Environ. Sci. Technol. 2004, 38, 202-209
Analysis of Ambient Particle Size
Distributions Using Unmix and
Positive Matrix Factorization
EUGENE KIM
Department of Civil and Environmental Engineering,
Clarkson University, Box 5708, Potsdam, New York 13699
PHILIP K. HOPKE*
Department of Chemical Engineering, Clarkson University,
Box 5708, Potsdam, New York 13699
TIMOTHY V. LARSON
Department of Civil and Environmental Engineering,
University of Washington, Seattle, Washington 98195
DAVID S. COVERT
Department of Atmospheric Science, University of
Washington, Seattle, Washington 98195
Hourly averaged particle size distributions measured at a
centrally located urban site in Seattle were analyzed
through the application of bilinear positive matrix factorization
(PMF) and Unmix to study underlying size distributions
and their daily patterns. A total of 1051 samples each with
16 size intervals from 20 to 400 nm were obtained from a
differential mobility particle sizer operating between December
2000 and February 2001. Both PMF and Unmix identify
four similar underlying factors in the size distributions. Factor
1 is an accumulation mode particle size spectrum that
shows a regular nocturnal pattern, and factor 2 is a larger
particle distribution. Factor 3 is assigned as a trafficrelated particle distribution, based on its correlations with
accompanying gas-phase measurements, and has a
regular weekday-high rush-hour pattern. Factor 4 is a trafficrelated particle size distribution that has a regular rushhour pattern on weekdays as well as weekends. Conditional
probability functions (CPF) were computed using wind
profiles and factor contributions. The results of CPF analysis
suggest that these factors are correlated with surrounding
particle sources of wood burning, secondary aerosol,
diesel emissions, and motor vehicle emissions.
Introduction
Many airborne particle measurements and epidemiology
studies have been undertaken since the association between
ambient particle concentrations and adverse health effects
has been shown in many studies (1-3). Recent epidemiological studies suggested that fine particles (particle diameter
< 2.5 µm), especially ultrafine particles (<100 nm), may cause
negative health effects because of their high number
concentrations in the ambient, high penetration, and deposition efficiencies in the lungs and their acidity or catalytically
active chemical properties (4-8). Many studies are monitor* Corresponding author phone: (315)268-3861; fax. (315)268-4410;
e-mail: [email protected].
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ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 38, NO. 1, 2004
ing the number concentrations to characterize local fine
particles (9-13).
Positive matrix factorization (PMF) (14) and Unmix (15)
have been shown to be powerful alternatives to traditional
receptor modeling methods for airborne particulate matter
source identification (16, 17). PMF has been used to assess
particle source contributions in the Arctic (18), Hong Kong
(19), Phoenix (20, 21), Thailand (22), Vermont (23), Atlanta
(24), and three northeastern U.S. locations (25). Unmix has
been applied to several aerosol data sets from Los Angeles
(26) and Phoenix (27). Also, PMF and Unmix were compared
in the northern Vermont aerosol study (28). All of these
applications have been to particle composition data. Particle
size distribution data measured in European cities (29, 30)
have been studied using principal component analysis (PCA)
as well as a constrained linear receptor model that has some
similarities to PMF. The results of these studies suggest that
particle sources produce characteristic size distributions that
are sufficiently stable in the atmosphere when measured at
a particular site to provide a problem suitable for factor
analysis.
Particle size distributions in the atmosphere are dynamic
with the potential for coagulation and size-dependent
deposition. Zhu et al. (31, 32) performed studies near major
highway sources. These results suggest that within a few
hundred meters of the roadway there are significant changes
in the size distributions as the smallest sizes coagulate and
dry deposit. However, at a reasonable distance from the road,
these processes slow significantly as the particle numbers
decrease, and thus, a quasistationary profile can be anticipated if the sampling location is not too near active sources
of ultrafine particles. Similar results have been observed in
studies of the size distributions in a dilution sampler (33);
examining the emissions of a boiler burning coal, oil, or
natural gas shows that at a sufficient residence time, a stable
size distribution appears to have developed. Previous laboratory studies of a variety of combustion sources showed that
they emitted monomodal, log-normal distribution (34). Thus,
although the potential for additional change in the size
distributions while the aerosol is in transit from the source
to the receptor site, it appears that there is sufficient stability
in the size distributions from the various sources that the
ambient aerosol size distribution can be considered to be a
superposition of the distributions arising from multiple
sources.
