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Workshop Statistical Extremes and Environmental Risk Faculty of Sciences University of Lisbon, Portugal February 15-17, PowerPoint Presentation
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Workshop Statistical Extremes and Environmental Risk Faculty of Sciences University of Lisbon, Portugal February 15-17,

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  1. Quantitative Methods for Flood Risk Management P.H.A.J.M. van Gelder $$ Faculty of Civil Engineering and Geosciences, Delft University of Technology THE NETHERLANDS Workshop Statistical Extremes and Environmental Risk Faculty of Sciences University of Lisbon, Portugal February 15-17, 2007

  2. Contents • Introduction • Extreme Value Statistics • Types of Uncertainties • Effect of Uncertainties on design • Case study • Conclusions

  3. Introduction • Events with small probabilities and large consequences • Estimating the quantiles of the order of 1/100 - 1/10,000 years of: • water levels • river discharges • precipitation levels • etc.

  4. “Staatscommissie voor den Waterweg, 1920

  5. Striking observations • Design of breakwater • ML estimate of 1/100 year quantile is below the largest observation during a 10 year period (see figure) • Optimal decision-making from which viewpoint?

  6. Threshold selection • 1/10,000 year quantiles of sea levels at Hook of Holland with 2 parameter estimation methods for GPA distribution

  7. River Meuse discharges (1/1250 years quantile)

  8. Homogeneity of datasets (generated by the same process?)

  9. Wave heights at Karwar India

  10. Karwar

  11. Karwar

  12. Extreme Value StatisticsMany available methods Moments Least Squares Maximum Likelihood L-Moments Minimum Entropy Bayesian all refined mathematics

  13. Lack of data • N = 101 – 102 observations • RP = 102 – 103 – 104 years • Homogeneity • Stationarity

  14. Not only mathematics, but physical insight • Discharge = water content x orographic x synoptic (Klemes, 1993) • Storm surge = tide + wind setup • Joint distribution of waves and storm surges (Vrijling, 1980)

  15. Still extrapolation with huge uncertainty • wait for more data; • postpone the constructions of the port, sea defence, or dam • the most rational way to decide on the size of the structure under uncertainties

  16. If we see the design as a decision problem under uncertainty, there are more uncertainties • extrapolation uncertainty • model uncertainty • uncertainty of the resistance • ...

  17. Types of Uncertainties

  18. Z = R – S – U ; • R: Resistance • S: Loads • U: Uncertainty

  19. Probability Distributions of 

  20. Policy Implications • Three Possible Reactions • 1 Accept the difference and do nothing. • 2 Heighten the dikes in order to lower the ‘new’ probability of flooding to the ‘old’ value. • 3 Reduce some uncertainties by research before deciding on the heightening of the dikes to the optimal probability of flooding.

  21. Case study • Lake IJssel • 1200 km2 • very shallow • steep waves

  22. Physical and reliability model • Wave run-up z2% (Van der Meer) • Wind surge  (Brettschneider) • Reliability function: • Z = K - M -  - z2% • Crest Level K • Lake Level M

  23. Uncertainties • Intrinsic • Lake Level • Wind Speed • Statistical • Lake Level • Wind Speed • Model • Surge • Oscillations • Significant wave height • Wave steepness • Wave run-up

  24. FORM Results of Rott. Hoek

  25. Contributions of Uncertaintiesat Rotterdamsche Hoek

  26. Rotterdamsche Hoek

  27. Reliability-based Optimization‘improve’ or ‘postpone’

  28. CONCLUSIONS • Extreme value theory in the most refined form is less fruitful • The limited amount of data and the various sources of uncertainty have to be seen in the context of the design decision • All uncertainties have to be taken into account in the design decision

  29. Conclusions • A method to get insight in the effect of uncertainty in hydraulic engineering problems is described. • The most influential random variables are generally the ones with inherent uncertainty (this uncertainty cannot be reduced).

  30. Conclusions • In case of exponential distribution + normal uncertainties, a simple expression for the economic optimal probability of failure can be derived • Larger location parameter leads to higher optimal design, but has no influence on the optimal probability of failure • Larger scale parameter leads to smaller optimal design and higher probability of failure

  31. Conclusions • More options than structural • reduce uncertainty by data collection or research • decrease loads (μ down or σ down) • increase resistance (μ up or σ down) • reduce damage in case of failure • Economic optimal decisions should be proposed for the height as well as the timing of the improvement