The Fractal Characteristics of Drainage Networks and Erosion Evolution Stages of Ten Kongduis in the Upper Reaches of the Yellow River, China

  • 1. Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101,China;
    2. University of Chinese Academy of Sciences, Beijing 100049, China

Received date: 2017-01-19

  Online published: 2017-03-28

Supported by

National Natural Science Foundation of China (41371036).


The fractal characteristics of drainage in the ten kongduis of the upper Yellow River were obtained using the box counting dimension, and the evolution stages of the watershed topography were defined by different ranges of the fractal dimensions of river networks (Dg). The results show that the fractal scaleless range of the Maobula River is 20–370 m based on a combination of artificial judgment, correlation coefficient test and fitting error. Other kongduis show good fractal characteristics in this fractal scaleless range as well. The box counting dimension can be used as a quantitative index of watershed topography fractal characteristics. The fractal dimension of stream networks is independent of the threshold contributing area used for extracting the drainage networks from the DEM. The values of Dg in the upper ten kongduis are in the range of 1.08?1.14. Both the runoff yield and the sediment yield are positively and linearly related with Dg. The positive relation between the sediment yield and Dg reflects the effect of landform features on sediment yield in the young and/or mature stages of landform evolution of the study area. By revising the critical value of Dg, the value of Dg of the basin in the young evolution stage is less than 1.06, while it is more than 1.06 for the basin in mature or old evolution stage. The upper ten kongduis are in the mature stage of landform evolution.

Cite this article

YANG Hui, SHI Changxing . The Fractal Characteristics of Drainage Networks and Erosion Evolution Stages of Ten Kongduis in the Upper Reaches of the Yellow River, China[J]. Journal of Resources and Ecology, 2017 , 8(2) : 165 -173 . DOI: 10.5814/j.issn.1674-764x.2017.02.007


