Distance of movement of coarse particles in gravel bed streams

Hassan, Marwan A.; Church, Michael; Schick, Asher P.

doi:10.1029/90wr02762

Cited by 163 publications

(193 citation statements)

References 6 publications

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“…The mean transport distance is the coefficient l D which we assume is inversely proportional to grain size [Hassan and Church, 1991],…”

Section: A2 Power Law Pdfs Via Mixing Distributionsmentioning

confidence: 99%

“…In reality, grains of bed sediment of variable mass are transported with a broad range of particle velocities over a wide range of distances by numerous flood discharges of varying magnitude [Stark et al, 2000]. Although the composite, long-term probability distribution of transport distances is not yet known empirically, studies such as those of Hassan and Church [1991] and Church and Hassan [1992] have recorded semiheavy (exponential or gamma) probability density functions (pdfs) of particle transport distances after one or two floods, and on theoretical grounds it is reasonable to deduce that it is heavy tailed. Probability distributions with heavy, power law tails arise in nature for one of (at least) three reasons: (1) because the governing process is self-similar, (2) through the mixing of distributions of constituent properties (Appendix A2), or (3) through summation of quantities with arbitary shape, broad-tailed distributions and convergence to a stable law pdf according to the Lévy limit theorem [Lévy, 1937;Feller, 1971].…”

Section: Introductionmentioning

confidence: 99%

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A nonlocal theory of sediment buffering and bedrock channel evolution

Stark¹,

Foufoula‐Georgiou²,

Ganti³

2009

J. Geophys. Res.

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[1] Bedrock erosion in mountain river channels ultimately sets the erosion rate of the surrounding hillslopes and the rate of sediment supply to the channels. The supply of coarse bed sediment acts as a dampening effect on further erosion by depositing an alluvial cover that temporarily obscures the bedrock. For landscapes where the residence time of the alluvial bed cover is comparable to the timescale of bedrock incision, coarse sediment supply and transport generate a strong negative feedback on fluvial downcutting and the coupled process of hillslope-channel erosion is inherently self-buffering. Here we study a simple model of self-buffered bedrock channel erosion that incorporates the spreading of bed sediment cover downstream in a way that allows for a broad-tailed, power law probability distribution of transport velocities of bed sediment over the long-term. This leads us to consider a nonlocal transport law (fractional advection) parameterized by a scaling exponent 0 a < 1 which collapses to local advection for a ! 1. For strong sediment buffering, we find that nonlocality 1 À a has a direct control on the power law scaling of channel slope S with upstream area A, giving S $ A À(1Àa)/2 at steady state. Empirical observations of slope-area scaling are consistent with a < 1 and nonlocal transport. In general, the model predicts linear, logarithmic, or power law stream profiles depending on the extent of buffering, the degree of nonlocality, and the scaling of the bedrock erosion law. It also predicts, somewhat counterintuitively, that bed cover should thicken with distance x downstream slower than linearly as x a , i.e., the more nonlocal the bed sediment spreading process (a ! 0), the slower the bed cover increases downstream. We deduce that long-range, heterogeneous transport of coarse sediment in mixed bedrock-alluvial rivers may be a key element of landscape scaling and an important factor in landscape dynamics.Citation: Stark, C. P., E. Foufoula-Georgiou, and V. Ganti (2009), A nonlocal theory of sediment buffering and bedrock channel evolution,

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“…The mean transport distance is the coefficient l D which we assume is inversely proportional to grain size [Hassan and Church, 1991],…”

Section: A2 Power Law Pdfs Via Mixing Distributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A nonlocal theory of sediment buffering and bedrock channel evolution

Stark¹,

Foufoula‐Georgiou²,

Ganti³

2009

J. Geophys. Res.

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“…The application of passive tracer particles has taken various forms, such as exotic lithologies (Houbrechts et al, 2011), painted bed material (Wilcock, 1997b), magnetic (Hassan et al, 1991), radioactive (Sayre and Hubbell, 1965;Bradley et al, 2010), and RFID (Lamarre et al, 2005;Bradley and Tucker, 2012;Phillips et al, 2013;Schneider et al, 2014). A benefit of RFID-equipped tracer particles is that each particle is uniquely identified, which allows its position to be measured at longer timescales with high recovery rates (Bradley and Tucker, 2012;Phillips et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Dynamics and mechanics of bed-load tracer particles

Phillips

Jerolmack

2014

Earth Surf. Dynam.

