[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) |