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Uncertainty analysis for strategic decision
making in the Thames Estuary
Jim Hall
Tyndall Centre for Climate Change Research
School of Civil Engineering and Geosciences
Newcastle University
Contents
1.
2.
3.
4.
5.
6.
7.
Background to the Thames Estuary 2100 project
Risk-based flood management decisions
The flood risk calculation in the Thames Estuary
Sources and implications of uncertainty
Uncertainties in climate change scenarios
Uncertainties in socio-economic change
Robust decision making under severe uncertainty
1953 slide
Bondi slide
The existing flood defence system
10
Thames Barrier
Teddington Richmond
Southend
9
8
North bank defence
Spring tide (aprox)
6
1000-year RP
10000-year RP
5
No closure
South bank defence
Spring tide (aprox)
1000-year RP
4
10000-year RP
1000-year RP: design
3
10000-year RP: design
2
1
F1
T1
T3
T2
0
0
5
10
15
20
25
30
35
40
45
50
55
60
65
Distance from Teddington (km)
70
75
80
85
90
95
100
Closure
Water Level (m AOD)
7
Thames Estuary 2100
The decision problem
A set of decision options or ‘acts’
A set of future states of nature
Depending on which state of nature in fact materialises, act di will
yield one of m possible outcomes
The net value associated with a given decision outcome yi,j can be
written as a scalar function
Decision making under certainty: The state of nature after the
decision is known i.e. m = 1. The decision maker chooses the
option with the highest value
Decision making under risk: Only the probabilities
are known. Choose the
option that maximises:
Decision making under uncertainty: There is no information about
the probabilities of states of nature .
The flood risk estimation
The state of the flooding system will be described by a vector of
continuous variables
The expected value of a given flood risk management option is:
Typically the quantities in yi(x) will extend though time, so it is
necessary to establish a method of aggregating a stream of
annual payments or losses
In any given year, t, the risk ri,t is given by
where
is a damage function
The flood risk management decision problem
The Present Value risk is:
In the case of purely economic decision making, commonplace
decision criteria are Net Present Value (NPV) and Benefit Cost
Ratio (BCR) in which case it is necessary to introduce the notion
of a ‘base case’ that involves no investment.
The Present Value risk corresponding to the base case is r0 and
expected to be unacceptably high, which is why investment in risk
reduction is being contemplated.
The Net Present Value is
The Benefit-Cost Ratio is
If the preference ordering between risk reduction options is
established on the basis of NPV then if
the preference ordering is denoted
and similarly for BCR.
The flood risk calculation
In order to estimate flood risks it is necessary to be able to:
1.
Estimate probability distributions, f(xt), for the sources of
2.
Relate given values of loading variables to probabilities of
flooding at locations where flooding may cause damage.
3.
Calculate the damage that is caused by floods of a given
severity.
Steps 2 and 3 are together contained in
The flood risk calculation in the Thames Estuary
1.
2.
3.
4.
5.
Joint probability distribution of boundary conditions at Southend (water
level) and Teddington (flow at weir)
1D hydraulic model of water levels in the estuary with the Thames
Barrier open and closed
Reliability analysis of each of the dike sections
Inundation models in the floodplain
Depth-damage functions for flooded locations
Dealing with uncertainty
1.
2.
Uncertainty is significant in its potential to change preference
orderings between options
Aleatory uncertainties:
Random variability, primarily in hydraulic loading conditions at the
system boundaries.
Integrate over jpdfs to obtain expectations.
Epistemic uncertainties:
Lack of knowledge due to:
 Limited statistical samples
 Choice of statistical distribution
 Limitations of physics-based models of underlying processes
 Potential for changes in future
Exhaustive inventory and evidence gathering for epistemic uncertainties
Robustness analysis under severe uncertainties
Hall, J.W. and Solomatine, D. A framework for uncertainty
analysis in flood risk management decisions, J. River Basin
Management, 6(2) (2008): 85-98.
Some examples of epistemic uncertainties:
Extracts from the Thames Estuary uncertainty inventory
Variable or function
Sources of uncertainty
Water level at Southend (probability distribution)
Statistical uncertainties in estimating extreme tide levels
Shape of tide/surge
Single representative surge used in analysis
Discharge at Teddington (probability distribution)
Hydrological uncertainty in estimating discharge
Water level at each defence in system: f(water level at
Southend and discharge Teddington)
Tidal/river model uncertainty
Defence crest level
