Implications of Hydraulic Geometry Exponents of Zambian Rivers
Keywords:
Hydraulic Geometry Exponents, At-a-station Hydraulic Geometry, Downstream Hydraulic Geometry, Tri-axial Ternary Diagram, Streambed, Sediment, Dambo, River Behaviour
Abstract
At-a-station and downstream hydraulic geometry exponents of rivers in Zambia, located in the central-southern African tropics, were analysed based on three power relations of width, depth and velocity plotted against discharge. Channel cross-sectional form and discharge data, for 55 gauging stations monitored by Department of Water Affairs between 1948 and 1984, the period with good data, were used. Of these stations, 12 were located in the Zambezi River sub-basin while 37 and 6 others were in the Kafue and Luangwa River basins, respectively. For downstream analysis, 14 stations located on the main channel of Kafue River were investigated. The objectives were to: (i) determine the hydraulic geometry relations of Zambian rivers for comparison with those of other regions of the world; (ii) assess the factors accounting for variations in the observed hydraulic geometry exponents; and (iii) draw some implications of Zambian rivers’ hydraulic geometry exponents. Results of analysis showed that the obtained average at-a-station hydraulic geometry exponents for width (b), depth (f) and velocity (m) of Zambian rivers were 0.15, 0.38 and 0.47, respectively, and accorded well with similar results in the literature. Similarly, ranges of downstream exponents on the Kafue River of b = 0.50, f = 0.30 and m = 0.20 were also within the ranges of reported values. The plotting of most of at-a-station hydraulic geometry exponents on the right side of the tri-axial (ternary) diagram (f>b), implies that Zambian rivers are generally adapted to the transportation of fine-grained sediment ostensibly caused by the entrenchment of the river channels. The observation of m>f in some cases was interpreted as evidence that such streams possessed greater capacity of transporting large calibre bed load sediment. It is concluded that the behaviour of Zambian rivers is comparable to others in different physiographic regions of the world. However, unlike in temperate areas, the existence and influence of dambos in Zambia provides a complicating factor in the understanding of the behaviour of rivers.References
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2. Acres, D. B, Blair, A., King, R. B., Lawton, R. M, Mitchell, A. J. B. and Rackham, L. J., 1985. ‘African dambos: their distribution, characteristics and use.’ Zeitschrift fur Geomorphologie New Folge Supplement band, 52, 63-86.
3. Allen, P. M., Arnold, J. G. and Byars, B. W., 1994. ‘Downstream channel geometry for use of in planning-level models.’ Water Resources Bulletin, 30, 4, 663-671.
4. Balek, J. and Perry, J. E., 1973. Hydrology of seasonally inundated African headwater swamps. Journal of Hydrology, 19, 227-249.
5. Carlston, C. W., 1969. ‘Downstream variations in the hydraulic geometry of streams: special emphasis on mean velocity.’ American Journal of Science, 267, 499-509.
6. Chang, H. H., 1980. ‘Geometry of gravel streams’. Journal of Hydraulic Division America Society of Civil Engineers106, HY9, 1443-1456.
7. Church, M., 1980. On the equation of hydraulic geometry. Department of Geography, University of British Columbia, Vancouver, Canada.
8. Coates, D. R., 1969. ‘Hydraulic geometry in a glaciated region.’ Transactions, American Geophysical Union, 50, 149.
9. Dalal-Clayton, D. B., English, E., Williams, G.J., and Spaargaren, O. 1985. A geomorphic legend for Zambia. Soil Survey Unit, Research Branch, Department of Agriculture, Lusaka, 65 p.
10. Darlymple, T., 1960. ‘Flood frequency analysis.’ US Geological Survey, Water Supply Paper,1543-A 77 pp.
11. Davis, T. R. H. and Sutherland, A. J., 1983. ‘Extremal hypotheses for river behavior.’ Water Resources Research19, 141-148.
12. Dodds, D. G. and Patton, D. R., 1968. Wildlife and Land use Survey of Luangwa Valley, FAO, Rome.
13. Drystal, A.R., Johnson, R.L., Moore, T.A. and Thieme, J.G., 1972. ‘Outline of the geology of Zambia', Geologie en Mijnbouw, 15, 263-276.
14. Dudley, R. W., 2004. ‘Hydraulic-geometry relations for rivers in coastal Central Maine.’ Scientific Investigations Paper 2004-5042. US Geological Survey, Augusta, Maine, 2004.
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16. FAO, 1968. Multipurpose Survey of the Kafue River basin, Zambia, Rome.
17. Ferguson, R.I., 1986, ‘Hydraulics and hydraulic geometry', Progress in Physical Geography 10, 1-31.
18. Giardino, J.R., 1973, 'Geomorphology and soils of the Luangwa Valley', Zambia Geographical Association, Conference Handbook: Eastern Province, Lusaka, p. 30-47.
19. Gilvear, D., Winterbottom, S. and Sichingabula, H., 2000. ‘Character of channel change and meander development: Luangwa River, Zambia.’ Earth Surface Processes and Landforms 25, 421-436.
