In this paper, we assess the risk of future coastal flooding in the Severn Estuary, examining the contribution from low probability extreme sea level rise scenarios resulting from the possibility of increased rates of ice sheet mass loss in the coming century. A simple asymmetric probability distribution is constructed to include sea level rise scenarios of up to 1.9 m by 2100, based on recent assessments of future sea level rise in the UK. A regular sampling procedure, sampling every 1 mm, is used to increase the boundary water levels associated with a current 1:200 year event to force a two-dimensional hydrodynamic model of coastal inundation to examine the influence of sea level rise on inundation of the Somerset Levels region. From the resulting ensemble of predictions an estimation of risk (conditioned upon the hazard and the probability of occurrence) by 2100 is established. The results indicate that although the likelihood of extreme sea level rise due to rapid ice sheet mass loss is low, the resulting hazard can be large, resulting in a significant (29.7%) increase to the projected risk. These findings clearly demonstrate that uncertainty in future sea level rise, mostly associated with the rate of ice sheet mass loss, is a vital component of coastal flood risk, and therefore, needs to be accounted for by decision makers when considering mitigation policies related to coastal flooding.
 More than a billion people and a significant proportion of the global gross domestic product (GDP) are located in coastal regions throughout the world [Small and Nicholls, 2003]. Continued development trends predicted for the next century are expected to result in an increase in the value of assets located near the coast [Nicholls, 1995; Turner et al., 1996; Zong and Tooley, 2003; Mokrech et al., 2012]. At the same time climatic changes, for instance, the alteration of storm tracks or an increase in storminess [Palmer and Ralsanen, 2002; Houghton, 2005; Bromirski et al., 2011], or local land subsidence [Wang et al., 2012; Wöppelmann and Marcos, 2012] may have significant impacts upon the likelihood of inundation along many coastal areas. The risk to a given region is a function of the probability of an event occurring and the consequence of its occurrence, therefore, both the environmental factors (such as climate change) and the human factors (such as urbanization at the coast and mitigation measures taken against flooding) will be influential in shaping the risk in a given region.
 Arguably, the greatest threat facing coastal communities throughout the world is the prospect of a rise in mean sea levels in the coming century, leading to an increase in the frequency and severity of coastal inundation [Houghton, 2005]. Given future projections Evans et al.  suggest that the average annual costs from flooding could increase to more than £20 billion by 2080 in England and Wales alone. To provide the most appropriate mitigation strategies against coastal flooding in a region, it is essential to accurately establish the future risk associated with sea level rise. By doing so, decision makers can be provided with vital information with which to define the best utilization of available resources.
 The UK Climate Impacts Program (UKCIP) provides an estimate of local future sea level rise for the UK. Regional projections of thermal expansion induced sea level rise from 11 atmospheric-ocean models, accounting for regional patterns in sea levels relative to the global mean [Lowe and Gregory, 2006], are provided by the Intergovernmental Panel on Climate Change Working Group 1 (IPCC) [Meehl et al., 2007]. These ensembles are then scaled into low to high scenarios using the methodology outlined by the IPCC [Nicholls et al., 2011] before being combined with the land ice melt contribution to provide an estimate of absolute sea level rise. Finally, using the predictions made by Bradley et al.  the local vertical land movement along UK coasts is considered in order to provide a prediction of the relative sea level rise, across the UK, which is shown to vary by more than 14 cm between London and Edinburgh when considering 2095 projections [Lowe et al., 2009].
 The future change in sea levels is, however, very uncertain. Numerous environmental processes which can both increase or decrease sea levels in a region, such as the thermal expansion of the oceans, ice cap melting, terrestrial storage, and local land movements, are considered. Furthermore, human factors, such as the degree to which societies reduce the rates of Greenhouse gas emissions, further increases the complexity involved in the prediction of future sea levels. To represent this, the latest predictions from the IPCC [Meehl et al., 2007] and UKCIP [Lowe et al., 2009] provide probability distributions of future sea levels derived from an ensemble of model simulations which aims to encapsulate the uncertainty contained in the predictions. For instance, in each of the three emission scenarios provided by Lowe et al.  a probability distribution of plausible relative sea level rise values is given. Considering all three scenarios, the range in plausible relative sea level rise at Cardiff in the coming century, within the 5th and 95th percentile probability bounds, falls between approximately 18 and 83 cm.
 Probability distributions such as those provided by Lowe et al.  have been used as boundary condition inputs to hydrodynamic inundation models to enable the estimation of future risk due to sea level rise [e.g., Purvis et al., 2008]. Such studies have provided an interesting assessment of future risk, explicitly accounting for the financial losses resulting from a given event and the associated probability of it occurring. However, recent research has indicated that many predictions may be underestimating the upper boundary of sea level rise in the coming century [Lowe et al., 2009]. The IPCC predictions [Meehl et al., 2007], from which the UKCIP projections are scaled, for instance, assumed a linear rate of mass loss in their predictions, which has been considered by many to lead to significant underestimation of the glacial contribution to sea level rise [Lowe et al., 2009].
