Pseudo multi-scaling model of intensity–duration–frequency (IDF) curves

Intensity–duration–frequency (IDF) curves are fundamental tools for analysis in hydrological field and design of hydraulic interventions and infrastructures, expressing the relationship between rainfall intensity and duration for various return periods (probabilities of exceedance). In this work, a simple, parsimonious approach is proposed to develop a single, accurate IDF model valid for durations below 1 h till 24 h, and various return periods, which embodies the scaling property of rainfall intensities. Besides the adoption of a three-parameter IDF power law formulation inside a simple scale invariance formulation, the main idea is to use a double coefficient of variation for the annual maximum rainfall intensities, which enables grouping, and better representing, the design durations that feature similar relative variability in the corresponding maximum extremes. The resulting formulation can be seen as a Pseudo-multiple scaling model. Application to four case studies at various latitudes in Europe shows a much better fit to the quantile predictions of extreme rainfall intensities for durations below and above one hour and for different return periods than the traditional simple scaling approach, with a still very parsimonious parameterization procedure.