Ronald C. Henry

Review of receptor model fundamentals

Abstract There are several broad classes of mathematical models used to apportion the aerosol measured at a receptor site to its likely sources. This paper surveys the two types applied in exercises for the Mathematical and Empirical Receptor Models Workshop (Quail Roost II): chemical mass balance models and multivariate models . The fundamental principles of each are reviewed. Also considered are the specific models available within each class. These include: tracer element, linear programming, ordinary linear least-squares, effective variance least-squares and ridge regression (all solutions to the chemical mass balance equation), and factor analysis, target transformation factor analysis, multiple linear regression and extended Q-mode factor analysis (all multivariate models). In practical application of chemical mass balance models, a frequent problem is the presence of two or more emission sources whose signatures are very similar. Several techniques to reduce the effects of such multicollinearity are discussed. The propagation of errors for source contribution estimates, another practical concern, also is given special attention.

PM source apportionment and health effects: 1. Intercomparison of source apportionment results

During the past three decades, receptor models have been used to identify and apportion ambient concentrations to sources. A number of groups are employing these methods to provide input into air quality management planning. A workshop has explored the use of resolved source contributions in health effects models. Multiple groups have analyzed particulate composition data sets from Washington, DC and Phoenix, AZ. Similar source profiles were extracted from these data sets by the investigators using different factor analysis methods. There was good agreement among the major resolved source types. Crustal (soil), sulfate, oil, and salt were the sources that were most unambiguously identified (generally highest correlation across the sites). Traffic and vegetative burning showed considerable variability among the results with variability in the ability of the methods to partition the motor vehicle contributions between gasoline and diesel vehicles. However, if the total motor vehicle contributions are estimated, good correspondence was obtained among the results. The source impacts were especially similar across various analyses for the larger mass contributors (e.g., in Washington, secondary sulfate SE=7% and 11% for traffic; in Phoenix, secondary sulfate SE=17% and 7% for traffic). Especially important for time-series health effects assessment, the source-specific impacts were found to be highly correlated across analysis methods/researchers for the major components (e.g., mean analysis to analysis correlation, r>0.9 for traffic and secondary sulfates in Phoenix and for traffic and secondary nitrates in Washington. The sulfate mean r value is >0.75 in Washington.). Overall, although these intercomparisons suggest areas where further research is needed (e.g., better division of traffic emissions between diesel and gasoline vehicles), they provide support the contention that PM2.5 mass source apportionment results are consistent across users and methods, and that todays source apportionment methods are robust enough for application to PM2.5 health effects assessments.

Multivariate receptor modeling by N-dimensional edge detection

The mathematical details of the Unmix multivariate receptor model for air quality data are given. Primary among these is an algorithm to find edges (more correctly hyperplanes) in sets of points in N-dimensional space. An example with simulated data is given.

Current factor analysis receptor models are ill-posed

Abstract Current factor models lack sufficient physical constraints to guarantee a unique, physically valid solution; in this sense they are ill-posed. Any realistic factor model must obey certain natural physical constraints, for example, the predicted source contributions and elemental compositions must be non-negative. Five such constraints are given in the paper. As shown by a simple example with only two sources and three elements, these natural constraints are insufficient to define a unique factor model. The same is shown to be true for a more complex example with seven sources and 10 elements. Since the examples use simulated data without observational or other errors, they prove that current factor models are, in general, biased in the statistical sense. The examples also show that the bias, or systematic error, can be very large. Thus, while factor analysis continues to be a valuable screening tool for unexpected sources, in the hands of the inexperienced it could lead to serious errors in source apportionment and derived source compositions.

Workgroup Report: Workshop on Source Apportionment of Particulate Matter Health Effects—Intercomparison of Results and Implications

Although the association between exposure to ambient fine particulate matter with aerodynamic diameter < 2.5 μm (PM2.5) and human mortality is well established, the most responsible particle types/sources are not yet certain. In May 2003, the U.S. Environmental Protection Agency’s Particulate Matter Centers Program sponsored the Workshop on the Source Apportionment of PM Health Effects. The goal was to evaluate the consistency of the various source apportionment methods in assessing source contributions to daily PM2.5 mass–mortality associations. Seven research institutions, using varying methods, participated in the estimation of source apportionments of PM2.5 mass samples collected in Washington, DC, and Phoenix, Arizona, USA. Apportionments were evaluated for their respective associations with mortality using Poisson regressions, allowing a comparative assessment of the extent to which variations in the apportionments contributed to variability in the source-specific mortality results. The various research groups generally identified the same major source types, each with similar elemental makeups. Intergroup correlation analyses indicated that soil-, sulfate-, residual oil-, and salt-associated mass were most unambiguously identified by various methods, whereas vegetative burning and traffic were less consistent. Aggregate source-specific mortality relative risk (RR) estimate confidence intervals overlapped each other, but the sulfate-related PM2.5 component was most consistently significant across analyses in these cities. Analyses indicated that source types were a significant predictor of RR, whereas apportionment group differences were not. Variations in the source apportionments added only some 15% to the mortality regression uncertainties. These results provide supportive evidence that existing PM2.5 source apportionment methods can be used to derive reliable insights into the source components that contribute to PM2.5 health effects.

