Multifractal scaling of soil spatial variability

Caniego, F. J.; Espejo, Rafael; Martı́n, Miguel Ángel; Fernando, José F.

doi:10.1016/j.ecolmodel.2004.04.014

Cited by 84 publications

(67 citation statements)

References 34 publications

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“…Attempts to explain such scale dependencies have focused in part on observed and/or hypothesized powerlaw behaviors of structure functions of variables such as hydraulic (or log hydraulic) conductivity (e.g. Painter, 1996;Liu and Molz, 1997a,b;Tennekoon et al, 2003), spacetime infiltration (Meng et al, 2006), soil properties (Caniego et al, 2005;Si, 2006, 2007), electrical resistance, natural gamma ray and spontaneous potential (Yang et al, 2009) and sediment transport data (Ganti et al, 2009). Power-law behavior means that a sample structure function ( 2) where Y (x) is the variable of interest (assumed to be defined on a continuum of points x in space or time), Y n (s) is a measured increment Y (s) = Y (x + s) − Y (x) of the variable over a separation distance (lag) s between two points on the x-axis, and N (s) is the number of measured increments.…”

Section: Introductionmentioning

confidence: 99%

Extended power-law scaling of air permeabilities measured on a block of tuff

Siena

Guadagnini

Riva

et al. 2012

Hydrol. Earth Syst. Sci.

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Abstract. We use three methods to identify power-law scaling of multi-scale log air permeability data collected by Tidwell and Wilson on the faces of a laboratory-scale block of Topopah Spring tuff: method of moments (M), Extended Self-Similarity (ESS) and a generalized version thereof (G-ESS). All three methods focus on q-th-order sample structure functions of absolute increments. Most such functions exhibit power-law scaling at best over a limited midrange of experimental separation scales, or lags, which are sometimes difficult to identify unambiguously by means of M. ESS and G-ESS extend this range in a way that renders power-law scaling easier to characterize. Our analysis confirms the superiority of ESS and G-ESS over M in identifying the scaling exponents, ξ(q), of corresponding structure functions of orders q, suggesting further that ESS is more reliable than G-ESS. The exponents vary in a nonlinear fashion with q as is typical of real or apparent multifractals. Our estimates of the Hurst scaling coefficient increase with support scale, implying a reduction in roughness (anti-persistence) of the log permeability field with measurement volume. The finding by Tidwell and Wilson that log permeabilities associated with all tip sizes can be characterized by stationary variogram models, coupled with our findings that log permeability increments associated with the smallest tip size are approximately Gaussian and those associated with all tip sizes scale show nonlinear variations in ξ(q) with q, are consistent with a view of these data as a sample from a truncated version (tfBm) of self-affine fractional Brownian motion (fBm). Since in theory the scaling exponents, ξ(q), of tfBm vary linearly with q we conclude that nonlinear scaling in our case is not an indication of multifractality but an artifact of sampling from tfBm. This allows us to explain theoretically how power-law scaling of our data, as well as of non-Gaussian heavy-tailed signals subordinated to tfBm, are extended by ESS. It further allows us to identify the functional form and estimate all parameters of the corresponding tfBm based on sample structure functions of first and second orders.

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Section: Introductionmentioning

confidence: 99%

Extended power-law scaling of air permeabilities measured on a block of tuff

Siena

Guadagnini

Riva

et al. 2012

Hydrol. Earth Syst. Sci.

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“…The same pattern has been observed in biodiversity studies for islands (MacArthur and Wilson 1967;May, 1975). Power law scalings of pedorichness-area relationships were first conjectured by Ibáñez and de Alba (2000) for earth soil systems and they have been reported for different soil classifications and geographical units (Ibáñez et al, 2005a;Caniego et al, 2005). They may be interpreted as indicators of the selfsimilarity of the pedorichness spatial distribution.…”

Section: Resultsmentioning

confidence: 99%

“…1 for q=2). The Berger-Parker index is introduced as a measure of dominance (Magurran, 1988) Following Pielou (1975) the ratio D 1 /D 0 can be interpreted as a measure of evenness in the context of multifractals (Caniego et al, 2003(Caniego et al, , 2006. The entropy dimension D 1 gauges the concentration degree of the distribution of abundances on the set supporting pedotaxa abundances whose geometrical size is characterized by D 0 .…”

Section: Diversity Indices Versus Rényi Dimensionsmentioning

confidence: 99%

Rényi dimensions and pedodiversity indices of the earth pedotaxa distribution

Caniego

Ibáñez

Martínez

2007

Nonlin. Processes Geophys.

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Abstract. Pedodiversity, the study and measurement of soil diversity, may be considered as a framework to analyze spatial patterns. Recently, selfsimilar multifractal patterns have been recently reported in the pedotaxa-abundance distributions at the planetary scale. This is the result to be expected from the complexity of earth soil systems. When the state of soil is understood as the outcome of nonlinear chaotic dynamic, highly irregular patterns with so-called multifractal behavior should be common. This opens the opportunity to use parameters of fractal theory to characterize pedodiversity. We compute Rényi generalized dimensions for the abundance distribution of pedotaxa for the five landmasses and the whole World drawn from the most detailed available global dataset based on the second level of the FAO 1974 classification units. We explore the effective relationship between diversity indices and Rényi dimensions. We show how multifractal analysis unifies diversity indices and how they should be interpreted offering a coherent perspective with a single mathematical procedure to analyze spatial patterns of the pedosphere.

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“…Numerous studies have documented scale invariance of soil and other porous earth materials over a broad range of scales (Oleschko et al, 2000;Caniego et al, 2005;Tarquis et al, Correspondence to: K. Oleschko (olechko@servidor.unam.mx) 2006; Meng et al, 2006;Di Domenico et al, 2006;Jawson and Niemann, 2007). Self-similarity, a most striking property of isotropic fractals, means that each piece of a shape is geometrically similar to the whole (Mandelbrot, 1983).…”

Section: Introductionmentioning

confidence: 99%

Mapping soil fractal dimension in agricultural fields with GPR

Oleschko¹,

Korvin

Muñoz³

et al. 2008

Nonlin. Processes Geophys.

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Abstract. We documented that the mapping of the fractal dimension of the backscattered Ground Penetrating Radar traces (Fractal Dimension Mapping, FDM) accomplished over heterogeneous agricultural fields gives statistically sound combined information about the spatial distribution of Andosol' dielectric permittivity, volumetric and gravimetric water content, bulk density, and mechanical resistance under seven different management systems. The roughness of the recorded traces was measured in terms of a single number H , the Hurst exponent, which integrates the competitive effects of volumetric water content, pore topology and mechanical resistance in space and time. We showed the suitability to combine the GPR traces fractal analysis with routine geostatistics (kriging) in order to map the spatial variation of soil properties by nondestructive techniques and to quantify precisely the differences under contrasting tillage systems. Three experimental plots with zero tillage and 33, 66 and 100% of crop residues imprinted the highest roughness to GPR wiggle traces (mean H R/S =0.15), significantly different to Andosol under conventional tillage (H R/S =0.47).

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Multifractal scaling of soil spatial variability

Cited by 84 publications

References 34 publications

Extended power-law scaling of air permeabilities measured on a block of tuff

Extended power-law scaling of air permeabilities measured on a block of tuff

Rényi dimensions and pedodiversity indices of the earth pedotaxa distribution

Mapping soil fractal dimension in agricultural fields with GPR

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