At-site flood frequency analysis in Brazil

Abstract

Governmental research agencies from Australia, Austria, Germany, Italy, Spain, and UK have suggested the use of specific 2- and 3-parameter Probability Density Functions (PDFs) to estimate the magnitude and frequency of annual maximum streamflow (AMS). There are no guidelines in Brazil concerning the most indicated PDFs to model AMS, however, two- and three-parameter PDFs have been used. Considering the worldwide promising results when using multiparameter PDFs, we were encouraged to evaluate ten candidate PDFs to model AMS at the scale of a continental country. The methodology of this study consisted of the: acquisition of streamflow data for the Brazilian territory and organization of the AMS series; screening of AMS series considering temporal and statistical criteria; fit of the following PDFs to the AMS series based on the L-moments method: Gumbel, Gamma, Generalized Logistic, Generalized Normal, Generalized Pareto, 3-parameter Log-Normal, Pearson type 3, Generalized Extreme Value, Kappa, and Wakeby; quantile estimation; and PDF performance according to the Filliben test and the Relative Absolute Error (RAE). Out of 3,826 AMS series initially considered, 707 were effectively used for the analysis. We concluded that: a) Gumbel and Gamma provided poor performance; b) the multiparameter PDFs (Wakeby and Kappa) outperformed the other PDFs to model AMS in Brazil; c) Gumbel and Generalized Extreme Value had the highest RAE values for quantile estimate; and d) this study has potential to contribute with the scientific advances reported in literature and can offer insights into the most indicated PDFs for the development of national guidelines.