Dynamic D-vine copula GAM quantile regression for boosting probabilistic streamflow forecasting reliability

Study Region: The Hanjiang River Basin, China Study Focus: Reliable and accurate streamflow forecasting is essential for effective water resources management, flood mitigation, and hydrological risk assessment. Deterministic forecasting approaches provide point predictions only and therefore fail to explicitly represent predictive uncertainty. To address this limitation and enhance forecast reliability, this study develops a probabilistic post-processing framework that transforms deep learning-based point forecasts (LSTM and Transformer) into probability forecasts by modeling the conditional error structure. The framework models forecast errors as the response variable and captures their regime-dependent dependence on hydrometeorological covariates using a dynamic D-vine copula generalized additive model quantile regression (DV-GAM-QR), enabling the generation of both median forecasts and probabilistic prediction intervals. New Hydrological Insights: The proposed DV-GAM-QR framework substantially improves probabilistic streamflow forecasting by explicitly modeling time-varying dependence between deep-learning forecast errors and hydrometeorological predictors. Compared with the stationary DVQR benchmark, DV-GAM-QR achieves marked gains in probabilistic performance, reducing the Continuous Ranked Probability Score (CRPS) by approximately 15% and producing sharper yet well-calibrated prediction intervals across flow regimes. This study demonstrates that forecast error dependence is not merely non-stationary over time, but rather varies systematically as a function of seasonal conditions and antecedent hydrologic memory. By integrating hydrologically meaningful covariates into a dynamic copula parameterization, the framework reveals regime-dependent dependence patterns that are obscured under stationary assumptions. These findings highlight the importance of dynamic dependence modeling for reliable uncertainty quantification and illustrate how copula-based post-processing can be effectively coupled with deep learning outputs to support risk-sensitive streamflow forecasting and water resources management.