1 Introduction

The storm called Xynthia hit the French Atlantic coast during the night of 27 to 28 February 2010. It was responsible for the death of 41 people by drowning and around 2.5 billion Euros of damage following the flooding of low-lying areas by the sea (Cour des Comptes 2012). Though the storm was not an extreme one (Feuillet et al. 2012), some of its characteristics (e.g. tide level, waves) (Bertin et al. 2012) resulted in a large sea surge in the Vendée and Charente-Maritime Departments, which are partly covered by polders or marshes (CETMEF et al. 2009).

Reviews of the storm show that the consequences of Xynthia (Anziani 2010; Bersani et al. 2010; Kolen et al. 2013; Pedreros et al. 2010; Devaux et al. 2012) were the result of people being located in hazardous areas. The development of tourism over the past 50 years has led to the uncontrolled growth of coastal towns and, in some cases, to the urbanization of low-lying areas. This is clearly shown by Vinet et al. (2012a), who point out the dynamics of urbanization in La Faute-sur-Mer (29 deaths by drowning during Storm Xynthia) to explain this death toll. It shows the inadequacy of houses with respect to the coastal flood hazard, along with poor land management in areas prone to coastal flooding due to the misjudgment of risk policy in France (Lumbroso and Vinet 2011; Douvinet 2011; Chadenas et al. 2013).

The inadequacy of buildings and the potential exposure of their occupants to lethal risks led the French State to implement an enforced relocation scheme and the demolition of homes at risk. Better known as the “black zone” policy, it was applied only to the Xynthia-impacted areas and has been widely criticized (Mercier and Chadenas 2012; Magnan and Duvat 2014). Nonetheless, it was the first attempt in France to implement a risk mitigation policy via the displacement of vulnerable people. Although of major importance, this policy measure has only had a limited impact because it was not extended to areas other than the ones impacted by Storm Xynthia. However, other French coastal regions display several characteristics in common with the areas impacted by Xynthia. It is therefore important to establish a diagnosis of these places in order to protect the population against similar catastrophic events. This issue is of great importance and will become increasingly relevant in the context of sea-level rise due to climate change, which could be responsible for the increase in storms similar to Xynthia (Cazenave and Le Cozannet 2013).

A review of the literature shows that there is no vulnerability index developed in France to evaluate, at a micro-scale (i.e. at the level of individual buildings), the vulnerability of houses for their occupants. The aim of the present publication is to propose a tool to identify places where people can be in danger of drowning during a coastal flood due to the inherent characteristics of their house. For this purpose, we have created the V.I.E. index (Vulnérabilité Intrinsèque Extrême), which can be translated as the Inherent Extreme Vulnerability index. The concept of “extreme vulnerability” refers to a lethal danger for people through the vulnerability of their house. The vulnerability of every individual building can be assessed using this index. The aim of the V.I.E. index is to be both simple to use and transposable to other regions in France.

We shall first consider the lessons learnt from Xynthia concerning vulnerability, the work done so far on vulnerability indices and the novelty of the V.I.E. index. Then, we shall describe the whole process of building the index and evaluate its robustness through a principal component analysis (PCA) and an ascending classification of buildings in the affected area in order to compare the resulting typology with the occurrence of casualties and the black zones selected by the government policy. We will present the first results using three small towns as examples, and finally discuss the potential and limitations of the index.

2 Vulnerability and human exposure to coastal flood hazard

2.1 Xynthia: the construction of human exposure to coastal flood hazard

The rare combination of high tide levels (coefficient of 102Footnote 1), low pressure (977 ha) and strong southwest winds (130 km/h) generated Xynthia and a dramatic sea surge along the departments of Vendée and Charente-Maritime (Bertin et al. 2012; Feuillet et al. 2012; Fig. 1). It resulted in the flooding of low-lying areas, mainly polders in the Poitevin marshes, the Charente estuary, and Ré and Oléron islands (Breilh et al. 2013). More than 50,000 ha were flooded due to Xynthia (Chauveau et al. 2011; Verger 2011; Magnan and Duvat 2014).

Fig. 1
figure 1

Area impacted by Storm Xynthia and location of the studied towns

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With the development of the “leisure society”, coastal areas have become much more attractive to people (Corbin 1990). Since the 1950, tourism has steadily increased, along with a rapid expansion in second homes. The French Atlantic coast is particularly affected by this because Vendée and Charente-Maritime are now amongst the most popular tourist departments of this coastline (Renard 2005; Chauveau et al. 2011).

The development of residential and second homes has increased the pressure on land in coastal towns. The population density of the French Atlantic coast has grown by 40 % since 1962, and the number of new buildings was three times higher than in other parts of France between 1990 and 2012 (Observatoire National de la Mer et du Littoral 2014). This phenomenon has contributed to the urbanization of low-lying areas, protected by dikes (Verger 2011; Perret and Sauzeau 2014). The occupation of low-lying areas for the development of housing estates is a sign of urbanization unaware of coastal hazards, which can be linked to the absence of any extreme coastal flood events in France for more than 60 years (Garnier and Surville 2010). This development was made possible by the lack of clear regulations to control urbanization in exposed areas, which can be observed in the inadequacy of the design of houses with respect to coastal flood risks (Vinet et al. 2012a; Chadenas et al. 2013).

Due to the lack of risk awareness, the French government decided to assess the vulnerability of houses with regard to some risk criteria and to buy back the most dangerous (Mercier and Chadenas 2012). This policy was known as the “black zone” or “solidarity zone” policy. It has been severely criticized by the people concerned because of a lack of information and the quick decision-making of the measure (Mercier and Chadenas 2012). Finally, approximately 1100 houses were purchased by the Government and destroyed (Cour des Comptes 2012). This was a first step in the assessment of vulnerability at a house-based micro-scale, but it concerned only towns that were impacted by Xynthia. Nevertheless, many other areas of the French coast are in the same situation (CETMEF et al. 2009).

