Description of soil micro-topography and fractional wetted area under runoff using fractal dimensions

María García-Serrana, John S. Gulliver, John L. Nieber

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Understanding the connections between the micro-topography of a surface and the patterns of shallow overland flow is important to the study of runoff and infiltration processes. In slopes with micro-topographic features parallel to the flow, water tends to concentrate in channels and only a fraction of the slope contributes to the overland flow. This study aimed to formulate the relevance of the fractal approach for understanding the relation of surface roughness to overland flow patterns. Laboratory experiments of simulated runoff over a bare soil slope were used to test the efficacy of two fractal parameters (fractal dimension [FD] and vertical intercept [VIC] from the Fourier power spectrum method) to describe how main surface micro-topographic features can influence runoff, infiltration and erosion processes. The fractal parameters behaved differently for the distinctive initial surface treatments (smooth, three rills, and five rills). The anisotropy of the surface was evident based on the change of the fractal parameters with direction. The rose plots of the fractal parameters provided important information about the magnitude of the concentrated flow erosion of a surface and its main direction; in the direction perpendicular to the rills, the FD values were lower and the VIC greater. The minimum FD decreased and the maximum VIC increased with runoff time. A linear relationship between the infiltration depth and the percentage of wetted area was observed. Furthermore, a relationship between the fraction of wetted area and the fractal parameters has been developed, indicating that vertical variations (VIC) in roughness had more impact on fraction of wetted area than horizontal variations (FD) of the surface. Finally, a decrease in the minimum FD and an increase in the maximum VIC were related to greater scour volumes. The scour volume of an initially smooth surface seems to be well-represented by a power relationship with the maximum VIC. By defining indicators of rill erosion and associating them with flow patterns through these fractal parameters, a better description of shallow overland flow can be achieved.

Original languageEnglish (US)
Pages (from-to)2685-2697
Number of pages13
JournalEarth Surface Processes and Landforms
Issue number13
StatePublished - Oct 2018

Bibliographical note

Funding Information:
Acknowledgements—The writers are grateful to the Minnesota Department of Transportation and Minnesota Local Road Research Board for funding this research under Contract No. 99008-97, with Barbara Loida as Technical Liaison. J.L. Nieber’s effort on this project was partially supported by the USDA National Institute of Food and Agriculture, Hatch/Multistate project 12-059.


  • erosion, micro-topography
  • fractal dimensions
  • fractional wetted area
  • infiltration
  • overland flow

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