ABSTRACTS

Preferential flow in water-repellent sands
TWJ Bauters, DA DiCarlo, TS Steenhuis and J-Y Parlange

Water-repellent soils occur all over the world and affect both groundwater pollution and crop yield. The finger-like wetting patterns in these soils have many similarities with unstable wetting fronts in coarse-grained sandy soils. Our objectives were to study the water movement in water-repellent sand and to examine how the theory for unstable wetting fronts applies to water-repellent sands. Infiltration experiments, in which moisture content and matric potentials were measured, were carried out in slab chambers with identical sands but with different levels of water repellence. Soil water characteristics were determined in separate experiments. Infiltration in the hydrophilic soil resulted in a uniform and horizontal front. All water-repellent sands showed a fingered flow pattern. For negative water-entry values, water infiltrated without delay. For positive values, water entered the soil only after the depth of the ponded water equaled or exceeded the water-entry pressure, which increased with increasing repellency. The finger widths predicted with the unstable flow theory agreed rather well with the observed values. In general, the research showed that the wetting patterns of water-repellent sands depended directly on the soil water characteristic curve. This implies that the type of wetting front and risk to groundwater pollution can be predicted based on laboratory-measured soil hydraulic properties.

Influence of image resolution and thresholding on the apparent mass fractal characteristics of preferential flow patterns in field soils
Baveye P, Boast CW, Ogawa S, Parlange JY, Steenhuis T

Preferential flow is ubiquitous in field soils, where it has important practical implications for water and contaminant transport. Dyes are frequently used to visualize preferential flow pathways. The fact that stain patterns in pictures of soil profiles often exhibit convoluted geometries, reminiscent of fractals, has encouraged a number of authors to use the principles of fractal geometry to describe stain patterns. This description typically involves two numbers, a mass and a surface fractal dimension. The evaluation of either one via image analysis requires numerous subjective choices to be made, including choices regarding image resolution, the definition adopted for the "fractal" dimension, and the thresholding algorithm used to generate binary images. The present article analyzes in detail the influence of these various choices on the mass fractal dimension of stained preferential flow patterns. A theoretical framework in which to envisage these choices is developed, using the classical quadratic von Koch island as an example. This framework is then applied to a set of pictures of an actual stain pattern in an orchard soil. The results suggest that the (apparent) mass fractal dimension of the stain pattern varies between 1.56 and 1.88, depending on choices made at different stages in the evaluation of the fractal dimension. In each case considered, the dimension, determined by a straight line fit in a log-log plot, has extremely high statistical significance, with R > 0.999. Of the various parameters subject to choice, image resolution seems to have the most pronounced influence on the value of the fractal dimension, which increases markedly at higher resolution (smaller-pixel size). By analogy with the case of the quadratic von Koch island, this dependence on image resolution, as well as the fact that the surface area of the stain pattern does not decrease with pixel size, suggests that the stain pattern is not a mass fractal; that is, there is no reason to believe that its various dimensions differ from 2. The approach adopted in the present article could be useful whenever fractal dimensions are evaluated via image analysis.

Lateral expansion of preferential flow paths in sands
DiCarlo DA, Bauters TWJ, Darnault CJG, Steenhuis TS, Parlange JY

The stability and persistence of preferential flow paths in sands can determine the flow paths of subsequent infiltration events. We have measured the evolution of preferential flow paths in a slab of sandy soil using an array of tensiometers and light transmission. The pressure and water content measurements show that the nonuniform moisture content exists even when the potentials are equalized horizontally and that then are the result of hysteresis in the soil's pressure-saturation relationship. The equalization of potential takes place over several days, if at all, and is consistent, initially, with estimates of vapor transport out of the finger cores. Once the soil is wet enough, the remainder of water movement takes place in liquid films. Hysteresis produces another interesting situation when the pack is drained. We find that the wetter portions of the soil can be at a lower potential than the drier portions, resulting in a horizontal driving force for a flow of water from the drier to the wetter soil.

