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Assessing coastal flood risk at specific sites and regional scales: Regional assessment of coastal flood risk This is the final report from Tyndall research project T2.46.

The following researchers worked on this project: Professor Robert Nicholls, Dr Mustafa Mokrech, Dr Julie Richards (University of Southampton) Professor Paul Bates (University of Bristol) Dr Richard Dawson, Professor Jim Hall, Dr Mike Walkden (University of Newcastle upon Tyne) Dr Mark Dickson (NIWA, New Zealand) Dr Andrew Jordan (University of East Anglia) Ms. Jessica Milligan (Tyndall Centre for Climate Change Research) Technical report No 45. October 2005

‘Assessing coastal flood risk at specific sites and regional scales’

Tyndall project T2.46 Technical Report

Abstract The research project ‘Assessing coastal flood risk at specific sites and regional scales’ has undertaken an integrated assessment of erosion and flood risk for the case study area of sub-cell 3b on the Norfolk coast. This project has worked closely with Tyndall Project T2.45 ‘Towards an integrated coastal sediment dynamics and shoreline response simulator’ and has used consistent scenarios of climate change (sea-level rise, wave height and direction), management strategies (from total to no coastal protection) and socio-economic scenarios using the DTI framework. To date, this is a unique study. The major flood-prone area within sub-cell 3b is the Norfolk Broads between Eccles and Winterton. The flood risk analysis carried out further develops the RASP intermediate level approach, which produces a snapshot of flood risk, considering temporal changes in loading conditions and floodplain development. The results show that future flood risk is sensitive to a number of different parameters, including climate change, primarily the rate of sea level rise; the future socio-economic development; and the management of the coast. The management decisions made in the future on this coast determine the amount of cliff protection in place, which in turn controls the amount of sediment supplied to down-drift beaches and hence influences the magnitude of the protective beach in front of flood defence dikes. Flood inundation modelling then analyses the impact of this resultant beach volume on flood risk. The aim of this approach is to emphasise the importance of coastal management in determining future flood risk in the light of climate change.

Keywords Coastal Simulator, climate change, regional assessment, flood risk.

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Table of Contents Part 1: Overview of project work and outcomes

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Summary Aim and objectives Work undertaken Results Relevance to Tyndall Centre research strategy and overall objectives Potential for further work

4 5 5 6 7 7

Part 2: Technical report

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1.

Introduction 1.1 Study Area

9 11

2.

Socio-Economic Scenarios 2.1 Global Sustainability Socio-Economic Scenario 2.2 Local Stewardship Socio-Economic Scenario 2.3 National Enterprise Socio-Economic Scenario 2.4 World Markets Socio-Economic Scenario

12 15 16 17 19

3.

Future Property Distribution 3.1 The implementation of urbanisation policies 3.1.1 Key datasets 3.1.2 Methodology 3.2 Results and Discussion

20 21 21 21 24

4.

Coastal Flood Risk Analysis 4.1 Modelling Methodology 4.2 Statistical estimation of extreme loads 4.3 Wave and water level time series 4.4 Measuring defence performance 4.5 Description of the Sub-Cell 3b Flood Defence System 4.6 Toe erosion 4.7 Wave overtopping and overflow 4.8 Defence Breaching 4.9 Inundation Modelling 4.10 Damage Estimation 4.11 Systems reliability analysis for a discrete system 4.12 Flood Risk Results

29 30 32 34 35 36 40 41 42 42 45 45 47

5.

Further work

56

6.

Conclusions

57

7.

References

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64 8. Appendix APPENDIX A. Socio-economic Storylines and Future Scenarios, linked to the RASP/Foresight drivers. 65

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Part 1: Overview of project work and outcomes Summary In the United Kingdom (and globally), increasing coastal flood risk due to accelerated sea-level rise and increasing storminess has been identified as a major challenge for the 21st Century. On the open coast, the impacts of climate change will often be superimposed on long-term trends of increasing flood risk due to a progressive reduction in beach levels. Historically, falling beach levels in the UK have largely been a result of human intervention in the coastal zone, especially protection of sediment sources, but erosion will also be exacerbated by climate change impacts, thereby further increasing the increased flood risk. Taking sub-cell 3b from Sheringham to Lowestoft in East Anglia as a case study, and working closely with Tyndall Project T2.45 (Towards an integrated coastal sediment dynamics and shoreline response simulator) an integrated assessment of erosion and flood risk has been undertaken for this area using consistent scenarios of climate change (sea-level rise, wave height and direction), management strategies (from total to no protection) and socio-economic scenarios developed using the DTI / Foresight framework. To date, this is a unique study exploring the combined erosion and flood risk and their interactions at the scale of a sub-cell. Flooding can occur at four major sites in sub-cell 3b from Eccles to Lowestoft, with the major flood-prone areas being the Norfolk Broads between Eccles and Winterton. Offshore wave conditions are transformed to the coast, and Project T2.45 also models the height of the beach, therefore a good understanding of the loads and flood system state are available. The goal is to understand the linkages between erosion and flooding within the sub-cell; flood defence upgrade is not considered. The flood risk analysis undertaken in this project further develops the Risk Assessment of Flood and Coastal Defence for Strategic Planning (RASP) intermediate level approach (Dawson and Hall, in review). RASP produces a snapshot of flood risk, whereas this project considers temporal changes in loading conditions and floodplain development. This comprises the following six steps: • • • • • •

statistical estimation of extreme loads; calculation of defence system reliability; estimation of defence breach properties; modelling of inundation depth and extent; estimation of damage to individual properties resulting from flooding; and, estimation of socio-economic and climatic changes to the system.

Socio-economic scenarios based on the Foresight framework are also developed into future urbanisation patterns using a set of attractors and repulsors for new households and non-residential properties. In all futures, there are more buildings in the floodplain, but the rate of expansion differs between futures and therefore flood risk changes according to the socio-economic future. The results show that future flood risk is sensitive to a number of different parameters, and emphasises the importance of future coastal management in controlling the magnitude of the protective beach fronting the flood-prone coastal lowlands. 4



Further work is suggested towards a more rigorous Earth Systems Simulator of regional coastal climate and socio-economic impact assessment and application of these techniques in shoreline management planning.

Aim and objectives The aims and objectives of the project evolved as the project developed and especially as the sister project (T2.45) produced morphological simulations for the coast from Weybourne to Winterton, allowing the combined flood and erosion risk to be explored at the scale of the sub-cell for the first time. In discussion with the Tyndall Centre, the research was refocused towards this major objective. 1. To develop consistent scenarios of long-term changes that will influence coastal flooding, including climate change, changes in societal values (e.g. pro- or antigovernment involvement), systems of governance (i.e. tools of future coastal zone policy, ranging from hard engineering technologies to managed retreat), as well as the availability of financial resources for flood protection. These scenarios would draw on related projects and recommendations within the Tyndall Centre to the largest degree possible. (and was combined with T2.45 for consistency) 2. To apply a flood risk assessment methodology to sub-cell 3b (from Weybourne to Lowestoft) 3. To evaluate the impacts and resulting vulnerability given the range of flood risk defined under objective 2.

Work undertaken Project management was done by Southampton University. Flood modelling and systems analysis was undertaken by Richard Dawson and Jim Hall at the University of Newcastle upon Tyne, in collaboration with Paul Bates at the University of Bristol. Regional socio-economic scenarios for East Anglia were developed by Andy Jordan and Jessica Milligan at the University of East Anglia, in collaboration with the University of Southampton. Detailed modelling of the socio-economic scenarios for sub-cell 3b based on these results was undertaken at the University of Southampton, by Mustafa Mokrech, Julie Richards and Robert Nicholls. To ensure consistency of analysis between this project and Project T2.45 (Towards an integrated coastal sediment dynamics and shoreline response simulator), there was close liaison between both projects and agreement on common scenarios and assumptions by all project partners. This report was mainly compiled by Robert Nicholls and Julie Richards at University of Southampton, and Richard Dawson at the University of Newcastle upon Tyne.

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Results The aim of the modelling and risk analysis work described in this report is to understand how coastal flood risk might evolve on a broad spatial scale (a sub-cell) over extended timescales under a range of plausible climate, management and socio-economic scenarios. In pursuit of strategic broad scale analysis a systems model of shoreline evolution is coupled with a reliability model of dike systems. The reliability analysis is driven by joint probability distributions of loading distributions, but long term morphological predictions mediate in the analysis of dyke reliability. A rapid flood inundation model is employed to generate flood risk estimates in the hinterland. Thus, a systematic appraisal of the effects of climate change on coastal morphological systems and coastal flood risk is described. As the focus is the interactions within the sub-cell, local adaptation of the flood risk areas is not considered. This has been achieved by coupled modelling of waves, morphodynamics and flood risk over the whole of a reasonably self-contained sedimentary system (sub-cell 3b). Such a broad scale simulation can never be complete, and one important element that has not been taken into account is the effect of changing offshore bathymetry of the Norfolk Banks, and this will be the subject of future research within the coastal research question of the Tyndall Centre Phase 2. In addition, it is not possible to deal with individual processes within this interacting system in the utmost detail. However, the rationale is that by representing the main interactions determining the long term behaviour of the system, the response to changes can be simulated with some degree of confidence, whether they are due to climate change or coastal management. Coastal flood risk is a complex function of loading, dike(s) properties, floodplain topography and the geographical location and type of assets in the floodplain. A limited assessment that considers conditions most likely to result in structural failure of the defence system, or a limited number of dike failure combinations would not, in the UK floodplain considered here, have adequately captured important system behaviour. In the application of this methodology to a coastal system, the maximum risk does not correspond to the location of the maximum failure probability. However, this can be neglected for systems where the consequences are likely to be similar for all system failure states. The long term impacts on flood risk are quantified for different scenarios of climate, management or socio-economic change. The down-drift impacts of coastal management options, such as the removal of erosion protection from cliffs whose foreshores are morphologically connected to those fronting floodplains some distance away, are quantified in terms of their impact on flood risk on the neighbouring coast. In systems of this complexity the effects of climate change on flood risk may be difficult to interpret, if increased erosion of soft cliffs increases sediment supply to low-lying down-drift coasts. Broad-scale integrated modelling tools of the type described in this paper are required to understand these interactions and enable comprehensive analysis of management options, as well as engaging broader stakeholder groups through appropriate interfaces and visualisation. The results of strategic coastal management options and climate change scenarios are presented in terms of changes in expected annual flood damage. This enables direct economic evaluation of local effects of modifying coastal cliff recession

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compared with the potential broader-scale effects on flood risk. The analysis indicates that the effect of climate change on low-lying coasts is dominated by rising sea levels and broader-scale morphodynamics that may lower or raise beach levels. This research provides the tools required to support strategic shoreline management, and has attracted interest from the Environment Agency, local authorities, Department for Environment, Food and Rural Affairs, and English Nature.

