Self‐Affinity in Braided Rivers

Sapozhnikov, Victor B.; Foufoula‐Georgiou, Efi

doi:10.1029/96wr00490

Cited by 111 publications

(97 citation statements)

References 22 publications

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“…In a recent paper [Sapozhnikov and Foufoula-Georgiou, 1996a] evidence was presented that natural braided rivers exhibit anisotropic scaling (self-affinity) in their geometrical structure, within a range of scales spanning the width of the narrowest channel to the width of the braid plain. In simple words, within these scales, if a small part of a braided river is stretched in a certain way along the mainstream direction and a certain different way along the perpendicular direction, then this stretched part looks statistically the same as a bigger part of the river.…”

Section: Introductionmentioning

confidence: 99%

“…In Sapozhnikov and Foufoula-Georgiou [1996a], three natural braided rivers of different scales and different hydrological and sedimentological characteristics (Aichilik and Hulahula in Alaska and Brahmaputra in Bangladesh) were analyzed for spatial scaling using the logarithmic correlation integral (LCI) method developed by Sapozhnikov and Foufoula-Georgiou [1995]. Interestingly enough, it was observed that despite their different scales (0.5-15 km in braid plain width), slopes (7 x of each river.…”

Section: Introductionmentioning

confidence: 99%

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Experimental evidence of dynamic scaling and indications of self‐organized criticality in braided rivers

Sapozhnikov

Foufoula‐Georgiou

1997

Water Resources Research

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Abstract. The evolution of an experimental braided river produced in our laboratory has been monitored and analyzed. It has been shown that in addition to the spatial scaling revealed by Sapozhnikov and Foufoula-Georgiou [1996a], braided rivers also exhibit dynamic scaling. This implies that a smaller part of a braided river evolves identically (in the statistical sense) to a larger one provided the time is renormalized by a factor depending only on the ratio of the spatial scales of those parts. The small value of the estimated dynamic exponent z is interpreted as an indication that the evolution of small channels in a braided river system is to a large extent forced by the evolution of bigger channels. The presence of dynamic scaling is further interpreted as indicating that braided rivers may be in a critical state and behave as self-organized critical systems. Braided rivers, besides their complex geometry at any instant of time, are also highly dynamic systems characterized by intensive erosion, sediment transport and deposition, and frequent channel shifting as they evolve. Predicting the evolution of braided rivers in terms of frequency and magnitude of channel shifting is of paramount importance where hydraulic structures or land developments are planned or where field use must be made of maps and air photos. It is of great practical and theoretical value therefore to study the evolution of braided rivers in addition to their spatial structure. In view of the evidence for spatial (static) scaling in braided rivers the question is asked here as to whether they also show dynamic scaling. The presence of dynamic scaling would imply that space and time can be appropriately rescaled such that the evolution of the spatial structure of parts of the river of different size would be statistically indistinguishable. The presence of dynamic scaling would also provide a highly desirable integrated framework for studying, simultaneously, the spatial and temporal structure of braided rivers. Dynamic Scaling: A Theoretical FrameworkThe idea of dynamic scaling can be qualitatively presented as follows. Suppose there is a fractal object, of fractal dimension D, which evolves in time such that its fractality is preserved at all times. In our case the fractal object is the spatial pattern of the active channels constituting a braided river which was shown to exhibit spatial scaling by Sapozhnikov and FoufoulaGeorgiou [1996a]. The fractality (spatial scaling) of the object implies that if one takes a picture of a part of the object of size L • x L • and a picture of a larger part of the same object of size L 2 X L 2 and projects these two pictures onto two screens of the same size, the images on the screens will be statistically 1983

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Experimental evidence of dynamic scaling and indications of self‐organized criticality in braided rivers

Sapozhnikov

Foufoula‐Georgiou

1997

Water Resources Research

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“…In a subsequent paper [10] they demonstrated the manner in which these models also capture the effects of random influences in driving the processes of landscape evolution. In particular, their results provided a physical basis for explaining various fundamental scaling relationships [44,70,55,42,60,61,59,48,54,69,62,58,32,56,21,22] that characterize fluvial landscapes and supply a bridge between deterministic and stochastic theories of drainage basin evolution.…”

Section: Complexity In Geomorphologymentioning

confidence: 99%

The Stochastic Theory of Fluvial Landsurfaces

2006

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A stochastic theory of fluvial landsurfaces is developed for transport-limited erosion, using well-established models for the water and sediment fluxes. The mathematical models and analysis is developed showing that some aspects of landsurface evolution can be described by Markovian stochastic processes. The landsurfaces are described by nondeterministic stochastic processes, characterized by a statistical quantity the variogram, that exhibits characteristic scalings. Thus the landsurfaces are shown to be SOC (Selforganized-critical) systems, possessing both an initial transient state and a stationary state, characterized by respectively temporal and spatial scalings. The mathematical theory of SOC systems is developed and used to identify three stochastic processes that shape the * and the University of Iceland, 107 Reykjavík 1 surface. The SOC theory of landsurfaces reproduces established numerical results and measurements from DEMs (digital elevation models).

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“…In addition, braided-river system outcrops do not show significant changes or trends in the dimensional characteristics of the deposits at one location. This medium to large scale stationarity of the deposit dimensions can be compared to the braided-river self-affinity described by Sapozhnikov and Foufoula-Georgiou [1996]. Therefore in absence of more specific information, it has been decided to keep the aggradation rate fixed in the algorithm for the moment.…”

Section: Algorithm and Main Parametersmentioning

confidence: 99%

A pseudo genetic model of coarse braided‐river deposits

Pirot

Straubhaar

Renard

2015

Water Resources Research

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A new method is proposed to produce three-dimensional facies models of braided-river aquifers based on analog data. The algorithm consists of two steps. The first step involves building the main geological units. The production of the principal inner structures of the aquifer is achieved by stacking Multiple-Point-Statistics simulations of successive topographies, thus mimicking the major successive flooding events responsible for the erosion and deposition of sediments. The second step of the algorithm consists of generating fine scale heterogeneity within the main geological units. These smaller-scale structures are generated by mimicking the trough-filling process occurring in braided rivers; the imitation of the physical processes relies on the local topography and on a local approximation of the flow. This produces realistic cross-stratified sediments, comparable to what can be observed in outcrops. The three main input parameters of the algorithm offer control over the proportions, the continuity and the dimensions of the deposits. Calibration of these parameters does not require invasive field measurements and can rely partly on analog data.

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Self‐Affinity in Braided Rivers

Cited by 111 publications

References 22 publications

Experimental evidence of dynamic scaling and indications of self‐organized criticality in braided rivers

Experimental evidence of dynamic scaling and indications of self‐organized criticality in braided rivers

The Stochastic Theory of Fluvial Landsurfaces

A pseudo genetic model of coarse braided‐river deposits

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