••= ** "•"t&^W'^Ji"?,
Ota- ICAN FTR 1-m AVE. IS O-OC Fm
STO' CCQ- CTTVlATtDJ 15 1-9E
TO TO5 CENT ff hfajSS HAVE DATA AVAIL-
AVERAGING TIME> HOURS
FIG- 4- CONCENTRATION VS • AVERAGING TIME AKO FREO-IElSCY <
PT5OM l&s l^Sl TO 1H'
SUL.FT-R QIDXIDE IM WASHINGTON
AVERAGING TIME
SECOND MINUTE HOUR DAY MONTH YEAR
1 1 5 10 15 30 i a|JT OF K1JJS WVE W
OOOi C.QOI 0-O1 0-1 1 1O 100 1.000 ID.000
AVERAGING TIME. HOURS
FIG- + CONCENTRATION VS - AVERAGING TIME AND FREQUENCY '
SLJ-FUR DIOXIDE IN WASHINGTON FROM IB-' l^Bl TO 12^ :
iECONO
MINUTE HOUR DAY MONTH YEAR
1 310153)1 2*8 IB 1 B 1 7 14 15361 3 10
an. I«AN FIR i-hfi Avt- is a-oc PPM
STD- &.0- DZVIATKN IS !•*
7O FO CWT Of KLFS H*VE OTA AVAIL-
O.QOQ1 0-001
AVERAGING TIME. MOURS
A MATHEMATICAL
MODEL FOR RELATING
AIR QUALITY
MEASUREMENTS
TO AIR QUALITY
STANDARDS
U.S. ENVIRONMENTAL
PROTECTION AGENCY
-------
AP89
A MATHEMATICAL MODEL FOR RELATING
AIR QUALITY MEASUREMENTS TO
AIR QUALITY STANDARDS
Ralph I. Larsen, Ph.D.
National Environmental Research Center
ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF AIR PROGRAMS
RESEARCH TRIANGLE PARK, NORTH CAROLINA
November 1971
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 - Price 60 cents
-------
The AP series of reports is published by the Technical
Publications Branch of the Informational Services Divi-
sion of the Office of Administration for the office
of Air and Water Programs, Environmental Protection
Agency, to report the results of scientific and engi-
neering studies, and information of general interest
in the field of air pollution. Information reported
in this series includes coverage of intramural activ-
ites and of cooperative studies conducted in conjunc-
tion with state and local agencies, research insti-
tutes, and industrial organizations. Copies of AP
reports are available free of charge to Federal em-
ployees, current contractors and grantees, and non-
profit organizations as supplies permit from the
Air Pollution Technical Information Center, Environ-
mental Protection Agency, Research Triangle Park,
North Carolina 27711 or from the Superintendent of
Documents.
3rd printing February 1973
Publication No. AP- 89
-------
ACKNOWLEDGMENTS
Sincere gratitude is expressed to George Morgan, Gerald Nehls,
Thomas Oliver, and their staff for providing the CAMP data listed
herein; and to Gene Lowrimore for providing the exact computer
solution for plotting position.
ill
-------
ABSTRACT
Analyses of air pollution data indicate that air quality measurements tend to fit a general mathematical model
having the following characteristics:
1. Pollutant concentrations are lognormally distributed for all averaging times.
2. Median concentrations are proportional to averaging time raised to an exponent.
3. Maximum concentrations are approximately inversely proportional to averaging time raised to an exponent.
The above characteristics have been used to develop equations that may be employed to calculate the geometric
mean, standard geometric deviation, maximum concentration, and various percentile concentrations of air
pollutants. To illustrate the predictive, as well as the interpretive value of the model, parameters have been first
calculated for one averaging time from actual data and then calculated for other averaging times by means of the
model. Maximum concentrations calculated with the model are compared with measured values for seven gaseous
pollutants obtained during continuous sampling for up to 7 years in eight cities. Averaging times for which the
model is most and least accurate are discussed.
The analytic techniques described can be used to compare ambient pollutant concentrations with air quality
standards and to calculate pollutant parameters for various averaging times. The resulting information can be used
in developing implementation plans and emission standards.
All the equations needed for performing the calculations are listed in the appendix.
Key Words: Air quality, statistical analyses, mathematical model, air quality criteria, ambient air quality
standards, carbon monoxide, hydrocarbons, nitric oxide, nitrogen dioxide, nitrogen oxides, photochemical
oxidants, sulfur dioxide.
IV
-------
TABLES
1. Relationship between Air Pollutant Exposure and Effects
2. National Primary and Secondary Ambient Air Quality Standards
3. Concentration (ppm) versus Averaging Time and Frequency for Sulfur Dioxide, Washington, D.C.,
December 1, 1961, to December 1, 1968 ......................................... 13
4. Carbon "Monoxide Concentration (ppm) at CAMP Sites, by Averaging Time and Frequency, 1962
through 1968 [[[ 14
5. Hydrocarbon Concentration (ppm) at CAMP Sites, by Averaging Time and Frequency, 1962 through
1968 [[[ 16
6. Nitric Oxide Concentration (ppm) at CAMP Sites, by Averaging Time and Frequency, 1962 through
1968 [[[ 18
7. Nitrogen Dioxide Concentration (ppm) at CAMP Sites, by Averaging Time and Frequency, 1962
through 1968 [[[ 20
8. Nitrogen Oxides Concentration (ppm) at CAMP Sites, by Averaging Time and Frequency, 1962
through 1968 [[[ 22
9. Oxidant Concentration (ppm) at CAMP Sites, by Averaging Time and Frequency, 1962 through 1968 . 24
10. Sulfur Dioxide Concentration (ppm) at CAMP Sites, by Averaging Time and Frequency, 1962 through
1968 [[[ 26
1 1. Plotting Position of Extreme Concentrations and Percentiles for Selected Averaging Times ........ 30
-------
FIGURES
1. Measured Ambient Air and Calculated Blood Carbon Monoxide Concentrations at the Lennox Site in
Los Angeles County from October 26 through 28, 1965 4
2. Estimated Frequency of Hourly Temperatures at CAMP Site, Washington, D.C., December 1, 1961, to
December 1, 1968 8
3. Frequency of 1-hour-average Sulfur Dioxide Concentrations Equal to or in Excess of Stated Values,
Washington, D.C., December 1, 1961, to December 1, 1968 11
4. Computer Plot of .Concentration versus Averaging Time and Frequency for Sulfur Dioxide at Site
256, Washington, D.C., December 1, 1961, to December 1, 1968 36
5. Expected Annual Maximum Sulfur Dioxide Concentrations at Sampling Site Where National Secondary
3- and 24-hour-standard Concentrations Occur Once a Year 40
VI
-------
CONTENTS
INTRODUCTION 1
EFFECTS VARIABLES 3
Exposure Duration 3
Frequency 4
AIR QUALITY STANDARDS 5
FREQUENCY ANALYSES 7
Normal Frequency Distribution 7
Lognormal Distribution 9
Cumulative Frequency Distribution 10
Comparing Data with Standards 12
Calculating the Standard Geometric Deviation 28
Calculating the Geometric Mean 29
Calculating the Expected Annual Maximum Concentration 31
Using Non-Continuous Data 32
AVERAGING-TIME ANALYSES 35
A Mathematical Model 35
Calculating the Standard Geometric Deviation • 37
Calculating the Geometric Mean 42
Plotting Results 43
Short-Cuts 44
Non-Lopnormally Distributed Data 45
SUMMARY 49
APPENDIX: WORKING EQUATIONS AND EXERCISES WITH ANSWERS 51
Equations 51
Exercises 52
Answers 53
REFERENCES 55
VII
-------
A MATHEMATICAL MODEL FOR RELATING
AIR QUALITY MEASUREMENTS TO
AIR QUALITY STANDARDS
INTRODUCTION
The setting of air quality standards is one of the major steps toward controlling widespread pollutants. I n the
United States, the Federal Government sets national minimum air quality standards for such pollutants,1 but the
states may set more stringent standards if they wish. The major purpose of air quality standard:; is to prevent the
occurrence of adverse effects such as those described in air quality criteria documents.2"5
In the criteria documents and in the national ambient air quality standards, allowable levels of eir pollution are
expressed in terms of the concentration of a specific pollutant and the duration of exposure to that pollutant.
Some air quality data cannot be compared directly to such standards, however, because pollutants are sampled
and analyzed by many different techniques and are sampled and averaged over different time periods (averaging
times). Nonetheless, a basis for reduction to uniformity exists inasmuch as air quality data tend to fit a
mathematical model having the following characteristics:
1. Pollutant concentrations are lognormally distributed for all averaging times.
2. Median concentrations are proportional to averaging time raised to an exponent.
3. Maximum concentrations are approximately inversely proportional to averaging time raised to an exponent.
These characteristics have been used to develop equations, given in this report, that can be used to calculate the
following air pollutant parameters, regardless of averaging time used: geometric mean, stiarvlard geometric
deviation, maximum concentration expected once a year, and frequency distribution of expected pollutant
concentrations.
The mathematical model presented in this report can be used not only for reducing real data, but also for
predicting pollutant concentrations; that is, parameters calculated for one averaging time from actual data can be
calculated for other averaging times by means of the model. Consequently, the model ran be used for
interpretation, comparison, and prediction.
When the model is used to achieve comparability of air quality data, ambient pollution concentrations
can be compared directly with air quality standards. The resulting information can be used in the development of
emission control strategies and implementation plans.
The following sections present the model and illustrate its interpretive and predictive value through sample
calculations and the treatment of real data.
-------
EFFECTS VARIABLES
EXPOSURE DURATION
The exposure time required to cause a particular pollutant effect depends upon the type of effect (Table 1).
Odor, for instance, can be detected in a 1-second whiff.6 On the other hand, a much longer exposure to carbon
monoxide is required to cause a different type of effect, impaired judgment. An 8-hour exposure to a carbon
monoxide concentration of 12 to 17 milligrams per cubic meter, mg/m3 (10 to 15 parts per million, ppm) can
impair a person's judgment of time intervals.2 Vegetation can be damaged by an exposure of less than 1 hour if
the concentrations of oxidant, sulfur dioxide, or some other toxicant are high enough; however, because of the
pattern of pollutant concentration variation in urban atmospheres, plant damage is usually caused instead by long
exposure (such as 8 hours) to low concentrations.
Table 1. RELATIONSHIP BETWEEN AIR POLLUTANT EXPOSURE AND EFFECTS
Approximate
exposure
duration
1 sec
1 hr
8hrs
1 day
4 days
1yr
Effect
Sensation
Odor
Taste
Eye irritation
Student athlete per-
formance impaired
Visibility reduced
Judgment impaired
Heart patients stressed
Vegetation damaged
Health impaired
Soiling
Health impaired
Health impaired
Vegetation damaged
Corrosion
Soiling
Pollutant
Carbon
monoxide
-
-
-
-
--
X
X
-
—
-
-
-
-
--
-
Oxidant
X
-
X
X
X
—
--
X
--
-
-
-
-
-
-
Particulate
matter
-
-
-
X
—
-
-
X
X
-
X
X
X
X
Sulfur
oxides
X
X
-
-
X
..
--
X
X
-
X
X
X
X
-
It is apparent from Table 1 that in order to relate pollutant effects to pollutant concentrations, the
concentrations should be analyzed as a function of exposure duration. This can be accomplished by averaging
ambient pollutant concentrations over time periods such as an hour, a day, or a year.
The close agreement between ambient concentrations and a particular effect, when the appropriate averaging
time is used, is shown in Figure 1.7 The highest ambient 8-hour-average carbon monoxide concentration for a day
agrees very closely with the highest carbon monoxide concentration expected in a man's blood stream for that
day. The maximum 1-hour ambient value, however, is a poor indicator of expected blood levels, for it fails to
show the relatively slow absorption and desorption of carbon monoxide that occurs over long periods.
-------
60
60
40
e
Q.
CL
111
Q
x
o
o
m
cr
<
o
2C
10
A 44
A 57
A 48
CALCULATED HOURLY BLOOD CONCENTRATION
8-HR AMBIENT AVERAGE .40
V24
V22
V 20
A AMBIENT 1-hr AVERAGE MAXIMUM FOR DAY-
V AMBIENT 1-hr AVERAGE MINIMUM FOR DAY
OCTOBER 26
OCTOBER 27
DATE
OCTOBER 28
Figure 1. Measured ambient air and calculated blood carbon monoxide concentrations at the Lennox site in
Los Angeles County from October 26 through 28, 1965.
FREQUENCY
Air pollutant concentrations vary as a function of meteorology and the number, strength, and location of
sources relative to a particular air sampling site. The frequency with which a particular pollutant concentration is
exceeded determines the frequency with which a particular effect can be expected. For example, the odor
threshold concentration for a particular pollutant at a particular location might be exceeded 1 percent of the
time. This frequency might not sound very objectionable, but since an odor can be detected in a 1-second whiff,
the odor might be smelled every few minutes.
Similarly, pollutant concentration data can be related to the frequency that plant damage might be expected.8
Sin:e commercial crops or ornamental plants can be permanently damaged by one exposure, damage might be
expected if a damaging concentration were exceeded even once a year.
n order to relate air pollutant concentrations to effects, air quality data should be analyzed as a function of
bolh averaging time and frequency.9
MODEL RELATING AIR QUALITY MEASUREMENTS TO STANDARDS
-------
AIR QUALITY STANDARDS
As mentioned earlier, the Federal Government sets minimum air quality standards for certain pollutants,
although the states may set more stringent standards if they wish. National primary ambient air quality standards
are set to protect the public health and secondary standards are set to protect the public welfare. Such primary
and secondary standards have been set for carbon monoxide, hydrocarbons, nitrogen dioxide, photochemical
oxidants, particulate matter, and sulfur dioxide (Table 2).1 Each standard specifies an averaging time, frequency,
and concentration. The averaging times are 1, 3, 8, and 24 hours, and 1 year. The frequency parameter column of
Table 2 specifies either annual maximum concentrations for averaging times of 24 hours or less, or an arithmetic
or geometric mean for a 1-year period. The standards specify that the maximum concentrations are not to be
exceeded more than once per year.
In order to relate measured air pollutant concentrations to air quality standards, measured concentrations
must be expressed as a function of averaging time and frequency. The next two major sections will deal with the
calculations needed to accomplish this task. The first major section will treat the frequency parameter. The
second major section will treat the averaging-time parameter.
Table 2. NATIONAL PRIMARY AND SECONDARY AMBIENT AIR QUALITY STANDARDS1
Pollutant
Carbon
monoxide
Hydrocarbons
(nonmethane)
Nitrogen
dioxide
Photochemical
oxidants
Particulate
matter
Sulfur
dioxide
Type of
standard
Primary and
secondary
Primary and
secondary
Primary and
secondary
Primary and
secondary
Primary
Secondary
Primary
Secondary
Averaging
time
1 hr
8hr
3hr
(6 to 9
a.m.)
1yr
1 hr
24 hr
24 hr
24 hr
24 hr
24 hr
1yr
3hr
24 hr
1yr
Frequency
parameter
Annual maximum3
Annual maximum
Annual maximum
Arithmetic mean
Annual maximum
Annual maximum
Annual geometric mean
Annual maximum
Annual geometric mean
Annual maximum
Arithmetic mean
Annual maximum
Annual maximum
Arithmetic mean
Concentration
M9/m3
40,000
10,000
160b
100
160
260
75
150
60C
365
80
1,300
260d
60
ppm
35
9
0.24b
0.05
0.08
-_
"
__
-
0.14
0.03
0.5
0.1d
0.02
al\lot to be exceeded more than once per year.
bAs a guide in devising implementation plans for achieving oxidant standards.
cAs a guide to be used in assessing implementation plans for achieving the annual maximum 24-hour standard.
'•'AS a guide to be used in assessing implementation plans for achieving the annual arithmetic mean standard.
-------
FREQUENCY ANALYSES
In order to make this discussion more meaningful, statistical parameters and specific examples are considered
together. Example data have been drawn from past studies in which concentrations have been expressed as parts
per million (ppm). Concentrations determined in future studies and analyses may tend to be reported in
micrograms per cubic meter (jug/m3).
NORMAL FREQUENCY DISTRIBUTION
Let us begin the discussion of frequency with an example. Assume that ambient temperature has been
recorded each hour at the Continuous Air Monitoring Program (CAMP) site operated by the Federal air pollution
control agency in downtown Washington, D.C. The estimated number of hours during the period from December
1, 1961, to December 1, 1968, that the hourly average temperature was a particular value has been plotted on
Figure 2. A December 1 starting date has been selected so that the three coldest months, December, January, and
February, could be kept together for calculating seasonal averages.
The data can be characterized mathematically by taking moments. A moment is merely a weight multiplied by
a levsr arm to a power. The first moment can be calculated about 0°F. In this case, the weight is the number of
hours and the lever arm is temperature. Since 40°F occurred for an estimated 860 hours during this period, the
moment at 40°F is 34,400. To obtain the arithmetic mean temperature, all of the moments for all of the
temperatures are added and then divided by the number of hours for which observations are available. The same
result could be obtained by adding all of the hourly observations together and dividing by the number of
observations.
n
where m = the arithmetic mean,
7JX = the summation of all the temperature values, and
n = the number of temperatures observed.
For the example given,
= 3,495,000
m ~ 61,320
m = 57°F
This calculation gives a very useful parameter, the arithmetic mean temperature at the Washington CAMP site;
but it does not tell how much the temperature fluctuates about the mean. For that information, a second
parameter is needed. The second moment about the mean can be calculated and used as follows:
(2)
where s = the standard deviation,
y"V2 = the summation of the squares of each observed temperature minus the mean temperature,
and
-------
5
2000 -
NUMBER OF STANDARD DEVIATIONS (z) FROM MEDIAN
-3-2-1 0 12
§1500
o
aj
"I
c
O
iiooo -
40 60
TEMPERATURE.'F
Figure 2. Estimated frequency of hourly temperatures at CAMP Site, Washington, D.C., December 1, 1961,
to December 1, 1968.
n = the number of observations.
For the example given.
n 3,800,000
5 61,320
s = 15°F
(3)
(4)
This processed second moment, the standard deviation, indicates how much the temperature fluctuates about
the mean. If the temperature were always the same, the standard deviation would be zero. If the temperature
fluctuated widely, then the standard deviation would be very large. Two parameters can thus be used to
characterize temperature at the Washington CAMP site, a mean and a standard deviation.
