Comparative evaluation of rating curve estimation methods for data-scarce mountainous rivers in the Indian Himalayas

Abstract

Abstract Direct gauging measurements are commonly used to estimate river discharge through stage-discharge relationships (rating curves). However, accurate rating curves are difficult to develop in high-gradient mountain rivers under data-scarce conditions. This study compares three methods for rating curve estimation across three gauging stations: the traditional power-law method, Heteroscedastic Maximum Likelihood Estimator (HMLE), and Bayesian inference methods. The stations include two located 40 km apart on the main stream and one on a highly dynamic tributary within a single 307 $$\:{\text{k}\text{m}}^{2}$$ catchment. We evaluated predictive performance using Leave-One-Out Cross-Validation (LOOCV) for both real-space and log-transformed measures of goodness of fit. Results show that model performance is highly sensitive to the assessment metric and cross-sectional stability. The classic power-law technique had the highest prediction accuracy for stable watershed outlets. Performance was mixed at geomorphologically unstable and data-scarce tributary stations, with the HMLE framework outperforming in statistical fits in log-space ( $$\:{\text{R}\text{M}\text{S}\text{E}}_{\text{l}\text{o}\text{g}}\:$$ of 0.311–0.333 vs. Bayesian 0.399–0.406) due to its effective optimization of data-dense low-flow regimes. However, purely statistical approaches such as HMLE produced hydrologically unrealistic, near-flat discharge paths during high-flow extrapolation. In contrast, the Bayesian approach, although slightly weaker in fit in log space, preserved hydraulic consistency during extreme occurrences through the formal integration of prior physical knowledge of channel geometry and roughness. These results show that statistical curve-fitting optimizes interpolation in low-flow regimes, but physically constrained probabilistic techniques are needed to provide trustworthy, hydrologically realistic discharge predictions when extrapolating hydrological information in dynamic mountainous catchments.