Modeling dependence of solar radiation and sky clearness index using a bivariate copula

Abstract

The total solar radiation received by a specific region in a day is a significant weather-related parameter for most areas of application. Obtaining correct information from irradiation models reduces uncertainty in solar resource estimations, leading to improvements in solar energy production. This study introduces a copula method to correlate the sky clearness index and solar radiation at two meteorology stations in Peninsular Malaysia. Six types of marginal likelihood distribution namely; gamma, logistic, Weibull, Burr, lognormal, and normal were fitted to the data of solar radiation and sky clearness index. Using information from the best-fit marginal distributions, six copula function types were then applied to evaluate the dependence between the sky clearness index and solar radiation. The copula functions used were the Gumbel, Joe, Frank, Clayton, Gaussian, and Student’s t copulas. The Gaussian copula most accurately represented the dependence between the sky clearness index and solar radiation as measured by Akaike s Information Criteria (AIC) for testing goodness of fit. These probabilistic properties can provide useful information for solar energy planning and management.