Skip to main content
SpringerLink
Log in

Statistical treatment of floods

  • Chapter
Stochastic Water Resources Technology

Abstract

A flood is an unusually high stage in a river that can cause damage to adjacent areas. Floods vary spatially and temporally in magnitude and are often measured through their peak discharges. The structural and hydraulic designs of dams and bridges are based on such extreme flows in water courses. Furthermore, the frequency of occurrence, the maximum stage reached, the volume of flood water, the area inundated and the duration of floods are of importance to the civil engineer when planning and designing roads, buildings and structures. In addition, there are dependent economic problems such as flood-plain zoning and flood insurance.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Abramowtiz, M., and Stegun, L. (eds) (1964). Handbook of mathematical functions. Natl Bur. Stand., Appl. Math. Ser. Publ., No. 55; Handbook of Mathematical Functions, Dover Publications, New York

    Google Scholar 

  • Aitchison, J., and Brown, J. A. C. (1957). The Lognormal Distribution, Cambridge University Press, London

    MATH  Google Scholar 

  • Alexander, G. N. (1963). Using the probability of storm transposition for estimating the frequency of rare floods. J. Hydrol., 1, 46–57

    Article  Google Scholar 

  • Alexander, G. N. (1965). Discussion of ‘hydrology of spillway design: large structures—adequate data’. J. Hydraul Div., Proc. Am. Soc. Civ. Eng., 91 (HY1), 211–19

    Google Scholar 

  • Anscombe, F. J. (1960). Rejection of outliers. Technometrics, 2, 123–47

    Article  MathSciNet  MATH  Google Scholar 

  • Barnett, V. (1975). Probability plotting methods and order statistics. Appl.Statist., 24, 95–108

    Article  MathSciNet  Google Scholar 

  • Benson, M. A. (1960). Characteristics of frequency curves based on a theoretical 1000-year record. U.S. Geol. Surv. Water-Supply Paper, No. 1543-A, 51–94

    Google Scholar 

  • Benson, M. A. (1962a). Factors influencing the occurrence of floods in a humid region of diverse terrain. U.S., Geol. Surv., Water-Supply Paper, No. 1580-B

    Google Scholar 

  • Benson, M. A. (1962b). Plotting positions and economics of engineering planning. J. Hydraul. Div., Proc. Am. Soc. Civ. Eng., 88 (HY6), 57–71.

    Google Scholar 

  • Benson, M. A. (1963). Discussion closure. J. Hydraul. Div., Proc. Am. Soc. Civ. Eng., 89 (HY6), 251–2

    Google Scholar 

  • Benson, M. A. (1968). Uniform flood-frequency estimating methods for federal agencies. Water Resour. Res., 4, 891–908.

    Article  Google Scholar 

  • Benson, M. A. (1969). Comments. Water Resour. Res., 5, 910–11.

    Google Scholar 

  • Benson, M. A. (1970) Comments. Water Resour. Res., 6, 998–9

    Google Scholar 

  • Benson, M. A. (1973). Thoughts on the design of design floods. Floods and Droughts, Proceedings of the 2nd International Hydrology Symposium, 11–13 September 1972, Water Resource Publications, Fort Collins, Colorado, pp. 27–33

    Google Scholar 

  • Berry, F. A., Bollay, E., and Beers, N. R. (eds) (1945). Handbook of Meteorology, McGraw-Hill, New York

    Google Scholar 

  • Bobée, B., and Robitaille, R. (1975). Correction of bias in the estimation of the coefficient of skewness. Water Resour. Res., 11, 851–4

    Article  Google Scholar 

  • Brown, J. P. (1972).The Economic Effect of Floods,Springer, Berlin

    Book  Google Scholar 

  • Burges, S. J., Lettenmaier, D. P., and Bates C. L. (1975). Properties of the three-parameter log normal probability distribution. Water Resour. Res., 11, 229–35

    Article  Google Scholar 

  • Bury, K. V. (1975). Statistical Models in Applied Science, Wiley, New York

    Google Scholar 

  • Carrigan, P. H., Jr. (1971). A flood frequency relation based on regional record maxima. U.S., Geol. Surv., Prof Paper, No. 434-F

    Google Scholar 

  • Chow, V. T. (1951). A general formula for hydrologic frequency analysis. Trans. Am. Geophys. Un., 32, 231–7. (1952). Discussion. Trans. Am. Geophys. Un., 33, 277–82

