It has been demonstrated in previously published results that large fourth Stokes parameter may be generated from a rough surface over multi-layered media, where only the top interface is rough while the others are all flat boundaries. In this paper, we consider the four Stokes parameters in microwave emission from a two-layer rough surface. In this case, there are two rough boundaries. The rough surfaces vary in one horizontal direction so that the azimuthal asymmetry exists in the 3-D problem. Periodic boundary conditions were assumed. The results are compared with the previously published results from a rough surface over multi-layered media. It is shown that the ``two-layer'' periodic rough surfaces can reduce the vertical and horizontal brightness temperatures remarkably; the interactions between the two rough surfaces also enhance the third and fourth Stokes parameters, which disappear in new structure for the large dips in the vertical and horizontal brightness temperatures presented in the former Sastrugi structure. In particular, the fourth Stokes parameter can be larger than that in previous layered structure. In addition, for the case of sinusoidal rough surface without large slope with snow's permittivities, the top boundary rough only layered structure cannot support the large third and fourth Stokes parameters any longer while the two-layer rough surface structure can do still up to -34 K and 15 K, respectively. It is also found that the reason resulting in the large fourth Stokes parameter is caused by relative magnitude of permittivities of the two layers, all cases with large fourth Stokes parameter should satisfy the upper layer's permittivity larger than the lower one due to total internal reflection from the lower layer.
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