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)
Linear-stability analysis of plane beds under flows with suspended loads
Koji Ohata, Hajime Naruse, and Norihiro Izumi
Earth Surf. Dynam., 11, 961–977, https://doi.org/10.5194/esurf-11-961-2023,https://doi.org/10.5194/esurf-11-961-2023, 2023
Short summary
Estimating surface water availability in high mountain rock slopes using a numerical energy balance model
Matan Ben-Asher, Florence Magnin, Sebastian Westermann, Josué Bock, Emmanuel Malet, Johan Berthet, Ludovic Ravanel, and Philip Deline
Earth Surf. Dynam., 11, 899–915, https://doi.org/10.5194/esurf-11-899-2023,https://doi.org/10.5194/esurf-11-899-2023, 2023
Short summary
Sediment source and sink identification using Sentinel-2 and a small network of turbidimeters on the Vjosa River
Jessica Droujko, Srividya Hariharan Sudha, Gabriel Singer, and Peter Molnar
Earth Surf. Dynam., 11, 881–897, https://doi.org/10.5194/esurf-11-881-2023,https://doi.org/10.5194/esurf-11-881-2023, 2023
Short summary
Spatiotemporal bedload transport patterns over two-dimensional bedforms
Kate C. P. Leary, Leah Tevis, and Mark Schmeeckle
Earth Surf. Dynam., 11, 835–847, https://doi.org/10.5194/esurf-11-835-2023,https://doi.org/10.5194/esurf-11-835-2023, 2023
Short summary
Ice-buttressing-controlled rock slope failure on a cirque headwall, Lake District, UK
Paul A. Carling, John D. Jansen, Teng Su, Jane Lund Andersen, and Mads Faurschou Knudsen
Earth Surf. Dynam., 11, 817–833, https://doi.org/10.5194/esurf-11-817-2023,https://doi.org/10.5194/esurf-11-817-2023, 2023
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.