Modelling rainfall event frequency through a temporal contagion model with external covariates

Physical modelling of atmospheric processes, such as rainfall events, is often difficult due to the complexity of the atmosphere and the large number of variables involved. At the same time, it is necessary to know, as carefully as possible, some characteristics of precipitation processes, such as rainfall magnitude and frequency, in order to better understand their impacts on the territory. For this reason, statistical frameworks able to use external covariates to explain the physical process could be a central point in research.

Starting from the rainfall events identified from continuous data series from about 40 rain gauges located in Sicily, this paper aims at assessing the occurrence of rainfall events in a fixed interval of time according to a temporal contagion model (branching process) with external covariates, within a regression-like framework (Adelfio and Chiodi, 2021).

In detail, we extend the model formulation proposed by Meyer et al. (2012) in the context of infectious disease transmission, suggesting the use of a specific branching-type model, born in seismic context (the ETAS model, (Ogata 1988, 1998)), in a regression-oriented version modelling. In the temporal ETAS model, the expected frequency of events in a time unit can be defined as the sum of a term that describes the long-term variation and a term that describes the short-term variation.

Accounting for further potential covariates in the model specification of the short-term variation component, may both explain some of the overall variability of the studied phenomenon (i.e., for decreasing the unpredictable variability) and provide a more realistic description of the observed activity. The Forward Likelihood for prediction (FLP) method (Chiodi and Adelfio 2011) is used for estimating the ETAS model components with the covariates.

In this application the mean rainfall intensity, the duration and the anomalies in temperature and relative humidity of the events have been considered as external covariates of the model in order to explain the events frequency. The first results of the model appear to be interesting, and special attention will be paid to the sample of convective precipitation events identified using the same dataset (Sottile et al. 2021).