Scaling models of intensity–duration–frequency (IDF) curves based on adjusted design event durations

This paper deals with intensity–duration–frequency (IDF) curves, which express the relationship between average rainfall intensity and event duration for various probabilities of non-exceedance (or return periods) for the design/analysis of hydraulic interventions and infrastructures in riverine and urban drainage contexts. New scaling models are proposed to develop a single IDF model valid for all durations, from below 1 h to 24 h. In these models, the scale invariance is applied to rainfall intensity to obtain a parsimonious IDF structure capable of defining a family of IDF curves at various return periods. The main novelty consists of the formulation of simple and multiple scale invariance based on adjusted design event durations. The parameterization is carried out in two phases: in the first phase, the adjustment size is searched for iteratively while the other parameters of the IDF structure are directly obtained in cascade; in the second phase, which enables considering different reliability levels for extreme rainfall data as a function of sample length at different durations, parameter refinement is carried out by means of a local optimization algorithm. The second step accommodates data samples of different extension as a function of available data at different durations. The application to four case studies at various latitudes in Europe, namely Helsinborg (Sweden), Frauenwald (Germany), Pavia and Erice (Italy), proves the IDF structure to fit well the quantile predictions of extreme rainfall data for specified durations below and above one hour.