Broken-cloud enhancement of solar radiation absorption

Two papers recently published in Science have shown that there is more absorption of solar radiation than estimated by current atmospheric general circulation models (GCMs) and that the discrepancy is associated with cloudy scenes. We have devised a simple model which explains this as an artifact of stochastic radiative transport. We first give a heuristic description, unencumbered by mathematical detail. Consider a simple case with clouds distributed at random within a single level whose upper and lower boundaries are fixed. The solar zenith angle is small to moderate; this is therefore an energetically important case. Fix the average areal liquid water content of the cloud layer, and take the statistics of the cloud distribution to be homogeneous within the layer