Source Identification of Volatile
Organic Compounds in Houston,
Texas
WEIXIANG ZHAO,
†
PHILIP K. HOPKE,*
,†
AND THOMAS KARL
‡
Department of Chemical Engineering, Clarkson University,
Box 5708, Potsdam, New York 13699-5708, and The National
Center for Atmospheric Research, Atmospheric Chemistry
Division, P.O. Box 3000, Boulder, Colorado 80307
The complexity of the volatile organic compound (VOC)
mixture in the Houston area makes studies of the air quality
in that area very challenging. In this paper, a novel
factor analysis model, where the normal chemical mass
balance model was augmented by a parallel equation that
accounted for wind speed and direction, temperature,
and weekend/weekday effects, was fitted with a multilinear
engine (ME) to provide identification and apportionment
of the VOC sources at the La Porte Municipal Airport site
in Houston during the Texas Air Quality Study (TexAQS)
2000. The analysis determined the profiles and contributions
of nine sources and the corresponding wind speed,
wind direction, temperature, and weekend factors. The
reasonableness of these results not only suggests the high
resolving power of the expanded factor analysis model
for source apportionment but also provides the novel and
effective auxiliary information for more specific source
identification. In addition, a new approach to estimate the

Hopke and co-workers (6), Heidam (7), Henry (8), and
Barrie and Barrie (9) applied principal component analysis
(PCA) to source identification, but Paatero and Tapper (10,
11) showed that PCAcannot provide a true minimal variance
solution since they are based on an incorrect weighting. In
view of the limitations of PCA, a new technique, positive
matrix factorization (PMF), was developed for sources
identification and apportionment (12). The distinct advan-
tages of PMF over PCA are that non-negative constraints are
built in PMF models and PMF does not rely on the
information from the correlation matrix but utilizes a point-
by-point least-squaresminimization scheme (12). It has been
reported (13) that the source profiles produced by PMF are
better andmore reasonable at describing thesource structure
than those by PCA. Over the past few years, PMF has been
applied to a number of particle composition data sets (e.g.,
14, 15).
Recently, the PMF analysis can be expanded by using a
more general model (16), and a new analysis tool called the
multilinear engine (ME) was developed (17) to solve such
problems. ME is very flexible and provides a general
framework for fitting any of the multilinear model (18, 19),
so it becomes possible to obtain not only the sourcesprofiles
but also other interesting parametric factors that may be
important forsource identification andpollution control and
planning. Forexample, winddirectional information can help
locate the potential sources. It was reported (16, 19) that in
some cases the expanded factor models could determine
more sources than PMF.
The coexistingsystem of VOCs is complex. A small change

†
Clarkson University.
‡
The National Center for Atmospheric Research.
Environ. Sci. Technol.
2004,
38,
1338-1347
1338
9
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 38, NO. 5, 2004 10.1021/es034999c CCC: $27.50  2004 American Chemical Society
Published on Web 01/28/2004
Expanded Factor Analysis Model
In general,the ordinarybilinear receptormodel canbe written
as
where X is the matrix ofVOCs’ concentrations, F isthe matrix
of source profiles, G is the matrix of source contributions,
and E is the residuals matrix. Their elements x
ij
, f
jp
, and g
ip
can be respectively understood as the concentration of
compound j measured in sample i, the concentration of
compound j in the emission of source p, and the strength
of source p on sample i (16, 19).
In this section, wind direction and wind speed will be
used to illustrate the construction of the expanded factor
analysis model(16,19). Inthe bilinear model, the contribution

direction range 0-360° are evenly divided into 18subranges)
should be a relatively larger value. S(s
i
,p) has a similar
definition for wind speed. Thus, z
ip
can be considered as a
multiplier that represents the comprehensive action of wind
direction and speed on the observed pollution. Obviously,
in different physical models, z
ip
can correspond to different
expressions. In this study, z
ip
corresponds to the factors for
wind speed, wind direction, temperature, and weekday/
weekend.
The expanded receptor model can then be expressed by
where W(w
i
,p) denotes the action of weekdays or weekends
by source p on the observed concentration, I is the number
of samples,and Jis the number ofmeasured chemicalspecies.
By fixing the weekday coefficient at unity, W(w
i
,p) is a vector
with n
p
(the number of sources) elements. T(t
i

