Flávia M S Maia

Solange Ribet

Céline Bailly

Mireia Grivé

Benoît Madé

Gilles F Montavon
email: montavon@subatech.in2p3.fr

Evaluation of thermodynamic data for aqueous Ca-U(VI)-CO3 species under conditions characteristic of geological clay formation

Keywords: Uranium, speciation, complexation, clay formation Highlights

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

complex formation and uranium retention on an anion-exchange resin. A modelling approach with PhreeqC was carried out to derive the thermodynamic data for the formation of these complexes. The Van't Hoff Equation can be applied to explain the variation in stability constant values as a function of temperature. This work suggests: log 10 K 113 o = 27.27 ± 0.04 and log 10 K 213 o = 29.8 ± 0.2 for CaUO 2 (CO 3 ) 3 2-and Ca 2 UO 2 (CO 3 ) 3 (aq) complexes, respectively, hence in good agreement with the literature data. The enthalpy of reaction determined here from experiments suggests that temperature does not facilitate the formation of CaUO 2 (CO 3 ) 3 2-(∆ r H m o = -24.4 ± 2.2 kJ mol -1 ), whereas it has very little effect on the stability of Ca 2 UO 2 (CO 3 ) 3 (aq) (∆ r H m o = -3 ± 10 kJ mol -1 ).

Introduction

Potential uranium contamination in nature, due to increased nuclear power generation and mining activities, raises distinct environmental concerns. Understanding the chemical behaviour of uranium is therefore essential to reliably predicting its migration [START_REF] Runde | The chemical interactions of actinides in the environment[END_REF].

This understanding becomes crucial in the context of deep geological radioactive waste disposal, where uranium is a ubiquitous component. In France, the Callovo-Oxfordian clay rock formation (COx) was chosen as a potential host rock for such a disposal site. According to the disposal concept, the formation plays an important role in preventing radionuclide migration to the natural environment. One consequence of disposing long-lived, high-level radioactive waste is the transient increase in temperature due to the exothermic nature of this waste [START_REF] Andra | Dossier 2005 Argile-Synthesis Evaluation of the feasibility of a geological repository in an argillaceous formation Meuse/Haute-Marne site[END_REF]. The thermal evolution may modify pore water chemical composition (pH, redox potential, gas pressure) and therefore speciation, solubility or even radionuclide migration.

In the past, geochemical models applied to radioactive waste disposal typically predicted that the most relevant redox state of uranium in pore water was U(IV), through use of available thermodynamic datasets, e.g. NEA-TDB [START_REF] Guillaumont | Update on the chemical thermodynamics of Uranium, Neptunium, Plutonium, Americium and Technetium[END_REF]. However, several data publications have confirmed the formation of aqueous Ca-U(VI)-CO 3 ternary complexes even under reducing conditions [START_REF] Bernhard | Speciation of Uranium in seepage waters of a mine tailing pile studied by Time-Resolved Laser-Induced Fluorescence Spectroscopy (TRLFS)[END_REF][START_REF] Bernhard | Uranyl(VI) carbonate complex formation: validation of the Ca 2 UO 2 (CO 3 ) 3 (aq.) species[END_REF][START_REF] Dong | Determination of the formation constants of ternary complexes of uranyl and carbonate with alkaline earth metals (Mg 2+ , Ca 2+ , Sr 2+ , and Ba 2+ ) using anion exchange method[END_REF][START_REF] Geipel | Mixed complexes of alkaline earth uranyl carbonates: A laser-induced time-resolved fluorescence spectroscopic study[END_REF][START_REF] Kalmykov | Mixed Ca 2+ /UO 2 2+ /CO 3 2complex formation at different ionic strengths[END_REF][START_REF] Lee | Formation of ternary CaUO 2 (CO 3 ) 3 2and Ca 2 UO 2 (CO 3 ) 3 (aq)[END_REF][START_REF] Shang | Determination of formation constants and specific ion interaction coefficients for Ca n UO 2 (CO 3 ) 3 (4-2n)complexes in NaCl solution by time-resolved laser-induced luminescence spectroscopy[END_REF], which increases the solubility of uranium in pore water [START_REF] Joseph | The ternary system U(VI) / humic acid / Opalinus clay, rerum naturalium[END_REF][START_REF] Tullborg | The occurrences of Ca 2 UO 2 (CO 3 ) 3 complex in Fe(II) containing deep groundwater at Forsmark, Eastern Sweden[END_REF][START_REF] Vercouter | A modelling exercise on the importance of ternary alkaline earth carbonate species of uranium(VI) in the inorganic speciation of natural waters[END_REF] and influences its mobility and sorption properties [START_REF] Dangelmayr | Laboratory column experiments and transport modeling to evaluate retardation of uranium in an aquifer downgradient of a uranium in-situ recovery site[END_REF][START_REF] Kautenburger | Insights into the retention behaviour of europium(III) and uranium(VI) onto Opalinus Clay influenced by pore water composition, temperature, pH and organic compounds[END_REF][START_REF] Mühr-Ebert | Speciation of uranium: Compilation of a thermodynamic database and its experimental evaluation using different analytical techniques[END_REF].

The formation conditions of aqueous Ca-U(VI)-CO 3 complexes are clearly established at room temperature, while only scarce information is available to predict the behaviour of uranium as temperature increases. To the best of our knowledge, just two studies address the effect of temperature on such species [START_REF] Endrizzi | Chemical speciation of Uranium(VI) in marine environments: Complexation of Calcium and Magnesium ions with [(UO 2 )(CO 3 ) 3 ] 4and the effect on the extraction of Uranium from seawater[END_REF][START_REF] Jo | Formation of CaUO 2 (CO3) 3 2and Ca 2 UO 2 (CO 3 ) 3 (aq) complexes at variable temperatures (10-70 °C)[END_REF]. Both these studies used calorimetric titration and showed an exothermal reaction driven by entropy. The aim of this study was to investigate in greater detail the temperature effect on the formation of Ca-U(VI)-CO 3 species under the clay geochemical conditions applicable to the French concept of radioactive waste disposal [START_REF] Gailhanou | Effects of a thermal perturbation on mineralogy and pore water composition in a clay-rock: An experimental and modeling study[END_REF], whereby Ca/pCO 2 /pH parameters are controlled by calcite dissolution/precipitation reactions (Figure 1). In this study, the Schubert-type method [START_REF] Schubert | Ion scattering as a probe of intermediate states in adsorption and reaction at surfaces[END_REF], which was also used by others [START_REF] Dong | Determination of the formation constants of ternary complexes of uranyl and carbonate with alkaline earth metals (Mg 2+ , Ca 2+ , Sr 2+ , and Ba 2+ ) using anion exchange method[END_REF][START_REF] Mühr-Ebert | Speciation of uranium: Compilation of a thermodynamic database and its experimental evaluation using different analytical techniques[END_REF], has been chosen to directly evaluate the competition between ternary complex formation and uranium retention. A specific experimental set-up has been designed in order to work in a biphasic solid/liquid system at various temperatures by means of controlling the temperature and pCO 2 .

Materials and Methods

Chemicals

All chemicals used herein were of analytical reagent grade or higher. Uranium solutions were prepared from 238 U(VI)-depleted ICP-MS standard solution (SCP Science, France). The anionic exchange resin used in the experiments was of the gel type Dowex-1x2 (Sigma-Aldrich, Merck), stable up to 99ºC. This strong resin initially in chloride form was converted to nitrate form after overnight equilibration at least three times with 1 M NaNO 3 at a solid-toliquid ratio of 10 g/L.

Analytical methods

The aqueous uranium concentration was analysed after filtration at 0.2 µm by Quadripole ICP-MS (Induced Coupled Plasma-Mass Spectrometry, ThermoScientific XSERIES 2), using an internal standard signal ( 205 Tl) to control any drift from the matrix effect. The organic carbon released by the tubes was measured by a Total Organic Carbon Analyser TOC V-CSH series (Shimadzu, Standalone, highly-sensitive method). The alkalinity was evaluated by colorimetric analysis using a Bromocresol green-methyl red indicator power pillow as a colour indicator and a digital titrator (Hach method 803), with a cartridge containing 0.16 N H 2 SO 4 . pH was measured at the target temperature with a dual dry bath system (Fisher Scientific) and a pH-meter combined with a red-rod pH electrode and thermometer detector (pHC285, Hach Lange) of hydrogen ion activity. 3% and 5% at 20, 40, 60 and 80 °C, respectively) to control the carbonate content in aqueous solution (see Figure 1 and Table 1).

The indirect Schubert-type method [START_REF] Schubert | Ion scattering as a probe of intermediate states in adsorption and reaction at surfaces[END_REF]) allows working at trace concentrations in order to limit potential mineral precipitation. All experiments were conducted at a controlled atmosphere and temperature in an electrolyte background of 0.1 M NaNO 3 and initial 5•10 -7 M of U(VI) (i.e. below the solubility of different U(VI)-bearing minerals so as to avoid any possible precipitation).

Two types of batch experiments were carried out:

(i) in the absence of calcium, as a function of the solid-to-liquid ratio (1 to 25 g/L). The objective of these experiments was to establish the model describing sorption of U(VI) on the resin;

(ii) and, as a function of the calcium concentration (0 to 5 mM) at a fixed solid-to-liquid ratio of 2.5 g/L. The objective of these experiments was to study the stability and temperature effect on Ca-U(VI)-CO 3 complex formation. The upper calcium concentration limit was calculated to avoid oversaturation of calcite in the experiments.

For each experimental set, two series of blank samples (no resin present) served to ensure that no precipitation of uranyl or sorption on the tube and filter surfaces occurred. Results

indicated that these processes can be neglected under the studied experimental conditions. The resin was weighed under room conditions in 35 mL PPCO (Polypropylene Copolymer, Nalgen) tubes (pre-washed at 20, 40, 60 or 80 °C with ultrapure water three times to limit the release of organic carbon during the experiments, i.e. < 1 ppm); next, the tubes were transferred into the Ar(g)/CO 2 (g) glovebox (with the % of CO 2 (g) dependent on the target temperature) and filled with the solution prepared from stock solutions of NaNO 3 , Ca(NO 3 ) 2 , NaHCO 3 and 238 U(VI). The tubes were sealed with Teflon tape, closed and transferred outside the glovebox, for confinement in aluminium foil bags under vacuum (20 mbar). Afterwards, the tubes were transferred into an incubator coupled to a reciprocate shaker (Thermotron InforsHT) and left in contact at the target temperature. After 5 days of contact, sufficient to reach a steady state (as proven by preliminary experiments), the aluminium foil bag was opened and the tubes introduced into an insulated Teflon/aluminium box, specially designed to maintain the temperature of the tubes, followed by rapid transfer into the glovebox. Once again inside the glovebox, an aliquot was sampled and preserved for subsequent analysis; moreover, pH was measured at the target temperature. After cooling the samples to room temperature, the alkalinity of the blank samples (without resin) was measured, assuming the same values for the whole series. Note that in considering the uncertainty of the analysis, pH measured after equilibrium was in the same range as that calculated, thus indicating that the pCO 2 /pH/temperature equilibrium was being relatively well controlled (see the "Modelling

Approach" section for additional information).

