Comparing grey formulations of the velocity-area method and entropy method for discharge estimation with uncertainty

Two methods, namely the velocity-area method and the entropy method, for assessing with uncertainty discharge measurements at gauged river sites are analysed and compared; uncertainty is represented through the grey number technique. Two different approaches for the ‘greyification’ of both methods are presented. In the first approach, the uncertainty affecting each measurement used to estimate the discharge is characterized by means of a grey number: all the grey uncertainty components are then combined through grey mathematics. In the second approach, greyification 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 three different gauged sections of the Tiber River, in central Italy, show that the first greyification approach leads to a broader discharge uncertainty estimate with respect to the second. Furthermore, as the greyification approach and the flow area quantification are 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 provided by the two methods are very similar. This testifies in favour of the entropy method, which is simpler than the other from an operative viewpoint.