Probabilistic envelope curves for design flood estimation at ungauged sites

Castellarin et al. (2005) introduced the probabilistic regional envelope curves (PRECs) of flood flows and formulated an empirical estimator of the recurrence interval T associated with the PREC for M synthetic cross-correlated and concurrent sequences of annual maxima with length n. In principle, a PREC can be used to estimate the T-year flood (design flood) for any basin in a given region as a function of the catchment area alone. A number of fundamental issues hamper the construction of PRECs and the estimation of their T for historical regional samples of flood flows. Some of these issues are addressed by this study, which presents an algorithm for the application of the empirical estimator of T to historical annual maximum series of unequal length and assesses how the selection of a particular cross-correlation formula and plotting position affects the accuracy of design flood estimates retrieved from PRECs (PREC flood quantiles). The reliability of the proposed algorithm and the accuracy of the flood quantiles are discussed through a comprehensive cross validation. The results show that the reliability of PREC flood quantiles for ungauged sites is comparable with the reliability of regional estimates produced by the application of the index flood approach. The results of the cross-validation also show that the selection of a particular correlation formula or plotting position may produce biased PREC flood quantiles, and suggest that the accuracy of the approach could be significantly enhanced by relaxing the assumption that the design flood scales with catchment area alone.