Regionalização hidrológica de vazões mínimas por meio do Método dos Mínimos Quadrados Generalizados aplicada à bacia do Alto SãoFrancisco

Abstract

Knowledge of flows at unmonitored sites is of great importance in hydrology. Hence the use of techniques that allow the transfer of information from monitored sites to unmonitored sites. Hosking and Wallis (1997) suggest the use of regional frequency analysis, since itincorporates more information than local analysis. Furthermore, the study of minimum flows plays an important role, since they are fundamental in assessing water availability, in the development of hydroelectric and irrigation projects, as well as being used as an authorization criterion. The methodology used in this study was structured based on an analysis of regionalization studies, primarily those involving minimum average flow rate statistics such as Q7,10. The regression model to be evaluated is the Generalized Least Squares (GLS) method proposed by Stedinger and Tasker (1985, 1986a, 1986b), in conjunction with the Ordinary Least Squares (OLS) method and the Weighted Least Squares (WLS) method, proposed by Tasker and Stedinger (1986). Such methods will be employed in a study of the regionalization of low flows over a 7-day and 10-year return period for the Alto São Francisco basin, subbasins40 and 41. Initially, the study area was divided into 4, supposedly homogeneous, regions (assigned the codes BA1, BA2, BA3 and BA4), although no statistical analysis was performed to corroborate that these regions actually are homogeneous from a hydrological and statistical standpoint. The criterion used to divide these regions was an analysis of the Water Resources Planning and Management Units (UPGRH) used by the Minas Gerais Institute of Water Management (IGAM). To determine the values of the low flow Q7,10, an analysis was performed of local frequency for all stations with more than 10 years of observed data using 2-parameter Weibull probability distribution. This distribution was also used to construct the covariance matrix, i.e. to determine the covariance of sampling errors. The analysis and determination of the final model for each of the 4 regions was undertaken by assessing the average variance of prediction (AVP) and the regression models generated were of the potential (quantile logarithm) type. The results obtained showed that the WLS method performed better than the GLS method in relation to the variance inflation ratio (VIR), as the VIR for the four homogeneous regions was less than 1. According to Griffis and Stedinger (2007), if the VIR is less than 1, then the WLS regression is sufficient, so there is no need touse the GLS model. In order to evaluate the criteria related to OLS method residuals, hypothesis tests for independence, normality, zero mean and constant variance at a significance level of 5% were applied. This analysis allowed it to be shown that, for the regions BA2 and BA4, the use of the OLS method is not recommended, since at least one assumption regarding the residuals was violated. Additionally, when evaluating the error variance ratio (EVR), it was found that the sample error variance is greater than the model error variance, therefore the OLS should not be employed. It should be noted that the GLS method is more appropriate, as the low flows are strongly correlated, given that the WLSmethod does not take into account correlations among concurrent flows. Nevertheless, where correlations are small, such a method could be adopted. However, in the region studied, the valuesof the cross-correlations are high. Therefore, it is concluded that, for the study inquestion, the GLS method is most appropriate. It is recommended, however, that the covariance matrix of the sampling errors be evaluated, as the method for estimating the covariance matrix is based on the quantiles themselves, and not on the quantile logarithm. This non-linear transformation certainly causes a change in the elements of the covariance matrix.