Relevance to Tyndall Centre research strategy and overall objectives The research described in this paper is directed towards development of the Tyndall Centre Regional Coastal Simulator (RCS), which aims to provide a coupled suite of process models for investigation of broad scale and long term influences upon the coastal system with a view to informing long term coastal management and adaptation to climate change. This research project integrates with other Tyndall Centre coastal modelling initiatives on the East Anglian coast (for example T2.45) by contributing to the coastal change element of the ‘Integrated Regional Coastal Simulator’ flagship project of Research Theme 4. Work on this project was conducted throughout in close collaboration with Tyndall project T2.45 (Towards an integrated coastal sediment dynamics and shoreline response simulator), utilising common future climate and management scenarios, wave modelling methods and GIS platforms.

Potential for further work The research represents an important step forward, as for the first time flood risk and erosion risk (in T2.45) have been linked at an extended spatial scale (a sub-cell) across a long temporal scale (100 years). Hence for the first time, the choices and trade-offs that society faces in terms responding to these evolving hazards under climate change can be explored in quantitative terms. As this links science and application questions, the issue of further work in both aspects is considered. While an integrated assessment has been achieved and the relative importance of a range of factors can be identified, the analysis is incomplete and a number of improvements are possible and desirable. Three elements are particularly important. First, the climate scenarios could be derived directly from downscaled climate models such as the HadRM3 which was used for the UKCIP02 scenarios (Hulme et al., 2002). This would provide consistent wave and surge parameters for the future climate that are consistent with the mean sea-level rise – these could then be transformed onshore as described above. Second, an important morphological element that has been treated quite simply are the sand banks, which in sub-cell 3b have a profound effect on the coastal wave climate. There is a need to model the dynamic response of the sand banks to climate change, as well as other issues such as dredging (which in the public mind is often the biggest concern). Third, the socioeconomic scenarios are an important element in quantifying both flood (and erosion) risk. Here, the socio-economic scenarios were modelled with a set of attractor/repulsion factors and consistent trajectories in time. Modelling approaches

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to scenario development need to be further developed, and if made into an interactive form, could provide the basis for working with communities and planners in ways that could minimise future risks (e.g., land use that recognises hazardous areas). In application, the next step is to take this forward to future shoreline management planning (DEFRA, 2001). This analysis has shown that these tools are ready to provide objective scientific support to these processes which should help stakeholders understand the difficult choices that they face. There are also important links to the concept of coastal simulator and visualisation of coastal change in general.

Communication Highlights Bates, P.D., Dawson, R.J., Hall, J.W., Horritt, M., Nicholls, R.J., Wicks, J. & Hassan, M.A.A.M. (2005) Simplified two-dimensional numerical modelling of coastal flooding and example applications. Coastal Engineering 52(9):793-810 One paper presented at the International Symposium on Stochastic Hydraulics 2005, Njimegen and subsequently to be published in the conference proceedings: Dawson, R.J., Hall, J.W., Nicholls, R.J., Bates, P.D., Dickson, M.E. & Walkden, M.J.A. Efficient broad scale flood risk assessment over multi-decadal timescales, in Proc. Int. Symposium Stochastic Hydraulics, Njimegen, May 2005, in press. One paper presented at Coastal Dynamics 2005, Barcelona (along with two papers from T2.45), and subsequently to be published in the conference proceedings: Hall, J.W., Dawson, R.J., Walkden, M.J.A., Dickson, M.E., Stansby, P., Zhou J., Nicholls R., Brown I. & Watkinson A. (2005) Broad-scale analysis of morphological and climate impacts on coastal flood risk. Proceedings of Coastal Dynamics, ASCE, New York, in press. Integrated paper with T2.45, presented at LOICZ II Inaugural Open Science Meeting, Egmond aan Zee, Netherlands: Nicholls R., Brown I., Dawson R., Dickson M., Hall J., Koukoulas S., Mokrech M., Pearson S., Rees J., Richards J., Stansby P., Walkden M., Watkinson A. & Zhou J. (2005) An Integrated Assessment of Erosion and Flooding in NorthEast Norfolk, England. LOICZ II Inaugural Open Science Meeting, Egmond aan Zee, Netherlands, 27-29 June 2005. Future journal submissions will include a paper describing in detail the coastal flood risk analysis and a paper describing the integrated assessment of erosion and flood risk. A further possibility may be a paper linking the work here with other research contributing to the Regional Coastal Simulator.

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Part 2: Technical report 1.

Introduction

In the United Kingdom (and globally), increasing coastal flood risk due to increasing storminess and accelerated sea-level rise has been identified as a major challenge for the 21st Century (McLean et al., 2001; Evans et al., 2004a; 2004b; Hall et al., 2005). The recent 50th anniversary of the 1953 ‘Big Flood’ and issues such as the eastward expansion of London as part of the Thames Gateway and the need to upgrade London’s defences have also focussed attention on the issue (McRobie et al., 2005). On the open coast, the impacts of climate change will often be superimposed on long-term trends of increasing flood risk due to a progressive reduction in beach levels. Historically, falling beach levels in the UK have largely been a result of human intervention in the coastal zone, especially protection of sediment sources, but erosion will also be exacerbated by climate change impacts, thereby further increasing the increased flood risk. Although aspects of the process of coastal flooding remain poorly understood, a range of methods for predicting coastal flood risk have been developed and applied both nationally and internationally. These include the Association of British Insurers (ABI) study (Reeve, 1998), the National Appraisal of Assets at Risk (Halcrow Maritime et al., 2000), the Regional Impact Study (RegIS) (Nicholls & Wilson, 2001; Holman et al., 2005a; 2005b), and the Risk Assessment of flood and coastal defence for Strategic Planning (RASP) methods, developed by HR Wallingford, the University of Bristol and Halcrow for the Environment Agency and DEFRA (e.g., Hall et al., 2003). RASP provides a three-tiered family of flood risk assessment tools. The high level RASP method is being designed to support national monitoring and prioritisation, whilst the more detailed methods (intermediate level and detailed level) will support strategic regional planning and detailed project design and optimisation, respectively. None of these methods comprehensively addresses the changing flood risk under climate change. RASP is designed to provide a ‘snap shot’ of flood risk, while RegIS assessed the impacts of climate change, but only for a limited number of change factors (mainly sea-level rise). The high level RASP method was applied to climate change analysis within the Foresight Flood and Coastal Defence (Evans et al., 2004a; 2004b), but developing the necessary scenarios of change is a challenge when using the limited number of RASP parameters. This project has built on the knowledge developed in the RASP/Foresight and RegIS projects for comprehensive assessment of changing flood risk under coastal climate and other long-term change. The methodology provides significant improvements through the use of process-based models of morphology and inundation to better capture the influence of past and future intervention options The study area is littoral sub-cell 3b in Norfolk, with the research focusing on marine flooding driven by extreme water levels (due to storm surges) and waves. The impacts of climate change on fluvial flooding are not considered, even where fluvial flooding will influence coastal flood plains, as this is a large research task in its own right. This project has been conducted in close conjunction with the sister Tyndall Project “Towards an integrated coastal sediment dynamics and shoreline response simulator” (T2.45) (Pearson et al., 2005) which has provided detailed morphological predictions for common climate change scenarios. Within this Flood Project, detailed socio-economic scenarios of land use and development have also been developed and applied, building on the experience in the Foresight Project. Hence, collectively

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these two projects provide important insights into the future evolution of this sub-cell under different climate, socio-economic and management scenarios. An overview of the framework for integrated coastal erosion and flood risk assessment is shown in Figure 1. This report considers those aspects of the framework relevant to the flooding impacts; the erosion impacts are reported elsewhere (T2.45 final report). In turn, the research described in this report, forms only a part of the development of the Regional Coastal Simulator (RCS) in the Tyndall Centre for Climate Change research. The RCS aims to provide a coupled suite of process models for investigation of broad scale and long term influences upon the coastal system (i.e. including environmental and other impacts as well as flooding and erosion) with a view to informing long term coastal management and adaptation to climate change. The socio-economic scenarios are developed from the National DTI / Foresight framework into regional and sub-cell 3b specific scenarios. These futures are applied using a new methodology for creating future urban development. This is based on a GIS methodology which calculates new property locations using possible attractors and repulsors, such as the coastline, floodplains, existing settlements and transport links. It is represented in Figure 1 as a land use change model, which will be developed further at a later stage. The main components of the methodology that the results described in this report depend upon are: 1. wave hindcasting from wind data and statistical simulation of time series of wave heights and water levels; 2. wave transformation modelling using TOMAWAC to propagate offshore waves over a complex bathymetry to shallow water; 3. broad scale modelling of shoreline erosion and beach evolution using the SCAPE (Soft Cliff and Platform Erosion) morphological model; 4. a reliability model of the flood defence system; 5. a fast inundation model to simulate the propagation of coastal flooding; 6. a GIS to calculate the economic impacts of coastal erosion and flooding. The outputs of the analysis are estimates of shoreline erosion (and resulting loss of cliff-top properties) and flood risk. The input conditions for the integrated assessment are changed according to the socio-economic and climate assumptions made about possible futures. A number of possible futures are considered in order to capture a broad range of (realistically) possible future development and climate scenarios. The main interactions between the above components are shown in Figure 1.

