Comparison of Two Source Apportionment Models for Fine
Particulate Matter In Chicago, Illinois
Michael Rizzoa and Peter Scheffb
a
United States Environmental Protection Agency, 77 W. Jackson Blvd., Chicago, IL 60604
b
University of Illinois – Chicago, School of Public Health, 2121 W. Taylor St., Chicago, IL
60612
INTRODUCTION
In 2000, the United States Environmental Protection Agency established the Fine Particulate
Speciation Trends Network to expand on its existing PM2.5 monitoring activities. The purpose
of the network is to characterize individual species which compose the total fine particulate
measured at the Agency's Federal Reference Method (FRM) PM2.5 monitoring sites. The data
from the speciation network serves an important role in aiding the Agency in determining which
species are the most prevalent in areas of the nation thus allowing for the formulation of control
strategies. Studies have already shown that secondary sulfates comprise a large part of the fine
particulate in the Eastern part of the United States while secondary nitrates dominate the total
PM2.5 in the Western United States. The Midwestern section of the country is dominated by
both secondary sulfates and nitrates. All areas of the country have been shown to have a large
portion of the total fine particulate comprised of organic carbon.1
Another use which has been planned for the data collected through the speciation network is to
determine possible fine particulate sources. Traditional source apportionment techniques have
centered around the use of the chemical mass balance model which utilizes source profiles and
speciated data to determine source contributions for either gaseous or particulate compounds or a
combination of both.2,3,4 There have been many analyses conducted regarding volatile organic
compounds.5,6,7,8,9,10,11 Recently, more studies have focused on implementing the chemical mass
balance technique for fine particulate matter. However, source profiles for many of the primary
PM2.5 sources need to be further developed to yield better results. A technique which has been
developed recently that does not require source profiles to provide an indication of possible
source impacts is Positive Matrix Factorization (PMF). This technique is related to factor
analysis where the underlying covariability of many variables is analyzed so that the original data
can be described by a smaller set factors to which the original variables are related. PMF has
already been used for a variety of source apportionment and spatial analyses.12,13,14,15,16,17 PMF is
advantageous in that one does not require profiles to determine the possible source contributions
as with the Chemical Mass Balance (CMB) model. Furthermore, CMB also assumes that none
of the fitting species used in the analysis is reactive or reacts significantly in the atmosphere
between the point of emission and the receptor location. However, it can be difficult to identify
potential sources without some sort of profile to which to compare the final results. This work
will examine the relationship between the PMF and CMB receptor models to determine their
similarities and differences using data from two sites within Chicago, Illinois metropolitan area.
METHODOLOGY
PMF Analysis
Positive Matrix Factorization is a tool similar to factor analysis but is able to provide nonnegative solutions for a variety of uses. PMF iteratively solves the following equation.
Equation 1.
X  GF  E
where:
X (n x Sp) = a matrix of observed fine particulate species concentrations
with the dimensions of number of observations by the number of species
G (n x f) = a matrix of source contributions by observation day whose sum is
normalized to the total number of observations in the analysis with the dimensions
of number of observations by the number of factors
F (f x Sp) = a matrix of source profiles normalized to the total fine
particulate with the dimensions of number of factors by the number of species
E (n x Sp) = a matrix of random errors with the dimensions of number of
observations by number of species
The Multilinear Engine 2 (ME2) is a piece of software capable of solving multivariate algorithms
including PMF and was used for this work. Equation 1 is solved by minimizing the error sum of
squares, Q, weighted inversely by the uncertainty in the measured value. The method of
calculating the uncertainties for the observed values can greatly affect the final solution PMF
calculates.
In addition to the main set of equations based the parametric factor analytic model in Equation 1,
two sets of auxiliary equations were also used during the iterative solving process. Equation 2
represents the normalization of the source contribution matrix where the sum of each source's
daily contributions are equal to the total daily observations.
Equation 2.
n
g
i 1
where:
ij
n
gij = the individual source contribution for day i and source j
n = the number of daily observations
The C1 uncertainty associated with the normalization of Equation 2 was set to 1% of the number
of observations which in this case was approximately 3. The C2 and C3 values were maintained
at zero.
