Abstract
This paper presents a heuristic probabilistic approach to estimating the size-dependent mobilities of nonuniform sediment based on the pre- and post-entrainment particle size distributions (PSDs), assuming that the PSDs are lognormally distributed. The approach fits a lognormal probability density function to the pre-entrainment PSD of bed sediment and uses the threshold particle size of incipient motion and the concept of sediment mixture to estimate the PSDs of the entrained sediment and post-entrainment bed sediment. The new approach is simple in physical sense and significantly reduces the complexity and computation time and resource required by detailed sediment mobility models. It is calibrated and validated with laboratory and field data by comparing to the size-dependent mobilities predicted with the existing empirical lognormal cumulative distribution function approach. The novel features of the current approach are: (1) separating the entrained and non-entrained sediments by a threshold particle size, which is a modified critical particle size of incipient motion by accounting for the mixed-size effects, and (2) using the mixture-based pre- and post-entrainment PSDs to provide a continuous estimate of the size-dependent sediment mobility.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abuodha JOZ (2003) Grain size distribution and composition of modern dune and beach sediments, Malindi Bay coast, Kenya. J Afr Earth Sci 36:41–54. https://doi.org/10.1016/S0899-5362(03)00016-2
Agrawal YC, Mikkelsen OA, Pottsmith HC (2012) Grain size distribution and sediment flux structure in a river profile, measured with a LISST-SL instrument. Sequoia Scientific, Inc, Bellevue
Armanini A, Di Silvio G (1988) A one-dimensional model for the transport of a sediment mixture in non-equilibrium conditions. J Hydraul Res 26:275–292. https://doi.org/10.1080/00221688809499212
Biron PM, Robson C, Lapointe MF, Gaskin SJ (2004) Comparing different methods of bed shear stress estimates in simple and complex flow fields. Earth Surf Process Landf 29:1403–1415. https://doi.org/10.1002/esp.1111
Bouchez J, Metivier F, Lupker M et al (2011) Prediction of depth-integrated fluxes of suspended sediment in the Amazon River: particle aggregation as a complicating factor. Hydrol Process 25:778–794. https://doi.org/10.1002/hyp.7868
Buscombe D, Conley DC (2012) Effective shear stress of graded sediments. Water Resour Res 48:1–13. https://doi.org/10.1029/2010WR010341
Church M, Wolcott J, Maizels J (1990) Palaeovelocity: a parsimonious proposal. Earth Surf Process Landf 15:475–480. https://doi.org/10.1002/esp.3290150511
Eisenberg B, Sullivan R (2008) Why is the sum of independent normal random variables normal? Math Mag 81:362–366. https://doi.org/10.2307/27643141
Fowlkes EB (1979) Some methods for studying the mixture of two normal (lognormal) distributions. J Am Stat Assoc 74:561–575. https://doi.org/10.2307/2286973
Graf WH, Song T (1995) Bed-shear stress in non-uniform and unsteady open-channel flows. J Hydraul Res 33:699–704. https://doi.org/10.1080/00221689509498565
Jafari M, Hemmat A, Sadeghi M (2011) Comparison of coefficient of variation with non-uniformity coefficient in evaluation of grain drills. J Agric Sci Technol 13:643–654
Lavelle JW, Mofjeld HO (1987) Do critical stresses for incipient motion and erosion really exist? J Hydraul Eng 113:370–385. https://doi.org/10.1061/(ASCE)0733-9429(1987)113:3(370)
Leopold LB, Emmettt WW (1976) Bedload measurements, East Fork River, Wyoming. Proc Natl Acad Sci USA 73:1000–1004
Lopez F, Garcia MH (2001) Risk of sediment erosion and suspension in turbulent flows. J Hydraul Eng 1:231–235
