Stochastic modeling of the cover effect and bedrock erosion

Water Resources Research

Volumn 45, Issue 3, 2009, Pages

  Turowski, Jens M ^a  

^a SWISS FEDERAL RESEARCH INSTITUTE WSL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

BED LOADS; BED-LOAD TRANSPORT RATES; BEDROCK EROSIONS; CONTROL VOLUMES; EROSION RATES; EXPERIMENTAL DATUM; LINEAR MODELS; MARKOV CHAINS; MODEL-BASED; SEDIMENT SUPPLIES; STOCHASTIC MODELING; TRANSPORT PROCESS;

EROSION; MARKOV PROCESSES; SEDIMENT TRANSPORT; SEDIMENTOLOGY; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC MODELS;

PROBABILITY DISTRIBUTIONS;

BEDLOAD; BEDROCK; EROSION; EXPERIMENTAL STUDY; HYDRAULICS; HYDROLOGICAL MODELING; MARKOV CHAIN; PROBABILITY; STOCHASTICITY;

EID: 65349158323     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2008WR007262     Document Type: Article

References (59)

1. Ancey, C, F. Bigillon, P. Frey, J. Lanier, and R. Ducret (2002), Saltating motion of a bead in a rapid water stream, Phys. Rev. E, 66, 036306, doi:10.1103/PhysRevE.66.036306.
2. Ancey, C, F. Bigillon, P. Frey, and R. Ducret (2003), Rolling motion of a bead in a rapid water stream, Phys. Rev. E, 67, 011303, doi: 10.1103/ PhysRevE.67.011303.
3. Ancey, C, T. Böhm, M. Jodeau, and P. Frey (2006), Statistical description of sediment transport experiments, Phys. Rev. E, 74, 011302, doi: 10.1103/ PhysRevE.74.011302.
4. Ancey, C, A. C. Davison, T. Böhm, M. Jodeau, and P. Frey (2008), Entrainment and motion of coarse particles in a shallow water stream down a steep slope, J. Fluid Mech., 595, 83-114, doi: 10.1017/ S0022112007008774.
5. Ashida, K., and M. Michiue (1972), Study on hydraulic resistance and bedload transport rate in alluvial streams (in Japanese), Trans. Jpn. Soc. Civ. Eng., 206, 59-69.
6. Bagnold, R. A. (1956), The flow of cohesionless grains in fluids, Philos. Trans. R. Soc. London, Ser. A, 249, 235-297, doi:10.1098/rsta. l956. 0020.
7. Bagnold, R. A. (1977), Bedload transport by natural rivers, Water Resour. Res., 13, 303-312, doi:10.1029/WR013i002p00303.
8. Benda, L., and T. Dunne (1997), Stochastic forcing of sediment supply to channel networks from landsliding and debris flow, Water Resour. Res., 33, 2849-2863, doi:10.1029/97WR02388.
9. Bitter, J. G. A. (1963a), A study of erosion phenomena, part I, Wear, 6,5 - 21, doi: 10.1016/0043-1648(63)90003-6.
10. Bitter, J. G. A. (1963b), A study of erosion phenomena, part II, Wear, 6, 169-190, doi:10,1016/0043-1648(63)90073-5.
11. Böhm, T., C. Ancey, P. Frey, J. Reboud, and C. Ducottet (2004), Fluctua- tions of the solid discharge of gravity-driven particle flows in a turbulent stream, Phys. Rev. E, 69, 061307, doi: 10.1103/PhysRevE.69. 061307.
12. Bolch, G, S. Greiner, H. de Meer, and K. S. Trivedi (2006), Queueing Networks and Markov Chains, 2nd ed., John Wiley, Hoboken, N. J. Charu, F., H. Mouilleron, and O. Eiff (2004), Erosion and deposition of particles on a bed sheared by a viscous flow, J. Fluid Mech., 519, 55-80, doi:10.1017/S0022112004001028.
13. Chatanantavet, P., and G. Parker (2008), Experimental study of bedrock channel alleviation under varied sediment supply and hydraulic condi- tions, Water Resour. Res., 44, W12446, doi:10.1029/2007WR006581.
14. Chen, L., and M. C. Stone (2008), Influence of bed material size hetero- geneity on bedload transport uncertainty, Water Resour. Res., 44, W01405, doi: 10.1029/2006WR005483.
15. Cowie, P. A., A. C. Whittaker, M. Attal, G. Roberts, G. E. Tucker, and A. Ganas (2008), New constraints on sediment-flux-dependent river incision: Implications for extracting tectonic signals from river profiles, Geology, 36, 535-538, doi:10.1130/G24681A.l.
16. Cudden, J. R., and T. B. Hoey (2003), The causes of bedload pulses in a gravel channel: The implications of bedload grain-size distributions, Earth Surf. Processes Landforms, 28, 1411-1428, doi:10.1002/esp.521.