The U concentration in solution was analysed in order to obtain the distribution coefficient (K D , in mL/g) (eq 1) characterising the distribution of uranium between the solid (in mol/g) and the aqueous solution (in mol/mL) at equilibrium:

K D = [U(VI)] resin [U(VI)] aq. = [U(VI)] 0 -[U(VI)] aq [U(VI)] aq (1)
The amount of uranium retained on the resin ([U(VI)] resin ) was determined by subtracting the initial concentration of uranium added to the system ([U(VI)] 0 ) and the concentration measured in the aqueous phase ([U(VI)] aq ).

Modelling approach

The modelling approach was defined so as to simulate the anionic exchange processes occurring between the resin and anionic species of U(VI) at different temperatures. A stepwise procedure was followed, with the first step quantifying uranium retention, as described by the following reaction

4XNO 3 + UO 2 (CO 3 ) 3 4-⇌ X 4 UO 2 (CO 3 ) 3 + 4NO 3 - 𝐾 𝑒𝑥 = { X 4 UO 2 (CO 3 ) 3 }{NO 3 -} 4 { UO 2 (CO 3 ) 3 4-}{XNO 3 } 4 (2)
where X is an ion-exchanger resin functional group and 𝐾 𝑒𝑥 corresponds to the exchange constant. In the presence of calcium (Ca), two additional reactions occur in solution

Ca 2+ + UO 2 2+ +3CO 3 2-⇌ CaUO 2 (CO 3 ) 3 2- 𝐾 113 = {CaUO 2 (CO 3 ) 3 2-} {Ca 2+ }{UO 2 2+ }{CO 3 2-} 3 (3) 2Ca 2+ + UO 2 2+ +3CO 3 2-⇌ Ca 2 UO 2 (CO 3 ) 3 (aq) 𝐾 213 = { Ca 2 UO 2 (CO 3 ) 3 (aq)} {Ca 2+ } 2 {UO 2 2+ }{CO 3 2-} 3 (4)
A change in the K D value with respect to the conditions without Ca (eq 2) provides an indirect evidence of ternary complex formation in the aqueous phase (eqs 3 and 4). Since the exchange constant describing U(VI) retention is fixed, it then becomes possible to obtain the constants describing the formation of ternary complexes by fitting the experimental data.

All simulations were performed using the PhreeqC code, version 3.1.4 [START_REF] Parkhurst | Description of input and examples for PhreeqC Version 3 -A computer program for speciation, batch-reaction, one-dimensional transport and inverse geochemical calculations[END_REF], and the ThermoChimie database [START_REF] Giffaut | Andra thermodynamic database for performance assessment: ThermoChimie[END_REF]www.thermochimie-tdb.com) with the Davies Equation for ionic strength corrections. The chemical thermodynamic data (Log 10 K) of pertinent aqueous complexation reaction at 20 °C, 40 °C, 60 °C, and 80 °C used in our modelling approaches are provided in Table S1. The reaction constants K ex , K 113 and K 213 from eqs 2-4 were fitted by implementing the PEST (Parameter ESTimation) code [START_REF] Doherty | PEST Model-Independent Parameter Estimation user manual[END_REF]) coupled with the batch version of PhreeqC. The PEST code is a public domain, open-source software suite that allows estimating both the model-independent parameters and the associated uncertainties. The first set of experiment (without calcium) allowed the determination of K ex , whereas K 113 and K 213 are the fitting parameters of the second set of experiments (in the presence of calcium). Please note that in the geochemical calculations, the system pCO 2 was allowed to vary freely and instead the measured alkalinity, pH and Ca concentration were set as the fixed parameters (see Table 1).

Temperature dependence

The Van't Hoff Equation (eq 5) was applied to account for the dependence of stability constants on temperature (T), assuming a constant enthalpy of reaction and so that the standard heat capacity change c p °=0 [START_REF] Puigdomenech | Temperature corrections to thermodynamic data and enthalpy calculations[END_REF] :

log 10 𝐾°(T) = log 10 𝐾°(T 0 ) - ∆ r H m o (T 0 )
𝑅ln( 10)

( 1 T - 1 T 0 ) (5)
When temperature dependence follows a straight line, the slope is directly correlated with the enthalpy of reaction ∆ r H m o (T 0 ) (J mol -1 ) at the reference temperature (298.15 K). log 10 𝐾°(T 0 )

is the intersection of this line with the vertical axis. R is the gas constant (8.31451 J K -1 mol -1 ).

Knowing both the standard stability constant and enthalpy of reaction from eq 5, the entropy can be determined from eq 6 and Gibbs free energy from eq 7

∆ r S m o (T 0 )= ∆ r H m o (T 0 ) T 0 + ln(10) 𝑅 • log 10 𝐾°(T 0 ) (6) ∆ r G m o (T 0 )=∆ r H m o -T 0 ∆ r S m o = -𝑅𝑇log 10 𝐾°(T 0 ) • ln(10) (7)

Results and Discussion

3.1 Application of the modelling approach to Dong and Brooks' ( 2006) experimental data

The model was used to explain the experimental data obtained by [START_REF] Dong | Determination of the formation constants of ternary complexes of uranyl and carbonate with alkaline earth metals (Mg 2+ , Ca 2+ , Sr 2+ , and Ba 2+ ) using anion exchange method[END_REF] (results given in Supporting Information, Figure S1). Results of the fitting approach yielded values of 27.26 ± 0.07 and 30.2 ± 0.5 for the stability constants, corresponding to reactions 3 and 4, respectively. These results differ very slightly from those proposed by [START_REF] Dong | Determination of the formation constants of ternary complexes of uranyl and carbonate with alkaline earth metals (Mg 2+ , Ca 2+ , Sr 2+ , and Ba 2+ ) using anion exchange method[END_REF], in which log 10 𝐾 113 o = 27.18 ± 0.07 and log 10 𝐾 213 o = 30.7 ± 0.06, although they lie in the same range. Emphasis must be focused on the uncertainty of the derived stability constant. This uncertainty is correlated with the predominant range of species relative to the concentration range of calcium in aqueous solution (limited by calcite precipitation). While the CaUO 2 (CO 3 ) 3 2-complex is predominant over the full range of calcium concentrations studied, the Ca 2 UO 2 (CO 3 ) 3 (aq) complex is only formed for [Ca 2+ ] > 1 mM and never as a major species (see an example in Figure S2). The error associated with the formation constant of the 1:1:3 complex is therefore smaller than that associated with the 2:1:3 complex. Special attention should then be paid to calculating the uncertainty of log 10 𝐾 213 o , which seems to be very low in the case of the work completed by [START_REF] Dong | Determination of the formation constants of ternary complexes of uranyl and carbonate with alkaline earth metals (Mg 2+ , Ca 2+ , Sr 2+ , and Ba 2+ ) using anion exchange method[END_REF].

Quantification of the sorption process

The speciation of U(VI) in the presence of carbonates and the absence of calcium is mainly controlled by the UO 2 (CO 3 ) 3 4-and UO 2 (CO 3 ) 2 2-species in the temperature range from 20 °C to 80 °C (Figure S3). At 80 °C, hydrolysed species UO 2 (OH) 3 -and UO 2 (OH) 2 (aq) are expected yet can be considered negligible. The experimental set-up and corresponding conceptual model proposed herein do not distinguish which aqueous species will control U(VI) sorption onto the resin. In fact, a description of the true ion exchange mechanism occurring on the anionic exchanger in the absence of calcium is not a priori necessary; considering a simple K D approach is sufficient to apply the Schubert-type method [START_REF] Schubert | Ion scattering as a probe of intermediate states in adsorption and reaction at surfaces[END_REF]. For purposes of completeness however, a mechanistic approach has been considered, assuming that UO 2 (CO 3 ) 3 4-present in all cases and displaying the highest anionic charge was the only species likely to be adsorbed onto the anionic exchange resin. This conclusion was also drawn from work conducted by [START_REF] Dong | Determination of the formation constants of ternary complexes of uranyl and carbonate with alkaline earth metals (Mg 2+ , Ca 2+ , Sr 2+ , and Ba 2+ ) using anion exchange method[END_REF] at room temperature.

The proposed model explains the sorption data in absence of calcium (see the lines in Figure S3). Agreement between the experimental data and calculated values at 20 °, 40 ° and 60 °C is excellent. In contrast, the fit between the estimated and experimental observations at 80 °C and 5% CO 2 (g) is less satisfactory, as the calculated uranium concentrations underestimate the values measured for the ratio S/L >10 g/L. However, even at 80 °C, for an S/L ratio equal to 2.5 g/L (which will be the ratio subsequently used in experiments in the presence of calcium), the agreement between model and experiments is good. Note that at 80 °C, the UO 2 (CO 3 ) 2 2complex is predominant in solution (Figure S3). Modelling tests were carried out in order to take into account the adsorption of the two complexes on the resin. In the end, the results were not modified: the experimental data were well described by the adsorption of the complex UO 2 (CO 3 ) 3 4-and the addition of the second one did not improve the results. This confirms the reliability of our initial hypothesis. This is also validated by the fact that the dependence of reaction constants K ex on temperature follows the Van't Hoff Equation (Figure 2A). This finding means that only one major species is interacting with the resin over the explored temperature range. If several U(VI) species were adsorbed, a linear relation would not be expected. Furthermore, these results show that the exchange of UO 2 (CO 3 ) 3 4-on the anionic- In conclusion, our simplified model serves to explain the sorption data and can thus be used as a reference state for describing uranium behaviour when calcium is present and the formation of Ca-U(VI)-CO 3 ternary complexes is being facilitated.

Sorption experiments in the presence of calcium

According to [START_REF] Dong | Determination of the formation constants of ternary complexes of uranyl and carbonate with alkaline earth metals (Mg 2+ , Ca 2+ , Sr 2+ , and Ba 2+ ) using anion exchange method[END_REF], in the presence of calcium, CaUO 2 (CO 3 ) 3 2-sorption onto the resin at room temperature may be neglected; this observation also constituted a fundamental assumption of our conceptual model. Sorption of the uncharged Ca 2 UO 2 (CO 3 ) 3 (aq) species was considered negligible. Results of the sorption experiments performed as a function of calcium concentration at different temperatures are given in Figure 3 (symbols). As expected, regardless of experimental temperature, the concentration of U(VI)

in the solution increases with calcium concentration in the system due to the formation of Ca-U(VI)-CO 3 complexes, which are not retained by the exchanger. The solid lines in Figure 3 account for the fitting results of the experimental data obtained from PEST on the two parameters: log 10 K 113 and log 10 K 213 . The level of agreement between model and experimental data proves to be excellent for each experimental set; results follow a non-linear model since two ternary aqueous species CaUO 2 (CO 3 ) 3 2-and Ca 2 UO 2 (CO 3 ) 3 (aq) are formed. Nonetheless, a qualitative comparison of the data is not straightforward since the equilibrium conditions (pH, alkalinity) of each experimental set differ from one temperature to the next.

