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OAR Box 1111 

Prepped by Ryan Dugan 

Document Number: 

•^Yd ll-A-2 

Docket Number: 

A-83-22 

Printed4/15/2008 1:25:18 PM Sheet 111 of 118 
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Final Report 

AN EXAMINATION OF AIR QUALITY 

DATA COMPLETENESS REQUIREMENTS 

SYSAPP-84/076 

29 May 1984 

Prepared for 

Monitoring and Reports Branch 

Office of Air Quality Planning and Standards 

U.S. Environmental Protection Agency 

Research Triangle Park, NC 27711 

Prepared by 

A. D. Thrall 

J. L. Baptista 

C. S. Burton 

Systems Applications, Inc, 

101 Lucas Valley Road 

San Rafael, CA 94903 

68306 ef 831U6T 
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DISCLAIMER 

This report has been reviewed by the Office of Air Quality Planning 

and Standards, U.S. Environmental Protection Agency, and approved for 

publication. Approval does not signify that the contents necessarily 

reflect the views and policies of the U.S. Environmental Protection 

Agency, nor does mention of trade names or commercial products constitute 

endorsement or recommendation for use. 

n 
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ACKNOWLEDGMENTS 

The authors are grateful to Scott Chaplin for his research on current data 

completeness criteria and to Mike Harper, Belle Hudischewskyj, and Gary 

Lundberg for assistance in computing. The authors also thank Bill Hunt, 

Neil Frank, and Tom Curran of the U.S. Environmental Protection Agency for 

their thoughtful comments. 

83i<+6 1 iii 
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CONTENTS 

Acknowl edgments ' iii 

List of Illustrations vi 

List of Tables x 

Notati on xi i i 

Executive Summary xv 

1 INTRODUCTION 1 

Background 1 

Methodology and Organization of Results 3 

2 STATISTICAL PROCEDURES FOR DETERMINING 

THE AIR QUALITY STATUS OF A SITE 6 

Annual or Quarterly (Long-Term) Averages 6 

Short-Term Concentrations 10 

The Observed Number of Short-Term Exceedances 10 

The Estimated Number of Short-Term Exceedances 15 

Current Practice in Determining the Short-Term 

Attainment Status of a Site 19 

Limiting the Maximum Probability of Type I Error 19 

Summary of Results and Alternative Approaches 27 

3 EMPIRICAL ESTIMATION OF THE PROBABILITY OF 

MISCLASSIFYING ATTAINMENT STATUS 31 

Long-Term Ambi ent Standards 31 

Short-Term Ambi ent Standards 43 

Summary 53 

83i46r i iv 
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STATISTICAL ESTIMATION OF THE STATUS AND 

TRENDS IN NATIONAL AIR QUALITY 

A Question of Bias , 

Variance of the Estimators, 

5 AN EMPIRICAL ASSESSMENT OF THE DATA COMPLETENESS 

NEEDED TO RELIABLY ESTIMATE NATIONAL TRENDS 

Sulfur Dioxide 

Carbon Monoxide , 

Nitrogen Dioxide 

Ozone , 

Lead 

Total Suspended Particulate, 

Summa ry , 

References , 

Appendix A SULFUR DIOXIDE DESCRIPTIVE STATISTICS 

Appendix B CARBON MONOXIDE DESCRIPTIVE STATISTICS 

Appendix C NITROGEN DIOXIDE DESCRIPTIVE STATISTICS 

Appendix D OZONE DESCRIPTIVE STATISTICS 

Appendix E LEAD DESCRIPTIVE STATISTICS 

Appendi x F PARTICULATE MATTER DESCRIPTIVE STATISTICS 

55 

55 

56 

58 

58 

58 

65 

65 

72 

72 

72 

80 

Appendix G SUMMARY OF CURRENT DATA COMPLETENESS CRITERIA 

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ILLUSTRATIONS 

2-1 Binomial approximation to a and 3 in the one-exceedance 

case, r = 1 21 

2-2 Binomial approximation to a and 3 in the three-exceedance 

case, r= 3 23 

2-3 Binomial approximation to a and 3 for r = 1 and a 

specification of ag = 0.2 '... 26 

2-4 Binomial approximation to a and 3 for r = 3 and a 

specification of ag = 0.2 28 

3-1 Lead: the probability of misjudging actual attainment status 

as determined by the mean, the coefficient of variation, 

and the proportion of data completeness 36 

3-2 TSP, annual geometric mean: the probability of misjudging 

actual attainment status as determined by the natural log 

of the geometric mean, the coefficient of variation, and 

the proportion of data completeness 37 

3-3 TSP, annual arithmetic mean: the probability of misjudging 

actual attainment status as determined by the mean, the 

coefficient of variation, and the proportion of data 

compl eteness 38 

3-4 Estimated probabilities a and 3 of misjudging attainment 

of the 24-hour sulfur dioxide standard as functions of the 

proporti on of data compl eteness 46 

3-5 Estimated probabilities a and 3 of misjudging attainment 

of the one-hour carbon monoxide standard as functions of 

the proportion of data completeness 47 

3-6 Estimated probabilities a and 3 of misjudging the 8-hour 

carbon monoxide standard as functions of the proportion of 

data compl eteness 48 

83146T 1 vi 
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3-7 Estimated probabilities a and 3 of misjudging attainment 

of the maximum daily one-hour ozone standard as functions 

of the proportion of data completeness 49 

3-8 Estimated probabilities a and 3 of misjudging attainment 

of the 24-hour TSP standard as functions of the proportion 

of data compl eteness 50 

5-1 Estimated long-term sulfur dioxide air quality parameters 

as functions of the required data completeness 60 

5-2 Estimated short-term sulfur dioxide air quality parameters 

as functions of the required data completeness 62 

5-3 Estimated one-hour carbon monoxide air quality parameters 

as functions of the required data completeness 64 

5-4 Estimated 8-hour carbon monoxide air quality parameters as 

functions of the required data completeness 67 

5-5 Estimated long-term nitrogen dioxide air quality parameters 

as functions of the required data completeness 69 

5-6 Estimated annual ozone air quality parameters as functions 

of the required data completeness 71 

5-7 Estimated long-term lead air quality parameters as functions 

of the required data completeness 74 

5-8 Estimated long-term TSP air quality parameters as functions 

of the required data completeness 76 

5-9 Estimated short-term TSP air quality parameters as functions 

of the required data completeness 78 

Appendix A: Sulfur Dioxide 

A-l Histogram of the percentage of data completeness for 

sites reporting sulfur dioxide concentrations in 1981 

A-2 Scatter plots of ambient air quality statistic s versus the 

percentage of total hours recorded in 1981 by sites 

reporting sulfur dioxide concentrations 

A-3 Histogram of expected primary exceedances for sites 

reporting 24-hour sulfur dioxide concentrations in 1981 

83mer 1 vi i 
A-4 Scatter plot of expected primary exceedances versus the 

percentage of total days recorded in 1981 by sites 

reporting 24-hour sulfur dioxide concentrations 

Appendix B: Carbon Monoxide 

B-l Histogram of the percentage of data completeness for 

sites reporting carbon monoxide concentrations in 1981 

B-2 Histogram of expected primary exceedances for sites 

reporting one-hour carbon monoxide concentrations in 1981 

B-3 Scatter plot of the number of expected primary exceedances 

versus the percentage of total hours recorded in 1981 by 

sites reporting one-hour carbon monoxide concentrations 

B-4 Histogram of expected primary exceedances for sites 

reporting 8-hour carbon monoxide concentrations in 1981 

B-5 Scatter plot of the number of expected primary exceedances 

versus the percentage of total hours recorded in 1981 by 

sites reporting 8-hour carbon monoxide concentrations 

Appendix C: Nitrogen Dioxide 

C-1 Histogram of the percentage of data completeness for 

sites reporting nitrogen dioxide concentrations in 1981 

C-2 Scatter plots of ambient air quality statistics versus the 

percentage of total hours recorded in 1981 by sites 

reporting nitrogen dioxide concentrations in 1981 

Appendix D: Ozone 

D-1 Histogram of the percentage of data completeness for 

sites reporting ozone concentrations in 1981 

D-2 Histogram of the number of expected primary exceedances 

for sites reporting ozone concentrations in 1981 

D-3 Scatter plot of the number of expected primary exceedances 

versus the percentage of data completeness for sites 

reporting ozone concentrations in 1981 

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Appendix E: Lead 

E-l Histogram of the percentage of data completeness for 

sites reporting lead concentrations in 1981 

E-2 Scatter plots of ambient air quality statistics versus the 

percentage of data completeness for sites reporting lead 

concentrations in 1981 

Appendix F: Total Suspended Particulate 

F-l Histogram of the percentage of data completeness for 

sites reporting TSP concentrations in 1981 

F-2 Scatter plots of ambient air quality statistics versus the 

percentage of data completeness for sites reporting TSP 

concentrations in 1981 

F-3 Histogram of the number of expected primary exceedances 

for sites reporting TSP concentrations in 1981 

F-4 Scatter plot of the number of expected primary exceedances 

versus the percentage of data completeness for sites 

reporting TSP concentrations in 1981 

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TABLES 

2-1 The required proportion of data completeness as a function 

of the total number of possible measurements, the coefficient 

of variation, and the prescribed maximum relative error 

occurring with 95 percent probability 8 

2-2 Relative error for data completeness proportions p^ = 0.50 

and p.j = 0.75 9 

2-3 The proportion of data completeness required to limit the 

risk to 3 of not detecting r + 1 exceedances 14 

2-4 The maximum probability of a Type I error and the binomial 

approximation to the probability, as functions of the proportion of data completeness 18 

2-5 Binomial approximations to probabilities a and 3 in the 

one-exceedance case, r = 1 20 

2-6 Binomial approximations to probabilities a and 3 in the 

three-exceedance case, r = 3 22 

2-7 Attainment status as a function of observed exceedances and 

the proportion of data completeness 25 

2-8 Attainment status for the one-exceedance form of the 

standard (r = 1) 25 

3-1 Estimated probability that a site' s attainment status for 

long-term standards is misclassified as a function of 

minimum data completeness proportion 34 

3-2 Estimated probability that a site' s attainment status for 

short-term standards is misclassified as a function of 

minimum data completeness proportion 51 

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5-1 Estimated composite annual average of one-hour sulfur dioxide 

and its estimated variance as functions of the required 

percentage of data completeness 59 

5-2 Estimated mean annual rate of 24-hour sulfur dioxide 

exceedance and its estimated variance as functions of the 

required percentage of data completeness 61 

5-3 Estimated mean annual rate of one-hour carbon monoxide 

exceedance and its estimated variance as functions of the 

required percentage of data completeness 63 

5-4 Estimated mean annual rate of 8-hour carbon monoxide 

exceedance and its estimated variance as functions of the 

required percentage of data completeness 66 

5-5 Estimated composite annual average of one-hour nitrogen 

dioxide and its estimated variance as functions of the 

required percentage of data completeness 68 

5-6 Estimated mean annual rate of maximum daily one-hour ozone 

exceedance and its estimated variance as functions of the 

required percentage of data completeness 70 

5-7 Estimated composite average of maximum quarterly lead and 

its estimated variance as functions of the required 

percentage of data completeness 73 

5-8 Estimated composite average of 24-hour TSP and its estimated 

variance as functions of the required percentage of data 

compl eteness 75 

5-9 Estimated mean annual rate of 24-hour TSP exceedance and its 

estimated variance as functions of the required percentage 

of data completeness 77 

Appendix A: Sulfur Dioxide 

A-l Number of sites recording one-hour sulfur dioxide during at 

least 75 percent of the total possible hours in 1981 

A-2 Number of sites recording one-hour sulfur dioxide during at 

least 50 percent of the total possible hours in 1981 

83iit6r l xi 
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A-3 Frequency table of the percentage of total days recorded in 

1981 versus expected primary exceedances for sites reporting 

24-hour sulfur dioxide averages 

Appendix B: Carbon Monoxide 

B-l Number of sites recording carbon monoxide during at least 

75 percent of the total possible hours in 1981 

B-2 Number of sites recording carbon monoxide during at least 

50 percent of the total possible hours in 1981 

B-3 Frequency table of the percentage of total days recorded in 

1981 versus expected primary exceedances for sites reporting 

one-hour carbon monoxide averages 

B-4 Frequency table of the percentage of data completeness in 

1981 versus expected primary exceedances for sites reporting 

8-hour carbon monoxide averages 

Appendix D: Ozone 

D-1 Frequency table of the percentage of data completeness in 

1981 versus expected primary exceedances for sites reporting 

maximum daily ozone concentrations 

Appendix F: Total Suspended Particulate 

F-l Number of sites recording 24-hour TSP during at least 75 

percent of the scheduled monitoring days in 1981 

F-2 Number of sites recording 24-hour TSP during at least 50 

percent of the scheduled monitoring days in 1981 

F-3 Frequency table of the percentage of total days recorded in 

1981 versus expected primary exceedances for sites reporting 

24-hour TSP averages 

Appendix G: Current Data Completeness Criteria 

G-1 National Aerometric Data Bank's criteria for validity 

of data 

G-2 California Air Resources Board's criteria for representativeness of air quality measurements and statistics 

G-3 Indiana Air Pollution Control Division's criteria for 

completeness of data 

83146r

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NOTATION 

Fixed or controlled parameters 

N = number of possible measurements in a year 

PQ = required data completeness proportion or percentage 

e = specified tolerance for estimating a site-specific long-term 

average concentration 

r = the maximum number of times short-term concentrations at a 

site may exceed a reference concentration without violating 

a given short-term air quality standard 

a = probability that the attainment status of a site will be 

incorrectly determined as nonattainment 

3 = probability that a site's failure to attain an air quality 

standard will go undetected 

Site-specific quantities (i = site index) 

p.j = proportion of possible measurements actually recorded during 

the year 

u- = average of the pn-N concentrations recorded during the year 

u-j = average of all N concentrations that could have been 

recorded during the year 

a- = standard deviation of the p^N concentrations recorded during 

the year 

0^ = standard deviation of all N concentrations that could have 

been recorded during the year 

k.j = the number of times a site is reported to have exceeded a 

short-term reference concentration 

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\. = the estimated number of short-term exceedances 

xi = the actual number of short-term exceedances (equal to k^ 

when p.,- = 1) 

Sample and population quantities 

IT = set of indices i of sites comprising the sample 

v(pg) = number of sites in the sample whose data completeness 

proportion equals or exceeds pg 

u(p0) = sample average of w- across sites with p. > pQ 

u(pg) = population mean of u- across sites with p. > PQ 

u = population mean of u^ 

"2 "2 

a (pn) = sample average of variance estimates oi across sites 

with p. > pQ 

2 2 

o (p0) = population mean of variances o^ across sites with p. > pQ 

2 2 

a = population mean of variances ai 

x(pn) = sample average of estimated site-specific exceedances (x^) 

for those sites with p. > pQ 

x(pQ) = population mean of site-specific exceedances (x..) for those 

sites with p. > pQ 

X = population mean of site-specific exceedances 

831t6 7 xn v 
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EXECUTIVE SUMMARY 

PURPOSE AND SCOPE OF THE STUDY 

The U.S. Environmental Protection Agency (EPA) stores ambient air quality 

data, obtained from a nationwide network of monitoring stations, in the 

National Aerometric Data Bank (NADB). Statistics summarizing the air 

quality at each monitoring station are also stored in the NADB. These 

summary statistics are made available to the government and public 

provided that certain data validity criteria are met, chief among these 

being requirements for data completeness (given in Appendix G) . 

This data screening policy helps to ensure that NADB summary statistics 

are reliable. Moreover, the policy of using one set of data validity 

criteria regardless of the intended use of the data is necessary since 

the EPA must respond quickly to numerous requests for NADB data. It is 

possible, however, that some information may be unnecessarily lost to the 

general NADB user because of the stringency of the criteria for data 

validity. Nevertheless, stringent criteria may be needed for some 

purposes, notably for determining whether National Ambient Air Quality 

Standards (NAAQS) have been attained. 

The purpose of this report is to examine data reliability as a function of 

data completeness in order to assist the EPA in its review of the adequacy 

and appropriateness of the current NADB data validity criteria. 

We consider two important cases at opposite ends of the spectrum of data 

usage: (1) the determination of NAAQS attainment at a site, which is 

essential to the implementation of the Clean Air Act and which depends 

heavily on complete data, and (2) the estimation of the status of, and 

831t6r 1 xv 
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trends in, air quality nationwide, for which much less complete data can 

be tolerated since data are pooled from a large number of sites. 

METHODOLOGY 

We take the view in this report that summary statistics based on incomplete data are estimates of the summary statistics that would have been 

obtained from complete data. Moreover, we treat the set of observations 

at a site as a random sample from the entire set of pollutant concentrations, even in the case of regular but intermittent sampling (so that a 

sampling schedule of once every six days produces at most 17 percent 

completeness). 

From this viewpoint, the correct NAAQS attainment status of a site depends 

solely on the complete set of measured pollutant concentrations, so that 

misciassification is possible only for those sites having incomplete 

data. Similarly, the accuracy of estimated trends in national air quality 

depends on the data completeness at each site as well as the set of sites 

used to form the estimates. We have thus set aside other important 

components of data reliability, i.e., measurement error (due to a variety 

of inherent limitations, such as instrument calibration and maintenance or 

recording and reporting practices) or the degree of spatial representativeness of measured concentrations. 

We adopt two forms of analysis: (1) we analyze hypothetical "mostsensitive" scenarios (in which sites barely attain or fail to attain 

short-term air quality standards, or where the hypothetical high variability of pollutant concentrations makes the estimation of long-term 

averages more difficult) and (2) we estimate actual error rates based on 

1981 NADB data (described in Appendixes A through F) . 

The criterion we use to evaluate the effect of data completeness requirements on the estimation of national air quality trends is the variance of 

the estimated national average in a single year. We show that strict data 

83m6r l xv i 
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completeness requirements affect the variance in two distinc t ways. That 

i s , excluding sites with less complete data has two effects : (1) an 

increase in the reliabilit y of those site-specifi c estimates included in 

the national estimate and (2) a reduction in the number of sites included 

in the national estimate. Using 1981 NADB data we evaluate these competing effects on the variance of the estimated national average. 

MAJOR FINDINGS 

In general, reliable determination of the short-term NAAQS attainment 

status of a site requires more complete data than the other data uses we 

consider. However, as several investigators have noted, increasing the 

data completeness proportion (up to a point) also increases the chance of 

misclassifying a site that, in fact , has one exceedance. This peculiarit y 

is due to the fact that the more complete the data, the greater the chance 

of including the exceedance in the sample and thus deriving an-expected 

exceedance rate greater than unity when correcting for the incompleteness 

of the data record. This scenario may be guarded against by requiring 

essentially complete data (more than 95 percent completeness), or by 

modifying the procedure for determining NAAQS attainment status. 

We used 1981 data in two ways to analyze data completeness needs: (1) we 

estimated the expected rate of misclassification for sites that met 

current and alternative completeness requirements in 1981, and (2) for 

long-term lead and particulate standards we estimated "critica l intervals " 

about the standards within which misclassification probabilities exceed 

10 percent, and we show how these intervals narrow as more complete data 

are required. (Critica l intervals are defined in Section 3, and should 

not be confused with confidence intervals.) 

Each form of analysis serves a different purpose. The firs t indicates 

rates of misclassification under current completeness requirements but is 

less useful for estimating the consequences of tightening or relaxing 

these requirements. The second form of analysis uses characteristics of 

83ii+6r i xvi i 
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the 1981 data to estimate the consequences of various data completeness 

requirements on the classification of lead or particulate monitoring sites 

whose long-term averages are near the standard. The second form thus 

focuses on those sites whose long-term average concentrations are near the 

standard without addressing the question of how many such sites there are 

likely to be (which cannot be done reliably in the absence of much more 

data or strong assumptions of uncertain validity). 

The probability of misclassifying an attainment site under current data 

completeness requirements is 1 percent for the 1-hour CO standard, 2 

percent for the 8-hour CO, 24-hour S02, and 24-hour TSP standards, and 

8 percent for the daily maximum ozone standard (see Table 3-2). Whenever 

reliable estimation was possible, we estimated the probability of misclassifying a nonattainment site. For the 24-hour SOg standard and the 

1-hour CO standard, reliable estimation was not possible due to the small 

number of nonattainment sites (less than 10). The probability is less 

than 1 percent for the 8-hour CO standard and the daily maximum ozone 

standard, and 6 percent for the 24-hour TSP standard. 

We attempted to use the first form of analysis to estimate the effects of 

alternative date completeness requirements on the probability of misjudging the attainment of short-term standards. This was done by restricting 

the analysis to those sites meeting the alternative requirements. For 

continuously monitored pollutants, a relaxation of the 75 percent requirement to 50 percent produced no appreciable difference in the probability 

of misclassification. It is theoretically possible, but impractical, to 

reduce the probability of a false determination of nonattainment to zero 

by requiring 95 percent complete data. For the current 24-hour TSP standard, we examined sites meeting completeness requirements of 5, 12, and 

25 percent, i.e., requirements of 5, 11, and 23 valid samples per quarter, 

respectively. Again, the analysis was insensitive to differences in data 

completeness, although the estimate for 5 and 25 percent completeness 

differed slightly. 

83146T i xvii i 
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For long-term standards, the 1981 data indicate that the probability of 

misclassifying the status of a site that has actually attained a standard 

and that meets current NADB completeness requirements is 2 percent for TSP 

and less than 1 percent for other pollutants (see Table 3-1). The chance 

of misclassifying the status of a TSP monitoring site that has not 

attained the annual standard is estimated to be 9 percent. The estimated 

chance of misclassification is greater for TSP sites that have not 

attained the standard than for those that have attained the standard 

because the nonattainment sites tend to be only slightl y above the 

standard, whereas the attainment sites tend to be well below the standard. For other long-term standards, there are too few nonattainment 

sites to reliably estimate the rate of misclassifying such sites . These 

results suggest that misclassifications are unlikely under current data 

completeness requirements. This is true provided that the 1981 data are 

representative of other years, i.e. , so that actual long-term averages are 

well below the standard for al l but a small fraction of sites . 

As in the case of short-term standards, the misclassification rate was 

approximately the same for sites meeting various data completeness 

requirements. The exception is that the estimated rate of misclassificatio n of TSP sites that have not attained the standard drops from 9 

percent to 3 percent when 25 percent completeness is required. 

Thus, direct estimation of expected rates of misclassification generally 

requires more data or stronger assumptions (of uncertain validity ) to 

distinguish the effects of alternative data completeness requirements. 

Using the second form of analysis, in which we estimated "critica l 

intervals " about a given standard, we analyzed the effec t of different 

completeness requirements on the accuracy of classifications of attainment 

of the quarterly lead standard and the annual TSP standard. We gave 

special attention to these two pollutants since they are typicall y sampled 

only once every six days. For each pollutant we estimated the expected 

total number of misclassifications (that is , misclassifications of both 

83i"+6r I xix 
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attainment and nonattainment) to be less than 5 percent; the estimated 

percentage for lead was less than that for TSP (see Figures 3-1 through 

3-3). For lead (quarterly standard = 1.5 pg/m3 ), the estimated critical 

interval when 12 samples per quarter are required is -17 percent to +27 

percent, i.e., 17 percent below to 27 percent above the standard. For TSP 

(annual standard = 75 ug/m3 ), the critical interval when five samples per 

quarter are required is -11 percent to +13 percent. If 12 TSP samples per 

quarter were required, the interval would narrow to -7 percent to +8 

percent. 

If our goal were to contain these critical intervals within ± 10 percent 

of the respective standards, then strengthened requirements should be 

considered for lead and possibly for particulates. Indeed, judging from 

our analysis of TSP, this goal would be achieved under a recently proposed 

revision to standards for particulate matter that includes a requirement 

of 12 valid observations per quarter (EPA, 1984; 49 FR 10434). 

A similar critical interval analysis of short-term standards is possible, 

although this would require additional assumptions about the frequency 

distribution of concentrations at individual sites. In the interests of 

time and project resources we did not conduct this analysis, although it 

may be useful to do so in the future. 

For reliable estimation of national trends, the benefits of relaxing data 

completeness requirements, i.e., broadening the base of sites from which 

to form the national average over successive years, outweigh the disadvantages of including the sites that have less complete data and 

therefore less reliable summary statistics (see Section 5) . This is 

because the variability in air quality among sites outweighs the sampling 

variability at individual sites. Although no optimum requirement can be 

identified from the analysis, the current 50 percent data completeness 

requirement used for the annual report on national air quality trends 

could be relaxed without increasing calculated variances. This conclusion 

is based on the distribution of the percentages of data completeness found 

83146T i xx 
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in the NADB records for 1981, and assumes that the distribution would not 

change substantially in future years if the current requirement for 

estimating national trends were relaxed. 

RELATED ISSUES 

We have attempted to be thorough within the scope of this study, however 

we must point out that data completeness requirements need to be evaluated 

in a broader context that includes 

(1) overall data quality; 

(2) the procedures used to determine the attainment status of a 

site, and 

(3) the ambient standards themselves. 

Some alternatives to the current procedure for determining short-term 

attainment status use a greater number of the high concentrations recorded 

at a site (see Section 2). Although these alternative procedures are 

somewhat more complicated, they appear to be less sensitive to incomplete 

data and avoid the counter-intuitive result, noted above, that the chance 

of misclassification increases with increasing data completeness. 

Although this report focuses on data completeness, there are other aspects 

of data reliability, e.g., quality assurance procedures. It is important 

to remember that requiring more complete data, e.g., requiring more 

frequent intermittent sampling, is not the only way to increase data 

reliability, and not necessarily the most cost-effective way. Thus all 

aspects must be considered together if enhanced data reliability is the 

objective. 

Similarly, the question of data reliability belongs to a larger circle of 

issues concerning effective air quality management. If increased data 

83it6r i xxi 
P.24 

reliability reduces the chance of misclassification, then the marginal 

costs of improved data reliability should be weighed against the economic 

and public health benefits of fewer misclassifications. If we reduce the 

chance that an attainment site will be misclassified as nonattainment, 

then unnecessary administrative and control costs will also be reduced. 

Likewise, if we reduce the chance that a nonattainment site will be 

misclassified as attainment, then presumably public health is better 

maintained. In evaluating the latter benefit, however, one should bear in 

mind that a margin of safety is incorporated into ambient standards so 

that actual pollutant concentrations at a nonattainment site may yet be 

below levels causing adverse health effects. Moreover, it is possible 

that with sufficient effort devoted to data reliability, our certainty 

about actual air quality could exceed our certainty about air quality 

health effects. 

In short, monitoring requirements (data completeness, quality assurance, 

numbers of monitors, frequency of sampling, etc.) and other regulatory 

issues, such as the margin of safety embodied in ambient standards, are 

interdependent. For example, the smaller the margin of safety used in 

deriving an air quality standard, the less we can afford to misjudge the 

attainment status of a site, and the greater the need for highly reliable 

data. 