Equation 3 represents the normalization of the F matrix.
Equation 3.
Sp
f
i 1
where:
ij
 Total Fine PM 2.5
fij = the individual profile value for specie i and source j
Sp = the total number of species in the analysis
Total Fine PM2.5 = total fine particulate matter from the speciation monitor
The C1 uncertainty associated with the normalization of Equation 2 was set to 10% of the
number of species which in this case was approximately 4. In cases where ME2 was having
trouble solving Equation 3 for a particular source, the C1 coefficient was set to half of the
original C1 uncertainty. The C2 and C3 values were maintained at zero.
Multivariate factor analytic techniques have been shown to be sensitive to variables with a high
proportion of data less than the minimum detectable limit (MDL). Thus, the uncertainty for each
value was based on the importantance of individual species given the number of samples each
was above the method detection limit. It has been shown that species which are consistently
below the detection limit and constitute mostly noise greatly influence the final result of a PMF
analysis.18 For the purpose of this work, a signal to noise ratio was calculated for each species
using Equation 4.
Equation 4.
0.2 

{i | x ij  j }
 j m DLj
x ij
2
where:
xij = the value of a specific variable j collected at time i which is greater than
the minimum detection limit
j = the minimum detection limit for variable j
mDLj = the number of values greater then the minimum detection limit
If the value from Equation 4 was greater than 2, then the variable was considered “good”. If the
value was between 0.2 and 2, the variable was considered “weak” and “bad” if it was less than
0.2. These categories were used to develop the uncertainties associated with each value used in
the analysis. Uncertainties for “good” variables were either the MDL or the root mean square
average of 10% of the measured concentration and MDL for that particular species whichever
was larger. “Weak” variables had uncertainties that were either the MDL or root mean square
average of 3 times the measured concentration and 3 times the MDL whichever was larger.
Figure 1. Example of a Scree Plot used for PMF
Species determined to be “bad” by the above criteria were removed from the analysis entirely.
Once the data had been processed, ME2 solved the PMF algorithm using the recommendations
given in the ME2 user's manual.19 The parameters listed in the following table were set according
to the recommendations given in the user's manual.
Parameter
Setting
Outlier-distance
4
Error Model
-12
C1, C2, C3
Calculated Uncertainty, 0, 0
In order to determine if PMF has truly found a global minimum solution, the program allows one
to repeat the analysis from random starting points. The final Q-statistics from these random
points are then compared to see if there is an significant difference between them. If there is,
then it may signify that a global minimum was not found. For this work, the analysis was
allowed to repeat three times from three pseudo-random starting points. In all three cases, the Qstatistics were not very different from one another, thus signifying that a global minimum
solution had been reached.
The possible number of factors to be included in the final solution was determined through the
following methods. First, a preliminary analysis was done using SAS PROC FACTOR where
the eigen values corresponding to the inclusion of each successive variable were plotted against
the number of variables included in the analysis. This is commonly known as a Scree plot and an
example of one is provided for Chicago, IL (Figure 2).
Usually, the Scree plot gives an indication of the number of factors appropriate for a solution
when the line begins to level considerably. For the Chicago example, a eight factors may be
enough to describe the data set. To investigate the possibility of a solution having more or less
than 8 factors, solutions of five to eleven factors were calculated in PMF.
To better determine how many factors provided the best solution, the final sum of squares metric
(Q) was used. The theoretical “Q” for the PMF solution would be the sum of all of the individual
observations which in this case is the total number of daily measurments times the total number
of species used. The observed “Q” cannot be less than the theoretical “Q” since this would mean
that the model predicted the observed data better than it could be based on the uncertainty. In
order to ensure that the solution is the global minimum, the model was run from 20 random
starting points and the lowest “Q” for the 20 runs was used as the final solution.
Final Normalization
The F and G matrices of the final solution are then normalized so that the sum of the species for
each source is unity according to the following equations.
Equation 5.