The log 10 𝐾 113 and log 10 𝐾 213 values obtained for the ternary complexes at each temperature from the fitting step are provided in Table S2. The temperature dependence on stability constants is shown as a function of (

1 T 0 - 1 T
) in Figure 2B and 2C. For the 1:1:3 complex the Van't Hoff Equation appears to be applicable since a linear relationship has been obtained (R 2 = 0.98). For the 2:1:3 complex, the coefficient of determination is low (R 2 = 0.04), showing no true dependence on temperature. However, fitting the data with the approximation of a constant heat capacity change [START_REF] Puigdomenech | Temperature corrections to thermodynamic data and enthalpy calculations[END_REF] show also a non-statistically significant values for c p ° and H r, °. These results indicate that aqueous species formation does not exhibit the same behaviour. Formation of the CaUO 2 (CO 3 ) 3 2-species is not promoted with an increase in temperature, whereas Ca 2 UO 2 (CO 3 ) 3 (aq) formation is only slightly affected by temperature changes.

The enthalpy of reaction (assumed to be constant over the temperature range explored) and standard stability constants (at 298.15 K) were therefore calculated from eq 5. The standard stability constants (±1) for ternary species CaUO 2 (CO 3 ) 3 2-and Ca 2 UO 2 (CO 3 ) 3 (aq) are: The aqueous speciation results indicate that the ternary complex CaUO 2 (CO 3 ) 3 2-is the main aqueous species of U(VI) at all temperatures studied for calcium concentrations below 1 mM (see Figure S2). The fraction of ternary complex Ca 2 UO 2 (CO 3 ) 3 (aq) increases with both calcium concentration and temperature yet is by no means the main species under the experimental conditions studied herein. As previously discussed for the fitting results of the published data reported in [START_REF] Dong | Determination of the formation constants of ternary complexes of uranyl and carbonate with alkaline earth metals (Mg 2+ , Ca 2+ , Sr 2+ , and Ba 2+ ) using anion exchange method[END_REF], the weak proportion of 2:1:3 complex explains the high degree of uncertainty related to log 10 K 213 , especially at the lowest temperatures where the contribution is smallest.

log
The standard enthalpy of reaction (±1) of CaUO 2 (CO 3 ) 3 2-and Ca 2 UO 2 (CO 3 ) 3 (aq) equal -24.4 ± 2.2 and -3 ± 10 kJ mol -1 , respectively. Based on the standard stability constant and enthalpy of reaction, both entropy (eq 6) and Gibbs free energy (eq 7) could also be determined (Table 2). Drawing the conclusion of an entropy-driven complexation therefore remains valid.

Furthermore, the exothermic reaction deduced from micro-calorimetry measurements, by studying the transition from UO 2 (CO 3 ) 3 4-to ternary complexes (CaUO 2 (CO 3 ) 3 2-and Ca 2 UO 2 (CO 3 ) 3 (aq)) [START_REF] Endrizzi | Chemical speciation of Uranium(VI) in marine environments: Complexation of Calcium and Magnesium ions with [(UO 2 )(CO 3 ) 3 ] 4and the effect on the extraction of Uranium from seawater[END_REF][START_REF] Jo | Formation of CaUO 2 (CO3) 3 2and Ca 2 UO 2 (CO 3 ) 3 (aq) complexes at variable temperatures (10-70 °C)[END_REF], has been recovered by values deduced from the Van't Hoff Equation directly targeting the formation of ternary complexes from UO 2 2+ as a function of temperature (eqs 3 and 4). For the 1:1:3 anionic complex, the enthalpy of reaction obtained in this study (-24.4 ± 2.2 kJ mol -1 ) is similar to previous published values (-47 ± 6 (Endrizzi and Rao, 2014) or -40.4 ± 4.1 [START_REF] Jo | Formation of CaUO 2 (CO3) 3 2and Ca 2 UO 2 (CO 3 ) 3 (aq) complexes at variable temperatures (10-70 °C)[END_REF])) although higher. For the 2:1:3 neutral species, this agreement is less satisfactory, (i.e. -3 ± 10 kJ mol -1 vs. -47 ± 7 [START_REF] Endrizzi | Chemical speciation of Uranium(VI) in marine environments: Complexation of Calcium and Magnesium ions with [(UO 2 )(CO 3 ) 3 ] 4and the effect on the extraction of Uranium from seawater[END_REF]Rao, 2014) or -42.3 ± 5.1 (Jo et al., 2019)). However, the low enthalpy value remains consistent with the fact that temperature does not exert a strong impact on formation (Figure 3).

The thermodynamic dataset proposed by [START_REF] Jo | Formation of CaUO 2 (CO3) 3 2and Ca 2 UO 2 (CO 3 ) 3 (aq) complexes at variable temperatures (10-70 °C)[END_REF] was tested to determine whether it could explain our experimental results. The modelling results are shown as dashed lines in Figure 3; reasonable results are obtained at low temperatures, yet a greater deviation can be observed as temperature increases, particularly at 80 °C. The possibility that 1:1:3 anionic complex could in fact be adsorbed onto the resin at temperature higher than 50°C could explain this discrepancy. However, this hypothesis is not trustworthy since it would lead to disagreement for temperatures below 40 °C.

It is important to recall that in this work, we describe the formation of 1:1:3 and 2:1:3 complexes from UO 2 2+ whereas in the previous work, the transition from species UO 2 (CO 3 ) 3 4-to 1:1:3 and 2:1:3 species is studied. In a last part, our data and those of Jo et al.

(2019) were compared using their formalism of reaction (2x-4) , 𝐾 𝑎𝑞 𝑥 ). The results are presented in Figure 4.

(x Ca 2+ + UO 2 (CO 3 ) 3 4-⇌ Ca x UO 2 (CO 3 ) 3
Overall, taking into account the dispersion of the points, similar trends are observed with the possibility of using Van't Hoff Equation. The fitting values derived for 2:1:3 complex (8.9 ± explain all the experimental data obtained as a function of temperature with regard to literature data. At this stage, it is difficult to explain these differences, given the very high sensitivity of the parameters, but the study does reveal the importance of testing various approaches, whether direct or indirect, under different experimental conditions. From an application point of view, under radioactive waste disposal conditions where temperatures around 80 °C are expected, experimental results indicate that the increase in temperature is not to promote the formation of ternary complexes. This could obviously have a potential impact on the prediction of U(VI) mobility near a radioactive waste disposal site. Additional work seems therefore necessary to further investigate/consolidate the effects of temperature increase on uranium behaviour.

Figure 1: Experimental conditions for this work (additional information can be found in Table S1) and in previous studies: END14: (Endrizzi and Rao, 2014); JO19: [START_REF] Jo | Formation of CaUO 2 (CO3) 3 2and Ca 2 UO 2 (CO 3 ) 3 (aq) complexes at variable temperatures (10-70 °C)[END_REF].

Calcium concentration range is controlled by calcite dissolution / precipitation. For all studies, an ionic strength of near 0.1 M was set with NaCl, NaClO 4 or NaNO 3 . 2 and Table S1). (1/T -1/T 0 )x1000 (K -1 )

2 Ca 2+ + UO 2 2+ + 3CO 3 2-= Ca 2 UO 2 (CO 3 ) 3aq (

Temperature (°C)

x Ca 2+ + UO 2 (CO 3 ) 3 4-= Ca x UO 2 (CO 3 ) 3 2x-4

x = 1 x = 2 Vant'Hoff eq.

  [START_REF] Jo | Formation of CaUO 2 (CO3) 3 2and Ca 2 UO 2 (CO 3 ) 3 (aq) complexes at variable temperatures (10-70 °C)[END_REF] also determined the stability constants of Ca-U(VI)-CO 3 complexes at various temperatures (10-70°C) in aqueous solution by applying spectroscopic techniques. However, the conclusions of this work indicate that an approximation of the constant enthalpy cannot explain the change in temperature of the thermodynamic constants. From an operational perspective, the formation of ternary complexes tends to be favoured by increasing the temperature and, depending on the conditions (pH, pCO 2 , Ca concentration), this may then lead to an increase in uranium(VI) mobility. The significance of this finding requires further validation under more realistic physicochemical conditions, such as those within the COx clay rock.

  exchange resin is enhanced by a temperature increase. The resultant log 10 𝐾 ex o (±1 ) equals 1.0 ± 0.1, and the ∆ r 𝐻 m,ex o (±1) is 26 ± 4 kJ mol -1 .

  respectively. These values are consistent with those found in the literature (see FigureS5), thus providing confidence in the proposed methodology and conceptual model.

3. 4

 4 Comparison with data from the literature For all three studies (i.e. the present work, Endrizzi and Rao (2014) and Jo et al. (2019)), the enthalpy values remain negative and low (> -50 kJ/mol) as compared to the entropy values.

Figure 2 :

 2 Figure2: Dependence on Temperature of the thermodynamic constant for (A) sorption of U(VI) on resin (R 2 =0.97), (B) 1:1:3 ternary complex (R 2 =0.98), (C) 2:1:3 ternary complex (R 2 =0.04). Solid lines represent fitted curves based on the Van't Hoff Equation (eq 5), dotted

Figure 3 Figure 4

 34 Figure 3 Uranium concentration (U(VI)) vs. calcium concentration in aqueous solution at I = 0.1 M NaNO 3 , total [U(VI)aq]  0.5 μM, with: pCO 2 = 10 -2.1 at 20 °C, pCO 2 = 10 -2.0 at 40 °C, pCO 2 = 10 -1.6 at 60 °C, and pCO 2 = 10 -1.5 at 80 °C. The lines represent the calculation

Table 1 :

 1 Summary of the batch experiments performed as part of the present work.. *) concentration set at 0.087 due to an experimental error. This situation has been taken into account in the modelling calculations.

	x=2
	x Ca 2+ + UO 2 (CO 3 ) 3	4-= Ca x UO 2 (CO 3 ) 3	2x-4
		Jo et al. 2019
		p.w.

(

Table 2 .

 2 Comparison of the thermodynamic parameters of the Ca-U(VI)-CO 3 ternary complex reactions (p.w.: present work) with data reported in END14[START_REF] Endrizzi | Chemical speciation of Uranium(VI) in marine environments: Complexation of Calcium and Magnesium ions with [(UO 2 )(CO 3 ) 3 ] 4and the effect on the extraction of Uranium from seawater[END_REF] and JO19[START_REF] Jo | Formation of CaUO 2 (CO3) 3 2and Ca 2 UO 2 (CO 3 ) 3 (aq) complexes at variable temperatures (10-70 °C)[END_REF]. .w.: present work. log 10 K 113 o = log 10 K 113 + log 10 K 013 o and log 10 K 213 o = log 10 K 213 + log 10 K 013 o . Corrected data considering the thermodynamic data obtained from NEA-TDB. (Guillaumont et al., 2003) log 10 K 013 o = 21.84 ± 0.04 ; ∆ r H m o = -39.2 ± 4.1

	Reaction	log 10 Kº ± σ	∆ r G m o ± σ (kJ/mol)	∆ r H m o ± σ (kJ/mol)	(kJ/mol) o ± σ 𝑻 𝟎 ∆ r S m	Reference
		27.27 ± 0.04	-155.6 ± 0.2	-24.4 ± 2.2	131± 5	p.w.
	Ca 2+ + UO 2 2+ + 3CO 3 2-= CaUO 2 (CO 3 ) 3 2-	27.00 ± 0.04	-154.1 ± 0.2	-47 ± 6	107 ± 6	END14
		27.02 ± 0.16*	-154.2 ± 0.9*	-40.4 ± 4.1* 114 ± 4*	JO19
		29.8 ± 0.2	-170.1 ± 0.9	-3 ± 10	167 ± 10	p.w.
	2 Ca 2+ + UO 2 = Ca 2 UO 2 (CO 3 ) 3 2+ + 3CO 3 2-	30.84 ± 0.04	-176.0 ± 0.2	-47 ± 7	129 ± 7	END14
		30.55 ± 0.16*	-174.4 ± 0.9*	-42.3 ± 5.1* 132 ± 5*	JO19

p*

Acknowledgments

This research was funded by ANDRA (France's National Radioactive Waste Management Agency) within the framework of the GL-CTEC Project.

