{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T04:26:55Z","timestamp":1768969615800,"version":"3.49.0"},"publisher-location":"Cham","reference-count":218,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319177182","type":"print"},{"value":"9783319177199","type":"electronic"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-17719-9_13","type":"book-chapter","created":{"date-parts":[[2015,6,30]],"date-time":"2015-06-30T04:15:30Z","timestamp":1435637730000},"page":"323-372","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Principles of Bedload Transport of Non-cohesive Sediment in Open-Channels"],"prefix":"10.1007","author":[{"given":"Rui M. L.","family":"Ferreira","sequence":"first","affiliation":[]},{"given":"Marwan A.","family":"Hassan","sequence":"additional","affiliation":[]},{"given":"Carles","family":"Ferrer-Boix","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,7,1]]},"reference":[{"issue":"HY11","key":"13_CR1","doi-asserted-by":"crossref","first-page":"2041","DOI":"10.1061\/JYCEAJ.0003791","volume":"99","author":"P Ackers","year":"1973","unstructured":"Ackers P, White WR (1973) Sediment transport: a new approach and analysis. J Hydraul Div 99(HY11):2041\u20132060","journal-title":"J Hydraul Div"},{"key":"13_CR2","doi-asserted-by":"crossref","unstructured":"Aleixo R, Maia R (2006) The beginning of sediment transport\u2014a different approach. In: Ferreira RML, Alves ECTL, Leal JGAB, Cardoso AH (eds) River flow 2006. Balkema, Lisse, pp 553\u2013563","DOI":"10.1201\/9781439833865.ch97"},{"key":"13_CR3","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1017\/S0022112007008774","volume":"595","author":"C Ancey","year":"2008","unstructured":"Ancey C, Davison AC, B\u00f6hm T, Jodeau M, Frey P (2008) Entrainment and motion of coarse particles in a shallow water stream down a steep slope. J Fluid Mech 595:83\u2013114","journal-title":"J Fluid Mech"},{"key":"13_CR4","doi-asserted-by":"crossref","first-page":"1225","DOI":"10.1130\/0016-7606(1983)94<1225:EOGFNS>2.0.CO;2","volume":"94","author":"ED Andrews","year":"1983","unstructured":"Andrews ED (1983) Entrainment of gravel from naturally sorted riverbed materials. Geol Soc Am Bull 94:1225\u20131231","journal-title":"Geol Soc Am Bull"},{"key":"13_CR5","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1029\/WR022i002p00191","volume":"22","author":"ED Andrews","year":"1986","unstructured":"Andrews ED, Erman DC (1986) Persistence in the size distribution of surficial bed material during an extreme snowmelt flood. Water Resour Res 22:191\u2013197","journal-title":"Water Resour Res"},{"key":"13_CR6","doi-asserted-by":"crossref","unstructured":"Ashida K, Michiue M (1972) Study on hydraulic resistance and bedload transport rate in alluvial streams. Trans Jpn Soc Civ Eng 206:59\u201369","DOI":"10.2208\/jscej1969.1972.206_59"},{"key":"13_CR7","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1029\/WR025i004p00627","volume":"25","author":"PJ Ashworth","year":"1989","unstructured":"Ashworth PJ, Ferguson RI (1989) Size-selective entrainment of bed-load in gravel bed streams. Water Resour Res 25:627\u2013634","journal-title":"Water Resour Res"},{"key":"13_CR8","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1098\/rspa.1954.0186","volume":"225","author":"RA Bagnold","year":"1954","unstructured":"Bagnold RA (1954) Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc R Soc Lond A 225:49\u201363","journal-title":"Proc R Soc Lond A"},{"key":"13_CR9","doi-asserted-by":"crossref","unstructured":"Bagnold, R. A. (1956). The flow of cohesionless grains in fluids. Phil. Trans. Roy. Soc. London, A, 249: 964","DOI":"10.1098\/rsta.1956.0020"},{"issue":"2","key":"13_CR10","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1080\/00221686.2013.869267","volume":"52","author":"F Ballio","year":"2014","unstructured":"Ballio F, Nikora V, Coleman SE (2014) On the definition of solid discharge in hydro-environment research and applications. J Hydraul Res 52(2):173\u2013184","journal-title":"J Hydraul Res"},{"key":"13_CR11","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1002\/esp.3290150508","volume":"15","author":"L Benda","year":"1990","unstructured":"Benda L (1990) The influence of debris flows on channels and valley floors in the Oregon Coast Range, U.S.A. Earth Surf Proc Land 15:457\u2013466","journal-title":"Earth Surf Proc Land"},{"issue":"12","key":"13_CR12","doi-asserted-by":"crossref","first-page":"2849","DOI":"10.1029\/97WR02388","volume":"33","author":"L Benda","year":"1997","unstructured":"Benda L, Dunne T (1997) Stochastic forcing of sediment routing and storage in channel networks. Water Resour Res 33(12):2849\u20132863","journal-title":"Water Resour Res"},{"key":"13_CR13","doi-asserted-by":"crossref","unstructured":"Bettess R (1984) Initiation of sediment transport in gravel streams. Proc Instn Civ Eng 77(Part 2, Technical Note 407):79\u201388","DOI":"10.1680\/iicep.1984.1275"},{"issue":"3","key":"13_CR14","first-page":"289","volume":"82","author":"B Binggeli","year":"1980","unstructured":"Binggeli B (1980) On the intrinsic shape of elliptical galaxies. Astron Astrophys 82(3):289\u2013294","journal-title":"Astron Astrophys"},{"key":"13_CR15","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1080\/00291958008545338","volume":"34","author":"J Bogen","year":"1980","unstructured":"Bogen J (1980) The hysteresis effect of sediment transport systems. Norsk Geogr Tidsskr 34:45\u201354","journal-title":"Norsk Geogr Tidsskr"},{"key":"13_CR16","doi-asserted-by":"publisher","unstructured":"Bradley DN, Tucker GE, Benson DA (2010) Fractional dispersion in a sand bed river. J Geophys Res 115:F00A09. doi:10.1029\/2009JF001268","DOI":"10.1029\/2009JF001268"},{"key":"13_CR17","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1130\/0016-7606(1980)91<135:COFNTT>2.0.CO;2","volume":"91","author":"WC Bradley","year":"1980","unstructured":"Bradley WC, Mears AI (1980) Calculations of flows needed to transport coarse fraction of boulder creek alluvium at boulder, Colorado\u2014summary. Geolog Soc Am Bull 91:135\u2013138","journal-title":"Geolog Soc Am Bull"},{"issue":"2","key":"13_CR18","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1029\/91WR02570","volume":"28","author":"JS Bridge","year":"1992","unstructured":"Bridge JS, Bennet SJ (1992) A model for the entrainment and transport of sediment grains of mixed sizes, shapes and densities. Water Resour Res 28(2):337\u2013363","journal-title":"Water Resour Res"},{"key":"13_CR19","unstructured":"Brownlie WR (1981) Prediction of flow depth and sediment discharge in open channels. W.M. Keck Laboratory of Hydraulics and Water Resources, Report no. KH-R-43A, California Institute of Technology, Pasadena, California"},{"issue":"4","key":"13_CR20","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1061\/(ASCE)0733-9429(1999)125:4(376)","volume":"125","author":"JM Buffington","year":"1999","unstructured":"Buffington JM (1999) The legend of shields. J Hydraul Eng 125(4):376\u2013387","journal-title":"J Hydraul Eng"},{"issue":"8","key":"13_CR21","doi-asserted-by":"crossref","first-page":"1993","DOI":"10.1029\/96WR03190","volume":"33","author":"JM Buffington","year":"1997","unstructured":"Buffington JM, Montgomery DR (1997) A systematic analysis of eight decades of incipient motion studies with special reference to gravel bedded rivers. Water Resour Res 33(8):1993\u20132029","journal-title":"Water Resour Res"},{"key":"13_CR22","doi-asserted-by":"publisher","unstructured":"Buffington JM, Montgomery DR (1999) Effects of hydraulic roughness on surface textures of gravel-bed rivers. Water Resour Res 35. doi:10.1029\/1999WR900138","DOI":"10.1029\/1999WR900138"},{"issue":"2","key":"13_CR23","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1029\/91WR02529","volume":"28","author":"JM Buffinton","year":"1992","unstructured":"Buffinton JM, Dietrich WE, Kirchner JW (1992) Friction angle measurements on a naturally formed gravel strembed. Implications for critical boundary shear stress. Water Resour Res 28(2):411\u2013425","journal-title":"Water Resour Res"},{"key":"13_CR24","doi-asserted-by":"publisher","unstructured":"Cao Z (1997) Turbulent bursting-based sediment entrainment functions. J Hydraul Eng 123(3):233\u2013236. doi:10.1061\/(ASCE)0733-9429(1997)123:3(233)","DOI":"10.1061\/(ASCE)0733-9429(1997)123:3(233)"},{"issue":"1","key":"13_CR25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/esp.3290080102","volume":"8","author":"PA Carling","year":"1983","unstructured":"Carling PA (1983) Threshold of coarse sediment transport in broad and narrow natural streams. Earth Surf Proc Land 8(1):1\u201318","journal-title":"Earth Surf Proc Land"},{"key":"13_CR26","unstructured":"Carling PA, Kelsey A, Glaister MS (1992) Effect of bed roughness, particle shape and orientation on initial motion criteria. In: