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Establishing reliable streamflow time series is essential for hydrological studies and water-related decisions, but it can be both time-consuming and costly since streamflow is typically calculated from water level using rating curves based on numerous calibration measurements (gaugings). It can take many years of gauging data collection to estimate reliable rating curves, and even then extreme-flow estimates often still depend on rating curve extrapolation. Hydraulically modeled rating curves are a promising alternative to traditional methods as they can be rapidly derived with few concurrent stage-discharge gaugings. We introduce a novel framework for Rating curve Uncertainty estimation using Hydraulic Modelling (RUHM), based on Bayesian inference and physically based hydraulic modeling for estimating stage-discharge rating curves and their associated uncertainty. The framework incorporates information from the river shape, hydraulic configuration, and the control gaugings as well as uncertainties in the gaugings and model parameters. We explored the interaction of uncertainty sources within RUHM by (1) assessing its performance at two Swedish stations, (2) investigating the sensitivity of the results to the number and magnitude of the calibration gaugings, and (3) evaluating the importance of prior information on the model parameters. We found that rating curves with constrained uncertainty could be estimated using only three gaugings for either low or low and medium flows that have a high probability of occurrence, thereby enabling rapid rating curve estimation. Prior information about the water-surface slope-stage relation, obtainable from site surveys, was needed to adequately constrain uncertainty estimates.

Plain Language Summary Reliable streamflow time series are essential for water-related decisions. However, it can take several years and numerous measurements to establish a reliable streamflow time series, and these may still be associated with large uncertainty. To address these issues, we developed a novel framework that couples uncertainty assessment with hydraulic modeling of the relation between water level and streamflow at a hydrological monitoring station using information about the physical characteristics of the channel. This relation between water level and streamflow, known as the rating curve, is the basis for calculating streamflow time series from the water level time series measured at hydrological monitoring stations. We explored the interaction of different uncertainty sources on rating curve estimation at two Swedish stations and found that rating curves could be modeled with high confidence (i.e., low uncertainty) using only three observations for either low flows or low and medium flows. Since such flow conditions occur often and are easy to measure (at least relative to the rare and hard-to-measure high flows) our framework has an advantage over traditional approaches by potentially allowing for more rapid rating curve estimation.