The objectives of this study are to apply these new
multivariate receptor modeling methods to particle size
distribution data and to estimate possible sources from model
identified particle size distributions. In the present paper,
PMF and Unmix were applied to a particle size distribution
data set from 20 to 400 nm collected during a ca. 2-month
period at a monitoring site in Seattle, WA. The same number
of factors were extracted from both PMF and Unmix to ensure
that these factors were stable and strong underlying features.
The resolved particle size distributions and their hourly
patterns as well as their possible sources are discussed.
Conditional probability functions were calculated using local
wind data to help identify the possible sources of particles.
The results could be used for the correlation study of local
fine particle sources and their adverse health effects.
Experimental Methods
Sample Collection. The particle size distribution data used
in this study consisted of hourly measurements collected
from December 2000 to February 2001 at an urban monitoring
site (Beacon Hill). As shown in Figure 1, the Beacon Hill site
10.1021/es030310s CCC: $27.50
 2004 American Chemical Society
Published on Web 11/25/2003
TABLE 1. Summary of 16 Particle Size Intervals Used for PMF
and Unmix (number of sample ) 1051)
Dp (µm)
vol. concentration
(µm3/cm3)
mean
median
standard
deviation
min
max
0.020
0.024
0.029
0.034
0.041
0.050
0.060
0.073
0.088
0.108
0.133
0.165
0.206
0.261
0.334
0.434
0.10
0.16
0.25
0.38
0.58
0.91
1.31
1.96
2.74
3.84
5.07
6.39
7.57
8.37
8.35
7.74
0.092
0.14
0.22
0.31
0.45
0.71
1.05
1.61
2.31
3.24
4.18
5.36
6.54
7.74
7.24
6.06
0.064
0.10
0.17
0.26
0.41
0.68
1.01
1.53
2.07
2.78
3.67
4.59
5.15
5.48
6.10
6.63
0.0031
0.0074
0.016
0.019
0.028
0.040
0.038
0.052
0.079
0.15
0.27
0.46
0.59
0.48
0.32
0.46
0.47
0.69
0.96
1.54
2.47
4.51
7.29
14.35
18.84
19.36
22.05
28.70
32.09
32.31
32.47
44.94
TABLE 2. Summary of Measurements Used for Conditional
Probability Function and Correlation Analysis
NOX (ppm)
CO (ppm)
bsp (10-4/m)a
bap (10-4/m)b
wind speed (m/s)
FIGURE 1. Location of the Beacon Hill monitoring site in Seattle,
WA.
is centrally located within the Seattle urban area on a hilltop,
99 m above sea level. The monitoring site is located inside
a water reservoir impoundment, located 5 km southeast of
the downtown business district. The sampling height of
particle size and gaseous measurements was 4 m above
ground. All instruments were closely located within a 2 m
radius. Wind data were measured at a 10 m tower located
in the site. The area to the immediate north and east of the
reservoir is residential. The hill is part of a larger ridge defining
the eastern edge of an industrialized valley. The Port of Seattle,
container shipping area, and warehousing area are located
northwest and west of the site. Highways that have a traffic
count of approximately 2 × 105 vehicles per day (35) are
closely situated about 2 km north and 1 km west of the site.
A total of 1051 particle size distributions, each with 17
size intervals from 20 to 600 nm, were measured using a
differential mobility particle sizer (DMPS). The last size
interval (Dp 0.571 nm) was not included in the analysis due
to the collection efficiency drop. The DMPS consists of a TSI
model 3080 Electrostatic Classifier with model 3081 long
column differential mobility analyzer (DMA) and a TSI model
3010 condensation nuclei counter (CNC). The DMPS steps
through the mobility size range by changing the voltage on
the DMA center rod from 40 to 10 000 over a period of 10
min. At the end of stepped scan sequence, the mobility data
are inverted with the charge probability matrix to get the
Stokes diameter (Dp) size distribution. The sample and sheath
flows, temperature, pressures, relative humidity in the sensing
volume, and scan voltages were checked twice weekly. It is
possible that significant changes in the ambient concentration at any size during a scan lead to distorted measurements
(36). In this study, the inversion scheme checks the number
concentration from one size interval to the next size interval
for continuity. The scan is discarded if the change exceeds
a given threshold. The inversion will not converge if the
a
no. of values
mean
min
max
830
821
875
876
878
0.059
0.58
0.38
0.27
2.55
0.002
0.10
0.03
0.01
0.18
0.38
2.8
1.86
2.54
9.07
Light scattering coefficient.
b
Light absorption coefficient.
measured size distribution is unrealistic. Most of the missing
values in the size distributions occurred when the inversion
failed or when the sampling pumps had problems.
