Schematic illustration of four cloud overlap assumptions: maximum, random, maximum-random (MAX-RAN), and exponential-random (EXP-RAN) overlap. The figure also shows the meaning of three important quantities: the cloud cover of a given layer, a_i; the pairwise cloud cover p_i+1/2; and the cumulative cloud cover c_i+1/2. For the EXP-RAN overlap, a schematic illustration of the exponentially decaying α parameter is also included, showing how it decreases with altitude as the separation between layers increases.