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Updated: May 16, 2026

Watershed Planning within a Quantitative Scenario Analysis Framework
Published on: July 24, 2016
Watersheds are Schramm-Loewner evolution curves
E Daryaei1, N A M Araújo, K J Schrenk
1Computational Physics for Engineering Materials, Institut f. Baustoffe, ETH Zurich, Wolfgang-Pauli-Street 27, 8093 Zurich, Switzerland. daryaei@physics.sharif.edu
Abstract:
We show that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner evolution (SLE) curves, being described by one single parameter κ. Several numerical evaluations are applied to ascertain this. All calculations are consistent with SLE(κ), with κ = 1.734 ± 0.005, being the only known physical example of an SLE with κ<2. This lies outside the well-known duality conjecture, bringing up new questions regarding the existence and reversibility of dual models. Furthermore, it constitutes a strong indication for conformal invariance in random landscapes and suggests that watersheds likely correspond to a logarithmic conformal field theory with a central charge c ≈ -7/2.
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