Theoretical derivation of the index flood

Abstract. The expected value of the annual flood is always needed for attaining reliable estimates of the return period of floods. In particular, the accuracy of its estimate is crucial for ungauged basins, where regional analysis is to be invoked.

The main goal of this research was to search for an index flood formula suitable to explicate the influence of basin characteristics such as geomorphology, vegetation, soil and climate. This formula, due to unavoidable overparameterization, more than being suggested for technical use, allows sensitivity analyses of simpler formulae to basin features.

This study was mainly based on the theoretical distribution of floods developed by Iacobellis and Fiorentino (2000). In particular, the relationship that they derived for the first order moment was analyzed and simplified by assuming the Gumbel distribution as a first order approximation for the distributions of floods and rainfall intensities. The results were validated with regard to data recorded in some basins located in Southern Italy, in a climatically end geologically heterogeneous territory.