Deep learning for the probabilistic prediction of semi-continuous hydrological variables – An application to streamflow prediction across CONUS
Year: 2026
Type: article
Abstract: This study introduces two new end-to-end probabilistic deep learning models for predicting semi-continuous hydrological variables with a physical lower bound of zero. Both models use long short-term memory networks (LSTMs) with probabilistic output layers to predict the parameters of a probability distribution that fit observed streamflow (target) and respect its physical lower bound of zero. The first model is based on the rectified Gaussian (RG) distribution, which is akin to a Gaussian distribution that converts negative values to zero. The second model is a hurdle model, which includes two parts. The first part predicts the probability of the target being non-zero (the hurdle) while the second part predicts the probability distribution over non-zero values. Both RG and hurdle models are benchmarked against a state-of-the-art deterministic LSTM and evaluated on a daily streamflow prediction case study across 421 catchments in the contiguous United States. The hurdle model outperformed the RG and deterministic models with improvements of 11% and 9%, respectively, in mean normalized root mean squared error. RG and hurdle models substantially outperformed the deterministic model in mean low flow accuracy by 17% and 36%, respectively. When compared against third-party benchmarks, the hurdle model outperformed a hybrid process-based DL model by over 30% in low flow root mean squared error and performed competitively with a probabilistic benchmark in terms of reliability, sharpness, and accuracy. Overall, the RG and hurdle models are promising probabilistic DL models for predicting semi-continuous hydrological variables. However, the hurdle model is recommended as a new probabilistic benchmark for daily streamflow prediction across CONUS due to its improved low flow accuracy, reliability, and sharpness.
Source: Journal of Hydrology
Authors: John Quilty, Mohammad Sina Jahangir
Institutions: University of Waterloo, Cornell University, McGill University
Language: English
Subfield: Environmental Engineering
Field: Environmental Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,030
OpenAlex ID: W7125427528