Introduction

Coastal flooding due to extreme sea levels (ESL, resulting from the combination of tides, storm surge and wave setup) is one of the most damaging natural hazards with massive consequences for human lives and property. The damage estimates for Hurricane Katrina (2005) and Hurricane Sandy (2012), which made landfall along the US Gulf and East coasts, are about $ 186.3 billion and $ 81.9 billion respectively1. Globally, the number of people that are at risk of coastal flooding by the present-day 100-year return period ESL event is estimated to be ~ $ 76 million2, while the global expected annual damage (EAD) from coastal flooding is estimated to be $ 19.6 billion per year3. This already bad situation is projected to get much worse in the future due to climate change, with the recent IPCC AR6 projecting, with high confidence, that coastal flooding will increase in almost all regions of the world by mid-century under all but the lowest emission scenarios4. Moreover, the present-day 100-year return period ESL event is projected to become one that occurs once- or more-than-once-a-year event in most of the world under the high emission SSP5-8.5 scenario, and under the moderate emission scenario SSP2-4.5, one that occurs at least once every 5 years in most of the world5. Given that approximately 10% of the world’s population currently lives in low elevation coastal zones, this means that urgent adaptation is required to protect coastal communities and assets.

Effective adaptation at local scale requires detailed numerical modelling of coastal flooding that adequately accounts for natural/artificial coastal defences (e.g. dunes, dikes) and nearshore hydrodynamics (e.g. tides, storm surge, wave setup). Considering currently available topographic data (DEM) at most places in the world and the high resource requirements of traditional hydrodynamic models (especially when using combined flow and wave forcing), these requirements thus present a double bottle-neck for detailed coastal flood modelling at local scale. In terms of the former, although high resolution LiDAR data may be available at some locations, most of the world must still rely on global DEMs, which mostly have resolutions ranging between 30 m and 90 m. At this horizontal resolution the DEMs will inevitably miss narrow-crested defence structures and coastal dunes. In terms of the latter, to accurately simulate the flooding induced by a hurricane or an extratropical cyclone (ETC) using traditional hydrodynamic models, the model domain will have to extend far offshore to capture the shelf region6,7,8, and will also need to have high grid resolution (10–20 m or finer) in the nearshore and over-land. Furthermore, as wave setup can make a substantial contribution to the total water level of ESL events9,10,11, especially when ESL events are accompanied by high waves, it is important to consider including flow-wave coupling in the model. All this is of course possible, but at substantial computational cost. For example, if one were to use one of the more commonly available models that use rectangular or curvilinear grids (e.g. Delft3D12,), facilitating a computational grid that minimises high resolution cells in the offshore (to maximise computational efficiency) and maximises resolution in the nearshore and over land would require domain decomposition. This adds complexity to the model. With respect to coupling waves to a flow model, most state-of-the-art models have this as a standard option, but adding waves does add some complexity to the simulation and also, for a typical hurricane model domain, would add at least 30% more computational time per simulation.

Over the last few decades, there have been numerous studies on river flood modelling and several studies that simulated local flood impacts of individual hurricanes or extratropical cyclones (ETCs) at high resolution, using models with different levels of sophistication10,13,14,15,16,17,18,19,20,21,22. The common feature of all these studies is that they used the best model and the best data that were available for the study, with the specific purpose of obtaining the best possible result. The general thinking in these applications is that the result is likely to be better with a sophisticated model setup (e.g. flow only vs flow plus short waves vs flow plus short waves plus infragravity waves) and as-detailed-as-possible representation of flood defences. This is true. However, more sophisticated modelling and detailed flood defence representation also come at an increasing resource cost, which likely increases exponentially as the level of sophistication/detail increases. But, as highlighted by the recent discussions of the “appropriate complexity modelling” philosophy23,24,25, if we can achieve 90% accuracy with, say, a moderate representation of flood defences and a flow only (i.e. no waves) model setup, then the additional resource cost borne to increase accuracy to, say, 95% may not represent efficient resource allocation (low return on the investment). However, this kind of comparative analysis has not been systematically done to date, and given the increased demand for detailed local scale coastal flooding that is almost certain to ensue as the frequency of ESL events increases as projected, in this study we aim to take an initial step towards addressing this knowledge gap. To this end, here we systematically investigate two aspects of coastal flood model complexity: level of detail at which flood defences are represented in the model (i.e. DEM augmentation), and the effect of accounting for wave setup on simulated coastal flooding (i.e. flow-wave coupling).

