Approximations on the Peano river network: application of the Horton-Strahler hierarchy to the case of low connections.

A network analysis is used to investigate the low connections of natural river channels. At the basin scale, the river networks are analyzed according to the Horton-Strahler hierarchy. We propose a quantitative criterion for the average junction degree as a function of a fixed hierarchical order of the network and independent of the usual scaling laws. The numerical results of this analysis are compared with exact results of the Peano river network, showing differences of the order of 10(-3). This aspect is especially relevant for the characterization of transport and diffusion processes at the basin scale.

[1]  R. Horton.  Drainage‐basin characteristics , 1932 .

[2]  A. Maritan,et al.  On the space‐time evolution of a cholera epidemic , 2008 .

[3]  P. Dodds,et al.  Unified view of scaling laws for river networks. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  A. N. Strahler.  Hypsometric (area-altitude) analysis of erosional topography. , 1952 .

[5]  A. N. Strahler.  DIMENSIONAL ANALYSIS APPLIED TO FLUVIALLY ERODED LANDFORMS , 1958 .

[6]  V. Gupta,et al.  Statistical self-similarity of width function maxima with implications to floods , 2001 .

[7]  R. L. Shreve,et al.  Stream Lengths and Basin Areas in Topologically Random Channel Networks , 1969, The Journal of Geology.

[8]  Vicenç Méndez,et al.  Transport on fractal river networks: application to migration fronts. , 2006, Theoretical population biology.

[9]  R. L. Shreve.  Infinite Topologically Random Channel Networks , 1967, The Journal of Geology.

[10]  R. L. Shreve.  Statistical Law of Stream Numbers , 1966, The Journal of Geology.

[11]  Alessandro Marani,et al.  A Note on Fractal Channel Networks , 1991 .

[12]  Thomas M. Over,et al.  River flow mass exponents with fractal channel networks and rainfall , 2001 .

[13]  P. Dodds,et al.  Geometry of river networks. II. Distributions of component size and number. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  P. Dodds,et al.  Geometry of river networks. I. Scaling, fluctuations, and deviations. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  R. Gaudio,et al.  Fixed-mass multifractal analysis of river networks and braided channels. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Hean-Teik Chuah,et al.  Allometric relationships between traveltime channel networks, convex hulls, and convexity measures , 2006 .

[17]  Exact analysis of the Peano basin , 1996 .

[18]  Peter Sheridan Dodds,et al.  Scaling, Universality, and Geomorphology , 2000 .

[19]  Enrico Bertuzzo,et al.  River networks and ecological corridors: Reactive transport on fractals, migration fronts, hydrochory , 2007 .

[20]  P. Dodds,et al.  Geometry of river networks. III. Characterization of component connectivity. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  A. N. Strahler.  Quantitative analysis of watershed geomorphology , 1957 .

[22]  R. Horton.  EROSIONAL DEVELOPMENT OF STREAMS AND THEIR DRAINAGE BASINS; HYDROPHYSICAL APPROACH TO QUANTITATIVE MORPHOLOGY , 1945 .

[23]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.