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

Abstract

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

Landscape reorganization under changing climatic forcing: Results from an experimental landscape

“…The exceedance probability, characterizing drainage organization and network connectivity, of upstream contributing areas is presented in Figure 4 showing a power law of slope 2 0.5 very similar to that of real landscapes [see e.g., Rodr ıguez-Iturbe et al, 1992; Rigon et al, 1996]. As previously noted by Hasbargen and Paola [2003] for experimental tributary networks and Sapozhnikov and Foufoula-Georgiou [1997] for experimental braided river networks, during steady state, our landscape exhibited a notable degree of internal variability (dynamic steady state) although the average basin erosion rate remained constant (see Figure 2 and also Reinhardt and Ellis [2015]). …”

The Stochastic Theory of Fluvial Landsurfaces

“…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.…”

Horizontal and vertical self‐organization of braided rivers toward a critical state

“…The main goal of this study was to provide more concrete evidence which would support or disprove our earlier hypothesis that braided rivers are self-organized critical systems [Sapozhnikov and Foufoula-Georgiou, 1997]. This hypothesis was based on our finding that in the statistical equilibrium state our experimental braided river showed dynamic scaling, and also on the fact that braided rivers are nonlinear systems with a high number of degrees of freedom, which is typical of SOC systems.…”

“…As the river evolved, it was recovering from the initial vertical disturbance by approaching a profile of a quasi-equilibrium shape, and at the same time it was developing toward the final equilibrium profile. This final equilibrium profile obtained by Sapozhnikov and Foufoula-Georgiou [1997] under the same conditions (same water and sand supply) is known to have a uniform slope of 0.15. We notice here, however, that by the time the dynamic scaling in the system had been achieved, the river was far from its final equilibrium profile.…”

“…The theoretical framework of testing for the presence of dynamic scaling based on changes in the analyzed objects is described in detail by Sapozhnikov and Foufoula-Georgiou [1997]. Here we present only in brief the essence of the theory.…”