Daniel Giménez

Fractal dimensions for volume and surface of interaggregate pores — scale effects

Geometrical attributes of pore systems in soil have shown fractal scaling. Scaling in natural materials is inherently statistical, i.e., fractal dimensions may change with scale. While fractal dimensions characterizing pore surface roughness, Ds, or scaling of pore sizes, Dv, have been reported, seldom are both measurements made at more than one scale. We examine a scale effect on Dv and Ds values, and relationships between fractal dimensions of both properties. Natural and artificial types of soil structure were studied in a Normania soil. Natural soil structure was sampled from experiments involving: (l) three primary tillage tools, sampled immediately after tillage; and (2) three tillage systems, sampled after consolidation. Artificial soil structure was formed in columns packed with aggregate assemblies that included two single aggregate-size fractions, and two mixtures of six aggregate-size fractions (each covering two ranges) made to obtain fractal aggregate-size distributions. Block-like samples from all sources were resin-impregnated in situ and a face was cut and polished. Images of UV-illuminated faces were obtained at three magnifications and then pooled into two groups. A box-counting technique was applied to area and outline of pores to obtain Dv-box, and Ds-box, respectively; Ds was also calculated from area-perimeter relations (Ds-AP). Box-count data showed two segments; Dv-box and Ds-box were evaluated in relation to each segment and to Ds-AP. Coefficients of determination in the relation Ds-AP vs Ds-box were relatively low, indicating discrepancies between the two methods. Fractal dimensions were not scale-invariant. Values of Ds-box for aggregate assemblies decreased with resolution, especially for single aggregate-size fractions. Values of Dv-box were more influenced by aggregate size than resolution. Both Ds-box and Dv-box varied with resolution for freshly tilled soil. For somewhat consolidated soil, variations in values of both fractal dimensions were related to tillage systems. Values of Ds-box and Dv-box were highly correlated, with linear relations depending on magnification and type of soil structure.

Scaling properties of saturated hydraulic conductivity in soil

Abstract Variability of saturated hydraulic conductivity, k sat , increases when sample size decreases implying that saturated water flow might be a scaling process. The moments of scaling distributions observed at different resolutions can be related by a power-law function, with the exponent being a single value (simple scaling) or a function (mutiscaling). Our objective was to investigate scaling characteristics of k sat using the method of the moments applied to measurements obtained with different sample sizes. We analyzed three data sets of k sat measured in: (1) cores with small diameter and increasing length spanning a single soil horizon, (2) columns with increasing cross sectional area and constant length, and (3) columns with increasing cross sectional area and length, the longest column spanning three soil horizons. Visible porosity (macroporosity) was traced on acetate transparency sheets prior to measurement of k sat in situation (2). Six moments were calculated assuming that observations followed normal ( k sat , macroporosity) and/or log-normal ( k sat ) distributions. Scaling of k sat was observed in all three data sets. Simple scaling was only found when flux occurred in small cross sectional areas of a simple soil horizon (data set (1)). Multiscaling of k sat distributions was found when larger soil volumes were involved in the flux process (data sets (2) and (3)). Moments of macroporosity distributions showed multiscaling characteristics, with exponents similar to those from ln k sat distributions. The scaling characteristics of k sat reported in this paper agree with similar results found at larger scales using semivariograms. Scaling exponents from the semivariogram and the moment techniques could be complemented, as demonstrated by the agreement between macroporosity scaling exponents found with both techniques.

Mass, surface, and fragmentation fractal dimensions of soil fragments produced by tillage

Structural units in freshly tilled soil are mainly fragments derived from tillage. Fractal geometry is potentially useful to model this structure. This research was designed to test the applicability of fractal models for mass– and number–size distributions, and surface roughness of soil fragments produced by tillage; and evaluate relationships among parameters of these fractal models. Fragments were sampled from the soil surface of three soil management experiments on a Normania clay loam: (1) moldboard, chisel, and disc as primary tillage tools, (2) three sequences of primary and secondary tillage, and (3) three crops followed by one tillage sequence. Air-dried samples were sieved to obtain eight fragment–size fractions with average diameters, xm, ranging from 0.4 to 28.0 mm. The size fraction with xm=0.4 mm had different patterns of fragmentation and mass distribution and was not used to estimate fractal parameters. Mass–size relations from size fractions and individual fragments did not show evidence of a fractal distribution of mass; but soil management influenced the estimated mass of fragments of unit diameter, km. Two-dimensional roughness of fragment surfaces measured on thin sections was fractal with dimensions, Ds, between 1.02 and 1.18. Disc tillage produced the highest Ds among primary tillage tools. Fragment number–size distributions were fractal with the fragmentation fractal dimension, Df, between 2.14 and 3.19, and sensitive to management effects. The number of fragments of unit diameter, kf, was inversely related to km, but relationships of Df–kf and Df–Ds were not consistent with present fragmentation fractal models. Parameters, Df and kf were valuable for characterizing freshly tilled soils. More research is needed to understand links between Df, kf, and the geometrical configuration of a tilled layer.