 The rate at which ice sheets will reduce in the future is of great interest due both to the uncertainty surrounding it, and to the potentially catastrophic consequences of relatively unlikely, rapid mass loss events. Of particular interest has been the possibility of a partial or complete collapse of the Western Antarctic Ice Sheet (WAIS) in the next 100–200 years, potentially leading to sea level rise at a rate of 1 m per century and absolute global sea levels increasing by up to 4 m [Mercer, 1978; Bentley, 1998; Oppenheimer, 1998; Vaughan and Spouge, 2002; Kasperson et al., 2005; Tol et al., 2006; Pfeffer et al., 2008; Lowe and Gregory, 2010]. Bamber et al.  suggest that the maximum contribution to sea level rise from a WAIS collapse is approximately 3.2 m, and would contain a significant degree of spatial variability around the Earth. Research has demonstrated a precedent for rapid sea level rise linked to glacial mass loss during previous interglacial periods [Mercer, 1968; Scherer, 1993; Scherer et al., 1998; Deschamps et al., 2012]. Furthermore, recent research has indicated that the rates of glacier mass loss have been increasing over the last two decades [Rignot et al., 2008; Gardner et al., 2011]. However, the degree to which these may be short-term trends is still uncertain. Moon et al.  examined 200 Greenland outlet glaciers velocities between 2000 and 2010 and found that although the overall trend was an increase in velocity, the rate of acceleration in many of the glaciers has slowed since 2005. Similarly, Bjørk et al.  examined over 80 years of data in southeast Greenland and found that the overall trend was punctuated with two particular periods of retreat (occurring in the last decade and in the 1930s) separated by periods of accumulation. Csatho et al. , Andresen et al. , and Kjær et al.  also provide evidence of complex, punctuated periods of rapid mass loss in Greenland, while Shepherd et al.  provide a robust analysis of Antarctic and Greenland ice sheet mass balances, also highlighting periods of both increase and decrease in mass, spatially variable between regions. Most authors report a lack of understanding of the processes related to changes in ice sheet mass loss, as well as a high degree of spatial and temporal variability in the response to environmental changes. Bjørk et al.  suggest that although mass loss is likely to continue with projected temperature increases, the rate may slow once the marine terminating glaciers reach grounding lines, at which point they will become less sensitive to climatic changes.
 These findings highlight that although a general increase in mass loss in response to climatic change does exist, a great deal of uncertainty in future contributions from the ice sheets to sea level rise in the coming century remains.
 The likelihood of rapid sea level rise due to the ice sheet collapse within the next 100–200 years has been described as extremely unlikely, but nevertheless not impossible [Vaughan and Spouge, 2002; Tol et al., 2006; Pfeffer et al., 2008; Bamber and Aspinall, 2013]. Due to the uncertainty in how ice sheets will respond to climate change, few authors have attempted to provide a probability estimate for such extreme projections. Bentley  provided a rough probability for the onset of rapid (1 m per century) sea level rise as one in a thousand, based upon such events occurring approximately once every major glacial cycle. However, Kasperson et al.  suggest this estimate is too high. Vaughan and Spouge  attempted to provide a probability estimate based on a set of expert opinions. Their findings led them to estimate that there was approximately a 5% chance of an onset of rapid sea level rise of 1 m per century within the next 200 years from the WAIS and a 5% chance of a 0.5 m contribution to sea level rise by 2100. A more recent expert elicitation by Bamber and Aspinall  concluded that although a great deal of uncertainty was present, the best representation of future sea level rise should be given by an asymmetric curve with an extended tail which includes the possibility of low probability extreme sea level rise events. They suggest that the sea level rise by 2100 due to ice sheet contributions contains a median value of 5.4 mm yr−1 but that there was a 5% likelihood of the rate reaching 17.6 mm yr−1 or greater.
