Streamflow estimation in real time is required for data assimilation by flood forecasting systems. Streamflow time series are established using 'rating curves' that approximate the stage-discharge relationship. A major problem is that the river bed at many hydrometric stations can evolve due to morphogenic floods, leading to rating changes, or 'shifts'. The methods proposed in the literature for updating the rating curve are based on a retrospective statistical analysis of calibration data (or gaugings). The aim of the proposed method is the automatic detection of shifts and the estimation of their magnitude in real time, using both observational data and hydraulic knowledge of the site. It is built on an existing Bayesian framework for estimating probabilistic stage-discharge rating curves with quantitative uncertainties. Before starting a real-time application, a retrospective analysis is performed to detect past changes typically based on available gaugings. The retrospective results are then used to calibrate the methods for detecting and estimating shifts and their magnitudes in real-time. To this aim, the method uses different sources of information available in real time, e.g. stage records, estimates of the sediment transport that affects the bed evolution, changes in the shape of recession curves, changes in correlations with neighbouring hydrometric stations, etc. The proposed method was applied to the Ardèche River at Meyras, France, a river with a gravel-bed degrading during each flood. Both retrospective analysis and real-time estimation of the stage-discharge rating curves yielded encouraging results, with consistent detection of shifts and estimation of their magnitudes. Further research includes testing the method at more challenging sites and the use of other useful information available in real-time. The final goal is to provide real-time streamflow estimates with uncertainties that can be assimilated in models and decision making.