Bidirectional enhanced quantile gated recurrent unit for short-term forecasting of PM2.5 with emphasis on extreme events in Sri Lanka

Anjana Jayasinghe , Chandima Tilakaratne 

Air quality forecasting is critical for mitigating the health impacts of fine particulate matter (PM2.5). This study introduces a hybrid deep learning model, the bidirectional enhanced quantile gated recurrent unit (BEQ-GRU), for short-term forecasting of PM2.5 concentrations with explicit emphasis on extreme pollution occurrences. This model was applied to forecast PM2.5 levels in two high-risk Sri Lankan cities, Colombo and Kandy, delivering 24-hour and 48-hour ahead forecasts. Unlike conventional point-estimation models that optimise for mean accuracy, the BEQ-GRU targets the upper tail of the conditional distribution through an asymmetric quantile objective engineered to capture the heavy-tailed distribution of pollution exceedances.
Beyond the architecture, this paper contributes a formal mathematical treatment of the method: (i) it is proved that the quantile loss function recovers the conditional quantile, and its 19:1 gradient asymmetry at τ = 0.95 is quantified; (ii) the “smoothing effect” of mean-optimal training is characterised through a peaks-over-threshold (POT) model, and it is proved that mean-trained detectors systematically miss an identifiable band of exceedances; and (iii) a decision-theoretic result (Theorem 1) is established, showing that thresholding a τ-quantile forecast is Bayes-optimal for cost-sensitive exceedance alarms, with the optimal level fixed by the public-health cost ratio as τ* = CFN/(CFN+CFP). This identity explains, rather than merely reports, the observed high-sensitivity, zero-false-alarm regime.
Hourly data from October 2022 to December 2023 were analysed, incorporating meteorological variables and co-pollutant concentrations as predictors. Statistical, machine learning, and deep learning models were compared. Deep learning consistently outperformed conventional approaches, capturing more than 70% of 24-hour and 60% of 48-hour extreme spikes at both stations. The proposed BEQ-GRU achieved the best performance for Colombo, while a standard Bidirectional GRU was most effective for Kandy. The framework can be adapted, with minor modifications, for proactive air-quality management and public-health early warning.