Skip to main content
SpringerLink
Log in

Types of probability distributions in the evaluation of extreme floods

  • The Methods and Methodology of Studies
  • Published:
Water Resources Aims and scope Submit manuscript

Abstract

The development of an optimal scheme for evaluation of maximal water discharges is discussed, including adequate probability distribution laws, an effective procedure for their approximation based on observational data, and reliable goodness-of-fit tests for analytical and empirical distributions. One-dimensional probability distribution laws are systematized. Promising distributions were identified, including generalized distribution of extreme values, lognormal distribution, Pearson type V power distribution, and GPD, for evaluating maximal discharges. The available methods for approximating analytical curves, including the up-to-date method of L-moments are considered. Parameter estimation algorithm based on L-moment method for Pearson type III distribution is considered. Pearson type III distribution, lognormal distribution, GEV, and GPD are compared in the approximation of maximal water discharges in rivers of Austria, Siberia, Far East, and the Hawaiian Islands.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bolgov, M.V., and Pisarenko, V.F., The Distribution of Peak Runoff Values in Maritime Territory Rivers, Water Resour., 1999, vol. 26, no. 6, pp. 636–646.

    Google Scholar 

  2. Vinogradov, Yu.B., Matematicheskoe modelirovanie protsessov formirovaniya stoka (Mathematical Modeling Runoff Formation Processes), Leningrad: Gidrometeoizdat, 1988.

    Google Scholar 

  3. Gartsman, B.I. and Stepanova, M.V., Specific Aspects of Hydrological Calculations of Maximal Runoff in Far East, Geogr. Prir. Resur., 1996, no. 4, pp. 103–110.

  4. Gartsman, B.I. and Bugaets, A.N., Application of a Model of Flood Cycle in a Small River Basin in Maximal-Runoff Calculations, in Gidrometeorologiya i ekologiya Dal’nego Vostoka (Hydrometeorology and Ecology of Far East), DVNIGMI Special Issue no. 4, Vladivostok: Dal’nauka, 2003, pp. 76–93.

    Google Scholar 

  5. Gartsman, B.I., Effect of Basin Counter-Regulation in the Formation of Extreme Rain Floods, Geogr. Prir. Resur., 2007, no. 1, pp. 14–21.

  6. Gubareva, T.S., Statistical Regularities in Maximal Runoff in Amur Basin Rivers, in Analiz i stokhasticheskoe modelirovanie ekstremal’nogo stoka na rekakh Evrazii v usloviyakh izmeneniya klimata. Tr. mezh. Sem. (Analysis and Stochastic Modeling of Extreme Runoff in Eurasian Rivers under Changing Climate. Proc. Int. Workshop), Irkutsk: Izd. Instituta geografii SO RAN, 2004, pp. 182–191.

    Google Scholar 

  7. Naidenov, V.I., Shveikina, B.I., and Vikhrova, M.A., Probabilistic Regularities in Catastrophic Floodds, Meteorol. Gidrol., 2003, no. 6, pp. 81–95.

  8. Naidenov, V.I., Nelineinaya dinamika poverkhnostnykh vod sushi (Nonlinear Dynamics of Continental Surface Water), Moscow: Nauka, 2004.

    Google Scholar 

  9. Rodkin, M.V., Typification of Catastrophic Manifestations of Natural Hazards, in Prirodnye opasnosti Rossii. T. 6. Otsenka i upravlenie prirodnymi riskami (Natural Hazards in Russia, vol. 6, Assessment and Control of Natural Risks), Moscow: KRUK, 2003, pp. 85–102.

    Google Scholar 

  10. Pisarenko, V.F., Bolgov, M.V., Osipova, H.V., and Rukavishnikova, T.A., Application of the Theory of Extreme Events to Problems of Approximating Probability Distributions of Water Flow Peaks, Water Resour., 2002, vol. 29, no. 6, pp. 593–604.

    Article  Google Scholar 

  11. Ben-Zvi, A., and Azmov, B., Joint Use of L-moment Diagram and Goodness-of-Fit Test: A Case Study of Diverse Series, J. Hydrology, 1997, vol. 198, pp. 245–259.

    Article  Google Scholar 

  12. Bernardara, P., Schertzer, D., Sauquet, E., Tchigirinskaya, I., and Lang, M., The Flood Probability Distribution Tail: How Heavy Is It?, Stochastic Environmental Research and Risk Assessment, 2007, vol. 22, no. 1, pp. 107–122.

