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.

摘要：强降雨信息对于环境研究与水利工程领域至关重要。本研究借助平稳降雨序列，对南里奥格兰德州（Rio Grande do Sul，简称RS）247个站点的强度-历时-频率（Intensity-Duration-Frequency，简称IDF）方程开展修正工作。研究采用曼-肯德尔（Mann-Kendall）检验法，对南里奥格兰德州271个雨量站的年最大日降雨量（Annual Maximum Daily Rainfall，简称AMDR）序列的时间趋势进行识别。针对无显著时间趋势的AMDR序列，分别拟合了卡帕分布、广义极值分布（Generalized Extreme Value，简称GEV）、耿贝尔分布、两参数对数正态分布与三参数对数正态分布等概率分布模型。通过安德森-达令（Anderson-Darling）检验筛选得到最优拟合分布后，将AMDR序列离散至5分钟分辨率。在RStudio中对IDF方程的系数进行拟合，并采用纳什-萨特克利夫效率系数（Nash-Sutcliffe’s Coefficient）与均方根误差（Root-Mean-Square Error）对拟合效果进行评估。研究结论如下：适配AMDR序列的最优分布为多参数卡帕分布与广义极值分布（GEV）；IDF方程系数的拟合效果被评定为"优秀"；系数a与b在南里奥格兰德州内存在空间差异，且与AMDR值及地理区位显著相关；而系数c与d则基本保持恒定。