D Lo

Hine Tong

Ph Minard

Ch Person

J Ph

Coupez

P Borel

D Izoard

Dipole Antenna Printed on Paper Substrate for WLAN Applications

Keywords: MIMO antenna, dipole antenna, paper substrate, balun. I

The design of a dipole antenna printed on a paper substrate is presented in this paper. The antenna which integrates a compact balun is devoted for dual-band 2.4/5 GHz WLAN applications. The antenna is based on a double-side printed multilayer paper substrate and is fed with a coaxial cable for the testing. The simulated results of the whole structure are also presented in detail and compared with the measured performances.

INTRODUCTION

The constant demand of higher and higher throughput requires new generation of home networking devices such as Internet gateways and routers to integrate more and more antennas with up to 8*8 MIMO schemes for instance. This calls to ever figure out innovating and low-cost solutions when consumer mass-market is addressed. So far, FR4 substrate is mostly used for the design of the antennas but, with the numerous promising results published in the recent years, paper substrate printing can also be an interesting alternative cost-effective solution [START_REF] Lo Hine Tong | Comparative Study of WLAN Dual-Band Monopole Antennas Printed and Etched on Paper and PET Substrates[END_REF][START_REF] Phan | Novel Ultra-Wideband "Robe" Antenna on High-Loss Paper Substrate[END_REF][START_REF] Nguyen | RF characterization of flexible substrates for new conformable antenna systems[END_REF][START_REF] Kim | Inkjet-printed antennas, sensors and circuits on paper substrate[END_REF][START_REF] Lakafosis | Progress towards the first wireless sensor networks consisting of inkjet-printed, paper-based RFID enabled sensor tags[END_REF].

Using this technology, we designed a dipole antenna for WLAN dual band applications, operating in the [2.4-2.5] GHz and [5.15-5.85] GHz bands of the IEEE.802.11.b/g/a/n/ac standard. This paper describes first the proposed novel concept of dipole antenna that integrates a balun, then the design of the dual-band antenna printed on paper substrate is discussed deeply in section III, showing the simulated and measured results. In the last section some perspectives of this work are given.

II. DIPOLE ANTENNA WITH INTEGRATED BALUN

A. Concept with via-hole for feeding

This study is based on an original concept of dipole that integrates a balun [START_REF] Minard | Dipole antenna with integrated balun[END_REF]. Compared to common approach where balun circuit is cascaded in series with the antenna [START_REF] Lindberg | Dual wideband printed dipole antenna with integrated balun[END_REF], in this novel approach the balun is integrated in one of the resonating element of the dipole, resulting in a much more compact design. Fig. 1 illustrates an example of a dual-band antenna designed according to this principle and meant for WLAN applications. The design comprises two cascaded dipoles, with A1&A2 resonating in the lower frequency band (2.4GHz) and B1&B2 resonating in the higher frequency band (5GHz). The antenna is fed through a modified Marchand balun formed by a microstrip to radial slot transition with the slot placed in one arm of the higher band dipole (B2). In this first mode of realization the feeding microstrip line is terminated by a via hole connecting this line to the radiating elements printed on the bottom layer.

B. Concept with direct feeding

In this second mode of realization (Fig. 2), which aims to get rid of the via-hole in order to reduce fabrication costs, the microstrip feeding line is extended to the upper side of the dipoles and interconnected to them by a U-shape transmission line. In practical, this design can be realized by using very common metal stamping process, where the feeding line and the radiating elements are stamped in a single metal plate and folded at 180° to form the suitable antenna design. In the following section it is described how the antenna can be realized by using printed paper substrate.

III. DIPOLE ANTENNA USING PAPER SUBSTRATE

A. Description

The proposed design of the dual-band dipole antenna is depicted in Fig. 3 and Fig. 4.

-First, the raw substrate used is based on the 200um-thick E4D paper (dielectric constant Dk=2.54, loss tangent Df=0.05 @6GHz), and the antenna patterns are printed by screen printing using a silver ink with a deposit thickness of 7um and a conductivity of 1.7MS/m. Performances of this technology were already demonstrated previously with the successful design of several kinds of antennas [START_REF] Lo Hine Tong | Comparative Study of WLAN Dual-Band Monopole Antennas Printed and Etched on Paper and PET Substrates[END_REF][START_REF] Phan | Novel Ultra-Wideband "Robe" Antenna on High-Loss Paper Substrate[END_REF][START_REF] Nguyen | RF characterization of flexible substrates for new conformable antenna systems[END_REF].

-Secondly, to ensure a proper rigidity of the paper-based antenna a total thickness of 1mm is set and to meet this request several sheets of papers are stacked. To this purpose, the stack-up comprises 3* inner type#2 papers (without any patterns printed apart the grounding pad#3) on which is wrapped the type#1 paper where the antenna pattern with the feeding line are printed. With this assembling process, a total of 1mm thickness paper is obtained, with the feeding line printed on the top layer and the radiating elements on the bottom side. -And finally, since the antenna is meant to be tested with a micro-coaxial cable (diameter 1.37mm), pads are added at the input port to guarantee a correct grounding of the cable through the multilayer structure. The via-holes are laserdrilled and metallized with a conductive glue. The geometrical parameters of the whole structure, including the coaxial cable, were optimized using the HFSS TM simulation tool to accommodate the required performances in both WLAN frequency bands.

B. Fabrication

Fig. 5 shows the realized circuits before cutting, stacking and assembling; L-shape patterns were added to ease the cutting. One can see the antenna pattern printed on the first area (Type#1) of the paper and only the grounding pad printed on both sides of the second area (Type#2) of the paper. The figure below shows the full design of the dipole antenna with the feeding and testing coaxial cable. The cable is attached to the paper with the help a conductive glue. Indeed, since this is done by hand with thus assembling tolerances the performances can be affected, especially in the higher band as it is shown in the following section.

C. Antenna performances

Fig. 7 shows the measured coefficient reflection response compared to the simulated one. As can be noticed, there is a rather good correlation in the WLAN 2.4GHz band, with dB(S11) <-12dB. However, in the 5GHz band the measured S11 level is higher than expected; this is certainly due to the fabrication and assembling tolerances, in particular, as aforementioned, the discontinuities introduced at the transition between the coaxial cable and the microstrip line. The radiated performances of the antenna were measured in near field with a StarLab TM testing system (Fig. 8). From the gain and efficiency performances plotted in the figures below, we find again a quite good agreement between the simulation and the measurement results in the 2.4GHz: the measured peak gains are around 0.5-1dBi and the efficiencies close to 70%.

In the 5GHz band, the peak gains are more sensitive to measurement uncertainties since around 1dB difference with the simulated gains are observed. In the high band, the measured gains are around 2dBi and the efficiencies close to 65%. The 3D radiation patterns plotted in Fig. 10 and Fig. 11, at respectively 2.45GHz and 5.5GHz, show that the antenna behaves like a dipole, exhibiting a null in the 0Y axis and a quite omnidirectional radiation in the ZX plan. One can also notice that the radiation pattern at 5.5GHz is a bit distorted by the presence of the 2.4GHz radiating arms.

IV. PERSPECTIVE

The achieved performances of the paper-based dipole antenna presented in this paper are comparable to the ones that can be obtained when using FR4 substrate as antenna carrier. Therefore, it could be an alternate low-cost solution for the development of home networking devices that requires many antennas to integrate. For instance, as illustrated in Fig. 12, several dual-band antennas can be mounted directly onto a main board to address the needs of a 4*4 MIMO system. In that case, the antennas will be excited directly from the board without using coaxial cables. By using the same concept of dipole integrating a balun as presented here, a single band 5GHz WLAN antenna is also under development, with expected effective size of 22mm*10mm (Fig. 13), peak gains around 1dBi and efficiencies close to 70% (Fig. 14). V. CONCUSION

The concept of compact dipole antennas integrating a balun and printed on paper substrate has been presented. The prototype realized has demonstrated the high potentialities of the design and of the printing technology used, especially for future applications in the field of wireless systems that require a massive integration of low-cost antennas.