 To account for the possibility of rapid ice mass loss, the latest assessment by UKCIP [Lowe et al., 2009] includes an extreme H++ scenario, which proposes the possibility of sea level rise in the UK of between 0.93 and 1.9 m by 2100 m, although no associated probabilities are given. The 1.9 m maximum is the local conversion from an upper estimate of 2.5 m global sea level rise defined from estimated rates of sea level rise during the last interglacial period, based on analysis of Red Sea sediment data [Rohling et al., 2008]. This estimate provides a reasonable upper limit to sea level rise in the coming century when compared to other research, such as that by Pfeffer et al.  who suggest a maximum global sea level rise of 2 m in the next century. The provision of the H2+ distribution provides a basis by which to estimate the consequences associated with possible, yet unlikely future sea levels, using a “what if” assessment [e.g., Dawson et al., 2005]. However, few if any studies have attempted to explicitly include such events in an estimation of future risk. Although the likelihood of sea level rise significantly greater than projected in the present UKCIP distributions is assumed to be low, the consequences might be relatively large, therefore contributing significantly to the predicted risk. The exclusion of such scenarios, therefore, may result in an important underestimation of risk.
 In this paper, we therefore examine the contribution of low probability extreme, yet plausible, sea level rise scenarios to the risk of coastal inundation along a section of coastline in the UK. To do this an asymmetrical curve [after Bamber and Aspinall, 2013] is fitted to the high-end sea level rise prediction for Cardiff by 2100 presented in the UKCIP fourth assessment including the recent H2+ scenarios [Lowe et al., 2009] to provide a probability distribution of future sea level rise in the region that includes the full range of plausible scenarios. These sea level rise scenarios are combined with a present 1:200 year event level to provide boundary conditions to the LISFLOOD-FP [Bates and De Roo, 2000] hydrodynamic model to estimate the inundation and financial loss associated with projected sea level rise induced defense overflow in the Somerset Downs. The LISFLOOD-FP model has been used in previous risk assessments in the region [Purvis et al., 2008] and has been validated for a 1:250 year flood event which occurred on the 13 December 1981 [Smith et al., 2012]. A description of the study site used in the research can be found in section 2, while full details of the methodology are provided in section 3. Model results and discussion, and a summary of the main conclusions are given in sections 4 and 5, respectively.
2. Study Site
 The focus of this research is a 20 km length of North Somerset coastline between Uphill (near Weston-Super-Mare) and Clevedon, lying on the Eastern side of the Severn Estuary in the UK. This section of the Severn provides the coastline to the Somerset Levels, an extensive region of low lying land (predominately below 7 m Ordnance Datum Newlyn) bounded inland by high ground. The study area contains three main towns: Weston-Super-Mare, Nailsea, and Clevedon, in addition to a variety of smaller villages, a section of the M5 motorway, extensive areas of farmland predominately used for grazing, and a variety of rivers including the mouths of two tidal rivers; the Axe and the Yeo (Figure 1).
 Approximately 90,000 people live in the study site, most of whom would currently be at risk from inundation were it not for an extensive array of coastline and river bank defenses, and a series of river lock gates, drainage channels and ditches that have been established. The current defenses are designed to 1:200 year event standards along the coast and 1:50 years along the major rivers. If no action is taken in the future, it is likely that rising sea levels would reduce the capacity for the present coastline and river defenses to prevent inundation in the region. Purvis et al.  suggest that due to the value of assets at risk from flooding, this region is a critical site for future flood risk assessment with which to inform mitigation policies.
3.1. Model Configuration
 To model the inundation associated with projected sea level rise, in conjunction with a current 1:200 year event, the LISFLOOD-FP hydrodynamic model [Bates and De Roo, 2000] was used. LISFLOOD-FP is a 2-D finite difference inundation model based upon a storage cell approach. The first model formulation was developed by Bates and De Roo  in order to provide a computationally efficient model capable of simulating large ensembles of predictions. A recent formulation described by Bates et al.  has been used in this research. The model is first order in space and explicit in time, but uses a semi-implicit treatment for the friction term to aid stability. The flow between cells is based upon the quasi-linearizes one-dimensional Saint-Venant equations, ignoring advection [after Hunter et al., 2007], and is given by:
where g is the acceleration due to gravity (ms−1), n is Manning's roughness coefficient (sm−1/3), h is depth (m), and z is cell elevation (m) such that Δ(ht + z) is the difference in water surface elevation between two cells (m), Δx is the cell resolution (m), Q is flow (m3 s−1), q is water flux (m2 s−1), and is the depth of flow between two cells (m) defined as the maximum water surface elevation in neighbouring cells minus the maximum bed elevation in neighboring cells.
 Stability in this method is approximated by the Courant-Freidrichs-Levy condition for shallow water models given by
where the nondimensional Courant number, Cr needs to be less than 1 for stability and V is a characteristic velocity given as the celerity of a long wavelength, small amplitude gravity wave.
 The flows across each face of every cell are summed and then multiplied by the time step to calculate a volume change, before dividing by the cell area to calculate the depth change in a cell [Neal et al., 2012].
