Comparison of scattered powers from a layer containing randomly distributed particles, calculated from a few radiative transfer equations

Let us consider the problem of active remote sensing for detecting water content in soil. A theoretical approach for this problem is one of the important subjects in civil and agricultural engineering as well as experimental approaches. Moist soil can be regarded as a mixture of air, soil, bound water and free water. Then it is considered as a dense random medium. A conventional radiative transfer equation (CRT) has been commonly used to analyze the propagation and scattering of wave intensity in a random medium, but it becomes invalid for a dense random medium. Another radiative transfer equation, which is called the dense medium radiative transfer equation (DMRT), has been derived from a wave equation with the quasi-crystalline approximation with coherent potential (QCA-CP) and ladder approximation. Under these approximations, the random medium can be replaced with a homogeneous medium with effective permittivity evaluated by QCA-CP. In this paper, we consider a three layered model, composed of air, moist soil layer and perfect conductor. The moist soil layer is assumed to be a homogeneous soil layer with densely distributed water particles. For this model, we have used a DMRT with effective permittivity evaluated by the method presented by Tateiba to calculate the backscattering cross section of the soil layer when a plane wave is incident on the moist soil layer. The numerical results of our method are compared with ones of QCA-CP