Fig. 1 .

 1 Fig. 1. Original dual-band dipole antenna including a balun.

Fig. 2 .

 2 Fig. 2. Dual-band dipole antenna fed directly via an interconnecting line.

Fig. 3 .

 3 Fig. 3. Paper-based dipole antenna fed with a coaxial cable.

Fig. 4 .

 4 Fig. 4. Constituent parts of the multilayer paper-based antenna.

Fig. 5 .

 5 Fig. 5. Realized dual-band printed antenna before assembling.

Fig. 6 .

 6 Fig. 6. The whole realized dual-band dipole antenna fed by a coaxial cable.

Fig. 7 .

 7 Fig. 7. Simulated and measured reflection coefficient of the dual-band antenna.

Fig. 8 .

 8 Fig. 8. The dipole antenna mesaured in near field with a compact StarLab TM measurement tool.

Fig. 9 .

 9 Fig. 9. Simulated and measured peak gain and effciency of the dual-band antenna.

Fig. 10 .

 10 Fig. 10. Measured 3D radiation pattern of dipole at 2.45GHz.

Fig. 11 .

 11 Fig. 11. Measured radiation pattern of dipole antenna at 5.5GHz.

Fig. 12 .

 12 Fig. 12. Example of application of the paper-based dipole antennas in an 4*4 dual-band MIMO system.

Fig. 13 .

 13 Fig. 13. Paper-based 5GHz WLAN dipole antenna with integrated balun, with the simulated S11 response.

Fig. 14 .

 14 Fig. 14. Simulated peak gain and efficiency of the 5GHz WLAN dipole antenna.

ACKNOWLEDGMENT

The authors acknowledge the French "Agence Nationale de la Recherche" for the financial support under the grant ANR-IG-CE26-0033-01 and the project name STICK'IT.


Axel Creach
email: axel.creach@univ-nantes.fr

Emilio Bastidas-Arteaga

Sophie Pardo
email: pardo@univ-nantes.fr

Denis Mercier
email: denis.mercier@paris-sorbonne.fr

Vulnerability and costs of adaptation strategies for housing subjected to flood risks: application to La Guérinière France

Keywords: Xynthia, coastal flood, human vulnerability, residential houses, climate change, adaptation strategies, economic assessment

Coastal flooding along the Atlantic coast caused by Storm Xynthia killed 41 people. The location and configuration of residential housing were the main factors affecting the vulnerability of people to flooding. The French government responded by destroying buildings in the most flood-prone areas and relocating residents to safer areas. This strategy attracted much criticism, in particular because of the high costs involved with demolition on this scale, and that not insufficient consideration was given to other possible solutions. In this study, the goal is to compare different adaptation strategies in terms of cost of implementation and efficiency in order to reduce the vulnerability of houses to flooding. The strategies are grouped based on: (i) protection, (ii) relocation, (iii) housing architectural adaptation, and (iv) preventive warning and evacuation. This work is applied to La Guérinière, an Atlantic coastal town at risk of coastal flooding, although it was not impacted by Storm Xynthia. The initial results show that the most efficient strategy to reduce housing vulnerability to coastal flooding is also the most expensive. Ranked from the most to the least efficient and expensive, the strategies are as follows: (i) relocation, (ii) housing architectural adaptation, (iii) protection, (iv) and preventive warning and evacuation. Until now, these strategies have been limited as they omit human behaviour in response to coastal flooding scenarios. Therefore, this study examines the role of human behaviour in relation to different mitigative strategies. The efficiency and costs of the strategies are then reappraised.

Introduction

Storm Xynthia hit the French Atlantic coast from the Loire in the north to the Gironde estuaries in the south in February 2010. The combination of strong winds and a high tide coefficient (102) produced an exceptionally high storm surge along the coasts of Vendée and Charente-Maritime that resulted in 50,000 hectares in low-lying areas being submerged [START_REF] Bertin | Importance of wave age and resonance in storm surges: The case Xynthia, Bay of Biscay[END_REF][START_REF] Verger | Digues et polders littoraux : réflexions après la tempête Xynthia, Physio-Géo[END_REF]. Despite the area having been classified as being at risk of coastal flooding, French stakeholders regarded the risk as being sufficiently low to warrant continued urban development [START_REF] Vinet | La mortalité comme expression de la vulnérabilité humaine face aux catastrophes naturelles: deux inondations récentes en France (Xynthia, Var, 2010)[END_REF][START_REF] Leone | A spatial analysis of the December 26th, 2004 tsunami-induced damages: Lessons learned for a better risk assessment integrating buildings vulnerability[END_REF] However, Storm Xynthia in 2010 led to 41 fatalities caused by drowning [START_REF] Vinet | La mortalité comme expression de la vulnérabilité humaine face aux catastrophes naturelles: deux inondations récentes en France (Xynthia, Var, 2010)[END_REF][START_REF] Leone | A spatial analysis of the December 26th, 2004 tsunami-induced damages: Lessons learned for a better risk assessment integrating buildings vulnerability[END_REF]. Notably, 93% of deaths occurred in residential buildings.

Subsequent investigations into the factors contributing to the 41 fatalities highlighted the importance of both the location and configuration of residential buildings [START_REF] Vinet | La mortalité comme expression de la vulnérabilité humaine face aux catastrophes naturelles: deux inondations récentes en France (Xynthia, Var, 2010)[END_REF][START_REF] Leone | A spatial analysis of the December 26th, 2004 tsunami-induced damages: Lessons learned for a better risk assessment integrating buildings vulnerability[END_REF]. Statistics show that: (i) 100% of deaths occurred in buildings subjected to water levels exceeding 1 m; (ii) 90% of deaths occurred in buildings located at less than 400 meters from the flood defences; and (iii) 78% of deaths were reported in single-storey buildings. Thus the location and configuration of residential buildings emerged as the most important variables contributing to human vulnerability to coastal flood events [START_REF] Creach | The use of a micro-scale index to identify potential death risk areas due to coastal flood surges: lessons from Storm Xynthia on the French Atlantic coast[END_REF].

Following Storm Xynthia, the French government decided to implement a "black area policy" which involved demolishing houses located in areas of high flood risk areas. This measure was criticized for its hasty implementation, the criteria used to delineate the black areas [START_REF] Mercier | La tempête Xynthia et la cartographie des « zones noires » sur le littoral français : analyse critique à partir de l'exemple de La Faute-sur-Mer (Vendée)[END_REF], and its high cost [START_REF]Cour des Comptes, Les enseignements des inondations de 2010 sur le littoral atlantique (Xynthia) et dans le Var[END_REF]. The "black areas policy" involves expensive 'relocation' in the short-term but is nonetheless effective in protecting human life against coastal flood risks. Nevertheless, several questions concerning the potential implementation and effectiveness of alternative measures remain. For instance, the elevation of flood defences could be increased to protect the more exposed areas instead of demolishing houses and relocating people. In addition, single-storey houses could be equipped with a "shelter floor." Against this backdrop, the main objective of this study is to evaluate the vulnerability and costs of different adaptation measures to protect occupied houses located in high flood risk areas on the French Atlantic coast.

