Critical Shields values in coarse-bedded steep streams

Water Resources Research

Volumn 49, Issue 11, 2013, Pages 7427-7447

  Bunte, Kristin ^a   Abt, Steven R ^a   Swingle, Kurt W ^b   Cenderelli, Dan A ^c   Schneider, Johannes M ^d  

^a Department of Environmental and Radiological Health Sciences   (United States)

^b University of Col orado   (United States)

^c USDA FOREST SERVICE   (United States)

^d WSL INSTITUTE FOR SNOW AND AVALANCHE RESEARCH SLF   (Switzerland)

Author keywords

critical shields values; flow competence; gravel bed load transport; mountain streams; particle mobility; relative bed mobility

Indexed keywords

CRITICAL SHIELDS VALUES; FLOW COMPETENCE; GRAVEL BED LOAD; MOUNTAIN STREAMS; PARTICLE MOBILITY;

SEDIMENT TRANSPORT;

STREAM FLOW;

BEDLOAD; CRITICAL FLOW; FLOW PATTERN; GRAVEL BED STREAM; MOBILITY; MOUNTAIN STREAM; PARTICLE MOTION; SEDIMENT TRANSPORT;

EID: 84887587833     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1002/2012WR012672     Document Type: Article

References (117)

1. Andrews, E. D., (1983), Entrainment of gravel from naturally sorted riverbed material, Geol. Soc. Am. Bull., 94, 1225-1231.
2. Andrews, E. D., (1994), Marginal bed load transport in a gravel bed stream, Sagehen Creek, California, Water Resour. Res., 30, 2241-2250. (Pubitemid 285302)
3. Andrews, E. D., and, J. D. Smith, (1992), A theoretical model for calculating marginal bedload transport rates of gravel, in Dynamics of Gravel-Bed Rivers, edited by, P. Billi, et al., pp. 41-52, John Wiley, Chichester, U. K.
4. Bathurst, J. C., W. H. Graf, and, H. H. Cao, (1983), Initiation of sediment transport in steep channels with coarse bed material, in Mechanics of Sediment Transport, edited by, B. M. Sumer, and, A. Müller, Proc. Euromech 156, Istanbul, pp. 207-213, Balkema, Rotterdam, The Netherlands. (Pubitemid 14518381)
5. Bathurst, J. C., W. H. Graf, and, H. H. Cao, (1987), Bedload discharge equations for steep mountain rivers, in Sediment Transport in Gravel-Bed Rivers, edited by, C. R. Thorne, J. C. Bathurst, and, R. D. Hey, pp. 453-491, John Wiley, Chichester, U. K.
6. Beschta, R. L., (1987), Conceptual models of sediment transport in streams, in Sediment Transport in Gravel-Bed Rivers, edited by, C. R. Thorne, J. C. Bathurst, and, R. D. Hey, pp. 387-419, John Wiley, Chichester, U. K.
7. Brayshaw, A. C., L. E. Frostick, and, I. Reid, (1983), The hydrodynamics of particle clusters and sediment entrainment in coarse alluvial channels, Sedimentology, 30, 137-143.
8. Brownlie, W. R., (1981), Prediction of flow depth and sediment discharge in open channels, Rep. KH-R-43A, 232 pp., W.M. Keck Lab. Hydraul. Water Resour., Calif. Inst. Technol., Pasadena, Calif.
9. Buffington, J. M., (2012), Changes in channel morphology over human time scales, in Gravel Bed Rivers: Processes, Tools, Environments, edited by, M. Church, P. M. Biron, and, A. G. Roy, pp. 435-463, John Wiley, Hoboken, N. J., ISBN 9781119952503.
10. Buffington, J. M., and, D. R. Montgomery, (1997), A systematic analysis of eight decades of incipient motion studies, with special reference to gravel-bed rivers, Water Resour. Res., 33, 1993-2029. (Pubitemid 27335796)
11. Buffington, J. M., and, D. R. Montgomery, (1999), Effects of hydraulic roughness on surface textures of gravel-bed rivers, Water Resour. Res., 35, 3507-3521.
12. Buffington, J. M., and, D. R. Montgomery, (2001), Reply to Comment on: "Effects of hydraulic roughness on surface textures of gravel-bed rivers" and "Effects of sediment supply on surface textures of gravel-bed rivers" made by P.R. Wilcock and to Comment on: "Effects of hydraulic roughness on surface textures of gravel-bed rivers" made by R.G. Millar and C.D. Rennie, Water Resour. Res., 37, 1529-1533.
