Analytical derivation of the flood frequency curve through partial duration series analysis and a probabilistic representation of the runoff coefficient

The authors propose a procedure for estimating the discharge with an assigned return period based on a probabilistic formulation of the rational formula referred to a generic flood event. In this manner it is possible to represent the natural variability in the runoff coefficient and at the same time to relate rainfall depths to the corresponding flood events. The link between the probability distributions of the annual maximum rainfalls and floods and the frequency of the corresponding events in partial duration series is established through relations deriving from the assumption of Poissonian occurrences of the relative events over the year. The proposed procedure makes it possible to display the effect of the first and second moments of the random variable ‘runoff coefficient’ on the shape of the flood frequency curve. In particular, it may be shown analytically that the second moment of the probability distribution of the runoff coefficient controls the third moment of the distribution of annual maximum peak discharges and hence its curvature. The procedure is applied to several basins of the Romagna–Marche region (Italy), for which the results of a regional analysis conducted using the index method were already available, both in relation to annual maximum rainfall depths and peak discharges. A comparison of the results obtained by the two different procedures provides a basis for advancing some considerations regarding the potential of the proposed procedure and highlights aspects, which warrant further investigation.