In February 2010 the Xynthia extratropical storm caused damage and casualties along the Atlantic coast of Spain and France (Slomp et al., 2010; Chauveau et al., 2011). The strong winds and low atmospheric pressure together with the landfall of the storm at high spring tide generated unprecedented water levels at La Rochelle and surroundings (Bertin et al., 2014). The present paper develops damage curves for buildings in the area where the storm surge and waves from the Xynthia storm caused the most damage. We draw on methods used to quantify damage due to hurricanes and tsunamis in the USA and Japan (Suppasri, 2013; Hatzikyriakou et al., 2018; Tomiczek et al., 2017) but for the first time apply these to modern masonry structures in Europe affected by storm surge and waves from an extratropical cyclone. Therefore, the main objective of the present study is to develop damage functions from insurance claims data supported by hydrodynamic modelling. A total of 423 reported claims in the area of study were used (Fig. 1). The damage ratio (DR) is defined as the ratio of damages claimed by each property to the total insured value of that property. More than 9 % of the structures had a damage ratio (DR) higher than 0.5 (considerable damages), 30 % had DR higher than 0.2 (medium damages), and 49 % had low damages. This is a typical distribution for damage claims (see for example Fuchs et al., 2019).

The damage curve is an important tool in risk assessment science related to the vulnerability of structures (Pistrika and Jonkman, 2010; Englhardt et al., 2019). From the structural point of view, damage curves depend on the construction materials that buildings are made of (Huizinga, et al., 2017; Postacchini et al., 2019; Masoomi et al., 2019). Damage curves also depend on construction methods, codes, and building layout, including the distance between buildings (Suppasri et al., 2013; Jansen et al., 2020; Masoomi et al., 2019). The current paper focuses on one–two-storey masonry buildings under the effect of storm surge and wave forces produced by an extratropical storm in northwest France. The Xynthia storm provided a rare dataset of empirical measured damage from coastal flooding in a European country. Similar analysis of damage from other storms with different return periods in the same region would help to reduce uncertainty (Breilh et al., 2014; Bulteau et al., 2015), but for now no other claims data are available.

In flood risk assessment, the relation between damage and hazard is quantified by fragility curves and damage curves. The difference between these two is that fragility curves express the probability that a structure is damaged to a specified structural state (Tsubaki et al., 2016), while damage curves instead assess the cost of damage incurred by flooding of a given structure (Englhardt et al., 2019; Huizinga et al., 2017). For both cases it is important to highlight the fact that these curves usually rely on the flood depth alone to quantify the hazard (Pregnolato et al., 2015), while there are fewer studies that attempt to represent the hazard by other quantities like the flow velocity, significant wave height, or wave force (Kreibich et al., 2009; De Risi et al., 2017). For instance, Tomiczek et al. (2017) related the flow velocity to the structure damage state (DS) in New Jersey for Hurricane Sandy. In the present study we relate eight different hydrodynamic variables to the damage ratio coming from insurance claims following extratropical storm Xynthia.

Damage curves are commonly developed by the correlation of field or laboratory measurements of damage, with numerical simulations of hazard level. Tsubaki et al. (2016) measured railway embankment and ballast scour in the field and correlated this damage with flood overflow surcharge calculated by a hydrodynamic flood simulation. Englhardt et al. (2019) and Huizinga et al. (2017) used big-data analytics to correlate tabulated damages with estimated flood levels over a large scale. Pregnolato et al. (2015) showed that most damage functions are based on flood depth alone, though a few also consider flow speed (De Risi et al., 2017; Jansen et al., 2020) or flood duration. The water depth is an important variable since it accounts for the static forces that act on a structure. Nevertheless, in storm events, structures close to the coast at a foreshore/backshore can be subjected to dynamical forces like the action of flow and waves (Kreibich et al., 2009; Tomiczek et al., 2017). For this reason, in order to consider other possible forces the following hydrodynamic parameters are analysed: water depth (h), flow speed (v), unit discharge (hv), flow momentum flux (ρhv2), significant wave height (Hsig), total water depth (h+Hsig), wave energy flux (Ef), and total force EfCg+ρhv2. The wave energy flux is defined via Eq. (1) as in Bricker et al. (2017). 1Ef=116ρgHsig2Cg, where Hsig (m) is the significant wave height, Cg (m s-1) is the wave group velocity, ρ (kg m-3) is the water density, g (m s-2) is the acceleration due to gravity, and Cg=gh over land where waves impact buildings.

Damage curves were developed by hindcasting the hazard with a meteorological model, followed by a hydrodynamic (tides and storm surge) and wave model, and then correlating the resulting flood conditions with claimed damages (Fig. 2).

After determining the model hydrodynamic and wave results (Fig. 6) at the location of each claim location, the data were subdivided into 10 categories according to damage ratio level, and box–whisker plots were built to display the entire dataset and analyse the trend of the data (Appendix A). Among the flow-only variables, the unit discharge (hv) appears to have the clearest trend and least scatter. From the variables related to both flow and waves, the total force EfCg+ρhv2 appears to have the clearest trend and correlation with the damage ratio.