13. Buffington, J. M., D. R. Montgomery, and, H. M. Greenberg, (2004), Basin-scale availability of salmonid spawning gravel as influenced by channel type and hydraulic roughness in mountain catchments, Can. J. Fish. Aquat. Sci., 61, 2085-2096, doi: 10.1139/F04-141.
14. Buffington, J. M., D. R. Montgomery, and, H. M. Greenberg, (2006), Erratum: Basin-scale availability of salmonid spawning gravel as influenced by channel type and hydraulic roughness in mountain catchments, Can. J. Fish. Aquat. Sci., 63, 2389, doi: 10.1139/F06-143.
15. Buffington, J. M., B. B. Roper, E. Archer, and, C. Moyer, (2009), Reply to Discussion by David L. Rosgen "The Role of Observer Variation in Determining Rosgen Stream Types in Northeastern Oregon Mountain Streams". J. Am. Water Resour. Assoc., 45 (5), 1298-1312, doi: 10.1111/j.1752-1688.2009. 00363.x.
16. Bunte, K., (1996), Analyses of the temporal variation of coarse bedload transport and its grain size distribution (Squaw Creek, Montana, USA), Gen. Tech. Rep. RM-GTR-288, 123 pp., U.S. Dep. of Agric., For. Serv., Rocky Mt. For. and Range Exp. Stn. Fort Collins, Colo.
17. Bunte, K., (2012a), Discussion of "Recent advances in the dynamics of steep channels" by F. Comiti and L. Mao, in Gravel Bed Rivers: Processes, Tools, Environments, edited by, M. Church, P. M. Biron, and, A. G. Roy, p. 374, John Wiley, Hoboken, N. J.
18. Bunte, K., (2012b), Discussion of "Semi-alluvial channels and sediment-flux-driven bedrock erosion" by J. Turowski, in Gravel Bed Rivers: Processes, Tools, Environments, edited by, M. Church, P. Biron, and, A. Roy, pp. 374-377, John Wiley, Hoboken, N. J.
19. Bunte, K., and, S. R. Abt, (2001a), Sampling surface and subsurface particle-size distributions in wadable gravel- and cobble-bed streams for analysis in sediment transport, hydraulics, and streambed monitoring, Gen. Tech. Rep. RMRS-GTR-74, 428 pp., U.S. Dep. of Agric., For. Serv., Rocky Mt. Res. Stn., Fort Collins, Colo.
20. Bunte, K., and, S. R. Abt, (2001b), Sampling frame for improving pebble count accuracy in coarse gravel-bed streams, J. Am. Water Resour. Assoc., 37 (4), 1001-1014. (Pubitemid 32948849)
21. Bunte, K., and, S. R. Abt, (2005), Effect of sampling time on measured gravel bedload transport rates in a coarse-bedded stream, Water Resour. Res., 41, W11405, doi: 10.1029/2004WR003880.
22. Bunte, K., and, L. H. MacDonald, (1999), Scale considerations and the detectability of sedimentary cumulative watershed effects, Tech. Bull. 776, 327 pp., Natl. Counc. of the Pap. Ind. for Air and Stream Impr., Triangle Research Park, N. C.
23. Bunte, K., S. R. Abt, J. P. Potyondy, and, S. E. Ryan, (2004), Measurement of coarse gravel and cobble transport using a portable bedload trap, J. Hydraul. Eng., 130 (9), 879-893. (Pubitemid 39196687)
24. Bunte, K., K. Swingle, and, S. R. Abt, (2007), Guidelines for using bedload traps in coarse-bedded mountain streams: Construction, installation, operation and sample processing, Gen. Techn. Rep. RMRS-GTR-191, 91 pp., U.S. Dep. of Agric., For. Serv., Rocky Mt. Res. Stn., Fort Collins, Colo.
25. Bunte, K., S. R. Abt, J. P. Potyondy, and, K. W. Swingle, (2008), A comparison of coarse bedload transport measured with bedload traps and Helley-Smith samplers, Geodin. Acta, 21 (1/2), 53-66.
26. Bunte, K., S. R. Abt, K. W. Swingle, and, J. P. Potyondy, (2009), Comparison of three pebble count protocols (EMAP, PIBO, and SFT) in two mountain gravel-bed streams, J. Am. Water Resour. Assoc., 45 (5), 1209-1227, doi: 10.1111/j.1752-1688.2009.00355.x.
