Random fields of broken clouds and their associated direct solar radiation, scattered transmission and albedo

To model fields of broken clouds, we consider two methods based on Gaussian random fields and one method based on truncated random paraboloids. These models are determined by a few parameters only: the amount of cloud, the mean cloud base diameter and the mean cloud height. A field of broken clouds is a realization of such a random field, it is obtained by stochastic simulation and special spectral methods for Gaussian fields. The direct solar radiation S, the scattered transmission T and the albedo A of such a field of broken clouds are obtained by solving the stationary radiation transfer equation. Numerically we do this by variance reduction Monte Carlo methods. Varying the cloud parameters, the angle of incidence of the solar radiation we get interesting new functional relations between S, T and A for visible and infrared wavelengths.