Effective radiative properties of bounded cascade absorbing clouds: Definition of an effective single-scattering albedo

We applied the equivalent homogeneous cloud approximation (EHCA) to the bounded cascade inhomogeneous absorbing clouds and defined their effective radiative properties. It is found that we have to introduce an effective single-scattering albedo in addition to an effective optical depth to treat the inhomogeneous absorbing clouds under the plane-parallel homogeneous cloud assumption. For an inhomogeneous absorbing cloud, a pair of the effective parameters can be estimated from each one of three possible pairs taken from the area-averaged reflectance, transmittance and absorptance. We found that the behavior of these effective properties was quite similar to those observed for the inhomogeneous non absorbing clouds except that two effective parameters were to be examined instead of only one effective parameter for the nonabsorbing clouds. Empirical relations for both the effective optical depth and the single-scattering albedo were given as a function of the local mean optical depth and relative local cloud inhomogeneity. We showed that title effective single-scattering albedo could not be properly introduced under the effective thickness approximation (ETA), which indicates an important conceptual difference between the EHCA and the ETA. Finally, we discussed possible consequences of the effective single-scattering albedo, defined in this study, with respect to the anomalous absorption phenomenon.