RESEARCH TRIANGLE INSTITUTE
Final Report
AN EVALUATION OF THE HIGH-VOLUME METHOD FOR DETERMINING
SUSPENDED PARTICULATES OVER SHORT SAMPLING TIMES
by
Reed S. C. Rogers
Franklin Smith
Research Triangle Institute
A. Carl Nelson, Jr.
Statistical Consultant
Contract No. 68-02-0294, Task 15
EPA Project Officer: Larry Purdue
Prepared for
Quality Assurance and Environmental Monitoring Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
November 1974
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27709
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ABSTRACT
Results of a field evaluation of the high volume method of measuring
suspended particulates in the ambient air for 4- and 6-hour sampling
periods and various combinations of equilibration parameters are reported.
Under the conditions tested, a short-term sampling procedure—namely, a
4-hour sampling period and a 2-hour equilibration period at about 25°C
and a relative humidity of 10 percent or less—is recommended. Results of
this field evaluation indicate that the precision, expressed as a relative
standard deviation, would be approximately 5.2 percent for the above
short-term sampling procedure.
iii
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ACKNOWLEDGMENTS
The authors wish to express appreciation to the project officer, Mr. Larry
Purdue, and staff members of the Environmental Monitoring Branch of the Quality
Assurance and Environmental Monitoring Laboratory for their assistance and
guidance in this project.
iv
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TABLE OF CONTENTS
SECTION PAGE
1.0 INTRODUCTION 1
2.0 TEST PLAN 2
2.1 Short-term Sampling Study 2
2.1.1 Apparatus 2
2.1.2 Description of Sampling Site 3
2.1.3 Procedure ' 3
2.1.4 Data Analysis for Short-term Sampling Periods 4
2.2 Filter Equilibration Study 10
2.2.1 Apparatus 10
2.2.2 Procedure 10
2.2.3 Data Analysis for the Equilibration Study 11
2.2.4 Validation of Data 12
3.0 RESULTS 15
4.0 CONCLUSIONS 18
5.0 RECOMMENDATIONS 18
5.1 Recommended Short-term Sampling Procedure 18
5.1.1 Recommended Sampling Procedure 19
5.1.2 Recommended Equilibration Procedure 19
5.2 Recommendations for Further Testing 19
6.0 REFERENCES 20
APPENDIX
A - PROPOSED REFERENCE METHOD FOR THE DETERMINATION OF 21
SUSPENDED PARTICULATES IN THE ATMOSPHERE OVER SHORT
SAMPLING TIMES (HIGH-VOLUME METHOD).
B - COMPILATION OF DATA FOR THE SHORT-TERM HIGH-VOLUME 33
SAMPLING STUDY.
C - DETERMINATION OF PRECISION FOR SHORT-TERM SAMPLING 43
PERIODS AND OPTIMUM EQUILIBRATION CONDITIONS.
v
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LIST OF TABLES
TABLE PAGE
1 Results from 4-hour sampling periods 6
2 Results from 6-hour sampling periods 6
3 Values of y (t_)/[Hy(t_)] and CV[l-ty(t )]
i- . ' Hi Hi •'Ci -,-7
for varyzng t 17
t
B-l Measured suspended particulate concentrations
from 4-, 6-, and 24-hour sampling periods 34
B-2 Data collected May 28-29, 1974 35
B-3 Data collected June 2-3, 1974 36
S~4 Sample weight as a function of equilibration
time, samples collected by Sampler B,
Environment 1 37
B-5 Sample weight as a function of equilibration
time, samples collected by Sampler C,
Environment 2 38
B-6 Sample weight as a function of equilibration
time, samples collected by Sampler D,
Environment 3 39
B-7 Sample weight as a function of equilibration
time, samples collected from Sampler E,
Environment 4 40
B-8 Values of "y (t^,) and s (y) for varying
equilibration time 41
B-9 Sample weight as a function of equilibration
time 42
C-l Values of B and B* such that E(B s1) = E(B*s) = a 44
n n n n
vi
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LIST OF FIGURES
FIGURE PAGE
1 Suspended particulate concentration levels, as
determined from short-term and 24-hour sampling
periods. 9
2 Average relative difference in particulate
weight, y" (t ), versus equilibration time, t^. 13
hi &
3 Average relative difference in particulate
weight versus equilibration time: Environments
2, 3, and 4 compared with Environment 1. 14
A-l Exploded view of typical high-volume air
sampler parts. 22
A-2 Assembled sampler and shelter. 23
A-3 Orifice calibration unit. 24
vii
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EXECUTIVE SUMMARY
Background
In order to facilitate a shorter reaction time in applying control
strategies during periods of air stagnation advisories, an acceptable
short-term method for the determination of suspended particulates in the
atmosphere is required. The objective of this study is to develop a
guideline document outlining proper operating procedures for the use of
a short-term method of measuring suspended particulates, following as
closely as possible the Environmental Protection Agency (EPA) reference
method for the determination of suspended particulates in the atmosphere.
The study was divided into three tasks as follows:
1. To estimate the precision associated with short-term (e.g., 4-
hour and 6-hour) sampling periods and to determine the comparability of
cumulative short-term sampling results to the 24-hour sampling period by
conducting field tests in the local area using standard high-volume
samplers and filters.
2. To evaluate the influence of the equilibration variables: a)
relative humidity, b) temperature, and c) duration on measurement
variability.
3. To specify a feasible procedure for short-term sampling based
on the results of 1 and 2 above.
Test Plan
The test plan was designed and conducted in such a manner that the
data could be subjected to statistical analysis allowing for the con-
struction of confidence limits on the final results. Individual test
plans were designed for the short-term sampling study and the filter
equilibration study.
The short-term sampling test plan was designed to allow for esti-
mating the precision of 4-hour, 6-hour, and 24-hour sampling periods and
for comparing the average 24-hour suspended particulate concentration
obtained by combining short-term samples with that resulting from one
24-hour sample. Six samplers were run concurrently with two collecting
24-hour samples, and the other four making consecutive short-term runs
of 4, 4, 6, 6, and 4 hours over the same 24-hour period. The test
ix
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was replicated, resulting in a total of 44 samples, including six sets
of four 4-hour samples, four sets of four 6-hour samples, and two sets
of two 24-hour samples for estimating precisions. It also provided two
sets of data for comparing cumulative short-term sampling period results
with 24-hour sampling period results.
The equilibration study consisted of conditioning exposed filters
o
(high-volume samples) in an environmental chamber set at 32 C and 100
percent relative humidity for a period of 24 hours. The filters were
then placed in equilibration chambers with different combinations of
relative humidity and temperature. Each filter was weighed after equilibra-
tion times of 1, 2, 4, and 24 hours. From these data, percent difference
in the instantaneous weight and the correct weight versus equilibration
time were determined for each equilibration environment. (The reference
weight was taken as the weight obtained after 24 hours of equilibration
in an environment of less than 50 percent relative humidity and about
25°C.)
Results
Results of this study are applicable only to the type of particulates
in the local area. Particulates with different chemical and physical
properties and/or atmospheres with different concentrations and combina-
tions of gaseous pollutants may give markedly different results.
Four-hour sampling periods with 2 hours of equilibration in a
o
controlled environment at 25 C and a relative humidity of less than 10
percent showed a precision, expressed as a relative standard deviation,
of 5.2 percent. (A collaborative test of the high volume method using
24-hour sampling and equilibration periods showed a relative standard
deviation of 3.0 percent).
Six-hour sampling periods with 2 hours of equilibration in a
o
controlled environment at 25 C and a relative humidity of less than 10
percent showed a relative standard deviation of 3.5 percent.
A potential bias between short-term and 24-hour sampling was
indicated by the second day's set of data showing the cumulative short-
term concentrations to be an average 8.3 percent higher than that given
by the 24-hour samplers. Only a 1.2 percent difference (in the same
direction) was observed on the first day's set of data.
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Suspended particulate concentrations calculated after a 2-hour
equilibration period averaged 1.5 percent higher than when calculated
after a 24-hour equilibration period.
Recommendations
The suggested short-term sampling procedure is a 4-hour sample
collection period followed by a 2-hour equilibration period in a con-
0
trolled environment at approximately 25 C and with a relative humidity
of 10 percent or less. Test results indicate that the precision expressed
as a relative standard deviation of such a short-term procedure would be
about 5.2 percent. The shorter equilibration period (2 hours) results
in an average positive relative bias of 1.5 percent in the measured
concentrations when compared to 24-hour equilibrated samples. A detailed
description of the suggested procedure is given in appendix A.
Results of this study are applicable only to the local area in
which the measurements were made. Therefore, before recommending the
short-term method for general use, it should be evaluated under the
various extremes that will be encountered in the field. For example,
atmospheres with high concentrations of particulates that plug the
filter, causing a nonlinear drop in the flow rate over a 4-hour period,
could result in errors in determining the average flow rate. Other
errors can result due to unequal sampling rates if the particulate
concentration as well as the flow rate is varying with time. Also,
since the precision appears to be a function of the sampling period
duration rather than the weight of collected particulates, the precision
could possibly be improved using continuous flow-rate recorders so that
a better estimate of the average flow rate could be obtained. This
possibility could be investigated with further testing.
Further study could be undertaken to determine the reasons for
differences in the concentrations determined by 24-hour sampling and
those determined by consecutive short-term sampling over a 24-hour
period. It appears from the results of this study that adverse weather
conditions (high humidity, dense fog, air stagnation) can cause a higher
daily average concentration to be measured by consecutive short-term
sampling than by 24-hour sampling over the same period. However, at
this point, there is no definite proof that 24-hour sampling results are
xi
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more accurate estimates of true concentrations than the consecutive
short-term sampling. It is therefore recommended that further testing
be done to examine the causes of differences in this type of comparison.
