The rapid development of UAV-based river surveying is creating new opportunities to efficiently survey river reaches and collect high-resolution topographic, hydraulic, and surface velocity data for hydraulic rating-curve modeling and discharge estimation. Hydraulic rating-curve modeling provides a physically based approach that can reduce extrapolation uncertainty and constrain rating curves with fewer stage–discharge gaugings. However, despite these advances, how such UAV-derived data can be integrated into rating-curve uncertainty estimation frameworks and the impact of different calibration-gauging datasets on uncertainty in derived hydrological signatures is largely unexplored, limiting understanding of the method's operational potential. This study provides the first application of the RUHM framework (Rating curve Uncertainty estimation using Hydraulic Modeling) using UAV-derived data and the first quantification of how RUHM-modeled rating-curve and discharge uncertainties propagate to hydrological signatures under different gauging strategies. We applied RUHM at two sites in northern Sweden. At the Rakkurijärvi site, RUHM was applied using UAV-derived data from LiDAR, Structure from Motion (SfM) photogrammetry, and surface-velocimetry videos together with bathymetric and water-surface slope data. At the Röån site, RUHM was evaluated under nine gauging scenarios to assess their impacts on uncertainty in hydrological signatures. RUHM constrained rating-curve uncertainty across the full flow range at Rakkurijärvi using only three calibration gaugings, with similar results for SfM and LiDAR topography; using UAV-derived discharge for calibration increased uncertainty but still yielded a reliable rating curve. At the Röån site, rating-curve, discharge, and hydrological signature uncertainties were generally well constrained when calibration included low- to mid-flow stage–discharge gaugings, including for extreme-flow and flow-variability metrics, but the resulting signature distributions did not necessarily overlap for all metrics. These results show that RUHM, combined with UAV-based surveys, can support rapid and cost-effective estimation of rating curves and their uncertainty using relatively few gaugings, while also demonstrating how gauging strategy influences the uncertainty in hydrological signatures derived from hydraulically modeled rating curves and discharge estimates. The approach is best suited to sites with near one-dimensional hydraulic conditions and a stable stage–discharge relation, and we found that careful flight planning was needed to obtain high quality UAV data.

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.

Establishing streamflow time series in unstable rivers is challenged by changes in the stage-discharge relation after floods. Then, the field hydrologist must develop a new stage-discharge rating curve using new calibration data but also using some information from previous calibration data and previous rating curves. The process includes a large amount of informal expert knowledge and hydraulic assumptions seldom made explicit. This paper develops a stage-period-discharge (SPD) model based on the physical interpretation of changes in the stage-discharge relation across a series of stability periods defined by known dates and times. Using simple hydraulic equations, the user provides prior knowledge on the controls, their static and varying parameters, and their possible changes. As a single model is used for all the periods, the estimation of all rating curves can be performed in one go: All gaugings hence provide information to estimate the static parameters and the varying parameters for the relevant periods. Bayesian inference is used, providing a natural way to include prior knowledge and to quantify uncertainty. The generality and some key properties of the method are demonstrated through application to two hydrometric stations, differing in hydraulic configuration and in number and type of changes. Specific experiments demonstrate the ability of the SPD model to transfer information across periods. Consequently, rating curves are more precisely estimated than by separately estimating them for each period. The SPD model provides a hydraulically based, transparent, and user-friendly approach to replace manual shift corrections traditionally applied in operational practice, with a quantification of uncertainties.

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 Is&e 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.

An original hydraulics-based Bayesian method is introduced for developing stage-fall-discharge (SFD) rating curves used at twin-gauge stations and estimating their uncertainties. A channel control with variable energy slope due to variable backwater is considered in combination with a backwater-unaffected control, usually another channel control. Succession between backwater-affected and backwater-unaffected controls is solved based on the continuity of the stage-discharge relation. The difference between the reference levels at the two stations is estimated as another uncertain parameter of the SFD model. Results at one typical twin-gauge station affected by the backwater of a run-of-the-river dam are presented. The accuracy and uncertainty of predicted discharges appear to be acceptable even when the uncertainty of the transition between backwater-affected and backwater-unaffected controls is high.

Hydraulic models can be useful tools for developing reliable rating curves, however, uncertainties in the input measurements can have implications for the model results. In this study, we investigate the impact of uncertain input field measurements (i.e. stream channel topography, water surface slope, vegetation density, stage, and discharge) on rating curves generated with a physically-based hydraulic model. This is the first-time measurement uncertainties have been assessed with the hydraulic model and we demonstrate the method at a regularly monitored catchment in central Sweden. The results show that the modeling approach, calibrated with three gauging measurements, acquired at low to median flows, was able to generate rating curves with relatively constrained uncertainty for the highest observed stage (i.e. -12% and +46%) when all uncertainty sources were accounted for. These results suggest that this modeling approach could be applied to quickly develop reliable rating curves and simultaneously estimate the uncertainty in the rating curves.