Throughout this study, we use the flexible mesh model Delft3D FM26, which allows the seamless integration of rectangular and triangular, large and small cells (here ranging from 50 km offshore to 10 m nearshore and over-land resolution), enabling the setup of a computationally efficient grid over a typical hurricane modelling domain, to hindcast the coastal flooding resulting from one of the most damaging ETCs that Europe has seen in the recent past (i.e. Xynthia storm, in 2010). We investigate the relative benefits of using different levels of detail when representing flood defences by performing simulations with (1) a 5 m resolution DEM that only captures large defences but misses small defences as well as small alongshore gaps in defences (hereon referred to as the base case DEM), (2) the same 5 m DEM augmented with defences extracted from a 1 m DEM and careful inspection of Google Earth images (hereon referred to as the moderately augmented DEM, and (3) the DEM in (2) further augmented with in-situ measurements of flood defences (hereon referred to as the highly augmented DEM). We investigate the added value of including waves by performing simulations with flow only and with flow-wave coupling. In all, here we perform 6 simulations of Xynthia using Delft3D FM, and analyse results in terms of four flood indicators: maximum flood depths, flood extents, flood velocities and flood damages.

Study area and the Xynthia storm

France was hit by extratropical cyclone Xynthia on 27th–28th February 2010, causing extensive flooding in parts of the Charente-Maritime, Deux-Sèvres, Vendée and Vienne regions27. The storm moved north from the Spanish border on 27th February 2010, passing over the Bay of Biscay toward the French coast, reduced in strength and crossed the English Channel on 28th February 2010. During the entire Xynthia event, the lowest eye-pressure was about 970 hPa and maximum wind speeds were greater than 30 ms−1. Xynthia induced a large storm surge, estimated at about 1.6 m at the La Rochelle tide gauge28, in phase with a high spring tide, which resulted in an extreme sea level with a return period of 200–300 years29. Flooding similar to that associated with Xynthia is reported to have occurred in the region during the 20th century as well30.

The study area considered in the present analysis is Île de Ré (Fig. 1A, B); one of the many areas flooded during Xynthia. Île de Ré is an 85 km2 island that is part of the Charente Archipelago in the Gulf of Gascogne. It consists of 10 communities, with a total of about 17,800 (2008) inhabitants31. The island is protected by dunes or revetments on the coast exposed to the Atlantic, while on the leeward side of the island, dikes are present around low-lying marshes. During Xynthia, breaches of the sea defences occurred in at least 5 locations, both on the Atlantic and leeward sides of the island, leading to the flooding of a large part of the island, and 2 casualties32.

Fig. 1: The study area and the locations of the measurement stations.
figure 1

A Study area: French Atlantic coast, Bay of Biscay and measurement stations during Xynthia, including: water level stations (red triangles) and wave stations (blue circles). B Location of Île de Ré island. C Flooded area (light blue) and observed flood extent (blue line) in Île de Ré during Xynthia33. D Residential areas (magenta) in Île de Ré. E Flood defence system in Île de Ré (black – from 1 m DEM data; green – 1 m DEM defences augmented by in-situ measurements; red – added from in-situ measurements (not present in DEM data)).

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The flooding caused by Xynthia was modelled previously by Bertin et al.33 using an online coupling of the unstructured SELFE circulation model34 with the third generation spectral wave model WWM-II35 in barotropic 2DH mode. The resolution of the triangular grid varied between 30 km in the deep ocean and 5 m over dikes and dunes. The overland topography was interpolated on the model grid from a post-storm LiDAR dataset, while the subtidal bathymetry was sourced from the French Hydrographic Office SHOM. Gaps in the data in shallow subtidal and intertidal areas were filled with local surveys. No information on breach locations was specifically considered in this application. Comparison with measured flood extent showed a reasonable agreement between model results and observations, although dike breaching and wave runup related processes were not modelled, and spatial resolution in many of the marsh areas was relatively coarse33.

Modelling framework

The modelling framework implemented in this study is described in detail in the Methods section, and therefore only a brief description is given here to ensure continuity. The models used here span from regional (i.e. Bay of Biscay) to local (Île de Ré) scale. Two coarse resolution regional models: the flow model (Regional Tide and Surge Model, RTSM) and the wave model (Regional Wave Model, RWM), are used to obtain input forcing (i.e. tide and wave boundary conditions) for the smaller and high resolution local flooding model (LFM). This local model simulates the total water levels (TWL) combining tide, storm surge and wave setup (in the simulations that incorporate waves - see Table 1), and consequent over-land flooding.