8
MODEL RELATING AIR QUALITY MEASUREMENTS TO STANDARDS
-------
Figure 2 is plotted as if temperature followed a normal frequency distribution. Because the distribution of
many variables tends to approximate this typical, bell-shaped plot, the number of samples expected for each value
can be expressed by the normal, or Gaussian, equation:
v ~ 7T^7^ exp
where y = the number of samples expected to have a certain x-value (e.g., x = 40°F, ranging from 39.50 to
40.50°F),
n = the total number of samples,
s = the standard deviation,
exp = the base of natural logarithms, 2.718, raised to the power that follows in brackets,
x = the value for which the frequency is desired, and
m = the arithmetic mean.
As one example, the number of hours when an observation of 40°F would be expected can be calculated.
61, c
y = 0-5 exp
y = 858 hours (7)
Equation 5 gives the number of samples with a given x-value. To determine the number of samples at or above
a particular x-value, all of the calculated values of y for all values of x at and above the selected value are merely
added together. Equation 5 can be integrated to accomplish this.
The area under any normal curve (Figure 2) can be set equal to unity or to 100 percent. Statistical texts
tabulate cumulative frequency as a function of the number of standard deviations by which a particular x-value
deviates from the median value. This type of information can be used to plot the cumulative frequency
distribution for a particular set of data, a type of distribution that will be discussed later.
LOGNORMAL DISTRIBUTION
Sulfur dioxide concentrations at the Washington CAMP site have been measured and recorded on
computer-readable punched paper tape every 5 minutes since shortly after December 1, 1961. If half or more of
the 5-minute measurements, or 6, were available for an hour and considered valid, an hourly average was
computed by adding the 5-minute observations available for that hour, dividing by the number of observations,
and rounding the quotient.
If hourly sulfur dioxide concentrations were plotted using axes similar to those in Figure 2, they would not
produce a frequency distribution of the same shape. The left tail would be quite short, the hump would be
skewed to the left, and the right tail would be very long. Such a shape indicates that many concentrations are
close to zero and that a few are very high. Unlike temperature, the sulfur dioxide values are blocked on the left,
for they cannot go below zero. This left-skewed distribution often results when many values are close to zero. It
can be readily normalized to the symmetrical curve shown in Figure 2 by plotting the frequency distribution of
the logarithms of the concentrations rather than the concentrations themselves. Equations 1, 2, and 5 can also be
normalized by replacing the concentration values with the logarithms of those values. Anti-logarithms can then be
calculated to obtain the two parameters needed to describe a lognormal distribution, the geometric mean and the
standard geometric deviation.
Frequency Analyses 9
-------
= exp
0.5
(9)
where mg = the geometric mean,
exp = the base of natural logarithms, 2.718, raised to the power that follows in brackets,
"^Inc = the summation of the logarithms of the concentrations,
n = the number of observations, and
Sg = the standard geometric deviation.
For a lognormal distribution, the arithmetic mean (m), geometric mean (mg), standard deviation (s), and
standard geometric deviation (sJ are related as follows:1 ° -11
sg = exp
In
0.5 ,
+ 1
i rn
(10)
m
m = —
9 exp (0.5 In2s )
Or, taking logarithms:
\nrrtg = \nm - 0.5 In2 sg
Rearranging to solve for In m gives:
\r\rn = \rtmg + 0.5 In2 sg
(11)
(12)
(13)
CUMULATIVE FREQUENCY DISTRIBUTION
A plot like Figure 2 gives little more than a qualitative idea of the distribution of pollutant concentrations.
The data could be evaluated much more easily if they were plotted so that a straight line is produced when the
data are lognormally distributed. On log-probability graph paper, concentration is plotted on a logarithmic
ordinate and the cumulative frequency distribution is plotted on the abscissa (Figure 3). The special probability
scale used on the abscissa will produce a straight line when the data are perfectly lognormally distributed.
Because the most valuable information is how often air pollutant concentrations equal or exceed certain
values, rather than how often concentrations are less than those values, the abscissa values in Figure 3 are used to
represent the frequency with which a certain concentration is equaled or exceeded. These data are from Table 3.
The following equation is used to determine which observation should be plotted at a particular frequency:
+ °'999
where r = the rank order of the observation, ranked from highest to lowest (r is truncated to give an integer
value),
MODEL RELATING AIR QUALITY MEASUREMENTS TO STANDARDS
-------
NUMBER OF STANDARD DEVIATIONS (z) FROM MEDIAN
21 0-1
CL
Q.
LLI
O
O
O
0.01
0.01
10 16
30 50 70
FREQUENCY, percent
90
99
Figures. Frequency of 1-hour-average sulfur dioxide concentrations equal to or in excess of stated values,
Washington, D.C., December 1, 1961, to December 1, 1968.
f = the selected frequency, in percent,
n = the number of observations, and
0.999 = a constant slightly less than 1, used to give uniform computer results.
If only one sample were available, such as a 1-year average for 1 year of data, then that concentration would
be plotted at the 50-percent frequency. If two samples were available, such as two 6-month averages for 1 year of
Frequency Analyses
11
-------
data, then the high value would be plotted for frequencies below 50.05 percent and the low value" would be
plotted for frequencies at and above 50.05 percent.
The frequency distribution for the 1-hour averages in Table 3 was obtained as follows. Column 5 of Table 3
indicates that sulfur dioxide concentration data were available from the Washington CAMP site for 70 percent of
the 61,300 hours in the 7-year period from December 1, 1961, to December 1, 1968, a total of about 43,000
hours. The hourly concentrations were arrayed from the highest to the lowest. A frequency of 0.1 percent is one
of the first listed for 1-hour averages in the table. Substitution of that frequency in Equation 14 gives 43. The
43rd value in the array was thus selected as the point for the 0.1 percent frequency. This value, 0.34 ppm, is
listed in Table 3 and plotted in Figure 3. This process was continued for each of the percentiles listed in Table 3.
All of the numbers in the array were then added together; the resulting sum was divided by the number of
observations and rounded to obtain the arithmetic mean of 0.05 ppm (column 2). The top value in the array is
listed in column 3 as the maximum 1-hour-average concentration, 0.62 ppm. The bottom value in the array is
listed in column 4 as the minimum concentration, 0.
CAMP information similar to that in Table 3 has been summarized in Tables 4 through 10 for the 7-year
period and for each individual year in that period for carbon monoxide, hydrocarbons, nitric oxide (NO),
nitrogen dioxide (NO2), nitrogen oxides (NO + NO2), oxidants, and sulfur dioxide.
The last 9 columns under Washington in Table 10 have been extracted from Table 3. Maximum concentrations
for each year are also shown. Column 5 in Table 10 indicates that the maximum 1-hour concentration measured
during the 7 years was 0.62 ppm. Column 9 indicates that it occurred in 1964 (December 1, 1963, to December
1, 1964). Column 6 indicates that the lowest annual maximum concentration measured was 0.35 ppm, which
occurred the next year, 1965. The highest annual maximum concentration during this 7-year period was thus
about twice the lowest annual maximum.
COMPARING DATA WITH STANDARDS
Sulfur dioxide will be used as an example pollutant in the discussion that follows. The national secondary
standards for sulfur dioxide specify an annual arithmetic mean, and maxima for averaging times of 3 and 24
hours. Some state standards specify a 1-hour maximum. Aerometric data analyses are needed that will accurately
depict statistical parameters for all of these averaging times.
The first task is to calculate the two parameters needed to describe 1-hour-average concentrations as a
lognormal distribution, the geometric mean and the standard geometric deviation. The goal is to use the
distribution data to calculate these parameters so that they in turn can be used to calculate expected
concentrations for comparison with standards.
As Figure 3 indicates, a lognormal distribution can be expressed as a straight line. A straight line, in turn, can
be characterized by two parameters, an intercept and a slope. The intercept in this case is the point where the
distribution line crosses the 50th percentile. This is the geometric mean or median. The slope is related to the
standard geometric deviation. The standard geometric deviation can be calculated as the 16-percentile
concentration (one standard deviation from the median, top abscissa on Figure 3) divided by the 50-percentile
concentration.
As noted, the geometric mean concentration for a lognormal distribution falls at the median or 50-percentile
point. Half of the concentration values are larger than the median and half are smaller. The arithmetic mean
concentration falls near the 30-percentile point for aerometric data, however, because of the heavier weight of
high concentration values in the calculation of arithmetic means. Thus, a distribution line drawn through the
30-percentile point for 1-hour averages should accurately estimate the arithmetic mean.
12 MODEL RELATING AIR QUALITY MEASUREMENTS TO STANDARDS
-------
I
CD
I
3
<"
Table 3. CONCENTRATION (ppm)VERSUS AVERAGING TIME AND FREQUENCY FOR SULFUR DIOXIDE, WASHINGTON, D.C., DECEMBER 1,
1961, TO DECEMBER 1, 1968
Aver-
aging
time
5 min
10
15
30
1 hr
2
4
8
12
1 day
2
4
7
14
1 mo
2
3
6
1yr
Arith-
metic
mean
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.04
0.05
0.04
0.05
Max
0.87
0.72
0.68
0.68
0.62
0.55
0.41
0.35
0.30
0.25
0.22
0.18
0.13
0.13
0.11
0.10
0.10
0.08
0.05
Min
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.01
0.01
0.04
Per-
cent
data
70
70
70
70
70
70
70
71
72
72
68
71
73
74
76
74
82
93
86
Percent of time concentration is equaled or exceeded
0.001
0.65
0.66
0.01
0.49
0.47
0.47
0.46
0.45
0.1
0.35
0.36
0.35
0.35
0.34
0.32
0.29
0.26
0.25
1
0.21
0.21
0.21
0.21
0.21
0.21
0.20
0.18
0.18
0.16
0.14
0.14
10
0.10
0.11
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.09
0.09
0.09
0.09
0.08
20
0.07
0.08
0.07
0.08
0.07
0.08
0.08
0.08
0.08
0.08
0.08
0.08
0.08
0.08
0.08
0.08
0.07
30
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
40
0.04
0.04
0.04
0.04
0.04
0.04
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.04
0.05
0.05
50
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
60
0.02
0.03
0.02
0.02
0.02
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.04
70
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.03
80
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.02
0.02
0.02
0.02
0.02
90
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
99
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
99.9
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
99.99
0.00
0.00
0.00
0.00
0.00
99.999
0.00
0.00
GO
-------
Table 4. CARBON MONOXIDE CONCENTRATION (ppm) AT CAMP SITES, BY AVERAGING TIME AND FREQUENCY, 1962 THROUGH 1968
City and
averaging
time
CHICAGO
5 min
1 hr
8hr
1 day
1 mo
1yr
CINCINNATI
5 min
1 hr
8hr
1 day
1 mo
1yr
DENVER
5 min
1 hr
8hr
1 day
1 mo
1yr
LOS ANGELES
5 min
1 hr
8hr
1 day
1 mo
1yr
Annual
maxi-
mum
81
53
38
32
18
13
103
52
29
22
9
5
114
61
37
28
12
8
72
46
32
26
15
11
1962 through 1968 Maximum for year
Geom.
mean
12.1
12.3
12.5
12.6
13.0
13.2
4.0
4.3
4.5
4.6
5.0
5.3
6.4
6.7
6.9
7.1
7.5
7.9
9.5
9.7
9.9
10.0
10.3
10.6
SGDa
1.54
1.46
1.40
1.36
1.22
1.00
2.09
1.92
1.77
1.69
1.41
1.00
1.93
1.79
1.66
1.60
1.35
1.00
1.58
1.50
1.43
1.39
1.24
1.00
Max
78
59
44
33
21
17
50
42
36
32
11
6
90
79
30
21
12
8
81
47
28
23
14
11
Min
43
28
20
16
7
6
26
20
12
9
5
4
63
40
27
16
9
5
70
35
27
22
13
9
1962
43
28
20
17
7
81
43
28
22
14
11
1963
50
36
22
19
10
70
35
28
22
13
9
1964
64
46
35
27
17
12
26
22
19
17
11
6
75
47
27
23
14
11
1965
61
44
37
32
21
17
50
34
21
16
5
4
70
40
27
16
10
7
1966
78
59
44
33
18
13
32
20
12
9
' 7
5
73
55
29
20
12
8
1967
63
56
33
23
11
47
27
17
13
8
5
63
43
30
20
10
8
1968
57
40
33
16
7
6
46
42
36
32
8
6
90
79
29
21
9
5
Percent
data
available
55
56
57
58
62
57
70
71
72
74
77
100
72
72
74
76
81
100
79
79
81
82
89
100
Percent of time concentration
is exceeded
0.01
56
51
40
36
62
53
50
43
0.1
44
40
34
32
32
32
44
40
29
36
34
27
1
33
30
27
25
16
15
14
14
26
24
18
16
25
25
21
19
10
21
21
20
20
18
9
9
8
8
7
13
13
12
11
9
16
16
15
15
13
30
15
15
14
14
13
6
6
6
6
6
9
9
8
8
8
12
12
12
12
12
50
10
10
10
10
10
12
5
5
5
5
5
5
6
6
6
7
7
7
10
10
10
11
11
11
70
6
7
7
7
7
3
4
4
4
4
4
4
5
5
6
9
9
9
9
9
90
3
3
4
5
6
2
2
2
3
3
2
2
3
4
4
7
7
8
8
9
o
o
m
i-
30
m
D
H
m
30
m
S
m
2
•A
H
O
C/J
O
>
33
O
CO
aStandard geometric deviation.
-------
CD
&
C.
CD
1
Table 4 (Continued). CARBON MONOXIDE CONCENTRATION (ppm) AT CAMP SITES, BY AVERAGING TIME AND FREQUENCY,
1962 THROUGH 1968
City and
averaging
time
PHILADELPHIA
5 min
1 hr
8hr
1 day
1 mo
1yr
ST. LOUIS
5 min
1 hr
8hr
1day
1 mo
lyr
SAN FRANCISCO
5 min
1 hr
8hr
1 day
1 mo
1yr
WASHINGTON
5 min
1 hr
8hr
1 day
1 mo
lyr
Annual
maxi-
mum
83
48
31
24
12
8
50
31
21
17
9
6
39
25
17
14
7
5
87
44
25
18
7
4
1962 through 1968
Geom.
mean
6.7
6.9
7.1
7.2
7.6
7.9
5.4
5.6
5.7
5.7
6.0
6.1
4.7
4.8
4.9
5.0
5.1
5.3
3.4
3.6
3.7
3.8
4.2
4.4
SGDa
1.77
1.66
1.56
1.50
1.30
1.00
1.65
1.56
1.48
1.tJ
1.26
1.00
1.62
1.53
1.46
1.41
1.25
1.00
2.10
1.93
1.78
1.70
1.41
1.00
Max
67
54
36
25
14
8
68
29
18
1 /
9
6
40
38
18
14
7
5
59
41
34
23
10
7
Min
43
35
23
14
9
6
45
25
12
9
6
5
38
22
14
10
6
5
29
25
17
11
5
3
Maximum for year
1962
51
47
36
23
30
25
19
14
7
1963
52
47
35
25
14
38
38
18
14
6
44
41
34
23
10
7
1964
43
37
27
21
13
7
45
25
18
17
9
6
40
22
14
10
7
5
29
28
18
13
6
6
1965
67
54
26
19
11
8
53
27
18
15
9
6
49
32
17
11
6
4
1966
47
43
34
20
10
7
68
29
18
12
8
6
47
38
22
15
5
3
1967
44
42
23
14
9
6
60
27
14
11
8
6
37
32
23
15
7
5
1968
49
35
26
23
11
8
47
26
12
9
6
5
59
27
21
14
7
3
Percent
data
available
58
58
59
60
62
71
86
87
88
89
95
100
67
68
68
69
67
50
71
71
72
73
76
86
Percent of time concentration
is exceeded
0.01
47
45
42
27
27
20
35
0.1
35
33
27
30
22
17
20
18
13
27
22
1
22
22
20
18
19
17
13
12-
14
13
11
9
27
17
15
13
10
13
13
12
12
10
10
10
9
9
8
9
8
8
7
6
8
8
8
8
7
30
9
9
9
9
8
7
7
7
7
6
6
6
6
6
6
5
5
5
5
5
50
7
7
7
7
7
7
5
5
5
6
5
6
5
5
5
5
5
5
4
4
4
4
4
4
70
5
5
5
6
6
4
4
4
5
5
4
4
4
4
5
3
3
3
3
3
90
3
3
3
4
5
2
2
3
3
4
2
2
3
3
4
1
2
2
2
2
aStandard geometric deviation.
-------
O)
O
O
m
r~
33
m
2
O
m
I
30
m
^
m
O
CO
D
>
33
O
CO
Table 5. HYDROCARBON CONCENTRATION (ppm) AT CAMP SITES, BY AVERAGING TIME AND FREQUENCY, 1962 THROUGH 1968
City and
averaging
time
CHICAGO
5 min
1 hr
8hr
1 day
1 mo
lyr
CINCINNATI
5 min
1 hr
8hr
1 day
1 mo
1yr
DENVER
5 min
1 hr
8hr
1 day
1 mo
1yr
LOS ANGELES
5 min
1 hr
8hr
1 day
1 mo
1yr
Annual
maxi-
mum
20
12
8
7
4
3
32
18
11
9
4
3
32
18
11
9
4
3
68
38
23
18
8
5
1962 through 1968
Geom.
mean
2.3
2.4
2.5
2.5
2.6
2.6
2.2
2.3
2.3
2.4
2.5
2.6
2.2
2.3
2.3
2.4
2.5
2.6
4.3
4.5
4.7
4.7
5.0
5.2
SGDa
1.62
1.53
1.46
1.41
1.25
1.00
1.84
1.72
1.61
1.54
1.33
1.00
1.84
1.72
1.61
1.54
1.33
1.00
1.87
1.74
1.63
1.56
1.34
1.00
Max
20
13
8
5
4
3
25
17
11
10
4
3
19
17
10
6
4
2
90
30
21
17
9
4
Min
14
8
6
5
3
2
12
9
6
4
2
2
18
13
6
5
3
2
90
30
21
17
9
4
Maximum for year
1962
17
10
8
5
4
3
15
11
7
6
3
1963
19
12
8
5
4
3
25
17
11
10
4
3
90
30
21
17
9
4
1964
20
8
6
5
3
3
20
16
11
8
3
3
1965
17
10
6
5
3
2
16
13
9
6
3
2
18
13
6
5
3
2
1966
14
11
7
5
3
2
12
9
6
4
3
2
19
15
9
6
3
2
1967
18
13
7
5
3
3
18
12
8
5
2
2
18
13
10
5
3
2
1968
17
12
7
5
3
2
18
14
8
5
3
2
18
17
9
6
4
2
Percent
data
available
78
78
80
81
88
100
74
74
75
75
80
86
79
80
81
83
90
100
85
85
86
87
100
100
Percent of time concentration
is exceeded
0.01
15
12
17
15
18
16
54
28
0.1
10
9
7
13
12
11
13
12
9
30
25
19
1
7
6
6
5
8
8
7
6
8
7
6
5
20
19
15
13
10
4
4
4
4
4
4
4
4
4
4
4
4
4
4
3
10
10
10
9
7
30
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
6
6
6
6
5
50
3
3
3
3
3
3
3
3
3
3
3
3
2
2
2
2
2
2
4
4
4
4
3
3
70
2
2
3
3
3
2
2
2
2
3
2
2
2
2
2
2
2
2
2
2
90
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
0
0
0
0
1
aStandard geometric deviation.
