Skip to main content
SpringerLink
Log in

Uncertainty analysis in statistical modeling of extreme hydrological events

  • Original Paper
  • Published:
Stochastic Environmental Research and Risk Assessment Aims and scope Submit manuscript

Abstract

With the increase of both magnitude and frequency of hydrological extreme events such as drought and flooding, the significance of adequately modeling hydrological extreme events is fully recognized. Estimation of extreme rainfall/flood for various return periods is of prime importance for hydrological design or risk assessment. However, due to knowledge and data limitation, uncertainty involved in extrapolating beyond available data is huge. In this paper, different sources of uncertainty in statistical modeling of extreme hydrological events are studied in a systematic way. This is done by focusing on several key uncertainty sources using three different case studies. The chosen case studies highlight a number of projects where there have been questions regarding the uncertainty in extreme rainfall/flood estimation. The results show that the uncertainty originated from the methodology is the largest and could be >40% for a return period of 200 years, while the uncertainty caused by ignoring the dependence among multiple hydrological variables seems the smallest. In the end, it is highly recommended that uncertainty in modeling extreme hydrological events be fully recognized and incorporated into a formal hydrological extreme analysis.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Beguería S (2005) Uncertainties in partial duration series modelling of extremes related to the choice of the threshold value. J Hydrol 303:215–230

    Article  Google Scholar 

  • Beirlant J, Goegebeur Y, Teugels J, Segers J (2004) Statistics of extremes, theory and applications. Wiley, England

    Book  Google Scholar 

  • Bernardara P, Schertzer D, Sauquet E, Tchiguirinskaia I, Lang M (2008) The flood probability distribution tail: how heavy is it? Stoch Environ Res Risk Assess 22:107–122

    Article  Google Scholar 

  • Booij MJ (2005) Impact of climate change on river flooding assessed with different spatial model resolutions. J Hydrol 303:176–198

    Article  Google Scholar 

  • Coles SG, Pauli F (2002) Models and inference for uncertainty in extremal dependence. Biometrika 89:183–196

    Article  Google Scholar 

  • Coles SG, Pericchi LR (2003) Anticipating catastrophes through extreme value modeling. Appl Stat 52:405–416

    Google Scholar 

  • Cui Y, Chen YS, Zhang L, Huang Y (2008) Hydrometric technology and development in China. In: Proceedings of symposium SK, Hydrometry China, February, 2008

  • Drees H, Kaufmann E (1998) Selecting the optimal sample fraction in univariate extreme value estimation. Stoch Process Appl 75:149–172

    Article  Google Scholar 

  • Genest C, Favre AC (2007) Everything you always wanted to know about copula modeling but were afraid to ask. J Hydrol Eng 12:347–368

    Article  Google Scholar 

  • Giupponi C (2007) Decision support systems for implementing the European Water Framework Directive: the MULINO approach. Environ Modell Softw 22:248–258

    Article  Google Scholar 

  • Goldstein J, Mirza M, Etkin D, Milton J (2003) Hydrologic assessment: application of extreme value theory for climate extreme scenarios construction. In: 14th symposium on global change and climate variations, California

  • Grimaldi S, Serinaldi F (2006) Asymmetric copula in multivariate flood frequency analysis. Adv Water Resour 29:1155–1167

    Article  Google Scholar 

  • Hadiani MO, Ebadi AG (2007) The role of land use changing in uncertainty of design flood of hydraulic Structures (the case study about Madarsoo Watershed Basin). World Appl Sci J 2(2):136–141

    Google Scholar 

  • Harremoës P, Mikkelsen PS (1995) Properties of extreme point rainfall I: results from a rain gauge system in Denmark. Atmos Res 37:277–286

    Article  Google Scholar 

  • Hill BM (1975) A simple general approach to inference about the tail of a distribution. Ann Stat 3:1163–1174

    Article  Google Scholar 

  • Hosking JRM, Wallis JR (1997) Regional frequency analysis: an approach based on L-moments. Cambridge University Press, New York

    Book  Google Scholar 

  • IPCC (2002) Workshop on changes in extreme weather and climate events. Workshop report, Beijing, China, 11–13 June, 2002, p 107

