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Establishing a reliable stage-discharge (SD) rating curve for calculating discharge at a hydrological gauging station normally takes years of data collection. Estimation of high flows is particularly difficult as they occur rarely and are often difficult to gauge in practice. At a minimum, hydraulicallymodelled rating curves could be derived with as few as two concurrent SD and water-surface slope measurements at different flow conditions. This means that a reliable rating curve can, potentially, be developed much faster via hydraulic modelling than using a traditional rating curve approach based on numerous stage-discharge gaugings. In this study, we use an uncertainty framework based on Bayesian inference and hydraulic modelling for developing SD rating curves and estimating their uncertainties. The framework incorporates information from both the hydraulic configuration (bed slope, roughness, vegetation) using hydraulic modelling and the information available in the SD observation data (gaugings). Discharge time series are estimated by propagating stage records through the posterior rating curve results. Here we apply this novel framework to a Swedish hydrometric station, accounting for uncertainties in the gaugings and the parameters of the hydraulic model. The aim of this study was to assess the impact of using only three gaugings for calibrating the hydraulic model on resultant uncertainty estimations within our framework. The results were compared to prior knowledge, discharge measurements and official discharge estimations and showed the potential of hydraulically-modelled rating curves for assessing uncertainty at high and medium flows, while uncertainty at low flows remained high. Uncertainty results estimated using only three gaugings for the studied site were smaller than ±15% for medium and high flows and reduced the prior uncertainty by a factor of ten on average and were estimated with only 3 gaugings.

The stage-discharge measurements and rating curves accumulated over decades at hydrometric stations are a valuable source of information on the long-term evolution of river bed levels. However, the methodology to extract meaningful geomorphic information from such hydrometric data is not straightforward. We introduce an original method to estimate the parameters of successive rating curves by Bayesian analysis in sequence. These parameters reflect the physical properties of the channel features that control the stage-discharge relation: low-flow riffles, main channel, floodway (bars), floodplain, etc. The dates of rating changes are assumed to be known in existing hydrometric records. The uncertainty interval of each parameter is estimated, assuming, however, that no rating change has been ignored by the station manager. It is thus possible to clearly distinguish overall trends of the channel bed level from the local evolution of riffles and to evaluate whether the observed temporal changes are significant compared to the estimation uncertainties.

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. Key Points: 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 [ABSTRACT FROM AUTHOR]

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. Plain Language Summary: 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. Key Points: 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 [ABSTRACT FROM AUTHOR]

Traditional methods for estimating stage–discharge rating curves and their uncertainties need numerous calibration gaugings. Years of data collection efforts are often needed to gauge the stage–discharge relation across the flow range to establish a reliable rating curve. In particular, high-flow discharge estimation is often highly uncertain since these flows rarely occur and are practically difficult to gauge. Therefore, the portion of the rating curve representing most extreme flows typically needs to be extrapolated. Hydraulic modelling can be used to derive rating curves based on only a few calibration gaugings and can therefore potentially be a good alternative for quickly estimating rating curves. In particular, they have potential to improve high flow discharge estimation as they are based on hydraulic theory rather than extrapolation techniques. However, rating curve estimation with hydraulic models is also associated with multiple sources of uncertainty that have not yet been comprehensively assessed. These uncertainties need to be accounted for and estimated to evaluate the full potential of hydraulic rating-curve modelling.We developed the Rating curve Uncertainty estimation using Hydraulic Modelling (RUHM) framework to investigate and estimate these uncertainties. The framework combines a one dimensional hydraulic model and Bayesian inference to incorporate information from both hydraulic knowledge (bed slope, roughness, topography and vegetation) and the (uncertain) calibration gauging data. The framework was applied at the Röån River catchment in Sweden. We investigated the number of gaugings needed to reliably calibrate the model, the sensitivity of the results to the prior hydraulic information quality (water-surface slope measurements and roughness), and the effect of the vegetation survey data on the high flow discharge estimation.We found that the rating curve uncertainty could be estimated reliably with only a few gauging and water-slope measurements, and that the uncertainty was insensitive to the number of gaugings as long as they covered low and medium flows. We found that at least one (uncertain) water-surface slope measurement was needed, and that precise information about the roughness parameter was not needed. The impact of the vegetation survey data on the high flow discharge estimation was investigated to assess its importance for extrapolation at extreme flows. Our results at this site show that hydraulic rating curve uncertainty estimation is a promising tool for quickly estimating rating curves and their uncertainties. It can be particularly useful at previously ungauged sites or at established sites that have experienced major temporal changes to the stage–discharge relation. [ABSTRACT FROM AUTHOR]

Obtaining reliable streamflow monitoring data is both costly and time-consuming. It typically takes many years to establish reliable streamflow data at a new hydrological monitoring station using traditional power-law rating curve approaches. This is because many control gaugings of the stage–discharge relation are required. The number of field gaugings and their distributions across the range of flow variability has a large impact on the uncertainty in the estimated rating curve, but there is little guidance on cost-effective gauging strategies in the literature. The aim of this study was to investigate the cost-effectiveness of different gauging strategies and rating-curve estimation methods in terms of leading to low rating-curve uncertainty for a low cost. Apart from traditional power-law rating curves, we assess hydraulic modelling of rating curves, which is a potentially more cost-effective strategy as only a few calibration gaugings are needed. We compared the RUHM framework for Rating curve Uncertainty estimation using Hydraulic Modelling and the BaRatin power-law method using nine different gauging strategies associated with different costs. The gauging strategies included for example those using only low, middle or high flow gaugings or those using different numbers of gaugings distributed throughout the flow range. We applied both methods to the 584 km2 River Röån station in Sweden, and we tested the BaRatin method for a further catchment, the 326 km2 Blairstown station on the River Paulins Kill in New Jersey, US. We found that there was a lower uncertainty for the low-cost gauging strategies (fewer gaugings) for the RUHM framework compared to BaRatin, and that there was a similar uncertainty for the high-cost gauging strategy (more gaugings) for the RUHM framework compared to BaRatin. We also found that traditional methods need gaugings with lower probability of occurrence (i.e. covering a larger part of the flow range) than when using hydraulic modelling (already 3–4 low and middle flow gaugings with high probability of occurrence gave good results). Our results suggest that hydraulic modelling of rating curves is a promising alternative for quickly and cost-effectively deriving streamflow data with low uncertainty. [ABSTRACT FROM AUTHOR]