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Figure 1. Conceptual diagram of the constituent components of the flood project. 1

1.1 Study Area The methodology is demonstrated using a flood analysis of littoral sub-cell 3b within East Anglia from Sheringham to Lowestoft, which includes the flood-prone coastal areas in the Norfolk Broads (from Eccles to Winterton) and smaller areas at Great Yarmouth and Lowestoft (Figure 2). East Anglia contains large areas of low-lying land such as the Fens and Broads, which were reclaimed from the sea over many centuries. Much of this land is below the level of mean high water spring tides and therefore highly susceptible to tidal flooding. The majority of this floodplain is defended along the coastline by a system of dunes, groynes and seawalls, combined with periodic beach renourishment. Extensive flooding of the Broads area within sub-cell 3b has occurred a number of times over the last 100 years, most notably in 1907, 1938 and 1953 (Mosby, 1938; Steers, 1953; Grieve, 1959).

1

It should be noted that the term model does not always imply a complex computer simulation, but is used to identify those parts of the assessment where the behaviour of the system has been abstracted, according to best available understanding, in order to make statements about likely future behaviour. For example, whilst the ‘morphology model’ is a process-based simulation, the ‘climate model’ refers to the use of established UKCIP climate predictions rather than a dynamically coupled GCM or RCM. Naturally, as our ability to better ‘model’ aspects of the coastal system grows, individual components can be upgraded. A number of these upgrades have been identified for future work in Tyndall Phase II and elsewhere.

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Eccles

Figure 2. Topographical map showing the flood risk study area (littoral sub-cell 3b). Box shows area subsequently shown in Figure 25.

2.

Socio-Economic Scenarios

In studies of this type, socio-economic scenarios provide the context in which flood management policy and practice will be enacted, and relate to the extent to which flooding may affect society (Evans et al., 2004a). Flood risk will change as socioeconomic conditions evolve, and activities in the coastal floodplain change: significant encroachment of new development in these areas has been the norm over the last 50 years. They also show that society has an important opportunity to manage impacts, as many of these changes can be controlled through appropriate policy choices (Holman & Loveland, 2001). The scenarios framework developed for the Office of Science and Technology (OST) Foresight Programme (Figure 3) has been used as a basis to produce four scenarios of the Anglian region to quantify the different risk of flooding and erosion (following Penning-Rowsell et al., 1993) with a

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particular focus on the area of Norfolk covered by the Shoreline Management Plan (SMP) sub-cell 3b. The study area is the coastline between the Humber and the Thames. The OST Foresight Futures scenarios examine alternative directions in which social, economic and technological change may evolve over the coming decades in the UK. These four worlds are described fully in “Foresight Futures 2020: Revised scenarios and guidance” (DTI, 2002). The OST Foresight scenarios have been widely used in a range of studies to assess climate change impacts (and extensively in government Foresight activities on flooding and coastal defence (Evans et al., 2004a; 2004b; http://www.foresight.gov.uk/). The scenarios allow the exploration of a set of only partially viewable alternative futures that describe “possibility space” and hence the ultimate aim of future studies is to explore future trends and potential discontinuities to inform decision-making (Berkhout & Hertin, 2002).

Figure 3. The four Foresight worlds, defined using interdependence and consumerism-community.

axes

of autonomy-

Existing trends will have a strong inertia that needs to be taken into account. According to the East of England Regional Housing Strategy (RHS) the population of East of England is expected to grow by 11.5% by 2021, with a corresponding increase in number of households by 18.5% by 2021. The figures have been adopted and extrapolated linearly to the 2030s and the 2080s for each socioeconomic future scenario. For more details of the methods used, see Appendix A. Some key future trends are given in Tables 1 and 2 for reference purposes. Note that the SCAPE morphological predictions used in this study supersede the results in Table 1. Table 1. Average future erosion over 100 years for England and Wales (from Evans et al., 2004a). Benchmark conditions 20-67m

World Markets 141-175m

National Enterprise 113-150m

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Local Stewardship 99-138m

Global Sustainability 82-123m



Table 2. Coastal indicators for the UK in the 2020s (from Berkhout et al., 2001). Today

Linear Trend 240,000 No data ha

Protected coastal zone Investment in coastal defence £200 million

£225 million

National Enterprise 235,000 ha

Local World Stewardship Markets 220,000 240,000 ha ha

Global Sustainability 225,000 ha

£230 million

£150 million

£200 million

£350 million

In the following text we explore the four socio-economic scenarios in turn. This analysis uses the different RASP/Foresight drivers for change analysis, following and hopefully improving on the Foresight analyses (Evans et al., 2004a; 2004b). This leads to a new methodology for creating scenarios based on a GIS methodology which calculates attractions or repulsions from possible attractors, such as the coast, floodplains, existing settlements and transport links. The drivers used in the analysis to determine the socio-economic futures are selected from the RASP/Foresight functional driver sets (Thorne, 2003). The functional driver sets considered are: flood and erosion management, specifically drivers of insurance and regulation; and socio-economic impacts attitudes and behaviour, characterised by individual drivers of urbanisation, infrastructure at risk, stakeholder behaviour and social impacts. The flood and erosion management driver insurance describes the payments to flood victims to compensate them for their losses and can be made by the government, charitable funds or insurance. The two components of the driver are how the compensation is funded and what the mechanism is to assess and make the payments. Both of these components may be undertaken by the government or the insurance industry, however, insurance is only possible through a public-private partnership including relevant flood management policies that need to continue to be effective for the provision of insurance to continue into the future (Thorne, 2003). The Foresight study concluded that the current UK government attitude for no compensation for victims of natural disasters is unlikely to remain under any of the four future scenarios. Regulation as a driver is the system of inducing behavioural change by a particular group of people, where incentives to induce such change may include regulations but also prices and subsidies. Radically different forms of regulation are likely under the different scenarios, for example, there will be an attempt to rely almost exclusively on environmental taxes, such as a carbon tax and other economic instruments. Urbanisation as a driver applies to the development of land and the resulting densities of development, building form and the nature of the future land use. The density of future urbanisation can significantly affect the magnitude of flood and erosion losses per unit area, which in turn justifies the amount of investment in flood and coastal defence. Infrastructure at risk includes the networks of physical services that support and enable the economy to convert materials into goods. The flooding of these networks can have consequences that occur outside of the area directly affected by flooding or erosion. As infrastructure adjustments require a large amount of capital it is expected that there will be considerable inertia to change in the future.

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Stakeholders are defined within the socio-economic functional driver set and within the Foresight scenarios (Thorne, 2003) as the individuals, groups or institutions with a direct or indirect interest in, or influence upon flood risk or coastal erosion. Their behaviour is highly interactive and driven by very different incentives. Stakeholders can influence flood risk and coastal erosion in diverse ways, from the type of agricultural practice adopted, the amount of consideration of ecological and conservation aims and pricing of insurance policies. The feedback possible between stakeholders and the interactions with other drivers means that it is difficult to predict the amount or type of influence likely. The social impact of flooding and coastal erosion driver encompasses all the impacts of flooding on households and communities that are not currently included in an economic assessment, including the risk to life, the intangible impacts in terms of health and stress, vulnerability of difference social groups and the impacts of flooding or erosion on the coherence of a community. However, what constitutes a social impact varies according to the scenario and under the World Markets scenario there are no social impacts (Thorne, 2003). A summary of the relevant drivers for each of the socio-economic scenarios is presented here; for a full description of each of the driver sets see Appendix A.

2.1 Global Sustainability Socio-Economic Scenario People aspire to high levels of welfare within communities with shared values, more equally distributed opportunities and a sound environment. There is a belief that these objectives are best achieved through active public policy and international cooperation within the European Union and at a global level. Social objectives are met though public provision, increasingly at an international level. Control of markets and people is achieved through a mixture of regulatory and norm-based mechanisms (Berkhout & Hertin, 2002). Coastal zone protection is seen from a national perspective, with East Anglia receiving a considerable amount of attention because it has such a vulnerable coastline (Shackley & Wood, 2000). There would be potentially strong local support networks and polled insurance to share costs in flood prone areas (Evans et al., 2004b). A shift to softer approaches such as realignment, energy generation and where necessary surrender of the most flood-prone areas would occur. There would be state compensation; tax credits and strong land-use planning to steer development away from flood-prone areas. Similarly to Local Stewardship, there may be scope to develop national floodplain charging schemes (Evans et al., 2004b). Under all four scenarios the potential shoreline erosion over the Anglian coastal region is classified as “extreme” in most places but as “very high” for the sub-cell 3b area (Evans et al., 2004a). However, the risk is lowest under Global Sustainability (see Table 1). There will be strict planning controls applied including managing hazards and no new floodplain or coastal development will be permitted (Holman & Loveland, 2001). There are requirements for the undertaking of compensatory actions for any negative environmental consequences and the frame of reference will be the enhancement of the functioning of the catchment or coastal zone rather than on flood or coastal defence. In general, regulators are more responsive to their perception of what stakeholders want and there is greater equity.

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This scenario proposes only small or minimal increases in population and household numbers in the Anglian coastal region and these developments will be mostly confined to existing urban areas (Holman & Loveland, 2001). Reduction in development on coasts and floodplains will arise partly through more planning and also through smaller growth in the number of households. Floodplain occupancy is kept stable under the Global Responsibility and Local Stewardship Scenarios. Flood risks will be minimised by planned retreat of coastal defences and less development on coasts and floodplains (Holman & Loveland, 2001). Due to strict development controls, housing construction is concentrated in existing urban centres and in ‘brownfield’ sites and kept away from environmentally sensitive areas (DTI, 2002). As well as the issue of urban spread the increase in the number of households may be exacerbated by a coastal attraction with a move of people from large urban areas like London to coastal regions. The focus for energy production moves away from fossil fuels to more renewable energies such as onshore and offshore wind, biomass and solar energy (DTI, 2002). Hence, two of the previous critical coastal infrastructures, Bacton Gas Terminal on the Norfolk coast and Sizewell nuclear power station near Leiston on the Suffolk coast, are no longer needed; however, Sizewell will continue to be defended due to its radioactive material, whereas Bacton is no longer defended. With regard to rail and road infrastructure there is an increased emphasis on public transport and new infrastructures may be developed. In this scenario stakeholders are more likely to respond to centralised commands and as such there are central government planning and awareness schemes linked to evacuation programmes and flood fighting (Evans et al., 2004b). The communitycentred nature of this scenario means that people affected by both flooding and erosion will help each other and those most vulnerable will become less vulnerable as a consequence of the increase of institutional and community support. Real income will increase and real spending on household durables rises but the real prices of household durables is likely to either cease to fall or increase as regulations governing water and energy efficiency, and for recycling of equipment, become increasingly rigorous. Coastal management will maintain or expand salt marshes, which act as natural flood defences (Holman & Loveland, 2001). Due to the greater reliance on managed realignment strategies, there will be more sediment available from eroding cliffs in the sub-cell 3b area and hence beaches will be nourished naturally and have wider profiles.