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1.0 INTRODUCTION
In order to facilitate a shorter reaction time in applying control
strategies during periods of air stagnation advisories, an acceptable short-
term method for the determination of suspended particulates in the atmosphere
is required. The objective of this study is to develop a guidelines document
outlining proper operating procedures for the use of a short-term method of
measuring suspended particulates, following as closely as possible the Environ-
mental Protection Agency (EPA) reference method for the determination of
suspended particulates in the atmosphere (ref. 1).
The study was divided into three tasks as follows:
1. Estimate the precision of short-term (e.g., 4-hour and 6-hour)
sampling periods and determine the comparability of cumulative short-term
sampling results to the 24-hour sampling period by conducting field tests in
the local area using standard high-volume samplers and filters.
2. Evaluate the influence of the equilibration variables! a) relative
humidity, b) temperature, and c) duration on measurement variability-
3. Specify a feasible procedure for short-term sampling based on the
results of 1 and 2 above.
Techniques for dynamic calibration of high-volume samplers using test
atmospheres containing known concentrations of particulates are not available.
Therefore, there is no way of knowing the accuracy of the values derived from
high-volume sampling. However, numerous experiments and studies have been
performed to identify and evaluate factors that influence the final results
(ref. 2) from which accuracy estimates can be deduced. This study then is
designed to determine system precision for different sampling period dura-
tions and to determine the relative error, if any, in estimating a 24-hour
average concentration by combining results from short-term sampling periods
and comparing them with the value obtained from a 24-hour sampling period.
Attached to this report as appendix A is a proposed reference method for
short-term sampling and sample equilibration based on the results of this
study.
Results of this study are applicable only to the type of particulates in
the local area. Particulates with different chemical and physical properties
and/or atmospheres with different concentrations and combinations of gaseous
pollutants may give markedly different results.
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2.0 TEST PLAN
The test plan was designed and conducted in such a manner that the data
could be subjected to statistical analysis allowing for the construction of
confidence limits on the final results. Individual test plans were designed
for the short-term sampling study and the filter equilibration study.
The short-term sampling test plan was designed to allow for estimating
the precision of 4-hour, 6-hour, and 24-hour sampling periods and for com-
paring the average 24-hour suspended particulate concentration obtained by
combining short-term samples with that resulting from one 24-hour sample.
Six samplers were run concurrently with two collecting 24-hour samples, and
the other four making consecutive short-term runs of 4, 4, 6, 6, and 4 hours
over the same 24-hour period. The test was replicated resulting in a total
of 44 samples, including six sets of four 4-hour samples, four sets of four
6-hour samples, and two sets of two 24-hour samples for estimating precisions.
It also provided two sets of data for comparing short-term sampling period
results with 24-hour sampling period results.
The equilibration study consisted of conditioning exposed filters
(high-volume samples) in an environmental chamber set at 32°C and 100 percent
relative humidity for a period of 24 hours. The filters were then placed in
an equilibration chamber with different combinations of relative humidity
and temperature. Each filter was weighed after equilibration times of 1, 2,
4, and 24 hours. From these data, percent difference in the instantaneous
weight and the correct weight versus equilibration time were determined for
each equilibration environment. (The reference weight was taken as the weight
obtained after 24 hours of equilibration in an environment of less than 50
percent relative humidity and about 25°C.) The curves developed from these
data were validated by collecting fresh samples under various temperature and
relative humidity combinations and equilibrating them as described above. A
compilation of the data collected for the short-term sampling study and
equilibration study is tabulated in appendix B.
2.1 Short-term Sampling Study
2.1.1 Apparatus. Apparatus used in the short-term sampling study included
the following:
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1. Six standard high volume samplers, each labeled and having a sepa-
rate flow measuring device.
2. Standard 8 x 10 inch fiberglass filters having a collection effi-
ciency of at least 99 percent for particles of 3 urn diameter.
3. Orifice calibration unit with different resistance plates as shown
in figure A-3 of appendix A.
4. Differential manometer capable of measuring 16 inches of water.
5. Relative humidity indicator.
6. Analytical balance capable of weighing to 0.1 mg.
7- Desiccating chamber.
8. Clean manila folders for the storage of filters.
9. Desiccant.
2.1.2 Description of Sampling Site. The sampling site was located near a
heavily traveled, four-lane highway in Durham, North Carolina. In the
immediate vicinity of the site was a large bus depot and some medium industry.
At the site—the roof of a one-story EPA air testing station—the six samplers
were placed approximately 10 feet apart in two rows of three. Feather con-
ditions during the sampling dates varied from 20 to 100 percent RH and 7°
to 30°C. The winds were variable in direction and speed, and during one
short-term period a dense fog was present.
2.1.3 Procedure. The procedure followed in making high-volume measurements
were essentially those recommended in the quality assurance document EPA-R4-
73-028b (ref. 2). The procedure consisted of these primary operations:
1. Clean filters were inspected for pinholes, marked with an identifica-
tion number, and equilibrated in an airtight disiccator chamber where a
relative humidity of less than 50 percent was controlled by the presence of
fresh Drierite (8 mesh). Each filter was equilibrated in this environment
for a period of 24 hours, weighed to the nearest 0.1 mg, and the tare weight
recorded. The equilibration temperature was 25°C ± 2°C.
2. The samplers were calibrated in the laboratory using the orifice
calibration unit and the differential manometer by the method described in
subsection 8.1.1 of appendix A. Rotameters (one per sampler) were the flow-
measuring devices used.
3. Filter changes for the short-term samplers were carried out as
follows:
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a) Record rotameter indications for short-term samplers.
b) Turn off short-term samplers and record the time.
c) Remove exposed filters, fold, and place in clean manilla
folders .
d) Install new filters.
e) Turn samplers on and record the time and relative humidity.
f) Wait 5 minutes and record rotameter indications.
This procedure minimized the time of sampler shutdown to 15 minutes for
filter changes for the short-term collecting period and allowed for samplers
to be started or stopped within 1 minute of each other.
4. Exposed filters were equilibrated for 24 hours under the same con-
ditions as described above for clean filters and then weighed to the nearest
0.1 mg.
2.1.4 Data Analysis for Short-term Sampling Periods. The data collected for
this section are tabulated in tables B-l and B-2 of appendix B, which contains
a qualitative study for the data analysis performed in this section and in
section 3.0.
Suspended particulate concentrations were calculated by
(W - W.) x 106
SPM "
where
Wf = Weight of filter and particulates after 24 hours of equilibra-
tion, g
W. = Tare weight of filter, g
o
Q_^ = Flow rate at beginning of sampling period, m /min
O
Qf = Flow rate at end of sampling period, m /min
T = Sampling time, min
SP = Measured suspended particulate concentration, yg/m3.
Samplers designated as B, C, D, and E collected short-term samples over
consecutive periods of 4, 4, 6, 6, and 4 hours, while samplers designated as
A and F collected continuously over the same 24-hour period. The resulting
information (presented in table B-l of appendix B) was analyzed to a) estimate
the precision of the weighted average concentrations based on suspended
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particulate concentrations determined from 4-hour and 6-hour sampling periods,
and b) compare the daily average concentration determined by consecutive
short sampling periods to the concentration determined by the 24-hour sampling
period.
The precision of the suspended particulate concentration measurements
for the short-term sampling periods was determined by calculating the average
concentration (SP.), the standard deviation (s.), and the coefficient of
variation (CV.) for each time period according to equations (2), (3), and
(4), respectively.
(2)
1/2
s = / , 3 (3)
J
4 (SP..-SP.)2
CV. = -J- (4)
p
"j
J SP.
where
SP.. = Suspended particulate concentration measured by the i sampler
J "*" th 3
(i = 1 - 4) during the j time period, yg/m . (Values of SP. .
determined during the short-term sampling study are reported
in table B-l of appendix B.)
Estimates of the true coefficients of variation for the short-term
sampling periods were found by the following:
6 ft
CV(4 hours) = V^ —^- (5)
/ j b
3=1
where
CV = Estimated coefficient of variation of the j 4-hour sampling
3
period,
and
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CV(6 hours) =
(6)
3=1
where
CV = Estimated coefficient of variation of the j 6-hour sampling
3
period.
Values of SP., s., and CV. for 4-hour sampling are given in table 1;
J J «J
for 6-hour sampling, the values are listed in table 2,
Table 1. Results from 4-hour sampling periods
Sampling
Day
May 28-29
June 2-3
Sampling
Day
May 28-29
June 2-3
Time
10 a.m.
2 p.m.
6 a.m.
10 a.m.
2 p.m.
6 a.m.
Table 2.
Time
6 p.m.
12 p.m.
6 p.m.
12 p.m.
Period
- 2 p.m.
- 6 p.m.
- 10 a.m.
2 p.m.
- 6 p.m.
- 10 a.m.
Results
Period
- 12 p.m.
— 6 a.m.
- 12 p.m.
- 6 a.m.
SP.. (yg/m3)
80.0
82.0
56.8
77.2
94.8
90.1
from 6-hour sampling
SP. (yg/m3)
J
.106.0
59.5
112.0
68.8
s (yg/m )
4.1
4.7
3.3
3.7
4.2
4.5
periods
s. (yg/m )
3.4
1.5
4.2
2.8
s^
CV3
0.051
0.057
0.058
0.048
0.044
0.050
XX
CTj
0.032
0.025
0.037
0.041
Using the values from table 1 in equation (5), an estimate of the
coefficient of variation for 4-hour sampling periods is
CV(4 hours) = 0.051 = 5.1 percent
For 6-hour sampling periods, an estimate of the coefficient of varia-
tion was calculated from the values in table 2 using equation (6) :
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CV(6 hours) = 0.034 =3.4 percent
According to subsection 2.2 of appendix C, the 90 percent confidence
interval for CV(4 hours) can be calculated in the following manner.