Billy P, Day RD, Thorne CR, Taconi P (eds) Dinamics of gravel-bed river. Wiley, New York, pp 23\u201337"},{"key":"13_CR27","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1046\/j.1365-3091.2000.00290.x","volume":"47","author":"PA Carling","year":"2000","unstructured":"Carling PA, Golz E, Orr HG, Radecki-Pawlik A (2000) The morphodynamics of fluvial sand dunes in the River Rhine near Mainz, Germany. Sedimentol Morphol Sedimentol 47:227\u2013252. doi:10.1046\/j.1365-3091.2000.00290.x","journal-title":"Sedimentol Morphol Sedimentol"},{"issue":"2","key":"13_CR28","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1061\/(ASCE)0733-9429(1998)124:2(232)","volume":"124","author":"N-S Cheng","year":"1998","unstructured":"Cheng N-S, Chiew Y-M (1998) Pickup probability for sediment entrainment. J Hydraul Eng 124(2):232\u2013235. doi:10.1061\/(ASCE)0733-9429(1998)124:2(232)","journal-title":"J Hydraul Eng"},{"key":"13_CR29","doi-asserted-by":"crossref","unstructured":"Chepil WS (1959) Equilibrium of soil grains at the threshold of movement by wind. Soil Sci Soc Am J 23(6):422\u2013428","DOI":"10.2136\/sssaj1959.03615995002300060019x"},{"key":"13_CR30","doi-asserted-by":"crossref","first-page":"343","DOI":"10.2136\/sssaj1961.03615995002500050011x","volume":"25","author":"WS Chepil","year":"1961","unstructured":"Chepil WS (1961) The use of spheres to measure lift and drag on wind-eroded soil grains. Proc Soil Sci Soc 25:343\u2013345","journal-title":"Proc Soil Sci Soc"},{"key":"13_CR31","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1146\/annurev.earth.33.092203.122721","volume":"34","author":"M Church","year":"2006","unstructured":"Church M (2006) Bed material transport and the morphology of alluvial river channels. Annu Rev Earth Planet Sci 34:325\u2013354","journal-title":"Annu Rev Earth Planet Sci"},{"issue":"1","key":"13_CR32","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1029\/91WR02523","volume":"28","author":"M Church","year":"1992","unstructured":"Church M, Hassan MA (1992) Size and distance of travel of unconstrained clasts on a streambed. Water Resour Res 28(1):299\u2013303","journal-title":"Water Resour Res"},{"key":"13_CR33","doi-asserted-by":"publisher","unstructured":"Church M, Hassan MA (2002) Mobility of bed material in Harris Creek. Water Resour Res 38:19-1\u201319-12. doi:10.1029\/2001WR000753","DOI":"10.1029\/2001WR000753"},{"key":"13_CR34","unstructured":"Church M (1978) Palaeohydraulic reconstructions from a Holocene valley fill. In: Miall AD (ed) Fluvial sedimentology. Canadian Society of Petroleum Geologists, Mem. 5, Calgary, Canada, pp 743\u2013772"},{"issue":"11","key":"13_CR35","doi-asserted-by":"crossref","first-page":"3169","DOI":"10.1029\/98WR00484","volume":"34","author":"M Church","year":"1998","unstructured":"Church M, Hassan MA, Wolcott JF (1998) Stabilizing self-organized structures in gravel-bed stream channels: Field and experimental observations. Water Resour Res 34(11):3169\u20133179","journal-title":"Water Resour Res"},{"key":"13_CR36","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1098\/rspa.1962.0069","volume":"266","author":"MJ Crickmore","year":"1962","unstructured":"Crickmore MJ, Lean GH (1962) The measurement of sand transport by means of radioactive tracers. Proc R Soc London Ser A 266:402\u2013421","journal-title":"Proc R Soc London Ser A"},{"key":"13_CR37","doi-asserted-by":"publisher","first-page":"W02030","DOI":"10.1029\/2004WR003568","volume":"41","author":"JC Curran","year":"2005","unstructured":"Curran JC, Wilcock PR (2005) Characteristic dimensions of the step-pool bed configuration: An experimental study. Water Resour Res 41:W02030. doi:10.1029\/2004WR003568","journal-title":"Water Resour Res"},{"key":"13_CR38","doi-asserted-by":"crossref","first-page":"2805","DOI":"10.1029\/2001WR000357","volume":"37","author":"PE DeVries","year":"2001","unstructured":"DeVries PE, Burges SJ, Daigneau J (2001) Measurements of the temporal progression of scour in a pool-riffle sequence in a gravel bed stream using an electronic scour monitor. Water Resour Res 37:2805\u20132816","journal-title":"Water Resour Res"},{"key":"13_CR39","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1061\/(ASCE)0733-9429(2002)128:11(983)","volume":"128","author":"P DeVries","year":"2002","unstructured":"DeVries P (2002) Bedload layer thickness and disturbance depth in gravel bed streams. J Hydraul Eng 128:983\u2013991","journal-title":"J Hydraul Eng"},{"key":"13_CR40","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/s12205-008-8045-3","volume":"12","author":"S Dey","year":"2008","unstructured":"Dey S, Papanicolaou AN (2008) Sediment threshold under stream flow: a state-of-the-art review. Water Eng KSCE J Civ Eng 12:45\u201360","journal-title":"Water Eng KSCE J Civ Eng"},{"key":"13_CR41","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1038\/340215a0","volume":"340","author":"WE Dietrich","year":"1989","unstructured":"Dietrich WE, Kirchner JW, Ikeda H, Iseya F (1989) Sediment supply and the development of the coarse surface layer in gravel-bedded rivers. Nature 340:215\u2013217","journal-title":"Nature"},{"key":"13_CR42","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1017\/S0022112088001831","volume":"192","author":"TG Drake","year":"1988","unstructured":"Drake TG, Shreve RL, Dietrich WE, Whiting PJ, Leopold LB (1988) Bed load transport of fine gravel observed by motion-picture photography. J Fluid Mech 192:193\u2013217","journal-title":"J Fluid Mech"},{"issue":"4","key":"13_CR43","first-page":"225","volume":"91","author":"IV Egiazaroff","year":"1965","unstructured":"Egiazaroff IV (1965) Calculation of non-uniform sediment concentrations. J Hydraul Eng 91(4):225\u2013248","journal-title":"J Hydraul Eng"},{"key":"13_CR44","unstructured":"Einstein HA (1950) The bed-load function for sediment transportation in open channel flows. Soil Conserv. Serv. Tech. Bull. 1026, US Department of Agriculture, 73\u00a0pp"},{"key":"13_CR45","unstructured":"Einstein HA (1937) Bedload transport as a probability problem. Ph.D. thesis, Colorado State University (In Sedimentation, Shen, H.W. (ed.) 1972, App. C)"},{"key":"13_CR46","doi-asserted-by":"crossref","unstructured":"Emmett, W.W. (1980). A field calibration of the sediment-trapping characteristics of the Helley-Smith bedload sampler: U. S. geological survey. Professional paper 1139, 44 p","DOI":"10.3133\/pp1139"},{"issue":"6","key":"13_CR47","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1061\/(ASCE)0733-9429(2004)130:6(477)","volume":"130","author":"R Ettema","year":"2004","unstructured":"Ettema R, Mutel CF (2004) Hans Albert Einstein: innovation and compromise in formulating sediment transport by rivers. J Hydraul Eng 130(6):477\u2013487","journal-title":"J Hydraul Eng"},{"key":"13_CR48","doi-asserted-by":"crossref","unstructured":"Fahnestock RK (1963) Morphology and hydrology of a glacial stream\u2014White River, Mount Rainier, Washington. U.S. geological survey professional paper 422A, 70\u00a0pp","DOI":"10.3133\/pp422A"},{"key":"13_CR49","volume-title":"An introduction to probability theory and its applications","author":"W Feller","year":"1968","unstructured":"Feller W (1968) An introduction to probability theory and its applications, vol 1, 3rd edn. Willey, New York","edition":"3"},{"key":"13_CR50","first-page":"523","volume":"352","author":"JD Fenton","year":"1977","unstructured":"Fenton JD, Abbott JE (1977) Initial movement of grains in a stream bed: the effects of relative protrusion. Proc R Soc A 352:523\u2013527","journal-title":"Proc R Soc A"},{"key":"13_CR51","doi-asserted-by":"crossref","unstructured":"Ferguson RI, Hoey TB (2002) Long-term slowdown of river tracer pebbles: generic models and implications for interpreting short-term tracer studies. Water Resour Res 38(8):17-1\u201317-11","DOI":"10.1029\/2001WR000637"},{"key":"13_CR52","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1002\/esp.3290190208","volume":"19","author":"RI Ferguson","year":"1994","unstructured":"Ferguson RI (1994) Critical discharge for entrainment of poorly sorted gravel. Earth Surf Proc Land 19:179\u2013186","journal-title":"Earth Surf Proc Land"},{"key":"13_CR53","doi-asserted-by":"crossref","first-page":"2031","DOI":"10.1029\/98WR01283","volume":"34","author":"RI Ferguson","year":"1998","unstructured":"Ferguson RI, Wathen SJ (1998) Tracer-pebble movement along a concave river profile: virtual velocity in relation to grain size and shear stress. Water Resour Res 34:2031\u20132038","journal-title":"Water Resour Res"},{"key":"13_CR54","doi-asserted-by":"publisher","first-page":"1045","DOI":"10.1029\/2001WR000254","volume":"38","author":"RI Ferguson","year":"2002","unstructured":"Ferguson RI, Bloomer DJ, Hoey TB, Werritty A (2002) Mobility of river tracer pebbles over different timescales. Water Resour Res 