The actual received signal in a mobile radio environment is often stronger than what is predicted by reflection and diffraction models alone.

This is because when a radio wave impinges on a rough surface, the reflected energy is spread out (diffused) in all directions due to scattering.

Objects such as lamp posts and trees tend to scatter energy in all directions, thereby providing additional radio energy at a receiver.

Flat surfaces that have much larger dimension than a wavelength may be modelled as reflective surfaces. However, the roughness of such surfaces often induces propagation effects different from the specular reflection described earlier in this chapter.

Surface roughness is often tested using the Rayleigh criterion which defines a critical height $(h_c)$ of surface protuberances for a given angle of incidence $\theta_i$ given by

$$h_{c}=\frac{\lambda}{8 \sin \theta_{i}}$$

A surface is considered smooth if its minimum to maximum protuberance h is less than $h_c$, and is considered rough if the protuberance is greater than $h_c$.

For rough surfaces, the flat surface reflection coefficient needs to be multiplied by a scattering loss factor, $\rho_{S}$, to account for the diminished reflected field.