27. Bunte, K., S. R. Abt, K. W. Swingle, and, J. P. Potyondy, (2010a), Bankfull mobile particle size and its predictions from a Shields-type approach, in Proc. 4th Fed. Interagency Hydrol. Model. Conf. and 9th Fed. Interagency Sediment. Conf., Advisory Committee on Water Information, [CD-ROM] ISBN 978-0-9779007-3-2.
28. Bunte, K., S. R. Abt, K. W. Swingle, and, J. P. Potyondy, (2010b), Functions to adjust transport rates from a Helley-Smith sampler to bedload traps in coarse gravel-bed streams (rating curve approach), in Proc. 4th Fed. Interagency Hydrol. Model. Conf. and 9th Fed. Interagency Sediment. Conf., Advisory Committee on Water Information, [CD-ROM] ISBN 978-0-9779007-3-2.
29. Bunte, K., K. W. Swingle, and, S. R. Abt, (2010c), Necessity and difficulties of field calibration of signals from surrogate techniques in gravel-bed streams: Possibilities for bedload trap samples, in Bedload-Surrogate Monitoring Technologies, U.S. Geol. Surv. Sci. Invest. Rep. 2010-5091, edited by, J. R. Gray, J. B. Laronne, and, J. D. G. Marr, pp. 107-129, Reston, Va.
30. Bunte, K., K. W. Swingle, J. P. Potyondy, and, S. R. Abt, (2011), Beaver dam effects on gravel transport patterns: A case study, Abstract EP21C-0711 presented at 2011 Fall Meeting, AGU, San Francisco, Calif.
31. Bunte, K., K. Swingle, S. Abt, and, J. Potyondy, (2012), Bedload traps for sampling gravel/cobble bedload and what we learned from them, Keynote talk, International Workshop Monitoring bedload and debris flows in mountain basins, Free University of Bolzano, Italy [Available at: http://www.unibz.it/EN/ SCIENCETECHNOLOGY/WELCOME/MONITORINGBEDLOADANDDEBRISFLOWSINMOUNTAINBASINS.html.]
32. Camenen, B., (2012), Discussion of "Understanding the influence of slope on the threshold of coarse grain motion: Revisiting critical stream power" edited by, C. Parker, N. J. Clifford, and, C. R. Thorne, Geomorphology, vol. 126, March 2011, pp. 51-65, Geomorphology, 139-140, 34-38, doi: 10.1016/j.geomorph.2011.10.033.
33. Carling, P. A., A. Kelsey, and, M. S. Glaister, (1992), Effect of bed roughness, particle shape and orientation on initial motion criteria, in Dynamics of Gravel Bed Rivers, edited by, P. Billi, et al., pp. 23-36, John Wiley, Chichester, U. K.
34. Church, M., and, M. A. Hassan, (2002), Mobility of bed material in Harris Creek, Water Resour. Res., 38 (11), 1237, doi: 10.1029/2001WR000753.
35. Church, M., M. A. Hassan, and, J. F. Wolcott, (1998), Stabilizing self-organized structures in gravel-bed stream channels: Field and experimental observations, Water Resour. Res., 34, 3169-3179. (Pubitemid 28494947)
36. CIRIA, CUR, CETMEF (2007), The Rock Manual. The Use of Rock in Hydraulic Engineering, 2nd ed., 1302 pp., C683, London.
37. Comiti, F., and, L. Mao, (2012), Recent advances in the dynamics of steep channels, in Gravel Bed Rivers: Processes, Tools, Environments, edited by, M. Church, P. M. Biron, and, A. G. Roy, pp. 353-377, John Wiley, Hoboken, N. J.
38. Duan, N., (1983), Smearing estimate: A nonparametric retransformation method, J. Am. Stat. Assoc., 87, 605-610.
39. Fenton, J. D., and, J. E. Abbott, (1977), Initial movement of grains on a stream bed: The effects of relative protrusion, Proc. R. Soc. London, Ser. A, 352 (1671), 523-537.
40. Ferguson, R. I., (1986), River loads underestimated by rating curves, Water Resour. Res., 22, 74-76. (Pubitemid 16153954)
41. Ferguson, R. I., (1987), Accuracy and precision of methods for estimating river loads, Earth Surf. Processes Landforms, 12, 95-104.
