The average distribution of solar radiation-correlations between diffuse and hemispherical and between daily and hourly insolation values

• Published in: Solar energy 1979, Vol.22 (2), p.155-164
• Main Authors: Collares-Pereira, Manuel, Rabl, Ari
• Format: Article
• Language: English
• ISSN: 0038-092X; 1471-1257
• DOI: 10.1016/0038-092X(79)90100-2

The correlations of Hottel, Whillier, Liu and Jordan between diffuse and hemispherical, and between instantaneous (hourly) values and daily totals of solar radiation are recalibrated against pyrheliometer data for five stations in the U.S. The validity of the Liu and Jordan approach is confirmed, and numerical inaccuracies of the original correlations are found to arise from three factors: (i) reliance on uncorrected measurements of diffuse insolation with pyranometer plus shade ring, (ii) use of a single value of extraterrestrial insolation for a whole month, and (iii) neglect of seasonal variations in the diffuse/hemispherical ratio. The new correlation for the daily total ratio of diffuse over hemispherical insolation agrees with results reported for India, Israel and Canada which included the shade ring correction. This suggests that latitude independence is a good approximation. The new correlations imply that the diffuse component is significantly larger than that predicted by the original formulas of Liu and Jordan. Analytical expressions are presented the parameters of which are obtained by a least squares fit to the data. The resulting formulas provide a complete description of the long term average insolation incident on surfaces of arbitrary orientation; the only meteorological input is the long term average daily total of hemispherical insolation on the horizontal surface. Comparison between model and data shows an accuracy better than 3 per cent for the long term average insolation available to solar correctors, both fixed and tracking. The model provides a framework for optimal matching between solar radiation and ideal concentrators (based on the principle of phase space conservation). In addition to computing radiation availability for solar collectors, the model can be used for calculating heating and cooling loads of buildings. Les corrélations établies par Hottel, Whillier, Liu et Jordan entre les radiations diffuse et hémisphérique (globale) et entre leurs valeurs instantanées (horaires) et journalières sont reajustées en les comparant avec les données expérimentales pour la radiation directe provenant de cinq localités diférentes aux Etats Unis. La validité de la méthode utilisée par Liu et Jordan est confirmée et les imprecisions numériques des corrélations établies auparavant sont corrigées. Trois facteurs sont à la source des problèmes associés avec ces corrélations: (i) des mesures non corrigées de la radiation diffuse obtenues ave