38:1045. doi:10.1029\/2001WR000254","journal-title":"Water Resour Res"},{"issue":"2","key":"13_CR55","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1080\/00221687609499677","volume":"14","author":"R Fernandez Luque","year":"1976","unstructured":"Fernandez Luque R, van Beek R (1976) Erosion and transport of bed-load sediment. J Hydraul Res 14(2):127\u2013144","journal-title":"J Hydraul Res"},{"key":"13_CR56","unstructured":"Ferreira RML (2005) River morphodynamics and sediment transport. Conceptual model and solutions. PhD thesis, IST, TULisbon"},{"issue":"10","key":"13_CR57","doi-asserted-by":"publisher","first-page":"1605","DOI":"10.1139\/L09-033","volume":"36","author":"RML Ferreira","year":"2009","unstructured":"Ferreira RML, Franca MJ, Leal JGAB, Cardoso AH (2009) Mathematical modelling of shallow flows: closure models drawn from grain-scale mechanics of sediment transport and flow hydrodynamics. Can J Civ Eng 36(10):1605\u20131621. doi:10.1139\/L09-033","journal-title":"Can J Civ Eng"},{"key":"13_CR58","doi-asserted-by":"publisher","unstructured":"Ferreira RML, Ferreira L, Ricardo AM, Franca MJ (2010) Impacts of sand transport on flow variables and dissolved oxygen in gravel-bed streams suitable for salmonid spawning. River Res Appl 26(4):414\u2013438. doi:10.1002\/rra.1307","DOI":"10.1002\/rra.1307"},{"key":"13_CR59","doi-asserted-by":"publisher","unstructured":"Ferreira RML, Franca MJ, Leal JGAB, Cardoso AH (2012) Flow over rough mobile beds: Friction factor and vertical distribution of the longitudinal mean velocity. Water Resour Res 48(5):W05529, 1944\u20137973. doi:10.1029\/2011WR011126","DOI":"10.1029\/2011WR011126"},{"key":"13_CR60","doi-asserted-by":"publisher","unstructured":"Foufoula-Georgiou E, Stark C (2010) Introduction to special section on stochastic transport and emergent scaling on earth\u2019s surface: rethinking geomorphic transport\u2014stochastic theories, broad scales of motion and nonlocality. J Geophys Res 115. doi:10.1029\/2010JF001661","DOI":"10.1029\/2010JF001661"},{"key":"13_CR61","doi-asserted-by":"publisher","first-page":"F03031","DOI":"10.1029\/2012JF002352","volume":"117","author":"DJ Furbish","year":"2012","unstructured":"Furbish DJ, Haff PK, Roseberry JC, Schmeeckle MW (2012a) A probabilistic description of the bed load sediment flux: 1. Theory. J of Geophys Res 117:F03031. doi:10.1029\/2012JF002352","journal-title":"J of Geophys Res"},{"key":"13_CR62","doi-asserted-by":"crossref","unstructured":"Furbish DJ, Ball AE, Schmeeckle MW (2012b) A probabilistic description of the bed load sediment flux: 4. Fickian diffusion at low transport rates. J Geophys Res Earth Surf 117","DOI":"10.1029\/2012JF002356"},{"key":"13_CR63","doi-asserted-by":"crossref","unstructured":"Ganti V, Meerschaert MM, Foufoula-Georgiou E, Viparelli E, Parker G (2010) Normal and anomalous diffusion of gravel tracer particles in rivers. J Geophys Res Earth Surf 115:F00A12. Doi:http:\/\/dx.doi.org\/10.1029\/2008JF001222","DOI":"10.1029\/2008JF001222"},{"key":"13_CR64","unstructured":"Garde RJ, Ranga Raju KG (1985) Mechanics of sediment transportation and alluvial stream problems, 2nd edn. Willey Eastern Limited, New Delhi"},{"key":"13_CR65","unstructured":"Gessler J (1965) The beginning of bedload movement of mixtures investigated as natural armouring in channels. Technical report no. 69, The Laboratory of Hydraulic Research and Soil Mechanics, Swiss Federal Institute of Technology, Zurich, (translation by W. M. Keck Laboratory of Hydraulics and Water Resources, California Inst. Technology)"},{"key":"13_CR66","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1002\/(SICI)1096-9837(199605)21:5<433::AID-ESP580>3.0.CO;2-P","volume":"21","author":"D Gintz","year":"1996","unstructured":"Gintz D, Hassan MA, Schmidt K-H (1996) Frequency and magnitude of bedload transport in a mountain river. Earth Surf Proc Land 21:433\u2013446","journal-title":"Earth Surf Proc Land"},{"issue":"1","key":"13_CR67","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1061\/(ASCE)0733-9429(2005)131:1(38)","volume":"131","author":"M G\u00f6\u011f\u00fc\u015f","year":"2005","unstructured":"G\u00f6\u011f\u00fc\u015f M, Defne Z (2005) Effect of shape in incipient motion of large solitary particles. J Hydraul Eng 131(1):38\u201345","journal-title":"J Hydraul Eng"},{"key":"13_CR68","doi-asserted-by":"crossref","first-page":"1161","DOI":"10.1029\/WR025i006p01161","volume":"25","author":"B Gomez","year":"1989","unstructured":"Gomez B, Church M (1989) An assessment of bed load sediment transport formulae for gravel bed rivers. Water Resour Res 25:1161\u20131186","journal-title":"Water Resour Res"},{"key":"13_CR69","doi-asserted-by":"publisher","unstructured":"Gomi T, Sidle RC (2003) Bed load transport in managed steep-gradient headwater streams of Southeastern Alaska. Water Resour Res 39. doi:10.1029\/2003WR002440","DOI":"10.1029\/2003WR002440"},{"key":"13_CR70","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1111\/j.1752-1688.2004.tb01068.x","volume":"40","author":"AS Gottesfeld","year":"2004","unstructured":"Gottesfeld AS, Hassan MA, Tunnicliffe JF, Poirier RW (2004) Sediment dispersion in fish bearing streams: the influence of floods and spawning salmon. J Am Water Resour Assoc 40:1071\u20131086","journal-title":"J Am Water Resour Assoc"},{"key":"13_CR71","unstructured":"Graf WH (1971) Hydraulics of sediment transport. McGraw_Hill Book Co., New York"},{"key":"13_CR72","doi-asserted-by":"crossref","unstructured":"Gray JR, Laronne JB, Marr JDG (2010) Bedload-surrogate monitoring technologies. U.S. geological survey scientific investigations report 2010\u20135091","DOI":"10.3133\/sir20105091"},{"issue":"HY 12","key":"13_CR73","doi-asserted-by":"crossref","first-page":"2501","DOI":"10.1061\/JYCEAJ.0002797","volume":"96","author":"NS Grigg","year":"1970","unstructured":"(Am Soc Civ Eng Proc)","journal-title":"J Hydraul Div"},{"issue":"4","key":"13_CR74","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1080\/00221689709498409","volume":"35","author":"A Gyr","year":"1997","unstructured":"Gyr A, Schmid A (1997) Turbulent flows over smooth erodible sand beds in flumes. J Hydraul Res 35(4):525\u2013544","journal-title":"J Hydraul Res"},{"key":"13_CR75","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1002\/hyp.147","volume":"15","author":"HM Habersack","year":"2001","unstructured":"Habersack HM (2001) Radio-tracking gravel particles in a large braided river in New Zealand: a field test of the stochastic theory of bed load transport proposed by Einstein. Hydrol Process 15:377\u2013391","journal-title":"Hydrol Process"},{"key":"13_CR76","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1002\/9781119952497.ch5","volume-title":"Gravel-bed river: processes, tools, environments","author":"JK Haschenburger","year":"2012","unstructured":"Haschenburger JK (2012) On gravel exchange in natural channels. In: Church M, Biron PA, Roy A (eds) Gravel-bed river: processes, tools, environments. Wiley, New York, pp 56\u201367"},{"key":"13_CR77","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1002\/(SICI)1096-9837(199809)23:9<791::AID-ESP888>3.0.CO;2-X","volume":"23","author":"JK Haschenburger","year":"1998","unstructured":"Haschenburger JK, Church M (1998) Bed material transport estimated from the virtual velocity of sediment. Earth Surf Proc Land 23:791\u2013808","journal-title":"Earth Surf Proc Land"},{"key":"13_CR78","doi-asserted-by":"crossref","first-page":"2857","DOI":"10.1029\/1999WR900153","volume":"35","author":"JK Haschenburger","year":"1999","unstructured":"Haschenburger JK (1999) A probability model of scour and fill depths in gravel-bed channels. Water Resour Res 35:2857\u20132869","journal-title":"Water Resour Res"},{"key":"13_CR79","doi-asserted-by":"publisher","unstructured":"Haschenburger JK (2011a) The rate of fluvial gravel dispersion. Geophys Res Lett 38(L24403). doi:10.1029\/2011GL049928","DOI":"10.1029\/2011GL049928"},{"key":"13_CR80","doi-asserted-by":"crossref","first-page":"1044","DOI":"10.1002\/esp.2130","volume":"36","author":"JK Haschenburger","year":"2011","unstructured":"Haschenburger JK (2011b) Vertical mixing of gravel over a long flood series. Earth Surf Proc Land 36:1044\u20131058","journal-title":"Earth Surf Proc Land"},{"key":"13_CR81","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.geomorph.2013.03.033","volume":"200","author":"JK Haschenburger","year":"2013","unstructured":"Haschenburger JK (2013) Tracing river gravels: insights into dispersion from a long-term field experiment. Geomorphology 200:121\u2013131","journal-title":"Geomorphology"},{"key":"13_CR82","doi-asserted-by":"crossref","first-page":"1885","DOI":"10.1029\/2000WR900055","volume":"36","author":"MA Hassan","year":"2000","unstructured":"Hassan MA, Church M (2000) Experiments on surface structure and partial sediment