Table 1 LFM scenarios simulated
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Here we use the process-based numerical model Delft3D Flexible Mesh (DFM) in 2DH mode and the spectral wave model SWAN36. The DFM flow module is used for the Regional Tide and Surge Model (RTSM) and SWAN is used for Regional Wave Model (RWM). The local flooding model (LFM) dynamically couples the DFM flow module and SWAN, in order to incorporate wave forcing on the flow field (wave forces driving wave setup is computed by SWAN and are fed into DFM via the dynamic coupling). Note that the flow-wave coupling done here represents only the effects of wave setup on flooding, and not that of wave-by-wave overtopping. More detailed descriptions of each of these 3 models are given in the Methods section. The RTSM, RWM and LFM are validated against measured data (see Methods), providing sufficient confidence to proceed with the scenario testing required to achieve the goals of this study.

To systematically investigate the impact of flow-wave coupling and the level of detail in representing flood defences, the LFM is run for the six different scenarios shown in Table 1. The flow only model is denoted F and the coupled flow-wave model is denoted FW. The simulations are numbered as: 01 – when defences are limited to those inherent to the 5 m DEM, 02 – 5 m DEM augmented with defences extracted from a 1 m DEM and careful inspection of Google Earth images, and 03 – the DEM in (02) further augmented with in-situ measurements of flood defences.

Results

Maximum flood depths

The differences in modelled maximum flood depths on the island between corresponding pairs of simulations were computed by subtracting the areal maximum flood depths between corresponding pairs of simulations (Fig. 2). Figure 2A, B show the maximum flood depth differences between flow only simulations (F01 vs F02 and F02 vs F03) and Fig. 2C, D show the differences between coupled flow-wave simulations (FW01 vs FW02 and FW02 vs FW03), demonstrating the effect of detailed representation of flood defences, without and with waves. Regardless of whether waves are included or not, the differences between Simulations 02 and 03 are less than 1 m (Fig. 2B, D). However, there are significant spatial differences in maximum flood depths between simulations with the base case DEM (F01 and FW01) and those with the augmented DEMs (F02, FW02, F03 and FW03). The difference between F01 and F02, is mostly in the range of 1–2 m, with the exception of larger differences (2–4 m) in the northwest part of the island (Fig. 2A). When waves are included in the model, the maximum flood depth differences between the simulations using the base case DEM (FW01) and the moderately augmented DEM (FW02) decrease by almost 50%, with differences of 0–1 m in most of the flooded area, while the highest difference in the northwest of the island decreases to 1–2 m (Fig. 2C). Clearly, both the more detailed representation of flood defences (to the level that is possible via a desktop study) and the inclusion of waves in the model has substantial impacts on modelled flood depths.

Fig. 2: Differences in computed maximum flood depths (m) on Île de Ré between corresponding pairs of simulations.
figure 2

A, C The differences between Base case DEM and moderately augmented DEM, without waves (F01-F02) and with waves (FW01-FW02). B, D The differences between Moderately augmented DEM and highly augmented DEM, without waves (F02-F03) and with waves (FW02-FW03). E The differences between Moderately augmented DEM with and without waves (FW02-F02). F The differences between Base case DEM without waves and moderately augmented DEM with waves (F01-FW02).

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The singular effect of waves on the maximum flood depth is further illustrated in Fig. 2E, which shows the differences in the maximum flood depths between simulations with and without wave forcing when using the same DEM (here, with the moderately augmented DEM) (i.e. FW02 vs F02; results for FW03 - F03 are very similar to FW02 - F02 and hence not shown here). Figure 2E shows that the inclusion of waves leads to increases of 1–2 m in maximum flood depth in a majority of the flooded area. The combined effect of detailed representation of flood defences and flow-wave coupling, as can be gleaned by contrasting F01 with FW02 (Fig. 2F), indicate that the non-inclusion of these phenomena could lead to overestimations of flood depths by up to 2 m, particularly in the northwest of the island.

