Controls on the spacing of first-order valleys

Journal of Geophysical Research: Earth Surface

Volumn 113, Issue 4, 2008, Pages

  Perron, J Taylor ^a,b   Dietrich, William E ^c   Kirchner, James W ^c,d,e  

^a HARVARD UNIVERSITY   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d SWISS FEDERAL RESEARCH INSTITUTE WSL   (Switzerland)

^e ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

BEDROCK; DRAINAGE BASIN; DRAINAGE NETWORK; HILLSLOPE; LANDSCAPE EVOLUTION; NUMERICAL MODEL; VALLEY;

EID: 61849114640     PISSN: None     EISSN: 21699011     Source Type: Journal    
DOI: 10.1029/2007JF000977     Document Type: Article

References (129)

1. Abrahams, A., A. D. Howard, and A. Parsons (1994), Rock-mantled slopes, in Geomorphology of Desert Environments, edited by A. Abrahams and A. Parsons, pp. 173-211, Chapman and Hall, London.
2. Ahnert, F. (1976), Brief description of a comprehensive three-dimensional process-response model of landform development, Z. Geomorphol., 25, 29-49.
3. Ahnert, F. (1987), Process-response models of denudation at different spatial scales, Catena Suppl., 10, 31-50.
4. Allen, P. (2005), Striking a chord, Nature, 434, 961, doi:10.1038/ 434961a.
5. Bagnold, R. A. (1941), The Physics of Blown Sand and Desert Dunes, Methuen, London.
6. Bull, W. B. (1975), Allometric change of landforms, Geol. Soc. Am. Bull., 86(11), 1489-1498.
7. Carson, M. A., and M. J. Kirkby (1972), Hillslope Form and Process, Cambridge Univ. Press, New York.
8. Castelltort, S., and G. Simpson (2006), River spacing and drainage network growth in widening mountain ranges, Basin Res., 18(3), 267-276.
9. Church, M. (2003), What is a geomorphological prediction?, in Prediction in Geomorphology, Geophys. Monogr. Ser., vol. 135, edited by P. R. Wilcock and R. M. Iverson, pp. 183-194, AGU, Washington, D. C.
10. Church, M., and D. M. Mark (1980), On size and scale in geomorphology, Prog. Phys. Geogr., 4(3), 342-390.
11. Costa-Cabral, M. C., and S. J. Burges (1994), Digital elevation model networks (DEMON): A model of flow over hillslopes for computation of contributing and dispersal areas, Water Resour. Res., 30(6), 1681-1692.
12. Culling, W. E. H. (1960), Analytical theory of erosion, J. Geol., 68(3), 336-344.
13. Culling, W. E. H. (1963), Soil creep and the development of hillside slopes, J. Geol., 71(2), 127-161.
14. Culling, W. E. H. (1965), Theory of erosion on soil-covered slopes, J. Geol., 73, 230-254.
15. Darwin, C. (1859), On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life, Murray, London.
16. Davis, W. M. (1992), The convex profile of badland divides, Science, 20, 245.
17. Densmore, A. L., M. A. Ellis, and R. S. Anderson (1998), Landsliding and the evolution of normal-fault-bounded mountains, J. Geophys. Res., 103, 15,203-15,219.
18. Dietrich, W. E., and T. Dunne (1993), The channel head, in Channel Network Hydrology, edited by K. Beven and M. J. Kirkby, pp. 175-219, John Wiley, New York.
19. Dietrich, W. E., and D. R. Montgomery (1998), Hillslopes, channels, and landscape scale, in Scale Dependence and Scale Invariance in Hydrology, edited by G. Sposito, pp. 30-60, Cambridge Univ. Press, Cambridge, U.K.
20. Dietrich, W. E., C. J. Wilson, D. R. Montgomery, J. McKean, and R. Bauer (1992), Erosion thresholds and land surface morphology, Geology, 20(8), 675-679.
21. Dietrich, W. E., C. J. Wilson, D. R. Montgomery, and J. McKean (1993), Analysis of erosion thresholds, channel networks, and landscape morphology using a digital terrain model, J. Geol., 101(2), 259-278.
