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This paper presents a model of microwave emissions from rough surfaces. We derive a more complete expression of the single-scattering terms in the integral equation method (IEM) surface scattering model. The complementary components for the scattered fields are rederived, based on the removal of a simplifying assumption in the spectral representation of Green's function. In addition, new but compact expressions for the complementary field coefficients can be obtained after quite lengthy mathematical manipulations. Three-dimensional Monte Carlo simulations of surface emission from Gaussian rough surfaces were used to examine the validity of the model. The results based on the new version (advanced IEM) indicate that significant improvements for emissivity prediction may be obtained for a wide range of roughness scales, in particular in the intermediate roughness regions. It is also shown that the original IEM produces larger errors that lead to tens of Kelvins in brightness temperature, which are unacceptable for passive remote sensing.