PERTURBATION SOLUTION FOR 3D RADIATIVE-TRANSFER IN A HORIZONTALLY PERIODIC INHOMOGENEOUS CLOUD FIELD

For a vertical homogeneous plane-parallel layer with horizontal cosinu soidal periodic variations of the extinction coefficient, k = k0 {1 epsilon[cos(ax) + cos(by)]} the first-order perturbation solution of t he three-dimensional radiative transfer equation has been obtained. Th e first-order perturbation correction in cloud albedo cancels when a h orizontal domain averaging is done. A correspondence exists between th e distribution of the extinction coefficient and the distribution of t he upwelling intensity. However, under certain conditions, the distrib ution of the upwelling intensity is opposite to the distribution of th e extinction coefficient. If the solar zenith angle is large, shifts i n the configurations of the distribution of the upwelling intensity ma y appear. The single scattering parameters can influence the distribut ion of the diffuse radiative intensity. The distribution of the heatin g rate inside the cloud and the distribution of the extinction coeffic ient are nearly coincident with each other.