Multi-City Bi-Pollutant Calibration of Low-Cost PM Sensors Using Machine Learning

Abstract

Low-cost sensor (LCS) networks can substantially enhance the spatial and temporal resolution of air pollutants, including particulate matter (PM) observations; however, their measurements are sensitive to meteorology, aerosol properties, and device heterogeneity. Consequently, LCS data require calibration against reference monitors (e.g., Tapered Element Oscillating Microbalance (TEOM), Fine Dust Analysis System (FIDAS), or other reference-grade instruments) before they can support exposure assessment or regulatory and policy-making decisions. We built and evaluated the calibration framework using two types of LCSs (PurpleAir (PA) and Alphasense OPC-N3) from three European cities (Antwerp (Belgium), Oslo (Norway), Zagreb (Croatia)) and two pollutants (PM2.5, PM10) using hourly averages data. We built Machine Learning (ML) calibration models using 1) a Random Forest (RF), 2) a compact feedforward Neural Network (NN), and 3) HybriCal-AQ (Hybrid Calibration for Air Quality)—a hybrid NN that appends a single standardized RF hint derived from out-of-fold predictions. To prevent information leakage and reflect operational practice, all models use a train-first pipeline consisting of split, impute, and encode. Models are evaluated under explicit reference grade instruments (TEOM, FIDAS, and generic reference) to mirror city-specific reference availability. We report R2, RMSE, and MSE with 5-fold cross-validation; for HybriCal-AQ, we also run a sparse-reference test that withholds 25% of random reference monitor observations, to evaluate model robustness under incomplete reference data. Across cities and reference grade instruments, HybriCal–AQ improves PM2.5 over NN and is competitive with RF (Antwerp/PurpleAir PM2.5: RMSE decreased from 2.02 to 1.93 with both R2=0.97; Oslo–FIDAS/PurpleAir PM2.5: RMSE decreased from 1.79 to 1.18 with R2 increasing from 0.94 to 0.97), while RF often remains preferable for PM10 (Antwerp/PurpleAir PM10: RF 4.76 versus HybriCal–AQ 6.58). In Oslo–TEOM, HybriCal–AQ yields lower PM2.5 RMSE (2.70 versus 3.06) with similar R2 (0.83 each), and under Oslo–FIDAS it attains R2=0.97. A notable PM10 exception occurs under Oslo–FIDAS, where HybriCal–AQ outperforms RF (RMSE 6.67 versus 9.52; R2=0.91 versus 0.78). For OPC–N3, HybriCal–AQ leads for PM2.5 for RMSE, R2 under FIDAS (Oslo: 1.57 vs 2.96, 0.95 vs 0.85), while RF perform better in Antwerp/Zagreb; for PM10, RF dominates in Antwerp/Zagreb but HybriCal–AQ matches or beats RF in Oslo (TEOM RMSE 7.77 vs 7.92; FIDAS RMSE 4.11 vs 7.90). The proposed calibration models are simple to implement, robust to reference grade instruments changes, and suitable for heterogeneous LCS networks.