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Abstract. Understanding the mechanics of bed load at the flood scale is necessary to link hydrology to landscape evolution. Here we report on observations of the transport of coarse sediment tracer particles in a cobblebedded alluvial river and a step-pool bedrock tributary, at the individual flood and multi-annual timescales. Tracer particle data for each survey are composed of measured displacement lengths for individual particles, and the number of tagged particles mobilized. For single floods we find that measured tracer particle displacement lengths are exponentially distributed; the number of mobile particles increases linearly with peak flood Shields stress, indicating partial bed load transport for all observed floods; and modal displacement distances scale linearly with excess shear velocity. These findings provide quantitative field support for a recently proposed modeling framework based on momentum conservation at the grain scale. Tracer displacement is weakly negatively correlated with particle size at the individual flood scale; however cumulative travel distance begins to show a stronger inverse relation to grain size when measured over many transport events. The observed spatial sorting of tracers approaches that of the river bed, and is consistent with size-selective deposition models and laboratory experiments. Tracer displacement data for the bedrock and alluvial channels collapse onto a single curve -despite more than an order of magnitude difference in channel slope -when variations of critical Shields stress and flow resistance between the two are accounted for. Results show how bed load dynamics may be predicted from a record of river stage, providing a direct link between climate and sediment transport.

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“…Available data suggest that particle step lengths at the intermediate scale (i.e., distances between long rests) are likely to follow exponential [7,8,13], gamma [12], or two-parameter gamma [11] distributions. In these references, it can also be found that the mean step lengths may vary, depending on travel conditions, from 100 to 150 particle diameters.…”

Section: Introductionmentioning

confidence: 99%

Diffusion of bedload particles in open-channel flows: distribution of travel times and second-order statistics of particle trajectories

et al. 2015

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The motion of bedload particles is diffusive and occurs within at least three scale ranges: local, intermediate and global, each of which with a distinctly different diffusion regime. However, these regimes, extensions of the scale ranges and boundaries between them remain to be better defined and quantified. These issues are explored using a Lagrangian model of saltating grains over the uniform fixed bed. The model combines deterministic particle motion dynamics with stochastic characteristics such as probability distributions of step lengths and resting times. Specifically, it is proposed that a memoryless exponential distribution is an appropriate model for the distribution of rest periods while the probability that a particle stops after a current jump follows a binomial distribution, which is a distribution with lack of memory as well. These distributions are incorporated in the deterministic Lagrangian model of saltating grains and extensive numerical simulations are conducted for the identification of the diffusive behavior of particles at different time scales. Based on the simulations and physical considerations, the local, intermediate, and global scale ranges are quantified and the transitions from one range to another are studied for a spectrum of motion parameters. The obtained results demonstrate that two different time scales should be considered for parameterization of diffusive behavior within intermediate and global scale ranges and for defining the localintermediate and intermediate-global boundaries. The simulations highlight the importance of the distributions of the step lengths and resting times for the identification of the boundaries (or transition intervals) between the scale ranges.

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Distance of movement of coarse particles in gravel bed streams

Cited by 163 publications

References 6 publications

A nonlocal theory of sediment buffering and bedrock channel evolution

A nonlocal theory of sediment buffering and bedrock channel evolution

Dynamics and mechanics of bed-load tracer particles

Diffusion of bedload particles in open-channel flows: distribution of travel times and second-order statistics of particle trajectories

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