these two problems for this case will be described in detail.
Because eq 3b will generate a poorer fit to the data than
eq 3a, the error estimate for eq 3b, σ′
ij
, must be (much) larger
than that for eq 3a, σ
ij
(16, 19). In this study σ′
ij
is 8 times of
σ
ij
and σ
ij
is represented as
where c
1
denotes the uncertainty of measurement and c
3
is
a constant. Here c
3
is valued at 0.2. Because of the complex
VOC mixture in the ship channel area and the potential
interference at low concentration, the experimental uncer-
tainties obtained by the measurement technique used here
were hard to access. An approach using the fast Fourier
transformation (FTT) was applied to solve this problem. The
procedure can be briefly described as follows. Xylene will be
used as an example from the species being studied in this

f
jp
) D(d
i
,p)S(s
i
,p)f
jp
(2)
x
ij
)
∑
p)1
N
g
ip
f
jp
+ e
ij
(3a)
x
ij
)
∑
p)1
N
z
ip

/σ
ij
)
2
+
∑
i)1
I
∑
j)1
J
(e′
ij
/σ′
ij
)
2
(4)
FIGURE 1. Illustration of FFT-based uncertainty estimation. (a) The
concentration series of xylene, c; (b) the magnitude spectrum of
concentration series, mfc; (c) the random data series, r; (d) the
magnitude spectrum of random data series, mfr.
σ
ij
) c
1
+ c
3
x
ij

was placed in an air-conditioned trailer situated next to a
10-m sampling tower at the southwest side of the municipal
airport at La Porte, TX, to identify and quantify the VOC
mixture in that area. A map showing the sampling site is
presented in Figure 2. The PTR-MS technique has been
previously described in detail (24), soonly a brief description
is given here. The principle of the PTR-MS is the reaction of
organic species in ambient air with H
3
O
+
ions, generated
from thehollow cathode discharge of watervapor, to produce
the protonated organic species (RH
+
). The concentration of
the product ions can be calculated from a reaction dynamic
equation (24). Only organic species with a proton affinity
greater than that of water can be detected by the mass
spectrometer. More details about the sampling procedure
can be found in ref 20.
The sampling period for the data in this study was from
08/20/00 to 09/08/00, and the most sampling frequencies
were about1/4-6 min
-1
, butthe frequenciesfor someperiods
were 1min
-1
. Allthe samples wereused for analysisto ensure
a sufficiency of samples. The concentrations of 14 VOCs

including methanol showed that methanol had a significant
contribution in each source profile, suppressing other
compounds such as vinyl acetate and c13-benzenes. Such
behavior typically suggested that there was a high variability
in the amounts of methanol associated with its sources. In
this case, an increase of the uncertainty of methanol could
not resolve this problem. Thus, methanol was excluded from
the final analysis. Figure 3 shows the concentration time
series for all compounds except methanol.
The determination of the number of sources is one of the
major problems in any factor analysis. In this study, three
rules were applied to decide the proper source number that
(1) the resolved source profiles should be explainable, (2) Q
value defined in eq 4 is expected to show a change in slope
with the number of sources from rapid to slow at the point
of the decidednumber, and (3) there should bea satisfactory
fit between the predicted concentrations and the measured
values. In detail, when the source number increased from 6
to 7, 7 to 8, 8 to 9, and 9 to 10, the decreases in Q were 6907,
8325, 5723, and 4915, respectively. Clearly, there is a change
in the slope at 9 sources.
In addition, there was a better fit between the predicted
concentrations and the measured values at that source
number. The fit between the predicted c13-benzenes con-
centration and the measured values increased exceptionally
quickly when the source number changed from 9 to 10. (The
correlation coefficient for 10 sources was 0.932 while that for
9 sources was 0.58.) However, actually more than 75% of the
c13-benzenes concentration measurements were below the
detection limit and replaced by half of the detection limit,

