A nonlocal theory of sediment buffering and bedrock channel evolution

Journal of Geophysical Research: Earth Surface

Volumn 114, Issue 1, 2009, Pages

  Stark, Colin P ^b   Foufoula Georgiou, Efi ^a   Ganti, Vamsi ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

^b Department of Earth and Environmental Sciences   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BEDROCK; BUFFERING; EROSION RATE; HILLSLOPE; LANDSCAPE CHANGE; LONG RANGE TRANSPORT; POWER LAW; RESIDENCE TIME; RIVER CHANNEL;

EID: 70349506874     PISSN: None     EISSN: 21699011     Source Type: Journal    
DOI: 10.1029/2008JF000981     Document Type: Article

References (58)

1. Baeumer, B., D. A. Benson, M. M. Meerschaert, and S. W. Wheatcraft (2001), Subordinated advection-dispersion equation for contaminant transport, Water Resour. Res., 37(6), 1543-1550. (Pubitemid 32480655)
2. Benson, D. A. (1998), The fractional advection-dispersion equation: Development and application, Ph.D. thesis, University of Nevada, Reno, Nev.
3. Benson, D. A., S. W. Wheatcraft, and M. M. Meerschaert (2000a), Application of a fractional advection-dispersion equation, Water Resour. Res., 36(6), 1403-1412.
4. Benson, D. A., S. W. Wheatcraft, and M. M. Meerschaert (2000b), The fractional-order governing equation of Lévy motion, Water Resour. Res., 36(6), 1413-1423.
5. Berkowitz, B., J. Klafter, R. Metzler, and H. Scher (2002), Physical pictures of transport in heterogeneous media: Advection-dispersion, random- walk, and fractional derivative formulations, Water Resour. Res., 38(10), 1191, doi:10.1029/2001WR001030. (Pubitemid 36111254)
6. Church, M., and M. A. Hassan (1992), Size and distance of travel of unconstrained clasts on a streambed, Water Resour. Res., 28(1), 299-303.
7. Cushman, J., and T. Ginn (2000), Fractional advection-dispersion equation: A classical mass balance with convolution-fickian flux, Water Resour. Res., 36(12), 3763-3766. (Pubitemid 32039925)
8. Dadson, S. J. (2004), Erosion of an active mountain belt, Ph.D. thesis, University of Cambridge, Cambridge, U. K.
9. Dadson, S. J., et al. (2004), Earthquake-triggered increase in sediment delivery from an active mountain belt, Geology, 32(8), 733-736.
10. 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.
11. Dodov, B., and E. Foufoula-Georgiou (2004), Generalized hydraulic geometry: Derivation based on multiscaling formalism, Water Resour. Res., 40, W06302, doi: 10.1029/2003WR002082. (Pubitemid 38947125)
12. Feller, W. (1971), An Introduction to Probability Theory and Its Applica-. tions, vol.2, 2nd ed., Wiley, New York.
13. Finnegan, N. J., L. S. Sklar, and T. K. Fuller (2007), Interplay of sediment supply, river incision, and channel morphology revealed by the transient evolution of an experimental bedrock channel, J. Geophys. Res., 112, F03S11, doi:10.1029/2006JF000569.
14. Flint, J. J. (1974), Stream gradient as a function of order, magnitude, and discharge, Water Resour. Res., 10, 969-973.
15. Gabet, E. J., D. W. Burbank, B. Pratt-Sitaula, J. Putkonen, and B. Bookhagen (2008), Modern erosion rates in the High Himalayas of Nepal, Earth Planet. Sci Lett., 267(3-4), 482-494.
16. Gorenflo, R. (1997), Fractional calculus: Some numerical methods, in Fractals and Fractional Calculus in Continuum Mechanics, edited by A. Carpinteri and F. Mainardi, pp. 277-290, Springer-Verlag, Wien, Germany.
