xvEPA
United States
Environmental Protection
Agency
Office of Air Quality
Planning and Standards
Research Triangle Park NC 27711
EPA-450/4-86-017
December 1986
Air
Procedures For
Estimating Probability
Of Nonattainment Of A
PM10 NAAQS Using
Total Suspended
Paniculate Or PMio
Data
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EPA-450/4-86-017
Procedures For Estimating Probability
Of Nonattainment Of A PIN/ho NAAQS Using
Total Suspended Paniculate Or
Data
By
Thompson G. Pace
Edwin L. Meyer
Air Management Technology Branch
And
Neil H. Frank
Stanley F. Sleva
Monitoring And Reports Branch
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office Of Air Quality Planning And Standards
Monitoring And Data Analysis Division
Research Triangle Park, North Carolina 27711
December 1986 _ _ _
U.S. Environmental Protection Agenc;
Region 5, Library (fi»l. -16)
230 S. IV--; ,i- 1-. :^~, i;,,,,.: 1.C.-7C
Cliicagj, i:. .j;.;l
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This report has been reviewed by the Office of Air Quality Planning and Standards, U. S. Environmental
Protection Agency, and approved for publication. Any mention of trade names or commercial products is
not intended to constitute endorsement or recommendation for use.
Technical Note
This document has been altered from the February 1984 version In order to
reflect public comments received in response to proposed regulations for
implementing revised particulate matter NAAOS (40 CFR Parts 50, 51, 52, 53,
58, 81) F]R (April 2, 1985), as well as the results of more recent studies.
In order adequately to illustrate the procedure described in this report,
it was necessary to assume a cutpoint and values for the annual and 24-hour
NAAQS. The decision concerning the appropriate values for the NAAOS has not
yet been published. We have arbitrarily chosen to illustrate the procedure,
assuming the following NAAOS: 150 wg/m^ 24-hour average not expected to be
exceeded more than once per year, and 50 yg/m^ annual arithmetic mean.
Should the NAAOS differ from those assumed in this report, several of the
curves (i.e., Figures A, R, 1, and 2) may have to be revised using Tables 1
and 2 as shown in this report. The procedure described herein would be
identical.
EPA -450/4-86-017
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TABLE OF CONTENTS
Page
List of Figures ....................................... . .......... v
List of Tables [[[ vi
Executi ve Summary ................................................ vi 1
1.0 Introduction ................................................ 1
2.0 Available Ambient Parti cul ate Matter Data ................... 2
2.1 Total Suspended Particulate (TSP) ...................... 2
2.2 PM10 [[[ 4
3.0 Use of Available Data to Draw Inferences About PMjQ Levels .. 5
3.1 Ratio of PM10 and IP to TSP .. .......................... 5
4.0 Methodology for Estimating the Probability of Nonattainment
for PM^Q NAAQS - Annual Standard ............................ 14
5.0 Methodology for Estimating the Probability of Nonattainment
for PM10 NAAQS - 24-hour Standard ........................... 18
5.1 Assessment Based on Adequate PM^g Data ................. 19
5.2 Assessment Without PMjg Data ........................... 23
5.2.1 Sampling Less Frequently Than Once in
Three Days ............ . ...... . ................... 23
5.2.2 Sampling Once in Three Days or More
Frequently ............................ . ......... 26
5.3 Assessment Based on TSP Data and One or More Years
of PM10 Data ............................................ 29
5.4 Use of IP Data .......................................... 34
6.0 Estimating the Spatial Extent of Nonattainment Situations ... 35
6.1 Introduction ........................................... 35
6.2 Use of Acceptable Air Quality Data ..................... 36
6.2.1 Type of Sampler ................................. 36
6.2.2 Sampler Location ................................ 37
6.2.3 Data Quality .................................... 37
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6.3.2 Spatial Interpolation of Air Monitoring Data .... 39
6.3.3 Air Quality Simulation by Dispersion Modeling ... 40
7.0 Acknowledgements 41
8.0 References 42
iv
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LIST OF FIGURES
Number Page
Relationship Between the Probability of Exceeding
a 50 yg/m3 Annual PM10 Concentration and Observed
TSP Annual Arithmetic Mean Concentration ix
Relationship Between the Probability of Exceeding
a 150 yg/m3 24-hour PM^Q Concentration and Observed
TSP 24-hour Concentration xi
Relationship Between the Probability of Exceeding a
50 yg/m3 Annual PMiQ Concentration and Observed TSP
Annual Arithmetic Mean Concentration 16
Relationship Between the Probability of Exceeding a
150 yg/m3 24-hour PMig Concentration and Observed
TSP 24-hour Concentration 25
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LIST OF TABLES
Number Page
A Summary of Methods for Using Available PMig. IP or
TSP Data to Assess PMjQ NAAQS Attainment/Nonattainment
Status [[[ xv
Cumulative Percentage of Ratios Greater Than a Given
Value (Annual) ........................................... 8
Cumulative Percentage of Ratios Greater Than A Given
Value (24-hour)
A Summary of Methods for Using Available PMig, IP or
TSP Data to Assess PMjg NAAQS Attainment/Nonattainment
Status [[[ 11
Allowable Observed Exceedances as a Function of Sample
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EXECUTIVE SUMMARY
The proposed primary National Ambient Air Quality Standards (NAAQS)
for participate matter (PM) specify ambient concentrations for particles
smaller than 10 micrometers (urn) aerodynamic diameter (PMjo). If meas-
ured PM^'o ambient concentrations are not available, ambient measurements of
other PM size fractions, such as total suspended particulate (TSP), may have
to be used to provide estimates of PM^Q concentrations. In this document,
emphasis is placed on a methodology for using available TSP measurements to
estimate whether or not the annual and/or 24-hour NAAQS for PMjg are likely
to be violated (probability of nonattainment). The probability of nonattain-
ment will be one of the criteria which may be used to specify action States
are to take in developing PM^Q monitoring requirements and State Implementation
Plans (SIP's). The document also suggests appropriate methods for determining
the spatial extent of the nonattainment situations.
The probability of nonattainment is defined by a series of calculations
which are based on data from a nationwide network of collocated ambient TSP
and PMjQ samplers and applied to TSP data collected at current monitoring loca-
tions. The PMjg samplers were operated by or for the U.S. Environmental
Protection Agency (EPA) during 1982-83 and the high volume samplers were
operated by State or local agencies during the same time period. These data
include TSP as measured by the high volume sampler and PMjo» as measured by
the dichotomous sampler. The calculated probability represents the likelihood
that either NAAQS for PM^n, was violated at the sampling site.
The following hierarchy is defined for using available ambient
measurements to determine attainment/nonattainment directly or to estimate
the probability of PMjQ nonattainment. The first preference is to use
vii
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ambient PM^g data, providing a site has complete sampling. PM^g data should
be used if sufficient [see Section 2.4 of Appendix K to 40 CFR, Part 50] data
are available.* The second preference is to use less than complete PMjg data
and Inhalable Particulate (IP) measurements obtained with the dichotomous
sampler.** A third preference is to use PMjg data with less than complete
sampling in conjunction with TSP data to draw inferences about PMjg nonattain-
ment. As described in this document, both preferences two and three may use
IP or TSP measurements together with a statistically defensible site specific
probability distribution for 24-hour PM^g/IP (or PM^g/TSP) ratios to estimate
likelihood of nonattainment, provided that sufficient IP (or TSP) data are
available. The sample size of concurrent PMjg and IP data in the IP National
Monitoring Network is insufficient for a default PM^g/IP distribution to be
presented in the document. The fourth preference is to use TSP data alone to
draw inferences about the probability of PM^g nonattainment. Such inferences are
drawn on the basis of PM^g to TSP ratios observed at sites in the National IP
Monitoring Network.
For the annual NAAOS, PMjg/TSP ratios have been computed from arithmetic
mean concentrations of PMjg and TSP using only days in which both PM^g and
TSP have been measured at collocated monitors. Frequency distributions of
the resulting PMjg/TSP ratios have been plotted and used to derive figures
such as Figure A. Using Figure A, the probability of nonattainment of the
*In some instances, PMjg observations within 20% of the NAAQS would not be
treated as exceedances. See Chapter 2 of the PMm SIP Development Guideline
for details.
**If size selective hi volume samples were collected on quartz fiber filters,
these concentrations may be treated as dichotomous sampler measurements.
Otherwise, the use of the term IP in this document refers to those particles
collected by the dichotomous sampler with a 15 \n size discriminating
inlet and teflon filters. It is anticipated that IP data will be used very
infrequently in conjunction with this guideline.
viii
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Figure A.
to
Relationship Between The Probability Of Exceeding A 50 ug/orAnnual PMJO Concentration
And Observed TSP Annual Arithmetic Mean Concentration
r-l
to
3
1.0 -i
k
f
at
u
X
Ul
o
>.
(D
A
o
Annual Arithmetic Mean TSP Concentration, ug/rrf
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annual PMjQ NAAQS can be estimated directly from the average TSP concentration
for the most recent three complete years of sampling. An example is presented
in Section 4.0.