RECOMMENDATIONS 

One use of the NADB data that we consider is the estimation of the status 

of and trends in air quality nationwide. Tightening the data requirements 

has two competing effects: (1) the sites meeting the stricter requirements (and therefore included in the national average) have more reliable 

air quality summary statistics, but (2) the exclusion of sites with less 

reliable statistics reduces the sample size used to form the national 

average. Our conclusion is that the current 50 percent data completeness 

requirement for determining national trends, which is a relaxation of the 

75 percent NADB requirement, should be further relaxed because the 

ssmer l xxii 
P.25 

advantage of a large sample size outweighs the advantage of reliable 

statistics at individual sites. Unfortunately, the optimum requirement 

cannot be identified from our analysis, so that any specific recommendation will require further consideration. 

The EPA staff responsible for the estimation and reporting of national air 

quality trends have direct access to NADB data. This is an example of a 

special group of NADB users who can apply data completeness requirements 

according to their particular needs. In considering the release of NADB 

data to the general user, however, it appears wise to continue the policy 

of using one set of data completeness requirements. Special users with 

direct access to NADB data, such as those responsible for the estimation 

of national air quality trends, should continue to determine the degree of 

data completeness needed for their particular application. 

Because of the practicality of using one set of requirements, the requirements should be based on the common application having the greatest need 

for complete data. On this basis, we have focused on the issue of whether 

current NADB criteria provide sufficient protection against misclassifying 

the attainment status of a site with respect to short-term or long-term 

standards. 

Certainly, accurate estimates of national trends require less complete 

data than do accurate classifications of individual sites (compare Figures 

5-1 through 5-9 with Tables 3-1 and 3-2). Of course, we cannot compare 

these data needs quantitatively until we prescribe the accuracies acceptable in each case, but the evidence supporting the statement is clear 

nevertheless. It is also clear that there are other possible data uses, 

not examined in this report, that depend even more heavily on complete 

data than does the determination of attainment status, e.g., inferring the 

maximum 10-minute concentration from hourly data. But, for the purpose 

of establishing appropriate NADB requirements for complete data, the 

determination of attainment status seems to be the most exacting use of 

air quality data that is common to all the pollutants for which we have 

national ambient air quality standards. 

83iJ+6r l xxiii 
P.26 

Direct estimates of the expected misclassification rate for continuously 

monitored pollutants do not change appreciably when the current NADB 

requirement of 75 percent data completeness is relaxed to 50 percent. 

Analyses of the most sensitive scenarios (which could become more common 

than they were in 1981) warn against this relaxation, however. In 

particular, if the procedures for determining the attainment of short-term 

standards remain unchanged, it seems best for the time being to also 

maintain current data completeness requirements for continuously monitored 

pollutants. 

Similarly, in the case of intermittent sampling, e.g., for lead and 

particulate matter, direct estimates of misclassification rates barely 

distinguish between the alternative data completeness requirements we 

consider. In general, the NADB data validity criteria require only five 

samples per quarter, and thus only 20 samples per year. For lead, 

however, 12 samples per quarter are required for attainment determinations 

(EPA, 1979; 43 FR 46266). In either case, it is much more difficult to 

ensure the correct classification of air quality status under an intermittent sampling. Critical interval analyses (Figure 3-1 through 3-3) 

demonstrate the advantages of strengthening data completeness requirements 

for lead and particulates. It is therefore advisable to adopt the 

recently proposed requirement of 12 particulate samples per quarter (EPA, 

1984; 49 FR 10434) and to consider even more frequent sampling of lead. 

Concerning the issues related to data completeness—less central to the 

scope of this study but no less important for effective air quality 

management—we recommend consideration of two changes in procedures. 

(1) A greater number of the high concentrations recorded at a site 

should be used in order to provide more robust short-term 

attainment inferences. 

83m6T i XXIV 
P.27 

(2) Data completeness considerations should be incorporated in the 

review, revision, and interpretation of air quality standards, 

along with such related issues as the cost of more complete 

data, other limitations on data reliability, the cost of 

misclassifying attainment status, and the existing margins of 

safety used to set thresholds for ambient concentrations. 

831t6r 1 

xxv 
P.28 

1 INTRODUCTION 

The U.S. Environmental Protection Agency (EPA) stores ambient air quality 

data, obtained from a nationwide network of monitoring stations, in the 

National Aerometric Data Bank (NADB). Statistics summarizing the air 

quality at each monitoring station are also stored in the NADB. These 

summary statistics are made available to the government and public 

provided that certain data validity criteria are met, chief among these 

being requirements for data completeness (given in Appendix G) . 

This data screening policy helps to ensure that NADB summary statistics 

are reliable. Moreover, the policy of using one set of data validity 

criteria regardless of the intended use of the data is necessary since the 

EPA must respond quickly to numerous requests for NADB data. It is 

possible, however, that some information may be unnecessarily lost to the 

general NADB user because of the stringency of the data validity 

criteria. Nevertheless, a stringent criteria may be needed for some 

purposes, notably, for determining whether National Ambient Air Quality 

Standards (NAAQS) have been attained. 

The purpose of this report is to examine data reliability as a function of 

data completeness in order to assist the EPA in its review of the adequacy 

and appropriateness of the current NADB data validity criteria. 

BACKGROUND 

Air quality data are provided to the National Aerometric Data Bank (NADB) 

primarily by state and local agencies. Included in the NADB record of air 

quality summary statistics for a monitoring station is a "criteria flag" 

83m6r

 2 1 
P.29 

indicating whether NADB data validity criteria are met. These (and other) 

data validity criteria are presented in Appendix G, but they may be 

roughly summarized as a 75 percent data completeness requirement. (Note 

that the monitoring schedule for lead and particulate matter is once every 

six days. In these cases of intermittent sampling of 24-hour concentrations, NADB criteria require five samples per quarter and thus 20 samples 

per year. 

In responding to typical requests for NADB data, the record of a site 

failing to meet the criteria may be written with question marks to 

indicate questionable data reliability, or the record may not be written 

at all. Thus, whereas authorized users of NADB data have access to all 

records, the records indicating that NADB criteria have been met constitute a common subset of NADB data that is reliable and widely available. 

In this report we consider the effect of excluding air quality data from 

sites that fail to meet certain data completeness requirements. More 

specifically, we consider whether current NADB requirements appear to be 

satisfactory or need to be changed, and, in the latter case, whether data 

completeness requirements should vary with data usage and type of monitoring (intermittent or continuous). 

We consider two important cases at opposite ends of the spectrum of data 

usage: (1) the determination of NAAQS attainment at a site, which is 

essential to the implementation of the Clean Air Act and which makes a 

heavy demand for data completeness, and (2) the estimation of the status 

of and trends in air quality nationwide, for which much less complete data 

can be tolerated (since data are pooled from a large number of sites). 

For each of these two data uses we consider summary statistics relevant to 

short-term and long-term air quality standards. That is, we consider the 

number of exceedances of the short-term standards (having an averaging 

time of 24 hours or less), and the annual or maximum quarterly average. 

Again, by treating both peak value summary statistics (where the effect of 

8311+6 2 
P.30 

incomplete data is pronounced) and long-term averages (where data completeness needs are minimal), we hope to provide useful benchmarks for 

other data uses. 

Currently, the attainment of most national ambient air quality standards 

is determined separately for each year of data. However, a three-year 

attainment period is used in the case of ozone, and multi-year periods are 

being considered for other short-term standards. We therefore address the 

data completeness needed for both single-year and multi-year attainment 

standards. 

METHODOLOGY AND ORGANIZATION OF RESULTS 

We take the view in this report that summary statistics based on incomplete data are estimates of the summary statistics that would have been 

obtained from complete data. Moreoever, we treat the set of observations 

at a site as a random sample from the entire set of pollutant concentrations, even in the case of regular but intermittent sampling (so that a 

sampling schedule of once every six days produces at most 17 percent 

completeness). 

From this viewpoint, the correct NAAQS attainment status of a site depends 

solely on the complete set of measured pollutant concentrations, so that 

misclassification is possible only for those sites having incomplete 

data. Similarly, the accuracy of estimated trends in national air quality 

depends on the data completeness at each site as well as the sample of 

sites used to form the estimates. We have thus set aside other important 

components of data reliability, i.e., measurement error (due to a variety 

of inherent limitations, such as instrument calibration and maintenance or 

recording and reporting practices) or the degree of spatial representativeness of measured concentrations. 

We adopt two forms of analysis. In Section 2 we analyze hypothetical 

"most-sensitive" scenarios (in which sites barely attain or fail to attain 

83146 2 3 
P.31 

short-term air quality standards, or in which the hypothetical high 

variability of pollutant concentrations makes the estimation of long-term 

averages more difficult). In Section 3 we assess the likely error rates 

based on 1981 NADB data (described in Appendixes A through F) . 

In our treatment of short-term NAAQS, the assigned status of a site is 

based on a quantity known as the "expected number of exceedances," that 

is, attainment status is determined assuming that the ratio of observed 

exceedances to total observations is maintained for the complete data set. 

The criterion we use to judge the degree of data completeness required to 

accurately determine NAAQS attainment is the chance of misclassifying the 

status of a site. The chance is zero for sites having 100 percent 

complete data or for sites having no exceedances. Otherwise the chance of 

misclassification depends on both the degree of data completeness and the 

actual number of exceedances. 

In Section 2 we consider the effect of data completeness on the chance of 

erroneously classifying the status of a site as nonattainment when in fact 

the reference concentration has been exceeded exactly once in the course 

of the year. We also consider the chance of erroneously classifying the 

status as attainment when the site has exactly two exceedances. This 

analysis is also carried out for air quality standards allowing no more 

than three exceedances in three years. 

In Section 3 we use 1981 NADB data to estimate the actual (but unknown) 

rates of misclassification. We first estimate the frequency distribution 

among sites of the actual number of exceedances. We then use this 

distribution to estimate the probability of misclassifying sites meeting 

various data completeness requirements. 

For long-term (annual or quarterly) ambient standards, the chance of 

misclassifying a site depends not only on the degree of data completeness 

at the site but also on the empirical frequency distribution of the entire 

year of pollutant concentrations at the site. In Section 2 we assess data 

83146 2 4 
P.32 

completeness requirements by assuming that the actual average concentration at the site is 10 percent above or below the standard, and that the 

standard deviation of the year of concentrations at the site is twice the 

average. In Section 3 we empirically estimate probabilities of misclassification using 1981 data. 

In Section 4 we introduce a criterion for evaluating the effect of data 

completeness requirements on the estimation of national air quality 

trends, namely the variance of the estimated national average in a single 

year. Excluding sites with less complete data has two effects: (1) the 

reliability of the site-specific estimates included in the national 

estimate is increased, and (2) the number of sites included in the 

national estimate is reduced. In Section 5, using 1981 NADB data, we 

evaluate these competing effects on the variance of the estimated national 

average. 

83146 2 
P.33 

STATISTICAL PROCEDURES FOR DETERMINING 

THE AIR QUALITY STATUS OF A SITE 

ANNUAL OR QUARTERLY (LONG-TERM) AVERAGES 

Suppose we wish to know (up to measurement error) the annual average 

concentration y^ of a pollutant at a particular site, with index i, based 

on a complete set of N measurements, but that only n^ valid measurements 

were recorded, the remaining m^ = N - n^ being either invalid or missing. 

Letting p^ denote the proportion, n^/N, of data completeness, it can be 

A 

shown (Cochran, 1963) that the sample average u. has expected value pH and 

2 variance (1 - pi)/pi

 (o^N): 

A 

E ji i = ui 

1

 " pi °i 

Moreover, annual air quality measurements usually entail large numbers of 

both missing and observed values (m^ and n^) with relatively few extreme 

values. Under these conditions, formulated more precisely by Cochran 

A 

(1963), who cites Hajek (1960), the sampling distribution of y, is 

approximately normal. 

Thus [(1 - p^ )/p-j]oi/N is a natural measure of the error in estimating the 

annual average (\ij) of all N measurements by the average of a proportion 

(p.j) of the N measurements. 

83146T 3 
P.34 

We may use these results—the expected value, variance, and approximate 

A 

normality of u^—to determine the minimum acceptable proportion of 

measurements, pg, provided that (1) we specify a relative error tolerance, 

e, such that errors of larger magnitude have, say, only a 5 percent of 

occurring, and (2) we have some idea of the coefficient of variation, 

Oi/\i-. Specifically we have 

1^ - u.| 

Pr I — — > e) = Pr 

eu. 

(Varu\) 1 / 2 (Var P . ) 1 / 2 

= 2 

1 - $ eu. 

.(Varuj) 1/2 

1 - $ e • — 

v< (NPi) l/2\-| 

. 1 - p. 1 H 

where $ is the standard normal cumulative distribution function. The 

above expression may be used to calculate either pg from a prescribed 

probability (e.g., 5 percent), or a confidence bound of a prescribed level 

(e.g., 95 percent) on the absolute relative error (|u. - u.|/u-) 

given the proportion of data completeness (p^) and the coefficient of 

variation (0^/u.j) at a particular site. 

Table 2-1 shows the minimum proportion pg corresponding to several 

combinations of e, o-j/u-j, and N. Table 2-2 shows e as a function of 

N, a*/\ii» and p.. Note that the 75 percent criterion used by the SAROAD 

system implies that partial annual averages are not likely to differ by 

more than appproximately one percent from complete annual averages if the 

coefficient of variation equals unity (100 percent). The corresponding 

error for the 50 percent completeness criterion commonly used in reporting 

trends in annual averages is approximately two percent (for an individual 

site). 

83146 3 
P.35 

TABLE 2-1. The required data completeness proportion (pg) as a function of 

the total number of possible measurements (N), the coefficient of variation (ai/y-j), and the prescribed maximum relative error (e) occurring 

with 95 percent probability. 

N = 8760 

(hrs/yr) 

N = 2920 

(3 hrs/yr) 

N = 1095 

(8 hrs/yr) 

N = 365 

(days/yr) 

N = 91 

(days/qtr) 

N = 30 

(days/mo) 

ai/yi 

0.5 

1.0 

2.0 

0.5 

1.0 

2.0 

0.5 

1.0 

2.0 

0.5 

1.0 

2.0 

0.5 

1.0 

2.0 

0.5 

1.0 

2.0 

.001 

0.99096 

0.99772 

0.99943 

0.99697 

0.99924 

0.99981 

0.99886 

0.99972 

0.99993 

0.99962 

0.99991 

0.99998 

0.99991 

0.99998 

0.99999 

0.99997 

0.99999 

1.00000 

.01 

0.52297 

0.81431 

0.94607 

0.76684 

0.92936 

0.98135 

0.89765 

0.97229 

0.99292 

0.96339 

0.99059 

0.99763 

0.99061 

0.99764 

0.99941 

0.99689 

0.99922 

0.99980 

e 

.05 

0.04201 

0.14923 

0.41233 

0.11626 

0.34479 

0.67793 

0.25971 

0.58390 

0.84878 

0.51278 

0.80805 

0.94394 

0.80848 

0.94409 

0.98541 

0.92756 

0.98085 

0.99514 

.10 

0.01084 

0.04201 

0.14923 

0.03184 

0.11626 

0.34479 

0.08063 

0.25971 

0.58390 

0.20831 

0.51278 

0.80805 

0.51346 

0.80848 

0.94409 

0.76197 

0.92756 

0.98085 

1.00 

0.00011 

0.00044 

0.00175 

0.00033 

0.00131 

0.00523 

0.00088 

0.00350 

0.01384 

0.00262 

0.01041 

0.04040 

0.01044 

0.04050 

0.14446 

0.03102 

0.11351 

0.33871 

83146 

83132 
P.36 

TABLE 2-2. Relative error (E) for data completeness 

proportions p. = 0.50 and pi = 0.75. 

N = 8760 

(hrs/yr) 

N = 2920 

(3 hrs/yr) 

N = 1095 

(8 hrs/yr) 

N = 365 

(days/yr) 

N = 91 

(days/qtr) 

N = 30 

(days/mo) 

cyy. 

0.5 

1.0 

2.0 

0.5 

1.0 

2.0 

0.5 

1.0 

2.0 

0.5 

1.0 

2.0 

0.5 

1.0 

2.0 

0.5 

1.0 

2.0 

.50 

0.01047 

0.02094 

0.04188 

0.01814 

0.03627 

0.07254 

0.02961 

0.05923 

0.11846 

0.05129 

0.10259 

0.20518 

0.10273 

0.20546 

0.41092 

0.17892 

0.35784 

0.71568 

.75 

0.00605 

0.01209 

0.02418 

0.01047 

0.02094 

0.04188 

0.01710 

0.03420 

0.06839 

0.02961 

0.05923 

0.11846 

0.05931 

0.11862 

0.23724 

0.10330 

0.20660 

0.41320 

83146 

83132 
P.37 

In interpreting the minimum proportions given in Table 2-1, note that a 

given maximum relative error e may seem either excessively stringent or 

too lenient depending on the particular application. For example, 10 

percent relative error may be too large if we need to determine the 

attainment status of a site whose annual average is typically within 10 

percent of the annual average ambient standard whereas for a site whose 

annual average is typically less than half the standard , a 10 percent 

relative error specification may be unnecessarily stringent. 

SHORT-TERM CONCENTRATIONS 

The Observed Number of Short-Term Exceedances 

Current national ambient air quality standards (NAAQS) for pollutant 

concentrations averaged over 24 hours or less influence the presentation 

and analysis of high short-term concentrations. The short-term standards 

for most pollutants stipulate an ambient concentration that should not be 

exceeded more than once per year, which implies that the second highest 

short-term concentration recorded at a site determines whether the site is 

in attainment of the standard. 

It is possible to treat the second highest value in a year's partial 

sample of short-term concentrations as an estimate of the second highest 

concentration in a complete sample, just as we treated long-term 

averages. This turns out to be a difficult approach from a statistical 

viewpoint, however, because of the great variability of the second highest 

concentration and the influence of the unknown tail distribution of shortterm concentrations on the sampling behavior of the second highest value. 

Another, more workable approach, at least from a statistical perspective, 

is to examine the sequence of short-term concentrations at a site over a 

one-year period and to simply count the number of times the ambient 

concentration exceeds the standard. If the count is no more than one, the 

short-term standard is attained; otherwise it is not. 

83146 3 10 
P.38 

In this approach the sequence of short-term concentrations is converted to 

a 0-1 valued sequence, in which 1 indicates that the concentration exceeds 

the standard and 0 indicates otherwise. The key question regarding the 

effect of data completeness on determining attainment status is whether an 

exceedance has been overlooked. More specifically, we wish to know the 

probability that a site has two or more exceedances but that no more than 

one exceedance is observed in our partial sample. We may formulate this 

as the following conditional probability: 

Pr (ki < 1 | X. = 2) 

where 

k.: = the number of exceedances in the observed sample of size n^ 

xi = the unknown total number of exceedances that occurred during the 

year. 

The reason for focusing on the case x. = 2 is that this is the most 

challenging problem for a fixed partial sample size, n^; we would do well 

to prescribe the chance, say 3, we are willing to take that we fail to 

observe the two exceedances, since for larger values of x^ our chance of 

detecting a violation only improves. More generally, for a standard 

allowing no more than r exceedances we would want to calculate the 

probability that r or fewer exceedances are observed in the partial sample 

when there are r + 1 exceedances in the complete sample. 

This conditional probability is given by the hypergeometric distribution: 

-"••".•-ft) t : *•:)/(:,)• 

For future reference we note that 

E (ki | X., Pj ) = piXi 

83146 3 11 
P.39 

and 

N - x. 

Var (k. | x., p ^ = TTT P i ( l - p ^ xi 

(see, for example, Johnson and Kotz, 1969). Returning to the chance that 

not all r + 1 exceedances are detected, we have 

or 

Noting that 

e=Pr(k i <r|x i =r+l ) 

1 - 3 = Pr (ki = r + 1 | xi = r + 1) 

'N - r - 1\ //N 

n,- r - l) / In, 

ni ni " 1 nT ' r 

N N - 1 •** N - r 

i ~

 j _ "i / N \ j 

- j " N \H - j/ ~ N - j 

N \ N - j / N - j 

=

 Pi -iHhr(1 - PI> 

83146 3 12 
P.40 

we see that 

1

 - s = Pi[p, - rh- ( i - oy] ••• h - N-TT

 (1

 - PI>] 

SP, [p, - i <1 - p,)] -[Pi-fi(l-pi> ] 

" Pi " ( 2 ) l Pi

 ( 1

 " pi> * • " 

+

 (- 1'

1

"

r !

 (i) p,(i-p,)' 

Pf1 * £ ^ j+1 ) (*)' Pi"J+1 d - Pi'' 

where the S^'+! are Stirling numbers of the first kind (Abramowitz and 

Stegun, 1964). 

Hence 

o • i r+1 3 = 1 - Pi 

1 2 

- 1 - Pi for r = 1 

Table 2-3 gives the data completeness proportion, pQ, required to reduce 

the risk of failing to detect two exceedances to a specified level, 3. 

For the 75 percent completeness criterion, there is an approximate 44 

percent chance that at least one of the two exceedances will not be 

detected. For the 50 percent completeness criterion the risk is 75 

percent. It would seem then that the determination of short-term attainment status requires either nearly (e.g., 95 percent) complete data, or 

else some method of inference other than merely counting the number of 

83146 3 13 
P.41 

TABLE 2-3. The proportion, pQ , of data completeness required 

to limit the risk to 3 of not detecting r + 1 exceedances. 

_ 

3 

0.01 

0.02 

0.05 

0.10 

0.20 

0.44 

0.75 

r = 1 

0.995 

0.990 

0.975 

0.949 

0.894 

0.748 

0.500 

r = 3 

0.997 

0.995 

0.987 

0.974 

0.946 

0.865 

0.707 

83146 8 14 
P.42 

exceedances in the partial sample (see EPA, 1979; Pace and Frank, 1982; 

Thrall and Burton, 1983). Table 2-3 also shows the required data 

completeness for a three-exceedance standard, a topic to which we now 

turn. 

The Estimated Number of Short-Term Exceedances 

An alternative procedure for determining whether short-term air quality 

standards have been attained at a site is to extrapolate from the observed 

exceedances, kn-, to the total number of exceedances, X-, i.e., to 

estimate X^ by 

^ - yPi • 

From the conditional moments derived for k^, we have 

E (Xi | Xv p.) = Xi 

.

 l ' Pi Var (x. | Xi S p.) --j — Xi 

so that x. is an unbiased estimate whose variance approaches zero as p^ 

approaches unity. 

For an r-exceedance short-term standard, we might judge a site to be in 

attainment of the standard only if 

1 

X. < r+ Y • 

This procedure reduces the risk of failing to detect nonattainment 

(X- > r + 1), since the estimate X^ is an extrapolation of the observed 

number of exceedances (k^) among n^ observed concentrations to the total 

number of exceedances (x.) in N concentrations. But we have also introduced the risk that x^ might be overestimated. 

83146 3 15 
P.43 

This procedure for determining whether a short-term air quality standard 

has been attained at a site can be cast as a statistical test of a 

hypothesis. A site is presumed to be in attainment of the standard (i.e., 

1 the null hypothesis is that x, < r) unless x. > r + j » in which case it 

is judged to have failed to attain the standard, i.e., we infer that the 

alternative hypotheis, x. > r + 1, holds. 

A "Type I" error occurs when the site has actually attained the standard 

but we incorrectly infer that it has not. Previously, when we determined 

attainment solely on the basis of the observed number of exceedances, k^, 

this was impossible, since k^ can never be greater than the actual number 

of exceedances, xi . Now, however, the probability of a Type I error is a, 

where 

Pr (vr + iiv r

) -

Whatever the proportion of data completeness, p^, the probability of a 

Type I error will be greatest when the site is just barely in attainment 

of the standard, i.e., when x. = r, in which case 

a = Pr (x-> r + Y | X. = r\ . 

1 Now if p^ > 2r/(2r + 1) it is impossible for x^ to equal or exceed r + j 

since 

1 Pi 

<

 r 

(2r)/(2r + 1) 

- 4 

so that 

a = 0 if p. > 2r/(2r + 1) 

83146 3 16 
P.44 

If 2(r - l)/(2r +1) < pi < 2r/(2r + 1) , xi will equal or exceed r + ^ 

only if k. = r. In general, as p^ becomes smaller, fewer observed 

' A 

exceedances (k^) are required to produce an estimate (x-) equaling 

or exceeding r + j , and the probability (a) of a Type I error increases, 

as shown in Table 2-4. Of course, when the sample size (n.,-) falls below 

r, the observed number of exceedances (k^) may be no more than n^ and the 

risk of a Type I error is reduced. (We assume throughout this discussion 

that N > (r + 1) (r + j) so that (r + 1)/N < 2/(2r + 1).) The binomial 

approximation given in Table 2-4 is accurate so long as N is large 

relative to r. 

A 

Thus, basing an attainment determination on x, rather than k^ introduces 

some probability (a) of a Type I error, but the maximum probability (3) of 

a Type II error is substantially reduced for small values of p^. We have 

(^i < r + | | Xi = r + l ) 

fc1 Ir + •SNT-i-iVW 

f or

 2 (J ' *? < p < ?j _ 

T o r

 2r + 1 p i * 2r + 1 

and for j = 1, 2, 3, ... , r + 1 

IIMP^-P,' r+l-k 

Of special interest are the cases r = 1, the one-exceedance form of 

short-term standards, and r = 3, a three-year, three-exceedance form of 

83146 3 17 
TABLE 2-4. The maximum probability , a, of a Type I error and the binomial approximation to 

functions of the proportion Pi of data completeness. 

Pi Interval Pr(xi > r + j \ x.. = r) 

irhr < Pi «! ° 

r

 - ••

 r

|IL^ 1 < p, < ^ , J . 2. 3. £ ( k

r

)(nV-V("i) 

N

 K

i N N 

83146 

r

 - - -

 r

i—» 

00

 n. 

i < D = !l l < L V /

r

\ /N - r \ // N \ V

S (k%VA)/w s 
the standards. Tables 2-5 and 2-6 show the binomial approximations to a 

and 3 for r = 1 and r = 3, respectively. The corresponding plots are 

shown in Figures 2-1 and 2-2. 

Current Practice in Determining the 

Short-Term Attainment Status of a Site 

In the previous section we calculated a and 3, the probabilities of 

misclassifying attainment or nonattainment sites, respectively, if the 

A 

estimated number of exceedances (x.= ) is rounded to the nearest integer and 

then compared to the allowed number of exceedances (r). This procedure 

generated the regularly spaced data completeness cutpoints 2j/(2r + 1) or 

j/(r + 0.5) of Table 2-4. 

In fact, the current EPA policy is to round \. to the nearest tenth and 

then compare the rounded value to r. That is, the status of a site is 

classified as nonattainment only if Xi , rounded to the nearest tenth, 

exceeds r. This procedure generates the data completeness cutpoints 

j/(r + .05) which are greater than the corresponding cutpoints j/(r + 0.5) 

of Table 2-4. 

