Condition for precise measurement of soil surface roughness

Whereas it is well known that electromagnetic scattering by a randomly rough surface is strongly influenced by the surface-height correlation function, it is not clear as to how long a surface-height profile is needed and at what interval it should be sampled to experimentally quantify the correlation function of a real surface. This paper presents the results of a Monte Carlo simulation conducted to answer these questions. It was determined that, in order to measure the rms height and the correlation length with a precision of ±10%, the surface segment should be at least 40l¯ long and 200l¯ long, respectively, where l¯ is the mean (or true) value of the surface correlation length. Shorter segment lengths can be used if multiple segments are measured and then the estimated values are averaged. The second part of the study focused on the relationship between sampling interval and measurement precision. It was found that, in order to estimate the surface roughness parameters with a precision of ±5%, it is necessary that the surface be sampled at a spacing no longer than 0.2 of the correlation length