Scarcity/accuracy of measurements.
Probability of breaching of flood defences (conditional
probability distribution)
Scarcity of information about defences
Limitations of quantified knowledge of failure modes
Breach width (discrete values)
Scarcity of information about defence materials.
Limitations of quantified knowledge of breaching
processes
Quantification of uncertainties
8
7.5
Southend water level (mOD)
JBA
7
r-largest
6.5
JPM
RJPM
6
SRJPM
5.5
Spatial model
Approach IV
5
Jones 2008
4.5
Suggested 95% bounds
for uncertainty analysis
4
3.5
10
100
1000
Return period
10000
Probabilistic treatment of epistemic uncertainties:
Distribution of EAD in the Thames Estuary
Spatial analysis of uncertainties
CV of EAD estimate (2005)
Variance-based sensitivity analysis
Consider a model of the form Y = g(X1,…, Xk)
The total variance V in the model output Y is apportioned to all the input
factors Xi as V  Vi  Vij  Vijl  ...  V12... k
i
i j
i  j l
The sensitivity index Ii represents the fractional
contribution of a given factor Xi to the total
variance:
V
Ii 
i
V
First order sensitivity indices
0.7
0.6
S ea level ris e
0.5
S ea level
F irs t order s ens itivity index
F low increas e
F low
0.4
In-river water levels
C res t level
W eir E qn C ons t.
0.3
B reach W idth
Multiplier
F ragility
0.2
C ondition grade
RFS M
T hres hold
0.1
D epth damage
Hydrograph multiplier
0
2005
-0.1
2100
Some examples of uncertainties in future changes :
Extracts from the Thames Estuary uncertainty inventory
Drivers
Explanation
Main Uncertainties
Relative sea
level
Increases in mean sea level due to climate change.
Uplift/subsidence of land.
GCM predictions of mean and local sea level rise
Future greenhouse gas emissions
Waves
Wave height and direction
GCM predictions of wind. Downscaled wave modelling
Future greenhouse gas emissions
Surges
Temporary increases in sea level above astronomic tide level,
resulting from reduced atmospheric pressure and the action of
strong winds
GCM predictions of wind. Downscaled surge modelling
Future greenhouse gas emissions
Precipitation
Quantity, spatial distribution of rainfall and intensity. Rain/snow
proportion.
GCM predictions of rainfall. Downscaling to Thames
catchment
Future greenhouse gas emissions
Runoff and
river
conveyance
Changes in land surface (e.g. construction of impermeable
surfaces and storm water drainage systems)
Changes (including engineering changes) in river morphology
and/or vegetation that influence flood storage and flood
conveyance
Changes in land surface cover in the Thames catchment
Future engineering works in the catchment that may alter
downstream fluvial discharges
Estuarial
morphology
Changes in the nearshore seabed, shoreline and estuaries. May
be the consequence of anthropogenic activities such as
dredging, reclamation and coastal protection.
Morphological evolution in the outer and inner Thames
estuary, including magnitude of and response to human
interventions e.g. dredging.
Flood defence
systems
Changes in the condition and reliability of the flood defence
system (including fixed and moveable components).
Rates of deterioration of the flood defence system e.g.
material deterioration, settlement of embankments and
deterioration of mechanical systems
Buildings and
contents
Changes in the cost of flood damage to domestic, commercial
and other buildings and their contents
Rate of increase of domestic wealth
Vulnerability of domestic and commercial buildings and
contents
Uncertainties: sea level rise
Uncertainties: projected changes in storm surges
from the UK Met Office Hadley Centre
Uncertainties: socio-economic change
Uncertainties: socio-economic change
Economics Scenarios
London geography:
633 admin zones
Population
socio-economic
Type
Economic
forecasts
(5 sectors)
Land-use
Spatial
Interaction
Model
633 zones:
Population
and employment
Planning Scenarios
Population
to
Land-use
100m grid
of landuse
change
Road
Rail
Light rail and
trams
Bus
Underground
Transport
Scenarios
Scenarios of economic change from the
Cambridge MDM model
Future land use change and vulnerability
Current Development
New development (2020, Low Economic Scenario, PDL
New development (2020, High Economic Scenario, PDL
desirable)
Info-gap analysis for dealing with severe
uncertainties
“So as to ensure better account is taken of climate change, Defra
and the Environment Agency will produce revised guidance for
use by those implementing flood and coastal erosion risk
management measures. The revised guidance, to be finalised by
the end of 2006, will ensure that adaptability to climate change
through robust and resilient solutions becomes an
integral part of all flood and coastal erosion management
decisions.”
Making space for water - Taking forward a new Government strategy for
flood and coastal erosion risk management in England, March 2005.