< CV(4 hours) < (7)
where
r = U
•y
CV(4 hours) = 0.051
Y = 0.90
U = 1.645
Y
N = Total number of 4-hour samples (no. of 4-hour sampling
periods x no. of samples collected in each period).
N = 24.
Therefore, the 90 percent confidence interval for CV(4 hours) is:
0.041 < CV(4 hours) < 0.067.
The 90 percent confidence interval for CV(6 hours) was determined in the same
manner. For this calculation
CV(6 hours) = 0.0341
Y = 0.90
U = 1.645
Y
N = Total number of 6-hour samples
N = 16
yielding
0.026 < CV(6 hours) < 0.048.
To compare the short-term with the 24-hour sampling period, an average
24-hour suspended particulate concentration was found for each short-term
sampler by the following equation:
-------
x lo6
where
W. = Particulate weight collected by the sampler during the j time
period, g
t*Vi ^
V. = Air volume sampled by the sampler during the j time period, m .
j
Five consecutive time periods with a total elapsed time of 24 hours
were sampled for this study. The values of SP for all short-term samplers
were averaged and compared with the average suspended particulate concen-
tration determined by the 24-hour samplers (see fig. 1).
The average daily particulate concentration levels as determined by short-
term sampling and 24-hour sampling, as well as the relative difference of the
concentration found by short-term sampling with respect to that found by 24-
hour sampling, are listed below for the respective sampling dates.
May 28-29
3
Average concentration from short-term sampling 77.6 yg/m
3
Average concentration from 24-hour sampling 76.7 yg/m
Relative difference 1.2 percent
June 2-3
3
Average concentration from short-term sampling 88.7 yg/m
Average concentration from 24-hour sampling 81.3 yg/m
Relative difference 8.3 percent
The data show good agreement for the May 28-29 sampling period. The
approximately 8-percent relative difference for the June 2-3 sampling period
is not greater than would be expected due to normal inprecision of the method
(at the .05 level). However, since -the agreement was good among the short-term
samplers and the two 24-hour samplers gave almost identical results (see table
B-l of appendix B for individual values) , the assumption can be made that some
condition adversely affected either all of the short-term samplers or the two
24-hour samplers equally.
Noticeable environmental differences in the two sampling periods were a
much higher relative humidity and more stagnant atmospheric conditions during
the June 2-3 sampling period than during the May 28-29 period. A possible
explanation is that under the conditions of June 2-3 the short-term samplers were
8
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CONCENTRATION DETERMINED
SUSPENDED PARTICULATE CONCENTRATION (^g/m3)
ncn-joitoO — C
JOOOOOO 0
f 1
120
CONCENTRATION DETERMINED
_^- BY SHORT-TERM SAMPLING
*> 110
C9
~ 100
z
Q
or
•t-
iu 90
p-
AVERAGE DAILY CONC. °
^-- FROM SHORT-TERM jil
.^--^ SAMPLING 5 80
. , -«sr^ _.__ .__ r>
^»>^ AVERAGE DAILY CONC. I
FROM 24-HOUR Q 70
SAMPLING o
UJ
OL
VI
\
I i an
-
~
-
^
BY SHORT-TERM SAMPLING
^
AVERAGE DAILY CONC.
FROM SHORT-TERM
^'^SAMPLING
j -^^ .,
^Ji.
AVERAGE^DAILY CONC.
FROM 24-HOUR
SAMPLING
"TOAM 2PM ' 6PM 12PM 6AM 10AM 10AM 2PM 6PM 12PM 6AM 10 AM
TIME
TIME
(A) May 28-29, 1974, sampling period (B) June 2-3, 1974, sampling period
Figure 1. Suspended particulate concentration levels, as determined
from short-term and 24-hour sampling periods.
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biased due to increased conversion of acid gases in the atmosphere to par-
ticulate matter at the surface of the clean alkaline filters (ref. 3).
(Filters used for the study had pH's ranging from about 8.5 to 9.) If this
assumption is true, larger biases can be expected if 1) more alkaline filters
are used, or 2) the atmosphere being tested has higher concentrations of acid
gases. This possibility could be evaluated in future testing by using neutral
filters and/or monitoring gaseous concentrations while sampling.
2.2 Filter Equilibration Study
2.2.1 Apparatus. Special apparatus used in the equilibration study included
the following:
1. Two airtight ovens capable of maintaining a constant temperature
(+ 2°C) and relative humidity (+ 5 percent) .
2. Two airtight desiccating chambers.
3. One airtight environmental chamber capable of maintaining a constant
temperature (+ 2°C) and relative humidity (+ 5 percent) at preset levels.
4. Four thermometers.
5. Four relative humidity indicators.
6. Clean manila folders.
7. Desiccant.
8. Analytical balance capable of measuring to 0.1 mg.
2.2.2 Procedure. After completion of the short-term sampling study, the samples
collected during that study were conditioned in an environment of 32°C and 100
percent relative humidity for a period of 24 hours and used for the equilibration
study. It was felt that this environment was representative of the more adverse
conditions under which high volume sampling is conducted. For the short-term
study, a total of 44 filters (11 per sampler) were used; therefore, in order to
make the best comparison of equilibration conditions, the samples were equilibrated
by sampler group in one of four conditions as listed below.
Filters from
Sampler
B
C
D
E
Environment
Numb er
1
2
3
4
Equilibr at ion
Condition
< 50% RH/25°C
< 10% EH/25°C
< 10% EH/50°C
< 50% RH/50°C
10
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The exposed filters after being conditioned at 32°C and 100 percent RH
were weighed and the weights recorded after 1, 2, 4, and 24 hours of equilibra-
tion. The filter weight after 24 hours of equilbration is defined and will be
referred to throughout this report as the equibrium weight. (Again the 24-
hour weight achieved in environment 1 is defined as the correct weight against
which all other weights are compared.)
2.2.3 Data Analysis for the Equilibration Study. The net collected particulate
wed
by
weight was found as a function of equilibration time, t (t = 1, 2, 4, 24 hours),
Jl SL
where
W (t ) = Net particulate weight at equilibration time, t , g
OJT XL ill
W-(t ) = Filter plus particulate weight at equilibration time,
V 8
W. = Tare weight of filter, g.
Blank filters subjected to the same equilibration procedures as the
samples indicated a negligible filter weight change therefore, W. for a
given filter is considered a constant independent of the equilibration en-
vironment throughout the procedure.
The relative difference of the particulate weight at equilibration time
t_ with respect to the equilibrium weight (the weight at t^ = 24 hours) for
r. £.
a given environment is given by
where
W (t ) = Particulate weight after equilibration for t < 24 hours, g
Oi III Ij
W (24) = Net particulate weight after 24 hours of equilibration, g
O-T
y(t ) = Error in particulate weight at t < 24 hours with respect to
III Hi
the weight at t^ = 24 hours.
£j
For each environment, an average relative difference, y(t ), and stan-
£j
dard deviation, s(y), were determined for t = 1, 2, and 4 hours. The
r.
average relative difference, y(t ), is subscripted with the number of the
11
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environment being considered, e.g., the average relative difference caused
by equilibration in environment 1 for time t is termed y (t ). Values of
*-* J. . E
y(t_). versus t for the respective environments were 'least-squares fitted
E E
to exponential functions and graphed in figure 2. The 90 percent confi-
dence limits for the curves presented in figure 2 were determined such that
a sample equilibration in a given environment for time t will yield a
measured value of y(O that will fall within the interval y(t£) + 1.645 s(y)
approximately 90 percent of the time (1.645 is value of the standard nor-
mal variable, U , whose absolute value is exceeded by 1 - y where-y = 0.90 =
the confidence level).
Since the equilibrium weight of a sample equilibrated in environment
1 (< 50% RH/25°C) is considered to be the correct weight of the collected
particulates (ref. 3), environment 1 is considered the reference equili-
bration environment. In order to compare the effect of equilibration in
environments 2, 3, and 4 with the effect of equilibration in environment 1,
the curves presented in figure 2 were shifted such that the initial values
of y2
-------
UI
o
S.O
40
Cj s •
tg \
ui _ ,
111
cc
1.0
QO
-IX!
-ZJO
ENVIRONMENT 1
U.C.L.
5.0r
ENVIRONMENT 2
-ZOL
o
z
Ul
i
o
Ul
>
> < JO
Ul
a:
1
ui
ENVIRONMENT
8.0
7.0
60
5.0
40
so'
1.0
0.0
-1.0
-2.0
Figure 2. Average relative difference in particulate weight, y(t ), versus
equilibration time, t .
u
Limits of 90 percent Confidence Interval
U.C.L. Upper Confidence Limit
L.C.L. Lower Confidence Limit
o validation data points
i z 3
Cclu "
13
-------
o ENVIRONMENT I
• ENVIRONMENT 2
* ENVIRONMENT 3
x ENVIRONMENT 4
UJ
O
UJ
o:
It!
u_
o
CD
i
UJ
uj 5
* 3
UJ
CD
UJ
-1.0
-2.0
o M24)
• y2(24)
* 73(24)
4567
EQUILIBRATION TIME, tE (hours)
24
Figure 3.
Average relative difference in participate weight versus equilibration time:
Environments 2, 3, and 4 compared with environment 1.
-------
1. Fresh filters were placed in the six high-volume samplers at the
sampling site and allowed to collect particulates for various sampling times
to obtain samples of varying weight.
