Abstract A model for incident solar radiation is developed. The sky is treated as if it were composed of two semi-grey layers, an upper passively attenuating medium, and a lower participating isotropically scattering medium. The radiative transfer equation is solved for the lower medium using an exponential kernel approximation. This solution is combined with a gamma distribution for the creation of cloud particles to obtain a probability distribution for optical thickness. The combined solution is fitted and compared to generalised radiation curves.