In reality, one random surface has multiple roughness scales, since the commonly used surface description based on single-scale roughness parameters does not comprise all the properties of natural surfaces relevant for describing wave scattering. Depending on the wavelength λ of the microwave sensor the dimension of the surface roughness parameters s and l correspond to specific roughness scales.
In case of multi-scale roughness, the equivalent RMS height is a composite of the individual RMS heights at different roughness scales (1).
A three-scale surface, as shown in Fig. 1, for example consists of a small-scale high-spatial frequency variation (c) ‘riding’ on top of the larger scales, the medium-scale perturbation (b) and the large-scale undulation (a).
At microwave frequencies, the centimeter scale is the scale of roughness of primary importance, since λ is on the order of centimeters to a few tens of centimeters. For natural surfaces it is very difficult to measure millimeter-scale roughness.