    Google Scholar 

  • Chow, V. T. (1954). The log-probability law and its engineering applications. Proc. Am. Soc. Civ. Eng., 80, paper 536, 1–25

    Google Scholar 

  • Chow, V. T. (1964). Handbook of Applied Hydrology, McGraw-Hill, New York

    Google Scholar 

  • Cole, G. (1966). An application of the regional analysis of flood flows. Proceedings of the Symposium on River Flood Hydrology, March 1965, Institution of Civil Engineers, London, session B, paper 3

    Google Scholar 

  • Collett, D., and Lewis, T. (1976). The subjective nature of outlier rejection procedures. Appl. Statist., 25, 228–37

    Article  Google Scholar 

  • Condie, R. (1977). The log Pearson type 3 distribution: the T-year event and its asymptotic standard error by maximum likelihood theory. Water Resour. Res., 13, 987–91

    Article  Google Scholar 

  • Court, A.(1952). Some new statistical techniques in geophysics. Adv. Geophys., 1, 45–85

    Article  Google Scholar 

  • Davis, D. R., Kisiel, C. C., and Duckstein, L. (1972). Bayesian decision theory applied to design in hydrology. Water Resour. Res., 8, 33–41

    Article  Google Scholar 

  • Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philos. Trans. A, 222, 309–68

    Article  MATH  Google Scholar 

  • Fisher, R. A., and Tippett, L. H. C. (1928). Limiting forms of the frequency distribution of the largest or smallest member of a sample. Proc. Camb. Philos. Soc., 24, 180–90

    Article  MATH  Google Scholar 

  • Foster, H. A. (1924). Theoretical frequency curves and their applications to engineering problems. Trans. Am. Soc. Civ. Eng., 87, 142–203

    Google Scholar 

  • Fréchet, M. (1927). Sur la loi de probabilité de l’écart maximum. Annales de la Société Polonaise de Mathematique, 6, 92–117

    Google Scholar 

  • Fryer, H. C. (1966). Concepts and Methods of Experimental Statistics, Allyn and Bacon, London

    Google Scholar 

  • Fuller, W. E. (1914). Flood flows. Trans. Am. Soc. Civ. Eng., 77, 564–617

    Google Scholar 

  • Giesbrecht, F., and Kempthorne, O. (1976). Maximum likelihood estimation in the three-parametric lognormal distribution.J. R. Statist. Soc. B, 38, 257–63

    MathSciNet  MATH  Google Scholar 

  • Gilroy, E. J. (1972). The upper bound of a log-Pearson type 3 random variable with negatively skewed logarithms. U.S., Geol. Surv., Prof. Paper, 800, B273–5

    Google Scholar 

  • Gray, D. A. (1974). Safety of dams—bureau of reclamation. J. Hydraul. Div., Am. Soc. Civ. Eng., 100 (HY2), 267–77

    Google Scholar 

  • Green, N. M. D. (1973). A synthetic model for daily streamflow. J. Hydrol., 20, 351–64

    Article  Google Scholar 

  • Gringorten, I. I.’ (1963). A plotting rule for extreme probability paper. J. Geophys. Res., 68, 813–4

    Article  Google Scholar 

  • Grubbs, F. E. (1950). Sample criteria for testing outlying observations. Ann. Math. Statist., 21, 27–58

    Article  MathSciNet  MATH  Google Scholar 

  • Gumbel, E. J. (1941). The return period of flood flows. Ann. Math. Statist., 12, 163–90

    Article  MathSciNet  MATH  Google Scholar 

  • Gumbel, E. J. (1943). On the reliability of the classical chi-square test. Ann. Math. Statist., 14, 253–63

    Article  MathSciNet  MATH  Google Scholar 

  • Gumbel, E. J.(1954). Statistical theory of extreme valves and some practical appli cations.Natl Bur. Stand., Appl. Math. Ser., Publ., No. 33

    Google Scholar 

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

    MATH  Google Scholar 

  • Gumbel, E. J. (1958b). Theory of floods and droughts. J. Inst. Water Eng., 12, 157–84

