Managing Hydrological Risks with Extreme Modeling: Application of Peaks over Threshold Model to the Loukkos Watershed, Morocco

Abstract

The peaks over threshold (POT) is a widely used technique to describe the exceedances of hydrological data above a threshold. It is well known that, under some conditions, the exceedances distribution can be approximated by a generalized Pareto distribution (GPD). The lack of a generally accepted methodology for selecting the optimal threshold is a major issue of the POT technique. In this paper an integrated approach is proposed that combines some graphical approaches with some analytical approaches to identify the optimal threshold and estimate the shape parameter of the exceedances distribution. Such a combination intends to reduce the subjectivity in graphical methods, and to refine their finding by using rigorous mathematical tools of analytical methods. First, a statistical test is used to select the appropriate GPD fitting the exceedances. Then, three numerical approaches, namely the likelihood ratio test, square error method, and multiple threshold method, are applied to detect the optimal threshold above which exceedances can be approximated by a GPD. These techniques are illustrated in a case study of Loukkos basin, a water resource of great importance in Morocco.