2. At the end of each sampling period, the samples were equilibrated
in environments described in subsection 2.2.2. Since environment 1 was
considered the reference environment, two filters were placed in that envi-
ronment and the remaining four filters were distributed to two of the other
environments for equilibration.
3. The exposed filters were weighed after 1, 2, 4, and 24 hours of
equilibration and the data analyzed according to equations (9) and (10) .
4. The values of yCt..,) versus t resulting from step 3 above were
£ £i
plotted in figure 2 for the respective environments.
As can be seen, the data collected during this section of the study
appear to validate all of the curves within the respective 90 percent con-
fidence intervals.
3.0 RESULTS
When a suspended particulate concentration has been determined by
sampling during a short sampling period and the sample has been equilibrated
under specified conditions, the 90 percent confidence interval of the true
average suspended particulate concentration for the specified sampling time,
i.e., the interval in which one can be 90 percent confident that the true
average concentration will fall, can be calculated (assuming no bias other
than that due to equilibration) by the following:
SPT = SPM ~ * - -1-*645 °
where
3
SP = True average suspended particulate concentration, yg/m
3
SP = Measured average suspended particulate concentration, yg/m
T = Estimated bias introduced by equilibration for t < 24 hrs ,
yg/m
a = Overall estimated standard deviation of measured samples; a
function of sampling period time and equilibration time.
Estimates of the bias, T, and standard deviation, a, are calculated by
equations (12) and (13) , respectively
15
-------
a = SPM x {CV2(sampling time) + CV2(l + y(tE))}1/2 (13)
xx 2
The square of the estimated relative standard deviation, CV , for single
operator variation for 4-hour sampling periods is
CV2 = CV2(4 hours) = (0.052)2,
and for 6-hour sampling periods
CV2 = CV2(6 hours) = (0.034)2.
Values of
-,2
can be determined from table 3 for the designated equilibration environments
and equilibration times.
The use of this method for determining the true average concentration
from a measured average concentration is illustrated as follows.
3
A measured average suspended particulate concentration of 100 yg/m has
been determined by sampling for 4 hours and equilibrating the sample for
t = 2 hours in environment 2.
ij
The true average suspended particulate concentration with 90 percent
confidence limits can be found by
SP_ = SPM - T + 1.645 a.
1 JM
Equations (12) and (13) state that
T = SP.
M
y(tE)
and a = SPM x {CV (sampling time) + CV [1 + y(t )]}
1/2
where from table 3 for t = 2 hours
16
-------
Table 3. Values of y(t )/[l + y(t_)] and CV[l + y(t )] for varying t
Environment t^
SL
I
1 2
4
1
2 2
4
1
3 2
4
1
4 2
4
y(tE)/[l + y(tE)]
0.0196
0.0143
I
0.0076
0.0221
0.0134
0.0049
0.0354
0.0267
0.0150
0.0240
0.0177
0.0096
CV[1 + y(tE)]
0.0142
0.0098
0.0060
0.0115
0.0081
0.0037
0.0242
0.0174
0.0150
0.0156
0.0117
0.0057
y(2)
= 0.0134 and CV2[1 + y(2)] = (0.0081)2
and for 4 hour sampling periods
CV2 = CV2(4 hours) = (0.051)2
Hence,
SPT = SPM " °'0134
(0.0081) ]
1/2
Therefore, given a measured average suspended particulate concentration,
o
SP , of 100 yg/m , the true average concentration for the specified sampling
time would fall within the following limits
90.1 yg/m3 < SPT < 107 yg/m3
with approximately 90 percent confidence assuming no bias other than that
due to equilibration times less than 24 hours.
17
-------
4.0 CONCLUSIONS
The Short-Term Sampling Study indicates that the coefficient of varia-
tion for single operator variation is a function of sampling time. Short
sampling times increase the variation from 3 percent for 24-hour sampling
(ref. 4), to an average of approximately 3.4 percent for 6-hour sampling, and
5.2 percent for 4-hour sampling.
For the sampling dates studied, the plots in figures 1A and IB show good
agreement between the daily average particulate concentration determined by
consecutive short-term sampling periods and that found by 24-hour sampling.
The percent difference (expressed as the relative difference) between the
results of the two methods varied from approximately 1 percent for May 28-29
to approximately 8 percent for June 2-3. It is felt, however, that further
study will be necessary in order to draw any definite conclusions based on
this type of comparison.
The recommended equilibration procedure for the type of particulates
studied is 2 hours of postsampling conditioning in an environment comparable
to environment 2 (i.e., at ~ 25°C and EH j£ 10 percent). While none of the
environments studies, with the possible exception of environment 3, con-
tributes extreme errors to the measured particulate concentration, environ-
ment 2 caused the instantaneous particulate weight to decrease more rapidly
and with less variability toward an equilibrium weight (i.e., the weight
after 24-hours of equilibration) for equilibration times less than 24 hours.
5.0 RECOMMENDATIONS
Recommendations are given in two areas. First, procedures for short-
term high volume sampling are recommended based on the data obtained from
this study. Secondly, recommendations are made for further evaluation of
short-term sampling in different atmospheres where the chemical and physical
properties of the particulate,matter adequately cover the spectrum of par-
ticulates encountered in high-volume sampling.
5.1 Recommended Short-term Sampling Procedure
The recommended short-term sampling procedures differ from the proce-
dures for the EPA reference method of measuring suspended particulates in
ambient air only in the length of the sample collection period and the
filter equilibration conditions. The recommended short-term method is given
in detail in appendix A. In this section the specific recommendations are
given along with the reasons for making the recommendation.
18
-------
Results from this study indicate that if these recommended procedures
are followed the reported values will be within ± 10 percent of the average
value with 90 percent confidence. The average value as used here represents
the average value that would result from several measurements made under
similar conditions. The average value will be the true value if there is
no bias in the measurement process.
5.1.1 Recommended Sampling Procedure. A 4-hour sampling period is recommended.
The data analysis indicated that for collected particulate weights greater
than about 20 mg the sampling period time is. more critical to precision than
is the actual particulate weight. A 4-hour sampling period appears to be
about the shortest possible for the results to be within ± 10 percent of the
average value with 90-percent confidence.
5.1.2 Recommended Equilibration Procedure. A 2—hour equilibration period in
a controlled environment with a relative humidity of 10 percent or less and a
temperature of approximately 25°C is recommended. These conditions are
recommended. These conditions are recommended for several reasons. First,
the desired conditions can be realized with simple equipment. A desiccator
with fresh Drierite will maintain a less than 10 percent relative humidity,
and the normal range of temperatures of a working area is acceptable. Also,
this set of conditions was selected because of the smaller variability in
the test data (see fig. 3, environment 2) and because the particulate weight
after 24-hours of equilibration in this set of conditions was not significantly
different from that obtained from the reference environment, i.e., that
recommended in reference 1.
5.2 Recommendations for Further Testing
Results of this study are applicable only to the local area in which
the measurements were made. Therefore, before recommending the short-term
method for general use, it should be evaluated -under the-various extremes
that will be encountered in the field. For example, atmospheres with high
concentrations of particulates that plug the filter, causing a nonlinear
drop in the flow rate over a 4-hour period, could result in errors in deter-
mining the average flow rate. Other errors can result due to unequal
sampling rates if the particulate concentration as well as the flow rate is
varying with time. Also, since the precision appears, to be a function of
19
-------
the sampling period duration rather than the weight of collected particu-
lates, the precision could possibly be improved using continuous flow-rate
recorders so that a better estimate of the average flow rate could be ob-
tained. This possibility could be investigated with further testing.
Further study could be undertaken to determine the reasons for dif-
ferences in the concentrations- determined by 24-hour sampling and those
determined by consecutive short-term sampling over a 24-hour period. It
appears from the results of this study that adverse weather conditions (high
humidity, dense fog, air stagnation) cause a higher daily average concen-
tration to be measured by consecutive short-term sampling than by 24-hour
sampling over the same period. However, at this point, there is no definite
proof that 24-hour sampling results are more accurate estimates of true
concentrations than the consecutive short-term sampling. It is therefore
recommended that further testing be done to examine the causes of differences
in this type of comparison.
6.0 REFERENCES
1. Appendix B, "National Primary and Secondary Ambient Air Standards."
Federal Register 36, No. 84, Part II CApril 30, 1971).
2. U.S. Environmental Protection Agency. Guidelines for Development of
a Quality Assurance Program; Reference Method for the Determination
of Suspended Particulates in the Atmosphere (High Volume Method).
EPA-R4-73-028b, Washington, B.C., June 1973.
3. Robert M. Burton et al. "Field Evaluation of the High-Volume Particle
Fractionating Cascade Impactor—A Technique for Reapirable Sampling."
Presented at the 65th. annual meeting of the Air Pollution Control
Association, June 18-22, 1972.
4. Herbert C. McKee et al. Collaborative Study of Reference Method for
the Determination of Suspended Particulates in the Atmosphere (High
Volume Method). Southwest Research Institute, Contract CAP 70-40,
SwRI Project 21-2811, San Antonio, Texas, June 1971.
20
-------
APPENDIX A PROPOSED REFERENCE METHOD FOR THE DETERMINATION
OF SUSPENDED PARTICULATES IN THE ATMOSPHERE
OVER SHORT SAMPLING TIMES.
(HIGH VOLUME METHOD)
1.0 PRINCIPLE AND APPLICABILITY
1. Air is drawn into a covered housing and through a filter by means
3
of a high-flow-rate blower at a flow rate (1.41 to 1.98 m /min; 50 to 70
3
ft /min) that allows suspended particles having diameters of less than 100
ym (Stokes equivalent diameter) to pass to the filter surface (ref. 1).
