Toolbox for accurate estimation and validation of PMF solutions in PM source apportionment

Abstract. Positive matrix factorization (PMF) is the most commonly used approach for particulate matter source apportionment; however, the implementation steps of the model require considerable user experience. Most studies apply PMF according to the recommendations of the Environmental Protection Agency and the European Commission, while relatively few studies focus on further developing the PMF methodology. This study aims to develop a systematic method that reduces some subjective aspects when performing a PMF study, providing recommendations and tools for its application and validation. A total of 13 targeted tests were conducted to address key sources of subjectivity in PMF, categorized into three critical aspects: preparation of the input matrix, selecting the number of sources, and validation of the PMF solution. The results of the first step highlighted that using a single source tracer reduces the tracer's dispersion into other sources, leading to more accurate results. The second stage tests suggested that the selection of a source tracer should be based on low uncertainty and specific temporal evolution, in order to facilitate the determination of a new source without compromising the PMF solution. Finally, the validation step was set up as an advanced comparison of the PMF-derived source profiles with those in the literature, including SPECIEUROPE database, using the ratio of chemicals and distance metrics. All outcomes of this study are compiled into a Python package providing essential tools to support the work from PMF implementation to solution validation, leading to less subjective solutions and more rigorous and reliable source apportionment.