The radiative transfer (RT) approach is widely used in remote sensing applications. Although this approach involves approximations, they are often not explicitly stated or explained. The RT approach for random media with nonscattering boundaries has been well studied, and the underlying assumptions are clearly documented. In contrast, our problem has scattering boundaries which are randomly rough. In order to better understand the RT approach to our problem, we adopt a statistical wave approach for modeling multiple scattering in the combined problem of random media and rough surfaces. The geometry of our problem consists of a multilayer discrete random medium with rough boundaries which are planar on the average. The statistical characteristics of the random medium in each layer are independent of each other and independent of the statistics describing the rough interfaces. Using the Green's functions of the problem without the volumetric fluctuations, we represent our problem as a system of integral equations. Employing the T-matrix description, we first average with respect to volumetric fluctuations to obtain a system of integral equations. We next average with respect to surface fluctuations, apply the weak surface correlation approximation, and arrive at a closed system of integral equations for the first and second moments of the electric fields. We use the Wigner transforms to relate the coherence functions to radiant intensities. On applying the quasi-uniform field approximation, we hence arrive at a system of equations identical to those used in the RT approach. In this process, we find that there are more conditions involved in the RT approach to our problem than widely believed to be sufficient. The important additional conditions are the following: (a) the thickness of layers are larger than the mean free path of the layer medium, and (b) the character of interface roughness is such that weak surface correlation approximation is applicable.
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