In the case of 24-hour data, this calculation depends on the number of
exceedances allowed by the standard. Attainment of the 24-hour standard,
expressed in terms of an expected number of exceedances, depends on the number
of sampling days and an adjustment for missing data. This adjustment, however,
is not made for the first observed exceedance, so that at least two exceedances
are required for nonattainment.
In order to estimate the probability of not attaining the 24-hour standard,
observed daily PMjQ/TSP ratios have been used to derive a frequency distribution
of ratios. The appropriate distribution is used in conjunction with TSP data
to estimate the likelihood of not attaining a 24-hour NAAOS for PM^Q. For
example, at sites sampling TSP less frequently than once every 3 days, these
estimates are made using Figure R and equations (a) - (d).
TT qi (a)
1=1
where
PO = probability of observing no PMjg concentrations greater
than the level of the 24-TiF. PM10 NAAOS
p-j = the probability that an observed TSP value (TSP^) will
correspond to a PMin level greater than the PMin 24-hr.
NAADS
q-j = (1-p-j) = the probability that an observed TSP value,
TSP-j, does not correspond with a PM^Q value greater
than the le^eT of the 24 hour PM10 NAAQS
n = the number of TSP values greater than the level of the
24 hour PMin NAAOS
3
~j~f = multiplication symbol such that ~[T Qi = (
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Figure B.
Relationship Between The Probability Of Exceeding A 150 ug/m3 24 Hour PM ..Concentration
And Observed TSP 24 Hour Concentration
(0
4-1
0)
U
c
o
o
O)
o
in
o>
o
a
to
1.0 -i
0.9 -
0.8 -
0.7 -
0.6 -
0.5 -
0.4 -
0.3 -
0.2 -
0.1 -
100
200
I
300
I
400
I
500
I
600
I
700
I
800
I
900
1000
1100
Observed 24 Hour TSP Concentration, ug/m'
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and
P(A (b)
n
Ci = I qi (c)
i = 1
, ,PF (D - i - (PO + PI) (d)
As equation (a) suggests, for each 24-hour TSP concentration greater than
150 vg/m3 there is an associated probability, p^ , that the corresponding PM^
concentration is also greater than the level of the NAAQS (i.e., 150 ug/m3).
This probability, p-,-, is determined for each high TSP value by using Figure
B. For example, if a site has three 24-hour TSP concentrations greater than
150 yg/m3, Figure B is used three times to estimate the probabilities
associated with each of the three high TSP values. The pj determined from
Figure B are then used in equation (a) to estimate the probability of observing
no PMjQ concentrations greater than the level of the PM^o NAAQS and in equation
(b) to estimate the probability of observing one PMjg concentration greater
than the level of the PM^Q NAAOS. For sites sampling less frequently than
once every 3 days over a 3-year period or less, there can be one observed
PM^Q concentration greater than the level of the PM^Q NAAOS according to the
proposed standard. Hence, the probability of violating the PM^Q NAAOS at a
site is simply the probability of observing two or more PMjf) concentrations
greater than 150 pg/m3 (i.e., the level of the NAAOS) at the site. This is
o
simply the complement of observing _< 1 PMjg value above 150 Mg/m , and is
computed using equation (d). This is illustrated by Example 5 in the text.
If samples are collected at a site at least as frequently as once every
2 days over a 3-year period, the NAAOS does allow two or more PM^g concentrations
xii
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greater than the level of the NAAQS to be observed. For example, if sampling
occurred every day over a 3-year period and produced 900 observations, two
observed exceedances would be allowed during the 3-year period. In this
case, the probability that a site is not in attainment with the NAAOS is
the probability of observing three or more PM^g concentrations greater than
the level of the NAAOS.
The 24-hour procedure is simplified somewhat if sufficient ambient PMjQ
data exist. In this case, the estimated number of exceedances in a given
year, E-j, is calculated by equation (e).
El = e1 (N)/ni (e)
where
EJ = the estimated number of exceedances for year i
e-j = the observed number of exeedances for year i
n-j = the number of data values observed for year i
N = total number of possible values in a year (e.g., 3fi5)
The estimated number of exceedances over a 3-year period would be based on
the average of the E-j for each of the 3 years, as shown in Examples 1 and
2 in the text. Based on the provision for the first observed exceedance,
Ei * 1, if ej = 1, or (f)
Ei = 1 + (ej - 1) x N/ni, if e, > 1 (g)
(provided that the first exceedance occurred in year i).
If statistically defensible site-specific or representative geographic
region-specific frequency distributions of PM^Q to TSP ratios can be developed,
either may be used in conjunction with the 24-hour NAAOS determination.
xm
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Similarly, site or area specific mean ratios may be used in conjunction with
the annual NAAOS. Otherwise, the national distribution should be used for
the years with TSP data. For both annual and 24-hour data, a site specific
relationship can be based on a nearby, similar site. To do this, it must
be demonstrated that the two sites are similar and that the ratio or distri-
i '
bution would be more applicable than the national distribution. Similar
rules apply with regard to the derivation and use of "site specific" distri-
butions for PM^g/IP ratios. Table A summarizes the use of national and more
locally specific frequency distributions.
A computer program has been developed to automate the calculations
necessary for estimating the probability of exceedance of both the annual
and 24-hour NAAOS.
Determining the spatial extent of a nonattainment area requires
subjective judgment. Three procedures are identified in Section 6.0
as useful in helping to arrive at this estimate. These are:
(1) a qualitative analysis of the area of representativeness of
the monitoring site, together with consideration of terrain, meteorology
and sources of emissions;
(2) spatial interpolation of air quality monitoring data;
(3) air quality simulation by dispersion modeling.
Choice of which procedure or combination of procedures to use depends on
the available information and the complexity of the PM^Q problem area.
xiv
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TABLE A
A SUMMARY OF METHODS FOR USING AVAILABLE PMi0, IP OR TSP DATA TO
ASSESS PM10 NAAQS ATTAINMENT/NONATTAINMENT STATUS
Procedure
Ambient Monitoring
Data Available5
1. PMjo data meeting
Appendix K sampling
completeness
requirement
Type of
Assessment
Yes/No
Determination
x
<
Annual NAAQS
Compare average annual
arithmetic mean
directly to annual
NAAQS
24-hour
(a) Multiply number of observed
exceedances in a given year
by the ratio of 365 to the
number of data values in that
year to estimate the number of
exceedances in that year, and
(b) calculate average number of
estimated exceedances per year
from the most recent 3 years
of data.b
2. PMjo data with less
than complete sampling
and IPC data available
Estimation
of probability
of nonattainment
(a) If sufficient PMjg data
are available at a site
or for a similar, nearby
site(s), use to derive
site-specific PMjo/IP
ratio for site of interest
(See Section 4.0)
(b) Use mean ratio derived in
(a) to estimate arithmetic
mean PMm for the most
recent 3 years
(c) Calculate average arithmetic
mean PMjQ and compare to
the annual NAAOS
Use observed PMjn, ex-
ceedances to estimate a re-
vised number of allowed ex-
ceedances. If the revised
number of allowed exceed-
ances is less than 0, the
site is in nonattainment.
Otherwise use IP data for
remaining years and a
statistically defensible
distribution for 24-hour
PMjQ/IP ratios using equa-
tions analagous to (6),
(10), and (11), in the
text and figures comparable
to Figure 2 in the text.
(See Section 5.4)
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TABLE A (Continued)
Procedure
Ambient Monitoring
Data Available3
3. PM10 data with
less than complete
sampling and TSP
data available
Type of
Assessment
Estimation of
probability of
nonattainment
Annual NAAQS
Same as #2, only
substitute "TSP" for
"IP". If data are
insufficient to
derive a site-
specific distribution,
use the national de-
fault distribution.
24-hour
Same as #2, only substitute "TSP"
for "IP". If data are insufficient
to derive a site-specific dis-
tribution, use the national
default distribution.
4. TSP data only
Estimation of
probability of
nonattainment
Calculate the average
arithmetic mean TSP level
using the most recent 3 years
of data; and estimate the
probability of nonattainment
using the above average and
the relationship between the
probability of exceeding
the annual PM^o NAAQS
level and observed annual
arithmetic mean TSP
concentration (based on
the national distribution of
annual arithmetic mean
PM10/TSP ratios).
Estimate the probability of indivi-
dual observed 24-hour TSP concen-
tration data to exceed the 24-hour
PMjQ standard level using observed
24-hour TSP data and the relation-
ship between the probability of ex-
ceeding the 24-hour TSP concen-
tration (based on the national
distribution of 24-hour PM^/
TSP ratios), and use the equations
(6), (10), or (11) in the text
to estimate the probability
of failing the attainment test.
aListed in the order of preference.
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TABLE A (Continued)
^Attainment/nonattainment estimates can also be made in terms of an allowable
number of observed exceedances for a specific number of sample days:
Allowable Number of Sample Size, Observations
Observed Exceedances in 3 Years
1 _< 509
2 510-1018
3 1019-1096
C0btained with a dichotomous sampler with a 15 ym size discriminating inlet
and teflon filters. Samples obtained on quartz filters with a size
selective hi-volume samplers may be treated as dichotomous sampler
< measurement.