directions (i.e., the longer the radius is, the bigger the
contribution at that direction). In addition, the emitter
location plots of acrylonitrile, toluene-xylene, benzene,
styrene, and propene are presented in Figures 10-14. The
plot showing emitter locations was produced by superim-
posing the wind directional plot (blue area) onto the map
where the corresponding emitters in the observed area were
displayed as circles, squares, or triangles. Emission rates for
2000 that were obtained from the Toxic Release Inventory
(26) were shown on the plots with the corresponding colors,
if available. The size of blue area in each plot does not
represent the distance between receptor site and emitter
but denotes the strengths of the identified source on the
pollution at different wind directions.
Activity can change considerably from weekdays to
weekends. Some production factories do not operate on
weekends, sothe emissions of these sourcesvary accordingly.
In addition, the pattern of motor vehicle use also changes
as fewerpeople commuteto workand fewerheavy-duty diesel
trucks will be operated on weekends. Thus, the weekend
factor should reflect changes in the human activities.
However, inthis study,the numberof weekendsamples (there
are only 3 weekends in this study and moreover they contain
many missingvalues) mightnot besufficient enoughto obtain
FIGURE 3. Concentration series of each compound.
FIGURE 4. Profiles ofthe identifiedVOC sources inLa Porte,Houston.
FIGURE 5. Time-resolved contribution ofeach identified VOC source
in La Porte, Houston.
KD
i

The wind directional plot for this source agrees with the
emitter locations as it shows a large contribution from the
northwest and a peak at about 150°. The high peaks of the
contribution plot for this source correspondto the nighttime
period when southerly winds dominate. No information is
available on the diurnal patterns of the source. In addition,
the KD value of this source in Table 1 is 0.404, so this source
is expectedto have asignificant weekend influence.However
such an influence does not agree with the result in Figure
9. As mentioned above, the limited number of weekend
measurements for analysis may notbe sufficient, which may
be the cause of this disagreement. Better results for the
weekend factor might be obtained if a larger data set were
available.
Source 2shows isopreneand M87 (vinylacetate). Isoprene
is atypical biogenicVOC (28),but the contribution of biogenic
isoprene is small in the immediate proximity of the La Porte
site (29).A numberof anthropogenic isoprene emitters (likely,
rubber industry) are located to the north and south of the
sampling site (20, 27). For M87, there are a number of vinyl
acetate emitters to the north and south of the sampling site,
and especially several large vinyl acetate emitters are located
to the north (27). These emitters are most likely the storage
tank and other equipment of chemical plants. The wind
directional plot for this source in Figure 6 largely confirms
the location of these emitters, as it shows some convexes in
FIGURE 6. Wind direction factor plots.
TABLE 1. Ratio of Mean Contribution of Weekend Samples to
That of Weekday Samples
a

and blue circles denote xylene and toluene emitters, respectively.
The blue area correspondsto the winddirection plot for thissource.
The red × at the center of the blue area is the sampling site.
FIGURE 12. Location ofbenzene emitters. Thegreen trianglesdenote
benzene emitters. The blue area corresponds to the wind direction
plot for this source. The red × at the center of the blue area is the
sampling site.
FIGURE 13. Location of styrene emitters. The black circles denote
styrene emitters. The blue area corresponds to the wind direction
plot for this source. The red × at the center of the blue area is the
sampling site.
FIGURE 14. Location of propene. The circles denote the propene
emitters. The blue area corresponds to the wind direction plot for
this source. The red × at the center of the blue area is the sampling
site.
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9
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 38, NO. 5, 2004
directional plot shows a broad contribution from that
direction. There are a number of peaks in the corresponding
contribution plot, but none of these peaks were on the
weekend. In addition, the KD value of this source is 0.599
and identical to the result of weekend factor.
Source 4 contains toluene and xylene. These emitters are
operation units and equipment of the chemical and refining
industry (e.g.,tanks, boilers, reactors, pyrolysis furnaces)(27).
Figure 11 shows the emitters are mainly located to the
northwest and south of the sampling. The wind directional
plot shows a large contribution from the north and a sharp
spike in the south, in agreement with the locations of the