 LISFLOOD-FP has been successfully used in coastal applications, including the Severn Estuary [Bates et al., 2005; Purvis et al., 2008] and has been shown to be computationally efficient [Aronica et al., 2002]; an important consideration when aiming to generate a large ensemble of model outputs. Furthermore, its ability to model coastal flooding in the region has been tested by Smith et al.  for a major event which occurred in 1981. Here the model provided a goodness of fit score [Bates et al., 2005] for flood extent of 0.85, which given uncertainty in the reconstructed flood shoreline (derived from eye witness accounts and postevent photography) is likely to be within the observed data error. This value was “as good as, or better then, values obtained for comparable applications to fluvial flooding problems using LISFLOOD-FP” [Smith et al., 2012]. Furthermore, at 30 spot water depths obtained from interviews, newspapers and photographs, the model was found to provide a reasonable agreement with very few major discrepancies.
 Recently, G. A. M. de Almeida and P. D. Bates (de Almeida and Bates, Applicability of the local inertial approximation of the shallow water equations to flood modeling, submitted to Water Resources Research, 2013, doi:10.1002/wrcr.20366) reviewed the capabilities of the local inertial LISFLOOD-FP model [Bates et al., 2010; de Almeida et al., 2012]. They reported that the model performed well in subcritical flow conditions (Froude values less than 1). However, as Froude values begin to exceed this point, model predictions, relative to analytical solutions, were shown to become increasingly uncertain. Unfortunately, flows over a defense structure, such as those of interest in this research, often result in flow conditions with Froude values exceeding 1. To reduce the potential errors associated with defense cells the flow along cell edges linking the defense structures and the floodplain within LISFLOOD-FP can be defined using standard weir equations [e.g., Ackers et al., 1978] in which the discharge between cells depends upon the weir width, gravity, the height of the head of water upstream of the weir, and a weir flow coefficient. This provides a series of point sources of water, representing the water flowing over defense structures, which are propagated over the floodplain using the standard LISFLOOD-FP formulations.
 The LISFLOOD-FP model was, therefore, considered to provide an appropriate tool to meet the objectives of this research, however, the results are considered to be model independent; other formulations could be used but would not be expected to significantly alter the main conclusions drawn.
 LISFLOOD-FP requires three key data sets to accurately model the flow of water over a coastal region; a digital elevation model (DEM), an estimation of the floodplain friction (Mannings n), and a boundary data set representing the water elevation along the coast. In order to demonstrate the methodology we assume, for simplicity, that inundation occurs only by overflowing of the defenses in a given cell, land use does not change from the present, and assess the risk from only a single probability event rather than all possible contributing events.
 The DEM used in this research was defined from airborne laser altimetry (LiDAR) with a spatial resolution of 2 m and vertical accuracy of ∼10 cm RMSE, obtained from the Environment Agency of England and Wales. This was then aggregated to 50 m resolution in order to reduce computational demands. Defense structures (and weir linkages, described above) were manually digitized back into the DEM after aggregation from information contained in UK Ordnance Survey maps [see Purvis et al., 2008; Lewis et al., 2011; and Smith et al., 2012]. The domain was centered on Weston-Super-Mare (indicated in Figure 1), giving a grid of 287 × 480 cells (Figure 2). The Land cover Map of Great Britain 2000 was used to define the Mannings n roughness throughout the domain. Smith et al.  recognized three dominant land cover types in the region; a largely unvegetated foreshore, managed grasslands, and urban areas. A value of n = 0.02 was assigned to the unvegetated foreshore areas, n = 0.03 was used for the managed grasslands after Arcement and Schneider , and a value of n = 0.09 was given to the urban regions as a result of their calibration and validation tests. Whilst the n value for urban areas appears high, Smith et al.  found that at 50 m grid resolution model the blockage effect of buildings significantly increases the effective resistance above typical skin friction values for urban surfaces (n = 0.01–0.02).
 It has been found in previous research [Yu and Lane, 2006a; Brown et al., 2007; Soares-Frazao and Zech, 2009] that errors can be introduced into hydraulic model predictions in urban areas where coarse spatial resolution grids are used due to the inability to explicitly represent blocking by buildings and the smoothing of topographic features. Some recent flood risk assessments [e.g., Stansby et al., 2012] have therefore utilized high resolution model domains (often defined with 2 m resolution LiDAR data sets) when simulating flows in urban areas. However, such studies often consider only local regions, often of a few square kilometers. This research considered 1900 simulations of an area composed of hundreds of square kilometers, and therefore, a coarser resolution domain was required for computational efficiency. Similar approaches have been used in previous research, both in the Somerset Levels [Purvis et al., 2008; Lewis et al., 2011; Smith et al., 2012] and in other coastal regions [Wadey et al., 2012]. Given a 50 m resolution, Smith et al.  found that a reasonable flood extent could be predicted by tuning the Manning roughness of urban cells to represent the blocking effect of buildings. Due to its success in the region, this approach has been used in this research, however, other approaches have been proposed that could equally have been used [e.g., Yu and Lane, 2006b]. It is expected that the effect of the modeling choices made upon the results will be largely insignificant relative to the influence of the boundary water level specification which was the focus of this research.