Particles within the size range of 0.1 to 100 ym diameter are ordinarily
collected on fiberglass filters. The mass concentration of suspended par-
3
ticulates in the ambient air (yg/m ) is computed by measuring the mass of
collected particulates and the volume of air sampled.
2. This method is applicable to measurement of 4-hour average mass con-
centrations of suspended particulates in ambient air. To assure measurements
of acceptable precision, this method should not be used to measure average
3
concentrations of less than about 50 yg/m (this yields 4-hour samples of
approximately 20 mg). The size of.the sample collected is usually adequate
3
for other analyses. Concentrations as low as 10 yg/m can be measured; however,
the relative error would probably be larger than that given in section 4.0.
2.0 RANGE AND SENSITIVITY
Weights are determined to the nearest 0.1 mg, airflow rates are deter-
3
mined to the nearest 0.1 m /min, times are determined to the nearest minute,
and mass concentrations are reported to three significant digits, e.g., 102
3 3
yg/m and 50.6 yg/m .
3.0 INTERFERENCES
1. Particulate matter that is oily, such as photochemical smog or wood
smoke, may block the filter and cause a rapid drop in airflow at a nonuniform
rate. Dense fog or high humidity in conjunction with certain types of par-
ticulates may severely reduce the airflow through the filter.
2. Fiberglass filters are comparatively insensitive to changes in
relative humidity but collected particulates can be hygroscopic (ref. 2).
3. Acid gases in the sample air may be converted to particulate matter
on the surface of alkaline filters (refs. 3, 4).
21
-------
4.0 PRECISION, ACCURACY, AND STABILITY
4.1 Precision
Based on the Short-term High-Volume Study, the estimated relative stan-
dard deviation (coefficient of variation) for single analyst variation (re-
peatability) for 4-hour sampling and 2-hour equilibration periods is 5.2 percent.
4.2 Accuracy
The accuracy with which the sampler measures the true average concentration
cannot be quantitatively determined. Measured values higher than the true values
may result when alkaline filters are used. A functional analysis of the method
indicates that other large biases should not occur in short-term sampling (ref. 5)
5.0 APPARATUS
5.1 Sampling
5.1.1 Sampler. The sampler consists of three units: 1) the faceplate and
gasket, 2) the filter adapter assembly, and 3) the motor unit. Figure A-l shows
an exploded view of these parts, their relationship to each other, and how they
are assembled. The sampler must be capable of passing environmental air through
3 2
a 406.5 on (63 in. ) portion of a clean 20.3 by 25.4 cm (8 by 10 in.) fiber-
3 3
glass filter at a rate of at least 1.70 m /min (60 ft /min). The motor must
Vnr-^
Figure A-l. Exploded view of typical high-volume air sampler parts.
22
-------
be capable of continuous operation for 4-hour periods with input voltages
ranging from 110 to 120 volts, 50-60 cycles alternating current and must have
third-wire safety ground. The housing for the motor unit may be of any con-
venient construction so long as the unit remains airtight and leak free.
5.1.2 Sampler Shelter. It is important that the sampler be properly
installed in a suitable shelter. The shelter is subjected to extremes of
temperature, humidity, and all types of air pollutants. For these reasons
the materials of the shelter must be chosen carefully. Properly painted
exterior plywood or heavy gauge aluminum serve well. The sampler must be
mounted vertically in the shelter so that the fiberglass filter is paral-
lel with the ground. The shelter must be provided with a roof so that the
filter is protected from precipitation and debris. The internal arrange-
ment and configuration of a suitable shelter with a gable roof are shown in
figure A-2. The clearance area between the main housing and the roof at its
2 2
closest point should be 580.5 + 193.5 cm (90 + 30 in. ). The main housing
should be rectangular, with dimensions of about 29 by 36 cm (11-1/2 by 14 in.)
5.1.3 Rotameter. A rotameter marked in arbitrary units, frequently 0 to 70,
and capable of being calibrated is acceptable for measuring sample flow rates.
Other devices of at least comparable accuracy may be used (see addendum A).
Figure A-2. Assembled sampler and shelter.
23
-------
5.1.4 Orifice Calibration Unit. Consisting of a metal tube 7.6 cm (3 in.)
ID and 15.9 cm (6-1/4 in.) long with a static pressure tap 5.1 cm (2 in.)
from one end. See figure A-3. The tube end nearest the pressure tap is
flanged to about 10.8 cm (4-1/4 in.) OD with a male thread of the same size
as the inlet end of the high-volume air sampler. A single metal plate
9,2 cm (3-5/8 in.) in diameter and 0.24 cm (3/32 in.) thick with a central
orifice 2.9 cm (1-1/3 in.) in diameter is held in place at the air inlet
end with a female threaded ring. The other end of the tube is flanged to
hold a loose female threaded coupling> which screws onto the inlet of the
sampler. An 18-hole metal plate, an integral part of the unit, is positioned
between the orifice and sampler to simulate the resistance of a clean fiber-
glass filter. An orifice calibration unit is shown in figure A-3.
5.1.5 Differential Manometer. Capable of measuring to at least 40 cm
(16 in.) of water.
5.1.6 Positive Displacement Meter. Calibrated in cubic meters or cubic
feet, to be used as a primary standard.
5.1.7 Barometer. Capable of measuring atmospheric pressure to the nearest
mm of Hg.
5.2 Analysis
5.2.1 Filter Conditioning Environment. Balance room or desiccator maintained
ORIFICE
RESISTANCE PLATES
Figure A-3. Orifice calibration unit.
24
-------
at approximately 25°C and less than 10 percent relative humidity. A
desiccator with fresh desiccant such as Drierite maintained in an air-
conditioned room provides a satisfactory conditioning environment.
5.2.2 Analytical Balance. Equipped with a weighing chamber designed to
handle unfolded 20.3 by 25.4 cm (8 by 10 in.) filters and having a sensi-
tivity of 0.1 mg.
5.2.3 Light Source. Frequently a table of the type used to view X-ray
films.
5.2.4 Number Device. Capable of printing identification numbers on the
filters.
6.0 REAGENTS
6.1 Filter Media
Neutral fiberglass filters having a collection efficiency of at least 99
percent for particles of 0.3 ym diameter, as measured by the DOP test, are
suitable for the quantitative measurement of concentrations of suspended
particulates (ref. 6), although some other medium, such as paper, may be
desirable for some analyses. If a more detailed analysis is contemplated,
care must be exercised to use filters that contain lox-/ background concen-
trations of the pollutant being investigated. Careful quality control is
required to determine background values of these pollutants.
7.0 PROCEDURE
7.1 Sampling
7.1.1 Filter Preparation. Expose each filter to the light source and inspect
for pinholes, particles, or other imperfections. Filters with visible imper-
fections should not be used. A small brush is useful for removing particles.
Print an identification number using the numbering device on the outer edge
of the filters. Equilibrate the filters in the filter conditioning environ-
ment of section 7.2 for 2 hours. Weigh the filters to the nearest 0.1 mg;
record tare weight and filter identification number. Do not bend or fold the
filter before collection of the sample.
7.1.2 Sample Collection. Open the shelter, loosen the wing nuts, and remove
the faceplate from the filter holder. Install a numbered, preweighed,
25
-------
fiberglass filter in position (rough side up), replace the faceplate
without disturbing the filter, and fasten securely. Undertightening will
allow air leakage; overtightening will damage the sponge rubber faceplate
gasket. A very light application of talcum powder may be used on the
sponge rubber faceplate gasket to prevent the filter from sticking. During
inclement weather the sampler may be removed to a protected area for filter
i
change. Close the roof of the shelter, run the sampler for about 5 minutes,
connect the rotameter to the nipple on the back of the sampler, and read
the widest part of the rotameter float with the rotameter in a vertical
position. Estimate to the nearest whole number. If the float is fluctuating
rapidly, tip the rotameter and slowly straighten it until the float gives
a constant reading. Disconnect the rotameter from the nipple; record the
initial rotameter reading, the starting time, and the date on the filter
or other suitable form folder. (The rotameter should never be connected
to the sampler except when the flow is being measured.) Sample for 4 hours
and take a final rotameter reading. Record the final rotameter reading,
ending time, and date on the filter folder or other suitable form. Remove
the faceplate as described above and carefully remove the filter from the
holder, touching only the outer edges. Fold the filter lengthwise so that
only surfaces with collected particulates are in contact, and place in a
manila folder. Record on the folder or other suitable form the filter number,
location, and any other factors, such as meteorological conditions or razing
of nearby buildings, that might affect the results. If the sample is defective,
void it at this time. In order to obtain a valid sample, the flow rate of
a high-volume sampler must be measured with the same rotameter and tubing that
were used during its calibration.
-7.2 Analysis
Equilibrate the exposed filters for 2 hours in a low relative humidity
(< 10 percent) and room temperature environment, then weigh to the nearest
0.1 mg. After they are weighed, the filters may be saved for detailed chem-
ical analysis.
7.3 Maintenance
7.3.1 Sampler Motor. Replace brushes before they are worn to the point
where motor damage can occur.
7.3.2 Faceplate Gasket. Replace when the margins of samples are no longer
26
-------
sharp. The gasket may be sealed to the faceplate with rubber cement or
double-sided adhesive tape.
7.3.3 Rotameter. Clean as required, using alcohol.
8.0 CALIBRATION
8.1 Purpose
Since only a small portion of the total air sampled passes through the
rotameter during measurement, the rotameter must be calibrated against ac-
tual airflow with the orifice calibration unit. Before the orifice cali-
bration unit can be used to calibrate the rotameter, the orifice calibra-
tion unit itself must be calibrated against the positive displacement
primary standard.