22. Dietrich, W. E., D. G. Bellugi, L. S. Sklar, J. D. Stock, A. M. Heimsath, and J. J. Roering (2003), Geomorphic transport laws for predicting landscape form and dynamics, in Prediction in Geomorphology, Geophys. Monogr. Ser., vol. 135, edited by P. R. Wilcock and R. M. Iverson, pp. 103-132, AGU, Washington, D. C.
23. Dunne, T. (1980), Formation and controls of channel networks, Prog. Phys. Geogr., 4, 211-239.
24. Dunne, T., and B. F. Aubry (1986), Evaluation of Horton's theory of sheet-wash and rill erosion on the basis of field experiments, in Hillslope Processes, edited by A. D. Abrahams, pp. 31-53, Allen and Unwin, Winchester, Mass.
25. Eaton, G. P. (1982), The basin and range province: Origin and tectonic significance, Annu. Rev. Earth Planet. Sci., 10(1), 409-440.
26. Fernandes, N. F., and W. E. Dietrich (1997), Hillslope evolution by diffusive processes: The timescale for equilibrium adjustments, Water Resour. Res., 33(6), 1307-1318.
27. Freeman, T. G. (1991), Calculating catchment area with divergent flow based on a regular grid, Comput. Geosci., 17(3), 413-422.
28. Gilbert, G. K. (1877), Report on the Geology of the Henry Mountains, U. S. Govt. Print. Off., Washington, D. C.
29. Gilbert, G. K. (1909), The convexity of hilltops, J. Geol., 17(4), 344-350.
30. Gioia, G., and F. A. Bombardelli (2002), Scaling and similarity in rough channel flows, Phys. Rev. Lett., 88(1), 014501, doi:10.1103/ PhysRevLett.88.014501.
31. Hack, J. T. (1957), Studies of longitudinal stream profiles in Virginia and Maryland, U.S. Geol. Surv. Prof. Pap., 294-B.
32. Hack, J. T., and J. C. Goodlett (1960), Geomorphology and forest ecology of a mountain region in the central Appalachians, U.S. Geol. Surv. Prof., 347.
33. Hallet, B. (1990), Spatial self-organization in geomorphology: from periodic bedforms and patterned ground to scale-invariant topography, Earth Sci. Rev., 29, 57-75.
34. Hanks, T. C., R. C. Bucknam, K. R. Lajoie, and R. E. Wallace (1984), Modification of wave-cut and faulting-controlled landforms, J. Geophys. Res., 89, 5771-5790.
35. Hanley, J. T. (1977), Fourier analysis of the Catawba Mountain knolls, Roanoke county, Virginia, Math. Geol., 9(2), 159-163.
36. Hasbargen, L. E., and C. Paola (2000), Landscape instability in an experimental drainage basin, Geology, 28(12), 1067-1070.
37. Hoey, T. B., P. Bishop, and R. I. Ferguson (2003), Testing numerical models in geomorphology: How can we ensure critical use of model predictions?, in Prediction in Geomorphology, Geophys. Monogr. Ser., vol. 135, edited by P. R. Wilcock and R. M. Iverson, pp. 241-256, AGU, Washington, D. C.
38. Horton, R. E. (1945), Erosional development of streams and their drainage basins: Hydrophysical approach to quantitative morphology, Geol. Soc. Am. Bull., 56(3), 275-370.
39. Hovius, N. (1996), Regular spacing of drainage outlets from linear mountain belts, Basin Res., 8, 29-44.
40. Howard, A. D. (1994a), A detachment-limited model of drainage basin evolution, Water Resour. Res., 30(7), 2261-2286.
41. Howard, A. D. (1994b), Badlands, in Geomorphology of Desert Environments, edited by A. Abrahams and A. Parsons, pp. 213-242, Chapman and Hall, London.
42. Howard, A. D. (1997), Badland morphology and evolution: Interpretation using a simulation model, Earth Surf. Processes Landforms, 22(3), 211-227.
43. Howard, A. D. (1998), Long profile development of bedrock channels: Interaction of weathering, mass wasting, bed erosion, and sediment transport, in Rivers Over Rock: Fluvial Processes in Bedrock Channels, Geophys. Monogr. Ser., vol. 107, pp. 297-319, AGU, Washington, D. C.