 A boundary sea level representing the current 1:200 year event was defined at each grid cell marking the seaward edge of the computational domain (Figure 2, Western boundary). The 1:200 year event was used as it represents the current coastal defense standard in the region. Peak water levels at each of these cells were defined by interpolating the values given at the Avonmouth and Hinkley Point class A tide gauges, after Purvis et al. , in which a 1:200 year water level at Avonmouth and Hinkley Point is defined as 9.09 m and 7.84 m ODN, respectively. A sine curve was fitted to the interpolated peaks to provide an approximation of the high and low phases of the tidal wave in region [after Smith et al., 2012].
3.2. Definition of an Asymmetric Sea Level Rise Distribution
 In order to provide an estimate of future coastal flood risk in the region, a distribution of sea level rise values with which to add to the current 1:200 year boundary conditions was required. This research focussed on the projected sea level rise by 2100, a date often used in the literature when discussing future risk for mitigation planning, and also a date for which the UKCIP currently provide sea level rise estimations. A lognormal distribution was fitted with a cumulative probability of 0% assigned to an increase in sea levels of 0 mm, 100% assigned to 1.9 m (representing the maximum possible after Lowe et al., 2009), and a central value of 53.1 cm (given as the central estimate at Cardiff in the high end projections by Lowe et al. ). A lognormal distribution was fitted, after Bamber and Aspinall , who indicated this as the most likely distribution representing future sea level rise, particularly when accounting for the inclusion of the possibility of increased rates of ice sheet loss.
 The choice of distribution is not without its uncertainties. The high-end UKCIP 95th percentile figure of 0.83 m is lower than other recent estimates, while the plausibility of 1.9 m sea level rise maximum is questioned by some. For instance, Bamber and Aspinall  suggest a global sea level rise 95th percentile of 1.32 m (scaling to approximately 1.05 m for the UK after Spada et al., 2013), while Vermeer and Rahmstorf  and Grinstead et al.  provide predictions of up to 1.9 m (1.52 m) and 1.3 m (1.04 m), respectively, by 2100 using an empirical model based upon global temperatures. Katsman et al.  provide a value of 1.15 m (0.92 m) and suggest that the 2 m sea level rise possibility proposed by Pfeffer et al.  is questionable due to the lack of evidence of glacier acceleration by an order of magnitude, and the possibility of negative feedbacks should such rates occur. Jevrejeva et al.  on the other hand, provide a 95th percentile estimate of seal level rise of 1.65 m (1.32 m) and use Pfeffer et al.  and Rignot et al.  to justify the required ice sheet contribution to meet such levels. Due to the imperfect knowledge of the physical processes, particularly those related to ice mass loss, it is impossible to precisely define the probability of a particular sea level rise scenario occurring, akin to “Knightian uncertainty” [Knight, 1921].
 This research has utilized the high end UKCIP projections as they are the regional transforms of the IPCC projections, both of which are commonly used in UK-based studies (e.g., see Stansby et al.  for a flood risk assessment in Norfolk, and DEFRA [2006a] and Department for Communities and Local Government (DCLG)  for defense height guidelines for the coming century) and are therefore of interest to policy makers within the UK. As this research is specifically focussed on the contribution of low probability events to overall risk, the extension of the distribution past the 95th percentile to an upper limit was desired. The use of the H2+ scenario was appealing as it includes global to regional adjustments to sea levels for the UK. Although the possibility of UK sea levels increasing by 1.9 m by 2100 is questionable, research suggests that it cannot be ruled out [Lowe and Gregory, 2010] and therefore, this value serves as a useful maximum possible scenario for the UK with which to constrain our distribution. The inclusion of such events is common in recent research related to future sea level rise [e.g., Chini and Stansby, 2012; Stansby et al., 2012].
 An ensemble of model simulations was conducted sampling the sea level rise scenarios associated with the distribution given in Figure 3. The sea level rise scenarios were sampled using a 1 mm sampling interval. This provided an ensemble of 1900 members. In each simulation the sea level rise scenario drawn from the distribution was added to the water levels in each of the seaward cells in the LISFLOOD-FP model, which was then used to force the LISFLOOD-FP model to predict the inundation throughout the domain. For simplicity the effect of a change in MSL upon an event return period was not examined; the current 1:200 year surge characteristics were assumed to be constant. Previous research has shown that an increase in MSL could affect the return period of a given event due to the interaction between the tide, surge and wave components of the storm tide [Chini et al., 2010; Haigh et al., 2011; Chini and Stansby, 2012; Stansby et al., 2012], while potential increased storminess may increase the likelihood of severe surge events, although Lewis et al.  demonstrated that within the Severn the latter, in particular, is unlikely to be a significant contribution to future risk. This research focusses only on the direct impacts from extreme MSL rise scenarios, which is considered to be the most significant component to future risk.
