Abstract
This paper presents an overview and synthesis of an extensive research effort to characterize and quantify scale invariances in the morphology and evolution of braided rivers. Braided rivers were shown to exhibit anisotropic spatial scaling (self-affinity) in their morphology, implying a statistical scale invariance under appropriate rescaling of the axes along and perpendicular to the main direction of flow. The scaling exponents were found similar in rivers of diverse flow regimes, slopes, types of bed material and braid plain widths, indicating the presence of universal features in the underlying mechanisms responsible for the formation of their spatial structure. In regions where predominant geologic controls or predominant flow paths were present, no spatial scaling was found. Regarding their spatiotemporal evolution, braided rivers were found to exhibit dynamic scaling, implying that a smaller part of a braided river evolves identically to a larger one provided that space and time are appropriately normalized. Based on these findings, and some additional analysis of experimental rivers as they approach equilibrium, it was concluded that the mechanism bringing braided rivers to a state where they show spatial and temporal scaling is self-organized criticality and inferences about the physical mechanisms of self-organization were suggested.
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REFERENCES
Alciatore, D., and Miranda, R., 1995, The best least-squares line fit, in Paeth, V. A. W., ed. Graphics Gems: Academic, San Diego, CA, p. 91–97.
Ashmore, P., 1985, Process and form in gravel braided streams: Laboratory modelling and field observations, unpubl. doctoral dissertation, University of Alberta, Edmonton.
Ashmore, P., and Parker, G., 1983, Confluence scour in coarse braided streams: Water Resour. Res., v. 19, p. 392–402.
Ashmore, P. E., Ferguson, R. I., Prestegaard, K. L., Ashworth, P. J., and Paola, C., 1992, Secondary flow in anabranch confluences of a braided, gravel-bed stream: Earth Surf. Processes Landforms, v. 17, p. 299–311.
Best, J. L., 1986, The morphology of river channel confluences: Prog. Phys. Georgr., v. 10, p. 157–174.
Bristow, C., and Best, J., 1993, Braided rivers: Perspectives and problems, in Best, J., and Bristow, eds., Braided Rivers: Geological Society, London, p. 1–11.
Bristow, C. S., Best, J. L., and Roy, A. G., 1993, Morphology and facies models of channel confluences, in Marzo, M., and Puigdefabregas, C., eds., Alluvial Sedimentation: Blackwell Scientific, Cambridge, MA, p. 91–100.
Foufoula-Georgiou, E., and Sapozhnikov, V., 1998, Anisotropic scaling in braided rivers: An integrated theoretical framework and results from application to an experimental river: Water Resour. Res., v. 34, no. 4, p. 863–867.
Howard, A. D., Keetch, M. E., and Vincent, C. L., 1970, Topological and geometrical properties of braided streams: Water Resour. Res., v. 6, p. 1674–1688.
Mandelbrot, B. B., 1982, The Fractal Geometry of Nature: W. H. Freeman, New York.
Mandelbrot, B. B., 1986, Self-affine fractal sets, in Fractals in Physics, in Petroniero, L., and Tosatti, E., eds., Proceedings of the Sixth Trieste International Symposium on Fractals in Physics, ICTP, Trieste, Italy: North-Holland, New York, p. 3–16.
Mosley, M. P., 1976, An experimental study of channel confluences: J. Geol., v. 84, p. 535–562.
Mosley, M. P., 1977, Stream junctions: A probable location for bedrock placers: Econ. Geol., v. 72, p. 691–697.
Murray, A. B., and Paola, C., 1994, A cellular model of braided rivers: Nature, v. 371, p. 54–57.
Nikora, V. I., 1994, On self-similarity and self-affinity of drainage basins: Water Resour. Res., v. 30, p. 133–137.
Nikora, V. I., and Sapozhnikov, V. B., 1993, River network fractal geometry and its computer simulation: Water Resour. Res., v. 29, p. 3569–3575.
Nikora, V. I., Sapozhnikov, V. B., and Noever, D. A., 1993, Fractal geometry of individual river channels and its computer simulation: Water Resour. Res., v. 29, p. 3561–3568.
Nykanen, D., Foufoula-Georgiou, E., and Sapozhnikov, V., 1998, Study of spatial scaling in braided river patterns using synthetic aperture radar imagery: Water Resour. Res., v. 34, no. 7, p. 1795–1807.
Robert, A., 1993, Bed configuration and microscale processes in alluvial channels: Prog. Phys. Geogr., v. 17, p. 123–136.
Sapozhnikov, V., and Foufoula-Georgiou, E., 1995, Study of self-similar and self-affine objects using logarithmic correlation integral: J. Phys. A: Math. Gen., v. 28, p. 559–571.
Sapozhnikov, V., and Foufoula-Georgiou, E., 1996a, Do the current landscape evolution models show self-organized criticality? Water Resour. Res., v. 32, no. 4, p. 1109–1112.
Sapozhnikov, V., and Foufoula-Georgiou, E., 1996b, Self-affinity in braided rivers: Water Resour. Res., v. 32, no. 5, p. 1429–1439.
Sapozhnikov, V., and Foufoula-Georgiou, E., 1997, Experimental evidence of dynamic scaling and indications of self-organized criticality in braided rivers: Water Resour. Res., v. 33, no. 8, p. 1983–1991.
Sapozhnikov, V., Brad Murray, A., Paola, C., and Foufoula-Georgiou, E. 1998, Validation of braided-stream models: Spatial state-space plots, self-affine scaling, and island shapes: Water Resour. Res., v. 34, no. 9, p. 2353–2364.
Sapozhnikov, V., and Foufoula-Georgiou, E., 1999, Horizontal and vertical self-organization of braided rivers toward a critical state: Water Resour. Res., v. 35, no. 3 p. 843–851.
Smith, L. C., Isacks, B. L., Forster, R. R., Bloom, A. L., and Presuss, I., 1995, Estimation of discharge from braided glacial rivers using ERS 2 synthetic aperture radar: First results: Water Resour. Res., v. 31, p. 1325–1329.
Smith, L. C., Isacks, B. L., Bloom, A. L., and Murray, A. B., 1996, Estimation of discharge from three braided rivers using synthetic aperture radar satellite imagery: Potential applications to ungaged basins: Water Resour. Res., v. 32, p. 2031–2034.
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Foufoula-Georgiou, E., Sapozhnikov, V. Scale Invariances in the Morphology and Evolution of Braided Rivers. Mathematical Geology 33, 273–291 (2001). https://doi.org/10.1023/A:1007682005786
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DOI: https://doi.org/10.1023/A:1007682005786