Probabilistic hydrological forecasting based on variational Bayesian deep learning

The field of deep learning research in hydrology primarily aims to enhance prediction capabilities. However, the intricate structure of deep learning models often leads to predictions that are difficult to explain and trust, making the development of trustworthy deep learning models a challenging and increasingly important topic. In this paper, we present a novel hybrid model that combines the strengths of deep learning and physical-based hydrological models to improve predictions in hydrology. Utilizing a framework of a residual error model, our approach develops a VB-LSTM (variational Bayesian deep learning model) to quantify hydrological uncertainty and enhance predictive reliability. We applied our model to predict streamflow in the source area of the Yellow River from 1961 to 2015, and the results demonstrate its superiority over traditional methods. Compared to long-short term memory networks (LSTM), the VB-LSTM model achieved stable performance and higher predictive accuracy in the validation period. Additionally, it outperforms the traditional probabilistic hydrological post-processing method that relies on a "linear-normal" assumption, by providing higher predictive accuracy and reliability, and reducing predictive uncertainty.