Modeling of Temperature and Rainfall of Tabriz Using Copulas

Because of nonlinear dependence between the random variables, probability distributions of multivariate random variables are generally more complex compared to their univariate counterparts. One approach to solve this problem is the use of copulas, which have more considered by researchers over recent years. In this study, the dependence of rainfall and temperature in Tabriz station was modeled using copulas. In this regard, monthly data of rainfall and temperature of Tabriz for a period of 1971-2008 was used. At the first step, by application of Kolmogorov–Smirnov test, exponential and generalized extreme value (GEV) distributions are selected as appropriate univariate distributions for rainfall and temperature, respectively. Then three type of copulas functions namely, Clayton, Gumbel and Frank are used for creating bivariate distribution of rainfall and temperature in Tabriz. The results indicated that the performances of all types of copulas are close together. However, an only Frank copula has capability to modeling the negative dependence between variables. Therefore, Frank function is selected as appropriate copulas for modeling dependence between rainfall and temperature in Tabriz station.