Avaliação de métodos para a regionalização de curvas de permanência de vazões na bacia do rio Iguaçu - Paraná

Abstract

Due to physical or economic factors, the absence or insufficiency of long and reliable fluviometric data series is one of the main challenges faced in hydrological studies. In order to overcome this problem, the present work aimed at applying the regionalization method of flow permanence curves for the part of the Iguaçu River basin located in the State of Paraná. In this context, the study region was divided into hydrologically homogeneous regions (RHH), defined by the methods of hierarchical clustering of Ward and fuzzy Fuzzy C-Means, and regional models of permanence flow curves were formulated. The Euclidean distance was used as a similarity measure, as well as the explanatory flow variables (the drainage area (A - km²), the length (L - km) and the river gradient (H - m), and the average basin slope (D - %)) as input data. The permanence curves were constructed for each river gauge station distributed in their respective regions and calibrated against six mathematical models (linear, power, exponential, logarithmic, quadratic, and cubic); linear and multiple regression were then applied. The correlation matrix showed that A and L, A and H, and H and L had a positive linear relationship. In the Ward method, the formation of HRH was spatially associated with the geomorphology of the watershed. On the other hand, the Fuzzy C-Means formed more clusters than Ward, verifying sharpness in the formation of the groups by the spatialization and proximity of the stations along the basin. However, in both methods, there was the presence of clusters composed of few fluviometric stations (below 4 units) and with correlated variables (correlation above 0.85), and the regional equations were not applied to them. Regarding the mathematical models for adjustment, the logarithmic method stood out in Ward and Fuzzy C-Means, with an average coefficient of multiple determination (R²) above 85%. In the regional models, only one equation showed R² and adjusted coefficient of determination (R²_a) above 60% in the Ward grouping and two in Fuzzy C-Means, but all with high Mean Square Error (MSE), outliers, and non-randomly distributed residuals. Finally, no model proved efficient in the validation for both methods tested, with an underestimation in the predicted values.