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.