Bayesian Neural Networks for Satellite Fog Detection: Quantifying Epistemic and Aleatoric Uncertainties

Conventional threshold-based dual-channel methods, as well as recent deep learning-based methods, can deterministically detect fog using satellite observations. However, stochastic processes like fog are best represented by probabilistic models. This study proposes a method for probabilistic fog detection from satellite data using the Bayesian neural network (BNN)-based model. The novelty of the method lies in quantifying fog detection uncertainty and disentangling its epistemic and aleatoric components. The model generates a probability of fog for each input, which can be thresholded into fog/no-fog status, if needed. Using data from the INSAT-3D geostationary satellite over 18 North Indian cities, we demonstrate that the proposed method significantly outperforms the operational fog detection product of the Indian Space Research Organization, INSAT-FOG. The critical success indices (CSI) of the proposed model during testing and the INSAT-FOG are 0.48 and 0.12, respectively, whereas their probabilities of fog detection (PoD) are 0.68 and 0.13, respectively. The diurnal evaluation of the results shows that the model performs better even during dawn and dusk, which is a critical challenge in satellite fog detection. Moreover, the proposed model can detect very dense fog observations (visibility < 50 m) accurately (with CSI 0.93). On average, the detection uncertainty is lower for correct detections than for incorrect detections, suggesting that the model is more confident about correct detections. The uncertainty analysis reveals that the aleatoric uncertainty is usually higher than the epistemic uncertainty, suggesting potential avenues for future improvements in satellite fog detection. It is concluded that the proposed BNN is a promising method for real-time operational fog detection.