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

Abstract

For water resources engineering and management, understand the extreme rainfall events it’s essential. Using rainfall frequency analysis, one can fit many Probability Density Functions (PDFs) to the rainfall series and identify the best fit through the goodness-of-fit tests, allowing the estimate of Annual Maximum Daily Rainfall (AMDR) quantiles for different Return Periods (RP). Recommendations regarding the best PDFs for this have been made for some countries, however, in the opposite direction, Brazil has no guidelines or recommendations such as the above mentioned, and Gumbel distribution still is the most used PDF for modeling AMDR, frequently without testing others. That said, we focus in modeling thousands of AMDR series in Brazil, evaluating ten PDF candidates to find the best fit and defining the most indicated to describe AMDR in the country. The methodology consisted of: acquisition, structuration and screening process by temporal and statistical criteria; fit of the 2-, 3- and multiparameter PDFs to the AMDR series based on the L-moments method; quantile estimation; and PDFs performance assessment by Filliben test and the relative absolute error. From the almost 4 thousand AMDR series investigated, we concluded that: Gumbel and Exponential provided the poorest performance (32.1–60.2% of non-satisfactory fits); multiparametric PDFs (Wakeby and Kappa) are the most indicated for modeling AMDR in Brazil; Gumbel had the highest error values for quantile estimate, especially for high RP; novelties and advances on probabilistic modeling of AMDR in Brazil were provided, helping decision makers with accurate and essential technical information for many purposes.