Flood extents

The modelled flood extents (in km2) for each scenario are shown in Table 2 (and in Fig. 12 - Methods). The flood extents simulated with the base case DEM is ~40% greater than that simulated with the moderately augmented DEM (F01 - F02). The difference between the extents simulated with the moderately augmented DEM and the highly augmented DEM is only ~0.5% (F02 - F03). When waves are included in the model, the flood extents simulated with the augmented DEMs are around 25% greater than that simulated without waves (FW02 - F02; FW03 - F03). Comparison of the computed flood extents in FW02 or FW03 with that in F01 indicates that the non-inclusion of both detailed representation of flood defences and flow-wave coupling will lead to increases of more than 10% in the modelled flood extent. Thus, in terms of flood extent too, both the more detailed representation of flood defences (to the level that is possible via a desktop study) and the inclusion of waves in the model have significant impacts on model results.

Table 2 Computed flood extents (km2) and flood damages (Mil Euros) on Île de Ré for the six considered scenarios: Base case DEM simulations without and with waves (F01 and FW01); Moderately augmented DEM simulations without and with waves (F02 and FW02); Highly augmented DEM simulations without and with waves (F03 and FW03)
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Maximum flood current velocities

In addition to flood depth and extent, current velocities during flood events can also contribute to flood damage37. Stronger currents can cause more damage to assets and additional loss of life. Therefore, here we also investigate the modelled current velocities on Île de Ré during Xynthia. The maximum current velocities in the flooded areas of the island from the six modelled scenarios are shown in Fig. 3 showing that, in general, maximum flood velocities can exceed 1 ms−1 in some areas, with the majority of the island experiencing flow velocities less than ~ 0.5 ms−1 (the white - yellow areas in Fig. 3).

Fig. 3: Computed maximum flood current velocity (ms-1) on Île de Ré for the six considered scenarios.
figure 3

A, B Maximum flood velocities of Base case DEM simulations, without and with waves (F01 and FW01). C, D Maximum flood velocities of Moderately augmented DEM simulations, without and with waves (F02 and FW02). E, F Maximum flood velocities of Highly augmented DEM simulations, without and with waves (F03 and FW03).

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Figure 4 which illustrates differences in the maximum current velocities between pairs of simulations shows that the level of representation of flood defences and the non-inclusion of waves in the model simulation have different effects on the current velocities on the island. First, similar to the above observations on maximum flood depths and flood extents, there is no significant difference between the maximum flood velocities in simulations with the moderately augmented DEM and the highly augmented DEM, with waves (FW02 - FW03, Fig. 4D) or without waves (F02 - F03, Fig. 4B). However, there are noteworthy differences in maximum flood velocities between simulations with the base case DEM and an augmented DEM, both with waves (Fig. 4C) and without waves (Fig. 4A). These differences constitute both increases and decreases of maximum flood velocities in different parts of the island.

Fig. 4: Differences in computed maximum flood current velocity (ms-1) on Île de Ré between corresponding pairs of simulations.
figure 4

A, C Differences in maximum flood velocity between Base case DEM and moderately augmented DEM, without waves (F01-F02) and with waves (FW01-FW02). B, D Differences in maximum flood velocity between Moderately augmented DEM and highly augmented DEM, without waves (F02-F03) and with waves (FW02-FW03). E Differences in maximum flood velocity between Moderately augmented DEM with and without waves (FW02-F02). F Differences in maximum flood velocity between Base case DEM without waves and moderately augmented DEM with waves (F01-FW02).

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Without the inclusion of waves, the use of the moderately augmented DEM decreases maximum current velocities (i.e. positive differences in Fig. 4A) in ~75% of the flooded area, relative to when the base case DEM is used. The same comparison between the two DEMs but with the inclusion of waves (Fig. 4C) shows decreases in maximum velocities in only ~60% of the flooded area.

The singular effect of including waves in the simulation is illustrated in Fig. 4E which compares simulations with the same DEM, but with and without waves. Here, it can be seen that including waves increases the maximum current velocities (positive values in this figure) in 77% of the flooded area. The combined effect of using an augmented DEM and including waves, relative to using the base case DEM without waves, is to increase maximum current velocities in approximately half of the flooded area and decrease them in the other half, with a slight bias towards decreasing (decreasing in ~55% of area, increasing in ~45% (Fig. 4F).