 The outputs from each model simulation in the ensembles were maps of water depths at each time step in the simulation, from which the maximum water depths in each cell, during each simulation, could be found and used to estimate the flood hazard.
 From the simulations conducted four statistics were produced:
 1. The area of inundation associated with each sea level rise scenario. A cell was said to be inundated if the maximum flood depth was 0.1 m or greater. Cells with depths below 0.1 m were not included as inundated as this is below the accuracy level of the LiDAR data, and unlikely to lead to significant and unpreventable flood damage [Purvis et al., 2008].
 2. The hazard (given in terms of £ loss) associated with each sea level rise scenario. The losses associated with building structure and content damage, and agricultural productivity disruption was given based on the methodology of Penning-Rowsell et al. . Damage to “urban” cells was estimated using average residential depth damage curves for the UK and the maximum inundation depth in a given LISFLOOD-FP simulation. A 10% increase to the structural damage was included due to the presence of saltwater inundation. Similarly, agricultural loss (dominated by grasslands used for grazing) was estimated based upon financial and economic gross margins for livestock enterprises [Penning-Rowsell et al., 2010] assuming that an inundated cell resulted in no productivity. Bare earth cells were assumed to have no value. DEFRA [2006b] highlight that the impact upon people is a fundamental aspect of flood risk assessment, while the Organisation for Economic Co-operation and Development (OECD) suggests that, in order to provide the most efficient mitigation strategies to cope with flooding, a monetary assessment of the hazard to people should also be included [Organisation for Economic Co-operation and Development (OECD), 2012]. The number of deaths and injuries for a given event, accounting for the severity of the flood conditions, the “area vulnerability” (which defines the susceptibility of a region based on factors such as the quality of flood warnings), and the “personal vulnerability” (which is conditioned by the proportion of old and infirm) was calculated using the methodology proposed by DEFRA [2006b]. Using the value of a statistical life, the corresponding economic loss valuation was given by
where Ci and Cd are the costs associated with injuries and deaths, respectively, Ni is the number of injuries, Nd is the number of deaths, VSL is the value of a statistical life given as approximately £2.4 million for EU-27 areas [OECD, 2012], and 0.06 is a scaling factor relating the cost of an injury relative to that of a death defined by the relative value of prevention per incident associated with fatal and nonfatal road accidents in the UK in 2010 [Department of Transport, 2012].
 Finally, an emergency service cost (given as 5.6% of the total residential property damage) was applied after Penning-Rowsell et al. .
 3. The per-cell probability of inundation was calculated. This was given by equation (1), in which Piflood is the probability of inundation in cell i given the range of sea level rise scenarios contained in the ensemble and the associated probability of their occurrence, fij is an indicator function which takes a value of 1 or 0 depending on whether the cell was inundated or not during simulation j, and P is the probability of the scenario j occurring, taken from the distribution in Figure 3.
 4. The risk (per year) was by multiplying the probability of inundation in each cell by the associated cell hazard value and dividing the resulting loss estimate over the 200 year return interval
4. Results and Discussion
 The current inundation extent (with no additional sea level rise) associated with a 1:200 year event was approximately 4.5 km2 (Figure 4). Flooding was predicted to occur only in grazing lands surrounding the river Yeo. These findings are consistent with the current standard of protection of the defenses and previous research by Purvis et al. , although, they predicted only 1.8 km2 would be flooded. This discrepancy is likely to be associated with the way in which the tidal wave was prescribed. In this research, a sine curve was used, while Purvis et al.  used a triangle form, which Smith et al.  suggest results in significant underprediction of the high tide water volume. Figure 4 also falls within the range of inundation extents expected in the region presented in Lewis et al. [2011, Figures 5c and 6a]. This consistent comparison with other studies helps to validate the models capabilities in the region, and therefore, provides confidence in the reliability of the subsequent assessment of the future risk from sea level rise.
