A fractal and entropy-based model for selecting the optimum spatial scale of soil erosion

  • Lemeng Ren
  • Jiejun Huang
  • Qiuping Huang
  • Guangdi Lei
  • Wei Cui
  • Yanbin Yuan
  • Youjia Liang
Original Paper


Soil erosion is an important issue of global climate change, which directly relates to the ecological environment quality and social sustainable development. Scale dependence is an intrinsic property of geographical phenomena and processes; therefore, it is scientifically significant to select an appropriate research scale for studying the driving mechanism and the ecological environment effect of soil erosion. The optimum scale selection model based on fractal and entropy theory was built in this paper. The model firstly used the entropy index from gray level co-occurrence matrix to evaluate the data redundancy, and adopted the similarity of Area-Weighed Mean Patch Fractal Dimension (AWMFD) to assess the expression ability of geographical intrinsic features. Then the correlation between each index and scale was computed, and finally the ratio of the correlation to their summation was taken as weight to calculate the weighted summation. In this paper, Danjiangkou reservoir area was taken as the case study. The results of the experiment show that the optimum scale for studying soil erosion in Danjiangkou reservoir area is 90 m, which means under this scale the optimum balance between data redundancy and the expression ability of intrinsic features is approached. Scalograms of landscape metrics were used to verify the rationality and feasibility of the optimum scale selection model.


Soil erosion Scale effect Optimum scale Entropy Fractal 



This work was supported by the National Natural Science Foundation of China (No. 41571514, 41601184) and the Wuhan Science and Technology Plan Program under Grant 2016010101010023.

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Saudi Society for Geosciences 2018

Authors and Affiliations

  • Lemeng Ren
    • 1
  • Jiejun Huang
    • 1
  • Qiuping Huang
    • 1
  • Guangdi Lei
    • 2
  • Wei Cui
    • 1
  • Yanbin Yuan
    • 1
  • Youjia Liang
    • 1
  1. 1.School of Resource and Environmental EngineeringWuhan University of TechnologyWuhanChina
  2. 2.School of Civil, Environmental and Mining EngineeringThe University of Western AustraliaPerthAustralia

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