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.