Aplicação da teoria de valores extremos para o índice pluviométrico da cidade de Juiz de Fora - MG

Abstract

The analysis of events, often critical, which are at the tails of the distributions is difficult because there is little information about them, due to their rarity. The extreme value theory presents methods for dealing with these events through limit distributions, allowing inference about them. This paper provides an introduction to this theory with the use of their most widespread univariate models, the generalized extreme value distribution (GEV) and the generalized Pareto distribution (GPD). A literature review on their properties, modeling techniques, estimation and evaluation of goodness-of-fit is shown. At the end, it is used for analysis of extreme events in the daily rainfall in the city of Juiz de Fora - MG. Such events are responsible for situations of floods, landslides and burials in the city and the knowledge about the behavior of precipitation extremes must be used to minimize their impact and prevent such tragedies. For this study, we used indices of daily rainfall between January 1, 1961 and December 31, 2014, provided by the Banco de Dados Meteorológicos para Ensino e Pesquisa (BDMEP) of the Instituto Nacional de Meteorologia. Through these data, it was concluded that potential harmful rains are expected to occur once between 0.99 and 2.4 years (GEV model) and between 1.17 and 2.24 years (GPD model). These results highlight the importance of preventive actions to be performed jointly by the government and community.