Bivariate frequency analysis of low flow using copula functions (case study: Dez River Basin, Iran)

Accurate estimation of low flow as a criterion for different objectives in water resource management, including drought is of crucial importance. Despite the complex nature of water deficits, univariate methods have often been used to analyze the frequency of low flows. In this study, low flows of Dez River basin were examined during period of 1956–2012 using copula functions at the upstream of headbranches’ junction. For this purpose, at first 7-day series of low flow was extracted at the studied stations, then their homogeneity was examined by Mann–Kendall test. The results indicated that 7-day low flow series of Dez basin were homogenous. In the next stage, 12 different distribution functions were fitted onto the low flow data. Finally, for Sepid Dasht Sezar (SDS), Sepid Dasht Zaz (SDZ), and Tang Panj Bakhtiyari (TPB) stations, logistic distribution had the best fit, while for Tang Panj Sezar (TPS) station, GEV distribution enjoyed the best fit. After specifying the best fitted marginal distributions, seven different copula functions including Ali–Mikhail–Haq (AMH), Frank, Clayton, Galambos, Farlie–Gumbel–Morgenstern (FGM), Gumbel–Hougaard (GH), and Plackett were used for bivariate frequency analysis of the 7-day low flow series. The results revealed that the GH copula had the best fitness on paired data of SDS and SDZ stations. For TPS and TPB stations, Frank copula has had the best correspondence with empirical copula values. Next, joint and conditional return periods were calculated for the low flow series at the upstream of branches’ junction. The results of this study indicated that the risk of incidence of severe drought is higher in upstream stations (SDZ and SDS) when compared with downstream stations (TPB and TPS) in Dez basin. Generally, application of multivariate analysis allows researchers to investigate hydrological events with a more comprehensive view by considering the simultaneous effect of the influencing factors on the phenomenon of interest. It also enables them to evaluate different combinations of required scenarios for integrated management of basin and planning to cope with the damages caused by natural phenomena.