Bivariate Flood Frequency Analysis Using the Copula Functions

In the conventional methods of flood frequency analysis, the flood peak variable is just considered and assumed that this variable follows some specific parametric distribution function. This assumption would restrict us and lead us to the limited available information to evaluate the flood risk. It is well known that a flood event has three variables of flood peak, volume and duration which are random in nature and are mutually dependent. In this research, the concept of the Copula function is briefly introduced and then used to modeling the dependency structure of the flood variables of the Karun River at the Ahvaz hydrometric stationand then estimate their joint probability distribution. We use three well-known and appropriate copulas, including Ali–Mikhail–Haq, Cook–Johnson and Gumbel–Hougaard which belong to the Archimedean class of copulas, to modeling the joint probability distribution of the flood variables, where the marginal distributions of the flood’s variables are selected from the parametric and non-parametric distributions. The Gumbel–Hougaard family led to better modeling of different combination of flood’s variables based on goodness of fit criteria. The selected copula is used to estimate conditional cumulative distribution function and joint return periods which lead to better estimation of flood risk.