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Positive matrix factorization (PMF) is a factor analysis based model that does not require source profiles as model inputs but it does require knowled...
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Environ. Sci. Technol. 2007, 41, 5763-5769

Positive Matrix Factorization (PMF) Analysis of Molecular Marker Measurements to Quantify the Sources of Organic Aerosols JEFFREY M. JAECKELS, MIN-SUK BAE, AND JAMES J. SCHAUER* Environmental Chemistry and Technology, University of Wisconsin, Madison, Wisconsin 53706

One hundred and twenty five particulate matter samples that were collected over a 2 year period at the St. Louis Midwest Supersite were analyzed for 24 hour average organic carbon (OC), elemental carbon (EC), and particle-phase organic compound (molecular markers) concentrations. Over 100 organic compounds along with measurements of silicon and aluminum were analyzed using a factor analysis based source apportionment model, positive matrix factorization (PMF), which has been widely used in the past with elemental data but not organic molecular markers. Four different solutions (7, 8, 9, and 10 factor solutions) to the PMF model were explored to consider the stability of the source apportionment results, which were found to be reasonably stable. The eight-factor solution was further explored and compared to a parallel chemical mass balance (CMB) source apportionment modeling result that used a subset of the PMF data. A base case eightfactor PMF solution resolved two point source factors, two winter combustion factors, a biomass-burning factor, a mobile source factor, a secondary organic aerosol factor, and a resuspended soil factor. An optimized eightfactor case was also examined, which was formulated by removing three extreme point source impacts observed in the base case, to better understand the nonpoint sources. In the optimized case, the daily OC explained by the biomass burning shows good agreement with the corresponding CMB source, with a slope of 0.93 ( 0.03. Likewise, the average OC explained by the optimized PMF resuspended soil factor showed good correlation with the CMB road dust apportionment, but there was a significant bias between the two results. The optimized PMF OC from one of the winter combustion factors showed good correlation with the CMB natural gas combustion apportionment but also has a significant bias. In both cases, PMF analysis factored one mobile source controlled by hopanes and streranes, which did not correlate well with any of the three CMB mobile sources. Although the most of the molecular markers were clustered with the PMF model in a manner consistent with prior knowledge of these organic compounds, one significant deviation was observed. Cholesterol, used in the past as a tracer for meat smoke, was found to largely associate with road dust, which raises questions on the suitability of cholesterol as a tracer for meat smoke in the midwestern U.S. * Corresponding author phone: (608)262-4495; fax (608)262-0454; email: [email protected]. 10.1021/es062536b CCC: $37.00 Published on Web 07/07/2007