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1.0 INTRODUCTION
The promulgation of the National Ambient Air Duality Standards (NAAQS)
for particulate matter (PM) will require the revision of State Implementa-
tion Plans (SIPs) to account for the new standards. The revised standards
include an annual and a 24-hour NAAQS specified in terms of PM nominally 10
t '
micrometers and smaller in terms of aerodynamic diameter (PM^o).* Unfortu-
nately, there are few measured data for this size fraction of PM. Other
ambient data, primarily TSP [and also possibly inhalable particulate (IP)],
which include PM10 but with larger particles as well, are available. The
purpose of this document is to describe a methodology for using these data
to estimate the probability of nonattainment of the annual and 24-hour NAAQS
for PMjQ at various sampling sites in the country. As described in the PMyn
SIP Development Guideline, the probability estimates will be used prior to
promulgation to help define where certain actions will be required.!
This document first discusses various measurement methods used to
obtain the underlying rationale and methodologies for inferring ambient
PM^Q levels from available data. Methodologies for estimating the likeli-
hood of not attaining PM^g NAAQS are presented, given ambient TSP data
obtained with a high volume sampler. A procedure for estimating PMjQ
levels using IP data obtained with a dichotomous sampler** is also possible.
Finally, limitations of the above methodologies are identified.
*A method of specifying particle diameter which considers both physical
diameter and particle density.
t For use of probability estimates, see Chapter 2 of PM-m SIP Development
Guideline. U.S. EPA, OAOPS.
** In this document, the term IP is used to denote particulate data collected
with a dichotomous sampler that has a 50% collection efficiency of 15 ym
particles. If size selective hi-volume samples were collected on quartz
fiber filters, these concentrations may be treated as dichotomous sampler
measurements.
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2.0 AVAILABLE AMBIENT PARTICIPATE MATTER DATA
The most desirable way to determine nonattainment of the proposed
NAAOS is to measure PMjo directly. Several monitoring instruments have
recently been developed and tested by the EPA. Unfortunately, sufficient data
collected by these instruments are not yet available at many locations. There-
fore, utilizing other particulate matter (PM) data as a means for estimating
the likelihood that one or more PM^Q NAAQS is not being attained would be useful
The principal data base measuring other PM is the total suspended particulate
(TSP) data base. In the following paragraphs, attributes of TSP which are used
in this report to derive relationships between PM^Q and TSP are described.
2.1 Total Suspended Particulate (TSP)
The most common measurement of PM concentration available is TSP,
as measured by the high volume sampler (hi-vol).(l) The hi-vol is generally
considered to measure PM less than 100 urn aerodynamic diameter, but the col-
lection efficiency (ability to capture) the very large particles is very
poor. With average wind speeds, the sampler is about 50% efficient in
collecting particles of 25-45 ym aerodynamic diameter. Thus, the sampler
is said to have a Ti^ of 30 vim, where DSQ is the particle diameter for 5Q%
collection efficiency. For the purpose of this discussion, the hi-vol is
considered to capture 100% or all particles smaller than 10 urn.
The hi-vol is generally considered to have several deficiencies which
can cause problems in data interpretation. The 059 is dependent on wind-
speed and the orientation of the sampler. Also, the glass fiber filter has
been shown to collect artifact sulfate of as much as 5 ug/m3 or higher
in high sulfate areas of the country.(2) Other artifact components such as
nitrate and organic particulates may be significant in some areas. Another
problem is the design of the hi-vol inlet which allows particles to be
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blown into the shelter and settle onto the filter during periods when the
sampler is not operating.(3) Despite these problems, the hi-vol has been
the standard reference method for TSP for many years and a vast data base
is available for immediate use in screening potential nonattainment areas.
Rasing PMj.Q estimates on empirically derived relationships between PMjg
and TSP lessens the degree to which these problems affect the validity of
the final designations.
2.2 PMin
PM^Q data are collected by a dichotomous sampler whose inlet is
designed to collect particles of 10 urn at 50% efficiency. The sampler
separates the particles which pass through the inlet into two flowstreams
(fine, <2.5 ym and coarse, 2.5-10 ym) and deposits them on two filters.
Potential problems which may bias reported results downward include
internal wall losses (believed to be small) and the loss of particles from
the coarse filter. This loss has been shown to occur on highly loaded fil-
ters during handling and shipment but is not believed to be a problem during
routine network operation.(8)
The national IP network operated 39 sites equipped with dichotomous
samplers measuring 10 ym. Recause of the switch in hi-vol filter media
manufacturers which occurred in 1981 and some dependence of PMjg/TSP relation-
ships on TSP concentrations, the data base used to derive distributions of
PM-LQ/TSP ratios is limited to 1982 and 1983 observations on days observing
high (_>100 yg/m3) TSP concentrations or sites observing high annual mean
TSP levels (_>55 yg/m3).(6) Further, all data used to derive the ratios
are based on the same hi volume sampler filter media that is being used by
State and local agencies at NAMS and SLAMS sites. These restrictions limit
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the size of the data base to 3bl site-days and 35 site-years for the 24-hour
and annual analyses respectively.
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3.0 USE OF AVAILABLE DATA TO DRAW INFERENCES ABOUT PMin LEVELS
The EPA Inhalable Participate Network mentioned previously provides
the available data base on TSP and PMjQ at collocated sites.(9) The sites
were located in urban and suburban locations to reflect maximum concentra-
tion and;population exposure due to urban and industrial sources, and at
nonurban sites to provide information on background levels. The data from
these sites are used, to draw conclusions about relationships between PM^Q
and TSP.
The data used for investigation of the individual observations were
collected from January 1982 - December 1983. These data from the IP network
were screened and validated by the EPA's Environmental Monitoring Systems
Laboratory (EMSL).
3.1 Ratio of PMin and IP to TSP
The ratio of PM^g/TSP was examined at the sites comprising the data
base in the hope that a simple ratio could be calculated which would permit
the direct adjustment of TSP to PMjg. However, upon scrutinizing the data
base, it is clear that a substantial degree of variability exists amongst
individual ratios. (The IP/TSP ratios were also examined, only to establish
that they confirmed the PMjQ/TSP analyses.) This variability includes inter-
as well as intra-site differences in the ratios. As described in Section
2.2, the PMjg/TSP ratio was also found to be somewhat sensitive to TSP
concentrations.(6) This sensitivity is diminished by focusing on site-days
observing TSP >_ 100 yg/m3 or, in the case of annual analyses, site-years
with TSP _> 55 ug/m3.
Several attempts have also been made to find an explanatory site
descriptor which could account for the disparity in the ratios among sites
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I
(i.e., inter-site variability). In the first attempt, such site descriptors
as urban versus suburban were compared; however, no statistically significant
difference was found. Geographic area (East, Southwest, West Coast, etc.)
and site type (industrial, commercial or residential) likewise revealed
insignificant differences in the ratios.(10) In a more recent and more
extensive investigation of geographic differences performed on the entire
1982 and 1983 data base, statistically significant differences were found
among individual sites as well as among larger groupings of sites. However,
the differences among larger groupings of sites are smaller and are difficult
to explain on a physical basis. These investigations conclude that unless
sufficient data to calculate a site specific PMio/TSP ratio are available,
the existing data base does not justify use of different distributions of
ratios for different parts of the country.(6)
The previously described investigations of geographic, climatological,
concentration range or site type classifiers were attempts to reduce or
account for part of the variability in PM^Q to TSP ratios. No doubt, a part
of the overall variance in ratios results from intra-site variation in
ratios arising from differences in the sources impacting the monitor site.
Also, as discussed in Section 2.0, there are several issues associated with
the precision of the TSP and PM^Q measurements which affect intra-site
variance. These factors include windspeed dependence, weighing problems,
artifact formation and sampler wall losses. Thus, the inter-site variance
can potentially be eliminated by the use of site specific data, but the
intra-site variance can only be partially reduced by careful operating
procedures.
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The previously described variance among PM^g/TSP ratios suggests the
need to examine the frequency distribution of ratios rather than relying on
a single value for the ratio. The cumulative frequency distribution for
PMio/TSP is presented in Table 1 for site average (arithmetic mean) ratios.
Table 2 contains a similar distribution for 24-hour ratios.
i '
Another factor to consider is the development and use of site specific
ratios or distributions for both annual and 24-hour cases. It seems logical
that, if an area can justify a statistically different site or area specific
distribution, its use should be encouraged. A site or area specific distri-
bution of PMjQ/TSP or of PMjo/IP may be developed if 1 year of PMjg and/or IP
dichotomous sampler data is available. A distribution based on another
site in the area may be used only if it is demonstrated on a physical basis
and by an appropriate statistical procedure that the sites are similar and
the specific distribution is a better representation of the data at that
site than is the national distribution.
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TABLE 1.