  • Jakeman AJ, Letcher RA, Norton JP (2006) Ten iterative steps in development and evaluation of environmental models. Environ Modell Softw 21:602–614

    Article  Google Scholar 

  • Kjeldsen TR, Jones DA (2004) Sampling variance of flood quantiles from the generalized logistic distribution estimated using the method of L-moments. Hydrol Earth Syst Sci 8(2):183–190

    Article  Google Scholar 

  • Klemes V (1993) Probability of extreme hydro meteorological events–a different approach. In: Kundzewicz ZW, Rosbjerg D, Simonovic SP, Takeuchi K (eds) Extreme hydrological events: precipitation, floods and droughts. IAHS Publication No. 213, New Zealand, pp 167–176

  • Klemes V (2000) Tall tales about tails of hydrological distributions. I. J Hydrol Eng 5(3):227–231

    Article  Google Scholar 

  • McNeil AJ (1997) Estimating the tail of loss severity distributions using extreme value theory. ASTIN Bull 27:117–137

    Article  Google Scholar 

  • Mendoza FJ, Izquierdo AG (2008) Environmental risk index: a tool to assess the safety of dams for leachate. J Hazard Mater 162(1):1–9

    Google Scholar 

  • Mikhailov VN, Morozov VN, Cheroy NI, Mikhailova MV, Zav’yalova YF (2008) Extreme flood on the Danube River in 2006. Russ Meteorol Hydrol 33(1):48–54

    Google Scholar 

  • Mueller DS, Abad JD, García CM, Gartner JW, García MH, Oberg KA (2007) Errors in Acoustic Doppler Profiler Velocity Measurements caused by flow disturbance. J Hydraul Eng 133(12):1411–1420

    Article  Google Scholar 

  • MWR (The Ministry of Water Resources of the People’s Republic of China) (2006) Regulation for calculating design flood of water resources and hydropower projects. China Water Power Press, Beijing, SL 44-2006

  • Nadarajah S (2003) Extreme value theory, models and simulation. In: Shanbhag DN, Rao CR (eds) Handbook of statistics 21: stochastic processes: modeling and simulation. Elsevier Science BV, Amsterdam

    Google Scholar 

  • Negrín MA, Vázquez-Polo FJ (2008) Incorporating model uncertainty in cost-effectiveness analysis: a Bayesian model averaging approach. J Health Econ 27(5):1250–1259

    Article  Google Scholar 

  • Nelsen RB (2006) An introduction to copulas. Springer, New York

    Google Scholar 

  • Pandey G, Lovejoy S, Schertzer D (1998) Multifractal analysis of daily river flows including extremes for basins of five to two million square kilometers, one day to 75 years. J Hydrol 208:62–81

    Article  Google Scholar 

  • Pandey MD, Van Gelder PHAJM, Vrijling JK (2004) Dutch case studies of the estimation of extreme quantiles and associated uncertainty by bootstrap simulations. Environmetrics 15:687–699

    Article  Google Scholar 

  • Parent E, Bernier J (2003) Bayesian POT modeling for historical data. J Hydrol 274:95–108

    Article  Google Scholar 

  • Rachev ST (2003) Handbook of heavy tailed distributions in finance (Handbooks in finance). Elsevier, North Holland

    Google Scholar 

  • Renard B, Lang M (2007) Use of a Gaussian copula for multivariate extreme value analysis: some case studies in hydrology. Adv Water Resour 30:897–912

    Article  Google Scholar 

  • Schlüter M, Rüger N (2007) Application of a GIS-based simulation tool to illustrate implications of uncertainties for water management in the Amudarya river delta. Environ Modell Softw 22:158–166

    Article  Google Scholar 

  • Shiau JT (2003) Return period of bivariate distributed extreme hydrological events. Stoch Environ Res Risk Assess 17:42–57

    Article  Google Scholar 

  • Shiau JT, Feng S, Nadarajah S (2007) Assessment of hydrological droughts for the Yellow River, China, using copulas. Hydrol Process 21:2157–2163

    Article  Google Scholar 

  • Shiklomanov AI, Yakovleva TI, Lammers RB, Karasev IP, Vörösmarty CJ, Linder E (2006) Cold region river discharge uncertainty-estimates from large Russian rivers. J Hydrol 326:231–256