0.1 for log 10 𝐾 aq 2 and +23 ± 7 kJ mol -1 for enthalpy) remain consistent with those obtained from our experiments (filled symbols; 7.96 ± 0.1 for log 10 𝐾 aq 2 and 36.5 ± 10 kJ mol -1 for enthalpy). The conclusion is also valid for the 1:1:3 complex if we compare the data from our work (5.42 ± 0.09 and 14.9 ± 5.1 kJ mol -1 for log 10 𝐾 aq 1 and the enthalpy, respectively) and those of [START_REF] Jo | Formation of CaUO 2 (CO3) 3 2and Ca 2 UO 2 (CO 3 ) 3 (aq) complexes at variable temperatures (10-70 °C)[END_REF] (5.22 ± 0.15 and 10.5 ± 9.5 kJ mol -1 for log 10 𝐾 aq 1 and the enthalpy, respectively). This illustrates the very high sensitivity of the parameters.

Moreover, all the values described in this work are dependent on the thermodynamic database used to perform the modelling analysis. It should be noted that the data in Thermochimie database for the HCO 3 -and CO 2 species deviate slightly at 60 °C and 80 °C from the one of Patterson and coll. [START_REF] Patterson | Second ionization of carbonic acid in NaCl media to 250°C[END_REF][START_REF] Patterson | Carbonate equilibria in hydrothermal systems: First ionization of carbonic acid in NaCl media to 300°C[END_REF] (See Table S1). Nevertheless, changing the values of the most pertinent reactions leads to almost the same conclusions on the enthalpy of reaction for the ternary complexes.

Conclusions

The present work focuses on the temperature effect on the formation of aqueous ternary "Ca-U(VI)-CO 3 " species under the clay geochemical conditions applicable to the French concept of radioactive waste disposal (COx clayrock), whereby Ca/pCO 2 /pH parameters are controlled by calcite dissolution/precipitation reactions. The anionic exchange method has been chosen to directly evaluate the competition between ternary complex formation and uranium retention. A specific experimental set-up has been designed in order to work in a biphasic solid/liquid system at various temperatures by means of controlling the temperature and pCO 2 . The Van't Hoff Equation can be applied to explain the variation in stability constant values as a function of temperature (20-80 °C). Increasing temperature does not facilitate the formation of CaUO 2 (CO 3 ) 3

2-

, whereas it has very little effect on the stability of Ca 2 UO 2 (CO 3 ) 3 (aq). Although similarities are found, it does not unfortunately seem possible to

Available Supporting Information

Additional details on experimental methods and modelling results are provided in the supporting information file.


Morgane Audère
email: morgane.audere@univ-nantes.fr

Marc Robin
email: marc.robin@unvi-nantes.fr

Assessment of the vulnerability of sandy coasts to erosion (short and medium term) for coastal risk mapping (Vendée, W France)

Highlights

-A study conducted on 109 km of sandy coastline -The measurement of instantaneous shoreline retreat during the 1999 and 2010 storms.

-A calculation of the parameter Lmax (retreat due to an extreme event).

Introduction

On a global scale, sandy coastlines are, as a result of climate change, increasingly exposed to the risks of coastal flooding and erosion [START_REF] Nicholls | Coastal systems and low-lying areas[END_REF]. Projected changes in climate would result in sea level rise, increased storminess in mid-latitudes, and changes in wave conditions with higher waves and storm surges [START_REF] Ranasinghe | Assessing climate change impacts on open sandy coasts: A review[END_REF]. According to [START_REF] Luijendijk | The State of the World's Beaches[END_REF], 24% of the world's sandy coasts have an erosion rate of more than 0.5 m/year and about 16% of more than 1 m/year. On the other hand, 27% of sandy coasts are undergoing accretion and about 18% have an accretion rate over 1 m/year. In France, 23% of sandy coasts are accreting, 40% are stable and 37% are eroding [START_REF] Cerema | Indicateur national de l'érosion côtière, Spécification technique du produit (version 1.0[END_REF].

In Vendée, sandy coasts represent 40% of the coastline, i.e. 109 km. According to the results of the National Erosion Indicator [START_REF] Cerema | Indicateur national de l'érosion côtière, Spécification technique du produit (version 1.0[END_REF], 27% of the Vendée coastline is historically retreating at an average rate of 0.1 to 0.5 m/year and 7% of 0.5 to 1.5 m/year. 21% of the coastline is accreting (over 0.1 m/year) and 48% is not significantly changing. Over the last 70 years, and despite significant erosion, the phenomenon of accretion remains predominant on the sandy coasts of Vendée [START_REF] Robin | Assessing Surface Changes between Shorelines from 1950 to 2011: The case of a 169-km Sandy Coast, Pays de la Loire (W France)[END_REF].

However, the erosion mechanism is not only characterized by average historical retreat speeds (Fenster et al., 2001). Indeed, instantaneous erosion during storms is an important phenomenon and it has to be precisely quantified in order to manage these coastal areas more easily [START_REF] Callaghan | Quantifying the storm erosion hazard for coastal planning[END_REF]. The Vendée coast has been impacted by numerous high intensity winter storms such as Lothar and Martin (1999), Johanna (2008), Xynthia (2010) or Joachim (2011). More recently, the 2013/2014 winter, for which 22 storms were recorded, has also been the subject of several studies showing the morphogenic impact of this succession of storms (Blaise et al., 2015, Masselink et al., 2015, Masselink et al., 2016). All these events have highlighted the fragility of this coastline by causing instant retreats of dune barriers, marine submersions, sometimes leading to significant material damage and even human casualties [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]Fattal et al., 2012;[START_REF] Bertin | Importance of wave age and resonance in storm surges: The case Xynthia, Bay of Biscay[END_REF]Castelle et al.,2015).

Thus, understanding the environmental processes and conditions that cause short-term shoreline mobility is important to protect the coasts, prevent damage and to understand the causes of chronic beach retreat [START_REF] Wright | Morphodynamics of beaches and surf zones in Australia[END_REF].

Over the past 30 years, various strategies have emerged to manage coastal risk. At the European scale, coastal erosion, and its link with climate change, was included for the first time in the 2002 Recommendation of the European Parliament and of the Council of the European Union, in the "Integrated Coastal Zone Management strategies" section. Following this recommendation, the Eurosion project (2002)(2003)(2004) was the first program to take stock of the situation of erosional coastal zones at the European scale. In the same way as in the United States, as part of the implementation of FEMA's coastal erosion management program (Leatherman, 2003), Eurosion project gave a lot of impetus to implement a coastal erosion policy and thus highlighted the need to consolidate knowledge on coastal erosion, to anticipate and to integrate it into management strategies (European Commission, 2004) forming a guideline for the implementation of regulations on national and local scales. Numerous studies have since recalled and insisted on the importance of an integrated and future-oriented coastal erosion management strategy [START_REF] Marchand | Concepts and science for coastal erosion management -An introduction to the Conscience framework[END_REF][START_REF] Rangel-Buitrago | How to make Integrated Coastal Erosion Management a reality[END_REF].

In France, there is a whole arsenal of measures to prevent and manage the risks linked to coastal erosion. The 1986 coastal law (loi "Littoral") for the development, protection and enhancement of the coastline prohibits urbanisation in the 100m strip from the upper limit of the shoreline in order to protect natural coastal areas. It indirectly reduces the number of issues subjected to coastal erosion. Thus, the Barnier law of 2 February 1995 relating to the reinforcement of environmental protection and the prevention of natural risks instituted the Coastal Risk Prevention Plan (PPRL). This spatial planning document, enforceable against third parties, is annexed to the Local Urban Planning Plan (PLU in French). It applies to the EPCI (a public establishment of cooperative urban areas) and limits or even prohibits urbanisation when the hazard and the stakes are high. Despite the pressures mentioned above, storm Xynthia was about to reveal the lack of PPRL on the coastal towns of Vendée. The sector of La Faute-sur-Mer, which would end up being the most affected, would be the first to get its PPRL in 2012. In 2017, all the towns along the Vendée coast, apart from Yeu Island, got an approved PPRL.

A methodological guide was published in 1997 (Gary et al., 1997) and updated in 2014 so as to help drawing up these PPRL (MEDDE, 2014). This guide offers food for thought concerning the methods determining the shoreline retreat hazard applied in the PPRL as well as ways of improving the methodology. The erosion hazard zone, built with a precautionary approach, aims to protect the stakes related to this phenomenon. This hazard zone (Lr) written as follow: "Lr = 100 Tx + Lmax". It results from the analysis of historical dynamics (Tx), projected to a 100-year horizon (100), to which is added the maximum retreat due to an extreme event (Lmax) (DDTM 85, 2015). The first parameter (100 Tx) aims at extrapolating the historical trends of the shoreline evolution in the future in order to know the shoreline position on a 100-year horizon. The second parameter (Lmax) is strategically added to define the most vulnerable areas during an extreme event.

There are several methods to measure the retreat due to an extreme event. The need to measure this erosion phenomenon during a storm was raised as early as 1968 by T. Edelman in the Netherlands who used a dune equilibrium model. In 2014, Ciavola et al. list and detail the principles and evolutions of empirical models for estimating dune retreat: 1) a first dune equilibrium model was created by Edelman in 1968. It was independent of time and pre-storm profile, and the post-storm profile's shape depended on wave and sediment properties. This method was then taken up and improved in other studies: DUROS method [START_REF] Dean | Equilibrium beach profiles: US Atlantic and the Gulf Coasts[END_REF], [START_REF] Van De Graaff | Dune erosion during a storm surge[END_REF], [START_REF] Vellinga | Beach and dune erosion during storm surges[END_REF]); 2) more advanced models taking into account the pre-storm profile and simulating the temporal evolution. It was particularly developed by Kriebel (1982), [START_REF] Kriebel | Convolution method for time-dependent beach-profile response[END_REF]; 3) a model estimating the potential retreat of the dune front was defined by Hallermeier and Rhodes in 1988 (also called Median Dune Erosion). This model related the erosion cross-sectional area which was relative to the return period of an extreme water level (FEMA, 2003). However, this model did not take into account beach morphodynamics such as beach slopes and run-up consequences. These three empirical approaches are the first of three existing methods estimating the retreat related to an extreme event. The second method is based on designing and using numerical models. These tools allow the simulation of hydrodynamic processes in order to better understand the morphological dynamics between the foreshore, the beach and the dune during extreme events. The XBeach, SBeach, Telemac models are the most commonly used [START_REF] Roelvink | Modelling storm impacts on beaches, dunes and barrier islands[END_REF][START_REF] Maspataud | L'apport de modèles numériques pour l'étude morphodynamique d'un système dune-plage macrotidal sous l'effet des tempêtes : plage de la dune Dewulf, Est de Dunkerque, France. XIèmes Journées[END_REF][START_REF] Corbella | Multivariate return periods of sea storms for coastal erosion risk assessment[END_REF][START_REF] Pender | An evaluation of methods available for quantifying extreme beach erosion[END_REF]. Finally, the third method is known as observation and measurement method. It consists in quantifying the impact of storms by measuring, using transects perpendicular to the shoreline, the distance between the pre-storm and post-storm shoreline which have been previously digitized on a database of aerial images. This method is more often used to assess historical trends in shoreline mobility [START_REF] Houser | Controls on coastal dune morphology, shoreline erosion and barrier island response to extreme storms[END_REF][START_REF] Thieler | The Digital Shoreline Analysis System (DSAS) version 4.0-an ArcGIS Extension for Calculating Shoreline Change[END_REF][START_REF] Moussaid | Using automatic computation to analyze the rate of shoreline change on the Kenitra coast, Morocco[END_REF][START_REF] Cellone | Coastal erosion and loss of wetlands in the middle Río de la Plata estuary (Argentina)[END_REF], than to assess the impact of a storm [START_REF] Harley | Extreme coastal erosion enhanced by anomalous extratropical storm wave direction[END_REF].

