROAD data; they are sorted in the table by the
number of sample days contributing to each ratio. The first column, K, is
the number of ratios included in each successive calculation. The second
column is the annual average PM10/TSP ratio, and the third column is the
number of sampling days for the ratio. The fourth column is the inverse
of the number of samples; these are successively summed in the fifth
column. The sixth column is the inverse of the square of K, the number of
ratios. The seventh column is the approximate variance of the mean ratio
(calculated from K ratios) without the common multiplier C, i.e.,
C . var(lT) "ir/V
and the seventh column is its square root, i.e., the standard deviation
without the multiplier /C. The final column is the successive means of
the ratios as each additional ratio is introduced.
The successive means and variances about the means are plotted against K,
the number of annual ratios included, in Figures C-l and C-2,
respectively. The vertical line on both plots corresponds to a cutoff
value of 10 sampling days required. At this cutoff the mean seems
relatively stable. The variance decreases continuously until ratios with
about 10 samples are included; then the variance increases as annual
ratios based on only a few samples are included. Of the 53 annual average
PM10/TSP ratios available, 14 (26 percent) are based on fewer than 10
sample days and were excluded from the analyses in this report.
Similar plots for annual average PM10/PM15 ratios are in Figures C-3 and
C-4 for the mean ratio and its variance, respectively. Again the vertical
line indicates the value of K that corresponds to at least 10 sample days
contributing to the annual average. At 10 samples the mean is relatively
stable and the variance begins its upward trend. Of the 20 annual ratios
available, 2 (10 percent) have fewer than 10 sample days and are therefore
excluded. Similar patterns can be seen in the mean PM15/TSP and variance
8506V 10
103
-------
of the mean plots in Figures C-5 and C-6, respectively. Of the 170
available PM15/TSP, 37 (22 percent) are based on fewer than 10 samples and
are therefore considered invalid.
Reference
Ku, H. H. 1966. Notes on the use of Propagation Error Formulas.
Precision Measurement and Calibration: Selected NBS Papers on
Statistical Concepts and Procedures, Harry H. Ku, ed. National
Bureau of Standards, United States Department of Commerce (NBS
Special Publication 300-Volume 1).
104
-------
TABLE C-l. Calculation of the mean and approximate variance of the average
of the annual average PM10/TSP ratios as ratios with fewer observations are
successively added.
K
1
2
3
4
5
6
7
8
9
10
11
12
13
U
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
4 a
41
42
43
44
45
4E
47
48
49
50
51
52
53
ratio
0.490300
0.280121
0.459348
0.545236
0.460069
0.678036
0.618555
0.412549
0.474548
0.510146
0.494091
0.652375
0.660701
0.321994
0.464458
0.623726
0.402997
0.584067
0.585117
0.56021 1
0.450649
0.685719
0.557745
0.545000
0.586320
0.404159
0.515386
0.575146
0.499870
0.432125
0.458420
0.404100
0.325678
0.508616
0.440820
0.416779
0.345503
0.432967
0.542340
0.470117
0.754780
0.578608
0.486979
0.607438
0.532089
0.667023
0.791877
0.666686
0.480677
0.747551
0.508341
0.322857
0.635886
nsamp
53
52
51
50
50
49
49
49
47
47
46
46
46
45
45
43
43
41
38
38 :
38
36
36
35
33
33
29
29
25
21
21
18
16
16
14
14
14
14
11
6
6
6
5
5
5
4
4
2
2
2
2
1
1
1/n
0.01887
0.01923
0.01961
0 . 02000
0.02000
0.02041
0.02041
0.02041
0.02128
0.02128
0.02174
0.02174
0.02174
0.02222
0.02222
0.02326
0.02326
0.02439
0.02632
0.02632
0.02632
0.02778
0.02778
0.02857
0.03030
0.03030
0.03448
0.03448
0.04000
0.04762
0.04762
0.05556
0.06250
0.06250
0.07143
0.07143
0.07143
0.07143
0.09091
0. 16667
0. 16667
0. 16667
0.20000
0 . 20000
0.20000
0.25000
0.25000
0.50000
0 . 50000
0 . 50000
0.50000
1 . 00000
1 . 00000
sum( 1/n )
0.01887
0.03810
0.05771
0. 07771
0.09771
0. 1 1811
0. 13852
0. 15893
0. 18021
0.20148
0.22322
0.24496
0.26670
0.28892
0.31115
0.33440
0.35766
0.38205
0.40836
0.43468
0.46100
