The shape of watersheds

Timothée Sassolas-Serrayet,Rodolphe Cattin,Matthieu Ferry

doi:10.1038/s41467-018-06210-4

Timothée Sassolas-Serrayet, Rodolphe Cattin + Show 1 more

Open Access

https://doi.org/10.1038/s41467-018-06210-4

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Abstract

Since the 1950s river networks have been intensely researched in geosciences and hydrology. This led to the definition of scaling laws that described the organisation of landscapes under fluvial incision and were later explored by statistical physics and fractal mathematics. The emblematic Hack’s Law proposes a power-law relationship between watershed area and main stream length. Though extensively documented, a wide range of values is still reported for Hack’s parameters. Some authors associate this dispersion to local geologic and climatic conditions. Here based on the analysis of large sets of river basins in various climatic and geological settings, we confirm the geometric similarity of river networks. We demonstrate that basin shape is mostly related to Hack’s coefficient and not to the exponent, independently of external forcing such as lithology and pluviometry.

Highlights

Since the 1950s river networks have been intensely researched in geosciences and hydrology
Basins shape gives a physical meaning to data dispersion
The use of Gravelius compactness coefficient[19] (GC) (Fig. 2) to define measures of catchment shape reveals that this dispersion is not related to data precision but rather to basin shape (Fig. 3)

Summary

Introduction

Since the 1950s river networks have been intensely researched in geosciences and hydrology. One of the best-known scaling laws of river network is Hack’s Law, which states that the length L of the longest channel of a river basin, measured from outlet to drainage divide, scales with the area A of this basin. Hack’s coefficient has rarely been studied[9] and its significance remains enigmatic In his original paper on river catchments in Midwestern United States[1], Hack found that for drainage areas inferior to 100 km[2], n = 0.6 but can be as large as 0.7 in some regions, whereas c ~ 1.5 but ranges between 1.1 and 2.7 (for L and A expressed in km and km[2], respectively). He interpreted this exponent greater than 0.5 as the result of an increase in basin elongation with the increasing catchment area

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