Derivation of a Solar Diffuse Fraction Model in a Bayesian Framework

Abstract

We propose a Bayesian statistical approach to deriving a simple logistic hourly diffuse fraction model. The model is calibrated with data that include northern as well as southern hemisphere sites. An independent dataset comprising seven worldwide locations is used to compare the model against several previous models such as Skartveit et al. (1998), Reindl et al. (1990), Erbs et al. (1982), and a version of the logistic model derived by Boland et al. (2008). On an overall basis, the new model performs better than the models of Erbs or Reindl, and exhibits similar performance to the Skartveit model but with a much simpler expression. In addition, the use of a Bayesian criterion for model selection confirms that the new proposed model achieves the best trade-off between goodness-of-fit and model complexity. Finally, it is shown that the use of Bayesian methods instead of classical statistical techniques lead to a less-biased model. Our presentation is accessible to readers with an intermediate level of statistics.

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