Cumulative Percentage of Ratios Greater Than a
Given Value (Annual)
PMio/TSP (annual)
Percentage
97.1 (minimum)
95
90
80
70
60
50
40
30
20
10
5
2.9 (maximum)
Ratio
0.28
0.32
0.34
0.40
0.43
0.46
0.47
0.51
0.54
0.56
0.59
0.63
0.66
Average
Standard deviation
Number of cases
0.48
0.09
35
-------
TABLE 2.
Cumulative Percentage of Ratios Greater
Than A Given Value (24-hour)
PM10/TSP (24-hour)
Percentage Ratio
99.7 (minimum) 0.029
99 0.140
95 0.223
90 0.275
80 0.334
70 0.396
60 0.433
50 0.472
40 0.507
30 0.547
20 0.597
10 0.687
5 0.754
1 U.960
0.3 (maximum) 1.181
Average 0.478
Standard deviation 0.165
Number of cases 351
-------
Table 3 below is a summary of the appropriate use of the various
methods available in descending order of preference. Sections 4 and 5 will
provide additional explanation and examples of these methods and will
establish procedures for combining the direct use of PM^o data with the
frequency distribution or probability approach.
10
-------
TABLE 3
A SUMMARY OF METHODS FOR USING AVAILABLE PM10, IP OR TSP DATA TO
ASSESS PM10 NAAQS ATTAINMENT/NONATTAINMENT STATUS
Procedure
Ambient Monitoring
Data Available3
1. PMjo data meeting
Appendix K sampling
completeness
requirement
Type of
Assessment
Yes/No
Determination
Annual NAAQS
Compare average annual
arithmetic mean
directly to annual
NAAQS
24-hour
(a) Multiply number of observed
exceedances in a given year
by the ratio of 365 to the
number of data values in that
year to estimate the number of
exceedances in that year, and
(b) calculate average number of
estimated exceedances per year
from the most recent 3 years
of data.b
2. PM10 data with less
than complete sampling
and IPC data available
Estimation
of probability
of nonattainment
(a)
If sufficient PMio data
are available at a site
or for a similar, nearby
site(s) , use to derive
site-specific PMjo/IP mean
ratio for site of interest
(See Section 4.0)
(b) Use mean ratio derived in
(a) to estimate arithmetic
mean PM^g for the most
recent 3 years
(c) Calculate average arithmetic
mean PM^g ar|d compare to
the annual NAAOS
Use observed PMjQ ex-
ceedances to estimate a re-
vised number of allowed ex-
ceedances. If the revised
number of allowed exceed-
ances is less than 0, the
site is in nonattainment.
Otherwise use IP data for
remaining years and a
statistically defensible
distribution for 24-hour
PMio/IP ratios using equa-
tions analagous to (6),
(10), and (11), in the
text and figures comparable
to Figure 2 in the text.
(See Section 5.4)
-------
TABLE 3 (Continued)
Procedure
Ambient Monitoring
Data Available3
3. PM10 data with
less than complete
sampling and TSP
data available
Type of
Assessment
Estimation of
probability of
nonattainment
Annual NAAOS
Same as #2, only
substitute "TSP" for
"IP". If data are
insufficient to
derive a site-
specific distribution,
use the national de-
fault distribution.
" 24-hour
Same as #2, only substitute "TSP"
for "IP". If data are insufficient
to derive a site-specific dis-
tribution, use the national
default distribution.
4. TSP data only
Estimation of
probability of
nonattainment
ro
Calculate the average
arithmetic mean TSP level
using the most recent 3 years
of data; and estimate the
probability of nonattainment
using the above average and
the relationship between the
probability of exceeding
the annual PMjQ NAAOS
level and observed annual
arithmetic mean TSP
concentration (based on
the national distribution of
annual arithmetic mean
PM10/TSP ratios).
Estimate the probability of indivi-
dual observed 24-hour TSP concen-
tration data to exceed the 24-hour
PM}Q standard level using observed
24-hour TSP data and the relation-
ship between the probability of ex-
ceeding the 24-hour TSP concen-
tration (based on the national
distribution of 24-hour PMjQ/
TSP ratios), and use the equations
(6), (10), or (11) in the text
to estimate the probability
of failing the attainment test.
aListed in the order of preference.
-------
TABLE 3 (Continued)
^Attainment/nonattainment estimates can also be made in terms of an allowable
number of observed exceedances for a specific number of sample days:
Allowable Number of Sample Size, Observations
Observed Exceedances in 3 Years
1 £ 509
2 510-1018
3 1019-1096
C0btained with a dichotomous sampler with a 15 urn size discriminating inlet
and teflon filters. Samples obtained on quartz filters with a size
selective hi-volume samplers may be treated as dichotomous sampler
measurement.
-------
4.0 METHODOLOGY FOR ESTIMATING THE PROBABILITY OF NONATTAINMENT FOR PM10
NAAOS - ANNUAL STANDARD
Concerning ambient levels of PM^Q it is preferable to have sufficient
measured ambient PMjQ data so that ambient concentrations are determined
directly. However, in the absence of complete PMjg data, the probability
of nonattainment of one or both PMjg NAAOS can also be estimated for any
location, given observed TSP data or observed IP data. The probability of
not attaining the proposed annual standard, given annual arithmetic mean
TSP data, is determined in a straightforward manner. A brief explanation
and example are provided herein. Calculating the probability of not attaining
the proposed 24-hour standard is more complicated. This requires a more
detailed explanation, and will be discussed in Section 5.0.
It is possible to obtain an estimate of the probability of nonattainment
of a 50 yg/nr level of the annual PM^Q NAAOS by using annual arithmetic
mean TSP data and the information in Table 1.* We can define TSP as:
TSP - PMm concentration
For any fixed level of PM^Q, such as a proposed NAAQS for PM^Q of
50 ug/m^, the value of TSP which would correspond to a given probability
of exceedance can be calculated. For example, in Table 1 there is a 70%
probability that the PM10/TSP ratio will be greater than .43. Substituting
into the above equation, a TSP concentration of 116 yg/m^ is found (i.e.,
*It should be noted that the Tables and curves in this document depicting
probability distribution or plotting exceedance probabilities as functions
of TSP levels are not to be applied if one's hi-vol measurements for TSP
were obtained with filters provided for local agency use prior to 1983.
This is a consequence of the data used to derive the relationships in this
document being based on this kind of a data base.
14
-------
50/.43 = 116). This is the TSP value that, if measured, would correspond
to a 70% probability that the proposed PM1Q NAAQS of 50 yg/m3 would be
exceeded. A series of these calculations was made to develop the plot in
Figure 1.
The relationship in Figure 1 can be used to estimate the probability
r '
of nonattainment at any site with annual arithmetic mean TSP data. To use
Figure 1, the average annual arithmetic mean TSP concentration is calculated
for the site. The figure is entered for that TSP value and a corresponding
probability of nonattainment is read. For example, if the average annual
mean TSP were 150 yg/m^, the probability of nonattainment would be .92 or
92%.
For the purpose of estimating the probability of nonattainment at a
specific site, the average of the annual arithmetic means of the most
recent three year's data should be used, if available. For example,
TSP • (TsT)ag + (Tsp)pd + (TSP)^ (1)
—
where (TsF)^ is the arithmetic mean TSP concentration observed
during 1985, yg/m^, etc.
As an example, if the arithmetic mean TSP concentrations for the
years 1983, 84 and 85 were 135, 142 and 158, the TsT would be (135 + 142 +
158)/3 = 145 yg/m3. Figure 1 would indicate a 90% likelihood of exceeding
an arithmetic mean PM1Q NAAQS of 50 yg/m3. This is quite different from a
determination of the attainment status for the current annual TSP primary
NAAOS. The current TSP NAAQS considers the geometric rather than arithmetic
15
-------
Figure 1.
CTi
to
3
i
CO.
at
o
in
•o
0>
0)
LI
X
LU
(0
.Q
O
Relationship Between The Probability Of Exceeding A 50 ug/m Annual PM.Q Concentration
And Observed TSP Annual Arithmetic Mean Concentration
1.0 -i
0.9 -
Annual Arithmetic Mean TSP Concentration, ug/nf
-------
mean. Further, no probability calculation is required since direct measure-
ments of TSP are available.
If 3 years of valid data (i.e., at least 75% data capture per quarter)
of PMjg is available, it may be used directly to determine whether the annual
NAAQS is being attained. The annual arithmetic mean should be computed by
taking the mean of the quarterly mean concentrations as described in Appendix
K to Part 50, Code of Federal Regulations (CFR).
If at least 1 full year of PM^Q data (having at least 75% data capture
for each of 4 quarters and a full year of valid TSP data (>_ 75% data capture)
exist for a site for the same year, a site or region-specific mean PMiQ/TSP
ratio should be developed and used in the following procedure:
= mean of full year of valid PMjg data for year i (2a)
l = TSPi-l x (mean site specific 24-hour ratio)i (2b)
PM10i-2 = TSP-j_2 x (mean site specific 24-hour ratio)j (2c)
where PMioi-l = estimated annual arithmetic mean PMjg concentration in
-2 = estimated annual arithmetic mean PM^g concentration in
year 1-2
TSPj_i = observed annual arithmetic mean TSP concentration in
year^!
