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?

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

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

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

10. Wave heights at Karwar India

11. Karwar

13. Extreme Value Statistics Many available methods Moments Least Squares Maximum Likelihood L-Moments Minimum Entropy Bayesian –all refined mathematics

14. Lack of data N = 10 1 – 10 2 observations RP = 10 2 – 10 3 – 10 4 years Homogeneity Stationarity

15. 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)

17. 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

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

19. Types of Uncertainties

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

21. Probability Distributions of 

22. 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.

23. Case study Lake IJssel 1200 km 2 very shallow steep waves

24. Physical and reliability model Wave run-up z 2% (Van der Meer) Wind surge  (Brettschneider) Reliability function: – Z = K - M -  - z 2% –Crest Level K –Lake Level M

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

26. FORM Results of Rott. Hoek

27. Contributions of Uncertainties at Rotterdamsche Hoek

28. Rotterdamsche Hoek

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

30. 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

31. 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).

32. 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

33. 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