44. Howard, A. D. (1999), Simulation of gully erosion and bistable landforms, in Incised River Channels: Processes, Forms, Engineering and Management, edited by S. Darby and A. Simon, pp. 277-299, John Wiley, Chichester, U.K.
45. Howard, A. D., and G. Kerby (1983), Channel changes in badlands, Geol. Soc. Am. Bull., 94(6), 739-752.
46. Howard, A. D., W. E. Dietrich, and M. A. Seidl (1994), Modeling fluvial erosion on regional to continental scales, J. Geophys. Res., 99, 13,971-13,986.
47. Izumi, N., and G. Parker (1995), Inception of channelization and drainage basin formation: Upstream-driven theory, J. Fluid Mech., 283, 341-363.
48. Izumi, N., and G. Parker (2000), Linear stability analysis of channel inception: Downstream-driven theory, J. Fluid Mech., 419, 239-262.
49. Kennedy, J. F. (1969), The formation of sediment ripples, dunes, and anti-dunes, Annu. Rev. Fluid Mech., 1(1), 147-168.
50. Kirkby, M. J. (1971), Hillslope process-response models based on the continuity equation, Inst. Br. Geogr. Spec. Publ., 3, 15-30.
51. Kirkby, M. J. (1980), The stream head as a significant geomorphic threshold, in Thresholds in Geomorphology, edited by D. R. Coates and J. D. Vitek, pp. 53-73, Allen and Unwin, Winchester, Mass.
52. Kirkby, M. J. (1986), A two-dimensional simulation model for slope and stream evolution, in Hillslope Processes, edited by A. D. Abrahams, pp. 203-222, Allen and Unwin, Winchester, Mass.
53. Kirkby, M. J. (1987), Modelling some influences of soil erosion, landslides and valley gradient on drainage density and hollow development, Catena Suppl., 10, 1-14.
54. Kirkby, M. J. (1993), Long term interactions between networks and hillslopes, in Channel Network Hydrology, edited by K. Beven and M. J. Kirkby, pp. 255-293, John Wiley, New York.
55. Kirkby, M. J. (1994), Thresholds and instability in stream head hollows: A model of magnitude and frequency for wash processes, in Process Models and Theoretical Geomorphology, edited by M. J. Kirkby, pp. 295-314, John Wiley, New York.
56. Knighton, D. (1998), Fluvial Forms and Processess: A New Perspective, Hodder Arnold, London.
57. Kooi, H., and C. Beaumont (1996), Large-scale geomorphology: classical concepts reconciled and integrated with contemporary ideas via a surface processes model, J. Geophys. Res., 101(B2), 3361-3386.
58. Leopold, L. B., and T. Maddock (1953), The hydraulic geometry channels and some physiographic implications, U.S. Geol. Surv. Prof. Pap., 252.
59. Loewenherz, D. S. (1991), Stability and the initiation of channelized surface drainage: A reassessment of the short wavelength limit, J. Geophys. Res., 96, 8453-8464.
60. Loewenherz-Lawrence, D. S. (1994), Hydrodynamic description for advective sediment transport processes and rill initiation, Water Resour. Res., 30(11), 3203-3212.
61. Luke, J. C. (1972), Mathematical models of landform evolution, J. Geophys. Res., 77, 2,460-2,464.
62. Luke, J. C. (1974), Special solutions for nonlinear erosion problems, J. Geophys. Res., 79, 4035-4040.
63. Luke, J. C. (1976), A note on the use of characteristics in slope evolution models, Z. Geomorphol., Suppl., 25, 114-119.
64. Malin, M. C., and K. S. Edgett (2000), Evidence for recent groundwater seepage and surface runoff on mars, Science, 288(5475), 2330-2335.
65. 10Be accumulations on a hillslope profile, Geology, 21(4), 343-346.
66. Melton, M. A. (1958), Geometric properties of mature drainage systems and their representation in an E4 phase space, J. Geol., 66(1), 35-54.
