La formula razionale rivisitata

Abstract

The Rational Formula (RF), also known as CIA formula, is probably the most applied equation in practical hydrology to compute the peak discharge, due to its simplicity and effective compromise between theory and data availability. The RF assumes the linearity of the hillslope response, neglects the time to ponding and the antecedent soil moisture condition (ASMC), concentrates the infiltration effect in the runoff coefficient (C) which estimation is highly controversial, since it is based on qualitative indications. This paper proposes an advanced rational formula that makes it possible to derive the peak discharge at the hillslope scale, where the above assumptions are relaxed and which depends on parameters with a clear physical meaning, thus measurable. It is based on three simplified and more or less consolidated models: i) the Green-Ampt model for infiltration (GA), ii) the kinematic wave model (KW) for infiltration excess transportation, and iii) the intensity-duration-frequency (IDF) model to described the yearly maximum rainfall intensity, for fixed return period.