Fi 
Spij
where:
FM i
Fi = the row of the source profile matrix for source i
Spij = the source profile value for specie j of source i
FMi = the calculated average total fine mass contribution for source i
Equation 6.
G i  N ik * FM i
where:
Gi = the column of the source contribution matrix for source i
Nik = the source contribution on day k for source i
FMi = the calculated average total fine mass contribution for source i
Finally, the relationship between the predicted total fine mass from PMF and the observed total
PM2.5 was examined. A linear regression between the two parameters was calculated using SAS
PROC REG in the form of the following equation:
Equation 5.
Predicted Mass(PMF)   0   1 * Measured Mass
where:
Predicted Mass (PMF) = sum of source contributions for specific site-day
b0 = Constant or y-intercept of relationship
b1 = Fraction of Measured Mass as predicted by PMF
Measured Mass = Measured total PM2.5 concentration from speciation
monitor
The fraction of Measured Mass statistic along with the R-square of the relationship was used to
determine which solution best described the data.
Chemical Mass Balance Model
The Chemical Mass Balance model has been widely used and is solved by an equation of the
form:
Equation 6.
X  PC  E
where:
X = a matrix of observed fine particulate species concentrations for a
particular sample period
P = a matrix of source profiles for each possible source whose contribution
being obtained
C = a matrix of potential source contributions in the form of the total fine
particulate concentration from each source and solved for the by model
E = a matrix of random errors
is
Equation 6 is solved using the variance weighted least squares algorithm as described in the
CMB8 User's Manual.20
Colinearity among sources is one issue which often causes a high degree of ill conditioning and
an inflation in the source contribution uncertainties. To remedy this problem, the CMB8
algorithm uses the Eligible Linear Space technique to obtain an average contribution from
colinear sources and a reasonable estimate of the contribution uncertainty.21 For the purpose of
this work, the variance weighted least squares algorithm was implemented using SAS PROC
IML.
A total of nine sources were used for the CMB model.22,23,24,25,26,27,28 An attempt was made to
distinguish contributions between diesel and gasoline powered motor vehicles. However, the
Speciation Trends Network data were not robust enough to accomplish this. Therefore, a motor
vehicle composite was created from the diesel and gasoline profiles and used as a single source.
Since one needs to investigate every possible combination of source contributions to obtain an
average contribution for a particular source, the SAS code was automated to hold motor vehicles
constant for each run and vary the remaining eight sources throughout the analysis for a total of
253 source combinations for each sampling day.
As with PMF, the CMB model requires some estimate of the uncertainties in the measured
species concentrations. However, CMB also requires uncertainty estimates for the various source
profiles used in the calculation. The uncertainties for the monitoring data were computed in the
same manner as described for the PMF model. The uncertainties in the CMB model were
calculated as the standard deviations of the composite values from the source profiles
utilized.22,23,24,25,26,27,28
For each sampling day, the average source contribution was calculated using the following
criteria. The solution's R2 had to be greater than or equal to 0.8. The percent mass explained
had to be greater than or equal to 80%. It was recognized that this would account for percent
mass explained values of greater than 100%. Because a major assumption of the CMB model is
that no secondary reactions occur, it is difficult to meet this assumption with fine particulate
since two of the major contributors, sulfates and nitrates, are primarily formed through secondary
reactions. This was accounted for by including two sources specifically for these compounds.
However, organic carbon is also formed secondarily in the atmosphere and cannot be accounted
for as easily. Therefore, the percent of explained mass was allowed to be above 100% to account
for this. Finally, the Chi square for an accepted solution had to be within 120% of the minimum
Chi square value for all of the solutions.
Once the groups of solutions had been chosen based on the above criteria, their individual source
contributions were averaged to obtain an average contribution for each source for each sampling
day. In cases where one solution did not contain the source found in another solution, the
contribution from the missing source was assumed to be zero and that value was averaged with
the remaining solutions.
