Diffuse fraction correlations

The influence of climatic and geometric variables on the hourly diffuse fraction has been studied, based on a data set with 22,000 hourly measurements from five European and North American locations. The goal is to determine if other predictor variables, in addition to the clearness index, will significantly educe the standard error of Liu- and Jordan-type correlations (IdI = f(k1)). Stepwise regression is used to reduce a set of 28 potential predictor variables down to four significant predictors: the clearness index, solar altitude, ambient temperature, and relative humidity. A piecewise correlation over three ranges of clearness indices is developed to predict the diffuse fraction as a function of these four variables. A second piecewise correlation is developed for predicting the diffuse fraction as a function of the clearness index and solar altitude, for use when temperature and relative humidity are not available. A third piecewise correlation of the Liu- and Jordan-type is developed from the same data set. Comparing this correlation with the new correlations provides a direct measure of the value of added predictor variables. The full diffuse fraction correlation reduced the residual sum squares by 14% when compared to the correlation that is a function of the clearness index only. The correlation including the clearness index and solar altitude diminished the residual sum squares by 9%. The correlations exhibited some degree of location dependence. This is expected, as the climates are quite different. The correlations also showed some seasonal dependence; the errors are higher in the fall and winter than on an annual basis.