Flood damage

Damage values (in Euro/m2) for the six considered model scenarios are estimated based on the computed maximum flood depths at each flooded grid cell and the constructed depth-damage curves for two land-use classes: residential buildings and agricultural areas (see Methods, Fig. 9). Here we do not consider damages due to current velocities, as the computed maximum flood velocities are rather small in most of the flooded area as shown in Fig. 3 above. The computed total flood damage values for flooded residential areas and for the entire island are shown in Table 2. Figure 5 shows the spatial variation of the flood damage values (in Mil Euros/m2) for the six modelled scenarios, together with corresponding values of the total damage for the entire island (in Mil Euro) for each scenario. Consistent with the much higher asset values (in Euro/m2) for the residential areas (magenta polygons in Fig. 5; also see Fig. 1D) as compared to agricultural areas (here taken to be all areas outside the residential areas), the computed damage due to the flooding of residential areas during Xynthia is also larger, with damage values of up to 100 Euro/m2 (red areas in Fig. 5) compared to only up to 25 Euro/m2 in agricultural areas (white areas in Fig. 5).

Fig. 5: Computed flood damage (Euros/m2) on Île de Ré for the six considered scenarios.
figure 5

A, B Flood damage of Base case DEM simulations, without and with waves (F01 and FW01). C, D Flood damage of Moderately augmented DEM simulations, without and with waves (F02 and FW02). E, F Flood damage of Highly augmented DEM simulations, without and with waves (F03 and FW03). Magenta polygons show the residential areas.

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The total flood damage values in Île de Ré for the six scenarios vary widely between ~282 Mil Euros (F03, Fig. 5E) and ~756 Mil Euros (FW01; Fig. 5B). As mentioned in Methods, it should be noted that these flood damage values are based on the global flood damage database of Huizinga et al.38, and the present-day insured market values could be much higher, but here we are interested in the relative differences between scenarios, and obtaining quantitatively accurate damage estimates is beyond the scope of this study. Figure 5 and Table 2 clearly show that detailed representation of flood defences reduces total flood damage substantially; by around 60% without flow-wave coupling (F02 - F01; F03 - F01) and by about 30% with flow-wave coupling (FW02 - FW01; FW03 - FW01) compared to the corresponding base case DEM simulations. In terms of the singular effect of waves on computed damages, inclusion of flow-wave coupling increases the computed total flood damage by about 80% in the simulations with detailed representation of flood defences (FW03 - F03 and FW02 - F02). The combined effect of detailed representation of flood defences and flow-wave coupling (comparing FW03 or FW02 with F01) is a decrease of about 25% in the computed total damage. Similar to modelled flood depths and flood extents, there are no appreciable differences between the damages computed with the moderately augmented DEM (F02 and FW02) and the corresponding computations with the highly augmented DEM (F03 and FW03).

The flooded area and damage in residential areas are compared against the total, island-wide flooded area and damage in the last 2 rows in Table 2. In all six scenarios, the flooded residential areas are less than one-third (i.e. ~17.12–23.37%) of the total flooded area (Table 2, 2nd last row). However, the residential flood damage is more than 99% of the total damage in all six scenarios (Table 2, the last row). And even though the flooded agricultural surface areas are much larger (~3.3–4.9 times the flooded residential areas), the total damage associated with the flooding of the agricultural areas is minor (less than 1% of the total damage), compared to hundreds of Millions of Euros of flood damage in residential areas. This is because the damage values (per m2) of agricultural land are much lower than that of residential land.

Discussion

This study applied the Delft3D Flexible mesh model to hindcast the flooding induced by the extratropical storm Xynthia (February 2010) in Île de Ré island, France. The unstructured grid approach enabled the simulation of over-land flooding at a high resolution of ~10 m with reasonable computational resources. The aim of the study was to investigate the benefits of (a) using different levels of detail when representing flood defences (both natural and artificial), and (b) inclusion of waves in the model, in simulating coastal flooding and associated damages. To investigate (a), we performed simulations with (i) a 5 m resolution DEM that only captures large defences but misses small defences as well as small alongshore gaps in defences (i.e. base case DEM), (ii) the same 5 m DEM augmented with defences extracted from a 1 m DEM and careful inspection of Google Earth images (i.e. moderately augmented DEM), and (iii) the DEM in (ii) further augmented with in-situ measurements of flood defences (i.e. highly augmented DEM). To investigate (b), we performed simulations with and without flow-wave coupling. The model was validated against the flood extents observed on Île de Ré during Xynthia. We used maximum flood depths, flood extents, maximum flood velocities and flood damages as indicators of flooding throughout the study.

