Title: 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
1Quantitative 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
2Contents
- Introduction
- Extreme Value Statistics
- Types of Uncertainties
- Effect of Uncertainties on design
- Case study
- Conclusions
3Introduction
- 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.
4Staatscommissie voor den Waterweg, 1920
5Striking 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?
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7Threshold selection
- 1/10,000 year quantiles of sea levels at Hook of
Holland with 2 parameter estimation methods for
GPA distribution
8River Meuse discharges (1/1250 years quantile)
9Homogeneity of datasets (generated by the same
process?)
10Wave heights at Karwar India
11Karwar
12Karwar
13Extreme Value StatisticsMany available methods
- Moments
- Least Squares
- Maximum Likelihood
- L-Moments
- Minimum Entropy
- Bayesian
- all refined mathematics
14Lack of data
- N 101 102 observations
- RP 102 103 104 years
- Homogeneity
- Stationarity
15Not 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)
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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
- ...
19Types of Uncertainties
20- Z R S U
- R Resistance
- S Loads
- U Uncertainty
21Probability Distributions of ?
22Policy 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.
23Case study
- Lake IJssel
- 1200 km2
- very shallow
- steep waves
24Physical 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
25Uncertainties
- Intrinsic
- Lake Level
- Wind Speed
- Statistical
- Lake Level
- Wind Speed
- Model
- Surge
- Oscillations
- Significant wave height
- Wave steepness
- Wave run-up
26FORM Results of Rott. Hoek
27Contributions of Uncertaintiesat Rotterdamsche
Hoek
28Rotterdamsche Hoek
29Reliability-based Optimizationimprove or
postpone
30CONCLUSIONS
- 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
31Conclusions
- 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).
32Conclusions
- 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
33Conclusions
- More options than structural
- reduce uncertainty by data collection or research
- decrease loads (µ down or s down)
- increase resistance (µ up or s down)
- reduce damage in case of failure
- Economic optimal decisions should be proposed for
the height as well as the timing of the
improvement