Material and methods

This section starts by describing and justifying the selection of the study site (Section 2.1). Section 2.2 describes and illustrates the methodology proposed to perform the vulnerability diagnosis of this site. Section 2.3 details the adaptation strategies that could be implemented to face flooding risks. Section 2.4 describes the discount rates used for cost analysis. Finally, section 2.5 presents the considered climate change scenarios.

Study site: La Guérinière town on the Noirmoutier Island

Noirmoutier Island: a low-lying area

Noirmoutier Island is a French Atlantic island (area of 49 km²), located in the Vendée department (Figure 1). It is a low-lying area. Around 68% of the island would have been under water during storm Xynthia if it had not been protected [START_REF] Creach | Vulnerability to coastal flood hazard of residential buildings on Noirmoutier Island (France)[END_REF]. The island is currently protected from the sea by a 24-km stretch of flood defences on the east coast and by a sand barrier on the west coast [START_REF] Fattal | Effets des tempêtes sur une plage aménagée et à forte protection côtière : la plage des Éloux (côte de Noirmoutier, Vendée, France)[END_REF]. Since 1968, the population of the island has increased by 19%. Meanwhile, the urbanization increased by +162% during the same period [START_REF] Creach | Cartographie et analyse économique de la vulnérabilité du littoral atlantique français face au risque de submersion marine (2 volumes)[END_REF]. This important growth is mainly due to the construction of leisure residential houses which represented 50% of the urbanized area in 2011 [START_REF] Insee | Recensement général de la population 2011[END_REF]. However, the new leisure housing is mainly located in low-lying areas [START_REF] Creach | Vulnerability to coastal flood hazard of residential buildings on Noirmoutier Island (France)[END_REF] and today one-half of the constructions is located in potential flooding areas.

Noirmoutier island was not severely affected by Storm Xynthia in 2010, with only 3% of the territory flooded [START_REF] Devaux | La tempête Xynthia du 28 février 2010 -Retour d'expérience en Loire-Atlantique et Vendée -Volet hydaulique et ouvrages de protection[END_REF]. Since the 1950s, no major flooding events have occurred, but 2/3 of the island were flooded in 1937; however, the relatively unpopulated nature of the island at that time resulted in minimal impacts on human life and infrastructure [START_REF] Garnier | Visions croisées de l'historien et du courtier en réassurance sur les submersions : recrudescence de l'aléa ou vulnérabilisation croissante ?[END_REF]. Taking into account the natural risk of flooding of this island, the additional risk related to sea-level rise and the present urbanization of the island, it is important to evaluate the potential consequences of an extreme event occurring today. This study focuses on one the most vulnerable towns of the island called La Guérinière.

La Guérinière: the most exposed town

La Guérinière covers 7.8 km² (16% of the island) with 80% of its territory located below the seawater level attained during Storm Xynthia (4.20 m NGF) [START_REF] Devaux | La tempête Xynthia du 28 février 2010 -Retour d'expérience en Loire-Atlantique et Vendée -Volet hydaulique et ouvrages de protection[END_REF]. The town is in the narrowest part of the island (less than 800 m between the west coast and the east coast) which increases the risk of coastal flooding. On the east coast, La Guérinière is protected from the Bay of Bourgneuf by flood defences which are 5 m high (following renovation in 2014) (Figure 1). On the west coast, the town is isolated from the Atlantic Ocean by a sand barrier which is high and wide on the north and the south, but narrow and less elevated in the central part of the town (approximately 5 m high and 50 m wide) and supported by a sea-wall.

The town had 2,667 houses with 1,460 inhabitants in 2011 [START_REF] Insee | Recensement général de la population 2011[END_REF]. The number of houses has increased by 144% since 1968 and presently 73% are located under the sea-water level reached during Storm Xynthia [START_REF] Creach | Cartographie et analyse économique de la vulnérabilité du littoral atlantique français face au risque de submersion marine (2 volumes)[END_REF]. Considering the fact that the town is in the narrowest part of the island and there is a large concentration of houses located in low-lying areas, La Guérinière is the most exposed town of Noirmoutier Island to coastal flooding.

Description of the Extreme Inherent Vulnerability (VIE) index

The VIE index is a method developed by [START_REF] Creach | Cartographie et analyse économique de la vulnérabilité du littoral atlantique français face au risque de submersion marine (2 volumes)[END_REF] [START_REF] Creach | The use of a micro-scale index to identify potential death risk areas due to coastal flood surges: lessons from Storm Xynthia on the French Atlantic coast[END_REF] to assess the vulnerability of residential buildings subjected to coastal flood risks. It is a micro-scale index that aims to identify houses in which people can be trapped inside during coastal flooding events as a function of building location and architecture.

Background

The method was developed in light of the number of deaths (100%) having occurred inside houses during Storm Xynthia Jonkman, and Kelman [START_REF] Jonkman | An analysis of the causes and circumstances of flood disaster deaths[END_REF] found that 6% of deaths were located inside houses for 13 flood events of relatively low magnitude compared to those generated by Storm Xynthia [START_REF] Boissier | La mortalité liée aux crues torentielles dans le sud de la France : une approche de la vulnérabilité humaine face au risque d'inondation[END_REF]. Jonkman et al. [START_REF] Jonkman | Loss of life caused by the flooding of New Orleans after Hurricane Katrina: analysis of the relationship between flood characteristics and mortality[END_REF] subsequently determined that 54% of fatalities had occurred inside houses during Storm Katrina. These data have prompted growing interest in the number of fatalities likely to occur during extreme events in the future.

For Storm Xynthia, the location and configuration of houses were the most important factors accounting for the number of deaths. According to Vinet [START_REF] Vinet | La mortalité comme expression de la vulnérabilité humaine face aux catastrophes naturelles: deux inondations récentes en France (Xynthia, Var, 2010)[END_REF], the 41 deaths resulting from Storm Xynthia occurred in buildings subjected to water levels in excess of 1 m. Furthermore, 90% of deaths occurred in houses within 400 m of flood defences, while 78% occurred in single-storey buildings. These results show that location (low-lying area, proximity of flood defences) and configuration (architecture) of residential buildings place people at greatest risk during major flood events.

Description of the method

The VIE index is based on four criteria used to identify the buildings in which death may occur during a coastal flood event. These criteria are outlined below (and see Figure 2):

•

The potential water level inside the building in case of flood (Cr1);

•

The distance between buildings and flood defences (e.g. dikes) (Cr2);

•

The architectural type of building (Cr3): (e.g. single or multi-storey);

•

The proximity of buildings to natural rescue points (Cr4) (e.g. areas of higher relief, margins of flood prone areas).

For each criterion, a mark between 4 (high vulnerability) and 0 (no vulnerability) is given for each building. To confirm the robustness of the VIE index, a correlation analysis was performed to check the independence between the criteria (non-redundancy) and the correlation of criteria with the results as this is recommended to generate good composite indicators [START_REF] Klugman | The HDI 2010: new controversies, old critiques[END_REF]. A Monte-Carlo test was then performed to confirm the robustness of the index [START_REF] Creach | The use of a micro-scale index to identify potential death risk areas due to coastal flood surges: lessons from Storm Xynthia on the French Atlantic coast[END_REF] on the basis of the formula in Figure 2 [5], This formula gives a score between 0 and 12 which represents the level of vulnerability of houses for people.

To map the results from the VIE index, four classes were identified (Figure 2):

•

Green class (VIE equal to zero) includes buildings where no vulnerability is identified (they are not exposed to coastal flooding). It is important to note that if the result of the first criterion (potential water level inside) is 0 (no water inside), the result of the VIE index is null.

• Yellow class (VIE index from 1-5) concerns buildings that are exposed to flooding but their location or characteristics do not result in high risk for people.