The location of buildings or their inherent characteristics can be sources of danger for their occupants. The rapid rise of the water and the surprise effect this has on occupants are important factors that can cause casualties. The effect of dike failure is paramount, as illustrated by the fact that 90 % of Xynthia deaths occurred within 400 m of dikes (Vinet et al. 2012b). Water depth also poses a danger to coastal populations. Beyond 1 m of water rise, it is recognized that a “healthy, fit” adult experiences great difficulty in moving (Ministère de l’écologie et al. 2011). In some places, the sea level reached 2.5 m high, reducing the opportunities for shelter. The architecture of the buildings can be an additional risk (Jousseaume et al. 2004; Jousseaume and Mercier 2009; Jonkman et al. 2009; Leone et al. 2011; Vinet et al. 2011, 2012a, b). Seventy-five percentage of the deaths by drowning during Xynthia occurred in single-storey houses, which acted as a trap for their occupants (Lumbroso and Vinet 2011; Vinet et al. 2012b). The absence of a window in the roof and the widespread presence of electric shutters that became stuck were aggravating factors that increased the risk.

Many other factors explain the death toll from Storm Xynthia, but these are not directly related to the characteristics of buildings. Not all human aspects are treated here. The age structure of the population had a negative impact on their ability to escape and be rescued (Vinet et al. 2011). The median age of people in La Faute-sur-Mer, where 29 people died during the Xynthia event, is significantly higher (52 years) than in the rest of France (38 years) (Vinet et al. 2012b). Eighty percentage of houses in this town are second homes, many of which were unoccupied during the storm outbreak.

2.2 How to assess vulnerability to coastal flood hazards?

The definition of the assessment of extreme vulnerability of houses is a key issue for the present study. However, many different definitions can be found in the literature. Birkmann (2006) proposed an inventory of more than 25 definitions of vulnerability. Consequently, there are as many different ways of assessing it, depending on the object studied (Barroca et al. 2006) and the goal of the study (Romieu et al. 2010). Khazai et al. (2014) used an ontology-based approach to discover a link between the different definitions of vulnerability assessments. Nevertheless, few procedures to assess the vulnerability to coastal flood hazards of houses for their occupants are available.

A few studies have dealt with the assessment of vulnerability regarding coastal risks (Cutter et al. 2000; Rygel et al. 2006; Meur-Férec et al. 2008), but there is still a lack of micro-scale assessment (Leone and Vinet 2006). Many studies are available in the UK or the Netherlands since the 1953 storm that was a dramatic event. They focus on the development of an agent-based loss-of-life-model (Di Mauro and Lumbroso 2008; Jonkman et al. 2008; De Bruijn and Klijn 2009; Di Mauro and De Bruijn 2012; Di Mauro et al. 2012). We can note Ramsbottom et al. (2003) and Priest et al. (2007) who proposed a methodology to assess and map fatalities caused by flooding or coastal flooding; they mainly focus on the risk of damage and collapse to buildings. The Social Flood Vulnerability Index, also developed in the UK, is applied at the building scale (Crone 2013). It focuses on social indicators to assess vulnerability of people to flood events, using census data.

Building assessments are also present in several other studies but mainly in connection with tsunamis (Dominey-Howes and Papathoma 2007; Reese et al. 2007; Dall’Osso et al. 2009; Gauraz et al. 2009; Leone et al. 2011; Mück et al. 2013; González-Riancho et al. 2014) and flood hazards (Kelman and Spence 2003; Priest et al. 2007; Eleuterio 2012).Their purpose relates more to the structural vulnerability of buildings. The coastal flood hazard is quite a different process from tsunami or flood hazards. Tsunamis follow a geological process while coastal floods are caused by a storm stemming from a hydrometeorological process. The latter is usually less powerful but can be very surprising for people when water begins to overflow the flood defences. Unlike building assessments for tsunami hazards, the destruction of buildings is not expected because the intensity of coastal floods is lower than that of tsunamis.

The literature on casualties induced by a flood outbreak is also extensive. According to Jonkman and Kelman (2005), pedestrians and drivers are the people most exposed to drowning. For these authors, only 6 % of deaths occur in houses. However, 54 % of deaths linked to the hurricane Katrina took place at home (Jonkman et al. 2009). Moreover, the particular feature of Xynthia was that it hit people at night and they were trapped in their houses.

This being said, our intention is not to work on the vulnerability of people but on the characteristics of buildings that can jeopardize their occupants in order to propose adaptation measures. Therefore, we emphasize the vulnerability of buildings for people exposed to coastal flood hazard, using the post-disaster analysis of Storm Xynthia, to propose a tool that can serve for pre-disaster strategies to define adaptation measures for buildings.

We define the concept of “extreme vulnerability” as possible exposure to mortal danger to people through the vulnerability of their home. The aim is to identify those houses that can lead to the death of people during flooding, because of their inadequacy with respect to the risk. We do not focus on the mere physical characteristics of buildings but on their closeness to the source of the hazard or their architectural characteristics, which can increase the vulnerability of their occupants. This work is developed at a micro-scale level, i.e. the building itself.

3 The V.I.E. index

The V.I.E. index is based on the lessons learned from Xynthia. It is a composite index of vulnerability to characterize the exposure of residential buildings to “extreme” vulnerability with four criteria, which can be applied at a micro-scale level (residential building). This tool is designed to be simply practicable; it is based on easily available data and the use of a GIS tool (Geographic Information System). To confirm its usefulness, we tested its statistical robustness and developed a comparative analysis with the actual consequences of Storm Xynthia.