transport on a gravel bed. Water Resour Res 36:1885\u20131895","journal-title":"Water Resour Res"},{"key":"13_CR83","doi-asserted-by":"crossref","unstructured":"Hassan MA, Zimmermann AM (2011) Channel response and recovery to changes in sediment supply. In: Church M, Biron PA, Roy A (eds) Gravel-bed river: processes, tools, environments, pp 464\u2013473 (Invited contribution)","DOI":"10.1002\/9781119952497.ch33"},{"key":"13_CR84","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1029\/90WR02762","volume":"27","author":"MA Hassan","year":"1991","unstructured":"Hassan MA, Church M, Schick AP (1991) Distance of movement of coarse particles in gravel bed streams. Water Resour Res 27:503\u2013511","journal-title":"Water Resour Res"},{"key":"13_CR85","doi-asserted-by":"crossref","unstructured":"Hassan M, Smith B, Hogan D, Luzi D, Zimmermann A, Eaton B (2008) Sediment storage and transport in coarse bed streams: scale considerations. In: Habersack H, Piegay H, Rinaldi M (eds) Gravel-bed rivers VI: from process understanding to river restoration. Elsevier, Amsterdam, pp 473\u2013496","DOI":"10.1016\/S0928-2025(07)11137-8"},{"key":"13_CR86","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1002\/esp.3290150405","volume":"15","author":"MA Hassan","year":"1990","unstructured":"Hassan MA (1990) Scour, fill, and burial depth of coarse material in gravel bed streams. Earth Surf Proc Land 15:341\u2013356","journal-title":"Earth Surf Proc Land"},{"key":"13_CR87","unstructured":"Hassan MA, Church M (1992) The movement of individual grains on the streambed. In: Billi P, Hey RE, Thorne CR, Tacconi P (eds) Dynamics of gravel bed rivers. Wiley, New York, pp 159\u2013175"},{"key":"13_CR88","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1029\/2000WR900346","volume":"37","author":"MA Hassan","year":"2001","unstructured":"Hassan MA, Church M (2001) Rating bedload transport in Harris Creek: seasonal and spatial variation over a cobble-gravel bed. Water Resour Res 37:813\u2013825","journal-title":"Water Resour Res"},{"key":"13_CR89","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1029\/93WR03351","volume":"30","author":"MA Hassan","year":"1994","unstructured":"Hassan MA, Church M (1994) Vertical mixing of coarse particles in gravel bed rivers: a kinematic model. Water Resour Res 30:1173\u20131185","journal-title":"Water Resour Res"},{"key":"13_CR90","doi-asserted-by":"crossref","unstructured":"Hassan MA, Ergenzinger P (2003) Tracers in fluvial geomorphology. In: Kondolf GM (ed) Tools in fluvial geomorphology. Wiley, Chichester","DOI":"10.1002\/0470868333.ch14"},{"key":"13_CR91","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1002\/esp.3290150807","volume":"15","author":"MA Hassan","year":"1990","unstructured":"Hassan MA, Reid I (1990) The influence of microform bed roughness elements on flow and sediment transport in gravel bed rivers. Earth Surf Proc Land 15:739\u2013750","journal-title":"Earth Surf Proc Land"},{"key":"13_CR92","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1002\/esp.3290170607","volume":"17","author":"MA Hassan","year":"1992","unstructured":"Hassan MA, Church M, Ashworth PJ (1992) Virtual rate and mean distance of travel of individual clasts in gravel-bed channels. Earth Surf Proc Land 17:617\u2013628","journal-title":"Earth Surf Proc Land"},{"key":"13_CR93","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/j.geomorph.2014.05.019","volume":"219","author":"MA Hassan","year":"2014","unstructured":"Hassan MA, Robinson SVJ, Voepel H, Lewis J, Lisle TE (2014) Modeling temporal trends in bedload transport in gravel-bed streams using hierarchical mixed-effects models. Geomorphology 219:260\u2013269","journal-title":"Geomorphology"},{"key":"13_CR94","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1002\/(SICI)1096-9837(199907)24:7<623::AID-ESP978>3.0.CO;2-2","volume":"24","author":"MA Hassan","year":"1999","unstructured":"Hassan MA, Schick AP, Shaw PA (1999) The transport of gravel in an ephemeral sandbed river. Earth Surf Proc Land 24:623\u2013640","journal-title":"Earth Surf Proc Land"},{"key":"13_CR95","doi-asserted-by":"crossref","unstructured":"Hassan MA, Voepel H, Schumer R, Parker G, Fraccarollo L (2013) Displacement characteristics of coarse fluvial bed sediment. J Geophys Res Earth Surf 118:155\u2013165","DOI":"10.1029\/2012JF002374"},{"key":"13_CR96","unstructured":"Hayward JA (1980) Hydrology and stream sediments in a mountain catchment. Special Publication 17, Tussock Grasslands and Mountain Lands Institutes, Lincoln College, Canterbury, New Zealnad, 236\u00a0pp"},{"key":"13_CR97","doi-asserted-by":"crossref","unstructured":"Helley EJ, Smith W (1971) The development and calibration of a pressure difference bed load sampler. U.S. geological survey, open file report, 18\u00a0pp","DOI":"10.3133\/ofr73108"},{"key":"13_CR98","doi-asserted-by":"publisher","unstructured":"Hill KM, DellAngelo L, Meerschaert MM (2010) Heavy\u2010tailed travel distance in gravel bed transport: An exploratory enquiry. J Geophys Res 115:F00A14. doi:10.1029\/2009JF001276","DOI":"10.1029\/2009JF001276"},{"key":"13_CR99","doi-asserted-by":"crossref","first-page":"1501","DOI":"10.1002\/esp.3258","volume":"37","author":"G Houbrechts","year":"2012","unstructured":"Houbrechts G, Campenhout JV, Levecq Y, Hallot E, Peeters A, Petit F (2012) Comparison of methods for quantifying active layer dynamics and bedload discharge in armoured gravel-bed rivers. Earth Surf Proc Land 37:1501\u20131517","journal-title":"Earth Surf Proc Land"},{"key":"13_CR100","unstructured":"Hu C, Hui Y, Xia Z (1992) Experimental study on saltation of solid grains in flowing water. Int J Sediment Res 7(2):23\u201351"},{"key":"13_CR101","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1061\/(ASCE)0733-9429(1985)111:4(677)","volume":"111","author":"DW Hubbell","year":"1985","unstructured":"Hubbell DW, Stevens HH, Skinner JV, Beverage JP (1985) New approach to calibrating bed load samplers. J Hydraul Eng 111:677\u2013694 (American Society of Civil Engineering)","journal-title":"J Hydraul Eng"},{"issue":"3","key":"13_CR102","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1029\/97RG00426","volume":"35","author":"R Iverson","year":"1997","unstructured":"Iverson R (1997) The physics of debris flows. Rev Geophys 35(3):245\u2013296","journal-title":"Rev Geophys"},{"key":"13_CR103","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1002\/esp.3290070602","volume":"7","author":"WL Jackson","year":"1982","unstructured":"Jackson WL, Beschta RL (1982) A model of two-phase bedload transport in an Oregon coast range stream. Earth Surf Proc Land 7:517\u2013527","journal-title":"Earth Surf Proc Land"},{"key":"13_CR104","unstructured":"Jaeggi MNR (1995) Sediment transport in mountain rivers\u2014a review. In: International conference on erosion control, 25\u201326 August, 1995, The Sabo Society of Japan, keynote address, 13\u00a0pp"},{"key":"13_CR105","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1061\/(ASCE)0733-9429(1995)121:11(766)","volume":"121","author":"JF Kennedy","year":"1995","unstructured":"Kennedy JF (1995) The albert shields story. J Hydraul Eng 121:766\u2013772","journal-title":"J Hydraul Eng"},{"key":"13_CR106","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1111\/j.1365-3091.1990.tb00627.x","volume":"37","author":"JW Kirchner","year":"1990","unstructured":"Kirchner JW, Dietrich WE, Iseya F, Ikeda H (1990) The variability of critical shear stress, friction angle, and grain protrusion in water-worked sediments. Sedimentology 37:647\u2013672","journal-title":"Sedimentology"},{"key":"13_CR107","doi-asserted-by":"publisher","unstructured":"Kleinhans M, van Rijn L (2002) Stochastic prediction of sediment transport in sand-gravel bed rivers. J Hydraul Eng 128:412\u2013425. doi:10.1061\/(ASCE)0733-9429(2002)128:4(412) (Special Issue: Stochastic Hydraulics and Sediment Transport)","DOI":"10.1061\/(ASCE)0733-9429(2002)128:4(412)"},{"issue":"2","key":"13_CR108","first-page":"203","volume":"57","author":"PD Komar","year":"1987","unstructured":"Komar PD (1987) Selective grain entrainment by a current from a bed of mixed sizes: a reanalysis. J Sediment Petrol 57(2):203\u2013211","journal-title":"J Sediment Petrol"},{"issue":"4","key":"13_CR109","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.1306\/74D7290F-2B21-11D7-8648000102C1865D","volume":"43","author":"PD Komar","year":"1973","unstructured":"Komar PD, Miller MC (1973) The threshold of sediment movement under oscilatorry water waves. J Sediment Petrol 43(4):1101","journal-title":"J Sediment Petrol"},{"key":"13_CR110","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1111\/j.1365-3091.1988.tb01244.x","volume":"35","author":"PD Komar","year":"1988","unstructured":"Komar PD, Li MZ (1988) Application of grain pivoting and sliding analyses to selective