A theory of robust decision
making under sever uncertainty
When probabilities are hard to
estimate
Incorporates approximate
information about the relative
magnitude of uncertainties
Can hybridise with probabilistic
representation of aleatory
uncertainties
V Hi
Climate change
Info-gap analysis
Hi

ũ
Med
Low
1%
2%
3%
Economic growth p.a.
Ben-Haim, Y.,“Information-Gap Decision Theory:
Decisions Under Severe Uncertainty”, 2nd Edition,
Wiley, New York, (2006).
Demonstration site: Dartford to Gravesend
Flood defence options
1.
2.
3.
4.
Optimising: Raise defences in 2025 to levels found to be optimal assuming an
annual rate of increase of relative mean sea level at the mouth of the Thames
consistent with current best estimates of 2100 level.
Precautionary: Raise defences in 2025 to levels found to be optimal assuming
an annual rate of increase of relative mean sea level at the mouth of the Thames
consistent with the upper bound on the IPCC range of 2100 levels.
Procrastinating: Raise defences in 2050 to levels optimal for actual sea level
rise, which is assumed to be known by the time works must begin.
Adaptive: As 3, but implement temporary works in 2025 to increase the standard
of defence.
Performance criterion
R(di,u): reward associated with option di and future conditions u
ri,y: flood risk associated with option i in year y
i = 0: base case “do nothing” option
ci,y: construction cost associated with option i in year y
N: appraisal period (years)
s: discount rate
Option
Base case
1. Raise 2025 1.4m, optimal for 0.56m mslr
2. Raise 2025 1.8m, optimal for 0.88m mslr
3. Raise 2050, optimal for actual slr
4. Raise 2050, optimal for slr, temporary works 2025
PV Damage £
1700×106
82×106
76×106
276×106
96×106
PV Cost £
57×106
65×106
24×106
36×106
NPV £
1.2×109
1.2×109
1.1×109
1.2×109
Info-gap uncertainty model
1.
2.
3.
Construction cost

Best estimate x1.6 (60% “optimism bias”)

At α=1 cost in [-14%, +220%]
Growth in flood damage potential

Foresight gives range [2.4%, 4.7%] annual growth
Sea level rise

Best regional estimate: 6.4mm/year

IPCC range (α=1) [2.1, 10.1]mm/year

Outer range of possibility (α=2) somewhere around [1.6,
22]mm/year
Info-gap uncertainty model
Robustness curves
..
Opportunity curves
FLOODrisk
The lessons
“Do something” options become less desirable at:
 Low rates of sea level rise
 Low rates of growth in vulnerability
 High cost over-runs
 Delaying to obtain better information yields more robust solutions,
but only if you can economically limit the risk in the meantime
 If you prefer to do something now, use the best estimate of sea
level rise, not a conservative estimate
The analysis is just for a sub-system: analysis of the whole system is
next.
Options are rather idealised: whole systems analysis will provide the
opportunity to explore a broader range of options

Conclusions

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
The principles of risk-based flood management decisions are well
established
Many critical uncertainties remain. These can be difficult to
quantify
Variance-based sensitivity analysis has been used to identify key
uncertainties
Systems of coupled models of long term change (e.g. climate
change, socio-economic change) are helping to understand how
flood risks may evolve in future
Info-gap decision theory is helping to identify robustness of
adaptation options under conditions of severe uncertainty
The Thames Estuary is an outstanding example of risk-based
decision making in the context of long term change
[email protected]
http://www.ceg.ncl.ac.uk/profiles2/njh57
http://www.tyndall.ac.uk/