Fractal dimension and geostatistical parameters for soil microrelief as a function of cumulative precipitation

Abstract

Surface roughness is influenced by type and intensity of soil tillage among other factors, and it changes considerably with rain. In microrelief studies the advantages of using indices such as the fractal dimension, D, and the crossover length, l, is that they allow the partition of the roughness characteristics into properties that depend purely on the scale and on a scale free component, respectively. On the other hand, some geostatistical parameters may provide different ways to understand soil surface variability not addressed with fractal parameters. Changes in fractal dimension and semivariogram parameters for surface roughness evolution were evaluated as a function of cumulative rainfall on Oxisol samples over six tillage treatments, namely, disc harrow, disc plow, chisel plow, disc harrow+disc level, disc plow+disc level and chisel plow+disc level. Measurements were taken in each tillage treatment after rainfall events yielding a total of 48 experimental surfaces measured with a pin microrelief meter. The plot had 135 cm by 135 cm and the sample spacing was 25 mm. Trends due to plot slope component with its concavities and convexities and to agricultural practices were removed from field data sets. A semivariogram model was fitted to each of the surfaces and the model parameters were analyzed and related to the fractal dimension, D, and crossover length, l. A relationship was found between the fractal dimension, D, and semivariogram model parameters. The cross over length, l, did not show as strong relationships with the semivariogram model parameters, even though there was a power relation between D and l. Key words: Oxisol, tillage, soil surface roughness, semivariogram, crossover lengthParâmetros fractais e geoestatística do microrrelevo do solo em função de chuva acumulada RESUMO: A rugosidade da superfície pode ser influenciada pelo tipo e pela intensidade do preparo do solo entre outros fatores. A vantagem de se usar índices fractais em estudos de microrrelevo é que eles permitem a partição das características da rugosidade em propriedades ou que dependem exclusivamente da escala ou que independem totalmente dela. Por outro lado, a geoestatística prove algumas ferramentas que podem ser úteis no estudo da dinâmica da variabilidade da superfície do solo, diferentes daquelas avaliadas pela dimensão fractal. Verificou-se se é possível aplicar geoestatística na análise da variação do microrrelevo de um Latossolo sob seis tratamentos de preparo do solo, a saber: grade de discos, arado de discos, escarificador, grade de discos+grade niveladora, arado de discos+grade niveladora e escarificador+grade niveladora. As medidas foram feitas logo após o preparo do solo e subseqüentemente após cumulativos eventos de chuva natural. Medições duplicadas foram feitas em cada tratamento para cada data, produzindo um total de 48 superfícies. Um rugosímetro de agulhas foi utilizado para as medidas da rugosidade da superfície. A área de cada parcela era 1,35 m por 1,35 m e as medidas espaçadas de 0,25 m, produzi...

Soil roughness indexes and their relationship with water erosion

“…agropec. bras., Brasília, v.53, n.6, p.756-764, June 2018 DOI: 10.1590/S0100-204X2018000600012 structural elements on soil surface (Vidal Vázquez et al, 2010b).…”

“…Two fractal indexes -fractal dimension (D) and intersection distance (l) -were obtained according to Paz-Ferreiro et al (2008) and Vidal Vázquez et al (2010b). The fractal analysis was carried out using a variational method, assuming autosimilar surfaces to describe the microrelief.…”

“…Therefore, when measuring roughness, spatial and scale dependence should also be considered, which does not occur when only a statistical index is used (Paz-Ferreiro et al, 2008). In this context, several other approaches have been presented, such as geostatistical indexes that consider the spatial distribution of microelevations on the terrain (Linden & Van Doren Jr, 1986;Paz-Ferreiro et al, 2008) and indexes based on the fractal theory, considering both the effects of space and of the measurement scale on soil surface roughness (Vidal Vázquez et al, 2007, 2010bPaz-Ferreiro et al, 2008). However, it should be noted that most of the runoff and erosion processes do not show an expressive correlation at small distances, indicating that the roughness indexes based on fractal parameters may not necessarily be more important than other indicators based on descriptive statistics or geostatistics (Paz-Ferreiro et al, 2008).…”

Effect of tillage on soil erosion before and after rill development

“…The spatiotemporal variations of SSR and its evolution during rainfall events have been the focus of recent studies (Bertol et al, 2006;Bramorski, Maria, Silva, & Crestana, 2012;Haubrock, Kuhnert, Chabrillat, Güntner, & Kaufmann, 2009;Vázquez, Bertol, Siqueira, Paz-Ferreiro, & Dafonte, 2010;Zhang et al, 2015), and researchers studying tillage have examined the spatial heterogeneity of the surface microtopography, not just SSR (Vázquez, Vieira, Maria, & Paz González, 2010;Zhang, Zhao, Wang, & Wu, 2014). In this case, the findings have shown that the dynamic processes and mechanisms involved in run-off and erosion on a tilled surface limit the use of SSR alone.…”

Fractal Analysis of Surface Microtopography and its Application in Understanding Hydrologic Processes

“…Abedini and Shaghaghian (2009) also found that surface detrending methods (e.g., linear, quadratic, and cubic fitting plane methods) had a minimal effect on D. Armstrong (1986) and Klinkenberg and Goodchild (1992) suggested that for fractal analysis of land surfaces, it is not necessary to remove the non-stationarity of the data in the semivariogram calculation since surface slope is a part of the topographic properties. However, Vázquez et al (2010) removed the slope of soil surface microrelief by finding a best fitting plane (linear, quadratic, or cubic fitting plane), and concluded that trend removal did affect the fractal indices (D and l). Thus, further studies are needed to evaluate the effect of surface trend removal on fractal analysis.…”