17. Gorenflo, R., and F. Mainardi (1997), Fractional calculus: Integral and differential equations of fractional order, in Fractals and Fractional Calculus in Continuum Mechanics, edited by A. Carpinteri and F. Mainardi, pp. 223-276, Springer-Verlag, Wien, Germany.
18. Gorenflo, R., and F. Mainardi (1998a), Feller fractional diffusion and Lévy stable motions, paper presented at 5th Conference on Levy processes: Theory and Applications, MaPhySto Cent., Dept. of Appl. Math, and Stat, Univ. of Aarhus, Copenhagen.
19. Gorenflo, R., and F. Mainardi (1998b), Random walk models for spacefractional diffusion processes, Fractional Calculus Appl. Anal, 1(2), 167-191.
20. Gorenflo, R., and F. Mainardi (1999), Approximation of Lévy-Feller diffusion by random walk, J. Anal. Appl, 18(2), 231-246.
21. Gorenflo, R., G. D. Fabritiis, and F. Mainardi (1999), Discrete random walk models for symmetric Lévy-Feller diffusion processes, Physica A, 269, 79-89.
22. Grünwald, A. K. (1867), Uber "begrenzte" derivation und deren anwendung, Z. Angew. Math. Phys., 12, 441-480.
23. Gupta, V. K., and E. Waymire (1989), Statistical self-similarity in river networks parameterized by elevation, Water Resour. Res., 25(3), 463-476.
24. Gupta, V. K., O. J. Mesa, and D. Dawdy (1994), Multiscaling theory of floods: Regional quantile analysis, Water Resour. Res., 30, 3405-3421.
25. Harp, E. L., and R. W. Jibson (1996), Landslides triggered by the 1994 Northridge, California, earthquake, Bull. Seismol Soc. Am., 86, S319-S332. (Pubitemid 27004600)
26. Hassan, M. A., and M. Church (1991), Distance of movement of coarse particles in gravel bed streams, Water Resour. Res., 27(4), 503-511.
27. Lague, D., N. Hovius, and P. Davy (2005), Discharge, discharge variability, and the bedrock channel profile, J. Geophys. Res., 110, F04006, doi: 10.1029/2004JF000259.
28. Levy, P. (1937), Théorie de l'Addition des Variables Aléatoires, GauthierVillars, Paris.
29. Lin, G W, C. L. Shieh, B. D. Yuan, Y.-C. Shieh, S. H. Liu, and S. Y. Lee (2003), Impact of the Chi-Chi earthquake on the occurrence of landslides and debris flows: Example from the Chenyulan River watershed, Eng. Geol, 71, 49-61.
30. Mainardi, F., P. Paradisi, and R. Gorenflo (1998), Probability distributions generated by fractional diffusion equations, in Econophysics, edited by J. Kertész and I. Kondor, Kluwer, Dordrecht, Netherlands.
31. Mantegna, R. N. (1994), Fast, accurate algorithm for numerical simulations of Lévy stable stochastic processes, Phys. Rev. E, 49, 4677-4683.
32. Mantegna, R. N., and H. E. Stanley (1994), Stochastic process with ultraslow convergence to a Gaussian: The truncated Lévy flight, Phys. Rev. Lett., 73, 2946-2949.
33. Meerschaert, M. M., D. A.- Benson, and B. Baeumer (1999), Multidimensional advection and fractional dispersion, Phys. Rev. E, 59(5), 5026-5028.
34. Miller, K. S., and B. Ross (1993), An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York.
35. Molnar, P., R. S. Anderson, G. Kier, and J. Rose (2006), Relationships among probability distributions of stream discharges in floods, climate, bed load transport, and river incision, J. Geophys. Res., 111, F02001, doi: 10.1029/2005JF000310. (Pubitemid 46542333)
36. Montgomery, D. R. (2001), Slope distributions, threshold hillslopes, and steady-state topography, Am. J. Sci, 301, 423-454.
37. Oldham, K. B., and J. Spanier (1974), The Fractional Calculus, Academic, New York.