8.1.1 Orifice Calibration Unit. Attach the orifice calibration unit to the
intake end of the positive displacement primary standard and attach a high-
volume motor blower unit to the exhaust end of the primary standard. Con-
nect one end of a differential manometer to the differential pressure tap
of the orifice calibration unit and leave the other end open to the atmos-
phere. Operate the high-volume motor blower unit so that a series of dif-
ferent, but constant, airflows (usually six) are obtained for definite time
periods. Record the reading on the differential manometer at each airflow.
The different constant airflows are obtained by placing a series of load-
plates, one at a time, between the calibration unit and the primary standard.
Placing the orifice before the inlet reduces the pressure at the inlet of
the primary standard below atmospheric; therefore, a correction must be made
for the increase in volume caused by this decreased inlet pressure. Attach
one end of a second differential manometer to an inlet pressure tap of the
primary standard and leave the other open to the atmosphere. During each of
the constant airflow measurements made above, measure the true inlet pres-
sure of the primary standard with this second differential manometer.
Measure atmospheric pressure and temperature. Correct the measured air
volume to true air volume as directed in subsection 9.1.1, then obtain true
airflow rate, Q, as directed in subsection 9.1.3. Plot the differential
manometer readings of the orifice unit versus 0.
8.1.2 High-volume Sampler. Assemble a high-volume sampler with a clean
filter in place and run for at least 5 minutes. Attach a rotameter, read
27
-------
the float, adjust so that the float reads 65} and seal the adjusting mech-
anism so that it cannot be changed easily. Shut off motor, remove the
filter, and attach the orifice calibration unit in its place. Operate the
high-volume sampler at a series of different, but constant, airflows
(usually six). Record the reading of the differential manometer on the
orifice calibration unit and record the readings of the rotameter at each
flow. Measure atmospheric pressure and temperature. Convert the differen-
tial manometer reading to m /min, Q, then plot rotameter reading versus Q.
8.1.3 Correction for Differences in Pressure or Temperature. See Addendum
9.0 CALCULATIONS
9.1 Calibration of Orifice
9.1.1 True Air Volume. Calculate the air volume measured by the positive
displacement primary standard.
(P - P )
v
a P v M'
a
where
3
V = True air volume at atmospheric pressure, m
3.
P = Barometric pressure, mm Hg
SL
P = Pressure drop at inlet of primary standard, mm Hg
V = Volume measured by primary standard, m .
9.1.2 Conversion Factors
Inches Hg x 25.4 = mm Hg.
_3
Inches water * 73,48 * 10 = inches of Hg.
Cubic feet air x 0.0284 = cubic meters air.
9.1.3 True Airflow Rate
V
where
3
Q = Flow rate, m /min
T = Time of flow, min.
28
-------
9.2 Sample Volume
9; 2.1 Flow Rate Conversion. Convert the initial and final rotameter readings
to true airflow rate, Q, using the calibration curve of subsection 8.1.2.
9.2.2 Volume of Air Sampled. Calculate the volume of air sampled by
V =
where
2
V = Air volume sampled, m
3
Q. = Initial airflow rate, m /min
1 3
Q,. = Final airflow rate, m /min
T = Sampling time, min.
9.3 Mass Concentration
Calculate mass concentration of suspended particulates by
(W - W-) x 106
where
3
SP = Mass concentration of suspended particulates, yg/m
W^ = Initial weight of filter, g
W = Final weight of filter, g
r 3
V = Air volume sampled, m
6
10 = Conversion of g to yg.
10.1 REFERENCES
1. C. D. Robson and K. E. Foster. "Evaluation of Air Particulate Sampling
Equipment." Am. Ind. Hyg. Assoc. J. 24(1962); 404.
2. G. P. Tierney and W. D. Conner. "Hygroscopic Effects on Weight Deter-
minations of Particulates Collected on Glass-Fiber Filters." Am. Ind.
Hyg. Assoc. J. 28 (1967): 363.
3. Robert M. Burton et al. "Field Evaluation of the High-Volume Particle
Fractionating Cascade Impactor—A Technique for Respirable Sampling."
Presented at the 65th Annual Meeting of the Air Pollution Control
Association, June 18-22, 1972.
4. Peter K. Mueller et al. "Selection of Filter Media: An Annotated
29
-------
Outline." Presented at the 13th Conference on Methods in Air Pollu-
tion and Industrial Hygiene Studies, University of California, Berkeley,
California, October 30-31, 1972.
5. F. Smith and A. C. Nelson, Jr., "Guidelines for Development of Quality
Assurance Programs and Procedures Applicable to Measuring Pollutants for
Which National Ambient Air Quality Standards Have Been Promulgated,"
Final Report, Research Triangle Institute, Contract No. EPA-Durham-
68-02-0598, Environmental Protection Agency, Research Triangle Park,
N.C. 27711, Aug. 1973.
6. J. B. Pate and E. C. Tabor. "Analytical Aspects of the Use of Glass-
Fiber Filters for the Collection and Analysis of Atmospheric Particu-
late Matter." Am. Ind. Hyg. Assoc. J. 23 (1962): 144-50.
30
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A. ALTERNATIVE EQUIPMENT
A modification of the high-volume sampler incorparating a method for
recording the actual airflow over the entire sampling period has been
described, and is acceptable for measuring the concentration of suspended
particulates (J. S. Henderson. Eighth Conference on Methods in Air Pollu-
tion and Industrial Hygiene Studies, Oakland, Calif, 1967). This modifi-
s
cation consists of an exhaust orifice meter assembly connected through a
transducer to a system for continuously recording airflow on a circular
chart. The volume of air sampled is calculated by the following equation:
V = Q x T
3
Q = Average sampling rate, m /min.
T = Sampling time, minutes.
The average sampling rate, Q, is determined from the recorder chart by estima-
3 3
tion if the flow rate does not vary more than 0.11 m /min. (4 ft /min) during
3 3
the sampling period. If the flow rate does vary more than 0.11 m (4 ft /min)
during the sampling period, read the flow rate from the chart at 2-hour inter-
vals and take the average.
B. PRESSURE AND TEMPERATURE CORRECTIONS
If the pressure or temperature during high-volume sampler calibration
is substantially different from the pressure or temperature during orifice
calibration, a correction of the flow rate, Q, may be required. If the
pressures differ by no more than 15 percent and the temperatures differ by
no more than 100 percent (°C), the error in the uncorrected flow rate will
be no more than 15 percent. If necessary, obtain the corrected flow rate as
directed below. This correction applies only to orifice meters having a con-
stant orifice coefficient. The coefficient for the calibrating orifice
described in 5.1.4 has been shown experimentally to be constant over the
3
normal operating range of the high-volume sampler (0.6 to 2.2 m /min; 20 to
3
78 ft /min). Calculate corrected flow rate:
31
-------
T P
21
T
I
1/2
where
Q? = Corrected flow rate, m /min
Q1 = Flow rate during high-volume sampler calibration (subsection
8.1.2), m3/min
TI = Absolute temperature during orifice unit calibration (subsection
8.1.1), K or °R.
P- = Barometric pressure during orifice unit calibration (subsection
8.1.1), mm. Hg.
!„ = Absolute temperature during high-volume sampler calibration
(subsection 8.1.2), K or °R.
7 = Barometric pressure during high-volume sampler calibration
(subsection 8.1.2), mm. Hg.
32
-------
APPENDIX B
COMPILATION OF DATA FOR THE SHORT-TERM HIGH-VOLUME SAMPLING STUDY
33
-------
1.0 DATA COLLECTED FOR THE SHORT-TERM SAMPLING STUDY
Table B-l. Measured suspended particulate concentrations
from 4-, 6-, and 24-hour sampling periods
Concentration (yg/m )
Sampler
B
C
D
E
A
F
SP.
s.
J
B
C
D
E
A
F
SP"
J
s .
~ ^a
j
10 a.m.-
2 p.m.
79.7
74.5
84.0
81.8
—
80.0
4.1 '
5.1
75.5
76.2
82.7
74.5
—
—
77.2
3.7
4.8
2 p.m.-
6 p.m.
75.5
82.6
86.8
83.0
—
—
82.0
4.7
5.8
89.1
95.4
99.1
95.8
—
—
94.8
4.2
4.4
6 p .m.—
12 p.m.
May
104.6
102.2
108.6
108.6
—
—
106.0
3.2
3.0
June
106.6
117.2
113.7
111.9
—
—
112.4
4.5
4.0
12 p.m.-
6 a.m.
28-29
58.4
58.1
60.3
61.2
—
—
59.5
1.5
2.6
2-3
64.7
71.3
69.5
69.7
__
—
68.8
2.8
4.1
6 a.m.-
10 a.m.
57.4
52.4
60.4
57.1
—
—
56.8
3.3
5.8
83.5
92.9
93.1
91.0
—
—
90.1
4.5
5.0
24-hr.
SPAVE (10 a.m.
10 a.m.)
76.1
74.9
80.3
79.3
78.5
75.0
77.7 76.8
2.6
3.3
83.9
90.9
91.3
88.8
81.3
81.7
88.7 81.5
3.4
3.8
34
-------
Table B-2. Data Collected May 28-29, 1974
Equilibration Conditions: < 50% Relative Humidity/ 25°C + 2°C
Sampling Period
Sampler
A
F
B
C
D
E
B
C
D
E
B
C
D
E
B
C
D
E
B
C
D
E
Filter
No.
5
2
3
7
4
1
8
10
6
9
12
14
11
13
15
20
16
19
18
21
17
22
Start
2:00
2:00
2:00
2:00
2:00
2:00
6:00
6:00
6:00
6:00
12:00
12:00
12:00
12:00
6:15
6:15
6:15
6:15
10:15
10:15
10:15
10:15
p .m.
p .m.
p .m.
p .m.
p .m.
p .m.
p .m.
p .m.
p .m.
p .m.
p .m.
p .m.
p .m.
p .m.
a.m.
a.m.
a.m.
a.m.
a.m.
a.m.
a.m.
a.m.