The particle volume size distributions were used in this
study for the direct comparisons with measured source size
distributions. It would be possible to use either number or
volume distributions since one can be derived from the other.
Since current particulate matter regulations are mass based,
it is more useful to examine volume distributions. Every 10min measured particle number concentration (dNi/dlog Dp)
for each size interval i was integrated to estimate hourly
particle number concentration, and then the particle volume
concentration (dVi/dlog Dp) was calculated for the analysis.
In addition, the local air pollution control agency (Puget
Sound Air Pollution Control Agency) provided hourly measurements of oxides of nitrogen (NOx, chemiluminescence
method) and carbon monoxide (CO, nondispersive infrared
method), light scattering coefficient (bsp, nephelometer), and
light absorption coefficient (bap, light absorption photometer).
Summaries of particle volume concentrations and other
measurements used in this study are presented in Tables 1
and 2, respectively.
Multivariate Receptor Modeling. The general receptor
modeling problem can be stated in terms of the contribution
from p independent sources to all size intervals in a given
sample (37, 38) as follows
p
xij )
∑g
ikfkj
(1)
k)1
where xij is the concentration in the jth size interval measured
in the ith sample, gik is the particle concentration from the
kth source contributing to the ith sample, and fkj is the particle
volume fraction in the jth size interval from the kth source.
This equation then assumes that there are stable size
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distributions that are emitted from the various source types
that contribute to the observed ambient aerosol size distribution.
As pointed out by Henry (39), there are infinite numbers
of possible solutions to the factor analysis problem outlined
in eq 1 (rotation of matrices). However, this problem is the
same as what exists in other areas of science. Particle size
distributions represent data that are similar to the problem
of spectrochemical separations. The absorption spectra for
individual components are sums of 1 or more Gaussian-like
peaks. These peaks can also be resolved by regression of the
spectral profiles if they are known and not changed by the
presence of the other absorbing species. However, for many
years back to the early work of Lawton and Sylvester (40),
factor analysis has been applied to these data with a high
level of success. Given the prior results of the analysis of
particle size data (29, 30), there do appear to be reasonably
stable source size profiles. There can be expected to be
substantial differences in the emission rates of various sources
at different times that will lead to the different sources
contributing quite different numbers of differently sized
particles. Because we have quite high time resolution,
variations in emissions such as morning and evening rush
hours, evening and weekend wood fires, and other timevarying activities can be expected to provide inputs of
particles at differing times. It was previously demonstrated
that higher time resolution sampling provides the ability to
identify increased number of sources (41). Thus, a series of
measurements that represent the superposition of the particle
size profiles with differing intensities as functions of time
will always permit a factor analysis to separate them.
To decrease rotational freedom, PMF and Unmix (version
2.3) use nonnegativity constraints on the factors. In addition,
parameter FPEAK is used to control the rotations in PMF
(42). By changing FPEAK values as one of the model input
parameters, rotations of matrices are visualized and then
best solutions can be found. Unmix uses the edges for which
source contributions are small or zero as an additional
constraint to find a unique solution (15, 43). PMF provides
a solution that minimizes an object function, Q(E), based
upon uncertainties for each observation (14, 44). This function
is defined as
[ ]
p
n
Q(E) )
m
∑∑
i)1 j)1
xij -
∑
k)1
uij
(2)
To use same input data for both PMF and Unmix, the
hourly particle size distributions in which concentrations
are missing are excluded from this analysis. Also, the
treatment of below detection limit values (45) for PMF and
Unmix were not used for the same reason. For the input data
for the PMF, the associated uncertainty with measured value
for each size interval is estimated by taking into account the
temporal variability of both measured particle number and
sampled air flow rates.
The results of PMF were then normalized by a scaling
constant, sk, so that the quantitative source contributions as
9
well as profiles for each source were obtained. Specifically
p
xij )
∑(s g
k ik)
k)1
()
fkj
sk
(3)
where sk is determined by regressing sum of volume
concentrations in the ith sample, vi, against estimated source
contribution values.
p
vi )
∑s g
k ik
(4)
k)1
In the Unmix, sum of volume concentrations shown in eq
4 were included as an input variable so that the model results
were normalized by Unmix directly.
