Hybrid VMD–BiGRU Framework for Multi-Step Forecasting of PM2.5 in Traffic-Intensive Cities of the Kingdom of Saudi Arabia

Fine particulate matter (PM2.5) poses major public health and environmental threats due to its capacity to enter deep respiratory passages and degrade urban air quality. In the Kingdom of Saudi Arabia (KSA), cities such as Riyadh, Dammam, and Jeddah show an elevated level of PM2.5 due to rapid urban growth, dense traffic activity, and wide industrial operations. This study proposes a hybrid Variational Mode Decomposition–Bidirectional Gated Recurrent Unit (VMD–BiGRU) framework for multi-horizon PM2.5 forecasts based on daily data from January 2022 to September 2024. The daily PM2.5 series was split through VMD into Intrinsic Mode Functions (IMFs) that represent multi-scale temporal patterns. A seven-day ahead forecast was carried out, and model performance was compared with VMD–GRU, VMD–LSTM, and VMD–TCN. For Riyadh, RMSE values for t + 1, t + 2, and t + 3 were 9.25, 12.26, and 16.05 µg/m3, with R2 above 0.90 up to the third day. For Dammam, RMSE values for the same horizons were 4.46, 7.24, and 11.34 µg/m3, and R2 remained above 0.90 up to the fourth day. For Jeddah, the corresponding values were 3.97, 6.09, and 9.36 µg/m3, and R2 remained above 0.90 up to the fourth day. The hybrid VMD–BiGRU model achieved higher accuracy for short horizons (t + 1 to t + 3). The study establishes a basis that aids short-term PM2.5 prediction and improves air quality assessment across major urban centers in KSA.