IJG  Vol.4 No.3 , May 2013
Studying Relationships between the Fractal Dimension of the Drainage Basins and Some of Their Geomorphological Characteristics
ABSTRACT

Complex nonlinear dynamic systems are ubiquitous in the landscapes and phenomena studied by earth sciences in general and by geomorphology in particular. Many natural landscape features have an aspect such as fractals. In the many geomorphologic phenomena such as river networks and coast lines this is visible. In recent years fractal geometry offers as an option for modeling river geometry and physical processes of rivers. The fractal dimension is a statistical quantity that indicates how a fractal scales with the shrink, the space occupied. This theory has the mathematical basis but also applied in geomorphology and also shown great success. Physical behavior of many natural processes as well as using fractal geometry is predictable relations. Behavior of complex natural phenomena as rivers has always been of interest to researchers. In this study using data basic maps, drainage networks map and Digital Elevation Model of the ground was prepared. Then applying the rules Horton-Strahler river network, fractal dimensions were calculated to examine the relationship between fractal dimension and some rivers geomorphic features were investigated. Results showed fractal dimension of watersheds have meaningful relations with factors such as shape form, area, bifurcation ratio and length ratio in the watersheds.


Cite this paper
Z. Khanbabaei, A. Karam and G. Rostamizad, "Studying Relationships between the Fractal Dimension of the Drainage Basins and Some of Their Geomorphological Characteristics," International Journal of Geosciences, Vol. 4 No. 3, 2013, pp. 636-642. doi: 10.4236/ijg.2013.43058.
References
[1]   B. B. Mandelbrot, “How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension,” Science, New Series, Vol. 156, No. 3775, 1967, pp. 636-638.

[2]   M. F. Barensley, “Fractals Everywhere,” Academic Press Professional, New York, 1993.

[3]   G. Cherbit, “Fractals-Non-In Integral Dimensions and Applacation,” Masson, Paris, 1993.

[4]   R. J. Huggett, “Dissipative System: Implications for Geomorphology,” Earth Surface Processes and Landforms, Vol. 13, No. 1, 1988, pp. 45-49.

[5]   G. P. Malanson, D. R. Butler and S. J. Walsh, “Chaos Theory in Physical Geography,” Physical Geography, Vol. 11, No. 4, 1990, pp. 293-304.

[6]   J. D. Phillips, “Earth Surface Systems: Complexity, Order and Scale,” Blackwell, Oxford, 1992.

[7]   I. Rodriguez and A. Rinaldo, “Fractal River Basins (Chance and Self-Organization),” Cambridge University Press, Cambridge, 1997.

[8]   J. D. Phillips, “Earth Surface Systems: Complexity, Order and Scale,” Blackwell, Oxford, 1999.

[9]   A. C. W. Baas, “Chaos, Fractals and Self-Organization in Coastal Geomorphology: Simulating Dune Landscapes in Vegetated Environments,” Geomorphology, Vol. 48, No. 2, 2002, pp. 309-328. doi:10.1016/S0169-555X(02)00187-3

[10]   S. Qin, et al., “A Nonlinear Dynamical Model of Landslide Evolution,” Geomorphology, Vol. 43, No. 1, 2002, pp. 77-87.

[11]   M. A. Fonstad and M. Marcus, “Self-Organized Criticality in Riverbank Systems,” Annals of Association of American Geographers, Vol. 93, No. 2, 2003, pp. 281-296.

[12]   J. D. Pelletier, “Qualitative Chaos in Geomorphic Systems, with an Example from Wetland Response to Sea Level Rise,” Journal of Geology, Vol. 100, No. 3, 2007, pp. 365-374.

[13]   M. H. Ramesht, “The Chaos Theory in Geomorphology,” 1382.

[14]   A. Karam, “The Chaos Theory, Fractal and Non Linear Systems in Geomorphology,” The Natural Geography Quarterly, Vol. 3, No. 8, 1389, 17 p.

[15]   A. Karam, “Quantitative Modeling and Danger Zonation of Earthquake in the WRINKLED ZAgross,” Ph.D. Thesis, Geographical Sciences and Remote Testing Department of Tarbiat Modarres University of Tehran, Tehran, 1381, 360 p.

[16]   A. Karam, “Analysis and Zonation of the Risks in Naghan and Its Surrounding Using AHP and Geographical Informative System,” The Scientific Pole of the Space Analysis of the Dangers in Tarbiat Moallem University, Tehran, 1388, 12 p.

[17]   Geological Survey of Iran.

[18]   M. G. Moghaddam, “A Dynamic Study of the Water and Fog Production Viewing the Fractal Theory,” Aab and Khak Leaflet of Ferdousi University of Mashhad, 1389, Mashhad.

[19]   M. Khakzand, “A Short Look at the Interaction between Nature and Architecture,” Baghe Nazar Magazine, Vol. 8, No. 3, 1386, 11 p.

[20]   T. Tekyeh, “Studying the Effects of Viscosity and Solution Trembling in the Fusion of Liquid-Gel of Laponite Nano Particles through Dispersing Light,” MS Thesis, the Department of Basic Sciences of Tarbiat Moddares University of Tehran, Tehran, 1387, 145 p.

[21]   A. Andalib, “Compressing the Figures by Waves and Fractals Theory,” MS Thesis, Engineering Department of Tarbiat Modarres University of Tehran, Tehran, 1381, 267 p.

[22]   A. M. Tayefeh, “Analyzing and Designing the Fractal Micro Strip Aerial with Wireless Dispatching Application,” MS Thesis, Engineering Department of Tarbiat Moddares University of Tehran, Tehran, 1383, 207 p.

[23]   A. Nikouee, “Fractal Geometry in River Engineering: Ideas, Basic Concepts, and the Achievements,” The 4th National Conference of Reconstruction Engineering, Tehran University, Tehran, 1387, 451 p.

[24]   B. B. Mandelbrot, “Fractal Geometry of Nature,” Freeman, San Francisco, 1982.

[25]   D. L. Turcotte, “Self-Organized Complexity in Geomorphology: Observations and Models,” Geomorphology, Vol. 91, No. 3-4, 2007, pp. 302-310. doi:10.1016/j.geomorph.2007.04.016

[26]   A. Adl, “The Fractal Dimension and the Hydrological Particularities of the Aquiferous Basins,” The 1st National Engineering Congress of Reconstruction, Sharif Industrial University, Sharif, 1383, 575 p.

[27]   A. Alizadeh, “The Rules of Applicable Hydrology,” Astane Ghodse Razavi Publications, Mashhad, 1389, 652 p.

 
 
Top