Analysis and propagation of uncertainties due to the stage–discharge relationship: a fuzzy set approach

River discharges are typically derived from a single-valued stage–discharge relationship. However, there is usually no one-to-one relationship between stage and discharge, and the use of a single-valued relationship may lead to uncertainties. This paper considers fuzzy set theory-based methods for analysis and propagation of uncertainties. The uncertainty analysis involves the application of fuzzy linear and nonlinear regression methods to define upper and lower bounds of the relationship, which expresses discharge values as fuzzy numbers. The resulting membership function of a peak discharge value is used for propagation of uncertainties in river channels and flood plains. This involves an application of the fuzzy alpha-level cut method together with a one-dimensional hydrodynamic model. The methods are demonstrated using data from the Lauffen gauging station on the River Neckar, Germany.