Abstract
Spatial variability of morphological characteristics and flow in river networks, and its relation to power distribution are analytically and empirically investigated. It is assumed, and positively tested, that Horton-type laws describe the downstream change in link morphological and topological characteristics. Accordingly, surrogates to the traditional stream length and area ratios are provided by the link number ratio, and the total link number ratio, respectively. The opposite statistical behaviour of stream and link length, as being dependent and independent variables, respectively, is found to be reversed in the case of link and stream heights. This property leads to an identical trend in the spatial variability of slope in both cases. On the other hand, assessment the of the self-similar model of link altitudinal geometry [Gupta & Waymire, 1989] reveals that previous testing, upon which the model has been refuted by Tarboton et al. [1989] was inadequately performed. However, our results show an increasing structured departure from simple-scaling for the n-th order moments. Finally, using Horton-type laws for height and flow yields the distribution of power to be characterized by a state of maximum spatial uniformity for a given flow quantile, for which the scaling exponent of mean link slope equals the one that describes mean flow pattern. This result is found to be implicitly explained by using the informational entropy principles as introduced by Kapoor [1990] for river networks.
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References
Andah, K., F. Siccardi, and P. La Barbera, ‘Is a drainage network from a digital terrain model a model for the real network?’, EOS Trans. AGU, 68 (44), 1272, 1987b.
Andah, K., and R. Rosso, ‘Hortonian approach to streamflow regionalization with particular reference to development of minihydroprojects in Ghana’, Proc. XIX Convegno di Idraulica e Costruzioni Idrauliche, Pavia, Italy, 6–8 September, 1984.
Band, L. E., ‘Topographic partition of watersheds with digital elevation models’, Water Resour. Res., 22, 15–24, 1986.
Cadavid, E., ‘Hydraulic geometry of channel networks: Test of scaling invariance’, M.S. thesis, Dept. of Civil Engineering, University of Mississippi, 1988.
Carrara, A, A., ‘Drainage and divide networks derived from high-fidelity digital terrrain models’, Proc. Sem., NATO-ASI, Pisa, Italy, 22 June-4 July, 1986.
Dawdy, D. R. R., ‘Variation of flood ratios with size of drainage area’, Geol Surv. Res. Paper, C-36–37, 1961.
Flint, J. J., ‘Stream gradient as a function of order, magnitude, and discharge, Water Resour. Res., 10 (5), 969–973, 1974.
Gupta V. K., and E. Waymire, ‘Statistical self-similarity in river networks parameterized by elevation’, Water Resour. Res., 25 (3), 463–476, 1989.
Gupta V. K., and E. Waymire, ‘Multiscaling properties of spatial rainfall and river flow distributions’, J. Geoph. Res., 95 (3), 1999–2009, 1990.
Horton, R. E.,’Erosional development of streams and their drainage basins: hydrophysical approach to quantitative morphology’, Bull. Geol. Soc. Am., 56, 275–370, 1945.
Kapoor, V., ‘Spatial uniformity of power and altitudinal geometry of river networks’, Water Resour. Res., 26 (10), 2303–2310, 1990.
Leopold. L. B., and T. Maddock, ‘The hydraulic geometry of stream channel and some physiographic implications, U.S. Geol. Survey Prof. Paper, 252, 1953.
Leopold, L. B., and J. P. Miller, ‘Ephemeral streams, hydraulic factors and their relation to the drainage network’, U.S. Geol. Survey Prof. Paper, 282-A, 1956.
Leopold, L. B., and W. B. Langbein, ‘The concept of entropy in landscape evolution’, U.S. Geol. Survey Prof. Paper, 500-A, 1962.
Leopold, L. B., M. G. Wolman, and J. P. Miller, Fluvial Processes in Geomorphology, Freeman and Co., San Francisco, 1964.
Mesa, O. J., ‘Analysis of channel networks parameterized by elevation’, Ph.D Dissertation, Dept. of Civil Engineering, University of Mississippi, 1986.
Morisawa, M. E., ‘Quantitative geomorphology of some watersheds in the Appalachian Plateau’, Geol. Soc. Amer. Bull., 73, 1025–1046, 1962.
Patton, P. C, and V. R. Baker, ‘Low frequency high magnitude floods and their relation to the morphology of sreams in central Texas (abstract), Geol. Soc. Amer. Abstr. Program, 7 (2), 224–225, 1975.
Rosso, R., Bacchi, B., and P. La Barbera, ‘Fractal relation of main-stream length to catchment area in river networks’ Water Resour. Res., 27 (3), 381–387, 1991.
Shreve, R. L., ‘Statistical law of stream numbers’, J. Geol., 74, 17–37, 1966.
Shreve, R. L., ‘Infinite topologically random channel networks’, J. Geol., 74, 178–186, 1967.
Strahler, A. N., ‘Quantitative geomorphology of drainage basins and channel networks’, in: Chow, V.T., Handbook of Applied Hydrology, Sec. 4, Mc Graw-Hill Book Company, New York, 1964.
Tarboton, D. G., Bras, R. L., and I. Rodriguez-Iturbe, ‘Scaling and elevation in river networks’, Water Resour. Res., 25 (9), 2037–2051, 1989.
Tarboton, D. G., Bras, R. L., and I. Rodriguez-It urbe, ‘On the extraction of channel networks from Digital Elevation Data’, Hydrological Processes, 5 (1), 81–100, 1990.
Wolman, M. G. G., ‘The natural channel of Brandywine Creek, Pennsylvania’, U.S. Geol. Survey Prof. Paper, 271-A, 1955.
Yang, C. T., ‘Potential energy and stream morphology’, Water Resour. Res., 7 (2), 311–322, 1971.
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© 1992 Springer Science+Business Media Dordrecht
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Elsheikh, S., Rosso, R., La Barbera, P. (1992). Analysis of Spatial Variability of River Network Morphology, Flow and Potential Energy. In: Singh, V.P., Fiorentino, M. (eds) Entropy and Energy Dissipation in Water Resources. Water Science and Technology Library, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2430-0_22
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DOI: https://doi.org/10.1007/978-94-011-2430-0_22
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