67. Moglen, G. E., and R. L. Bras (1995), The effect of spatial heterogeneities on geomorphic expression in a model of basin evolution, Water Resour. Res., 31(10), 2613-2623.
68. Moglen, G. E., E. A. B. Eltahir, and R. L. Bras (1998), On the sensitivity of drainage density to climate change, Water Resour. Res., 34(4), 855-862.
69. 10Be chronometry of bedrock-to-soil conversion rates, Earth Planet. Sci. Lett., 111, 483-492.
70. Montgomery, D. R., and W. E. Dietrich (1988), Where do channels begin?, Nature, 336, 232-234.
71. Montgomery, D. R., and W. E. Dietrich (1989), Source areas, drainage density, and channel initiation, Water Resour. Res., 25(8), 1907-1918.
72. Montgomery, D. R., and W. E. Dietrich (1992), Channel initiation and the problem of landscape scale, Science, 255(5046), 826-830.
73. Nash, D. (1980), Morphologic dating of degraded normal fault scarps, J. Geol., 88, 353-360.
74. O'Callaghan, J. F., and D. M. Mark (1984), The extraction of drainage networks from digital elevation data, Comput. Vision Graph. Image Process., 28(3), 323-344.
75. Orange, D. L., R. S. Anderson, and N. A. Breen (1994), Regular canyon spacing in the submarine environment: the link between hydrology and geomorphology, GSA Today, 4(2), 35-39.
76. Parsons, A. J., and A. D. Abrahams (1992), Field investigations of sediment removal in interrill overland flow, in Overland Flow: Hydraulics and Erosion Mechanics, edited by A. J. Parsons and A. D. Abrahams, pp. 307-334, Chapman and Hall, New York.
77. Parsons, A. J., A. D. Abrahams, and J. Wainwright (1994), On determining resistance to interrill overland-flow, Water Resour. Res., 30(12), 3515-3522.
78. Pelletier, J. D. (2004), Persistent drainage migration in a numerical landscape evolution model, Geophys. Res. Lett., 31, L20501, doi:10.1029/2004GL020802.
79. Perron, J. T., W. E. Dietrich, A. D. Howard, J. A. McKean, and J. R. Pettinga (2003), Ice-driven creep on Martian debris slopes, Geophys. Res. Lett., 30(14), 1747, doi:10.1029/2003GL017603.
80. Perron, J. T., J. W. Kirchner, and W. E. Dietrich (2008), Spectral signatures of characteristic spatial scales and nonfractal structure in landscapes, J. Geophys. Res., 113, F04003, doi:10.1029/ 2007JF000866.
81. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (1992), Numerical Recipes in C: The Art of Scientific Computing, Cambridge Univ. Press, New York.
82. Prosser, I. P., and W. E. Dietrich (1995), Field experiments on erosion by overland flow and their implication for a digital terrain model of channel initiation, Water Resour. Res., 31(11), 2867-2876.
83. Quinn, P., K. Beven, P. Chevallier, and O. Planchon (1991), The prediction of hillslope flow paths for distributed hydrological modelling using digital terrain models, Hydrol. Processes, 5(1), 59-79.
84. Reid, L. M. (1989), Channel incision by surface runoff in grassland catchments, Ph.D. thesis, Univ. of Washington, Seattle.
85. Rinaldo, A., W. E. Dietrich, R. Rigon, G. K. Vogel, and I. Rodriguez-Iturbe (1995), Geomorphological signatures of varying climate, Nature, 374, 632-635.
86. Roering, J. J., J. W. Kirchner, and W. E. Dietrich (1999), Evidence for nonlinear, diffusive sediment transport on hillslopes and implications for landscape morphology, Water Resour. Res., 35(3), 853-870.
87. Roering, J. J., J. W. Kirchner, and W. E. Dietrich (2001a), Hillslope evolution by nonlinear, slope-dependent transport: Steady state morphology and equilibrium adjustment timescales, J. Geophys. Res., 106, 16,499-16,514.
88. Roering, J. J., J. W. Kirchner, L. S. Sklar, and W. E. Dietrich (2001b), Hillslope evolution by nonlinear creep and landsliding: An experimental study, Geology, 29(2), 143-146.