-------
c
CD
O
BJ_
I
Table 5 (Continued). HYDROCARBON CONCENTRATION (ppm) AT CAMP SITES, BY AVERAGING TIME AND FREQUENCY,
1962 THROUGH 1968
City and
averaging
time
PHILADELPHIA
5 min
1 hr
8hr
1 day
1 mo
lyr
ST. LOUIS
5 min
1 hr
8hr
1 day
1 mo
lyr
SAN FRANCISCO
5 min
1 hr
8hr
1 day
1 mo
1yr
WASHINGTON
5 min
1 hr
8hr
1 day
1 mo
1yr
Annual
maxi-
mum
20
12
8
7
4
3
28
16
10
8
4
3
24
14
9
7
4
3
28
16
10
8
4
3
1962 through 1968
Geom.
mean
2.3
2.4
2.5
2.5
2.6
2.6
2.2
2.3
2.4
2.4
2.5
2.6
2.3
2.4
2.4
2.4
2.5
2.6
2.2
2.3
2.4
2.4
2.5
2.6
SGDa
1.62
1.53
1.46
1.41
1.25
1.00
1.77
1.66
1.56
1.50
1.30
1.00
1.70
1.60
1.51
1.46
1.28
1.00
1.77
1.66
1.56
1.50
1.30
1.00
Max
17
13
8
6
3
2
20
16
13
9
4
3
17
14
9
8
4
3
20
17
13
8
3
3
Min
10
9
7
4
2
2
11
11
8
6
3
2
16
12
8
6
4
2
12
9
7
4
2
2
Maximum for year
1962
12
9
7
5
3
17
14
9
8
4
2
15
12
8
7
3
1963
15
12
7
6
3
2
17
12
8
6
4
3
20
17
13
8
3
2
1964
17
11
8
6
2
2
20
13
8
6
4
3
16
12
9
7
4
3
17
14
10
7
3
3
1965
10
9
7
5
2
2
15
13
10
7
3
2
12
9
7
4
3
2
1966
14
11
8
5
2
2
14
12
9
7
3
3
14
12
8
6
2
2
1967
14
13
7
6
2
2
11
11
10
8
4
3
15
15
11
5
3
2
1968
13
11
8
4
2
2
17
16
13
9
4
3
18
13
8
5
3
2
Percent
data
available
70
71
72
73
75
86
70
70
71
72
77
100
79
79
80
81
86
100
77
77
78
79
83
86
Percent of time concentration
is exceeded
0.01
12
11
16
15
14
12
15
14
0.1
9
9
7
12
11
11
11
10
9
12
11
9
1
6
6
5
5
8
8
8
7
7
7
6
6
7
7
6
5
10
4
4
3
3
3
5
5
5
4
4
4
4
4
4
3
3
3
3
3
3
30
3
3
3
3
3
3
3
3
3
4
3
3
3
3
3
3
3
3
3
3
50
2
2
2
2
2
2
3
3
3
3
3
3
2
2
2
3
2
2
2
2
2
2
2
2
70
2
2
2
2
2
2
2
3
3
3
2
2
2
2
2
2
2
2
2
2
90
1
1
2
2
2
2
2
2
2
2
1
1
1
1
2
1
1
2
2
2
aStandard geometric deviation.
-------
CO
Table 6. NITRIC OXIDE CONCENTRATION (ppm) AT CAMP SITES, BY AVERAGING TIME AND FREQUENCY, 1962 THROUGH 1968
City and
averaging
time
CHICAGO
5 min
1 hr
8hr
1 day
1 mo
1yr
CINCINNATI
5 min
1 hr
8hr
1 day
1 mo
1yr
DENVER
5 min
1 hr
8hr
1 day
1 mo
1yr
LOS ANGELES
5 min
1 hr
8hr
1 day
1 mo
1yr
Annual
maxi-
mum
1.45
0.77
0.46
0.35
0.15
0.10
3.83
1.25
0.50
0.31
0.07
0.03
1.84
0.74
0.35
0.24
0.07
0.04
3.84
1.54
0.72
0.49
0.15
0.08
1962 through 1968
Geom.
mean
0.077
0.081
0.084
0.086
0.092
0.096
0.014
0.017
0.019
0.021
0.027
0.032
0.023
0.025
0.028
0.029
0.034
0.037
0.045
0.050
0.055
0.058
0.067
0.075
SGDa
1.94
1.80
1.68
1.61
1.36
1.00
3.59
3.10
2.70
2.49
1.81
1.00
2.72
2.43
2.18
2.04
1.59
1.00
2.75
2.45
2.20
2.06
1.60
1.00
Max
0.97
0.91
0.49
0.36
0.17
0.10
1.46
1.38
0.86
0.37
0.10
0.04
0.68
0.61
0.33
0.23
0.08
0.04
2.11
1.42
0.60
0.46
0.25
0.08
Min
0.63
0.60
0.34
0.21
0.11
0.07
0.54
0.50
0.22
0.15
0.06
0.03
0.46
0.36
0.16
0.11
0.05
0.03
0.97
0.79
0.49
0.38
0.18
0.07
Maximum for year
1962
0.66
0.61
0.41
0.36
0.17
0.10
0.60
0.58
0.38
0.29
0.06
0.03
2.11
1.42
0.60
0.46
0.25
0.08
1963
0.63
0.60
0.39
0.35
0.15
0.10
0.54
0.50
0.22
0.15
0.06
0.03
0.97
0.79
0.49
0.38
0.18
0.08
1964
0.97
0.91
0.49
0.35
0.16
0.10
0.68
0.65
0.34
O.I,
0.10
0.04
1.32
1.24
0.60
0.44
0.19
0.07
1965
0.67
0.62
0.34
0.28
0.13
0.10
0.63
0.62
0.40
0.31
0.07
0.03
0.46
0.40
0.16
0.14
0.05
0.03
1966
0.74
0.64
0.42
0.34
0.14
0.10
1.18
1.00
0.46
0.37
0.07
0.04
0.59
0.54
0.30
0.23
0.08
0.04
1967
0.69
0.63
0.41
0.26
0.15
0.08
1.46
1.38
0.86
0.36
0.06
0.03
0.48
0.36
0.19
0.11
0.07
0.04
1968
0.66
0.61
0.40
0.21
0.11
0.07
1.26
1.02
0.58
0.34
0.08
0.68
0.61
0.33
0.21
0.07
0.04
Percent
data
available
79
79
83
86
94
100
70
71
74
77
80
86
68
68
72
74
79
100
72
72
78
81
92
100
Percent of time concentration is exceeded
0.01
0.67
0.64
1.08
0.98
0.55
0.52
1.23
1.12
0.1
0.52
0.50
0.40
0.57
0.55
0.40
0.42
0.39
0.24
0.85
0.80
0.55
1
0.33
0.32
0.27
0.23
0.29
0.29
0.24
0.19
0.23
0.22
0.17
0.13
0.54
0.53
0.41
0.36
10
0.18
0.18
0.17
0.15
0.13
0.09
0.09
0.08
0.08
0.06
0.09
0.09
0.08
0.08
0.07
0.23
0.23
0.21
0.19
0.16
30
0.11
0.11
0.11
0.11
0.11
0.03
0.03
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.05
0.08
0.08
0.09
0.10
0.09
50
0.08
0.08
0.08
0.09
0.08
0.10
0.02
0.02
0.02
0.03
0.03
0.03
0.02
0.02
0.02
0.03
0.03
0.04
0.03
0.03
0.04
0.05
0.06
0.07
70
0.05
0.05
0.06
0.07
0.07
0.01
0.01
0.01
0.02
0.02
0.01
0.01
0.02
0.02
0.02
0.01
0.01
0.02
0.03
0.03
90
0.02
0.02
0.03
0.04
0.06
0.00
0.00
0.01
0.01
0.02
0.00
0.00
0.01
0.01
0.01
0.00
0.00
0.01
0.01
0.02
o
D
m
m
r-
>
Z
O
>
30
D
m
1
m
m
Z
V)
O
V)
>
D
33
D
in
aStandard geometric deviation.
-------
Table 6 (Continued). NITRIC OXIDE CONCENTRATION (ppm) AT CAMP SITES, BY AVERAGING TIME AND FREQUENCY,
1962 THROUGH 1968
CD
O
2L
1
City and
averaging
time
PHILADELPHIA
5 min
1 hr
8hr
1 day
1 mo
1yr
ST. LOUIS
5 min
1 hr
8hr
1 day
1 mo
lyr
SAN FRANCISCO
5 min
1 hr
8hr
1 day
1 mo
1yr
WASHINGTON
5 min
1 hr
8hr
1 day
1 mo
lyr
Annual
maxi-
mum
6.54
2.12
0.84
0.52
0.12
0.05
1.27
0.55
0.28
0.20
0.07
0.04
2.23
1.03
0.54
0.39
0.14
0.08
4.64
1.46
0.56
0.34
0.07
0.03
1962 through 1968
Geom.
mean
0.023
0.028
0.032
0.035
0.044
0.053
0.024
0.026
0.028
0.030
0.033
0.036
0.057
0.061
0.065
0.067
0.075
0.081
0.013
0.016
0.019
0.021
0.027
0.033
SGDa
3.61
3.12
2.71
2.50
1.81
1.00
2.46
2.22
2.01
1.90
1.52
1.00
2.30
2.09
1.91
1.81
1.47
1.00
3.78
3.25
2.81
2.59
1.85
1.00
Max
1.98
1.87
1.00
0.58
0.13
0.06
0.84
0.75
0.26
0.25
0.07
0.04
1.64
1.30
0.52
0.32
0.13
0.09
1.26
1.14
0.55
0.41
0.10
0.04
Min
1.03
0.89
0.52
0.25
0.07
0.04
0.44
0.37
0.17
0.12
0.05
0.03
0.50
0.42
0.26
0.15
0.06
0.09
0.68
0.62
0.39
0.21
0.06
0.03
Maximum for year
1962
1.58
1.57
0.93
0.46
0.08
0.04
0.50
0.42
0.26
0.15
0.06
0.68
0.65
0.39
0.22
0.07
0.03
1963
1.72
1.51
0.91
0.58
0.08
0.05
1.64
1.30
0.52
0.32
0.11
0.09
0.73
0.68
0.51
0.26
0.08
0.04
1964
1.35
1.15
0.52
0.25
0.09
0.04
0.84
0.75
0.22
0.14
0.05
0.03
0.81
0.63
0.41
0.23
0.13
0.09
1.03
0.88
0.54
0.29
0.07
0.03
1965
1.03
0.89
0.53
0.31
0.07
0.04
0.52
0.37
0.17
0.12
0.06
0.03
0.74
0.62
0.39
0.21
0.06
0.03
1966
1.98
1.87
1.00
0.48
0.13
0.06
0.61
0.57
0.26
0.25
0.05
0.03
1.15
1.02
0.55
0.41
0.09
0.04
1967
1.74
1.49
0.72
0.34
0.10
0.06
0.45
0.41
0.23
0.17
0.07
0.04
1.26
1.14
0.55
0.36
0.08
0.04
1968
1.68
1.44
0.87
0.37
0.12
0.06
0.44
0.41
0.18
0.13
0.05
0.03
0.89
0.69
0.43
0.31
0.10
0.04
Percent
data
available
75
76
80
82
87
100
76
76
81
84
87
100
72
72
77
77
83
67
79
80
84
86
93
100
Percent of time concentration is exceeded
0.01
1.60
1.49
0.51
0.41
1.25
0.87
0.88
0.1
0.95
0.93
0.72
0.33
0.31
0.22
0.64
0.60
0.43
0.62
0.48
1
0.37
0.36
0.31
0.25
0.19
0.18
0.14
0.10
0.43
0.42
0.31
0.22
0.42
0.33
0.27
0.20
10
0.12
0.12
0.11
0.10
0.09
0.08
0.08
0.07
0.07
0.05
0.18
0.18
0.18
0.15
0.11
0.10
0.09
0.09
0.08
0.07
30
0.05
0.05
0.06
0.06
0.06
0.04
0.04
0.04
0.04
0.04
0.09
0.09
0.09
0.10
0.09
0.03
0.03
0.04
0.04
0.04
50
0.03
0.03
0.03
0.04
0.05
0.04
0.02
0.02
0.02
0.03
0.03
0.03
0.05
0.05
0.06
0.07
0.08
0.09
0.01
0.01
0.02
0.02
0.03
0.03
70
0.01
0.01
0.02
0.02
0.03
0.01
0.01
0.01
0.02
0.03
0.03
0.03
0.03
0.05
0.06
0.01
0.01
0.01
0.01
0.02
90
0.00
0.00
0.01
0.01
0.02
0.00
0.00
0.01
0.01
0.02
0.01
0.01
0.01
0.02
0.05
0.00
0.00
0.00
0.01
0.01
aStandard geometric deviation.
CO
-------
N)
O
Table 7. NITROGEN DIOXIDE CONCENTRATION (ppm) AT CAMP SITES, BY AVERAGING TIME AND FREQUENCY,
1962 THROUGH 1968
City and
averaging
time
CHICAGO
5 min
1 hr
8hr
1 day
1 mo
1yr
CINCINNATI
5 min
1 hr
8hr
1 day
1 mo
1yr
DENVER
5 min
1 hr
8hr
1 day
1 mo
1yr
LOS ANGELES
5 min
1 hr
8hr
1 day
1 mo
1yr
Annual
maxi-
mum
0.45
0.26
0.17
0.13
0.07
0.04
0.38
0.22
0.14
0.11
0.05
0.03
0.47
0.26
0.16
0.12
0.05
0.03
1.48
0.69
0.36
0.26
0.09
0.05
1962 through 1968
Geom.
mean
0.037
0.039
0.040
0.040
0.042
0.044
0.030
0.031
0.032
0.032
0.034
0.035
0.029
0.030
0.031
0.032
0.033
0.035
0.038
0.041
0.044
0.045
0.050
0.054
SGDa
1.76
1.65
1.55
1.49
1.30
1.00
1.79
1.67
1.57
1.51
1.31
1.00
1.89
1.76
1.64
1.57
1.34
1.00
2.30
2.09
1.91
1.81
1.47
1.00
Max
0.79
0.47
0.22
0.15
0.08
0.06
1.19
0.56
0.16
0.10
0.05
0.04
0.38
0.33
0.18
0.12
0.05
0.04
1.27
0.68
0.37
0.26
0.10
0.06
Min
0.21
0.18
0.12
0.09
0.05
0.04
0.21
0.17
0.10
0.07
0.04
0.03
0.30
0.25
0.12
0.08
0.04
0.03
0.57
0.52
0.27
0.20
0.07
0.05
Maximum for year
1962
0.26
0.22
0.16
0.12
0.06
0.04
0.26
0.23
0.12
0.07
0.04
0.03
1963
0.23
0.21
0.17
0.13
0.06
0.04
0.30
0.25
0.14
0.09
0.04
0.03
0.57
0.52
0.37
0.20
0.10
0.06
1964
0.79
0.47
0.22
0.15
0.07
0.05
1.00
0.34
0.14
0.10
0.05
0.03
1.27
0.68
0.27
0.26
0.07
0.05
1965
0.21
0.18
0.15
0.09
0.05
0.04
0.21
0.17
0.10
0.08
0.04
0.03
0.31
0.28
0.14
0.09
0.04
0.04
1966
0.35
0.31
0.20
0.15
0.08
0.06
0.30
0.24
0.13
0.09
0.05
0.04
0.30
0.27
0.18
0.09
0.04
0.03
1967
0.29
0.25
0.15
0.11
0.07
0.05
0.70
0.24
0.13
0.07
0.04
0.03
0.37
0.33
0.17
0.08
0.04
0.04
1968
0.29
0.18
0.12
0.10
0.06
0.05
1.19
0.56
0.16
0.10
0.05
0.03
0.38
0.25
0.12
0.12
0.05
0.04
Percent
data
available
79
80
84
87
93
100
79
79
83
86
94
100
71
72
76
79
81
100
63
63
67
71
79
100
Percent of time concentration is exceeded
0.01
0.28
0.25
0.26
0.24
0.31
0.27
0.66
0.55
0.1
0.18
0.18
0.16
0.16
0.15
0.12
0.18
0.17
0.13
0.44
0.40
0.27
1
0.13
0.12
0.12
0.10
0.09
0.09
0.08
0.07
0.11
0.10
0.09
0.08
0.25
0.24
0.23
0.18
10
0.07
0.07
0.07
0.07
0.06
0.05
0.05
0.05
0.05
0.04
0.06
0.06
0.05
0.05
0.04
0.12
0.11
0.11
0.10
0.09
30
0.05
0.05
0.05
0.05
0.05
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.06
0.06
0.06
0.07
0.05
50
0.04
0.04
0.04
0.04
0.04
0.04
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.04
0.04
0.04
0.05
0.05
0.04
0.05
70
0.03
0.03
0.04
0.04
0.04
0.02
0.02
0.02
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.04
0.04
90
0.02
0.02
0.03
0.03
0.03
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.03
0.01
0.01
0.02
0.02
0.03
O
O
m
r~
33
m
O
O
m
>
OT
C
33
m
2
m
Z
V)
33
O
C/5
aStandard geometric deviation.