entrainment of gravel and to flow competence evaluations. Sedimentology 35:681\u2013695","journal-title":"Sedimentology"},{"key":"13_CR111","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1017\/S002211209400114X","volume":"267","author":"A Kovacs","year":"1994","unstructured":"Kovacs A, Parker G (1994) A new vectorial bedload formulation and its application to the time evolution of straight river channels. J Fluid Mech 267:153\u2013183","journal-title":"J Fluid Mech"},{"key":"13_CR112","doi-asserted-by":"crossref","first-page":"798","DOI":"10.1061\/TACEAT.0004653","volume":"100","author":"H Kramer","year":"1935","unstructured":"Kramer H (1935) Sand mixtures and sand movement in fluvial models. Trans Am Soc Civ Eng 100:798\u2013878","journal-title":"Trans Am Soc Civ Eng"},{"key":"13_CR113","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1002\/esp.3290170206","volume":"17","author":"RA Kuhnle","year":"1992","unstructured":"Kuhnle RA (1992) Bedload transport during rising and falling stages on two small streams. Earth Surf Proc Land 17:191\u2013197","journal-title":"Earth Surf Proc Land"},{"key":"13_CR114","doi-asserted-by":"publisher","first-page":"W05502","DOI":"10.1029\/2006WR005027","volume":"43","author":"RWJ Lacey","year":"2007","unstructured":"Lacey RWJ, Roy AG (2007) A comparative study of the turbulent flow field with and without a pebble cluster in a gravel bed river. Water Resour Res 43:W05502. doi:10.1029\/2006WR005027","journal-title":"Water Resour Res"},{"key":"13_CR115","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/j.geomorph.2007.11.005","volume":"99","author":"H Lamarre","year":"2008","unstructured":"Lamarre H, Roy AG (2008) The role of morphology on the displacement of particles in a step\u2013pool river system. Geomorphology 99:270\u2013279","journal-title":"Geomorphology"},{"key":"13_CR116","doi-asserted-by":"crossref","unstructured":"Lamb MP, Scheingross JS, Amidon WH, Swanson E, Limaye A (2011) A model for fire-induced sediment yield by dry ravel in steep landscapes. J Geophys Res: Earth Surf 116(F3)","DOI":"10.1029\/2010JF001878"},{"key":"13_CR117","unstructured":"Laronne JB, Reid I, Yitshak Y, Frostick LE (1992) Recording bedload discharge in a semiarid channel, Nahal Yatir, Israel. In: Bogen J, Walling DE, Day TJ (eds) Erosion and sediment transport monitoring programmes in river basins, vol 210. IAHS Publication, Wallingford, pp 79\u201386"},{"key":"13_CR118","unstructured":"Lauffer H, Sommer N (1982) Studies on sediment transport in mountain streams of the eastern Alps. In: Proceeding of 14th congress international commission on large dams, Rio de Janeiro, pp 431\u2013453"},{"key":"13_CR119","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/S0341-8162(99)00016-8","volume":"36","author":"MA Lenzi","year":"1999","unstructured":"Lenzi MA, D\u2019Agostino V (1999) Bedload transport in the instrumented catchment of the Rio Cordon, Part II: analysis of bedload rate. CATENA 36:191\u2013204","journal-title":"CATENA"},{"key":"13_CR120","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/S0341-8162(99)00016-8","volume":"36","author":"MA Lenzi","year":"1999","unstructured":"Lenzi MA, D\u2019Agostino V, Billi P (1999) Bedload transport in the instrumented catchment of Rio Cordon, part I: analysis of bedload records, conditions and threshold of bedload entrainment. Catena 36:171\u2013190","journal-title":"Catena"},{"issue":"3","key":"13_CR121","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1111\/j.1365-3091.1986.tb00545.x","volume":"33","author":"Z Li","year":"1986","unstructured":"Li Z, Komar PD (1986) Laboratory measurements of pivoting angles for applications to selective e ntrainment of gravel in a current. Sedimentology 33(3):413\u2013423. doi:10.1111\/j.1365-3091.1986.tb00545.x","journal-title":"Sedimentology"},{"issue":"6","key":"13_CR122","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1061\/(ASCE)0733-9429(1995)121:6(472)","volume":"121","author":"C-H Ling","year":"1995","unstructured":"Ling C-H (1995) Criteria for incipient motion of spherical sediment particles. J Hydraul Eng 121(6):472\u2013478. doi:10.1061\/(ASCE)0733-9429(1995)121:6(472)","journal-title":"J Hydraul Eng"},{"issue":"12","key":"13_CR123","doi-asserted-by":"crossref","first-page":"3743","DOI":"10.1029\/2000WR900238","volume":"36","author":"TE Lisle","year":"2000","unstructured":"Lisle TE, Nelson JM, Pitlick J, Madej MA, Barkett BL (2000) Variability of bed mobility in natural, gravel-bed channels and adjustments to sediment load at local and reach scales. Water Resour Res 36(12):3743\u20133755","journal-title":"Water Resour Res"},{"issue":"8","key":"13_CR124","doi-asserted-by":"crossref","first-page":"1971","DOI":"10.1029\/97WR01180","volume":"33","author":"TE Lisle","year":"1997","unstructured":"Lisle TE, Pizzuto JE, Ikeda H, Iseya F, Kodama Y (1997) Evolution of a sediment wave in an experimental channel. Water Resour Res 33(8):1971\u20131981","journal-title":"Water Resour Res"},{"key":"13_CR125","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1111\/j.1752-1688.1992.tb04003.x","volume":"28","author":"TE Lisle","year":"1992","unstructured":"Lisle TE, Hilton S (1992) The volume of fine sediment in pools: an index of sediment supply in gravel bed streams. Water Resour Bull 28:371\u2013383","journal-title":"Water Resour Bull"},{"issue":"12","key":"13_CR126","doi-asserted-by":"publisher","first-page":"2169","DOI":"10.1002\/2014JF003308","volume":"119","author":"H Ma","year":"2014","unstructured":"Ma H, Heyman J, Fu X, Mettra F, Ancey C, Parker G (2014) Bed load transport over a broad range of timescales: determination of three regimes of fluctuations. J Geophys Res Earth Surf 119(12):2169\u20139011. doi:10.1002\/2014JF003308","journal-title":"J Geophys Res Earth Surf"},{"key":"13_CR127","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1016\/j.geomorph.2010.10.031","volume":"125","author":"BJ MacVicar","year":"2011","unstructured":"MacVicar BJ, Roy AG (2011) Sediment mobility in a forced riffle-pool. Geomorphology 125:445\u2013456","journal-title":"Geomorphology"},{"key":"13_CR128","doi-asserted-by":"publisher","unstructured":"Martin R, Jerolmack D, Schumer R (2012) The physical basis for anomalous diffusion in bed load transport. J Geophys Res 117:F01018, 18\u00a0pp. doi:10.1029\/2011JF002075","DOI":"10.1029\/2011JF002075"},{"key":"13_CR129","unstructured":"Mavies W, Ho C-H, Tu Y-C (1935) The transportation of detritus by flowing water\u2013I. University of Iowa Studies in Engineering, Bulletin 5, 54\u00a0pp"},{"issue":"2","key":"13_CR130","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1061\/(ASCE)0733-9429(2004)130:2(129)","volume":"130","author":"I McEwan","year":"2004","unstructured":"McEwan I, S\u00f8rensen M, Heald J, Tait S, Cunningham G, Goring D, Willetts B (2004) Probabilistic modeling of bed-load composition. J Hydraul Eng 130(2):129\u2013139. doi:10.1061\/(ASCE)0733-9429(2004)130:2(129)","journal-title":"J Hydraul Eng"},{"issue":"10","key":"13_CR131","doi-asserted-by":"crossref","first-page":"1871","DOI":"10.1002\/hyp.1453","volume":"18","author":"JP McNamara","year":"2004","unstructured":"McNamara JP, Borden C (2004) Observations on the movement of coarse gravel using implanted motion-sensing radio transmitters. Hydrol Process 18(10):1871\u20131884","journal-title":"Hydrol Process"},{"key":"13_CR132","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/BF02509922","volume":"7","author":"RH Meade","year":"1985","unstructured":"Meade RH (1985) Wavelike movement of bedload sediment, East Fork River, Wyoming. Environ Geol Water Sci 7:215\u2013255","journal-title":"Environ Geol Water Sci"},{"key":"13_CR133","unstructured":"Meyer-Peter E, M\u00fcller R (1948) Formulas for bed-load transport. In: Proceedings of 2nd meeting, IAHR, Stockholm, Sweden, pp 39\u201364"},{"key":"13_CR134","unstructured":"Milhous, R.T. (1973). Sediment transport in a gravel-bottomed stream, PhD thesis, Oregon State University, Corvallis, Oregon, 232\u00a0pp"},{"key":"13_CR135","doi-asserted-by":"crossref","first-page":"1814","DOI":"10.1130\/0016-7606(2000)112<1814:EOPSSO>2.0.CO;2","volume":"112","author":"DJ Miller","year":"2000","unstructured":"Miller DJ, Benda LE (2000) Effects of punctuated sediment supply on valley-floor landforms and sediment transport. Geolog Soc Am Bull 112:1814\u20131824","journal-title":"Geolog Soc Am Bull"},{"issue":"4","key":"13_CR136","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1111\/j.1365-3091.1966.tb01897.x","volume":"6","author":"RL Miller","year":"1966","unstructured":"Miller RL, Byrne RJ (1966) The angle of repose for a single grain on a fixed rough bed. Sedimentology 6(4):303\u2013314. doi:10.1111\/j.1365-3091.1966.tb01897.x","journal-title":"Sedimentology"},{"key":"13_CR137","unstructured":"Mizuyama T (1977) Bedload transport in steep