For a site with data completeness proportion between j/(r + 0.5) and 

j/(r + .05), rounding to the nearest tenth rather than to the nearest 

integer thus increases the chance of misclassifying the status of the site 

as nonattainment if in fact the total number of exceedances is r. On the 

other hand, rounding to the nearest tenth decreases the chance of misclassifying the status as attainment if the total number of exceedances is 

actually r + 1. 

Limiting the Maximum Probability of a Type I Error 

A 

The effect of determining attainment status by comparing X- to the fixed 

1

 1 

value r + y is to create the regularly spaced data completeness cutpoints 

2j/(2r + 1) of Table 2-4. If Pi = 2r/(2r + 1) , the maximum probability a 

83146 3 19 
TABLE 2-5. Binomial approximations to 

probabilities ot and 3 in the one-exceedance 

case, r = 1. 

Pi interval 

2/3 < Pi < 1 

0 < pi < 2/3 

Binomial 

a 

0 

Pi 

App roximation 

3 

i-p, 2 

d - Pj) 2 

83146 8 20 
• 

• 

• 

• 

• 

• 

• 

• 

• 

• 

• 83146 

i n -

1 . u 

0.6 

0.6 

Q. 

TJ 

0.4 

0.2 

°-8. 

' i ' i i i < i 

: A 

. / 

/ ! 

0 0.2 0.4 0.6 0.3 

Pi 

(a) a versus p^ 

1.0 

0. s 

0. 6 

*-> 

XJ 

0. 4 

0. 2 

°-8 

\ 

; \ 

_ \ 

: \ \ 

• \ J 

i i i i > i i i 

0 0.2 0.4 O.S 0. b 

Pi 

(b) 3 versus pi 

FIGURE 2-1. Binomial approximation to a 

the one-exceedance case, r = 1. 

21 

-

-

-

-

] . .-, 

1 o 

and e in 
TABLE 2-6. Binomial approximations to probabilities a and 3 in the three-exceedance case, r = 

Pi Interval 

Binomial Approximation 

6/7 < p. 1 1 - Pi 

PO 

ro 

4/7 < pi < 6/7 6 Pi

2 (1 - Pi)2 + 4 p. (1 

2/7 < p. < 4/7 p.

3 + 3 p.2 (1 - p.) 4 Pi (1 - Pi)

3 + (1 - Pi)

3/N < p. < 2/7 1 - (1 - Pi)' (1 - Pi) 

Pi = 2/N 3 Pi

2 (1 - .p.) + 3 p. (1 - Pi )2 (1 - Pi) 

Pi = 1/N 3 Pj (1 - Pj)' (1 - Pj) 

83146 
1.0 

0.8 

0.6 

Q. 

0.4 

0.2-

"i 1 1 i 1 1 1 r 

(a) a versus pi 

1.0 

o.e0.6L 

cu 

.D 

0. 4 

0.2r 

0.0 

0.0 0. 

(b) 3 versus Pi 

FIGURE 2-2. Binomial approximations to a and 6 in 

the three-exceedance case, r = 3. 

83146 

23 
P.51 

of a Type I error will be between 0.60 and 0.67, depending on r. The 

point is that by using this method of determining the short-term attainment status of a site we run a high risk that the status might be erroneously determined as nonattainment. 

It is possible to modify the method so that the probability of a Type I 

error never exceeds a prescribed level, ag, at the cost of increasing the 

probability of a Type II error (in which a site's failure to attain the 

short-term standard goes undetected). The modification is to simply shift 

the data completeness cutpoints to smaller values, n,, n2, ..., n , which 

are obtained from ag. The procedure is depicted in Table 2-7. 

The resulting maximum probability of a Type I error is that given in Table 

2-4, with 2j/(2r + 1) replaced by IT,, for j = 1, 2, ..., r. The maximum 

J 

probability, 3, of a Type II error is also obtained in this way from 

previous expressions. Below we demonstrate the derivation of nj from a 

prescribed level of risk, ag, for the cases r = 1 and r = 3. 

The procedure for the current one-exceedance form of a standard (r = 1) is 

depicted in Table 2-8. We see that a Type I error can only occur if ki = 

1, Pi < Ttj, and Xi = 1. The probability of a Type I error is thus zero if 

pn- > TTJ. If Pi < it. then 

Pp(ki = 1 | xi = 1) = p., 

so the absolute maximum (i.e., across all sites) occurs at Pi = n^. We 

may therefore limit the risk of a Type I error to ag simply by setting n1 

= ag. Figure 2-3 depicts a and 3 as functions of Pi when the prescribed 

absolute maximum probability of a Type I error is ag = 0.20. 

In the case r = 3, ki will be taken at face value if Pi > 113, i.e., we 

will only declare the status to be nonattinament if we observe ki > 4 

83146 3 24 
P.52 

TABLE 2-7. Attainment status as a 

function of observed exceedances (ki) and 

the proportion (pi) of data completeness. 

* 

0 

1 

1 

2 

0 < p . < 1 

0 < Pi < TTj 

*1 < Pi < 1 

0 < Pn- < TT2 

Assigned 

ki Pi Interval Status 

A 

N 

A 

N 

ir2 < Pi < 1 A 

r 0 < pi < irr N 

r TTP < pi < 1 A 

> r + 1 0<Pi< l N 

A = attainment, N = nonattainment 

TABLE 2-8. Attainment status for the 

one-exceedance form of the standard (r = 1) 

k

i 

0 

1 

1 

> 2 

Pi Interval 

0 < Pi < 1 

0 < Pi < TTj 

T^X < Pi < 1 

0 < Pi < 1 

Assigned 

Status 

A 

N 

A 

N 

A = attainment, N = nonattainment 

25 

83146 8 
P.53 

1.0 

O.Br 

0.6 

sz 

a. 

0.4 -

0.2 

1.0 

(a) a versus pi 

(b) 3 versus p. 

FIGURE 2-3. Binomial approximation to a and 3 

for r = 1 and a specification of aQ = 0.2. 

83146 26 
P.54 

exceedances. Hence there is no chance of a Type I error. If ng < Pi < 

113, three observed exceedances are required for a nonattainment determination, and the maximum probability of an incorrect nonattainment determination is approximately p*. Continuing, we obtain a modified Table 2-6 with 

cutpoints 2j/7 replaced by HJ for j = 1, 2, 3. Close approximations to 

the required n; are obtained by solving 

3 

a 0 " *3 

a 0 = ^2 + 3ir 2 ^ " v2^ 

ag = 1 - (1 - Hj) 

For ag = 0.20, we obtain 

it3 = 0.585 

ir2 = 0.287 

ir1 *= 0.072 

Figure 2-4 shows the resulting a and 3. 

Summary of Results and Alternative Approaches 

In discussing attainment of air quality standards at an individual site 

during a specified year (or other attainment period), we have adopted the 

view that a complete set of measured ambient concentrations at the site 

for the year would unambiguously define the status of the site to be 

either that of attainment or nonattainment. We have also adopted the view 

that, however incomplete the data may be, we must come to a decision 

regarding whether, on the basis of a partial set of observations, the 

status appears to be either that of attainment or nonattainment, i.e., we 

have excluded an "indeterminate" status. Rather than prescribing a data 

83146 3 27 
P.55 

1.0 

0.6 

0.6-

CL 

0.4 

0.2 

0.0 

1.0 

(a) a versus p. 

1 . ~! 

(b) 3 versus p. 

FIGURE 2-4. Binomial approximation to a and 3 

for r = 3 and a specification of an = 0.2. 

83146 28 
P.56 

completeness threshhold, pg, above which we may reliably asssign attainment status, we have addressed the chance of coming to an erroneous 

decision as a function of the data completeness proportion, Pi, whatever 

it may be. Moreover, we have focused on situations in which the total 

number of exceedances (x.) is just within or just above that prescribed by 

the standard, i.e., situations in which the chance of misjudging the 

attainment status is greatest. 

Within this context, we examined three procedures for judging attainment 

status: (1) based solely on the observed number of exceedances, k-; (2) 

based solely on the estimated number of exceedances, x. = k./p.; and (3) 

based on both ki and the data completeness proportion, Pi. In the first 

procedure there is no possibility of a Type I error, in which the status 

is erroneously determined to be that of nonattainment. In the second 

procedure the maximum probability, a, of a Type I error is greater than 

0.6, but the probability, 3, of a Type II error, in which the status is 

erroneously determined to be that of attainment, is reduced for moderate 

data completeness porportions. In the third procedure a is limited to a 

preassigned level ag at the cost of increasing 3. 

The Type I/Type II error analysis does not give a definitive answer 

regarding which of the three procedures is preferable, because this 

depends on the priorities of the decisionmaker. For example, if a Type I 

error is to be completely avoided, the first procedure is preferable. It 

is hoped that the analysis will nevertheless be useful in considering the 

interplay between the proportion of data completeness and the likelihood 

of an erroneous attainment determination. 

Frank and Curran (1982) present a similar analysis in the case of particulate matter, which is typically sampled once every six days. Their 

results correspond to those we have obtained (although they explicitly 

treat a five-exceedances-per-year, three-year standard, which we treat 

only implicitly in Table 2-4, setting r = 15). Moreover, the theoretical 

probabilities they calculate correspond to those they obtained empirically 

83146 3 29 
P.57 

from a subset of sites having nearly complete data. Their study emphasizes a comparison of the first two procedures, based on ki and 

X., respectively. They show that when the number of exceedances is well 

above the number (r) allowed in the standard, our enhanced ability to 

detect nonattainment using the second procedure is even greater than that 

shown by the present worst-case analysis (in which x, = r + 1) . 

A different form of theoretical analysis is presented by Davidson and 

Hopke (1983). The authors construct a probability distribution of 

pollutant concentrations at a given site having a characteristic concentration, c, that is exceeded on average once per year. They define the 

status of a site as "attainment" if c is at or below the standard; 

otherwise it is "nonattainment." 

It should be noted that theoretical analysis of the most sensitive 

scenarios is not the only possible way to view the interplay between data 

completeness and procedures for inferring attainment status. An alternative is to empirically estimate the probability of misclassifying a site 

with a given proportion of data completeness. This approach is discussed 

in Section 3. 

There are other procedures for determining attainment. Breiman, Gins, and 

Stone (1978) substantially ameliorate the effects of incomplete data using 

a different estimate, X-, of the actual number of exceedances, Xi« Their 

approach is to fit an exponential distribution to the highest 20 percent 

observed concentrations and to use this fitted tail exponential distribution to estimate the expected number of exceedances among the missing 

concentrations (also see Breiman and Stone, 1983). It might prove 

worthwhile to include a procedure based on x. in future investigations of 

the effects of incomplete data on the chance of misclassification. 

83146 3 30 
P.58 

EMPIRICAL ESTIMATION OF THE PROBABILITY OF 

MISCLASSIFYING ATTAINMENT STATUS 

LONG-TERM AMBIENT STANDARDS 

Using the statistical framework introduced in Section 2, we consider the 

ith site to have attained a long-term ambient standard if the average of a 

complete set of concentrations, \x^, does not exceed the reference 

concentration, C NAAQS* Typically, a complete set of concentrations is not 

recorded, i.e., the data completeness proportion (Pi) is less than unity, 

so that the average of the recorded concentrations (u•) is used instead of 

u^ to classify the site as attainment or nonattainment. 

If Pi is less than unity and the site has in fact attained the standard, 

there is a chance, denoted by ai, that the site will be misclassified as 

nonattainment. Similarly, if the site has in fact failed to attain the 

standard, there is some chance, 3., that the site will be misclassified as 

' A 

attainment. Using the approximate normality of yi discussed in Section 2, 

i f

 "1

 < SAAQS we have 

a

i

 = p r

 <"1 > SAAQS) 

* 1 

= $ 

Np, 

,1/2 

1

 " Pi 

Np, 

vl/2 

CNAAQS " M i 

U

1 " SAAQS 

°1 

83146 10 31 
P.59 

and if Ui > C NAA Q S we have 

*1

 = Pr K < CNAAQS} 

-[(AT 

,1/2 

,1/2 

1 

NAAQS '"j 

a 

wi " CNAAQS 

Setting 

N p i \1/2 "1 " CNAAQS 

1 " Pi 

i 

A 

where a. is the standard deviation of the recorded concentrations, we may 

estimate ai and 3. as 

ai = *(H} if pi < CNAAQS 

ei =»(- C l ) i f u1 >c NAAQ S 

We then estimate a(pg) and 3(pQ)» the probability of misclassifying a site 

whose actual status is attainment and nonattainment, respectively, as 

a(pQ ) = average a^ , pi > pQ and Ui < C NAAQS 

3(p0 ) = average jj. , P i > pQ and u. > CNAAQS 

83146 10 32 
P.60 

The calculation of a(pQ) and 3(pQ) requires that each site be tentatively 

classified as attainment or nonattainment based on ui prior to the 

A A ' 

calculation of ai or 3.. This tentative classification may be erroneous 

* ' A 

for a given site, particularly if p. is near CmA AQ$, but averaging over a 

large number of sites produces estimates a(pQ ), 8(p0) whose reliability is 

much greater than the corresponding estimates, ai or 3., at a given site. 

Table 3-1 summarizes the results of these calculations for sulfur dioxide, 

nitrogen dioxide, lead, and total suspended particulate matter. In some 

cases no estimate is given because the number of sites is insufficient for 

reliable estimation. In the cases where reliable estimation is possible, 

A A 

we see that a(pg) and 3(Pg) are less than one percent. For sulfur dioxide 

and nitrogen dioxide, data completeness requirements of 50, 75, and 95 

percent were examined. For lead and total suspended particulate, which 

are typically monitored once per six days, we examined data completeness 

requirements of 5 percent (corresponding to the current requirement of 

five recorded concentrations per quarter), 12 percent (which may be 

interpreted as requiring a 75 percent data recovery from a once per six 

day sampling schedule), and 25 percent (75 percent recovery from a once 

per 3 day sampling schedule). 

When interpreting Table 3-1 it is important to distinguish between rates 

of misclassification that are possible under various data completeness 

requirements and rates that are estimated from 1981 data. The distinction 

is especially important for lead and particulate matter since their onceper-six-day sampling schedules limit the data completeness proportion to 

one-sixth. Figures 3-1 through 3-3 illustrate this point for, respectively, 

the quarterly lead standard, the annual TSP standard (based on the annual 

geometric mean concentration), and a hypothetical TSP standard based on 

the annual arithmetic mean concentration. The last figure is included 

because an annual particulate (PM 10) standard based on an arithmetic mean 

is currently under consideration. 

Each figure consists of a set of curves, a set of plotted points, and a 

bar chart. Each curve shows possible misclassification probabilities for 

83146r 10 33 
P.61 

TABLE 3-1. Estimated probability that a site's attainment status for longterm standards is misclassified as a function of minimum data completeness 

proportion, pg. The table entries are the estimated percentages of attainment sites (A) meeting a given data completeness requirement, p0, likely to 

be misjudged as nonattainment, or the percentage of nonattainment sites (N) 

likely to be misjudged as attainment. No estimate is made if the number of 

sites is insufficient. (Note: there are no known specific instances of 

misclassified sites—see text for a discussion of the estimation procedure.) 

S02 (annual): 891 sites 

Assigned Status 

Actual p0 = .50 (85%)a pQ = .75 (71%) p0 = .95° (8%) 

Status A N A N A N 

A (99%) c < l%d < 1% < 1% 

N (1%) 

N02 (annual): 324 sites 

Actual 

Status 

A (97%) 

N (3%) 

p0 = .50 (78%) 

A N 

< 1% 

p0 = .75 (54%) 

A N 

< 1% 

pg = .95 (8%) 

A N 

< 1% 

Pb (maximum quarterly): 696 sites 

Actual p0 = .05 (61%) p0 = .12 (39%) pQ = .25 (1%) 

Status A N A N A N 

A (97%) < 1% < 1% 

N (3%) 

TSP (annual): 3654 sites 

Actual 

Status 

A (87%) 

N (13%) 

p0 = .05 (92%)e 

A N 

2% 

9%f 

Pg = .12 (77%) 

A N 

2% 

8% 

Pg = .25 (6%) 

A N 

< 1% 

3% 

Notes on next page. 

83146T 8 34 
P.62 

a 

d 

Notes for Table 3-1 

The number in parentheses is the percentage of sites meeting the required 

data completeness proportion, pg. 

By 0.95 the value y^g- = 0.9524 is meant. 

The number in parentheses is the estimated percentage of sites that have 

attained or failed to attain the standard. Estimates are based on reported 

long-term averages. 

This is the estimated a-probability that a site in attainment and meeting 

the data completeness proportion pg = 0.5 would be misjudged 

as nonattainment. This entry can also be interpreted as an estimate of the 

percentage of such sites expected to be misclassified. 

e Note that intermittent monitoring in itself results in less than complete 

data. The data completeness requirements of 0.05, 0.12, and 0.25 correspond 

approximately to five recorded 24-hour measurements per quarter, and 75 

percent data recovery from once-per-six-day and once-per-three-day sampling 

schedules, respectively. 

' This is the estimated 3-probability that a site not in attainment of the 

standard and meeting data completeness proportion pg = 0.05 would be 

misjudged as attainment. Alternatively, we can interpret this entry as an 

estimate of the percentage of such sites expected to be misclassified. 

83146T 8 35 
P.63 

(A) fQ = 1/18, N = 91; (1/18) < = Pi < (1/12), 50 sites 

E.5 

5:. 

o/v 

o/v 

o/v 

0.36 (10% tile) 

0.59 (50% tile) j 

0.93 (90% tile) 

E.5 

(B) fQ = 1/12, N = 91 ; (1/12) < = p. < (1/8), 86 sites . 

1 E. 

'C£-- .IS 

E.5 -

a ss Miscl 

*•-

o > > 

* -> 

•-

<D 

o 

E 

2 

Z 

E 

E 

--r 

-7 

O • 

T . i _ 

? .-^ 

i 

I 

o/v = 0.36 (10% tile ) J 

o/v = 0.59 (50% tile ) \ 

o/v = 0.93 (90% tile ) ~~ 

I 

i 

E.3 .2 2. 4 

(C) pQ = 1/8, N= 

E.~-

! 

0 . 4 ; 

9 1 ; (1/8) < = p. < = (1/6), 180 sites, 

o 

J3 

O 

0. 1 

0 . 2 

-0. 1 

0 . 0 1.2 

o/p = 0.36 (10% tile ) -j 

o/v = 0.59 (50% tile ) | 

o/v = 0.93 (90% tile ) I 

h 3 . 3 

Figure 3-1. Lead: the probability of misjudging actual attainment status as 

determined by the mean (y), the coefficient of variation (o/p), and the 

proportion of data completeness (p). Continuous curves show probabilities 

determined by fixed combinations of p and o/p, whereas the plotted points 

are determined by combinations obtained from 1981 data. 

35 
P.64 

(A) pn = 1/18, N 

c 

o 

• J 

IO 

o 

Hvt 

vt 

m 

r— 

U 

yt 

X. 

HO 

>> * J 

r— 

J 3 

«0 

O 

0 

0. 

0. 

0. 

0. 

B. 

0. 

6 

5 

4 

3 

2 

1 

0 

365; (1/18) < = p. < (1/12), 199 sites. 

i ». 

Percent 00s 

se. 

"

0

- 0 . 

j _ 

30.0 

_L 

l n og/l n yg « 0.08 (10% tile ) 

l n og/l n yg = 0.10 (50% tile ) 

l n o g / l n yg = 0.15 (90% tile ) 

_L 

60.0 90.0 

_L 

120.0 

w,#//Mv .'TWA -'AM is?#r >TM 

150.0 

(B) pQ = 1/12, N = 365; (1/12) < = pi < (1/8), 432 sites, 

§ 0.6 

S 0.5 

T; 0.4 

tA 

n 

a 0-3 

<^ 0.2 

o 

Percent Obs 

5B. 

I 

.£> 

O 

0.1 

0.0 

-0. , 

_L 

30.0 

rititih 

J_ 

In o g / l n yg = 0.08 (10% tile ) -

In og/l n vg = 0.10 (50% tile ) _ 

l n o g / l n ug = 0.15 (90% tile ) 

mirrW-y. 

_L _L 

60.0 90.0 120.0 150.0 

(C) pn = 1/8, N = 365; (1/8) < = Pi

 K (1/6), 2125 sites, 

0.6 

Percent ODs 

se. 

i 

In og/l n yg •= 0.08 (10% tile ) -

l n og/l n vg = 0.10 (50% tile ) 

— l n o g / l n yg = 0.15 (90% tile ) 

150.0 

Figure 3-2. TSP, annual geometric mean: the probability of misjudging 

actual attainment status as determined by the natural log of the geometric 

mean (pq ). the coefficient of variation (ln og/ln p g ) , and the proportion 

of data completeness (p). Continuous curves show probabilities determined 

by fixed combinations of p and (In Og/ln pn), whereas the plotted points are 

determined by combinations obtained Trom 1981 data. 

37 
P.65 

(A) pQ = 1/18, N = 365; (1/18) < 

0.6 j 

p. < (1/12), 199 site s Percent Obs 

SB. 

o 

g 0.5 -

£ 0. 4 -

•s 

o 0. 3 -

*_ B.2 

o 

2 B.l 

•S 0- 0 

O 

£ -0.1 

30. 0 

i 

o/v ' 0.32 (10% tile ) 

o/v ' 0.42 (50% tile ) 

o/v • 0.61 (90% tile ) 

£** • •>*'") » #*••* • 

_L J_ 

60. 0 90. 0 120.0 

M S I 

150.0 

(B) pQ = 1/12, N = 365; (1/12) < = p. < (1/8), 432 sites, 

0 . 6 1 

o/v = 0.32 (10% tile) -

o/v = 0.42 (50% tile ) 

o/y = 0.61 (90% tile ) 

Percent Obs 

5B. IBB. 

-H 

°- -0. : 

0 . 0 30. 0 60. 0 90. 0 

_L 

120.0 150. 0 

g-0. 6 

S 0.5 

< 4 -

s

 0

-

4 

a 0.3 

(C) P 0 = 1/8, N = 365; 

i 

(1/8) < = p. < = (1/6) , 2125 sites . 

e 

i i i 

m o/v = 0.32 (10% tile ) -

S o/v - 0.42 (50% tile) 

* * S o/v - 0.61 (90% tile) " 

* fir* 

Percent Obs 

5B. 

I 

IBB 

1 

1 

<t 0.2! -

O i 

••? B. l U 

•o 0. 0 

o 

I. 

°- -B J.0 

MTX. VP T 

I 

'-<(".. CI 60. 0 90. 0 120.0 150. 0 

Figure 3-3. TSP, annual arithmetic mean: the probability of misjudging 

actual attainment status as determined by the mean (p), the coefficient of 

variation (a/p), and the proportion of data completeness (p). Continuous 

curves show probabilities determined by fixed combinations of p and a/p, 

whereas the plotted points are determined by combinations obtained from 

1981 data. 

38 
P.66 

a range of mean concentrations by combining a given data completeness 

proportion (1/18, 1/12, or 1/8) with a given coefficient of variation 

(obtained from the 10th, 50th, or 90th percentile of the 1981 distribution). The given data completeness proportions approximately correspond 

to 5, 8, and 12 samples per quarter, respectively. The last proportion, 

1/8, may also be interpreted as a 75 percent data recovery rate from a 

once-per-six-day sampling schedule. 

The plotted points in each figure represent sites whose data completeness 

proportions fall with a specified interval. Parts (A), (B), and (C) of 

each figure represent completeness intervals of 1/18 to 1/12, 1/12 to 1/8, 

and 1/8 to 1/6, respectively. For each site the estimated misclassification probability (in part determined by the coefficient of variation 

reported for that site) is plotted against the reported mean concentration. Within each data completeness interval the bar chart shows the 

percentages of sites having a given probability of misclassification. 

The figures show that the data completeness requirements by themselves do 

not limit probabilities of misclassification. It can be seen, however, 

that for the great majority of 1981 sites, reported mean values are 

sufficiently far above or below the standard and coefficients of variation 

are sufficiently small so that the estimated probabilities are effectively 

zero. Thus, misclassifications are not ruled out by these data completeness requirements but they are unlikely, assuming that the means and 

coefficients of variation reported in 1981 are representative of other 

years. 

We can also use the figures to infer the benefits of requiring 12 rather 

than 5 samples per quarter from intermittent samplers. In the case of 

lead we are assessing the benefits of current requirements since 12 

samples per quarter are required to determine attainment status (see Table 

G-1). The bar charts of parts (A) and (C) of Figure 3-1 show that the two 

groups of sites have nearly the same low susceptibility to misclassification. The curves distinguish parts (A) and (C) more clearly, however, and 

are probably more indicative of the future consequences of strengthening 

83l46r 1 0 

39 
P.67 

or relaxing data requirements for al l sites . We can express thi s difference by comparing "critica l concentration intervals," i.e. , by noting the 

interval of maximum quarterly mean concentrations within which the 

probability of misclassification exceeds 0.10 for a site having a typical 

(i.e. , median) coefficient of variation. 

This definitio n of a "critica l interval" bears some explanation. We are 

interested in correctly classifying the attainment status of a sit e whose 

actual long-term average concentration, p, is estimated by p based on 

incomplete data. For simplicity , we assume the coefficient of variation , 

a/p, to be the median of the coefficients of variation calculated for our 

sample of sites . If p is very close to the reference concentration, 

^NAAQS'

 t^1en

 w w ^ l be above or below C^/ms with nearly equal probability . Therefore, i f p is only slightl y above or below CN ^g$, the risk 

of misclassification wil l be close to 50 percent. As p moves away from 

^NAAQS»

 t,1 e

 probability of misclassification decreases until , at some 

point above and below C^g^ , the probability drops below 10 percent. The 

critica l interval i s thus the set of p for which attainment determinations 

are subject to error with nonnegligible probability . 

In mathematical notation we define the critica l interval as the union of 

intervals A and B where 

A = { u : P < CNAAQS and Prp (p > CNAAQS) > a } 

B = { p : P > CNAAQS and Prp(p < CNAAQS) > a j 

so that the critica l interval is 

A U B = { p : a < Pr y (J > CNAAQ$) < 1 - a } . 

In the framework of testing the statistica l hypothesis that p <. Cw/\ngc 

based on p, the critica l interval is the set of p for which the power of 

83146T 10 4 Q 
P.68 

the test , i.e. , the probability that p exceeds CN ^ AQ$, is between 

a and 1 - a, i.e. , setting a equal to 0.1 , between 10 and 90 percent. 

We may also describe the critica l interval as the interval within which 

the probabilities of apparent attainment and nonattainment (based on a 

comparison of p and CNAAQS ) are both between 10 and 90 percent. I t is 

thus an interval within which the determination of attainment status is 

unreliable. We may therefore use critica l intervals to judge the adequacy 

of completeness requirements—the more stringent the requirement, the 

narrower the critica l interval . 

The critica l interval for a sit e recording only five valid lead samples 

per quarter is 1.13 to 2.23 pg/nr (25 percent below to 49 percent above 

•3 

the standard of 1.5 pg/m ), whereas the interval narrows to 1.24 to 1.90 

pg/nr (17 percent below to 27 percent above the standard) for a site that 

records 12 valid samples per quarter. 