TSP-j.2 = observed annual arithmetic mean TSP concentration in
Thus, the PM1(1 for the 3 years' data would be
+ PMmi-i + PM10i-2)/3.
In effect, if PM^g is greater than the level of the proposed NAAOS, the
probability of nonattainment is 1.0. Otherwise, the probability of non
attainment is 0.
17
-------
Procedures similar to those described for estimating PM^Q attainment
status given TSP data can be used to estimate PM^g attainment given IP data,
providing sufficient data exist to develop a site-specific PMjg/IP mean
ratio (see data requirements for TSP above). This site specific distribution
would be used to construct a figure analogous to Figure 1. This analogous
figure would then be used as described above. Since few sites are likely
to have 3 years of IP data, it is anticipated that IP data will be used
very infrequently to estimate PMjg attainment status.
In summary, the annual PMjQ NAAQS attainment status may be estimated
directly using PMjg data or the probability of nonattainment may be estimated
using TSP (or IP) data and the frequency distribution method described above.
The following steps apply in inferring PMjg levels at sites in which
only TSP data are measured:
(1) calculate the average arithmetic mean TSP, as described in
the proposed Appendix K to Part 50, Code of Federal Regulations;
(2) enter Figure 1 (for TSP) and read the corresponding
probability of nonattainment of the annual arithmetic mean NAAOS for PMjg.
If PM^g data are available for fewer than 3 years, a statistically
defensible site specific ratio for PM^g/TSP ratios may be developed. This
mean ratio is used to convert mean TSP observations (in years with insuffi-
cient PMjg data) to equivalent mean PMjg values. Probability of nonattainment
with the annual NAAOS is estimated by comparing the average of 3 yearly mean
"PM10" values with the level of the NAAOS.
18
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5.0 METHODOLOGY FOR ESTIMATING THE PROBABILITY OF NONATTAINMENT FOR
PM1Q NAAOS - 24-HOUR STANDARD
The proposed 24-hour NAAOS for particulate matter (PM) specifies that
the expected number of exceedances must be less than or equal to one per
year. The proposed attainment test consists of using monitoring data to
estimate'the average number of exceedances expected with complete sampling
over a 3-year time period. The test specifies that the average number of
estimated exceedances be rounded to the nearest tenth (.05 rounds up).
Thus, an estimated number of 1.05 (which becomes 1.1) exceedances per year
would be required in order to fail the attainment test.
According to Appendix K to Part 50 and Part 58.13 of the proposed
standards and the PMjQ SIP Development Guideline, the first observed exceed-
ance shall not be adjusted for incomplete sampling if everyday sampling is
initiated thereafter. To be consistent with the intent of the proposed
provisions of the standards, the procedures for estimating the probability
of nonattainment of the proposed 24-hour standard include the provision
that the first observed exceedance in the 3-year time period shall not be
adjusted for incomplete sampling. Based on these considerations, the number
of allowable exceedances as a function of data completeness is presented in
Table 4. Use of the information in Table 4 is illustrated in Section 5.1.
Prior to the availability of 3 complete years of PM^g monitoring data,
it may be useful to estimate the probability of not attaining the 24-hour
NAAOS through use of TSP data. As PM^Q monitoring continues, these data would
also be incorporated into the nonattainment probability assessment. The fol-
lowing discussion addresses procedures for estimating attainment/nonattainment
for three cases: (1) adequate PM10 data, (2) no PM10 data, and (3) some PM10
data.
19
-------
5.1 Assessment Rased on Adequate PM1Q Data
If 3 years of valid PM^g data (i.e., at least 75% data capture
per quarter) are available, the assessment of attainment/nonattainment is
relatively straightforward. The approach is described in Appendix K to
40 CFR50? and consists of estimating the number of exceedances per year from
the observed monitoring data and then averaging these estimates over a 3-year
period. Thus, the probability of nonattainment is certainty (i.e., defined
as 1.0) if the proposed attainment test is failed. Otherwise, the probability
of nonattainment is zero.
For the purposes of this guideline, the adjustment for incomplete sampling
shall be performed on an annual basis. The formula for estimation of exceedances,
F.J from a year of PM^Q monitoring data is as follows:
E1 = e1 x N / n1 (2)
where
E.J = the estimated number of exceedances for year i,
assuming complete sampling
e.j = the observed number of exceedances for year i
n.j = the number of data values observed in year i, and
N = the total number of possible values in year (e.g., 3fi5)
Rased on the provision for the first observed exceedance,
Ei = 1, if ei = 1, or (2a)
EJ = 1 + (ej - 1) x N/ni, if e1 > 1 (2b)
(provided that the first exceedance occurred in year i).
Note that E-j is also called the estimated exceedance rate.
20
-------
Example 1
The 3-year period 1983-1985 is being evaluated. In 1983, a hypothetical
site measured 292 PM^Q values with at least 75% data capture in each quarter.
Two exceedances of the level of the NAAQS were observed. The recorded con-
centrations were 220 and 260 yg/m3. Since more than one exceedance was
i '
observed in the first evaluation year, the estimated number of exceedances
is calculated using equation (2b) as
r _ i , 1*365 _ o OC
too - I + - £.£0
no 292
Note that the concentration magnitudes of the observed exceedances were not
considered. The magnitudes would be important, however, when the amount of
required control is evaluated*.
The estimated exceedance rate over a 3-year period would be based on
the average of the estimated number of exceedances for each year. If the
numbers of estimated exceedances (E-j) for 1984 and 1985 were 0 and 2.5,
respectively, then the average number of estimated exceedances, rounded
to the nearest tenth, would be l.fi. Since 1.6 is greater than 1.0, this
site would fail the attainment test.
Although attainment of the 24-hour expected exceedance NAAQS using PM^Q
data can be determined in terms of the average number of estimated exceedances
(as in the above example), the procedure can also be done in terms of an
allowable number of observed exceedances for a specific number of sampling days,
*In some instances, PM10 observations close to the level of the NAAQS would be
subject to special interpretations, depending on the PMjg monitoring instru-
ment used. See Chapter 2 of the PMin SIP Development Guideline, U.S. EPA,
OAQPS, for details.
21
-------
The number of allowable observed exceedances over 3 years Is shown as a
function of sample size in Table 4. With the use of this table, it is assumed
that the sampling rates are similar in each year. For the once in 6-day sam-
pling rate historically applied to TSP and allowing for the first exceedance
provision, one observed exceedance would be allowed. This follows because
a site with a sample size as small as 183 (i.e., 3 x 61 samples/year) would
fail the proposed attainment test only if it had 2 or more observations
greater than the level of the NAAQS, according to Table 4.
Example ?.
(a) As stated in Example 1, two exceedances were observed for a site in
1983 that sampled 292 PMjQ values. Suppose that in the two subsequent years,
1 and 0 PMjQ exceedances were observed and that the number of sampling days
was 120 in both of these years. For the 3 years, there was a total sample
size of 532 observations and from Table 4, we see that two exceedances are
allowed at this sampling rate. Thus, the three observed exceedances cause
a failure of the proposed attainment test.
(b) Suppose that PMjo data was not produced in 1983. In this case, over
the 2-year period, 1984-1985, there was one observed exceedance. Results of
the attainment test are now inconclusive. That is, the number of observed
exceedances is consistent with the allowable number specified in Table 4.
However, data from 2 years are insufficient to conclusively demonstrate
attainment according to provisions in Appendix K. The situation described
in part (b) of this example is addressed in Section 5.3.
22
-------
TABLE 4. Allowable Observed Exceedances as a Function of Sample Size
for a One Expected Exceedance Standard.
Allowable Number of Sample Size, Observations
Observed Exceedances in 3 Years
1 <_ 509
2 510-1018
3 1019-1096
-------
5.2 Assessment Without PMm Hata
Unlike the 'yes-no' situation with actual PM^g monitoring data,
the failure of the proposed PM^g attainment test using TSP data will be
expressed as a probability. This probability will take into account the
chance of ,a PMjg NAAOS exceedance on each TSP sampling day. The probability
of nonattainment is defined in terms of the likelihood of observing more
than the number of allowable PM^g NAAOS exceedances. The conditions specifying
failure of the attainment test depend on TSP sampling frequency as outlined
in Section 5.1 (see Table 4).
The chances of a PMjg NAAOS exceedance on each TSP sampling day is
derived from the estimated probability distribution of the relative PM^g
portion of TSP (Table 2). This distribution specifies the probability
that the PMjg portion of the TSP would have exceeded a stated fraction.
For a specific TSP concentration, these ratio probabilities translate into
the probability that the concentration of the PM^g portion of the TSP would
have exceeded a given PM^g concentration level. A curve of "exceedance"
probabilities for a PM1Q concentration _> 150 yg/m3 is shown in Figure 2.