channels. Ph.D. thesis, Kyoto University, Japan, 118\u00a0pp"},{"key":"13_CR138","first-page":"289","volume":"19","author":"H Nakagawa","year":"1976","unstructured":"Nakagawa H, Tsujimoto T (1976) Experimental Study on Evolution of Sand Waves from an Initially Flattened Bed. Disaster Prev Res Inst Ann 19:289\u2013309","journal-title":"Disaster Prev Res Inst Ann"},{"key":"13_CR139","doi-asserted-by":"crossref","first-page":"2071","DOI":"10.1029\/95WR00976","volume":"31","author":"JM Nelson","year":"1995","unstructured":"Nelson JM, Shreve RL, McLean SR, Drake TG (1995) Role of near-bed turbulence in bedload transport and bedform mechanics. Water Resour Res 31:2071\u20132086","journal-title":"Water Resour Res"},{"issue":"6","key":"13_CR140","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2001WR000513","volume":"38","author":"V Nikora","year":"2002","unstructured":"Nikora V, Habersack H, Huber T, McEwan I (2002) On bed particle diffusion in gravel bed flows under weak bed load transport. Water Resour Res 38(6):1\u20139","journal-title":"Water Resour Res"},{"key":"13_CR141","unstructured":"Novak ID (1973) Predicting coarse sediment transport: the Hjulstrom curve revisited. In: Morisawa M (ed) Fluvial geomorphology. Binghampton New York State University, New York, pp 13\u201326"},{"issue":"1","key":"13_CR142","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1080\/00221687109500339","volume":"9","author":"AS Paintal","year":"1971","unstructured":"Paintal AS (1971a) Concept of critical shear stress in loose boundary open channels. J Hydraul Res 9(1):91\u2013113","journal-title":"J Hydraul Res"},{"issue":"4","key":"13_CR143","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1080\/00221687109500371","volume":"9","author":"AS Paintal","year":"1971","unstructured":"Paintal AS (1971b) A stochastic model of bed load transport. J Hydraul Res 9(4):527\u2013554","journal-title":"J Hydraul Res"},{"issue":"4","key":"13_CR144","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1080\/00221689009499058","volume":"28","author":"G Parker","year":"1990","unstructured":"Parker G (1990) Surface bedload transport relation for gravel rivers. J Hydraul Res 28(4):417\u2013436","journal-title":"J Hydraul Res"},{"key":"13_CR145","doi-asserted-by":"crossref","unstructured":"Parker G (2008) Transport of gravel and sediment mixtures. In: Garc\u00eda MH (ed) Sedimentation engineering. Processes, measurements, modeling and practice, ASCE, Reston, pp 165\u2013251","DOI":"10.1061\/9780784408148.ch03"},{"issue":"9","key":"13_CR146","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1029\/WR021i009p01361","volume":"21","author":"G Parker","year":"1985","unstructured":"Parker G, Andrews E (1985) Sorting of bed load sediment by flow in meander bends. Water Resour Res 21(9):1361\u20131373","journal-title":"Water Resour Res"},{"key":"13_CR147","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1029\/WR018i004p01049","volume":"18","author":"G Parker","year":"1982","unstructured":"Parker G, Klingeman PC (1982) On why gravel-bed streams are paved. Water Resour Res 18:1049\u20131423","journal-title":"Water Resour Res"},{"issue":"11","key":"13_CR148","doi-asserted-by":"publisher","first-page":"1264","DOI":"10.1029\/2001WR000669","volume":"38","author":"G Parker","year":"2002","unstructured":"Parker G, Toro-Escobar CM (2002) Equal mobility of gravel in streams: the remains of the day. Water Resour Res 38(11):1264. doi:10.1029\/2001WR000669","journal-title":"Water Resour Res"},{"key":"13_CR149","doi-asserted-by":"crossref","first-page":"818","DOI":"10.1061\/(ASCE)0733-9429(2000)126:11(818)","volume":"126","author":"G Parker","year":"2000","unstructured":"Parker G, Paola C, Leclair S (2000) Probabilistic form of Exner equation of sediment continuity for mixtures with no active layer. J Hydraul Eng 126:818\u2013826","journal-title":"J Hydraul Eng"},{"issue":"HY4","key":"13_CR150","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1061\/JYCEAJ.0005854","volume":"108","author":"G Parker","year":"1982","unstructured":"Parker G, Klingeman PC, McLean DG (1982) Bedload and size distribution in paved gravel-bed streams. J Hydraul Div 108(HY4):544\u2013571","journal-title":"J Hydraul Div"},{"issue":"7","key":"13_CR151","doi-asserted-by":"crossref","first-page":"1183","DOI":"10.1029\/2001WR001253","volume":"39","author":"G Parker","year":"2003","unstructured":"Parker G, Seminara G, Solari L (2003) Bed load at low shields stress on arbitrarily sloping beds: alternative entrainment formulation. Water Resour Res 39(7):1183","journal-title":"Water Resour Res"},{"key":"13_CR152","doi-asserted-by":"crossref","unstructured":"Proffitt GJ, Sutherland AJ (1983) Transport of non-uniform sediment. J Hydraul Res IAHR 21(1):33\u201343","DOI":"10.1080\/00221688309499448"},{"key":"13_CR153","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1002\/esp.498","volume":"28","author":"RS Pyrce","year":"2003","unstructured":"Pyrce RS, Ashmore PE (2003a) Particle path length distributions in meandering gravel-bed streams: results from physical models. Earth Surf Proc Land 28:951\u2013966","journal-title":"Earth Surf Proc Land"},{"key":"13_CR154","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/S0169-555X(03)00077-1","volume":"56","author":"RS Pyrce","year":"2003","unstructured":"Pyrce RS, Ashmore PE (2003b) The relation between particle path length distributions and channel morphology in gravel-bed streams. Geomorphology 56:167\u2013187","journal-title":"Geomorphology"},{"key":"13_CR155","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1111\/j.1365-3091.2005.00714.x","volume":"52","author":"RS Pyrce","year":"2005","unstructured":"Pyrce RS, Ashmore PE (2005) Bedload path length and point bar development in gravel-bed river models. Sedimentology 52:839\u2013857","journal-title":"Sedimentology"},{"key":"13_CR156","doi-asserted-by":"crossref","unstructured":"Ramette M, Heuzel M (1962) Le Rh\u00f4ne \u00e0 Lyon. Etude de l\u2019entra\u00eenement des galets \u00e0 l\u2019aide de traceurs radioactifs. Essai poor l\u2019extension de la formule de Mayer-Peter au domaines du charriage partiel. Houille Blanche, pp 289\u2013399","DOI":"10.1051\/lhb\/1962011"},{"key":"13_CR157","unstructured":"Reid I, Frostick LE (1984) Particle interaction and its effect on the thresholds of initial and final beldoad motion in coarse alluvial channels. Can Soc Pet Geo 19:61\u201368 (Koster EH, Steel RJ (eds) Sedimentary of gravels and conglomerates)"},{"key":"13_CR158","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1029\/94WR02233","volume":"31","author":"I Reid","year":"1995","unstructured":"Reid I, Laronne JB (1995) Bedload sediment transport in an ephemeral stream and a comparison with seasonal and perennial counterparts. Water Resour Res 31:773\u2013781","journal-title":"Water Resour Res"},{"key":"13_CR159","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1002\/esp.3290100107","volume":"10","author":"I Reid","year":"1985","unstructured":"Reid I, Frostick LE, Lyman JL (1985) The incidence and nature of bedload transport during flood flows in coarse-grained alluvial channels. Earth Surf Proc Land 10:33\u201344","journal-title":"Earth Surf Proc Land"},{"key":"13_CR160","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1080\/00221688009499550","volume":"18","author":"I Reid","year":"1980","unstructured":"Reid I, Layman JT, Frostick LE (1980) The continuous measurement of bedload discharge. J Hydraul Res 18:243\u2013249","journal-title":"J Hydraul Res"},{"key":"13_CR161","unstructured":"Ribberink JS (1987) Mathematical modeling of one-dimensional morphological changes in rivers with non-uniform sediment. Ph.D. thesis, Delft University of Technology, 200 p"},{"key":"13_CR162","unstructured":"Rickenmann D (1990) Bedload capacity of slurry flows at steep slopes. In: Mitteilung der Versuchsanstalt fur Wasserbau, Hydrologie und Glaziologie, Rep. 103, Eidg. Tech. Hochsch, Zurich, Zurich, Switzerland, 249\u00a0pp"},{"key":"13_CR163","doi-asserted-by":"crossref","first-page":"3295","DOI":"10.1029\/2001WR000319","volume":"37","author":"D Rickenmann","year":"2001","unstructured":"Rickenmann D (2001) Comparison of bedload transport in torrents and gravel bed streams. Water Resour Res 37:3295\u20133305","journal-title":"Water Resour Res"},{"key":"13_CR164","first-page":"1092","volume":"16","author":"RJ Roberts","year":"1986","unstructured":"Roberts RJ, Church M (1986) The sediment budget in severely disturbed watersheds, Queen Charlotte Ranges, British Columbia. Can J Earth Sci 16:1092\u20131106","journal-title":"Can J Earth Sci"},{"key":"13_CR165","doi-asserted-by":"crossref","unstructured":"Roseberry JC, Schmeeckle MW, Furbish DJ (2012) A probabilistic description of the bed load sediment flux: 2. Particle activity and motions. J Geophys Res Earth Surf 