89. Roering, J. J., J. T. Perron, and J. W. Kirchner (2007), Functional relationships between denudation and hillslope form and relief, Earth Planet. Sci., Lett., 264, 245-258.
90. Rosenbloom, N. A., and R. S. Anderson (1994), Hillslope and channel evolution in a marine terraced landscape, Santa Cruz, California, J. Geophys. Res., 99, 14,013-14,029.
91. Schorghofer, N., B. Jensen, A. Kudrolli, and D. H. Rothman (2004), Spontaneous channelization in permeable ground: theory, experiment, and observation, J. Fluid Mech., 503, 357-374.
92. Seidl, M. A., and W. E. Dietrich (1992), The problem of channel erosion into bedrock, in Functional Geomorphology, edited by K. Schmidt and J. de Ploey, Catena Suppl., 23, 101-124.
93. Seidl, M. A., W. E. Dietrich, and J. W. Kirchner (1994), Longitudinal profile development into bedrock: An analysis of Hawaiian channels, J. Geol., 102(4), 457-474.
94. Shaler, N. S. (1899), Spacing of rivers with reference to the hypothesis of base-levelling, Geol. Soc. Am. Bull., 10, 263-276.
95. Shreve, R. L. (1967), Infinite topologically random channel networks, J. Geol., 75, 178-186.
96. Simpson, G., and F. Schlunegger (2003), Topographic evolution and morphology of surfaces evolving in response to coupled fluvial and hillslope sediment transport, J. Geophys. Res., 108(B6), 2300, doi:10.1029/2002JB002162.
97. Sklar, L., and W. E. Dietrich (1998), River longitudinal profiles and bedrock incision models: Stream power and the influence of sediment supply, in Rivers Over Rock: Fluvial Processes in Bedrock Channels, Geophys. Monogr. Ser., vol. 107, edited by K. Tinkler and E. Wohl, pp. 237-260, AGU, Washington, D. C.
98. 26Al from an alpine hillslope, Geomorphology, 27(1), 131-150.
99. Smith, T. R., and F. P. Bretherton (1972), Stability and the conservation of mass in drainage basin evolution, Water Resour. Res., 8(6), 1506-1529.
100. Smith, T. R., and G. E. Merchant (1995), Conservation principles and the initiation of chainnelized surface flows, in Natural and anthropogenic influences in fluvial geomorphology, Geophys. Monogr. Ser., vol. 89, edited by A. J. Miller, K. W. Potter, and P. R. Wilcock, pp. 1-25, AGU, Washington, D. C.
101. Smith, T. R., B. Birnir, and G. E. Merchant (1997a), Towards an elementary theory of drainage basin evolution: I. The theoretical basis, Comput. Geosci., 23(8), 811-822.
102. Smith, T. R., G. E. Merchant, and B. Birnir (1997b), Towards an elementary theory of drainage basin evolution: II. A computational evaluation, Compute. Geosci., 23(8), 823-849.
103. Snyder, N. P., K. X. Whipple, G. E. Tucker, and D. J. Merritts (2003), Importance of a stochastic distribution of floods and erosion thresholds in the bedrock river incision problem, J. Geophys. Res., 108(B2), 2117, doi:10.1029/2001JB001655.
104. Stock, J., and W. E. Dietrich (2003), Valley incision by debris flows: Evidence of a topographic signature, Water Resour. Res., 39(4), 1089, doi:10.1029/2001WR001057.
105. Stock, J., and W. Dietrich (2006), Erosion of steepland valleys by debris flows, Geol. Soc. Am. Bull., 118(9), 1125-1148.
106. Stock, J. D., D. R. Montgomery, B. D. Collins, W. E. Dietrich, and L. Sklar (2005), Field measurements of incision rates following bedrock exposure: Implications for process controls on the long profiles of valleys cut by rivers and debris flows, Geol. Soc. Am. Bull., 117, 174-194.
107. Strahler, A. N. (1958), Dimensional analysis applied to fluvially eroded landforms, Geol. Soc. Am. Bull., 69, 279-300.
108. Strahler, A. N. (1964), Quantitative geomorphology of drainage basins and channel networks, in Handbook of Applied Hydrology, edited by V. T. Chow, pp. 4.39-4.76, McGraw-Hill, New York.