42. Ferguson, R. I., (2012), River channel slope, flow resistance, and gravel entrainment thresholds, Water Resour. Res., 48, W05517, doi: 10.1029/2011WR010850.
43. Fisher, J. S., B. L. Sill, and, D. F. Clark, (1983), Organic detritus particles: Initiation of motion criteria on sand and gravels, Water Resour. Res., 19, 1627-1631.
44. Gomez, B., (1983), Temporal variations in bedload transport rates: The effect of progressive bed-armouring, Earth Surf. Processes Landforms, 8, 41-54. (Pubitemid 13506728)
45. Gordon, N. D., T. A. McMahon, and, B. L. Finlayson, (1992), Stream Hydrology: An Introduction for Ecologists, 526 pp., John Wiley, Chichester, U. K.
46. Halwas, K. L., and, M. Church, (2002), Channel units in small, high gradient streams on Vancouver Island, British Columbia, Geomorphology, 43, 243-256. (Pubitemid 34170280)
47. Hassan, M. A., and, M. Church, (2000), Experiments on surface structure and partial sediment transport on a gravel bed, Water Resour. Res., 36, 1885-1895. (Pubitemid 30651202)
48. Hassan, M. A., and, M. Church, (2001), Sensitivity of bedload transport in Harris Creek: Seasonal and spatial variation over a cobble-gravel bar, Water Resour. Res., 37, 813-825. (Pubitemid 32532591)
49. Helley, E. J., and, W. Smith, (1971), Development and calibration of a pressure-difference bedload sampler, USDI, U.S. Geol. Surv. Water Resour. Div. Open File Rep., 18 pp.
50. Hirsch, R. M., D. R. Helsel, T. A. Cohn, and, E. J. Gilroy, (1993), Statistical analysis of hydrological data, in Handbook of Hydrology, edited by, D. R. Maidment, p. 17.1-17.55, McGraw-Hill, New York.
51. Inman, D. L., (1952), Measures for describing the size distribution of sediments, J. Sediment. Petrol., 22, 125-145.
52. Isaak, D. J., W. A. Hubert, and, K. L. Krueger, (1999), Accuracy and precision of stream reach water surface slopes estimated in the field and from maps, North Am. J. Fish. Manage., 19, 141-148. (Pubitemid 29311564)
53. Isbash, S. V., (1936), Construction of dams by depositing rocks in running water Transactions, Second Congress on Large Dams, Vol. 5, p. 123-136, Washington, DC.
54. Kappesser, G. B., (2002), A riffle stability index to evaluate sediment loading to streams, J. Am. Water Resour. Assoc., 38 (4), 1069-1081.
55. Kaufmann, P. R., J. M. Faustini, D. P. Larson, and, M. A. Shirazi, (2008), A roughness-corrected index of relative bed stability for regional stream surveys, Geomorphology, 99, 150-170.
56. Kaufmann, P. R., D. P. Larsen, and, J. M. Faustini, (2009), Bed stability and sedimentation associated with human disturbances in Pacific Northwest streams, J. Am. Water Resour. Assoc., 45 (2), 434-459, doi: 10.1111/j.1752-1688. 2009.00301.x.
57. Kellerhals, R., and, D. I. Bray, (1971), Sampling procedures for coarse fluvial sediments, J. Hydraul. Div., 97 (HY 8), 1165-1180.
58. 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.
59. Koch, R. W., and, G. M. Smillie, (1986), Bias in hydrologic prediction using log-transformed prediction models, Water Resour. Bull., 22 (5), 717-723.
60. Komar, P. D., and, Z. Li, (1986), Pivoting analysis of the selective entrainment of sediments by shape and size with application to gravel threshold, Sedimentology, 33, 425-436.
61. Lamb, M. P., W. E. Dietrich, and, J. G. Vendetti, (2008), Is the critical Shields stress for incipient sediment motion dependent on channel slope? J. Geophys. Res., 113, F02008, doi: 10.1029/2007JF000831.
62. Leopold, L. B., (1994), A View of the River, 298 pp., Harvard Univ. Press, Cambridge, Mass.
63. Lepp, L. R., C. J. Koger, and, J. A. Wheeler, (1993), Channel erosion in steep gradients, gravel-paved streams, Bull. Assoc. Eng. Geol., 30 (4), 443-454. (Pubitemid 24403550)
