Multifractal modeling of soil microtopography with multiple transects data

Soil complexity and environmental heterogeneity may be viewed as a consequence of deterministic chaotic dynamics and therefore highly irregular patterns with so-called multifractal behavior should be common. This approach introduces a distinct viewpoint as compared with fractal models for soil surface roughness based on fractional Brownian motion. It suggests that it would be useful to move away from the fractal geometry of sets towards the multifractal description of singular probability measures, as well as going beyond second order statistics. The goal of this study was to investigate the multifractal behavior of soil microtopography measured on transects. On rectangular 200 cm × 40 cm plots, point elevation values were obtained and soil microtopography was examined as two-dimensional probability measure. A well-defined multifractal behavior similar to multinomial measures was observed in all cases. The multinomial measures were simulated with a multifractal spectrum close to the spectra of the experimental plots to obtain the synthetic multifractals to evaluate the level of uncertainty in the estimates of the multifractal spectrum of natural roughness as a consequence of the transect rather than grid sampling. We found that the transect separation used to collect the experimental data in this work generates a realistic multifractal spectrum but it cannot precisely define its tails that correspond to asymptotic values of the singularity exponents.