The present paper considered the influence of flow-only variables (h,v,hv,ρhv2) and combined flow-wave parameters (Hsigh+Hsig,Ef,EfCg+ρhv2). Flow depth and total (flow plus wave) force produce the best fits with analytical functions. Goodness of fit to damage curves improves with quality of the topographic data used (Table 1). However, when applying damage curves in practice, it is important to base predictions off a similar model setup to that used when calculating the damage curves in the first place (Brussee et al., 2021). For example, if damage curves are built using coarse topography that neglects the presence of thin seawalls (i.e. sheet pile/cantilever walls, or T or L walls), then the buildings protected by these walls might experience more intense hydrodynamic conditions in the simulation than if the walls had been present in the simulation. Since the actual recorded damage does not depend on the model used to calculate the hydrodynamic forcing conditions, damage curves developed using the coarse-resolution topography will be shifted to the right relative to damage curves generated with the thin flood walls present. If these damage curves generated using a coarse-resolution simulation are then applied for damage prediction by an external user who applies a high-resolution simulation that resolves flood walls, the reduced forcing (due to the presence of these flood walls) will generate a non-conservative result (too little damage), because the damage curves had been generated using forcing data from a simulation where the flood walls had not been present. Therefore, when damage curves are reported in the literature, it is important to quantify how these vary with the topography used in the simulations on which the damage curves are based. However, in the current paper, Fig. 7 shows that damage curves do not vary consistently leftward or rightward as topographic data are improved. This is because the response of forcing to the presence of these walls is more complex than simply reducing wave height. If not overflowed, walls reduce damage greatly. However, water depth can be exacerbated in front of walls, and flow can be channelled and intensified along walls, all increasing hydrodynamic forcing in some locations, preventing a simple relation between topographic resolution and damage curve robustness.

In addition to the general sensitivity of damage curves to topographic data quality, the damage curves displayed in Fig. 7 do not consider certain physical wave-driven phenomena such as wave overtopping of structures (Lashley et al., 2020a; Ke et al., 2021) or infragravity waves generated by waves breaking in shallow water (Roeber and Bricker, 2015). For instance Lashley et al. (2019) discussed the importance of dike overtopping due to infragravity waves on nearshore developments that can induce wave-driven coastal inundation. The wave model used here, SWAN, does not include infragravity waves, nor does the combined Delft3D–SWAN flow–wave model simulate wave overtopping of dikes, possibly leading to an underestimation of the hydrodynamic forces on buildings, which would affect the resulting damage functions. However, consideration of wave overtopping and infragravity effects requires either phase-resolving wave simulations or empirical relations specific to the local topography (Lashley et al., 2020b), though this is beyond the scope of the current study and is similarly neglected by most other large-scale inundation studies (i.e., Sebastian et al., 2014; Kress et al., 2016; Kowaleski et al., 2020). Nonetheless, the effect of infragravity oscillations and wave overtopping on resulting damage is an important item for future research.

Another important factor mentioned by Bertin et al. (2015) was the particular track direction of the storm that for the Xynthia event induced a young sea state, enhancing the surface stress, and adding up to 40 cm to the theoretical surge and tide of their model. The uncertainty and variability within this methodology can be explained by two factors: (1) the hydrodynamic modelling, and consequently uncertainty in the hydrodynamic variables, and (2) uncertainty in the claims data. Regarding the first point, there is a trend that indicates that better topography/bathymetry data give hydrodynamic variables that correlate better with the damage ratio. This is because higher-resolution data generally more accurately reproduce the actual flood conditions (Luppichini et al., 2019; Ettritcha et al., 2018). Damage curves developed with a better representation of the topography (IGN + structures) improve the accuracy indicators (Table 3), though scatter in the data themselves (Figs. A1, A2 or A3) is large for all topographies. This first point is also related to the mesh resolution and the roughness coefficients used. The second point deals with the quality of the damage ratio data. It is known that insurance claims can sometimes be subject to fraud or information distortion. In addition, variables related to the vulnerability of the assets like the construction characteristics, the materials, the quality, and the age of the structures (Paprotny et al., 2021) play important roles in determining whether a particular hydrodynamic is related to damage. This adds a degree of complexity to the analysis. Finally, it is worth mentioning that if more detailed information from the claims data is available (like structure type, number of floors, and damage stage), then a more detailed fragility functions can be generated instead of the bulk damage functions determined here.

Insurance claims data facilitated generation of damage curves for structures located in La Rochelle and surroundings. This provides valuable information for predicting future damages that can be expected from an extratropical storm strike on the French Atlantic coast. In the present study, the hydrodynamic variables that correlated best with the damage ratio are the flow depth and the total (flow plus wave) force for the flow-only and flow-plus-wave-related variables respectively. In addition to the sensitivity of results to resolution of the topographic and bathymetric data, the inclusion of thin flood walls via a land survey carried out by the authors also had a significant effect on the damage functions generated. This is important to note, as thin steel or concrete structures like flood walls are typically only a few decimetres thick and therefore do not appear in digital elevation models. The effect of these thin structures on the resulting damage functions shows the importance of locally sourcing elevation data for the thin structures that are present when conducting risk analyses for coastal regions. However it is imperative to keep in mind agreement between the simulations used for developing the damage relations in the first place and those where the damage relations are applied for further risk analysis.