 2007 American Chemical Society

Introduction Carbonaceous particulate matter is an important component of fine particulate matter in both urban and rural locations (1-4). Receptor based models have been used in the past to different degrees of success to understand sources of elemental carbon and organic carbon (ECOC), which comprise carbonaceous aerosols (2, 5-8). Two types of receptorbased models are commonly used to determine the origin of fine organic aerosols: (1) chemical mass balance (CMB) models using molecular markers, ECOC data, and a few crustal elements (9, 10) and (2) factorization techniques using measurements of ECOC, secondary inorganic ions, and trace elements (11, 12). Although these models are becoming more and more widely used by researchers and regulators, there have been very limited efforts to validate these models due to the lack of other definitive methods for the source apportionment. Recently, Held et al. (13) showed good agreement between a mechanistic air quality transport model and the molecular marker based CMB model for two studies in California. However, there is a great need to implement other intercomparison efforts among receptor-based models with mechanistic air quality transport models. Historically, data sets have not been collected that allow direct comparisons of PMF and molecular marker CMB models because the different data sets used by the two models are based on very different study designs. Molecular marker CMB models require measurements of organic tracers, which have been previously identified to have relatively unique association with specific sources of atmospheric fine particulate matter. Relatively unique organic tracers have been identified for sources including wood smoke (14, 15), mobile sources (6, 16), road dust (5), and biomass burning (15, 17). A disadvantage with CMB source apportionment is the requirement of a priori knowledge of the source profiles. To this end, questions are always raised with CMB models as to the accuracy of the source profiles and the ability to quantify errors associated with using source profiles that may not have been representative of the sources impacting receptor sites. Positive matrix factorization (PMF) is a factor analysis based model that does not require source profiles as model inputs but it does require knowledge of source profiles to determine the relationship of factors derived from the model with air pollution sources. A PMF source apportionment analysis, however, does require an assumption of the number of significant factors affecting the monitored data. Because robust PMF analysis typically uses at least 60-200 required sets of observations, the model has typically been driven by trace elements, ECOC measurements, and secondary inorganic ions, which are less specific than the organic compounds used in molecular marker based CMB source apportionment. As was done for previous studies, receptor observations need not be a continuous string of data for PMF analysis (18-21). Historically, molecular marker data sets have not been large enough for PMF based analysis and have been limited to use in CMB models. Recently, PM2.5 molecular markers have been measured for 120 days at the St. Louis Midwest Supersite that includes observations of 111 organic aerosol species. These measurements were used in a PMF model to apportion sources of organic carbon, which could be compared directly to the CMB based source apportionment of the same data set. These results demonstrate the broader abilities of the PMF software that should not be limited to data sets comprised of only trace elements, ECOC, and secondary ions. VOL. 41, NO. 16, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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Materials and Methods Sampling and Chemical Analysis. Daily PM2.5 samples were collected at the St. Louis Midwest Supersite were analyzed for 24 hour average organic carbon (OC), elemental carbon (EC) and trace elements for approximately 2 years (10). The samples for ECOC analysis were collected on prebaked quartz fiber filters and were analyzed for ECOC as described by Schauer (22). Trace elements were collected with a Harvard Impactor (23) and were analyzed by XRF. Additionally, the daily medium volume samplers that were used comprised of 92 lpm PM2.5 cyclones (URG Inc., Chapel Hill, NC) and 90 mm quartz filter holder with baked quartz fiber filters to collect particulate matter on alternating days from midnight to midnight. Daily samples collected every sixth day between May 13, 2001 through June 8, 2003 were analyzed for the molecular markers listed in Table S1 using gas chromatography mass spectrometry (GCMS) methods (24, 25). The target analytes included n-alkanes, cycloalkanes, alkanoic acids, resin acids, aromatic diacids, alkanedioic acids, steranes, hopanes, PAHs, oxy-PAHs, phthalates, levoglucosan, and cholesterol. Although only the 24 hour average ECOC, molecular marker, and silicon and aluminum data from XRF were used in the CMB and PMF analysis, hourly EC/OC data from two semicontinuous ECOC analyzers (25) were used as external checks to evaluate the molecular marker based PMF model predictions of point source impacts on carbonaceous aerosols. CMB Source Apportionment. The U.S. EPA computer code, CMB8.2, was used to solve the CMB source apportionment model using the effective variance solution (26) to obtain daily source apportionment results for the 120 days with complete sets of ambient observations. Ambient measurements and source profiles were input into the model that were comprised of silicon, aluminum, EC, and 33 molecular markers as mass balance species. The selection of these tracers as mass balance species is based on prior molecular marker based CMB modeling results (9, 25, 27) and the molecular marker based PMF results of this study. The source profiles used in the model are vegetative detritus (28), biomass burning (14), diesel engine exhaust, gasoline and smoking gasoline engine exhaust (29), tire wear debris and road dust (30), and particulate matter emissions from residential natural gas combustion (31). Details of the CMB analysis have been published by Bae (29). PMF Procedures. Positive matrix factorization (PMF) (18) is a factor analysis method that utilizes non-negativity constraints for the analysis of environmental data and associated error estimates. PMF solves the mass balance equations for each observation xij made for the jth species on the ith day. The model assumes factor profiles fkj consisting of the jth species in the kth factor, and factor contributions gik consisting of the kth factor on the ith day. Mathematically stated, the mass balance equations are as follows: p

xij )

∑g

ikfkj

+ eij

k)1

Where eij is the residual concentration for each observation. By incorporating an uncertainty for each observation sij, a function of the residual and uncertainty is created and is minimized using weighted least-squares. n

Q)

m

∑∑ i)1 j)1

(

)

p xij - Σk)1 gikfij

sij

The PMF model seeks to minimize this function. The theoretical minimum Q value is on the order of the number 5764

