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

Abstract

The univariate analysis of hydrological extremes is a well-established practice in developing countries such as Ethiopia. However, for the design of hydrological and hydraulic systems, it is essential to have a thorough understanding of flood event characteristics, including volumes, peaks, time of occurrence, and duration. This study utilizes copula functions for bivariate modeling of flood peak and volume characteristics, examining the performance of four Archimedean copulas in the Guder basin located in Ethiopia from 1987 to 2017. Flood peak and volume were extracted using the theory of runs for analysis of their joint characteristics with the truncation level chosen as equal to the lowest annual maximum event. Univariate distributions with the best fitness on both variables were determined, and results showed that gamma and GEV-fitted flood peaks and lognormal-fitted flood volumes are the most suitable. Four Archimedean copulas were evaluated, and the Gumbel-Hougaard copula was found to be the best fit for the data based on graphical and measurable tests. Bivariate probability and return period were computed in “AND” and “OR” states. The joint return period for flood peak (97.49 m3/s) and volume (77.35 m3/s) was found to be 15 years in the “AND” state and approximately 4 years in the “OR” state. The study also evaluates univariate and conditional return periods, comparing them with the primary one. The copula method was an effective method for distributing marginal variables, highlighting its potential as a valuable tool in flood management.