Uncertainty analysis for strategic decision making in the Thames Estuary

1. 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

2. Contents • 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

3. 1953 slide

4. Bondi slide

6. The existing flood defence system

7. Thames Estuary 2100

8. 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 .

9. 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

10. 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.

11. The flood risk calculation In order to estimate flood risks it is necessary to be able to: • Estimate probability distributions, f(xt), for the sources of • Relate given values of loading variables to probabilities of flooding at locations where flooding may cause damage. • Calculate the damage that is caused by floods of a given severity. Steps 2 and 3 are together contained in

12. The flood risk calculation in the Thames Estuary • 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

13. Dealing with uncertainty 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.

14. Some examples of epistemic uncertainties: Extracts from the Thames Estuary uncertainty inventory

15. Quantification of uncertainties

16. Probabilistic treatment of epistemic uncertainties: Distribution of EAD in the Thames Estuary

17. Spatial analysis of uncertainties CV of EAD estimate (2005)

18. 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 Xias The sensitivity index Iirepresents the fractional contribution of a given factor Xi to the total variance:

19. First order sensitivity indices

20. Some examples of uncertainties in future changes : Extracts from the Thames Estuary uncertainty inventory

21. Uncertainties: sea level rise

22. Uncertainties: projected changes in storm surges from the UK Met Office Hadley Centre

23. Uncertainties: socio-economic change

24. Uncertainties: socio-economic change Economic forecasts (5 sectors) Economics Scenarios Road London geography: 633 admin zones Land-use Spatial Interaction Model Rail Population socio-economic Type Transport Scenarios 633 zones: Population and employment Light rail and trams Bus Population to Land-use Planning Scenarios Underground 100m grid of landuse change

25. Scenarios of economic change from the Cambridge MDM model

26. Future land use change and vulnerability

27. New development (2020, Low Economic Scenario, PDL desirable) Current Development

28. New development (2020, High Economic Scenario, PDL desirable)

30. 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.

31. Climate change V Hi Hi ũ Med Low 1% 2% 3% Economic growth p.a. Info-gap analysis • 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  Ben-Haim, Y.,“Information-Gap Decision Theory: Decisions Under Severe Uncertainty”, 2nd Edition, Wiley, New York, (2006).

32. Demonstration site: Dartford to Gravesend

33. Flood defence options • 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.

34. Performance criterion R(di,u): reward associated with option diand 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

35. 35

36. Info-gap uncertainty model • 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

37. Info-gap uncertainty model

38. Robustness curves . .

40. Opportunity curves

41. 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

42. Conclusions • 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

43. jim.hall@ncl.ac.uk http://www.ceg.ncl.ac.uk/profiles2/njh57 http://www.tyndall.ac.uk/