Bayesian Proxy Modelling for Estimating Black Carbon Concentrations using White-Box and Black-Box Models

Black carbon (BC) is an important component of particulate matter (PM) in urban environments. BC is typically emitted from gas and diesel engines, coal-fired power plants, and other sources that burn fossil fuel. In contrast to PM, BC measurements are not always available on a large scale due to the operational cost and complexity of the instrumentation. Therefore, it is advantageous to develop a mathematical model for estimating the quantity of BC in the air, termed a BC proxy, to enable widening of spatial air pollution mapping. This article presents the development of BC proxies based on a Bayesian framework using measurements of PM concentrations and size distributions from 10 to 10,000 nm from a recent mobile air pollution study across several areas of Jordan. Bayesian methods using informative priors can naturally prevent over-fitting in the modelling process and the methods generate a confidence interval around the prediction, thus the estimated BC concentration can be directly quantified and assessed. In particular, two types of models are developed based on their transparency and interpretability, referred to as white-box and black-box models. The proposed methods are tested on extensive data sets obtained from the measurement campaign in Jordan. In this study, black-box models perform slightly better due to their model complexity. Nevertheless, the results demonstrate that the performance of both models does not differ significantly. In practice, white-box models are relatively more convenient to be deployed, the methods are well understood by scientists, and the models can be used to better understand key relationships.