    Google Scholar 

  • Gumbel, E. J. (1959). Communications. J. Inst. Water Eng., 13, 71–102

    Google Scholar 

  • Gumbel, E. J. (1967). Extreme value analysis of hydrologic data. Statistical Methods in Hydrology, Proceedings of the 5th Hydrology Symposium, McGill University, 1966, Queen’s Printer, Ottawa, pp. 147–81

    Google Scholar 

  • Hardison, C. H. (1973). Probability distribution of extreme floods, highways and the catastrophic floods of 1972. Proceedings of the 52nd Annual General Meeting of the Highway Research Board, National Academy of Sciences, Washington, D.C., No. 479, pp. 42–5

    Google Scholar 

  • Hardison, C. H. (1974). Generalized skew coefficients of annual floods in the United States and their application. Water Resour. Res., 10, 745–52

    Article  Google Scholar 

  • Harter, H. L. (1969). A new table of percentage points of the Pearson type III distribution. Technometrics, 11, 177–87

    Article  MATH  Google Scholar 

  • Hazen, A. (1914). Storage to be provided in impounding reservoirs for municipal water supply. Trans. Am. Soc. Civ. Eng., 77, 1539–640

    Google Scholar 

  • Hazen, A. (1930). Flood Flows, Wiley, New York

    Google Scholar 

  • Hershfield, D. M. (1961). Estimating the probable maximum precipitation. J. Hydraul. Div., Am. Soc. Civ. Eng., 87 (HY5), 99–116

    Google Scholar 

  • Holtzman, W. H. (1950). The unbiased estimate of the population variance and standard deviation. Am. J. Psychol., 63, 615–17

    Article  Google Scholar 

  • Horton, R. E. (1914). Discussion on ‘Flood flows’ by W. E. Fuller. Trans. Am. Soc. Civ. Eng., 77, 663–70

    Google Scholar 

  • Horton, R. E. (1936). Hydrologic conditions as affecting the results of the application of method of frequency analysis to flood records. U.S., Geol. Surv., Water-Supply Paper, No. 771, 433–50

    Google Scholar 

  • Huxham, S. H., and McGilchrist, C. A. (1969). On the extreme value distribution for describing annual flood series. Water Resour. Res., 5, 1404–5

    Article  Google Scholar 

  • Jenkinson, A. F. (1955). The frequency distribution of the annual maximum (or minimum) values of meteorological elements. Q. J. R. Meteorol. Soc., 81, 158–71

    Article  Google Scholar 

  • Jenkinson, A. F. (1969). Estimation of maximum floods. World Meteorol. Organ., Tech. Note, No. 98, chapter 5, 183–257

    Google Scholar 

  • Kaczmarek, Z. (1957). Efficiency of the estimation of floods with a given return period, vol. 3, International Association of Scientific Hydrology, Toronto, pp. 145–59

    Google Scholar 

  • Kalinske, A. A. (1946). On the logarithmic-probability law. Trans. Am. Geophys. Un., 27, 709–11

    Article  Google Scholar 

  • Kazmann, R. G. (1972). Modern Hydrology, 2nd edn, Harper and Row, New York

    Google Scholar 

  • Kendall, M. G., and Stuart, A. (1977). The Advanced Theory of Statistics, vol. 2, 4th edn, Griffin, London

    MATH  Google Scholar 

  • Kimball, B. F. (1960). On the choice of plotting positions on probability paper. J. Am. Statist. Assoc., 55, 546–60

    Article  MATH  Google Scholar 

  • Kirby, W. (1974). Algebraic boundedness of sample statistics. Water Resour. Res., 10, 220–2

    Article  Google Scholar 

  • Kottegoda, N. T. (1972). Flood evaluation—can stochastic models provide an answer? Proceedings of the International Symposium on Uncertainties in Hydrology and Water Resources Systems, vol. 1, 11–14 December 1972, University of Arizona, Tucson, pp. 105–14

    Google Scholar 

  • Kottegoda, N. T. (1973). Flood estimation by some data generation techniques. Floods and Droughts, Proceedings of the 2nd International Hydrology Symposium, 11–13 September 1972 , Water Resource Publications, Fort Collins, Colorado, pp. 189–99

    Google Scholar 

  • Kritsky, S. N. and Menkel, M. F. (1969). On principles of estimation methods of maximum discharge. Floods and their Computation, vol. 1, International Association of Scientific Hydrology, Belgium, No. 84, pp. 29–41

