Estimativa de vazões de projeto com o método GRADEX: avaliação e alternativas metodológicas

Abstract

The study of floods allows the quantification of the magnitude of the maximum streamflows, which represents a very important variable for the management of water resources, control and prediction of floods and works of hydraulic structures. The estimate of maximum streamflows depends on historical series of streamflows, which are scarce, mainly in developing countries. Therefore, methods for estimating maximum streamflows have been developed. An alternative is the GRADEX method, a probabilistic method that proposes the extrapolation of the flood volume frequency curve, applying probability density functions from rainfall series. Despite being a consolidated method in the European literature, there are few studies and applications of it in Brazil. The objective of this study was to evaluate the GRADEX method in the way it was conceived and, also, with changes proposed in the present study referring to other probability distributions and alternatives for defining the method’s parameters, taking as reference watersheds located in the southeast region and, in an unprecedented way, watersheds in the extreme south of Brazil in the State of Rio Grande do Sul. For this, historical series from 70 rain gauges (29 in Rio Grande do Sul and 41 in Minas Gerais) and from 9 fluviometric stations were used in this study. The existence of trends or variations in the historical series was verified using the Mann-Kendall’s stationarity test and Pettitt's homogeneity test. Aiming at applying the GRADEX method, it was necessary to establish a time duration t for the organization of historical series of rainfall and annual maximum daily discharge. Two methodologies consolidated in the GRADEX literature were applied: t equal to the time of concentration (tc) of the watersheds and t equal to the average base time of the flood hydrographs (tbase). To compute the aerial annual average daily rainfall depth for each watershed, the Thiessen polygon technique was applied. Then, the probability distributions of Gumbel, Generalized Extreme Value (GEV) and Pearson Type III (P3) were adjusted to the data of maximum annual rainfall depth and maximum annual discharge and their adherence was verified in relation to the sample data through the Filliben test (Fi). Finally, the extrapolation of the flood volume frequency curve was carried out at the points corresponding to the TR equal to 10, 50 and 100 years and the maximum streamflows were computed. For illustrative purposes, it was decided to simulate the flood levels derived from the maximum streamflows obtained by extrapolating the GRADEX at the point corresponding to TR equal to 10 years and t equal to t base, considering the three probability distributions, in the environment of the HEC-RAS. Based on the results obtained, the main conclusions of this study were: a) the Gumbel and GEV distributions showed better adherence to rainfall data, and for streamflow the best adherence was presented when applying GEV and P3; b) the estimated values of maximum streamflows applying Gumbel were lower than those obtained by GEV and P3 and c) in general, P3 presented high values of maximum streamflows; d) the duration of time adopted for the events of rainfall and maximum streamflow and the point of extrapolation of the runoff over time had a great influence on the results of the estimates of the maximum streamflows; and e) the methodology used in the application of the GRADEX influences the results of the estimation of maximum streamflows.