Generalized Pareto distribution applied to the analysis of maximum rainfall events in Uruguaiana, RS, Brazil
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Generalized Pareto distribution applied to the analysis of maximum rainfall events in Uruguaiana, RS, Brazil Amanda Larissa Alves Martins1 · Gilberto Rodrigues Liska2 · Luiz Alberto Beijo3 · Fortunato Silva de Menezes4 · Marcelo Ângelo Cirillo4 Received: 23 March 2020 / Accepted: 9 July 2020 © Springer Nature Switzerland AG 2020
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. Keywords Extreme value theory · Probability distribution · Rain amount · Inundation · Environmental concern
1 Introduction Rainfall is vital for life on Earth [1], but its occurrence in high magnitude can cause damage and losses, usually causing flooding, destruction of buildings and crops, soil erosion, breaches of dikes and dams, among others [2, 3]. Damage in cities tends to be more severe because of the rapid urbanization and installation of complex infrastructure [4]. In addition, the frequency of extreme weather events has shown an increasing trend in various regions of the planet [2, 5]. In addition, the frequency of extreme
weather events has shown an increasing trend in several regions of the planet [6–8], and the southern region of Brazil has suffered from the occurrence of these events [2, 5]. To minimize negative impacts or avoid economic, social and environmental losses, it is necessary to plan activities and constructions based on the probabilistic forecast of the occurrence of maximum precipitation in a given location [9]. For the forecasting process the fit of mathematical statistical models to the data, which can study the phenomena with different approaches, as well as the occurrence of extreme values, temporal dis
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