Multivariate Hydrological Drought Severity-Duration-Frequency Analysis in Gilvan Watershed by Copula Models

Hydrological droughts are characterized by the combination of the multi correlated attributes of severity, duration and frequency. This study aims to investigate hydrological drought by considering daily streamflow discharge and Q7,10 index applied to the Gilvan watershed. An integrated Severity-Duration Frequency, (SDF), analysis of hydrological drought is proposed by applying copula functions. The drought periods were extracted in terms of 7,10, and characterized by attributes of severity and duration. Various univariate marginal distributions were fitted to the drought severity and duration data sets; with Gamma and generalized Pareto distributions being selected for the drought severity and duration respectively, in accordance with the Kolmogorov-Smirnov test. To model the joint distribution of drought severity and duration, two classes of bivariate Archimedean and Elliptical copula functions were fitted to the aforementioned data sets, with Frank copula being selected as the best copula, based on the performance evaluation criteria. The selected copula was then used for multivariate analysis of droughts. The results of fitting Frank copula to the severity and duration data sets, imply that, the most extreme hydrological drought in the region is characterized by the severity of 1045.36 m3/s, with a duration of 134 days and return period of 2.36 years.