38. Podlubny, I. (1999), Fractional Differential Equations, vol.198, Academic, San Diego.
39. Rhoads, B. (1987), Stream power terminology, Prof. Geogr, 39(2), 189-195.
40. Saichev, A. I., and G. M. Zaslavsky (1997), Fractional kinetic equations: Solutions and applications, Chaos, 7(4), 753-764. (Pubitemid 127368185)
41. Samko, S. G., A. A. Kilbas, and O. I. Marichev (1993), Fractional Integrals and Derivatives: Theory and Applications (translated from Russian), Gordon and Breach, Zurich.
42. Samorodnitsky, G., and M. S. Taqqu (1994), Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman and Hall, London.
43. 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. J. Tinkler and E. E. Wohl, pp. 237-260, AGU, Washington, D. C.
44. Sklar, L., and W. E. Dietrich (2001), Sediment and rock strength controls on river incision into bedrock, Geology, 29, 1087-1090, doi:10.1130/ 0091-7613(2001)029<1087:SARSCO>2.0.CO;2. (Pubitemid 34060647)
45. Sklar, L., and W. E. Dietrich (2004), A mechanistic model for river incision into bedrock by saltating bedload, Water Resour. Res., 40, W06301, doi: 10.1029/2003 WR002496. (Pubitemid 38947124)
46. Sklar, L., and W. E. Dietrich (2006), The role of sediment in controlling steady-state bedrock channel slope: Implications of the saltation-abrasion incision model, Geomorphology, 1-2, 58-83. (Pubitemid 44696138)
47. Snyder, N. P., K. X. Whipple, G. E. Tucker, and D. M. 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.
48. Stark, C. P. (2006), A self-regulating model of bedrock river channel geometry, Geophys. Res. Lett., 32, L04402, doi:10.1029/2005GL023193.
49. Stark, C. P., J. K. Weissel, and P. S. Dodds (2000), A Levy diffusion model of sediment transport and landscape evolution, EOS, Trans. AGU, 81(48), Fall Meet. Suppl, Abstract H12B-13.
50. Stock, J. D., and D. R. Montgomery (1999), Geologic constraints on bedrock river incision using the stream power law, J. Geophys. Res., 104(B3), 4893-4993.
51. Tarboton, D. G., R. L. Bras, and I. Rodriguez-Iturbe (1989), Scaling and elevation in river networks, Water Resour. Res., 25(9), 2037-2051.
52. Tinkler, K. J., and E. E. Wohl (Eds.) (1998), Rivers Over Rock: Fluvial Processes in Bedrock Channels, Geophys. Monogr. Ser., vol.107, AGU, Washington, D. C.
53. Tucker, G. E., and R. L. Bras (2000), A stochastic approach to modeling the role of rainfall variability in drainage basin evolution, Water Resour. Res., 36(7), 1953-1964.
54. Turowski, J. M., N. Hovius, A. Wilson, and M.-J. Homg (2008), Hydraulic geometry, river sediment and the definition of bedrock channels, Geomorphology, 99(1-4), 26-38, doi:10.1016/j.geomorph.2007.10.001.
55. Whipple, K. X. (2004), Bedrock rivers and the geomorphology of active orogens, Annu. Rev. Earth Planet. Sci, 32, 151-185.
56. 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, 17,661-17,674.
57. Wobus, C. W, G. E. Tucker, and R. S. Anderson (2006), Self-formed bedrock channels, Geophys. Res. Lett., 33, L18408, doi:10.1029/ 2006GL027182, 1-6.
58. Zhang, Y., D. A. Benson, M. M. Meerschaert, and E. M. LaBolle (2007), Space-fractional advection-dispersion equations with variable parameters: Diverse formulas, numerical solutions, and application to the Macrodispersion Experiment site data, Water Resour. Res., 43, W05439, doi: 10.1029/2006 WR004912. (Pubitemid 46998239)