Univariate and multivariate extreme value analysis of Düsseldorf hydrological data

Abstract

The rise in catastrophic climate events during the late 20th century prompted an increase in the application of statistical methods based on extreme value theory (EVT) in the fields of hydrology, climate, and meteorology. Several statistical models have been developed over the years. This dissertation presents an in-depth review of the fundamental univariate and multivariate techniques that rely on asymptotic EVT results. This dissertation focuses on univariate methods, including the Block Maxima (BM) method, the K largest Order Statistics (KLOS) method, and the Peak over Threshold (POT) method. Also, the Component-wise Block Maxima (CWBM) method and the General Copula-based (GCB) method are covered as multivariate methods. These methods are applied to the monthly mean of river discharge observations and the collective impact of snow melt and precipitation excess observations that were collected from Düsseldorf stations. Through these models, the return period and return level metrics are used to assess whether flood risk mitigation measures are sufficient for Düsseldorf and if the univariate analysis is still important to be taken into consideration when implementing flood protection measures in light of the inter-relationship between extreme events.