Modelling the frequency distribution of inter-arrival times from daily precipitation time-series in North-West Italy

The discrete three-parameter Lerch distribution is used to analyse the frequency distribution of inter-arrival times derived from 26 daily precipitation time-series, collected by stations located throughout a 28,000 km2 area in NW Italy (altitudes ranging from 113 m to 2,170 m a.s.l.). The precipitation regime of these Alpine regions is very different (latitude 44.5 to 46.5 N) from the typical Mediterranean precipitation regime of the island of Sicily (latitude 37 to 38 N), where the Lerch distribution has already been tested and whose results are compared with. In order to verify the homogeneity of the precipitation time series, the Pettitt test was preliminarily performed. In this work, a good fitting of the Lerch distribution to NW Italy is shown, thus evidencing the wide applicability of this kind of distribution, also allowing to jointly model dry spells and wet spells. The three parameters of the Lerch distribution showed rather different values than the Sicily ones, likely due to the very different precipitation regimes. Finally, a relevant spatial variability of inter-arrival times in the study area was revealed from the regional scale application of the probability distribution here described. The outcomes of this study could be of interest in different hydrologic applications.