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Growth laws for channel networks incised by groundwater flow


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.


  1. 1

    Dunne, T. Runoff Production in a Humid Area. Thesis (Johns Hopkins Univ., 1969). Also published as US Department of Agriculture Report ARS 41–160 (1970).

  2. 2

    Dunne, T. in Hillslope Hydrology (ed. Kirkby, M. J.) 227–293 (Wiley, 1978).

    Google Scholar 

  3. 3

    Dunne, T. Formation and controls of channel networks. Prog. Phys. Geogr. 4, 211–239 (1980).

    Article  Google Scholar 

  4. 4

    Dunne, T. in Groundwater Geomorphology: The Role of Subsurface Water in Earth-Surface Processes and Landforms Vol. 252 (eds Higgins, C. G. & Coates, D. R.) 1–28 (Geol. Soc. Am. Special Paper, Geological Society of America, 1990).

    Book  Google Scholar 

  5. 5

    Dietrich, W. E. & Dunne, T. in Channel Network Hydrology (eds Beven, K. & Kirby, M. J.) 175–219 (Wiley, 1993).

    Google Scholar 

  6. 6

    Horton, R. E. Erosional development of streams and their drainage basins: Hydrophysical approach to quantitative morphology. Geol. Soc. Am. Bull. 56, 275–370 (1945).

    Article  Google Scholar 

  7. 7

    Wentworth, C. K. Principles of stream erosion in Hawaii. J. Geol. 36, 385–410 (1928).

    Article  Google Scholar 

  8. 8

    Laity, J. E. & Malin, M. C. Sapping processes and the development of theater-headed valley networks on the Colorado plateau. Geol. Soc. Am. Bull. 96, 203–17 (1985).

    Article  Google Scholar 

  9. 9

    Orange, D. L., Anderson, R. S. & Breen, N. A. Regular canyon spacing in the submarine environment: The link between hydrology and geomorphology. GSA Today 4, 1–39 (1994).

    Google Scholar 

  10. 10

    Schorghofer, N., Jensen, B., Kudrolli, A. & Rothman, D. H. Spontaneous channelization in permeable ground: Theory, experiment, and observation. J. Fluid Mech. 503, 357–374 (2004).

    Article  Google Scholar 

  11. 11

    Lamb, M. P. et al. Can springs cut canyons into rock? J. Geophys. Res. 111, E07002 (2006).

    Google Scholar 

  12. 12

    Higgins, C. G. Drainage systems developed by sapping on Earth and Mars. Geology 10, 147–152 (1982).

    Article  Google Scholar 

  13. 13

    Malin, M. C. & Carr, M. H. Groundwater formation of martian valleys. Nature 397, 589–591 (1999).

    Article  Google Scholar 

  14. 14

    Malin, M. C. & Edgett, K. Evidence for recent groundwater seepage and surface runoff on Mars. Science 288, 2330–2335 (2000).

    Article  Google Scholar 

  15. 15

    Lamb, M. P., Howard, A. D., Dietrich, W. E. & Perron, J. T. Formation of amphitheater-headed valleys by waterfall erosion after large-scale slumping on Hawaii. GSA Bull. 19, 805–822 (2007).

    Article  Google Scholar 

  16. 16

    Lamb, M. P., Dietrich, W. E., Aciego, S. M., DePaolo, D. J. & Manga, M. Formation of Box Canyon, Idaho, by megaflood: Implications for seepage erosion on Earth and Mars. Science 320, 1067–1070 (2008).

    Article  Google Scholar 

  17. 17

    Howard, A. D. in Sapping Features of the Colorado Plateau: A Comparative Planetary Geology Field Guide (eds Howard, A. D., Kochel, R. C. & Holt, H. E.) 71–83 (NASA Scientific and Technical Information Division, 1988).

    Google Scholar 

  18. 18

    Schumm, S. A., Boyd, K. F., Wolff, C. G. & Spitz, W. J. A ground-water sapping landscape in the Florida Panhandle. Geomophology 12, 281–297 (1995).

    Article  Google Scholar 

  19. 19

    Montgomery, D. R. & Dietrich, W. E. Channel initiation and the problem of landscape scale. Science 255, 826–830 (1992).

    Article  Google Scholar 

  20. 20

    Schmidt, W. Alum Bluff, Liberty County, Florida. Open File Report 9 (Florida Geological Survey, 1985).

  21. 21

    Rupert, F. R. The Geomorphology and Geology of Liberty County, Florida. Open File Report 43 (Florida Geological Survey, 1991).

  22. 22

    Polubarinova-Kochina, P. I. A. Theory of Ground Water Movement (Princeton Univ. Press, 1962).

    Google Scholar 

  23. 23

    Bear, J. Dynamics of Fluids in Porous Media (Dover, 1972).

    Google Scholar 

  24. 24

    Culling, W. E. H. Analytic theory of erosion. J. Geol. 68, 336–344 (1960).

    Article  Google Scholar 

  25. 25

    McKean, J. A., Dietrich, W. E., Finkel, R. C., Southon, J. R. & Caffee, M. W. Quantification of soil production and downslope creep rates from cosmogenic 10Be accumulations on a hillsope profile. Geology 21, 343–346 (1993).

    Article  Google Scholar 

  26. 26

    Rosenbloom, N. A. & Anderson, R. S. Hillslope and channel evolution in a marine terraced landscape, Santa Cruz, California. J. Geophys. Res. 99, 14013–14029 (1994).

    Article  Google Scholar 

  27. 27

    Fernandes, N. F. & Dietrich, W. E. Hillslope evolution by diffusive processes: The timescale for equilibrium adjustments. Wat. Resour. Res. 33, 1307–1318 (1997).

    Article  Google Scholar 

  28. 28

    Small, E. E., Anderson, R. S. & Hancock, G. S. Estimates of the rate of regolith production using 10Be and 26Al from an alpine hillslope. Geomorphology 27, 131–150 (1999).

    Article  Google Scholar 

  29. 29

    Howard, A. D. & McLane, C. F. Erosion of cohesionless sediment by groundwater seepage. Wat. Resour. Res. 24, 1659–1674 (1988).

    Article  Google Scholar 

  30. 30

    Lobkovsky, A. E., Jensen, B., Kudrolli, A. & Rothman, D. H. Threshold phenomena in erosion driven by subsurface flow. J. Geophys. Res.-Earth 109, F04010 (2004).

    Google Scholar 

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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).

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