Dependence on cloudiness of the relation between the ratio of diffuse to global radiation and the ratio of global to extraterrestrial radiation for average daily values

Abstract

The following linear correlation proposed by Page can be used to estimate values of H d if values of c, d, H , and H o are known H d H = c + d H H o where H , H d , and H o are, respectively, the mean daily global, diffuse, and extraterrestrial radiation on a horizontal surface, and c and d are empirical constants. Usually, values of H and H d are obtained for each month, but in the present work the values obtained for the first, second, and third decades of each month have been used. Page's correlation is generally established using all the measured values of global and diffuse radiation (independently of the state of the sky). The corresponding values of H , H d , c and d may be referred to as “average skies” values. In the present work we have computed the best values of c and d (in a least squares sense) using values of H and H d obtained at Uccle (latitude 50°48′N, longitude 4°21′N, E) for 11 different classes of days: days with S S o = 0 ; 0 < S S o ⩽ 0.1 ;…; S S o > 0.9 , where S is the daily number of sunshine hours and S o is the astronomical daylength. Quadratic correlations relating the values of c and d with the middle values of S S o for each of the ranges considered, are established. Values of c and d are also computed for “average skies” and “clear skies” ( S S o = 1 ), and the corresponding linear correlations are compared to those obtained for the mentioned classes of days.