Estimation of fractal dimension for Seolma creek experimental basin on the basis of fractal tree concept

This study presents a methodology to estimate two distinct fractal dimensions of natural river basin by using fractal tree concept. To this end, an analysis is performed on fractal features of a complete drainage network which consists of all possible drainage paths within a river basin based on the growth process of fractal tree. The growth process of fractal tree would occur only within the limited drainage paths possessing stream flow features in a river basin. In the case of small river basin, the bifurcation process of network is more sensitive to the growth step of fractal tree than the meandering process of stream segment, so that various bifurcation structures could be generated in a single network. Therefore, fractal dimension of network structure for small river basin should be estimated in the form of a range not a single figure. Furthermore, the network structures with fractal tree from this study might be more useful information than stream networks from a topographic or digital map for analysis of drainage structure on small river basin.

[1]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[2]  David G. Tarboton,et al.  A Physical Basis for Drainage Density , 1992 .

[3]  I. Rodríguez‐Iturbe,et al.  The fractal nature of river networks , 1988 .

[4]  F. D'asaro,et al.  Scaling properties of topologically random channel networks , 1996 .

[5]  Joo-Cheol Kim,et al.  Hack's Law and the Geometric Properties of Catchment Plan-form , 2009 .

[6]  S. Schumm.  EVOLUTION OF DRAINAGE SYSTEMS AND SLOPES IN BADLANDS AT PERTH AMBOY, NEW JERSEY , 1956 .

[7]  Stephen C. Medeiros,et al.  Wet channel network extraction by integrating LiDAR intensity and elevation data , 2015 .

[8]  T. Beer,et al.  HORTON'S LAWS AND THE FRACTAL NATURE OF STREAMS , 1993 .

[9]  Giha Lee,et al.  Comparative Analysis of Geomorphologic Characteristics of DEM-Based Drainage Networks , 2011 .

[10]  Carlos E. Puente,et al.  On the fractal structure of networks and dividers within a watershed , 1996 .

[11]  A. Maritan,et al.  On Hack's Law , 1996 .

[12]  R. Rosso,et al.  On the fractal dimension of stream networks , 1989 .

[13]  James W. Kirchner,et al.  Dynamic, discontinuous stream networks: hydrologically driven variations in active drainage density, flowing channels and stream order , 2014 .

[14]  Jaehan Kim,et al.  The Geometric Properties of the Drainage Structures based on Fractal Tree , 2008 .

[15]  D. Maidment,et al.  A GIS assessment of nonpoint source pollution in the San Antonio-Nueces coastal basin , 1996 .

[16]  R. Bras,et al.  Scaling regimes of local slope versus contributing area in digital elevation models , 1995 .

[17]  Peter Sheridan Dodds,et al.  Scaling, Universality, and Geomorphology , 2000 .

[18]  David G. Tarboton,et al.  Terrain Analysis Using Digital Elevation Models in Hydrology , 2003 .

[19]  Joo-Cheol Kim,et al.  Fractal Tree Analysis of Drainage Patterns , 2015, Water Resources Management.

[20]  R. L. Shreve.  Statistical Law of Stream Numbers , 1966, The Journal of Geology.

[21]  Jaehan Kim,et al.  Morphological Representation of Channel Network by Dint of DEM , 2007 .

[22]  John F. O'Callaghan,et al.  The extraction of drainage networks from digital elevation data , 1984, Comput. Vis. Graph. Image Process..

[23]  William I. Newman,et al.  Fractal Trees with Side Branching , 1997 .

[24]  Maritan,et al.  Scaling laws for river networks. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  R. Horton.  EROSIONAL DEVELOPMENT OF STREAMS AND THEIR DRAINAGE BASINS; HYDROPHYSICAL APPROACH TO QUANTITATIVE MORPHOLOGY , 1945 .

[26]  R. Moussa.  On morphometric properties of basins, scale effects and hydrological response , 2003 .

[27]  K. Paik,et al.  NEW FINDINGS ON RIVER NETWORK ORGANIZATION: LAW OF EIGENAREA AND RELATIONSHIPS AMONG HORTONIAN SCALING RATIOS , 2017 .

[28]  L. B. Leopold,et al.  Ephemeral streams; hydraulic factors and their relation to the drainage net , 1956 .

[29]  E. Foufoula‐Georgiou,et al.  Channel network source representation using digital elevation models , 1993 .

[30]  Renzo Rosso,et al.  Fractal relation of mainstream length to catchment area in river networks , 1991 .

[31]  S. Peckham.  New Results for Self‐Similar Trees with Applications to River Networks , 1995 .