Abstract
The modern analysis of channel patterns in nature over a wide range of scales, be it a tree-like river, braided landforms or the complex incisures of a tidal network, relies on accurate digital mapping technologies and on objective manipulations of remotely sensed imaging. Such analyses reveal extraordinary diversity of natural forms, and yet deep regularity and symmetry, regardless of a variety of environmental factors — what strikes is diversity of hydro-and morpho-dynamics, adapting to (and coevolving with) geology, climate, vegetation or exposed lithology. Our observations strongly suggest that river networks are indeed a paradigm of scale-invariant, or fractal, forms ubiquitous in nature, whereas tidal networks bear rather strikingly the signatures of scale-dependence. Here we review a somewhat subjective choice of linked results, chiefly observational, that are deemed helpful towards a theory of the dynamic origin of scale invariance in the fluvial landscape referring to a common mechanism of growth and stabilization of open, dissipative systems with many degrees of freedom.
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References
Bak, P. (1996) How Nature Works: the Science of Self-Organized Criticality (New York: Copernicus-Springer).
Dietrich W.E., Wilson C.J., Montgomery D.R., McKean J, and Bauer R. (1992) Erosion thresholds and land surface morphology. J. Geology 20, 675–679.
Eden, M. (1961) A two-dimensional growth process, Fourth Berkeley Symposium on Mathematical Statistics and Probability. In Biology and Problems of Health, ed. R Neyman, 4, 223–239. ( Berkeley: Univ. of California Press ).
Fagherazzi, S., Bortoluzzi, A., Adami, A., Marani, M., Lanzoni, S., and Rinaldo, A. (1999) Tidal Networks 1. Automatic extraction from digital terrain maps, Water Resources Research,35, 3891–3904.
Hack, J.T. (1957) Studies of longitudinal profiles in Virginia and Maryland, U.S. Geological Survey Paper 294-B, Washington.
Howard, A.D. (1971) Simulation model of stream capture, Geol. Soc. Am. Bulletin 82, 1355–1363.
Howard, A.D. (1994) Detachment-limited model of drainage basin evolution, Water Resources Research 30, 2261–2285.
Kirchner, J.W. (1993) Statistical inevitability of Horton’s laws and the apparent randomnness of stream channel networks, Geology 21, 591–594.
Knighton, A.D., Woodroffe, C.D. and Mills, K. (1992) The evolution of tidal creek networks, Mary River, Northern Australia, Earth Surface Processes and Landforms 17, 167–190.
Leopold, L.B., Langbein, W.B. (1962) The concept of entropy in landscape evolution, U.S. Geological Survey Prof. Paper 500-AWashington.
Leopold L.B., Wolman MG, Miller J.P. (1964)Fluvial Process in Geomorphology (San Francisco: Freeman and Co.).
Mandelbrot, B.B. (1967) How long is the coast of Britain? Statistical self-similarity and fractional dimension, Science 156, 636–638.
Mandelbrot, B.B. (1983)The Fractal Geometry of Nature (San Francisco: Freeman).
Maritan A, Rinaldo A, Giacometti A, Rigon R, and Rodriguez-Iturbe I. (1996) Scaling in river networks, Physical Review E 53, 1501–1512.
McMahon, T.A. and Bonner, J.T. (1983) On Size and Life ( New York: Scientific American Library).
Montgomery, D.R., and Dietrich W.E. (1988) Where do channels begin, Nature 336, 232–234.
Montgomery, D.R., and Dietrich W.E. (1992) Channel initiation and the problem of landscape scale, Science 255, 826–830.
Murray, A.B., and Paola, C. (1994) A cellular model of braided rivers, Nature 371 54–57.
Niemeyer, L., Pietronero, L., and Wiesmann, H.J. (1984) Fractal Dimension of Dielectric Breakdown, Physical Review Letters 52, 1033–1036.
Pestrong, R. (1965) The development of drainage patterns on tidal marshes, Stanford Univ. Publ. Geol. Sci., Tech. Rep. 10, 87 pp.
Pethick, J.S. (1992) Salt marsh geomorphology, In Salt Marshes: Morphodynamics, Conservation and Engineering Significance, ed. Allen, J.R.L. and Pye, K., Cambridge University Press, p. 184.
Rigon R., Rodriguez-Iturbe I., Giacometti A., Maritan A., Tarboton D., and Rinaldo, A. (1996) On Hack’s law, Water Resources Research 32, 3367–3374.
Rinaldo, A. Dietrich, W.E., Vogel, G., Rigon, R., and Rodriguez-Iturbe, I. (1995) Geomorphic signatures of varying climate, Nature 374, 632–636.
Rinaldo, A., Maritan, A., Flammini, A., Colaiori, F., Rigon, R., and RodriguezIturbe, I. (1996) Thermodynamics of Fractal Networks, Physical Review Letters 76, 1501–1513.
Rinaldo, A., Rodriguez-Iturbe, I., and Rigon, R. (1998) Channel Networks, Annual Review of Earth and Planetary Sciences 26 289–327.
Rinaldo, A., S. Fagherazzi, Lanzoni, S., Marani, M., Dietrich, W.E. (1999) Tidal Networks 2. Watershed delineation and comparative network morphology, Water Resour. Res. 35, 3905–3918.
Rodriguez-Iturbe I., Ijjasz-Vasquez E., Bras RL, and Tarboton D.G. (1992) Power-law distributions of mass and energy in river basins, Water Resources Research 28, 988–993.
Rodriguez-Iturbe, I. and Rinaldo, A. (1997) Fractal River Basins: Chance and Self-Organization (New York: Cambridge University Press).
Sander, L.M. (1987) Fractal Growth, Scientific American 256, 94–100.
Sapozhnikov, V.B. and Foufoula-Georgiou, E. (1998) Study of spatial scaling in braided river patterns using synthetic aperture radar imagery, Water Resources Research 34, 1795–1804.
Scheidegger, A.E. (1967) Theoretical Geomorphology, 3rd edition ( Berlin: Springer-Verlag).
Schumm, S.A. (1977) The Fluvial System ( New York: J. Wiley )
Shreve, R.L. (1966) Statistical law of stream numbers, J. Geology 74, 17–37.
Shreve, R.L. (1967) Infinite topologically random channel networks, J. Geology 77, 397–414.
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Rinaldo, A., Lanzoni, S., Marani, M. (2001). River and Tidal Networks. In: Seminara, G., Blondeaux, P. (eds) River, Coastal and Estuarine Morphodynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04571-8_9
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DOI: https://doi.org/10.1007/978-3-662-04571-8_9
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