EGU23-10027, updated on 26 Feb 2023
EGU General Assembly 2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.

Eikonal approximation for landscapes dominated by threshold hillslopes

Shashank Kumar Anand1, Matteo B. Bertagni2, Arvind Singh3, and Amilcare Porporato1,2
Shashank Kumar Anand et al.
  • 1Department of Civil and Environmental Engineering, Princeton University, Princeton, United States of America
  • 2High Meadows Environmental Institute, Princeton University, Princeton, United States of America
  • 3Department of Civil, Environmental and Construction Engineering, University of Central Florida, United States of America

Steep landscapes maintain predominantly planar hillslopes over a range of spatial scales. These hillslopes are bounded at a typical angle, beyond which shallow landslides or slope failures remove the excess sediment influx. The evolution of such steep topographies with threshold hillslopes is well approximated by the eikonal equation, which is well-known in problems of geometry, optics, and mechanics. According to this approximation, hillslopes meet upstream to construct a network of sharp ridges and join downstream at the boundary to produce a complementary valley network. We find a good agreement between the proposed approximation and the spatial organization of landscapes with a dominant control of landslide erosion and negligible fluvial erosion. We also show that the eikonal approximation can be utilized to reconstruct the landscapes with threshold hillslopes where fluvial erosion sets the downstream free boundary.

How to cite: Anand, S. K., Bertagni, M. B., Singh, A., and Porporato, A.: Eikonal approximation for landscapes dominated by threshold hillslopes, EGU General Assembly 2023, Vienna, Austria, 24–28 Apr 2023, EGU23-10027,, 2023.

Supplementary materials

Supplementary material file