Figure 2 shows the location of speciation sites in Region 5 and the surrounding States. Data
were obtained from the USEPA Air Quality System for two sites in the Chicago Metropolitan
Area for the years 2001 through 2003. The data consist of speciated metals, nitrate, sulfate,
organic carbon, and elemental carbon measurements. Data is collected on a national schedule
with most speciation sites operating every sixth day. Each State is required to run a trends site
which operates on a once every third day basis.
Figure 2. Location of Fine Particulate Speciation Sites within Region 5 and Surrounding States
Data were combined from the two sites within Chicago to create a data set of 372 observations.
The first site is the Lawndale site on the Southwest side of the City. The second site is located
approximately 7 miles north of Lawndale at the Springfield Pumping Station. Concerns were
raised about whether the two sites were measuring similar air masses. The results of the analysis
demonstrate that the two sites alone gave similar results as combined. Each measurement
observation contained a total of 41 species which were usable after conducting the signal to noise
ratio analysis described above. Of these 40 species, 27 were categorized as “good” variables
with the remaining 14 characterized as “weak”. Four the data points centered around the 4th of
July holiday had their uncertainties downweighted to the same weights associated with the
“weak” variables because emissions from fireworks were having a large bias on the final PMF
results.
Quality assurance criteria were imposed on the data to filter potentially detrimental data. Any
observations flagged '5' meaning an outlier of unknown cause were removed from the data set.
In the final analysis, a total of 351 out of the 372 valid observations were used because of the '5'
flag. Observations with a flag of '4' meaning possible laboratory contamination were
downweighted with uncertainties associated with “weak” variables. A summation of all of the
species concentrations was used to determine if the measured total fine particulate mass was at
least the same if not greater than the sum of the species. In cases where this was not true, the
total mass concentration for a particular observation was downweighted in the same manner as
the “weak” variables. This was done in order to place a constraint on the model where the sum
of the species would equal or be less than the total fine particulate.
RESULTS AND DISCUSSION
A total of ten factors or sources were obtained from PMF. The theoretical Q for the 351
observation data set was 10023. The observed Q for the ten factor solution was 12025. Using
Equation 5, the total explained mass from the PMF model was approximately 98% and an
average of 108% from the CMB model results. The value greater than 100% for the CMB results
could possibly be explained by secondarily formed organic carbon for which it was unaccounted.
Table II shows the resulting source matrix from the PMF analysis.
Table II: PMF Computed Source Profiles as Percentage of Total PM2.5 (F-matrix) for
Chicago, IL
Specie
Al
Factor 1
0.28%
Factor 2
0.00%
Factor 3
0.00%
Factor 4
0.00%
Factor 5
0.02%
Factor 6
0.00%
Factor 7
0.00%
Factor 8
6.19%
As
0.00%
0.02%
0.02%
0.02%
0.00%
0.06%
0.00%
0.00%
0.00%
0.16%
Ba
0.22%
0.35%
0.00%
0.17%
0.00%
0.08%
0.00%
0.00%
0.01%
1.03%
Br
0.01%
0.03%
0.04%
0.02%
0.02%
0.04%
0.03%
