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Risk of Extreme Events Under Nonstationary Conditions

Author

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  • J. Rolf Olsen
  • James H. Lambert
  • Yacov Y. Haimes

Abstract

The concept of the return period is widely used in the analysis of the risk of extreme events and in engineering design. For example, a levee can be designed to protect against the 100‐year flood, the flood which on average occurs once in 100 years. Use of the return period typically assumes that the probability of occurrence of an extreme event in the current or any future year is the same. However, there is evidence that potential climate change may affect the probabilities of some extreme events such as floods and droughts. In turn, this would affect the level of protection provided by the current infrastructure. For an engineering project, the risk of an extreme event in a future year could greatly exceed the average annual risk over the design life of the project. An equivalent definition of the return period under stationary conditions is the expected waiting time before failure. This paper examines how this definition can be adapted to nonstationary conditions. Designers of flood control projects should be aware that alternative definitions of the return period imply different risk under nonstationary conditions. The statistics of extremes and extreme value distributions are useful to examine extreme event risk. This paper uses a Gumbel Type I distribution to model the probability of failure under nonstationary conditions. The probability of an extreme event under nonstationary conditions depends on the rate of change of the parameters of the underlying distribution.

Suggested Citation

  • J. Rolf Olsen & James H. Lambert & Yacov Y. Haimes, 1998. "Risk of Extreme Events Under Nonstationary Conditions," Risk Analysis, John Wiley & Sons, vol. 18(4), pages 497-510, August.
  • Handle: RePEc:wly:riskan:v:18:y:1998:i:4:p:497-510
    DOI: 10.1111/j.1539-6924.1998.tb00364.x
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    Cited by:

    1. Jianzhu Li & Senming Tan, 2015. "Nonstationary Flood Frequency Analysis for Annual Flood Peak Series, Adopting Climate Indices and Check Dam Index as Covariates," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(15), pages 5533-5550, December.
    2. Ritika & Himanshu & Nawal Kishor, 2023. "Modeling of factors affecting investment behavior during the pandemic: a grey-DEMATEL approach," Journal of Financial Services Marketing, Palgrave Macmillan, vol. 28(2), pages 222-235, June.
    3. S. Parey & T. T. H. Hoang & D. Dacunha-Castelle, 2019. "Future high-temperature extremes and stationarity," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 98(3), pages 1115-1134, September.
    4. Gabi Hufschmidt & Michael Crozier, 2008. "Evolution of natural risk: analysing changing landslide hazard in Wellington, Aotearoa/New Zealand," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 45(2), pages 255-276, May.
    5. Luis Fernando Melo‐Velandia & Camilo Andrés Orozco‐Vanegas & Daniel Parra‐Amado, 2022. "Extreme weather events and high Colombian food prices: A non‐stationary extreme value approach," Agricultural Economics, International Association of Agricultural Economists, vol. 53(S1), pages 21-40, November.
    6. Lei Yan & Lihua Xiong & Qinghua Luan & Cong Jiang & Kunxia Yu & Chong-Yu Xu, 2020. "On the Applicability of the Expected Waiting Time Method in Nonstationary Flood Design," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(8), pages 2585-2601, June.
    7. Yiming Hu & Zhongmin Liang & Vijay P. Singh & Xuebin Zhang & Jun Wang & Binquan Li & Huimin Wang, 2018. "Concept of Equivalent Reliability for Estimating the Design Flood under Non-stationary Conditions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(3), pages 997-1011, February.
    8. Andrea Gioia & Maria Francesca Bruno & Vincenzo Totaro & Vito Iacobellis, 2020. "Parametric Assessment of Trend Test Power in a Changing Environment," Sustainability, MDPI, vol. 12(9), pages 1-18, May.
    9. Rongrong Li & Lihua Xiong & Xini Zha & Bin Xiong & Han Liu & Jie Chen & Ling Zeng & Wenbin Li, 2022. "Impacts of climate and reservoirs on the downstream design flood hydrograph: a case study of Yichang Station," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 113(3), pages 1803-1831, September.
    10. Jianzhu Li & Yuming Lei & Senming Tan & Colin D. Bell & Bernard A. Engel & Yixuan Wang, 2018. "Nonstationary Flood Frequency Analysis for Annual Flood Peak and Volume Series in Both Univariate and Bivariate Domain," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(13), pages 4239-4252, October.
    11. Dong-dong Zhang & Deng-hua Yan & Yi-Cheng Wang & Fan Lu & Shao-hua Liu, 2015. "GAMLSS-based nonstationary modeling of extreme precipitation in Beijing–Tianjin–Hebei region of China," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 77(2), pages 1037-1053, June.
    12. R. Gerrard & A. Tsanakas, 2011. "Failure Probability Under Parameter Uncertainty," Risk Analysis, John Wiley & Sons, vol. 31(5), pages 727-744, May.

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