A DeepAR-Based Modeling Framework for Probabilistic Mid-Long Term Streamflow Prediction

Mid–long term streamflow prediction (MLSP) plays a critical role in water resource planning amid growing hydroclimatic and anthropogenic uncertainties. Although AI-based models have demonstrated strong performance in MLSP, their capacity to quantify predictive uncertainty remains limited. To address this challenge, a DeepAR-based probabilistic modeling framework is developed, enabling direct estimation of streamflow distribution parameters and flexible selection of output distributions. The framework is applied to two case studies with distinct hydrological characteristics, where combinations of recurrent model structures (GRU and LSTM) and output distributions (Normal, Student’s t, and Gamma) are systematically evaluated. Results indicate that models employing the Gamma distribution consistently outperform those using Normal and Student’s t distributions. In the Upper Wudongde Reservoir area, the model using LSTM structure and Gamma distribution reduces RMSE from 1407.77 m³/s to 1016.54 m³/s. As the forecast horizon extends, the Gamma-based models demonstrate more reliable probabilistic predictions, reflected by sharper and better-calibrated prediction intervals. This is evidenced by substantially reduced CRPS values at the 18th forecast horizon (521.4 and 1746.6 m³/s), compared to Normal-based models (747.6 and 1877.5 m³/s). Although the improvements in predictive performance achieved by the proposed modeling framework vary depending on the RNN model architecture used and the specific application region, it generally delivers consistent enhancement in forecasting accuracy, thereby providing stronger support for practical applications.