Deep Chaulya
Department of Computer Science and Engineering, Indian Institute of Technology Patna, Patna 801106, India
Fog significantly affects aviation, transportation, agriculture, and energy in North India during winter. Accurate prediction is difficult due to nonlinear meteorological interactions and uncertainty. Traditional models provide point estimates without uncertainty, while Bayesian methods offer probabilistic outputs but struggle to capture complex temporal dependencies in atmospheric time-series data effectively. To address these limitations, this study proposes a hybrid long-term forecasting framework that integrates a three-layer Bidirectional Long Short-Term Memory (BiLSTM) network with a Modified Bayesian Beta Regression model. The model is trained and evaluated using 24 years (2000–2023) of meteorological observations from Lucknow Airport, representing a fog-prone region within the Indo-Gangetic Plains. Fog behaviour was represented through a normalized Fog Index (0–1) that incorporates both intensity and persistence, offering a more stable and informative forecast target than raw visibility. The BiLSTM component captures temporal dependencies and produces accurate point forecasts, achieving a root mean square error (RMSE) of 0.125 for a three-day prediction horizon. The Bayesian layer enhances reliability by generating calibrated uncertainty intervals. The resulting model achieved an average interval width of approximately 0.59 and a prediction interval coverage close to 80%, effectively representing both aleatoric and epistemic uncertainty. Additional techniques, including Min-Max normalization, sequence windowing, Fast Fourier Transform (FFT) feature augmentation, learning-rate scheduling, and Monte Carlo dropout, improved generalization and model stability. The proposed hybrid framework outperforms standalone models and shows strong potential for operational fog forecasting, offering both accurate predictions and uncertainty-aware confidence estimates for aviation, transportation, and early-warning systems.
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Copyright © 2026 Deep Chaulya
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