Stop Elapsed Time
(min)
2:00
2:00
5:45
5:45
5:45
5:45
11:45
11:45
11:45
11:45
6:00
6:00
6:00
6:00
10:00
10:00
10:00
10:00
2:00
2:00
2:00-
2:00
p .m.
p .m.
p .m.
p .m.
p .m.
p .m.
p .m.
p .m.
p .m.
p .m.
a.m.
a.m.
a.m.
a.m.
a.m.
a.m.
a.m.
a.m.
p.m.
p.m.
p.m.
p .m.
1440
1440
225
225
225
225
345
345
345
345
360
360
360
360
225
225
225
225
225
225
225
225
Flow
Rate
, 3, . ,
(m '/nun)
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
66
80
72
98
79
89
71
95
79
86
67
95
86
86
72
93
80
87
65
95
80
83
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
Weights (g)
w.
i
.6460
.8249
.6048
.6187
.8082
.6358
.8342
.8183
.8382
.6392
.8167
.8562
.6316
.6591
.5838
.8520
.8292
.5592
.8385
.5917
.5619
.8424
Wf
3.8333
4.0198
3.6341
3.6556
3.8432
3.6711
3.8958
3.8871
3.9053
3.7089
3.8518
3 . 89 70
3.6721
3.7001
3.6061
3.8748
3.8537
3.5833
3.8681
3.6244
3.5960
3.8761
35
-------
Table B-3. Data Collected June 2-3, 1974
Equilibration Conditions: < 50% Relative Humidity/ 25°C + 2°C
Sampling Period
Sampler
A
F
B
C
D
E
B
C
D
E
B
C
D
E
B
C
D
E
B"'
C
D
E .
Filter Start
No.
23
24
28
26
25
27
32
30
29
31
36
34
33
35
40
38
37
39
44
42
41
43
10:00
10:00
10:00
10:00
10:00
10:00
2:00
2:00
2:00
2:00
6:00
6:00
6:00
6:00
12:00
12:00
12:00
12:00
6:15
6:15
6:15
6:15
a.m.
a.m.
a.m.
a.m.
a.m.
a.m.
p .m.
p .m.
p .m.
p .m.
p.m.
p .m.
p .m.
p .m.
p .m.
p .m.
p .m.
p .m.
a.m.
a.m.
a.m.
a.m.
Stop Elapsed Time
(min)
10:00
10:00
1:45
1:45
1:45
1:45
5:45
5:45
5:45
5:45
11:45
11:45
11:45
11:45
6:00
6:00
6:00
6:00
10:00
10:00
10:00
10:00
a.m.
a.m.
p .m.
p .m.
p .m.
p.m.
p .m.
p.m.
p .m.
p .m.
p.m.
p.m.
p .m.
p .m.
a.m.
a.m.
a.m.
a.m.
a.m.
a.m.
a.m.
a.m.
1440
1440
225
225
225
225
225
225
225
225
345
345
345
345
360
360
360
360
225
225
225
225
Flow Rate
(m /min)
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
.83
.90
.82
.90
.85
.93
.78
.87
.86
.95
.76
.77
.85
.92
.78
.78
.88
.90
.80
.78
.89
.93
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
•Weights (g)
Wi
.6341
.8228
.7533
.7858
.5885
.6124
.7650
.7330
.5905
.6214
.7517
.7411
.6248
.5956
.7682
.8069
.6113
.5841
.7521
.7644
.5815
.6037
Wf
3.8490
4.0467
3.7842
3.7984
3.6230
3.6448
3.8007
3.7731
3.6321
3.6634
3.8165
3.8126
3.6975
3.6699
3.8097
3.8527
3.6583
3.6319
3.7859
3.8017
3.6211
3.6433
36
-------
2.0 DATA COLLECTED FOR THE EQUILIBRATION STUDY
Table B-4. Sample weight as a function of equilibration time,
samples collected by Sampler B,
Environment 1
Equilibration Conditions: < 50% RH/ 25°C
Weight, W (t ), in grams.
r EJ
t^ = Equilibration time, hours.
Filter No.
44
40
36
3
15
18
8
12
32
28
2 (Sampler F)
47 (Blank)
48 (Blank)
Wf (1)
3.7860
3.8102
3.8175
3.6337
3.6054
3.8668
3.8972
3.8511
3.7999
3.7838
4.0289
3.6244
3.7737
Wf (2)
3.7858
3.8093
3.8164-
3.6335
3.6052
3.8666
3.8963
3.8502
3.7996
3.7835
4.0222
3.6245
3.7739
Wf (4)
3.7849
3.8086
3.8157
3.6328
3.6045
3.8661
3.8956
3.8497
3.7992
3.7831
4.0179
3.6245
3.7740
Wf(24)
3.7855
3.8088
3.8160
3.6331
3.6045
3.8664
3.8962
3.8503
3.7996
3.7833
4.0179
3.6250
3.7742
W.
i
3.7521
3.7682
3.7517
3.6048
3.5838
3.8385
3.8342
3.8167
3.7650
3.7533
3.8249
37
-------
Table B-5. Sample weight as a function of equilibration time,
samples collected by Sampler C,
Environment 2
Equilibration Conditions: < 10% EH/ 25°C
Weight, Wf(tE), in grams.
t« = Equilibration time, hours.
Filter No.
10
21
7
20
14
42
38
34
26
30
5 (Sampler A)
49 (Blank)
50 (Blank)
Wf (1)
3.8866
3.6231
3.6542
3.8741
3.8948
3.8009
3.8522
3.8122
3.7969
3.7715
3.8322
3.6214
3.6457
Wf (2)
3.8860
3.6224
3.6541-
3.8736
3.8943
3.8006
3.8516
3.8110
3.7962
3.7710
3.8303
3.6217
3.6453
Wf(4)
3.8856
3.6219
3.6536
3.8732
/ 3.8938
3.8004
3.8513
3.8106
3.7960
3.7706
3.8295
3.6217
3.6456
Wf(24)
3.8859
3.6222
3.6535
. 3.8730
3.8935
3.8001
3.8512
3.8112
3.7959
3.7706
3.8294
3.6220
3.6459
w.
i
3.8183
3.5917
3.6187
3.8520
3.8562
3.7644
3.8069
3.7411
3.7658
3.7330
3.6460
38
-------
Table B-6. Sample Weight as a function, of equilibration time,
samples collected by Sampler D,
Environment 3
Equilibration Conditions: < 10% RH/ 50°C
Weight, Wf(tE), in grams.
t = Equilibration time, hours.
Filter No.
6
17
4
11
16
41
37
33
25
29
23 (Sampler A)
51 (Blank)
52 (Blank)
Wf (1)
3.9029
3.5938
3.8416
3.6697
3.8520
3.6205
3.6570
3.6964
3.6215
3.6303
3.8462
3.7772
3.6086
Wf (2)
3.9029
3.5929
3,8416-
3.6693
3.8513
3.6202
3.6561
3.6957
3.6209
3.6300
3.8444
3.7772
3.6086
Wf (4)
3.9019
3.5936
3.8412
3.6685
3.8500
3.6194
3.6551
3.6949
3.6211
3.6293
3.8424
3.7772
3.6087
Wf (24)
3.9012
3.5920
3.8414
3.6679
3.8503
3.6198
3.6538
3.6949
3.6208
3.6285
3.8422
3.7774
3.6089
Wi
3.8382
3.5619
3.8082
3.6316
3.8292
3.5815
3.6113
3.6248
3.5885
3.5905
3.6341
39
-------
Table B-7. Sample weight as a function of equilibration time,
samples collected by Sampler E,
Environment 4
Equilibration Conditions: < 50% RH/ 50°C
Weight, Wf(tF), in grams.
t = Equilibration time, hours.
Filter No.
13
35
9
22
27
31
19
1
43
39
24 (Sampler F)
53 (Blank)
54 (Blank)
Wf (1)
3.6965
3.6678
3.7063
3.8747
3.6431
3.6614
3.5820
3.6699
3.6423
3.6298
4.0427
3.7737
3.6286
Wf (2)
3.6968
3.6676
3.7058°
3.8738
3.6422
3.6609
3.5815
3.6690
3.6420
3.6291
4.0410
3.7738
3.6283
Wf (4)
3.6963
3.6667
3.7054
3.8738
3.6422
3.6605
3.5812
3.6684
3.6413
3.6278
4.0391
3.7735
3.6287
Wf(24)
3.6961
3.6658
3.7050
3.8735
3.6428
3.6607
3.5816
3.6685
3.6417
3.6271
4.0376
3.7741
3.6388
Wi
3.6591
3.5956
3.6392
3.8424
3.6124
3.6214
3.5592
3.6358
3.6037
3.5841
3.8228
40
-------
Table B-8. Values of y(t ) and s(y) for varying equilibration times
Environment t_,
K
i
1 2
4
24
1
2 2
4
24
1
3 2
4
24
1
4 2
4
24
Actual
y(tE)
(fig. 4)
0.0200
0.0145
0.0077
0.0000
0.0226
0.0136
0.0049
0.0000
0.0367
0.0274
0.0153
0.0000
0.0246
0.0180
0.0097
0.0000
Comparative
y(t£)
(fig. 3)
0.0200
0.0145
0.0077
0.0000
0.0200
0.0110
0.0023
-0.0026
0.0200
0.0107
-0.0014
-0.0167
0.0200
0.0134
0.0051
-0.0046
s(y)
0.0145
0.0100
0.0061
—
0.0118
0.0082
0.0037
—
0.0251
0.0179
0.0152
—
0.0160
0.0119
0.0058
—
41
-------
3.0 DATA COLLECTED FOR VALIDATION OF EQUILIBRATION STUDY RESULTS
Table B-9. Sample weight as a function of equilibration time
Weight, W (t ) , in grams.
