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

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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

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Contents

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

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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.

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Staatscommissie voor den Waterweg, 1920
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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?

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Threshold selection

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

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River Meuse discharges (1/1250 years quantile)
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Homogeneity of datasets (generated by the same
process?)
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Wave heights at Karwar India
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Karwar
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Karwar
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Extreme Value StatisticsMany available methods

• Moments
• Least Squares
• Maximum Likelihood
• L-Moments
• Minimum Entropy
• Bayesian
• all refined mathematics

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Lack of data

• N 101 102 observations
• RP 102 103 104 years
• Homogeneity
• Stationarity

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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)

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• 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

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

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Types of Uncertainties
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• Z R S U
• R Resistance
• S Loads
• U Uncertainty

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Probability Distributions of ?
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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.

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Case study

• Lake IJssel
• 1200 km2
• very shallow
• steep waves

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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

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Uncertainties

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

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FORM Results of Rott. Hoek
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Contributions of Uncertaintiesat Rotterdamsche
Hoek
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Rotterdamsche Hoek
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Reliability-based Optimizationimprove or
postpone
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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

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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).

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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

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Conclusions

• 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