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Growth laws for channel networks incised by groundwater flow

Abstract

The re-emergence of groundwater at the surface shapes the Earth’s topography through a process known as seepage erosion1,2,3,4,5. In combination with flow over land6, seepage erosion contributes to the initiation and growth of channel networks1,2,3,4,5. Seepage processes have also been invoked in the formation of enigmatic amphitheatre-headed channel networks on both Earth7,8,9,10,11 and Mars12,13,14. However, the role of seepage in producing such channels remains controversial11,15,16. One proposed growth law for channel development suggests that the velocity at which channel heads advance is proportional to the flux of groundwater to the heads17. Here we use field observations and physical theory to show that this simple model, combined with a second linear response that relates channel branching to the total groundwater flux to the network, is sufficient to characterize key aspects of the growth and form of a kilometre-scale seepage-driven channel network in Florida18. We find that the dynamics for the advance of channel heads are reversible, which allows us to estimate the age of the channel network and reconstruct the history of its growth. Our theory also predicts the evolution of the characteristic length scale between channels19, thereby linking network growth dynamics to geometric form.

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Figure 1: Topographic map of networks of steephead channels draining into the Apalachicola River, located on the Apalachicola Bluffs and Ravines Preserve, near Bristol, Florida.
Figure 2: Water table geometry.
Figure 3: Geometric drainage areas and the curvature–area relation.
Figure 4: Reconstruction of network growth.

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Acknowledgements

We would like to thank The Nature Conservancy for access to the Apalachicola Bluffs and Ravines Preserve, and K. Flournoy, B. Kreiter, S. Herrington and D. Printiss for guidance on the Preserve. We would also like to thank D. Forney, D. Jerolmack and J. T. Perron for helpful suggestions and assistance in the field, and T. Dunne and J. T. Perron for critical reviews of the manuscript. This work was supported by Department of Energy Grants FG02-99ER15004 and FG02-02ER15367. D.H.R. also thanks the Radcliffe Institute for Advanced Study for providing a year-long fellowship during which much of this work was completed.

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D.M.A., A.E.L., A.P.P., K.M.S. and D.H.R. contributed equally to this work. D.M.A., A.E.L., A.P.P. and D.H.R. developed theory and carried out field work and data analysis. K.M.S. and A.K. carried out field work and data analysis. B.M. and D.C.M. carried out field work and analysed regional sedimentology. D.H.R. wrote the paper, with input from D.M.A., A.E.L., A.P.P., K.M.S. and B.M.

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Correspondence to Daniel H. Rothman.

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Abrams, D., Lobkovsky, A., Petroff, A. et al. Growth laws for channel networks incised by groundwater flow. Nature Geosci 2, 193–196 (2009). https://doi.org/10.1038/ngeo432

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