Does the flow of information in a landscape have direction?

Voller, V. R.; Ganti, Vamsi; Paola, Chris; Foufoula‐Georgiou, Efi

doi:10.1029/2011gl050265

Cited by 24 publications

(19 citation statements)

References 13 publications

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“…A better, more general approach is then to model the flux at a given point as a weighted sum of an appropriate function of hydrogeomorphic measures (e.g., slope, discharge) taken over an area around the point of interest. A model like this is “nonlocal”, and when used in the balance of equation , has been demonstrated to reproduce natural large‐scale topography and reduce curvature anomalies [ Foufoula‐Georgiou et al ., ; Voller and Paola , ; Voller et al ., ].…”

Section: Background On Nonlinear and Nonlocal Approachesmentioning

confidence: 99%

“…To build a general nonlocal flux treatment, we also account for hydrogeomorphic measures at points upstream and downstream of x = A [ Voller et al ., ; Furbish and Roering , ]. A convenient and general means of achieving this is to define the nonlocal flux in terms of the convolution integral

q (x) = \int_{0}^{1} W ((),, x, ξ) q^{L} ((), ξ) italicdξ,

where W ( x , ξ ) are appropriate weights and in this general case q L ( x ) is a reference flux whose physical interpretation requires some care.…”

Section: A General Nonlocal Framework For Modeling Sediment Fluxmentioning

confidence: 99%

“…To move forward, we narrow our choice of local hydrogeomorphic measures to the topographic slope. In this way, for the specific case when q L ( x ) is a linear function of this slope, the nonlocal framework in equation will be consistent with previous fractional calculus models of nonlocality [ Foufoula‐Georgiou et al ., ; Voller and Paola , ; Voller et al ., ]. Given that our goal is to develop a combined nonlocal, nonlinear model, our next step is, through the use of basic sediment transport relations and reasonable physical assumptions, to arrive at a general local , nonlinear sediment transport model in terms of the topographic slope.…”

Section: A General Nonlocal Framework For Modeling Sediment Fluxmentioning

confidence: 99%

“…Following appropriate scaling, a simple but relevant test model for our proposed NLNL framework can be constructed by considering a steady state surface in a unit domain subjected to (1) no subsidence ( σ = 0) [ Postma et al ., ] or (2) a piston subsidence of unit magnitude ( σ = − 1) [ Voller et al ., ]. From the Exner mass balance equation , the governing sediment transport equation for this system is

\frac{d}{italicdx} (q) = \{\begin{matrix} left \\ 0, zero \\ - 1 piston \end{matrix} 0 \leq x \leq 1,

with boundary conditions

q (0) = 1, h (1) = 0,

where q is the sediment flux defined by the nonlocal and/or nonlinear forms above.…”

Section: A Steady State Model For Depositional Systemsmentioning

confidence: 99%

“…Although there have been numerous analyses proposing different ways to relate flux to topographic slope [ Paola , ], until recently, there was little question that the slope to use in such models was the one at the point of interest. This view, however, has been challenged in a series of recent papers [e.g., Bradley et al ., ; Foufoula‐Georgiou et al ., ; Ganti et al ., ; ; Ganti , ; Schumer et al ., ; Stark et al ., ; Voller and Paola , ; Voller et al ., ], which propose that in some cases the sediment flux at a point might also depend on values of the slope (or other topographic measures) away from that point. This dependence, typically expressed via some form of convolution integral, i.e., weighted average over space and/or time, takes into account the fact that probabilistic sediment motion may span a wide range of transport length scales.…”

Section: Introductionmentioning

confidence: 99%

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A combined nonlinear and nonlocal model for topographic evolution in channelized depositional systems

et al. 2013

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[1] Models for the overall topographic evolution of erosional and depositional systems can be grouped into two broad classes. The first class is local models in which the sediment flux at a point is expressed as a linear or nonlinear function of local hydrogeomorphic measures (e.g., water discharge and slope). The second class is nonlocal models, where the sediment flux at a point is expressed via a weighted average (i.e., convolution integral) of measures upstream and/or downstream of the point of interest. Until now, the nonlinear and nonlocal models have been developed independently. In this study, we develop a unified model for large-scale morphological evolution that combines both nonlinear and nonlocal approaches. With this model, we show that in a depositional system, under piston-style subsidence, the topographic signatures of nonlinearity and nonlocality are identical and that in combination, their influence is additive. Furthermore, unlike either nonlinear or nonlocal models alone, the combined model fits observed fluvial profiles with parameter values that are consistent with theory and independent observations. By contrast, under conditions of steady bypass, the nonlocal and nonlinear components in the combined model have distinctly different signatures. In the absence of nonlocality, a purely nonlinear model always predicts a bypass fluvial profile with a spatially constant slope, while a nonlocal model produces a nonconstant slope, i.e., profile curvature. This result can be used as a test for inferring the presence of nonlocality and for untangling the relative roles of local and nonlocal mechanisms in shaping depositional morphology.Citation: Falcini, F., E. Foufoula-Georgiou, V. Ganti, C. Paola, and V. R. Voller (2013), A combined nonlinear and nonlocal model for topographic evolution in channelized depositional systems,

