Eikonal Equation Reproduces Natural Landscapes With Threshold Hillslopes

Shashank Kumar Anand, Matteo B. Bertagni, Arvind Singh, Amilcare Porporato

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Many natural landscapes maintain steep planar hillslopes bounded at a typical angle, beyond which shallow landslides or slope failures remove the excess sediment volume by mass wasting. Here we show that the celebrated eikonal equation, derived from a landscape evolution model in conditions of negligible soil diffusion and fluvial erosion, accurately portrays the organization of these topographies. Referred to as “eikonal landscapes,” such solutions feature constant-slope hillslopes originating from downstream boundary conditions and culminating in sharp upstream ridges. We demonstrate that the eikonal landscapes reproduce well a variety of natural landforms, including small islands, a volcano, and an extended mountain ridge. The boundary condition for the eikonal representation is specified through the natural landscape's slope-area relation. Going beyond merely representing landscape statistical features, the present results provide a first-of-kind direct match of mathematical and natural landscapes.

Original languageEnglish (US)
Article numbere2023GL105710
JournalGeophysical Research Letters
Issue number21
StatePublished - Nov 16 2023

All Science Journal Classification (ASJC) codes

  • Geophysics
  • General Earth and Planetary Sciences


  • debris flow
  • eikonal equation
  • landscape evolution model
  • landslide erosion
  • slope area relation
  • threshold hillslope


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