Effective radiative properties of bounded cascade nonabsorbing clouds: Definition of the equivalent homogeneous cloud approximation

In the present study we investigated the radiative properties of inhomogeneous nonabsorbing clouds under the Equivalent plane‐parallel Homogeneous Cloud Approximation (EHCA), by using the one‐dimensional (1‐D) bounded cascade inhomogeneous clouds. The effective optical depth was defined under the EHCA by requiring the identity of the radiant flux components of the radiation budget between the inhomogeneous clouds and their equivalent homogeneous counterparts. Such requirement provides a rational framework to define the effective optical depth of the inhomogeneous nonabsorbing clouds. We analyzed the dependency of the effective optical depth on the horizontal scale of averaging and solar incidence angle and specified the conditions under which an inhomogeneous cloud segment could be treated as a plane‐parallel homogeneous cloud. A parameterization of the effective optical depth was proposed as a function of the mean optical depth and a relative cloud inhomogeneity parameter. Finally, we compared the EHCA with the effective thickness approximation, both based on the definition of the effective optical depth, and discussed the difference between their respective effective optical depths.