Results show that both detailed representation of flood defences as well as the inclusion of waves in the model have substantial effects on all four indicators of flooding, with the former having a more pronounced impact on results than the latter. In terms of the level of detail in representing flood defences, results show that while there are marked differences in all four flood indicators between the simulations using the base case DEM and the moderately augmented DEM, there are hardly any differences between the simulations using the moderately augmented DEM and the highly augmented DEM – with or without waves. This indicates that there might not always be a reasonable return on the investment in going to the lengths of acquiring/implementing highly detailed in-situ measurements to represent flood defences in models, and that a DEM that is carefully augmented via a desktop study may well suffice.

In simulating flooding due to Xynthia at Île de Ré, improving only the representation of flood defences (without adding waves) from the base case DEM to the moderately augmented DEM (comparing simulation F01 with F02) leads to decreases of: 1–2 m of maximum flood depths in most of the island, ~29% in flood extent, maximum current velocities in ~75% of the flooded area, and a decrease of ~60% (~€ 425 million) in total flood damage. When waves are added to the simulation with the moderately augmented DEM (comparing simulation FW02 with F02), maximum flood depths increase by 1–2 m in a majority of the flooded area, the flood extent increases by ~25%, maximum current velocities increase in 77% of the flooded area, and the computed total flood damage increases by about 82% (~€ 236 million).

The combined effect of using the moderately augmented DEM and wave forcing is quite different to the above described singular effects of augmenting the DEM or including waves, relative to using the base case DEM without waves (FW02 - F01): maximum flood depths decrease by up to 2 m, particularly in the northwest of the island, the flood extent decreases by about 10%, maximum current velocities increase in approximately half of the flooded area and decrease in the other half, while the computed flood damage decreases by about 27% (~€ 188 million).

Finally, it should be noted that the flood damage values on the island in this study were estimated based on 2 types of land-use classes, comprising residential buildings and agriculture. Huizinga et al.38, developed a database for flood damage of total 6 damage classes, including: residential buildings, commercial buildings, industrial buildings, transport, infrastructure (roads), and agriculture. For a more detailed estimation of flood damage, an investigation of the possible presence and distribution of all 6 land-use classes on Île de Ré can be implemented in order to estimate their associated damages, provided a relatively accurate land-use map on the island is made available. In addition, the spatial variation of roughness values specified in the models was based on the land-use types considered. A sensitivity analysis carried out here showed that the flooding results are somewhat sensitive to the specified roughness values. Any changes in the spatial map of the roughness, for example, due to changes in land-use or adopting different values of roughness for different land-use types, can have a direct impact on computed flooding and consequent damages.

Methods

Data

Measured water levels at 2 tide gauge stations, La Rochelle and Les Sables d’Olonne, were obtained from SHOM (https://www.shom.fr/) for model validation. The locations of these 2 stations are shown by red triangles in Fig. 1A, B. These data are at a time interval of 10 min, and were corrected to mean sea level (MSL) following the instructions in the Références Altimétriques Maritimes (RAM) Report39. At Les Sables d’Olonne station, however, data was missing for a short period during Xynthia.

Uninterrupted wave measurements during Xynthia are available at 3 stations - Île d’Yeu Nord, Plateau Du Four and Gascogne (indicated by blue circles in Fig. 1A, B) and were obtained from European Marine Observation and Data Network (EMODnet, available at: https://portal.emodnet-physics.eu/) for wave model validation. The measured wave data includes significant wave height (Hs, in m) and mean wave period (Tm, in s).

The observed flood extent for Île de Ré was obtained from Bertin et al.33 and shown by the blue line in Fig. 1C. This information was compiled from observations after Xynthia, from several sources of satellite images and field observations of storm deposits (see Bertin et al.33 for more details). These data, while not precise, provide some means of quantitatively validating modelled flood extents.

The residential areas (magenta) on Île de Ré are shown in Fig. 1D. This information was obtained from the French Cadastre web page (https://cadastre.data.gouv.fr/) at building level. Based on this information, Île de Ré is here considered to have mainly two types of land-use: residential and agricultural. This spatial information is also used here to define the spatial roughness for the over-land flood modelling and to estimate associated flood damage.

