Multifractal modeling of soil microtopography with multiple transects data

Authors: SAN JOSE MARTINEZ, FERNANDO - POLYTECHNIC U.,MADRID; CANIEGO, JAVIER - POLYTECHNIC U.,MADRID; GUBER, ANDREY; Pachepsky, Yakov; REYES, MARTIN - POLYTECHNIC U.,MADRID

Submitted to: Ecological Complexity
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 5/11/2009
Publication Date: 6/17/2009
Citation: San Jose Martinez, F., Caniego, J., Guber, A.K., Pachepsky, Y.A., Reyes, M. 2009. Multifractal modeling of soil microtopography with multiple transects data. Ecological Complexity. 6(3):240-245.

Interpretive Summary: Soil surface microtopography controls the overland transport of water and chemicals, and the micrometerological conditions within crop canopies. A correct model of the spatial variability of soil microtopography is needed to account for the soil surface roughness in environmental and crop models. The multifractal model of the microtopography spatial variability has been shown to be superior to other models. The objective of this work was to see whether parameters of the multifractal model could be adequately evaluated across a turfgrass soil surface if the microtopography was measured along transects. The multifractal model gave an excellent representation of soil surface microtopography variations. Synthetic surfaces with the same multifractal properties as the soil surfaces in experiments were created to evaluate the effect of the transect spacing on parameters of the multifractal variability model. It was found that the transect sampling allowed one to find reliable values of the multifractal parameters that reflected typical variations. A larger uncertainty is to be expected in the values of the multifractal parameters that reflect rare microtopographic features. This uncertainty depends on the transect density. These finding are important for researchers and practitioners using surface roughness parameters in that the work has shown the benefits of using a preliminary modeling of the multifractal microtopography to design transect microrelief measurements that account for rare microtopographic features.

Technical Abstract: 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 new viewpoint as compared with fractal models for soil surface roughness based on fractional Brownian motion and 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. Recently, it has been reported that topography exhibits multifractal behavior over a wide range of scales from 1 to 107 meters. The goal of this study is to investigate the multifractal behavior of soil microtopography. On rectangular plots of soil of 200 cm by 40 cm, point elevation values were obtained and soil microtopography was examined as a two-dimensional probability measure in order to determinate its possible multifractal behavior. A well defined multifractal behavior similar to multinomial measures was observed in all cases and afterwards, multinomial measures were simulated with a multifractal spectrum close to the spectra of the experimental plots. The synthetic multifractals for simulating soil roughness were used to evaluate the level of uncertainty in the estimates of the multifractal spectrum of natural roughness as a consequence of the distance between two consecutive transects. 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. At the same time, comparisons of entropy dimensions seem to be achievable when the change in the variance with the distance between transects are taken into account.