0.19%
0.01%
0.09%
COg
19004.88% 24221.93%
0.00%
23303.26% 5426.29% 51484.06%
0.00%
Factor 9 Factor 10
0.00%
0.00%
18809.96% 1512.80%
0.00%
Ca
5.10%
0.00%
0.31%
0.31%
0.01%
0.00%
0.52%
1.87%
0.03%
0.16%
Cl
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
12.30%
0.00%
0.00%
0.00%
Co
0.00%
0.00%
0.01%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.03%
Cr
0.01%
0.00%
0.00%
0.01%
0.00%
0.22%
0.02%
0.06%
0.00%
0.00%
Cu
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.01%
0.00%
0.00%
6.26%
EC
9.31%
1.02%
10.74%
10.57%
0.21%
99.87%
1.05%
0.00%
1.13%
17.29%
Eu
0.05%
0.00%
0.00%
0.02%
0.01%
0.00%
0.03%
0.43%
0.00%
0.00%
Fe
1.31%
0.36%
0.53%
0.24%
0.00%
65.49%
0.31%
1.96%
0.06%
1.32%
K
0.52%
5.89%
0.00%
0.00%
0.14%
4.70%
0.43%
2.14%
0.00%
0.00%
K+
0.00%
5.18%
0.59%
0.17%
0.14%
0.00%
0.14%
0.00%
0.02%
0.00%
Mg
0.15%
0.00%
0.00%
0.10%
0.01%
0.00%
0.00%
0.00%
0.00%
0.57%
Mn
0.01%
0.01%
0.00%
0.00%
0.01%
2.76%
0.03%
0.00%
0.00%
0.00%
Mo
0.01%
0.00%
0.00%
0.02%
0.00%
0.00%
0.00%
0.04%
0.00%
0.01%
NH4
0.00%
0.00%
0.00%
0.00%
17.99%
42.86%
18.20%
0.00%
20.58%
0.00%
NO3
1.88%
7.79%
0.00%
1.53%
65.72%
92.81%
48.75%
0.00%
1.41%
0.00%
NOx
1134.00%
0.00%
0.00%
1264.38%
230.14%
2455.71% 869.45%
0.00%
0.00%
42.15%
Na
0.00%
0.00%
0.04%
1.15%
0.30%
0.00%
1.48%
4.19%
0.00%
0.00%
Na+
0.76%
0.58%
0.60%
0.37%
0.04%
5.45%
0.90%
0.00%
0.01%
2.58%
Ni
0.01%
0.00%
0.00%
0.00%
0.00%
0.04%
0.01%
0.01%
0.00%
0.02%
OC
33.96%
37.42%
42.08%
59.60%
0.00%
0.00%
12.65%
48.93%
8.16%
116.60%
P
0.00%
0.00%
0.06%
0.02%
0.01%
0.00%
0.00%
0.01%
0.00%
0.00%
Pb
0.00%
0.08%
0.42%
0.02%
0.01%
1.66%
0.02%
0.04%
0.01%
0.56%
S
0.66%
1.28%
4.58%
2.96%
0.31%
0.00%
0.71%
12.32%
18.67%
8.62%
SO2
154.95%
105.28%
0.00%
152.82%
2.84%
0.00%
0.00%
476.83%
22.05%
0.00%
Specie
SO4
Factor 1
0.00%
Factor 2
3.24%
Factor 3
11.45%
Factor 4
8.09%
Factor 5
1.56%
Factor 6
31.09%
Factor 7
1.64%
Factor 8
31.29%
Factor 9 Factor 10
57.20%
1.06%
Sb
0.01%
0.00%
0.00%
0.04%
0.00%
0.00%
0.01%
0.22%
0.01%
0.00%
Sc
0.00%
0.01%
0.00%
0.00%
0.00%
0.02%
0.00%
0.00%
0.00%
0.01%
Se
0.00%
0.00%
0.00%
0.01%
0.00%
0.16%
0.00%
0.01%
0.01%
0.00%
Si
2.95%
0.65%
0.00%
0.00%
0.00%
0.86%
0.00%
20.12%
0.10%
0.89%
Sn
0.06%
0.03%
0.00%
0.07%
0.00%
0.28%
0.00%
0.16%
0.01%
0.09%
Sr
0.02%
0.02%
0.00%
0.01%
0.00%
0.00%
0.00%
0.04%
0.00%
0.00%
Ta
0.00%
0.10%
0.00%
0.04%
0.01%
0.17%
0.00%
0.24%
0.00%
0.00%
Ti
0.18%
0.02%
0.00%
0.03%
0.01%
0.49%
0.00%
0.26%
0.01%
0.10%
V
0.02%
0.01%
0.00%
0.01%
0.00%
0.02%
0.00%
0.02%
0.00%
0.04%
Zn
0.10%
0.00%
5.76%
0.00%
0.02%
5.62%
0.00%
0.00%
0.00%
0.00%
Possible
Source
Soil
Vegetative
Burning
Steel
Vehicles
Nitrates
Fe/Mn
Rock Salt
Industry
Sulfates
Copper
All of the values are normalized to the total fine particulate. The last row in Table II gives a
possible identification for the type of source based on the resulting profile structure obtained
from PMF. Sources were identified using a variety of methods. First, the nitrates and sulfates
which are formed secondarily in the atmosphere due to photochemical reactions were identified
using the mass ratios of ammonium ion to the nitrate and sulfur which is approximately 1:3 and
1:1, respectively. The steel source always had the highest loading for zinc as well as higher
loadings for manganese, lead and iron than the other factors. The vegetative burning factor has
the highest loadings for potassium ion and elemental potassium than any of the other sources.