 The area of inundation and the associated hazard (given as £ million loss) with the various estimations of future sea level rise are given in Figure 5. The area of inundation relative to the increase in sea levels was well represented, in this case, by a linear trend (r2 0.96), while the hazard (given as £ million loss) curve presented in Figure 5 showed an increase in slope beginning from approximately 0.5 m sea level rise. The change in the slope of the hazard curve was associated with the onset of inundation of urban cells in the Weston-Super-Mare and Clevedon regions, due to overflow of sea defenses (Figure 6), while costs continued to escalate even once all urban cells were inundated, due to the effect of depth on the hazard, associated with increasingly severe sea level rise scenarios. These findings can provide coastal managers with valuable information relating to mitigation policies, highlighting both the change in the nature of the hazard through time and providing a time frame within which one might need to implement mitigation strategies. For instance, the results indicate that inundation of urban areas (and therefore a rapid escalation in the hazard) would begin between 0.4 and 0.5 m sea level rise. Using the projections given by Lowe et al.  for Cardiff, it can be estimated that this level would be contained within the 95th percentile bounds by the 2070s, 2060s, and 2050s in the low, medium and high emission distributions, respectively. Given that the planning and implementation of alterations to sea defenses can take many years, such indications are useful in highlighting the urgency of action required.
 The results presented in Figures 5 and 6 enable one to ascertain the hazard of a given sea level rise, which is of great value to coastal managers, as discussed. Similar deterministic “what-if” scenario-based approaches have been used by Lewis et al.  and Dawson et al. . However, the expected future sea level rise is very uncertain. A more detailed assessment of the effect of future sea level rise in a region can be given when one accounts for such uncertainty, provided by calculating risk (a product of the hazard and the likelihood of an event occurring). Given the probability distribution presented (Figure 3), the probability of inundation in each cell can be calculated using equation (1). The estimated inundation probability for the region, highlighting the contribution of low probability scenarios, described in section 3.3, is presented in Figure 7. Contrasting the two inundation probability maps indicates that in the grazing areas directly surrounding the river Yeo the inclusion of the low probability tails of the distribution reduced the probability of inundation. This demonstrated that without inclusion of the scenarios prior to the fifth percentile sea level rise estimate, the probability of inundation in this region would be overestimated as not all sea level rise scenarios between 0 m and 1.9 m would induce inundation. Alternatively, the underestimation of the probability of inundation, due to the exclusion of the 95th–100th percentile portion of the distributions, was found to influence a significant proportion of the model domain. Of particular relevance in terms of future inundation risk was the increase in likelihood of inundation throughout many of the urban areas when the low probability tails of the distribution were included. Without inclusion of the distribution tails, many of the urban cells would have been predicted to have had a probability of inundation of zero.
 The findings highlighted in Figure 7 were extended to assess the significance of the low probability tails to the predictions of risk. This was examined by calculating the risk associated with three methods by which one may ascertain the probability of inundation. In the first instance, the central sea level rise estimate (0.531 m) only was used, assuming a probability of 100% (representing a deterministic approach to future risk). This resulted in a risk of £0.77 million. Second, using the probability of inundation given from the 5th to 95th percentile of the distribution [after Purvis et al., 2008], the risk was given as £1.17 million. Finally, a risk of £1.66 million was predicted when the full distribution, including low probability scenarios, was considered. These results indicated that the exclusion of the low probability tails of the sea level rise projections would decrease the risk by 29.7% and 53.6%, relative to those obtained using only the scenarios contained between the 5th and 95th percentile boundaries, and the deterministic approach, respectively. Considered from a defense design perspective, the current best practice guidelines from the Department for Communities and Local Government (DCLG) for the construction of defense structures for the future suggests that planners should allow for a 96 cm increase in mean sea levels for regions in the south west of the UK by 2100 [DEFRA, 2006a; DCLG, 2012]. This is a conservative value based upon the IPCC third assessment high emissions, high model sensitivity scenario, with a local adjustment to include vertical land movements for the UK. The results from this research indicate that increasing defense structure heights to this level would be expected to protect against approximately 96% of the sea level rise scenarios in the estimated distribution. However, the remaining projected sea level rise scenarios beyond this height, although unlikely, would be expected to contribute a residual risk of approximately £0.38 million. To further demonstrate the importance of the inclusion of extreme event risk, Table 1 provides the contribution to the overall risk for every 10% of the distribution, while Figure 8 plots the probability of occurrence and the risk for each sea level rise scenario in the distribution. From these findings, it can be demonstrated that although the likelihood of extreme sea level rise, such as that contained in the UKCIP H2+ scenario, is unlikely, the associated hazard is large, resulting in a significant contribution to the overall risk, and therefore this should be an important consideration to mitigation decisions.
Table 1. The Contribution to Risk From Each 10 Percentile Bin
Portion of the Probability Distribution (Percentile Range)
Contribution to Risk (%)
 Although the results presented in this paper cannot be directly applied to other coastal regions due to the complexity in the response of risk to an increase in sea levels, the methods used could be easily transferred to other locations or applied to less extreme estimates of future MSL rise than that used in this research. The main findings of this research will be of interest to those interested in inundation to coastal areas throughout the world, particularly coastal megacities such as those discussed by Nicholls , in which millions of people and billions of dollars of urban developments are found.