-------
a
CD
I
Table 7 (Continued). NITROGEN DIOXIDE CONCENTRATION (ppm) AT CAMPSITES, BY AVERAGING TIME AND FREQUENCY,
1962 THROUGH 1968
City and
averaging
time
PHILADELPHIA
5 min
1 hr
8hr
1 day
1 mo
1yr
ST. LOUIS
5 min
1 hr
8hr
1 day
1 mo
1yr
SAN FRANCISCO
5 min
1 hr
8hr
1 day
1 mo
1yr
WASHINGTON
5 min
1 hr
8hr
1 day
1 mo
1yr
Annual
maxi-
mum
0.52
0.28
0.17
0.13
0.06
0.04
0.36
0.20
0.12
0.09
0.04
0.03
0.87
0.46
0.27
0.20
0.09
0.05
0.38
0.22
0.14
0.11
0.05
0.03
1962 through 1968
Geom.
mean
0.028
0.030
0.031
0.031
0.033
0.035
0.021
0.022
0.023
0.024
0.025
0.026
0.041
0.044
0.046
0.047
0.050
0.053
0.030
0.031
0.032
0.032
0.034
0.035
SGDa
1.94
1.80
1.67
1.60
1.36
1.00
1.90
1.77
1.65
1.58
1.35
1.00
2.00
1.85
1.71
1.64
1.38
1.00
1.79
1.67
1.57
1.51
1.31
1.00
Max
0.44
0.32
0.19
0.14
0.06
0.04
0.31
0.22
0.14
0.12
0.04
0.04
0.52
0.41
0.31
0.18
0.08
0.06
0.37
0.30
0.14
0.10
0.05
0.05
Min
0.22
0.20
0.10
0.07
0.04
0.04
0.17
0.13
0.08
0.05
0.03
0.02
0.38
0.27
0.16
0.10
0.04
0.03
0.19
0.18
0.09
0.07
0.04
0.03
Maximum for year
1962
0.24
0.22
0.14
0.10
0.05
0.04
0.50
0.27
0.16
0.10
0.04
0.03
0.37
0.30
0.10
0.07
0.04
0.03
1963
0.36
0.32
0.19
0.14
0.06
0.04
0.38
0.33
0.23
0.13
0.06
0.05
0.24
0.22
0.11
0.09
0.04
0.03
1964
0.37
0.26
0.14
0.10
0.05
0.04
0.31
0.22
0.14
0.12
0.04
0.04
0.52
0.41
0.31
0.18
0.08
0.06
0.24
0.23
0.14
0.10
0.04
0.04
1965
0.24
0.20
0.10
0.07
0.04
0.04
0.28
0.13
0.08
0.05
0.03
0.03
0.25
0.23
0.10
0.07
0.04
0.03
1966
0.29
0.23
0.15
0.10
0.05
0.04
0.21
0.20
0.14
0.10
0.04
0.03
0.19
0.18
0.09
0.07
0.04
0.03
1967
0.44
0.23
0.13
0.10
0.05
0.04
0.17
0.16
0.09
0.06
0.03
0.03
0.24
0.21
0.14
0.09
0.05
0.04
1968
0.22
0.20
0.12
0.09
0.05
0.04
0.20
0.18
0.09
0.05
0.04
0.02
0.26
0.24
0.13
0.08
0.05
0.05
Percent
data
available
79
79
84
86
90
100
81
81
87
89
92
100
70
70
75
75
83
100
79
79
84
86
95
100
Percent of time concentration is exceeded
0.01
0.25
0.23
0.21
0.20
0.43
0.38
0.22
0.21
0.1
0.18
0.18
0.13
0.13
0.13
0.11
0.31
0.29
0.23
0.16
0.15
0.11
1
0.11
0.11
0.10
0.08
0.08
0.08
0.07
0.07
0.18
0.18
0.16
0.12
0.10
0.10
0.09
0.08
10
0.07
0.07
0.06
0.06
0.05
0.05
0.05
0.05
0,04
0.04
0.08
0.08
0.08
0.07
0.07
0.06
0.06
0.06
0.06
0.05
30
0.04
0.04
0.05
0.05
0.04
0.03
0.03
0.03
0.03
0.03
0.06
0.06
0.06
0.06
0.05
0.04
0.04
0.04
0.04
0.04
50
0.03
0.04
0.04
0.04
0.04
0.04
0.03
0.03
0.03
0.03
0.03
0.03
0.04
0.04
0.04
0.04
0.05
0.03
0.03
0.03
0.03
0.04
0.04
0.03
70
0.03
0.03
0.03
0.03
0.03
0.02
0.02
0.02
0.02
0.02
0.03
0.03
0.03
0.03
0.04
0.03
0.03
0.03
0.03
0.03
90
0.02
0.02
0.02
0.02
0.03
0.01
0.01
0.01
0.01
0.02
0.01
0.01
0.01
0.02
0.02
0.02
0.02
0.02
0.02
0.03
ro
aStandard geometric deviation.
-------
ro
Ni
Table 8. NITROGEN OXIDES CONCENTRATION (ppm) AT CAMP SITES, BY AVERAGING TIME AND FREQUENCY,
1962 THROUGH 1968
City and
averaging
time
CHICAGO
5 min
1 hr
8hr
1 day
1 mo
1yr
CINCINNATI
5 min
1 hr
8hr
1 day
1 mo
1yr
DENVER
5 min
1 hr
8hr
1 day
1 mo
1yr
LOS ANGELES
5 min
1 hr
8hr
1 day
1 mo
1yr
Annual
maxi-
mum
1.43
0.85
0.55
0.44
0.22
0.15
2.83
1.18
0.57
0.39
0.12
0.06
1.78
0.84
0.45
0.33
0.12
0.07
3.69
1.68
0.88
0.63
0.22
0.13
1962 through 1968
Geom
mean
0.128
0.132
0.136
0.138
0.144
0.149
0.041
0.045
0.049
0.051
0.059
0.065
0.052
0.055
0.059
0.060
0.066
0.071
0.088
0.095
0.101
0.105
0.116
0.126
SGDa
1.73
1.62
1.53
1.48
1.29
1.00
2.62
2.35
2.12
1.99
1.56
1.00
2.24
2.04
1.87
1.78
1.45
1.00
2.34
2.12
1.94
1.84
1.48
1.00
Max
1.12
1.06
0.62
0.50
0.22
0.16
1.51
1.42
0.90
0.46
0.12
0.08
0.80
0.72
0.44
0.31
0.13
0.07
1.49
1.39
0.78
0.55
0.28
0.13
Min
0.72
0.68
0.41
0.30
0.15
0.12
0.49
0.45
0.29
0.21
0.09
0.06
0.61
0.56
0.27
0.17
0.09
0.06
1.12
1.07
0.71
0.54
0.23
Maximum for year
1962 1963
0.78 0.72
0.69 0.68
0.54 0.51
0.42 0.43
0.21 0.18
0.14 0.14
0.69 0.49
0.68 0.45
0.50 0.29
0.37 0.21
0.09 0.10
0.06 0.06
1.12
1.07
0.71
0.54
0.28
0.12 0.13
1964
1.12
1.06
0.62
0.50
0.22
0.15
1.02
0.73
0.51
0.39
0.12
0.07
1.49
1.39
0.78
0.55
0.23
0.12
1965
0.74
0.68
0.41
0.34
0.17
0.14
0.74
0.73
0.51
0.39
0.12
0.07
0.61
0.56
0.27
0.22
0.09
0.06
1966
0.86
0.75
0.52
0.44
0.19
0.16
1.35
1.22
0.67
0.46
0.11
0.08
0.68
0.62
0.36
0.28
0.13
0.07
1967
0.81
0.74
0.46
0.31
0.19
0.13
1.51
1.42
0.90
0.39
0.10
0.06
0.62
0.59
0.33
0.17
0.11
1968
0.78
0.73
0.49
0.30
0.15
0.12
1.26
0.95
0.46
0.32
0.11
0.80
0.72
0.44
0.31
0.13
Percent
data
available
73
74
78
81
89
100
65
66
69
72
74
86
61
62
65
68
63
50
61
61
64
68
79
100
Percent of time concentration is exceeded
0.01
0.79
0.75
1.20
1.03
0.64
0.60
1.28
1.09
0.1
0.62
0.59
0.49
0.66
0.63
0.49
0.53
0.50
0.33
0.97
0.97
0.71
1
0.40
0.39
0.34
0.30
0.35
0.34
0.29
0.23
0.31
0.30
0.24
0.20
0.67
0.67
0.53
0.48
10
0.23
0.23
0.22
0.20
0.17
0.13
0.13
0.12
0.12
0.10
0.14
0.14
0.13
0.13
0.12
0.31
0.31
0.29
0.26
0.23
30
0.16
0.17
0.16
0.16
0.15
0.07
0.07
0.07
0.07
0.07
0.08
0.08
0.08
0.08
0.09
0.14
0.14
0.14
0.15
0.11
50
0.13
0.13
0.13
0.13
0.13
0.14
0.05
0.05
0.05
0.06
0.06
0.06
0.05
0.06
0.06
0.06
0.06
0.06
0.08
0.08
0.09
0.09
0.09
0.12
70
0.09
0.09
0.10
0.11
0.12
0.04
0.04
0.04
0.04
0.05
0.04
0.04
0.05
0.05
0.05
0.05
0.05
0.05
0.06
0.08
90
0.06
0.06
0.07
0.09
0.10
0.02
0.02
0.03
0.03
0.05
0.02
0.02
0.03
0.04
0.04
0.02
0.02
0.03
0.04
0.05
o
D
m
r~
3D
m
r™
O
s
m
c
30
m
^
m
z
CO
CO
>
z
0
>
30
D
CO
aStandard geometric deviation.
-------
I
CD
O
03
CD
Table 8(Continued). NITROGEN OXIDES CONCENTRATION (ppm) AT CAMP SITES, BY AVERAGING TIME AND FREQUENCY,
1962 THROUGH 1968
City and
averaging
time
PHILADELPHIA
5 min
1 hr
8hr
1 day
1 mo
1yr
ST. LOUIS
5 min
1 hr
8hr
1 day
1 mo
1yr
SAN FRANCISCO
5 min
1 hr
8hr
1 day
1 mo
1yr
WASHINGTON
5 min
1 hr
8hr
1 day
1 mo
1yr
Annual
maxi-
mum
4.80
1.92
0.90
0.61
0.18
0.09
1.18
0.60
0.34
0.25
0.10
0.06
1.96
1.05
0.62
0.48
0.21
0.13
3.44
1.37
0.64
0.43
0.13
0.07
1962 through 1968
Geom.
mean
0.056
0.063
0.069
0.072
0.084
0.094
0.047
0.050
0.052
0.054
0.058
0.062
0.105
0.110
0.115
0.117
0.125
0.131
0.039
0.044
0.048
0.051
0.059
0.066
SGDa
2.75
2.45
2.20
2.06
1.60
1.00
2.08
1.91
1.77
1.69
1.40
1.00
1.94
1.80
1.68
1.61
1.36
1.00
2.77
2.46
2.21
2.07
1.60
1.00
Max
2.16
2.02
1.11
0.70
0.18
0.10
1.02
0.92
0.39
0.35
0.09
0.07
1.69
1.35
0.56
0.36
0.20
0.14
1.47
1.30
0.69
0.45
0.14
0.09
Min
1.14
0.97
0.45
0.28
0.10
0.08
0.52
0.44
0.21
0.14
0.07
0.05
0.58
0.49
0.31
0.23
0.10
0.14
0.79
0.68
0.41
0.27
0.10
0.06
Maximum for year
1962
1.81
1.79
1.06
0.56
0.13
0.08
0.58
0.49
0.31
0.23
0.10
0.79
0.74
0.43
0.27
0.11
0.06
1963
1.93
1.69
1.06
0.70
0.12
1.69
1.35
0.56
0.36
0.16
0.14
0.86
0.76
0.58
0.35
0.13
0.07
1964
1.50
1.27
0.45
0.28
0.10
0.08
1.02
0.92
0.26
0.25
0.08
0.07
0.91
0.76
0.52
0.31
0.20
0.14
1.16
1.00
0.69
0.38
0.12
0.07
1965
1.14
0.97
0.60
0.38
0.10
0.08
0.59
0.44
0.21
0.14
0.07
0.05
0.84
0.71
0.45
0.27
0.10
0.07
1966
2.16
2.02
1.11
0.58
0.18
0.10
0.72
0.66
0.39
0.35
0.09
0.07
0.85
0.68
0.41
0.30
0.12
0.07
1967
1.87
1.62
0.79
0.42
0.15
0.10
0.52
0.48
0.28
0.22
0.08
0.06
1.47
1.30
0.56
0.45
0.11
0.08
1968
1.82
1.61
0.98
0.44
0.15
0.10
0.52
0.46
0.21
0.15
0.08
0.06
1.00
0.78
0.49
0.38
0.14
0.09
Percent
data
available
70
71
75
76
81
83
73
73
78
82
85
100
65
65
69
68
75
67
71
71
75
78
86
100
Percent of time concentration is exceeded
0.01
1.81
1.69
0.61
0.55
1.31
0.92
1.00
0.97
0.1
1.04
1.00
0.80
0.39
0.37
0.27
0.72
0.68
0.49
0.70
0.71
0.54
1
0.42
0.41
0.36
0.29
0.24
0.23
0.18
0.15
0.52
0.51
0.41
0.30
0.38
0.38
0.31
0.25
10
0.17
0.17
0.16
0.15
0.12
0.12
0.12
0.11
0.10
0.07
0.26
0.26
0.25
0.22
0.16
0.14
0.14
0.13
0.12
0.10
30
0.10
0.10
0.10
0.10
0.09
0.07
0.07
0.07
0.07
0.07
0.15
0.15
0.15
0.15
0.14
0.07
0.07
0.07
0.08
0.08
50
0.07
0,07
0.07
0.08
0.08
0.08
0.05
0.05
0.06
0.06
0.06
0.06
0.10
0.10
0.11
0.12
0.13
0.14
0.05
0.05
0.05
0.06
0.06
0.07
70
0.05
0.05
0.05
0.06
0.07
0.03
0.03
0.04
0.04
0.05
0.06
0.06
0.07
0.09
0.10
0.03
0.04
0.04
0.05
0.05
90
0.03
0.03
0.03
0.04
0.06
0.02
0.02
0.02
0.03
0.04
0.03
0.03
0.03
0.06
0.07
0.02
0.02
0.03
0.03
0.04
IV}
CO
3Standard geometric deviation.
-------
O
D
m
i—
30
m
JO
D
m
>
CO
c
30
m
S
m
2
O
OT
30
O
C/J
Table 9. OXIDANT CONCENTRATION (ppm) AT CAMP SITES, BY AVERAGING TIME AND FREQUENCY, 1962 THROUGH 1968
City and
averaging
time
CHICAGO
5 min
1 hr
8hr
1 day
1 mo
1 yr
CINCINNATI
5 min
1 hr
8hr
1 day
1 mo
1 yr
DENVER
5 min
1 hr
8hr
1 day
1 mo
1yr
LOS ANGELES
5 min
1 hr
8hr
1 day
1 mo
1yr
Annual
maxi-
mum
0.36
0.20
0.12
0.09
0.04
0.03
0.46
0.24
0.14
0.10
0.04
0.03
0.47
0.26
0.16
0.12
0.05
0.03
1.47
0.62
0.31
0.21
0.07
0.04
1962 through 1968
Geom.
mean
0.021
0.022
0.023
0.024
0.025
0.026
0.021
0.022
0.023
0.023
0.025
0.026
0.029
0.030
0.031
0.032
0.033
0.035
0.024
0.026
0.028
0.029
0.033
0.037
SGDa
1.90
1.77
1.65
1.58
1.35
1.00
2.03
1.87
1.73
1.66
1.39
1.00
1.89
1.76
1.64
1.57
1.34
1.00
2.56
2.30
2.08
1.96
1.55
1.00
Max
0.47
0.23
0.14
0.11
0.05
0.03
0.32
0.26
0.16
0.10
0.06
0.03
0.43
0.26
0.13
0.09
0.04
0.03
1.40
0.49
0.31
0.16
0.07
i
Min
0.17
0.12
0.08
0.03
0.01
0.02
0.13
0.12
0.08
0.05
0.03
0.01
0.26
0.21
0.12
0.07
0.03
0.03
0.53
0.41
0.25
0.1-3
0.06
Maximum for year
I962b
0.25
0.23
0.09
0.07
0.01
0.20
0.14
0.10
0.06
0.03
0.01
0.53
0.49
0.31
0.16
0.06
1963b
0.24
0.21
0.08
0.03
0.01
0.24
0.20
0.14
0.09
0.04
0.02
1.40
0.49
0.25
0.14
0.06
1964
0.17
0.12
0.09
0.08
0.05
0.03
0.32
0.26
0.16
0.09
0.06
0.03
0.88
0.41
0.26
0.13
0.07
1965
0.19
0.13
0.10
0.08
0.04
0.03
0.19
0.17
0.12
0.10
0.04
0.03
1966
0.23
0.19
0.12
0.08
0.03
0.02
0.13
0.12
0.08
0.06
0.04
0.30
0.23
0.13
0.07
0.04
0.03
1967
0.21
0.16
0.12
0.08
0.04
0.03
0.25
0.20
0.13
0.09
0.05
0.03
0.26
0.21
0.12
0.09
0.03
1968
0.47
0.18
0.14
0.11
0.04
0.02
0.19
0.14
0.10
0.05
0.03
0.43
0.26
0.13
0.08
0.04
Percent
data
available
60
61
66
68
75
100
59
59
63
65
60
60
54
55
59
62
53
33
47
69
53
66
28
0
Percent of time concentration is exceeded
0.01
0.19
0.16
0.20
0.19
0.25
0.23
0.52
0.47
0.1
0.14
0.13
0.12
0.15
0.15
0.13
0.19
0.17
0.12
0.38
0.34
0.25
1
0.09
0.09
0.08
0.07
0.11
0.10
0.09
0.07
0.11
0.11
0.09
0.07
0.23
0.21
0.19
0.12
10
0.05
0.05
0.05
0.05
0.04
0.06
0.06
0.05
0.05
0.04
0.06
0.06
0.06
0.05
0.04
0.12
0.10
0.12
0.07
0.06
30
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.04
0.04
0.04
0.03
0.04
0.03
0.04
0.04
0.05
0.06
0.06
50
0.02
0.02
0.02
0.03
0.03
0.02
0.02
0.02
0.02
0.03
0.03
0.03
0.02
0.02
0.03
0.03
0.03
0.03
0.02
0.02
0.03
0.04
0.06
0.06
70
0.01
0.01
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0..02
0.01
0.01
0.02
0.03
0.04
90
0.00
0.00
0.00
0.01
0.01
0.01
0.01
0.01
0.01
0.02
0.01
0.01
0.01
0.01
0.01
0.00
0.00
0.01
0.01
0.02
Standard geometric deviation.