    Article  Google Scholar 

  • Singh VP, Zhang L (2007) IDF curves using the Frank Archimedean copula. J Hydrol Eng 12(6):651–662

    Article  Google Scholar 

  • Sivakumar B (2001) Is a chaotic multi-fractal approach for rainfall possible? Hydrol Process 15(6):943–955

    Article  Google Scholar 

  • Sivakumar B, Sharma A (2008) A cascade approach to continuous rainfall data generation at point locations. Stoch Environ Res Risk Assess 22:451–459

    Article  Google Scholar 

  • Tung YK, Yen BC, Melching CS (2005) Hydrosystems engineering reliability assessment and risk analysis. McGraw-Hill, New York

    Google Scholar 

  • Turner DP, Dodson R, Marks D (1996) Comparison of alternative spatial resolutions in the application of a spatially distributed biogeochemical model over complex terrain. Ecol Modell 90(1):53–67

    Article  CAS  Google Scholar 

  • Van Asselt MBA (2000) Perspectives on uncertainty and risk: the PRIMA approach to decision support. Kluwer, Dordrecht, The Netherlands

    Google Scholar 

  • Vreugdenhil CB (2002) Accuracy and reliability of numerical river models. J Am Water Resour Assoc 38(4):1083–1095

    Article  Google Scholar 

  • Walker WE, Harremoes P, Rotmans J, Van de Sluis JP, Van Asselt MBA, Janssen P, Krayer von Krauss MP (2003) Defining uncertainty, a conceptual basis for uncertainty management in model-based decision support. Integr Assess 4(1):5–17

    Article  Google Scholar 

  • Wang GA (1999) Principles and methods of PMP/PMF calculations. China Water Power Press, Beijing (in Chinese)

    Google Scholar 

  • Wasserman L (2000) Bayesian model selection and model averaging. J Math Psychol 44:92–107

    Article  Google Scholar 

  • Williems P, Guillou A, Beirlant J (2007) Bias correction in hydrologic GPD based extreme value analysis by means of a slowly varying function. J Hydrol 338:221–236

    Article  Google Scholar 

  • Wilson EB, Hilferty MM (1931) The distribution of chi-square. Proc Natl Acad Sci U S A 17:684–688

    Article  CAS  Google Scholar 

  • Xu YP, Booij MJ (2007) Propagation of discharge uncertainty in a flood damage model for the Meuse River. In: Begum S, Hall J, Stivem M (eds) Flood risk management in Europe: innovation in policy and practice (Advances in natural and technological hazards research series). Kluwer, Dordrecht

    Google Scholar 

  • Yen BC, Cheng ST, Melching CS (1986) First order reliability analysis. In: Yen BC (ed) Stochastic and risk analysis in hydraulic engineering. Water Resources Publications, Littleton

    Google Scholar 

  • Zhang L, Singh VP (2006) Bivariate flood frequency analysis using the copula method. J Hydrol Eng 11:150–164

    Article  Google Scholar 

Download references

Acknowledgements

This paper has been produced with the support of the Chinese National Nature Science Foundation ‘Uncertainties in Hydrological Extreme Analysis and their impact on flood risk assessment’ (Project No. 50809058) and Zhejiang Provincial Natural Science Foundation of China ‘Design Flood Estimation for Ungauged River Basins’ (No. Y507071). The authors would like to thank Rijkswaterstraat in the Netherlands for providing data for the first case study and Prof. Y. K. Tung from Hong Kong University of Science and Technology for providing data for the third case study.

Author information

Authors and Affiliations

  1. Institute of Hydrology and Water Resources, Department of Civil Engineering, Zhejiang University, Hangzhou, 310058, China

    Yue-Ping Xu & Yang-Bin Tong

  2. Water Engineering and Management, Faculty of Engineering, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Martijn J. Booij

Authors
  1. Yue-Ping Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martijn J. Booij
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yang-Bin Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yue-Ping Xu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, YP., Booij, M.J. & Tong, YB. Uncertainty analysis in statistical modeling of extreme hydrological events. Stoch Environ Res Risk Assess 24, 567–578 (2010). https://doi.org/10.1007/s00477-009-0337-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00477-009-0337-8

Keywords

Search

Navigation