• Red class (VIE index from 5-8) encompasses buildings in which risk particularly vulnerable people (young, elder, disabled) are at risk of drowning.

• Black class (VIE index from 8-12) concerns buildings in which death is highly likely to occur in case of flooding due to the location and configuration of the building.

For purposes of validation, the VIE index was applied to three towns impacted by Storm Xynthia and compared to the death toll for this event [START_REF] Creach | The use of a micro-scale index to identify potential death risk areas due to coastal flood surges: lessons from Storm Xynthia on the French Atlantic coast[END_REF]. It was found that 83% of deaths were in buildings identified in the black class by the VIE Index and 17% in the red class. For this study, the VIE index is used to assess the vulnerability of people in houses subjected to different flood scenarios (defined in Section 2.5). The VIE index is then applied to estimate the efficiency of four adaptation strategies (Section 2.3) to reduce the vulnerability of people residing in houses to death by flooding.

Adaptation strategies

Various adaptation strategies can be implemented to reduce the vulnerability of houses for people and to protect human life from coastal flood risk. Table 1 summarizes the classification of structural adaptation strategies found in the literature which could be applied to buildings [START_REF] Paskoff | Potential Implications of Sea-Level Rise for France[END_REF][START_REF] Klein | Technological Options for Adaptation to Climate Change in Coastal Zones[END_REF][START_REF] Nicholls | Planning for the Impacts of Sea Level Rise[END_REF]. Moreover, prevention and warning are also crucial to prevent fatalities [START_REF] Priest | Building a model to estimate Risk to Life for European flood events[END_REF][START_REF] Lumbroso | A comparison of the causes, effects and aftermaths of the coastal flooding of England in 1953 and France in 2010[END_REF][START_REF] Kolen | The impacts of storm Xynthia February 27-28, 2010 in France: lessons for flood risk management[END_REF][START_REF] Lumbroso | Use of an agent-based model and Monte Carlo analysis to estimate the effectiveness of emergency management interventions to reduce loss of life during extreme floods[END_REF]. In this way, this study considers protection, retreat and two accommodation strategies. The first accommodation strategy encompasses housing architectural adaptation that aims to protect the population, and the second includes those actions that facilitate preventive warning and evacuation in case of an imminent flooding event.

Table 1: Adaptation strategies for housing subjected to coastal flooding risks (adapted from [START_REF] Nicholls | Planning for the Impacts of Sea Level Rise[END_REF]) Adaptation strategy Scheme Protection: construction of a protective structure that reduces the probability of flooding in a particular zone.

Retreat: moving an exposed building to safe zones [START_REF] Medde | Stratégie nationale de gestion intégrée du trait de côte -Vers la relocalisation des activités et des biens[END_REF]. This strategy was adopted after Storm Xynthia via the "black areas policy." Accommodation: minimization of flood impact by renovating housing at the original location.

Protection: dike reinforcement and rising

Objectives and implementation

This strategy artificially aims at maintaining the position of the shoreline permanently (construction of a dike or a protective wall), or sand dunes to reduce the likelihood of floods [START_REF] Paskoff | Potential Implications of Sea-Level Rise for France[END_REF][START_REF] Klein | Technological Options for Adaptation to Climate Change in Coastal Zones[END_REF][START_REF] Nicholls | Planning for the Impacts of Sea Level Rise[END_REF]. Nevertheless, protection structures can fail for three key reasons: (i) structural failure, (ii) over-topping, and (iii) improper maintenance or degradation during their life-time. Despite criticisms regarding the exponential costs of adapting flood defences [START_REF] Jonkman | Costs of Adapting Coastal Defences to Sea-Level Rise-New Estimates and Their Implications[END_REF] and the false sense of security that they provide to people living behind these structures [START_REF] Vinet | Le risque inondation. Diagnostic et gestion[END_REF], this strategy is popular in developed countries [START_REF] Klein | Technological Options for Adaptation to Climate Change in Coastal Zones[END_REF].

This study considers only the adaptation of existing protection facilities to overcome sea-level rise due to climate change. In France, since 2015 and the introduction of the GEMAPI law (GEstion des Milieux Aquatiques et Prévention des Inondations, i.e. Water Environment and Floods Prevention Management), local authorities are now responsible for management of flood defences. This signifies a considerable change because prior to 2010, 3000 km of pre-existing flood defences were not managed or maintained properly. [START_REF] Lumbroso | A comparison of the causes, effects and aftermaths of the coastal flooding of England in 1953 and France in 2010[END_REF].

Costs

Dollet and Sylla [START_REF] Dollet | Techniques de renforcement et coûts d'adaptation des digues face à des nouveaux risques en lien avec le changement climatique -Application au cas de l'Ile de Noirmoutier[END_REF] quantified the reinforcement and rising costs for a segment of a dike located in Noirmoutier island, France. A dike rise of 120 cm was considered sufficient to raise the dike crest to an altitude higher than the present sea level (4.20 m NGF), but also with extra protection (60 cm) to mitigate against future sea level rise. The new altitude is 5 m NGF as recommended by Noirmoutier's Council. The total cost of this work was estimated at €500 per m, plus an annual maintenance allowance equivalent to 2% of the investment (€10 per m, annually). Although this price range is similar to those outlined in other studies [START_REF] Goeldner-Gianella | Depolderisation policy against coastal flooding and social acceptability on the French Atlantic coast: The case of the Arcachon Bay[END_REF], it is important to note that these costs vary depending on the initial state of the structure, required elevation increase, and/or availability and proximity of necessary construction materials.

Impact on VIE Index calculation

This strategy affects the second criterion of the index which concerns the distance between flood defences and buildings. This study considers that flood defences are reinforced and therefore the probability of collapse is less important in reducing the risk of flooding (0.5 is retrenched to the mark considering that the defence is in a good functional state). In contrast, raising the elevation of flood defences could increase the surprise effect in case of failure and therefore increase flood vulnerability of houses and their occupants.

Retreat: relocation

Objectives and implementation

In some cases, implementation of protective strategies for high-risk exposure levels becomes very expensive and accommodation strategies cannot guarantee a significant decrease in the vulnerability of houses and their occupants. Consequently, it is necessary to relocate vulnerable buildings outside hazard areas. This measure has been previously implemented for housing and facilities placed in zones where coastal erosion is unavoidable [START_REF] Klein | Technological Options for Adaptation to Climate Change in Coastal Zones[END_REF]. Regarding the marine flooding risk, this approach is still new in Francei.e., the "black areas policy" was the first example of the application of this strategy following the Xynthia event. The application of the policy led to the demolition of 1628 houses supposedly within a high flood-risk zone, resulting in a total cost of €315.7 million. In the context of sea level rise due to climate change, this strategy should become widely employed in the future, as proposed in the French national strategy for shoreline management [START_REF] Medde | Stratégie nationale de gestion intégrée du trait de côte -Vers la relocalisation des activités et des biens[END_REF].

The implementation of this type of strategy requires the purchase and destruction of more exposed buildings and facilities. Although retreat is expensive in the short-term, it should eliminate future flooding consequences. Like protection, this strategy also concerns mainly public authorities and is carried out by friendly takeovers or expropriations.

Costs

Housing relocation costs after the Xynthia event are not considered in this study. Therefore, the costs for this adaptation strategy are estimated based on available information as the sum of purchase and demolition costs. Purchase costs in coastal zones are influenced by larger land pressure that differs for each construction located in a given location. To account for these variations, this study estimates a mean cost per m 2 for La Guérinière from information available from three specialized websites (http://www.meilleursagents.com/prix-immobilier, http://prix-immobilier.drimki.fr and htpp://Efficity.com). Data for seven towns located around La Guérinière zone indicate a mean purchase cost of €2,366/m 2 with a standard deviation of €555/m 2 . This cost can then be multiplied by the surface area of the buildings shortlisted for demolition to estimate the overall purchase cost.