Sulfur dioxide interference caused low concentration readings for oxidant in
1962 and 1963. This fact shows especially for maximum concentrations for
averaging times of 1 month and 1 year. Data for these 2 years were not used for the
frequency distributions above, except in Los Angeles and San Francisco, where the
interference was much less serious. Interference was controlled after 1963.
-------
I
CD
O
CD
Table 9(Continued). OXIDANT CONCENTRATION (ppm) AT CAMP SITES, BY AVERAGING TIME AND FREQUENCY,
1962 THROUGH 1968
City and
averaging
time
PHILADELPHIA
5 min
1 hr
8hr
1 day
1 mo
1yr
ST. LOUIS
5 min
1 hr
8hr
1 day
1 mo
1 yr
SAN FRANCISCO
5 min
1 hr
8hr
1 day
1 mo
1 yr
WASHINGTON
5 min
1 hr
8hr
1 day
1 mo
1yr
Annual
maxi-
mum
0.93
0.41
0.21
0.15
0.05
0.03
0.43
0.24
0.15
0.12
0.05
0.03
0.54
0.24
0.13
0.09
0.03
0.02
0.46
0.24
0.14
0.10
0.04
0.03
1962 through 1968
Geom.
mean
0.018
0.020
0.021
0.022
0.025
0.027
0.029
0.030
0.031
0.032
0.034
0.035
0.012
0.013
0.014
0.015
0.017
0.018
0.021
0.022
0.023
0.023
0.025
0.026
SGDa
2.45
2.21
2.01
1.89
1.51
1.00
1.84
1.72
1.61
1.54
1.33
1.00
2.35
2.13
1.94
1.84
1.49
1.00
2.03
1.87
1.73
1.66
1.39
1.00
Max
0.60
0.52
0.35
0.18
0.06
0.03
0.62
0.35
0.14
0.10
0.06
0.04
0.42
0.26
0.16
0.09
0.04
0.02
0.32
0.26
0.17
0.11
0.04
0.03
Min
0.12
0.10
0.08
0.05
0.02
0.01
0.25
0.20
0.08
0.05
0.03
0.02
0.29
0.17
0.10
0.05
0.03
0.02
0.17
0.13
0.10
0.06
0.03
0.01
Maximum for year
I962b
0.12
0.10
0.08
0.05
0.02
0.01
0.32
0.26
0.16
0.09
0.03
0.02
0.17
0.13
0.10
0.06
0.03
0.01
1963b
0.13
0.11
0.08
0.05
0.02
0.01
0.29
0.17
0.10
0.08
0.04
0.02
0.25
0.22
0.16
0.08
0.03
0.01
1964
0.25
0.21
0.14
0.09
0.04
0.02
0.42
0.17
0.11
0.05
0.03
0.02
0.19
0.18
0.11
0.08
0.04
0.03
1965
0.25
0.21
0.14
0.09
0.04
0.03
0.62
0.35
0.12
0.07
0.04
0.03
0.24
0.21
0.12
0.09
0.04
0.03
1966
0.60
0.52
0.35
0.18
0.06
0.03
0.25
0.22
0.11
0.09
0.06
0.04
0.22
0.16
0.12
0.10
0.04
0.03
1967
0.29
0.17
0.13
0.08
0.05
0.03
0.27
0.20
0.14
0.10
0.05
0.04
0.32
0.26
0.17
0.11
0.04
0.03
1968
0.31
0.21
0.13
0.08
0.03
0.37
0.23
0.08
0.05
0.03
0.02
0.29
0.25
0.13
0.10
0.04
0.03
Percent
data
available
72
72
78
79
89
100
69
70
75
79
79
100
65
65
69
69
72
100
75
76
80
83
89
100
Percent of time concentration is exceeded
0.01
0.51
0.44
0.32
0.23
0.26
0.25
0.20
0.20
0.1
0.24
0.23
0.18
0.17
0.16
0.12
0.15
0.14
0.11
0.15
0.15
0.12
1
0.13
0.13
0.11
0.08
0.10
0.10
0.09
0.07
0.07
0.07
0.06
0.06
0.11
0.11
0.10
0.07
10
0.06
0.06
0.05
0.05
0.04
0.06
0.06
0.06
0.05
0.04
0.04
0.04
0.03
0.03
0.02
0.06
0.06
0.06
0.05
0.04
30
0.03
0.03
0.03
0.03
0.03
0.04
0.04
0.04
0.04
0.04
0.02
0.02
0.02
0.02
0.02
0.03
0.03
0.03
0.04
0.03
50
0.02
0.02
0.02
0.02
0.03
0.02
0.03
0.03
0.03
0.03
0.03
0.03
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.03
0.03
0.03
70
0.01
0.01
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.02
0.02
0.02
90
0.00
0.00
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.02
0.00
0.00
0.01
0.01
0.01
0.00
0.00
0.01
0.01
0.01
NJ
"Standard geometric deviation.
Sulfur dioxide interference caused low concentration readings for oxidant in
1962 and 1963. This fact shows especially for maximum concentrations for
averaging times of 1 month and 1 year. Data for these 2 years were not used for the
frequency distributions above, except in Los Angeles and San Francisco, where the
interference was much less serious. Interference was controlled after 1963.
-------
O)
Table 10. SULFUR DIOXIDE CONCENTRATION (ppm) AT CAMP SITES, BY AVERAGING TIME AND FREQUENCY,
1962 THROUGH 1968
City and
averaging
time
CHICAGO
5 min
1 hr
8hr
1 day
1 mo
1yr
CINCINNATI
5 min
1 hr
8hr
1 day
1 mo
1yr
DENVER
5 min
1 hr
8hr
1 day
1 mo
1yr
LOS ANGELES
5 min
1 hr
8hr
1 day
1 mo
1 yr
Annual
maxi-
mum
3.27
1.58
0.86
0.63
0.24
0.14
1.68
0.65
0.30
0.20
0.06
0.03
0.47
0.22
0.12
0.09
0.03
0.02
0.47
0.22
0.12
0.09
0.03
0.02
1962 through 1968
Geom.
mean
0.104
0.112
0.118
0.121
0.133
0.142
0.016
0.018
0.020
0.022
0.025
0.029
0.013
0.014
0.015
0.015
0.017
0.018
0.013
0.014
0.015
0.015
0.017
0.018
SGDa
2.19
2.00
1.84
1.75
1.44
1.00
2.87
2.54
2.27
2.12
1.63
1.00
2.28
2.07
1.90
1.80
1.46
1.00
2.28
2.07
1.90
1.80
1.46
1.00
Max
1.94
1.69
1.02
0.79
0.35
0.18
1.49
0.57
0.38
0.18
0.06
0.04
1.81
0.36
0.14
0.07
0.03
0.02
0.68
0.29
0.13
0.10
0.03
0.02
IViin
1.11
0.86
0.45
0.36
0.18
0.09
0.65
0.38
0.14
0.08
0.03
0.02
0.33
0.17
0.05
0.02
0.01
0.01
0.24
0.13
0.08
0.06
0.02
0.02
Maximum for year
1962
1.13
0.86
0.45
0.36
0.18
0.10
0.84
0.46
0.14
0.11
0.04
0.03
0.24
0.13
0.08
0.06
0.03
0.02
1963
1.94
1.69
0.87
0.71
0.33
0.14
0.99
0.48
0.23
0.11
0.06
0.03
0.51
0.19
0.09
0.07
0.03
0.02
1964
1.62
1.12
1.02
0.79
0.35
0.18
0.88
0.55
0.27
0.14
0.06
0.04
0.68
0.29
0.13
0.10
0.02
1965
1.59
1.14
0.74
0.55
0.27
0.13
1.15
0.57
0.38
0.18
0.06
0.03
0.95
0.36
0.14
0.06
0.03
0.02
1966
1.11
0.98
0.63
0.48
0.26
0.09
0.70
0.41
0.18
0.10
0.05
0.03
0.96
0.26
0.10
0.05
0.02
0.01
1967
1.62
1.11
0.80
0.65
0.32
0.12
0.65
0.42
0.18
0.13
0.04
0.02
0.33
0.17
0.05
0.02
0.01
1968
1.33
0.91
0.63
0.51
0.26
0.12
1.49
0.38
0.18
0.08
0.03
0.02
1.81
0.24
0.10
0.07
0.03
0.01
Percent
data
available
83
83
84
86
94
100
80
80
81
82
86
100
78
78
79
81
83
100
59
67
71
71
64
67
Percent of time concentration is exceeded
0.01
1.31
1.11
0.68
0.53
0.38
0.26
0.38
0.25
0.1
1.01
0.95
0.74
0.41
0.33
0.22
0.18
0.13
0.10
0.15
0.13
0.10
1
0.67
0.64
0.56
0.49
0.19
0.16
0.12
0.10
0.08
0.07
0.05
0.04
0.08
0.08
0.07
0.06
10
0.32
0.32
0.31
0.30
0.27
0.06
0.06
0.06
0.06
0.05
0.03
0.03
0.03
0.03
0.02
0.04
0.04
0.04
0.04
0.02
30
0.16
0.16
0.16
0.16
0.18
0.03
0.03
0.03
0.04
0.03
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.02
50
0.08
0.08
0.09
0.09
0.09
0.12
0.02
0.02
0.02
0.03
0.03
0.03
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.02
0.02
0.02
0.02
70
0.03
0.03
0.04
0.05
0.06
0.01
0.01
0.01
0.02
0.02
0.00
0.00
0.00
0.00
0.01
0.01
0.01
0.01
0.01
0.01
90
0.01
0.01
0.01
0.02
0.03
0.00
0.00
0.00
0.01
0.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.01
O
O
m
r~
33
m
33
D
m
1
33
m
^
m
Z
en
O
C/5
D
>
33
O
V)
aStandard geometric deviation.
-------
CD
.Q
C
CD
3
n
2L
V)
Table 10 (Continued). SULFUR DIOXIDE CONCENTRATION (ppm) AT CAMP SITES, BY AVERAGING TIME AND FREQUENCY,
1962 THROUGH 1968
City and
averaging
time
PHILADELPHIA
5 min
1 hr
8hr
1 day
1 mo
1 yr
ST. LOUIS
5 min
1 hr
8hr
1 day
1 mo
1yr
SAN FRANCISCO
5 min
1 hr
8hr
1 day
1 mo
1yr
WASHINGTON
5 min
1 hr
8hr
1 day
1 mo
1yr
Annual
maxi-
mum
2.67
1.19
0.61
0.43
0.15
0.08
2.32
0.94
0.44
0.30
0.09
0.05
0.56
0.22
0.10
0.07
0.02
0.01
1.14
0.56
0.31
0.23
0.09
0.05
i
1962 through 1968
Geom.
mean
0.055
0.060
0.064
0.067
0.075
0.081
0.028
0.032
0.034
0.036
0.042
0.047
0.005
0.006
0.007
0.007
0.008
0.010
0.040
0.042
0.045
0.046
0.050
0.053
SGDa
2.41
2.18
1.99
1.88
1.50
1.00
2.72
2.43
2.18
2.05
1.59
1.00
2.87
2.54
2.27
2.12
1.63
1.00
2.14
1.96
1.81
1.72
1.42
1.00
Max
1.25
1.03
0.71
0.46
0.16
0.10
1.42
0.96
0.36
0.26
0.08
0.06
0.33
0.26
0.10
0.08
0.03
0.02
0.87
0.62
0.35
0.25
0.11
0.05
Min
0.79
0.66
0.43
0.35
0.12
0.06
0.85
0.55
0.23
0.16
0.05
0.03
0.16
0.11
0.06
0.05
0.01
0.01
0.42
0.35
0.22
0.15
0.07
0.04
Maximum for year
1962
1.25
1.03
0.56
0.35
0.13
0.09
0.16
0.11
0.06
0.05
0.01
0.42
0.38
0.23
0.18
0.10
0.05
1963
1.05
0.85
0.58
0.46
0.12
0.06
0.33
0.26
0.07
0.05
0.02
0.01
0.56
0.48
0.35
0.25
0.11
0.05
__.
1964
1.00
0.84
0.54
0.43
0.15
0.09
1.16
0.73
0.31
0.26
0.08
0.06
0.26
0.16
0.10
0.08
0.03
0.02
0.87
0.62
0.32
0.22
0.09
0.04
1965
1.11
0.94
0.71
0.35
0.13
0.08
1.42
0.96
0.36
0.19
0.06
0.05
0.44
0.35
0.27
0.20
0.08
0.05
1966
0.79
0.66
0.43
0.36
0.13
0.09
1.25
0.84
0.33
0.18
0.06
0.04
0.47
0.45
0.34
0.25
0.10
0.04
1967
1.12
0.77
0.56
0.35
0.13
0.10
0.85
0.55
0.24
0.21
0.05
0.03
0.44
0.37
0.22
0.15
0.07
1968
1.10
0.88
0.55
0.36
0.16
0.08
1.33
0.68
0.23
0.16
0.06
0.03
0.53
0.42
0.22
0.18
0.10
0.04
Percent
data
available
77
78
79
81
88
100
83
83
84
86
90
100
64
64
65
65
75
67
70
70
71
72
76
86
Percent of time concentration is exceeded
0.01
0.96
0.85
0.94
0.73
0.18
0.16
0.49
0.45
0.1
0.72
0.67
0.52
0.56
0.49
0.29
0.13
0.11
0.09
0.35
0.34
0.26
1
0.48
0.45
0.37
0.31
0.28
0.25
0.18
0.14
0.07
0.07
0.06
0.05
0.21
0.21
0.18
0.16
10
0.20
0.20
0.19
0.17
0.12
0.10
0.10
0.09
0.08
0.06
0.03
0.03
0.03
0.03
0.02
0.10
0.10
0.10
0.10
0.09
30
0.09
0.09
0.10
0.10
0.10
0.04
0.05
0.05
0.05
0.05
0.01
0.01
0.02
0.02
0.01
0.06
0.06
0.06
0.06
0.06
50
0.05
0.05
0.06
0.07
0.08
0.08
0.02
0.02
0.03
0.03
0.04
0.03
0.01
0.01
0.01
0.01
0.01
0.01
0.03
0.03
0.04
0.04
0.04
0.04
70
0.03
0.03
0.04
0.04
0.07
0.01
0.01
0.02
0.02
0.03
0.00
0.00
0.00
0.00
0.01
0.02
0.02
0.02
0.02
0.02
90
0.01
0.01
0.01
0.02
0.04
0.00
0.00
0.00
0.01
0.01
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.01
0.01
NJ
Standard geometric deviation.
-------
The next item to consider is the annual maximum 1-hour concentration. There are 8760 hours in a year. If an
hourly value were available for every one of these hours, and if one were certain that each of the values were
completely accurate, then the maximum observed value could be used as an accurate expression for the maximum
1-hour concentration for that year. Data are not available, however, for 100 percent of the hours, and the
accuracy of the 8760th highest value might be questioned, even if all values were available. One alternative is to
select a frequency close to the actual maximum, but far enough away to compensate for the possibility of
inaccuracy in higher observations. The 0.1-percent frequency has been selected for this purpose. It represents the
ninth highest value in the year, if data are available for 100 percent of the hours. A line drawn through the 0.1-
and 3Opercenti/e points (*points on Figure 3) should thus give a good estimate of both the annual maximum
1-hour and the arithmetic mean concentrations.
If each year had the same meteorology and source-strnegth pattern, then the same frequency distribution
could be expected each year. This is not the case, as witnessed by severe air pollution episodes in London and
New York, which, fortunately, do not occur every year.12 This variation from year to year is also shown by the
fact that the highest maximum 1-hour concentration observed during 1 of the 7 years shown in Tables 4 through
10 is often about twice as great as the maximum observed in the lowest year for the same city. Since the most
polluted year may have several hours of high pollution, it can markedly affect the calculated annual maximum
1-hour concentration. In fact, the annual maximum values calculated in column 2 of Tables 4 through 10 are
often about the same as the maximum observed during the 7-year period (column 5). Although the distribution is
markedly affected by the high concentrations during the most polluted years, it is these same concentrations that
need to be controlled if an air pollution problem is to be alleviated and air quality standards are to be met. The
calculated annual maximum concentration is thus suggested as a good design value to use when determining
control strategies and implementation plans.
Some air quality standards may specify maximum values that are not to be exceeded. In order to treat these
data statistically, however, some frequency limit must be assigned to the maxima, whether the frequency be once
a year, once a decade, or once a century. A frequency of once a year is suggested here. Although some sets of
data depart from lognormality, use of the lognormal distribution is recommended because most aerometric data
tend to fit this distribution better than any other.
CALCULATING THE STANDARD GEOMETRIC DEVIATION
The standard geometric deviation is presented graphically on Figure 3,13 in which it is shown as the
16-percentile concentration (1 standard deviation from the median) divided by the 50-percentile concentration.
Actually, the standard geometric deviation can be calculated from any two points on the distribution, as will now
be shown.
As mentioned before, the slope of the plotted line is analogous to the standard geometric deviation. The
ordinate on Figure 3 is logarithmic. The abscissa, expressed as the number of standard deviations from the median
(top axis), is arithmetic. The slope, p, of a line on such a semi-logarithmic plot12 is
p = lnc/7-|nc/
zh — zi
or
In (cn/Cj)
where p = slope,
Cfj = the concentration at point/;,
Cf = the concentration at point /,
Zfj = the number of standard deviations between h and the median, and
Zj = the number of standard deviations between / and the median.
28 MODEL RELATING AIR QUALITY MEASUREMENTS TO STANDARDS
-------
The standard geometric deviation is the antitogarithm of the slope, p.
in(cu
sg = exp
*(17)
Note that Equation 17 is set in boldface type and marked with an asterisk. Only these boldface equations are
needed for analyzing aerometric data. The other equations are used to derive the working equations from
fundamental concepts. The working equations are summarized at the end of this paper.
Carefully note that Equation 17 is a special definition of the standard geometric deviation. If a particular set
of data is perfectly lognormally distributed, the same value of Sg will result regardless of the points selected for
the computation; but if a particular set of data departs significantly from lognormality, the value of sg calculated
by Equation 17 will be strongly affected by the two points selected.