3.1 The four criteria

Xynthia has provided many lessons on how a coastal storm that causes flooding can become a disaster. Our index is based on four characteristics of the storm, resulting in four criteria. They are divided into two categories: the exposure of the building to coastal floods and the inherent characteristics of the building producing greater vulnerability.

Because one aspect of this work concerns residential houses, a database (BD Topo, Institut Géographique National) was used to collect the geometry of buildings.

The first parameter, i.e. exposure of buildings to coastal flood hazard, includes two criteria: the potential water depth in the building during flooding, and its closeness to flood defences.

3.1.1 The potential water depth (Cr1: “Appendix 1”)

This is the first parameter that can explain the vulnerability of a building to coastal flood hazard (Ramsbottom et al. 2003; Jonkman 2007; Jonkman et al. 2009). As seen above, all the deaths by drowning caused by Storm Xynthia occurred in a water depth higher than 1 m (Vinet et al. 2012b). To calibrate this criterion, we used the sea water level baseline defined in the risk prevention plan (RPP—Chadenas et al. 2013). It usually corresponds to a 1 in 100 years event or a higher measured historical event if known. In the present case, the 1 in 100 years theoretical event is lower (3.90 m NGFFootnote 2—Pineau-Guillou 2012) than Xynthia sea water level (4.70 m NGF), it is the second one which is used. We used a “static” floods method (Breilh et al. 2013) to transpose this water level to coastal lands, and light detection and ranging data (LiDAR—from the French Litto-3D program) to create a digital terrain model (DTM). For each residential building, we calculated the difference between the ground and water levels: this figure gives the potential water depth rise for each house. To avoid overestimating the number of houses that can be flooded, we selected only those located in a low-lying area in contact with the sea (<100 m from the sea). It is considered that above the 0.5 m water depth, rescue teams cannot use terrestrial vehicles, making rescue operations more difficult. Above 1 m, it is agreed that a person in good health cannot move easily (Ministère de l’écologie et al. 2011). Above 2 m, in a single-storey construction, people are trapped under the roof (Vinet et al. 2012b).

3.1.2 The distance to flood defences (Cr2: “Appendix 2”)

Flood defences creates a false feeling of safety for people living behind it (Vinet et al. 2011). If it can prevent regular coastal flood events, people may forget about the major risk of inundation of overflowed dikes, which can dramatically increase rare and large coastal floods. This is what happened in La Faute-sur-Mer during Storm Xynthia since people were surprised during their sleep by a very large rise in the water level. All the people of this town who died were living <400 m behind the dikes (Vinet et al. 2012b). With this criterion, we intended to assess the speed of water rising in houses. The closer a house is to a flood defence structure, the higher its vulnerability. For the same reason, we considered that the higher the dike, the riskier the situation in the case of a sudden collapse of the flood defence. We also paid attention to the current structural integrity of the structure: if it is in poor condition, the risk of collapse is greater. Moreover, the fact that houses are located or not in a basin was taken into account because basins concentrate water flows. On the basis of previous work of Jonkman et al. (2008) who distinguish three hazard zones behind a breach (i.e. breach zone; zone with rapidly rising water and remaining zone), we propose three security strips behind dikes, considering lessons from Storm Xynthia (Vinet et al. 2011). As far as the rating procedure is concerned, the principle of the RPP regulation was used (Ministère de l’écologie et al. 2011), i.e. one strip, of high vulnerability (breach zone), equal to 100 m behind the dike; another adjacent one whose width is equal to the dike height (h) in metres multiplied by 100 (zone with rapidly rising water); and a last one, of lower vulnerability, between h × 100 and 400 m. The remaining zones are located beyond 600 m from the flood defence, where the rise of water level is relatively slow and cannot be considered dangerous for people in residential houses as demonstrate in Charron.

The calculation of this criterion is a little bit different from the three others because it has two additional “sub-options” which can increase the final score itself. First, the state of the structure which concerns the house (−0.5 to +0.5) and secondly, the presence of the house in the basin (+0.5). For instance, the maximum score is 4 points for a house located in the 100 m strip behind a weak dike, located in a basin.

To locate dikes and flood defences, the BD Topo dataset from IGN was used, which includes a dike layer. It excludes natural dunes from flood defences. The data about the state of structures came from RPPs, while basins were identified with the DTM.

The second parameter, inherent characteristics of buildings, refers to house features that are likely to increase the extreme vulnerability. This parameter is split into two criteria: the architectural type of houses and their closeness to a point of rescue.

3.1.3 The architectural typology of buildings (Cr3: “Appendix 3”)

As demonstrated during Storm Xynthia, single-storey constructions can be a trap for people during flooding, whereas a house equipped with an upper floor is safer (Vinet et al. 2012b; Lumbroso and Vinet 2011; Dominey-Howes and Papathoma 2007). For this reason, the architectural typology is a very important factor of vulnerability for buildings exposed to coastal flood hazard. We first built a typology according to previous works (Jousseaume and Mercier 2009; Leone et al. 2011; Mercier and Chadenas 2012; Chevillot-Miot et al. 2013) and collected field data for each individual house.

The majority of houses in French coastal zones are constructed in such a way (e.g. from concrete, concrete blocks or bricks) that they are not easily damaged during tidal surges (André 2013). This is the reason that building materials have not been considered in this paper.

This architectural typology is divided in five types:

  • Single-storey constructions without roof evacuation: this type of dwelling is typical on the French Atlantic coast (Vinet et al. 2012b). Without an upper floor, this type of dwelling appears to be a trap for people during Xynthia. Seventy-eight percentage of deaths occurred in single-storey buildings, in which water depth reached 2.50 m in some cases (Vinet et al. 2011; Devaux et al. 2012). Without roof evacuation, people have no chance to escape from their house if they are surprised by rising water.

