Assessment of an annual maximum flow regional method applied to different basins of mexico using the double Gumbel distribution

Abstract The limited availability of streamflow records, compared to rainfall data, poses a recurring challenge in hydraulic facility planning. This study applied a year-station regionalization method to estimate the distribution function of annual maximum flows across four previously defined regions. These include coastal basins vulnerable to hurricanes, an intermediate region where lowlands are exposed to hurricanes while highlands are protected, and highland basins naturally shielded against these events. The main objective of this paper was to verify the hypothesis that the behavior of these groups can be considered homogeneous by comparing the empirical data position of the maximum annual floods recorded at each gauging station with confidence intervals for a probability of approximately 90% obtained from maximum and minimum values of synthetic series generated from the probability distribution functions obtained for each region under test. The probability distribution functions used to describe the probabilistic behavior in each region include the Gumbel distribution function, the generalized extreme value distribution, and particularly the Double Gumbel distribution developed by González (Contribución al análisis de frecuencias de valores extremos de los gastos máximos en un río Publicación N° 277, Instituto de Ingeniería UNAM, México, 1970), which is widely used in Mexico. The results obtained show that the vast majority of the measured records in the clustered regions fall within the confidence intervals obtained with the probability distribution corresponding to each region, confirming the applicability of the regionalization method.