The dependence on solar elevation of the correlation between monthly average hourly diffuse and global radiation

Abstract

In the present work, the dependence on γ of the correlation between K d = I d I o and K t = I I o is studied, I , I d , and I o respectively being the monthly average hourly values of the global, diffuse, and extraterrestrial radiation, all of them on a horizontal surface, and γ the solar elevation at midhour. The dependence is studied for Uccle for the following sky conditions. Condition A: clear skies (fraction of possible sunshine = 1) and the maximum values of direct radiation measured during the period considered (each of the hours before or after the solar noon for which radiation is received); Condition B: corresponding to all the values of radiation measured when the sunshine fraction is 1 during the period considered; Condition C: corresponding to all the data collected, independently of the state of the sky; Condition D: corresponding to overcast skies ( I = I d ). From the available values of I and I D (monthly average hourly direct radiation on a horizontal surface), values of K d and K t for 5° ≤ γ ≤ 45° and Δ γ = 5° are calculated using Newton's divided difference interpolation formula. The interpolated K d− K t values occupy three clearly different regions in the K d− K t plot, one for each of the conditions A,B, and C. For Condition A and each value of γ best linear fits with high correlation coefficients are obtained for the K d− K t correlation. The influence of the Linke turbidity factor on the correlation for Condition A is studied for 5° ≤ γ ≤ 35°, Δ γ = 5°.