17. Einstein, H. A. (1937), Der Geschiebetrίeb als Wahrscheinlichkeitsproblem, Mitt. Versuchsanst. Wasserbau Eidg. Tech. Hochsch. Zürich, Rascher, Zurich, Switzerland.
18. Einstein, H. A. (1950), The bed-load function for sediment transportation in open channel flows, Tech. Bull, 1026, pp. 1-78, U.S. Dep. of Agric, Washington, D. C.
19. Engelund, F., and J. Fredsøe (1976), A sediment transport model for straight alluvial channels, Nord. Hydrol., 7, 293-306.
20. Fernandez Luque, R., and R. van Beek (1976), Erosion and transport of bed-load sediment, J. Hydraul. Res., 14, 127-144.
21. Finnegan, N. J., L. 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.
22. Frey, P., C. Ducottet, and J. Jay (2003), Fluctuations of bed load solid discharge and grain size distribution on steep slopes with image analysis, Exp. Fluids, 35, 589-597, doi:10.1007/s00348-003-0707-9.
23. Gilbert, G. K. (1877), Land sculpture, in The Geology of the Henry Mountains, chap. V, pp. 99-150, U.S. Gov. Print. Off., Washington, D. C.
24. Gomez, B. (1983), Temporal variations in bedload transport rates: The effect of progressive bed armouring, Earth Surf. Processes Landforms, 8, 41-54, doi:10.1002/esp.3290080105.
25. Gomez, B., and M. Church (1989), An assessment of bedload transport formulae for gravel bed rivers, Water Resour. Res., 25(6), 1161-1186, doi: 10.1029/WR025i006p01161.
26. Gomez, B., R. L. Naff, and D. W. Hubbell (1989), Temporal variations in bedload transport rates associated with the migration of bedforms, Earth Surf. Processes Landforms, 14, 135-156, doi:10.1002/esp.3290140205.
27. Hassan, M. A., and M. Church (2001), Sensitivity of bed load transport in Harris Creek: Seasonal and spatial variation over a cobble-gravel bar, Water Resour. Res., 37(3), 813-825, doi:10.1029/2000WR900346.
28. Hegg, C, and D. Rickenmann (1998), Short-time relations between runoff and bed load transport in a steep mountain torrent, in Modelling Soil Erosion, Sediment Transport and Closely Related Hydrological Pro- cesses, edited by W. Summer, E. Klaghofer, and W. Zhang, IAHS Publ., 249, 317-324.
29. Hodge, R., K. Richards, and J. Brasington (2007), A physically based bedload transport model developed for 3-D reach-scale cellular model- ling, Geomorphology, 90, 244-262, doi:10.1016/j.geomorph.2006. 10.022.
30. Iseya, F., and H. Ikeda (1987), Pulsations in bedload transport rates induced by a longitudinal sediment sorting: A flume study using sand and gravel mixtures, Geogr. Ann., Ser. A, 69, 15-27, doi:10.2307/521363.
31. Johnson, J. P., and K. X. Whipple (2007), Feedbacks between erosion and sediment transport in experimental bedrock channels, Earth Surf. Pro- cesses Landforms, 32, 1048-1062, doi:10.1002/esp.l471.
32. Kalinske, A. A. (1947), Movement of sediment as bed load in rivers, Eos Trans. AGU, 28, 615-620.
33. Kirchner, J. W., W. E. Dietrich, F. Iseya, and H. Ikeda (1990), The variability of critical shear stress, friction angle, and grain protrusion in water-worked sediments, Sedimentology, 37, 647-672, doi:10.1111/j. 1365-3091.1990. tb00627.X.
34. Kleinhans, M. G., and L. C. van Rijn (2002), Stochastic prediction of sediment transport in sand-gravel bed rivers, J. Hydro!. Eng., 128, 412-425, doi:10.1061/(ASCE)0733-9429(2002)128:4(412).
35. Kuhnle, R. A., and J. B. Southard (1988), Bed load transport fluctuations in a gravel bed laboratory channel, Water Resour Res., 24, 247-260, doi: 10.1029AVR024i002p00247.
36. Lee, H.-Y., J.-Y. You, and Y.-T. Lin (2002), Continuous saltating process of multiple sediment particles, J. Hydrol. Eng., 128, 443-450, doi: 10.1061/ (ASCE)0733-9429(2002)128:4(443).
37. Lisle, T. E., Y. Cui, G. Parker, J. E. Pizzuto, and A. M. Dodd (2001), The dominance of dispersion in the evolution of bed material waves in gravel- bed rivers, Earth Surf. Processes Landforms, 26, 1409-1420, doi:10.1002/esp.300.
