Comparison of conventional and intelligent methods in estimating Copula Function Parameters for multivariate frequency analysis of low flows (Case Study: Dez River Basin)

Document Type : Research Article


1 PhD Candidate of Water Resources Engineering. Shahid Chamran University, Ahvaz, Iran

2 Water Engineering Department, Shahid Chamran University, Ahvaz, Iran

3 Department of Statistics, Shahid Chamran University, Ahvaz, Iran

4 Water Engineering Department, Shahre Kord University, Shahre Kord, Iran


Over the recent years, the dependence structure among hydrological variables has been taken into consideration and it resulted in employment of 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. First, 7-d series of low flow was extracted from measured daily flows at the studied stations over the period of 1956-2012. In the next stage, 11 different distribution functions were fitted into the low flow data whereby 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 outperformed IFM in estimating the copula parameter. Among the Ali - Mikhail – Haq, Clayton, Frank, Galambos and Gumbel-Hougaard copulas, the Frank copula function had the lowest error and the 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”.


Main Subjects

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Volume 4, Issue 2
June 2017
Pages 315-329
  • Receive Date: 24 January 2017
  • Revise Date: 04 March 2017
  • Accept Date: 15 March 2017
  • First Publish Date: 22 June 2017