  • Single-storey constructions with roof evacuation: it is the same type as above but the roof evacuation gives a chance for people to evacuate from their house if they are surprised by rising water. It also makes it easier for a rescue team to intervene.

  • “Rescue” level constructions: it can be defined as “a less dangerous building because it allows people to find refuge in case of rising water; however, the inside access is not always guaranteed, and cannot always accommodate all occupants” (Vinet et al. 2012a). During Storm Xynthia, four deaths occur in this type of dwelling (Vinet et al. 2012b).

  • One floor or more: in this type of dwelling, the upstairs floor “can accommodate all occupants of the housing” (Vinet et al. 2012a). During Storm Xynthia, one death occurs in this type of constructions (Vinet et al. 2012b).

  • Ground floor unoccupied: in this type of dwelling, the ground floor is not a living room, people are expected to be upstairs in case of flooding.

3.1.4 The closeness to a rescue point (Cr4: “Appendix 4”)

We defined a rescue point as a piece of land larger than 100 m2 that cannot be flooded (Sahal 2011). The proximity to a rescue point is a factor that reduces vulnerability because people can move to a safer place during a coastal flood warning (Jonkman et al. 2008). Moreover, if rescue teams need to evacuate people, having a rescue point in the area makes rescue operations easier, reducing the time of intervention. We also assumed that in housing estates, the spatial concentration of houses allows the assistance of neighbours. Therefore, we considered that the closeness to a rescue point is an important feature of house vulnerability, as well as the isolation of a building.

At less than 100 m, it is possible to reach the rescue point. Between 100 and 200 m, it becomes harder. Beyond 200 m, it is nearly impossible, especially if water rises rapidly. This criterion could be improved by using time rather than distance, i.e. the time needed to reach the rescue point. In the present study, we do not have the means to do that but it will be considered in future improvements. Rescue points were defined on the basis of the DTM.

3.2 V.I.E. methodology

Based on these four criteria, the aim of the V.I.E. index is to score every house with regard to its vulnerability to coastal flood hazard. As presented in Fig. 2, the scores range from 0 to 4 for each criterion. To classify houses, the scores obtained for each criterion are added together to give a sum that defines the overall level of vulnerability. Criteria 1 and 4 are weighted because they are based on a DTM and could therefore be correlated, resulting in redundancy. To avoid this problem, we referred to the Human Development Index (HDI) literature (Klugman et al. 2011) to propose a composite criterion: Cr1 × 2/3 + Cr4 × 1/3. The formula of the V.I.E. index thus becomes:

$${\text{V.I.E}}\,{\text{index}} = \left( {{\text{Cr}}1 \times \frac{2}{3} + {\text{Cr}}4 \times \frac{1}{3}} \right) + {\text{Cr}}2 + {\text{Cr}}3$$
Fig. 2
figure 2

The V.I.E. index methodology

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The final result can vary between 0 and 12. It should be noted that houses that are out of flood reach are automatically marked as 0, and therefore not considered to be vulnerable. The power of the index is shown better by the use of maps. A colour-based scale divided into four categories is used as follows:

  • Class A (green): buildings are not located in a potential coastal flood area, so they are not vulnerable to this hazard;

  • Class B (orange): buildings are located in a potential coastal flood area; although the water depth is low, the architecture is suited to the risk level and buildings are not too close to a flood defence;

  • Class C (red): the risk level of buildings is high but not lethal if people behave in a “safe manner”, such as looking for a shelter upstairs; the water height is compensated in this class thanks to appropriate buildings or closeness to a rescue point;

  • Class D (black): buildings are subject to a potential lethal risk due to a high water depth, closeness to a flood defence and inappropriate architecture with respect to the risk level.

Initially, the index was applied using the current coastal flood hazard as it is defined in the RPP. It relates to a known historical sea level (for example the Xynthia level) or 1 in 100 years events if historical events are fewer (Chadenas et al. 2013). This scenario is named the “current scenario”. The resulting maps are presented in the preliminary results section.

In a second stage, it is proposed to focus on a projection of the current vulnerability to year 2100 to look at the effects of sea-level rise due to climate change. This scenario will be calculated using the “current scenario” event and adding 0.6 m for the sea-level rise (but not including all changes of parameters if a “genuine” 2100 scenario were to be tested). This value is recommended by ONERC (Observatoire National des Effets du Réchauffement Climatique) for the implementation of RPP. This corresponds to the 2100 “worst-case” scenario of sea-level rise proposed by the Ministère de l’écologie et al. (2011). This will affect both Cr1 and Cr4 (Fig. 2). This scenario will be named the “2100 scenario”. Results of this scenario are not presented here. All this work was done through a GIS application.

4 V.I.E. index validation

4.1 Statistical validation and limitations of automatic classification

On the basis of our first results obtained with the current scenario, we carried out a statistical validation of the work.

Two conditions are expected from a good composite indicator: firstly, a relative pairwise independence between all the criteria included in the index, and second, that each criterion is correlated with the overall index (Klugman et al. 2011). Consequently, we applied a first correlation analysis to the actual scores obtained in our sample of 5234 houses subject to coastal flood hazards (i.e. excluding those houses that are not vulnerable), over the three towns covered by the study. Concerning the first condition, it can be seen (Table 1) that the criteria are not too highly correlated between themselves (the maximum value is 0.219); this confirms the non-redundancy of all selected criteria. The second condition is also met by the index: each criterion is correlated with the overall index (the minimum value is 0.584), showing a good contribution of each of them to the calculation of the final index.

Table 1 Correlation matrix of the V.I.E. index
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To confirm the robustness of the V.I.E. index, we ran a Monte Carlo test on hypothetical values of the index. The aim was to assign random values to the criteria to perform a large number of random samples (e.g. 10,000) by combining these values and looking at the distribution of index values thus obtained. The results are presented in Table 2.

