Advancing Rating Curve Generation in High-Gradient Rivers: Comparing Power Law, Spline, and Bayesian Approaches of Rating Curve Generation

Reliable estimation of river discharge is constrained by uncertainties in stage-discharge rating curves, particularly in steep, high-gradient catchments where channel morphology is highly dynamic. Conventional approaches often fail to capture the complexity of these systems. To synthesize a more robust understanding of Rating Curve generation, this study evaluates three methods, the conventional power law, spline interpolation, and Bayesian inference, across multiple sites within a mountainous headwater catchment.

We use two years of high-frequency stage data and corresponding gauged discharge measurements from a primary field site, with ongoing validation at two additional sites. The methods are compared in terms of different performance metrics (e.g., RMSE, NSE), their ability to extrapolate low and high flow conditions, and their treatment of uncertainty.

Initial results show that the Bayesian approach substantially outperforms deterministic power law and spline methods in simulating discharge time series. Its strength lies in explicitly accounting for measurement error and structural uncertainty, which are pronounced in high-gradient environments. Posterior parameter distributions further provide physically meaningful insights linked to reach characteristics such as roughness and bed slope. Testing across additional sites will enable synthesis of generalized patterns: if consistent Bayesian priors prove effective across geomorphologically similar reaches, this suggests common hydraulic-hydrological controls operating within this catchment type.

This comparative study advances a probabilistic framework for Rating Curve generation in steep river systems. By demonstrating the transferability of Bayesian methods across multiple sites, we highlight a pathway for operational hydrology to move beyond deterministic curve fitting toward more robust, uncertainty-aware, and physically grounded discharge estimation.