2.2 Local Stewardship Socio-Economic Scenario People aspire to sustainable levels of welfare in local communities. Markets are subject to social regulation to ensure more equally distributed opportunities and a high-quality local environment. Active public policy aims to promote economic activities that are small-scale and regional in scope and acts to constrain large-scale markets and technologies. Local communities are strengthened to ensure participative and transparent governance in a complex world (Berkhout & Hertin, 2002). There will be stronger opposition to large-scale scheme and also limited government investment may curtail other large scale schemes (e.g. managed realignment).

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Potentially strong local networks and pooled insurance will exist to share costs in the flood prone areas as well as the possibility of local floodplain charging schemes (Evans et al., 2004b). Whilst erosion risk is very high for the area, it is lower under this scenario than those of World Markets and National Enterprise (see Table 1). The urbanisation of the countryside comes to a halt as planning controls are tightened (DTI, 2002) and strong land-use control policy avoiding flood prone areas. The environment will act as a constraint, limiting what actions can be done, and simultaneously a primary concern will be to undertake works that can improve the environmental functioning of the catchment. In any case, there is a presumption in favour of what are understood to be ‘natural’ forms of flood management; in particular ‘room for rivers’. There is a sharp conflict between the desire to give room to rivers and ensuring a sustainable food supply. A conservationist ethic and lower demand for new development contributes to the continuing dominance of traditional housing (DTI, 2002). New buildings are located in existing towns and cities, leading to a denser urban environment around places like Great Yarmouth, Lowestoft and Southend-on-sea. Energy resources diverse and are focussed on local energy sources hence the continued reliance on power produced from critical coastal infrastructures such asBacton Gas Terminal and Sizewell nuclear power station. Bacton may continue to be defended or may be relocated further back from the coast. There is possibility of asset removal from the floodplains and effective evacuation programmes (Evans et al., 2004b). Governance will be local and participative with a lack of central control. Flood plain occupancy is kept stable in the Global Sustainability and Local Stewardship Scenarios. Although a more community-based society than that of World Markets or National Enterprise there is a view that those who have chosen to live in flood-prone areas will have to deal with the consequences themselves. Real income increases relatively slowly and the expected lives of consumption durables and the real cost of goods will increase. However, the susceptibility of some of these goods to damage through flooding might be lower. Large scale defence schemes are opposed by the community (Evans et al., 2004b) and hence there would be more sediment available to naturally nourish beaches. However, tourism is a declining sector under this scenario and most visits would be from local people on day trips. Attempts may be made to restore declining resorts such as Great Yarmouth and Lowestoft, to protect pristine areas from new development.

2.3 National Enterprise Socio-Economic Scenario People aspire to personal independence and material wealth within a nationally rooted cultural identity. Liberalised markets together with a commitment to build capabilities and resources to secure a high degree of national self-reliance and security are believed to best deliver these goals. Political and cultural institutions are strengthened to buttress national autonomy in a more fragmented world. (Berkhout & Hertin, 2002). Similarly to the World Markets scenario, here will be strong preferences for largescale schemes of river and coastal engineering to protect nationally economic areas. Also the management of flood losses will be achieved mainly through property level

17



actions with self insurance supplemented by charitable donations (Evans et al., 2004b). The erosion risk, nationally, under National Enterprise is only slightly lower than that of the World Markets scenarios. Coastal defences would be focussed on protecting important economic areas, for the sub-cell 3b area these would include Cromer, Sheringham, Great Yarmouth and Lowestoft. It is unlikely that insurance would be available to those properties that would be at risk, with self-insurance being the norm. Planning controls at a local level are weakened in order to encourage economic development (DTI, 2002). Under this scenario planning controls are relaxed and this will allow more building and more people to live in river and coastal flood plains (Holman & Loveland, 2001). This scenario has an increase in population, households, urban areas, and second homes in the area, particularly in the sub-cell 3b area. However, the increase will not be as high as that of the World Markets Scenario since there are lower levels of investment in housing (DTI, 2002). As well as the issue of urban spread the increase in the number of households may be exacerbated by a coastal attraction with a move of people from large urban areas like London to coastal regions. Bacton Gas Terminal and Sizewell nuclear power station will continue to be defended. Transport links such as coastal roads and railways will be maintained but there is a continuing reliance on private transport and lower levels of investment in infrastructure (DTI, 2002). Under this scenario there is less co-ordinated forecasting with local/individual floodproofing and temporary defences in the most economically important areas (Evans et al., 2004b). However, due to the level of personal independence that society under this scenario aspires to it may be the case that few individuals actually respond to centralised demands. Large increases in the number of people occupying the floodplain in the UK are envisioned in the relatively loosely regulated World Markets and National Enterprise scenarios. Hence, the continued development under this scenario (although at a lower level than World Markets) increases exposure to flooding (Holman & Loveland, 2001). Some settlements on the sub-cell 3b coastal area may be “forgotten” as the major defences are concentrated on more economically important areas. With regard to damage to residential and commercial properties the increase in consumption under this scenario and the change in technologies will increase the susceptibility of these items to flood damage. The buildings and contents value will also vary with regard to changes in the distribution of wealth. Tourism is one of the fastest growing sectors under this scenario. However, continued coastal development on cliff-top locations will lead to continued growth of the length of cliff protection and will reduce sediment supply for beaches (Holman & Loveland, 2001). There will therefore be a loss of beaches and subsequent effects on lowering the tourist volume.

18



2.4 World Markets Socio-Economic Scenario People aspire to personal independence, material wealth and mobility to the exclusion of wider social goals. Integrated global markets are presumed to best deliver these goals. Internationally co-ordinated policy sets framework conditions for the efficient functioning of markets. The provision of goods and services is privatised wherever possible under a principle of “minimal government”. Rights of individuals to personal freedoms are emphasised (Berkhout & Hertin, 2002). Under this scenario there is a strong preference for large-scale coastal engineering schemes that will protect nationally important economic areas. Hence, the major settlements of such as Grimsby, Great Yarmouth, Lowestoft and Southend-on-sea will continue to be defended. In terms of managing flood losses there will be mainly property level actions and self-insurance supplemented by charitable donations (Evans et al., 2004b). In East Anglia, sea level rise will be highest in the Fens and the Norfolk Broads because of localised land subsistence as the remaining peat wastes away (Holman & Loveland, 2001). Erosion risk is highest under this scenario, with losses of land and assets within the coastal strip increasing by a factor of seven from the baseline. Coastal defences would be focussed on protecting important economic areas, for the sub-cell 3b area these would include Cromer, Sheringham, Great Yarmouth and Lowestoft. It is unlikely that insurance would be available to those properties that would be at risk, with self-insurance being the norm. There is a general decrease in planning controls and a weakening of environmental regulations under this scenario. Since there is little incentive to implement environmentally-oriented flood management measures then development would occur within the floodplain and would concentrate in major developments such as the Thames Gateway. Building in areas of the Anglian coastal strip that could be vulnerable to flooding and in cliff areas prone to erosion would be of particular concern. Since a market-based climate regime has developed and this has failed to reduce greenhouse gases (DTI, 2002) there is an increased probability of sea level rise and associated flooding and coastal erosion. In the World Markets Scenario there is a continued pressure to build more houses and due to the lack of planning regulations these will occur in all areas even in flood plains. As well as the issue of urban spread the increase in the number of households may be exacerbated by a coastal attraction with a move of people from large urban areas like London to coastal regions. Critical coastal infrastructures with regard to energy distribution, e.g. Bacton Gas Terminal and Sizewell nuclear power station will continue to be defended at all costs. Transport links such as coastal roads and railways will be maintained to meet the demands for increased goods and passenger transport, since high mobility and housing developments create a need for new investments in these services. Effective forecasting will be in place but a strong reliance then placed on local/individual flood-proofing and temporary defences in the most economically important areas such as the Thames region (Evans et al., 2004b). However, due to the level of personal independence that society under this scenario aspires to it may be the case that few individuals actually respond to centralised demands. There will

19



also be an increased role in the use of technology (e.g. the internet) to pass on information about flood risk. Large increases in the number of people occupying the floodplain in the UK are envisioned in the relatively loosely regulated World Markets and National Enterprise scenarios. Hence, flood vulnerability will increase. Under this selfish “Everyman for himself” society there is little sense of community with a shrinking role of government in the provision of social services. Hence, with increased development in flood prone areas there will be a greater number of individuals at risk and these individuals will have to deal with that risk on their own. As a consequence those that are the socially vulnerable will become even more vulnerable. Some settlements on the sub-cell 3b coastal area may be “forgotten” as the major defences are concentrated on more economically important areas. With regard to damage to residential and commercial properties the increase in consumption under this scenario and the change in technologies will increase the susceptibility of these items to flood damage. The buildings and contents value will also vary with regard to changes in the distribution of wealth. Leisure is one of the fast growing sectors under World Markets and yet there is a widening of inequality and divergence between the wealthy and those that are disadvantaged. While the wealthy go afford to go abroad on holiday, others continue to visit run down resorts in the UK. Hence, for the Anglian coastal region there are many day trip visits but few people holiday here for any length of time. Another factor in the level of tourism, especially with regard to the sub-cell 3b coastal area, is the beaches. Due to the heavy defences in some parts there will be a decrease in sediment transport and so beaches will become narrower. Overall, the total level of tourism will stay the same.