5.2.1 One Allowable Exceedance
Typically, TSP monitoring sites sample on a once in fi day schedule and
thus the number of TSP samples is usually less than 61 per year or 183 over
a 3-year period. For these and other sites producing fewer than 510 observa-
tions in 3 years, one exceedance is allowed and thus the probability of
failing the attainment test is the probability of observing at least two
PM^o exceedances over the sampling time period (from Table 4). Stated another
way, this is the probability of not observing zero or one exceedances as
shown below in equations (3) - (6).
24
-------
Figure 2.
Relationship Between The Probability Of Exceeding A ISO ug/m3 24 Hour PM ..Concentration
And Observed TSP 24 Hour Concentration
(0
C.
.
i.O
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1 -
100
I
200
I
300
I
400
I
500
I
600
I
700
I
800
I
900
1000
I
1100
Observed 24 Hour TSP Concentration, ug/nf
-------
If p-j represents the PMjQ exceedance probability for the ith TSP sample, then
the probability, P0, of observing zero allowable exceedances is
PO = TT qi (3)
1 = 1
; '
where q^ = I-PJ (the probability that an observed TSP value,
TSP-j , does not correspond to a PMjo value
greater than the level of the 24-hour PMjo
standard), and
n = the number of TSP values greater than the level
of the 24-hour PM standard.
Example 3
In this example, the level of the PMjQ NAAQS is assumed to be
'150 yg/m3. TSP data greater than 150 yg/m3 observed during the most
recent 3 years are as follows:
Observed TSP Concentrations
Year Sample Size Greater Than 150 ug/m3
1983 60 250
1984 50 290,200
1985 50 400,280
Using Figure 2, the PMjQ exceedance probabilities for each TSP value
are as follow:
TSP PMm Exceedance Probability
400 .72
290 .38
280 .32
250 .20
200 .05
26
-------
Rased on equation (3), the probability of observing no exceedance is
P0 = (1-0.72)(1-0.38)'"(1-0.05), or
P0 = .0897
The probability of observing exactly one exceedance is
P! = P0 Ci (4)
where P0 is defined in equation (3) and
n .
= I qi (5)
Example 4
Suppose the data is the same as used in Example 3. Using equation (4)
and (5), the probability of observing one exceedance, Pj, is
£i
q-j , where P0 is the same as derived in Example 3
[.72 + .38 + .32 + .20 + .05]
Thus, P! = (.09) C.28" .61 ~38 ~M Ml
= (.09) (3.96)
= .36
As indicated earlier, the probability of failing the attainment test for
sites producing fewer than 509 observations in 3 years is the probability of
observing more than one PMjg exceedance over the sampling period. This
probability is equivalent to the probability of not observing zero or one
exceedance, or
27
-------
PF (i) = i - (PO + PI) (fi)
Example 5
Using the data and calculations performed in examples 3 and 4,
PF (1) = 1 - (P0 + PI)
= 1 - (.09 + .36)
= .55
Thus, the probability of failing the attainment test is 0.55, i.e., 55%
probability of nonattainment.
5.2.2 Two or More Allowable Exceedances
If the TSP data were sampled at least once in 2 days (or otherwise
more than 509 days in 3 years), then two or more exceedances may be allowed
by the standard over a 3-year period. For example, with 600 TSP samples
over a 3-year period, Table 4 indicates that two observed exceedances are
allowed by the standard. For this situation, the failure probability is
defined as the probability of observing more than two exceedances.
With 3 years of TSP data (sampling every day), up to three exceedances
may be allowed (Table 4). Depending on TSP sample size, the failure
probability guide may be defined as the probability of observing more than
two or three exceedances. These probability computations depend on the
chance of observing exactly zero, one, two or three exceedances. The
remainder of this section provides the equations for these calculations.
Their use assumes that the annual TSP sampling rates are similar, as defined
by the ranges in Table 4.
The formulas for the probability of exactly two exceedances, ?2» anc'
exactly three exceedances, ?3, are
28
-------
1
Pj> = 2 FPiCi - P0C2"I» and (7)
1
= 3" CpC - PC + P0Cl> (8)
n /£l\r
-r =.E VH/. f = i,
where Cr = Z \qi/, r = 1, 2 or 3 (9)
1=1
The probability of failing the attainment test for two or three
allowable exceedances is
PF (2) = 1 - (P0 + PI + ?2) (10)
PF (3) = 1 - (P0 + P! + P2 + PS) (ID
The computational form of equations 4, 5, 7, 8, and 9 follows from the
probability generating function of a Bernoulli process with variable
probabilities and have been derived elsewhere. (13, 14)
5.3 Assessment Based on TSP Data and One or More Years of PMm Hata
If three years of PMjQ data do not exist (according to Section 5.1) to
determine the probability of nonattainment directly, then available PM^Q
data shall be combined with prior TSP data to estimate the probability for
the 3-year period. This procedure shall be discussed for two situations:
first, when a partial year of PM^Q data is available and second, when 1 or 2
years of PMjQ data are available. In either case, minimum annual data com-
pleteness requirements for 3 years of data would be applicable.
When a partial year of PMjg data is available, then actual, PMjg
concentrations, may be substituted for concurrent, collocated TSP measure-
ments. If the PM1Q value (rounded to the nearest 10 yg/m3, as specified by
Appendix K) is less than or equal the level of the standard, then the
29
-------
exceedance probability would be 0.0, and is therefore not considered in
equations (3)-(ll). If any PMjg values are greater than the level of the
standard, then the number of allowable exceedances, as per Table 4, are
reduced by the number of observed exceedances.* The revised number of
allowable exceedances is defined as
i '
A1 = A - E, (12)
where A is the allowable number of exceedances based on the total number
of sampling days, and
E is the observed number of actual PM^g exceedances.*
The revised allowable number of exceedances can now be zero. When this is
the case, the probability of nonattainment becomes
PF (0) = 1 - Pn (13)
When the number of observed exceedances exceed the allowable number (i.e.,
A'<0), the probability of nonattainment becomes 1.0. If this is not the
case, then equations (3)-(13) are applied on the basis of the reduced number
of allowable exceedances. In effect, the days when PMjg measurements were
made would not be included in the computation. With this approach, the
estimated PMjg exceedances derived from the actual PM^g data are viewed as
being fixed, while the estimated PM^g exceedances derived from the TSP data
are viewed as a random variable. Thus, the probability of failing the
attainment test can be defined solely in terms of the additional PM^g
exceedances estimated from the TSP data. This procedure is illustrated by
the following example.
*In some instances, PM^g observations close to the level of the NAAQS would be
subject to special interpretations, depending on the PMjg monitoring instru-
ment used. See Chapter 2 of the PMin SIP Development Guideline, U.S. EPA,
OAOPS, for details.
30
-------
Example 6
Following example 5, suppose that some PM^g data were collected in 1985
and that PMjg data were available for the days on which TSP concentrations of
400 yg/m3 and 280 yg/m3 were recorded. The day which recorded a value of
400 had a PM10 value of 180 yg/m3, an exceedance of the 150 yg/m3 standard
level. This was the only PM^g exceedance recorded at this site. According
to Table 4, one exceedance would have been allowed. Now, however, because
of the single observed PM^g exceedance, no additional PM^g exceedances would
be permitted (i.e. A '= 1-1 = 0).
Thus the probability of nonattainment is the probability of observing
one or more additional exceedances, and there are only three TSP values
(290 yg/m3, 250 yg/m3 and 200 yg/m) for which exceedance probabilities
are needed.
Using equation (3), then
P0 = (1-0.38) (1-0.20) (1-0.05), or
= .4712
Using equation (13), the failure probability is
PF(0) = 1-.471? = .5233 or .53
The development of the PM^g nonattainment probability using 1 or 2
years of PM^g data is based on a similar approach. For this situation, a
site specific frequency distribution of ratios could be used to develop a
revised Figure 2, providing that the site specific frequency distribution is
statistically defensible. Otherwise, the national distribution is used.
The distribution should be used to estimate the probabilities (i.e., the
p-j) for use in equations (6), (10), (11), or (13).
31
-------
When 1 or 2 years of PM^Q data are available, and PM^g and TSP were
sampled at the same frequency, then equations (3-12) will again be used to
estimate the probability of failing the attainment test. An adjustment to
the allowable number of exceedances using equation (13) would be required
if any actual PM10 exceedances were observed, as discussed previously. The
following example illustrates the calculations needed when PMjg and TSP
have the same sampling rates.
Example 7
Suppose there are 180 PMjQ samples in 1985 showing 2 NAAQS exceedances
and 180 TSP samples collected annually during 1983-1984. Based on 540 PMin
plus TSP samples, the allowable number of exceedances, A, is equal to 2 (from
Table 4, Section 5.2). Since two actual PMjQ NAAQS exceedances were observed,
the revised allowable number, A1, is 2 - 2 = 0. Therefore for this case,
failure of the attainment test is defined as the probability of observing 1
or more exceedances (equation 13).
When PMm and TSP are sampled at different rates, the allowable number
*v
of exceedances, A, in Table 4 and equation (12) may not be used directly.
