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<br />UI"V'\f'"I U
<br />
<br />I
<br />
<br />"000
<br />
<br />I
<br />I
<br />
<br />. Malnstraam design quantiles
<br />. Tribulal)'designqIJantiles
<br />-Fitted log-Normal distribution
<br />
<br />o
<br />i
<br />~
<br />m ~OOO
<br />"-
<br />"0
<br />8
<br />u:
<br />
<br />
<br />
<br />I
<br />I
<br />
<br />100
<br />20
<br />
<br />'.5
<br />
<br />50
<br />
<br />55
<br />
<br />2.5
<br />
<br />2.5
<br />
<br />2.0
<br />
<br />'.0
<br />
<br />AEP (Standardised Nonnal Variate)
<br />
<br />I
<br />
<br />Figure 18 Fitted log-Normal flood frequency curves for
<br />mainstream and tributary design flows.
<br />
<br />I
<br />
<br />= 2.638 10g(m'/s)
<br />
<br />440 m'/s
<br />
<br />The computed design flood estimates from the fitted
<br />distribution are shown in columns 8 and 10; these are then
<br />back-transformed into the arithmetic domain, as shown in
<br />columns 9 and 11.
<br />
<br />I
<br />
<br />I
<br />I
<br />
<br />(c) Estimation of concurrent tributary flows
<br />
<br />Computation of the average concurrent flow in the
<br />tributary (m"..) for varying design floods in the mainstream
<br />(x) are determined from Equation 9, as follows:
<br />
<br />myjx = 1251
<br />
<br />+ 0.5 0.376 (x -1.796)
<br />0.362
<br />
<br />I
<br />I
<br />
<br />where 0.5 represents the correlation between the log-
<br />transformed flows calculated for the largest floods on
<br />record. The average concurrent flow in the tributary
<br />corresponding to a 1 in 50000 AEP event in the
<br />mainstream is thus calculated by:
<br />
<br />mw = 1.251 + 0.5 0.376 (3.465-1.796)
<br />0.362
<br />= 2.118 10g(m'/s)
<br />= 131 m'/s
<br />The computed figures for all AEPs are shown in columns
<br />12, and the back-transformed values are shown in columns
<br />13. It is of interest to calculate the AEPs of the concurrent
<br />tributary flows, and these may be calculated by first
<br />calculating the standard normal deviate using:
<br />z = (x-m)ls
<br />For example, to calculate the AEP of the 74 m'/s design
<br />flood estimate in the tributary:
<br />z = (log(74) -1.251)1 0.376
<br />= 1.644
<br />
<br />I
<br />
<br />I
<br />
<br />I
<br />I
<br />
<br />I
<br />
<br />The corresponding standard normal cumulative distribution
<br />for this value of z is 0.95, which corresponds to an AEP of 1
<br />in 20. Values for the other estimates are shown in column
<br />14.
<br />
<br />I
<br />
<br />7 REFERENCES
<br />
<br />Abramow~z, M. -and Stegun, IA (ads) (1964, 1974):
<br />Handbook of mathematical functions with Fonnulas,
<br />graphs, and Mathematical Tables. National Bureau of
<br />
<br />I
<br />
<br />DUUI\ VI - L..~UJIJQ"U'1 VJ L.cll!:jC LV t:^\IQII'C"' ............."
<br />
<br />Standards Applied Mathematics Series 55, Washington
<br />DC.
<br />
<br />AUSTROADS (1994): Waterway design, A guide to the
<br />hydraulic design of bridges, culverts and floodways.
<br />Publication No. AP-23194. AUSTROADS, Sydney, 137
<br />pp.
<br />American Meteorological Society (1992): Proceedings of
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<br />
<br />Australian National Committee on Large Dams (ANCOLD;
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<br />
<br />. Baker, V.R. and Pickup, G. (1987): Flood geomorphology of
<br />the Katherine Gorge, Northern Territory, Australia.
<br />Geological Society of America Bulletin, 98: 635-646.
<br />
<br />. Baker, V.R., Kochel, R.C., and Patton, P.C. eds. (1988):
<br />Flood geomorphology. John Wiley and Sons, New York,
<br />503pp.
<br />
<br />Baron, B.C., Pilgrim, D.H. and Cordery, I. (1980)
<br />Hydrological relationships between small and large
<br />catchments. Dept of Nail. Devel. and Energy, Aust
<br />Water Resources Council Tech Paper Nfl. 54.
<br />
<br />Binley, A.M., Beven, K.J., Calver, A., and Watts, L.G.
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<br />WaterResour. Res. 27(6): 1253-1261.
<br />
<br />Bloschl, G. and Sivapalan, M. (1996): Process Controls on
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<br />Properties and Return Period. Water Resources
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<br />
<br />Beran, M.A. (1973): Estimation of Design Fioods and the
<br />Problem of Equating the Probability of Rainfall and
<br />Runoff. Symp. on the Design of Water Resour. Projects
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<br />
<br />Bergstrom, S., Harlin, J., Lindstrom, G. (1996): Spillway
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<br />J. 37(5): 505-519.
<br />
<br />Body, D.N. (1962) Significance of peak runoff intensity in
<br />the application of the unit graph method to flood
<br />estimation. J. Inst Engrs. Aust., Vol. 34, pp. 25-31.
<br />
<br />Boughton, W.C., Hill, P.I., (1997): A Design Flood
<br />Estimation Procedure using Data Generation and a
<br />Daily Water Balance Model. CRC for Catchment
<br />Hydrology Research Report No. 97/8.
<br />
<br />Boyd, M.J., Bates, B.C., Pilgrim, D.H. and Cordery, I.
<br />(1987): WBNM: a general runoff-routing model-
<br />programs and user manual. Univ. of New South Wales,
<br />Water Resour. Lab. Report No. 170.
<br />
<br />Brown, JAH. (1982): A review of flood estimation
<br />procedures. Proc. of the Workshop on Spillway Design,
<br />Dept of Nail Devel. and Energy, AWRC Cant. Series
<br />No.6, pp. 84-108.
<br />
<br />Bureau of Meteorology (1994) The estimation of probable
<br />maximum precipitation in Australia: Generalised Short
<br />Duration Method. Department of the Environment Sport
<br />and Territories, Bureau of Meteorology Bulletin 53,
<br />AGPS, 48pp. (supplement issued in December 1996).
<br />
<br />Bureau of Meteorology (1998'): Development of temporal
<br />distributions of rainfall antecedent to large and extreme
<br />design bursts over southeast Australia, Hydrology
<br />Report Series Report No.5, Hydrometeorological
<br />Advisory Service, Bureau of Meteorology.
<br />
<br />Bureau of Meteorology (1998'): Climatic Atlas of Australia,
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<br />
<br />,J-
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