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Part of the book series: The University of Western Ontario Series in Philosophy of Science ((WONS,volume 37))

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Abstract

The usual approach to the calculation of x(T), the annual maximum daily streamflow associated with recurrence interval T, is to fit a probability distribution to a set of observations of annual maxima. The choice of the probability distribution is often based on asymptotic results. We investigate this model selection criterion through evaluation of the errors in estimating of x(T) for a Markovian daily flow stochastic process.

The design of spillways or flood control storage requires the complete calculation of the T flood hydrograph, rather than just the peak value. Questions regarding the evolution of reservoir storage could be solved if a large number of daily streamflow sequences were available to be used in the evaluation of the frequency of failure of each tentative design. The utility of stochastic daily streamflow models is discussed, particularly the question of how to reduce the computer time necessary to generate a large number of synthetic daily sequences.

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References

  • Beard, L. R. (1963), “Flood control operation of reservoirs.” Journal of the Hydraulics Division, Proceedings of the American Society of Civil Engineers 89, 1–23.

    Google Scholar 

  • Bryson, M. C. (1974), “Heavy tailed distributions: properties and tests.” Technometrics 16, 61–68.

    Article  MathSciNet  MATH  Google Scholar 

  • Bulu, A. (1979), “Flood frequency analysis based on a mathematical model of daily flows.” In Modeling Hydrologic Processes. Fort Collins, Colorado: Water Resources Publications.

    Google Scholar 

  • Cohn, T. A. (1984), “The incorporation of historical information in flood frequency analysis.” M.Sc. Thesis, Cornell University.

    Google Scholar 

  • Costa, J. P., J. M. Damazio, M. V. F. Pereira, and J. Kelman (1983), “Optimal allocation of flood control storage in a system of reservoirs.” In Proceedings of the 7th National Seminar on Production and Transmission of Electric Energy, Brasilia, Brazil, in Portuguese.

    Google Scholar 

  • Cramer, H., and M. R. Leadbetter (1967), Stationary and Related Stochastic Processes. New York: Wiley and Sons.

    MATH  Google Scholar 

  • Damazio, J. M. (1984), ‘Comment on “Quantile estimation with more or less flood-like distributions” by J. M. Landwehr, N. C. Matalas and J. R. Wallis’. Water Resources Research 20, 746–750.

    Article  Google Scholar 

  • Damazio, J. M., and J. Kelman (1984), “Use of historical information for the estimation of the streamflow with a recurrence interval of 10000 years”. Technical Report, CEPEL 650/84, in Portuguese.

    Google Scholar 

  • Damazio, J. M., J. C. Moreira, J. P. Costa, and J. Kelman (1983), “Selection of a method for estimating streamflows with a large recurrence interval.” Proceedings of the 5th Brazilian Symposium of Hydrology and Water Resources 2, 145, Blumenau, in Portuguese.

    Google Scholar 

  • Gomide, F. L. S. (1975), “Range and deficit analysis using Markov chains.” Hydrology Paper no. 79, Colorado State University.

    Google Scholar 

  • Grigoriu, M. (1979), “On the prediction of extreme flows.” In Inputs for Risk Analysis in Water Systems, ed. E. A. McBean, K. W. Hipel, and T. E. Unny, pp. 27–46. Fort Collins, Colorado: Water Resources Publications.

    Google Scholar 

  • Gumbel, E. J. (1958), Statistics of Extremes. New York: Columbia University Press.

    MATH  Google Scholar 

  • Hammersley, J. M., and D. C. Handscomb (1964), Monte Carlo Methods. London: Methuen.

    MATH  Google Scholar 

  • Henriques, A. G. (1981), “Analysis of the frequency distribution of the annual maximum.” National Laboratory of Civil Engineering (LNEC), Lisbon, Portugal, in Portuguese.

    Google Scholar 

  • Hosking, J. R. M., and J. R. Wallis (1984), “Palaeoflood hydrology and flood frequency analysis.” AGU Fall Meeting.

    Google Scholar 

  • Hosking, J. R. M., J. R. Wallis, and E. F. Wood (1985), “An appraisal of the regional flood frequency procedure in the U.K.” Flood Studies Report, Hydrological Sciences Journal 30, 85–109.

    Article  Google Scholar 

  • Houghton, J. C. (1977), Robust Estimation of the Frequency of Extreme Events in a Flood Frequency Context. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Kelman, J. (1977), “Stochastic modeling of hydrologic intermittent daily processes.” Hydrology Paper no. 89, Colorado State University, Fort Collins.

    Google Scholar 

  • Kelman, J. (1980), “A stochastic model for daily streamilow.” Journal of Hydrology 47, 235–249.

    Article  Google Scholar 

  • Kelman, J. (1983), “Floods and hydroplants.” Thesis submitted in the competition for the full professorship in the hydraulics department of the Federal University of Rio de Janeiro.

    Google Scholar 

  • Kelman, J., J. P. Costa, J. M. Damazio, and V. M. S. Barbalho (1985b), “Flood control in a multireservoir systems.” Fourth International Hydrology Symposium, Fort Collins, Colorado.

    Google Scholar 

  • Kelman, J., and J. M. Damazio (1983), “Synthetic hydrology and spillway design.” XX Congress of the International Association for Hydraulic Research, Moscow.

    Google Scholar 

  • Kelman, J., and J. M. Damazio (1984), “The 1982 flood of the Iguaçu River at Salto Santiago.” Brazilian Journal of Engineering, Water Resources, Vol. 2—no. 2, in Portuguese.