3.

Future Property Distribution

The current baseline property distribution has been augmented with new properties based on the current regional housing policy forecasts and according to the four socio-economic scenarios. The distribution of the new development is influenced by four attraction factors: existing settlements, transport networks, the coastline and floodplain. These attraction factors reflect the urbanisation policies and the levels of attraction that areas and infrastructures are likely to generate under the different socio-economic scenarios. Table 3 shows the importance of the four attraction factors represented by a categorical scale of --, -, 0, +, and ++. The 0 indicates an equal importance of the attraction factor, the negative side of the scale indicates less importance, while the positive side indicates more importance of the attraction factor. Table 3. Summary of the attraction/repulsion factors under the socio-economic scenarios.

Local Stewardship Global Sustainability National Enterprise World Markets

Existing Settlements -+ 0 0

Transport Networks 0 0 +

20

Coast

Floodplains

+ + ++

-+ ++



These attraction factors show that the pattern of urbanisation under the Local Stewardship scenario tends towards avoiding both floodplains and existing settlements and moving away from the coast and transport networks. This indicates a significant trend of moving development into the countryside. This scenario contrasts in many aspects to the urbanisation under the extreme scenario of World Markets, where urban developments will expand across much of the countryside, floodplain and the coastal zone, with a corresponding desire to be close to transport networks.

3.1 The implementation of urbanisation policies 3.1.1 Key datasets The datasets described in Table 4 have undergone extensive processing in order to obtain the locations of the new Residential Properties (RP), and the locations and Multi-Coloured Manual (MCM) code (Penning-Rowsell et al., 2003) of the new NonResidential Properties (NRP) based on the attraction factors listed in Table 3. Table 4. Summary of datasets. Data Indicative Floodplain Map 2003: tidal and fluvial National Property Database (NPD) Transport data: A Roads Coastline Inland water layer Major settlement layer Postcode polygon layer

Source Environment Agency Environment Agency Ordnance Survey data Extracted from Ordnance Survey data Ordnance Survey data Digitized from Ordnance Survey data Ordnance Survey data

Figure 4 shows the study area and maps the four attraction factors. The Indicative Floodplain Map 2003 is used to represent the maximum extent of flood hazard zones in the region, and includes the outlines for the 1:100 year fluvial floodplain and the 1:200 year tidal floodplain. The National Property Database is used to identify the location of existing properties and to identify the MCM of existing NRP. The transport networks are a significant attraction under the World Markets scenario as people express a desire to be close to major road links for easy commuting. Therefore, the layer of A-roads has been extracted from Ordnance Survey (OS) data. The coastline was also extracted from OS data for the study area from Weybourne in North Norfolk to Aldeburgh in Suffolk. A layer of inland water bodies was extracted from OS data and used to limit the extent of new development. The existing major settlements have been obtained based on expert judgment by on-screen digitization using the OS Address Point layer. A layer of postcode polygons was obtained from OS data and used as a base map for the relocation of new properties.

3.1.2 Methodology The developed methodology is implemented in a Geographic Information Systems (GIS) environment. The objectives are to obtain the locations of Residential Properties (RP), and the locations and Multi-Coloured Manual code of NonResidential Properties (NRP) based on the attractions factors reported in the storylines of the socio-economic scenarios. The methodology uses the postcode

21



polygon layer as a base map, where the total numbers of both RP and NRP are quantified for each postcode polygon and then distributed randomly within each polygon excluding areas of inland water bodies.

Figure 4. The study area and attraction factors. The first step towards the implementation of this methodology is to quantify the total number of new properties, both RP and NRP, under each socio-economic scenario. The storylines of the socio-economic scenarios provided most of the change rates in RP and NRP from the present baseline, see Table 5. The change in NRP under the local stewardship scenario is obtained by applying a correction factor of – to the change of RP. This correction factor is interpreted (based on expert judgment) as a decrease of 10% from the RP rate, which makes the rate of increase in NRP as +18%. Similarly, the change in NRP under the World Markets scenario is obtained by applying a correction factor of + to the change of RP, which is interpreted as an increase of 10% from the RP rate. This makes the rate of the increase in NRP as + 87%.

22



Table 5. The percentage growth of RP and NRP, and the total numbers of new properties created under each socio-economic scenario. Change in RP

Change NRP

Local Stewardship

+28%

Global Responsibility National Enterprise World Markets

in

Implemente d change in NRP +18%

Total no. of new RP 62607

Total no. of new NRP 4069

+44%

Correction factor of – on the increase in RP +44%

Implemente d change in RP +28%

+44%

+44%

98158

9939

+61%

+61%

+61%

+61%

136053

13785

+77%

Correction factor of + on the increase in RP

+77%

+87%

171790

19662

It has been assumed that there is no spatial correlation between the new RP and NRP that could influence the spatial distribution of the properties. Therefore, the single objective multi-criteria decision making technique (Eastman et al., 1993) is implemented in order to determine the locations of both RP and NRP. This technique was first implemented in raster GIS and it has been modified to make it applicable in vector GIS. It is based on combining the criteria in order to produce a single quota map, which is used to extract the number of new properties in each postcode polygon. The criteria are split into two types, constraints and factors: •

Constraints: used to exclude some areas from consideration for the location of new properties by applying constraint mapping using Boolean algebra. The inland water bodies are excluded by giving them a zero code (0) and those areas open for consideration are coded with one (1). Then, the binary coded map is intersected with the postcode polygon map to exclude the inland water bodies.

•

Factors: enhance or detract from the suitability of postcode polygons to accommodate new properties. Four factors are used to influence the distribution of RP and NRP, as described above: major existing settlements, transport network, the coastline and floodplain.

The decision rule is structured to quantify the single quota score (number) of new properties (i.e. RP or NRP) for each postcode polygon. This is achieved by using the weighted linear combination: ∑WiXi

(1)

where Wi is the weight of factor i and Xi the criterion score of factor i. The criterion scores are quantified using the proximity of the postcode polygons to the factors. Standardisation of the criteria is essential before combination in this equation as they represent different entities (Voogd, 1983; Carver, 1991). The centre of postcode polygons are used to calculate the proximity to major settlements, roads and coastline and then equation 2 is applied in order to standardise the outputs, 23



using the minimum and maximum values as scaling points of the factor scores, and to rescale the final scores. Thus, the closer the polygon to an attraction factor, the higher the criterion score will be. Xi =1-[(Di - Dmin )/(Dmax -Dmin )]

(2)

where Di is the proximity of a factor I, Dmin the minimum value of proximity of a factor I and Dmax the maximum value of proximity of a factor i. It is clear that the standardisation process has an important role in quantifying the criterion score and the scaling points and deserves closer attention (Saaty, 2000; Harker & Vargas, 1987). The criterion weights are quantified considering the duplication pattern reported in the storylines of the socio-economic scenarios, as in Table 6. Table 6. The quantification of criterion weights. 1/16 --

1/8 Less important -

1 equally important 0

8

16 More important

+

++

In the case of the floodplain, a postcode polygon or portion of a postcode polygon is given a weight factor associated with each socio-economic scenario if it is located inside the floodplain, while it is considered equally important and given a value of 1 if it is located outside the floodplain. In addition, as postcode polygons have different sizes, the area of postcode polygon is used as an additional factor in the decision rule in order to allocate the new properties proportionally by area. Once the weights and the factor scores are linearly combined, they are rescaled to 1 in order to produce the quota scores that reflect the number of the new properties in each postcode polygon. The MCM codes of the new NRP are identified based on the existing codes within the postcode polygons. They are determined in a proportional manner of the existing MCM codes and then distributed randomly within postcode polygons.

3.2

Results and Discussion

The weights that represent how people are attracted to areas and infrastructures under each socio-economic scenario are combined with the attraction criteria in order to determine how many properties will be created inside each postcode polygon. The areas of the postcode polygons are taken into account in order to allow more properties into larger postcode polygons. The possibility of abandonment of some properties under some socio-economic scenarios such as Local Stewardship, where people prefer to move outside of major settlements into the countryside, is not considered as it seems to be unrealistic with the high values of properties and future pressures on housing through increasing populations. The spatial distributions of the final outputs show consistency with the urbanisation policies and the attraction factors described in the storylines of the socio-economic scenarios. For example, Figures 5 & 7 show the spatial distributions of all properties under the World Markets and the Local Stewardship scenarios, respectively. Under 24



the World Markets scenario there are significant urban developments everywhere in the region including floodplains, coastal areas, and countryside, while there are a limited number of developments in the floodplain, in the coastal areas and inside the existing major settlements under the Local Stewardship scenario. These patterns can be seen more clearly if only the new properties are shown. In Figures 6 & 8 only the new properties (both RP & NRP) created under the Local Stewardship and the World Markets scenarios respectively, are shown. Table 5 above shows the total numbers of properties created under each socioeconomic scenario, and Table 7 shows the numbers of both residential and nonresidential properties located within the floodplain. The total number of properties within the floodplain is shown to increase under all four socio-economic scenarios. Table 7. Summary of the new properties inside the floodplains. Scenarios Baseline Local Stewardship Global Sustainability National Enterprise World Markets

Number of new properties inside floodplains RP NRP 16766 3160 2241 99 20654 2140 36053 3830 37853 4414

% of properties RP 7.5% 3.5% 21% 26.5% 22%

NRP 14% 2.4% 21.5% 27.8% 22.4%

The highest number of properties is created within the floodplain, as expected, under the World Markets scenario, while the lowest number of properties in the floodplain are created under the Local Stewardship scenario. However, the highest percentages of new properties inside the floodplains are created under the National Enterprise scenario. This is due to the combination of all the attractions. Under the World Markets scenario, although there is a desire to live within the floodplain as properties could be cheaper than elsewhere, other factors also act as attractants, including the coast and transport networks, whereas under the National Enterprise scenario the only other attraction is the coast (see Table 3). This creates an increase in the proportion of new properties within the floodplain.

