TY - JOUR
T1 - New findings on river network organization
T2 - Law of eigenarea and relationships among hortonian scaling ratios
AU - Yang, Soohyun
AU - Paik, Kyungrock
N1 - Publisher Copyright:
© 2017 World Scientific Publishing Company.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017/5/1
Y1 - 2017/5/1
N2 - 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.
AB - 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.
KW - Horton's Law
KW - River Network
KW - Self-Similarity
KW - Tokunaga's Law
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U2 - 10.1142/S0218348X17500293
DO - 10.1142/S0218348X17500293
M3 - Article
AN - SCOPUS:85019226027
SN - 0218-348X
VL - 25
JO - Fractals
JF - Fractals
IS - 3
M1 - 1750029
ER -