Soil surface roughness modelling with the bidirectional autocorrelation function
Résumé
Surface roughness is a major part of soil surface condition. It results from tillage operations and weathering. Surface roughness parameterisation is still a scientific lock and the object of many studies. An efficient parametrisation of soil surface roughness by modelling the bidirectional autocorrelation function estimated from 2.5D digital elevation models of soil surfaces is introduced. It not only provides geostatistical parameters that can be related to other soil surface characteristics, but let us emphasise that it reproduces the autocorrelation function with very good accuracy. The autocorrelation function is often modelled by a function of three parameters, the height variance, a single correlation length, and a roughness exponent. We added two parameters in order to take into account the anisotropy of soil surfaces and to align the coordinate system in the direction of the maximum correlation length. We propose the way to estimate roughness parameters and show its robustness for soil surfaces using laboratory tests with repeated rainfall events. One soil surface evolves from isotropy to anisotropy, and the other undergoes a reduction of initial anisotropy. The improvement brought by a second correlation length is thus highlighted. Under rainfall impact, the variation of the correlation lengths is more marked than that of the usual roughness parameter that is the root mean squared of the heights. Both parameters are complementary, capturing horizontal or vertical variation respectively. The evolution of the roughness exponent showed a slight increasing trend, which can be related to surface smoothing.
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