Share This Article:

On Return Periodof the Largest Historical Flood

Abstract Full-Text HTML Download Download as PDF (Size:421KB) PP. 144-152
DOI: 10.4236/gep.2014.23019    2,870 Downloads   3,854 Views   Citations

ABSTRACT

The use of nonsystematic flood data for statistical purposes depends on reliability of assessment both flood magnitudes and their return period. The earliest known extreme flood year is usually the beginning of the historical record. Even though the magnitudes of historic floods are properly assessed, a problem of their retun periods remains unsolved. Only largest flood (XM) is known during whole historical period and its occurrence carves the mark of the beginning of the historical period and defines its length (L). So, it is a common practice of using the earliest known flood year as the beginning of the record. It means that the L value selected is an empirical estimate of the lower bound on the effective historical length M. The estimation of the return period of XM based on its occurrence, i.e. , gives the severe upward bias. Problem is to estimate the time period (M) representative of the largest observed flood XM. From the discrete uniform distribution with support of the probability of the L position of XM one gets  which has been taken as the return period of XM and as the effective historical record length. The efficiency of using the largest historical flood (XM) for large quantile estimation (i.e. one with return period T = 100 years) has been assessed using maximum likelihood (ML) method with various length of systematic record (N) and various estimates of historical period length  com- paring accuracy with the case when only systematic records alone (N) are used. The i-th simula- tion procedure incorporates systematic record and one largest historic flood (XMi) in the period M which appeared in the Li year backward from the end of historical period. The simulation result for selected distributions, values of their parameters, different N and M values are presented in terms of bias (B) and root mean square error (RMSE) of the quantile of interest and widely discussed.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Strupczewski, W. , Kochanek, K. and Bogdanowicz, E. (2014) On Return Periodof the Largest Historical Flood. Journal of Geoscience and Environment Protection, 2, 144-152. doi: 10.4236/gep.2014.23019.

References

[1] Benson, M. A. (1950). Use of Historical Data in Flood-Frequency Analysis. EOS Transaction on AGU, 31, 419-424. http://dx.doi.org/10.1029/TR031i003p00419
[2] Bernieur, I., Miquel, J., Lebosse, A., & Griffet, A. (1986). Use of Additional Historical Information for Estimation and Goodness of Fit of Flood Frequency Model. Int. Symp. On Flood Frequency and Risk Analysis, L.S.U., Baton Rouge, 14-17 May 1986.
[3] Cohn, T. A. (1986). Flood Frequency Analysis with Historical Information. Ph.D. Thesis, Cornell University.
[4] Dalrymple, T. (1960). Flood Frequency Analysis. U.S. Geol. Surv. Water Supply Pap., 1543-A.
[5] Frances, F., Salas, J. D., & Boes, D. C. (1994). Flood Frequency Analysis with Systematic and Historical or Paleoflood Data Based on the Two-Parameter General Extreme Value Models. Water Resources Research, 30, 1653-1664. http://dx.doi.org/10.1029/94WR00154
[6] Girgu?, R., & Strupczewski, W. (1965). Excerpts from the Historical Sources Dealing with Extraordinary Hydro-Meteorological Phenomena on the Polish Territories from X-XVI c. Instr. i Podr., 87, 216 (in Polish).
[7] Hirsch, R. M. (1985). Probability Plotting Positions for Flood Records with Historical Information. China Bilateral Symposium on the Analysis of Extraordinary Flood Events, Nanjing, 21-23 October 1985. http://dx.doi.org/10.1029/WR023i004p00715
[8] Hirsch, R. M., & Stedinger, J. R. (1987). Plotting Positions for Historical Floods and Their Precision. Water Resources Research, 23, 715-727. http://dx.doi.org/10.1029/WR022i004p00543
[9] Hosking, J. R. M. and Wallis, J. R. (1986). Paleoflood Hydrology and Flood Frequency Analysis. Water Resources Research, 22, 543-550.
[10] Interagency Advisory Committee on Water Data (IACWD) and U.S. Water Research Council Hydrology Committee (1982). Guidelines for Determining Flood Flow Frequency. Bull 17B, (Revised) Hydrol Subcomm, Office of Water Data Coord., U.S. Geol. Surv., Reston, Va.U.S. Gov. Print. Off. Washington D.C.
[11] Natural Environment Research Council (NERC) (1975). Flood Studies Report. Vol. 1, London.
[12] Naulet, R., Lang, M., Ouarda, T. B. M. J., Coeur, D., Bobee, B., Recking, A., & Moussay, D. (2005). Flood Frequency Analysis on the Ardèche River Using French Documentary Sources from the Last Two Centuries. Journal of Hydrology, 313, 58-78. http://dx.doi.org/10.1016/j.jhydrol.2005.02.011
[13] Stedinger, J. R. and Cohn, T. A. (1986). Flood Frequency Analysis with Historical and Paleoflood Information. Water Resources Research, 22, 785-793. http://dx.doi.org/10.1029/WR022i005p00785
[14] Stedinger, J. R., & Baker, V. R. (1987). Surface Water Hydrology: Historical and Paleoflood Information. Review of Geophysics, 25, 119-124. http://dx.doi.org/10.1029/RG025i002p00119
[15] Strupczewski, W. G., Singh, V. P., & Weglarczyk, S. (2002a). Asymptotic Bias of Estimation Methods Caused by the Assumption of False Probability Distribution. Journal of Hydrology, 258, 122-148. http://dx.doi.org/10.1016/S0022-1694(01)00563-7
[16] Strupczewski, W. G., W?glarczyk, S., & Singh, V. P. (2002b). Model Error in Flood Frequency Estimation. Acta Geophysica Polonica, 50, 279-319.
[17] Wang, S. X., & Adams, B. J. (1984). Parameter Estimation in Flood Frequency Analysis. Publ. 84-02. Dep. Of Civ. Eng., Univ. of Toronto.
[18] W?glarczyk, S., Strupczewski, W. G., & Singh, V. P. (2002). A Note on the Applicability of log-Gumbel and log-Logistic Probability Distributions in Hydrological Analyses: II. Hydrological Sciences Journal, 47, 123-137. http://dx.doi.org/10.1080/02626660209492912
[19] Zhang, Y. (1982). Plotting Positions of Annual Flood Extrems Considering Extraordinary Values. Water Resources Research, 18, 859-864. http://dx.doi.org/10.1029/WR018i004p00859
[20] Zhang, Y. (1985). On the Role and Treatment of Outliers in Probability Estimation Method of Flood Frequency Analysis. China Bilateral Symposium on the Analysis of Extraordinary Flood Event, Nanjing, 21-25 October 1985.

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.