  The hierarchical organization and self-similarity in river basins have been
topics of extensive research in hydrology and geomorphology starting with the
pioneering work of Horton in 1945. Despite significant theoretical and applied
advances however, the mathematical origin of and relation among Horton laws for
different stream attributes remain unsettled. Here we capitalize on a recently
developed theory of random self-similar trees to introduce a one-parametric
family of self-similar critical Tokunaga trees that elucidates the origin of
Horton laws, Hack's laws, basin fractal dimension, power-law distributions of
link attributes, and power-law relations between distinct attributes. The
proposed family includes the celebrated Shreve's random topology model and
extends to trees that approximate the observed river networks with realistic
exponents. The results offer tools to increase our understanding of landscape
organization under different hydroclimatic forcings, and to extend scaling
relationships useful for hydrologic prediction to resolutions higher that those
observed.
