A grey-based method for evaluating the effects of rating curve uncertainty on frequency analysis of annual maxima

A grey-based technique for characterizing 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 and discharge measurements, the grey parameters of the rating curve are estimated by using a grey non-linear regression. Commencing with this grey rating curve and a set of annual maximum stages, we show how the probability distribution (here assumed of EV1 type) of the grey annual maximum discharges can be estimated. The grey EV1 distribution can be estimated through two approaches, the first of which directly exploits the grey discharges corresponding to the annual maximum stages, whereas with the second approach two different sets of extreme (crisp) discharges, and therefore two EV1 distributions of extreme (crisp) values which delimit the grey discharges of a given return period, are obtained by considering the lower and upper limits of the grey parameters of the rating curve. The methodology is illustrated using data pertaining to a gauged section of the River Po (Italy). The results show that the first approach yields a wider grey EV1 distribution with respect to that resulting from the second approach: physical justification of this is given.