Abstract
What is the best way to divide a rugged landscape? Since ancient times, watersheds separating adjacent water systems that flow, for example, toward different seas, have been used to delimit boundaries. Interestingly, serious and even tense border disputes between countries have relied on the subtle geometrical properties of these tortuous lines. For instance, slight and even anthropogenic modifications of landscapes can produce large changes in a watershed, and the effects can be highly nonlocal. Although the watershed concept arises naturally in geomorphology, where it plays a fundamental role in water management, landslide, and flood prevention, it also has important applications in seemingly unrelated fields such as image processing and medicine. Despite the far-reaching consequences of the scaling properties on watershed-related hydrological and political issues, it was only recently that a more profound and revealing connection has been disclosed between the concept of watershed and statistical physics of disordered systems. This review initially surveys the origin and definition of a watershed line in a geomorphological framework to subsequently introduce its basic geometrical and physical properties. Results on statistical properties of watersheds obtained from artificial model landscapes generated with long-range correlations are presented and shown to be in good qualitative and quantitative agreement with real landscapes.
Highlights
Both start in the mountains of Switzerland, the Rhine and Rhone rivers diverge while flowing toward different seas
When looking at a landscape, how to identify the regions draining toward one side or the other? When rain falls or snow melts on a landscape, the dynamics of the surface water is determined by the topography of the landscape
WATERSHEDS IN THREE AND HIGHER DIMENSIONS Up to now, we have focused on the watershed line that divides the landscape into drainage basins for water on the surface
Summary
Both start in the mountains of Switzerland, the Rhine and Rhone rivers diverge while flowing toward different seas. For every landscape, several outlets can be defined, each one with a corresponding drainage basin. Sets of small drainage basins eventually drain toward the same outlet forming a even larger basin. Such hierarchy results in a larger number of watersheds. Schramm-Loewer Evolution (SLE) curves in the continuum limit [16] This association explains why watersheds on uncorrelated landscapes as well as other statistical physics models, such as, optimal path cracks [17,18,19], fuse networks [20], and loopless percolation [15], belong to the same universality class of optimal paths in strongly disordered media
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