Copula Based Joint Flood Frequency Analysis: the Case of Guder River, Upper Blue Nile Basin, Ethiopia

Abstract

AbstractThe study of univariate frequency of hydrological extremes is well established in developing countries such as Ethiopia. However, the design of hydrological and hydraulic systems necessitates a thorough understanding of the flood event's characteristics, such as volumes, peaks, time of occurrence, and duration. The majority of researches use a univariate approach rather than a more realistic approach that acknowledges the multivariate nature of the underlying phenomenology. In addition to the uncertainty involved with the occurrence in both space and time, these events may frequently bear various degrees of association. As a result, the major objective of this study is to address the problem of quantifying flood events in terms of frequency of occurrence utilizing the 'Copula' based bivariate approach to analyze the joint distributions of associated flood variables with a special focus on two Guder River stations in Ethiopia. Using a 'Theory of Runs' based on a set threshold flow value, the concept was applied to flood parameters such as flood peaks and volume. Various bivariate copulas from Archimedean families were used and compared with various statistical and graphical tests. The Clayton and Gumbel-Hougaard copulas were chosen as the best fit for the flood peak and volume for stations 1 and 2, respectively. The chosen copula approach was used to determine the joint cumulative distribution, conditional distribution, and return periods required for hydrologic design. Various primary, secondary, and conditional return durations were computed and compared, and some correlations between them were established.