Probabilistic distribution of solar irradiation frequency using copulas

In order to provide accurate solar irradiation approximation, and to quantify solar energy; the dependencies between solar irradiation, sunshine hours and ambient temperature must be taken into account. The amount of daily irradiation received for a particular area is among the most important meteorological parameters for numerous application fields. The utilization of accurate distribution minimizes the degree of uncertainty in solar resource estimates. This study applies the copula method for solar radiation estimation. This particular method is useful where probability of marginals fit into various families of distributions. The Archimedean copula and Gaussian copula were applied to evaluate solar irradiation in Johor Bharu, Malaysia. The solar irradiation, sunshine hours and ambient temperature were fit into five marginal probability distributions, namely, Gamma, Lognormal, Burr, Weibull and Normal distributions. The optimal fit marginal probability distribution was assessed by selecting the lowest possible value for Akaike Information Criterion (AIC). Finally, the bivariate copula best fit distribution was combined to obtain at the triavariate joint probability distribution. The results indicate that the best fit of joint probability between solar irradiation, sunshine hours and ambient temperature is Clayton copula.