25



Figure 5. The spatial distribution of all properties under the World Markets scenario.

26



Figure 6. The new properties created under the World Markets scenario.

27



Figure 7. The spatial distribution of all properties under the Local Stewardship scenario.

Figure 8. The locations of new properties created under the Local Stewardship scenario.

28


4.


Coastal Flood Risk Analysis

Structural reliability analyses are now commonplace in coastal engineering. For a system consisting of n basic variables X ( X 1 ,..., X n ) which characterise the behaviour of the system, the probability of failure, pf, can be expressed as: p f = P[G ( X) ≤ 0] = ∫ ...

∫

ρ ( x ) dx

(3)

G ( X)≤0

where ρ(x) is the joint probability density function (j.p.d.f.) of X and G(X)≤0 denotes the violation set of the limit state function. Equation 1 can be solved using first order reliability methods (FORM). FORM, and other Level II methods (Note: traditional design uses Level I methods (see JCSS (1981) for discussion on these levels), in which safety factors are imposed on the loading and resistance variables) approximate the failure surface with a first or higher order Taylor series expansion around the failure point closest to the origin (the 'design point'), after the j.p.d.f. describing the random input variables has been transformed into independent normally distributed variables. Despite being both efficient and elegant, the approximation of the failure surface can be inaccurate for highly non-linear limit state functions and is dependent on the availability of an explicit limit state function, which may not exist. Conversely, numerical approximations to the equation using so-called level III methods such as Monte Carlo analysis provide greater flexibility as they are not bound by these constraints. However, Level III methods are more computationally demanding, and despite everincreasing computer power they still need to be implemented efficiently. The risk, R, associated with the system is: R = ∫ ...∫ ρ (x).C (x)dx

(4)

where C(x) is a function describing the consequences associated with the occurrence of a given state of the basic variables and may be expressed in terms of economic damage or some other quantified measurement of harm. For the analysis of coastal flood risk, the function C(x) is usually implicit, highly non-linear and, for each point in X, computationally expensive to estimate as inundation models are required to obtain realistic damage estimates. Dawson and Hall (submitted) and Dawson et al. (2005) have developed an adaptive risk-based importance sampling strategy to efficiently estimate this integral for a single instance in time – a ‘snapshot’ of risk. An estimate of risk after N samples N is obtained by intermittently updating a sampling distribution, fR(x), by from X, R N →R: fitting it to known points of the function R(x). This is repeated until R N = 1 R N

N

(x ) R i ( x R i)

∑f i =1

(5)

29



4.1 Modelling Methodology In this research, this method is extended to consider the influence of a changing climate on coastal flood risk: i.e. temporally variable systems. Typically a coastal defence system is characterised by: • • • • •

two (partially correlated) loading variables, wave height, Hs, and water level, W; a system of n coastal defence components that can breach individually or in any combination and are susceptible to failure by different modes and may fail to a different degree depending on the loading (e.g. breach width); spatially variable density and type of assets susceptible to damage in the floodplain; and temporally (and possibly spatially) variability in climatic conditions, and, temporally and spatially changing floodplain development.

The six main requirements for simulating a coastal flood system are: • • • • • •

statistical estimation of extreme loads; calculation of system reliability; estimation of defence breach properties; model inundation depth and extent; estimation of damage to individual properties resulting from this depth; and, estimation of changes to the system.

An overview of the flood risk analysis methodology used as applied to the coastal defence system is shown in Figure 9.

30



Identify the system of q components

Construct a j.p.d.f. φ (L,t) of loading

Describe the resistance of each component in terms of its fragility, P(D| L,t).

Sample m points from L.

No k0 sufficiently low?

Calculate the measure of spread, k0.

Yes

Calculate the conditional probability P(Sp| L,t) of each system state

Identify r system states which have nonnegligible probability.

Sample 500 points from fR,i(L,t)

Update and run the inundation model to represent the system failure state, water level and wave overtopping conditions Fit the risk-based sampling function, fR,i(L,t), to C(Sj,L,t).P(Sp| L,t)

No

Estimate the associated economic damages, C(Sj,L,t)

Estimate the (t ) risk R

Risk sufficiently converged?

N

Yes

Calculate final risk estimate and extract other useful indices

Figure 9. Overview of coastal flood risk analysis methodology.

31



4.2 Statistical estimation of extreme loads A joint probability density function φ(Hs, W) for extreme events is constructed using simultaneous measurements of wave height, Hs, and water level, W, using the approach of Hawkes et al. (2002), and the salient points of this methodology are reproduced below. A typical joint distribution is illustrated in Figure 10. 1. The input data are prepared; each record consists of a simultaneous record of wave height, Hs, wave period, Tm, and water level, W, at a given location. Each high water is extracted and taken to be an independent record. 2. Statistical distributions are fitted to Hs, W and wave steepness, γ. Below a user-defined threshold (for Hs, W and γ) the distribution is represented empirically by observed values. Above this threshold (i.e. extreme values) a Generalised Pareto Distribution (GPD) is used. The threshold level must be selected with care: too high and there are insufficient extreme events to estimate the GPD parameters accurately; too low and the asymptotic justification for the GPD does not hold (HR Wallingford & Lancaster University, 1998). 3. A dependence function is fitted to the extreme data. Distributions of Hs and W are transformed to standard Normal distributions, N~(0,1). A correlation coefficient, ρ, is calculated from the bivariate normal distribution that defines the relationship between the two parameters. 4. Thousands of years of sea conditions are simulated for Hs, W and γ (which can be transformed back to Tm) using the population distribution for nonextreme events and the bivariate normal distributions for extreme events. 5. A j.p.d.f. is fitted to the distribution of the sea conditions. For the evaluation of climate change impacts the distribution shape is assumed to remain constant, but is transformed (Figure 10) in the loading space to represent rising sea levels and increased storminess.

Sea level rise Storminess and Sea level rise

Figure 10. Contour plot of φ (Hs,W) showing the effect of sea-level rise, and increasing storminess and sea-level rise combined.

32



Sea level rise equates to a direct transformation of the j.p.d.f. along the W axis of the plot. The sea level rise scenarios used here are not assumed to be linear (see Figure 11), and are the same as used by Pearson et al. (2005) to make the two studies comparable. The sea level rise scenarios correspond to the low, medium and high scenarios derived from the UKCIP02 scenarios (Hulme et al., 2002). The low scenario is similar to present trends, while the high scenario assumes both a high global-mean rise in sea level due to climate change and a large positive regional effect on sea levels in the North Atlantic, giving a rise approaching 1.2 m by 2100.

1200

low sea level rise

Sea level (mm above 2000 level)

med sea level rise

1000

high sea level rise

800 600 400 200 0 2000

2020

2040

2060

2080

2100

Year

Figure 11. The sea level rise scenarios used over the 21st century. Wave height and wave direction changes were also considered. This comprises a sensitivity analysis as there are no detailed scenarios, and they were assumed to be linear over the 100 year study period (Table 8). Increases in wave height were only applied to winter wave heights. Thus winter wave heights in 2100 are 10% larger under the high growth scenario than in 2000; whilst summer wave heights in 2100 are the same as in 2000 under all sea level rise scenarios. Similarly, possible changes in direction are also considered as shown in Table 8. Table 8. Sea level rise and offshore wave condition scenarios. Relative Sea level rise Low: 0.2m higher by 2100 Continue present trends Medium 0.45m higher by 2100 UKCIP02 ‘Medium-High’ High 1.2m higher by 2100 UKCIP02 ‘High’

Change in offshore wave conditions None No change Medium High High + High -

33

7% increase in winter wave height by 2100 10% increase in winter wave height by 2100 High scenario plus clockwise rotation of wave rose (10°) High scenario plus anticlockwise rotation of wave rose (10°)



The change in wave conditions were applied to offshore waves, which are subsequently transformed onshore using the Manchester University model described below and the new nearshore series are then used to derive an updated j.p.d.f.s.

4.3 Wave and water level time series For the complex coastal bathymetry of East Anglia the inshore wave climate is only slightly affected by directionality, tidal currents and wave forcing over the propagation area. Therefore for a range of offshore conditions, it is reasonable to define the inshore wave climate by wave height, period, direction and tidal level (Kuang & Stansby, 2004). The wave series at a single offshore point was obtained by passing recorded wind time series through the hindcasting model HINDWAVE (Hawkes, 1987). This was then transformed to eight nearshore points using the Manchester University TELEMAC model (Kuang & Stansby, 2004), shown in Figure 2. Concurrent time series of wave and water level data were derived at the four points that occur directly in front of the floodplain areas being investigated (Points 4, 5, 6 and 7 in Figure 2). Water level measurements from the Admiralty tide gauges at Lowestoft and Cromer were provided by the National Tidal & Sea Level Facility (POL). Water levels at each of the loading points were estimated through linear interpolation based on the distance of each loading point between the two Admiralty tide gauges (c.f. HR Wallingford, 2002). The results of this wave transformation modelling have been compared with measured wave and water level data at points shown in Figure 12. Thus, the concurrent wave and water level series were used to generate time series to drive the foreshore erosion model and in the reliability analysis. The data were altered to explore climate change scenarios using the inputs described in the following section.

34



Figure 12. Wave, water level and wind measurement points on the East Anglian coast.

4.4 Measuring defence performance The performance of each defence in the system is described in terms of its fragility (Dawson & Hall, 2003), defined as the conditional probability of a defence breach conditional on the loading. The failure probability of a defence, P(D), can be established by integrating the fragility function P(D|Hs,W) over the loading distribution, φ(Hs,W) (see Figure 13): ∞

P( D) = ∫ f ( H s , W ) P( D | H s , W )dH s dW

(6)

0

The loading assigned to each defence corresponded to the nearest loading point taken from the wave transformation model. The function P(D|Hs,W) is usually constructed from a reliability analysis where the failure mode can be described using a limit state function. However, for failure modes where this is not possible, subjective judgements can be used to construct the function.