We suggest using the last method to assess the impacts of the storms of December 1999 (Lothar and Martin) and February 2010 (Xynthia). In Vendée, Xynthia is considered as the reference storm in the PPRL because of the exceptional water levels measured through La Rochelle's tide gauge. Indeed, the local rise in water levels was due to the concomitance between the storm, which happened during a high spring tide [START_REF] Pineau-Guillou | Caractérisation des niveaux marins et modélisation des surcotes pendant la tempête Xynthia[END_REF]. However, in meteorological terms, Xynthia was not as exceptional as Lothar, Martin (1999) or Klaus storms (2009) [START_REF] Bertin | Importance of wave age and resonance in storm surges: The case Xynthia, Bay of Biscay[END_REF][START_REF] Genovese | Xynthia : le déroulement de la tempête et ses conséquences en France[END_REF]. This implies that other storms such as Lothar and Martin may have had a more significant impact than Xynthia. It also aims to show that considering other extreme events could affect the erosion hazard zones of the PPRL. This work aims to improve the definition of the erosion hazard in PPRL maps by showing the relevance of including the impacts at least two extreme events for the definition of Lmax and to provide leads to improve the realization of the erosion hazard bands of the PPRL.

First, the study area will be presented, then the method of realization of the erosion hazard zone will be explained. In a third part the results will be presented and then discussed in the last section by taking into account a specific example of « La Tranche-sur-Mer ».

Study area

The Vendée coastline is located on the French mid-Atlantic coast and is generally oriented along a NW-SE axis [START_REF] Robin | Assessing Surface Changes between Shorelines from 1950 to 2011: The case of a 169-km Sandy Coast, Pays de la Loire (W France)[END_REF]. It stretches for nearly 276 km from the bay of Bourgneuf to the Aiguillon cove. The Vendée coast is composed of 109 km of sandy coast, 64 km of rocky coast and 103 km of sea defences. The erosional sandy coasts are generally characterized by eroding cliffs (Fig 1-G). The foredunes are representative of accretion (or healing) sectors (Fig 1-F). In some areas, such as Noirmoutier, dunes play an essential role and are the only barrier between the sea and the low areas (Fig 1-A). Other sectors are more characterized by important seasonal sedimentary dynamics. The outlet of the Goulet de Fromentine (Fig 1-B), is the part of the mouth whose morphology is the most dynamic (Le Mauff, 2019). , 2017). According to the coast classification developed in Davies (1964), the coast can be considered macro-tidal. Concerning the hydrodynamic parameters, between 1979 and 2016, an annual predominance of winds from the NW to SW sectors (about 42%) was observed with a W to SW trend (about 25%) in the winter period (September to February). The strongest winds are mainly from the S-SW sector (Fig. 2-a). Concerning the wave climate, the majority of the significant wave between 1979 and 2016 comes from the NW (40%) and W (35%) sectors (Fig. 2-a). In the winter period, the significant swells mainly come from the W sector (38%). The observation is the same for the highest Hs (above 4m). The inventory of the most relevant storm events has been achieved for the whole survey period . The most notable storms in terms of sea-weather conditions since 1979 are listed in Table 2.

For each event, the hydrodynamic and meteo-atmospheric characteristics and the storm index, according to Dolan and Davis in 1992 (Table 1), were calculated. This index takes into account significant wave heights (hs) and storm duration (hr).

The waves and wind data come from the HOMERE database [START_REF] Accensi | HOMERE. Ifremer -Laboratoire Comportement des Structures en Mer[END_REF] whose extraction point is located between the islands of Yeu and Noirmoutier (Fig. 1). Atmospheric pressure data come from the meteorological record station (METEO FRANCE) on Yeu island. The water levels measured are from tide gauge of Saint-Gildas (Loire-Atlantique department) because tide gauges of Vendée (L'Herbaudière, Les Sables d'Olonne, La Rochelle-La Palice) did not operate during one of the two storms.

In this paper, we chose to study the storms Lothar (December 26-27, 1999) and Martin (December 27-28, 1999) and Xynthia (February 2010). The December 1999 storms were unusually violent and caused a lot of damage on the coastline of the Pays de la Loire and especially in Vendée. These storms are often mentioned together as they hit the French coasts two days apart. Nevertheless, we note Lothar crossed France at a rather northerly position than Martin (Ulbrich et al., 2001), causing less damage in Vendée. However, as we are unable to differentiate precisely the impact of each storm, we will combine both storms and refer to the event of December 1999. The significant wave average over the duration of these events is 7.9 m for Lothar and 7 m for Martin with maximum heights of 8.7 m and 10.4 m respectively (Table 1). Lothar peaked at mid-tide, Martin at low tide, both during a phase of decreasing tidal range from spring to neap tide. These storms lasted 22 and 28 hours respectively. According to the severity index of Dolan and Davis (1992), both of them are classified as category 4, or "severe" storms.

Storm Xynthia, which occurred during the night of 27-28 February 2010, caused significant swells (over 27 hours) of 3.9 m on average with a maximum height measured at 5.9 m. According to the severity index, Xynthia is classified as a category 3 or "significant" storm, with a lower storm surge 170 than Martin (table 1). However, this storm surge, combined with high tide (table 1), generated extreme water levels.

These two events were chosen for 1) the available data. Indeed, both events are sufficiently documented (archives, aerial images, feedback, photographs, forcing data) to carry out this work. 2) Their morphogenic character. Beyond the numerous damage and human casualties, their impact on sandy coasts makes them suitable study objects for measuring Lmax. The December 1999 storms were chosen for their particularly intense meteorological conditions manifested by strong waves, high water level and storm surge (Table 1, Fig. 2-b) as well as Xynthia considered as a "reference storm" in Vendée, characterized by extreme water levels and a particularly high storm surge (table 1, Fig. 2-b). 180 3. Method 3.1. Data

The aerial images are produced by the French institute of geographic and forest information (IGN). Their resolution varies between 0.5 and 1 m depending on the date of the aerial images. These images have been georeferenced and then mosaicked over the entire departmental coastline. The analysis of the historical evolution of the shoreline was carried out over a period of 66 years, using aerial images from 1950 (BD ORTHO Historique) and 2016 (BD ORTHO). For the short term analysis of the shoreline's mobility evolution, the before and after storm aerial images were taken 14 months apart for Lothar and Martin and 10 months apart for Xynthia. The before and after storm aerial images are mosaicked. Then shorelines are digitized. The shoreline changes are measured using a vegetation line and/or a morphological line both strongly related depending on the context. After an erosive storm event, the selected line is a morphological line. The edge of the dune -as the erosion reference feature (ERF)-is always selected in such a context because it is highly relevant. The line corresponds to the toe of a nearly vertical dune cliff carve by erosion processes, which clearly demarcates the vegetated dune (which comes until the top dune cliff) from the backshore [START_REF] Crowell | Historical Shoreline Change: Error Analysis and Mapping Accuracy[END_REF]Zuzeck et al., 2003;[START_REF] Boak | Shoreline Definition and Detection: A Review[END_REF][START_REF] Suanez | Monitoring of recent morphological changes of the dune of Vougot beach (Brittany, France) using differential GPS. Shore and beach[END_REF]. After a recovery period, the limit between backshore and dune is different because dune recovery process associated with sediment supply on the backshore build a foredune with pioneer vegetation. In such a context, the foredune vegetation line proxy is chosen which also correspond to the morphological line between foredune and backshore in such an sedimentary accretion context. The shorelines have been digitized at a scale of 1:1000 in order to achieve a good level of accuracy.

When the shoreline is artificial, the marker used is the base of the structure. These structures are built to protect currently non-relocatable assets situated in the coastal strip and potentially subject to erosion.

Measurement of the retreat due to an extreme event

The evaluation of the maximum retreat related to an extreme event (Lmax), consists of measuring the distance between the shorelines before and after a storm using an extension of the ArcGis 10.5 software (Digital Shoreline Analysis System (DSAS) [START_REF] Thieler | The Digital Shoreline Analysis System (DSAS) version 4.0-an ArcGIS Extension for Calculating Shoreline Change[END_REF]. The transects are generated at a right angle from the shoreline and the spacing is variable according to the authors. It is generally less than 100 meters [START_REF] Aernouts | L'évolution du rivage et des petits-fonds en baie de Wissant pendant le XXe siècle (Pas-de-Calais, France). Géomorphologie : relief, processus[END_REF][START_REF] Hapke | National assessment of shoreline change: Part 3: Historical shoreline changes and associated coastal land loss along the sandy shorelines of the California coast[END_REF][START_REF] Abdellaoui | Etude diachronique et historique de l'évolution du trait de côte de la baie de Tanger (Maroc)[END_REF][START_REF] Faye | Évolution du trait de côte à Nouakchott (Mauritanie) de 1954 à 2005 par photo-interprétation[END_REF]. The spacing of the transects in this study is 20 meters [START_REF] Houser | Controls on coastal dune morphology, shoreline erosion and barrier island response to extreme storms[END_REF][START_REF] Moussaid | Using automatic computation to analyze the rate of shoreline change on the Kenitra coast, Morocco[END_REF][START_REF] Cellone | Coastal erosion and loss of wetlands in the middle Río de la Plata estuary (Argentina)[END_REF] as this distance is best suited to small beaches in the study area. 5 000 transects are thus implemented along the Vendée coastline. Finally, the distance between the oldest and the most recent shoreline (pre and post storm) is measured for each transects using the Net Shoreline Measurement (NSM) method in DSAS.

