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 i s that the radiative properties of a cirrus cloud may be represented by tho se associated with a specific ice crystal shape (or habit) and a single par ticle size distribution. However, observations of cirrus clouds have shown that the shapes and sizes of ice crystals may vary substantially with heigh t within the clouds. In this study we investigate the sensitivity of the to p-of-atmosphere bidirectional reflectances for two Moderate-Resolution Imag ing Spectroradiometer (MODIS) bands centered at 0.65 mum and 2.11 mum to ci rrus models composed of either a single homogeneous layer or three distinct , but contiguous, layers. First, we define the single- and three-layer cirr us cloud models with respect to ice crystal habit and size distributions on the basis of in situ replicator data acquired during the First Internation al 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 singl e-scattering and the bulk radiative properties of the cirrus cloud. For rad iative transfer computations we present a discrete form of the adding/doubl ing principle that is computationally straightforward and efficient. For th e 0.65 mum band, at which absorption by ice is negligible, there is little difference between the bidirectional reflectances calculated for the one- a nd three-layer cirrus models. This result suggests that the vertical inhomo geneity effect is relatively unimportant at 0.65 mum. At 2.11 mum the bidir ectional reflectances computed for both optically thin (tau = 1) and thick (tau = 10) cirrus clouds show significant differences between the results f or the one- and three-layer models. The reflectances computed for the three -layer cirrus model are substantially larger than those computed for the si ngle-layer cirrus. Furthermore, our analysis shows that the cirrus reflecta nces 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 t hree-layer cirrus model. It is critical to define the most realistic geomet ric shape for the small "quasi-spherical" ice crystals in the top layer for obtaining reliable single-scattering parameters and bulk radiative propert ies of cirrus.