Modelling Wet and Dry Spells with Mixture Distributions

Abstract

The object of the study is to develop a discrete precipitation model which is able to simulate local, daily series of precipitation occurrences. The model is fitted to the observed data of two stations, Szeged and Szombathely, in Hungary (1951–1995), with pronounced attention to the reproduction of long dry periods, as characteristic features of the climate in Central Europe. The point of the approach is to model the duration of consecutive dry and wet series, i.e., spells, instead of individual wet or dry days. After having comparisons of three different aspects performed, the selected precipitation threshold is 0.1 mm. This threshold keeps the duration of dry and wet periods more or less balanced, whereas the value of the threshold does not fundamentally influence either the conditional distribution of macrocirculation types or the local weather statistics related to the so defined wet or dry days. The duration of both wet and dry spells are found to be independent of the length of either the preceding (opposite) or the last, but one (identical) state. It is also demonstrated that mixed distributions fairly fit to the wet and dry spells, whereas the simple geometric does not, especially due to the erroneous lack of long dry sequences. Weighted sum of two geometric distributions, as well as that of one geometric and one Poisson distribution exhibits good fitting for the dry spells, whereas only the latter one can be advised to employ for the wet periods. Parameters of the distributions obviously depend on the season and the site, in question.