3.4. Assessment of the uncertainties 3.4.1. Uncertainty of the shoreline position

The uncertainty on the shoreline's position involves potential location errors. These errors may accumulate when there is a comparison between the positions of two shorelines at two different times [START_REF] Robin | Assessing Surface Changes between Shorelines from 1950 to 2011: The case of a 169-km Sandy Coast, Pays de la Loire (W France)[END_REF]. A margin of uncertainty has therefore been calculated. The accuracy with which the position of the shoreline is determined depends on the quality of the images (image resolution or "pixel error"), the quality of the georeferencing (orthorectification error) and the accuracy and regularity with which the shoreline has been digitized (digitization error). The final result corresponds to an interval in which it is impossible to define whether the sandy coastline portion is stable or whether the error is related to the uncertainty of the method. The overall position error for a shoreline is calculated by taking the square root of the sum of the squares of each error [START_REF] Fletcher | Mapping Shoreline Change Using Digital Orthophotogrammetry on Maui, Hawaii[END_REF][START_REF] Hapke | National assessment of shoreline change: Part 3: Historical shoreline changes and associated coastal land loss along the sandy shorelines of the California coast[END_REF]. The overall error for both events is estimated to be 2.8m. When the evolution rates are calculated between two dates and over a longer period (more than one year), these values can be annualized by calculating the square root of the sum of the squares of the global error for each date, divided by the time passed between these two dates [START_REF] Faye | Évolution du trait de côte à Nouakchott (Mauritanie) de 1954 à 2005 par photo-interprétation[END_REF][START_REF] Bagdanavičiūtė | Assessment of shoreline changes along the Lithuanian Baltic Sea coast during the period 1947-2010[END_REF]Oyedotun, 2014;[START_REF] Cellone | Coastal erosion and loss of wetlands in the middle Río de la Plata estuary (Argentina)[END_REF][START_REF] Dada | Seasonal shoreline behaviours along the arcuate Niger Delta coast: Complex interaction between fluvial and marine processes[END_REF][START_REF] Fossi Fotsi | Temporal (1948-2012) and Dynamic Evolution of the Wouri Estuary Coastline within the Gulf of Guinea[END_REF][START_REF] Robin | Assessing Surface Changes between Shorelines from 1950 to 2011: The case of a 169-km Sandy Coast, Pays de la Loire (W France)[END_REF].

Temporal uncertainty

Temporal uncertainty is related to the gap between pre-storm and post-storm aerial images. For the December 1999 event, almost 14 months separate the aerial images before the storm (19/06/1999) and after the storm (01/08/2000) (Fig. 3-A). Wave and wind conditions recorded during these 14 months show that both Lothar and Martin storms are the only most severe events. We therefore assume that the results in terms of measured retreats on the aerial photographs are mainly caused by the impact of both storms.

The time between the passage of the storms and the images, taken either immediately afterwards or a few months later, interferes little with the measurement of the setback because resilience is taken into account. In fact, aerial images sometimes reveal markers of resilience such as the formation of benches or the re-growth of vegetation on the fore dune. However, when the actual traces of storm impact (notch formation or erosion cliffs) are visible, these markers are used to digitize the poststorm shoreline. The historical evolution of the shoreline was measured between 1950 and 2016. The 1950 shoreline was digitized from IGN aerial photographs recorded in 1950 and supplemented with a few 1952 photographs to provide aerial continuity over the entire area [START_REF] Robin | Assessing Surface Changes between Shorelines from 1950 to 2011: The case of a 169-km Sandy Coast, Pays de la Loire (W France)[END_REF].

The shoreline position indicators selected are the same as for Lmax. However, the digitization scale for the 1950s is set at 1:2500 due to the poor quality of the aerial photographs. The transect method is also used in this case in order to measure an average annual change between two dates. On each transect, the EPR (End Point Rate) method is used [START_REF] Thieler | The Digital Shoreline Analysis System (DSAS) version 4.0-an ArcGIS Extension for Calculating Shoreline Change[END_REF]. 270 3.5.2. Projection to 2050

The projection to 2050 is based on the observation of shoreline evolution between 1950 and 2016. This approach, based on the one applied in the PPRL, consists in carrying back the current shoreline linearly towards the back of the range, taking into account the historical evolution value of each transect. This historical evolution integrates the various processes that explain the observed dynamics: hydrodynamic and climatic factors (the role of tides, the impact of extreme events), longterm sea level rise (eustatism), and human intervention.

To the value of the historical evolution calculated on each transect is then added the maximum measured retreat value linked to an extreme event (Lmax). This addition (value of the historical evolution and Lmax) corresponds to the value of the projection to 2050 on each transect. Finally, the line connecting each point on each transect corresponding to the value of the 2050 projection delimits the erosion hazard strip.

For all of Vendée, two scenarios have been carried out. The first one is the projection of the current shoreline to 2050 to which the retreat values measured after the storms Lothar and Martin are added. The second scenario also consists of projecting the shoreline to the year 2050, but this time taking into account the retreat values generated by the storm Xynthia. By comparing these two scenarios, we will be able to determine which of them shows the most significant retreat.

The IPCC's work published in 2019 [START_REF] Oppenheimer | Sea Level Rise and Implications for Low-Lying Islands, Coasts and Communities[END_REF] justifies the choice of a projection to 2050 by the small divergence of RCP scenarios. Indeed, the average divergence in the projection of sea level rise by 2100 is 33cm between RCP 2.6 and RCP 8.5, whereas by 2050 it is only 4cm. The uncertainty is therefore lower by 2050: the risk of obtaining an erroneous shoreline positioning in 2050 is therefore much lower than trying to position the shoreline in 2100 with a much higher risk of error.

In this paper, the projection of the current shoreline is calculated by multiplying an average annual rate of shoreline change (accretion or erosion) by the number of years between 2016 and 2050 (i.e. 34 years). In the PPRL, only negative average annual rates of shoreline change are projected, thus corresponding to an erosive trend.

In areas where the shoreline is "fixed" by sea defences, we consider that the shoreline will be the same in 2050. However, a storm like Xynthia can have an overflow effect and bring sand behind the structure (Fig. 4), which should not to be confused with a retreat of the shoreline. In areas where the shoreline is "fixed" by coastal protection works, we consider that the shoreline will remain the same in 2050. In addition, the State ensures that the owners, managers and operators of these protection structures meet the regulatory requirements and thus guarantee a certain level of reliability. Nevertheless, the ante and post-storm shoreline remain digitized at the base of the structure. On the other hand, simple walls delimiting property lines are not considered to be sea defences. They were moreover destroyed by wave action during Xynthia (Fig. 5). In this case, we take into account the 310 retreat behind these property lines. In PPRL, the erosion hazard strip defined on the 100-year horizon is composed of two elements: the historical retreat of the shoreline to which is added the maximum retreat due to an extreme event [START_REF] Ddtm | Plan de Prévention des Risques Naturels Prévisibles Littoraux « Pays d'Olonne[END_REF]. The 2050 projection from 2016 onwards will therefore be written as follows:

Lr = 34 * Tx + Lmax with Lr = the width of the hazard zone, 34 is the number of years between the "current" shoreline used in this study ( 2016) and the 2050 horizon, Tx = the average annual retreat rate, Lmax = the value of the maximum retreat following an extreme event. The parameter Lmax retained for all sections of the coastline is thus based on two steps : (i) on the section-by-section comparison of the setback observed for each storm and (ii) from which the Lmax for all storms compared is retained. The Lmax value corresponds to the strongest setback resulting from the comparison of the setback of the various storms. Thus, the Lmax for a given section can come from the Xynthia storm impact which is stronger than the Lothar one and for the next section, the Lmax can come from the Lothar storm impact if this one is stronger than the Xynthia one (Fig. 6-a). The historical retreat and Lmax are calculated for each transect. The final result is transcribed as a hazard zone according the PPRL method (pink shaded area, Fig. 6-c). 12). In addition, some towns saw much of their shoreline retreat during the Xynthia storm, as in Saint-Jean-de-Monts, where 90% of the coastline eroded as a result of the storm with retreat values of up to -12m.

Even if the storm's most serious consequences have not been found in Vendée, the impact of Lothar and Martin remains consequential. Indeed, as far as our study area is concerned, the 1999 storms caused retreats over 20.5 km, i.e. 21.6% of the sandy coasts of Vendée. The results show an uneven impact of the storms on the sandy coasts of the Vendée. Some sectors were more affected during Xynthia than during Lothar and Martin as is the case for the local council community "Océan Marais de Monts". This local community includes the coastal towns of La Barre-350 de-Monts, Notre-Dame-de-Monts and Saint-Jean-de-Monts. Its coastline is particularly exposed to storms. The impact of Xynthia on this sandy coast was greater than Lothar's and Martin's, both in terms of length of the eroded shoreline and the distance of landwards retreat (cross-shore). On this coast, the retreats due to Xynthia were measured over 9.5 km, i.e. 68.7% of the three towns' coastline against 23% for Lothar and Martin. Much of the retreats measured during this storm are of less than 5 m and constitute 50.4% of the eroded coastline. It is also observed that 26.8% of the erosion values are between 5 m and 10 m and 1.3% between 10 m and 20 m after Xynthia (Fig. 8). Generally speaking, Lothar and Martin have impacted the coastline three times less than Xynthia; 22.8% of the coastline was hit against 68.5% in 2010. Despite Xynthia's undeniable impact, some areas were nevertheless more affected by the storms Lothar and Martin as in the town Noirmoutier-en-île. Approximately 30% of the sandy coasts of the town eroded after the 1999 storms, i.e. almost 1.5 km. Retreat values of less than 5 m are equivalent for both storms. We note that retreats between 10 m and a maximum retreat value reaching 19.7 m were measured only during Lothar and Martin whereas the retreat values did not exceed 6 m following of Xynthia.In addition, erosion values measured between 5 m and 10 m are observed on 11.8% of the town's sandy coasts after Lothar and Martin against 3.3% after Xynthia (Fig. 7-b).

In the sector located in both Longeville-sur-Mer and La Tranche-sur-Mer, 56% of this sector has 370 retreated following Xynthia against 46.5% in December 1999 (Fig. 9). However, in the area of the Grouin du Cou tip, in the southern part of the sector, Lothar and Martin caused the most significant retreats of up to 13 m, whereas no significant retreats were measured following Xynthia. Although Xynthia affected a larger portion of this area, the percentage of retreats between 10 m and 20 m is higher (5.3%) for Lothar and Martin than after Xynthia (3.1%). We have previously noted that the two extreme events studied had different at department scale. However, some sectors suffered a similar impact both in terms of eroded coastline and depth of 380 retreat. This is the case of La Faute-sur-Mer, one of the most severe impacted sectors in this department (Fig. 7-c). This section of the coastline was particularly sensitive to the storms Lothar, Martin and Xynthia. Its coastline was affected to the same extent by both events: 70% by Xynthia and 74% by Lothar and Martin. The retreat values exceeded 20 m in the northern part of the town during the storms of December 1999, whereas they did not exceed 10 m during Xynthia

Consequences on projection scenarios

The study of the two extreme events Lothar & Martin and Xynthia, added to the historical evolution of the shoreline, makes it possible to compare the hazard strip for each scenario and to see which one has the greatest impact. This approach also aims to target vulnerable and erosional areas. In the example of La Tranche-sur-Mer (Fig. 10-a), the most important hazard strip corresponds to the 390 Xynthia scenario and is therefore selected. In this sector, there is a difference of up to 11 m between the two scenarios. For the Xynthia scenario, the hazard strip extends over a maximum of 36 m compared to 28 m for the Lothar and Martin scenario, starting from the 2016 shoreline. In other areas, Xynthia is not the most morphogenic storm. This reveals the importance of taking into account another more impactful event such as the storms Lothar and Martin. In the sector of La Guérinière (Noirmoutier Island) (Fig. 10-b), the retreats measured are greater after the December 1999 storms than after Xynthia. The "Lothar and Martin" scenario is therefore the most relevant 400 scenario to be taken into account. A difference of up to 9 m between the two scenarios is observed.

