Intensity-Duration-Frequency equations for Rio Grande do Sul - Brazil, based on stationary rainfall series

Abstract

Heavy rainfall information is essential for environmental studies and water engineering. This study therefore aimed to adjust Intensity-Duration-Frequency (IDF) equations for 247 locations in the Rio Grande do Sul (RS) using stationary rainfall series. Mann-Kendall’s test was applied to identify the temporal trends in the Annual Maximum Daily Rainfall (AMDR) series of 271 rain gauges in RS. The Kappa, Generalized Extreme Value (GEV), Gumbel, two-parameters Log-Normal and three-parameters Log-Normal probabilistic distributions were adjusted to the AMDR series without significant temporal trend. The best distribution fit was given by Anderson-Darling’s test, so the AMDR was discretized up to 5 minutes. IDF equations coefficients were adjusted in RStudio, using Nash-Sutcliffe’s Coefficient and the Root-Mean-Square Error to evaluate them. In conclusion: the most suitable distributions for the AMDR were the multiparametric Kappa and GEV; the IDF equations coefficients adjustment was classified as “excellent”; coefficients a and b varied across the RS and are correlated with the AMDR and geographical positions; and the c and d coefficients were practically constant.
 Keywords: goodness of fit test, Kappa probabilistic distribution, trends test.

Frequency analysis of annual maximum daily rainfall in Brazil with multiparameter probability density functions

“…Our results corroborate with other studies (Beskow et al 2015;Moccia et al 2020;Mendes et al 2020;Ogarekpe et al 2020;Ballarin et al 2022;Rodrigues et al 2023b) that aimed to compare 2-and 3parameter PDFs with others for different hydrological purposes, been those PDFs even recommended for it in some countries, such as Nigeria, Italy, Poland, Spain, Australia, China, Canada, South Korea, and UK (Rahman et al 2015;Nguyen et al 2017;Młyński et al 2019;Ogarekpe et al 2020;Moccia et al 2020;Yeo et al 2021).…”

“…In the case of KAP, this result is due to the upper and lower PDF limits, making it impossible to fit it to series with data outside these boundaries. Beskow et al (2015) and Rodrigues et al (2023b) also used KAP distribution to model the AMDR in Rio Grande do Sul state -Brazil, and reached the same conclusion.…”

“…In Brazil, the PDFs most commonly used for modeling extreme rainfall are the simpler ones, such as Gumbel, Gama, Exponential, and the 2 and 3 parameters Log-Normal (Caldeira et al 2015;Souza et al 2017;Back et al 2020). However, studies carried out in several countries (Beskow et al 2015;Alemaw and Chaoka 2016;Mamoon and Rahman 2017;Ye et al 2018;Coronado-Hernandez et al 2020;Ogarekpe et al 2020;Heo et al 2020;Lima et al 2021;Moccia et al 2021;Das 2022;Ibrahim 2022;Rodrigues et al 2023b) have shown that PDFs with more than three parameters (p.e Wakeby -WAK and Kappa -KAP) outperform the others in the probabilistic modeling of extreme rainfall and, consequently, produce more accurate and reliable estimates.…”