A parameterized model for global insolation under partially cloudy skies

A simple and efficient parameterization of insolation under partially cloudy skies is discussed and compared with a set of exact radiative transfer results for clear skies, an empirical equation and observations. The parameterization is physically based and requires, as input variables, the ozone path length, precipitable water, Angstrom turbidity, surface air pressure and albedo, fractional cloud-cover and cloud thickness. Multiple reflection between the surface and the overlying atmosphere, and clouds are considered. The albedo of the earth-atmosphere system is also formulated and compared with a set of exact radiative transfer results. As compared to the exact radiative transfer results, the errors in the insolations are generally less than 1 per cent, and in the albedo of the earth-atmosphere system less than 10 per cent. The errors in the calculated insolations using climatological data are 2–3 per cent when compared with many years averaged observations at Maudheim (Antarctica) and at Rockville (U.S.A.). A parametric equation for calculating directly the daily total insolation is also given.