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