Articles | Volume 9, issue 2
https://doi.org/10.5194/esurf-9-317-2021
https://doi.org/10.5194/esurf-9-317-2021
Research article
 | 
16 Apr 2021
Research article |  | 16 Apr 2021

Hack distributions of rill networks and nonlinear slope length–soil loss relationships

Tyler H. Doane, Jon D. Pelletier, and Mary H. Nichols

Related authors

Rarefied particle motions on hillslopes – Part 1: Theory
David Jon Furbish, Joshua J. Roering, Tyler H. Doane, Danica L. Roth, Sarah G. W. Williams, and Angel M. Abbott
Earth Surf. Dynam., 9, 539–576, https://doi.org/10.5194/esurf-9-539-2021,https://doi.org/10.5194/esurf-9-539-2021, 2021
Short summary
Rarefied particle motions on hillslopes – Part 2: Analysis
David Jon Furbish, Sarah G. W. Williams, Danica L. Roth, Tyler H. Doane, and Joshua J. Roering
Earth Surf. Dynam., 9, 577–613, https://doi.org/10.5194/esurf-9-577-2021,https://doi.org/10.5194/esurf-9-577-2021, 2021
Short summary
Rarefied particle motions on hillslopes – Part 3: Entropy
David Jon Furbish, Sarah G. W. Williams, and Tyler H. Doane
Earth Surf. Dynam., 9, 615–628, https://doi.org/10.5194/esurf-9-615-2021,https://doi.org/10.5194/esurf-9-615-2021, 2021
Short summary
Rarefied particle motions on hillslopes – Part 4: Philosophy
David Jon Furbish and Tyler H. Doane
Earth Surf. Dynam., 9, 629–664, https://doi.org/10.5194/esurf-9-629-2021,https://doi.org/10.5194/esurf-9-629-2021, 2021
Short summary

Related subject area

Physical: Geomorphology (including all aspects of fluvial, coastal, aeolian, hillslope and glacial geomorphology)
Stream hydrology controls on ice cliff evolution and survival on debris-covered glaciers
Eric Petersen, Regine Hock, and Michael G. Loso
Earth Surf. Dynam., 12, 727–745, https://doi.org/10.5194/esurf-12-727-2024,https://doi.org/10.5194/esurf-12-727-2024, 2024
Short summary
Time-varying drainage basin development and erosion on volcanic edifices
Daniel O'Hara, Liran Goren, Roos M. J. van Wees, Benjamin Campforts, Pablo Grosse, Pierre Lahitte, Gabor Kereszturi, and Matthieu Kervyn
Earth Surf. Dynam., 12, 709–726, https://doi.org/10.5194/esurf-12-709-2024,https://doi.org/10.5194/esurf-12-709-2024, 2024
Short summary
Geomorphic risk maps for river migration using probabilistic modeling – a framework
Brayden Noh, Omar Wani, Kieran B. J. Dunne, and Michael P. Lamb
Earth Surf. Dynam., 12, 691–708, https://doi.org/10.5194/esurf-12-691-2024,https://doi.org/10.5194/esurf-12-691-2024, 2024
Short summary
Evolution of submarine canyons and hanging-wall fans: insights from geomorphic experiments and morphodynamic models
Steven Y. J. Lai, David Amblas, Aaron Micallef, and Hervé Capart
Earth Surf. Dynam., 12, 621–640, https://doi.org/10.5194/esurf-12-621-2024,https://doi.org/10.5194/esurf-12-621-2024, 2024
Short summary
Riverine sediment response to deforestation in the Amazon basin
Anuska Narayanan, Sagy Cohen, and John R. Gardner
Earth Surf. Dynam., 12, 581–599, https://doi.org/10.5194/esurf-12-581-2024,https://doi.org/10.5194/esurf-12-581-2024, 2024
Short summary

Cited articles

Bennett, S. and Liu, R.: Basin self-similarity, Hack's law, and the evolution of experimental rill networks, Geology, 44, 35–38, 2016. a
Carslaw, H. and Jaeger, J.: Conduction of heat in solids, chap. 2, Clarendon Press, Oxford, UK, 1959. a
Damron, M. and Winter, C. L.: A non-Markovian model of rill erosion, arXiv: preprint, arXiv:0810.1483, 2008. a, b
Doane, T. H. and Pelletier, J. D.: Rill Network Data and Codes, Zenodo, https://doi.org/10.5281/zenodo.3952897, 2020. a, b
Dodds, P. S. and Rothman, D. H.: Geometry of river networks. I. Scaling, fluctuations, and deviations, Phys. Rev. E., 63, 016115, https://doi.org/10.1103/PhysRevE.63.016115, 2000. a, b, c, d, e, f, g, h, i, j, k, l, m, n, o
Download
Short summary
This paper explores how the geometry of rill networks contributes to observed nonlinear relationships between soil loss and hillslope length. This work develops probability functions of geometrical quantities of the networks and then extends the theory to hydraulic variables by relying on well-known relationships. Theory is complemented by numerical modeling on numerical and natural surfaces. Results suggest that the particular arrangement of rill networks contributes to nonlinear relationships.