A new model that synthesizes sky luminance angular distribution from routine irradiance measurements for all insolation conditions was recently presented by the authors[1]. The model produces continuous sky luminance distribution patterns representative of specific insolation conditions from overcast to clear through partly cloudy. In this article we address the discontinuous aspects of skylight, created by “one of a kind” cloud patterns. We show that these patterns, which are superimposed on the continuous luminance distributions, have predictable physical characteristics that can be parameterized as a function of insolation conditions. We present a method for incorporating these random but predictable luminance effects as an option in the continuous skylight distribution model.