Surface fractal characteristics of preferential flow patterns in field soils: evaluation and effect of image processing

In the last few decades, preferential flow has become recognized as a proce ss of great practical significance for the transport of water and contamina nts in field soils. Dyes are frequently used to visualize preferential flow pathways, and fractal geometry is increasingly applied to the characteriza tion of these pathways via image analysis, leading to the determination of 'mass' and 'surface' fractal dimensions. Recent work by the authors has sho wn the first of these dimensions to be strongly dependent on operator choic es (related to image resolution, thresholding algorithm, and fractal dimens ion definition), and to tend asymptotically to 2.0 for decreasing pixel siz e. 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-count ing, information, and correlation dimensions of the stain pattern are evalu ated via non-linear regression, they vary anywhere between 1.31 and 1.64, d epending on choices made at different stages in the evaluation. Among the p arameters subject to choice, image resolution does not appear to exert a si gnificant influence on dimension estimates. A similar lack of dependency on image resolution is found in the case of a textbook surface fractal, the q uadratic von Koch island. These parallel observations suggest that the obse rved stain pattern exhibits characteristics similar to those of st surface fractal. The high statistical significance (R > 0.99) associated with each dimension estimate lends further credence to the fractality of the stain pa ttern. However, when proper attention is given to the fact that the theoret ical definition of the surface 'fractal' dimension, in any one of its embod iments, involves the passage to a limit, the fractal character of the stain pattern appears more doubtful. Depending on the relative weight given to t he available pieces of evidence, one may conclude that the stain pattern is or is net a surface fractal. However, this conundrum may or may not have p ractical significance. Indeed, whether or not the stain pattern is a surfac e fractal, the avenging method proposed in the present article to calculate surface dimensions yields relatively robust estimates, in the sense that t hey are independent of image resolution. These dimensions, even if they are not 'fractal', may eventually play an important role in future dynamical t heories of preferential flow in field soils. (C) 1999 Elsevier Science B.V. All rights reserved.