Source Apportionment of Phoenix PM2.5 Aerosol with the Unmix Receptor Model

Abstract The multivariate receptor model Unmix has been used to analyze a 3-yr PM2.5 ambient aerosol data set collected in Phoenix, AZ, beginning in 1995. The analysis generated source profiles and overall average percentage source contribution estimates (SCEs) for five source categories: gasoline engines (33 ± 4%), diesel engines (16 ± 2%), secondary SO4 2− (19 ± 2%), crustal/soil (22 ± 2%), and vegetative burning (10 ± 2%). The Unmix analysis was supplemented with scanning electron microscopy (SEM) of a limited number of filter samples for information on possible additional low-strength sources. Except for the diesel engine source category, the Unmix SCEs were generally consistent with an earlier multivariate receptor analysis of essentially the same data using the Positive Matrix Factorization (PMF) model. This article provides the first demonstration for an urban area of the capability of the Unmix receptor model.

PM source apportionment and health effects. 3. Investigation of inter-method variations in associations between estimated source contributions of PM2.5 and daily mortality in Phoenix, AZ

As part of an EPA-sponsored workshop to investigate the use of source apportionment in health effects analyses, the associations between the participants estimated source contributions of PM2.5 for Phoenix, AZ for the period from 1995–1997 and cardiovascular and total nonaccidental mortality were analyzed using Poisson generalized linear models (GLM). The base model controlled for extreme temperatures, relative humidity, day of week, and time trends using natural spline smoothers. The same mortality model was applied to all of the apportionment results to provide a consistent comparison across source components and investigators/methods. Of the apportioned anthropogenic PM2.5 source categories, secondary sulfate, traffic, and copper smelter-derived particles were most consistently associated with cardiovascular mortality. The sources with the largest cardiovascular mortality effect size were secondary sulfate (median estimate=16.0% per 5th-to-95th percentile increment at lag 0 day among eight investigators/methods) and traffic (median estimate=13.2% per 5th-to-95th percentile increment at lag 1 day among nine investigators/methods). For total mortality, the associations were weaker. Sea salt was also found to be associated with both total and cardiovascular mortality, but at 5 days lag. Fine particle soil and biomass burning factors were not associated with increased risks. Variations in the maximum effect lag varied by source category suggesting that past analyses considering only single lags of PM2.5 may have underestimated health impact contributions at different lags. Further research is needed on the possibility that different PM2.5 source components may have different effect lag structure. There was considerable consistency in the health effects results across source apportionments in their effect estimates and their lag structures. Variations in results across investigators/methods were small compared to the variations across source categories. These results indicate reproducibility of source apportionment results across investigative groups and support applicability of these methods to effects studies. However, future research will also need to investigate a number of other important issues including accuracy of results.

Origins of fine aerosol mass in the Baltimore-Washington corridor: implications from observation, factor analysis, and ensemble air parcel back trajectories

Chemically speciated fine particulate matter (PM2.5) and trace gases (including NH3, HNO3, CO, SO2 ,N O y) have been sampled at Fort Meade (FME: 39.101N, 76.741W; elevation 46 m MSL), Maryland, since July 1999. FME is suburban, located in the middle of the Baltimore–Washington corridor, and generally downwind of the highly industrialized Midwest. The PM2.5 at FME is expected to be of both local and regional sources. Measurements over a 2year period include eight seasonally representative months. The PM2.5 shows an annual mean of 13m gm � 3 and primarily consists of sulfate, nitrate, ammonium, and carbonaceous material. Day-to-day and seasonal variations in the PM2.5 chemical composition reflect changes of contribution from various sources. UNMIX, an innovative receptor model, is used to retrieve potential sources of the PM2.5. A six-factor model, including regional sulfate, local sulfate, wood smoke, copper/iron processing industry, mobile, and secondary nitrate, is constructed and compared with reported source emission profiles. The six factors are studied further using an ensemble back trajectory method to identify possible source locations. Sources of local sulfate, mobile, and secondary nitrate are more localized around the receptor than those of other factors. Regional sulfate and wood smoke are more regional and associated with westerly and southerly transport, respectively. This study suggests that the local contribution to PM2.5 mass can vary from o30% in summer to >60% in winter. r 2002 Elsevier Science Ltd. All rights reserved.

Extension of self-modeling curve resolution to mixtures of more than three components: Part 1. Finding the basic feasible region

Abstract Henry, R.C. and Kim, B.M., 1990. Extension of self-modeling curve resolution to mixtures of more than three components. Part 1. Finding the basic feasible region. Chemometrics and Intelligent Laboratory Systems , 8: 205–216. Self-modeling curve resolution attempts to find all possible solutions to a mixture problem which obey certain natural physical constraints expressed as linear inequalities in an eigenspace. The basic feasible region is the region of the eigenspace defined by the intersection of these constraints. A method is given to determine this region for a mixture of any number of components. The outer boundary of the region is found using linear programming methods to determine all its vertices. The vertices of the inner boundary are also found by linear programming; however, the constraints are formulated in a different eigenspace. The method is demonstrated on a set of simulated airborne particulate composition data. A more complete solution to the mixture problem requires additional physical constraints on the solutions. Incorporating these in the model will be the subject of a later paper. The effects of random errors in the data will also be considered at a later time.

Multivariate analysis of trace element data from moss samples used to monitor atmospheric deposition

Abstract Data from a national survey of trace element atmospheric deposition in Norway comprising 26 elements in 512 moss samples were examined using principal component analysis with a VARIMAX rotation. Ten factors explaining 78.4% of the total variance were identified. The three dominant principal components represent long-range atmospheric transport of polluted aerosol to southern Norway (Pb, Sb, As, V, Cd, Se, Zn, Cr, Mo, Ag and Th), soil particles (Sc, Al, Na, Fe and Sm) and contribution from trace-element enriched marine aerosols (I, Br and Se). Furthermore components representing local and regiona; air pollution phenomena, specific geological components in the soil particle fraction, and factors related to specific uptake mechanisms in the moss are identified.