A nonlocal theory of sediment buffering and bedrock channel evolution

Stark, C. P.; Foufoula‐Georgiou, Efi; Ganti, Vamsi

doi:10.1029/2008jf000981

Cited by 53 publications

(59 citation statements)

References 49 publications

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“…We can draw some comfort from well-established principles such as Fourier's law of heat conduction and the kinetic theory of gases, which work in part because there is a clear separation between micro and macro scales. On the other hand, not all systems have such a clear separation (West et al, 2003), which can lead to problems in the use of standard differential-equation formulations for sediment transport (Stark et al, 2009;Foufoula-Georgiou et al, in press;Tucker and Bradley, in press). One possibility is that, in many cases, our models of complex geomorphic systems may have to rest upon a statistical approach to translate microscopic (e.g.…”

Section: Up-scaling Of Geomorphic Processesmentioning

confidence: 97%

Modelling landscape evolution

Tucker

Hancock

2010

Earth Surf Processes Landf

478

438

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Geomorphology is currently in a period of resurgence as we seek to explain the diversity, origins and dynamics of terrain on the Earth and other planets in an era of increased environmental awareness. Yet there is a great deal we still do not know about the physics and chemistry of the processes that weaken rock and transport mass across a planet's surface. Discovering and refi ning the relevant geomorphic transport functions requires a combination of careful fi eld measurements, lab experiments, and use of longer-term natural experiments to test current theory and develop new understandings. Landscape evolution models have an important role to play in sharpening our thinking, guiding us toward the right observables, and mapping out the logical consequences of transport laws, both alone and in combination with other salient processes. Improved quantitative characterization of terrain and process, and an ever-improving theory that describes the continual modifi cation of topography by the many and varied processes that shape it, together with improved observation and qualitative and quantitative modelling of geology, vegetation and erosion processes, will provide insights into the mechanisms that control catchment form and function. This paper reviews landscape theory -in the form of numerical models of drainage basin evolution and the current knowledge gaps and future computing challenges that exist.

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Section: Up-scaling Of Geomorphic Processesmentioning

confidence: 97%

Modelling landscape evolution

Tucker

Hancock

2010

Earth Surf Processes Landf

478

438

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“…Long step lengths of bedload particles in the field may result from any bed pattern that induces preferential paths for transport, including grain size mixtures , bedforms, scour and fill, and intermittent bedrock exposure (Stark et al, 2009). Thus our results may be applicable to these cases.…”

Section: Discussionmentioning

confidence: 99%

“…However, certain sediment dynamics, such as (i) particle diffusion in river bedload (e.g., Nikora et al, 2002;Bradley et al, 2010;Ganti et al, 2010;Martin et al, 2012), (ii) bed sediment transport along bedrock channels (Stark et al, 2009) and (iii) particle displacements on hillslopes may show nonlocal behavior that is not easily captured by the classical form of the Exner equation (the notation used throughout the manuscript is defined and listed after the conclusions).…”

Section: Introductionmentioning

confidence: 99%

Morphodynamics of river bed variation with variable bedload step length

Pelosi

Parker

2014

Earth Surf. Dynam.

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Abstract. Here we consider the 1-D morphodynamics of an erodible bed subject to bedload transport. Fluvial bed elevation variation is typically modeled by the Exner equation, which, in its classical form, expresses mass conservation in terms of the divergence of the bedload sediment flux. An entrainment form of the Exner equation can be written as an alternative description of the same bedload processes, by introducing the notions of an entrainment rate into bedload and of a particle step length, and assuming a certain probability distribution for the step length. This entrainment form implies some degree of nonlocality, which is absent from the standard flux form, so that these two expressions, which are different ways to look at same conservation principle (i.e., sediment continuity), may no longer become equivalent in cases when channel complexity and flow conditions allow for long particle saltation steps (including, but not limited to the case where particle step length has a heavy tailed distribution) or when the domain of interest is not long compared to the step length (e.g., laboratory scales, or saltation over relatively smooth surfaces). We perform a systematic analysis of the effects of the nonlocality in the entrainment form of the Exner equation on transient aggradational/degradational bed profiles by using the flux form as a benchmark. As expected, the two forms converge to the same results as the step length converges to zero, in which case nonlocality is negligible. As step length increases relative to domain length, the mode of aggradation changes from an upward-concave form to a rotational, and then eventually a downward-concave form. Corresponding behavior is found for the case of degradation. These results may explain anomalously flat, aggradational, long profiles that have been observed in some short laboratory flume experiments.

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“…Recently, modeling Earth surface processes that possess variability over a large range of space time scales and exhibit heavy-tailed statistics has received considerable attention [e.g., Stark et al, 2009;Ganti et al, 2009Ganti et al, , 2010Foufoula-Georgiou and Stark, 2010;Bradley et al, 2010;Harman et al, 2010]. In a recent study, Voller and Paola [2010] acknowledged the deviation of fluvial profiles from ones predicted by classical diffusion and proposed the exploration of fractional diffusive model to describe the observed steady state fluvial profiles in a depositional system.…”

Section: Modeling Of Surface Evolution and Sediment Surface Elevationmentioning

confidence: 99%

Space‐time dynamics of depositional systems: Experimental evidence and theoretical modeling of heavy‐tailed statistics

et al. 2011

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[1] In depositional systems, channels migrate from one location to another, causing erosion and deposition at any given point in the domain. The durations of depositional and erosional events, as well as their magnitudes, control the structure of the stratigraphic record. In this study, we use high-resolution temporal surface elevation data from a controlled experiment to quantify the probability distributions of the processes that govern the evolution of depositional deltaic systems. Heavy-tailed statistics of erosional and depositional events are documented, indicating that a small but significant chance exists for the occurrence of extreme events. We show that the periods of inactivity, when neither deposition nor erosion occurs, follow a truncated Pareto distribution whose truncation scale is set by the mean characteristic avulsion time scale in the system. Further, we show that the heavy tails in the magnitudes of the erosional and depositional events are not preserved in the stratigraphic record, resulting instead in an exponential distribution for the bed sediment thickness. It is also shown that the temporal evolution of surface elevation exhibits self-similarity with a nonlinear spectrum of scaling exponents (multifractality) quantifying the complex dynamics of the system. Finally, we show how the results of this study can lead to improved diffusional models for surface evolution using the tools of fractional calculus.Citation: Ganti, V., K. M. Straub, E. Foufoula-Georgiou, and C. Paola (2011), Space-time dynamics of depositional systems: Experimental evidence and theoretical modeling of heavy-tailed statistics,

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A nonlocal theory of sediment buffering and bedrock channel evolution

Cited by 53 publications

References 49 publications

Modelling landscape evolution

Modelling landscape evolution

Morphodynamics of river bed variation with variable bedload step length

Space‐time dynamics of depositional systems: Experimental evidence and theoretical modeling of heavy‐tailed statistics

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