Figures 3-1 and 3-2 support similar conclusions regarding TSP long-term 

standards. Since long-term average concentrations are well below the 

standard at most sites, the benefits of 12 versus five samples per quarter 

are clearer from the curves depicting possible misclassification 

probabilities than by a direct comparison of sites with different proportions of data completeness. We consider two forms of annual TSP standard, 

both having a reference concentration of 75 pg/m , namely, the current 

standard based on the geometric mean and a hypothetical standard based on 

an arithmetic mean (the latter is relevant to the recently proposed PM-10 

standard). For the current standard, the critical interval for the case 

of five valid samples per quarter is 67 to 85 pg/m3 (11 percent below to 

13 percent above the standard), which narrows to 70 to 81 pg/m (7 percent 

below to 8 percent above the standard) for the case of 12 valid samples 

per quarter. These results are the same (to two-digit accuracy) for the 

hypothetical standard concentration represented in Figure 3-3. 

It is instructive to compare the cases of lead and TSP represented by 

Figures 3-1 and 3-2, respectively. The probability of misclassification 

is determined not solely by the proportion of data completeness, but also 

83146r io 41 
P.69 

by the number of valid observations to be used in judging attainment. 

For example, 5.5 percent complete data yields 20 observations with 

which to judge attainment of an annual standard, but only five 

observations for assessing the attainment of a quarterly standard. 

Therefore, a given number of lead samples per quarter with which to judge 

attainment of the quarterly lead standard leads to higher 

misclassification probabilities than the same number of TSP samples per 

quarter (i.e. , four times that number per year) with which to judge 

attainment of the annual TSP standard, other factors being equal. Thus, 

the critica l interval corresponding to the 12 lead samples per quarter 

required for attainment determinations is relativel y wider (17 percent 

below to 26 percent above the quarterly lead standard) than the interval 

corresponding to the required 5 TSP samples per quarter (10 percent below 

to 13 percent above the annual TSP standard). 

Therefore, i f our goal were to contain the 0.10 probability critica l 

interval within , say, + 10 percent of the standard, then the requirement 

of five TSP samples per quarter nearly achieves the goal whereas the 

requirement of 12 lead samples per quarter does not. This suggests that 

any tightening of current data completeness requirements to improve 

attainment assessments of long-term standards should begin with lead. 

On the other hand, i f our goal were to restric t the fraction of sites 

vulnerable to misclassification, e.g. , sites for which the misclassification probability exceeds 0.10, i t appears from the 1981 data that any 

tightening of completeness requirements should be directed at TSP rather 

than lead, since the observed fraction of "vulnerable" sites is greater 

for TSP than for lead. This difference between TSP and lead may be solely 

a consequence of the smaller sample of lead sites , however. 

The two goals thus lead to different conclusions about which pollutant, 

lead or TSP, warrants the most consideration for strengthened data 

completeness requirements. Since the "critica l interval" analysis seems 

to be more reliable than the "vulnerable sites" analysis, i t seems that 

requirements for lead warrant firs t consideration. This is especially so 

since strengthed requirements for particulates have already been 

42 83146r i o **• 
P.70 

considered; proposed revisions to the particulate NAAQS include a 

requirement of 12 valid observations per quarter (EPA, 1984). 

The recommendation that strengthened completeness requirements be considered for lead is offered only as a point of departure, however, since 

realisti c recommendations must include many practical considerations 

outside the scope of our analysis. For example, we have not attempted to 

distinguish in general between data completeness proportions resulting 

from good data recovery from intermittent sampling, on the one hand, 

versus poor data recovery from continuous sampling on the other. The 

latte r case may be indicative of generally unreliable data. Pending a 

more comprehensive review of data completeness requirements, however, the 

results presented in Table 3-1 and Figures 3-1 through 3-3 should be 

useful because they show that current requirements are adequate to render 

reliable determinations of the attainment of long-term standards at al l 

but a small fraction of sites . 

SHORT-TERM AMBIENT STANDARDS 

Correctly classifying the short-term attainment status of a site having a 

certain data completeness proportion is much more difficul t than classify -

ing the long-term attainment status. That is , the estimated long-term 

average is a more stable statisti c than the observed number of short-term 

exceedances or the estimated total number of exceedances. Because of 

this , i t is not possible to reliabl y estimate the chance of misclassifying 

the status of most sites . We can, however, estimate the average chance of 

misclassifying sites whose proportion of data completeness meets a 

required proportion. 

This can be done i f we make the reasonable assumption that the actual 

number of short-term exceedances (x.) and the data completeness proportion 

(p.j) are statisticall y independent. That is , we may use an estimate of 

the total number of exceedances at each site to estimate the statistica l 

distributio n of short-term exceedances across al l sites . We then apply 

83146r io 43 
P.71 

this statistical distribution to those sites having data completeness 

proportions, p^, near a given proportion, p, and thereby estimate the 

fraction of these sites having a given number of exceedances 

(x = 0, 1, 2, ...) . For a one-exceedance standard (for which r = 1 in 

the notation of Section 2) , we may therefore estimate the probability of 

misclassified attainment and nonattainment sites, respectively, a and 3 , 

associated with a given proportion of data completeness. The estimates of 

a„ and 3„ are 

P P 

a = Pr(x. > 1.05 | p. = p, xi = 1) Pr(xi = 1 | Xi < 1) 

= p.Pr(xi = 1 | Xi < 1), if p <y-^ -

= °. if P>-O F 

and 

max 

3p = £ Pr(*i <

 l

-

05 I Pi

 = P» xi = x ) pr(xi = x Uj > 2) 

X ^x

 \ - 1 

= E d " P) Pr(Xi = X | Xi > 2) , if p < T - i F 

A C 

m a x > 1 * 1 

= L C d - P) X + xp(l - p)*"1] Pr(xj = X | X. > 2) , if p > y- ^ 

A —£ 

We then estimate a(pQ) and 3(pQ) as 

a(p0) = average ap , Pi > P0 

3(p0) = average 3p , Pi > Pg 

In estimating the statistical distribution of the total number of exceedances, instead of using X- = k./p. we use X-, obtained by fitting an 

83146T

 1 0 44 
P.72 

exponential distribution to the upper 10 percent of the distribution of 

concentrations at a site (the exponential tail is fitted using available 

statistics—the 90th percentile and the maximum concentration). This is 

done to avoid a certain lumpiness in the distribution of x, (e.g., the 

minimum positive estimate obtained from a once per six day sampling 

schedule is 6) , and results in a larger estimate in several cases. The 

formula for x is 

x=k+(N-n + 1)(1 - y) exp 

'

CNAAQS " X A ln 

xm,„ - x / max y I 

where we have suppressed the index i for ease of notation and where 

k = the number of recorded exceedances 

N = the number of observations in a complete data set 

n = the number of recorded concentrations 

•y = 0.9, corresponding to the use of the upper 10 percent of the 

concentration distribution 

x = xg#g, the 90th percentile of the concentration distribution 

xmax = t'1e max im u m recorded concentration 

n = n/(n + 1) 

Provision is made in the calculation of x for cases in which either x > 

^NAAOS

 o r x a = x . In these cases x was set equal to x = k/p. 

It should also be noted that X is rounded to the nearest integer to estimate 

the statistical distribution of the total number of exceedances among all 

sites. 

The results of these calculations are shown in Figures 3-4 through 3-8 and 

in Table 3-2. The figures indicate the chance a that a site randomly 

selected from a group of attainment sites having data completeness 

proportion p would be misclassified as nonattainment, or the chance 3 that 

a nonattainment site would be misclassified. In contrast to the most 

sensitive scenarios treated in Section 2, Figures 3-4 through 3-8 indicate 

83146T 10 45 
P.73 

(a) a versus p 

0.06 1-

0.06-

a. 

0.04r 

0.02-

0.C 

(b) 3 versus p 

~> r 

FIGURE 3-4. Estimated probabilities a and 3 of 

misjudging attainment of the 24-hour sulfur dioxide 

standard as functions of data completeness proportion, p. 

83146 46 
P.74 

(a) a versus p 

O.OB 

0.06r 

XI 

£ 

0.04 

0.02 -

O.C 

0.06 

0.06 

JD 

0.04 

0.02 

0. OC 

(b) 3 versus p 

-i 1 1 j 1 1 1 r 

1 ' ' 

0 0.2 0.4 0.6 O.B 1.0 

P 

FIGURE 3-5. Estimated probabilities a and 3 of 

misjudging attainment of the one-hour carbon monoxide 

standard as functions of data completeness proportion, p. 

83146 47 
(a) a versus p 

P.75 

0.08 

-i 1 1 1 r "i 1 r 

0.06 -

Q 

0 . 04 

0.02 -

(b) 3 versus p 

0.08 -

0.06 r 

0) 

0.04 -

0.02 L 

0.0 

FIGURE 3-6. Estimated probabilities a and 3 of 

misjudging the 8-hour carbon monoxide standard as 

functions of the data completness proportion, p. 

83146 48 
P.76 

(a) a versus p 

1. 0 i 1 1 1 1 1 1 r 

0.8 

0.6 

.c 

Q. 

0.4 

0.2 -

(b) g versus p 

QJ 

X) 

1 . u 

0.8 

0.6 

0.4 

0.2 

n n 

1 ' ' ' ' 

- \ 

i 1 i 1 

i | i | i 

-

-

-

7 1 -H —J !_- . 

0.0 0.2 0.4 0.6 0.8 1.0 

P 

FIGURE 3-7. Estimated probabilities a and 3 of 

misjudging attainment of the maximum daily one-hour 

ozone standard as functions of the data completeness 

proportion, p. 

83146 49 
(a) a versus p 

P.77 

0.08 -

0.06 

o 

sz 

a 

0.04 

0.02 

0.0 

-i 1 r "1 1 1 r 

0.08 

0.06 

o 

V 

XJ 

0.04 

0.02 

0.0 8.o 

FIGURE 3-8. Estimated probabilities a and 3 of 

misjudging attainment of the 24-hour TSP standard as 

functions of the data completeness proportion, p. 

83146 50 
P.78 

TABLE 3-2. Estimated probability that a site's attainment status for shortterm standards is misclassified as a function of minimum data completeness proportion, p0 . The table entries are the estimated percentages of attainment sites (A) meeting a given data completeness requirement, pg, likely to 

be misjudged as nonattainment, or the percentage of nonattainment sites (N) 

likely to be misjudged as attainment. No estimate is made if the number of 

sites is insufficient. (Note: There are no known specific instances of 

misclassified sites—see text for a discussion of the estimation procedure.) 

S02 (24 hours): 891 sites 

Assigned Status 

Actual p0 = .50 (85%)a pQ = .75 (71%) p0 = .95b (8%) 

Status A N A N A N 

A (98%) c 2%d 2% 0% 

N (1%) 

CO (1 hour): 480 sites 

Actual p0 = .50 (79%) p0 = .75 (65%) p0 = .95 (22%) 

Status A N A N A N 

A (99%) < 1% < 1% 0% 

N (1%) 

CO (8 hours): 480 sites 

Actual pg = .50 (79%) p0 = .75 (65%) p0 = .95 (26%) 

Status A N A N A N 

A (57%) 2% 2% 0% 

N (43%) < l%e < 1% < 1% 

O3 (Daily maximum 1-hour): 723 sites 

Actual p0 = .50 (86%) pQ = .75 (70%) pQ = .95 (16%) 

Status A N A N A N 

A (63%) 8% 8% 0% 

N (37%) < 1% < 1% < 1% 

Continued 

83146T 8 bl 
P.79 

TABLE 3-2. (Concluded) 

TSP (24-hours): 3667 sites 

Assigned Status 

Actual 

Status 

A (79%) 

N (21%) 

p0 = .05 (92%)f 

A N 

2% 

6% 

Pg = .12 (77%) 

A N 

2% 

6% 

p0 = .25 (6%) 

A N 

3% 

4% 

a The number in parentheses is the percentage of sites meeting the required 

data completeness proportion, PQ. Under current procedures for determining 

the attainment of short-term standards, this completeness requirement rules 

out the possibility of a false nonattainment determination. 

b By 0.95 the value y ^ = 0.9524 is meant. 

c The number in parentheses is the estimated percentage of sites that have 

attained or failed to attain the standard. These estimated percentages are 

based on the tail-exponential method discussed in the text. 

d This is the estimated a-probability that a site in attainment and meeting 

the data completeness proportion pg = 0.5 would be misjudged 

as nonattainment. This entry can also be interpreted as an estimate of the 

percentage of such sites expected to be misclassified. 

e This is the estimated 3-probability that a site not in attainment of the 

standard and meeting data completeness proportion pg = 0.5 would be 

misjudged as attainment. Alternatively, we can interpret this entry a 

estimate of the percentage of such sites expected to be misclassified. 

' Note that intermittent monitoring in itself results in less than complete 

data. The data completeness requirements of 0.05, 0.12, and 0.25 correspond 

approximately to five recorded 24-hour measurements per quarter, and 75 

percent data recovery from once-per-six-day and once-per-three-day sampling 

schedules, respectively. 

as an 

83146r 8 5 2 
P.80 

that a and 3 are for the most part well below 10 percent. This is 

because most sites are estimated to have no exceedances, in which case 

there is no chance of misclassification, and those sites estimated to have 

more than one exceedance frequently appear to have more than two exceedances. In short, the most difficult cases treated in Section 2 appear to 

be rare in actuality. It should be noted that the data are from 1981, so 

that, for purposes of comparison, ozone is treated as having the same oneyear one-exceedance form of standard as the other pollutants. 

Table 3-2 shows an approximate 1 or 2 percent probability of misclassifying sulfur dioxide and carbon monoxide sites. The a- and 3-probabilities 

of misclassification are estimated to be 8 percent and less than 1 

percent, respectively, for ozone sites. For particulate sites a and 3 

are estimated to be 2 and 6 percent, respectively. 

SUMMARY 

The 1981 data indicate that under current data completeness requirements, 

the rate of misjudging the attainment of either long-term or short-term 

standards is under 10 percent, and in several instances the estimated 

misclassification rate is under one percent. The current completeness 

requirements therefore seem to be adequate for generally reliable attainment determinations. This conclusion should be regarded as tentative, 

however, pending development of specific objectives for limiting rates of 

misclassification. 

We have also conducted what must be regarded as a preliminary analysis of 

the benefits of strengthened requirements for data completeness. In 

general, direct estimates of the expected percentages of misclassified 

sites reveals virtually no change resulting from the changes in requirements that we consider. Taking a less direct approach in the case of 

long-term standards, however, we have estimated a critical interval about 

the standard, within which misclassification probabilities exceed 10 

percent, and we have shown how these critical intervals narrow as more 

831l+6 r 1 0 53 
P.81 

complete data are required. The analysis suggests that strengthened 

requirements be considered for lead and possibly for particulates (the 

recently proposed revisions to the particulate standards include such a 

strengthened requirement). A similar analysis is possible for short-term 

standards, although the analysis would require some assumptions about the 

frequency distribution of concentrations at individual sites. 

In any case, realistic recommendations for strengthened data completeness 

requirements must address the broader issues concerning data reliability 

and cost-effective air quality management. For example, we should 

probably consider the benefits of strengthened quality assurance procedures along with strengthened data completeness requirements. Similarly 

we might consider whether more accurate attainment determinations might be 

achieved under current data completeness requirements by changing the form 

of current short-term standards. We have not attempted to include such 

issues in the present analysis, although these issues certainly deserve 

future consideration. 

83146T 10 54 
STATISTICAL ESTIMATION OF NATIONAL 

AIR QUALITY STATUS AND TRENDS 

We now consider the estimation of national averages of site-specific 

annual averages, p., and site-specific exceedance rates, x... We face the 

choice of a minimum data completeness proportion, pg, such that only those 

sites in our sample with p. > pn will be used to estimate the national 

average. 

A QUESTION OF BIAS 

Let 

1

 v(P?> . 

P(PQ )

 = v(Pg) E v. 

and 

v(Pg) 

X(Pg) = v(p0) E xi 

where p. and x. are estimates of the site-specific long-term average, \i-, 

and exceedance rate, X-, respectively, and where the summation is over 

sites in the sample with p. > pQ . If we assume that from site to site the 

air quality parameters pi and x. are independent of the proportion p^ of 

data completeness, and if we regard the set a of sites in our sample as 

having been randomly drawn from the population of sites of interest, then 

for each p0 , p(pg) and x(pQ) should be unbiased, i.e., we should have 

A 

E y(Pg)

 B u = E(u.j) 

83146 4 55 
P.83 

and 

A 

E x(pQ) = X = E (x^ . 

A A 

This lack of bias follows from the unbiasedness of pi and x., 

E pn- = Pi 

E I. = Xi 

as discussed in Section 2. 

A A 

Under these assumptions, p(pQ) and x(pQ) are approximately normally 

distributed unbiased estimators of p and x, respectively. Thus, a natural 

criterion to use in selecting pg is the variance of these estimators. 

VARIANCE OF THE ESTIMATORS 

A A 

In Chapter 2 we obtained expressions for the variance of Pi and xi5 

conditional on the choice of site, i, and thus conditional on p., x-, and p. 

Extending the conditional variance to the averages taken over the set (/ 

of sites in our sample, we have 

v(Pn) i _ „ 2 

Var(p(p0) | JI) *-| E 

9' 1 - P« o i l 

v

fc(pn) 1=1 pi 

and 

1

 V( 'o)l - P i 

Var (x(p0) | J/) i- 1 E - T r

L x 1 

v (pQ) 1=1

 Kl 

83146 4 56 
P.84 

To obtain the unconditional variance, we must allow for site-to-sit e 

differences in Pi and x. . Thus (see, for example, Brillinger, 1966) 

Var (P( P Q ) ) = E {var (A9Q) | ^) } + Var{E(p(pQ) | &)} 

v

(Pn) i . n J- \ i v(Pn) 

i_ V 1 " Pi °1 

2, , H, D, N * ^{-f 2J -^— L

-^> + Var 

v (pQ) i= l 

which may be estimated as 

v(P0> 1 - p. 2 , »<P0> 

Var (;(p0» --j-J - E -j-l-J * 1 E (.,-;(P0 )) 2 

v (p Q ) 1=1

 K l v (p Q ) 1=1 

Similarly , we have 

X(p 0}

 1 - p. \ I ,

 v(p 0} 

( i HQ / 1 " PH ) ( i ^ 

which may be estimated as 

u (P[)' 1 - p. , v(Po> 

Jar U(p ) . "L- E —J-x , + -jX y E (X, -lip,,))1 

V (Pn) 1=1

 r l V r •(P 0 ) 0 ' 1=1 

The variance expressions are similar for p(pQ) and x(p Q ). In both cases, 

the second term may be expected to be proportional to l/v(p Q ) while the 

firs t term depends on the distributio n of Pi (as p0 increases to unity , 

(1 - Pi)/Pi approaches zero but l/v(p Q ) increases). 

83146 4 57 
AN EMPIRICAL ASSESSMENT OF THE DATA COMPLETENESS 

NEEDED TO RELIABLY ESTIMATE NATIONAL TRENDS 

SULFUR DIOXIDE 

A 

Table 5-1 and Figure 5-1 show p(pQ ), the estimated composite annual 

average sulfur dioxide (SO2) concentration, and Var (p(p0)), its estimated 

variance as discussed in Section 4, for several values of required data 

A 

completeness proportion pg. The estimator p(pn) is fairly constant with 

Pg, but its estimated variance increases substantially for pQ > 80 percent, consistent with the discussion in Section 4. 

Similarly, Table 5-2 and Figure 5-2 show a substantial increase in the 

A 

estimated variance of x(pQ) for pQ > 80 percent. In addition, Figure 5-2a 

suggests that increasing the required percentage, pg, may induce a 

positive bias in the estimate of the national average exceedance rate. 

A 

The increase in x(pQ) accelerates for pg > 80 percent. 

In summary, it appears that no more than an 80 percent data completeness 

requirement should be used to estimate the national status and trend in 

SO2 concentrations. 

CARBON MONOXIDE 

A 

Table 5-3 and Figure 5-3 show the estimated exceedance rate, x(pn ), and 

A A U 

its estimated variance, Var (x(pQ)), for hourly averaged carbon monoxide 

(CO) concentrations. Interestingly, sites with more complete data have no 

A A A 

observed exceedances, so that both x(pQ) and Var (x(pQ)) are calculated 

to be zero for pg > 94 percent. For smaller values of pg, however, both 

A A A 

x(p0) and Var (x(pQ)) increase with p0, with a fairl y sharp rise in 

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Var (x(pQ)) beginning at p0 = 60 percent. The results suggest that no 

more than 65 percent data completeness is needed to estimate the national 

hourly CO exceedance rate. 

Table 5-4 and Figure 5-4 show results for 8-hour CO exceedances. Both the 

A 

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A A *J 

Var (x(pQ)) sharply increase for p^ > 90 percent, suggesting that no more 

than a 90 percent data completeness requirement should be used to estimate the 

national 8-hour CO exceedance rate. 

NITROGEN DIOXIDE 

A 

Table 5-5 and Figure 5-5 show p(pn ), the estimated composite annual 

^ A A 

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estimated variance, for several values of the required data completeness 

A 

proportion, PQ . The estimator P(PQ ) is fairly constant with PQ, but its 

estimated variance increases substantially for PQ > 90 percent. This 

suggests that no more than a 90 percent data completeness requirement 

should be used to estimate the national status and trend in NO2 

concentrations. 

OZONE 

Table 5-6 and Figure 5-6 show the estimated exceedance rate, x(pn ), and 

A A ^ 

its estimated variance, Var (x(pn)), for daily maximum 1-hour ozone (Oo) 

concentrations. Both x(pQ) and Var (x(pQ)) increase with PQ, with a 

fairly sharp rise in Var (x(p0)) beginning at PQ = 85 percent. The 

results suggest that no more than a 90 percent data completeness 

requirement should be used to estimate the national daily maximum ozone 

exceedance rate. 

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TABLE 5-5. Est 

of one-hour N02 

variance, Var(0 

requi red percen 

p0 

96.50000 

95.09999 

93.79999 

92.39999 

90.50000 

88.20000 

85.70000 

82.00000 

78.20000 

75.20000 

69.70000 

65.50000 

58.39999 

51.39999 

45.30000 

37.10000 

31.80000 

26.90000 

23.10000 

17.50000 

0.30000 

0.30000 

imated composite annual average 

, P(PQ), and its estimated 

^pn)), as functions of the 

u 

tage, pQ, of 

I(P0) 

33.44099 

34.75300 

41.21500 

44.69399 

44.60000 

44.89600 

44.36099 

44.71400 

45.92799 

45.62500 

44.94700 

44.63499 

45.01400 

44.45399 

43.99200 

44.30199 

44.23399 

43.65500 

43.77599 

43.56400 

43.36700 

43.24699 

68 

data completeness. 

Var(y(p0)) 

14.59878 

6.81544 

11.62743 

10.46519 

6.89711 

5.32763 

4.35964 

3.41974 

3.34880 

3.19546 

2.92656 

2.74853 

2.56410 

2.42393 

2.24541 

2.22146 

2.05578 

1.92911 

1 .78446 

1.64982 

1.57100 

1.57575 
(A) u(p0 ) versus pQ 

(B) Var(p(pQ)) versus 

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Required Percent 

FIGURE 5-5. Estimated long-term N02 air quality parameters 

as functions of the required data completeness, Pg. 

83l't6 
P.97 

TABLE 5-6. Estimated mean annual rate of 

maximum daily one-hour ozone exceedance, 

x(p„), and its estimated variance, Var(x(p0)): 

as functions of the required percentage, 

P Q , of data completeness. 

p0 

98.89999 

97.79999 

96.39999 

95.29999 

93.89999 

92.89999 

91.50000 

90.09999 

88.29999 

86.89999 

85.00000 

83.00000 

80.29999 

78.00000 

73.79999 

67.20000 

61.20000 

50.89999 

40.00000 

26.80000 

3.70000 

0.40000 

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X(P0) 

12.82300 

20.10000 

19.90200 

18.18400 

15.01800 

13.10600 

12.83500 

11.58300 

10.65700 

9.71900 

9.16100 

8.53400 

8.17600 

7.83800 

7.43100 

7.45200 

7.36400 

7.20000 

7.78500 

7.93800 

7.92600 

7.91500 

". A 

Var(x(pQ)) 

30.20399 

22.94687 

15.08907 

10.62845 

7.01568 

5.04998 

4.27442 

3.30427 

2.67449 

2.18219 

1.82070 

1.53777 

1.32614 

1.16137 

1.01475 

1.00815 

0.89779 

0.82834 

0.93169 

0.95963 

0.96646 

0.96394 

83146 

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FIGURE 5-6. Estimated annual ozone air quality parameters 

as functions of the required data completeness, pg. 

8 3 I '• f) 
LEAD 

Table 5-7 and Figure 5-7 show p(pn ), the estimated composite maximum 

*»» A A 

quarterly lead (pb) concentration, and Var (p(pn)), its estimated variA A *•* 

ance. Both p(pQ) and Var (p(pQ)) are fairly constant for pQ <; 17 percent 

(corresponding to complete data recovery from a once-per-six-day sampling 

schedule). Only a small number of sites have more than 17 percent data 

completeness. The consequent rise in the estimated variance suggests that 

no more than a 17 percent data completeness requirement should be used to 

estimate the national status and trend in lead concentrations under 

current sampling requirements. 

TOTAL SUSPENDED PARTICULATE 

A 

Table 5-8 and Figure 5-8 show p (pQ)» the estimated composite annual 

average concentration of total suspended particulate (TSP), and its 

A A A 

estimated variance, Var (p(p0)). The estimator p(pfi) is fairly constant 

with pg, and its estimated variance shows no pattern for increasing pg. 

Therefore, it is not possible to judge the effect that an increased data 

A 

completeness requirement would have on the variance of p(p 0 ) . 

Similarly, Table 5-9 and Figure 5-9 show no appreciable pattern in the 

A 

estimated variance of x(pQ ). Figure 5-9, however, suggests that increasing the required percentage, PQ, may induce a positive bias in the 

estimate of the national average exceedance rate. Because of this 

possible bias, it appears that no more than a 17 percent data completeness 

requirement should be used to estimate the national status and trend in 

TSP concentrations. 

SUMMARY 

In general, we see that the advantages of including a large number of 

sites in the estimation of national air quality trends outweighs the 

83146 9 72 
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TABLE 5-8. Estimated composite average of 

24-hour TSP, u(pQ), and its estimated 

variance, Var(p(pn)), as functions of the 

required percentage, pQ, of data completeness. 

p o 

30.68500 

16.71200 

16.71200 

16.43800 

16.43800 

16.16400 

15.89000 

15.89000 

15.61600 

15.34200 

15.06800 

14.79500 

14.24700 

13.97300 

12.87700 

12.05500 

10.41100 

8.21900 

6.02700 

3.83600 

0.27400 

0.27400 

A 

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51.08199 

53.59200 

56.05000 

56.52800 

56.72600 

56.57700 

57.10899 

57.17000 

57.28699 

57.48299 

57.43500 

57.27200 

57.13400 

57.28999 

57.31000 

57.41100 

57.20499 

56.97199 

56.78200 

56.70900 

56.52599 

56.52599 

A ". 