0.48877
0.51655
0.54512
0.57543
0.60573
0.64021
0.67469
0.71469
0.76231
0.80993
0.86549
0.92799
0.99049
1 .06192
1 . 13334
1 .20477
1.27620
1 .36711
1 .53378
1 .70044
1.86711
2.0671 1
2.26711
2.46711
2.71711
2.96711
3.46711
3.96711
4.46711
4.96711
5.96711
6.96711
1/K**2
1 .00000
0.25000
0.11111
0.06250
0.04000
0.02778
0.02041
0.01563
0.01235
0.01000
0.00826
0.00694
0.00592
0.00510
0.00444
0.00391
0.00346
0.00309
0. 00277
0.00250
0.00227
0.00207
0.00189
0.00174
0.00160
0.00146
0.00137
0.00128
0.00119
0.00111
0.00104
0.00098
0.00092
0.00087
0.00082
0.00077
0.00073
0.00069
0.00066
0.00063
0.00059
0.00057
0.00054
0.00052
0.00049
0.00047
0.00045
0.00043
0.00042
0.00040
0.00038
0.00037
0.00036
var(m>
0.0188679
0.0095247
0.0064116
0.0048567
0.0039083
0.0032810
0.0028270
0.0024833
0.0022248
0.0020148
0.0018448
0.0017011
0.0015781
0.0014741
0.0013829
0.0013063
0.0012376
0.0011792
0 . 00 1 1 3 1 2
0.0010867
0.0010453
0.0010099
0.0009765
0.0009464
0.0009207
0.0008960
0.0008782
0.0008606
0.0008498
0.0008470
0.0008428
0.0008452
0.0008521
0.0008566
0.0008669
0.0008745
0.0008800
0.0008838
0.0008988
0.0009586
0.00101 16
0.0010585
0.0011180
0.001 1710
0.0012183
0.0012841
0.0013432
0.0015048
0.0016523
0.0017868
0.0019097
0.0022068
0.0024803
stdevdn )
0.137361
0.097594
0.080074
0.069690
0.062516
0.057280
0.053170
0.049833
0.047168
0.044887
0.042951
0.041245
0.039726
0.03B394
0.037187
0.036142
0.035179
0.034339
0.033633
0.032965
0.032332
0.031778
0.031246
0.030764
0.030343
0.029934
0.029625
0.029336
0.029152
0.029104
0.029031
0.029072
0.029192
0.029272
0.029443
0.029572
0.029665
0.029729
0.029980
0.030961
0.031805
0.032534
0.033436
0.034220
0.034905
0.035834
0.036650
0.038792
0.040648
0.042271
0.043700
0.046976
0.049802
mean
0.490300
0.385210
0.409923
0.443751
0.447015
0.465518
0.504524
0.493027
0.490974
0.492891
0.493000
0.506281
0.518160
0.504148
0.501502
0.509141
0.502897
0.5074#7
0.511497
0.513932
0.510919
0.518864
0.520555
0.521573
0.524163
0.519548
0.519393
0.521385
0.520643
0.517692
0.515780
0.512290
0.506635
0.506693
0.504811
0.502366
0.498126
0.496412
0.497589
0.496903
0.503192
0.504988
0.504569
0.506907
0.507467
0.510935
0.516913
0.520033
0.519230
0.523796
0.523493
0.519635
0.521828
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-------
Appendix D
RECOMMENDATION OF A CONSTANT TO USE FOR
CONVERTING PM15 TO PM10 FOR USE WITH
PM15/TSP RATIOS
-------
Appendix D
RECOMMENDATION OF A CONSTANT TO USE FOR
CONVERTING PM15 TO PM10 FOR USE
WITH PM15/TSP RATIOS
In some situations PM15/TSP ratios may be used to determine attainment
status for the PM10 standards rather than PM10/TSP ratios. In this case,
a multiplier is needed to convert the PM15 data to PM10 data. The dis-
tributions of PM10/PM15 ratios are variable and should not be considered
constant. However, a single conversion factor has been used in the past
and in this study because of the limited availability of PM10 data on days
having both PM15 and TSP data. This appendix contains justification for
our recommendation of 0.85 as the multiplier.
Four data sets of PM10/PM15 ratios were examined: all 24-hour ratios,
24-hour ratios corresponding to high TSP values (> 100 Mg/nr), all valid
annual ratios, and valid annual ratios corresponding to high annual aver-
age TSP concentrations (> 55 pg/m3). For each of these four data setss
the number of available ratios, mean and median ratio, and TSP to PM10
regression slope are given in Table D-l. The regression slope is the
linear regression estimate of the best multiplier for predicting PM10 from
PM15; i.e., it is the constant a that minimizes the sum of squared differ-
ences
n ?
£ (PM10 - a • PM15T •
i = l
The multipliers in the table cover a very small range from a minimum of
0.84 to a maximum of 0.87. Recognizing that most of the sample sizes in
Table D-l are small and therefore that the variances about these estimates
are not small, we chose 0.85 as a rounded number in the middle of the
range of multipliers.
113
-------
TABLE D-l. Summary statistics for 24-hour and annual PM10/TSP ratios.