The above method for calculating the standard geometric deviation, in addition to having other advantages
that will be mer tioned later, eliminates the problem of dealing with concentrations at or near zero. The logarithm
of zero is minus infinity. Equations 8 and 9 cannot be used with zero values. Observations near zero may not be
accurate, but they can affect the calculated standard geometric deviation significantly if Equation 9 is used.
Employing Equation 17 would eliminate the problem of inaccurate low values, since only the higher
concentrations associated with the top third of the distribution would usually be used. In a relatively clean
atmosphere only 15 percent of the concentrations measured might be above the instrument's minimum
detectable level. In such cases, the 0.1- and 10-percentile points could be used for calculating the standard
geometric deviation.
Table 11 shows the plotting positions of various percentiles in terms of the number of standard deviations
between these percentiles and the median (top abscissa of Figure 3). This type of information is available for
various percentiles in any standard statistical text. For 1-hour averages, Figure 3 and Tables 3 and 10 show that a
sulfur dioxide concentration of 0.34 ppm was equaled or exceeded at the Washington CAMP site for 0.1 percent
of the measurements during the period shown, and that 0.06 ppm was equaled or exceeded for 30 percent.
Substituting this information into Equation 17 gives
[In (0.34/0.06)"!
3.09 - 0.52J
sghr = 1.96 (19)
CALCULATING THE GEOMETRIC MEAN
A line plotted on semi-logarithmic paper (Figure 3) can be expressed by the general equation12
y = jk* (20)
where y = the ordinate value,
x = the abscissa value,
/ = the intercept value of y when x = 0, and
k = the antilogarithm of the slope of the line (Equation 17).
Applying these concepts to Figure 3,
c = mgSgZ *(2D
OQ
Frequency Analyses ^
-------
Table 11. PLOTTING POSITION OF EXTREME CONCENTRATIONS AND PERCENTILES FOR
SELECTED AVERAGING TIMES
Averaging time.
hr
1 sec
1 min
5 min
8.8 min
10 min
15 min
30 min
1 hr
1 .46 hr
2 hr
3 hr
8 hr
12 hr
14.6 hr
1 day
2 day
4 day
5.9 day
7 day
14 day
1 mo
2 mo
3 mo
6 mo
1 yr
0.000278
0.0166
0.0833
0.146
0.166
0.25
0.5
1
1.46
2
3
8
12
14.6
24
48
96
146
168
346
730
1460
2190
4380
8760
No. of samples
in year
31,500,000
525,000
105,000
60,000
52,500
35,000
17,500
8,760
6,000
4,380
2,920
1,095
730
600
365
183
91
60 .
52
26
12
6
4
2
1
Plotting position
Frequency (60%/N),
percent
of time
0.0000019
0.0001142
0.000571
0.001
0.001142
0.001715
0.00343
0.00685
0.01
0.0137
0.02055
0.0548
0.0822
0.1
0.1644
0.328
0.657
1
1.153
2.31
5
10
15
30
50
No. of standard
deviations (z)
from median
5.50
4.73
4.39
4.27
4.24
4.14
3.98
3.81
3.72
3.63
3.53
3.26
3.14
3.09
2.94
2.72
2.48
2.33
2.27
1.99
1.64
1.28
1.04
0.52
0.00
where z = the number of standard deviations between the particular frequency and the median (top abscissa of
FigureS).
The arithmetic mean can be used instead of the geometric mean by substituting Equation 1 1 into Equation 21 .
c = ms
z ~
Equation 21 can be rearranged to solve for the geometric mean.
(22)
*(23)
Taking logarithms,
In mg = In c - z In sg
Equation 23 can be used to solve for mQ for the example.
(24)
30
MODEL RELATING AIR QUALITY MEASUREMENTS TO STANDARDS
-------
0.06
fftn hi- = -
0nr L960-S2
mg hr = 0.042 ppm (25)
This concentration is listed in column 3 of Table 10.
CALCULATING THE EXPECTED ANNUAL MAXIMUM CONCENTRATION
The frequency at which the expected annual maximum 1-hour concentration should be plotted (Figure 3) will
now be treated. Consider a simpler situation first, that of plotting the frequency distribution for two 6-month
average samples collected in a 12-month period. The first thought might be that the higher of the two values
represents 50 percent of the data and that this value should thus be plotted at the 50-percentile point. The same
reasoning would also place the low value at the 50-percentile point and thus an impossible vertical distribution
line would be produced. The most probable location, however, for the high point should actually be somewhere
between a frequency of 0 and 50 percent, and the low point should be plotted the same distance from the median
on the opposite side of the distribution. An analysis of the data from a table of mean positions of ranked normal
deviates14 reveals that the high point should be plotted at a frequency of about 30 percent. If it were equally
probable that the point could occur at 0 percent or at 50 percent, then the most probable location of the plotting
position would be midway between the two, at 25 percent. Concentrations near the median, however, are
expected to occur more frequently than are concentrations near the extremes. This fact moves the plotting
position for the point in the example from the 25th percentile to a point near the 30th percentile. A simple
empirical equation13 for locating the plotting position for each point up to but not including the median has
been developed from an analysis of the mentioned table.14
1 r — 0 4
f = 100% - — — *(26)
n
where f = the plotting position frequency, in percent,
r = the rank order (highest, second, third, fourth, etc.), and
n = the number of samples.
The plotting position for the highest 1-hour averaging-time concentration in a year would thus be
(27)
f = 0.00685% (28)
Th[s frequency is a statistical z-value of 3.81 deviations from the median (Table 1 1 and Figure 3).
Now that the z-value is known, the expected annual maximum concentration can be calculated by using
Equation 21.
6>3-81 (29)
cmaxhr = °'55 PPm (30)
When more significant digits are carried in a computer, a rounded value of 0.56 ppm results (Table 10, column 2).
Plotting positions, in terms of z-values, are available in statistical tables for sample sizes up to 50. 14 An exact,
complex equation has been used to calculate z-values for any sample size by means of computerized numerical
integration.15 In almost all cases, the resulting z-values are within 0.01 of those determined with Equation 26.
Resulting maximum concentrations for averaging times of 1 second to 1 month (such as those calculated in
Equation 29, but using sg flr = 2) are within 1 percent of what they would be if Equation 26 were used. For
Frequency Analyses 31
-------
averaging times of 5 minutes to 1 day the accuracy is within 0.3 percent. Since these accuracies are sufficient for
air quality data, Equation 26 is recommended for use in all cases, instead of the exact, complex equation.
USING NON-CONTINUOUS DATA
Calculations thus far have been based on continuous air sampling data. The same results can be obtained using
data from non-continuous sampling. The accuracy of the results will be related to the number of samples
collected, compared with the number that would have been available had sampling been continuous. Equations
and tables can be used to calculate confidence limits when non-continuous data are used.16
The standard geometric deviation and the geometric mean can be calculated from any two percentile points, as
discussed previously. For smaller sets of data, a better fit to the arithmetic mean and the expected
annual-maximum concentration might be determined by using the observed arithmetic mean and the observed
maximum.
For instance, assume that a 24-hour sample of sulfur dioxide was taken every third day for a year. Since
sampling every third day permits all days of the week to be sampled equally, this program would give completely
randomized data. If all samples had been collected and analyzed successfully, the program would produce 121
samples. Assume that a dozen of them were lost, leaving 109 samples; that the highest 24-hour concentration
measured was 0.15 ppm; and that the arithmetic mean was 0.05 ppm. The standard geometric deviation and the
geometric mean can be calculated from these two values.
The plotting position for the maximum is first determined by using Equation 26.
f = 100% 1 ~090'4 (31)
f = 0.5505% (32)
Statistical tables similar to Table 11 indicate that this frequency is 2.54 deviations from the median.
The arithmetic mean can be used in these calculations if the right halves of Equations 12 and 23 are set equal
to each other, terms are gathered, and the resulting quadratic equation is solved for In $„. The resulting equation
to use (since c is greater than m) is
HO.s
(33)
VV_|
Taking antilogarithms,
r -|0.5)
"(34)
where Sg = the standard geometric deviation,
z = the number of deviations the selected value is from the median,
c = the concentration of the selected value, and
m = the arithmetic mean concentration.
32 MODEL RELATING AIR QUALITY MEASUREMENTS TO STANDARDS
-------
For the example.
sg day = exP
2.542 - 2 In
, 0-5
0.15'
,0.05
(35)
sg day = 1-61 (36)
The geometric mean can now be calculated from Equation 23.
0.15
<37>
mg day = °-045 PPm (38)
The expected annual maximum 1-day concentration can now be calculated from Equation 21.
cmax day = 0.045 (1.61 )2"94 (39)
cmaxday = 0.18ppm (40)
The methods discussed in this section thus present an alternate technique, especially suited to non-continuous
sampling, that can be used to calculate the standard geometric deviation, the geometric mean, and the expected
annual maximum concentration for a particular averaging time, given the arithmetic mean concentration and a
measured maximum or near-maximum concentration.
Several precautions must be taken when one is using non-continuous data. The first has already been
mentioned— the fact that since somewhat less accurate results are obtained with non-continuous than with
continuous sampling, the needed accuracy must be balanced against sampling program cost.1 6
A second precaution is required to ensure that the sampling program adequately represents the data. For
instance, sulfur dioxide contributions from fuel combustion will be large in the winter and small in the summer.
A program with sampling spaced equally throughout the year would give the most accurate representation for the
year, although some evidence indicates that the annual mean may be close to the spring mean (March, April, and
May) or the fall mean (September, October, and November), and that the standard geometric deviations obtained
from spring-only or fall-only sampling may be comparable to those obtained from all-year sampling.1 7
Frequency Analyses 33
-------
AVERAGING-TIME ANALYSES
Data analyses and statistical parameters for a single averaging time have been treated in previous sections. The
following sections show how statistical parameters for one averaging time can be related to those for another
averaging time. As one example, frequency distributions for 19 averaging times (Table 3) have been determined in
the same manner as those described for 1-hour average concentrations and have been plotted by computer as the
"+" points on Figure 4. Measured maximum and minimum values have been plotted as triangles. Each averaging
time is about twice the previous one; thus, when plotted on logarithmic paper, they are approximately equally
spaced along the abscissa.
For these analyses, all sampling times begin at midnight on December 1, 1961. The first 8-hour sample, for
instance, is an average (rounded) of all the 5-minute values available from midnight to 8 a.m., the next from 8
a.m. to 4 p.m., the third from 4 p.m. to midnight, the fourth from midnight to 8 a.m. on December 2, etc. An
average is calculated for a period only if half or more of the 5-minute values are available.
Because December, January, and February are the three coldest months of the year, fuel combustion for space
heating and, thus, the concentrations of some combustion-related pollutants are highest during these months. For
the particular analyses shown, a sampling period has been selected to begin on December 1 so that the 3-month
averages shown in Table 3 will relate to winter (December, January, and February), spring (March, April, and
May), summer (June, July, and August), and fall (September, October, and November). Splitting data into two
calendar years causes some problems in data processing and computer programming, however; and, since past
analyses have served the purpose of providing seasonal analyses for seven pollutants in eight cities (summarized in
Tables 4 through 10), it no longer seems worth the trouble to continue analyzing data on a "pollution-year"
rather than a calendar-year basis. For future analyses, therefore, the Federal Government is recommending, and
using, sampling periods that begin on January 1 and end on December 31, whether for a single- or several-year
period.
A MATHEMATICAL MODEL
Data have been analyzed and plotted by computer as a function of averaging time and frequency (Figure 4) for
each year, and up to a 7-year period, for concentrations of carbon monoxide, hydrocarbons, nitric oxide,
nitrogen dioxide, nitrogen oxides (NO + NO2), oxidants, and sulfur dioxide for the CAMP sites in downtown
Chicago, Cincinnati, Denver, Los Angeles, Philadelphia, St. Louis, San Francisco, and Washington. Analysis of
these plots has resulted in a general mathematical model with the following characteristics:1 3
1. Concentrations are lognormally distributed for all averaging times.
2. The median concentration is proportional to averaging time raised to an exponent (and thus plots as a
straight line on logarithmic paper).
3. The arithmetic mean concentration is the same for all averaging times.
4. For the longest averaging time calculated (usually 1 year), the arithmetic mean, geometric mean, maximum
concentration, and minimum concentration are all equal (and thus plot at a single point on Figure 4).
5. Maximum concentration is approximately inversely proportional to averaging time raised to an exponent
for averaging times of less than 1 month.
As mentioned previously, a model constructed "from the 0.1- and 30-percent-frequency concentrations for
1-hour averages (* points on Figures 3 and 4) is expected to fit short-term maxima and the annual arithmetic
35
-------
00
O
O
m
i—
30
m
30
D
m
I
30
m
2
m
Z
c/j
100*000 ..
. 1O?000 ..
U
\
Z
D
H
h
=3 Dt
Z
llJ
U
D
U
1*000 ..
100 ..
10 ..
1 -
SECOND
1
15077
5-759
AVERAGTNG TIME
MINUTE HOUR
1 5 10 15 30 1 2 4 6
12 1
DAY
2 4 7 14
MONTH
23 E 12
LJG/CU M
PPM
A I I 1 ±r
1
-+-f-
E3-44
1-125
1447
0-553
H05 533 233 133
0-307 0-227 0-OH3 0-053
EXPECTED ANNUAL MAXIMUM CONC
.. 10
-t-
GED- MEAN FOR 1-HR = 110 LJG/CU M = 0-042 PPM
STANDARD GEOMETRIC DEVIATION = 1-3B
70 PER CENT OF HOURS HAVE DATA AVAILABLE
i 1^
0-0001 O-001 0-01 0-1 1 10
AVEIRAGING TIMEs HOURS
1—
100
100
0.
Z
D
H
ft:
h
z
D
U
.. 0-001
o-oooi
1.000
10?000
Figure 4. Computer plot of concentration versus averaging time and frequency for sulfur dioxide at site 256, Washington, D.C., December 1, 1961, to
December 1, 1968.
-------
mean very closely. A computer has been programmed with these two points and the above characteristics to plot
the lines describing the model (Figure 4). If a particular set of data does not fit lognormality well, the model may
inaccurately predict maxima for intermediate averaging times such as a week or a month. Fortunately, few air
quality standards are specified for those averaging times, and the model thus seems especially suitable for the
short-term (less than a few days) and long-term (1-year) averaging times that are commonly used.
For averaging times shorter than 1 hour, the maximum observed values are often less than the model predicts.
An analysis of oxidant concentrations shows, for instance, that 5-minute maxima are about 1.2 to 1.6 times the
1-hour maxima, rather than about 2 times, as the model predicts.4 One possible reason for this fall-off in oxidant
concentration for short averaging times is that oxidant is a secondary rather than a primary pollutant; time is
required for the photochemical reaction needed to produce oxidants. The reaction time may tend to dampen the
fluctuations in concentrations and make them less than the fluctuations observed in primary pollutants.
Another effect on short-averaging-time concentrations results from instrument response time.18 For instance,
the nitrogen oxides instruments at the CAMP sites have a time constant of 10 minutes; this means that in each
10-minute period the sampler reading moves 63.2 percent of the remaining distance from the old concentration
toward the new concentration to which the sampler is then being exposed. If the sampled concentration were
abruptly changed from 0 to 1 ppm, in 10 minutes the sampler would read 0.63 ppm. Ten minutes later it would
read 0.86 ppm. After 30 minutes, it would read 0.95 ppm, and so on. Although a computer could be used to
compensate for instrument response time, the data reported here have not been so processed.
Another limitation of instrumentation appears as shorter and shorter averaging times are used, and the limit is
finally reached when a sampler is measuring one molecule at a time; if the sampled molecule is the pollutant, then
the concentration for that instant is 1 million ppm (100 percent). If the molecule is not the pollutant, the
concentration is 0.
CALCULATING THE STANDARD GEOMETRIC DEVIATION
With the mathematical model, one can calculate the standard geometric deviation for any averaging time if it is
known for another. The equation used to accomplish this was developed as follows: First, model characteristic
number 2 states that the median concentration is proportional to averaging time raised to an exponent (and thus
plots as a straight line on logarithmic paper). The slope,p, of a straight line on logarithmic graph paper12 (Figure
4, 50-percentile line) is
In X2 - I" Xi ,.,,
P = : 1 (41)
In x2 — In Xj
For*! at averaging time tg and x2 at averaging time ffotal the equation becomes
In m - In mga (42)
P ~ In Unt - In ta
or
(43)
where p = the slope of the median line (50th percentile),
m = the arithmetic mean,
rrifjg = the geometric mean at averaging time a.,
Averaging -Time Analyses 37
-------
ttot = the total averaging time (usually 1 year), and
f0 = averaging time a_.
a
Equation 13 can be rearranged as
m \ ~ r- , ,2
In
~ 0.5 In2 s_
Substituting this expression into Equation 43, and expressing the results at two averaging times, tg and tb,
0.5 In2 s
P =
0.5 In2 s
P =
(44)
(45)
(46)
Setting the right halves of these two equations equal to each other and solving for s b gives:
"gb s
-------
A substitute variable, w, can be used as the coefficient for the second term.
w = z_ - z. v
,0.5
a
:bv "(54)
The quadratic equation can be solved for In s to give:
w ± [w2 - 2(1 - i/) ln(c /c. )]°'5
ln S9a = ^~v (55)
Antilogarithms can be taken to give:
( •> \
\w ± [w2 - 2(1 - v) In (c /cb)l /
sga = expj __ '- \ .(B6)
When cb is greater than cy use the positive radical. When cb is less than cg, use the negative radical.
Equation 56 is used when the two input values to the mathematical model are from different averaging times.
For instance, point a might be the 30-percentile concentration for 1-hour averages (previously used in Equation
18) and point 6might be the 1-percentile concentration for 1-day averages (0.16 ppm, from Tables 3 and 10).
The standard geometric deviation for the 1-hour averaging time at point a could then be calculated as follows.
Equation 49 could be used first to solve for v:
In (8760/24)
In (8760/1) (57)
v = 0.65 (58)
Equation 54 could be used next to solve for w:
w = 0.52 - 2.33(0.65)°'s (59)
w = -1.36 (60)
Finally, the standard geometric deviation for the averaging time at point a could be determined with Equation 56.
i-1.36 + [(-1.36)2 - 2(1 - 0.65)(ln 0.06/0.16)] °'5)
1 - 0.65
(61)
(62)
which is very close to the 1.96 calculated by Equation 19 from the 0.1- and 30-percentile concentrations of
1-hour averages.
