Probabilistic deep learning models for streamflow forecasting: A case study in the Rhine basin

Abstract. Along the Rhine River, low-flow conditions are among the most frequent and economically significant constraints on inland waterway transport. Reliable and accurate forecasts are critical for informed decision-making. Although deep learning has shown great promise in hydrological modelling, process-based models remain the operational standard at many institutions, including the German Federal Institute of Hydrology.

In this study, we show that a regionally trained probabilistic deep learning model improves operational streamflow forecasts for the Rhine basin. We further investigate a hybrid configuration that combines data-driven and process-based modelling by incorporating operational forecasts as inputs to the deep learning model. Both approaches provide more accurate and reliable forecasts than the current operational system. Improvements are most pronounced for low flows, where the models reach skill levels that the operational system attains only at substantially shorter lead times, corresponding to an effective gain of approximately 2 forecast days. The hybrid approach achieves the highest overall performance by combining the short-term strengths of the operational system with the long-term generalization capabilities of deep learning.

These findings highlight that deep learning can complement established operational systems without replacing them, offering a practical pathway to integrate data-driven methods into operational practice. This, in turn, enables safer and more efficient inland waterway transport and facilitates planning under low-flow conditions.