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of observations (32). The model requires data for all concentration and uncertainty values for all j species and i days. Data confidence can be maintained by adjusting the uncertainties for questionable observations. This allows the user to downgrade the importance of these data in the leastsquares fit. PMF is more thoroughly described in previous publications (33). For the current analysis, the U.S. EPA version of PMF was used (EPA PMF 1.1), which is based on the multilinear engine ME-2 developed by Paatro (34). The original set of 1 in 6 day organic data from May 13, 2001 through June 8, 2003 was reviewed and five of the 112 organic compounds were eliminated from use in PMF due to incomplete observations. The compounds eliminated were alkanes (iso-nonacosane, anteiso-triacontane, iso-hentriacontane, ateiso-dotriacontane, and iso-tritriacontane). ECOC, silicon, and aluminum observations were included with the organic observations. Analytical uncertainties derived in the organic analysis (24) were used as uncertainties in the molecular marker PMF model. EPA PMF 1.1 allows the user to review concentration statistics, which includes the signalto-noise ratio, and downgrade the importance of a species, if necessary, to “weak” or “bad” status. Weak species have uncertainties increased by a factor of 3, and bad species are removed from the analysis. In the current study, species with a signal-to-noise ratio equal to or less than 0.5 were marked as “bad” and species with signal-to-noise ratio equal to or less than 1.0 were marked as “weak”. Eight compounds were downgraded to “weak” compounds via control in the model. Two compounds, 9-hexadecenoic acid and squalene, were downgraded to “bad” and therefore not used in the model.

Results and Discussion A total of 109 aerosol species were evaluated in the PMF model. A summary of the individual species is presented in the Supporting Information as Table S1 along with the 2 year average ambient concentrations measured at the St. Louis Supersite, an indication of which compounds are tracers used the CMB analysis, and expected sources of each species from the literature. Twenty runs were made for each model. From the twenty runs the convergent run with the minimum Qrobust reported by EPA PMF1.1 was used for the solutions presented in this study. As an exploratory analysis PM2.5 OC contributions for seven, eight, nine, and ten factor PMF solutions were explored. Initially, the tentative identification of the factors was largely based on the distribution of molecular markers among the source profiles and the temporal characteristics of the source contributions to OC. The molecular markers associated with each factor for 7, 8, 9, and 10 factor models are presented in the Supporting Information as Table S2. The different solutions were very similar in terms of the derived profiles and the source contributions. The main difference between the seven-factor solution and the eightfactor solution was the splitting of the winter combustion factor into two different winter combustion factors. The ninefactor model resolved eight factors very similar in profiles as the eight-factor solution but included a ninth factor whose key feature was the eight resin acids. Due to the fact that the ninth factor dominated the variability in the resin acids but had little association with levoglucosan, hopanes, steranes, silicon, or aluminum, the factor did not appear to be associated with a physical air pollution source. Since the additions of a 9th and 10thtenth factor are largely the splitting of the biomass burning factor into subfactors that do not have a clear connection with current knowledge of biomass burning emissions, the eight factor model was chosen as the best solution to the PMF model. Residual OC contributions for each of the different models were stable across the solutions varying from 0.33 to 0.38 ug-m-3 (See the Supporting Information for additional information and a direct comparison of the different models).

FIGURE 1. Contributions to atmospheric organic carbon concentrations from the base case eight factor PMF model. Based on the analysis presented in the Supporting Information, the eight-factor model was chosen as a base case. OC contributions for some of the factors have important temporal characteristics, which are presented in Figure 1 as daily source contributions over the entire study period. The winter combustion and wood combustion factors are significant contributors to OC during the winter season. The two point sources have significant short-term (episodic) OC contributions, which make them important factors for local air pollution control. In order to explore the effect of these extreme observations, an optimized eight-factor case is also evaluated in which the two highest point source days and a high SOA day were taken out of the analysis (6/24/01, 11/ 15/01, and 12/10/02). The optimized case is used for the factor comparison to CMB derived sources and CMB tracers. In general, the secondary organic aerosol factor is characterized by alkanedioic acids, phthalates, aromatic diacids, and alkanoic acids; the biomass combustion factor by levoglucosan, resin acids, and steranes; the first winter combustion factor by PAH and oxygenated PAH; the second winter combustion factor by cholesterol and PAH; the mobile factor by steranes, hopanes, and EC; the first point source