As an additional application for Equations 49 through 56, the three national secondary standards for sulfur
dioxide (Table 2) might be studied. These three standards have been plotted on Figure 5. The annual maximum
concentration line has been drawn through the 3- and 24-hour standards. This line thus depicts the air quality
expected at an air sampling site where these two concentrations are expected to occur once a year. The standard
geometric deviation for such a site for 24-hour averages can be calculated by using Equations 49 through 56.
Point a will be the 24-hour standard and point b will be the 3-hour standard. Equation 49 can be used to
calculate v:
= In (8760/3) (63)
" In (8760/24)
v = 1.35 <64>
Averaging-Time Analyses 39
-------
AVERAGING TIME
100
100,000 —
0.0001
0.0001 0.001 0.01 0.1 1 10
AVERAGING TIME, hours
100 1,000 10,000 100,000
FigureB. Expected annual maximum sulfur dioxide concentrations at sampling site where national secondary
3- and 24-hour-standard concentrations occur once a year.
Equation 54 can be used to calculate w. The value of za is 2.94 (Table 11). Equation 26 is used to determine z^:
(65)
1 - 0.4
2920
f = 0.02055%
(66)
Most statistics texts list frequency as a portion of 1 rather than as a portion of 100 percent. Expressed in these
terms.
f = 0.0002055
(67)
Most statistics texts also measure frequency starting with the low values and going to the high values, whereas
here we are going in the opposite direction. The statistics texts would thus list this value as
f = 1 - 0.0002055 (68)
f = 0.9997945 (69)
Thez value associated with this frequency is 3.53. This information can now be substituted into Equation 54:
w = 2.94 - 3.530.35)0'5 (70)
w = - 1.16
40 MODEL RELATING AIR QUALITY MEASUREMENTS TO STANDARDS
-------
The standard-tjeometric deviation for 24-hour averages can now be calculated with Equation 56:
zld6jLjM-16)2 - 2(1 - 1.35)(ln260/1300)l°-s)
1 - 1.35
sgday = 7'22
Thus, for 24-hour averages at an air sampling site, if the standard geometric deviation were 7.22 and the
annual maximum concentration were 260 M9/m3, then the annual maximum concentration expected for 3-hour
averages would be 1300 /ig/m3 .
The expected annual mean could be calculated by rearranging Equation 22 to solve for m,
m =csg°-5<"sg-* (72)
m = 260(7.22) °-5ln7-22 - 2-94
m = 5.5 |ug/m3
i
Thus, if the 3- and 24-hour standard concentrations each occurred at a given site once a year, then the annual
arithmetic mean concentration expected at that site would be 5.5 M9/m3, which is far below the allowable
standard of 60 jug/m3 .
Any two air quality standards for a given pollutant can be inserted into the mathematical model to determine
the standard geometric deviation that occurs when both standards are achieved simultaneously. This deviation can
be compared with the deviation determined by analyzing aerometric data for a particular air sampling site. If the
measured deviation is less than that calculated from the two standards, then the longer averaging time standard
will require the greatest source reduction at that site and could be called the "controlling standard." If the
measured deviation is greater than the one calculated from the two standards, the shorter averaging time standard
will control.
If one of the standards is an arithmetic mean, then Equation 34 can be used to determine the standard
geometric deviation at which the "controlling standard" will switch from one standard to the other. This
equation could be used to determine when the controlling standard switches from the 24-hour sulfur dioxide
standard of 260 M9/m3 to the annual arithmetic mean standard of 60 ;ug/m3.
sgday = «xP 2.94 -
2.942 - 2 In
o.sf
(73)
V day - 1'73 (74)
Thus, if the standard geometric deviation for 24-hour averages is less than 1.73, the annual mean standard is the
"controlling standard," and if the deviation is more than 1.73, the 24-hour standard controls.
The standard geometric deviation at which the "controlling standard" switches from one standard to another
has been calculated for the national standards and listed in Table 12 for the three pollutants that have two or
more standards (carbon monoxide, paniculate matter, and sulfur dioxide). These deviations can be compared
with the minimum, median, and maximum deviations measured for the CAMP stations for carbon monoxide
(Table 4) and sulfur dioxide (Table 10). Such a comparison can suggest how frequently one of the two standards
is expected to "control" implementation plans and control strategies for achieving the standards. The controlling
deviation for carbon monoxide is 4.60. Since this is greater than the median value of 1.47, the 8-hour standard is
expected to apply more than half of the time. In fact, the controlling deviation of 4.60 is so much higher than the
1.70 maximum measured at any CAMP station that the 1-hour standard will probably never affect any outdoor
source reduction plans.
Averaging-Time Analyses 41
-------
Table 12. STANDARD GEOMETRIC DEVIATIONS AT WHICH "CONTROL" SWITCHES FROM ONE
STANDARD TO ANOTHER
Pollutant
Carbon
monoxide
Hydrocarbons
(nonmethane)
Nitrogen
dioxide
Oxidants
Particulate
matter
Sulfur
dioxide
Type of
standard
Primary and
secondary
Primary and
secondary
Primary and
secondary
Primary and
secondary
Primary
Secondary
Primary
Secondary
Standards
Annual maximum for avg. time,
/ug/m3
1 hr
40,000
160
3hr
160
(6 to 9
a.m.)
1300
8hr
10,000b
24 hr
260
150b
365b
260b
260b
1yr
100
80
60
Annual
geom. mean
of 24-hr
averages,
Hg/m3
75b
60
sg day if
both stds
achieved
at same
time
4.60
1.53
1.37
1.77
7.22
1.73
CAMP3
S0day
Min
1.36
1.25
1.72
Med
1.47
1.50
1.84
Max
1.70
2.00
2.12
Approximate Deviations observed on National Air Surveillance Network data are listed for paniculate matter.
"Air quality standard that is expected to "control" at more than half of air sampling sites.
A similarly high deviation, 7.22, is calculated for the 3- and 24-hour sulfur dioxide standards; thus the 24-hour
standard would always be expected to control source reduction plans. This calculation is, however, based on the
assumption that the aerometric data fit the mathematical model. The model in turn has been based on
concentrations in urban atmospheres that are affected by many sources of a pollutant. It is conceivable that
concentration patterns near an isolated, strong, high source of sulfur dioxide might cause the 3-hour standard to
control at a few sites in the Nation.
The controlling standard deviation for the 24-hour and annual arithmetic mean sulfur dioxide standards is
1.73, almost the same as the minimum deviation of 1.72 observed at the CAMP stations. This observation coupled
with that from the previous paragraph suggests that the 24-hour sulfur dioxide standard will almost always be the
controlling standard when implementation plans for achieving the standards are being devised.
CALCULATING THE GEOMETRIC MEAN
The geometric mean for one averaging time can be calculated from information for another averaging time by
use of the equations that follow.
Model characteristic number 2 states that the median concentration is proportional to averaging time raised to
an exponent (and thus plots as a straight line on logarithmic paper). The slope of this median (geometric mean)
line expressed as a function of parameters for averaging times (Equation 42) can also be written with parameters
for averaging time b. Since the slope is the same at both averaging times, the right halves of both equations can be
set equal to each other and solved for In m
42
'gb>
MODEL RELATING AIR QUALITY MEASUREMENTS TO STANDARDS
-------
(75)
Antilogarithms can be taken to give:
where v =
(49>
Equation 76 thus gives the geometric mean at averaging time b as a function of the arithmetic mean (the same for
all averaging times), v, and the geometric mean at averaging time a.
The geometric mean at averaging time b can also be expressed as a function of the geometric mean and
standard geometric deviation at a. Equation 75 is first rearranged as:
\nmgb = (In m)(1 - v) + v In mgg (77)
By using Equation 13, In m can be replaced. Solving for In m ^ then gives:
In mgb = In mga + 0.5(1 - v) In2 sga (78)
Taking antilogarithms gives:
mgb
or
= mg exp [0.5(1 - v) In2 i ] *(79)
(80)
For 1-hour averages of sulfur dioxide concentrations in Washington, Equation 19 and Table 10 indicate that
the standard geometric deviation is 1.96 and that the geometric mean is 0.042 ppm (Equation 25 and column 3
of Table 10).
The geometric mean for 1-day averages can be calculated by using Equation 79:
= I" (8760/24)
In (8760/1) (B1)
v = 0.65
= °-042(1-96> exp [0.5 (1 - 0.65) In2 1.96] (82)
= °'045 (83)
which is very close to the value of 0.046 ppm calculated by computer and listed in column 3 of Table 10.
PLOTTING RESULTS
Equations 17, 21, 23, 48, and 79 have been used, together with the 0.1- and 30-percentile concentrations
measured for 1-hour averages, to plot all of the lines on Figure 4 and to calculate all of the values in columns 2
through 4 in Tables 4 through 10 (the other values in Tables 4 through 10 were measured). The data have been
plotted and tabulated for a total time (ftot) of 1 year so that the expected annual maximum concentrations could
be easily compared with air quality standards. The model could have been used to predict maxima expected for
Averaging -Time Analyses 43
-------
any other period, such as a decade. For most instances, however, it is suggested that the model be used as shown
in Figure 4 to depict expected annual maximum concentrations.
Figure 4 shows expected annual maximum concentrations both graphically (as the top plotted line) and
digitally (along the top abscissa). Concentrations are given both in ^g/m3 and in ppm. The values along the top
abscissa indicate, for instance, that the annual maximum 1-second concentration is expected to be 5.76 ppm. This
parameter could be used if the odor of sulfur dioxide were to be controlled, for instance.6 The values on the top
abscissa in Figure 4 and in Table 10 indicate that the expected annual maximum 1-hour concentration is 0.56
ppm, the expected annual maximum 1-day concentration is 0.23 ppm, and the expected annual mean is 0.053
ppm. Values in Figure 4 and Table 10 vary to a slight but unimportant degree because of slightly different
sequences in computer calculations.
As mentioned earlier, the values in column 2 of Tables 4 through 10 are suggested as design values for use in
relating aerometric data to air quality standards, control strategies, and implementation plans.
SHORT CUTS
Model characteristic number 5 indicates that the expected annual maximum concentration is approximately
inversely proportional to averaging time raised to an exponent for periods of less than 1 month. If the standard
geometric deviation and the expected annual maximum concentration for a particular averaging time at a
particular sampling site are known, then the expected annual maxima for other averaging times can be
estimated1 3 by using the equation:
cmax = cmax hr^ *(84)
where cmax = tne expected annual maximum concentration for a particular averaging time,
cmax hr = t'le exPe(;ted annual maximum 1-hour concentration,
t - the averaging time, and
q = the slope of the maximum line on logarithmic paper (Figure 4).
The slope of the annual maximum line can be determined from any two points. To illustrate the use of the
equation, averaging times of 1 hour and 1 day have been selected and the slope has been calculated as a function
of the standard geometric deviation for 1-hour averaging time (Table 13). 13 The expected annual maximum
1 -month concentration could be calculated by using Table 13 and the previously calculated maximum 1-hour
concentration (Equation 30):
(85)
cmax mo = °'087 PPm (86)
which is quite close to the 0.089 ppm read from the top abscissa of Figure 4.
Relationships among standard geometric deviations and expected annual maximum concentrations have been
calculated for several averaging times (Table 14). 7 Calculations have been made for 0.05-unit increments of
1-hour standard geometric deviations. For example, the 1-hour standard geometric deviation for sulfur dioxide at
the Washington CAMP site is 1.96 and the annual mean is 0.053 ppm (top abscissa. Figure 4). The expected
annual maximum concentration for 1-day averages at that site can be determined by using Table 14. The 1.96
value is one-fifth of the distance from the 1.95 value toward the 2.00 value listed in column 3 of Table 14.
Similarly, the maximum-to-mean ratio of 4.25 is one-fifth of the distance between the values of 4.21 and 4.42
listed under 1-day ratios. The expected annual maximum 1-day concentration would thus be 4.25 times the
annual mean of 0.053 ppm, or 0.23 ppm, which agrees with the 0.227 read from the top abscissa on Figure 4.
44 MODEL RELATING AIR QUALITY MEASUREMENTS TO STANDARDS
-------
Table 13. SLOPE OF MAXIMUM CONCENTRATION LINE FOR 1-HR AVERAGE STANDARD
GEOMETRIC DEVIATIONS FROM 1.0 THROUGH 4.99
SGDa
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
2.10
2.20
2.30
2.40
2.50
2.60
2.70
2.80
2.90
3.00
3.10
3.20
3.30
3.40
3.50
3.60
3.70
3.80
3.90
4.00
4.10
4.20
4.30
4.40
4.50
4.60
4.70
4.80
4.90
0.00
0.000
-0.042
-0.080
-0.114
-0.145
-0.174
-0.200
-0.224
-0.246
-0.267
-0.287
-0.305
-0.322
-0.338
-0.353
-0.368
-0.382
-0.395
-0.407
-0.419
-0.430
-0.441
-0.451
-0.461
-0.471
-0.480
-0.489
-0.497
-0.506
-0.514
-0.521
-0.529
-0.536
-0.543
-0.549
-0.556
-0.562
-0.568
-0.574
-0.580
0.01
-0.004
-0.046
-0.083
-0.117
-0.148
-0.176
-0.202
-0.226
-0.248
-0.269
-0.288
-0.307
-0.324
-0.340
-0.355
-0.369
-0.383
-0.396
-0.408
-0.420
-0.431
-0.442
-0.452
-0.462
-0.472
-0.481
-0.490
-0.498
-0.506
-0.514
-0.522
-0.529
-0.536
-0.543
-0.550
-0.556
-0.563
-0.569
-0.575
-0.580
0.02
-0.008
-0.050
-0.087
-0.121
-0.151
-0.179
-0.205
-0.229
-0.251
-0.271
-0.290
-0.308
-0.325
-0.341
-0.356
-0.371
-0.384
-0.397
-0.410
-0.421
-0.432
-0.443
-0.453
-0.463
-0.473
-0.482
-0.491
-0.499
-0.507
-0.515
-0.523
-0.530
-0.537
-0.544
-0.551
-0.557
-0.563
-0.569
-0.575
-0.581
0.03
-0.012
-0.054
-0.090
-0.124
-0.154
-0.182
-0.207
-0.231
-0.253
-0.273
-0.292
-0.310
-0.327
-0.343
-0.358
-0.372
-0.386
-0.398
-0.41 1
-0.422
-0.434
-0.444
-0.454
-0.464
-0.474
-0.483
-0.492
-0.500
-0.508
-0.516
-0.523
-0.531
-0.538
-0.545
-0.551
-0.558
-0.564
-0.570
-0.576
-0.582
0.04
-0.017
-0.057
-0.094
-0.127
-0.157
-0.184
-0.210
-0.233
-0.255
-0.275
-0.294
-0.312
-0.329
-0.344
-0.359
-0.373
-0.387
-0.400
-0.412
-0.424
-0.435
-0.445
-0.455
-0.465
-0.475
-0.484
-0.492
-0.501
-0.509
-0.517
-0.524
-0.531
-0.539
-0.545
-0.552
-0.558
-0.565
-0.571
-0.576
-0.582
0.05
-0.021
-0.061
-0.097
-0.130
-0.160
-0.187
-0.212
-0.235
-0.257
-0.277
-0.296
-0.314
-0.330
-0.346
-0.361
-0.375
-0.388
-0.401
-0.413
-0.425
-0.436
-0.446
-0.456
-0.466
-0.476
-0.485
-0.493
-0.502
-0.510
-0.517
-0.525
-0.532
-0.539
-0.546
-0.553
-0.559
-0.565
-0.571
-0.577
-0.583
0.06
-0.025
-0.065
-0.101
-0.133
-0.163
-0.190
-0.214
-0.238
-0.259
-0.279
-0.298
-0.315
-0.332
-0.347
-0.362
-0.376
-0.390
-0.402
-0.414
-0.426
-0.437
-0.447
-0.457
-0.467
-0.477
-0.485
-0.494
-0.502
-0.510
-0.518
-0.526
-0.533
-0.540
-0.547
-0.553
-0.560
-0.566
-0.572
-0.578
-0.583
0.07
-0.029
-0.069
-0.104
-0.136
-0.165
-0.192
-0.217
-0.240
-0.261
-0.281
-0.299
-0.317
-0.333
-0.349
-0.364
-0.378
-0.391
-0.403
-0.415
-0.427
-0.438
-0.448
-0.458
-0.468
-0.477
-0.486
-0.495
-0.503
-0.51 1
-0.519
-0.526
-0.533
-0.541
-0.547
-0.554
-0.560
-0.566
-0.572
-0.578
-0.584
0.08
-0.034
-0.072
-0.107
-0.139
-0.168
-0.195
-0.219
-0.242
-0.263
-0.283
-0.301
-0.319
-0.335
-0.350
-0.365
-0.379
-0.392
-0.405
-0.417
-0.428
-0.439
-0.449
-0.459
-0.469
-0.478
-0.487
-0.496
-0.504
-0.512
-0.520
-0.527
-0.534
-0.541
-0.548
-0.555
-0.561
-0.567
-0.573
-0.579
-0.584
0.09
-0.038
-0.076
-0.111
-0.142
-0.171
-0.197
-0.222
-0.244
-0.265
-0.285
-0.303
-0.320
-0.337
-0.352
-0.366
-0.380
-0.393
-0.406
-0.418
-0.429
-0.440
-0.450
-0.460
-0.470
-0.479
-0.488
-0.497
-0.505
-0.513
-0.520
-0.528
-0.535
-0.542
-0.549
-0.555
-0.562
-0.568
-0.574
-0.579
-0.585
aStandard geometric deviation for a particular slope is the sum of the left and top margin values.
NON-LOGNORMALLY DISTRIBUTED DATA
Model characteristic number 1 states that concentrations are lognormally distributed over all averaging times.
This general trend, subject to the limitations noted earlier, is based on data collected at CAMP stations near the
centers of large cities. The model has also been designed so that accurate predictions of expected annual maxima
will be made for the most frequently used averaging times even if a particular set of data departs markedly from
lognormality. Aerometric data sampled from sites near strong, isolated sources are often not lognormally
distributed, however, and one must ensure that grossly inaccurate predictions are not made from model
characterizations of these data. At some future time, a special mathematical model may be developed for
describing air quality as a function of averaging time and frequency for these strong, isolated sources.
