Systematic Evaluation of Two Classical Receptor Models in Source Apportionment of Soil Heavy Metal(loid) Pollution Using Synthetic and Real-World Datasets

Due to the lack of a priori knowledge on true source makeup and contributions, whether the source apportionment results of Unmix and positive matrix factorization (PMF) are accurate cannot be easily assessed, despite the availability of built-in indicators for their goodness of fit and robustness. This study systematically evaluated, for the first time, the applicability and reliability of these models in source apportionment of soil heavy metal(loid)s with synthetic datasets generated using known source profiles and contributions and a real-world dataset as well. For eight synthetic datasets with different pollution source characteristics, feasible Unmix solutions were close to the true source component compositions (R² > 0.936; total mean squared errors (MSEs) < 0.04), while those of PMF had significant deviations (R² of 0.484-0.998; total MSEs of 0.04-0.16). Nonetheless, both models failed to accurately apportion the sources with collinearity or non-normal distribution. Unmix generally outperformed PMF, and its solutions showed much less dependence on sample size than those of PMF. While the built-in indicators provided little hint on the reliability of both models for the real-world dataset, their sample-size dependence indicated that Unmix probably yielded more accurate solutions. These insights could help avoid the potential misuse of Unmix and PMF in source apportionment of soil heavy metal(loid) pollution.