Describing soil surface microrelief by crossover length and fractal dimension
Authors: Vidal Vázquez E. , Miranda J. G. V. , Paz González A. 
Published: April 2010

Abstract. Accurate description of soil surface topography is essential because different tillage tools produce different soil surface roughness conditions, which in turn affects many processes across the soil surface boundary. Advantages of fractal analysis in soil microrelief assessment have been recognised but the use of fractal indices in practice remains challenging. There is also little information on how soil surface roughness decays under natural rainfall conditions. The objectives of this work were to investigate the decay of initial surface roughness induced by natural rainfall under different soil tillage systems and to compare the performances of a classical statistical index and fractal microrelief indices. Field experiments were performed on an Oxisol at Campinas, São Paulo State (Brazil). Six tillage treatments, namely, disc harrow, disc plow, chisel plow, disc harrow + disc level, disc plow + disc level and chisel plow + disc level were tested. Measurements were made four times, firstly just after tillage and subsequently with increasing amounts of natural rainfall. Duplicated measurements were taken per treatment and date, yielding a total of 48 experimental surfaces. The sampling scheme was a square grid with 25×25 mm point spacing and the plot size was 1350×1350 mm, so that each data set consisted of 3025 individual elevation points. Statistical and fractal indices were calculated both for oriented and random roughness conditions, i.e. after height reading have been corrected for slope and for slope and tillage tool marks. The main drawback of the standard statistical index random roughness, RR, lies in its no spatial nature. The fractal approach requires two indices, fractal dimension, D, which describes how roughness changes with scale, and crossover length, l, specifying the variance of surface microrelief at a reference scale. Fractal parameters D and l, were estimated by two independent self-affine models, semivariogram (SMV) and local root mean square (RMS). Both algorithms, SMV and RMS, gave equivalent results for D and l indices, irrespective of trend removal procedure, even if some bias was present which is in accordance with previous work. Treatments with two tillage operations had the greatest D values, irrespective of evolution stage under rainfall and trend removal procedure. Primary tillage had the greatest initial values of RR and l. Differences in D values between treatments with primary tillage and those with two successive tillage operations were significant for oriented but not for random conditions. The statistical index RR and the fractal indices l and D decreased with increasing cumulative rainfall following different patterns. The l and D decay from initial value was very sharp after the first 24.4 mm cumulative rainfall. For five out of six tillage treatments a significant relationship between D and l was found for the random microrelief conditions allowing a covariance analysis. It was concluded that using RR or l together with D best allow joint description of vertical and horizontal soil roughness variations.