Climatic a priori information for the GEV distribution’s shape parameter of annual maximum flow series

The Generalized Extreme Value (GEV) distribution encompasses various models with unique characteristics, such as upper or lower bounds, complicating the application of the maximum likelihood algorithm in hydrological frequency analysis. When proposed, the Generalized Maximum Likelihood (GML) approach addressed some computational challenges in maximum likelihood estimation but remains sensitive to constraints on the shape parameter. These constraints on the support of the shape parameter do not consider the variability on the tail behavior of annual maximum flow series in various hydroclimatic regions. To mitigate this, we introduce the Extended GML (EGML), which incorporates a priori information on the shape parameter to reduce model specification bias in annual maximum flows, particularly when working with short data records. Based on the statistical characteristics of the monthly flows for the training set of the data series and a classification by Fuzzy C-Means (FCM) we developed four classes representing similar hydrological behaviors. This classification analysis was then combined with the Koppen climate regions to propose the a priori distributions for the GEV shape parameter across the four classes to better characterize the tail behaviour of annual maximum flow series distribution. A comparison of the 100-year return period quantile estimated with the EGML and GML methods reveals significant differences, particularly for the arid climate class.