Is there a physical coherence between the problems of wave scattering from absolutely soft and impedance rough surfaces?

For over than thirty years it has been believed that the scattering of waves by a randomly rough surface with sufficiently small elevations runs similarly to the scattering by an ideal (unperturbed) surface but having a random impedance. Based on this belief, many of authors applied a habitual simplifying trick from the very outset of handling the wave scattering problem: they replaced the exact boundary condition by its Taylor expansion in terms of the irregularities height keeping only linear term. Following a thorough analysis the authors conclude that a necessary condition for the replacement of an absolutely soft-wall scattering problem with the corresponding impedance approach is the firm certainty that the physical quantities sought are mainly formed by the natural modes whose wavelengths far exceed the average height of the surface elevations.