    Google Scholar 

  • Kelman, J, J. M. Damazio, and J. P. Costa (1985a), “A multivariate synthetic daily streamflow generator.” Fourth International Hydrology Symposium, Fort Collins, Colorado.

    Google Scholar 

  • Kelman, J., J. M. Damazio, J. P. Costa, and M. V. F. Pereira (1980), “Reservoir operation for flood control.” Brazilian Journal of Hydrology and Water Resources 2, in Portuguese.

    Google Scholar 

  • Kelman, J., J. M. Damazio, M. V. F. Pereira, and J. P. Costa (1982), “Flood control restrictions for a hydroelectric plant.” In Decision Making for Hydrosystems Forecasting, Water Resources Publications.

    Google Scholar 

  • Kottegoda, N. T. (1980), Stochastic Water Resources Technology. New York: Macmillan.

    Google Scholar 

  • Landwehr, J. M., N. C. Matalas, and J. R. Wallis (1980), “Quantile estimation with more or less flood-like distributions.” Water Resources Research 16, 547–555.

    Article  Google Scholar 

  • Mazumdar, M. (1975), “Importance sampling in reliability estimation.” Reliability and Faulty Tree Analysis, SIAM, Philadelphia, pp. 153–163.

    Google Scholar 

  • Moreira, J. C., J. M. Damazio, J. P. Costa, and J. Kelman (1983), “Estimation of extreme flows: partial series or annual maxima?” Proceedings of the 5th Brazilian Symposium of Hydrology and Water Resources, vol. 5, pp. 135, Blumenau, Brazil, in Portuguese.

    Google Scholar 

  • Myers, V. A. (1981), “Estimation of probable maximum precipitation in tropical regions.” Conference presented at ELETRONORTE, Brazilia, Brazil, on December 16, 1981.

    Google Scholar 

  • N.E.R.C. (Natural Environment Research Center) (1975), Flood Studies Report, United Kingdom.

    Google Scholar 

  • O’Connell, P., and D. A. Jones (1979), “Some experience with the development of models for the stochastic simulation of daily flows.” In Inputs for Risk Analysis in Water Systems, ed. E. A. McBean, K. W. Hipel and T. E. Unny, pp. 287–312. Fort Collins, Colorado: Water Resources Publications.

    Google Scholar 

  • Plate, E. (1979), “Extreme values models”. In Inputs for Risk Analysis in Water Systems, ed. E. A. McBean, K. W. Hipel and T. E. Unny, pp. 3–26. Fort Collins, Colorado: Water Resources Publications.

    Google Scholar 

  • Quimpo, R. G. (1967), “Stochastic model of daily flow sequences.” Hydrology Paper No. 18, Colorado State University.

    Google Scholar 

  • Rosbjerg, D. (1979), “Analysis of extreme events in stationary dependent series.” In Inputs for Risk Analysis in Water Systems, ed. E. A. McBean, K. W. Hipel and T. E. Unny, pp. 69–75. Fort Collins, Colorado: Water Resources Publications.

    Google Scholar 

  • Rubinstein, R. Y. (1981), Simulation and the Monte Carlo Method. New York: Wiley and Sons.

    Book  MATH  Google Scholar 

  • Slack, J. R., Wallis, J. R., and N. C. Matalas (1975), “On the value of information to flood frequency analysis.” Water Resources Research 11, 629–647.

    Article  Google Scholar 

  • Treiber, B., and E. J. Plate (1975), “A stochastic model for the simulation of daily flows.” Symposium and Workshop on the Application of Mathematical Models in Hydrology and Water Resources, Bratislava, Czechoslovakia.

    Google Scholar 

  • USWRC (U.S. Water Resources Council) (1967), Uniform Technique for Determining Flood Flow Frequency. Bulletin no. 15.

    Google Scholar 

  • USWRC (U.S. Water Resources Council) (1977), Guidelines for Determining Flood Flow Frequency. Bulletin no. 17A.

    Google Scholar 

  • Wallis, J. R. (1981) “Hydrologic problems associated with oilshale development.” IFIP Conference, Italy.

    Google Scholar 

  • Weiss, G. (1977), “Shot noise models for the generation of synthetic streamflow data.” Water Resources Research 13, 101–108.

    Article  Google Scholar 

  • World Meteorological Organization (WMO) (1983), “Manual for estimation of probable maximum precipitation.” Operational Hydrology Report no. 1, WMO, no. 332, Genova, 190 pp.

    Google Scholar 

  • Yakowitz, S. J. (1979) “A nonparametric Markov model for daily river flow.” Water Resources Research 15, 1035–1043.

    Article  Google Scholar 

  • Yevjevich, V., and V. Taesombut (1979), “Information on flood peaks in daily flow series.” In Inputs for Risk Analysis in Water Systems, ed. E. A. McBean, K. W. Hipel, and T. E. Unny, pp. 171–192. Fort Collins, Colorado: Water Resources Publications.

    Google Scholar 

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© 1987 D. Reidel Publishing Company, Dordrecht, Holland

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Kelman, J. (1987). Statistical Approach to Floods. In: MacNeill, I.B., Umphrey, G.J., McLeod, A.I. (eds) Advances in the Statistical Sciences: Stochastic Hydrology. The University of Western Ontario Series in Philosophy of Science, vol 37. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4792-4_12

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  • DOI: https://doi.org/10.1007/978-94-009-4792-4_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8625-7

  • Online ISBN: 978-94-009-4792-4

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