A grey-based methodology for representing uncertainty in discharge measurements at a gauged river site

The velocity-area method and entropy method for assessing with uncertainty discharge measurements at a gauged river site are analysed and compared; uncertainty is represented through the grey number technique. Two different approaches for greyfication of both the methods are presented. In the first approach, the uncertainty affecting each measurement used to estimate the discharge is characterized by a grey number: all the grey uncertainty components are then combined through the grey mathematics. In the second approach, greyfication is applied to the relationship expressing the total uncertainty on the discharge measurement, provided by the EN ISO 748 guidelines. Results of the application of the proposed methods to measurement data pertaining to a gauged Tiber river section show that the first greyfication approach leads to a larger discharge uncertainty estimate with respect to the latter. Furthermore, being the greyfication approach and the flow area quantification the same, the velocity-area and entropy methods provide nearly the same estimate of the uncertainty affecting the discharge measurements, i.e. the grey discharges they provide are fairly similar.