Averaging-Time Analyses 45
-------
Table 14. RATIO OF EXPECTED ANNUAL MAXIMUM POLLUTANT CONCENTRATION TO
ARITHMETIC MEAN CONCENTRATION FOR VARIOUS AVERAGING TIMES
AND STANDARD GEOMETRIC DEVIATIONS
Standard geometric deviation for
averaging times of:
1 sec
1.00
1.07
1.14
1.21
1.29
1.36
1.44
1.51
1.59
1.67
1.75
1.83
1.91
1.99
2.08
2.16
2.25
2.34
2.42
2.51
2.60
2.69
2.78
2.87
2.97
3.06
3.15
3.25
3.34
3.44
3.54
3.64
3.74
3.83
3.93
4.04
4.14
4.24
4.34
4.45
4.55
4.66
476
4.87
4.97
5 min
1.00
1.06
1.11
1.17
1.23
1.29
1.34
1.40
1.46
1.52
1.58
1.64
1.70
1.76
1.82
1.88
1.94
2.00
2.06
2.12
2.19
2.25
2.31
2.37
2.43.
2.50
2.56
2.62
2.69
2.75
2.81
2.88
2.94
3.00
3.07
3.13
3.20
3.26
3.33
3.39
3.46
3.52
3.59
3.65
3.72
1 hr
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
1.55
.60
.65
.70
.75
.80
.85
.90
1.95
2.00
2.05
2.10
2.15
2.20
2.25
2.30
2.35
2.40
2.45
2.50
2.55
2.60
2.65
2.70
2.75
2.80
2.85
2.90
2.95
3.00
3.05
3.10
3.15
3.20
3hr
1.00
1.05
1.09
1.14
1.19
1.23
1.28
1.32
1.37
1.42
1.46
1.51
1.55
1.60
1.64
1.69
1.74
1.78
1.83
1.87
1.92
1.96
2.00
2.05
2.09
2.14
2.18
2.23
2.27
2.32
2.36
2.41
2.45
2.49
2.54
2.58
2.63
2.67
2.71
2.76
2.80
2.84
2.89
2.93
2.98
8hr
1.00
1.04
1.09
1.13
1.17
1.22
1.26
1.30
1.34
1.39
1.43
1.47
1.51
1.55
1.59
1.63
1.68
1.72
1.76
1.80
1.84
1.88
1.92
1.96
2.00
2.04
2.08
2.12
2.16
2.20
2.24
2.27
2.31
2.35
2.39
2.43
2.47
2.51
2.55
2.59
2.62
2.66
2.70
2.74
2.78
1 day
1.00
1.04
1.08
1.12
1.16
1.20
1.24
1.27
1.31
1.35
1.39
1.42
1.46
1.50
1.53
1.57
1.61
1.64
1.68
1.71
1.75
1.78
1.82
1.85
1.89
1.92
1.96
1.99
2.03
2.06
2.09
2.13
2.16
2.19
2.23
2.26
2.29
2.33
2.36
2.39
2.42
2.46
2.49
2.52
2.55
4 days
1.00
1.04
1.07
1.10
1.14
1.17
1.20
1.24
1.27
1.30
1.33
1.36
1.39
1.42
1.45
1.48
1.51
1.54
1.57
1.60
1.63
1.66
1.69
1.72
1.74
1.77
1.80
1.83
.85
.88
.91
.93
.96
.99
2.01
2.04
2.07
2.09
2.12
2.14
2.17
2.20
2.22
2.25
2.27
1 mo
1.00
1.03
1.05
1.08
1.10
1.12
1.15
1.17
1.19
1.21
1.24
1.26
1.28
1.30
1.32
.34
.36
.38
.40
.42
1.44
1.46
1.47
1.49
1.51
1.53
1.55
1.56
1.58
1.60
.62
.63
.65
.67
.68
.70
.71
1.73
1.75
1.76
1.78
1.79
1.81
1.82
1.84
Ratio of annual maximum concentration to mean
concentration for averaging times of:
1 sec
1.00
1.44
2.04
2.83
3.86
5.18
6.85
8.94
11.53
14.69
18.53
23.14
28.65
35.16
42.83
51.78
62.18
74.18
87.96
103.70
121.61
141.88
164.73
190.39
219.09
251.07
286.61
325.94
369.37
417.15
469.60
527.00
589.67
657.92
732.07
812.47
899.45
993.34
1094.51
1203.31
1320.11
1445.27
1579.16
1722.17
1874.68
5 min
1.00
1.27
1.59
1.97
2.42
2.93
3.51
4.18
4.93
5.77
6.71
7.76
8.92
10.19
11.58
13.11
14.76
16.56
18.50
20.59
22.83
25.24
27.81
30.55
33.47
36.56
39.84
43.31
46.97
50.82
54.88
59.14
63.60
68.28
73.17
78.28
83.61
89.16
94.94
100.94
107.17
113.64
120.34
127.28
134.46
1 hr
.00
.20
.43
.69
.97
2.28
2.63
3.00
3.41
3.84
4.32
4.82
5.37
5.95
6.56
7.21
7.90
8.62
9.39
10.19
11.03
11.91
12.83
13.78
14.78
15.81
10.89
18.00
19.15
20.34
21.57
22.84
24.14
25.49
26.87
28.29
29.75
31.24
32.78
34.35
35.95
37.60
39.28
40.99
42.74
3hr
1.00
1.17
1.37
1.57
1.80
2.05
2.31
2.60
2.90
3.22
3.56
3.92
4.30
4.70
5.12
5.55
6.01
6.49
6.98
7.49
8.03
8.58
9.15
9.74
10.34
10.97
11.61
12.27
12.94
13.64
14.35
15.07
15.82
16.58
17.35
18.14
18.95
19.77
20.60
21.45
22.32
23.20
24.09
25.00
25.92
8hr
1.00
1.15
1.31
1.48
1.66
1.86
2.06
2.28
2.51
2.75
3.00
3.26
3.53
3.81
4.10
4.40
4.71
5.03
5.36
5.70
6.04
6.40
6.76
7.14
7.52
7.91
8.30
8.71
9.12
9.54
9.97
10.40
10.84
11.28
11.74
12.20
12.66
13.13
13.61
14.09
14.58
15.07
15.57
16.07
16.57
1day
1.00
1.12
1.25
1.38
1.52
1.67
1.82
1.98
2.14
2.31
2.48
2.65
2.84
3.02
3.21
3.40
3.60
3.80
4.00
4.21
4.42
4.64
4.85
5.07
5.29
5.52
5.75
5.98
6.21
6.44
6.68
6.92
7.16
7.40
7.64
7.89
8.13
8.38
8.63
8.88
9.13
9.38
9.64
9.89
10.15
4 days
1.00
1.09
1.18
1.27
1.36
1.46
1.56
1.65
1.75
1.85
1.95.
2.05
2.15
2.26
2.36
2.46
2.57
2.67
2.77
2.88
2.98
3.09
3.19
3.30
3.40
3.51
3.61
3.72
3.82
3.93
4.03
4.13
4.24
4.34
4.44
4.55
4.65
4.75
4.86
4.96
5.06
5.16
5.26
5.36
5.46
1 mo
1.00
1.04
1.08
1.12
1.16
.20
.24
.28
.31
.35
.38
.42
.45
1.48
1.52
1.55
1.58
.61
.64
.67
.70
.73
.75
.78
1.81
1.83
1.86
1.88
1.91
1.93
1.96
1.98
2.00
2.03
2.05
2.07
2.09
2.11
2.13
2.16
2.18
2.20
2.22
2.24
2.25
46
MODEL RELATING AIR QUALITY MEASUREMENTS TO STANDARDS
-------
Table 14(Continued). RATIO OF EXPECTED ANNUAL MAXIMUM POLLUTANT CONCENTRATION TO
ARITHMETIC MEAN CONCENTRATION FOR VARIOUS AVERAGING TIMES
AND STANDARD GEOMETRIC DEVIATIONS
Standard geometric deviation for
averaging times of:
1 sec
5.08
5.19
5.30
5.41
5.52
5.63
5.74
5.85
5.96
6.08
6.19
6.30
6.42
6.53
6.65
5 min
3.78
3.85
3.91
3.98
4.05
4.11
4.18
4.24
4.31
4.38
4.44
4.51
4.58
4.65
4.71
1 hr
3.25
3.30
3.35
3.40
3.45
3.50
3.55
3.60
3.65
3.70
3.75
3.80
3.85
3.90
3.95
3hr
3.02
3.06
3.11
3.15
3.19
3.24
3.28
3.32
3.37
3.41
3.45
3.50
3.54
3.58
3.63
8hr
2.81
2.85
2.89
2.93
2.97
3.00
3.04
3.08
3.12
3.15
3.19
3.23
3.27
3.30
3.34
1 day
2.59
2.62
2.65
2.68
2.71
2.75
2.78
2.81
2.84
2.87
2.90
2.93
2.96
3.00
3.03
4 days
2.30
2.32
2.35
2.37
2.39
2.42
2.44
2.47
2.49
2.52
2.54
2.56
2.59
2.61
2.63
1 mo
1.85
1.87
1.88
1.90
1.91
1.93
1.94
1.95
1.97
1.98
2.00
2.01
2.02
2.04
2.05
Ratio of annual maximum concentration to mean
concentration for averaging times of:
1 sec
2037.07
2209.73
2393.06
2587.45
2793.31
301 1 .02
3241.01
3483.66
3739.39
4008.61
4291.72
4589.13
4901.25
5228.49
5571.26
5 min
141.87
149.53
157.43
165.58
173.97
182.61
191.50
200.63
210.02
219.65
229.54
239.67
250.06
260.70
271.59
1 hr
44.53
46.35
48.20
50.09
52.01
53.96
55.95
57.97
60.02
62.11
64.22
66.37
68.55
70.75
72.99
3hr
26.85
27.79
28.75
29.72
30.71
31.70
32.71
33.72
34.75
35.79
36.84
27.90
38.97
40.05
41.14
8hr
17.09
17.60
18.12
18.65
19.17
19.71
20.24
20.78
21.32
21.87
22.42
22.97
23.53
24.09
24.65
1 day
10.40
10.66
10.92
11.18
11.44
11.70
11.96
12.22
12.48
12.74
13.00
13.26
13.53
13.79
14.05
4 days
5.56
5.66
5.76
5.86
5.96
6.05
6.15
6.25
6.34
6.44
6.53
6.63
6.72
6.82
6.91
1 mo
2.27
2.29
2.31
2.33
2.35
2.36
2.38
2.40
2.41
2.43
2.45
2.46
2.48
2.49
2.51
Averaging-Time Analyses
47
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SUMMARY
Information on air quality measurements, air pollutant effects, air quality criteria, and air quality standards
can all be expressed as a concentration function of averaging time and frequency. This type of information has
been presented here in tables and on graphs.
The frequency with which certain concentration values are equaled or exceeded has been discussed in terms of
the lognormal distribution. Air quality data have been related to air quality standards with calculated geometric
means, standard geometric deviations, and the expected annual maximum concentrations from both continuous
and non-continuous data.
Air pollutant effects vary with exposure durations, and these durations can be related in turn to current air
quality data by averaging measured pollutant concentrations over various time periods. A mathematical model for
describing the relationship among concentration values for various averaging times has been described. Results of
calculations with the model have been plotted and various short cuts for speeding the analysis of aerometric data
have been discussed.
49
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APPENDIX: WORKING EQUATIONS
AND EXERCISES WITH ANSWERS
EQUATIONS
Many equations have been used here in order to establish the fundamental concepts needed to develop the
working equations actually used in analyzing aerometric data. The twelve working equations that follow are the
only ones actually needed for analysis.
The following five equations can be used to analyze data collected for one averaging time:
(17)
sg = exp
sg = exp
*
In (ch/c
2h ~ zi
(34)
(23)
c = rrigSg* (21)
f = 100% r ~ °-4 (26)
n
The following seven equations can be used to calculate values for one averaging time from values that are
available for another averaging time.
'gb - */'5 (48)
(w ± [i/i/2 - 2(1 -v) ln(c/c.)]°-5)
I ___ a U \
- —- -
I ___ a \ /c/M
sgg = exp - ^—-v - (56)
(49)
w =
(54)
51
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mgb = mga exP[°-5 « - "> ln2 V1 (79>
cmax = cmax hrf<7 <84>
The parameters used in these equations have been arranged alphabetically and are defined as follows:
a = one averaging time,
b = a second averaging time,
c = concentration,
cm_ = maximum concentration, usually the maximum expected once a year,
max
exp = base of natural logarithms, 2.718, raised to the power that follows in brackets,
f = frequency, in percent, with which a particular concentration is equaled or exceeded,
h = one given concentration point,
/ = a second given concentration point at the same averaging time as h,
In = natural logarithms, base e,
m = arithmetic mean,
m = geometric mean,
y
n = number of samples,
q = slope of the maximum concentration line on logarithmic paper,
r = rth value in a set of aerometric data ranked from the highest concentration to the lowest
concentration,
s = standard geometric deviation,
y
t = averaging time,
ftot = total averaging time, usually 1 year (8760 hours), and
z = number of deviations a point is located away from the median.
EXERCISES
The following exercises are recommended for increasing proficiency with the techniques discussed in this
paper. The example used involves only 11 samples in order to reduce the amount of computation needed. It has
been assumed that 1-month sulfur dioxide samples have been taken in front of the U.S. Capitol for each month of
1 year and that the concentrations, in jug/m3, from January through December are 300, 250, 180, missing, 150,
60, 120, 100, 140, 160, 190, and 220, respectively.
1. What is the arithmetic mean concentration for the year?
52 MODEL RELATING AIR QUALITY MEASUREMENTS TO STANDARDS
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2. Calculate the geometric mean by using all values.
3. What is the maximum 1-month observed concentration, and at what frequency should it be plotted on
log-probability paper?
4. What is the minimum 1-month observed concentration and at what frequency should it be plotted on
log-probability paper?
5. At what frequency should each of the observed values, from January through December, be plotted on
log-probability paper?
6. Plot the 11 values on log-probability paper (e.g., Keuffel & Esser Co. paper 46 8040, probability x 2-log
cycles).*
7. Use the arithmetic mean and the maximum to calculate the standard geometric deviation (a frequency of
5.5 percent is a z-value of 1.60).
8. Calculate the geometric mean from the calculated standard geometric deviation and the maximum.
9. Use the answers from 7 and 8 to calculate the standard geometric deviation and geometric mean for
1-hour average concentrations.
10. Use the answers from 9 to calculate the expected annual maximum 1-hour concentration.
11. Compare the answers in 9 and 10 with values in Table 14.
12. Plot the expected annual maximum concentration on logarithmic paper as a function of averaging time.
Draw the curve through the hourly maximum, monthly maximum, and annual mean. Read the 24-hour
maximum from the graph and compare it with the value calculated by using Table 14.
ANSWERS
1. m = 170/xg/m3.
2- ^ month = 156M9/m3.
3- 'max month -300/ig/mV = 5.5%.
4-
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REFERENCES
1. National Primary and Secondary Ambient Air Quality Standards. Federal Register. 36:8186-8201. April 30,
1971.
2. Air Quality Criteria for Carbon Monoxide. U.S. DHEW, PHS, EHS, National Air Pollution Control
Administration. Washington, D.C. Publication No. AP-62. March 1970.
3. Air Quality Criteria for Particulate Matter. U.S. DHEW, PHS, EHS, National Air Pollution Control
Administration. Washington, D. C. Publication No. AP-49. January 1969.
4. Air Quality Criteria for Photochemical Oxidants. U.S. DHEW, PHS, EHS, National Air Pollution Control
Administration. Washington, D.C. Publication No. AP-63. March 1970.
5. Air Quality Criteria for Sulfur Oxides. U.S. DHEW, PHS, EHS, National Air Pollution Control
Administration. Washington, D.C. Publication No. AP-50. January 1969.
6. Larsen, R. I. Relating Air Pollutant Effects to Concentration and Control. J. Air Poll. Contr. Assoc.
20:214-225, April 1970.
7. Larsen, R. I. and H. W. Burke. Ambient Carbon Monoxide Exposures. APCA Paper 69-167. Presented at the
annual meeting of the-Air Pollution Control Association, New York City, June 22-26, 1969.
8. Larsen, R. I., C. E. Zimmer, D. A. Lynn, and K. G. Blemel. Analyzing Air Pollutant Concentration and
Dosage Data./ Air Poll. Contr. Assoc. 17:85-93, February 1967.
9. Guidelines for the Development of Air Quality Standards and Implementation Plans. U.S. DHEW, PHS,
CPEHS, National Air Pollution Control Administration. Washington, D.C. May 1969.
10. Aitchison, J. and J. A. C. Brown. The Lognormal Distribution. Cambridge University Press, New York.
1966. p. 8.
11. Drinker, P. and T. Hatch. Industrial Dust (2nd Ed.). McGraw-Hill, New York. 1954. p. 194.
12. Larsen, R. I. Determining Basic Relationships Between Variables. Symposium on Environmental
Measurements. U.S. DHEW, PHS, Division of Air Pollution. PHS Publication 999-AP-15. Cincinnati, Ohio.
July 1964. p. 251-263.
13. Larsen, R. I. A New Mathematical Model of Air Pollutant Concentration, Averaging Time, and Frequency. J.
Air Poll. Contr. Assoc. 19:24-30, January 1969.
14. Pearson, E. S. and H. O. Hartley. Biometrika Tables for Statisticians. Vol. 1. Cambridge University Press,
New York. 1962. p. 175.
15. Lowrimore, Gene R., statistician, Effects Studies, Environmental Protection Agency. Personal Com-
munication.
16. Hunt, W. F., Jr. The Precision Associated with the Sampling Frequency of Log-Normally Distributed Air
Pollutant Measurements. APCA Paper 70-99. Presented at the annual meeting of the Air Pollution Control
Association, St. Louis, Missouri, June 14-19, 1970.
17 Stalker W. W., R. C. Dickerson, and G. D. Kramer. Sampling Station and Time Requirements for Urban Air
Pollution Surveys. J. Air Poll. Contr. Assoc. 12:361-375, August 1962.
55
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18. Larsen, R. I., F. B. Benson, and G. A. Jutze. Improving the Dynamic Response of Continuous Air Pollutant
Measurements with a Computer. J. Air Poll. Contr. Assoc. 15:19-22, January 1965.
56 MODEL RELATING AIR QUALITY MEASUREMENTS TO STANDARDS,
U.S. GOVERNMENT PRINTING OFFICE: 1973 746-767/4143 - Region 4
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