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A solution for the problem of horizontally polarized radio waves propagating in a surface duct situated over a perfectly conducting, sinusoidally shaped ground with small amplitudes is obtained. The solution contains the assumption that the source is a horizontal line source perpendicular to the roughness variation. It is found that the specular contribution may be derived using an equivalent matrix with an effective reflection coefficient that accounts for scattering both out of and into the specular direction. The accuracy of a method for obtaining the rough Earth waveguide eigenvalues as a perturbation of those for the smooth Earth case is analyzed. Numerical field results are compared using the different approaches, demonstrating an attenuation effect due to the roughness.