A very substantial effort was made in this study to correctly identify flood defences in Île de Ré. The base case DEM used in this study is the 5 m DEM from Institut National De L’Information Géographique et Forestière (IGN, France), which only captures very large natural and artificial defences, and even in these, the elevations may not be accurate due to the 5 m maximum resolution, while small gaps between adjacent defences (or within a given defence) would be missed. In this study, the representation of flood defences in Île de Ré was augmented in two sequential steps. First, all natural and artificial flood defences that are not captured by the 5 m DEM were identified by a careful time history analysis of Google Earth images and the 1 m resolution IGN DEM and manually added to the 5 m DEM, resulting in the moderately augmented DEM used in this study. The elevations of all these additional defence systems were derived from the 1 m DEM. Second, a 2-week long (01 August 2020 – 15 August 2020) in-situ measurement campaign was undertaken, in order to further augment the representation of flood defences in the moderately augmented DEM. During this field campaign, the crests of the flood defences were measured using a Leica GNSS-GPS GS14 instrument (a compact and powerful GNSS (Global Navigation Satellite System) smart antenna, with integrated mobile communications and UHF (Ultra High Frequencies) modem and RTK DGPS). A comparison of the above moderately augmented DEM with these in-situ measurements indicated crest level differences in some defences, while some defences, especially along the southeast coast in the lee of the island, had not been captured in the moderately augmented DEM. Using these in-situ data, these issues in the moderately augmented DEM were addressed, resulting in the highly augmented DEM used in this study. Figure 1E shows all the flood defence systems considered in this study.

Modelling approach

The overall modelling approach adopted in this study is illustrated in (Fig. 6).

Fig. 6: Modelling framework implemented to estimate storm damage from Xynthia.
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At regional scale, total water levels and waves are simulated independently by RTSM and RWM, respectively. At local scale, a fully coupled flow-wave model, LFM, is used to estimate flood depths in the study area, which are then used to compute flood damage.

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Regional Tide and Surge Model (RTSM)

Regional Tide and Surge Model (RTSM) is the large scale, coarse grid resolution DFM flow model, covering the entire French Atlantic coast. The RTSM domain is shown in Fig. 7A (black dashed line). This model provides the tidal input conditions for local flooding model (LFM).

Fig. 7: The grid system of the modelling framework.
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A Bathymetry and Topography of the study area (m). B Flow grid of the Regional Tide and Surge Model (RTSM). C Wave grids of the Regional Wave Model (RWM): overall wave grid (in grey) and local nested wave grid (in blue), with a zoom-in shown in D. E Flow grid of the Local Flooding Model (LFM). F Wave grids of the Local Flooding Model (LFM): lower resolution wave grid (in grey) and finer nested wave grid (in blue).

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The RTSM grid is shown in Fig. 7B. This grid is a cut-out grid for the Bay of Biscay from the Global Tide and Surge Model unstructured grid (GTSM)2, with grid resolution varying from ~50 km in deep water to ~1 km in the nearshore area. This cut-out grid was modified to ensure smooth grid resolution transitions and to exclude triangular cells on open boundaries (i.e. in the Bay of Biscay and the English Channel) for numerical stability. The grid was also refined further towards the nearshore, and extended to cover the land area on Île de Ré. The highest grid resolution within the RTSM is ~250 m. The bed level of RTSM (Fig. 7A) is generated by combining the GTSM cut-out bathymetry, which is from EMODnet (https://emodnet.ec.europa.eu/en/bathymetry) and General Bathymetric Chart of the Oceans (https://www.gebco.net/); and for the sub-aerial part, the digital terrain model topography data (at 75 m resolution) from IGN is used. Prior to interpolating the data to derive the final RTSM bed levels, these two datasets (bathymetry - negative values and topography - positive values) are merged in such a way that there is a smooth transition between the two.

For validation purposes, the RTSM is implemented here in 2 different modes: (a) a tide model with only tidal forcing with the aim of validating the model for tides only during summer (01 July 2010–01 August 2010), and (b) a TWL (tide plus surge) model, forced with tides and atmospheric winds and pressure fields (shown in Fig. 8) during Xynthia (27 February 2010–01 March 2010) with the aim of validating the model for total water level. Both of these RTSM simulations are started several days before the target model durations (i.e. tide only model starting from 25th June, and TWL model starting from 22nd February) to allow adequate model spin-up. The offshore tidal forcing is derived from global GTSM model results in the form of water level time series. The atmospheric forcing for the TWL model is derived from the downscaled WRF model for Xynthia (described below) and is imposed in DFM as spatially and temporally varying winds and pressure fields.

Fig. 8: WRF model derived surface pressure (hPa) and 10 m wind field (m/s) during Xynthia.
figure 8

Time is Central European Time (CET).