= Equilibration time, hours.
Environment Filter No.
59
60
1 61
62
67
68
57
58
2 63
64
73
74
55
56
3 69
70
75
76
65
66
4 71
72
77
wf (l)
3.8787
3.7102
3.8777
3.7447
3.9715
3.8040
3.8670
3.7407
3.9051
3.7636
4.2537
4.0899
3.8680
3.7098
3.9629
3.7999
4.2754
4.2239
3.9059
3.7551
3.9824
3.7882
4.2551
Wf (2)
3.8770
3.7090
3.8771
3.7445
3.9704
3.8029
3.8657
.3.7390
3.9048
3.7636
4.2466
4.0846
3.8652
3.7074
3.9589
3.7938
4.2755
4.2185
3.9057
3.7549
3.9801
3.7870
4.2491
Wf (4)
3.8759
3.7067
3.8748
3.7422
3.9671
3.8000
3.8644
3.7380
3.9032
3.7621
4.2404
4.0787
3.8634
3.7057
3.9554
3.7907
4.2719
4.2116
3.9040
3.7549
3.9785
3.7849
4.2411
Wf(24)
3.8755
3.7064
3.8739
3.7410
3.9657
3.7986
3.8641
3.7380
3.9030
3.7620
4.2353
4.0743
3.8630
3.7049
3.9554
3.7906
4.2682
4.2092
3.9022
3.7506
3.9767
3.7820
4.2382
W.
3.7650
3.6032
3.7316
3.5972
3.7810
3.6113
3.7564
3.6275
3.7623
3.6178
3.7676
3.5996
3.7523
3.5992
3.7693
3.6032
3.8121
3.7606
3.7675
3.6240
3.7956
3.6133
3.7907
42
-------
APPENDIX C DEIEFfWJION OF PRECISION FOR SHORT-TEW SWUNG
PERIODS M) VARIOUS EOl'ILIPPATION CONDITIONS
1.0 INTRODUCTION
The material presented in this section will detail the construction
of confidence limits for the coefficients of variation of the 4-hour and
6-hour sampling periods and will propose a technique by which, given a
measured suspended particulate concentration determined from either 4-
or 6-hour sampling and equilibrated in one of the four environments
studied, one can determine with 90 percent confidence the interval in
which the true concetration can be found.
2.0 SHORT-TERM SAMPLING STUDY
2.1 Estimation of CV
The sample coefficient of variation (relative standard deviation) is
*
an estimate of the population coefficient, CV = a/y .
This estimate is biased and ref. 1 suggests that following estimate of
the population CV based on k samples of size n each:
(1)
X
where
s'(x) = An estimator of the standard deviation of x
x = Average of all x.
B = The value such that E{B s'V = a (see table 2 in ref. 1).
n n
*It is assumed that the population of measurements is normally distri-
buted with mean y and standard deviation a.
tE{x} is read as average or expected value of x.
43
-------
Since the usual estimator of the standard deviation (as defined in the
short-term sampling study) is given in the form
s(x) =
- x)
n - 1
1/2
1/2
(3)
The values of B listed in ref. 1 were corrected by
- B
n n \ n
(4)
Table C-l lists B and B for a few values of n.
n n
Table C-l. Values of B and B such that E(B s')
n n n
E(B s) = a
n
n
B
n
B
n
2
3
4
5
6
10
15
20
1.2533
1.1284
1.0854
1.0638
1.0509
1.0281
1.0180
1.0132
0.8861
0.9213
0.9400
0.9515
0.9593
0.9754
0.9834
0.9876
Table C-l indicates that CV based on
k CV
= / ^
(5)
where
s.
CV. =
SP.
J
(6)
44
-------
will in fact yield a more conservative estimate of the true coefficient of
variation than the suggested form of
(7)
Hence, equation (6) is recommended for determining the precision of short
sampling periods.
2.2 Confidence Interval of CV
The construction of confidence intervals for the true coefficient of
s\
variation, CV, based on an estimate, CV, was determined by a simple and
accurate approximation presented in ref. 2. For values of CV < 0.2 and
assuming that CV is normally distributed, the approximation of the confi-
denct interval for CV is given by the following.
CV < 7 (8)
(1 + r) "'Ml - r)
where
r = UY -JL— (9)
/ZN
Uy = The standard normal variable whose absolute value (two-tail
value) is exceeded with probability 1 - y where y i-s tne
confidence level
N = Total number of measurements used in obtaining CV.
3.0 FILTER EQUILIBRATION STUDY
Measured suspended particulate concentrations are determined from
samples that have been equilibrated for 24 hours by the following calculation:
(W- - W.) x 106
x T
where
45
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3
SP = Measured average suspended particulate concentration, yg/m
W. = Tare weight of filter, g
Wf = Weight of filter plus particulates after 24 hours of
equilibration, g
3
Q. = Initial airflow rate, m /min
1 3
Q,- = Final airflow rate, m /min
T = Sampling time, min.
The equilibration study has indicated that the term Wf varies as the
equilibration time, i.e., that Wf decreases exponentially from the beginning
of equilibration to reach some equilibrium value as the equilibration time,
t_, approaches 24 hours. Writing W,. as a function of equilibration time,
£i I
W. = W,_(O with W,.(24) as the equilibrium value, equation 10 becomes:
I I ,h I
[W (t ) - W ] x 106
_ —±—£ i
M Q + Q
-^—- * T
with W = W (24) in equation 10. •
The net collected particulate weight at anytime t can then be written
WSP(tE) * Wf (V - Wi
where W (t ) = Net collected particulate weight at equilibration time, t_-, g.
or r. £
Since the reference method for high-volume sampling (ref. 1) indicates 24
hours as the optimum time to allow samples to reach an equilibrium weight,
the relative difference between the particulate weight at t < 24 hours and
£i
the equilibrium weight at t-., = 24 hours can be given by
" WSP(24)
where yCt^,) = Error introduced, into the measured particulate weight by
£
equilibrating for tp < 24 hours.
Hence, if a sample is equilibrated for less than 24 hours, the equilibrium
particulate weight can be estimated by
46
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w (t )
+ , ,-E,
Assuming that 24 hours of postsampling equilibration yields the best
estimate of the true average suspended particulate concentration, the
combination of equations (11), (12), and (14) allows an unbiased estimate
of the true average concentration.
x lo6
T Q + Q 1 + y(t )
• 2 x T x [1 + y(tE)J h
where SP = Unbiased estimate of the true average suspended particulate
3
concentration, yg/m .
The 90 percent confidence interval of the true average suspended par-
ticulate concentration based on the measured average concentration was de-
rived by taking the natural log of equation (15) and differentiating the
resulting expression.
= £ [W,(t_) - W.] - £n(Q. + Q,) - JinT - £n[l + y(t )] (16)
ntJix II £
d[Wf (t£) - W±] d(Qi + Qf) d y(t£) (17)
SPT = Wf(tE) - W± Q.,. + Qf " 1 + y(tE)
r\ fj ^^^ f\
Since the estimated variance of dx/x is defined as s (x)/x = CV (x)
CV2(SPJ = CV2f¥.(t ) - W.] + CV2(Q. + Q,) + CV2(T) + CV2[1 + y(t )] (18)
i 1 SL 1 1 I >->
The quantities CV2[Wf (t£) - W±]
CV2(Q + Q ), and
•^2
CV (T)
are discussed in reference 3 and will be combined as
CV (sampling time) = {CV2[W£(O - W.] + CV2(Q. + Q_) + CV2(T)}1/2 (19)
i hi i it
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CV(sampling time) is the estimated coefficient of variation which
describes the variability of measured concentrations resulting from the
various sampling period times, i.e., 4-hour, 6-hour, 24-hour sampling.
Therefore,
CV(SPT) = {CV2(sampling time) + CV2[1 +
(20)
where
(21)
4.0 COMBINED RESULTS
In order to be 90 percent confident that a measured value of the
average suspended particulate concentration will be an estimate of a true
average of suspended particulate concentration, confidence intervals for
the true concentrations which need_ to be constructed take into account the
error in the measured values caused when samples are equilibrated for less
than 24 hours and variability which is a function of sampling time.
The bias, the difference between the measured average concentration,
^x
SP' , and the estimated true average concentration, SP , is determined in the
following manner:
Since
= SPM - SPT
(22)
and
SPT ~
SP.
M
(15)
it follows that
T = SP.
M
t
(23]
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Hence, the confidence interval for the true average suspended par-
ticulate concentration based on a measured average concentration is
calculated by
SP,,, = SP,, - T + U a (24)
where
a = SP x {CV2 + CV2[1 + y(0}}1/2
JXL JSi
and U for 90 percent confidence is 1.645.
Y
5.0 REFERENCES
1. R. K. Ziegler. "Estimators of Coefficients of Variation Using k Samples."
Technometrics 15, No. 2 (May 1973).
2. B. Iglewicz and R. H. Myers. "Comparison of Approximations to the
Percentage Points of the Sample Coefficients of Variation/' Technometrics
12(1970):166-70.
3. U.S. Environmental Protection Agency. Guidelines for Development of a
Quality Assurance Program; Reference Method for the Determination of
Suspended Particulates in the Atmosphere (High Volume Method). EPA-
R4-73-028b, Washington, D.C., June 1973.
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