Validation of quasi-invariant ice cloud radiative quantities with MODIS satellite-based cloud property retrievals.

Similarity relations applied to ice cloud radiance calculations are theoretically analyzed and numerically validated. If (1-) and (1-) are conserved where is optical thickness, the single-scattering albedo, and the asymmetry factor, it is possible that substantially different phase functions may give rise to similar radiances in both conservative and non-conservative scattering cases, particularly in the case of large optical thicknesses. In addition to theoretical analysis, this study uses operational ice cloud optical thickness retrievals from the Moderate Resolution Imaging Spectroradiometer (MODIS) Level 2 Collection 5 (C5) and Collection 6 (C6) cloud property products to verify radiative similarity relations. It is found that, if the MODIS C5 and C6 ice cloud optical thickness values are multiplied by their respective (1-) factors, the resultant products referred to as the effective optical thicknesses become similar with their ratio values around unity. Furthermore, the ratios of the C5 and C6 ice cloud effective optical thicknesses display an angular variation pattern similar to that of the corresponding ice cloud phase function ratios. The MODIS C5 and C6 values of ice cloud similarity parameter, defined as [(1-)/(1-)], also tend to be similar.