IMMISCIBLE DISPLACEMENT IN POROUS-MEDIA - STABILITY ANALYSIS OF 3-DIMENSIONAL, AXISYMMETRICAL DISTURBANCES WITH APPLICATION TO GRAVITY-DRIVEN WETTING FRONT INSTABILITY
GLASS RJ, PARLANGE JY, STEENHUIS TS

As water infiltrates downward into an air-filled, water wettable porous medium, the wetting front which forms may become unstable and allow the formation of downward moving fingers within the vadose zone. In this paper we first review stability criteria and estimated finger widths determined from linear stability theory in two-dimensional systems. Two approaches reported in the literature which employ different formulations for the interfacial boundary conditions, yield different estimates of the finger width. We extend the analyses to investigate finger diameter in three-dimensional systems by considering axisymmetric disturbances. Results of the three-dimensional analyses are illustrated through comparison to previously reported experimental results in three-dimensional systems. Because either approach gives similar results for low system fluxes, in practice, it probably will not matter which formulation is used. However, one approach represents the data better and contains only traditionally measured porous media properties.

Surface fractal characteristics of preferential flow patterns in field soils: evaluation and effect of image processing
Susumu Ogawa a, Philippe Baveye, Charles W. Boast, Jean-Yves Parlange, Tammo Steenhuis

In the last few decades, preferential flow has become recognized as a process of great practical significance for the transport of water and contaminants in field soils. Dyes are frequently used to visualize preferential flow pathways, and fractal geometry is increasingly applied to the characterization of these pathways via image analysis, leading to the determination of 'mass' and 'surface' fractal dimensions. Recent work by the authors has shown the first of these dimensions to be strongly dependent on operator choices related to image resolution, thresholding algorithm, and fractal dimension definition , and to tend asymptotically to 2.0 for decreasing pixel size. A similar analysis is carried out in the present article in the case of the surface fractal dimension of the same stained preferential flow pathway, observed in an orchard soil. The results indicate that when the box-counting, information, and correlation dimensions of the stain pattern are evaluated via non-linear regression, they vary anywhere between 1.31 and 1.64, depending on choices made at different stages in the evaluation. Among the parameters subject to choice, image resolution does not appear to exert a significant influence on dimension estimates. A similar lack of dependency on image resolution is found in the case of a textbook surface fractal, the quadratic von Koch island. These parallel observations suggest that the observed stain pattern exhibits characteristics similar to those of a surface fractal. The high statistical significance R)0.99 associated with each dimension estimate lends further credence to the fractality of the stain pattern. However, when proper attention is given to the fact that the theoretical definition of the surface 'fractal' dimension, in any one of its embodiments, involves the passage to a limit, the fractal character of the stain pattern appears more doubtful. Depending on the relative weight given to the available pieces of evidence, one may conclude that the stain pattern is or is not a surface fractal. However, this conundrum may or may not have practical significance. Indeed, whether or not the stain pattern is a surface fractal, the averaging method proposed in the present article to calculate surface dimensions yields relatively robust estimates, in the sense that they are independent of image resolution. These dimensions, even if they are not 'fractal', may eventually play an important role in future dynamical theories of preferential flow in field soils.

A SOIL-WATER HYSTERESIS MODEL FOR FINGERED FLOW DATA
LIU YP, PARLANGE JY, STEENHUIS TS, HAVERKAMP R

Wetting and drying boundaries of a hysteresis loop were measured for fingered flow in a uniform sand, as well as drying scanning curves within the loop. The data are described by a soil water hysteresis model that uses a Brooks and Corey (1964) type main wetting boundary curve to predict the boundaries and scanning curves. The model requires as input parameters the bulk density, matric potential, water content at the two intersection points between the wetting and drying boundary curves, and one parameter obtained by curve fitting. The analysis is used to explain a fingered flow pattern in an uniform sand with different initial moisture contents.