35



Figure 13. Example of a fragility function plotted on Hs × W. The fragility of the defence at time t, is given by P(D|Hs,W,t). The fragility of the defence may change due to maintenance or structural degradation. However, a number of defence failure modes are mediated by the level of the beach that fronts the structure. These levels were predicted using a shore evolution model based on a coupling of the one-line approach (see Pelnard-Considere, 1956) with an erosion model developed by Walkden and Hall (2005). This coupling describes feedback between eroding shores and the beach, and produces credible predictions of the shoreline evolution over the 20th Century, and consequently enables century scale predictions of future beach volume to be modelled (Pearson et al., 2005). For very long defences, the parameters describing defence resistance, for example crest height or geotechnical properties, will show strong dependency nearby. However, CUR/TAW (1990) suggest that these parameters become more or less independent over distances of about 500m so longer defences are sub-divided into sections of ~500m long for the purposes of the analysis, so they can be considered as independent sections. A total of 25 dike sections were used in this analysis.

4.5 Description of the Sub-Cell 3b Flood Defence System There are four major lengths of flood defences in sub-cell 3b: (1) Eccles to Winterton, (2) Great Yarmouth, (3) Great Yarmouth-Lowestoft, and (4) Lowestoft, and details of the system are taken from the Sea Defence Survey (1998/9) with summaries in Table 9. Figure 14 shows a typical defence cross-section.

36



Figure 14. Example of 1998/9 Sea Defence Survey (courtesy of Environment Agency) showing typical flood defence cross-section between Eccles and Winterton (in this study: defence no. 5). The extensive flood defence system fronting the Norfolk Broads starts at Eccles and stretches for 15km southwards to Winterton Ness (Figure 2). This coastal length consists of seven major flood defence structures, which are all similar in that they are a hybrid sloped embankment with a concrete seawall (Figure 15), with either concrete front slopes or vegetated sand dunes (Figure 14). The crest levels range from 9-12.4 m O.D. The most likely mode of failure for these defences is through toe erosion.

Figure 15. Winterton.

Example of the flood defences at Sea Palling between Eccles and

37



Areas of Great Yarmouth are sufficiently low to have been inundated during previous extreme events, such as the 1953 flood. In this study, only wave overtopping and overflow volumes of the harbour walls at Great Yarmouth are considered. Failure, through undermining or wave overtopping of the structures protecting the promenade of Great Yarmouth, is unlikely to lead to inundation due to the relative level of the hinterland. However, extreme sea levels in the tidal flats of Breydon Water could result in inundation in areas of Great Yarmouth, such as Southtown (as occurred in 1953). South of Great Yarmouth, and just North of Lowestoft, there are four sections of seawall, totalling 2.3km in length, with a crest height of 5-5.5m. The seawall is protected by a sand/shingle foreshore for 1.7km and rock armour for a length of 600m. The defences protect an area of low lying land approximately 800m × 200m in size that is predominantly occupied by a caravan park. This stretch of land was included in the flood risk analysis in order to consider the entirety of SMP (Shoreline Management Plan) sub-cell 3b. However, although the morphological model was not extended this far south, the influence of cliff retreat on this region is unlikely to be as significant as for the Eccles to Winterton section due to the presence of several barriers to longshore transport (for example, the estuary and associated harbour breakwaters at Great Yarmouth). Whilst a more thorough risk assessment would be desirable, this was not possible as the morphological behaviour is not yet modelled fully. However, some understanding of the risk over the entire sub-cell is useful and the floodplain at Sea Palling is potentially connected as far south as Lowestoft (although the complex network of embankments in the Broads means only a surge level greatly in excess of 3 m could result in inundation of entire area). Furthermore, a full morphological-flood risk analysis coupling for the benefit of a relatively (compared to the entire system) low impact area is arguably an inefficient use of resources. Therefore, toe erosion is not considered as rigorously in the analysis of this section: the beach over the 21st century is assumed to erode using a Bruun-rule based recession model. This means that the probability of failure due to toe erosion will only be influenced by changing sea level and wave conditions. Failure from overtopping is considered for this system of defences. Areas of Lowestoft are sufficiently low as to have been inundated in previous extreme events. However, they are currently protected by harbour walls. Likewise a lock gate controls flow into and out of Oulton Broad and consequently the rest of the Broads system. The lock gates and harbour walls are assumed to fail only by overflow. Mechanisms of failure will be explained further.

38



Table 9. Summary of flood defence system in sub-cell 3b from Eccles to Lowestoft. Description 1 2 3 4 5 6 7 A B C D 8 9 10 11 E

Concrete defences in front of sand dunes at Eccles Well vegetated, advancing sand dunes Concrete Return Wall and Sand Dune Concrete Return Wall and Sand Dune Concrete Return Wall and Sand Dune Concrete Return Wall and Sand Dune Concrete Return Wall and Sand Dune Winterton-Caister cliff protection Caister-Yarmouth coastal protection River Yare estuary walls Gorleston-Lowestoft Denes cliff protection Concrete Sea Wall and Promenade Concrete Sea Wall and Promenade Low Level Apron and Concrete Sea Wall Rock armour and concrete return wall. Lowestoft harbour walls

Approximate central co-ordinate

Length (km)

Average crest level (m AOD)

Foreshore

Easting

Northing

640635

329340

2.0

Sand

644821

325839

1.7

645975

324739

646806

Failure modes Toe

Overtopping

Overflow

10.73

•

•

n/a

Sand

11.04

•

•

n/a

1.4

Sand

9.53

•

•

n/a

323910

0.9

Sand

9.28

•

•

n/a

647603

322976

1.5

Sand

10.555

•

•

n/a

648374

322060

0.8

Sand

10.02

•

•

n/a

649292

320744

2.3

Sand

8.935

•

•

n/a

652000

314500

~10

-

n/a

n/a

n/a

n/a

653500

308000

~5

-

3.5-5

-

•

•

652500

306000

~9

-

2.5-3.85

-

•

•

654000

299000

~9

-

n/a

n/a

n/a

n/a

655210

295099

0.5

5.225

½

•

n/a

5.32

½

•

n/a

5.435

½

•

n/a

655408 655554

294379 293782

Sand shingle Sand shingle Sand shingle

1.0 0.2

and and and

655540

293412

0.6

None

5.455

½

•

n/a

652300

292600

~8

n/a

3-3.8m

-

•

•

(½ implies limited consideration of morphological interaction)

39



4.6 Toe erosion Toe erosion is a complex failure mechanism and is not especially well understood in terms of its likelihood of occurrence and potential to lead to breaching. However, erosion at the toe is one of the most common and serious causes of damage to coastal defences (CIRIA, 1986). Toe failure is represented by the reliability function: Z=Rd-Rc

(7)

where Rd is the level of the beach and Rc is the critical beach level. Both these variables are stochastic. Rd is derived by modelling the beach response to a full range of loads. Using the description of the beach from the SCAPE model (Project T2.45), a Vellinga beach profile (Vellinga, 1983) is derived for each combination of the loading variables. The level in front of the defence is extracted from the crosssection and assigned the appropriate probability form φ(L) giving an indication of the variability of the depth of the sand in front of a structure for a given initial beach state. The predicted impact of beach morphology on the probability of toe erosion is shown in Figure 16. (Note that large fluctuations in beach level have been reported at the site). However, Rc is difficult to calculate correctly, even if all information about the defence is known. Invariably, the most important parameter, the toe depth is unknown. When this is true, the critical depth is assumed to behave as a cumulative normal density function such that Bc~N(Rd,0.35) where Rd is the assumed (or measured if available) toe depth of -1m.

Figure 16. The impact of beach morphology on defence failure probability. As described above, a Bruun-rule based recession model was employed to allow limited consideration of the effects of sea level rise on defence reliability. Because of the presence of a number of sediment disruption structures (the estuary and harbour walls at Great Yarmouth and other groynes etc.) the morphological connectivity south of Great Yarmouth (to the Cromer cliffs at least) is greatly reduced. Therefore, employment of a more simplistic approach to model future recession is justifiable, and indeed, this approach has been used in many other studies (c.f. Bruun, 1954, 1962; Leatherman, 1990; Dean, 1991; Bray and Hooke, 1997).

40


R=


xc h (d b + d c )

(8)

where R is the beach recession, xc is the distance to the closure depth (i.e. width of active profile), db is the beach height and dc is the depth of closure. The rule can be rewritten as (e.g. Pilkey and Cooper, 2004):

R=

S tan φ

(9)

where S is the amount of sea level rise, and φ is the angle of the beach profile. It is evident from Equation 9, that this rule does not allow the sensitivity of wave climate to be explored fully as the impact of changing wave conditions are not considered in this recession model (although they are still considered in terms of their impact on defence reliability). Likewise, offshore sediment movement from tides, currents and gravity are not considered.

4.7 Wave overtopping and overflow The Overtopping Manual (HR Wallingford, 1999) is used to calculate the wave overtopping volumes for each defence section. The manual lists functions to define the overtopping discharges for sea walls depending on their roughness, permeability, slope and whether they have a berm or crown wall. The height of the defences, relative to even an extreme storm surge results in very small overtopping volumes (although the models suggest more overtopping is likely at those defences south of Great Yarmouth). However, the probability of failure from overtopping was considered. Owen’s equation (HR Wallingford, 1980; Equation 4.19) and later adaptations (HR Wallingford, 1999) are used to estimate overtopping volumes. For example, the overtopping rate, Q, for an impermeable seawall is given by:

⎡ − b( h − h ) ⎤ c w ⎥ Q = gH T a exp ⎢ s m ⎢ T ⎥ gH ⎢⎣ m s ⎥⎦

(10)

where Hs is the significant wave height, Tm is the mean wave period, hc is the crest level, hw is the still water level and a and b are coefficients based on the slope and berm. For rough and armoured slopes, a roughness coefficient is required. This is based on the type of material and where this is unknown a value can be assigned based on the limited defence revetment material classification information used for high level risk assessment (e.g. turf front face corresponds to a roughness coefficient of 0.9-1.0). The fragility is estimated around the threshold at which damage starts to occur (~2 l/sec/m for an unprotected clay embankment, ~50 l/s/m for an armoured seawall and ~200 l/s/m for a paved apron revetment with no backslope (HR Wallingford, 1980; CIRIA and CUR, 1991; HR Wallingford, 1999)). Thus the reliability function for wave overtopping is: Z=Qth-Q

(11)

where Qth is typically the threshold at which damage occurs. 41



4.8 Defence Breaching Prediction of dike breach location, geometry and growth rate is highly uncertain (Wahl, 1998). A number of simplified rules for breach width have been proposed, including: Bw = min {10h.a, B}

(12)

where B is the dike length, h is the overflow depth and a is as little as 3 for cohesive materials (HR Wallingford, 2004b) and as great as 15 for non-cohesive materials (Visser, 1998); here a = 12.

