Fractal River Networks

David G Tarboton
Utah State University

Abstract of Presentation at European Geophysical Society XXVI General Assembly, Nice, France, March 25-30, 2001.

River networks are the fundamental organizing structure of river basins.  They are the pathways through which water and sediment move to the outlet.  River Networks are among the earliest natural objects studied using fractals.  Mandelbrot in his first books suggested Peano curves that provided a space filling interpretation of river networks, with each river (and complementary interlocked drainage divide) having a dimension D=1.129.  The scaling exponent in Hack's empirical law relating mainstream length to drainage area was also predicted by Mandelbrot's early geometric models.  Much work has followed from these first inspiring steps.  Our understanding of the empirical geometry of river networks has been renewed through analysis from the perspective of fractal geometry.  Scaling descriptors (most notably Horton ratios) have been related to fractal dimensions, providing insights into their basis and interrelationships.  Research on the dynamics of the evolution of landforms and river networks has revealed the natural emergence, or self organization, of fractal river networks.  In this paper no new results will be presented.  The paper will review existing empirical and theoretical results on fractal river networks, highlighting the connections between different results and different fractal river network descriptors.  The paper will then present thoughts on future directions for research involving fractals and river networks