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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. 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. An uncertainty framework using physically based hydraulic modeling was developed for rapid rating curve estimationRating curves with constrained uncertainty were estimated using only three gaugings for either low or low and medium flowsPrior information about the water‐surface slope‐stage relation was needed to obtain reliable results

Streamflow time series are commonly derived from stage‐discharge rating curves, but the uncertainty of the rating curve and resulting streamflow series are poorly understood. While different methods to quantify uncertainty in the stage‐discharge relationship exist, there is limited understanding of how uncertainty estimates differ between methods due to different assumptions and methodological choices. We compared uncertainty estimates and stage‐discharge rating curves from seven methods at three river locations of varying hydraulic complexity. Comparison of the estimated uncertainties revealed a wide range of estimates, particularly for high and low flows. At the simplest site on the Isère River (France), full width 95% uncertainties for the different methods ranged from 3 to 17% for median flows. In contrast, uncertainties were much higher and ranged from 41 to 200% for high flows in an extrapolated section of the rating curve at the Mahurangi River (New Zealand) and 28 to 101% for low flows at the Taf River (United Kingdom), where the hydraulic control is unstable at low flows. Differences between methods result from differences in the sources of uncertainty considered, differences in the handling of the time‐varying nature of rating curves, differences in the extent of hydraulic knowledge assumed, and differences in assumptions when extrapolating rating curves above or below the observed gaugings. Ultimately, the selection of an uncertainty method requires a match between user requirements and the assumptions made by the uncertainty method. Given the significant differences in uncertainty estimates between methods, we suggest that a clear statement of uncertainty assumptions be presented alongside streamflow uncertainty estimates. Knowledge of the uncertainty in streamflow discharge measured at gauging stations is important for water management applications and scientific analysis. This paper shows that uncertainty estimates vary widely (typically up to a factor of 4) when comparing seven recently introduced estimation methods. A clear understanding of the assumptions underpinning different uncertainty estimation methods and the sources of uncertainty included in their calculations is needed when selecting a method and using and presenting its uncertainty estimates. Methods for estimating the stage‐discharge rating curve and its uncertainty were compared for stream gauges with varying hydraulic complexityUncertainty estimates varied widely at high and low flows for the different methodsCareful description of the assumptions behind uncertainty methods is needed

Reliable information about hydrological behavior is needed for water-resource management and scientific investigations. Hydrological signatures quantify catchment behavior as index values, and can be predicted for ungauged catchments using a regionalization procedure. The prediction reliability is affected by data uncertainties for the gauged catchments used in prediction and by uncertainties in the regionalization procedure. We quantified signature uncertainty stemming from discharge data uncertainty for 43 UK catchments and propagated these uncertainties in signature regionalization, while accounting for regionalization uncertainty with a weighted-pooling-group approach. Discharge uncertainty was estimated using Monte Carlo sampling of multiple feasible rating curves. For each sampled rating curve, a discharge time series was calculated and used in deriving the gauged signature uncertainty distribution. We found that the gauged uncertainty varied with signature type, local measurement conditions and catchment behavior, with the highest uncertainties (median relative uncertainty ±30–40% across all catchments) for signatures measuring high- and low-flow magnitude and dynamics. Our regionalization method allowed assessing the role and relative magnitudes of the gauged and regionalized uncertainty sources in shaping the signature uncertainty distributions predicted for catchments treated as ungauged. We found that (1) if the gauged uncertainties were neglected there was a clear risk of overconditioning the regionalization inference, e.g., by attributing catchment differences resulting from gauged uncertainty to differences in catchment behavior, and (2) uncertainty in the regionalization results was lower for signatures measuring flow distribution (e.g., mean flow) than flow dynamics (e.g., autocorrelation), and for average flows (and then high flows) compared to low flows. We quantify impact of data uncertainty on signatures and their regionalizationMedian signature uncertainty ±10–40%, and highly variable across catchmentsNeglecting gauging uncertainty causes overconditioning of regionalization