Demolition costs are estimated at €20,000 per building, corresponding to the mean cost estimated from the website: http://www.renovationettravaux.fr/cout-demolition-maison-prix-devis. Retreat costs could be completed by considering additional costs such as those related to land restoration or the building costs associated with new "retreat" areas.

Impact on VIE Index calculation

This strategy has no direct impact on any of the VIE index criteria. In this study, buildings identified in the black class without considering adaptation measures are considered too dangerous and consequently it is supposed that they need to be demolished.

Accommodation 1: housing architectural adaptation

Objectives and implementation

This strategy focuses on adapting the buildings to reduce occupants' vulnerability to coastal flood events. The different types of solutions can be classified into two categories:

•

measures that reduce or avoid potential flooding zones: increase the level of the first floor by using of stilts, construction mounds around the building, use a floating foundation, etc.

• measures that provide a safe zone in case of a flooding event: addition of a refuge floor, conversion of loft, etc.

The implementation of these solutions depends on both the use and temporality of construction. For example, the first category would be more suitable for new buildings while the second could be more appropriate for existing or secondary constructions. The present study only considers architectural adaptation of existing buildings. It will then focus specifically on the construction of a refuge floor, as proposed by the French repository for flood prevention works in existing houses [START_REF] Medde | Référentiel de travaux de prévention du risque d'inondation dans l'habitat existant[END_REF] (Figure 3). Considering that 17% of deaths occurred in single-storey buildings during the Xynthia event [START_REF] Vinet | La mortalité comme expression de la vulnérabilité humaine face aux catastrophes naturelles: deux inondations récentes en France (Xynthia, Var, 2010)[END_REF][31]), the implementation of this adaptation strategy could be cost-effective. However, it should be noted that it does not guarantee fully effective security for occupants in case of a coastal flooding event. In some cases they could be trapped on the ground floor despite the presence of a refuge. The application of the strategy concerns mainly private individual initiatives but it may also be supported by public financial incentives.

Costs

The solution takes into account the recommendation of the French ministry for flood prevention works in relation to existing housing [START_REF] Medde | Référentiel de travaux de prévention du risque d'inondation dans l'habitat existant[END_REF]. It consists of constructing a refuge floor with the following characteristics: (i) surface area varying from 9-20 m 2 , (ii) a floor level higher than 4.2 m above the sealevel, and (iii) external access (roof window or balcony) allowing evacuation by helicopter or boat. On the basis of these requirements, Festuot and Guillaume [START_REF] Festuot | R&D : Etude technico économique sur la réduction de la vulnérabilité des constructions de plain pied soumise à des risques de submersions[END_REF] estimated that the minimum construction cost of a refuge floor of 20 m 2 is €19,000. However, this cost may vary depending on the type of existing foundation and structure as well as the selection of construction materials. Potential benefits include the use of the new space as an active part of the house and to increase the economic value of the building.

Impact on VIE Index calculation

The measure of housing architectural adaptation has impacts the third criteria of the index: the architectural configuration of the house. Single-storey buildings identified in red and black classes in the initial results could be adapted by building a rescue level.

Accommodation 2: preventive warning and evacuation

Objectives and implementation

This strategy aims to facilitate preventive evacuation in case of an alert of a coastal flooding event. Kolen et al. [START_REF] Kolen | The impacts of storm Xynthia February 27-28, 2010 in France: lessons for flood risk management[END_REF] affirmed that such an evacuation would significantly reduce human fatalities during Storm Xynthia. Moreover, Chadenas et al. [START_REF] Chadenas | The impact of storm Xynthia in 2010 on coastal flood prevention policy in France[END_REF] showed that prevention could be greatly improved for coastal floods in France. However, at the time of Storm Xynthia, no real-time monitoring

Roof window

Balcony access Refuge floor of coastal surges and warning was available along the French Coast [START_REF] Lumbroso | A comparison of the causes, effects and aftermaths of the coastal flooding of England in 1953 and France in 2010[END_REF]. In 2017, the only existing system was capable of providing information at the department scale.

Nevertheless, the effectiveness of an evacuation depends on: (i) the number of people who effectively evacuate, which can be extremely variable [START_REF] Priest | Building a model to estimate Risk to Life for European flood events[END_REF]; and (ii) the time available between the beginning of the alert and the occurrence of the storm event as well as evacuation logistics [START_REF] Parker | Understanding and enhancing the public's behavioural response to flood warning information[END_REF].

A successful warning and evacuation, in case of a coastal flooding event, requires that people have awareness of flooding-risk and that previous preparation has been undertaken. This necessitates that appropriate guidelines are issued regarding evacuation procedures and drills conducted every so often. The difficulty with such a measure is maintaining risk awareness as an ongoing process. This strategy can be executed at two levels:

•

Implementation of preventive measures for population information and education: this task could be carried out by disseminating regulatory documents for information and prevention (risk prevention plan, communal information document on major risks, communal safeguard plan, etc.) and conducting evacuation drills regularly. These actions would facilitate the successful evacuation of inhabitants in case of an alert.

• Development of evacuation equipment or refuge structures: since the total evacuation of an area is unrealistic, provision of compulsory household equipment such as the 'standby emergency kit' (http: //www.developpement-durable.gouv.fr/Kit-d-attente-des-secourspendant.html) could be made available following the recommendation of the Ministry of Ecology. Specific structures like shelter platforms could also be installed for use as a refuge. Various types of refuge platforms have been already implemented elsewhere [START_REF] Creach | Cartographie et analyse économique de la vulnérabilité du littoral atlantique français face au risque de submersion marine (2 volumes)[END_REF].

The application of this strategy depends primarily on public authorities. Nevertheless, several private facilities such as holiday centres have already built refuge platforms [START_REF] Creach | Cartographie et analyse économique de la vulnérabilité du littoral atlantique français face au risque de submersion marine (2 volumes)[END_REF].

Costs

This study considers the implementation of information and educational measures as well as the construction of a refuge shelter platform. Preventive actions are defined at the municipal level. The costs of the production and dissemination of the various documents and evacuation training for the Flood Prevention Action Plan (PAPI in French) for La Rochelle (France) are €357,000 [START_REF] La | Programme d'Action de Prévention des Inondations « Agglomération Rochelaise[END_REF]. An update every five years is envisaged to maintain and adapt risk awareness.

The installation of shelter platforms is compulsory in certain holiday centres and campgrounds. According to one company that constructed and installed them (TDEM company), the cost of a platform with a capacity of 150-200 people is about €80,000. This cost varies depending on the size and structure of equipment (staircases, lifts, etc.). Finally, the cost of household equipment 'standby emergency kit' is estimated at €250 (personal estimation on the basis of the list given by Ministry of Ecology).

Impact on VIE Index calculation

This adaptation measure impacts on the proximity of buildings to a rescue point criterion of the VIE index. We consider one adaptation scenario where each house is located within 200 m of a natural or artificial shelter or safe haven.