    Google Scholar 

  • Lane, F. W. (1948). The Elements Rage, Country Life, London

    Google Scholar 

  • Langbein, W. B. (1949). Annual floods and the partial-duration flood series. Trans. Am. Geophys. Un., 30, 879–81

    Article  Google Scholar 

  • Langbein, W. B.(1960). Plotting positions in frequency analysis. U.S., Geol. Surv., Water Supply Paper, No. 1543-A, 48–51

    Google Scholar 

  • Larson, C. L., and Reich, B. M. (1973). Relationships of observed rainfall and runoff intervals. Floods and Droughts, Proceedings of the 2nd International Hydrology Symposium, 11–13 September 1972, Water Resource Publications, Fort Collins, Colorado, pp. 34–43

    Google Scholar 

  • Linsley, R. K., Kohler, M. A., and Paulhus, J. L. H. (1949). Applied Hydrology, McGraw-Hill, New York

    Google Scholar 

  • Lloyd, E. H. (1970). Return periods in the presence of persistence. J. Hydrol., 10, 291–8

    Article  Google Scholar 

  • Lowery, M. D., and Nash, J. E. (1970). A comparison of methods of fitting the double exponential distribution. J. Hydrol., 10, 259–75

    Article  Google Scholar 

  • Majumdar, K. C., and Sawhney, R. P. (1965). Estimates of extreme values by different distribution functions. Water Resour. Res., 1, 429–34

    Article  Google Scholar 

  • Markowitz, E. M. (1971). The chance a flood will be exceeded in a period of years. Water Resour. Bull., 7, 40–53

    Article  Google Scholar 

  • Matalas, N. C. (1967). Mathematical assessment of synthetic hydrology. Water Resour. Res., 3, 937–45

    Article  Google Scholar 

  • Matalas, N. C., Slack, J. R., and Wallis, J. R. (1975). Regional skew in search of a parent. Water Resour. Res., 11, 815–26

    Article  Google Scholar 

  • Miller, J. F. (1973). Probable maximum precipitation—the concept, current, procedures and the outlook. Floods and Droughts, Proceedings of the 2nd International Hydrological Symposium, 11–13 September 1972, Water Resource Publications, Fort Collins, Colorado, pp. 50–61

    Google Scholar 

  • Moran, P. A. P. (1957). The statistical treatment of flood flows. Trans. Am. Geophys. Un., 38, 519–23

    Article  Google Scholar 

  • Myers, V. A. (1969). The estimation of extreme precipitation as the basis for design flood—resume of practice in the United States. Floods and their Computation, vol. 1, International Association of Scientific Hydrology, Belgium, No. 84, pp. 84–104

    Google Scholar 

  • Nash, J. E., and Shaw, B. L. (1966). Flood frequency as a function of catchment characteristics. Proceedings of the Symposium on River Flood Hydrology, March 1965, Institution of Civil Engineers, London, session C, paper 6

    Google Scholar 

  • Natural Environmental Research Council (1975). Flood Studies Report, Natural Environment Research Council, London

    Google Scholar 

  • Panchang, C. M. (1969). Improved precision of future high floods. Floods and their Computation, vol. 1, International Association of Scientific Hydrology, Belgium, No. 84, pp. 51–9

    Google Scholar 

  • Powell, R. W. (1943). A simple method of estimating flood frequencies. Civ. Eng., 13, 105–6

    Google Scholar 

  • Quimpo, R. G. (1967). Stochastic model of daily river flow sequences. Colo. St. Univ., Fort Collins, Hydrol. Papers, No. 18

    Google Scholar 

  • Sangal, B. P., and Biswas, A. K. (1970). The 3-parameter lognormal distribution and its application in hydrology. Water Resour. Res. 6, 505–15

    Article  Google Scholar 

  • Santos, A., Jr. (1970). The statistical treatment of flood flows. Water Power, 22, 63–7

    Google Scholar 

  • Schulz, E. F., Koelzer, V. A., and Mahmood, K. (eds) (1973). Floods and Droughts, Proceedings of the 2nd International Hydrology Symposium, 11–13 September 1972, Water Resource Publications, Fort Collins, Colorado

    Google Scholar 

  • Schuster, J. (1973). A simple method of teaching the independence of X and s2. Am. Statist., 27, 29–30

