A multifractal approach to characterize cumulative rainfall and tillage effects on soil surface micro-topography and to predict depression storage
Authors: Vidal Vázquez E. , Miranda J. G. V. , Paz-Ferreiro J. 
Published: April 2010

Abstract. Most of the indices currently employed for assessing soil surface micro-topography, such as random roughness (RR), are merely descriptors of its vertical component. Recently, multifractal analysis provided a new insight for describing the spatial configuration of soil surface roughness. The main objective of this study was to test the ability of multifractal parameters to assess decay of initial surface roughness induced by natural rainfall under different soil tillage systems in field conditions. In addition, we evaluated the potential of the joint use of multifractal indices plus RR to improve predictions of water storage in depressions of the soil surface (MDS). Field experiments were performed on an Oxisol at Campinas, São Paulo State (Brazil). Six tillage treatments, namely, disc harrow, disc plough, chisel plough, disc harrow + disc level, disc plough + disc level and chisel plough + disc level were tested. In each treatment soil surface micro-topography was measured four times, with increasing amounts of natural rainfall, using a pin meter. The sampling scheme was a square grid with 25×25 mm point spacing and the plot size was 1350×1350 mm (≈1.8 m2), so that each data set consisted of 3025 individual elevation points. Duplicated measurements were taken per treatment and date, yielding a total of 48 experimental data sets. MDS was estimated from grid elevation data with a depression-filling algorithm. Multifractal analysis was performed for experimental data sets as well as for oriented and random surface conditions obtained from the former by removing slope and slope plus tillage marks, respectively. All the investigated microplots exhibited multifractal behaviour, irrespective of surface condition, but the degree of multifractality showed wide differences between them. Multifractal parameters provided valuable information for characterizing the spatial features of soil micro-topography as they were able to discriminate data sets with similar values for the vertical component of roughness. Both, rough and smooth soil surfaces, with high and low roughness values, respectively, can display similar levels of spectral complexity. Although in most of the studied cases trend removal produces increasing homogeneity in the spatial configuration of height readings, spectral complexity of individual data sets may increase or decrease, when slope or slope plus tillage tool marks are filtered. Increased cumulative rainfall had significant effects on various parameters from the generalized dimension, Dq, and singularity spectrum, f(α). Overall, micro-topography decay by rainfall produced was reflected on a shift of the singularity spectra, f(α) from the left side (q>>0) to the right side (q<<0) and also on a shift of the generalized dimension spectra from the right side (q>>0) to the left side (q<<0). The use of an exponential model of vertical roughness indices, RR, and multifractal parameters accounting for the spatial configuration such as D1, D5, and D10 improved estimation of water stored in surface depressions.