Table 2 Results of the Monte Carlo analysis of hypothetical V.I.E. index values on a sample of 10,000 trials
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The main features are the closeness between the mean value (6.49) and the median value (6.67) and the low skewness (0.02), which tend to show that the index follows a fairly normal distribution. The particular construction of the index by summing several criteria means that all the dimensions of vulnerability remain perfectly substitutable among themselves: it is possible to compensate a low value obtained in one criterion by a higher value obtained in another one. The negative kurtosis gives insight into the importance of mean values compared to extreme ones (elongated distribution).

In order to check the fitness of the V.I.E. index with actual observations, we then applied a PCA with the four criteria, entering the V.I.E. scoring of the 5,234 observations of the three towns mostly hit by Storm Xynthia: La Faute-sur-Mer, L’Aiguillon-sur-Mer and Charron.

The PCA displays a good scattered distribution of buildings on the factorial map: the horizontal axis is preliminary explained by Criteria 1–4 and 2, the vertical one by Criterion 3. The two first factors cumulate 75 % of the sum of Eigen values. The multivariate analysis was followed by an ascending hierarchical classification (AHC) based on the Ward criterion (maximizing the distance between classes and minimizing it within classes), using the test values and error probabilities of the SPAD© software (i.e. normal distribution tests around the sample means and frequencies).

Using the dendrogram and the histogram of level indices (“Appendix 5”), a good classification could be obtained with three classes (without Class A whose observations were excluded from the PCA). If we apply this classification to the case of La Faute-sur-Mer, L’Aiguillon-sur-Mer and Charron, we can describe each group by the following characteristics (“Appendix 6”):

  • Class B = V.I.E. results between 1 and 8.667, its mean value is 5.3 (SD = 1.6). It covers 1,198 buildings. Fifty-five percentage of them have a potential water depth above 1 m; 27 % of buildings are not protected by a flood defence structure and/or are located beyond the 400 m-strip; and 99 % have one upper floor (“rescue” level or a complete floor) and 47 % of them are close (<100 m) to a rescue point;

  • Class C = V.I.E. results between 4 and 8.5, its mean value is 7 (SD = 0.9). It covers 2229 houses, 70 % of them face a potential water depth between 0.5 and 2 m; 50 % are not protected by a flood defence structure and/or are located beyond the 400 m-strip; 99 % of them are single-storey constructions; and 60 % are <100 m from a rescue point;

  • Class D = V.I.E. results between 7.5 and 11.7, its mean value is 9.6 (SD = 0.8). It covers 1804 buildings, 85 % of them can be impacted by a potential water depth above 1 m; 65 % have results between 3 and 4 for Criterion 2, which means a high vulnerability in the case of an overflowed dike; 97 % are single-storey constructions; and more than 80 % are located further than 200 m from a rescue point.

With this classification method, classes are well balanced in terms of size. However, Class B is not totally in line with expectations. Fifty-five percentage of the buildings in this class have a potential water depth above 1 m, and yet it is recognized that above this level a healthy, fit person cannot move easily (Ministère de l’écologie et al. 2011). This is demonstrated by the fact that six people died in a house belonging to this class, with one floor or more (Vinet et al. 2011). They were trapped during their sleep without the ability to move upstairs. This cannot therefore be considered a safe place or a less vulnerable house.

With the aim of providing a more accurate tool, we re-defined another classification, based on the actual consequences of Xynthia.

4.2 Validation using a known storm event

As seen previously, Xynthia was the most significant coastal flood in the last 50 years in terms of casualties. The 41 deaths linked to the flood give the event an exceptional character.

Beyond the statistical aspects shown by the PCA results, the V.I.E. index still needed to be validated by the actual consequences of Xynthia in terms of casualties and post-event policies. To be more accurate in the definition of classes, we manually adjusted the limits of the classes in order to fit them as closely as possible with the definition of classes in part 3.2. This adjustment has a limited impact on the transposition of the index to other territories presenting characteristics close to those of the French Atlantic coast: low-lying territories protected by dikes or weak dunes, with a majority of single-storey constructions.

Based on the four classes identified previously, we delimited each class as follows (“Appendix 7”):

  • Class A concerns the buildings that are not subject to flooding. Thus, Criterion 1 = 0 and this condition is considered sufficient to put these houses into the A class (not vulnerable). 1958 are included in this class;

  • Class B: V.I.E. varies between 1 and 5; its mean value is 4.07. It covers 655 buildings that can be flooded but for which the human risk is limited. In this class, 75 % of buildings face a potential water depth under 1 m; 70 % of them are not concerned by the presence of a flood defence structure; 75 % have one upper floor (“rescue” level or a complete floor); and 75 % of them are close to a rescue point;

  • Class C: V.I.E. comprised between 5 and 8; its mean value is 6.76. It covers 2,440 buildings for which the risk can be high but not lethal if people have good reactions. Ninety percentage of the houses have a potential water depth between 0.5 and 2 m; 70 % of them are single-storey constructions; and 75 % are less than 200 m from a rescue point;

  • Class D: V.I.E. has values between 8 and 12; its mean value is 9.41. It encompasses 2,139 buildings where a risk of death cannot be excluded during a coastal flood event. It is composed of 80 % of houses in which the potential water depth can reach more than 1 m; 70 % are close to a flood defence; 98 % are single-storey constructions; and more than 50 % are located further than 200 m from a rescue point.

With this delineation, the classes are less balanced in size than with the PCA and automatic clustering, but Class B is more representative of buildings facing a low level of risk.

