In this paper, the exact solution of scattering off a flat surface with a single semielliptical cylindrical boss of infinite extent is developed. The cylindrical boss approximates the geometric shape of an ice‐ridge keel. A far‐field approximation and the results to a grid of randomly distributed scatterers are applied. First, the case where the simulated keels have a single, constant depth is examined. In the frequency range below 200 Hz, energy is scattered mostly into steep angles, where it is eventually lost to bottom absorption. Above 200 Hz, a significant fraction of the scattered energy is directed into shallow angles, where it becomes a propagating incoherent component. Statistics are developed that describe a Rayleigh distribution of keel depths. A formula is developed that relates the standard deviation of surface roughness to mean keel depth and mean ice‐ridge spacing. Then the model is applied to find that for a given ice roughness, a Rayleigh distribution yields less coherent reflection loss, and slightly less scattering loss, than a field of constant keel depths.