Discount rates

There is some uncertainty about the level of discount rate, particularly for climate change economic assessments (e.g. [START_REF] Dasgupta | Discounting Climate Change[END_REF]. France used a discount rate of 8% to evaluate public investments from 1985 to 2005. However, following the 2005 Lebègue report [START_REF] Lebègue | Révision du taux d'actualisation des investissements publics[END_REF], the 'Commissariat Général au Plan' has recommended a 4% discount rate for short term investments and a lower discount rate of 2% for cash flows occurring after more than 30 years [START_REF] Gollier | Pricing the Planet's Future: The Economics of Discounting in an Uncertain World[END_REF]. These discount rates were revised in 2013 by the 'Commissariat Général à la Strategie et à la Prospective' recommending 2.5% and 1.5% discount rates for short term (lifetime less than 70 years) and long term investments, respectively [START_REF] Quinet | L'évaluation socioéconomique des investissements publics, Commissariat Général à la Strategie et à la Prospective[END_REF]. Quinet et al.

[39] also recommends carrying out a sensitivity analysis with a 4.5% discount rate to compare new and old approaches. Other countries and institutions use different discount rates. The European Commission recommends a 5% discount rate [START_REF] Harrison | Valuing the Future: the social discount rate in cost-benefit analysis[END_REF]; Infrastructure Australia recommends discount rates of 4%, 7% and 10% for infrastructure projects [START_REF] Ia | Outline of Infrastructure Australia's Prioritisation Methodology, Infrastructure Australia[END_REF]; and other discount rates vary from 3% (Germany) to over 10% (World Bank) [START_REF] Harrison | Valuing the Future: the social discount rate in cost-benefit analysis[END_REF].

Discount rates are generally assumed to be constant with time. However, this may not be appropriate when considering intergenerational effects often associated with climate change policy decisions (e.g. [START_REF] Boardman | Cost-Benefit Analysis: Concepts and Practice[END_REF]. Projects with significant effects beyond 30-50 years are considered intergenerational, and so for example, the British Treasury recommends the following time-decreasing discount rates [START_REF] Hm Treasury | The Green Book: Appraisal and Evaluation in Central Government[END_REF]: 3.5% (0-30 years), 3.0% (31-75 years), 2.5% (76-125 years), 2.0% (126-200 years), 1.5% (201-300 years), and 1.0% (300+ years). However, there is some controversy about timedecreasing discount rates (e.g. [START_REF] Viscusi | Rational Discounting for Regulatory Analysis[END_REF], and the Australian Office of Best Practice and Regulation (OBPR) states that 'there is no consensus about how to value impacts on future generations' and 'Rather than use an arbitrarily lower discount rate, the OBPR suggests that the effects on future generations be considered explicitly' [START_REF] Obpr | Best Practice Regulation Handbook[END_REF]. Nonetheless, the 2006 U.K. Stern Review adopted a discount rate of 1.4% [START_REF] Stern | The Economics of Climate Change: The Stern Review[END_REF], and the Australian Garnaut Review adopted discount rates of 1.35% and 2.65% [START_REF] Garnaut | The Garnaut Climate Change Review: Final Report[END_REF]. These relatively low discount rates were selected so as not to underestimate climate impacts on future generations. However, others suggest higher discount rates when assessing economic impacts of climate change (e.g, [START_REF] Nordhaus | A Review of the Stern Review on the Economics of Climate Change[END_REF]).

The above quantification of discount rates relates mainly to public-sector investments in infrastructure. Private investments in infrastructure, such as the owners of a port, power station or airport (etc), tend to include a risk premium which leads to a higher discount rate [START_REF] Btre | Report 110: Risk in cost-benefit analysis[END_REF]. The marginal rate of return of private investments is suggested as one method to derive discount rates for private investments (e.g. [START_REF] Boardman | Cost-Benefit Analysis: Concepts and Practice[END_REF]). According to [START_REF] Boardman | Cost-Benefit Analysis: Concepts and Practice[END_REF], the best 'proxy' for the marginal rate of return of private investments is the before-tax rate of return on corporate bonds -or approximately 4.5%.

The present study considers the discount rate recommended by the 'Commissariat Général à la Strategie et à la Prospective' in 2005 in the Lebègue report [START_REF] Lebègue | Révision du taux d'actualisation des investissements publics[END_REF].

Climate change scenarios

This study analyses the vulnerability of houses for people and costs of adaptation strategies for four scenarios of coastal flooding: frequent, medium, medium including sea level rise in 2100 and extreme. These scenarios have been defined on the basis of studies made by the French administration to implement the Flood Directive [START_REF]2007 relative à l'évaluation et à la gestion des risques d'inondation[END_REF]. We use the values proposed in a study carried out in Fromentine which is close to La Guérinière [START_REF]DREAL Pays de la Loire, Rapport de présentation de la cartographie du risque de submersion marine sur le secteur Noirmoutier -Saint Jean de Monts (Directive inondations Bassins Loire-Bretagne)[END_REF]. Table 2 describes the characteristics of each scenario. Based on the sea levels presented in Table 2, the potentially flooded areas were determined using a "static" flood model [START_REF] Breilh | Assessment of static flood modeling techniques: application to contrasting marshes flooded during Xynthia (western France)[END_REF] that uses high resolution topographic datasets (Lidar Litto-3D) [START_REF] Ign | Litto3D®v 1.0 -Spécifications techniques[END_REF] and considers that inland areas located below sea level are inundated within 100 m of the seashore. The difference between sea level and the ground level of the house permits the potential water level in case of flooding to be estimated. This method is relatively simple but has some limitations that are discussed in Section 4.

Results

VIE Index for existing housing configuration

For each flood scenario, we calculated the results of the VIE index for every house (2817 houses identified in total) of La Guérinière. Table 3 summarizes the results for the flood scenarios. As expected, vulnerability of houses for people increases with the intensity of the coastal flood event. For frequent, low magnitude events, half of the buildings (47%) are located outside the flooded zone whereas only 26% are outside during high magnitude, low frequency events. This means that 74% of the houses in La Guérinière could be flooded during an extreme flood. Houses within the red and black classes are the most vulnerable. In particular, for the black class, the number of houses increases from 469 (frequent, low magnitude event) to 758 (infrequent, high magnitude event).

VIE index considering adaptation strategies

In the second instance, the VIE index was calculated considering the adaptation strategies presented in Section 2.3. These results allow us to compare the results with and without adaptation measures. For example, Figure 4 shows the result of VIE index for the medium hazard event, without measures (above map) and with architectural adaptation of houses (below map). 60% of La Guérinière houses are single-storey constructions that lack adaptation. This percentage is reduced to 2% when the adaptation measure is included. This difference has a significant impact on the VIE index; for instance, the black class is reduced from 25% (without adaptation) to 4% (after architectural adaptation), thus representing a significant decrease in the vulnerability of houses and their occupants to flooding. Tables 4 to 7 summarize the VIE indexes for each of the adaptation strategies. Each adaptation strategy has a different performance depending on the hazard level. In a global manner, retreat is the most efficient measure because all the houses considered as the most dangerous (black class) are demolished. As seen in Table 4, the black class is empty. However, from political, economical and social points of view, it is harder to implement when considering the destruction of 16% (frequent event) to 29% (extreme event) of the municipality buildings [START_REF] King | Voluntary relocation as an adaptation strategy to extreme weather events[END_REF].

The second most efficient measure is that of housing architectural adaptation (Table 5). It reduces the number of dangerous houses from 95% (for a frequent event) to 42% (for an extreme event) with respect to the initial situation (Table 3). The protection measure (Table 6) reduces this part from 46% (frequent event) to 26% (extreme event). Finally, warning and evacuation measures appear to be less efficient (Table 7), but their efficiency increases with the intensity of the coastal flood hazard. For example, for a frequent event, it reduces the portion of black class houses from 2.3%, whereas this portion reaches 14% for an extreme event. This inefficiency is because of human behaviour rather than housing architectural adaptation while the efficiency is, here, only measured in terms of the number of "dangerous" houses.

