An explainable Bayesian gated recurrent unit model for multi-step streamflow forecasting

Study region: In the middle and lower reaches of the Yangtze River Basin of China Study focus: We propose an explainable Bayesian gated recurrent unit (EB-GRU) model for reliable multi-step streamflow forecasting. The proposed model introduces Bayesian inference into a gated recurrent unit (GRU) to quantify the uncertainty of streamflow prediction, and uses SHapley Additive exPlanations (SHAP) method to analyze the importance of hydrometeorological indices on streamflow prediction. The EB-GRU is examined by forecasting the multi-step streamflow at Hukou and Qilishan stations in the middle and lower reaches of the Yangtze River Basin, and compared with the Transformer (TSF), multi-layer perceptron (MLP) and support vector machine (SVM). New hydrological insights for the region: The comparative results show that the performance of the proposed EB-GRU surpasses that of the TSF, except for the streamflow forecast at the Hukou station with a 1-day lead time. The EB-GRU outperforms the MLP and SVM at each lead time, particularly at shorter lead times, highlighting its effectiveness in capturing short-term streamflow dynamics. The analysis of uncertainty quantization shows that noise in the input data is the primary source of overall uncertainty in model prediction, whereas a notable increase is observed in the uncertainty caused by the model in the flood season. Furthermore, the application of the SHAP method reveals the critical role of water level in streamflow prediction. • An explainable deep learning is proposed for multi-step streamflow forecasting. • Bayesian inference is utilized to quantify the streamflow forecast uncertainty. • SHAP provides transparency for streamflow forecasting. • The proposed model shows its excellent performance in streamflow forecasting.