Fractal Analysis of Surface Microtopography and its Application in Understanding Hydrologic Processes

Abstract

Fractal analysis provides a useful way to characterize the spatial complexity of surface microtopography. In this study, six random roughness soil surfaces and two field plot surfaces were created. Anisotropic properties of these surfaces were examined by using the directional semivariogram method and a modified anisotropy index (a). Multifractal analysis was performed to identify the dissimilar changing patterns of fractal dimension (D) and crossover length (l) for these surfaces at different scales. It has been found that D and l at smaller scales describe topographic surfaces in more detail, while the overall topographic features of the surfaces can be captured by D and l at larger scales. Surface slope removal has a considerable effect on the fractal calculation using the semivariogram method. This study also demonstrates that fractal parameters D and l have clear and meaningful relationships with some hydrotopographic parameters, such as random roughness (RR), maximum depression storage (MDS), and number of connected areas (NCA). More importantly, fractal and anisotropic analyses enable better understanding of the overland flow generation process. A surface with a small D value has the potential to retain more water in its depressions, which in turn redistributes surface runoff water, enhances infiltration in depressions, and delays surface runoff initiation. The dominant roughness exists along the directions of smaller D values. Along those directions, surface runoff is prone to be hindered or blocked by ridges, while better hydrologic connections occur along other directions.