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
Contents • Introduction • Extreme Value Statistics • Types of Uncertainties • Effect of Uncertainties on design • Case study • Conclusions
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.
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?
Threshold selection • 1/10,000 year quantiles of sea levels at Hook of Holland with 2 parameter estimation methods for GPA distribution
Extreme Value StatisticsMany available methods Moments Least Squares Maximum Likelihood L-Moments Minimum Entropy Bayesian all refined mathematics
Lack of data • N = 101 – 102 observations • RP = 102 – 103 – 104 years • Homogeneity • Stationarity
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)
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
If we see the design as a decision problem under uncertainty, there are more uncertainties • extrapolation uncertainty • model uncertainty • uncertainty of the resistance • ...
Z = R – S – U ; • R: Resistance • S: Loads • U: Uncertainty
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.
Case study • Lake IJssel • 1200 km2 • very shallow • steep waves
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
Uncertainties • Intrinsic • Lake Level • Wind Speed • Statistical • Lake Level • Wind Speed • Model • Surge • Oscillations • Significant wave height • Wave steepness • Wave run-up
Reliability-based Optimization‘improve’ or ‘postpone’
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
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).
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
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