Application of Archimedean Copula Functions in Flood Frequency Analysis (Case Study: Dez Basin)

Most of hydrological phenomena have a stochastic and probabilistic nature and the relationship governing on these phenomena are almost unknown and ambiguous. Therefore, the theories of statistic and probability apply for describing and forecasting of such phenomena. One of the hydrological phenomena which have a complicated nature and causes too much damage is the flood. In the present study, flood frequency analysis in the Dez basin at the junction of two hydrometric stations of Sepid Dasht Sezar (SDS) and Sepid Dasht Zaz (SDZ) was performed during the period of 1957-2012 using the copula functions. The copula is a function which joint the univariate marginal distribution to form a bivariate or multivariate distribution function. For this purpose, first the partial series of flood at studied stations were extracted using the Malmoud-Tookart method. In the next step, 11 different distribution functions were fitted on the extracted flood series and the Generalized Logistic (SDS station) and Generalized Extreme Value (SDZ station) distribution functions were selected as the best fitted ones. After selecting the suitable marginal distributions, some of Archimedean copula functions (Ali - Mikhail – Haq, Frank and Clayton) were used for joint flood frequency analysis in Dez basin. Results showed that the Frank copula had the highest match with empirical copula for paired flood data of SDS and SDZ stations. For investigating the return period of events the joint return periods in two states “AND” and “OR” and also the conditional return period were considered. Based on the results obtained from joint analysis of flood series in two river branches, it was found that the severe flood events may occur simultaneously at SDS and SDZ River branches every 70 years.