The influence of horizontal inhomogeneity on radiative characteristics of clouds: an asymptotic case study

The paper is devoted to analytical studies of the influence of horizontal inhomogeneity of clouds on their radiative properties in the framework of the asymptotic radiative transfer theory. It is assumed that a cloud field is optically thick. Thus, only overcast cloud fields are under consideration. The study is based on the independent column approximation, assuming Gamma distribution of cloud optical thickness (COT) in the cloud field under study. This paper confirms all essential findings of cloud optics, concerning the influence of horizontally inhomogeneous clouds on transmitted, reflected, and absorbed solar light. For instance, we found the decrease of light reflection and absorption (negative biases) and the increase of light transmission (positive biases) for inhomogeneous clouds as compared to the case of a homogeneous cloud field with the value of optical thickness equal to that of an average COT of an inhomogeneous cloud field. Analytical equations for biases of radiative characteristics (e.g. the reflection function, spherical albedo, transmittance, and absorptance) are derived. Also, for the first time, we established the relationships between biases of different radiative characteristics. Analytical equations proposed are simple and highly accurate for optically thick weakly absorbing cloud fields. They can be incorporated in large-scale atmospheric models for the simplification of radiation blocks both for homogeneous and inhomogeneous cloud fields in visible and near-infrared spectral regions.