Physical interpretation of gray cloud observed from airplanes

When obliquely observed from an airplane, gray clouds near the horizon are sometimes observed to overlap with white clouds. Photographic observation from an airplane and simulations using a three-dimensional radiative transfer model are conducted to understand why such clouds appear gray. From observations, the brightness depression rate of gray clouds relative to surrounding whitish clouds is about 25%, whereas in simulations, it is as high as about 30%. Conditions necessary for the observation of gray clouds are as follows: (1) two clouds at different altitudes do not overlap, but the higher cloud overlaps with the lower cloud along the line of sight when these clouds are observed in near-horizontal direction, and (2) the higher cloud is optically thin in the vertical direction, but optically thick along the line of sight.