Conditional Probability Function. The conditional probability function (CPF) (46) was calculated using source
contribution estimates from PMF and Unmix coupled with
wind direction values measured at the site. The source
impacts from various wind directions can be analyzed by
CPF. The sources are likely to be located to the direction that
have high conditional probability values. To minimize the
effect of atmospheric dilution, the hourly fractional particle
volume contribution from each source relative to the total
of all sources was used rather than using the absolute source
contributions. Specifically, the CPF is defined as
CPF )
m∆θ
n∆θ
(5)
2
gikfkj
where uij is an uncertainty estimate in the jth size interval
measured in the ith sample. The application of PMF depends
on the estimated uncertainties for each of the data values.
The uncertainty estimation provides a useful tool to decrease
the weight of missing and below detection limit data in the
solution as well as account for the variability in the source
profiles.
204
FIGURE 2. FPEAK versus Q value for PMF.
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 38, NO. 1, 2004
where m∆θ is the number of occurrences from wind sector
∆θ that exceeded the threshold criterion and n∆θ is the total
number of data from the same wind sector. In this study, ∆θ
was set to be 11.3°. Calm winds (<1 m/s) were excluded
from this analysis due to the isotropic behavior of wind vane
under calm winds. From the trials of several different
percentile of the fractional contribution from each source,
the threshold criterion of upper 25% was decided to show
clear directionality.
Results and Discussion
Unmix identified four profiles from the given data set. In
Unmix, the tracer variable was not chosen for this study. In
the PMF, different numbers of factors need to be tested and
the optimal number is the one that adequately fits the data
with the most physically meaningful results. In this study,
however, only four factor solutions were used in order to
extract stable and common factors to compare the results
between PMF and Unmix. Also, since rotational ambiguity
exists in the PMF solutions, PMF was run several times with
different FPEAK values to determine the range within which
the objective function Q(E) value in eq 2 remains essentially
constant (38). The optimal solution should lie in this FPEAK
range. As shown in Figure 2, FPEAK values between -0.3 and
TABLE 3. Pearson Correlation Coefficients between Factor
Contributions and Independently Measured Variables
factor 1
factor 2
factor 3
factor 4
variable PMFa Unmix PMF Unmix PMF Unmix PMF Unmix
bap
bsp
NOX
CO
a
0.74
0.69
0.69
0.60
0.60
0.62
0.48
0.42
0.61
0.95
0.56
0.64
0.45
0.86
0.42
0.52
0.53
0.28
0.70
0.60
0.51
0.29
0.67
0.59
0.42
0.11
0.58
0.44
0.29
0.05
0.43
0.31
FPEAK values ) 0.
FIGURE 4. Normalized factor profiles and standard deviation
resolved from particle size distributions using Unmix.
FIGURE 3. Normalized factor profiles (mean ( standard deviation)
resolved from particle size distributions using PMF. FPEAK values
from -0.3 to 0.3 were used.
0.3 were likely to provide relatively constant Q(E) values, so
that the PMF solution from default rotation (FPEAK ) 0) as
well as from six FPEAK values between -0.3 and 0.3 were
considered in this study. For the PMF, the robust mode was
used to reduce the influence of extreme values on the solution.
Table 3 shows the Pearson correlations of the contributions from PMF and Unmix against on-site measured
variables. The comparisons of the hourly volume contributions from all factors for 16 size intervals reconstructed by
PMF and Unmix with measured values show that the resolved
factors by both methods effectively reproduce the measured
values and account for most of the variation in the particle
concentrations (slope ) 0.988 and r2 ) 0.99 for PMF; slope
) 0.992 and r2 ) 0.99 for Unmix). Figure 3 presents the PMF
identified feature profiles. Mean and standard deviation
values are estimated based on the variability in seven FPEAK
solutions. Figure 4 presents the Unmix identified profiles
(value ( standard deviation resolved by Unmix). In Unmix,
“edges” are used to fix the profiles. Edges are defined by
points of nearly pure contributions of only a single source.
The idea is discussed by Henry and co-workers (15, 25, 26).
Thus, Unmix has reduced the rotational ambiguity in the
solution by assuming the edges serve as constraints on several
factors. In the PMF analysis, the range of rotational ambiguity
(i.e., the region over which FPEAK can be varied with
essentially no change in the value of Q in eq 2) has been
explored. Thus, the PMF error bars represent the range of
uncertainty including measurement error and rotational
FIGURE 5. CPF plots for the highest 25% of the volume contribution
from model resolved underlying factors.
ambiguity while the Unmix solution only reflects the
measurement errors, which are much smaller.