64. Li, Z., and, P. D. Komar, (1986), Laboratory measurements of pivoting angles for application to selective entrainment of gravel in a current, Sedimentology, 33, 413-423.
65. Lorang, M. S., and, F. R. Hauer, (2003), Flow competence and streambed stability: An evaluation of technique and application, J. N. Am. Benthol. Soc., 22 (4), 475-491. (Pubitemid 37481640)
66. Mao, L., (2012), The effect of hydrographs on bed load transport and bed sediment spatial arrangement, J. Geophys. Res., 117, F03024, doi: 10.1029/2012JF002428.
67. Meshkova, L. V., P. A. Carling, and, T. Buffin-Bélanger, (2012), Nomenclature, complexity, semi-alluvial channels and sediment-flux-driven bedrock erosion, in Gravel-Bed Rivers: Processes, Tools, Environments, edited by, M. Church, P. M. Biron, and, A. G. Roy, p. 424-431, John Wiley, Hoboken, N. J., doi: 10.1002/9781119952497.ch31.
68. Meyer-Peter, E., and, R. Müller, (1948), Formulas for bed-load transport, in Proc. Intl. Assoc. Hydraul. Structures Res., 2nd Meeting, Stockholm, p. 39-64, Delft, The Netherlands.
69. Milhous, R., (1973), Sediment transport in a gravel-bottomed stream, Ph.D. thesis, Oreg. State Univ., Corvallis, Oreg.
70. Miller, D. M., (1984), Reducing transformation bias in curve fitting, Am. Stat., 38 (2), 124-126, doi: 10.1080/00031305.1984.10483180.
71. Miller, M. C., I. N. McCave, and, P. D. Komar, (1977), Threshold of sediment motion in undirectional currents, Sedimentology, 24, 507-527.
72. Molnar, P., A. L. Densmore, B. W. McArdell, J. M. Turowski, and, P. Burlando, (2010), Analysis of changes in the step-pool morphology and channel profile of a steep mountain stream following a large flood, Geomorphology, 124, 85-94.
73. Montgomery, D. R., and, J. M. Buffington, (1997), Channel-reach morphology in mountain drainage basins, Geol. Soc. Am. Bull., 109 (5), 596-611.
74. Mueller, E. R., J. Pitlick, and, J. M. Nelson, (2005), Variation in the reference Shields stress for bedload transport in gravel-bed streams and rivers, Water Resour. Res., 41, W04006, doi: 10.1029/2004WR003692.
75. Neill, C. R., (1968), A reexamination of the beginning of movement for coarse granular bed materials, Rep. no. INT 68, Hydraul. Res. Stn., Wallingford, U. K.
76. Nelson, P. A., J. G. Venditti, W. E. Dietrich, J. W. Kirchner, H. Ikeda, F. Iseya, and, L. S. Sklar, (2009), Response of bed surface patchiness to reductions in sediment supply, J. Geophys. Res., 114, F02005, doi: 10.1029/2008JF001144.
77. Nelson, P. A., W. E. Dietrich, and, J. G. Venditti, (2010), Bed topography and the development of forced bed surface patches, J. Geophys. Res., 115, F04024, doi: 10.1029/2010JF001747.
78. Olsen, D. S., A. C. Whitaker, and, D. F. Potts, (1997), Assessing stream channel stability thresholds using flow competence estimates at bankfull stage, J. Am. Water Resour. Assoc., 33 (6), 1197-1207. (Pubitemid 28052119)
79. Paintal, A. S., (1971), A stochastic model of bedload transport, J. Hydraul. Res., 9 (4), 527-553.
80. Parker, C., N. J. Clifford, and, C. R. Thorne, (2011), Understanding the influence of slope on the threshold of coarse grain motion: Revisiting critical stream power, Geomorphology, 126, 51-65, doi: 10.1016/j.geomorph.2010.10.027.
81. Parker, G., (1979), Hydraulic geometry of active gravel-bed rivers, J. Hydraul. Div., ASCE, 105 (HY 9), 1185-1201. (Pubitemid 9465373)
82. Parker, G., P. C. Klingeman, and, D. G. McLean, (1982), Bedload and the size distribution of paved gravel-bed streams, J. Hydraul. Div. Am. Soc. Civ. Eng., 108 (HY 4), 544-571. (Pubitemid 12477398)
