Influence of Subpixel Scale Cloud Top Structure on Reflectances from Overcast Stratiform Cloud Layers

Recent observational studies have shown that satellite retrievals of cloud optical depth based on plane-parallel model theory suffer from systematic biases that depend on viewing geometry, even when observations are restricted to overcast marine stratus layers, arguably the closest to plane parallel in nature. At moderate to low sun elevations, the plane-parallel model significantly overestimates the reflectance dependence on view angle in the forward-scattering direction but shows a similar dependence in the backscattering direction. Theoretical simulations are performed that show that the likely cause for this discrepancy is because the plane-parallel model assumption does not account for subpixel, scale variations in cloud-top height (i.e., "cloud bumps"). Monte Carlo simulation, comparing ID model radiances to radiances from overcast cloud field with 1) cloud-top height variation, but constant cloud volume extinction; 2) flat tops but horizontal variations in cloud volume extinction; and 3) variations in both cloud top height and cloud extinction are performed over a approximately equal to 4 km x 4 km domain (roughly the size of an individual GAC AVHRR pixel). The comparisons show that when cloud-top height variations are included, departures from 1D theory are remarkably similar (qualitatively) to those obtained observationally. In contrast, when clouds are assumed flat and only cloud extinction is variable, reflectance differences are much smaller and do not show any view-angle dependence. When both cloud-top height and cloud extinction variations are included, however, large increases in cloud extinction variability can enhance reflectance difference. The reason 3D-1D reflectance differences are more sensitive to cloud-top height variations in the forward-scattering direction (at moderate to low, sun elevations) is because photons leaving the cloud field in that direction experience fewer scattering events (low-order scattering) and are restricted to the topmost portions of the cloud. While reflectance deviations from 1D theory are much larger for bumpy clouds than for flat clouds with variable cloud extinction, differences in cloud albedo are comparable for these two cases.