Oh J, Tsai CW (2017) A stochastic multivariate framework for modeling movement of discrete sediment particles in open channel flows. Stoch Environ Res Risk Assess. https://doi.org/10.1007/s00477-017-1410-3
Rhodes DG (1995) Newton–Raphson solution for gradually varied flow. J Hydraul Res 33:213–218. https://doi.org/10.1080/00221689509498671
Rilstone P (2002) Econometric analysis of count data. J Am Stat Assoc 97:361–362. https://doi.org/10.1198/jasa.2002.s458
Safik A, Safak M (1994) Moments of the sum of correlated log-normal random variables. In: Vehicular technology conference. IEEE, Stockholm, pp 140–144
Schulte AM, Chaudhry MH (1987) Gradually-varied flows in open-channel networks. J Hydraul Res 25:357–371. https://doi.org/10.1080/00221688709499276
Shrestha NK, Leta OT, De Fraine B et al (2013) OpenMI-based integrated sediment transport modelling of the river Zenne, Belgium. Environ Model Softw 47:193–206. https://doi.org/10.1016/j.envsoft.2013.05.004
Soulsby R, Whitehouse R (1997) Threshold of sediment motion in coastal environments. In: Pacific coasts and ports’ 97: proceedings of the 13th Australasian coastal and ocean engineering conference and the 6th Australasian port and harbour conference, vol 1. Centre for Advanced Engineering, University of Canterbury, p 145
Sun Z, Donahue J (2000) Statistically derived bedload formula for any fraction of nonuniform sediment. J Hydraul Eng 126:105–111
Sundborg A (1956) The River Klarälven: a study of fluvial processes author(s): Åke Sundborg Published by: Wiley on behalf of Swedish Society for Anthropology and Geography Stable. http://www.jstor.org/stable/520140. Accessed 14 April 2016. 14: 10 UTC. Geogr Ann 38:125–237
Tayfur G, Singh VP (2007) Kinematic wave model for transient bed profiles in alluvial channels under nonequilibrium conditions. Water Resour Res. https://doi.org/10.1029/2006WR005681
Vanoni VA, Brooks NH (1957) Laboratory studies of the roughness and suspended load of alluvial streams. California Institute of Technology, Pasadena
Wilcock PR, Mcardell BW (1997) Partial transport of a sand/gravel sediment flume. Water Resour Res 33:235–245. https://doi.org/10.1029/96WR02672
Wilcock PR, Southard JB (1988) Experimental study of incipient motion in mixed-size sediment. Water Resour Res 24:1137–1151. https://doi.org/10.1029/WR024i007p01137
Wilcock PR, Southard JB (1989) Bed-load transport of mixed-size sediment: fractional transport rates, bed forms, and the development of a coarse bed-surface layer. Water Resour Res 25:1629–1641
Wu F-C, Wang C-K (1998) Higher-order approximation techniques for estimating stochastic parameter of a sediment transport model. Stoch Hydrol Hydraul 12:359–375. https://doi.org/10.1007/s004770050025
Wu W, Wang SSY (2000) Movable bed roughness in alluvial rivers. J Hydraul Eng 125:1309–1312
Wu F-C, Yang K-H (2004a) A stochastic partial transport model for mixed-size sediment: application to assessment of fractional mobility. Water Resour Res 40:1–18. https://doi.org/10.1029/2003WR002256
Wu F-C, Yang K-H (2004b) Entrainment probablities of mixed-size sediment incorporating near-bed coherent flow structures. J Hydraul Eng 130:1187–1197
Wu W, Wang SAMSY, Jia Y (2000) Nonuniform sediment transport in alluvial rivers Transport de sédiments non uniformes en rivière alluviale. J Hydraul Res 38:427–434. https://doi.org/10.1080/00221680009498296
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Woldegiorgis, B.T., Wu, FC., Van Griensven, A. et al. A heuristic probabilistic approach to estimating size-dependent mobility of nonuniform sediment. Stoch Environ Res Risk Assess 32, 1771–1782 (2018). https://doi.org/10.1007/s00477-017-1471-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00477-017-1471-3