Soil resistance to penetration (PR) is an indirect measure of the state of soil compaction. Thus, the objective of this study was to characterize PR in vertical profiles in an area cultivated with sugarcane using multifractal models for different relief units. The experiment was carried out in an Oxisol with a clay texture, with 6.85 ha in the municipality of Coelho Neto (Maranhão state, Brazil), where 60 sampling points were demarcated. The area was divided into four relief units (Type A > 74 m, Type B from 71 to 74 m, Type C from 68 to 71 m and Type D from 65 to 68 m). The PR was measured at the 60 sampling points using an impact penetrometer, and the PR determined in the 0-0.60 m depth layer every 0.01 m. The multifractal analysis was performed considering the scale property of each profile and typified the singularity and Rènyi spectra estimated using the current method. Multifractal analysis allowed the identification of patterns at different scales and with high heterogeneity. The multifractal behavior was represented by the singularity spectrum (α), versus f(α), and the generalized dimension (Dq). The multifractal analysis allowed the differentiation between the profiles of the relief units (Types A, B, C and D), resulting in an important tool for studies of soil resistance to penetration.

The objective of this study was to evaluate the spatial variability of soybean yield, carbon stock, and soil physical attributes using multivariate and geostatistical techniques. The attributes were determined in Oxisols samples with clayey and cohesive textures collected from the municipality of Mata Roma, Maranhão state, Brazil. In the study area, 70 sampling points were demarcated, and soybean yield and soil attributes were evaluated at soil depths of 0-0.20 and 0.20-0.40 m. Data were analysed using multivariate analyses (principal component analysis, PCA) and geostatistical tools. The mean soybean yield was 3,370 kg ha-1. The semivariogram of productivity, organic carbon (OC), and carbon stock (Cst) at the 0-0.20 m layer were adjusted to the spherical model. The PCA explained 73.21% of the variance and covariance structure between productivity and soil attributes at the 0-0.20 m layer [(PCA 1 (26.89%), PCA 2 (24.10%), and PCA 3 (22.22%)] and 68.64% at the 0.20-0.40 m layer [PCA 1 (31.95%), PCA 2 (22.83%), and PCA 3 (13.85%)]. The spatial variability maps of the PCA eigenvalue scores showed that it is possible to determine management zones using PCA 1 in the two studied depths; however, with different management strategies for each of the layers in this study.

Soils are highly variable across landscapes, which can be assessed and characterized according to scale, as well as fractal and multifractal concepts of scale. Thus, the objective of this study was to analyze the multifractality of the penetration resistance (PR) of vertical profiles from different slope forms (concave and convex). The experimental plot incorporated 44.75 ha, and the PR was measured at 70 sampling points in the 0-0.6 m layer, distributed in concave (Type A: 38 sampling points) and convex pedoforms (Type B: 32 sampling points). Data analysis was performed using the PR value (every 0.01 m depth) for each of the sampling points (PRmean), and their respective maximum (Prmaximun) and minimum (PRminimum) values. Multifractal analysis was performed to assess the changes in the structure, heterogeneity, and uniformity of the vertical profiles according to the scale, characterizing the partition function, generalized dimension, and singularity spectrum. The multifractal parameters of the generalized dimension and singularity spectrum demonstrated greater homogeneity and uniformity in the vertical PR profiles of pedoform B (convex) compared to those of pedoform A (concave). The minimum PR values in pedoform A (PRminimum) showed the greatest scale heterogeneity, indicating that in terms of soil management, it is more relevant to monitor the minimum values than the maximum values. The fractal analysis allowed us to describe the heterogeneity of the data on scales not evaluated by conventional analysis methods, with high potential for use in precision agriculture and the delimitation of specific management zones.