Rating curve uncertainty effects on extreme discharge frequency analysis evaluated through a grey-based technique

A grey-based technique for characterizing both the rating curve uncertainty due to discharge measurement errors and its effect on flood frequency analysis is here presented. On the basis of river stage measurements (affected by negligible errors) and corresponding discharge measurements (affected by uncertainty here represented through grey numbers) made in a gauged section, the grey parameters of the rating curve are estimated by using a grey non-linear regression. The rating curve with grey parameters can be interpreted both (a) as a grey function which provides an uncertain (grey) estimation of the discharge for a given river stage and (b) as a sheaf of crisp rating curves whose crisp parameters are included within the corresponding grey parameters. Given a set of annual maximum stages observed in the section, the frequency distribution (here assumed of EV1 type) of the annual maximum grey discharges is thus estimated through two approaches consistent with the two interpretations of the rating curve, i.e. exploiting the definition of grey function a) of the grey discharges and b) of the rating curve grey parameters. The application of the methodology proposed to the data pertaining to a gauged section of the river Po (Italy) shows that the first approach yields a wider grey EV1 distribution with respect to that resulting from the second approach; this is due to the fact that, unlike the former, the latter explicitly takes into account the hydraulic consistency between discharges associated with different stages.