Bayesian analysis of stage‐fall‐discharge rating curves and their uncertainties

Stage‐fall‐discharge (SFD) rating curves are traditionally used to compute streamflow records at sites where the energy slope of the flow is variable due to variable backwater effects. We introduce a model with hydraulically interpretable parameters for estimating SFD rating curves and their uncertainties. Conventional power functions for channel and section controls are used. The transition to a backwater‐affected channel control is computed based on a continuity condition, solved either analytically or numerically. The practical use of the method is demonstrated with two real twin‐gauge stations, the Rhône River at Valence, France, and the Guthusbekken stream at station 0003⋅0033, Norway. Those stations are typical of a channel control and a section control, respectively, when backwater‐unaffected conditions apply. The performance of the method is investigated through sensitivity analysis to prior information on controls and to observations (i.e., available gaugings) for the station of Valence. These analyses suggest that precisely identifying SFD rating curves requires adapted gauging strategy and/or informative priors. The Madeira River, one of the largest tributaries of the Amazon, provides a challenging case typical of large, flat, tropical river networks where bed roughness can also be variable in addition to slope. In this case, the difference in staff gauge reference levels must be estimated as another uncertain parameter of the SFD model. The proposed Bayesian method is a valuable alternative solution to the graphical and empirical techniques still proposed in hydrometry guidance and standards.