The limitation of this method is that some houses in Class D can be flooded by less than 1 m. For example, a score of 9 can be obtained in the following situation: Cr1 = 1, Cr2 = 4, Cr3 = 4, Cr4 = 1. This means that a house can be in Class D if it is close to a weak dike, is a single-storey house and is near a rescue point with <0.5 m of water. However, as can be seen in “Appendix 7”, only 3 % of the houses in this class have a water depth under 0.5 m. This combination is not very probable.

In order to validate this choice, we then applied the V.I.E. index again to the three towns studied in 4.1.: La Faute-sur-Mer, L’Aiguillon-sur-Mer and Charron. Although these towns are quite close to each other, they exhibit distinct features and the consequences of the storm were not at all similar. We compared the results of the V.I.E. index with the map highlighted by the “black zone” policy and the areas where casualties occurred. The correlations between the V.I.E. index and the impact of Xynthia are fairly good (Fig. 3). Figure 3 shows the results of V.I.E. index for two different black zones for three municipalities defined successively in April and October 2010 (3a, b, d, e and f) and for houses where deaths have occurred in La Faute-sur-Mer. It is expected that V.I.E. index shows a majority of black houses in these different areas.

Fig. 3
figure 3

Validation of the V.I.E. index using the Xynthia event

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Twenty-nine deaths occurred in La Faute-sur-Mer during Xynthia. Eighty-three percentage of them were located in houses classified as black buildings (D) by the V.I.E. index (Fig. 3c, and map Fig. 4). The other 17 % obtained a red score (C) according to the V.I.E., showing that the V.I.E. critical scores fit well with casualties. The town of Charron was also hit by casualties, but they occurred outside houses: three people were trapped by the water flow when escaping. This provides further evidence that the V.I.E. index captures the vulnerability of people living in at risk houses, but not the individual vulnerability of people, since no criterion dealing with the social aspects or behaviours of residents has been taken into consideration.

Fig. 4
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Mapping validation of the V.I.E. index on La Faute-sur-Mer using the Xynthia event

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In addition, our definition of vulnerable classes gave better results than the automatic classification of houses in which people died. With the manual classification, 25 of the 29 deaths were located in houses marked as black buildings (marked D) by the V.I.E. index. In the automatic classification, only 19 of the 29 deaths were located in black houses included in the most vulnerable class of houses.

For the black zones identified by the state scheme, we also obtained good results from the V.I.E. index (Fig. 3a, b, d–f). Two zones were successively delineated in La Faute-sur-Mer and L’Aiguillon-sur-Mer: the first one, in April 2010, was strongly contested by inhabitants and led to a second smaller zone in October 2010. For the first zone, 71 and 93 % of houses matched a black (D) V.I.E. score in La Faute-sur-Mer and L’Aiguillon-sur-Mer, respectively. Logically, the second one, which is smaller than the first one, was more accurate with 83 and 94 % of V.I.E.-blacked houses, respectively.

In Charron, only one black zone was defined in January 2011. It included only 5 % of black houses (100 % of which were identified by the V.I.E. index) and 74 % of red houses. The main difference is in La Faute-sur-Mer (Fig. 4). In the north of the town, the V.I.E. index identified a large housing estate that is potentially vulnerable to coastal flood hazard (La Chenolette), but this was not included in the black zones of the state scheme. After Xynthia, this area was reported as highly vulnerable (Pitié and Puech 2010), particularly during flooding of the Lay river. In the southern area, there is a good overlap of the V.I.E. critical area with the policy black zone.

5 Preliminary results

In Sect. 4, the V.I.E. index was applied to three towns impacted by Storm Xynthia (current scenario): La Faute-sur-Mer, L’Aiguillon-sur-Mer and Charron. The results are relatively different between the three towns as shown in Table 3.

Table 3 Results of the V.I.E. index for residential buildings of three municipalities
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5.1 La Faute-sur-Mer (Fig. 5)

La Faute-sur-Mer is a seaside town located in south Vendée. In 2006, there were 1008 permanent residents, 80 % of second homes and nearly 8,000 places for camping (Vinet et al. 2012a). It became independent from La Tranche-sur-Mer in 1953 and has expanded significantly since; its population has trebled and the number of buildings has increased sevenfold.

As reported in Vinet et al. (2012a), La Faute-sur-Mer is a perfect example of the possible errors and mistakes which have led to an increase in the risk level for populations. The town has developed on the sandy spit of Arçay and is isolated from the Lay estuary by dikes, hence artificially isolated from the sea. The dike was constructed by farmers to protect land from coastal floods. However, in 1957, engineers reported that this dike was not able to protect buildings (Perret and Sauzeau 2014). While the original village of La Faute-sur-Mer is located on a relatively high point of the town, expanding urbanization has reached the lowest part of the southern tip of Arçay. The lack of planning documents has enabled the urbanization of the lower areas without special architectural requirements (Pigeon 2012). Single-storey construction is traditional because of the need to be protected against the wind (Perret and Sauzeau 2014). The housing estate where 28 people died by drowning because of Xynthia was built after the year 2000. The most recent buildings were flooded by more than 2 m of water.

Fig. 5
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V.I.E. index application to La Faute-sur-Mer

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These characteristics give La Faute-sur-Mer an inherent exposure to coastal flood risk. The application of the V.I.E. index confirms such an analysis. For the current baseline hazard, 4.70 m NGF (Xynthia level), only 8 % of the buildings are not affected by any coastal inundation. These are located on one side of the dune. Conversely, nearly 90 % of the buildings display a high degree of exposure to very high (and potentially lethal) risk for their occupants.

Two areas classified as D (black) by the V.I.E. index are clearly identified. The first is located in the south and was the most affected zone during Xynthia (28 deaths occurred here). The second, located in the north, also corresponds to recent concerns. It was flooded in February 2010 without lethal consequences. Nevertheless, the expert delegation (Pitié and Puech 2010) stated the particularly vulnerable configuration of this area, questioning the consequences of a sea-level rise related to climate change and the effects of a flood of the Lay river on this area. Indeed, some buildings are located around 2.50 m NGF.