The soil factor has larger loadings for silicon, calcium, titanium and iron than the other seven
factors. The high loadings for the sodium ion, elemental sodium and chlorine in factor 1 indicate
that this could possibly be associated with road salt which is a PM2.5 source in the winter in
Chicago.
Figures 3 – 12 show the time series of the G-scores or source contributions for each of the ten
factors at each site over the time period examined.
Figure 3. Soil Contributions
Figure 4. Burning Contributions
Figure 3. Soil Contributions
Figure 4. Burning Contributions
Figure 5. Steel Contributions
Figure 6. Vehicle Contributions
Figure 7. Nitrate Contributions
Figure 7. Fe/Mn Contributions
Figure 8. Rock Salt Contributions
Figure 9. Industry Contributions
Figure 10. Sulfate Contributions
Figure 11. Copper Contributions
The time series plots show some interesting features. The Sulfates and Nitrates plots show the
seasonal patterns seen for sulfates and nitrates which are peaks in the summer and winter
respectively for the two secondarily formed particle categories. Rock Salt shows the seasonal
variability associated with reintrained salting materials which are spikes during the winter. The
Soil factor shows a spike near the beginning of July 2002 which may be a large transported dust
event. The Vehicle source shows a steady contribution throughout the studied time period. This
makes sense due to the vast transportation infrastructure surrounding the Chicago metropolitan
area.
Table III shows the summary of the results of the CMB and PMF analyses for the two sites in
Chicago, IL. The results reflect the combined average source contributions from both sites.
Table III. Summary of CMB and PMF results from the two sites in Chicago, IL
Model
Source
Minimum Maximum
Median Mean StdDev
% of
Total
CMB
PMF
Coal
Soil
Steel
Burning
Vehicle
Road Salt
Refinery
Sulfate
Nitrate
Refinery/
Utility
Soil
Steel
Fe/Mn
Copper
Burning
Vehicle
Road Salt
Sulfate
Nitrate
0.000
0.000
0.000
0.000
0.642
0.000
0.000
0.335
0.143
1.46
4.05
4.26
11.6
12.6
6.16
1.1
30.2
23.9
0.14
0.28
0.2
1.41
4.41
0.01
0.05
3.18
2.1
0.19
0.39
0.31
1.71
4.8
0.21
0.07
4.79
3.18
0.18
0.42
0.44
1.35
2.24
0.64
0.08
4.29
3.43
1%
2%
2%
11%
31%
1%
0%
31%
20%
0.000
1.49
0.19
0.28
0.27
2%
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
6.32
4.16
0.72
1.05
8
11.23
12.51
38.47
25.56
0.69
0.24
0.07
0.06
0.56
3.51
0.06
3.61
1.91
0.9
0.41
0.1
0.09
0.85
3.53
0.45
5.66
3.2
0.85
0.48
0.11
0.12
0.91
1.74
1.31
5.55
3.78
6%
3%
1%
1%
5%
23%
3%
37%
21%
As can be seen by the results in Table III, the two models yielded the same three sources for the
highest fine particulate contributions: sulfates, nitrates and vehicles. The difference between the
two models shows that the sulfates and vehicles were tied for their individual percentages of the
total fine mass with nitrates the third highest contribution for the CMB model. The PMF results
show that sulfates had the highest overall contribution with nitrates and vehicles tied at
approximately 20% of the total PM2.5. Other differences include a minimum of zero (no
contribution) from nitrates, sulfates and vehicles for the PMF model which is not seen in the
CMB model. This can be explained by the fact that a factor analytic model assumes that one or
more sources are not present in a sufficient fraction of data points [paatero et al, chemometrics
and intell systems]. Another possibility to consider is the rotational ambiguity in the PMF
results. One would need to further examine the PMF results for possible rotations which could
affect the results thereby making the PMF results more comparable to the CMB values.