109. Syvitski, J. P., and M. D. Morehead (1999), Estimating river-sediment discharge to the ocean: Application to the eel margin, northern california, Mar. Geol., 154(1), 13-28.
110. Talling, P. J., and M. J. Sowter (1999), Drainage density on progressively tilted surfaces with different gradients, Wheeler Ridge, California, Earth Surf. Processes Landforms, 24(9), 809-824.
111. Talling, P. J., M. D. Stewart, C. P. Stark, S. Gupta, and S. J. Vincent (1997), Regular spacing of drainage outlets from linear fault blocks, Basin Res., 9, 275-302.
112. Tarboton, D. G. (1997), A new method for the determination of flow directions and upslope areas in grid digital elevation models, Water Resour. Res., 33(2), 309-319.
113. Tarboton, D., R. L. Bras, and I. Rodriguez-Iturbe (1989), Scaling and elevation in river networks, Water Resour. Res., 25(9), 2037-2051.
114. Tarboton, D. G., R. L. Bras, and I. Rodriguez-Iturbe (1992), A physical basis for drainage density, Geomorphology, 5(1-2), 59-76.
115. Tucker, G. E., and R. L. Bras (1998), Hillslope processes, drainage density, and landscape morphology, Water Resour. Res., 34(10), 2751-2764.
116. Tucker, G. E., and R. Slingerland (1996), Predicting sediment flux from fold and thrust belts, Basin Res., 8(3), 329-349.
117. Tucker, G. E., and R. Slingerland (1997), Drainage basin responses to climate change, Water Resour. Res., 33(8), 2031-2047.
118. Tucker, G. E., and K. X. Whipple (2002), Topographic outcomes predicted by stream erosion models: Sensitivity analysis and intermodel comparison, J. Geophys. Res., 107(B9), 2179, doi:10.1029/ 2001JB000162.
119. van der Beek, P., and J. Braun (1998), Numerical modelling of landscape evolution on geological time-scales: A parameter analysis and comparison with the south-eastern highlands of Australia, Basin Res., 10, 49-68.
120. Whipple, K. X., and G. E. Tucker (1999), Dynamics of the stream-power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs, J. Geophys. Res., 104(B8), 17,661-17,674.
121. Willgoose, G. (1994a), A statistic for testing the elevation characteristics of landscape simulation models, J. Geophys. Res., 99(B7), 13,987-13,996.
122. Willgoose, G. (1994b), A physical explanation for an observed area-slope-elevation relationship for catchments with declining relief, Water Resour. Res., 30(2), 151-160.
123. Willgoose, G. (2005), Mathematical modeling of whole landscape evolution, Annu. Rev. Earth Planet. Sci., 33(1), 443-459.
124. Willgoose, G., R. L. Bras, and I. Rodriguez-Iturbe (1991a), Results from a new model of river basin evolution, Earth Surf. Processes Landforms, 16(3), 237-254.
125. Willgoose, G., R. L. Bras, and I. Rodriguez-Iturbe (1991b), A coupled channel network growth and hillslope evolution model: 1. Theory, Water Resour. Res., 27(7), 1671-1684.
126. Willgoose, G., R. L. Bras, and I. Rodriguez-Iturbe (1991c), A coupled channel network growth and hillslope evolution model: 2. Nondimensionalization and applications, Water Resour. Res., 27(7), 1685-1696.
127. Willgoose, G., R. L. Bras, and I. Rodriguez-Iturbe (1991d), A physical explanation of an observed link area-slope relationship, Water Resour. Res., 27(7), 1697-1702.
128. Willgoose, G., R. L. Bras, and I. Rodriguez-Iturbe (1992), The relationship between catchment and hillslope properties: implications of a catchment evolution model, Geomorphology, 5(1-2), 21-37.
129. Willgoose, G. R., G. R. Hancock, and G. Kuczera (2003), A framework for the quantitative testing of landform evolution models, in Prediction in Geomorphology, Geophys. Monogr. Ser., vol. 135, edited by P. R. Wilcock and R. M. Iverson, pp. 195-216, AGU, Washington, D. C.