20. Hey, R.D., 1978. 'Determinate hydraulic geometry of river channels'. Journal of Hydraulic Division of America Society of Civil Engineers, 104, 869-885.
21. Hickin, E. J., 1995. Hydraulic geometry and channel scour, Fraser River, British Columbia, Canada’, In: Hickin, E.J. (ed.) River Geomorphology. John Wiley & Sons, 155-167.
22. Huang, H. Q. and Nanson, G., 1995, 'Hydraulic geometry and bank strength on selected streams in southeastern Australia: Abstract', International Association of Geomorphologists, Southeast Asia Conference, Programme with Abstracts, 18-23 June, 1995, National University of Singapore & Nanyang Technological University, Singapore, p. 47.
23. Huang, H. Q. and Nanson, G. C., 2000. ‘Hydraulic geometry and maximum flow efficiency as products of the principle of least action.’ Earth Surface Processes and Landforms, 25, 1-16.
24. Karabasis, E. N., 1988. The morphology of the Kakumbi concave bank bench on Luangwa River. Undergraduate dissertation, Geography Department, University of Zambia, Lusaka, 54 pp.
25. Knighton, A.D., 1975. 'Variations in at-a-station hydraulic geometry'. American Journal of Science, 275, 186-218.
26. Langbein, W.B., 1964. 'Geometry of river channels'. Journal of Hydraulic Division America Society of Civil Engineers, 90, 301-312.
27. Langbein, W.B., 1965, 'Geometry of river channels: Close of discussion', Journal of Hydraulic Division of America Society of Civil Engineers, 91, 297-313.
28. Leopold, B. and Langbein, W.B., 1962. 'The concept of entropy in landscape evolution', U.S. Geological Survey Professional Paper, 500-A, 20 pp.
29. Leopold, B. and Langbein, W.B., 1964. ‘Quasi-equilibrium states in channel morphology.’ American Journal of Science 262: 782-794.
30. Leopold, L.B., and Maddock, T., 1953. 'The hydraulic geometry of stream channels and some physiographic implications', U.S. Geological Survey Professional Paper, 252, 1-57.
31. Leopold, L.B., Wolman, M.G. and Miller, J.P., 1964. Fluvial Processes in Geomorphology. Freeman, San Francisco.
32. Mäckel, R., 1971, ‘The physiographic regions of Zambia', Geographical Association Magazine, Lusaka, 19, 1-20.
33. Mäckel, R., 1985. ‘Dambos and related landforms in Africa - an example for the ecological approach to tropical geomorphology.’ Z. Geormorph. N. F. Suppl.-Bd 52, 1-23.
34. Mäckel, R., 1986. ‘Dambo environments of the Central Plateau Region of Zambia.’ Zambia Geographical Journal, 36, 28-47.
35. Maddock, T., 1969. 'The behavior of straight open channels with movable beds', U.S. Geological Survey Paper Professional Paper, 622-A, 70 pp.
36. Money, N.J., 1972. ‘An outline of the geology of western Zambia', Records: Geological Survey of Zambia, 12, 103-123.
37. Morisawa, M., 1968. Streams: their dynamics and morphology. McGraw-Hill, New York, 175 pp.
38. Osterkamp, W.R., Lane, L.J., and Foster, G.R., 1983. ‘An analytical treatment of channel-morphology relations', U.S. Geological Survey Professional Paper, 1288, 21 pp.
39. Park, C.C., 1977. ‘World-wide variations in hydraulic geometry exponents of stream channels: An analysis and some observations', Journal of Hydrology, 33, 133-146.
40. Parker, G., 1979. Hydraulic geometry of active gravel rivers. Journal of Hydraulic Division (Proceeding American Society Civil Engineers), 105 (HY9), 1185-1201.
41. Phillips, J.D., 1990, ‘The instability of hydraulic geometry', Water Resources Research, 26, 739-744.
42. Ponton, J. R., 1972, Hydraulic geometry in the Green and Birkenhead river basins, British Columbia. Mountain Geomorphology: Geomorphological Processes in the Canadian Cordillera, pp. 151-160, Tantalus Research Limited, Vancouver, Canada.
43. Richards, K.S., 1973, ‘Hydraulic geometry and channel roughness: A non-linear system', American Journal of Science, 273, 877-896.
44. Richards, K.S., 1976. ‘Complex width-discharge relations in natural river sections.’ Geological Society of America Bulletin, 87, 199-206.
45. Richards, K.S., 1982. Rivers: form and process in alluvial channels, Methuen, London.
46. Rhoads, B. L., 1991. ‘A continuously varying parameter model of downstream hydraulic geometry.’ Water Resources Research, 27, 8, 1865-1872.
47. Rhodes, D.I.D., 1977. 'The b-f-m diagram: Graphical representation and interpretation of at-a-station hydraulic geometry'. American Journal of Science, 277, 73-96.
48. Rhodes, D.D., 1978. 'Discussion: worldwide variation in hydraulic geometry exponents of stream channels: An analysis and some observations'. Journal of Hydrology, 39, 193-197.
