Bivariate Flood Frequency Analysis: A case study of Rib River, Upper Blue Nile Basin, Ethiopia

Abstract

Hydrological design, planning and design of flood mitigation structures require detailed knowledge of the characteristics of the flood event, i.e. peaks, volumes, occurrence times and duration. In addition to the uncertainty associated with the occurrence in both space and time, these events may often have a correlation of varying strengths. The literature study interestingly reveals that the majority of studies are based on a univariate approach rather than a more realistic approach that recognizes the multivariate nature of the underlying phenomenology. Therefore, the main objective of this study is to revisit the topic of sizing of flood events in terms of their frequency of occurrence using the ‘Copula’ based bivariate approach to analyze the joint distributions of correlated flood variables with a special focus on Ribb sub basin, Upper Blue Nile (Ethiopia) as the case study. The methodology was applied to flood attributes, i.e. flood peaks and volume generation from partial duration series (PDS) by applying run theory. The Joint Cumulative Distribution Function, the Conditional Cumulative Distribution Function and the associated Return Periods can be easily achieved based on the bivariate distribution of the copula and compared to the univariate analysis.