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Section: Background On Nonlinear and Nonlocal Approachesmentioning

confidence: 99%

q (x) = \int_{0}^{1} W ((),, x, ξ) q^{L} ((), ξ) italicdξ,

where W ( x , ξ ) are appropriate weights and in this general case q L ( x ) is a reference flux whose physical interpretation requires some care.…”

Section: A General Nonlocal Framework For Modeling Sediment Fluxmentioning

confidence: 99%

Section: A General Nonlocal Framework For Modeling Sediment Fluxmentioning

confidence: 99%

\frac{d}{italicdx} (q) = \{\begin{matrix} left \\ 0, zero \\ - 1 piston \end{matrix} 0 \leq x \leq 1,

with boundary conditions

q (0) = 1, h (1) = 0,

where q is the sediment flux defined by the nonlocal and/or nonlinear forms above.…”

Section: A Steady State Model For Depositional Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A combined nonlinear and nonlocal model for topographic evolution in channelized depositional systems

et al. 2013

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A direct simulation demonstrating the role of spacial heterogeneity in determining anomalous diffusive transport

Voller

2015

Water Resources Research

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Typically the spreading length-scale in a diffusion process increases in time as ' $ t n ; n5 1 2 . In the presence of spatial heterogeneities, however, so-called anomalous diffusion can occur, here the time exponent n 6 ¼ 1 2 . The objective of this paper is to present a numerical simulation that directly demonstrates the link between spacial heterogeneity and anomalous diffusion. The simulation is of the infiltration of a fluid into a horizontal unit area Hele-Shaw cell in which the permeability at specified locations, laid out as a Sierpinski fractal carpet pattern, can differ from the nominal value K 5 1. When there is no permeability contrast, the fluid infiltration has a diffusion-like behavior, i.e., the filled plan-form area increases in time as F5At n ; n5 1 2 . When there is a permeability contrast, however, although the evolution of infiltration still follows a power law, anomalous behavior is observed; subdiffusive (n < 1 2 ) when K < 1 and superdiffusive (n > 1 2 ) when K > 1. These anomalous behaviors persist, even when the permeability contrast is only imposed over the largest sized fractal pattern element. But, if the pattern over which the permeability contrast is imposed has a subdomain length scale (obtained by filling in the largest sized element in the Sierpinski carpet with the smaller sized elements), normal diffusion n5 1 2 behavior is recovered. In the special case that the imposed permeability in the pattern elements is K ( 1, an approximate model, directly relating the coefficient and exponent in the infiltration power law to the porosity and fractal dimension of the carpet pattern, is derived and validated.

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Backward fractional advection dispersion model for contaminant source prediction

Zhang

Meerschaert

Neupauer

2016

Water Resources Research

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The forward Fractional Advection Dispersion Equation (FADE) provides a useful model for non‐Fickian transport in heterogeneous porous media. The space FADE captures the long leading tail, skewness, and fast spreading typically seen in concentration profiles from field data. This paper develops the corresponding backward FADE model, to identify source location and release time. The backward method is developed from the theory of inverse problems, and then explained from a stochastic point of view. The resultant backward FADE differs significantly from the traditional backward Advection Dispersion Equation (ADE) because the fractional derivative is not self‐adjoint and the probability density function for backward locations is highly skewed. Finally, the method is validated using tracer data from a well‐known field experiment, where the peak of the backward FADE curve predicts source release time, while the median or a range of percentiles can be used to determine the most likely source location for the observed plume. The backward ADE cannot reliably identify the source in this application, since the forward ADE does not provide an adequate fit to the concentration data.

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Does the flow of information in a landscape have direction?

Cited by 24 publications

References 13 publications

A combined nonlinear and nonlocal model for topographic evolution in channelized depositional systems

A combined nonlinear and nonlocal model for topographic evolution in channelized depositional systems

A direct simulation demonstrating the role of spacial heterogeneity in determining anomalous diffusive transport

Backward fractional advection dispersion model for contaminant source prediction

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