83. Parker, G., C. M. Toro-Escobar, M. Ramey, and, S. Beck, (2003), The effect of floodwater extraction on mountain stream morphology, J. Hydraul. Eng., 129 (11), 885-895. (Pubitemid 37447139)
84. Parker, G., P. R. Wilcock, C. Paola, W. E. Dietrich, and, J. Pitlick, (2007), Physical basis for quasi-universal relations describing bankfull hydraulic geometry of single-thread gravel bed rivers, J. Geophys. Res., 112, F04005, doi: 10.1029/2006JF000549.
85. Pitlick, J., E. R. Mueller, C. Segura, R. Cress, and, M. Torizzo, (2008), Relation between flow, surface-layer armoring and sediment transport in gravel-bed rivers, Earth Surf. Processes Landforms, 33 (8), 1192-1209, doi: 10.1002/esp.1607.
86. Potyondy, J. P., K. Bunte, S. R. Abt, and, K. W. Swingle, (2010), Bedload movement in mountain channels: Insights gained from use of portable bedload traps, in Proc. 4th Fed. Interagency Hydrol. Model. Conf. and 9th Fed. Interagency Sediment. Conf., Advisory Committee on Water Information, [CD-ROM] ISBN 978-0-9779007-3-2.
87. Recking, A., (2009), Theoretical development on the effects of changing flow hydraulics on incipient bedload motion, Water Resour. Res., 45, W04401, doi. 1029/2008WR006826.
88. Recking, A., and, J. Pitlick, (2013), Shields versus Isbash. J. Hydraul. Eng., 139 (1), 51-54, doi: 10.1061/(ASCE)HY.1943-7900.0000647.
89. Reid, I., L. E. Frostick, and, J. T. Layman, (1985), The incidence and nature of bedload transport during flood flows in coarse-grained alluvial channels, Earth Surf. Processes Landforms 10, 33-44. (Pubitemid 15474249)
90. Rice, S., and, M. Church, (1996), Sampling surficial fluvial gravels: The precision of size distribution percentile estimates, J. Sediment. Res., 66 (3), 654-665.
91. Rickenmann, D., J. M. Turowski, B. Fritschi, A. Klaiber, and, L. Andreas, (2012), Bedload transport measurements at the Erlenbach stream with geophones and automated basket samplers, Earth Surf. Processes Landforms, 37 (9), 1000-1011, doi: 10.1002/esp.3225.
92. Roper, B. B., J. M. Buffington, E. Archer, C. Moyer, and, M. Ward, (2008), The role of observer variation in determining Rosgen stream types in northeastern Oregon mountain streams, J. Am. Water Resour. Assoc., 44 (2), 417-427, doi: 10.1111/j.1752-1688.2008.00171.x. (Pubitemid 351432380)
93. Rosgen, D. L., (1994), A classification of natural rivers, Catena, 21, 169-199.
94. Rosgen, D. L., (1996), Applied River Morphology, Wildland Hydrol., Pagosa Springs, Colo.
95. Rouse, H., (1939), An analysis of sediment transportation in light of fluid turbulence, SCS-TP-25, Sediment Div., U.S. Dep. of Agric., Soil Conserv. Serv., Washington, D. C.
96. Ryan S. E., L. S. Porth, and, C. A. Troendle, (2005), Coarse sediment transport in mountain streams in Colorado and Wyoming, USA, Earth Surf. Processes Landforms, 30, 269-288, doi: 10.1002/esp.1128. (Pubitemid 40435775)
97. Schmid, B., (2011), Geschiebetransportuntersuchungen in einem Gebirgsbach. Messungen und Berechnungen für den Riedbach im Kt. Wallis, MS thesis, The Swiss Fed. Inst. Technol. (ETH), Zürich, Switzerland.
98. Shields, A., (1936), Anwendung der Ähnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung [Application of similarity principles and turbulence research to bedload movement.], Mitt. Preuss. Ver. Wasserbau Schiffbau, Berlin, Germany, 26, 26 pp.
99. Shvidchenko, A. B., and, G. Pender, (2000), Flume study of the effect of relative depth on the incipient motion of coarse uniform sediment, Water Resour. Res., 36, 619-628. (Pubitemid 30065553)
100. Stelczer, K., (1981), Bed-load Transport. Theory and Practice, Water Resour. Publ., Littleton, Colo.
