Watersheds in disordered media

• Main Authors: José S. Andrade Jr., Nuno A. M. Araújo, Hans eHerrmann, Julian eSchrenk
• Format: Article
• Language: English
• Published: Frontiers Media S.A. 2015-02-01
• Series: Frontiers in Physics
• Subjects: Fractals; Watersheds; invasion percolation; Drainage basin; Catchment basins
• Online Access: http://journal.frontiersin.org/Journal/10.3389/fphy.2015.00005/full

What is the best way to divide a rugged landscape? Since ancient times, watershedsseparating adjacent water systems that flow, for example, toward different seas, have beenused to delimit boundaries. Interestingly, serious and even tense border disputes betweencountries 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 awatershed, and the effects can be highly nonlocal. Although the watershed concept arisesnaturally in geomorphology, where it plays a fundamental role in water management, landslide,and flood prevention, it also has important applications in seemingly unrelated fields suchas image processing and medicine. Despite the far-reaching consequences of the scalingproperties on watershed-related hydrological and political issues, it was only recently that a moreprofound and revealing connection has been disclosed between the concept of watershed andstatistical physics of disordered systems. This review initially surveys the origin and definition of awatershed line in a geomorphological framework to subsequently introduce its basic geometricaland physical properties. Results on statistical properties of watersheds obtained from artificialmodel landscapes generated with long-range correlations are presented and shown to be ingood qualitative and quantitative agreement with real landscapes.