When the errors associated with profiles are considered,
Figures 3 and 4 indicate that both methods resolved very
similar profiles. Since the conditional probabilities for the
possible source locations between PMF and Unmix are the
same, only PMF-resolved conditional probabilities are presented in Figure 5. In Figure 6, the hourly contribution
patterns estimated for both weekdays and weekends by PMF
are shown for the same reason.
Factor 1 is an accumulation mode (0.1 µm < Dp < 2.5 µm)
particle distribution that has the highest concentration
between 0.2 and 0.3 µm. As shown in Figure 6, this factor
shows a weak nocturnal pattern during weekdays. This
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FIGURE 6. Comparisons of model resolved hourly contributions between weekday and weekend.
nocturnal pattern is distinct during weekends. The origin of
this factor is likely to be residential wood burning. The CPF
plots in Figure 5 indicate that the source of this factor is
located in a residential area that is immediately north and
east of the site. Wood burning is prevalent in the northwestern
United States (47). In this study, wood burning in winter is
consistent with emissions from fireplace and woodstoves,
which are ubiquitous ground-level sources whose emissions
are frequently trapped by nighttime temperature inversion.
The daytime contributions from this factor during the
weekends are lower than those of weekdays. Both PMF- and
Unmix-estimated contributions from this factor have associations with bap and bsp in common as shown in Table 3.
The particle size distribution of this factor is similar to the
measured size distribution of vegetative burning influences
aerosols (the highest concentration between 0.4 and 0.5 µm
in the volume size distribution) by Morawska et al. (48).
Factor 2 is a larger particle distribution. This factor is
strongly associated with bsp for both methods. Figure 6 shows
that this factor has a noon and evening high pattern. The
CPF plots show that the source of this factor is located
northeast-southeast of the site. Although sea salt and traffic
produced airborne soil can be possible sources of these larger
particles (45), the source associated with this factor is likely
to be secondary aerosol. This assignment is made because
the extracted size distributions compare well with those from
prior measurements (49). Sulfate, nitrate, and ammonium
measured in Claremont, CA, have the highest concentrations
between 0.6 and 0.7 µm (47). Nitrate-rich secondary aerosol,
in which most of nitrates originate from combustion emissions, has seasonal variations with its maximum in the winter
when these samples were obtained. Low temperature and
high relative humidity in winter help the formation of nitrate
aerosols in urban areas (24). In addition, the direction for
the ocean (west of the site) and nearby highways are not
consistent with the CPF plot.
Factor 3 has the highest concentration at approximately
0.1 µm. The association with NOx, CO, and bap indicate that
this is a traffic-related particle feature. The hourly pattern in
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Figure 6 shows that this factor has a regular weekday rushhour pattern. The source of this factor can be diesel emissions.
In Figure 5, the high values of conditional probability point
northwest of the site, indicating the possibility of contributions from heavy-duty diesel emissions from the Port of
Seattle, which is located about 5 km northwest of the site.
In addition, the roads and freeways close to the Beacon Hill
site have high traffic of commuter buses and delivery trucks
that contribute diesel emissions to the site. Factor 3 shows
similar size distribution to measured mass size distribution
of heavy-duty diesel (50) and diesel passenger car exhaust
particles (51) that has the highest concentration at approximately 0.1 µm. Park et al. (52) found that diesel engine
exhaust is monomodal with a mass mode mean around 100200 nm. Also, particle volume distribution of 1995 diesel
engine exhaust shows the geometric volume mean diameter
of 0.125 µm (53).
Factor 4 has high concentrations in nucleation (Dp < 0.05
µm) and accumulation mode. As shown in Table 3, the
association with NOx indicates that this is also a traffic-related
particle feature. Figure 6 shows that this factor has a regular
rush-hour pattern during weekdays as well as on weekends.
In the CPF plots, three high peaks of conditional probability
point to the nearby freeways and junctions. For the possible
source of this factor, motor vehicle emissions are suggested.
The volume size distribution of this factor shows bimodality
that has the highest concentration at approximately 0.04 and
0.3 µm. The peak in the accumulation mode is very similar
to those in a previous study (44). From the measurements
near the freeway during peak traffic condition, Morawska et
al. (44) showed two peaks at 0.3 and 3 µm in volume size
distribution of the traffic-influenced aerosol. As they expected
to see near a major motor vehicle traffic concentration, a
nucleation mode peak is shown in the distribution of factor
4. As discussed with respect to factor 3, diesel engines typically
emit particles in the accumulation mode range. Maricq and
co-workers (54) found on-road vehicles emitted particles with
number distributions that would correspond well to the
volume size found in this factor. Thus, a mixture of vehicles
FIGURE 7. PMF-deduced factor contributrions versus Unmix-deduced factor contributions.
on local highways appears to be a good assignment for this
factor.
