The roles of scattering, absorption, and air mass on the diffuse-to-global correlations

Abstract

Monthly plots of the ratio K d of daily diffuse to daily total extraterrestrial irradiation versus the daily clearness index K t , have shown that points of large K t tend to be placed nearly on a straight line K t + K d = C (constant C < 1). This straight line exhibits a parallel displacement for different periods of the year. The same line is found in monthly plots of hourly K d versus K t values. A possible physical interpretation for this linear relationship is that on days of low cloudiness level, nearly half of the direct solar irradiance stopped by cloudiness is scattered downward and nearly half upward. However, cloudiness in this paper includes both turbidity (haze) and actual clouds. It is shown that the entire shape of the K d versus K t relationship can be explained by scattering alone. Variations in absorption caused by air mass, or by changes in absorbing constituents, account for seasonal variability, and for variations as a function of solar altitude. An apparent anomaly at very high K t accompanied by high K d is shown to be a natural consequence of unshaded sun periods during partly cloudy conditions. This region of the correlation is also found to tend to a straight line but with a positive slope: K t - K d = C. It is shown that for space or time averaged data this “anomalous” stretch tends to disappear. A useful distinction is made between local correlations and regional correlations, the former display the “anomalous” extension but the latter do not. The authors recommend the use of the K d = H d H o versus K t graphs instead of the K = H d H t versus K t for future investigations.