Abstract
A procedure based on the method of derived distributions is proposed for the estimation of flood frequency from ungauged watersheds. The results of previous research on rainfall characteristics and watershed response are incorporated into the proposed procedure. These rainfall characteristics are storm depth, storm duration, space and time distribution. A simplified watershed model is used which has previously given good simulation of the watershed response. Some of the rainfall and watershed model parameters are stochastic in nature and are assumed to follow various probability distributions. Monte Carlo simulation is used for the generation of the various parameter values and simulation of the peak flow hydrographs. After 5000 realizations, the frequency of the hourly and daily peak flow and the flood volume is estimated. The proposed procedure is applied to eight coastal British Columbia watersheds and the results compare well with the observed data and with fitted probability distributions. The method is easy to apply, requires limited data and is shown to be reliable. Sensitivity analysis shows that the procedure is not very sensitive to uncertainty of the parameter values and is not dependent on the parameter probability distributions used.
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References
Blazkova, S.: 1992, Empirical study of nonlinearity in direct runoff on 100 km2 basin, Hydrol. Sc. J., IAHS 37(4), 347–358.
Cadavid, L., Obeysekera, J. T. B. and Shen, H. W.: 1991, Flood-frequency derivation from kinematic wave, J. Hydr. Engrg., ASCE 117(4), 489–510.
Chapman, A., Reksten, D. and Nuhof, R.: 1992, Guide to Peak Flow Estimation for Ungauged Watersheds in the Vancouver Island Region, British Columbia Ministry of Environment, Lands and Parks, Water Management Division, Hydrology Section, Victoria.
Chuptha, P. and Dooge, J. C. I.: 1990, The shape parameters of the geomorphologic unit hydrograph, J. Hydrol. 117, 81–97.
Consuegra, D., Meylan, P. and Musy, A.: 1993, A probabilistic approach to estimate design parameters for flood control projects, in C.Y. Kuo (ed.), Engineering Hydrology, ASCE, San Francisco, pp. 455–460.
Diaz-Granados, M. A., Valdes, J. B. and Bras, R. L.: 1984, A physically based flood frequency distribution, Water Resour. Res. 20 (7), 995–1002.
Dickinson, W. T., Kelly, P. N. and Whiteley, H. R.: 1992, Extremes for rainfall and streamflow, how strong are the links?, Can. Water Resour. J. 17(3), 224–236.
Eagleson, P. S.: 1972, Dynamics of flood frequency, Water Resour. Res. 8(4), 878–898.
Garcia-Guzman, A. and Aranda-Oliver, E.: 1993, A stochastic model of dimensionless hyetograph, Water Resour. Res. 29(7), 2363–2370.
Haan, C. T.: 1978, Statistical methods in hydrology, The Iowa State University Press, Ames.
Haan, C. T. and Edwards, D. R.: 1988, Joint probability estimates of return period flows, Trans. ASAE 31(4), 1115–1119.
Hebson, C. and Wood, E. F.: 1982, A derived flood frequency distribution using Horton order ratios, Water Resour. Res. 18(5), 1509–1518.
Hershfield, D. M.: 1961, Rainfall frequency atlas of the United States, Technical Paper 40, U.S. Department of Commerce, Weather Bureau, Washington, DC.
Hogg, W. D., and Carr, D. A.: 1985, Rainfall Frequency Atlas for Canada, Canadian Government Publishing Centre, Ottawa.
Larson, C. L. and Reich, B. M.: 1972, Relationship of observed rainfall and runoff recurrence intervals, in E. F. Schulz, V. A. Koelzer, and K. Mahmood (eds), Floods and Droughts, Water Resources Publications, Fort Collins, pp. 34–43.
Linsley, R. K., Kohler, M. A. and Paulhus, J. L. H.: 1982, Hydrology for Engineers, McGraw-Hill, New York.
