Chemical sparsity in Bayesian receptor models for aerosol source apportionment

Abstract. Aerosol source apportionment is a key tool for understanding the origins of atmospheric particulate matter and for guiding effective air quality management strategies. However, source apportionment techniques still struggle to properly separate highly correlated sources without relying on restrictive a priori information, possibly skewing the solution and adding subjective operator input, with varying degrees of benefit. This study introduces sparsity into the Bayesian Autocorrelated Matrix Factorisation (BAMF) model with the aim of removing non-essential species contribution in the unconstrained profiles, which is expected to improve the separation of factors compared to BAMF. The regularised horseshoe prior (HS) has been added to BAMF (BAMF+HS) to promote composition matrix F sparsity, shrinking low-signal contributions to the solutions. BAMF+HS was evaluated using three synthetic datasets designed to reflect increasing levels of data complexity (Toy, representing a highly simplified dataset; Offline, representing a filter dataset; and Online, representing an Aerosol Chemical Speciation Monitor (ACSM)-like dataset), and a real-world multi-site filter dataset. The results demonstrate that BAMF+HS effectively enforces sparsity in offline datasets and that this improves accuracy in reconstructing source profiles and time series compared to BAMF and Positive Matrix Factorisation (PMF). However, its application to higher-complexity ACSM datasets revealed sensitivity to sampling instability hindering sparsification. With that, even though sparsity was not achieved, the quality of the BAMF+HS solution metrics were not deprecated compared to BAMF. Overall, this work underscores the value of incorporating profile sparsity as a solution property in Bayesian source apportionment, and positions BAMF+HS as a promising model for source apportionment.