Fractal modeling of airborne laser altimetry data

Abstract Airborne laser altimetry is a remote sensing technique that can provide high resolution data on the roughness of the landscape both for estimating water balance components and for distinguishing between landscapes. Models of the scale-dependent roughness are needed to find scales most appropriate for these purposes. Our objectives were to apply fractal scaling to high-resolution profiling laser altimetry data and to determine fractal parameters for differentiating land cover. Data were collected at the USDA-ARS jornada Experimental Range in New Mexico over grass-dominated and shrub-dominated sites along four transects at each site. Scale-dependent root-meansquare (RMS) roughness and data power spectrums were computed from 100,000 data points (∼2 km) from each transect. A linearity measure and piecewise linear approximation were applied to find intervals of the fractal scaling. The RMS roughness data had two intervals of self-affine fractal scaling on grass transects and four such intervals on shrub transects. Reduction in the number of data points did not lead to a decrease in roughness but caused a smoothing dependency of fractal dimension on scale. Ten- and hundred-meter scales were appropriate for distinguishing between grass and shrub transects on the basis of fractal dimensions.

Estimation of spatial and spectral properties of phytophthora root rot and its effects on cranberry yield

Abstract Current agricultural practices are aimed at maximizing productivity while minimizing the area of cultivated land. This is especially important in cranberry production because strict federal guidelines curtail development of new cranberry acreage on wetlands. A major component of this research is focused on the chronic effects of phytophthora root rot (PRR) because of the difficulties in detection and the significant impact on yields. PRR causes a reduction in root mass, which results in reduced canopy biomass and alters the spectral reflectance characteristics of the canopy. Detection of acute cases of PRR using color-infrared (CIR) aerial photography is straightforward from apparent bare soil on May images; however, the level of detectable chronic infection is unknown. The objectives of this study are to investigate the relationships between soil characteristics, spectral properties of the crop surface, and the severity of Phytophthora effects on cranberries. Soil, pathogen, and crop data were entered in a GIS and the relationships among the factors were studied using geostatistical methods and surface maps of the relevant GIS layers. These maps were then compared and incorporated with the data derived from remotely sensed images (CIR aerial photographs—May, 2001 and July, 2001). The spatial pattern of stressed vegetation was fairly consistent through 5 years and corresponded to spread of PRR chronic injury and low yield. The disease develops in surface depressions with low infiltration rates, which have high soil water content during July–August. The results suggest that early-season (May) CIR images have more predictive power for the yield and vine density, whereas late-season (July) images are more correlated with PRR and soil infiltration rate.

Impact of roots on ground water quality

Preferential flow is perhaps the major chemical transport process influencing the rapid and typically unexpected movement of agricultural chemicals to ground water. Plant roots are a major contributor to preferential flow mechanics as they form spatial voids which can be used as preferential flow pathways. Chemical transport of atrazine, deethylatrazine, and bromide solutions concentrations under tilled and no-tilled corn fields was evaluated below the active root zone. Additionally, the impact of roots on flow pathways was visualized using a soluble dye (Brilliant Blue FCF). Pictures of the dye-stained pattern were subsequently digitized to determine the cross-sectional area used for transport as a function of depth. Bromide transit times through the field soils were not influenced by tillage practice, whereas atrazine transport was strongly influenced by tillage practice. Under no-till field conditions, atrazine was rarely detected but deethylatrazine concentrations were greater than those observed under tilled field conditions. Visual observation indicated that the dye under no-tillage was more predominant in the corn row, indicative of transport through void root channels. No-tillage practices may decrease the likelihood of ground water contamination through leaching due to the formation of stable root channels where an organic carbon source and microbial population are preferentially located to degrade pesticides.

Sorption of acetochlor, S‐metolachlor, and atrazine in surface and subsurface soil horizons of Argentina

Understanding herbicide sorption within soil profiles is the first step to predicting their behavior and leaching potential. Laboratory studies were conducted to determine the influence of surface and subsurface soil properties on acetochlor, atrazine, and S-metolachlor sorption. Soil samples were taken from horizons A, B, and C of two loamy soils of the humid pampas of Argentina under no-till management; horizon A was divided into two layers, A(0) (0-5 cm) and A(1) (5 cm to the full thickness of an A horizon). Sorption isotherms were determined from each sampled horizon using the batch equilibrium method and seven concentrations (0, 0.1, 0.5, 2.0, 5.0, 10.0, and 20.0 mg L(-1)). Sorption affinity of herbicides was approximated by the Freundlich equation. The sorption strength K(f) (mg(1 - 1/n) kg(-1) L(1/n) ) over the soils and horizons studied followed the order S-metolachlor (16.51-29.19) > atrazine (4.85-12.34) ≥ acetochlor (5.17-11.97), which was closely related to the hydrophobicity of herbicides expressed as octanol-water partition coefficient (K(OW) ). The K(f) values of the three herbicides were positively correlated with soil organic carbon, with a significance of p < 0.01. Values of K(f) for the three herbicides decreased with depth in the two soils, indicating greater sorption onto surficial soil horizons and possibly a delayed transport toward subsurface soils and subsequent pollution of groundwater.

