New findings on river network organization: Law of eigenarea and relationships among hortonian scaling ratios

Soohyun Yang, Kyungrock Paik

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Horton's laws have long served as fundamental principles for fractal organization of a drainage basin. Scaling ratios of stream number, length, area, and side tributary have been proposed but the definitions of these basic variables are inconsistent. The concept of eigenarea can be utilized to resolve this issue. Here, we investigated the relationships among Hortonian scaling ratios using the concept of eigenarea. We found that the eigenarea ratio, likewise other scaling ratios, is invariant within a stream network, the law of eigenarea. We analytically revealed that the eigenarea ratio is equivalent to the stream length ratio. Our examination implies that Horton's original two ratios of stream number and length can represent most Hortonian scaling ratios except Tokunaga ratio.

Original languageEnglish
Article number1750029
JournalFractals
Volume25
Issue number3
DOIs
Publication statusPublished - 2017 May 1

Keywords

  • Horton's Law
  • River Network
  • Self-Similarity
  • Tokunaga's Law

ASJC Scopus subject areas

  • Modelling and Simulation
  • General
  • Geometry and Topology
  • Applied Mathematics

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