The PMF and Unmix estimated particle volume contributions are compared in Figure 7, indicating high correlations
(r2 ) 0.89-0.98) and similar contributions (slope ) 0.8-1.1),
except for factor 3 (slope ) 2.1). From the principal
component analysis of particle number size distributions
from 10 to 700 nm measured at the urban street canyon,
Wahlin et al. (29) identified three sources: traffic, diesel, and
secondary particles. The traffic source contributed to the
total number of particles the most, and the secondary
particles contributed to the total number of particles the
least. For this study, the average source contributions of each
factor to the particle volume concentration for 2-month
period are summarized in Figure 8. Factor 1 (residential wood
burning) has the highest contribution to the particle volume
concentrations (PMF 48%; Unmix 44%). For the PMF, the
second contributor is factor 2 (secondary aerosol), accounting
for 21% of the particle volume concentration, and the third
contributor is factor 3 (diesel emissions), accounting for 20%.
For the Unmix, the second contributor is factor 3 (diesel
emissions), accounting for 30% of the particle volume
concentration, and the third contributor is factor 2 (secondary
aerosol), accounting for 16%. Factor 4 (motor vehicle) is the
fourth contributor (PMF 11%; Unmix 10%). When the errors
associated with average contributions are considered, significant differences only occur for factor 3, in which Unmix
estimates higher contribution than PMF does.
In the analysis of particle size distribution, a factor can
be a combined size distribution of surrounding sources if
those are co-located and the temporal emission patterns are
similar. Unmix did not find a five-factor solution, but it is
possible to extract an additional factor by PMF. The factor
5 extracted from the five-factor PMF model is shown in Figure
9. There is a peak in the volume distribution at 20-30 nm.
Thus, there is a very high number count in sizes near 10 nm.
FIGURE 8. Average contributions to particle volume concentration
estimated by PMF and Unmix. FPEAK values from -0.3 to 0.3 were
used for PMF.
It appears that this factor is another representation of freshly
nucleated particles. Examination of the distributions has
shown that there are no nucleation and growth events, as
seen at other locations (55). Motor vehicle emissions do
produce different sized particles including nucleation mode
particles. The CPF plots for factors 4 and 5 (Figure 10) show
similar directional patterns. The contributions of factors 4
and 5 are plotted against the wind speed in Figure 11. It can
be seen that factor 5 contributed less than factor 4 at low
wind speeds, suggesting that factor 5 is fresher motor vehicle
emissions from nearby freeways. Although this factor contributes very little to the total volume of the ambient
particulate matter, it is the largest factor contributing to the
particle number concentrations.
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Acknowledgments
This study was partly funded by the University of Washington/
EPA Northwest Research Center for Particulate Air Pollution
and Health (R827355) and by the University of Rochester/
EPA Particulate Matter and Health Center (R827354). This
support does not constitute an endorsement by the U.S. EPA
of the views expressed. We also thank Dr. Pentti Paatero for
his helpful discussions of the work presented in this paper.
We would also like to thank the anonymous reviewer A for
the useful comments on this manuscript.
Literature Cited
FIGURE 9. Normalized factor profiles (mean ( standard deviation)
resolved from particle size distributions using PMF 5-factor model.
FPEAK values from -0.3 to 0.3 were used.
FIGURE 10. CPF plots for the highest 25% of the volume concentrations deduced by PMF 5-factor model.
FIGURE 11. Wind speed versus particle volume concentrations
deduced by PMF 5-factor model.
The sources and their profiles are not clearly identified
in detail without costly chemical speciation data, and
therefore, the source identifications of the factors shown in
this study are tentative. However, the comparisons between
PMF- and Unmix-predicted and measured volume concentration over all samples show that the extracted factors from
both methods effectively reproduce the original size distributions. This study suggested that PMF and Unmix are useful
methods to extract underlying features from ambient particle
size distribution data and possibly cost-effective tools to
identify their possible sources.
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Received for review January 9, 2003. Revised manuscript
received September 22, 2003. Accepted September 23, 2003.
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