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Abstract
A semi-analytic iterative series solution for the radiative transfer equations in a discrete inhomogeneous random layer is developed and then exploited in assessing multiple scattering contributions to the layer radiometry. The solution is based on discretizing the layer into sub-layers. Explicit expressions for the zero and first iterative orders of the brightness temperatures at the sub-layer interfaces are derived. As for higher iterative orders, they are summed giving the diffuse brightness temperature that is obtained through solving two sets of integral equations. The integral equations are based on an analytic formulation for the diffuse brightness temperature within the sub-layers. As an application, the magnitude of the diffuse brightness temperature is calculated for a layer of circular discs, and the factors affecting this magnitude are investigated.