Loukas, A. and Quick, M. C.: 1995, A 24-hour design storm for coastal British Columbia, ASCE J. Hydr. Engrg. (Dec. 1995).
Loukas, A. and Quick, M. C.: 1993a, Storm precipitation in southwest British Columbia, in C. Y. Kuo (ed.), Engineering Hydrology, ASCE, San Francisco, pp. 13–18.
Loukas, A. and Quick, M. C.: 1993b, Hydrologic behaviour of a mountainous watershed, Can. J. Civil. Engrg. 20(1), 1–8.
Moughamian, M. S., McLaughlin, D. B., and Bras, R. L.: 1987, Estimation of flood frequency: An evaluation of two derived distribution procedures, Water Resour. Res. 23(7), 1309–1319.
Muzik, I.: 1993, The method of derived distributions applied to peak flows, in C. Y. Kuo (ed.), Engineering Hydrology, ASCE, San Francisco, pp. 437–442.
Phillip, J. R.: 1960, General method of exact solution of the concentration-dependent diffusion equation, Aust. J. Phys. 13(1), 1–12.
Quick, M. C.: 1993, U.B.C. Watershed Model Manual, Version 2.0, Department of Civil Engineering, University of British Columbia, Vancouver.
Raines, T. H. and Valdes, J. B.: 1993, Estimation of flood frequencies for ungauged catchments, J. Hydr. Engrg., ASCE, 119(10), 1138–1154.
Reich, B. M.: 1970, Flood series compared to rainfall extremes, Water Resour. Res. 6(6), 1655–1667.
Rodriguez-Iturbe, I., Gonzalez, M. and Bras, R. L.: 1982, A geomorphologic climate theory of instantaneous unit hydrograph, Water Resour. Res. 18(4), 877–886.
Rodriguez-Iturbe, I. and Valdes, J. B.: 1979, The geomorphologic structure of hydrologic response, Water Resour. Res. 15(6), 1409–1420.
Rosso, R.: 1984, Nash model relation to Horton order ratios, Water Resour. Res. 20(7), 914–920.
Russell, S. O.: 1982, Flood probability estimation, J. Hydr. Engrg. ASCE 108(1), 63–73.
Sabol, G. V.: 1993, Lag relations for semi-arid regions and urban areas, in: C. Y. Kuo (ed.), Engineering Hydrology, ASCE, San Francisco, pp. 168–173.
Sarino and Serrano, S. E.: 1990, Development of the instantaneous unit hydrograph using stochastic differential equations, Stoch. Hydrol. Hydr. 4, 151–160.
U.S. Soil Conservation Service, 1972, Hydrology, Section 4, National Engineering Handbook, Soil Conservation Service. U.S. Department of Agriculture, Washington, DC.
U.S. Army Corps of Engineers, 1990, HEC-1 Flood hydrograph Package, Hydrologic Engineering Center, Davis.
Watt, W. E., Lathem, K. W., Neill, C. R., Richards, T. L. and Rousselle, J. (eds.): 1989, Hydrology of Floods in Canada-A Guide to Planning and Design, National Research Council of Canada, Ottawa.
Watt, W. E. and Chow, K. C. A.: 1985, A general expression for basin lag time, Can. J. Civil. Engrg. 12, 294–300.
Weiss, L. L.: 1964, Ratio of true to fixed-interval maximum rainfall, J. Hydr. Div. ASCE 90, 77–82.
Yang, J. C., Tarng, S. Y. and Tung, Y. K.: 1993, Analyzing uncertainty of IUH of Nash, in H. W. Shen, S. T. Su, and F. Wen (eds.), Hydraulic Engineering, ASCE, San Francisco, pp. 1927–1932.
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Loukas, A., Quick, M.C. & Russell, S.O. A physically based stochastic-deterministic procedure for the estimation of flood frequency. Water Resour Manage 10, 415–437 (1996). https://doi.org/10.1007/BF00422548
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DOI: https://doi.org/10.1007/BF00422548