Sensitivity of cirrus bidirectional reflectance to vertical inhomogeneity of ice crystal habits and size distributions for two Moderate-Resolution Imaging Spectroradiometer (MODIS) bands

A common assumption in satellite imager-based cirrus retrieval algorithms is that the radiative properties of a cirrus cloud may be represented by those associated with a specific ice crystal shape (or habit) and a single particle size distribution. However, observations of cirrus clouds have shown that the shapes and sizes of ice crystals may vary substantially with height within the clouds. In this study we investigate the sensitivity of the top-of-atmosphere bidirectional reflectances for two Moderate-Resolution Imaging Spectroradiometer (MODIS) bands centered at 0.65 mum and 2.11 mum to cirrus models composed of either a single homogeneous layer or three distinct, but contiguous, layers. First, we define the single- and three-layer cirrus cloud models with respect to ice crystal habit and size distributions on the basis of in situ replicator data acquired during the First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment (FIRE-II), held in Kansas during the fall of 1991. Subsequently, fundamental light-scattering and radiative transfer theory is employed to determine the single-scattering and the bulk radiative properties of the cirrus cloud. For radiative transfer computations we present a discrete form of the adding/doubling principle that is computationally straightforward and efficient. For the 0.65 mum band, at which absorption by ice is negligible, there is little difference between the bidirectional reflectances calculated for the one- and three-layer cirrus models. This result suggests that the vertical inhomogeneity effect is relatively unimportant at 0.65 mum. At 2.11 mum the bidirectional reflectances computed for both optically thin (tau = 1) and thick (tau = 10) cirrus clouds show significant differences between the results for the one- and three-layer models. The reflectances computed for the three-layer cirrus model are substantially larger than those computed for the single-layer cirrus. Furthermore, our analysis shows that the cirrus reflectances at both the 0.65 and 2.11 mum bands are very sensitive to the optical properties of the small crystals that predominate in the top layer of the three-layer cirrus model. It is critical to define the most realistic geometric shape for the small "quasi-spherical" ice crystals in the top layer for obtaining reliable single-scattering parameters and bulk radiative properties of cirrus.