Var(y(p0)) 

3.17931 

1.35666 

0.90998 

0.69591 

0.52045 

9.22075 

2.12360 

1.13663 

0.75091 

0.56889 

0.44404 

4.18731 

1.42163 

0.86768 

0.65872 

0.56483 

0.45510 

3.04553 

1 .37268 

0.87463 

0.66334 

0.66334 

8311+6 75 
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P.7 

disadvantages of including sites having a low data completeness proportion, p.:. The broad inference from these 1981 results—which seems likely 

to hold even if more frequent intermittent samples or more complete data 

are required--is that the wide variability between sites argues against 

the exclusion of a large fraction of sites solely on the basis of data 

completeness requirements. Thus, the requirement for estimating national 

trends should be more relaxed than that for determining the attainment 

status of an individual site. 

83146 9 79 
P.8 

REFERENCES 

Abramowitz, M., and I. A. Stegun. 1964. Handbook of Mathematical 

Functions . Dover, New York. 

Brillinger, D. R. 1969. The calculation of cumulants via conditioning. 

Annals Inst. Stat. Math., 21:215-218. 

Breiman, L., J. Gins, and C. J. Stone. 1978. "Statistical Analysis and 

Interpretation of Peak Air Pollution Measurements." Technology 

Service Corporation, Santa Monica, CA (TSC-PD-A190-10). 

Breiman, L., and C. J. Stone. 1983. "Approximate confidence bounds for 

extreme quantiles." In progress (will be submitted in 1984 to 

J. Amer. Stat. Assoc.). 

Cochran, W. G. 1963. Sampling Techniques, 2nd ed. Wiley, New York. 

Davidson, J. E., and P. K. Hopke. 1983. "Implications of Incomplete 

Sampling in a Statistical Form of the Ambient Air Quality Standard 

for Particulate Matter." Paper presented at the 76th Annual Meeting 

of the Air Pollution Control Association, Atlanta, Georgia. 

EPA. 1979. "Guideline for the Interpretation of Ozone Air Quality 

Standards." Environmental Protection Agency, Research Triangle Park, 

NC (EPA-450/4-79-003). 

EPA. 1981. "U.S. Environmental Protection Agency Intra-Agency Task Force 

Report on Air Quality Indicators." Environmental Protection Agency, 

Research Triangle Park, NC (EPA-450/4-81-015). 

Frank, N. H., and T. C. Curran. 1982. "Statistical Aspects of a 24-Hour 

National Ambient Air Quality Standard for Particulate Matter." Paper 

presented at the 75th Annual Meeting of the Air Pollution Control 

Association, New Orleans, Louisiana, June 1982. 

83146 6 30 
P.9 

Hajek, J. 1960. Limiting distributions in simple random sampling from a 

finite population. Pub. Math. Inst. Hungarian Acad. Sci., 5:361-374. 

Johnson, N. L., and S. Kotz. 1969. Discrete Distributions, Wiley, New 

York. 

83146 6 

ol 
P.10 

Appendix A 

SULFUR DIOXIDE DESCRIPTIVE STATISTICS 

83146 5 
P.11 

APPENDIX A 

SULFUR DIOXIDE DESCRIPTIVE STATISTICS 

Using program NA282 of the EPA's Storage and Retrieval of Aerometric Data 

(SAROAD) system, various summary files of 1981 data were obtained. Figure 

A-l shows the distribution of data completeness among air monitoring 

stations. Table A-l shows the number of sites meeting an annual quota of 

75 percent data completeness and meeting a corresponding quarterly quota 

in a specified number of quarters. Table A-2 shows the same information 

for an annual quota of 50 percent. In considering whether a quarterly 

quota should be required so that an even distribution of data would be 

guaranteed throughout the seasons of the year, it is of interest to note 

that roughly 70 percent of the sites that met an annual quota also met a 

corresponding quarterly quota in each of the four quarters of 1981. 

There are low correlations between the percentage of data completeness and 

reported annual averages, standard deviations, and coefficients of 

variation (Figure A-2). 

Histograms of "expected" exceedances (i.e., X.* or k./p. in the notation of 

Section 2) show that zero expected exceedances were reported by 96 percent 

of the stations (Figure A-3). The greatest number of expected exceedances 

were reported by the stations that had the most complete data (Figure A-4 

and Table A-3). 

83146 5 
SY1S30L COUNT 

A 4 I2 

EACII SYMBOL REPRESENTS 

MEAN ST.DEV . 

70.98 7 23.05 8 

1 OBSERVATIO N 

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45 

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80 

FREQUENCY 

INT. CUM. 

3 

0 

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6 

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9 

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17 

25 

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59 

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68 

71 

78 

82 

91 

100 

108 

111 

126 

138 

154 

175 

201 

241 

29 2 

358 

4 33 

471 

472 

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4 72 

4 72 

472 

PERCENTAGE 

INT. CUM. 

0.6 

0.0 

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61 

75 

91 

99, 

100.0 

100.0 

100.0 

100.0 

1 00 . 0 

Number of Sites 

8314 6 

FIGURE A-la. Histogram of the percentage, p, 

reporting one-hour S09 concentrations in 1981 

of data completeness for those sites 

: SLAMS (including NAMS). 
P.13 

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00 
P.14 

TABLE A-l. Number of sites recording one-hour S0£ during at least 

75 percent of the total possible hours in 1981, by the number of 

quarters in which at least 75 percent of the total hours per quarter 

are recorded. 

Site Type 

SLAMS 

(includes 

Other 

No. of Quarters 

with at Least 

75% Hours/Quarter 

0 

NAMS) 1 

2 

3 

4 

Total 

0 

1 

2 

3 

4 

Total 

No. of 

> 75% 

0 

0 

17 

79 

244 

340 

0 

0 

8 

48 

117 

173 

Sit 

< 

es 

75% 

35 

48 

38 

9 

0 

130 

49 

89 

51 

59 

0 

248 

Total 

35 

48 

55 

88 

244 

470 

49 

89 

59 

107 

117 

421 

TABLE A-2. Number of sites recording one-hour S02 during at 

least 50 percent of the total possible hours in 1981, by the 

number of quarters in which at least 50 percent of the total 

possible hours per quarter are recorded. 

Site Type 

SLAMS 

(includes 

Other 

No. 

wi 

50% 

NAMS) 

of Quarters 

th at Least 

Hours/Quarter 

0 

1 

2 

3 

4 

Total 

0 

1 

2 

3 

4 

Total 

No. of 

> 50% 

0 

0 

19 

42 

343 

~404 

0 

1 

15 

102 

170 

"288 

Sites 

< 50% 

11 

30 

25 

0 

0 

66f 

24 

48 

59 

2 

0 

"l33~ 

Total 

11 

30 

44 

42 

343 

"470" 

24 

49 

74 

104 

170 

"421 

83146 8 
P.15 

SLAMS 

OTHER 

N= 891 

COR = .0500 

SYMBOL' 

SYMBOL' 

MEAN 

70.-J 93 

25.026 

ST.DEV. 

25.782 

16.539 

REGRESSION 

X= ..0SG73*Y + 

Y= .03313*X+ 

LINE 

68.328 

22.479 

RE S.MS. 

603.36 

276.30 

co 

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to 

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00 OS"OO 

SSS 00 * 

00 00 *0 

0 O S 

0 0*0 0"S' 

0 00 S 0 

s 

s 

s 

ss s 

S O S 

s s 

OS SOS 0 

sssso 

OSS ** 

0 s s ss 

• ssssossss 

ss s*ssos 

s s*s*ss***o 

s s*ss•=**** 

*os***s***o* 

* ft 2 * * 2 * ft -.V ft ft ft 

•.1 ft S ****** s * s 

00******0**0 

ft ft Q * * * * ft ft g ft 2 

ss**sos*so 

ooss * *•••• ••SSS 

o*s* s *S*SSS 

0.000 + 

7.500 22.50 37.50 52.50 67.50 82 

r.000 15.00 30.00 45.00 60.00 75.00 

h ... . + ... . + .. . . 

.50 9 7.50 

90.00 105.0 

FIGURE A-2a. Scatter plots of ambient air quality statistics versus 

the percent of total hours recorded in 1981 (p) by sites reporting 

one-hour S0 2 : annual average versus p. 

831'*6 
P.16 

SL/VMS 

OTHER 

N» 891 

CUR= .071 2 

SYMBOL-S 

SYMBOL=0 

liEAN ST.DEV. REGRESSION LI.M" RES. MS. 

X 7.V.493 25.73 2 X= . ,:C C J 3 - Y + G'J.iSa 632.0 7 

Y 39.20 5 32.73 8 Y= ..0iz.J3oV;X + 32.^ 5 10G7.6 

A 0 0 

3 5 0 + 

3 0 0 

ir-.7 

5 0 . 

0 . 0 

, + .X. . + * 

s 

0 

00 

s s 

0 0 

0 0' 

OS 

0 

' 0 

S 0 

0 0 

* 

SS 

so 

OS 

OS 

. + . . 

S 0 0 OS 

* 0 0 

00 OSO 0 

003 S Sz'O-'O 

*••* S SO 0 Ou'-* 

•••OS OO — SS 'J'J'-S 

SCO SO '•60-':/00t 

0 SO 00S00S;' o -

00 OSS 0 

0 

s s 

00 

it 

0 0 0 

s 

00 0 0 ooo s 

o-os s 

30 * OSOOOO 0 ••• 

0 0 SS S SOOOO—'OS 

'••00 OOS SSOSSOO *:-0-'Ov 

•• 0S 00 •• 003 * S * S * ••' * - •'•• S03 S 

'SS "0* S';3S 0 0

 T3-'-3S3 

00 * *0S0 00 OSO 0 

0 00 S 

+ ... . + ... . + .. . .X.... + 

s 

0 

0 * 

s 

OS * 3 

1.13*0* 

s**~ s 

**s* * 

ft * 0 - -

0 00 

. . . + . 

s 

s 

O O S 

00 

0 OS 

OS 0 

*SSSS 

S*S — * 

3**** * 

pf * * ft ft ft 

.-. ft ft s * ft 

3-*S*- : 

SS s 

s 

0 s 

50 

ft 

**o o 

ftQft* 

s * o 

pV rt rt rt 

• • s * s 

••* s * s 

••SSS 

OSSS 

+ . , 

7.50.7 22.5.7 37.5.7 52.50 67.50 02.50 97.50 

.7.70 1 5 . .70 30.00 45.00 60.00 7 5 .00 90 .00 105.0 

FIGURE A-2b. Standard deviation versus p. 

83146 
P.17 

SLAMS 

OTHER 

M- 891 

COR=-.0330 

MEAN 

X 70.-193 

Y 1.6345 

SYMBOL-S 

SYMBOL-0 

ST.DEV. REGRESSION LINE RES.MS 

25.732 X = -1.0_'73*Y+ 72.173 664.72 

.82749 Y--..O0106*X+ 1.7071 .684/7 

C 

0 

ti 

12.0 + 

.7.5 

7 . 5.7 

3.00 

1 . 30 

0.00 

+....+....+....+. ,X+. 

OO 

0 

so 

OS 

OOOO 

O S O 

OOO 

*OSOO s 

OS 

so 

00 

0 

OS 

OS 

O-O 

0* 

0 

0 000 

OS 0 

0* 

0 0 

0 0 00 

0 

0 000 0 

00 

SO 0 

0 0 SOO 

S 0 

0 

0 

0*00 

000 

0*0*0"* 

OS 

s 

so 

SOO • 

*0-0 s 

*-'-0-5S; 

SOS 

0 

OS 0 03 00 

•S'-30*"f 

s "3'0-:: 

: OS 0"" 

0 S l 

0 

•s 

ft 

OSO 0*'00 OOSS 0**3**0""S 

00 500-0"* 

00 0 0003 *000"000s 

• i .'5 

S0'-: 

* * S SSS-S"Z:0"S*S* 

•3 SSS*- SO 0 S3 SS 

0 s 

00 

. . . + + ... . + ..X . + . 

O J *' 

s* 

s s 

s ss 

00 0 

00 s 

Q rt -.v a 

* s * * 

ft * * o * 

ft0ftsft* 

s**s** 

S**S3 * SS' 

s 

*0 

0 0* s 

00 -* o 

*os*o s 

S*0 "* 0 

ft ft :': '.•.• * ft ft 

ft ft ft ft * ft rt 

"*-"*SS 

SS**SSS 

00 0 

7.500 22.5.7 37.3.7 52.50 67.50 82.50 97.50 

0.000 15.00 30.00 4 5.00 60.00 7 5.00 90.00 105.0 

FIGURE A-2c. Coefficient of variation (standard deviation divided by annual 

average) versus p. 

83146 
E 

* . 6000.00 

* 1.20000 

* 1 . 00000 

* 2 . 100,0.7 

*3.000r''0 

•3.000.00 

* 4 . 200.00 

* 4. 8 00.00 

*5 . 4.000.0 

* 6.00.0.00 

* 6.60000 

* > .20.0,00 

* 7.00000 

*3.4 0000. 

-'J. '"?ri70 

* 7.60000 

-10.2.000 

-10.000,7 

*J 1 . '1.000 

* 1 2 .070.7 

-l 2 . an 'TO 

* 1 3 . 20.00 

-13 . 000.7 

-14.4.0: 0 

rt ] 5 ,0.000 

••15. 6'.:-..' 

••'••16 . 2r'"'( 

« 16.80.00 

* 17 . 4 >•'"•/ 

* 1 8 . .O0/..0 

* 18 . 6.'00.7 

* 1 9 . 2.0.0.7 

* 19.0°"J 

"20.4000 

-21.0.0.00 

*21 .0.0.0:7 

-2 2.2.000 

-2 2.8000 

•AAA 

• AAA 

+AAA 

+AA 

+A 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+A 

+ A 

+ A A 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+A 

+ 

+ 

+A 

+ 

+ 

t-

+ 

+ 

+ 

5 

'.AAA; 

^ 

' 

5 

10 

.AAA, 

10 

SYMBOL COUNT MEAN ST.DEV. 

A 4 70 0.180 1.424 

EACH SYMBOL REPRESENTS 1 OBSERVATION 

15 20 25 30 35 40 45 50 55 60 65 70 75 80 

\AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA* 

15 20 25 30 35 40 45 50 55 60 65 70 75 80 

FREQUENCY 

INT. 

454 

4 

3 

2 

1 

0 

0 

0 

0 

0 

0-

0 

1 

1 

2 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

1 

0 

0 

0 

0 

0 

0 

CUM. 

454 

458 

4C1 

463 

464 

464 

454 

4 6 4 

464 

464 

464 

4 6 4 

4 0 5 

4GG 

46 8 

4 08 

4 0 8 

4 0 o 

4 0 8 

4 6 8 

4 08 

4 0 {i 

4 50 

4 G 8 

40?! 

4 0 8 

4 '.'- 8 

4 C 8 

4 0 *J 

4 07 

4 Ci 7 

4/0 

4/0 

4 70 

4/0 

4 70 

4 70 

4 70 

PERCENTAGE 

INT. 

96.6 

0.9 

0.6 

0.4 

0.2 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.2 

0.2 

0.4 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

w. 1,1 

0.0 

0.0 

0.2 

0.0 

0.0 

0.2 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

CUM. 

96.6 

97.4 

98. 1 

98.5 

98.7 

98.7 

98.7 

98.7 

98.7 

98.7 

98.7 

98.7 

93.9 

9 9. 1 

99.6 

99.6 

9 9.6 

9 9.6 

9 9.6 

99.6 

9 7.6 

9 9.6 

9 9.6 

97.6 

97.6 

9 7 . 6 

9 7.6 

9 7.6 

9 7 . 8 

9 9 . 8 

9 9 . 8 

10.7.0 

1 00 .0 

100.0 

100.0 

1.0.7.0 

100.0 

1 00 .0 

Number of Site: 

FIGURE A-3a. Histogram of expected primary exceedances, E, for those sites 

reporting 24-hour S02 concentrations in 1981: SLAMS (including NAMS). 

83146 
E 

* . G 0.700.0 

- 1 . 20.000 

* i , o.i;.i.!.o.o 

* 2 . 4.000.00 

* 3 . 0 0 0 O'O 

* 3. 60.900 

* 4. 2 000:7 

* 4.87 0 00 

* 5. 40.000 

* 6.00000 

•"6.0.7.0 00 

* 7. 200:70 

'•7.00000 

* 0.40000 

V;9 .00.00.7 

* 7 . 60,000 

* 10 . 20.00 

* irr.U'107 

*11 . '10.00 

* 12.0.0.00 

* 1 2 . 0.0.00 

ft i 3 , 2.7.0.7 

* 1.3 . 8.0.00 

* 14 . 40.00 

* 1 5 .0.0.0.7 

* 15 . o.o.o.'"/ 

* 16 . 2.0.00 

* 1 6 . 8.00.7 

* 17 . 4.0.00 

•18.0000 

-18. 6,0.0.7 

* 19.2000 

* 19.8000 

* 20.4000 

* 2 1 .000.7 

*21.OOOO 

* 2 2 . 2 0.00 

* 22.8000 

5 

+13IJ 0 B C B B' 

+BBBBBEB1 

+ 0u 

+ 8 

+ I3B 

+ B 

+ B 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

•i-

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ ' 

+ 

+ 

+ 

+ 

+ 

5 

S' 

EACH SYMBOL 

10 15 20 25 

• G 3 B 13 C G li 13 £ '3 1313 D 5 u 'J •_> L 

• 1313 

10 15 20 25 

'M30L COUNT MEAN ST.DEV. 

B 421 0.067 0.380 

REPRESENTS 1 OBSERVATION 

3.7 35 40 45 50 55 60 65 70 75 80 

.'uUoOBBIj'.-BUBBUBBBOCUoBC-BBBBOBBBBUBBBBBBBBBBBBBBBBBBBBBB* 

30 35 40 45 50 55 60 65 70 76 80 

FREQUENCY 

INT. 

404 

10 

2 

1 

2 

1 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

CUM. 

404 

414 

416 

417 

419 

4 20 

421 

421 

421 

421 

421 

421 

421 

421 

421 

42 1 

421 

421 

421 

421 

421 

421 

421 

421 

421 

421 

421 

42 1 

421 

421 

421 

421 

421 

421 

421 

421 

421 

421 

PERCENTAGE 

INT. 

96.0 

2.4 

0.5 

0.2 

0.5 

0.2 

0.2 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

CUM. 

96.0 

98.3 

9 3.8 

9 7.0 

99.5 

99.8 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100 .0 

100.0 

100.0 

100 .0 

1 00 .0 

100 .0 

10.7.0 

1 00 . 0 

100. ti 

100.0 

10.7.0 

1 07.0 

10.7.0 

100.0 

10.7.0 

107.0 

1 0.7.0 

1XI. kl 

1 00 .0 

FIGURE A-3b. Other sites 

8314 6 
P.20 

SLAMS , SYMBOL=S 

OTHER , SYMBOL=0 

N= 891 

COR= .0813 

MEAN ST.DEV. REGRESSION LINZ RES.MS. 

X 70.457 26.0-33 X= 1.S335-Y+ 70.205 675.55 

Y .12682 1.0679 Y= .00333*X-.107S0 1.1341 

20.0 + 

17.5 + 

15.0 + 

lZ.5 + 

E 10.0 

7 .5.0 + 

5. .7.7 + 

2 . 5.7 + 

, +* 

00 

SOOS 

0 

ss 

0 

0 

s s 

0*00* 0** 

0.00 y * o * 0 * * * * 00 * * 0 ***************** 0 ***** 0 ********************'•***"*"* * * S Y 

+....+....+....+....+....+....+....+....+....+X. .. + .... + .... + .. ,. + ....+ . 

7.500 22.50 37.50 52.50 67.50 82.50 97.50 

0.70 15.00 30.00 45.00 60.00 75.00 90.00 105.0 

FIGURE A-4. Scatter plot of the percentage of total days recorded in 1981 

(p) versus expected primary exceedances (E) for sites reporting 24-hour 

average SOp. 

831«*6 
TABLE A-3. Frequency table of the percentage of total days recorded in 1981 (p) 

versus expected primary exceedances (E) for sites reporting 24-hour SCL averages, 

0 - 28X <= 43X <«= 60.5X 71X 80X <- 86X <- 89.5X <- 93X <- 96.5X <- 100X TOTAL 

0 

1 

<- 2 

<- 5 

<» 20 

TOTAL 

87 

pff 

0 

1 

0 

88 

88 

er 

0 

0 

0 

88 

87 

0 

0 

0 

0 

87 

88 

0 

1 

2 

0 

91 

88 

0 

5 

1 

0 

94 

81 

0 

1 

1 

0 

83 

77 

0 

3 

0 

0 

80 

87 

2 

1 

0 

3 

93 

102 

2 

0 

2 

2 

108 

73 

4 

1 

0 

1 

79 

858 

e 

12 

7 

6 

891 

83146 
P.22 

Appendix B 

CARBON MONOXIDE DESCRIPTIVE STATISTICS 

83146 5 
P.23 

APPENDIX B 

CARBON MONOXIDE DESCRIPTIVE STATISTICS 

Figure B-l shows the distribution of data completeness among air monitoring stations. Table B-l shows the number of sites meeting an annual quota 

of 75 percent data completeness and meeting a corresponding quarterly 

quota in a specified number of quarters. Table B-2 shows the same 

information for an annual quota of 50 percent. Note that roughly 80 

percent of the sites that met an annual quota also met a corresponding 

quarterly quota in each of the four quarters of 1981. 

Histograms of one-hour expected exceedances show that zero expected 

exceedances were reported by 99 percent of the stations (Figure B-2). A 

scatter diagram of expected one-hour exceedance versus percentage of data 

completeness is presented in Figure B-3 and in Table B-3. 

Similar information for overlapping eight-hour exceedances is shown in 

Figures B-4 and B-5 and in Table B-4. More than 10 percent of the 

stations reported over 40 expected exceedances. No clear relationship 

between expected exceedances and data completeness is evident. 

83146 5 
SYMBOL COUNT 

A 364 

EACH SYMBOL REPRESENTS 

MEAN ST.DEV. 

80.353 23.138 

1 OBSERVATION 

P 5 10 15 20 25 3.7 35 40 45 50 55 60 65 70 

+ v + + + + + + + + + + + + + . 

* 3..70000 +A 

* 6..00.: 070 +A 

* 7.000,7. J +A 

* 12 .000.J +AAA 

*15.00:.-.z +AA 

* 1 8 .07.'.'. J + 

* 2 l A)X.!.i +A 

* 2-i.H :.<•<.! + AAAAAA 

*2V .0. •-.; +AAAAAAAA 

*-l/ . 0..O.7 +AAA 

* 3 '.3.0.77.7 +AA 

* 3 0 .:).'i.0',7 +AAAA 

* 3 7.0.'.' 0.0 +AAA 

* 4 2 .0,00.7 + AAAAAAA 

* 4 5.00.00 +A 

* 4 o . .1)00.7 + AAAAAA 

* 6 1 .0.0:07 +AA 

'* 5 4 .0.'.':.'.'.'' + 

* 5 7.0.0:.'. J +AAA 

*-30.0.1.'0.7 +AAA 

* 6 3.0.0.00 +AAA ".AAA 

*uu.0.0.70 + AAAAAAAA 

*G7 .0.Z-.'...;i + AAA/-.AAAAA 

*'/2.0.7'.-JJ * AAAAAA 

*7 5 .0:070 +AAAAAAAAAAA 

* 78.00.00 +AAAAAAA 

* 3 1 .000.7 +AAAAAA 

*8--! .:):".•.! +A.'•..".AAA.".AAAAAAAA 

* 8 / . .000.7 + A.'\ AAA AAAA AAA 

* yJJ ..';.-.'0:7 + AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 

*

:

 7 3 .0 7 0 '.7 + AAA A.V.A A AAA A AAA AAA AAAA AAAAA AAAA A AAAAAA AAAAAAAAA 

* 70.07.00 + AAAAAA. .AAA.V.AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 

*9'J ..O.oi'0 +A."..'z.\AA.^..'zAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 

* 102 . .0.0.7 +AAAAAAAAAAAAAAA 

*l.l:'i..0.0.tf + 

* 1 JL< 8 . .7.00 + 

* 1 1 1 . 00.7 + 

* 114.00 0 + 

+ + + + + + + + + + + -

5 10 15 20 25 30 35 40 45 50 

75 

-- + -

80 

-- + 

-- + -

i;i; 60 

-- + -

65 

- + -

70 75 80 

FREQUENCY 

INT. CUM. 

1 

1 

1 

3 

' 2 

0 

1 

6 

8 

3 

2 

4 

3 

7 

1 

6 

2 

0 

3 

3 

7 

8 

9 

6 

11 

7 

6 

15 

12 

33 

47 

61 

70 

15 

0 

0 

0 

0 

1 

2 

3 

6 

8 

8 

9 

15 

23 

26 

28 

32 

35 

42 

43 

49 

51 

51 

54 

57 

64 

7 2 

81 

87 

98 

105 

U l 

126 

138 

171 

218 

279 

349 

364 

364 

364 

364 

364 

PERCENTAGE 

INT. CUM. 

0.3 

0.3 

0.3 

0.8 

0.5 

0.0 

0.3 

1 .6 

2.2 

0.8 

0.8 

1 .9 

0. 

1. 

0. 

0.0 

0.8 

0.8 

1 .9 

2, 

2, 

1 . 

3, 

1 . 

1, 

4, 

3, 

9. 

12, 

16.8 

19.2 

4. 1 

0.0 

0.0 

0.0 

0.0 

0.3 

0.5 

0.8 

8.8 

9.6 

11 .5 

11 .8 

13.5 

14.0 

14.0 

14.8 

15.7 

17.6 

19.8 

22.3 

23.9 

26.9 

28.8 

30.5 

34.6 

37.9 

47.0 

59.9 

76.6 

95.9 

100.0 

100.0 

100.0 

100.0 

100.0 

Number of Sites 

8314 6 

FIGURE B-la. Histogram of the percentage, p, of data completeness 

for those sites reporting CO in 1981: SLAMS (including NAMS). 
p 

*3.00000 

* 6..0.7000 

* 9.07.70.7 

* 12 .0000 

*•' 1 !i. 0.7.7.7 

* 18.0000 

* 21.0000 

*2-J Qr<>'t 

* 2 7. 000:7 

* 3 0.0.O..) .7 

*33..O.j00 

*36.0.7.J0 

* 3 9. 0.0.70 

* 4 2.0.O.7J 

"4 5.0.7:,'.7 

* 4 8 .00.7.0' 

•51.000.7 

* 5 4 .0.7.7.7 

•57.00.70 

* 6 0.00.0.7 

* 6 3.000.7 

•66.007.7 

•69.0000 

•72. 0.0 00 

*75.0n-'7 

* 7 8.0.0 0.7 

• 3 1 .0.0.7.7 

•34.0070 

•3 7.00.0.7 

•90.0.0.0.7 

* 9 3.0.0.0.7 

* 9 6.0.0 0 0 

•97.000.7 

* 102 . fi,70 

* 1.75 .0770 

*1IZP3..O:70 

*l11.000 

* 1 1 4 . .0.70 

5 

+ BB 

+ 8HB 

+ 0 3 

+ B 

+ L; 8 

+;:c 

+Li:..r,B 

+ .V:.!.A,;33 

+ U0B B 

+ 8i;C 

+ !!'.'i.:!!B'3 

+ i;u.BU 

+ R01A..B 

•t-UI.LiB 

+ 88 

+ 

+ B 

+ 

+ B 

+ 

+ H3B 

+ D 

+ !A.'L;3 

+ 8iiBBB 

+ BB 

+ 

+I;L.[,B 

+ BL.LI 

+ 8 

10 

+ G:v1;833BBBBBB 

+ 8 0 6B'. 

