Modelling the occurrence of rainy days under a typical Mediterranean climate

Abstract

The statistical inference of the alternation of wet and dry periods in daily rainfall records can be achieved through the modelling of inter-arrival time-series, IT, defined as the succession of times elapsed from a rainy day and the one immediately preceding it. In this paper, under the hypothesis that ITs are independent and identically distributed random variables, a modelling framework based on a generalisation of the commonly adopted Bernoulli process is introduced. Within this framework, the capability of three discrete distributions, belonging to the Hurwitz–Lerch-Zeta family, to reproduce the main statistical features of IT time-series was tested. These distributions namely Lerch-series (Lerch), polylogarithmic- series (Polylog) and logarithmic-series (Log) were selected thanks to their capability to describe some peculiar properties usually observed in IT series derived from daily rainfall records: very high standard deviation and skewness, relatively high frequency associated to the unitary IT, monotonically decreasing frequencies with a slow decay. Both Polylog and Log distributions are special cases of the 3-parameter Lerch distribution with a decreasing number of free parameters (2- and 1-parameter, respectively). The analysis, performed on 55 raingauges located in Sicily (Italy) under a typical Mediterranean climate, suggests that a reliable statistical representation of IT can be attained with the 3-parameter Lerch distribution. Despite the marked seasonality of rainfall in the study area, a simple subdivision of the year into two 6-month periods, roughly corresponding to the dry ‘‘semester’’ (D-sem) and the wet ‘‘semester’’ (W-sem), allows a satisfactory reproduction of IT, as well as of wet spells (WS) and dry spells (DS), separately. It was also noticed that the 2-parameter Polylog distribution could be successfully used to reconstruct the DS frequency distribution only. This result suggests that the additional parameter of the Lerch distribution is required by the inclusion of WS into the analysis. Finally, considering that Polylog outperforms the commonly adopted Log, a noteworthy step forward in DS modelling can be achieved by using Polylog distribution rather than Log one.