Simultaneous Stochastic Simulation of Monthly Mean Daily Global Solar Radiation and Sunshine Duration Hours Using Copulas

In this paper, copula functions are used to model the dependence structure of monthly mean solar radiation $R$ and sunshine duration hours $D$. The efficiency of five well-known bivariate parametric copula functions, including (1) normal, (2) student’s $t$, (3) Clayton, (4) Frank, and (5) Gumbel, are evaluated in a seasonal basis for nine radiometric stations in Iran. First, the most appropriate marginal probability distributions for $R$ and $D$ were individually selected from 16 univariate distributions; then, performance of the parametric copulas for modeling the dependence structure of $R\text{-}D$ joint empirical probability distribution was assessed using two criteria. Finally, based on appropriate parametric copulas, the joint simulation of marginal variables was accomplished using the conditional sampling technique. The results show that the best marginal distribution fitted on the original data $D$ and $R$ is normal distribution when transformed with Johnson function (in more than a half of cases). Because of high (low) correlation of $R$ and $D$ in the left (right) tail of scatter diagram, the Clayton model had better fitting on the empirical copula than other models. The joint simulation using appropriate parametric copula functions indicated that the Clayton yield a better performance in terms of the slope of relation between $R$ and $D$. Besides, this model does not introduce unreasonable data. Therefore, the Clayton model is proposed as an appropriate copula model for simulating $R$ and $D$ data.