Fig. 2: The cross-validation results at National Air Pollution Monitoring Network (NABEL) stations.

a–e display cross-validation predictions for each of the five different sites, with dashed lines marking the 1:2 (or 2:1) ratio lines. Each plot is labeled in bold with the station omitted during the training process. Although each model was trained by excluding one station, predictions were generated for all five stations during testing. f presents a comparative radar plot showing results with and without the exclusion of specific sites, along with a scenario where all five sites were included in training (indicated by the red dashed line). The site name in brackets identifies the station excluded from training. To ensure comparability, hourly metrics were normalized across test stations, with further adjustments applied so values closer to 1 indicate lower actual values, reflecting improved predictive accuracy and generalization. Notably, f displays Stem-PNC metrics based on hourly normalized results, in contrast to the monthly time scales in (a)–(e). The metrics include Coefficient of Determination (R²), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Square Error (MSE), Explained Variance Score (EVS), and Mean Bias (M-Bias). Additional daily and weekly results are provided in Supplementary Note 4.1.