Virtual Sensing of Equivalent Black Carbon in the Context of Urban Automatic Monitoring Sensor Networks

Black carbon (BC) is an important urban air pollutant of emerging concern with documented health and climate effects, yet direct BC measurements remain unavailable at the majority of automatic monitoring stations in typical urban sensor networks. Virtual sensing has been recently proposed as a complementary approach, using statistical relationships between routinely measured air quality parameters to provide indicative estimates of unmeasured quantities. In this study, regression models based on multiple linear regression (MLR), random forests (RFs) and support vector regression (SVR) are explored for equivalent BC estimation using reference-grade signals from a newly established urban background pilot supersite (Ada Marina, Belgrade). Three seasonal cases were considered: heating season, non-heating season, and the complete ~1-year dataset. Predictors for the models were derived using two approaches: a greedy algorithm based on stepwise linear regression, and a non-greedy algorithm based on adaptive best subset selection, yielding: NOx and CO for the heating season; NO₂ and PM_2.5 for the non-heating season; and NOx and PM_2.5 for the complete period. Models achieved the following R² and RMSE performance metrics for 50/50 training/test split: heating season R² = 0.87–0.94 and RMSE = 0.65–0.95 μg/m³; non-heating season R² = 0.57–0.60 and RMSE = 0.87–0.90 μg/m³; and complete period R² = 0.70–0.72 and RMSE = 0.78–0.80 μg/m³. Model performance is discussed in the context of published BC virtual sensor results from other European cities. A network applicability assessment indicates that the majority of Belgrade monitoring stations record the predictor signals required by the developed models, suggesting potential applicability for indicative BC estimation across the monitoring network, pending site-specific validation. We also present a preliminary, exploratory assessment of the models’ transferability to two external sites, where models achieved 0.6–0.8 R² for the heating season, and 0.5–0.6 R² for non-heating and the complete period.