Quantification of Data and Model Uncertainty for Deep Learning-based Streamflow Prediction

Abstract. Accurate and timely flood warnings are essential for reducing flooding risks. Achieving this objective requires both accurate data and careful model parameterization. The absence of high-resolution ground-based precipitation observations in many locations leaves relatively low-accuracy satellite-based precipitation products as one of the few alternatives. At the same time, advancements in deep learning-based flood prediction have led to improvements in both accuracy and computational efficiency. Despite the progress made by integrating satellite-based precipitation data and a deep learning-based hydrologic model, the quantification of uncertainty—stemming from both data and model—remains largely unexamined. This gap results in less reliable predictions, as overfitting and limited explainability are common concerns in deep learning. In this paper, uncertainties arising from satellite-based precipitation inputs, streamflow observations, training data variability, and model parameters are jointly addressed. The basin-averaged precipitation uncertainty is represented by a parametric probabilistic distribution function, whose parameters can be inferred from the deep learning-based hydrologic model, without the need for higher-accuracy precipitation “ground truth”. Streamflow observation uncertainty is characterized by a multiplicative Gaussian noise. Training data variability is quantified by using a mixture density network, while uncertainty in model parameters is captured through variational inference. Our results demonstrate that this integrated approach to uncertainty quantification enhances both the prediction accuracy and the explainability of ensemble streamflow predictions. It provides a foundation for “uncertainty-aware” deep learning-based streamflow prediction.