Figure 13 shows the correlation matrix for the relationships between the CMB and PMF sources.
Figure 12. Correlation Matrix between the CMB and PMF Mode
Table IV: Regression Parameters and R2 for the Relationships between the PMF and CMB
Results*
Factor
PMF
Soil
Parameter
Intercept
Slope
R2
PMF
Intercept
Vegetative
Slope
Burning
R2
PMF Steel Intercept
Slope
R2
PMF
Intercept
Vehicles
Slope
R2
PMF
Intercept
Nitrates
Slope
CMB
CMB
CMB
CMB
CMB
Vegetative Nitrates Petroleum Rock Sulfates
Burn
Refineries Salt
0.65
0.94
0.59
0.86
0.77
0.15
-0.01
4.79
0.23
0.03
0.0499
0.0023
0.1139
0.0298 0.0188
0.19
0.82
0.69
0.79
0.51
0.36
-0.01
1.63
0
0.06
0.3296
0.0010
0.0150
0.0000 0.1059
0.24
0.32
0.32
0.39
0.32
0.1
0.03
1.47
0.1
0.02
0.0637
0.0379
0.0307
0.0182 0.0296
2.89
3.33
3.52
3.54
3.7
0.42
0.09
1.29
0.3
-0.02
0.0935
0.0303
0.0020
0.0124 0.0030
2.36
-0.21
3.82
2.88
2.44
0.48
1.06
-9.99
1.47
0.15
CMB
Soil
CMB
Steel
CMB
Utilities
CMB
Vehicles
0.47
1.08
0.3118
0.32
1.19
0.4297
0.23
0.46
0.1610
3.67
-0.17
0.0017
3.59
-1.03
0.43
1.61
0.3883
0.46
1.13
0.2204
0.21
0.68
0.1997
3.59
0.03
0.0000
3.43
-0.87
0.46
2.34
0.2223
0.8
-0.02
0.0000
0.37
0.2
0.0048
3.68
-0.43
0.0018
3.46
-1.53
0.19
0.15
0.1605
0.26
0.11
0.1008
-0.25
0.14
0.3952
1.03
0.53
0.4910
1.49
0.35
Factor
PMF
Fe/Mn
PMF
Rock Salt
PMF
Industry
PMF
Sulfates
PMF
Copper
Parameter
R2
Intercept
Slope
R2
Intercept
Slope
R2
Intercept
Slope
R2
Intercept
Slope
R2
Intercept
Slope
R2
CMB
CMB
CMB
CMB
CMB
Vegetative Nitrates Petroleum Rock Sulfates
Burn
Refineries Salt
0.0250
0.9465
0.0240
0.0613 0.0303
0.07
0.09
0.08
0.1
0.08
0.02
0
0.39
0.01
0
0.0552
0.0130
0.0434
0.0020 0.0395
0.29
-0.09
0.75
0.03
0.43
0.07
0.15
-5.51
1.82
-0.01
0.0048
0.2067
0.0753
0.9704 0.0006
0.24
0.28
0.06
0.27
0.2
0.02
0
3.24
-0.01
0.01
0.0065
0.0023
0.5514
0.0011 0.0532
3.83
4.76
4.23
5.81
-0.62
1.1
0.29
22.81
-0.5
1.29
0.0602
0.0329
0.0562
0.0031 0.9961
0.06
0.08
0.07
0.08
0.08
0.02
0
0.2
0.01
0
0.0336
0.0039
0.0095
0.0013 0.0037
CMB
Soil
CMB
Steel
CMB
Utilities
CMB
Vehicles
0.0137
0.04
0.17
0.4613
0.52
-0.3
0.0124
0.19
0.19
0.1038
4.37
3.36
0.0655
0.07
0.03
0.0100
0.0055
0.05
0.19
0.3216
0.52
-0.42
0.0130
0.19
0.28
0.1225
4.91
2.7
0.0239
0.04
0.15
0.1671
0.0046
0.07
0.17
0.0692
0.66
-1.41
0.0406
0.13
0.75
0.2409
4.62
5.8
0.0298
0.09
-0.01
0.0002
0.0432
-0.05
0.03
0.4396
-0.25
0.13
0.0663
0.2
0.01
0.0167
2.19
0.73
0.0844
0.03
0.01
0.0517
 The regression equation for each PMF and CMB source was the following:
 PMF Factor = CMB Source * Slope + Intercept
The results show that for some of the corresponding PMF and CMB source relationships, there is
a bias toward the CMB results to be greater than the PMF contributions. This is the case for the
Soil, Vegetative Burning and Steel sources. Other sources such as Nitrates and Sulfates have
slopes close to one demonstrating a rather good agreement between the two models. The PMF
Industry and Rock Salt sources both have slopes greater than one when compared to their
respective CMB sources.
