Comparison of Conventional and Intelligent Methods in Estimating Copula Function Parameters for Multivariate Frequency Analysis of Low Flows (Case Study: Dez River Basin)

In the recent years, the dependence structure among hydrological variables is taken into consideration and it led to employ the multivariate analysis as a suitable alternative for univariate methods. In this study, the copula functions were employed for multivariate frequency analysis of low flows of Dez River basin at Tange Panj-Bakhtiari (TPB) and Tange Panj-Sezar (TPS) hydrometric stations. At the first, at first 7-d series of low flow was extracted from measured daily flows at the studied stations in the period of 1956-2012. In the next stage, 11 different distribution functions were fitted onto the low flow data which logistic distribution had the best fit on the TPB station and the GEV distribution had the best fit on the low flow data of TPS station. After specifying the best fitted marginal distributions, the copula parameter should be estimated. In this study, two methods of inference function for margins (IFM) and particle swarm optimization (PSO) were used to estimate copula parameter. The results showed that the PSO method had outperform than IFM in estimating the copula parameter. Among the Ali - Mikhail – Haq, Clayton, Frank, Galambos and Gumbel-Hougaard copulas, the Frank copula function had lowest error and highest accuracy in constructing the joint distribution of paired 7-d low flows data and was used for calculating the joint return periods in two states of “OR” and “AND”.