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

摘要

An analysis was carried of the surface fractal dimension of a stained preferential flow pathway, observed in an orchard soil in New York, USA. The results indicate that when the box-counting, information, and correlation dimensions of the stain pattern are evaluated via non-linear regression, they vary 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 exert a significant influence on dimension estimates. A similar lack of dependency on image resolution was found in 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. However, when it is realised 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. Whether or not thestain 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.