Constrained positive matrix factorization: Elemental ratios, spatial distinction, and chemical transport model source contributions

Source apportionment models attempt to untangle the relationship between pollution sources and the impacts at downwind receptors. Two frameworks of source apportionment models exist: source-oriented and receptor-oriented. Source based apportionment models use presumed emissions and atmospheric processes to estimate the downwind source contributions. Conversely, receptor based models leverage speciated concentration data from downwind receptors and apply statistical methods to predict source contributions. Integration of both source-oriented and receptor-oriented models could lead to a better understanding of the implications sources have on the environment and society. The research presented here investigated three different types of constraints applied to the Positive Matrix Factorization (PMF) receptor model within the framework of the Multilinear Engine (ME-2): element ratio constraints, spatial separation constraints, and chemical transport model (CTM) source attribution constraints. PM10-2.5 mass and trace element concentrations were measured in Winston-Salem, Chicago, and St. Paul at up to 60 sites per city during two different seasons in 2010. PMF was used to explore the underlying sources of variability. Information on previously reported PM10-2.5 tire and brake wear profiles were used to constrain these features in PMF by prior specification of selected species ratios. We also modified PMF to allow for combining the measurements from all three cities into a single model while preserving city-specific soil features. Relatively minor differences were observed between model predictions with and without the prior ratio constraints, increasing confidence in our ability to identify separate brake wear and tire wear features. Using separate data, source contributions to total fine particle carbon predicted by a CTM were incorporated into the PMF receptor model to form a receptor-oriented hybrid model. The level of influence of the CTM versus traditional PMF was varied using a weighting parameter applied to an object function as implemented in ME-2. The resulting hybrid model was used to quantify the contributions of total carbon from both wildfires and biogenic sources at two Interagency Monitoring of Protected Visual Environment monitoring sites, Monture and Sula Peak, Montana, from 2006 through 2008.