Publication

Scaling laws for river networks

1996
Journal Articles

Abstract

Seemingly unrelated empirical hydrologic laws and several experimental facts related to the fractal geometry of the river basin are shown to find a natural explanation into a simple finite-size scaling ansatz for the power laws exhibited by cumulative distributions of river basin areas. Our theoretical predictions suggest that the exponent of the power law is directly related to a suitable fractal dimension of the boundaries, to the elongation of the basin, and to the scaling exponent of mainstream lengths. Observational evidence from digital elevation maps of natural basins and numerical simulations for optimal channel networks are found to be in good agreement with the theoretical predictions. Analytical results for Scheidegger's trees are exactly reproduced.

Official source

https://infoscience.epfl.ch/entities/publication/8fd755da-8f8c-4ff3-8e55-3f51eb6d683c

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1996
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/8fd755da-8f8c-4ff3-8e55-3f51eb6d683c

About this result

Related concepts (32)

Drainage basin

A drainage basin is an area of land where all flowing surface water converges to a single point, such as a river mouth, or flows into another body of water, such as a lake or ocean. A basin is separated from adjacent basins by a perimeter, the drainage divide, made up of a succession of elevated features, such as ridges and hills. A basin may consist of smaller basins that merge at river confluences, forming a hierarchical pattern. Other terms for a drainage basin are catchment area, catchment basin, drainage area, river basin, water basin, and impluvium.

Endorheic basin

An endorheic basin (ˌɛndoʊˈriː.ɪk; also endoreic basin and endorreic basin) is a drainage basin that normally retains water and allows no outflow to other, external bodies of water (e.g. rivers and oceans), instead, the water drainage flows into permanent and seasonal lakes and swamps that equilibrate through evaporation. Endorheic basins also are called closed basins, terminal basins, and internal drainage systems. Endorheic regions contrast with open lakes (exorheic regions), where surface waters eventually drain into the ocean.

Power law

In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to a power of the change, independent of the initial size of those quantities: one quantity varies as a power of another. For instance, considering the area of a square in terms of the length of its side, if the length is doubled, the area is multiplied by a factor of four.

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Scaling laws for river networks

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