Generalized Pareto distribution applied to the analysis of maximum rainfall events in Uruguaiana, RS, Brazil

Abstract

The rainfall monitoring allows us to understand the hydrological cycle that not only influences the ecological and environmental dynamics, but also affects the economic and social activities. These sectors are greatly affected when rainfall occurs in amounts greater than the average, called extreme event; moreover, statistical methodologies based on the mean occurrence of these events are inadequate to analyze these extreme events. The Extreme Values Theory provides adequate theoretical models for this type of event; therefore, the Generalized Pareto Distribution (Henceforth GPD) is used to analyze the extreme events that exceed a threshold. The present work has applied both the GPD and its nested version, the Exponential Distribution, in monthly rainfall data from the city of Uruguaiana, in the state of Rio Grande do Sul in Brazil, which calculates the return levels and probabilities for some events of practical interest. To support the results, the goodness of fit criteria is used, and a Monte Carlo simulation procedure is proposed to detect the true probability distribution in each month analyzed. The results show that the GPD and Exponential Distribution fits to the data in all months. Through the simulation study, we perceive that the GPD is more suitable in the months of September and November. However, in January, March, April, and August the, Exponential Distribution is more appropriate, and in the other months, we can use either one.