    Google Scholar 

  • Singh, K. P., and Sinclair, R. A. (1972). Two-distribution method for flood-frequency analysis. J. Hydraul Div., Proc. Am. Soc. Civ. Eng., 98 (HY1), 29–44

    Google Scholar 

  • Slack, J. R., Wallis, J. R., and Matalas, N. C. (1975). On the value of information to flood frequency analysis. Water Resour. Res., 11, 629–47

    Article  Google Scholar 

  • Stripp, J. R., and Young, G. K., Jr. (1971). Plotting positions for hydrologic frequencies. J. Hydraul. Div., Proc. Am. Soc. Civ. Eng., 97 (HY1), 219–22

    Google Scholar 

  • Tennessee Valley Authority (1961). Floods and Flood Control, Tennessee Valley Authority, Knoxville, Tennessee

    Google Scholar 

  • Todorovic, P. (1978). Stochastic models of floods. Water Resour. Res., 14, 345–56

    Article  Google Scholar 

  • Todorovic, P., and Rouselle, J. (1971). Some problems of flood analysis. Water Resour. Res., 7, 1144–50

    Article  Google Scholar 

  • Treiber, B., and Plate, E. J. (1975). A stochastic model for the simulation of daily flows. Proceedings of the International Symposium and Workshop on the Application of Mathematical Models in Hydrology and Water Resources System, International Association of Scientific Hydrology, Bratislava, preprints

    Google Scholar 

  • Tribus, M. (1969). Rational Descriptions, Decisions and Designs, Pergamon, New York

    Google Scholar 

  • Wallis, J. R., Matalas, N. C., and Slack, J. R. (1974). Just a moment! Water Resour. Res., 10, 211–19

    Article  Google Scholar 

  • Wallis, J. R. (1976). Effect of sequence length n on the choice of assumed distribution of floods. Water Resour. Res., 12, 457–71

    Article  Google Scholar 

  • Watson, G. S. (1954). Extreme values in samples from M-dependent stationary stochastic processes. Ann. Math. Statist., 25, 798–800

    Article  MathSciNet  MATH  Google Scholar 

  • Weisner, C. J. (1970). Hydrometeorology, Chapman and Hall, London

    Google Scholar 

  • Weiss,G. (1977). Shot noise models for synthetic generation of multisite daily streamflow data. Water Resour. Res. 13, 101–8

    Article  Google Scholar 

  • Whipple,G. C.(1916).The element of chance in sanitation. J. Franklin Inst., 182, 205–27.

    Article  Google Scholar 

  • Whittaker, J. (1973). Discussion on ‘Relationship of observed rainfall and runoff recurrence intervals’ by C. L. Larson and B. M. Reich. Floods and Droughts, Proceedings of the 2nd International Hydrology Symposium, 11–13 September 1972, Water Resource Publications, Fort Collins, Colorado, pp. 108–9

    Google Scholar 

  • Wilk, M. B., Gnanadesikan, R., and Hugett, M. J. (1962). Probability plots for the gamma distribution. Technometrics, 4, 1–20

    Article  MathSciNet  MATH  Google Scholar 

  • Wilson, E. M. (1974). Engineering Hydrology, 2nd edn, Macmillan, London

    Book  Google Scholar 

  • World Meteorological Organisation (1973). Manual for estimation of probable maximum precipitation. Oper. Hydrol. Rep., No. 1, World Meteorol. Organ., Geneva, Publ., No. 332.

    Google Scholar 

  • Wilson, E. M. (1974). Guide to hydrometeorological practices. World Meteorol. Organ., Geneva, Publ. No. 168

    Google Scholar 

  • Yevjevich, V. (1968). Misconceptions in hydrology and their consequences. Water Resour. Res., 4, 225–32.

    Article  Google Scholar 

  • Yevjevich, V. (1969). Comments and reply. Water Resour. Res., 5, 535–41

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, University of Birmingham, UK

    N. T. Kottegoda

Authors
  1. N. T. Kottegoda
    View author publications

    You can also search for this author in PubMed Google Scholar

Copyright information

© 1980 N. T. Kottegoda

About this chapter

Cite this chapter

Kottegoda, N.T. (1980). Statistical treatment of floods. In: Stochastic Water Resources Technology. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-03467-3_6

Download citation

Publish with us

Policies and ethics

Search

Navigation