For the Lothar and Martin scenario, the hazard strip extends to a depth of 20 m compared to 12 m for the Xynthia scenario. In the eastern part of this area, the shorelines' projections to 2050 are located " in front of" the initial coastline. These sectors's evolution trends have been positive since 1950. Therefore, they won't be in a situation of erosion by 2050.

A Lmax definition based on two extreme events

Noting that the December 1999 storms sometimes caused greater retreats than Xynthia, it seems relevant to take both events into account to define Lmax at a department level. Fig. 12 shows the sectors that were most sensitive to either storm. These results can provide necessary information to analyse and explain the responses of the beaches to extreme events. 410

For example, the 1999 storms caused greater retreats than Xynthia in the northern part of La Fautesur-Mer, with an average retreat of 18m and a maximum retreat of 25m (box, Fig. 11) compared to an average of 10m and a maximum retreat of 15m after Xynthia. Fig. 11: Maximum retreat due to extreme events (Lmax) in south of Vendée Fig. 12 shows, on the one hand, the maximum retreat value measured during the two events and, on the other hand, the percentage of sandy coasts impacted per town and per urban area, indicating the zones covered by a PPRL in the department. This table also includes the values for Yeu Island, which does not have a PPRL. We note that of the fourteen towns, four (Noirmoutier-en-île, l'Epine, la Guérinière and la Faute-sur-Mer) show a higher maximum retreat value for Lothar and Martin than 420 for Xynthia. In most cases, the town or urban area with the highest retreat value also has the greatest impact. La Barre de Mont is an exception since, while the maximum retreat was measured after Xynthia, it was Lothar and Martin that affected a larger portion of the sandy coasts in this town (50.8% compared to 46.2% in Xynthia). In various more recents studies, the shoreline's projection to a given location in futur time is estimated according to the historical dynamic of the shoreline and sea level rise. [START_REF] Durand | Impact de l'élévation du niveau marin sur l'évolution future d'un cordon littoral lagunaire : une méthode d'évaluation. Exemple des étangs de Vic et de Pierre Blanche (littoral méditerranéen, France)[END_REF] proposed a mathematical approach to fix the future shoreline location (site of Lido, in the Mediterranean Sea). This study was taken up by [START_REF] Suanez | Méthode d'évaluation du risque de submersion des côtes basses appliquée à la plage du Vougot, Guissény (Bretagne)[END_REF] and [START_REF] Cariolet | Cartographie de l'aléa de submersion marine et PPR : éléments de réflexion à partir de l'analyse de la commune de Guissény (Finistère, France)[END_REF] and applied to a few sites in Brittany).

Other studies, on the contrary, only focus on the analysis of extreme events and their impact on sandy coasts. These works are mainly based on numerical and/or statistical modelling methods aiming to estimate erosion following a storm as proposed by Callagan et al. (2009) or Corbella & Stretch (2012a). In this study, the originality is the computation of the Lmax taking into account 440 observations of shoreline location before/after an extrem event. This Lmax can be added to a projection of a future shoreline taking into account the historical trend of the shoreline motion as recommended in the PPR or even be added to the historical trend coupled with the future sea level rise as recommended in studies already mentioned. The projection of the shoreline to which this Lmax is added thus allows the spatialization of a truly exhaustive erosion risk hazard strip.

The impact of the two extreme events studied differs from one sector to another. This can be explained in particular by the different characteristics of each storm (waves, winds, and atmospheric pressure), the tidal conditions at the time of impact (tidal coefficients, time of tide), the morphodynamic and anthropogenic context (presence/absence of coastal defences, type of beach sediments, orientation and slope of the beaches). The work of [START_REF] Pereira | Numerical modelling of shoreline evolution in the Aveiro coast, Portugal -climate change scenarios[END_REF] shows that coastline projection scenarios vary according to storm types. This work supports the idea that taking into account a single event is not sufficient to define the vulnerability of a sandy coast to extreme events. Indeed, this would be tantamount to considering only one category of storm.

As these extreme retreat values have a direct impact on the elaboration of the erosion hazard strip, it is fundamental to question the possibility of taking into account several extreme events. In Vendée, a 2007 study [START_REF] Dhi | Etude de connaissance des phénomènes d'érosion sur le littoral vendéen[END_REF] considered the following Lmax values for the South Vendée sector (towns of Longeville-sur-Mer, La Tranche-sur-Mer and La Faute-sur-Mer): a maximum retreat of 20m applied to the entire South Vendée coastline (including behind the longitudinal structures) and an exceptional value of 35m in La Belle Henriette sector (Fig. 11). These values are therefore included in the Coastal Risk Prevention Plans. Thus, contrary to the PPRL, which maintains a single Lmax value of 20 m along the entire coastline, we suggest keeping a retreat value calculated every 20 m in order to qualify the impact of storms on this shoreline, as shown in Fig. 7-c.

Concerning the use of aerial images for the evaluation of Lmax, two biases can be mentioned. Firstly, the before and after storm aerial images used are spaced several months apart (14 months for Lothar and Martin and 10 months for Xynthia) on account of availability and spatial completeness. Therefore, this time interval does not allow for the measurement of regression due to a storm alone. Within a few months, other smaller events may affect the coastline and contribute to the shoreline's mobility. In addition, the time between the storms' occurrence and the images taken either immediately after or a few months later can generally affect the measurement of storm impact. However, even if traces of resilience are visible, we take into account the markers of storms' impact (formation of erosion notches or cliffs) as soon as possible.

Then, the shots following Xynthia were taken after the breach-filling work on the beach of La Belle Henriette. This work damaged part of the upper beach and the vegetated dune. As a result, the high retreat values measured in this area must be taken with caution.

This work aims to improve the definition of the erosion hazard in PPRL maps based on observations. This land use planning document is legally rely on against third parties. It aims at protecting natural coastal area and above all limiting or even prohibiting urbanization when the hazard is high. It therefore seems necessary to highlight the weakness in the method applied in the PPRL and to propose other approaches to improve this protection zoning and ultimately encourage its updating. With this in mind, we compare our results with those of the PPRL in order to highlight the differences between the PPRL's 100-year hazard strip and this study's projection to 2050. Choosing 2050 allows us to reduce the uncertainty (see Method) and is well taken into account in the comparison of the results. This comparison therefore shows significant differences, particularly on the Clémenceau beach in La Tranche-sur-Mer. Depending on the method chosen, the erosion hazard may be underestimated or overestimated. Thus, in this sector, the PPRL zoning "100-year horizon" underestimates the erosion hazard when compared to our hazard zone "2050 horizon". Four elements explain these differences: 1) The time frame used to define the historical evolution of the shoreline in this sector is 31 years in the PPRL whereas it is 66 years in this paper . Consequently, the historical dynamics of the PPRL, between 1975 and 2006, do not take 490 into account the accretion that occurred on Clémenceau beach (between 0m and +0.70m/year).

Conversely, for the period considered here (from 1950 to 2016), we observe an average erosion rate of 0.20m/year. 2) The choice of the earliest date for both of the selected methods also conditions the analysis of the historical dynamics of the shoreline. To this end, in La Tranche-sur-Mer, urbanisation in the coastal strip began in the 1960s and contributed to the fixation of the shoreline. Consequently, a shoreline digitized in 1975 takes into account the property lines and thus biases the measurement of the historical evolution of the shoreline.

3) The difference between the two approaches is also due to the value of Lmax. Indeed, in La Tranche-sur-Mer, the Lmax used in the PPRL is 20 m for the entire coastline. With the method chosen in this article, we averaged all the transects' Lmax values in this range and obtained a retreat of 8.2m during Xynthia. The maximum retreat is 12.4m. 4) The initial 500 shoreline from which the projection to 2050 is made is also different (2006 in PPRL and2016 in this paper). As a result, the shoreline between these two dates varies from 10 to 15 m on the whole beach (Fig. 13). Consequently, it would probably be appropriate to update the hazard zoning with more recent data.

Conclusion

This paper provides new proposals regarding the creation of erosion risk bands based upon observation, which could be considered in the revision of a PPRL if necessary, as a revision is expected in any case when a change in the level of risk is observed (MEDDE, 2014). Three suggestions are thus put forward: i) updating the risk zoning using more recent data and taking into account observed trends, whether erosion or accretion ; ii) studying the impact of several storms to define an observed and measured Lmax at any point along the shoreline in order to propose a Lmax locally calculated in steps of 20m corresponding to the maximum change actually caused by the strongest of the extreme events studied; iii) proposing shorter term (2050) shoreline projections (2050) that are reasonable in the context of climate change to reduce the margin of uncertainty. Greater precision in terms of spatialization of erosion risk may thus justify the updating of these regulatory coastal strips.

Fig. 1 :

 1 Fig. 1: Location map of Vendée (W France department). The map shows the location of the different types of coasts (illustrated by seven photographs) as well as the current status of the Coastal Risk Prevention Plans. (HOMERE point : X 309753.801597 ; Y 6658415.559416) The Vendée coast is exposed to the North Atlantic marine weather patterns. Tides are semi-diurnal 130 with a range varying form 2.3 m during neap tides to 4.80 m during spring tides and reach up to 6.3 m during highest astronomical tides (from tide gauge of Saint Gildas) (SHOM, 2017). According to the coast classification developed in Davies(1964), the coast can be considered macro-tidal. Concerning the hydrodynamic parameters, between 1979 and 2016, an annual predominance of winds from the NW to SW sectors (about 42%) was observed with a W to SW trend (about 25%) in the winter period (September to February). The strongest winds are mainly from the S-SW sector (Fig.2-a).

Fig. 2

 2 Fig. 2: a : Percentage and direction of wind and wave data over the 1979-2016 period (annual and seasonal) , b : Wind and wave data during storms Lothar & Martin and Xynthia

Fig. 3 :

 3 Fig. 3: Hydrodynamic characteristics over the period between the two aerial images for A) Lothar and Martin, B) XynthiaThis observation is also available for the storm Xynthia. The 2009 and 2010 aerial campaigns were carried out 10 months apart. The highest wind speeds were indeed recorded during Xynthia (Fig.3-B). Concerning the wave climate, a few days before the storm hit, we observe two set of wave whose heights exceed those measured during the storm. In spite of these important values, these sets of wave occurred during neap tides so the impact on the coast was definitely not significant. 260 3.5. Projection of the shoreline to 2050 3.5.1. Assessment to historical mobility of the shoreline

Fig. 4 :

 4 Fig. 4: The shoreline's retreat and damage on protection works in the aftermaths of Xynthia. La Tranche-sur-Mer -South of the Clémenceau beach

Fig. 5 :

 5 Fig. 5: Oblique aerial and ground photographs following Xynthia. Town of la Tranche-sur-Mer. Left : 2009. Right : 2010 3.5.3. Erosion hazard

Fig. 6 :

 6 Fig. 6: Steps of the realization of the "erosion hazard" zone. 4. Results 4.1. Impact of the two storms on the Vendée shoreline Over all the sandy coasts of Vendée, 43.2% (i.e 41 km) of the sandy coastline were eroded during storm Xynthia. Regardless of the range of erosion, Xynthia was more morphogenic than Lothar and Martin (Fig. 7-a). The most remarkable erosion values are measured in the town of La Tranche-sur-Mer (up to 40 m) (Fig.12). In addition, some towns saw much of their shoreline retreat during the Xynthia storm, as in Saint-Jean-de-Monts, where 90% of the coastline eroded as a result of the storm with retreat values of up to -12m.