4.9 Inundation Modelling Numerical models of floodplain flows range in complexity from fully threedimensional solutions of the Navier-Stokes equations (Cugier & Le Hir, 2002) to models that treat flow as one-dimensional. Simulation of inundation over lowgradient floodplains with significant dike structures requires at least a twodimensional modelling approach with relatively high spatial resolution to represent the complex geometry of the floodplain. However, full two or three-dimensional modelling remains computationally prohibitive on a broad scale, particularly if multiple scenarios are to be modelled. The risk assessment methodology presented in this project is not dependent on the use of a particular inundation model, the only requirement being that the model can produce a spatial distribution of flood depths within the floodplain. However, to reduce the computational burden of the hydrodynamic calculations for this study a simple 2D raster based inundation model called LISFLOOD-FP was selected. Bates and De Roo (2000) describe the model in detail; however, a number of key points are reproduced here. Flood wave propagation is represented as an approximation to a 2D diffusive wave. The floodplain is discretised as a grid of rectangular cells and flow between cells ‘Q’ is calculated simply as a function of the free surface height difference across each cell face: h5 3 ⎛ hi −1, j − hi , j ⎜ Q= n ⎜⎝ Δx

12

⎞ ⎟ Δy ⎟ ⎠

(13)

Change in water depth in a cell over time t is calculated by summing the fluxes over the four cell faces: i −1, j i, j i , j −1 i,j dh i , j Q x − Q x + Q y − Q y = dt ΔxΔy

(14)

where hi,j is the water free surface height in cell (i,j), Δx and Δy are the cell dimensions, n is a friction coefficient, and Qx and Qy describe the volumetric flow rates between floodplain cells. These equations give similar results to a more accurate finite difference discretisation of the diffusive wave equation but with much reduced computational cost, and have been shown to perform as well as full two-

42



dimensional codes (Horritt & Bates, 2001). Flow over dikes is described by standard weir equations (e.g. Chadwick & Morfett, 1993). A DEM for this region was constructed from LiDAR data with a horizontal resolution of 2m and vertical accuracy of ~0.15m rmse. The LiDAR data were passed through a standard vegetation removal algorithm, although visual inspection of the data revealed that in urban areas some features still remained. The model covered the coastline from Sea Palling to Lowestoft and extended inland as far as Norwich (see Figure 2). This region was discretised on a 250m cell grid consisting of 161 x 168 cells, giving a total of ~27k cells, covering an area of 1700km2. Flow within the floodplain is heavily influenced by a complex series of embankments; some constructed around rivers and drainage channels to provide fluvial flood protection and others to support road or rail infrastructure. However, their presence often restricts the flow of water within the floodplain, particularly for lower return period flood events. Spatial averaging of the 2m resolution LiDAR data to the model grid scale results in these features being ‘smeared out’, so their influence was simulated by defining weirs at the appropriate crest elevation and location within the floodplain. Both the 1938 and 1953 flood events were simulated with the LISFLOOD-FP model. For the 1938 event the DEM was modified at Winterton to include the breach dimensions given by Mosby (1938). Unfortunately, no dynamic time series of water levels over the course of the 1938 event was available and the only boundary condition information consisted of the maximum recorded water level at Winterton. To allow a dynamic simulation we therefore took the time series of water levels for the 1953 event as recorded at Sheerness (see Figure 17) and re-scaled this to the maximum water level given by Mosby (1938). We assumed that the shape of the 1953 event was typical of storm surge waves along the eastern coast of the UK and believe, despite the uncertainty introduced by this procedure, this to be the best approximation available given the lack of data. The entire 10 hour dynamic event was simulated using 36000 time steps of 1s duration. On a 2.5GHz processor, simulation time was 5 minutes. This is predominantly because the floodplain has a low gradient, and initially there is a negative gradient before the land starts to rise to high ground. As at other sites a number of values of Manning’s number (n) were tested and n=0.025 gave a very good model performance of F value of 0.91 on a scale of 0 to 1, where 1 implies a perfect match between the simulation and actual event (Bates et al., 2005). Application of a planar water surface model led to large areas of the coastal floodplain being predicted as flooded compared to the relatively limited extent of flooding suggested by the observed data. This process yielded an F value of only 0.11 and suggests that the planar method is even more susceptible to failure in wide area applications where there is a greater possibility of low points in the DEM being below the elevation of maximum flood level but not hydraulically connected to the flood. Figure 18 shows the comparison of the observed inundation extent for the 1938 Horsey flood with that predicted by the LISFLOOD-FP model and the planar water surface elevation method (sometimes termed the ‘bath-tub’ method). For the 1953 surge event model boundary conditions consisted of the water elevation time series shown in Figure 17 without re-scaling of the maximum elevation. At Great Yarmouth, the landward extent of inundation was not available. However, flood information within Yarmouth town centre was known and using n=0.025 the model correlates well with the areas known to have been inundated, providing further confidence in the calibration.

43



For each inundation simulation run, the boundary conditions were updated to reflect any defence breaches, conditions, extreme water level and wave overtopping volumes.

Figure 17. The 1953 storm surge as measured at Sheerness (Rossiter, 1954, Smith & Ward, 1998).

Figure 18. Comparison of observed inundation extent for the 1938 Horsey flood from Mosby (1938) with that predicted by the LISFLOOD-FP model and the planar water surface elevation method.

44



4.10 Damage Estimation A national database (known as the National Property Database) combines information on property type and location in England and Wales. For each property type, defined by a Multi-Coloured Manual (MCM) code for non-residential properties, Penning-Rowsell et al. (2003) have defined a depth-damage relationship (Figure 19). 3.00 2.50

Depth (m)

2.00 1.50 1.00 0.50 0.00 0

10

20

30 Damage (£ 000s)

40

50

60

Figure 19. Depth-damage curve of a residential property (Penning-Rowsell et al., 2003).

4.11 Systems reliability analysis for a discrete system In the context of coastal defence system with n components there are 2n dike system states, Sj: j = 1,…, 2n each with probability P(Sj). Given a loading, L ( H s , W ) on the system in terms of wave height, Hs, and water level, W, and a dike state Sj there is a damage function C(Hs,W, Cj). The total flood risk is therefore given by: ∞

R = ∫ ∑ j =1 P ( S j | H s , W ) f ( H s ,W )C ( H s , W , S j )dH s dW 2n

(15)

0

∞

2n

where by definition

∑ P( S j =1

j

| H s ,W ) = 1 and

∫ f ( H ,W )dH dW = 1 . s

s

0

Defences within a linear system such as that demonstrated in this study interact with each other in series (i.e. failure of one or more components results in system failure). The conditional probability of failure of one or more components failing in series is defined as: n

P( S s | L) = 1 − ∏ ⎡⎣1 − P ( Di | L ) ⎤⎦

(16)

i =1

45



The value at which P(Ss|L). φ (L) is maximised is also known as the system design point. This provides useful information about the overall system behaviour, however, the concern here is the contribution towards flood risk from individual system failure states. For example, in a series system with components that have fully independent failure probabilities conditional upon the loading, the probability of any given state Sj corresponding to the event D1 ∩ ... ∩ Dd ∩ Dd +1 ∩ ... ∩ Dn can be calculated: d

n

i =1

i = d +1

P( S j | L) = ∏ P( Di ) ∏ [1 − P( Di ) ]

(17)

For a system with components that exhibit a degree of dependency, correlation coefficients may be used (CUR/TAW, 1990). Little is known about R(x) at the outset, so the initial exploratory analysis of R(x) necessarily spans the whole of the region A ⊂ n where R(x) is known to be nonnegligible. The region A may be quite large. In the absence of further information an exploratory sample should be reasonably uniform throughout A. This could be achieved by pre-selecting samples on a regular grid over A, or by randomly sampling from a uniform distribution over A: f0(L)~U(A). Starting with a random sample from a known distribution is attractive because the m initial samples can subsequently contribute to the pool of samples used in the integral estimation. This initial sample would ideally be reasonably evenly spread over A so in practice it is possible to take k (where k can be large) sets of m samples from f0(L) and select the set of samples that best minimises the following quantity: n m −1 ⎛ l ⎞ k0 = ∑∑ ⎜ i − di , j ⎟ ⎠ i =1 j =1 ⎝ m − 1

2

(18)

where li is the length of the projection of A onto the xi-axis and di,j is the distance on the xi-axis between points xj and xj+1. By doing so it is ensured that the samples from U(A) are reasonably evenly spread over A and extend towards the boundaries of the (L) , is calculated for each sample: region. The contribution towards risk, R (L) = ρ (L).C (L) R

(19)

The initial risk-based importance sampling distribution (after m samples), fR,m(L), is (L) : j=1,…,m and normalising as necessary so obtained by fitting a surface over R that fR,m(L) is a j.p.d.f. fR,m(L) is sampled to obtain the next set of points, Lj: (L) is evaluated. For each realisation of L and Sj, the j=m+1,…,N at which R damage, C(Sj,L), needs to be estimated. In order to reduce the number of failure states analysed to manageable proportions for each value of L, whilst still capturing the dominant behaviour of the system, the r failure combinations that make a nonnegligible contribution to

2n

∑ P(S j =1

j

n | L) = 1 (generally r