Bayesian Modeling of PM10 in Kraków Using Meteorological and Seasonal Factors

Short-term particulate-matter forecasts are strongly influenced by temporal persistence, which can obscure the incremental value of meteorological covariates and seasonality. This study evaluates that incremental value using 42,823 hourly observations of PM10 and meteorological conditions from Kraków, Poland, collected during 2020–2024. Four interpretable Bayesian lognormal regression models were compared with historical-median, persistence, and rolling one-step-ahead ARX(1) dynamic-regression references. The models progressively incorporated lagged PM10, standardized meteorological predictors, and annual and daily Fourier terms. The evaluation used four rolling-origin validation folds and an untouched final 20% test period. On the final test set, the full Bayesian model achieved MAE 4.865 µgm−3, RMSE 7.454 µgm−3, CRPS 3.602 µgm−3, and 0.884 coverage of its nominal 90% predictive interval. Its point accuracy was statistically indistinguishable from persistence, the lag-only Bayesian model, and ARX(1) under moving-block bootstrap. The full model had the highest PSIS-LOO expected log predictive density and the lowest observed test-set CRPS, but its CRPS difference from ARX(1) was small (0.020 µgm−3) and the paired 95% bootstrap interval included zero. The meteorological effects were strongly attenuated after including lagged PM10, while persistence remained the best point predictor during high-pollution hours. Temporal persistence therefore dominates one-hour-ahead point prediction. Meteorology and cyclic seasonality changed distributional summaries more than MAE or RMSE, but the held-out CRPS differences among the persistence-aware models were small and inconclusive at the 95% level.