+GLBBBL 

•*- LJ C L 3 B t> 

+ 

+ 

+ 

+ 

+ 

5 

EACi 

15 

BBBBBBBB 

3 

BB 

10 15 

1 SY 

20 

20 

SYMBOL 

•IBOL 

25 

25 

B 

COUNT 

1 16 

REPRESENTS 

30 

30 

35 

35 

40 

40 

MEAN 

58.952 

1 

45 

45 

ST.DEV 

31 . 

, 

631 

OBSERVATION 

50 

50 

55 

55 

60 

60 

65 

65 

70 

70 

75 

75 

80 

80 

FREQUENCY 

INT. 

2 

3 

2 

,1 

2 

2 

4 

6 

4 

3 

6 

4 

5 

4 

2 

0 

1 

0 

1 

0 

3 

1 

4 

5 

2 

0 

4 

3 

1 

12 

14 

7 

8 

0 

0 

0 

0 

0 

CUM. 

2 

5 

7 

8 

10 

12 

16 

22 

26 

29 

35 

39 

44 

48 

50 

50 

51 

51 

52 

52 

55 

56 

60 

65 

67 

67 

71 

74 

75 

87 

101 

108 

116 

1 16 

116 

116 

1 16 

116 

PERCENTAGE 

INT. 

1.7 

2.6 

1 .7 

0.9 

1 .7 

1 .7 

3.4 

5.2 

3.4 

2.6 

5.2 

3.4 

4.3 

3.4 

1 .7 

0.0 

0.9 

0.0 

0.9 

0.0 

2.6 

0.9 

3.4 

4.3 

1 .7 

0.0 

3.4 

2.6 

0.9 

10.3 

12. 1 

6.0 

6.9 

0.0 

0.0 

0.0 

0.0 

0.0 

CUM. 

1 .7 

4.3 

6.0 

6.9 

8.6 

10.3 

13.8 

19.0 

22.4 

25.0 

30.2 

33.6 

37.9 

41 .4 

43. 1 

43. 1 

44.0 

44.0 

44.8 

44.8 

47.4 

48.3 

51 .7 

56.0 

57.8 

57.8 

61 .2 

63.8 

64.7 

75.0 

87. 1 

93. 1 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

Number of Sites 

FIGURE B-lb. Other sites , 

83146 
P.26 

TABLE B-l. Number of sites recording CO during at least 75 percent 

of the total possible hours in 1981, by the number of quarters in 

which at least 75 percent of the total hours per quarter 

are recorded. 

Site Type 

SLAMS 

(includes 

Other 

No 

wi 

75% 

NAMS) 

. of Quarters 

th at Least 

Hours/Quarter 

0 

1 

2 

3 

4 

Total 

0 

1 

2 

3 

4 

Total 

N o. of Sites 

> 75% 

0 

0 

5 

53 

212 

270 

0 

0 

0 

17 

33 

50 

< 75% 

15 

37 

33 

9 

0 

94 

17 

35 

8 

6 

0 

66 

Total 

15 

37 

38 

62 

212 

364 

17 

35 

8 

23 

33 

116 

TABLE B-2. Number of sites recording CO during at least 50 percent of 

the total possible hours in 1981, by the number of quarters in which 

at least 50 percent of the total hours per quarter are recorded. 

No, of Quarters 

with at Least 

Site Type 50% 

SLAMS 

(includes NAMS) 

Other 

Hours/Quarter 

0 

1 

2 

3 

4 

Total 

0 

1 

2 

3 

4 

Total 

N o. of 

> 50% 

0 

0 

10 

42 

261 

lu 

0 

0 

1 

16 

49 

"66" 

Sites 

< 50% 

7 

23 

20 

1 

0 

IT 

9 

30 

11 

0 

0 

"50 

Total 

7 

23 

30 

43 

261 

364 

9 

30 

12 

16 

49 

"116" 

83146 8 
• • 

E 

•--.300000 

'•• .0;; 0.0 0 0 

•': . 7.00.00.7 

* 1 . 20.0.00 

* 1 . 50.00.7 

* 1 . 80.0.0.7 

•'2 . I.O.OJJPJ 

" 2 . 40.0.•..'.7 

:'-2. AOO0.7 

"3.0.0.0 0 0 

••• 3 . 30.1.10.7 

•••3. '.'J.O.0.7 

"3.70.00.7 

* 4 . 20.00.7 

- 4 . 0'0.i.0)0 

* 4 .8.0.0.0.7 

* 5 . 10.00.7 

•5.40.0.0.7 

*5.7.U.0.u.7 

•6.00000 

•6.30000 

* 6 . 600.0.7 

•6 . 70.0.00 

* 7 . 2.0''07 

* 7. 500.0.7 

* 7. 3.0.000 

* 3 . 10i'•'•'7 

•3.40.0.7.7 

* 3 . 70,0.00 

* 9. "i)u 0 0 

* 9 . 30.000 

* 9.60000 

* 9. 9 0.0 00 

•10.2.0.00 

* 10. 5.000 

* 10. 8.000 

*1 1 . 1000 

*11.4000 

83146 

+ A A 

+ 

+ 

+ 

+A 

+ 

+ A 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

t-

+ 

+ 

+ 

+ 

•t-

+ 

+ 

+A 

+ 

+ 

+ 

+ 

+ 

+ 

+A 

+ 

+ 

+ 

+ 

• •••• • 

SYMBOL COUNT MEAN ST.DEV. 

A OD ) 0.060 0.691 

EACH SYMBOL REPRESENTS 1 OBSERVATION 

5 10 13 2,7 2 5 3.7 3 5 40 4 5 50 55 60 65 70 7 5 80 

• 

FREQUCNCY 

INT. 

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA* 360 

5 10 13 20 25 30 35 40 45 50 56 60 66 70 76 80 

Number of Sites 

FIGURE B-2a. Histoqram of expected primary exceedances, E, for those 

sites reporting one:hour CO concentrations in 1981: SLAMS (including NAMS) 

0 

0 

0 

1 

0 

l 

0 

0 

0 

0 

0 

0 

I'l 

0 

0 

0 

0 

0 

ti 

ti 

ti 

ti 

ti 

ti 

0 

1 

0 

0 

ti 

kl 

a 

0 

I 

ti 

ti 

kl 

0 

CUM. 

300 

3 00 

3 00 

300 

361 

361 

•jc:i 

302 

3 0 2 

3'.. 2 

30 2 

30 2 

36 2 

30 2 

3.'. 2 

362 

762 

3 0 2 

302 

30 2 

3-72 

3 72 

372 

30 2 

3 0 2 

30 2 

30 3 

8 03 

3 0 3 

J (.1 z' 

8 0 3 

8 (J 3 

363 

30 4 

304 

374 

3 G 4 

304 

• 

PERCE 

HIT. 

9 8.9 

0.0 

0.0 

0.0 

0.3 

0.0 

a. 3 

ti .ti 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.3 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.3 

0.0 

0.0 

0.0 

0.0 

NTA^E 

CUM. 

9 8 . 9 

9 8.9 

9 8 . 9 

9 8.9 

9 7.2 

99.2 

0 0 . D 

9 7.5 

9 3 . 5 

9 7.5 

9 7.5 

9 7 . 5 

97.5 

97.5 

9 7.5 

9 9.5 

9 7.5 

9 7.5 

9 7.5 

9 7 . 5 

9 7 . 5 

9 7.5 

9 7.5 

9 7.5 

9 7.6 

9 7 . 5 

9 9 . 7 

9 7 . 7 

9 7.7 

97.7 

9 7 . 7 

9 7.7 

9 7.7 

1.70 .0 

100.0 

100.0 

1 00 .0 

1 00 .0 

• 
«M 

- . IA 

• fciz 

> • o 

UJ —• « 

D

•

 H 

 < 

I- > 

vt ai 

Ul 

l/> 

ca 

f

Oi 

 o 

ZBj -

< • 

Ul S3 

3

•Z-'OIA 

 — H 

O - Z 

O ui 

U

IA 

l 

_i ai 

O ilea Ul 

S co Qi 

> • 

(A _l 

c

o 

a 

IA 

> 

L

OL 

J X 

I

1

 u 

- < 

O ui 

63 

CO 

in 

is 

LP 

IC 

LO 

uo 

UO 

UO 

• « • 

«s 

tn 

ro 

ro 

Bl 

CM 

BJ + 

c

« 

a 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

c

m 

a 

c

ca 

ca 

ca 

ea 

a 

a 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

e

ca 

ca 

a 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

co 

=3 

ca 

ca 

ca 

ca 

=i 

ca 

ca 

ca 

ca 

ca 

c

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

ca 

a> 

o 

ca 

ca 

c

+ 

o 

+ Bl 

CO 

+ in 

+ S3 

+ in 

U3 

+ B! 

in 

+ tn 

in 

+ Bl 

in 

+ Bi 

+ in 

ro 

to 

cu 

+-> 

< + -

<

O 

E 

D 

3 

l/l 

dl 

4-> 

$-

(11 

.Q 

CMI 

I 

CO 

=

a: 

3 

+ Bl 

po 

+ tn 

+. Bi 

(M 

+ Bl 

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 

GlO^^O&^iSO^OQOQ^OOOQQO^Q^QCJiSO^^O^^&i^^^t

fcaQ&>S3^^C5fi353^C3BlBl^^3BlSJfc!OQt3^£3C3taiS!^Q£P^O^ta^i3Bl^ia 

S 

&1 ia to S O GiQ^Q^QiS&^Q^i^utQ^QOiSlSJQ&IQQQ^OOS ) O ^ Bj ^ Bl ^ 

&25j£iBlBiQO&J^t^QB!^Sl^£j^^5JQ^&lB!SlO^Bi^Q^^BlBJCMinC0~* ^ 

BispOCMtnco — nrr«.QroincTiCMinc3-.-«»r^{acou30-icMinco — •<* r^ ta ro m on 

niOO l .....fc$tiat9-« ^ 

• • .-»,-_<rp|NN(onnnfnnL'iininioiDioiDr>h.N»coc3!jioMJioi-<rt'" p — 

to 

j -
P.29 

SLAMS 

OTHER 

N- 480 

COR=-.0068 

MEAN 

X 75.234 

Y .06792 

SYMBOL=S 

SYMBOL=0 

ST.DEV. 

27.015 

.77943 

REGRESSION LINE RES.MS. 

X=-.23588*Y+ 75.250 731.29 

Y=-195E-6*X+ .08269 .60876 

,X. + . 

12.0 + 

10.5 + 

9.00 + 

7.50 

6.00 

4.50 

3.00 

1.50 + 

0.00 Y*0 0** S**0 0****** **0*S***0* SS* * SSS***S*****SSS**************S Y 

.+....+....+....+....+....+....+....+....+....+....X... . + ... . + ... . + ... . + . 

7.500 22.50 37.50 52.50 67.50 82.50 97.50 

0.000 15.00 30.00 45.00 60.00 75.00 90.00 105.0 

FIGURE B-3. Scatter plot of the number of expected primary exceedances 

(E) versus the percentage (p) of total hours recorded in 1981 for sites 

reporting one-hour CO concentrations. 

8311+6 
TABLE B-3. Frequency table of the percentage of total days recorded in 1981 (p) 

versus expected primary exceedances (E) for sites reporting 1-hour CO averages. 

E 

0 

<- n 

TOTAL 

0 -- 26X 

46 

1 

47 

<= 46.5X 

48 

0 

48 

<= 71% 

50 

1 

51 

<- 83X 

46 

0 

46 

<- 90X 

65 

1 

66 

P 

<- 91.5X 

28 

1 

29 

<- 94X 

50 

1 

51 

<- 96X 

48 

0 

48 

O 97.5X <- \B0X 

43 51 1 

0 0 1 

43 51 1 

TOTAL 

475 

6 

480 

83146 
E 

* 40.0000 

* 80.0000 

* 120.000 

* 160.000 

* 200.000 

*240.000 

*280.000 

•320.000 

•360.000 

•400.000 

•440.000 

•4 80.000 

•520.000 

•560.000 

•600.000 

•640.000 

•680.000 

•7 20.000 

•760.000 

•800.000 

•840.000 

•880.000 

•920.000 

•960.000 

•1000.00 

•1040.00 

•1080.00 

•1120.00 

•1160.00 

•1200.00 

•1240.00 

•1280.00 

•1320.00 

•1360.00 

•1400.00 

•1440.00 

•1480.00 

•1520.00 

SYMBOL COUNT MEAN ST.DEV. 

A 364 34.301 112.449 

EACH SYMBOL REPRESENTS 1 OBSERVATION 

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 

+AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA* 

+AAAAAAAAAAAAAAAAAAA 

+AAAAAAA 

+AAAAAAAA 

+AAA 

+ AAAA 

+A 

+ AAA 

+AA 

+AA 

+ AAA 

+ 

+ 

+ 

+ A 

+ 

+ 

+ 

+ 

+ 

+ 

+A 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+A 

+ 

+ 

+ 

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 

FREQUENCY 

INT. 

309 

19 

7 

a 

3 

4 

1 

3 

2 

2 

3 

0 

0 

0 

1 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

CUM. 

309 

328 

335 

343 

346 

350 

351 

354 

356 

358 

381 

361 

361 

361 

3G2 

362 

362 

362 

3G2 

362 

362 

363 

363 

363 

363 

3G3 

363 

363 

363 

3G3 

363 

363 

363 

363 

364 

3G4 

3G4 

364 

PERCENTAGE 

INT. 

84.9 

5.2 

1.9 

2.2 

0.8 

1 . 1 

0.3 

0.8 

0.5 

0.5 

0.8 

0.0 

0.0 

0.0 

0.3 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.3 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.3 

0.0 

0.0 

0.0 

CUM. 

84.9 

90. 1 

92.0 

94.2 

95. 1 

96.2 

96.4 

97.3 

97.8 

98.4 

99.2 

99.2 

99.2 

99.2 

99.5 

99.5 

99.5 

99.5 

99.5 

99.5 

99.5 

99.7 

99.7 

99.7 

99.7 

99.7 

99.7 

99.7 

99.7 

99.7 

99.7 

99.7 

99.7 

99.7 

100.0 

100.0 

100.0 

100.0 

Number of Sites 

FIGURE B-4a. Histogram of expected primary exceedances, E, for those 

sites reporting 8-hour CO concentrations in 1981: SLAMS (including NAMS) 

83146 
E 

•40.0000 

•30.0000 

•120.000 

•160.000 

•200.000 

•2 40.000 

•280.000 

•320.000 

•3G0.000 

•400.000 

•440.000 

•4 80.000 

•520.000 

•560.000 

•600.000 

•640.000 

•680.000 

•7 20.000 

•760.000 

•800.000 

•840.000 

•880.000 

•9 20.000 

•960.000 

* 10.00 .00 

•1040.00 

•1080.00 

•1120.00 

•1160.00 

* 1200.00 

•1240.00 

•1280.00 

•1320.00 

•1360.00 

•1400.00 

•1440.00 

•1480.00 

•1520.00 

SYMBOL COUNT MEAN ST.DEV. 

OTHER B 116 28.348 90.30G 

EACH SYMBOL REPRESENTS 1 OBSERVATIONS 

5 10 15 20 25 30 35 40 45 " 50 55 60 65 70 75 80 

+BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB6B* 

+ BBBB 

+ B 

+ B 

+ B 

+ 

+ B 

+ B 

+ B 

+ B 

+ B 

+ 

+ 

+ 

+ B 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 

FREQUENCY 

INT. 

103 

4 

• 1 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

CUM. 

103 

107 

108 

109 

110 

1 10 

1 11 

1 12 

113 

114 

115 

115 

115 

115 

116 

116 

116 

116 

116 

116 

116 

116 

116 

116 

116 

116 

116 

116 

116 

1 16 

116 

116 

1 16 

116 

116 

116 

116 

116 

PERCENTAGE 

INT. 

88.8 

3.4 

0.9 

0.9 

0.9 

0.0 

0.9 

0.9 

0.9 

0.9 

0.9 

0.0 

0.0 

0.0 

0.9 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

CUM. 

83.8 

92.2 

93. 1 

94.0 

94.8 

94.8 

95.7 

96.6 

97.4 

98.3 

99.1 

99.1 

99. 1 

99. 1 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

10.0 .0 

100.0 

Number of Sites 

FIGURE B-4b. Other sites , 

83H46 
P.33 

1400 + 

1225 

1050 + 

875. 

700. 

525. 

350. 

175. 

0.00 

SLAMS 

OTHER 

N= 480 

COR=-.0376 

MEAN 

X 75.482 

Y 32.862 

SYMBOL=S 

SYMBOL»0 

ST.DEV. 

27.260 

107.46 

REGRESSION LINE RES.MS 

X=-.00953*Y+ 75.795 743.63 

Y=-.14812*X+ 44.043 11555 

,+X. 

Y S O OS* 

+*0 0** S*00 00****S0*** * *s*so*s s 

.+....+....+....+....+....+....+.. . 

S S S 

SSOSS S S 

OSSS**OS********S**S*S*********S 

i-.. . . + ... . + .. . ,+X. . . + .. . . + ... . + . . 

0 s 

s 

s 

s 

0 s 

s 

s 

O S s 

ss 

s s ss 

s ss ss 

S OS ss 

o s*s** s**s s 

7.500 22.50 37.50 52.5 0 67.50 82.50 97.50 

0.00 0 15.00 30.00 45.00 60.00 75.00 90.00 105.0 

FIGURE B-5. Scatter plot of the number of expected primary exceedances 

(E) versus the percentage (p) of total hours recorded in 1981 for sites 

reporting 8-hour CO concentrations. 

8311+6 
TABLE B-4. Frequency table of the percentage of total days recorded in 1981 (p) 

versus expected primary exceedances (E) for sites reporting 8-hour CO averages. 

0 25.5 <- 46X <= 70.5X <- 82.5X <- 89X <- 91.5X <- 94.5X <- 96.5X <- 98.5X <- IBBX TOTAL 

0 

1 - 5 

<- 10 

<- 50 

<- 100 

<- 1400 

TOTAL 

36 

0 

1 

3 

0 

6 

46 

31 

0 

5 

7 

1 

5 

49 

31 

3 

3 

7 

3 

3 

50 

29 

3 

6 

6 

1 

3 

48 

27 

5 

4 

5 

1 

4 

46 

31 

1 

3 

9 

0 

2 

46 

26 

7 

5 

4 

2 

6 

50 

21 

6 

5 

12 

0 

1 

45 

25 

5 

0 

15 

3 

4 

52 

21 

2 

1 

11 

4 

9 

48 

278 

32 

33 

79 

15 

43 

4 80 

83146 

co 

fc 
P.35 

Appendix C 

NITROGEN DIOXIDE DESCRIPTIVE STATISTICS 

83146 5 
P.36 

APPENDIX C 

NITROGEN DIOXIDE DESCRIPTIVE STATISTICS 

Figure C-1 shows the distribution of data completeness among air monitoring stations. There are low correlations between the percentage of data 

completeness and reported annual averages, standard deviations, and 

coefficients of variation (Figure C-2). 

83146 5 
UJ • in *3 S; cn iji cn < co ro i^ .NI CM O -< Si LO «PJ ui OO -^I co CM O 5; 55 J\ r- ~ TT CVJ LO P- LO S> SI S; S) Si 

us: 

< S> Sl - H CM CM CM CM < O u l Ca —P 01 LO O CTl S; CM CO o jv. Cl CM O ,'0 —P LO —p .-«. CO —p —. CM Cd ;-- 5J Cr-p 5 ; Bj 

H O -<-< « — «— • CM CM CM CM CM CM PI CO CO sc - » LO LO O p"^ CO Cl C7P ' 5 S: S! Sl Sl 

QL Iin LO Sl Sl Sj Sl li! t -=f LO LO 5} "3- SI ul LO ^ LO Tf LO 51 -"J ST u") cn cn cn "3- CO CO CM CM CO LO S) Sl & S} 

l 2 Sl^«-«^!a»-CMC M — 5CMCMSlCM-HCM«CM-<CMCM'q--.CM-S-L0L0Or~.S>—PVDS1S151C55 1 

CJ Z -PCM'>flIJOPOOITC!lMCON\n^MOC7P'PtN-,-JL.1CO^-^^NSlCN5)-S^-. .l^lLli.1 

Zl Z> — —' CM CM CM CO CO CO "3- -sf "=f -0 LO wO O P^ .""- CO 0". Z£) -< CO *C O u'. 5; 3 'C: Sp 5^ '^5 

UJ O «-« « —< "• —< rn CM CJi :o. CM zr co 

=> 

a • 

pj! - rH-HcsjcM^JsciLOLoro—<"CLOr-voro'<3-coLOcO'!r„ocncooSiPOrH,-oo-.c)'^-H5i55SiSi 

SO 

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LJ 

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+ ta 

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+ 55 

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1 

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OTHER , SYMDOL=0 

N = 324 

COR= .092 4 

MEAN' ST.DEV. REGRESSION L I NZ RES. !>-:;. 

X 64.231 28..'j.'7 K= . 1 14 c".a--Y+ 59.275 7U!.J G 

Y 43.247 22.5J7 Y= .0/443:-I' + 3C.4G5 507. 3-J 

,+X. 

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,x+. 

7.50.7 2 2.50 3 7.50 5 2.50 57.50 02.50 97.50 

0.00 0 15.00 30.00 4 5.00 60.00 75.00 90.00 105.0 

FIGURE C-2a. Scatter plots of ambient air quality statistics versus 

the percentage of total hours recorded in 1981 (p) by sites reporting 

NO?: annual average versus p. 
SLAMS , 5YMB0L=S 

OTHER , 5YMBOL=0 

N= 324 ) 

COP.= .004 4 

MEAN ST.DEV. REGRESSION LINE RES.MS. 

X 54.231 23.027 X= .0.;792* Y + 63.9G5 737.9G 

Y 2 7.505 13.3-35 Y= ..J.J2 i 9")!+ 2/.-! 4 5 193.39 

,X. + . 

0 S O 

0 0 0 so s 

0 0 OS S 03 

SS 0*0' ' 0 s* 

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ss 

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S 'JOGS S S* SO OSS 0-0 0 -SSS 

S S S i.."0c-:'3 

0 0 SO 00 

0 0 SO O 

7.30 0 22.3 0 37.3 0 52.5 0 (57.3.7 32.5 0 97.5 0 

00.0 15.0 0 30.0 0 45.0 0 C-0.00 75.0 0 90.0 0 105. 0 

FIGURE C-2b. Standard deviation versus p. 
P.41 

SLAMS , SYMBOL'S 

OlMlc'R , 3YHBOL = 0 

N= 324 

COR--.143 0 

;;EAN ST.DEV . REG^ZSSIO N LT>;- iziis.i-ii. 

X 61.231 23.027 X = -27. 1 39* Y + 77..0G //.J./I 

.37304 .2,0331 Y = -. ...J7.J9*X + .74277 .0;;.',3 

2 . 1 

0 0 

0 0 0 

0 0 

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0 3 SOO'J 

0 S zO S 0 0 

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S 0005SO S 

30 COS 3 -'•J * 0 

S O S3 

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0 0 

0 S 

0 0 

s * s 

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s * 

s s s 

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3 SO S SS SS 3S0 OSS S 

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S S SO 

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7.o.Z'0 22.3 0 3 7.3 0 52.3 0 67 . 

0.70 0 13.00 30.00 45.00 60.00 

; 32.c-0 9/ . 5.0 

75.00 90.00 105, 

FIGURE C-2c. Coefficient of variation (standard deviation 

divided by annual average) versus p. 
P.42 

Appendix D 

OZONE DESCRIPTIVE STATISTICS 

83146 5 
P.43 

APPENDIX D 

OZONE DESCRIPTIVE STATISTICS 

Figure D-1 shows the distribution of data completeness among air monitoring stations. 

Histograms of "expected" exceedances (i.e., \. or ki/pi in the notation of 

Section 2) show that roughly 85 percent of the stations reported seven or 

fewer expected exceedances in 1981 (Figure D-2). (These statistics are 

purely for descriptive and comparative purposes and do not directly 

pertain to the attainment of the ambient standard, since this is 

determined from three years of data, not from a single year.) Somewhat 

greater expected exceedances were reported by stations having nearly 

complete data; 4 percent of the stations reported zero expected exceedances (Figure D-3 and Table D-1). Judging by Table D-1 and the low 

correlation given in Figure D-3, no clear relationship is evident between 

expected exceedancs and data completeness. 

831»*6 5 
* 3.00000 

* 6.00000 

* 9.00000 

* 12.0000 

* 15.0000 

* 10.0000 

00.00 

0000 

0000 

0000 

0000 

0000 

0000 

*21 

*24 

*27 

*30 

*33 

*36 

*39 

*42 

*45 

*48 

*51 

*54 

00.00 

0000 

0000 

0000 

0000 

* 57.0000 

* 6 0.000.0 

* 6 3 . .0000 

*56.0000 

*69.0000 

* 72.0000 

"75.0000 

* 7 8 .00,00 

*81.0000 

* 3 4.0000 

* 3 7.0000 

* 90.0000 

* 9 3.0000 

* 96.0000 

* 99.0000 

* 102.000 

•105.000 

* 100.000 

* 1 1 1 .00.0 

* 114.000 

SYMBOL COUNT 

A 548 

EACH SYMBOL REPRESENTS 

MEAN ST.DEV. 

81.767 18.528 

1 OBSERVATION 

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 

+AAAAAAA 

+ A 

+A 

+ AAA 

+ AAAA 

+ A 

+ AA 

+ AA 

+ AAA 

+ AAA 

+AAAAAAAAA 

+AAA 

+AAAAAAAA 

+AAAAAAA 

+AAAAAAAAA 

+AAAAA 

+AAAAAAAAAA 

+AAAAAAAAAAAAAA 

+AAAAAAAAA 

+AAAAAAAAAAA 

+AAAAAAAAAAAA 

+AAAAAAAAAAAAAAAAAAAAAAAAAA 

+AAAAAAAAAAAAAAAAAAAAAAAAAAA 

+AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 

+AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 

+AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 

+AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 

+AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 

+AAAAAAAAAAAAAAAA.V.AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 

+AAAAAAAAAAAAAAAAAAAAA 

1.0 20 

-- + -

30 

• - + -

35 

._ + . 