For the most part, however, several of the PMF sources correlate very well with their CMB
counterparts. For example, the secondary nitrates and sulfates as well as the road salt sources
have a very high R2 correlation greater than 0.9. This demonstrates the ability of the PMF model
to give results comparable to those from CMB before examining the PMF results for possible
rotational ambiguity. Other CMB sources showed moderate correlations with their PMF
counterparts as well as other PMF sources which would suggest the intermixing of source
emissions or the close proximity of sources to one another. This is seen between CMB Vehicles
and the PMF Vehicles, Steel and Fe/Mn sources. This can also be seen between the CMB Soil
source and the PMF Soil, Vegetative Burning and Vehicles sources. These moderate correlations
between a single CMB source and multiple PMF sources suggest similarities in profiles for the
PMF sources.
Figures 14 through 17 show the profiles for the PMF Vehicles, Steel and Fe/Mn sources.
The profile plots show similar values for As, Ca, elemental carbon, Fe, Na+, organic carbon and
sulfates for the Steel and Vehicles sources. Likewise, there are similar values for NOx and
carbon monoxide when comparing the Vehicles and Fe/Mn sources. Species with similarities
between Steel and Fe/Mn included Pb and Zn.
Many of the other PMF and CMB sources correlate well with sources other than their identified
counterparts. For example, the PMF Industry source correlates well with the CMB Petroleum
Refineries and has a smaller correlation with the CMB Utilities source. Other sources like the
PMF Steel source correlates better with the CMB Vehicles than it does with the CMB Steel.
This can be explained in part because the CMB Steel profile which was used represents steel
processes in South Africa and could infer that the local steel source is not well represented by the
South African profile.
The PMF soil source is correlated the greatest with the CMB Steel and Soil sources, but there are
also weaker correlations with the CMB Utilities, Vehicles and Petroleum Refineries. This could
signify that many of the CMB profiles are similar to one another or that the PMF profile
represents a sort of composite of the individual CMB source profiles. This is not the case for the
PMF Nitrates, Sulfates or Rock Salt which have specific mass ratios and species which are more
unique to each source.
CONCLUSIONS
1. The two models yield the same source categories as the maximum sources of fine
particulate with sulfates, nitrates and motor vehicles being the top three sources for each
model.
2. The source contributions obtained from the 10 factor PMF and 9 source CMB models
compare relatively well when examining corresponding sources.
3. Several PMF sources correlate well with a single CMB source suggesting the similarities
in profiles of the PMF sources or the relatively close proximity of these sources to one
another.
4. Several CMB sources also correlate well with a single PMF source suggesting the PMF
source represents a composite of CMB sources. However, this could also signify possible
rotational ambiguity in the PMF results which need to further investigated.
DISCLAMER
The views expressed in this work are those of the authors and do not necessarily reflect those of
the United States Environmental Protection Agency.
ACKNOWLEDGEMENTS
The authors would like to acknowledge Shelly Eberly of the United States Environmental
Protection Agency Office of Research and Development and Dr. Pentti Paatero of the University
of Helsinki for their aid.
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