49. Rhodes, D.D., 1987. 'The b-f-m-diagram for downstream hydraulic geometry'. Geografisca Annaler, 69A, 147-161.
50. Riley, S. J., 1978. ‘The role of minimum variance theory in defining the regime characteristics of the lower Namoi-Gwydir basin.’ Water Resources Bulletin, 14, 1-11.
51. Schumm, S.A., 1960. 'The shape of alluvial channels in relation to sediment type', U.S. Geological Survey Professional Paper, 352-B, 15 pp.
52. Sharma, T. C., 1984. Characteristics of runoff processes in the Upper Kafue basin. National Council for Scientific Research, Water Resources Report, No. 25, Lusaka.
53. Sichingabula, H. M., Walling, D. E., Collins, A. L. and Leeks, G. G. L., 2007. ‘Suspended sediment transport characteristics of Upper Kaleya River, southern Zambia.’ Paper presented to the 8th WATERNET/WARFSA/GWP-SA Symposium: IWRM Concept to Practice, 31 October – 2 November 2007, Lusaka, Zambia.
54. Sichingabula, H. M., 1999b. ‘Clastic sediment flux into the Indian and Pacific oceans by rivers in central southern Africa and western Canada.’ Proceedings of the Hydrological and Geochemical Processes in Large Scale River Basins, 15-19 November 1999, Manaus, Brazil, 7 pp.
55. Sichingabula, H. M., 1999a. Analysis and results of discharge and sediment monitoring activities in the southern Lake Tanganyika basin: Final Report. Lake Tanganyika Biodiversity Project funded by UNDP/GEF/RAF/G32. [http://www.ltbp.org/FTP/SSS4.PDF](http://www.ltbp.org/FTP/SSS4.PDF).
56. Sichingabula, H. M., 1996. Estimation of contemporary suspended sediment loads on Kafue and Luangwa Rivers, Zambia. In: B. W. Webb (ed.) Erosion and Sediment Yield: Global and Regional Perspectives, Poster booklet report, (Proceedings, Exeter International Symposium, July 1996), pp. 96-99.
57. Singh, V. P., 2003. ‘On the theories of hydraulic geometry’, International Journal of Sediment Research, 18, 3, 196-218.
58. Slingerland, R., 1981, 'Qualitative stability analysis of geologic systems with an example from river hydraulic geometry', Geology 9, 491-493.
59. Smith, T. R., 1974. ‘A derivation of the hydraulic geometry of steady-state channels from conservation principles and sediment transport laws.’ Journal of Geology, 82, 98-104.
60. Stewardson, M., 2005. ‘Hydraulic geometry of stream reaches.’ Journal of Hydrology 306, 97-111. http://dx.doi.org/10.1016/j.jhydro.2004.09.004.
61. Thorne, C.R., 1979, 'Bank processes, bed movement and planform development in a meandering river’. In: D. D. Rhodes and G. P. Williams (Eds.). Adjustments of the Fluvial System. Kendall Hunt, Dubuque, Iowa, pp. 117-137.
62. Thornes, J. B., 1970. ‘The hydraulic geometry of stream channels in the Xingu-Araguaia headwaters.’ The Geographical Journals, 136, 376-382.
63. Thornes, J.B., 1977. ‘Hydraulic geometry and channel change', In: K.J. Gregory, River Channel Change. John Wiley, Chichester, p. 91-100.
64. Wharton, G., 1995. ‘The channel-geometry method: Guidelines and applications.’ Earth Surface Processes and Landforms 20, 649-660.
65. White, G., 1973. Soil resources of Eastern Province. Zambia Geographical Association Conference Handbook Series, Eastern Province, Lusaka, pp. 54-65.
66. Wilcock, D.N., 1971. 'Investigations into relations between bed transport and channel shape.’ Geological Society of America Bulletin, 82, 2159-2176.
67. Wolman, M. G., 1955. The natural channel of Brandywine Creek, Pennsylvania. U.S. Geological Survey Professional Paper 271, Washington, D.C.
68. Whitlow, R., 1984. ‘A survey of Dambos in Zimbabwe.’ Zimbabwe Agricultural Journal 81, 4, 129-138.
69. Whitlow, R., 1985. ‘Dambos in Zimbabwe: a review.’ Z. Geomorph. N. F., Suppl.-Bd 52, 115-146.
70. Wolman, M.G., 1955. 'The natural channel of Brandywine Creek, Pennsylvania', U.S. Geological Professional Paper, 271, 50 pp.
71. Young, C. T. and Song, C. C.S., 1979. ‘Theory of minimum rate of energy dissipation.’ Journal of Hydraulic Division of American Society of Civil Engineering 105 (HY7), 769-784.
Published
2020-12-18
How to Cite
[1]
H. Sichingabula, “Implications of Hydraulic Geometry Exponents of Zambian Rivers”, Journal of Natural and Applied Sciences, vol. 2, no. 1, pp. 4-26, Dec. 2020.
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