The Case Study of the Alluvium Affecting Funchal City (Madeira Island, Portugal): Bivariate Modelling of Short-Duration Extreme Rainfall Events

Intense rainfalls and alluvium flooding are recurrent occurrences in Madeira Island. However, the understanding of how intense rainfalls relate to alluvium flooding is limited. The present research is intended to characterise the extreme rainfalls measured at the Funchal ObservatOrio rain gauge and how they relate to the alluvium flooding in the region. While other studies on the subject applied univariate approaches to rainfall data, in this study the relationship between extreme events of rainfall and alluvium was addressed based on a copula approach as a way of describing the return periods of coupled extreme rainfalls with different durations. The AMS technique applied over a 34-year recording period was used to identify the extreme rainfall events and to assign to each of those events cumulative rainfalls in periods immediately before or/and after the same. By applying bivariate copulas to the coupled AMS-cumulative rainfall series, joint and conditional return periods were calculated and their relationship with alluvium flood events was analysed, including the deadly alluvium in late February 2010. The results obtained showed that the copula approach may contribute to a better understanding of the extreme rainfalls capable of triggering alluvium events. The coupled rainfall events that originated alluvium flood events tend to have higher return periods than those with no reports on such type of flood. It also proved the extreme exceptionality of the February 2010 event. This work also assists in understanding how intense rainfall events relate to alluvium flood events and the adequacy of copulas in hydrological studies.