PMF Source Contribution Uncertainty Estimation via Effective Variance Least Squares

Understanding the sources of atmospheric particulate matter (PM) through reliable source apportionment methods is essential to support effective pollution control policies. Positive matrix factorization (PMF) has become the most widely used source apportionment method worldwide. However, conventional PMF analysis provides source profiles with uncertainties but contributions (g-value) without uncertainties limiting the utility of the resolved source-specific PM. This study estimates the g-value uncertainties in PMF-resolved PM2.5 source contributions by combining PMF with an effective variance least-squares (EVLS) analysis. Data from daily PM2.5 samples collected in Tianjin, China, were analyzed with the EPA PMF to identify the major sources. The EVLS method calculated the uncertainties in the g-value using the displacement intervals as the profile uncertainties. The primary PM2.5 contributors in Tianjin during 2013 to 2019 included secondary sulfate (25.39 ± 7.51 μg/m3), coal combustion (22.07 ± 9.41 μg/m3), secondary nitrate (19.88 ± 4.74 μg/m3), dust (16.12 ± 7.36 μg/m3), vehicle emissions (12.46 ± 5.04 μg/m3), the steel industry (12.32 ± 8.58 μg/m3), biomass burning (5.93 ± 2.61 μg/m3), and the galvanizing industry (3.37 ± 2.89 μg/m3). PMF-EVLS provided more comprehensive insights by better quantifying the contributions and uncertainties for each source, as shown by the more accurate reproduction of the original concentrations, particularly the higher concentration samples. Secondary sulfate and coal combustion had the highest uncertainties. This three-step method presents a significant advancement in PM source apportionment by allowing contribution uncertainty estimation, thus enhancing the reliability of source apportionment results and supporting data-driven air quality management decisions.