117","DOI":"10.1029\/2012JF002353"},{"key":"13_CR166","unstructured":"Rouse H (1939) An analysis of sediment transportation in light of fluid turbulence. Report no. SCS-TP-25, Sediment Division, U.S. Department of Agriculture, Soil Conservation Service, Washington, DC"},{"key":"13_CR167","doi-asserted-by":"crossref","unstructured":"Ryan SE, Emmett WW (2002) The nature of flow and sediment movement in Little Granite Creek near Bondurant, Wyoming. U. S. Forest Service, General technical report RMRS-GTR -90, 48 p","DOI":"10.2737\/RMRS-GTR-90"},{"key":"13_CR168","unstructured":"Ryan SE (2001) The influence of sediment supply on rates of bed load transport: a case study of three streams on the San Juan National Forest. In: Proceeding of the seventh federal interagency sedimentation conference, March 25\u201329, 2001, Reno, Nevada, pp III-48\u2013III-54"},{"key":"13_CR169","unstructured":"Ryan SE, Troendle CA (1996) Bed load transport patterns in coarse-grained channels under varying conditions of flows. In: Proceeding of the sixth federal interagency sedimentation conference on sedimentation technologies for management of natural resources in the 21st century, vol 2, March 10\u201314, 1996, Las Vegas, pp VI-22\u2013VI-27"},{"key":"13_CR170","unstructured":"Ryan SE, Troendle CA (1997) Measuring bedload in coarse-grained mountain channels procedures, problems, and recommendations. In: Water resources education, training, and practice. Opportunities for the next century, American Water Resources Association, Keystone, Colorado, pp 949\u2013958"},{"key":"13_CR171","unstructured":"Sawada T, Ashida K, Takahashi T (1983) Relationship between channel pattern and sediment transport in a steep gravel bed river. Z Geomorph NF Suppl Bd 16:55\u201366"},{"key":"13_CR172","unstructured":"Sawada T, Ashida K, Takahashi T (1985) Sediment transport in mountain basins. Paper presented at international symposium on erosion, debris flow and disaster prevention, Tsukuba, Japan"},{"key":"13_CR173","doi-asserted-by":"crossref","unstructured":"Sayre WW, Hubbell DW (1965) Transport and dispersion of labeled bed material. U.S. Geology survey professional paper 433-C, North Loup River, Nebraska, 48\u00a0pp","DOI":"10.3133\/pp433C"},{"key":"13_CR174","first-page":"73","volume":"10","author":"AP Schick","year":"1987","unstructured":"Schick AP, Hassan MA, Lekach J (1987) A vertical exchange model for coarse bedload movement: numerical considerations. Catena Suppl 10:73\u201383","journal-title":"Catena Suppl"},{"key":"13_CR175","doi-asserted-by":"crossref","unstructured":"Schmidt K-H, Ergenzinger P (1992) Bedload entrainment, travel lengths, step lengths, rest periods\u2014studied with passive (iron, magnetic) and active (radio) tracer techniques. Earth Surf Process Land 17:147\u2013165","DOI":"10.1002\/esp.3290170204"},{"key":"13_CR176","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1002\/2013JF002874","volume":"119","author":"JM Schneider","year":"2014","unstructured":"Schneider JM, Turowski JM, Rickenmann D, Hegglin R, Arrigo S, Mao L, Kirchner JW (2014) Scaling relationships between bed load volumes, transport distances, and stream power in steep mountain channels. J Geophys Res Earth Surf 119:533\u2013549. doi:10.1002\/2013JF002874","journal-title":"J Geophys Res Earth Surf"},{"key":"13_CR177","volume-title":"Handbuch des Wasserbaues","author":"A Schoklitsch","year":"1962","unstructured":"Schoklitsch A (1962) Handbuch des Wasserbaues, 3rd edn. Springer, Vienna","edition":"3"},{"key":"13_CR178","doi-asserted-by":"publisher","first-page":"1296","DOI":"10.1029\/2003WR002141","volume":"39","author":"R Schumer","year":"2003","unstructured":"Schumer R, Benson DA, Meerschaert MM, Baeumer B (2003) Fractal mobile\/immobile solute transport. Water Resour Res 39:1296. doi:10.1029\/2003WR002141","journal-title":"Water Resour Res"},{"key":"13_CR179","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1002\/(SICI)1096-9837(199603)21:3<241::AID-ESP623>3.0.CO;2-1","volume":"21","author":"DA Sear","year":"1996","unstructured":"Sear DA (1996) Sediment transport processes in pool-riffle sequences. Earth Surf Proc Land 21:241\u2013262","journal-title":"Earth Surf Proc Land"},{"issue":"11","key":"13_CR180","doi-asserted-by":"crossref","first-page":"1249","DOI":"10.1029\/2001WR000681","volume":"38","author":"G Seminara","year":"2002","unstructured":"Seminara G, Parker G, Solari L (2002) Bed load at low shields stress on arbitrarily sloping beds: failure of the Bagnolg hypothesis. Water Resour Res 38(11):1249","journal-title":"Water Resour Res"},{"key":"13_CR181","unstructured":"Shields A (1936) Anwendung der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung, Mitt. Preuss. Versuchsanst.Wasserbau Schiffbau; english translation by W. P. Ott and J. C. van Uchelen, 36\u00a0pp, U.S. Dep. of Agric. Soil Conser. Serv. Coop. Lab., California, Institute of Technology, Pasadena"},{"key":"13_CR182","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1029\/WR024i002p00207","volume":"24","author":"RC Sidle","year":"1988","unstructured":"Sidle RC (1988) Bedload transport regime of a small forested stream. Water Resour Res 24:207\u2013218","journal-title":"Water Resour Res"},{"key":"13_CR183","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1002\/esp.3290180507","volume":"18","author":"RD Smith","year":"1993","unstructured":"Smith RD, Sidle RC, Porter PE (1993a) Effects on bedload transport of experimental removal of woody debris from a forest gravel-bed stream. Earth Surf Proc Land 18:455\u2013468","journal-title":"Earth Surf Proc Land"},{"key":"13_CR184","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/0022-1694(93)90144-X","volume":"152","author":"RD Smith","year":"1993","unstructured":"Smith RD, Sidle RC, Porter PE, Noel JR (1993b) Effects of experimental removal of woody debris on the channel morphology of a forest, gravel bed stream. J Hydrol 152:153\u2013178","journal-title":"J Hydrol"},{"key":"13_CR185","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1061\/(ASCE)0733-9429(2000)126:3(185)","volume":"126","author":"L Solari","year":"2000","unstructured":"Solari L, Parker G (2000) The curious case of mobility reversal in sediment mixtures. J Hydraul Eng 126:185\u2013197","journal-title":"J Hydraul Eng"},{"key":"13_CR186","unstructured":"Stelczer K (1981) Bedload transport: theory and practice. Littleton, Colorado, Water Resources Publication, 295\u00a0pp"},{"key":"13_CR187","doi-asserted-by":"publisher","unstructured":"Sterling S, Church M (2002) Sediment trapping characteristics of a pit trap and a Helley-Smith sampler in a cobble-gravel bed river. Water Resour Res 38:19-1\u201319-11. doi:10.1029\/2000WR000052","DOI":"10.1029\/2000WR000052"},{"key":"13_CR188","doi-asserted-by":"publisher","unstructured":"Sun Z, Donahue J (2000) Statistically derived bed load formula for any fraction of nonuniform sediment. J Hydraul Eng ASCE 126(2):105\u2013111. doi:10.1061\/(ASCE)0733-9429(2000)126:2(105)","DOI":"10.1061\/(ASCE)0733-9429(2000)126:2(105)"},{"key":"13_CR189","doi-asserted-by":"crossref","first-page":"1036","DOI":"10.1130\/0016-7606(2002)114<1036:EOALIS>2.0.CO;2","volume":"114","author":"DG Sutherland","year":"2002","unstructured":"Sutherland DG, Ball MH, Hilton SJ, Lisle TE (2002) Evolution of a landslide-induced sediment wave in the Navarro River, California. Geol Soc Am Bull 114:1036\u20131048","journal-title":"Geol Soc Am Bull"},{"key":"13_CR190","doi-asserted-by":"crossref","unstructured":"Swanson FJ, Janda RJ, Dunne T, Swanston DN (eds) (1982a). Sediment budgets and routing in forested drainage basins. United States Department of Agriculture, Forest Service, General technical report PNW-141, 165\u00a0pp","DOI":"10.2737\/PNW-GTR-141"},{"key":"13_CR191","doi-asserted-by":"crossref","unstructured":"Swanson FJ, Janda RJ, Dunne T (1982b) Summary: sediment budgets and routing in forested drainage basins. In: Swanson FJ, Janda RJ, Dunne T, Swanston DN (eds) Sediment budgets and routing in forested drainage basins. United States Department of Agriculture, General Technical Report Number PNW-141, pp 157\u2013165","DOI":"10.2737\/PNW-GTR-141"},{"key":"13_CR192","unstructured":"Troendle CA, Nankervis JM, Ryan SE (1996) Sediment transport from small, steep-gradient watersheds in Colorado and Wyoming. In: Sixth federal interagency sedimentation conference on sedimentation technologies for management of natural resources in the 21st century, March 10\u201314, 1996, Las Vegas, NV, pp IX-39\u2013IX-45"},{"key":"13_CR193","doi-asserted-by":"publisher","first-page":"W08501","DOI":"10.1029\/2009WR008488","volume":"46","author":"JM Turowski","year":"2010","unstructured":"Turowski JM (2010) Probability distributions of bed load transport rates: a new derivation and comparison with field data. Water Resour Res 46:W08501. doi:10.1029\/2009WR008488","journal-title":"Water