Stochastic point models of rainfalls and their extremes

The increasing number of disastrous phenomena caused by heavy rains growed the interest toward the study of rainfall behaviour. A reliable protection from flooding and landslide events could be reached through two different approaches: a structural approach, that is the realization of infrastructures of active protection, in order to decrease the possibility that the feared phenomenon occurs, and a not structural approach, whose objective is mainly the preannouncement of the event occurrences, in order to avoid the loss of human life and to reduce the economic damages. These protection strategies could even be performed jointly. Stochastic models play a fundamental role in the preannouncement of disastrous events. Inside these models, a conceptual difference can be made between purely interpretative and physically based models. Briefly it can be said that the purely interpretative models try to reproduce the main characteristics of autocorrelation observed in the time series. On the contrary, the physically based ones hypothesize a physical schematization of the rainfall generation and usually they are built upon stochastic point process, so they are also indicated as stochastic point models of rainfall. An important feature of these models is their capability in reproducing the behaviour of extremes values, that is surely one of the most important aspects in the prevention of natural disasters. In the following paragraphs various stochastic point models of rainfall are described and analysed, with particular regard to their properties of extremes.