by oxygenated PAHs, PAHs, and resin acids; the second point source by alkanes aromatic diacids and alkanoic acids; and the resuspended soil factor by silicon, aluminum, and cholesterol. Secondary Organic Aerosol Factor. The secondary organic aerosol (SOA) factor is characterized with the majority of alkanedioic acids, 1,2-benzenedicarboxcylic acid, 1,3benzenedicarboxylic acid, 4-methyl-1,2-benzenedicarboxylic acid, benzenetricarboxylic acid, benzenetetracarboxcylic acid, alkanoic acids, and phthalates (Table S2). Previous work has suggested aliphatic diacids and aromatic di-, tri-, and tetra-acids as indicators of secondary organic aerosols (SOA) (24, 35, 36). Both the base-case and optimized case contributions over time (Figures 1 and S2), respectively, illustrate the contributions of this factor are more significant in early spring and summer. OC contributions from the SOA factor and measured 1,2benzenedicarboxylic acid are plotted in Figure 3a for the base case. This plot (r2 ) 0.47) suggests this aromatic diacid is important in developing profiles for SOA. Secondary organic aerosols were not directly included in the CMB analysis. VOL. 41, NO. 16, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 2. Hourly organic carbon concentrations for day with high point contributions to organic carbon concentrations for the base case model: (a) February 7, 2002, (b) December 10, 2002, (c) June 24, 2001, and (d) November 3, 2001. Wood Combustion Factor. Levoglucosan has been identified as a unique and strong molecular marker for wood combustion and biomass buring (15). It has been used in source profiles of this source in several CMB analyses including the St. Louis Supersite and is resolved as a unique factor in the PMF analysis. This PMF factor has strong contributions in late fall to early spring (Figures 1 and S1), and it is very low in the summer months. These characteristics are strong evidence that this is a wood combustion factor. OC contributions from the wood combustion factor are plotted against monitored levoglucosan concentrations in Figure 3b for the optimized case to show good correlation (r2 ) 0.88) including the high-predicted contribution for 11/ 1/01. The PMF wood combustion factor for the optimized case is also compared to the CMB wood combustion source in Figure 4a. The correlation (r2 ) 0.88) is strong confirmation of the wood combustion source profile used in the CMB analysis. Winter Combustion Factors. One of the PMF factors is characterized by PAH and oxygenated PAH. The majority of fluoranthene and pyrene are in this factor (Table S2). This 5766

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factor is significant in the winter months and almost nonexistent in the summer months (Figure 1). This factor was termed the first of two winter combustion factors. OC contributions from the first winter combustion factor are plotted against measured pyrene concentrations in Figure 3c for the optimized case. Good correlation (r2 ) 0.91) exists. Natural gas use is considerably higher in winter months due to residential heating and is a possible contribution to this factor (37). This factor was plotted against the CMB natural gas combustion source in Figure 4b showing correlation (r2 ) 0.42) but bias (m ) 3.8) suggesting disagreement with the CMB source profile. The fifth PMF factor also has PAH characteristics (acephenanthrylene, benzo(j)fluoranthene, and perylene) and 9,12-octadecanedienoic acid. Contributions are very similar to the previous factor and are referred to as the second winter combustion factor. OC contributions from this factor are plotted against methyl substituted PAH (Figure 3d) indicating correlation (r2 ) 0.62). The combination of the two winter combustion factors is plotted in Figure 4c with the CMB natural gas source also showing correlation (r2 ) 0.61)

FIGURE 3. Relationships among the key measured atmospheric tracer concentrations and the organic carbon source contributions determined by the optimized case eight factor PMF model: (a) SOA factor and 1,2-benzenedicarboxylic acid, (b) wood combustion factor and levoglucosan, (c) winter combustion 1 factor and pyrene, (d) winter combustion 2 factor and methyl substituted PAH with molecular weights of 226, (e) mobile source factor and 17r(H)-21β(H)-hopane, and (f) resuspended soil factor and Silicon. suggesting both factors are related to the CMB natural gas source, which serve as an indication of wintertime combustion. Mobile Source Factor. One of the factors is clearly dominated by the majority of hopanes and steranes. These molecular markers are known to be dominated from the crankcase of internal combustion engines including gasoline and diesel engines (9). Hopanes and steranes have been used in source profiles for mobile sources in previous CMB analysis. This PMF factor is referred to as a mobile factor. OC contributions from the PMF mobile factor and measured 22S, 17R(H)-21β(H)-30-homohopane are plotted in Figure 3e. Correlation is evident between this factor and tracer (r2 ) 0.43). The PMF mobile factor has poor correlation with both the diesel and spark ignition CMB sources but has reasonable correlation with each of these sources when combined with the CMB “smoker” source. The mobile source factor has similar correlation with the CMB smoker source and a combination of diesel, spark ignition, and smoker sources. These figures are presented in Figure S5 and provide little insight into the specific impact of diesel, spark ignition, and smoker vehicles and cannot be used to further assess the accuracy of the CMB analysis. However, they do support the notion that total mobile source apportionment for the CMB analysis is reasonable.

