Uncertainty assessment of non-stationary stage-discharge relationship with hydrodynamic extensions across flow regimes

Study region : Asia Pacific region, Taiwan. Study focus : Accurate discharge estimation in river systems is fundamentally hindered by the scarcity of high-flow measurements and the complexities of channel non-stationarity. This study introduces an integrated framework that reconciles historical in-situ observations with hydrodynamically derived synthetic relationships to bridge critical data gaps. We employ a dual-methodology paradigm, utilizing both a Bayesian inference model (BaRatin) and a fuzzy regression framework to simultaneously address probabilistic variability and inherent measurement uncertainty. This approach ensures a comprehensive evaluation across the full spectrum of flow regimes at two gauging stations in the Wu River Basin. New hydrological insights : This research explicitly incorporates high-flow extensions generated via the Height Above the Nearest Drainage (HAND) method into the uncertainty assessment, offering a physically consistent approach that utilizes hydraulic constraints rarely explored in rating-curve literature. Results demonstrate that while uncertainty is most pronounced under low-flow conditions due to channel irregularities, the bounds converge significantly to within ± 35%–75% in high-flow regimes. The Bayesian method effectively captures structural errors in complex channel–floodplain reaches, whereas fuzzy regression offers a computationally efficient alternative for data-scarce scenarios. Notably, integrating HAND-based hydrodynamic information reduces high-flow bias and enhances the continuity between empirical and synthetic segments. This framework establishes a statistically defensible basis for discharge estimation, significantly improving uncertainty quantification in both gauged and ungauged catchments.