A Transformer-Based Probabilistic Deep Learning Framework for Uncertainty-Aware Long-Range Flood Forecasting Using Satellite-Derived Mesoscale Inputs

The uneven spatiotemporal distribution of precipitation, exacerbated by climate change, poses significant challenges to sustainable water resource management and flood forecasting. Deterministic models often fail to address the uncertainties inherent in long-term hydrological predictions. To address this gap, this study introduces a novel probabilistic flood forecasting framework that integrates a distribution head into attention-based architectures (Transformer and Informer) to capture long-range spatiotemporal dependencies. A second contribution is the implementation of a cascaded principal component analysis (PCA)-based data fusion approach that incorporates satellite-derived mesoscale inputs for long-horizon forecasting. The framework was evaluated across forecasting horizons of 7, 30, 60, and 180 d in two hydrologically distinct basins in the USA. Experimental results show that the Transformer achieved the best overall performance, with Continuous Ranked Probability Scores (CRPS) up to 35% lower than those of the baseline Bayesian LSTM in extended forecasting scenarios. In addition, the attention-based models maintained high reliability, with Prediction Interval Coverage Probabilities (PICP) exceeding 90% for the 95% prediction interval even at the 180-d lead time. Although the probabilistic LSTM showed greater error accumulation at longer horizons, the Informer provided a computationally efficient alternative, with accuracy remaining within 5% of the Transformer while reducing computational complexity. These findings highlight the potential of attention-based architectures for stable, uncertainty-aware flood forecasting in hydrologically dynamic basins.