Approximate self-affine model for cultivated soil roughness

We consider laser profiler measured soil profiles and show that the roughness of the cultivated soil can be viewed as an approximately self-affine structure. This conclusion is drawn from the limited range scaling behaviour found in both the variance and the second-order structure function of the profiles. We then propose and test a model for the radial part of the roughness spectra the explicitly incorporates the approximate self-affinity. A comparison of the model with data renders the values of the roughening exponent, the pertinent statistical parameters, the topothesy and the large-scale correlation length. Some technical details of the statistical analysis used to ascertain the model are also discussed.