On the derivation of the areal reduction factor of storms

A stochastic derivation of the areal reduction factor (ARF) of the storm intensity is presented: it is based on the analysis of the crossing properties of the rainfall process aggregated in space and time, As a working hypothesis, the number of crossings of high rainfall intensity levels is assumed to be Poisson-distributed and a hyperbolic tail of the probability of exceedances of rainfall intensity has been adopted. These hypotheses are supported by the analysis of radar maps during an intense storm event which occurred in Northern Italy. The reduction factor derived from this analysis shows a power-law decay with respect to the area of integration and the duration of the storm. The areal reduction results as a function of the storm duration and of its frequency. A weak, but significant decrease of the areal reduction factor with respect to the return period is shown by the functions derived, and this result is consistent with that of some recent studies on this topic. The results derived, although preliminary, may find useful applications for the definition of the design storm in urban catchments of a size greater than some square kilometres and with duration of some hours.