101. Swingle, K. W., K. Bunte, and, S. R. Abt, (2012), Hysteresis in gravel transport rates and particle sizes in mountain streams, poster presented at International Workshop Monitoring Bedload and Debris Flows in Mountain Basins, Free University of Bolzano, Italy [Available at: http://www.unibz.it/EN/ SCIENCETECHNOLOGY/WELCOME/MONITORINGBEDLOADANDDEBRISFLOWSINMOUNTAINBASINS.html.]
102. Trush, W. J., S. M. McBain, and, L. B. Leopold, (2000), Attributes of an alluvial river and their relation to water policy and management, Proc. Natl. Acad. Sci. U. S. A., 97 (22), 11,858-11,863.
103. Turowski, J. M., E. M. Yager, A. Badoux, D. Rickenmann, and, P. Molnar, (2009), The impact of exceptional events on erosion, bedload transport and channel stability in a step-pool channel, Earth Surf. Processes Landforms, 34, 1661-1673.
104. Turowski, J. M., A. Badoux, and, D. Rickenmann, (2011), Start and end of bedload transport in gravel-bed streams, Geophys. Res. Lett. 38, L04401, doi: 10.1029/2010GL046558.
105. Vanoni, V. A., P. C. Benedict, D. C. Bondurant, J. E. McKee, R. F. Piest, and, J. Smallshaw, (1966), Sediment transportation mechanics: Initiation of motion, J. Hydraul. Div. Am. Soc. Civ. Eng., 92 (HY 2), 291-314.
106. Whitaker, A. C., (1997), The initiation of coarse bedload transport in gravel bed streams, Ph.D. Diss., 148 pp., Univ. of Montana, Missoula.
107. Whitaker, A. C., and, D. F. Potts, (1996), Validation of two threshold models for bedload initiation in an upland gravel-bed stream, in Watershed Restoration Management: Physical, Chemical, and Biological Considerations, edited by, J. J. McDonnell, et al., pp. 85-94, Proc. Ann. Symp. Am. Water Resour. Assoc., New York City Water Supply Stud., Syracuse, New York.
108. Whitaker, A. C., and, D. F. Potts, (2007a), Coarse bedload transport in an alluvial gravel bed stream, Dupuyer Creek, Montana, Earth Surf. Processes Landforms, 32, 1984-2004, doi: 10.1002/esp.1512. (Pubitemid 350177122)
109. Whitaker, A. C., and, D. F. Potts, (2007b), Analysis of flow competence in an alluvial gravel bed stream, Dupuyer Creek, Montana, Water Resour. Res., 43, W07433, doi: 10.1029/2006WR005289.
110. White, C. M., (1940), The equilibrium of grains on the bed of a stream, Proc. R. Soc. London, Ser. A, 174, 322-338.
111. Wiberg, P. L., and, J. D. Smith, (1987), Calculations of the critical shear stress for motion of uniform and heterogeneous sediments, Water Resour. Res., 23, 1471-1480. (Pubitemid 17634281)
112. Wilcock, P. R., (1988), Methods for estimating the critical shear stress of individual fractions in mixed-sized sediment, Water Resour. Res., 24, 1127-1135. (Pubitemid 19299936)
113. Wilcock, P. R., (2001), Toward a practical method for estimating sediment transport rates in gravel-bed rivers, Earth Surf. Processes Landforms, 26, 1395-1408. (Pubitemid 34010687)
114. Yager, E. M., J. W. Kirchner, and, W. E. Dietrich, (2007), Calculating bed load transport in steep boulder bed channels, Water Resour. Res., 43, W07418, doi: 10.1029/2006WR005432.
115. Yager, E. M., J. M. Turowski, D. Rickenmann, and, B. W. McArdell, (2012), Sediment supply, grain protrusion, and bedload transport in mountain streams, Geophys. Res. Lett., 39, L10402, doi: 10.1029/2012GL051654.
116. Yalin, M. S., and, E. Karahan, (1979), Inception of sediment transport, J. Hydraul. Div. Am. Soc. Civ. Eng., 105 (HY 11), 1433-1443. (Pubitemid 9480699)
117. Zimmermann, A., M. Church, and, M. A. Hassan, (2010), Step-pool stability: Testing the jammed state hypothesis, J. Geophys. Res., 115, F02008, doi: 10.1029/2009JF001365.