Bivariate analysis of short-duration extreme rainfalls. Application to the study of the debris floods (alluviums) in the Funchal region (Madeira Island)

Abstract

Intense rainfalls and debris floods are familiar occurrences in Madeira Island (Portugal); but, understanding how intense rainfall relates to this type of floods is limited. This research seeks to characterise extreme rainfall events measured at the Funchal rain gauge station and to analyse their relationship with the region’s debris flood records. Contrary to other studies, a multivariate approach was performed to describe those relationships. To identify the extreme hourly rainfall events, the annual maximum series (AMS) technique was applied to a record of hourly time-series data covering a period of 34 years. By applying bivariate copula analysis to coupled AMS and cumulative rainfall series, joint and conditional return periods were calculated. The results suggested that the extreme rainfall events causing debris flood events tend to have higher return periods than those with no debris flow generation. The exceptionality of the late February 2010 deadly event is reaffirmed. This work assists our understanding as to how intense rainfall events relate to debris flood events, and shows the benefit of copulas in providing new insights in hydrologic studies.