Probability Distribution of Peak Discharge at the Hillslope Scale Generated by Hortonian Runoff

In this work, the probability distribution of peak discharge at the hillslope bottom is determined hypothesizing a prevalent Hortonian mechanism of runoff production for a given rainfall duration. As is well known, the probability distribution of peak discharge depends on the probability of both the rainfall event as well as that of the antecedent soil moisture conditions. In particular, the probability of the rainfall event is calculated according to the familiar rainfall duration–intensity–frequency approach, whereas the ecohydrological method from the literature is used here to define the probability of the antecedent soil moisture conditions. The latter depends on a set of parameters describing the dynamic interactions between average climate, soil and vegetation. By using the Monte Carlo procedure, the peak discharge is derived for a given rainfall duration and for each antecedent moisture condition/rainfall intensity pair from a physical-based model from the literature, by coupling the analytical solution of the overland flow equations over a hillslope with an established model that accounts for the infiltration process. Thus, the probability of peak discharge is evaluated via the typical multivariate probability distribution procedure. The methodology proposed was applied to three soil classes, i.e., silty clay loam (SCL), silty clay (SC), and silty loam (SL), for three climatically diverse Sicilian localities, namely Acireale (eastern Sicily, along the Ionian coast), Enna (central mountainous region), and Trapani (westernmost coast). For each of these places, precipitation and temperature data sets are widely available.