A two-step electromagnetic detection procedure is proposed to characterize a dielectric obstacle buried at low depth under a rough surface from single frequency and multiple incidence data. First, a properly defined correlation function is constructed to provide an estimation of the surface roughness. Second, this surface profile geometry is introduced into a finite element code thanks to a conformal mapping in order to compute the associated scattered field with this additionnal information. An iterative process is than used, based on a level-set formulation, to obtain the shape of the buried target. To understand the impact of the supplemental information added by estimating the roughness profile, we will compare throughout numerical experiments the reconstructed images with or without this supplemental information.