At-site flood frequency analysis in Brazil

Governmental research agencies from Germany, Italy, Spain, and UK have suggested the use of specific two- and three-parameter probability density functions (PDFs) for estimating the magnitude and frequency of annual maximum streamflow (AMS). In Brazil, there are no guidelines concerning the use of multiparameter PDFs to model AMS, with most applications relying on two-parameter distributions. Considering the worldwide promising results when using multiparameter PDFs, here we focused on the evaluation of ten PDFs to model AMS over all gauged streams of Brazil. The methodology developed for this study consisted of the: (i) acquisition of streamflow data; (ii) organization of the AMS series; (iii) screening of AMS series considering temporal and statistical criteria; (iv) fit of the following PDFs to the AMS series based on the L-moments method: Gumbel, Gamma, Generalized Logistic, Generalized Normal, Generalized Pareto, three-parameter Log-Normal, Pearson type 3, Generalized Extreme Value, Kappa, and Wakeby; (v) quantile estimation; and (vi) PDF performance assessment according to the Filliben test and the relative absolute error (RAE). Based on the almost 4 thousand AMS series considered on this study, we concluded that: (i) Gumbel and Gamma provided poor performance (more than 17% of non-satisfactory fits); (ii) the multiparameter PDFs (Wakeby and Kappa) outperformed all other PDFs; (iii) Gumbel and Generalized Extreme Value had the highest RAE values for quantile estimate; and (iv) this study contributes to the scientific advances reported in the recent statistical hydrology literature and can provide local decision makers with the necessary technical information for developing national design flood guidelines. .