MULTIFRACTAL ANALYSIS OF SOIL RESISTANCE TO PENETRATION IN DIFFERENT PEDOFORMS

LEIVA, JAIRO OSVALDO RODRIGUEZ; SILVA, RAIMUNDA ALVES; SILVA, ÊNIO FARIAS DE FRANÇA E; SIQUEIRA, GLÉCIO MACHADO

doi:10.1590/1983-21252021v34n119rc

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Agronomy • Rev. Caatinga 34 (1) • Jan-Mar 2021 • https://doi.org/10.1590/1983-21252021v34n119rc copy

MULTIFRACTAL ANALYSIS OF SOIL RESISTANCE TO PENETRATION IN DIFFERENT PEDOFORMS

ANÁLISE MULTIFRACTAL DA RESISTÊNCIA DO SOLO À PENETRAÇÃO EM DIFERENTES PEDOFORMAS

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

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 (PR_mean), and their respective maximum (Pr_maximun) and minimum (PR_minimum) 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 (PR_minimum) 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.

Keywords:
Scale heterogeneity; Precision agriculture; Soil compaction; Soil management; Spatial variability

Equations
Partition function	$p_{i} (δ) = \frac{N_{i} (δ)}{N_{t}}$	(1a)
	$ϰ (q, δ) = \sum_{i = 1}^{n (δ)} p_{i}^{q} (δ)$	(1b)
	$τ (q) = \lim_{δ \to 0} \frac{\log χ (q, δ)}{\log (1 / δ)}$	(1c)
Generalized dimension (Dq)	$Dq = τ (q) / (q - 1)$	(2a)
	$Dq = \frac{1}{q - 1} \lim_{δ \to 0} \frac{\log [χ (q, δ)]}{\log δ} = \frac{τ (q)}{q - 1} para q = 1$	(2b)
	$D_{1} = \lim_{δ \to 0} \frac{\sum_{i = 1}^{n (δ)} p_{i} (δ) \log [p_{i} (δ)]}{\log δ} para q = 1$	(2c)
Singularity spectrum	$α (q) \propto \frac{\sum_{i = 1}^{N (δ)} μ_{i} (q, δ) \log [p_{i} (δ)]}{\log (δ)}$	(3a)
Singularity spectrum	$f (α (q)) \propto \frac{\sum_{i = 1}^{N (δ)} μ_{i} (q, δ) \log [μ_{i} (q, δ)]}{\log (δ)}$	(3b)

	-------- 70 points --------			--------Type A --------			-------- Type B --------
	Mean	Maximum	Minimum	Mean	Maximum	Minimum	Mean	Maximum	Minimum
Mean	2.333	4.801	0.852	2.374	4.533	0.914	2.277	4.355	0.935
Variance	0.922	4.855	0.153	1.175	4.597	0.239	0.710	3.652	0.186
Standard deviation	0.960	2.203	0.391	1.084	2.144	0.489	0.843	1.911	0.431
CV %	41.168	45.890	45.864	45.648	47.303	53.518	37.021	43.886	46.104
Asymmetry	-0.545	-0.078	1.715	-0.418	-0.041	1.881	-0.665	-0.051	1.022
Kurtosis	-1.373	-0.917	1.819	-1.568	-0.896	2.204	-1.068	-0.537	-0.454
D	0.278Ln	0.136n	0.396Ln	0.274Ln	0.161n	0.438Ln	0.224Ln	0.132n	0.36Ln

			Generalized dimension
	D_-5-D₅	D_-5	D₅	D₀	D₁	D₂
			70 points
PR_mean	0.359	0.939 ± 0.020	1.297 ± 0.010	1.000 ± 0.000	0.971 ± 0.005	0.956 ± 0.011
PR_maximum	0.367	0.910 ± 0.008	1.278 ± 0.023	1.000 ± 0.000	0.968 ± 0.004	0.946 ± 0.006
PR_minimum	0.920	0.507 ± 0.104	1.427 ± 0.189	1.000 ± 0.000	0.642 ± 0.006	0.545 ± 0.090
			Pedoform A
PR_mean	0.377	0.930 ± 0.025	1.307 ± 0.019	1.000 ± 0.000	0.966 ± 0.008	0.948 ± 0.014
PR_maximum	0.410	0.910 ± 0.014	1.320 ± 0.019	1.000 ± 0.000	0.963 ± 0.004	0.942 ± 0.008
PR_minimum	0.921	0.511 ± 0.103	1.432 ± 0.186	1.000 ± 0.000	0.648 ± 0.068	0.550 ± 0.090
			Pedoform B
PR_mean	0.340	0.945 ± 0.016	1.285 ± 0.011	1.000 ± 0.000	0.975 ± 0.004	0.962 ± 0.008
PR_maximum	0.333	0.925 ± 0.006	1.258 ± 0.025	1.000 ± 0.000	0.972 ± 0.003	0.955 ± 0.005
PR_minimum	0.333	0.925 ± 0.006	1.258 ± 0.025	1.000 ± 0.000	0.972 ± 0.003	0.955 ± 0.005
			Singularity spectrum
	q-	q+	α₀		α₅	α₅
			70 points
PR_mean	5.000	-4.000	1.038 ± 0.007		1.515 ± 0.022	0.927 ± 0.036
PR_maximum	5.000	-3.500	1.039 ± 0.007		1.461 ± 0.047	0.876 ± 0.014
PR_minimum	1.500	-5.000	1.365 ± 0.124		1.593 ± 0.297	0.532 ± 0.116
			Pedoform A
PR_mean	5.000	-4.000	1.044 ± 0.010		1.520 ± 0.036	0.917 ± 0.042
PR_maximum	5.000	-4.000	1.047 ± 0.007		1.539 ± 0.035	0.879 ± 0.025
PR_minimum	1.500	-5.000	1.359 ± 0.123		1.603 ± 0.292	0.536 ± 0.116
			Pedoform B
PR_mean	5.000	-3.500	1.032 ± 0.004		1.483 ± 0.030	0.933 ± 0.029
PR_maximum	5.000	-3.500	1.034 ± 0.006		1.432 ± 0.051	0.894 ± 0.009
PR_minimum	5.000	-3.500	1.034 ± 0.006		1.432 ± 0.051	0.894 ± 0.009

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						0-0.2 m
Sand	Silt	Clay	SD	Macro	Micro	TP	OM	PH	P	K	Ca	Mg	CEC
---- g kg^-1 ----			mg m^-3	---- m³ m^-3----			g dm^-3		mg dm^-3	--- mmol_c dm^-3---
745.58	138.214	117.143	1.268	0.169	0.378	0.547	22	5	49	0.7	18	3	46.7
						0.2-0.4 m
Sand	Silt	Clay	SD	Macro	Micro	TP	OM	PH	P	K	Ca	Mg	CEC
---- g kg^-1 ----			mg m^-3	--- m³ m^-3----			g dm^-3		mg dm^-3	--- mmol_c dm^-3---
737.772	141.7	120.629	1.291	0.16	0.372	0.532	19	4.7	47	0.5	17	3	45.6