A rational runoff coefficient for a revisited rational formula

The Rational Formula (RF) is probably the most frequently applied equation in practical hydrology to compute the peak discharge, due to its simplicity and effective compromise between theory and data availability. Thus, after more than a century, the estimation of peak discharge through the RF is still an important and challenging issue in hydrology. The RF assumes response linearity and sometimes assumes that the return period does not depend on the runoff coefficient and neglects the time to ponding and the antecedent moisture condition. Moreover, the RF requires the critical duration of rainfall and the runoff coefficient to be estimated, both of which are highly controversial. This paper proposes an advanced RF that makes it possible to derive the peak discharge at the hillslope scale, where the above RF assumptions are mostly relaxed. Physically based runoff coefficient tables, which are not affected by subjectivity, are presented and application of the derived procedure is performed.