Quantitative Methods for Flood Risk Management P.H.A.J.M. van Gelder $ $ Faculty of Civil...
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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
Quantitative Methods for Flood Risk Management P.H.A.J.M. van Gelder $ $ Faculty of Civil Engineering and Geosciences, Delft University of Technology THE
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
Slide 2
Contents Introduction Extreme Value Statistics Types of
Uncertainties Effect of Uncertainties on design Case study
Conclusions
Slide 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.
Slide 4
Staatscommissie voor den Waterweg, 1920
Slide 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?
Slide 6
Slide 7
Threshold selection 1/10,000 year quantiles of sea levels at
Hook of Holland with 2 parameter estimation methods for GPA
distribution
Slide 8
River Meuse discharges (1/1250 years quantile)
Slide 9
Homogeneity of datasets (generated by the same process?)
Slide 10
Wave heights at Karwar India
Slide 11
Karwar
Slide 12
Slide 13
Extreme Value Statistics Many available methods Moments Least
Squares Maximum Likelihood L-Moments Minimum Entropy Bayesian all
refined mathematics
Slide 14
Lack of data N = 10 1 10 2 observations RP = 10 2 10 3 10 4
years Homogeneity Stationarity
Slide 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)
Slide 16
Slide 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
Slide 18
If we see the design as a decision problem under uncertainty,
there are more uncertainties extrapolation uncertainty model
uncertainty uncertainty of the resistance ...
Slide 19
Types of Uncertainties
Slide 20
Z = R S U ; R: Resistance S: Loads U: Uncertainty
Slide 21
Probability Distributions of
Slide 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.
Slide 23
Case study Lake IJssel 1200 km 2 very shallow steep waves
Slide 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
Slide 25
Uncertainties Intrinsic Lake Level Wind Speed Statistical Lake
Level Wind Speed Model Surge Oscillations Significant wave height
Wave steepness Wave run-up
Slide 26
FORM Results of Rott. Hoek
Slide 27
Contributions of Uncertainties at Rotterdamsche Hoek
Slide 28
Rotterdamsche Hoek
Slide 29
Reliability-based Optimization improve or postpone
Slide 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
Slide 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).
Slide 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
Slide 33
Conclusions More options than structural reduce uncertainty by
data collection or research decrease loads ( down or down) increase
resistance ( up or down) reduce damage in case of failure Economic
optimal decisions should be proposed for the height as well as the
timing of the improvement
