Depth-duration-initial soil state-frequency curves: A new paradigm for hydrology

This paper proposes a new paradigm for hydrology, i.e., the depth-duration-initial soil state-frequency (DDSF) curves, which are capable of describing rainfall depth as a function of event duration and initial soil conditions, expressed for instance in terms of initial infiltration capacity, for given return periods. They are obtained by applying a multi-step methodology based on processing the yearly extrema in the event depth-initial infiltration capacity space for various design event durations, analysing them probabilistically and fitting them with regressive equations relating rainfall depth to event duration. The iteration of these steps for various initial soil infiltration capacity values yields, for a desired return period, a group of DDSF curves, which can be effectively used in hydrologic applications. The applications show the easy derivation of DDSF curves at two Italian sites, namely Pavia (Lombardy in Northern Italy) and Erice (Sicily in Southern Italy), considering two different kinds of soil. The usefulness of these curves is then proven in the estimation of the peak water discharge on a small catchment, as they offer a sound tool for generating multiple equally probable scenarios of rainfall/initial soil conditions, to identify the most critical one for a given return period.