40 

-- + -

5.0 55 

-- + -

60 

-- + -

65 

._ + -

70 

-- + -

75 

• - + 

80 

FREQUENCY 

INT. CUM. 

0 

0 

0 

0 

7 

1 

1 

3 

4 

1 

2 

2 

3 

3 

9 

3 

8 

7 

9 

5 

10 

14 

9 

11 

12 

26 

27 

31 

55 

51 

62 

73 

78 

21 

0 

0 

0 

0 

0 

0 

0 

0 

7 

8 

9 

12 

16 

17 

19 

21 

24 

27 

36 

39 

47 

54 

63 

68 

78 

92 

101 

112 

124 

150 

177 

20S 

263 

314 

376 

4 49 

527 

548 

548 

540 

548 

5 4 0 

PERCENTAGE 

INT. CUM. 

0.0 

0.0 

0.0 

0.0 

1 .3 

2 

2 

5 

7 

2 

4 

4 

5 

5 

6 

5 

5 

3 

6 

9 

8 

6 

G 

0 

2 

7 

9 

7 

10.0 

9.3 

11.3 

13.3 

14.2 

3.8 

0.0 

0.0 

0.0 

0.0 

0. 

0. 

0. 

0. 

0. 

0. 

0. 

0. 

0. 

1 . 

0. 

1 . 

1 . 

1 . 

0. 

1 , 

2. 

1 , 

2. 

2. 

4, 

4. 

5. 

0.0 

0.0 

0.0 

0.0 

1 .3 

1 .5 

1 . 

2. 

2. 

3, 

3. 

3, 

4. 

4, 

6. 

7. 

8. 

9, 

11, 

12. 

14. 

20, 

22. 

27. 

32. 

16.8 

18.A 

38.0 

49.0 

57.3 

68.6 

81 .9 

96. 2 

100.0 

100.0 

100.0 

100..0 

100.0 

Number of Sites 

H o, ] i, c, 

FIGURE D-la. Histogram of the percentage, p, of data completeness for those sites 

reporting 0-, concentrations in 1981: SLAMS (including NAMS). 
* 3.00000 

* 6.00000 

*9.00000 

* 12.0000 

* 15.0000 

* 1 8 .00.0.0 

0000 

0000 

0000 

*21 

*24 

*27 

*30 

•33 

*36 

*39 

*42 

*45 

*48 

*51 

*54 

0000 

0000 

0000 

0000 

0000 

0000 

0000 

0000 

.00.00 

'5 7.000.0 

*G0 

*63 

*66 

*G9 

*72 

*75 

*73 

*81 

*8 4 

*87 

*90 

*93 

*96 

*99 

*102 

*105 

M 0 B 

*11 1 

*114 

000,0 

0000 

0000 

000.0 

0000 

0000 

0000 

0.000 

0000 

0000 

0000 

0000 

000.0 

0000 

000 

000 

000 

000 

000 

SYMBOL COUNT 

B 175 

EACH SYMBOL REPRESENTS 

MEAN ST.DEV. 

64.906 27.499 

1 OBSERVATION 

5 10 

+ + + 

+ B 

+ BB 

+ B 

+ 

+BBBBB 

+ BBB 

+ EU 

+ BB 

+ BBBB 

+GBGCBB 

+BBBGBBBB 

+ BBBB 

+ BBB 

+BBBBBB 

+ GB 

+BBBBB 

+ BBBB 

+ B 

+ BB 

+ BB 

+BBBBBBBB 

+BBBBB 

+ BB 

+BBBBBBBB 

+BBBBBBBB 

+BBBBB 

+BBBBBBBBBB 

+BBBBBGB 

+BBBBBB 

+BBBBBBBBBBB 

+BBBBBBBBB8BBBB 

+CBBSBCEBBBBBB 

+BBBBBBB3BB 

+BBBBB 

+ 

+ 

+ 

+ 

i + + 

15 20 25 30 35 40 

-- + -

50 

-- + -

55 60 65 70 75 80 

10 15 

-- + -

20 

-- + -

30 

-- + -

35 40 

-- + -

45 

-- + -

50 55 

-- + -

60 

-- + -

65 

-- + -

70 

- - + -

75 

-- + 

80 

Number of Sites 

FREQUENCY PERCENTAGE 

INT. CUM. INT. CUM. 

1 

2 

1 

0 

5 

3 

2 

2 

4 

6 

0 

4 

3 

6 

2 

5 

4 

1 

2 

2 

8 

5 

2 

8 

8 

5 

10 

7 

6 

11 

14 

13 

10 

5 

0 

0 

0 

0 

1 

3 

4 

4 

9 

12 

14 

16 

20 

26 

34 

38 

41 

47 

49 

54 

50 

59 

61 

63 

71 

7 6 

78 

OG 

94 

99 

109 

H G 

122 

133 

147 

160 

170 

175 

175 

175 

175 

175 

0.6 

1 . 1 

0.6 

0.0 

2.9 

1 .7 

1 . 1 

1 . 1 

2.3 

1 . 1 

2.9 

0.6 

1 .7 

2.3 

2.3 

5. 1 

6.9 

8 . Gf 

9.1 

11.4 

14.9 

19.4 

21 , 

23, 

26, 

2 0.0 

30.9 

2 

0 

1 

1 

4 

2 

1 

4 

4 

2 

5 

4 

3 

6 

8 

7 

5 

2 

0 

0 

0 

0 

3 

6 

1 

1 

6 

9 

1 

6 

6 

9 

7 

0 

4 

3 

0 

4 

7 

9 

0 

0 

0 

0 

33 

33 

34 

36 

40 

43 

44 

49 

53 

55 

62 

66 

69 

76 

0 4 

91 

9 7 

1 00 

1 00 

1 00 

100 

1 00 

1 

7 

o 

0 

G 

4 

G 

1 

7 

6 

3 

3 

7 

0 

ti 

4 

1 

ti 

ti 

ti 

ti 

ti 

FIGURE D-lb. Other sites, 

8 iM'it. 
SYMBOL COUNT 

A 540 

EACH SYMBOL REPRESENTS 

MEAN ST.DEV. 

7.445 22.398 

1 OBSERVATION 

E 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 

+ + + + + + + + + + + + + + + + + 

* 7.00000 +AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA* 

* 14.0000 +AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 

* 21.0000 +AAAAAAAAAAAA 

* 28.0000 +AAAA 

* 35.0000 +AAAAAA 

* 42.0000 +AA 

* 49.0000 +A 

* 56.0000 +AA 

*63.0000 +AAAA 

* 70.0000 + 

*7 7.0000 +A 

*84.0000 + 

*91.0000 +A 

•98.0000 +AAA 

•105.000 +AAA 

•112.000 + 

•119.000 +AA 

•126.000 +AAA 

•133.000 + 

•140.000 +AA 

•147.000 +AAA 

•154.000 +A 

•161.000 + 

•168.000 + 

•175.000 + 

•182.000 + 

•189.000 + 

•196.000 + 

•203.000 + 

•210.000 + 

•217.000 + 

•224.000 + 

•231.000 + 

•238.000 + 

•245.000 + 

•252.000 + 

•259.000 + 

•266.000 + 

+ + -

FREQUENCY PERCENTAGE 

INT. CUM. INT. CUM. 

•- + -

10 

• - + -

15 

• - + -

20 

-- + -

25 

-- + -

30 

-- + -

40 

-- + -

50 

-- + -

55 

-- + -

60 

-- + -

65 

-- + -

70 

-- + -

75 

-- + 

80 

463 

35 

12 

4 

6 

2 

1 

2 

4 

0 

1 

0 

1 

3 

3 

0 

2 

3 

0 

2 

3 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

463 

498 

510 

514 

520 

52 2 

523 

525 

529 

529 

530 

530 

531 

534 

537 

537 

539 

542 

542 

5 44 

547 

540 

540 

540 

540 

540 

540 

540 

540 

540 

540 

540 

548 

548 

548 

548 

540 

548 

34. 

6. 

2. 

0. 

1 , 

0. 

0, 

0. 

84.5 

90. 9 

93. 1 

93.8 

94.9 

0.7 

0.0 

0.2 

0.0 

0.2 

0.5 

0.5 

0.0 

0.4 

0.5 

0.0 

95 

95 

95 

96 

96 

96 

96 

9 6 

97 

98.0 

98.0 

0. 

0. 

0. 

4 

.5 

.2 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

98.4 

98.9 

93.9 

99.3 

99.8 

100.0 

100.0 

100.0 

100.0 

100.0 

100 .0 

100. 0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

Number of Sites 

(3146 

FIGURE D-2a. Histogram of the number of expected primary exceedances 

(E) for sites reporting 03 concentrations in 1981: SLAMS (including NAMS) 
E 

* 7 .0000.0 

•14.0000 

•21.000.0 

•28.0000 

•35.0000 

•4 2.0000 

•49.0000 

•56.0000 

•63.0000 

* 70.0000 

•77.0000 

•84.0000 

•91.0000 

•90.0000 

•105.000 

•112.000 

•119.000 

•126.000 

•133.000 

•14 0.000 

•14 7.00.9 

•15 4.000 

*161.000 

•168. OD.- J 

•17 5.0.00 

•18 2.000 

•18 9.000 

•19G.000 

•203.000 

•210.000 

•217.000 

•224.000 

•231.000 

•238.000 

•245.000 

•252.000 

•259.000 

•266.000 

SYMBOL COUNT MEAN ST.DEV. 

B 175 9.383 35.657 

EACH SYMBOL REPRESENTS 1 OBSERVATION 

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 

+B3BBBBBBBBBBBBBB5 3BBBBBBB3BBQBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB8BBBBBBBBBBBBB* 

+BBBBB3BBB 

+BBBBB 

+ BB 

+ BBB 

+ B 

+ BB 

+ 

+ 

+ 

+ 

+ B 

+ 

+ 

+ 

+ 

+ 

+ B 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ B 

+ 

+ 

+ 

+ B 

+ 

+ 

+ B 

+ 

+ 

+ B 

+ 

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 

FREQUENCY 

INT. 

147 

9 

5 

2 

3 

1 

2 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

1 

0 

0 

1 

0 

0 

1 

0 

CUM. 

147 

156 

161 

163 

166 

167 

169 

169 

169 

169 

169 

170 

170 

170 

170 

170 

170 

171 

171 

17 1 

171 

171 

171 

171 

171 

171 

172 

172 

172 

172 

173 

173 

173 

174 

174 

174 

175 

175 

PERCENTAGE 

INT. 

84.0 

5. 1 

2.9 

1 . 1 

1 .7 

0.6 

1 . 1 

0.0 

0.0 

0.0 

0.0 

0.G 

0.0 

0.0 

0.0 

0.0 

0.0 

0.G 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.6 

0.0 

0.0 

0.0 

0.G 

0.0 

0.0 

0.G 

0.0 

0.0 

0.G 

0.0 

CUM. 

84.0 

89. 1 

92.0 

93. 1 

94.9 

95.4 

96.6 

96.6 

96.6 

96.6 

96.6 

97. 1 

97. 1 

97. 1 

97. 1 

97. 1 

97. 1 

97.7 

97.7 

97.7 

97.7 

97.7 

97.7 

9 7.7 

97.7 

97.7 

90.3 

90.3 

90.3 

98.3 

93.9 

90.9 

9 0.9 

9 9.4 

9 9.4 

99.4 

100. ti 

1 00 . ti 

Number of Sites 

FIGURE D-2b. Other sites. 

p. (, 
P.48 

SLAMS 

OTHER 

M- 723 

COR- .0073 

MEAN 

X 77.685 

Y 7.9154 

SYMBOL=S 

SYMBOL=0 

ST.DEV. 

22.238 

26.214 

REGRESSION LINE 

X= .00621*Y+ 77.636 

Y= .00863*X+ 7.2452 

.. + +..X.+ + .. 

RES.MS. 

495.19 

688.08 

280 

245 

210 

175 

140 

105 

70. 

35. 

0.0 

OO 

S 

S 

S 

s 

s s 

s 

SSS 

s 

s 

s 

so 

s 

S S S 

s 

s s 

s s 

s s 

s s s 

0 s osossss ss s s 

ssssss*s«s*s*sss 

0 • O S 0 s 

s so 

0 0 OOS 0 S S SOS ss 

Y 0 SSOOO s s * s s**os ssssss*s*s*s*sss Y 

+0 0 0 **o*o*o s** **s o****ss*s*ss* **«**s*S*********************s + 

.+....+....+....+....+....+....+....+....+....+....+.X..•....+....+....• . 

7.500 22.50 37.50 52.50 67.50 82.50 97.50 

0.00 0 15.00 30.00 45.00 60.00 75.00 90.00 105.0 

FIGURE D-3. Scatter plot of the percentage of data completeness in 1981 

(p) versus the number of estimated primary exceedances (E) for sites 

reporting 0 3 concentrations. 

83146 
TABLE D-1. Frequency table of the percentage of total days recorded in 1981 (p) 

versus expected primary exceedances (E) for sites reporting 1-hour ozone averages. 

83146 

0 - 41* <= 62.5X <» 75X <- 81.5X 86X 89X <- 92X <- 95X <- 97.5X <- 100X TOTAL 

0 

1 - 2 

<^ 5 

<--255 

101 AL 

51 

jar 

9 

12 

72 

41 

G 

5 

20 

71 

42 

a 

10 

14 

75 

43 

1 0 

7 

10 

70 

36 

12 

16 

9 

73 

29 

ii. 

13 

9 

63 

34 

12 

16 

17 

79 

37 

14 

16 

11 

78 

25 

12 

8 

20 

65 

30 

13 

15 

19 

77 

368 

99 

115 

141 

723 
P.50 

Appendix E 

LEAD DESCRIPTIVE STATISTICS 

83146 5 
P.51 

APPENDIX E 

LEAD DESCRIPTIVE STATISTICS 

Figure E-l shows the distribution of data completeness among air monitoring stations. For SLAMS, the mode of the data completeness distribution 

is in the interval of 15-18 percent, corresponding to nearly complete data 

recovery from a once-per-six-day sampling schedule. There are low 

correlations between the percentage of data completeness and reported 

annual averages, standard deviations, and coefficients of variation 

(Figure E-2). 

83146 5 
EAC 

SYMBOL COUNT 

A 171 

il SYMBOL REPRESENTS 

MEAN ST.DEV. 

11.917 10.059 

1 OBSERVATION 

.00000 

. 000.00 

,00000 

, 0000 

. 0000 

, 0000 

. 0000 

. 0000 

. 0000 

•30.0000 

*33.0000 

.0000 

, 0000 

.0000 

, 0000 

.0300 

'3. 

lG. 

'9, 

'12. 

'1! 

M 3 , 

*21 . 

"24, 

'27. 

'36. 

'39. 

'42, 

= 45. 

'40, 

•51.0000 

•54.0000 

*57 

*G0 

*G3 

•66 

•69 

•72 

. 0000 

. 0.Cf 0 

.0000 

.000-; 

.0.0.00 

. 00.00 

•75 

•70 

•31 

*G4 

•87 

•90 

"93 

•96 

0.00.7 

00 00 

00.00 

0000 

0000 

000;/ 

0000 

000 0 

*99.0000 

* 102.0,00 

105 

100 

111 

114 

000 

000 

000 

000 

5 

+AAAAAA 

+AA 

+ AAA 

+AAAAA 

+AAAAAA 

+AAAAAA 

+ AAA 

+ 

+ 

+ A 

+ A 

+ AA 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+A 

+ 

+ 

+ 

+ 

+ 

+ 

10 15 

AAAAAAAAAAA/1 

-\AAAAAAAAAA," 

••.AAAAAAAAAA,' 

20 

.AAAA,' 

,A 

2 5 30 35 

AAAAAAAAAAAAA. 

.AAAAAAAAA. 

40 45 50 

XAAAAAAAAAAAA 

\AAAAAAAAAAAAAA 

55 60 65 70 75 80 

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA* 

INT. 

49 

2 

3 

5 

19 

B5 

3 

0 

0 

1 

1 

2 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

0 

0 

0 

CUM. 

49 

51 

54 

59 

78 

1G3 

1G6 

1G6 

166 

167 

1G8 

170 

170 

170 

170 

170 

170 

170 

170 

170 

170 

170 

170 

170. 

17.0 

170 

170 

170 

170 

170 

170 

171 

171 

171 

171 

171 

171 

171 

INT. 

28.7 

1 .2 

1 .0 

2.9 

11.1 

49.7 

1 .0 

0.0 

0.0 

0.6 

0.6 

1 .2 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0. 6 

0.0 

0. ti 

0.0 

0.0 

0.0 

0.0 

CUM. 

28.7 

29.8 

31.6 

34.5 

45.6 

95.3 

97.1 

97.1 

97. 1 

97.7 

90.2 

99.4 

99.4 

99.4 

9 9.4 

99.4 

99.4 

99.4 

99.4 

99.4 

99.4 

9 9.4 

99.4 

99.4 

99.4 

9 9.4 

99.4 

99.4 

9 9.4 

93.4 

99.4 

\titi.ti 

100. ti 

1 00 .0 

1 00 . ti 

100.0 

100. ti 

\titi,ti 

10 20 30 35 40 45 50 

Number of Sites 

60 70 75 00 

FIGURE E-la. 

reporting Pb 

Histogram of the percentage, p, of 

in 1981: SLAMS (including NAMS). 

data completeness for those sites 

fni'ir, 
p 

* 3 . .00000 

•6.00000 

•9.0000J 

•12.0000 

•15.0000 

•13.0000 

•21.0000 

•24.0000 

•2 7.0000 

•30.0000 

•33.0.900 

•36.0000 

•39.0000 

•4 2.0000 

•45.00.00 

•4 8.0000 

•51 .00.0.7 

•54.0000 

•57.0000 

•50.070.7 

•63.000.7 

*G 6. 000,7 

•69.0,000 

•72 .00.00 

•75.0,i.'0,7 

•7 8.0000 

•81.0000 

•3 4 Cf-.-rvyj 

•8 7.000.7 

•90.000.7 

•93.0000 

•96.0000 

•99.0000 

•102.000 

•105.000 

•103.00.7 

•HI . 00.7 

•114.000 

SYM30L COUNT MEAN ST.DEV. 

B 525 7.G14 7.023 

EACH SYMBOL REPRESENTS 1 OBSERVATION 

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 

+BBBBBEBBBBBBBBBBB3BBBBB3BBBBBBBBBBBBB3B3BBBBBBB3BBBBBBBBB3BBBBBBBBBBBBBBBBBBBCBB* 

+GBECBBBBBBBBBOBB 

+B3BEBBBUBBBBBBBB63BBBBDBBBBBBBBBBBBBBSEB3BBBBBBBBBBBBBBBBBBBBBBBBBB5BBBBBBBBBBBB* 

+ BBC 

+ BCB 

BBE-3'r -BBBBEBBCF'-iBBCBE.!}BBBBBBBBB 

BBBBBBBBBBBBBBJ-BBCBCBBBBBBBBBBB 

+BBBBBB5 3BBBBBBBB3 3BBB3 3BUBD33BC3BBBBBBBBBBBBBDB3BBBBCBBBBBBBBBBBBBBBBBBBBBBB3B3B* 

+ 

+ 

• 

+ B 

+ B 

+ B 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 

FREQUENCY 

INT. 

212 

16 

95 

33 

34 

132 

0 

0 

0 

1 

1 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

CUM. 

212 

220 

323 

356 

390 

522 

522 

52 2 

5 22 

52 3 

524 

52 5 

525 

52 5 

L-2 5 

525 

5>!5 

5 2 5 

525 

5 2 5 

52 5 

525 

525 

525 

5 25 

5 25 

5 2 5 

525 

5 Z 5 

525 

5 2 5 

525 

525 

525 

525 

5 25 

525 

525 

PERCENTAGE 

INT. 

40.4 

3.0 

18. 1 

6.3 

6.5 

25. 1 

0.0 

0.0 

0.0 

0.2 

0.2 

0.2 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

CUM. 

40.4 

43.4 

61.5 

67.8 

74.3 

99.4 

99.4 

99.4 

9 9.4 

99.G 

S 9 . 0 

1 00 . 0 

1 00 . ii 

1 00 . ti 

10.7. ti 

100. ti 

1 00 . ti 

i0H.fi 

100. ti 

1 00. 0 

1 00 . ti 

1 00 . ti 

1 00 . 0 

100.0 

l'XJ.ti 

1 00 . 0 

100.0 

100./:' 

10.7. ti 

1 yj ti . ti 

100.0 

ltiti.ti 

1 titi. ti 

1 titi. ti 

1 titi. ti 

1 00 . ti 

1 '7.7. ti 

1 titi. .'.1 

Number of Sites 

FIGURE E-lb. Other sites, 

H ''• I 'i l . 
P.54 

SLAMS 

OTHER 

N- 696 

COR=-.0080 

MEAN 

X 8.6711 

V .44578 

SYMBOL-S 

SYMBOL-0 

ST.DEV. 

8.0850 

.67639 

X 

Y 

REGRESSION LINE RES.MS. 

=-.09538*Y+ 8.7136 65.457 

=-668E-6*X+ .45157 .45814 

12.0 + 

10.5 

9.00 

<. 7.50 + 

Oi 

a. 

JD 

a. 

c 

to 

cu 

6.00 + 

4.50 

3.00 + 

1.50 +S 

• S 

0.0 0 

SSO 

S 0 

0 • 

SS* 

s** 

0 

• 0 0 00 

** *00*0***** S 

**oo**o******s 

**oo*oo*o*o** 

+ + x. . . + + , 

s s 

OS * 

. + . 

7.500 22.50 37.50 52.50 67.50 82.50 97.50 

000 15.00 30.00 45.00 60.00 75.00 90.00 105.0 

FIGURE E-2a. Scatter plots of ambient air quality statistics versus the 

percent (p) of data completeness for sites reporting Pb concentrations in 

1981: maximum quarterly average versus p. 

8 314 6 
P.55 

10.0.7 + 

3.75,7 + 

7.50,7 + 

S G.25.7 + 

.ti~ti + 

5.7 + 

, X... . + ... . + . 

3.75.7 +S 

2.5.70 + S 

0 0 

s 

S OS 3 

O O O 

•0 0 OS O 

•' 50 0 SS*" 

* OOOO3* ""••••• S 

Y-*00'-0'--S*-;'---S 

ti.tiZti +-000 " -O-O--*-'"-

SLAMS 

OT;-:ER 

, SYMBOL'S 

, SYMBOL=0 

N- 670 

COR=-.0068 

f i E A N 

0.9734 

.31G10 

ST.DEV. REGRESSION LINE RES.MS. 

8.0'.-..'l X = -.08129*Y+ 8.9991 65.545 

.67630 Y = -559E-G*:;+ .32120 .45072 

•S 

7.50,3 22.5 0 37.5 0 52.5 0 67.5 0 82.5 0 97.5 0 

Z.utiti 15.0 0 30.0 5 45.0 0 60.0 0 75.0 0 90.0 0 105. 0 

FIGURE E-2b. Standard diviation versus p. 

3i>e 
P.56 

SLAMS 

OT.IER 

N= 67 0 

COR=-.025 2 

I1EAM 

X 8.973 4 

Y .5431 1 

SVMBOL=S 

SYMBOL=0 

ST.DEV. 

0..u9.;i 

.31213 

RECESSION LINE RCS.;;3. 

X=-.S522S*Y* 9.3329 6 5.5.-J7 

Y -• - 9 7 1 E - 5 "••";(+ .55102 .09734 

C 

0 

E 

F 

F 

V 

A 

R 

3.2 + 

2.8 

2. 4 

2.0 

1 .6 

1.2 

,30 

40 

0.0 

0 

0 

+ S 

0 

00 

+ '•* 

0 

0 S 

• 0 

0 

00 s 

0 

*s 

so 

ss 0 

S 0 

S 00 

** 0 

OOOOO OCO'-'S 

0 00:--"-;"S 

* soo - ••••'••••••-•s 

* OOOOOO o"•••* 

'••0 rt ooo *•••»** 

- 0 OOOOO* *••-

+ * OOuOOOO* ••••••• 

*0 oo-:-o o----* 

* s 000 0 0 * 

0 0 ss 

* 0 0 

00 0 

+....+x...+....+ . 

0 s 

s 

S 0 

7.50.7 22.5 0 37.5 0 52.5 0 67.5 0 82.5 0 97.5 0 

0 0 0 15..70 30.0 0 45.0 0 60.0 0 75.0 0 90.0 0 105. 0 

FIGURE E-2c. Coefficient of variation (standard deviation divided by 

maximum quarterly average) versus p. 
P.57 

Appendix F 

TSP DESCRIPTIVE STATISTICS 

83146 5 
P.58 

APPENDIX F 

TSP DESCRIPTIVE STATISTICS 

Figure F-l shows the distribution of data completeness among air monitoring stations. The mode of the distribution is the interval of 15-18 

percent data completeness, corresponding to nearly complete data recovery 

from a once-per-six-day sampling schedule. Table F-l shows the number of 

sites meeting an annual quota of 75 percent data completeness and meeting 

a corresponding quarterly quota in a specified number of quarters. Table 

F-2 shows the same information for an annual quota of 50 percent. Note 

that roughly 70 percent of the sites that met an annual quota also met a 

corresponding quarterly quota in each of the four quarters of 1981. 

There are low correlations between the percentage of data completeness and 

reported annual averages, standard deviations, and coefficients of 

variation (Figure F2). 

Histograms of "expected" exceedances (i.e., \- or k./p. in the notation of 

Section 2) show that roughly 95 percent of the stations reported eight or 

fewer expected exceedances in 1981 (Figure F-3). The greatest number of 

expected exceedances were reported by the stations having relatively less 

complete data; 91 percent of the stations reported zero expected exceedances (Figure F-4 and Table F-3). Judging by Table F-3 and the low 

correlation given in Figure F-4, no clear relationship is evident between 

expected exceedances and data completeness. 

83146 5 
• 

83 1 'if 

• 

P 

•3.00000 

•6.00000 

•9.00000 

•12.0000 

•15.0000 

•18.0000 

*2 1.0000 

•24.0000 

•2 7.0000 

•30.0000 

•33.0000 

•36.0000 

•39.0000 

•42.0000 

•4 5.0000 

•48.0000 

•51.0000 

•54.0000 

•57.0000 

•60.0000 

•63.0000 

•66.0000 

•69.0000 

•72.0000 

•75.0000 

•78.0000 

•81.0000 

•8 4.0000 

•87.0000 

•90.0000 

•93.0000 

•96.0000 

•99.0000 

•102.000 

•105.000 

•108.000 

•111.000 

•114.000 

SYMBOL COUNT MEAN ST.DEV. 

