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The expected value of the annual flood is always needed for attainingreliable estimates of the return period of floods. In particular, theaccuracy of its estimate is crucial for ungauged basins, where regionalanalysis is to be invoked.<P  style="line-height: 20px;">The main goal of this research was to search for an index flood formulasuitable to explicate the influence of basin characteristics such asgeomorphology, vegetation, soil and climate. This formula, due tounavoidable overparameterization, more than being suggested for technicaluse, allows sensitivity analyses of simpler formulae to basin features.<P  style="line-height: 20px;">This study was mainly based on the theoretical distribution of floodsdeveloped by Iacobellis and Fiorentino (2000). In particular, therelationship that they derived for the first order moment was analyzed andsimplified by assuming the Gumbel distribution as a first orderapproximation for the distributions of floods and rainfall intensities. Theresults were validated with regard to data recorded in some basins locatedin Southern Italy, in a climatically end geologically heterogeneousterritory

Theoretical derivation of the index flood