Bivariate Analysis of Duration and Severity of Drought in Sanandaj and Saqez Stations

Drought is one of the natural events that has a great impact on the environment. The severity and duration of drought are two important characteristics for the detection of drought and are usually derived from the weather data such as precipitation. In this study, two-dimensional copulas were used to construct bivariate distribution of drought characteristics for Sanandaj and Saqez stations located in the western part of Iran. Two important characteristics of drought including; duration and severity were derived from the standardized precipitation index (SPI) time series. In order to use copulas functions, Spearman’s rho and Kendall’s tau correlation coefficients were first calculated to assess correlation between variables of severity and duration of drought for both of considered stations. The results showed that there is a significant correlation between severity and duration of drought. After determining the best fitted marginal distributions on drought characteristics, the fittness of five different copulas for developing the bivariate distribution of severity and duration of drought was examined and the dependency parameter of each copula was calculated using the inference function for the margins technique (IFM). The results showed that for both stations (i.e. Sanandaj & Saqez) Frank copula function, due to having the highest log-likelihood (-328.9137 & -339.3758) and NSE (0.9393 & 0.9174), and the lowest values of RMSE (0.0655 & 0.0763) and AIC (695.8280 & 680.7516), is the most appropriate function for constructing the bivariate distribution of duration and severity of drought. Finally, the conditional probability of drought, joint and conditional returns periods of drought were calculated. The obtained results can provide useful information for planning and management of water resources over the studied area.