Analytical derivation of rain intensity–duration–area–frequency relationships from event maxima

The annual maximum amount of rainfall over a fixed duration, area, and level of occurrence is generally described by intensity–duration–area–frequency (IDAF) curves. The annual maxima analysis can provide poor estimates of quantiles associated to high return periods when the sample size is short. Here, IDAF curves are derived analytically from the statistical properties of event maxima of rainfall intensity in area and duration, which are assumed scale invariant in time and space and Lognormal distributed, with a Poissonian chronology of rain events. The event maxima methodology is applied to the Reno basin, Emilia-Romagna, Italy, and its IDAF curves are compared in terms of goodness-of-fit to those obtained through the annual maxima analysis, showing better performances. In particular, we found that the absolute difference, in %, between model and data, is 20% in average, and 7% in standard deviation, using the method based on the event maxima analysis, while it is 27% in average, and 12% in standard deviation, using the method based on the annual maxima analysis.