Receptor models such as the chemical mass balance (CMB) family and factor-analytic methods (PMF and relatives) apportion ambient PM2.5 to emission sources, but different models applied to the same chemical-composition dataset resolve different numbers of sources and different contribution magnitudes. Shi et al. (2018), comparing seven receptor models on Tianjin PM2.5 data, combined them by a simple unweighted average of the available model estimates. Weighted and Bayesian ensembles have been demonstrated at single sites (Atlanta, St. Louis), but the underlying methodology remains unresolved — how to weight member models, how to treat sources that some models fail to resolve, how to propagate uncertainty across correlated models, and how to validate the ensemble when no ground-truth source impacts exist. The open problem is to establish and validate a principled procedure for combining multiple receptor-model source apportionments of the same dataset, replacing the ad hoc unweighted average.

Background

PM2.5 designates airborne particulate matter with aerodynamic diameter below 2.5 micrometers, a dominant air pollutant in Chinese megacities and a leading health concern. Source apportionment (SA) estimates the contribution of each emission source category (e.g., crustal dust, coal combustion, vehicle exhaust, secondary sulfate and nitrate formed in the atmosphere from SO2 and NOx) to measured PM2.5 mass, and its results feed directly into air-quality control policy. Receptor models perform SA at a measurement ("receptor") site by solving a mass-conservation relation between the ambient chemical composition and source profiles, i.e., the relative chemical composition of PM emitted by each source category.

Two families dominate. Chemical mass balance (CMB) is a weighted least-squares fit of ambient species concentrations to known source profiles, applicable when the sources and their profiles are known; factor-analytic models such as positive matrix factorization (PMF) decompose the ambient data matrix into factors that the user interprets as sources without requiring profiles in advance. Variants used in the seven-model comparison include CMB-Iteration (iterative reweighting incorporating source-profile and receptor-data uncertainties); CMB-GC and CMBGC-Iteration (gas-constrained CMB, which adds ambient gas concentrations such as SO2, CO and NOx, through their ratios to PM2.5, as constraints on the solution, with a bound factor n, recommended as three, allowing for gas-phase chemical transformations during transport); WALSPMF (weighted alternating least squares PMF); and NCAPCA (non-negative-constrained absolute principal-component analysis).

A persistent structural difficulty is collinearity: chemically similar sources such as cement dust and crustal dust share marker species (e.g., Ca, Si, Al), so receptor models cannot reliably separate their contributions. Receptor-model SA is also not identifiable in a unique mathematical sense: different models, and even different runs of one model, yield different numbers of resolved sources and different contribution estimates for the same dataset, and no ground-truth time series of source impacts exists at a receptor to judge which model is correct.

Against this background, the idea of combining multiple SA results into an ensemble estimate has emerged. Shi, Liu, Wang, Tian, Wen, Shi, Feng, Ivey and Russell (2018) proposed CMBGC-Iteration, applied it and six other receptor models to 114 PM2.5 samples collected in Tianjin (April 2014 to January 2015), and computed ensemble-average source impacts as the unweighted arithmetic mean of whichever of the seven models provided an estimate for each source category, noting only that this average avoided negative and zero estimates that individual models produced. Earlier, related ensembles had been built with explicit weighting: Lee, Balachandran, Pachon, Shankaran, Lee, Mulholland and Russell (2009) combined four SA methods for health-effect studies using weights inversely proportional to method uncertainty; Balachandran, Pachon, Hu, Lee, Mulholland and Russell (2012) analyzed ensemble method uncertainty and sensitivity to which member methods are included; Balachandran, Chang, Pachon, Holmes, Mulholland and Russell (2013) formulated a Bayesian ensemble averaging of multiple SA methods; and Maier, Balachandran, Sarnat, Turner, Mulholland and Russell (2013) applied an ensemble-trained approach at a site impacted by multiple industrial point sources. None of these established a general, validated procedure for the combination step itself.

Problem Statement

Given several receptor-model source apportionments of the same ambient PM2.5 chemical-composition dataset — e.g., the seven models compared by Shi et al. (2018) on the Tianjin data, which resolve different numbers of source categories (four to six) and different contribution magnitudes — establish and validate a principled procedure for combining them into ensemble source-impact estimates. The procedure must specify: (i) a weighting scheme for member models and the criterion it optimizes, in a setting where member-model estimates are mutually correlated and no ground-truth source impacts exist at the receptor; (ii) how a source category that some member models fail to resolve (e.g., secondary organic carbon, i.e., particulate carbon formed in the atmosphere by oxidation of volatile organic compounds, or cement dust) is treated in the ensemble estimate and its uncertainty; and (iii) how uncertainty is propagated across member models to yield quantitative uncertainty bounds on ensemble source impacts. Validation must demonstrate, against defined performance criteria (e.g., mass closure, i.e., agreement of the sum of apportioned source contributions with the measured PM2.5 mass; agreement with independent constraints such as tracer species or emission-inventory changes; robustness to member inclusion and exclusion; comparison of ensemble uncertainty against individual-model uncertainties), whether and when the ensemble estimate is more accurate or better calibrated than both the individual member models and the unweighted average of available estimates that current practice uses, which the ensemble is meant to replace — with an executed comparison.

References

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