Because 80 % of buildings are second homes, fortunately most of them were unoccupied during the Xynthia event (end February 2010) (Lumbroso and Vinet 2011); otherwise, the death toll could have been higher.

As shown in Fig. 4, La Faute-sur-Mer is a very special case. It is the most vulnerable town that we have analysed.

5.2 L’Aiguillon-sur-Mer (Fig. 6)

L’Aiguillon-sur-Mer is close to La Faute-sur-Mer and has experienced the same growth pattern. In 2011, this town had 2261 inhabitants but more than 40 % of second homes (INSEE 2011). Its population has grown by 50 % since the middle of the twentieth century. The town is mainly known for tourism, which represents the first industry in economic value (around 40 % of the town’s activity is linked to shops, transport and other services—INSEE 2011).

L’Aiguillon-sur-Mer is located on the other side of the Lay river from La Faute-sur-Mer so its seafront is shorter. The original village has changed location three times in the past because of the movement of the Aiguillon sandy spit (Perret and Sauzeau 2014) and is now located on a former “island”. The Aiguillon spit is oriented south from this point. It is a narrow spit, 13 km long, which protects the polders behind it. Because of its natural movement, the combination of the Lay river changes and the growth of the Arçay spit, the Aiguillon spit is defended by large dikes, the biggest being the Génie (i.e. the “Genius”) dike.

With the development of the town around the former island, houses have been progressively built in the surrounding low-lying areas (Les Grandes Vignes, Les Sables). The houses closest to the seaside are particularly exposed to coastal flood hazard. Other developments have been constructed more recently, like La Baie, a little further south, which is known as a higher vulnerability zone. Further south, there are houses on the narrow sandy spit, like Les Glaireaux, Les Caves and Les Sablons, which is located at the mouth of the spit. Les Sablons is an interesting example of the free development of the tourism industry in the French coastal area and of the difficulty of the French government in managing these constructions. Les Sablons has followed the development of “popular” tourism and that of temporary houses, shelters and other weak constructions. It has been made very vulnerable because of self-made constructions without planning (Perret and Sauzeau 2014).

Fig. 6
figure 6

V.I.E. index application to L’Aiguillon-sur-Mer

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Storm Xynthia impacted the town of L’Aiguillon-sur-Mer without any casualties occurring but with large flooded areas, mainly in the polders. The Génie dike, being too weak, was partly overtopped by the sea surge. As a result, 1590 houses were flooded, with water depths above 1.50 m in some cases (Pitié and Puech 2010). After the event, L’Aiguillon-sur-Mer was particularly concerned by black zones, like its neighbour La Faute-sur-Mer. One-hundred and eighty-nine houses and hundred shelters were bought back by the state and destroyed (Pitié and Puech 2010). Houses in Les Sablons were almost entirely destroyed. This is again well represented by the V.I.E. index. The absence of casualties can be explained by the large number of second homes, with very few people being present in their home during the storm.

L’Aiguillon-sur-Mer can be considered less vulnerable than La Faute-sur-Mer because of its location behind the Arçay spit, although the town could be exposed to a sea surge in the Lay estuary added to a flooding of the river. The most exposed area, Les Sablons, lies south of the spit because of its location in front of the sea. It was the most impacted town zone during Storm Xynthia but, as said above, it was totally destroyed by the French government.

5.3 Charron (Fig. 7)

Charron is a little south of La Faute-sur-Mer and L’Aiguillon-sur-Mer and is also located in the Aiguillon bay. In 2011, there were 1,893 inhabitants (INSEE 2011). Its social and demographic profile is very different to those of La Faute-sur-Mer and L’Aiguillon-sur-Mer: the proportion of second homes is far lower than in the two other towns (3.4 % in 2011). It is due to the fact that many of its inhabitants work in the nearby city of La Rochelle, Charron is their principal home.

The town has expanded on two different sites, which are two former islands of the Pictons gulf: Charron and Bourg-Chapon (Perret and Sauzeau 2014). Two small sandy spits connected the two islands at this time. Since 1771, the Poitevin marsh has become gradually disconnected from the sea by polders (Perret and Sauzeau 2014). The last period of dike construction took place in the nineteenth century and led to the two islands having around 2 km of seaside (Perret and Sauzeau 2014). Buildings that were concentrated on the two islands have progressively reached the former spits since the 1970s (red houses between the two islands—Perret and Sauzeau 2014). Other constructions were built on the edge of the islands. Finally, the two most recent expansions are located in the low-lying areas of the polder, namely La Marina on the western part and Les Sables de Bourg Chapon (i.e. The Sands of Bourg Chapon) on the northern part. Houses were built at around 2–3 m above 0 m NGF. However, without architectural obligations, 80 % of them are single-storey buildings. The dikes, which protect the town from the sea, should have been reinforced since 1999, but this has not been achieved because it was not considered as a priority project by stakeholders (Garnier and Surville 2010).

Fig. 7
figure 7

V.I.E. index application to Charron

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During Xynthia, dikes were overflowed and breached. The whole former marsh, on which houses had been built, was flooded. Around 250 houses were affected. Three people were trapped by water when escaping from their houses.

Considering the V.I.E. index, Charron is less vulnerable than the other two towns due to its greater distance from the sea. This advantage partly reduces the surprise effect during a coastal flood: 70 % of the constructions are located on the two islands and cannot be flooded, 18 % of the houses are in red and are located in the lowest part of the town, and 1 % of the houses are classified black. This latter proportion concerns the houses closest to the sea in La Marina. The lower vulnerability of this town is representative of its situation, where people were less exposed to the coastal flood hazard.