Costs of adaptation scenarios

Underpinning the theoretical efficiency, each adaptation strategy has a cost which is estimated according to the values described in Section 2.3. This section provides the overall cost for the implementation of the strategies. The detailed costs per strategy and for the different hazard scenarios, are detailed in Appendix A. These costs are given for investment and maintenance over total lifetimes of 20, 50 and 100 years, considering the discount rates defined in Section 2.4.

Figure 5 summarizes the costs for the considered adaptation strategies and hazard scenarios. The evolution of cost is also given for the two strategies that are concerned with maintenance (protection, warning and evacuation) as a function of the expected lifetime. There are major differences in the costs of each of the four strategies. The cost and efficiency trends follow the same pattern: the most efficient strategies are the most expensive. Retreat is the most efficient and expensive adaptation strategy. Its cost varies between €138 billion (469 houses in the black class to be demolished), and €228 billion (758 houses in the black class to be demolished) for frequent and extreme coastal flood events, respectively. These costs are around ten times greater than the cost of housing architectural adaptation that ranges from €17 billion (adaptation of 860 single-story houses) to €22.5 billion (adaptation of 1,167 singlestory houses) for frequent and extreme coastal flood events, respectively. The initial cost of protection is €3.8 billion. Depending on the envisaged maintenance and lifetime of the coastal defences, the total cost could reach €5.9 billion in 100 years. Finally, the less efficient strategy, warning and evacuation, appears to be around 100 times cheaper than the retreat strategy. The initial investment costs vary from €1.6 billion to €2.4 billion for frequent to extreme events, respectively. As mentioned in Section 0, to be efficient, this measure needs to maintain population risk awareness with updates every 5 years (documents and evacuation training). In consequence, for a lifetime of 100 years, the cost increases from €3.9 billion to €4.9 billion for frequent and extreme events, respectively. These first results estimate the level of efficiency and costs for each adaptation strategy. A measure is proposed in the following section to relate both indicators. Cost and efficiency results separately do not provide sufficient information for policy makers. The European Commission [START_REF]2007 relative à l'évaluation et à la gestion des risques d'inondation[END_REF] recommends performing an economic analysis in flood management projects to ensure transparency [START_REF]L'évaluation environnementale stratégique[END_REF] and to provide firm choices in the context of SLR [START_REF] Giec | Climate Change 2014: Impacts, Adaptation and Vulnerability[END_REF]. Different methods are used for economic analysis [START_REF] Markantonis | Review Article "Valuating the intangible effects of natural hazards -review and analysis of the costing methods[END_REF]: (i) cost-benefit analyses, (ii) cost-effectiveness analyses, and (iii) multicriteria analyses, etc. In this study, we propose to link (i) the adaptation cost with (ii) the reduction of risk related to the implementation of an adaptation strategy, Δrisk. Δrisk (as a percentage) is estimated as a function of the number houses in the black class with and without the implementation of the adaptation strategy by using the following equation:

= 𝑛𝑏 𝑤𝑖𝑡ℎ 𝑎𝑑𝑎𝑝 -𝑛𝑏 𝑤𝑖𝑡ℎ𝑜𝑢𝑡 𝑎𝑑𝑎𝑝 𝑛𝑏 𝑤𝑖𝑡ℎ𝑜𝑢𝑡 𝑎𝑑𝑎𝑝 × 100 (1)
where 𝑛𝑏 𝑤𝑖𝑡ℎ 𝑎𝑑𝑎𝑝 and 𝑛𝑏 𝑤𝑖𝑡ℎ𝑜𝑢𝑡 𝑎𝑑𝑎𝑝 are respectively the number of houses in the black class with and without considering the adaptation strategy. 𝑛𝑏 𝑤𝑖𝑡ℎ 𝑎𝑑𝑎𝑝 and 𝑛𝑏 𝑤𝑖𝑡ℎ𝑜𝑢𝑡 𝑎𝑑𝑎𝑝 are estimated from the results presented in Section 3.

Figure 6 shows the adaptation costs and Δrisk of the considered adaptation strategies. The analysis also indicates that the reduction of risk is most important for the more expensive adaptation strategies. Strategies when ranked from the most efficient and expensive to the less efficient and expensive are as follows: (i) retreat; (ii) housing architectural adaptation; and (iii) protection, warning and evacuation. These results indicate that the choice of the adaptation strategy revolves around the goal which is either to maximize efficiency or minimize costs. Nevertheless, these results (and therefore the ranking) could have some limitations, especially for efficiency assessments for which there are many uncertainties.

The main uncertainty is related to human behaviour. Indeed, to assess the efficiency of strategies to protect human life we used an index based on the vulnerability of houses for people. However, human behaviour can increase or lower vulnerability. During Storm Xynthia, there were five deaths in houses where people had the possibility of escaping to a higher floor. As a consequence it can be concluded that architectural adaptation is not sufficient to prevent death in the case of flooding because human behaviour is a key factor [START_REF] Vinet | La mortalité comme expression de la vulnérabilité humaine face aux catastrophes naturelles: deux inondations récentes en France (Xynthia, Var, 2010)[END_REF][START_REF] Jonkman | An analysis of the causes and circumstances of flood disaster deaths[END_REF][START_REF] Parker | Understanding and enhancing the public's behavioural response to flood warning information[END_REF].

Figure 6: Summary of the cost/efficiency evaluation Thus, prevention, warning and evacuation can be viewed as an important strategy to reduce loss of life. The fact that it appears to be the less efficient strategy in the present work is because efficiency is measured as a reduction of building's vulnerability for people. To be more realistic, efficiency should be measured as a number of lives potentially saved with adaptation strategies. Several existing methods could be used [START_REF] Mauro | Quantitative methods for estimating flood fatalities: towards the introduction of loss-of-life estimation in the assessment of flood risk[END_REF]. By measuring efficiency in terms of the number of lives saved, prevention warning and evacuation would probably appear far more efficient and at an affordable cost.

Uncertainties regarding costs also need to be considered. First, he cost of protection had been estimated for reinforcement and increasing the elevation of flood defences to 5 m NGF, which is below the projected sea level for an extreme event (5.20 m NGF). It would be useful to estimate the costs associated with increasing the elevation of flood defences to over 5 m NGF which would undoubtedly increase the total cost of the strategy. Sea level rise may necessitate further upgrades in coastal defences that result in exponential costs [START_REF] Jonkman | Costs of Adapting Coastal Defences to Sea-Level Rise-New Estimates and Their Implications[END_REF]. Second, the cost of retreat is an average cost of different websites based on real-estate estimation. The sources of their dataset are not clearly explained in the websites which introduces uncertainties regarding future costs.

Other limitations of this study include the efficiency of the protection strategy in relation to an extreme event. For a sea-water level of 5.20m NGF, 5 m high flood defences are likely to be overtopped, and consequently, the strategy is not sufficient to cope with high magnitude flooding events.

Finally, this study addresses the cost/efficiency of adaptation strategies separately. However, the best way to reduce the vulnerability of houses for people is to combine prevention of inhabitants with different levels of adaptation and protection. Combining these measures could contribute to the increased awareness of inhabitants in flood-prone coastal areas. The utilisation of structural strategies to reduce the vulnerability of houses and the occupants could help to optimise costs [START_REF] Creach | Cartographie et analyse économique de la vulnérabilité du littoral atlantique français face au risque de submersion marine (2 volumes)[END_REF].

The VIE index: limits of datasets and method

The VIE index is a key issue for this study because it estimates the vulnerability of houses and their occupants to flooding as well as considering the efficiency of the different adaptation strategies. Nevertheless, some limits need to be highlighted regarding both the methods and datasets used.