Transport of Atrazine and Metribuzin in Three Soils of the Humid Pampas of Argentina1

Widespread groundwater contamination has prompted studies on the fate and transport of solute through soil. Large quantities of atrazine and metribuzin are applied annually in the Humid Pampas of Argentina, creating the need to study the fate of these herbicides in soils of the region. The objective of this work was to study the vertical transport of atrazine and metribuzin in packed soil columns for three loam soils representative of the Humid Pampas of Argentina. Bromide was used as a nonreactive tracer. The convection dispersion equation was fitted to chemical breakthrough data to obtain a parameter characterizing chemical transport. Bromide breakthrough curves (BTCs) were similar among soils. BTCs for atrazine and metribuzin revealed significant interaction among soils and herbicides. The average values for the organic carbon (OC) partition coefficients (Koc) derived from column flow experiments were 119 and 48 ml/g for atrazine and metribuzin, respectively. Metribuzin in leachate was 97.3% of the total recovered, whereas atrazine was 3.5%. This behavior can be explained by their different affinities to OC. The OC contents of the Balcarce, Necochea, and Nueve de Julio soils were 4.1, 3.4, and 1.9%, respectively. The lowest leaching values of herbicides were found in the Balcarce soil, suggesting that OC content was the main factor in controlling herbicide transport in these soils. Nomenclature: Atrazine; bromide; metribuzin. Additional index words: GC/MS, groundwater contamination, herbicide transport, soil columns. Abbreviations: BTC, breakthrough curve; CDE, convection dispersion equation; OC, organic carbon; PV, pore volume; PVC, polyvinyl chloride.

Fractal dimensions of mass estimated from intact and eroded soil aggregates

Scaling of mass within soil aggregates is characterized with a power-law model relating mass, M, and radius, r, of aggregates. When distribution of mass is fractal, the constants of the power-law model are the fractal dimension of mass, Dm, with a value 1 cm and r 1Þ of the Gladstone and Holmdel soils. For the wooded Gladstone and Holmdel soils, mass scaling of intact and eroded aggregates was statistically characterized by the same values of Dm and km, suggesting a concentric arrangement of mass, but only within aggregates that are not subjected to tillage. The km values of intact and eroded aggregates were correlated ðR ¼ 0:97Þ to aggregate bulk density of intact aggregates. Typically, small aggregates ðr < 1c mÞ, aggregates from wooded sites, and intact aggregates had larger values of lacunarity than their corresponding counterparts. This study indicates that fractal scaling of mass cannot be assumed for all soils, but it can be maintained in cultivated soils despite changes in mass scaling introduced by tillage. # 2002 Elsevier Science B.V. All rights reserved.

Prediction of A pore distribution factor from soil textural and mechanical parameters

Soil-water retention properties (WRC) are required for modeling purposes, but data availability is restricted by the high cost of measurements. Prediction of WRC from particle size distribution (PSD) is a useful approach that could be improved by accounting for soil structure. Mechanical parameters can characterize soil structure in situ. Our objective was to use mechanical and PSD parameters to estimate a pore distribution factor, λ, from a power-law model of WRC. Samples for WRC and PSD determinations were taken in pre-wetted horizons after characterization of soil structure with multiple measurements of a single-vane shear test (SB) and penetration resistance (PR). Mechanical parameters were the mean, M, and standard deviation, σ, of SB and PR. Parameters characterizing a PSD were the power exponent of a cumulative exponential function, β; the geometric mean, μ(r) = eμln(r) and standard deviation, σln(r), of a log-normal distribution; and clay content. Models of λ were built with the Group Method of Data Handling (GMDH) first using textural and mechanical parameters separately and then using each textural variable with all mechanical parameters. Both μ(r) and σln(r) were consistently selected as the best textural estimators of λ. The best mechanical estimators were log(MSB) and σSB. In models that included textural and mechanical parameters, σPR was selected consistently regardless of the textural parameter used. Textural parameters were better predictors than mechanical parameters, even though the latter alone provided a reasonable estimate of λ. Mechanical parameters improved textural estimates of λ only when clay content was used to characterize a PSD.