A 2295 15.722 9.718 

EACH SYMBOL REPRESENTS 1 OBSERVATION 

FREQUENCY 

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 INT 

+AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 40 

+AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 76 

+AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA * 86 

+AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA* 165 

+AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA * 534 

+AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAM240 

+AAAAAAAAAAAAAAAAA 17 

+AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 4 7 

+AAAAAAAAA 9 

+AAAAAAAA 8 

+AAAAAAAAAAAAAAAAAAAAAAAAAAA 2 7 

+ 0 

+AA 2 

+AA 2 

+A 1 

+ AA 2 

+ AA 2 

+A 1 

+ A 1 

+ 0 

+ A 1 

+ A 1 

+AAAAAA 6 

+ AAA 3 

+ 0 

+A 1 

+AAAA 4 

+A 1 

+ 0 

+AA 2 

+AAAA 4 

+AAAAAAA 7 

+ AAA 3 

+AA 2 

+ 0 

+ 0 

+ 0 

+ 0 

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 

Number of Sites 

FIGURE F-la. Histogram of the percentage, p, of data completeness for those 

sites reporting TSP concentrations in 1981: SLAMS (including NAMS). 

CUM. 

40 

116 

202 

367 

901 

2141 

216 9 

2205 

2214 

2222 

2249 

2249 

2251 

2253 

2254 

2256 

2258 

2259 

2260 

2260 

2261 

2262 

2268 

2271 

2271 

2272 

2276 

2277 

2277 

2279 

2283 

2290 

2293 

2295 

2295 

2295 

2295 

2295 

• 

PERCENTAGE 

INT. 

1 .7 

3.3 

3.7 

7.2 

2 3.3 

54.0 

JBT . 7 

2.0 

0.4 

0.3 

1 .2 

0.0 

0. 1 

0. 1 

0.0 

0. 1 

0. 1 

0.0 

0.0 

0.0 

0.0 

0.0 

0.3 

0. 1 

0.0 

0.0 

0.2 

0.0 

0.0 

0. 1 

0.2 

0.3 

0. 1 

0. 1 

0.0 

0.0 

0.0 

0.0 

CUM. 

1 .7 

5. 1 

8.8 

16.0 

39.3 

93.3 

9 4 .BS 

96. 1 

96.5 

96.8 

98.0 

98.0 

98. 1 

98.2 

98.2 

98.3 

98.4 

98.4 

98.5 

98.5 

98.5 

98.6 

93.8 

99.0 

99.0 

99.0 

99.2 

99.2 

99.2 

99.3 

99.5 

99.8 

99.9 

100.0 

100.0 

100.0 

100.0 

100.0 

• 
* 3.00000 

* 6.000.00 

* 9.00000 

•12.0000 

, 0000 

, 0000 

. 0000 

. 0000 

•27.0000 

* 30.0000 

•33.0000 

•36.0000 

•39.0000 

'15. 

'18. 

'21 

'24. 

. 0000 

, 0000 

. 0000 

. 0000 

. 0000 

•57.0000 

•60.0000 

.00.0.0 

'42. 

'45. 

'48. 

'51 . 

'54. 

•63 

•GG 

•63 

•72 

•75 

•78 

•31 

•84 

•37 

•90 

•93 

•96 

•99 

•102 

•105 

•108 

•111 

00>z0 

00.00 

0000 

0000 

0000 

0000 

0000 

0000 

0000 

0000 

0000 

0.0.70 

000 

000 

000 

000 

EACH 

SYMBOL COUNT 

B 1372 

SYMBOL REPRESENTS 

MEAN ST.DEV. 

15.845 15.563 

1 OBSERVATION 

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 

FREQUENCY PERCENTAGE 

INT. CUM. INT. CUM. 

+ -

+ B 

+ B 

+ B 

+ B 

+ B 

+ B 

+ B 

+ B 

+ B 

+ B 

+ B 

+ B 

+ B 

+ B 

+ 

+ 3 

+ B 

+ B 

+ B 

+ B 

+ B 

+ D 

+ B 

+ B 

+ B 

+ B 

+ B 

+ B 

+ B 

+ B 

+ B 

+ B 

+ B 

+ B 

BBBB3BBBBBBBBBBBBBBBt-BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB* 

BBBB3BBBBBBBBBBBBBBBCBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB* 

6BBBBBBBBBBBBBBBBBBBOBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB* 

BBBBBE3BBBBBBB3BBBBBBBr,BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBEBBBBBBBBB* 

BBBB3BBBBBBBBEBBBBBBBBGBBBBBBBBBBBBBBBBBBBBBUBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB* 

BBBBSBBBBBBBBB3BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB3BBBBBBBBBBBBBBB* 

BBBBBBBBBBBBB 

BBBB3BBBBBBBBB 

BBBBBBBBBBB 

BBBBBBBBBBBBBBBBBBBBBBBBBBB 

BB 

BB 

BB 

BB 

BB 

BB 

BB 

BB 

BB 

BB 

BB 

BB 

BB 

BB 

BBBBB 

BBBB 

B 

BBB 

BBBB 

BBB 

B 

B 

BBBBBB 

BBBBBB 

BBBBBB 

B 

BBB 

BBBBBBB 

•114.000 + 

- + -

10 

• - + -

15 

-- + -

20 25 

-- + -

30 

-- + -

35 

-- + -

40 

-- + -

45 50 

-- + -

55 

-- + -

60 

• - + -

65 

-- + -

70 

-- + -

75 

-- + 

80 

87 

145 

135 

119 

259 

468 

16 

17 

14 

3 

30 

3 

1 

3 

0 

3 

6 

1 

5 

1 

2 

4 

5 

4 

2 

2 

7 

7 

7 

2 

1 

4 

8 

1 

0 

0 

0 

0 

87 

232 

367 

456 

745 

1213 

1229 

1246 

1260 

1263 

1293 

1296 

1297 

1300 

1300 

1303 

1309 

1310 

1315 

1316 

1318 

1322 

13 2 7 

1331 

1333 

13 35 

1342 

1349 

1356 

1358 

1359 

1363 

1371 

1372 

1372 

1372 

1372 

1372 

6. 

10. 

9. 

8. 

18. 

34. 

1 . 

1 . 

1 . 

0. 

2. 

0. 

0. 

0.2 

0.0 

0.2 

0.4 

0. 1 

0. 

0. 

0. 1 

0.3 

0. 

0. 

0. 

0. 1 

0.5 

0.5 

0.5 

0. 1 

0. 1 

0.3 

0.6 

0. 1 

0.0 

0.0 

0.0 

0.0 

6. 

16. 

26. 

35. 

54, 

83. 

89. 

90.8 

91 .8 

92.1 

94.2 

94.5 

94.5 

94.8 

94.8 

95.0 

95.4 

95. 

95. 

95. 

96. 

96. 

96. 

97.0 

97.2 

9 7.3 

97.8 

98.3 

98.8 

99.0 

99. 1 

99.3 

99.9 

100.0 

107.0 

100.0 

100.0 

100.0 

Number of Sites 

FIGURE F-lb. Other sites 
P.61 

TABLE F-l. Number of sites recording 24-hour TSP during at least 

75 percent of the scheduled monitoring days in 1981, by the number of 

quarters in which at least 75 percent of the scheduled days per quarter 

are recorded. 

Site Type 

SLAMS 

(includes 

Other 

No. of Quarters 

with at Least 

75% Days/Quarter 

0 

NAMS) 1 

2 

3 

4 

Total 

0 

1 

2 

3 

4 

Total 

No. of 

> 75% 

0 

2 

69 

452 

1335 

1858 

0 

0 

70 

185 

590 

845" 

Sites 

< 75% 

79 

148 

145 

65 

0 

437 

160 

204 

119 

44 

0 

527 

Total 

79 

150 

214 

517 

1335 

2295 

160 

204 

189 

229 

590 

1372 

TABLE F-2. Number of sites recording 24-hour TSP during at least 

50 percent of the scheduled monitoring days in 1981, by the number 

of quarters in which at least 50 percent of the scheduled days 

per quarter are recorded. 

Site Type 

SLAMS 

(includes 

Other 

No. 

wi 

50% 

NAMS) 

of Quarters 

th at Least 

Days/Quarter 

0 

1 

2 

3 

4 

Total 

0 

1 

2 

3 

4 

Total 

No. of 

> 50% 

0 

0 

52 

235 

1825 

2112 

0 

3 

62 

175 

785 

1025 

Sites 

< 50% 

32 

89 

61 

1 

0 

"183" 

75 

186 

83 

3 

0 

W 

Total 

32 

89 

113 

236 

1825 

2295 

75 

189 

145 

178 

785 

1372 

83146 8 
P.62 

SLAMS 

OTHER 

SYMBOL=S 

SYMBOL=0 

N= 3654 

COR=-.0122 

MEAN 

15.821 

56.526 

ST.DEV. 

12.220 

20.827 

REGRESSION 

X=-.00714*Y+ 

Y=-.02074*X+ 

LINE 

16.225 

55.854 

RE S.MS. 

149.34 

433.31 

o i 

3. 

Q00 

c 

to 

oi 

E 

O 

Ol 

4 0 0 

3 5 0 

3 0 0 

250 

2 0 0 

150 

100 

5 0 . 

0 . 0 

,X+. 

0 

S 

S 

s 

*s* 

s o * 

s s**s 

o oo*o*s* 

o o*s* 

+ S *0S**S**** 0 

* * * * 2 A ft A ft A 2 

Q Q pp.- * '.-.- ft ft ft * rt rt ft 

* V; -.': rt ft ft * * ft ft rt * 

YO***"**-"******Q S S*OS*00 

+ Qftrtft:'c*rtrtft**rtftCrtrt* * C it ft ft Q C 

g Q ft ft ft I- ft ft * rt * * ft ft Q ft ft ft Q 0 * S 0 

.0**'"0******* S 0 00 0 00 

. 0'-* *o**** * 00 00 0* * c 

. * 0 00 * S 0 S 0 

+ 0 

. + ... . + ....+X . . . + .. . . + .... H 

s s s 

s 

sss s SOS 

* S * s** s 

OS 

3 

s 

0 

00 

00 

0 

s 

00 

• 0 

0 

s s 

SOS s 

ss 

»oo s 

0 so 

3 00 0 

00 0 

0 

s 

00 

s 

SOS 0 

0 

0 00 

00*00 0 

00 

s so 

s « 

S OOS 

ssss 

so • 0 

00 

0 

7.50 0 22.5 0 37.5 0 52.5 0 67.5 0 82.5 0 97.5 0 

0.00 0 15.0 0 30.0 0 45.0 0 60.0 0 75.0 0 90.0 0 105. 0 

FIGURE F-2a. Scatter plots of ambient air quality statistics versus the 

percent of data completeness (p) for sites reporting TSP concentrations 

in 1981: annual geometric mean versus p. 

83146 
P.63 

SLAMS 

OTHER 

SYMBOL=S 

SYMBOL=0 

N- 3654 

COR= .0797 

MEAN 

15.821 

1 .5G70 

ST.DEV. 

12.220 

.22200 

REGRESSION 

X= 4.3S43--Y + 

Y = .0014 5 * X + 

LINE 

8.9511 

1.5441 

RES.MS. 

148.42 

.04599 

5.0 

4.5 

4.0 

3.5 + 

3.0 + 

2.5 + 

2.0 + 

1.5 Y * 

1 .0 + 

0 

,+X, 

SO 

S 

0 0 

0 0 

S 0 

0 

0 coo 

0 OOS 

• 0 * 

*0 0* 0 

0 00 * * 

S0S00*3a 

QpVS O ftftp*.V 

QftS-O**** 

* fc Q rt ft :•; :t iV 

* * :•: A *; •/: * -.': 

S * * -* * * * * * 

* ;": •/; rt * * rt :t 

* :\ .V Ki'ftA S 

Q rt V: fc * -A' -ii •-* 

o*oso 

0* 

0 

+....+.. . 

7 . 500 

000 1 

s s 

s s 

s s 

ss 

*os 

ft * rt 

* ft ft 

ft ft rt 

ft * ft 

* rt ft 

ft ft rt 

ft ft rt 

* * ft 

x+, 

0 

00 

00 

SSO 000 

S O 0 

• s o 0 

so«*s * 00 0 

•ooss oocos 

* ••'•SO S*S ' 

SS*S*S*S0**0S 

ft*ft*OOOS**S 

ft* S *Q 

OS 

0 0 

s 

0 

S 0* 

SSO 

s 

0 

s 

0 

0 

0 0 

0 0 0 0 

0 

0 000 

•osos so 

ss s 

s 

0 

OOOO 

oosooo 

0 S 00 

s s 

•0 

osos *oss 

s ss *os 

ss ss s 

SO 0 

,+....+....+....+....+....+....+....+....+....+....+....+ . 

22.50 37.50 52.50 67.50 82.50 97.50 

5.00 30.00 45.00 60.00 75.00 90.00 105.0 

FIGURE F-2b. Geometric standard deviation versus p. 

i 4 6 
P.64 

SLAMS 

OTHER 

N° 3654 

COR= .0082 

SYMBOL=S 

SYMBOL=0 

MEAN 

15.821 

.03262 

ST.DEV. 

12.220 

.03931 

REGRESSION 

X= 2.52S4*Y+ 

Y= 268E-7*X+ 

LINE RE S.MS. 

15.739 149.3 5 

.03219 .00159 

.*....+ . 

2 . 4 

2 . 1 

1.8 + 

C 

0 

E 

F 

F 

V 

A 

R 

1.5 + 

1.2 + 

. 9 0 

, 6 0 

.30+ 0 S 

0 OS 

0 * OO S 

0*S 00'*** * OS O 000 0 0 00 

YO*********x.i*rt***0*o**fto* 00 OOOO *0 *00 00*000 00*000 0 OS *0 Y 

0.0 +*rt****ftftftft*ftftft**ft5*s**.<o S S* S**'SS 0 0 SOSS S OS S SO 0 sss*s*os* + 

. + .... + ....X . ... + .... + .... + .... + .... + ... . + .... + .... + .... + .... + ... . + .... + . 

7.500 22.50 37.50 52.50 67.50 82.50 97.50 

0.000 15.00 30.00 45.00 60.00 75.00 90.00 105.0 

FIGURE F-2c. Coefficient of variation (geometric stnadard deviation 

divided by the annual geometric mean) versus p. 

;i45 
SYMBOL COUNT MEAN ST.DEV. 

E 

* 8 .0000.0 

* 16.0000 

•24.0.U'00 

*32.0000 

•40.0000 

•48.0000 

•56.0000 

•64.0000 

* 7 2.0000 

* 80.0000 

* 33.0000 

* 9 6 .000.0 

* 104.000 

* 112.000 

•120.000 

•12 8.000 

•136.000 

•144.000 

•15 2.000 

•160.000 

•163.000 

•17 6.000 

•184.000 

•192.000 

•200.000 

•203.000 

•216.000 

•22 4.000 

•232.000 

•2 40.000 

•24 8.000 

•256.000 

•264.000 

•272.000 

•2 80.000 

*288.000 

•296.000 

•304.000 

5 10 

EACH 

15 

SYMBOL 

20 25 

A 2295 

REPRESENTS 

30 35 40 

1 .489 

1 

45 

9. 438 

OBSERVATION 

50 55 60 65 70 75 80 

+AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA* 

+AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA 

+AAAAAAAAAAAAAAAA 

+AAAAAAA 

+ AA 

+AAA 

+ AAAA 

+AA 

+ 

+ AA 

+ AA 

+ AA 

+ 

+ 

• 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+A 

+ 

+ 

+ 

+A 

+ 

+ 

+ 

+ 

+ 

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 

FREQUENCY 

INT 

2196 

57 

16 

7 

2 

3 

4 

2 

0 

2 

2 

2 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

0 

0 

0 

1 

0 

0 

0 

0 

0 

CUM. 

2196 

2253 

2269 

2276 

2278 

2281 

2285 

2287 

2287 

2289 

2291 

2293 

2293 

2293 

2293 

2293 

2293 

2293 

2293 

2293 

2293 

2293 

2293 

2293 

2293 

2293 

2293 

2293 

2294 

2294 

2294 

2294 

2295 

2295 

2295 

2295 

2295 

2295 

PERCENTAGE 

INT. 

95.7 

2.5 

0.7 

0.3 

0. 1 

0. 1 

0.2 

0. 1 

0.0 

0. 1 

0. 1 

0. 1 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

CUM. 

95.7 

98.2 

98.9 

99.2 

99.3 

99.4 

99.6 

99.7 

99.7 

99.7 

99.8 

99.9 

99.9 

99.9 

99.9 

99.9 

99.9 

99.9 

99.9 

99.9 

99.9 

99.9 

99.9 

99.9 

99.9 

99.9 

99.9 

99.9 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

Number of Sites 

FIGURE F-3a. Histogram of the number of estimated primary exceedances (E) 

for sites reporting TSP concentrations in 1981: SLAMS (including NAMS). 

13 14 6 
E 

* 8.00.000 

•16.00.00 

* 2 4.0000 

* 3 2.00.00 

* 40.0000 

* 4 8.0000 

•56.0000 

•6 4.0000 

•72.0000 

•80.0000 

•8 8.0000 

•96.0000 

•104.000 

•112.000 

•120.000 

•12 8.000 

•136.000 

•14 4.000 

•152.000 

•160.000 

•168.000 

•176.1.00 

•184.000 

•192.000 

•200.000 

•203.0.00 

•216.000 

•22 4.000 

•232.000 

•240.000 

•243.000 

•25 5.000 

•264. .700 

•2 7 2.000 

•230 .

C,P<] 

•2 8B.000 

•2 30.000 

•304.000 

5 10 

EACH 

15 

SYMBOL 

SYMBOL 

20 25 

B 

COUNT 

1372 

REPRESENTS 

30 35 40 

MEAN 

1 .483 

1 

45 

ST.DEV 

8. 

. 

144 

OBSERVATION 

50 55 60 65 70 75 80 

+BBBBBBBBBBBBBBBBBBBBBBBBB3BBBBBBBBBBB8BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB* 

+BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB 

+BBBBBBBBBB 

+BBBBBB 

+ BBBB 

+ BBB 

+ B 

+ 

+ BB 

+ B 

+ B 

+ 

+ 

+ B 

+ B 

+ 

+ B 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 

FREQUENCY 

INT. 

1302 

39 

10 

6 

4 

3 

1 

0 

2 

1 

1 

0 

0 

1 

1 

0 

1 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

CUM. 

1302 

1341 

1351 

1357 

1361 

1364 

1365 

1365 

1367 

1368 

1369 

1369 

1369 

1370 

13 71 

1371 

1372 

1372 

1372 

1372 

1372 

1372 

1372 

1372 

1372 

1372 

1372 

13 7 2 

1372 

1372 

1372 

1372 

1372 

1372 

1372 

1372 

1372 

1372 

PERCENTAGE 

INT. 

94.9 

2.8 

0.7 

0.4 

0.3 

0.2 

0. 1 

0.0 

0. 1 

0. 1 

0. 1 

0.0 

0.0 

0. 1 

0. 1 

0.0 

0. 1 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

CUM. 

94.9 

97.7 

98.5 

98.9 

99.2 

99.4 

99.5 

99.5 

99.6 

99.7 

99.8 

99.8 

99.8 

99.9 

99.9 

99.9 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

1 00.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

1 00 .0 

100.0 

100.0 

1 00.0 

1 00.0 

100.0 

100.0 

100.0 

Number of Sites 

FIGURE F-3b. Other sites. 

8 'j I '!<> 
P.67 

SLAMS 

OTHER 

N= 3667 

COR= .0125 

SYMBOL=S 

SYMBOL=0 

MEAN 

15.766 

1 .4867 

ST.DEV. 

12.233 

8.9745 

REGRESSION 

X= .0I703*Y+ 

Y= .00919*X+ 

LINE RES.MS. 

15.741 149.66 

1.3418 80.551 

280 + 

245 + 

2io + 

175 

140 

105 

70. 

35. 

0.0 

0 

,X+. 

0 

0 

s s 

0 OS * 

S ss 

3 0 OO S 0 

0 so so 

0 osss** 

o** s***0 

ss 

so 00 

s s 

s s 

****** sss* s 000 OS s S 0 0 0 

Y**« ftft** ******«*****Q**Qso S0*0*0 *0 *0*0S*0*00* *0*000 *S**S*OS* Y 

+ .... + .. ..X. ... + .... + .... + .... + .... + .... + .... + .... + .... + .... + .... + .... + . 

7.500 22.50 37.50 52.50 67.50 82.50 97.50 

000 15.00 30.00 45.00 60.00 75.00 90.00 105.0 

FIGURE F-4. Scatter plot of the percentage of data completeness (p) 

versus the number of estimated exceedances (E) for sites reporting 

TSP concentrations in 1981. 

83146 
TABLE F-3. Frequency table of the percentage of total days recorded in 1981 (p) 

versus expected primary exceedances (E) for sites reporting 24-hour TSP averages. 

83146 

SS - SX <= 10.5X <= 13X <- 14.5X 15% 15.5X 16X 16. 5X 17X <- 100X TOTAL 

0 

1 - 10 

<= 20 

<- 260 

TOTAL 

339 

0 

2 

7 

348 

326 

7 

16 

6 

355 

308 

28 

3 

8 

347 

308 

27 

8 

5 

348 

231 

13 

2 

2 

248 

367 

23 

10 

3 

403 

426 

23 

6 

5 

460 

542 

21 

12 

8 

583 

219 

17 

10 

3 

249 

257 

52 

9 

8 

326 

3323 

21 1 

78 

55 

3667 
P.69 

Appendix G 

SUMMARY OF CURRENT DATA COMPLETENESS CRITERIA 

83146 5 
P.70 

APPENDIX G 

SUMMARY OF CURRENT DATA COMPLETENESS CRITERIA 

The present data completeness criteria used to establish valid air quality 

summary statistics vary by use and organization. Tables G-l through G-3 

summarize criteria for NADB, the California Air Resources Board, and the 

Indiana Air Pollution Control Division. In addition, the EPA Trends 

Report (EPA, 1983) requires 50 percent or 4380 hourly observations per 

year (or in some cases 4000 hours per year is used). 

The "EPA fact book" in the Trends Report, which summarizes air quality 

levels in Standard Metropolitan Statistical Areas, uses the same criteria 

as in the Trends Report but notes if the volume of annual data is less. 

Summaries from intermittent measurements based on less than 30 days or 

less than the NADB criteria are also noted. 

REFERENCES 

CARB. 1983. California Air Quality Data, Summary of 1982 Air Quality 

Data, Gaseous and Particulate Pollutants. California Air Resources 

Board, Sacramento, CA. 

EPA. 1977. Aeros Manual Series Volume III: Summary and Retrieval. U.S, 

Environmental Protection Agency, Research Triangle Park, NC (EPA450/2-76-009a). 

EPA. 1979a. "Implementation Plans for Lead National Ambient Air Quality 

Standards." 43 Federal Register, 46266. 

83146 5 
P.71 

EPA. 1979b. Guideline for Lead Monitoring in the Vicinity of Point 

Sources. U.S. Environmental Protection Agency (EPA-450/4-01-006). 

EPA. 1983. National Air Quality and Emission Trends Report, 1981. U.S, 

Environmental Protection Agency, Research Triangle Park, NC. 

EPA. 1984. "Proposed Revisions to the National Ambient Air Quality 

Standards for Particulate Matter." 49 Federal Register, 10434. 

83146 5 
P.72 

TABLE G-l . National Aerometric Data Bank's criteri a 

for validit y of data. (Source: EPA, 1977) 

Continuous Sampling (1 , 2, and 4-hour data) 

Quarterly statistics--75% or 1642 hours 

Annual statistics--75% or 6570 hours 

Intermittent Sampling (24-hour data) * 

Quarterly statistics—fiv e samples per quarter 

( I f one month has no values, at least two 

values in other months) 

Annual statistics—four valid quarters 

Note that 12 samples per quarter are required to 

demonstrate attainment of the NAAQS for lead 

(EPA, 1979a, b). This requirement is also under 

consideration for particulates (EPA, 1984). 

83146T 8 
P.73 

TABLE G-2. California Air Resources Board's criteri a for representativeness 

of air qualit y measurements and statistics . (Source: CARB, 1983) 

Representative 

Calendar 

Statistic 

/ 

Year J 

( 

/ 

Quarter j 

( 

/ 

Month 1 

( 

Sampling Time 

Period 

4 

representative 

calendar 

quarters 

24 hours 

Or 

< 24 hours 

24 hours 

Or 

< 24 hours 

Day 

Mean of 

N Hour 

Period 

1-hour 

Or 

2-hour; or 

3-hour; or 

24-hour 

H_ 

24 

8 

6 

4 

3 

2 

1 

Basis of Statistic or 

Requirement 

Number of 

Representative Hours 

or Days Required 

3 representative months 

Based on a daily 

statistic; or 

Based on hourly statistics 

4 or more 24-hour samples 

Based on a daily 

statistic; or 

Based on all hourly 

statistics; or 

Based on all 2-hour 

statistics; or 

Based on all 3-hour 

statistics 

No more than 2 consecutive 

samples missing in each 

1/3 day (hours 0 thru 7, 

8 thru 15, 16 thru 23) 

69 or more calendar 

days 

1,638 or more hours 

23 or more calendar 

days 

548 or more hours 

274 or more 2-hour 

statistics 

183 or more 3-hour 

statistics 

6 or more hours in 

each 1/3 day 

11 or more samples 

7 or more samples 

22 but not more than 26 hours of sampling 

Number of Samples Needed 

22 or more hourly samples 

7 or more hourly samples 

5 or more hourly samples 

4 hourly samples 

3 hourly samples 

2 hourly samples 

30 minutes or more of sampling* 

* ARB Quality Assurance Manual Section 2.0.23. 

83146 
P.74 

TABLE G-3. Indiana Air Pollution Control Division's 

criteria for completeness of data. (Source: Buch, 1983) 

Time Interval Minimum Number of Valid Observations 

A. Continuous 

Hour 

Day 

Month 

Quarter 

Year 

Three-Hour Running Average 

Eight-Hour Running Average 

At least forty-five (45) minutes* 

At least eighteen (18) hours 

At least twenty-one (21) days 

Three (3) months 

At least nine (9) months with 

at least two (2) months per quarter 

Three (3) consecutive hours 

Six.(6) hours out of eight (8) 

consecutive hours 

B. Six-Day Sampling Schedule 

Quarter 

Year 

At least ten (10) samples unless one 

(1) month has zero (0) valid samples, 

then the remaining two (2) months must 

have at least four (4) samples each. 

At least nine (9) months with at least 

two (2) months per quarter and at least 

forty-five (45) samples. 

C. Daily Sampling Schedule 

Quarter 

Year 

At least sixty (60) samples unless one 

(1) month has zero (0) valid samples, 

then each remaining month must have at 

least twenty-four (24) samples. 

At least nine (9) months witn at least 

two (2) months per quarter and at least 

two-hundred seventy-three (273) samples 

*If an hour includes the daily zero/span sequence, the hour is 

considered valid if at least fifty percent (50.0%) of the hour 

is valid. 

83146