    Article  Google Scholar 

  13. De Haan, L., On Regular Variation and Its Applications to Weak Convergence of Sample Extremes, Math. Centre Tracts., vol. 32, Amsterdam: Math. Centrum, 1970.

    Google Scholar 

  14. Fisher, R., and Tippett, L., On the Estimation of the Frequency Distributions of the Largest or Smallest Member of a Sample, Proc. Cambridge Philosoph. Soc., 1928, Iss. 24, pp. 180–190.

  15. Frequency and Risk Analysis in Hydrology, Kite, G.W., Ed., Littleton. Colorado. USA: Water Resources Publications, 1988.

    Google Scholar 

  16. Gingras, D., and Adamowski, K., Coupling of Non-Parametric and L-moment Analysis for Mixed Distribution Identification, Water Res. Bull., 1992, vol. 28, no. 2, pp. 263–272.

    Google Scholar 

  17. Greenwood, J.A., Landwehr, J.M., Matalas, N.C., and Wallis, J.R., Probability Weighted Moments: Definitions and Relation to Parameters of Several Distributions Expressible in Inverse Form, Water Resour. Res., 1979, vol. 15, pp. 1049–1054.

    Article  Google Scholar 

  18. Hosking, J.R.M., and Wallis, J.R., Regional Frequency Analysis. An Approach Based on L-moments, Cambridge: Cambridge Univ. Press, 1997.

    Book  Google Scholar 

  19. Jenkinson, A.F., The Frequency Distribution of the Annual Maximum (or Minimum) Value of Meteorological Elements, The Quarterly J. Royal Meteorological Society, 1955, vol. 81,Iss. 350, pp. 158–171.

    Article  Google Scholar 

  20. Malamud, B.D., and Turcotte, D.L., The Applicability of Power-Law Frequency Statistics to Floods, J. Hydrology, 2006, vol. 322, nos. 1–4, pp. 168–180.

    Article  Google Scholar 

  21. Nathan, R.J., and Weinmann, P.E., Application of at-Site and Regional Flood Frequency Analysis, Proc. Int. Hydrology and Water Resources Symp., Australia: Inst. of Engineers, 1991, pp. 769–774.

    Google Scholar 

  22. Pearson, C.P., New Zealand Regional Flood Frequency Analysis Using L-moments, J. Hydrology, 1991, vol. 30, no. 2, pp. 53–63.

    Google Scholar 

  23. Pickands, J., Statistical Inference Using Extreme Order Statistics, The Annals of Statistics, 1975, vol. 3, no. 1, pp. 119–131.

    Article  Google Scholar 

  24. Pilon, P.J. and Adamowski, K., The Value of Regional Information To Flood Frequency Analysis Using the Method of L-moments, Canad. J. Civil Engineering, 1992, no. 19, pp. 137–147.

  25. Rao, A.R., and Hamed, K.H., Regional Frequency Analysis of Wabash River Flood Data By L-moments, J. Hydrologic Engineering, 1997, vol. 2,Iss. 4, pp. 169–179.

    Article  Google Scholar 

  26. Turcotte, D.L., Modelling Geomorphic Processes, Physica D: Non-linear Phenomena, 1994, vol. 77, nos. 1—4, pp. 229–237.

    Article  Google Scholar 

  27. Vogel, R.M., McMahon, T.A., and Chiew, F.H.S., Floodflow Frequency Model Selection in Australia, J. Hydrology, 1993, vol. 146, pp. 421–449.

    Article  Google Scholar 

  28. Vogel, R.M., Thomas Jr.W.O., and McMahon, T.A., Flood Flow Frequency Model Selection in Southwestern United States, J. Water Resources Planning and Management, 1993, vol. 119,Iss. 3, pp. 353–366.

    Article  Google Scholar 

  29. Vogel, R.M., and Wilson, I., Probability Distribution of Annual Maximum, Mean, and Minimum Streamflows in the United States, J. Hydrologic Engineering, 1996, vol. 1,Iss. 4, pp. 69–76.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Pacific Institute of Geography, Far Eastern Branch, Russian Academy of Sciences, ul. Radio 7, Vladivostok, 690041, Russia

    T. S. Gubareva

Authors
  1. T. S. Gubareva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. S. Gubareva.

Additional information

Original Russian Text © T.S. Gubareva, 2010, published in Geoekologiya, 2010, No. 5, pp. 446–457.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gubareva, T.S. Types of probability distributions in the evaluation of extreme floods. Water Resour 38, 962–971 (2011). https://doi.org/10.1134/S0097807811070074

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0097807811070074

Keywords

Search

Navigation