The standard deviation of the surface height variation (or RMS height), denoted by s (or hRMS), describes the statistical variation of a random surface with height z(x). In case of an azimuthally symmetrical surface, the single-scale RMS height of the one dimensional case for discrete profile values is given by (1), where N is the number of samples, and z ̅ the mean surface height (2).
As roughness depends not only on the soil surface properties but also the wavelength λ of the electromagnetic signal, the roughness parameters are scaled by the wave number k. Hence, the electromagnetic roughness ks for surface roughness parameter s is (2π/λ)*s (3). In order to determine if a random surface may be considered as electromagnetically smooth, one common definition is given by the Rayleigh roughness criterion, where s < λ / 8*cosθ, or ks < 0.8, at incidence angle θ = 0. This criterion has been revised for the microwave region, where the wavelength is usually of the order of the RMS height, called the Fraunhofer roughness criterion, where s < λ / 36*cosθ, or ks < 0.2, at incidence angle θ = 0. Additionally, surfaces are considered as electromagnetically rough for 1 < ks < 3.