First, an inherent limitation of the dataset used is the architectural type of house, which is used for the calculation of the third criterion of the index. It was obtained by [START_REF] Creach | Vulnerability to coastal flood hazard of residential buildings on Noirmoutier Island (France)[END_REF]. This study performed field observations in order to determine the type of building. Nevertheless, this work was only carried out for houses exposed to flood for the medium + SLR scenario (4.80 m NGF) and more frequent scenarios. Houses outside the flood zone in this scenario are expected not to be vulnerable according to the VIE index and so no field observations were made for it. For the present study, the vulnerability of houses was analysed for people in relation to an extreme coastal flooding event (5.20 m NGF). Logically, more houses are included than for the previously mentioned scenario; however, due to the data available, no architectural type is known for these houses which introduce errors when recalculating the VIE index for these buildings. Thus, there are 191 houses (7% of buildings) for which the VIE Index is calculated based on the other scenarios. In consequence, for the extreme scenario, the non-identified class is more important than for the other scenarios.

Second, Creach et al. [START_REF] Creach | The use of a micro-scale index to identify potential death risk areas due to coastal flood surges: lessons from Storm Xynthia on the French Atlantic coast[END_REF] presented limits of the VIE index method and proposed different ways to improve it. The main limit is the use of a static flood method which increases the potential water level, particularly in extensively flooded areas like marshes [START_REF] Breilh | Assessment of static flood modeling techniques: application to contrasting marshes flooded during Xynthia (western France)[END_REF]. To be more realistic, a twodimensional hydraulic model coupled with a probabilistic model of the failure of the flood defences could be utilised [START_REF] Mauro | Hydrodynamic and loss of life modelling for the 1953 Canvey Island flood[END_REF]. However, the static method allows every building in a potentially flooded area to be ranked equally and to focus more on the vulnerability than the hazard. It offers the possibility of modelling the worst case scenario, which is the focus of emergency planning efforts [START_REF] Lumbroso | Use of an agent-based model and Monte Carlo analysis to estimate the effectiveness of emergency management interventions to reduce loss of life during extreme floods[END_REF].

Finally, two additional parameters overestimate the potential water level inside the buildings and could increase the result of the first parameter of the VIE index. This level is estimated on the basis of the flood level and the ground level of the house. The ground level of the house is taken from the ground level derived from LiDAR datasets. [START_REF] Cooper | Sea-level rise vulnerability mapping for adaptation decisions using LiDAR DEMs[END_REF] identify several uncertainties for LiDAR datasets, particularly in marshes for which the accuracy could be lower owing to the presence of water. Urbanized areas could also be sources of uncertainty. For example, the Litto-3D program [START_REF] Ign | Litto3D®v 1.0 -Spécifications techniques[END_REF] gives an accuracy of +/-20 cm in elevation for the Digital Elevation Model in the worst cases. Moreover, we used the ground level as the reference for the ground floor of houses. Nevertheless, there is in some cases a difference of 20-60 cm between the ground level and the ground floor. This difference is automatically added to the potential water level which is probably overestimated.

Conclusions

In this study we have identified four strategies to reduce the vulnerability of houses for people in the context of SLR: (i) protection with the reinforcement and increased height of existing flood defences, (ii) retreat of buildings most at risk of flooding, (iii) housing architectural adaptation, and (iv) preventive warning and evacuation. These four strategies were applied on a virtual basis to La Guérinière town which is particularly susceptible to coastal flooding. This was carried out to compare the costs and the efficiency of their implementation for four coastal flood events: frequent, medium, medium + SLR and extreme. Assessments of probable costs are rooted in other estimates provided in the literature. Efficiency was assessed using the VIE Index method [START_REF] Creach | The use of a micro-scale index to identify potential death risk areas due to coastal flood surges: lessons from Storm Xynthia on the French Atlantic coast[END_REF] which evaluates the vulnerability of houses for people. It was observed that the costliest strategies are also the most efficient. Ranked from the most to the least expensive and efficient, they are: (i) retreat (more than €138 billion), (ii) housing architectural adaptation (more than €17 billion), (iii) protection (more than €3.8 billion), and (iv) prevention (more than €1,6 billion). Costs increase and efficiency decreases for greater coastal flood intensity. Despite its cost, the retreat strategy is necessary for the most exposed houses. Housing architectural adaptation is a less expensive strategy which can be adopted for the least exposed houses.

Protection and preventive warning and evacuation are less efficient. However, it is important to highlight that the way to measure efficiency of the strategies has some limitations. Although we measure it in terms of the reduction in the proportion of dangerous houses (black class of the VIE Index), the preventive warning and evacuation strategy is more focused on the improvement of human behaviour than on the reduction of the level of vulnerability of houses for people. The best way would be to assess the efficiency in terms of the number of lives saved when each strategy is employed. This could be done using methods of estimating flood fatalities and introducing a parameter of vulnerability of houses for people which can increase or decrease the risk of death. This may be a viable way to assess the costefficiency of adaptation strategies to coastal flooding within the context of SLR.

Figure 1 :

 1 Figure 1: Location of La Guérinière town

Figure 2 :

 2 Figure 2: Summary of the VIE Index method

Figure 3 :

 3 Figure 3: Example of creation of a refuge floor (according to [30])

Figure 4 :

 4 Figure 4: Maps showing the results of the VIE Index on La Guérinière for a medium coastal flood event, without adaptation measures (above) and with housing architectural adaptation (below).

Figure 5

 5 Figure 5 also indicates that the cost of protection is not influenced by the coastal flood hazard level. Rather it is controlled by an arbitrary renovation of dike elevation (+5 m -NGF) imposed for all hazard scenarios in keeping with work done previously by Noirmoutier Council.

Figure 5 : 4 Discussion 4 . 1

 5441 Figure 5: Summary of the costs of various adaptation measures, depending on the hazard scenario

Table 2 :

 2 Description of the considered coastal flood scenarios (based on[START_REF]DREAL Pays de la Loire, Rapport de présentation de la cartographie du risque de submersion marine sur le secteur Noirmoutier -Saint Jean de Monts (Directive inondations Bassins Loire-Bretagne)[END_REF])

	Scenario	Return period	Sea water level at Fromentine (in front of Noirmoutier Island)
	Frequent	10 years	3.6 m NGF
	Medium	100-300 years	4.2 m NGF
	Medium + SLR *	Same as above + 0.6 m	4.8 m NGF
	Extreme	1000 years or more	5.2 m NGF

Table 3 :

 3 Results of the VIE index without measures, depending on the hazard scenarios

Table 4 :

 4 Results of the VIE index for retreat measures, depending of the hazard scenarios

Table 5 :

 5 Results of the VIE index for housing architectural adaptation measures, depending on the hazard scenarios

Table 6 :

 6 Results of the VIE index for protection measures, depending on the hazard scenarios

Table 7 :

 7 Results of the VIE index for warning and evacuation measures, depending on the hazard scenarios

* SLR means Sea Level Rise

Acknowledgements

The authors are grateful to Martin Paillart from the Communauté de Communes de l'île de Noirmoutier for material support on the island, and all the PhD students who helped with data collection in the field. In particular, we thank Elie Chevillot-Miot, and the Geopal program for all their help with dataset collection. We also thank Oumar Sylla, Vincent Dollet, Romain Festuot, Laura Guillaume, and TDEM construction company for providing useful information to estimate the costs of adaptation strategies. Thanks to Jan Bloemendal for the careful rereading of the manuscript. This was supported by COSELMAR research program, funded by the Regional Council of Pays de la Loire.

Appendix A: Costs of adaptation strategies