38. Métivier, F., P. Meunier, M. Moreira, A. Crave, C. Chaduteau, B. Ye, and G. Liu (2004), Transport dynamics and morphology of a high mountain stream during the peak flow season: The Ürümqi River (Chinese Tian Shan), in River Flow, vol. 1, edited by R. M. L. Ferreira, E. C. T. L. Alves, and J. G. A. B. Leal, pp. 761-777, Taylor and Francis, London.
39. Niño, Y., and M. Garcia (1994), Gravel saltation: 2. Modeling, Water Resour. Res., 30, 1915-1924, doi:10.1029/94WR00534.
40. Niño, Y., M. Garcia, and L. Ayala (1994), Gravel saltation: 1. Experiments, Water Resour. Res., 30, 1907-1914, doi:10.1029/94WR00533.
41. Paintal, A. S. (1970), A stochastic model of bed load transport, J. Hydraul. Res., 9, 528-554.
42. Parker, G" G. Seminara, and L. Solari (2003), Bed load at low Shields stress on arbitrarily sloping beds: Alternative entrainment formulation, Water Resour. Res., 39(7), 1183, doi:10.1029/2001WR001253.
43. Schmeeckle, M. W., J. M. Nelson, and R. L. Shreve (2007), Forces on stationary particles in near-bed turbulent flows, J. Geophys. Res., 112, F02003, doi: 10.1029/2006JF000536.
44. Seminara, G., L. Solari, and G. Parker (2002), Bed load at low Shields stress on arbitrarily sloping beds: Failure of the Bagnold hypothesis, Water Resour. Res., 38(11), 1249, doi:10.1029/2001WR000681.
45. Shepherd, R. C. (1972), Incised river meanders: Evolution in simulated bedrock, Science, 178, 409-411, doi:10.1126/science.178.4059.409.
46. 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.
47. 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.
48. Sklar, L., and W. E. Dietrich (2004), A mechanistic model for river incision into bedrock by saltating bed load, Water Resour. Res., 40, W06301, doi: 10.1029/2003WR002496.
49. Sumer, B. M., H. C. Lloyd, C. Chua, N.-S. Cheng, and J. Fredsøe (2003), Influence of turbulence on bed load sediment transport, J. Hydrol. Eng., 129(8), 585-596, doi:10.1061/(ASCE)0733-9429(2003)129:8(585).
50. Turowski, J. M., and D. Rickenmann (2009), Tools and cover effects in bedload transport observations in the Pitzbach, Austria, Earth Surf. Pro- cesses Landforms, 34, 26-37, doi: 10.1002/esp. 1686.
51. Turowski, J. M., D. Lague, and N. Hovius (2007), Cover effect in bedrock abrasion: A new derivation and its implications for the modeling of bed- rock channel morphology, J. Geophys. Res., 112, F04006, doi:10.1029/ 2006JF000697.
52. Turowski, J. M., N. Hovius, M.-L. Hsieh, D. Lague, and M.-C. Chen (2008a), Distribution of erosion across bedrock channels, Earth Surf. Processes Landforms, 33, 353-363, doi:10.1002/esp.1559.
53. Turowski, J. M., N. Hovius, A. Wilson, and M.-J. Homg (2008b), Hydrau- lic geometry, river sediment and the definition of bedrock channels, Geomorphology, 99(1-4), 26-38, doi:10.1016/j.geomorph.2007. 10.001.
54. Warburton, J. (1992), Observations of bed load transport and channel bed changes in a proglacial mountain stream, Arct. Alp. Res., 24(3), 195 - 203, doi:10.2307/1551657.
55. Whipple, K. X. (2004), Bedrock rivers and the geomorphology of active orogens, Annu. Rev. Earth Planet. Sci., 32, 151-185, doi:10.1146/ annurev.earth.32.101802.120356.
56. Whipple, K. X., and G. E. Tucker (2002), Implications of sediment-flux- dependent river incision models for landscape evolution, J. Geophys. Res., 107(B2), 2039, doi:10.1029/2000JB000044.
57. Wiberg, P. L., and J. D. Smith (1985), A theoretical model for saltating grains in water, J. Geophys. Res., 90, 7341-7354, doi:10.1029/ JC090iC04p07341.
58. Wilcock, P. R., and J. C. Crowe (2003), Surface-based transport model for mixed-size sediment, J. Hydraul. Eng, 129(2), 120-128, doi:10.1061/ (ASCE)0733-9429(2003)129:2(120).
59. Wohl, E. E., and H. Ikeda (1997), Experimental simulation of channel incision into a cohesive substrate at varying gradients, Geology, 25, 295-298, doi:10.1130/0091-7613(1997)025<0295:ESOCΠ>2.3.CO;2.