Number Mean Median Regression
Date Set of Ratios Ratio Ratio Slope
All 24-hour ratios 567 0.87 0.87 0.85
24-hour ratios corresponding 122 0.85 0.84 0.84
to TSP > 100 yg/m3
All valid annual ratios 18 0.87 0.87 0.84
Valid annual ratios corre-, 17 0.85 0.86 0.84
spending to annual average
TSP > 55
85061* 2 114
-------
Appendix E
DETERMINATION OF CUTOFF VALUES FOR HIGH TSP
85061+ 10
-------
Appendix E
DETERMINATION OF CUTOFF VALUES FOR HIGH TSP
PM10/TSP and PM15/TSP ratios, both 24-hour and annual, are more variable
at low TSP concentrations. Most of the usually large ratios occur at low
TSP concentrations, where sampling errors have a greater relative effect
than at high TSP concentrations. Because of these outlying ratios, the
variances of the ratio distributions are large. Rather than arbitrarily
omit all ratios greater than a specified level, we chose to consider
ratios corresponding to a TSP concentration above a fixed level. In this
appendix, justification for the choice of the high TSP cutoff values of
•3 O
100 yg/m for 24-hour concentrations and 55 yg/nr for annual average
concentrations is given.
Figure E-l contains a plot of 24-hour PM10/TSP ratios versus 24-hour TSP
concentrations. The extremely high PM10/TSP ratios occur at less than 60
•5
yg/nr TSP, but even beyond that cutoff value there are ratios greater than
one. Figure E-2 is a plot of PM15/TSP ratios versus TSP, also 24-hour
concentrations. Here, too, the largest ratios occur at low TSP
•5
concentrations, below approximately 90 yg/m TSP.
The higher the TSP cutoff value, the more ratios are excluded. In general
variances decrease with larger sample sizes, but in these cases the
variance about the mean most likely decreases as more low TSP ratios are
excluded, because they are the more variable ratios. A wide range of
cutoff values for TSP concentrations, from 50 to 150 yg/m , was
considered. The means and standard deviations of the 24-hour PM10/TSP
and PM15/TSP ratio distributions corresponding to each of the 24-hour TSP
cutoff values considered are shown in Figures E-3 and E-4, respectively.
8506^
116
-------
Because of the relationship between high ratios and low TSP
concentrations, the mean ratio decreases almost monitonically. The
standard deviations of the ratio distributions, however, decrease when
high ratios are omitted but then increase as there are fewer and fewer
ratios. For both PM10/TSP and PM15/TSP ratios, the standard deviation is
minimized at 100 yg/m , the chosen cutoff value.
Annual average PM10/TSP and PM15/TSP ratios are also dependent on TSP
levels (i.e., annual average TSP), but the relationships shown in Figures
E-5 and E-6 are not as striking as those of E-l and E-2, because averaging
over multiple sample days reduces the effects of outliers. There are no
annual average PM10/TSP ratios above one, and only one annual average
PM15/TSP ratio above one. There are, however, some unusually high
o
ratios. Cutoff values for annual average TSP of 40 to 80 yg/m were
considered. The means and standard deviations of the resulting ratio
distributions for each cutoff value considered are shown in Figures E-7
and E-8, respectively. As with the 24-hour ratios, the mean decreases
almost monotonically with increasing cutoff values. Except for the very
o
highest cutoff values above 75 yg/m , where most of the data are excluded,
the standard deviations of the ratio distributions are minimized at 55
•3
yg/m , the chosen cutoff value.
8506^ 10
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TECHNICAL REPORT DATA
/Please read Instructions on the reverse before completing]
13. RECIPIENT'S ACCESSION NO.
4.TTLE AND SUBTITLE
An Examination of 1982-83 Participate
Matter Ratios and Their Use In The Estimation of PM
NAAQS Attainment Status
10
|5. REPORT DATE
August 1985
6. PERFORMING ORGANIZATION CODE
AUTHOR(S)
8. PERFORMING ORGANIZATION REPORT NO.
A.K. Pollack et al
9 PERFORMING ORGANIZATION NAME AND ADDRESS
Systems Applications, Inc.
San Rafael, California 94903
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO
68^02-4306
12. SPONSORING AGENCY NAME AND ADDRESS
Air Management Technology Branch (MD-14)
U. S. Environmental Protection Agency
Research Triangle Park, N.C. 27711
13. TYPE OF REPORT AND PERIOD COVERED
14 SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
EPA Project Officer: Edwin L. Meyer, Jr.
16. ABSTRACT
The U. S. Environmental Protection Agency is proposing new short- and long-term
National Ambient Air Quality Standards (NAAQS) for particulate matter having an
aerodynamic diameter of less than 10 -micrometers (PM,0). The current NAAQS for
particulate matter refers to total suspended particuiate matter (TSP) concentrations
without a size specification. Until PM,Q data are more widely available, TSP
monitoring data must be used to estimate the likelihood of attainment of the PM ~
NAAQS. Pace and Frank (1984) have developed a method for estimating that like-1
lihood. Their approach relies on the distributions of particulate matter ratios.
KEY WORDS -NIT DOCUMENT AKiAl_VSiS
NAAQS
PM
mio
Attainment
Particulate
Particulate Matter Ratios
.'.3 SECL-f T f' CLASS , .V;;.< \i~.,r:, ,21 \O ^e'^GES
1 20 St
K > '*• Ci-AiS • ,> n:s p
, 22 pP ' CE
-------