Generative deep learning for probabilistic streamflow forecasting: Conditional variational auto-encoder

•Generative Deep learning models were developed for streamflow forecasting.•A specific generative model, conditional variational auto-encoder was selected.•Conditional variational auto-encoder models were tested on 75 basins in Canada.•Generative models outperformed long short-term memory networks.•Examining more than 9000 models proved models produce reliable forecasts. Probabilistic hydrological forecasting has gained increasing importance in recent years, as it offers essential information for risk-based decision-making and flood management. Traditional hydrological models often produce deterministic forecasts, which do not account for the inherent uncertainties in hydrological systems. Although many previous studies have investigated using deep learning (DL) models for hydrological prediction, the development of probabilistic DL models (especially, generative models) has not yet been thoroughly examined for hydrological forecasting. The present study investigates the efficacy of a generative DL model, namely, conditional variational auto-encoder (CVAE). CVAE is applied for one-seven day(s) ahead probabilistic streamflow forecasting in 75 basins from the Canadian model parameter experiment (CANOPEX) database. The CVAE forecast model, which outputs forecasts in the form of a probability distribution, was benchmarked against two state-of-the-art quantile-based DL models: quantile-based encoder-decoder (ED) and quantile-based CVAE (QCVAE). The latter outputs forecasts for specific quantiles of a probability distribution (here, q = 0.05, 0.5, 0.95). More than 9000 models were developed based on different basins, input variable sets, and model structures. The models were evaluated in terms of point forecast accuracy and forecast reliability. The results indicate that the CVAE model generally outperforms the benchmark models in terms of reliability at a 90 % confidence level (median reliability of 92.49 % compared to 87.35 % and 84.59 % for ED and QCVAE, respectively). However, the quantile-based forecast models produce slightly more accurate point forecasts than the CVAE (median Kling-Gupta efficiency (KGE) of 0.88 compared to 0.90 for both ED and QCVAE). Notably, the CVAE model exhibits superior probabilistic forecasts in basins with poor point forecast accuracy, highlighting its usefulness over benchmark methods in difficult-to-forecast basins. Overall, CVAE is a promising probabilistic DL model for streamflow forecasting, and it can be readily applied for