located to the northwest and south of the sampling site (27).
Particularly there is a large styrene emitter at about 210°.
The corresponding wind directional plot in Figure 6 agrees
with thelocation informationas itshows a broad contribution
from the northand also a sharpspike at the directionof 210°.
Most of the high peaks in the contribution plot were at
nighttime when the southerly wind was dominant. The KD
FIGURE 15. Distribution plot for scaled residual errors.
VOL. 38, NO. 5, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
1345
value of this source is 0.662, which agrees with the weekend
factor result that this source has a weekend effect.
Source 7 is represented by M61 whose kernel component
is acetic acid. Acetic acid is a typical photochemical reaction
product (30), so the wind direction plot shows a relatively
smooth shape.Meanwhile, a number of anthropogenicacetic
acid emitters (e.g., acetic acid storage tanks, boilers, and
exhausted liquid tanks) are located to the north and south
of the sampling site (27). The KD value of this source is 0.738
and identicalto theweekend factorresult. The photochemical
sources should not have weekend effect, so the variation
between weekday and weekend may be due to the changes
of theemission ratesof the anthropogenic acetic acidsources.
Source 8 is characterized by c9-benzenes and c10-
benzenes. A number of c9- and c10-benzenes emitters (e.g.,
the operation units of chemical or petrochemical plants) are
located to the north of the sampling site (27). The wind
directional plot for this source shows a broad contribution
from the northwest and a spike in the south. The motor

have a reasonable distribution. Although the weekend data
are not sufficient enough to make a correct conclusion on
weekend effect for each source, the weekend factors of most
sources (7 out of 9) are identical with the defined KD values.
These results suggest the feasibility ofincluding the weekend
effect analysis.
Wind speed and temperature are two potentially impor-
tant meteorological factors that can help interpret the
observed VOCconcentrations. Figure 7 shows thewind speed
factor. Formost factors,the wind speed factor valuesdecrease
with increasing wind speed. This trend suggests a dilution
effect that the same emitted mass is released into a larger
volume of air as wind speed increases; the concentration
therefore decreases (16). However, the factors of sources 2
and 9increase withincreasing wind speed and source3 shows
an almost flat curve. The possible reasons for these phe-
nomena mightbe (1) forthese sources that may becomposed
of pointemitters (e.g.,high-concentration storagetank), there
may be more coherent plume effect at higher wind speed
(higher wind speed makes these emitted VOCs gathered
together ratherthan dispersed) and (2) high-speed wind may
enhance the evaporations of some VOCs.
The influence of temperature on pollutants is more
complex than that of wind speed because increasing tem-
perature will not only speed up the vaporization of VOCs but
also change the chemical properties of VOCs and enhance
the reactions between VOCs and oxidants in the air. It is
relatively difficult to summarize the action of temperature
on the observed concentration. For some sources (e.g., Nos.
2, 3,and 7), the temperature factor values in Figure 8 increase

The Universityof Texas atAustin (UT). Althoughthe research
described in this article has been funded wholly or in part
by the United States Environmental Protection Agency, it
has not been subjected to the Agency’s required peer and
policy review and, therefore, does not necessarily reflect the
views of the Agency and no official endorsement should be
inferred. Themeteorological data for this studywere supplied
by NOAA Aeronomy Lab.
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(26) Toxic ReleaseInventory, U.S. EnvironmentalProtection Agency,
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Received for review September 11, 2003. Revised manuscript
received December 8, 2003. Accepted December 18, 2003.
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