First, intermediate calculations must be performed to produce adjusted
** -v
allowable number of exceedances, A, and adjusted PM^Q exceedances, E
according to the average TSP sampling rate. The total number of exceedances
allowed in 3 years is 3.14. The first observed exceedance is not adjusted
for incomplete sampling. If nTSp and nPMin represent the number of TSP and
PMjQ samples per year, respectively, then the total number of observed
allowable exceedances is
•%*
A = 1 + 2.14 n-rsp (14)
~
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and,
E = 1 + (E-l)nTsP *
nPM (15)
10
The revised number of allowable exceedances for the remaining years is
defined as
i '
A1 = A - E (16)
The probability of nonattainment is the chance of observing more than
A1 PMjQ exceedances during the TSP sampling period. To be consistent
with equations (3)-(13), the number of allowable exceedances are interpreted
as the integer values of A1 (for example, the integer value of 1.7 is 1).
Note that with this approach, the number of allowable exceedances for
the 1 or 2 years with TSP data cannot be more than what would be permitted
for 3 years of TSP data at that same sampling rate (i.e. E must be less
than or equal to A). Depending on the PMjo sampling rate, however, 1-3
actual PM^Q exceedances may be permitted for purposes of estimating
nonattainment probabilities.
Example 8
In this example, assume TSP was sampled 60 times per year in 1982 and
1983. Suppose that PM}Q was sampled 180 days in 1984 and showed two
exceedances. What is the probability of PMjg nonattainment? First, we
calculate A, on the basis of 3 years of data with 60 observations per year:
A = 1 + 2.14(60) = 1.35
365
Next, we calculate the adjusted number of exceedances,
*Note that E is the actual number of observed exceedances, as defined
in Equation 12.
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E = 1 + (l)x 60 = 1.33
***
Therefore, A1 = 1.35 - 1.33 = 0.02
The integer value of A' equals zero, so no additional exceedances
would have been permitted during the TSP sampling period (i.e. one addi-
tional exceedance would be sufficient for nonattainment). For this example,
therefore, equations (3) and (13) would be used with 1982 and 1983 TSP data.
If three PM^Q exceedances were observed in 1984, the site would
automatically fail the attainment test and have a nonattainment probability
of one. If the revised number of allowable exceedances, A', were estimated
to be "1", however, Equations (3) - (6) would be used with 1983 and 1984
TSP data to estimate the probability of nonattainment.
5.4 Use of Site or Region-Specific Distributions
Section 4.0 made provision for the development of an annual site
or region-specific ratio using at least 1 full year of concurrent PM^g and
TSP data. Analogously, a site or region-specific frequency distribution of
ratios should be developed (provided it is statistically defensible) and
used in conjunction with the 24-hour NAAOS attainment determination. This
distribution would then be used in place of the national distribution when
PMjg data are available for partial years or not available at all as provided
for in Section 5.3.
5.5 Use of IP Data
Similar procedures to those described in Sections 5.1 - 5.3 can
be followed using IP and some PM^Q data provided the data are sufficient to
develop a site-specific PMin/IP distribution. One would simply substitute
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the term "IP" for "TSP" in the preceding discussion. Since few sites would
have current IP data, it is anticipated that this procedure would be used
very infrequently.
5.6 Software Support
t .A computer program has been developed to automate the calculations
necessary for estimating the probability of exceedance of both the annual
and 24-hour NAAQS.(15)
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6.0 ESTIMATING SPATIAL EXTENT OF NONATTAINMENT SITUATIONS
6.1 Introduction
As described in earlier sections, assessing attainment/nonattainment
of the National Ambient Air Duality Standards (NAAOS) for PM10 requires the
use of ambient monitoring data. If the data and the assessment procedures
described earlier identify a nonattainment area and result in the requirement
for control strategy development, the question remains as to what is the
spatial extent of the nonattainment problem. Defining the spatial extent
of the problem is not a simple, straightforward technical matter, as is
evidenced by the differences in the size of boundaries for nonattainment
areas for the other criteria pollutants and the original TSP NAAQS. For
example, some nonattainment area boundaries are county or citywide, some
include entire townships or parishes, while others encompass the central
business district or an area bounded by designated streets.
Such differences occur because the size of the boundaries are
influenced by a variety of technical factors such as the pollutant itself,
its reactivity, type and density of emissions, meteorology, topography,
etc. In addition to these technical considerations, final boundaries are
also influenced by nontechnical factors such as the amount of time and
resources available to effectively define their limits, as well as the
jurisdictional borders of the areas surrounding the nonattainment
monitoring site.
States have used several techniques, including dispersion modeling,
isopleth analysis, source receptor models, and monitoring site scales of
representativeness in defining nonattainment boundaries for other pollutants.
These techniques are also used for other purposes and are fairly complex
and detailed. Since they are not unique to nonattainment boundary
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definitions, and are adequately described and discussed elsewhere in the
literature, they are not covered here in any great detail; rather, they are
listed as techniques or approaches that are recommended for use as guidance
in defining the extent of a nonattainment problem.
6.2_ .Use of Acceptable Air Quality Data
The use of acceptable air quality data is required in determining
the attainment/nonattainment status of a monitoring site. In determining
data acceptability, three items which need to be evaluated are: the type of
sampler used, sampler location, and quality of the data.
6.2.1 Type of Sampler
When using TSP data for estimating the probability of
nonattainment for PMjg, the TSP sampler must be a reference method, as defined
in Appendix B to 40 CFR Part 50. For those situations where inhalable parti-
culate (IP) data will be used for estimating the probability of nonattainment
for PMio or PM^Q data will be used directly, the determination of the accepta-
bility of the type of IP or PM^Q sampler will have to be done on a case-by-
case basis, as there is no existing designated reference method for IP or
PM^Q. Data collected from dichotomous samplers used in EPA's national
sampling network for inhalable particulates are considered acceptable. As
a general rule when using IP or PMjQ data, the sampler should be similar to
those used in the EPA IP network or EPA supplied PMjg samplers which are
based on the principles of inertia! separation and filtration. The Environ-
mental Monitoring Systems Laboratory (EMSL), Research Triangle Park, North
Carolina, will provide guidance to assist in making this determination.
37
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6.2.? Sampler Location
Appendices D and E of 40 CFR 58 included network design and
siting criteria for TSP samplers and PM^g samplers, but not for IP. If TSP
data are to be used in the assessment of attainment/nonattainment for PMjn»
then these samplers must conform to the requirements of Appendices D and E.
6.?.3 Data Quality
The Agency's quality assurance policy is that all environ-
mental data generated, processed, or used for implementing Clean Air Act
requirements, will be of known precision and accuracy and, to the extent
possible, be complete, comparable, and representative.
Consistent with this policy, TSP samplers must conform to the
reference method requirements and the data must be collected in accordance
with the quality assurance criteria contained in Appendix A of Part 58.
For PM^o and IP data, the samplers must be similar to those used in the EPA
national sampling network for inhalable particulates, except that size-selective
hi-volume samples collected with glass fiber filters should not be used.
Minimum quality assurance activities that should have been conducted during
the PMjQ or IP measurement process are quality control checks, data review
and validation activities. The quality control activities include regularly
scheduled flow calibrations where the flow measurement devices used to
measure sampling rate were also calibrated. Data review and validation
procedures should be similar to those established for the other criteria
pollutants.
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6.3 Determining the Boundaries of a Nonattainment Area
As noted in Section 6.1, several techniques have been used by
States to define the spatial extent of NAAOS violations expressed as boundaries
of nonattainment areas. Basically, the approaches used can be placed into
three categories:
i '
1. a qualitative analysis of the area of representativeness of
the monitoring site, together with consideration of terrain, meteorology
and sources of emissions;
2. spatial interpolation of air monitoring data;
3. air quality simulation by dispersion modeling.
In determining the extent of a PM^g nonattainment situation, the use of
any one or a combination of the above categories would be considered accept-
able to the EPA. The choice of which technique to use depends on the
complexity of the PM^ problem area.
6.3.1 Qualitative Analysis
This approach, unlike the others discussed below, is not
intended to define any single analytical procedure for defining the extent
of a nonattainment problem. On the contrary, it is intended to recognize
as acceptable various approaches that consider such factors as ambient
monitoring data, the spatial scales of representativeness of the monitoring
station, the number of areas in the community similar to that being measured
by the monitoring station, the type of terrain, meteorology, and sources
of PM}Q emissions. Revisions to Appendix n of Part 58 describe the topic
of spatial scales of repesentativeness for PM^Q stations, as well as pro-
cedures for locating such stations. The predominant spatial scales for
PM10 stations include micro, middle and neighborhood, with a fewer number of
39
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stations represented by the urban and regional scale. Properly located
stations that are specifically classified according to their spatial scale
could, in certain instances, be solely used to define the limits of the
nonattainment area. Other situations obviously will require a more detailed
review and analysis of sources, pollutant transport and receptor.
6.3.2 Spatial Interpolation of Air Monitoring Data
Although it would be desirable to ensure that the entire
area of a designated nonattainment area is actually nonattainment, air
monitoring costs are so high as to prohibit full coverage of a large non-
attainment area. There are, however, two methods available to arrive at
refined estimates of the spatial variation of air quality. One method is
spatial interpolation of air monitoring data, the other which will be
discussed in Section 6.3.3, is air quality simulation by dispersion modeling.
