Using multi-parameters distributions to assess the probability of occurrence of extreme rainfall data

Abstract

Soil erosion, soil saturation and floods are frequently associated with extreme rainfall events. Thus, the scientific literature agrees on the need to carry out studies that improve the assessment of the probability of occurrence of extreme rainfall values. The main goal of this study was to compare the performance of the multi-parameters distributions Wakeby, Kappa and Generalized Extreme Value in fitting the annual maximums of daily, 2-day and 3-day rainfall amounts obtained from the weather station of Campinas, located in the State of São Paulo, Brazil (1890-2012. As a secondary aim, the presence of climate trends and serial correlation in these series was also evaluated. The auto-correlation function and the Mann-Kendall tests have shown the presence of no serial correlation and climate trends in the above mentioned series. The results obtained from goodness-of-fit procedures allowed us to conclude that the Kappa and the Generalized Extreme Value distributions present the best performance in describing the probabilistic structure of the series under analysis.Distribuições multi-paramétricas para avaliar a probabilidade de ocorrência de eventos extremos de precipitação pluvial R E S U M O Erosão e saturação hídrica do solo estão frequentemente associadas a eventos extremos de precipitação pluvial, tal como as enchentes. Desta forma, a literatura científica indica a necessidade de se realizar estudos que aprimorem a determinação da probabilidade de ocorrência desses eventos. O objetivo principal do estudo foi comparar o desempenho das distribuições multiparamétricas Wakeby, Kappa e Generalizada dos Valores Extremos na estimativa dos máximos anuais de totais de precipitação (diários, dois e três dias) da localidade Campinas-SP (1890-2012. O objetivo secundário foi avaliar a presença de tendências climáticas e a correlação serial nessas variáveis. A função autocorrelação e o teste de Mann-Kendall não indicaram a presença de significativas tendências climáticas e correlações serias em nenhuma das séries. Com base nos resultados dos testes de aderência concluiu-se que as distribuições Kappa e Generalizada dos Valores Extremos apresentam os melhores desempenhos na descrição probabilística das séries do estudo.

Modeling of probability in obtaining intensity-duration-frequency relationships of rainfall occurrence for Pelotas, RS, Brazil

“…The stationarity and independence of the maximum intensities obtained for different durations were verified using the non-parametric Mann-Kendall test and the sample autocorrelation function (Kendall & Stuart, 1967;Blain & Camargo, 2012;Blain & Meschiatti, 2014), respectively. An empirical frequency analysis was applied through the Weibull method to the maximum annual intensities associated with return periods (RP) of 2, 5, 10, 20, and 25 years; on the other hand, for return periods of 50 and 100 years, the probability distributions (Normal, Log-Normal, Gumbel and Gamma) were adjusted by the maximum likelihood method, composing hybrid series.…”

Inadequacy of the gamma distribution to calculate the Standardized Precipitation Index

“…Therefore, it was applied the same algorithm proposed by Wu et al (2007) The parametric distributions used in this study, 2-parameter gamma, general extreme value, generalized logistic, 3-parameter generalized normal, generalized Pareto, Pearson Type III, 4-parameter Kappa and 5-parameter Wakeby are described in Table 1. The greek characters are the parameters of the distributions that were estimated from all available data by means of the L-moments method (Guttman, 1999;Queiroz & Chaudhry, 2006;Blain & Meschiatti, 2014). (3) assumption of the SPI series.…”

Multiparameter probability distributions for heavy rainfall modeling in extreme southern Brazil

“…In the study of Franco et al (2014) in Minas Gerais state, they concluded from adequacy tests that the GEV, with parameters estimated by the L-moments method, was that with the best fit. Blain and Meschiatti (2014) compared the performance of GEV, Kappa and Wakeby distributions to model maximum annual rainfall of 1, 2 and 3 days through data from São Paulo state. They concluded that the Kappa, with parameters estimated by the L-Moments method, and GEV with parameters estimated by the maximum likelihood and L-moments methods, presented the best adjustments.…”

“…In Brazil, the fit of more simplified theoretical probability models has been commonly observed, such as 2 and 3 parameter Log-Normal distribution, and Asymptotic Extreme Value Type I, also known as Gumbel (Silva et al, 2002;Sansigolo, 2008;Santos et al, 2009;Back et al, 2011;Souza et al, 2012;Caldeira et al, 2015). However, several studies associated with heavy rainfall events have sought also evaluate other probability distributions, such as the 2-parameter Gamma (Franco et al, 2014), Generalized Extreme Value (Durrans and Kirby, 2004;Nadarajah and Choi, 2007;Blain and Camargo, 2012;Blain and Meschiatti, 2014), Kappa (Parida, 1999;Park and Jung, 2002;Norbiato et al, 2007;Ahmad et al, 2013;Blain and Meschiatti, 2014), Wakeby (Park et al, 2001;Blain and Meschiatti, 2014), Generalized Logistic (Norbiato et al, 2007;Hailegeorgis et al, 2013;Rahman et al, 2013) and Generalized Pareto (Hailegeorgis et al, 2013;Rahman et al, 2013).…”