[1] Ariza-Villaverde A B, Jiménez-Hornero F J, Gutiérrez de Ravé E. 2013. Multifractal analysis applied to the study of the accuracy of DEM-based stream derivation. Geomorphology, 197: 85–95.
[2] Barbera L, Rosso R. 1989. On the fractal dimension of stream networks. Water Resources Research, 25(4): 735–741.
[3] Barreiro-Lostres F, Moreno A, González-Sampériz P, et al. 2016. Erosion in Mediterranean mountain landscapes during the last millennium: a quantitative approach based on lake sediment sequences (Iberian Range, Spain). Catena, 28(24): 1–17.
[4] Beer T, Borgas M. 1993. Horton's laws and the fractal nature of streams. Water Resources Research, 29(5): 1475–1487.
[5] Cámara J, Gómez-Miguel V, Martín M A. 2016. Identification of bedrock lithology using fractal dimensions of drainage networks extracted from medium resolution LiDAR digital terrain models. Pure and Applied Geophysics, 173(3): 945–961.
[6] Claps P, Oliveto G. 1994. Fractal structure, entropy and energy dissipation in river networks. Journal of Hydrology, 17(3/4): 38–51.
[7] Claps P, Oliveto G. 1996. Reexamining the determination of the fractal dimension of river networks. Water Resources Research, 32(10): 3123– 3135.
[8] Cui L Z, Li Z B, Guo Y B. 2004. Fractal-information-dimension-based relationship between sediment yield and topographic feature of watershed. Acta Pedologica Sinica, 18(2): 41–44. (in Chinese)
[9] Davis W M. 1899. The geographical cycle. The Geographical Journal, 14(5): 41–58.
[10] De Bartolo S G, Gabriele S, Gaudio R. 2000. Multifractal analysis of river networks. Hydrology and Earth System Sciences, 4(1): 105–112.
[11] De Bartolo S G, Veltri M, Primavera L. 2006. Estimated generalized dimensions of river networks. Journal of Hydrology. 322(1-4): 181–191.
[12] Feng J L, Zhang W. 1999. River network fractal of the Haihe and Luanhe river drainage basin. Journal of Sediment Research, 1999(1): 62–65. (in Chinese)
[13] Jin D S, Chen H, Guo Q W. 2000. An experimental study on influence of material component to non-linear relation between sediment yield and drainage network development. Acta Geographica Sinica, 55(4): 439–448. (in Chinese)
[14] He L H, Zhao H. 1996. The fractal dimension of river networks and its interpretation. Scientia Geographica Sinica, 16(2): 124–128. (in Chinese)
[15] Lashermes B, Foufoula-Georgiou, E. 2007. Area and width functions of river networks: New results on multifractal properties. Water Resources Research, 43(9): 405–423.
[16] Li M, Zhu L R. 2002. Fractal characteristics of topographic isoline and dynamic interpretation. Northwest Seismological Journal, 24(2): 97–103. (in Chinese)
[17] Liu R X. 2013. Analysis of water and soil conservation in the ten kongduis of the Jin-Shan-Meng soft sandstone area. Inner Mongolia Water Resources, 2013(6): 68–69. (in Chinese)
[18] Liu T. 1992. Fractal structure and properties of stream networks. Water Resources Research, 28(11): 2981–2988.
[19] Lin X Z, Guo Y, Hou S Z. 2014. Estimation of sediment discharge of ten tributaries of Yellow River in Inner Mongolia. Journal of Sediment Research, 2014(2): 15–20. (in Chinese)
[20] Lu A F, Chen X, Wang G S. 2002. Study on calculation methods of watershed fractal dimension based on DEM. Arid Land Geography, 25(4): 345–320. (in Chinese)
[21] Mandelbrot B B. 1967. How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science, 155(3775): 636–638.
[22] Mandelbrot B B. 1983. The Fractal Geometry of Nature. New York: W H Freeman and Company. 495.
[23] Martinez-Casasnovas J A. 2003. A spatial information technology approach for the mapping and quantification of gully erosion. Catena, 50(2-4): 293– 308.
[24] Moussa R, Bocquillon C. 1996. Fractal analyses of tree-like channel networks from digital elevation model data. Journal of Hydrology, 187(1-2): 157–172.
[25] Norton D, Sorenson S. 1989. Geometric characteristics of fractured granite surface. Pure Applied and Geophysics, 131(1): 107–116.
[26] Pan B T, Pang H L, Zhang D, et al. 2015. Sediment grain-size characteristics and its source implication in the Ningxia-Inner Mongolia sections on the upper reaches of the Yellow River. Geomorphology, 246: 255– 262.
[27] Peckham S D. 1995. New results for self-similar trees with applications to river networks. Water Resources Research, 31(4): 1023–1029.
[28] Rinaldo A, Rodriguez-Iturbe I, Rigon R, et al. 1993. Self-organized fractal river network. Physical Review Letters, 70(6): 822–826.
[29] Sayles R S, Thomas T R. 1978. Topography of random surfaces. Nature, 273(5663): 573.
[30] Strahler A N. 1952. Hysomotric analysis of erosional topography. Geological Society of America Bulletin, 63: 25–34.
[31] Scheidegger A E. 1979. The principle of antagonism in the earth’s evolution. Tectonophysics, 55(3): 7–10.
[32] Tarboton D G. 1996. Fractal river networks, Horton’s laws and Tokunaga cyclicity. Journal of Hydrology, 187(3): 105–117.
[33] Tarboton D G, Bras R L, Rodriguez-Iturbe I. 1989. The Analysis of River Basins and Channel Networks Using Digital Terrain Data. Ralph M. Parsons Laboratory, Massachusetts Institute of Technology.
[34] Wang B, Tian F Q, Hu H P. 2009. Relationship between fractal dimension of river networks and their climates. Journal of Tinghua University (Science &Technology), 49(12): 1948–1953. (in Chinese)
[35] Wang F Q, Cao S Y, Ding J. 2002. Fractal self-organization and its physical mechanism of river networks. Advances in Water Science, 13(3): 368 – 376. (in Chinese)
[36] Wang X C, Wu S, Bi X L, et al. 2004. Fractal dimensions of Jinghe river channels and ecological significance. Journal of Beijing Normal University (Natural Science), 40(3): 364–368. (in Chinese)
[37] Willgoose G, Hancock G. 1998. Revisiting the hypsometric curve as an indicator of form and process in transport limited catchments. Earth Surface Processes and Landforms, 23(7): 611–623.
[38] Wu Z C. 2002. Determination of fractal scaleless range. Acta Geodaetica Et Cartographica Sinica, 31(3): 240–244. (in Chinese)
[39] Xin Z B, Xu J X, Ma Y X. 2008. Hypsometric integral analysis and its sediment yield implications in the Loess Plateau, China. Journal of Mountain Science, 26(3): 356–363. (in Chinese)
[40] Zhang J X, Ma X Y, Zhao W J. 2008. Analysis on fractal characteristics of river networks of key watersheds in the Loess Plateau. Journal of Sediment Research, 2008(5): 9–14. (in Chinese)
[41]Zhu S J, Tang G A, Li F Y, et al. 2013. Spatial variation of hypsometric integral in the Loess Plateau based on DEM. Acta Geographica Sinica, 68(7): 921–932. (in Chinese)