The use of spatial interpolation of air monitoring data is the method
most appropriate for situations in which monitors are located at relatively
close proximity to one another. Over the past years, most cities and urban
areas have established fairly dense air monitoring networks which enabled
the technique to become more widely applicable. A complete description of
the method is described in the publication, "Guideline on Procedures for
Constructing Air Pollution Isopleth Profiles and Population Exposure Analysis,"
U.S. Environmental Protection Agency, Office of Air Quality Planning and
Standards, Research Triangle Park, North Carolina 27711, EPA-450/2-77-024a,
October 1977 (OAOPS No. 1.2-083).
The basic procedure involves the plotting of station locations and
measured concentrations from these stations. For those areas of the map
not covered by monitoring stations, a spatial interpolation scheme is used
40
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to estimate air quality concentrations. The technique can be done manually
or through the use of computer mapping programs.
6.3.3 Air Quality Simulation by Dispersion Modeling
Determining the extent of the PM NAAOS nonattainment can
also be accomplished by using dispersion models to simulate the spatial
distribution of air quality under various conditions. Dispersion modeling
is more appropriate than spatial interpolation of air monitoring data in
areas where actual monitoring data are scarce. In order to use a dispersion
model, source data, air quality data, and meteorological data are required.
For dispersion modeling purposes, PMjg is treated as a nonreactive gas. The
type of source (point, area, mobile, or stationary), type of standard
(short term or annual), type of terrain (flat or rough), and the type of
area (urban or rural) will of course affect the decision as to which model
to use. The document, Guideline on Air Quality Models, (16), includes
specific recommendations concerning air quality models, and also describes
circumstances for which models, data and techniques other than those
recommended in the guideline may be applied.
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7.0 ACKNOWLEDGEMENTS
The authors wish to acknowledge reviews of preliminary versions of
this document by Dr. William P. Smith of the Statistical Policy Staff of
OPRM, Mr. Jack Suggs of the EMSL, and Dr. William F. Biller. Special
thanks i,s. given to Mr. Roger Powell of the Control Programs Development
Division, OAQPS, for advice in ensuring the consistency of this document
with the overall regulatory effort. Finally, the excellent typing and
clerical support by Mrs. Carole Mask, Mrs. Cathy Coats, Mrs. Josephine
Harris and Mrs. Helen Hinton is greatly appreciated.
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8.0 REFERENCES
1. U.S. Environmental Protection Agency, "National Primary and Secondary
Ambient Air Quality Standards. Appendix B - Reference Method for the
Determination of Suspended Particulates in the Atmosphere (high volume
method)," 40 CRF 50: 12-16, July 1, 1979.
2. R. W. Countant, "Effect of Environmental Variables on Collection of
Atmospheric Sulfate." Environmental Science and Technology 11:
873-878, 1977.
3. Hardial S. Chalal and David J. Romano, "High Volume Sampling: Effect
of Windborne Particulate Matter Deposited During Idle Periods."
Journal of the Air Pollution Control Association, Volume 26, No. 9,
pages 885-886, 1976.
4. A. R. McFarland and C. E. Rodes, "Characteristics of Aerosol Samplers
Used in Ambient Air Monitoring." Presented at 86th National Meeting,
American Institute of Chemical Engineers, Houston, Texas, April 2,
1979.
5. B. W. Loo, R. S. Adachi, C. P. Cork, F. S. Goulding, J. M. Jaklevic,
D. A. Landis, and W. L. Searles, "A Second Generation Dichotomous
Sampler for Large Scale Monitoring of Airborne Particulate Matter,"
LBL-8725, Lawrence Berkeley Laboratory, Berkeley, California,
January 1979.
6. A. K. Pollack, A. B. Hudischewskyj and A. D. Thrall, An Examination of
1982-83 Particulate Matter Ratios and Their Use in the Estimate of
PMm NAAQS Attainment Status. EPA-450/4-85-010, (August, 1985).
7. J. B. Wedding, M. Weigand, W. John, and S. Wall, "Sampling Effectiveness
of the Inlet to the Dichotomous Sampler." Environmental Sciences and
Technology, !L4: 1367-1370, 1980.
8. Kenneth Axetell, Jr. and Chatten Cowherd, Jr., Improved Emission
Factors for Fugitive Dust from Western Surface Coal Mining Sources.
Final Report to U.S. Environmental Protection Agency, Cincinnati,
Ohio by PEDCo Environmental under Contract Number 68-02-2924, Volume I,
page 4-1, July 1981.
9. Jack C. Suggs, Charles E. Rodes, E. Gardner Evans, and Ralph E.
Baumgardner, Inhalable Particulate Network Annual Report: Operation
and Data Summary (mass concentrations only), April 1979 - June 1980.
U.S. Environmental Protection Agency Report Number EPA-600/4-81-037,
Research Triangle Park, North Carolina, May 1981.
10. Thompson G. Pace, "Estimating PM^o Concentrations from IP and TSP
Data," APCA Paper 82-45.2, Presented at Annual Meeting of the Air
Pollution Control Association, New Orleans, Louisiana, June 1982.
43
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11. John G. Watson, Judith Chow and Jitindra Shah, Analysis of Inhalable
and Fine Participate Matter Measurements. Final Report to U.S.
Environmental Protection Agency, Research Triangle Park, North Carolina,
by ER&T under Contract No. 68-02-2542, Task Order 6, pages 8-18,
December 198?.
12. Neil H. Frank and Thomas C. Curran, "Statistical Aspects of a 24-hour
National Ambient Air Ouality Standard for Particulate Matter,"
Paper 82-23.8, 75th Annual APCA Conference, New Orleans, Louisiana,
June 1Q82.
13. W. Feller, An Introduction to Probability Theory and Its Application,
Volume I, 3rd Edition, John Wiley and Sons, 19fi8, page 282.
14. Memorandum from W. P. Smith to N. P. Ross, subject: "Recursive
Algorithms for Computing Compliance Probabilities," November 1, 1982.
15. W. Freas, User's Guide for PM-|n Probability Guideline Software,
Version 2.0, U.S. Environmental Protection Agency, Research Triangle
Park, North Carolina 27711, in preparation.
Ifi. U.S. Environmental Protection Agency, Guideline on Air Ouality Models
(Revised). F.PA-450/2-78-027R, (July
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TECHNICAL REPORT DATA
(Please rtsd Instructions on the reierse before completing}
1 RtPORT NO. 2
EPA-450/4-86-017
4. TITLE ANDSUBTITLE
Procedures For Estimating Probability Of Nonattainment
Of A PM NAAOS Using Total Suspended Particulate
Or PM10iData
7 AUTHOR(S)
T. G. Pace, E. L. Meyer, N. H. Frank and S. F. Sleva
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Monitoring And Data Analysis Division
Office Of Air Quality Planning And Standards
U. S. Environmental Protection Agency
Research Triangle Park, NC 27711
12. SPONSORING AGENCY NAME AND ADDRESS
3. RECIPIENT'S ACCESSION NO.
5. REPORT DATE
December 1986
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION' REPORT tvO.
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
13. TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
The proposed primary National Ambient Air Quality Standards (NAAOS) for participate
matter (PM) specify ambient concentrations for particles smaller than 10 micrometers
(pm) aerodynamic diameter (PM^). This document describes a methodology for
using available PMjn measurements in conjunction with TSP data to estimate whether
or not the annual and/or 24-hour NAAQS for PMjg are likely to be violated (probability
of nonattainment). The probability of nonattainment is one of the criteria which
are used to specify action States are to take in developing PMjo monitoring require-
ments and State Implementation Plans (SIP's). The document also addresses appropriate
methods for determining the spatial extent of the nonattainment situations. The
following hierarchy is described in the document for using available ambient measure-
ments to determine attainment/nonattainment directly or to estimate the probability
of PM}Q nonattainment: (1) use ambient PM^Q data alone; (2) use less than complete
PM}g data and Inhalable Particulate (IP) measurements obtained with the dichotomous
sampler; (3) use PM^Q data with less than complete sampling in conjunction with TSP
data to draw inferences about PMjg nonattainment. Alternatively, IP or TSP measure-
ments together with a statistically defensible site specific probability distribution
for 24-hour PM^/IP (or PM^Q/TSP) ratios to estimate likelihood of nonattainment;
(4) use TSP data to draw inferences about the probability of PM^Q nonattainment.
This document describes the above hierarchy and provides guidance for application.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
PMio
Particulate Matter
Total Suspended Particulate
Estimating Procedures
Nonattainment
National Ambient Air Quality Standards
18. DISTRIBUTION STATEMENT
b. IDENTIFIERS/OPEN ENDED TERMS
19. SECURITY CLASS (This Report}
2O SECURITY CLASS (This page}
c. COSATI Held/Group
21 NO. OF PAGES
62
22. PRICE
EPA Form 2220-1 (Rev. 4-77)
PREVIOUS EDITION IS OBSOLETE
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