Fig. 7 :

 7 Fig. 7: Percentage of the shoreline impacted by storms per erosion phase on sandy coast of a) Vendée, b) Noirmoutier-en-île, c) La Faute-sur-Mer 4.2. The uneven effects of the two events on sandy coasts

Fig. 8 :

 8 Fig. 8: Retreats measured during both events on the local council community "Océan Marais de Monts". Left strip: Lothar and Martin (December 1999) Right strip : Xynthia (February 2010)

Fig. 9 :

 9 Fig. 9: Retreats measured during both events on La Pointe du Grouin du Cou. Left strip : Lothar and Martin (December 1999). Right strip : Xynthia (February 2010)

Fig. 10 :

 10 Fig. 10: Projection to 2050 with both scenarios (Lothar & Martin / Xynthia) a) La Tranche-sur-Mer, b) La Guérinière -Noirmoutier island

Fig. 12 :

 12 Fig. 12: Summary of the impact of storms per town and urban area 5. DiscussionIn various studies, the shoreline's projection to a given point in time is estimated only according to the historical dynamics of the shoreline. The works of[START_REF] Pereira | Numerical modelling of shoreline evolution in the Aveiro coast, Portugal -climate change scenarios[END_REF] andMukhopadhyay et al. 430 (2012), offer methods for projecting the shoreline at various times based on the historical evolution in the Northwest coast of Portuga and on Puri Coast, Bay of Bengal. In various more recents studies, the shoreline's projection to a given location in futur time is estimated according to the historical dynamic of the shoreline and sea level rise.[START_REF] Durand | Impact de l'élévation du niveau marin sur l'évolution future d'un cordon littoral lagunaire : une méthode d'évaluation. Exemple des étangs de Vic et de Pierre Blanche (littoral méditerranéen, France)[END_REF] proposed a mathematical approach to fix the future shoreline location (site of Lido, in the Mediterranean Sea). This study was taken up by[START_REF] Suanez | Méthode d'évaluation du risque de submersion des côtes basses appliquée à la plage du Vougot, Guissény (Bretagne)[END_REF] and[START_REF] Cariolet | Cartographie de l'aléa de submersion marine et PPR : éléments de réflexion à partir de l'analyse de la commune de Guissény (Finistère, France)[END_REF] and applied to a few sites in Brittany).Other studies, on the contrary, only focus on the analysis of extreme events and their impact on sandy coasts. These works are mainly based on numerical and/or statistical modelling methods aiming to estimate erosion following a storm as proposed byCallagan et al. (2009) orCorbella & Stretch (2012a). In this study, the originality is the computation of the Lmax taking into account 440 observations of shoreline location before/after an extrem event. This Lmax can be added to a

Fig. 13 :

 13 Fig. 13: Comparison of erosion hazard zones by 2050 and 2120. Clémenceau beach, La Tranche-sur-Mer.

FIGURESFig. 1 :

 1 FIGURES Fig. 1: Location map of Vendée (W France department). The map shows the location of the different types of coasts (illustrated by seven photographs) as well as the current status of the Coastal Risk Prevention Plans. (HOMERE point : X 309753.801597 ; Y 6658415.559416) ......................................... 4 Fig. 2: a : Percentage and direction of wind and wave data over the 1979-2016 period (annual and seasonal) , b : Wind and wave data during storms Lothar & Martin and Xynthia .................................. 5 Fig. 3: Hydrodynamic characteristics over the period between the two aerial images for A) Lothar and Martin, B) Xynthia .......................................................................................................................... 10 Fig. 4: The shoreline's retreat and damage on protection works in the aftermaths of Xynthia. La Tranche-sur-Mer -South of the Clémenceau beach ............................................................................ 12 Fig. 5: Oblique aerial and ground photographs following Xynthia. Town of la Tranche-sur-Mer. Left : 2009. Right : 2010 .................................................................................................................................. 12 Fig. 6: Steps of the realization of the "erosion hazard" zone. ............................................................... 13 Fig. 7: Percentage of the shoreline impacted by storms per erosion phase on sandy coast of a) Vendée, b) Noirmoutier-en-île, c) La Faute-sur-Mer ............................................................................ 14 Fig. 8: Retreats measured during both events on the local council community "Océan Marais de Monts". Left strip: Lothar and Martin (December 1999) Right strip : Xynthia (February 2010) ........... 15 Fig. 9: Retreats measured during both events on La Pointe du Grouin du Cou. Left strip : Lothar and Martin (December 1999). Right strip : Xynthia (February 2010) .......................................................... 17Fig. 10: Projection to 2050 with both scenarios (Lothar & Martin / Xynthia) a) La Tranche-sur-Mer, b) La Guérinière -Noirmoutier island ....................................................................................................... 18 Fig. 11: Maximum retreat due to extreme events (Lmax) in south of Vendée ..................................... 19 Fig. 12: Summary of the impact of storms per town and urban area ................................................... 20

Fig. 10 :TABLESTable 1 :

 101 Fig. 1: Location map of Vendée (W France department). The map shows the location of the different types of coasts (illustrated by seven photographs) as well as the current status of the Coastal Risk Prevention Plans. (HOMERE point : X 309753.801597 ; Y 6658415.559416) ......................................... 4 Fig. 2: a : Percentage and direction of wind and wave data over the 1979-2016 period (annual and seasonal) , b : Wind and wave data during storms Lothar & Martin and Xynthia .................................. 5 Fig. 3: Hydrodynamic characteristics over the period between the two aerial images for A) Lothar and Martin, B) Xynthia .......................................................................................................................... 10 Fig. 4: The shoreline's retreat and damage on protection works in the aftermaths of Xynthia. La Tranche-sur-Mer -South of the Clémenceau beach ............................................................................ 12 Fig. 5: Oblique aerial and ground photographs following Xynthia. Town of la Tranche-sur-Mer. Left : 2009. Right : 2010 .................................................................................................................................. 12 Fig. 6: Steps of the realization of the "erosion hazard" zone. ............................................................... 13 Fig. 7: Percentage of the shoreline impacted by storms per erosion phase on sandy coast of a) Vendée, b) Noirmoutier-en-île, c) La Faute-sur-Mer ............................................................................ 14 Fig. 8: Retreats measured during both events on the local council community "Océan Marais de Monts". Left strip: Lothar and Martin (December 1999) Right strip : Xynthia (February 2010) ........... 15 Fig. 9: Retreats measured during both events on La Pointe du Grouin du Cou. Left strip : Lothar and Martin (December 1999). Right strip : Xynthia (February 2010) .......................................................... 17Fig. 10: Projection to 2050 with both scenarios (Lothar & Martin / Xynthia) a) La Tranche-sur-Mer, b) La Guérinière -Noirmoutier island ....................................................................................................... 18 Fig. 11: Maximum retreat due to extreme events (Lmax) in south of Vendée ..................................... 19 Fig. 12: Summary of the impact of storms per town and urban area ................................................... 20

Table 1 :

 1 List of significant storms since 1979.

														Stor
				Wind			Waves						m class
														(Dola
										Atmosp	Maximu	Stor		n &
										heric	m water	m	Power	Davis
						Hs		Tp		pressur	level (St	surg	index	,
		Storm	Duration	Speed		(mean/	Hs	(peak		e (min)	Gildas'	e	(Hs²hr	1992
	Date	name	(h)	(mean/hr) Dir	hr)	max	)	Dir	(hPa)	station)	(m)	)	)
	15/12 /1979	-	18	19	W	9.4	10.2 16.9	W	1001.1	5.3	0.7	1590. 48	4
	23/11
	/1984 24/11	-	18	14.5	WS W	7.3	8.6	16.1	W	1001.4	6.3	1.1	959.2 2	4
	/1984
	24/03
	/1986 25/03	-	15	18.1	W	9.4	10	16.9	W	994	5.6	0.5	1325. 4	4
	/1986
	15/10
	/1987 16/10	-	27	16.5	SW	5.9	7	12.4	SW	980.8	-	-	939.8 7	4
	/1987
	26/12 /1999	Lothar	22	19.4	W	7.9	8.7	14.5	W	993.6	6.5	1.1	1373. 02	4
	27/12
	/1999 28/12	Martin	28	17.8	WN W	7	10.4 14.7	WN W	969.6	5.4	1.2	1372	4
	/1999

Table 2 :

 2 The 2010 photographs were also produced by the IGN as part of the "Xynthia feedback" conducted by the Directorate General for Risk Prevention (DGPR) (table 2).

		Date of	Number of
	Events	flight	georeferenced	Resolution	Scale	Data	Source
		campaigns	images
		From
		06/19/1999 to	25	1	1/30000	Aerial images	"Go back in time" (IGN)
		07/11/1999
	Lothar et
	Martin	From
		07/30/2000 to	-	0.5	1/25000	OrthoLittorale ®	Geolittoral (IGN)
		08/01/2000
		07/09/2009	-	0.2	1/25000	BD ORTHO®	Géovendée
	Xynthia
		03/04/2010	70	0.2	1/10000	Aerial images	Geolittoral (IGN)

Characteristics of the aerial photographs survey dataset for the Lothar & Martin and Xynthia storms 3.2. Shoreline detection

Acknowledgments

The authors wish to thank the UMR 6554 LETG-Nantes and OR2C (Regional Observatory of Coastal Risks of Region Pays de la Loire) for providing research facilities. This study was conducted as part of the PhD grant of Morgane Audere supported by the Region Pays de la Loire and the University of Nantes. Thanks to the reviewers for their wise remarks and their help in the construction of this article, and especially Serge Suanez for his in-depth comments. We also thank Paul Fattal and Cassandra Carnet for proofreading this paper, Martin Juigner and Riwan Kerguilec for many advices throughout this research.

ACKNOWLEDGMENTS

The authors wish to thank the UMR 6554 LETG-Nantes and OR2C (Regional Observatory of Coastal Risks of Region Pays de la Loire) for providing research facilities. This study was conducted as part of the PhD grant of Morgane Audere supported by the Region Pays de la Loire and the University of Nantes. Thanks to the reviewers for their wise remarks and their help in the construction of this article, and especially Serge Suanez for his in-depth comments. We also thank Paul Fattal and Cassandra Carnet for proofreading this paper, Martin Juigner and Riwan Kerguilec for many advices throughout this research.