Forecasting hourly size-resolved ambient ultrafine particles with size-specific historical windows

Ultrafine particles (UFPs; diameter ≤100 nm) vary rapidly in number concentration, but the history length associated with the lowest hourly prediction error may differ among particle sizes. We measured eight nominal size bins (10, 14, 19, 27, 37, 52, 72, and 100 nm) using a Mini-Wide-Range Aerosol Spectrometer (Mini-WRAS) at an urban site in Shenzhen, China (September 2023-June 2025), obtaining 8,982 quality-controlled hourly observations (89.6% of acquired monitoring hours) for analysis. We compared multiple linear regression (MLR), random forest (RF), extreme gradient boosting (XGBoost), long short-term memory (LSTM), and bidirectional LSTM (BiLSTM) across six historical windows (1, 2, 4, 6, 12, and 24 h) for one-hour-ahead prediction of each bin and their sum. All 270 model-window-target configurations were evaluated on the same 533 observed testing hours using normalized root mean square error (NRMSE) as the primary metric. The lowest NRMSE values were 60.2% at 10 nm and 22.1% at 14 nm versus 13.4-14.8% at 19-100 nm. A 2 h history yielded the lowest or co-lowest NRMSE at 10-19 nm, compared with 4 h at 27-100 nm. Multiple model classes shared the lowest NRMSE for several prediction targets. For total selected-channel UFPs, defined as the sum of the eight bins spanning approximately 8.8-118 nm, the lowest NRMSE was 13.7% at 12 h. The contrast between errors for the summed concentration and smallest bins highlights the importance of size-resolved forecasting evaluation.