Resour Res"},{"issue":"9","key":"13_CR194","doi-asserted-by":"publisher","first-page":"W09512","DOI":"10.1029\/2010WR010236","volume":"47","author":"M Valyrakis","year":"2011","unstructured":"Valyrakis M, Diplas P, Dancey CL (2011) Entrainment of coarse grains in turbulent flows: an extreme value theory approach. Water Resour Res 47(9):W09512. doi:10.1029\/2010WR010236","journal-title":"Water Resour Res"},{"issue":"10","key":"13_CR195","doi-asserted-by":"crossref","first-page":"1431","DOI":"10.1061\/(ASCE)0733-9429(1984)110:10(1431)","volume":"110","author":"LC Van Rijn","year":"1984","unstructured":"Van Rijn LC (1984) Sediment transport, part I: bed load transport. J Hydraul Eng 110(10):1431\u20131456","journal-title":"J Hydraul Eng"},{"key":"13_CR196","doi-asserted-by":"crossref","unstructured":"Vanoni VA (1966) Sediment transportation mechanics: Initiation of motion. J Hydraul Div ASCE 92(2):291\u2013314","DOI":"10.1061\/JYCEAJ.0001416"},{"issue":"8","key":"13_CR197","doi-asserted-by":"crossref","first-page":"1022","DOI":"10.1061\/(ASCE)0733-9429(1984)110:8(1021)","volume":"110","author":"VA Vanoni","year":"1984","unstructured":"Vanoni VA (1984) Fifty years of sedimentation. J Hydraul Eng 110(8):1022\u20131057","journal-title":"J Hydraul Eng"},{"issue":"8","key":"13_CR198","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1029\/95WR01229","volume":"31","author":"SJ Wathen","year":"1995","unstructured":"Wathen SJ, Ferguson RI, Hoey TB, Werrity A (1995) Unequal mobility of sand and gravel in weakly bimodal river sediments. Water Resour Res 31(8):287\u2013296. doi:10.1029\/95WR01229","journal-title":"Water Resour Res"},{"key":"13_CR199","unstructured":"White FM (2011) Fluid mechanics, 7th edn. McGaw-Hill International Editions"},{"key":"13_CR200","unstructured":"White WR, Day TJ (1982) Transport of graded gravel bed material. In: Hey RD, Bathurst JC, Thorne CR (eds) Gravel-bed rivers, fluvial processes, engineering and management. Wiley, New York, pp 181\u2013223"},{"key":"13_CR201","first-page":"545","volume-title":"Sediment transport in gravel-bed rivers","author":"JG Whittaker","year":"1987","unstructured":"Whittaker JG (1987) Sediment transport in step-pool streams. In: Thorne CR, Bathurst JC, Hey RD (eds) Sediment transport in gravel-bed rivers. Wiley, Chichester, pp 545\u2013579"},{"key":"13_CR202","doi-asserted-by":"crossref","first-page":"1471","DOI":"10.1029\/WR023i008p01471","volume":"23","author":"PL Wiberg","year":"1987","unstructured":"Wiberg PL, Smith JD (1987) Calculations of the critical shear stress for motion of uniform and heterogeneous sediments. Water Resour Res 23:1471\u20131480","journal-title":"Water Resour Res"},{"issue":"2","key":"13_CR203","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1061\/(ASCE)0733-9429(2003)129:2(120)","volume":"129","author":"PR Wilcock","year":"2003","unstructured":"Wilcock PR, Crowe JC (2003) Surface-based tranport model for mixed-size sediment. J Hydraul Eng 129(2):120\u2013128. doi:10.1061\/(ASCE)0733-9429(2003)129:2(120)","journal-title":"J Hydraul Eng"},{"key":"13_CR204","doi-asserted-by":"publisher","unstructured":"Wilcock PR (1998) Two-fraction model of initial sediment motion in gravel-bed rivers. Science 280(410). doi:10.1126\/science.280.5362.410","DOI":"10.1126\/science.280.5362.410"},{"issue":"10","key":"13_CR205","doi-asserted-by":"publisher","first-page":"1194","DOI":"10.1029\/2001WR000684","volume":"38","author":"PR Wilcock","year":"2002","unstructured":"Wilcock PR, Kenworthy ST (2002) A two-fraction model for the transport of sand\/gravel mixtures. Water Resour Res 38(10):1194. doi:10.1029\/2001WR000684","journal-title":"Water Resour Res"},{"issue":"7","key":"13_CR206","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1029\/WR024i007p01137","volume":"24","author":"PR Wilcock","year":"1988","unstructured":"Wilcock PR, Southard JB (1988) Experimental study of incipient motion in mixed-size sediment. Water Resour Res 24(7):1137\u20131151","journal-title":"Water Resour Res"},{"issue":"1","key":"13_CR207","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1029\/96WR02666","volume":"33","author":"PR Wilcock","year":"1997","unstructured":"Wilcock PR (1997a) The components of fractional transport rate. Water Resour Res 33(1):247\u2013258. doi:10.1029\/96WR02666","journal-title":"Water Resour Res"},{"issue":"4","key":"13_CR208","doi-asserted-by":"publisher","first-page":"1297","DOI":"10.1029\/92WR02748","volume":"29","author":"PR Wilcock","year":"1993","unstructured":"Wilcock PR, McArdell BW (1993) Surface-based fractional transport rates: mobilization thresholds and partial transport of a sand-gravel sediment. Water Resour Res 29(4):1297\u20131312. doi:10.1029\/92WR02748","journal-title":"Water Resour Res"},{"issue":"1","key":"13_CR209","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1029\/96WR02672","volume":"33","author":"PR Wilcock","year":"1997","unstructured":"Wilcock PR, McArdell BW (1997) Partial transport of a sand\/gravel sediment. Water Resour Res 33(1):235\u2013245. doi:10.1029\/96WR02672","journal-title":"Water Resour Res"},{"key":"13_CR210","doi-asserted-by":"crossref","first-page":"1125","DOI":"10.1002\/(SICI)1096-9837(199712)22:12<1125::AID-ESP811>3.0.CO;2-V","volume":"22","author":"PR Wilcock","year":"1997","unstructured":"Wilcock PR (1997b) Entrainment, displacement and transport of tracer gravels. Earth Surf Proc Land 22:1125\u20131138","journal-title":"Earth Surf Proc Land"},{"key":"13_CR211","doi-asserted-by":"crossref","first-page":"2897","DOI":"10.1029\/96WR01628","volume":"32","author":"PR Wilcock","year":"1996","unstructured":"Wilcock PR, Barta AF, Shea CC, Kondolf GM, Matthews WVG, Pitlick JC (1996) Observations of flow and sediment entrainment on a large gravel-bed river. Water Resour Res 32:2897\u20132909","journal-title":"Water Resour Res"},{"key":"13_CR212","unstructured":"Williams GR et al.\u00a0(1937). Selected bibliography on erosion and silt movement. Water supply paper 797, US Department of Interior Geological Survey"},{"key":"13_CR213","doi-asserted-by":"publisher","first-page":"W03440","DOI":"10.1029\/2006WR005172","volume":"43","author":"M Wong","year":"2007","unstructured":"Wong M, Parker G, DeVries P, Brown TM, Burges SJ (2007) Experiments on dispersion of tracer stones under lower-regime plane-bed equilibrium bed load transport. Water Resour Res 43:W03440. doi:10.1029\/2006WR005172","journal-title":"Water Resour Res"},{"key":"13_CR214","doi-asserted-by":"publisher","first-page":"W04501","DOI":"10.1029\/2003WR002256","volume":"40","author":"F-C Wu","year":"2004","unstructured":"Wu F-C, Yang K-H (2004) A stochastic partial transport model for mixed-size sediment: application to assessment of fractional mobility. Water Resour Res 40:W04501. doi:10.1029\/2003WR002256","journal-title":"Water Resour Res"},{"issue":"2","key":"13_CR215","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1061\/(ASCE)0733-9429(2003)129:2(110)","volume":"129","author":"F-C Wu","year":"2003","unstructured":"Wu F-C, Chou Y-J (2003) Rolling and lifting probabilities for sediment entrainment. J Hydraul Eng 129(2):110\u2013119. doi:10.1061\/(ASCE)0733-9429(2003)129:2(110)","journal-title":"J Hydraul Eng"},{"key":"13_CR216","unstructured":"Yalin MS (1977) Mechanics of sediment transport. 2nd edn. Pergamon Press, Oxford"},{"key":"13_CR217","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/S0169-555X(01)00057-5","volume":"40","author":"A Zimmerman","year":"2001","unstructured":"Zimmerman A, Church M (2001) Channel morphology, gradient profiles and bed stresses during spring runoff in a step-pool channel. Geomorphology 40:311\u2013328","journal-title":"Geomorphology"},{"key":"13_CR218","doi-asserted-by":"publisher","first-page":"F02008","DOI":"10.1029\/2009JF001365","volume":"115","author":"AE Zimmermann","year":"2010","unstructured":"Zimmermann AE, Church M, Hassan MA (2010) Step-pool stability: testing the jammed state hypothesis. J Geophys Res 115:F02008. doi:10.1029\/2009JF001365","journal-title":"J Geophys Res"}],"container-title":["GeoPlanet: Earth and Planetary Sciences","Rivers \u2013 Physical, Fluvial and Environmental Processes"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-17719-9_13","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,9]],"date-time":"2024-06-09T19:27:32Z","timestamp":1717961252000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-17719-9_13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319177182","9783319177199"],"references-count":218,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-17719-9_13","relation":{},"ISSN":["2190-5193","2190-5207"],"issn-type":[{"value":"2190-5193","type":"print"},{"value":"2190-5207","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]},"assertion":[{"value":"1 July 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}