Our results reproduce the black zones identified by the state scheme relatively well. The French government destroyed 245 houses in Charron (Pitié et al. 2011). La Marina, Les Sables de Bourg Chapon, La Maison Neuve and the two sandy spits were all concerned by this measure.

6 Discussion

In this paper, we have presented the first steps of the V.I.E. index: its background, theoretical and statistical aspects, its validation and some preliminary results.

As shown, the first results are promising and give a quite realistic view of the consequences of Storm Xynthia. However, this approach requires several improvements.

First, we used a “static” method of superposition of a marine baseline to elevation data to estimate the potential water depth. This method has the advantage of being simple in its implementation but some points could be improved.

Firstly, the DTM based on LiDAR data is very accurate for our needs. The French Litto-3D project gives a DTM with vertical accuracy of 20 cm (IGN and SHOM 2012). But it has some limitations. Uncertainties vary, depending on the type of vegetation or human occupation (Cooper et al. 2013). This is true for marshes where water gives potentially wrong measurements leading to overestimated altimetry. In a first step, we can consider that this effect is insignificant for urbanized areas.

Secondly, the use of LiDAR data to measure the ground level of buildings is responsible for an error because houses are often raised above the ground. This elevation varies from 20 to 60 cm, but no accurate measure has been made to estimate the margin of uncertainty.

Thirdly, the method tends to overestimate the water depth, particularly for extensive marshes, by not taking into account the kinetics of flooding (Breilh et al. 2013). To refine the calculation of water depths and getting velocities data, it would be an interesting improvement to use a two-dimensional hydraulic model coupled with a probabilistic model of the failure of the dikes (Di Mauro and Lumbroso 2008). One other way would be the application of the alternative method proposed by Breilh et al. (2013), in which surge overflowing volumes are calculated. This would be particularly valuable for the Marais Poitevin.

However, our results are not problematic because the Poitevin marshes were flooded, 8 km from the sea at some points during Storm Xynthia. Moreover, the static method offers the advantage of being independent of any hypothesis used by a numerical modelling approach. Such hypotheses may concern the breaks in the levees, when water overflows the protection, the tide level, the river flow, etc. Only a probabilistic method would be useful in this case, independent of a specific event.

We decided to focus on the architectural characteristics of the buildings to assess the degree of vulnerability of populations during a coastal flood event. To be more accurate, it would be useful to complement the index with social data on how houses are occupied.

Firstly, it would be interesting to know how many people are living in the houses. We can assume that the more inhabitants there are, the higher the risk.

Secondly, the age of people matters in assessing their vulnerability. Many studies (Jonkman and Kelman 2005; Vinet et al. 2012b, Lumbroso and Vinet 2011) have shown the danger for very young, elderly or disabled people during flooding. The presence of an upper floor in the house is useless if people cannot reach it.

Thirdly, it would be useful to know whether houses are principal or second homes. According to the seasonality of storms, more people can be affected by a potential coastal flood event. For example, 80 % of residential houses in La Faute-sur-Mer are second homes (Vinet et al. 2012a). Many of them are likely to be unoccupied at the end of February, thus having a limited impact on the human death toll. This is particularly true for Les Sablons in L’Aiguillon-sur-Mer, where there are only temporary houses, and which were unoccupied during Xynthia.

This information can be obtained by finer occupation data, particularly available in the census data of the population. However, it is difficult in France to obtain census data at such a micro-scale.

To improve this work, it could also be interesting to use data from other coastal flood events that resulted in casualties, in order to compare the robustness of the methodology. A few big storms have hit France in the last 20 years (Lothar and Martin in 1999, Johanna in 2008, Klaus in 2009), but none led to such a large coastal flood as Storm Xynthia (Cariolet 2010). For instance, Xynthia could be compared with the storm of 1953, which had dramatic consequences in the Netherlands and the UK (Gerritsen 2005; Lumbroso and Vinet 2011).

The objective of this work was to provide an assessment of a fatal exposure of residential buildings to the risk of coastal flooding by going further than the mere analysis provided by the French government. The first results offer interesting additional inputs to the state policy regarding coastal flood hazards.

The next step could be the application of the V.I.E. index to other coastal towns that were not affected by Xynthia to identify areas with a high degree of exposure to coastal flood hazard. This work is ongoing to make a prospective application to the Island of Noirmoutier (Vendée). This island presents similar characteristics to those of Île de Ré, but it was not impacted by Storm Xynthia (Devaux et al. 2012), although it was strongly affected by a storm in 1937. Garnier et al. (2012) estimated the nominal cost of that storm as fourfold higher than Xynthia. It will be particularly relevant to consider mitigating measures aimed at reducing the vulnerability of buildings identified as highly exposed to marine submersion.

7 Conclusion

Storm Xynthia has highlighted the high vulnerability of coastal towns to coastal flood surges. More than the storm itself that resulted in the coastal flood event, the increasing human settlement in low-lying areas since the 1950s is responsible for this high vulnerability. Moreover, the inadequacy of houses towards coastal flood hazards is a second argument to adopt a micro-scale approach in the mitigation process. The creation of the V.I.E. index is a response to the necessary preventive diagnosis of extremely vulnerable sites for people. Based on four simple criteria (potential water depth, distance to a flood defence, architectural typology and closeness to a rescue point), this composite index is well balanced and offers good preliminary results for the towns impacted by Storm Xynthia. The next step will be the application of the V.I.E. index to a non-flooded area.

The destruction of extremely dangerous houses cost the French government more than 315.7 million Euros (Cour des Comptes 2012). With appropriate planning regulations, these buildings may not have been so vulnerable, and the adaptive measures would not have cost so much. In the context of global change and a tendency for sea-level rise, it is necessary to improve the assessment of highly exposed houses in order to reduce their vulnerability before a new tragic event occurs.