 This paper examined the risk facing the Somerset Levels due to projected future sea level rise, with a particular focus on the importance of the inclusion of low probability, extreme scenarios associated with the onset of a rapid ice sheet mass loss. The research provides a valuable insight into the nonlinearity of changing hazard in response to the change in projected sea level rise and demonstrates the significant contribution of low probability, high consequence scenarios to the overall estimation of risk. Further research could extend the examination of the influence of rapid ice sheet mass loss to the estimation of risk in the region by providing more accurate predictions of future ice sheet contributions to sea level rise in the coming century. For instance, the historical record of ice sheet mass loss has been shown to contain punctuated periods of short-term increases and decreases in the rate of loss [Bentley, 1998; Hansen, 2007; Rignot et al., 2008; Bjørk et al., 2012; Moon et al., 2012]. The presence of such events could significantly alter the expected future risk, particularly over time scales of relevance to mitigation policy. Increasing our understanding of the processes controlling the onset of rapid mass loss, and the duration over which they occur, and therefore, the likelihood of rapid sea level rise occurring in the future, is fundamental in improving our estimates of future risk. Due to the complexity and often nonuniform response of different ice masses to climatic drivers, recent work such as that by M. Siddall et al. (Sea level hazard from increased dynamic ice loss from ice sheets, submitted to Global and Planetary Change, 2012), which aims to provide an estimate of dynamic ice loss contributions to sea level rise based upon the estimated recurrence intervals of the onset of rapid ice mass loss associated with individual glaciers, including the effect to onset likelihoods from increasing temperatures, could provide more useful projections of sea level rise at a variety of lead times than are currently available from methods assuming a steady rate of ice mass loss. Coupling such estimates with flood risk models, such as that used in this paper, could provide more robust estimates of risk for a given lead time. They further suggest that continued collection of paleo-proxy data with which to define recurrence intervals of dynamic ice loss events is a key task in increasing the accuracy of future sea level rise predictions. This is particularly important as short records can lead to biases in the predicted rates of change where decadal variability in the measured rates of ice mass loss can be found. Haigh et al.  for instance, found that decadal variations in mean sea levels resulted in bias in their projections unless at least 50 years of data were included when using a traditional linear regression approach to the estimation of rates of mean sea level rise throughout the 20th century.
 Future work could also relax a number of the risk analysis assumptions used in this study. In particular, risk could be assessed for a greater range of events including those against which we currently do not protect ourselves (i.e., events with a recurrence interval >200 years) and for loss induced by overtopping, breaching and fluvial inputs rather than those purely due to storm tide overflow [Brown et al., 2007; Gouldby et al., 2008; Stansby et al., 2012; Wadey et al., 2012]. Future economic and social scenarios could also be considered, while the number of receptors to risk considered could be expanded. For instance, the KULTURisk project (http://www.kulturisk.eu), currently in progress, aims to provide a robust methodology with which to estimate risk, accounting for a wide variety of factors contributing to risk not considered in this research, such as economic losses due to business closure related both to businesses directly impacted by flooding and those affected through trade connectivity. However, it is anticipated that none of these refinements are likely to change the overall nature of the conclusions drawn in this research.
 This paper assessed the coastal flood risk to the Somerset Levels region due to projected future sea level rise by 2100 using an asymmetric distribution with a central value derived from the latest UKCIP high end estimate for the Severn Estuary. The contribution of plausible low probability sea level rise scenarios, due to the possibility of increased rates of ice sheet mass loss, was examined. The results indicated that there was a significant (29.7%) increase to the projected risk in the region due to the relatively large hazard associated with such scenarios. These findings clearly demonstrate that any estimation of future coastal flood risk in the region is likely to be underestimated unless it accounts for the possibility of the onset of rapid sea level rise in the coming century. Due to the global nature of sea level rise, these findings are expected to be applicable to coastal flood risk analysis in other regions throughout the world. Furthermore, it is expected that the significance of low probability scenarios to risk will be even greater in many of the most at risk regions of the world.
 The research presented in this paper was funded by the KULTURisk FP7-ENV-2010 project. More information about the KULTURisk project can be found at http://www.kulturisk.eu. The authors are grateful to the Environment Agency of England and Wales for the provision of LiDAR data, and would like to acknowledge the previous work by R. Smith and M. Purvis on the FLISFLOOD-FP model data sets used in this research. Finally, the authors are grateful to M. Trigg, G. De Almeida, and J. Neal of Bristol University for their assistance.