Point Source Factors. Two of the PMF factors are characterized by episodic contributions with minor contributions existing throughout the remainder of the 2 year period (Figure 1). These two factors have the highest single daily OC contributions resolved by the PMF model at 10.8 µg-m-3 for one and 7.4 µg-m-3 for the second factor in the base case of the model. From these characteristics it is clear that these factors are localized point sources. Point source 1 has a number of PAH and oxygenated PAH as dominant species. Point source 2 is characterized by the majority of n-alkanes and 1,4-benzenedicarboxcylic acid. Hourly meteorological data available for the St Louis Supersite indicate calm and variable winds for these episodes. Figure 2 plots the hourly OC observations from the St. Louis Supersite with the point source OC contributions for the two highest episodes for each point source. Hourly OC observations are included for the preceding day and the day following the PMF-resolved episodes. It is clear that the episodes identified by the PMF model correspond with severe spikes in OC concentrations consistent with point source impacts. These 2 days and the high SOA day are removed for the optimized PMF analysis. The consequence of removing these days is a redistribution of the OC contributions as shown in Table S1 and Figure S1. The two point sources together VOL. 41, NO. 16, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 4. Comparison of the organic carbon contributions determined from the optimized eight factor PMF model and the CMB Model. lose the most and SOA gains the most OC mass in moving from the base case to optimized case. Resuspended Soil. Aluminum and silicon were included in the PMF analysis as they are important markers for resuspended dust. Both aluminum and silicon were used as tracers for CMB modeling at the site which is based on a source profile from California (30). Both elements resolved almost exclusively into one factor. Most of the OC, cholesterol, and stigmasterol also are in this factor. Although cholesterol is used as a meat smoke tracer in CMB studies, cholesterol previously has been associated with soil (38, 39). OC contributions of the PMF resuspended soil factor are plotted against the monitored silicon concentrations in Figure 3f showing a strong correlation (r2 ) 0.93). This suggests silicon is an important tracer for resuspended soil in this area. To compare the OC contributions from the PMF resuspended soil factor to the CMB road dust source, OC contributions are plotted against one another in Figure 4d. Good correlation exists between the two sources (r2 ) 0.66) suggesting agreement that silicon is an important tracer for this source. The plot has bias, however (m ) 1.9), which suggests the profiles differ between the PMF resuspended dust factor and the CMB road dust source. This is likely due to the use of a California road dust profile in the CMB analysis, which emphasizes the need for local resuspended soil profiles for use in CMB analysis. The majority of cholesterol and stigmasterol is also in this factor, which contradicts the profile and apportionment of meat cooking smoke in the prior CMB analysis. From the contributions plotted in Figure 1 one can see the resuspended dust factor contributions are slightly lower in the winter months consistent with seasonal variations in wind blown soil. The PMF analysis agrees well and supports CMB tracers and profiles for wood combustion (levoglucosan) and mobile sources (hopanes). PMF also is in agreement with the CMB analysis regarding tracers for resuspended soil (silicon) and combustion (pyrene, PAH). Further, the PMF analysis confirmed the ability of the molecular marker CMB model to accurately quantify the contributions from resuspended 5768

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dust and biomass burning and confirmed the importance of smoking vehicles in the mobile source profile. The PMF analysis raised questions about the apportionment of meat cooking smoke by the CMB model. The use of factor analysis identified four important factors not previously used in the CMB analysis. These are the two point source factors, a second winter combustion source, and the secondary organic aerosol source. In removing three extreme observations, two important points are highlighted. First, using all data fully characterizes all factors contributing to the observed data. Second, removing extreme events reduces the importance of the point source factors and redistributes mass among the remaining factors. Although it is difficult to assess which case is more accurate, it is clear that the combination of the two cases provides reasonable quantitative information on important sources of OC at the sampling site. This analysis is the first to directly compare the use of molecular markers in CMB and PMF to gain insight into the uncertainties of these source apportionment applications. In the context of the goals of source apportionment, the models agree reasonably well and provide an important baseline to better evaluate the accuracy and biases of the source apportionment models using molecular markers and other particulate matter tracers. The data collection used in this analysis was funded by the United States Environmental Protection Agency through cooperative agreement R-82805901-0 and the Electric Power Research Institute (EPRI). We gratefully acknowledge members of the St. Louis-Midwest Supersite consortium, who were instrumental in the design and implementation of the measurements made at the St. Louis-Midwest Suprsite.

Supporting Information Available Additional details are shown in six figures and two tables. This material is available free of charge via the Internet at http://pubs.acs.org.

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Received for review October 22, 2006. Revised manuscript received June 2, 2007. Accepted June 5, 2007. ES062536B

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