Electromagnetic Wave Scattering from Rough Boundaries Interfacing Inhomogeneous Media and Application to Snow-Covered Sea Ice

In this study a new analytical formulation for electromagnetic wave scattering from rough boundaries interfacing inhomogeneous media is presented based on the first-order approximation of the small perturbation method. First, we considered a scattering problem for a single rough boundary embedded in a piecewise continuously layered medium. As a key step, we introduced auxiliary wave propagation problems that are aimed to link reflection and transmission coefficients in the layered media with particular solutions of one-dimensional wave equations at the mean level of the rough interface. This approach enabled us to express the final solution in a closed form avoiding a prior discretization of the inhomogeneous medium. Second, we naturally extended the obtained solution to an arbitrary number of rough interfaces separating continuously layered media. As a validation step, we demonstrated that available solutions in the literature represent special cases of our general solution. Furthermore, we showed that our numerical results agree well with published data. Finally, as a particular special case, we presented a formulation for scattering from inhomogeneous snow-covered sea ice when the dominant scattering occurs at the snow-ice and air-snow interfaces.