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Figure 8 shows the dynamically downscaled surface pressure and wind fields during Xynthia. This dynamical downscaling was performed using the regional climate model Weather Research and Forecasting model (WRF)40 with the United States National Centre for Environmental Prediction (NCEP) Climate Forecast System Reanalysis (CFSR) data41. The regional non-hydrostatic WRF model (version 3.4) is used for a simulation run spanning from 15 February 2010 until 05 March 2010. The initial and lateral boundary conditions are taken from the CFSR reanalysis at 0.5° resolution, updated every 6 h. The horizontal resolution is 7 km, and a vertical resolution of 35 sigma levels is used with a top-of-atmosphere at 50 hPa. The simulation domain was chosen to be large enough for WRF to fully simulate the large-scale atmospheric features of Xynthia. A spin-up time of 5 days was used in the study to remove spurious effects of the top layer soil moisture adjustment even though most of the analyses here are performed over the ocean. Land surface processes are resolved by using the NOAA Land Surface Model scheme with four soil layers. The WRF outputs are generated every 3 h.

The Regional Wave Model (RWM)

The Regional Wave Model (RWM) is a large scale, stand-alone SWAN wave model, of which the computational domain covers the entire Bay of Biscay (Fig. 7A, blue dashed line). This regional wave model is a 2-stage nested model with a smaller domain with finer resolution grid embedded in the larger model, to obtain nearshore waves as input for the local flooding model (LFM).

These SWAN grids are structured rectangular grids. The larger grid (Fig. 7C) has a resolution of ~ 8 km and the nested grid (Fig. 7D) has a minimum resolution of 500 m × 200 m. The bathymetries for both the larger and nested grids are generated by combining higher resolution (0.001°) SHOM data in the nearshore42 and GEBCO in deeper water. The SHOM data covers a part of the North Sea, the English Channel and the Bay of Biscay and extends offshore to approximately 4800 m depth.

The RWM is run for the Xynthia duration (27 February 2010–01 March 2010). The model is forced with temporally and spatially varying downscaled wind fields from the WRF model and with offshore wave conditions from the ERA5 hindcast database43. Twenty ERA5 points are used here as offshore wave input points, from which wave heights, wave periods and wave directions are used as open boundary forcing for the RWM.

The Local Flooding model (LFM)

The Local Flooding model (LFM) is the high resolution (~10 m) coupled flow-wave model for local scale flood modelling on Île de Ré. The LFM domain is shown by the red dashed line box in Fig. 7A. The aim of the LFM model is to derive high resolution coastal flooding due to the combined effect of tide, surge and (when activated) waves.

The LFM comprises a DFM unstructured grid flow model (Fig. 7E) and a SWAN rectangular grid model (Fig. 7F). The unstructured flow grid is refined up to ~10 m resolution in the residential areas on the island as well as along the island’s coastline to represent the topography on the island at high resolution, which is essential in detailed flood modelling. Elsewhere, coarser resolution grid cells are used to optimise the computational effort required. The LFM also has a larger structured (rectangular) wave grid, which extends farther to North, South and West directions compared to the LFM flow grid (to avoid boundary artefacts), and a nested finer resolution (~20 m) wave grid for high resolution wave computations near and, when flooded, on the island, (blue grid in Fig. 7F). The bed levels of the LFM are generated by combining nearshore bathymetry data from SHOM at 0.001° (or ~111 m) resolution and the IGN digital terrain model topography data at 5 m resolution. The bathymetry and topography are merged such that the combined dataset is smooth to ensure seamless interpolation of the data points onto the computational grids.

The LFM is run for the Xynthia storm’s duration (27 February 2010–01 March 2010) and forced with tidal forcing derived from the RTSM (as water level time series), wave input forcing derived from the RWM (including significant wave heights, peak wave periods and wave directions), and atmospheric forcing (i.e. spatial temporal wind and pressure fields) from the WRF model. In implementing wind forcing, the model adopts Smith and Banke’s44 formulations for the wind drag coefficient with two breakpoints at U10 = 0 m/s (drag coefficient Cd = 6.3 × 10−4) and at U10 = 100 m/s (Cd = 7.23 × 10−3). Accounting for the spatial variability of surface roughness is important in flood modelling. Therefore, considering the two main types of land-use on Île de Ré, residential and agricultural, spatially varying Manning roughness coefficients are used in the LFM, with a roughness coefficient of 0.12 for residential areas and 0.04 elsewhere (following ref. 13).

To model over-land flooding, it is important to adequately represent the natural topography, as well as all natural and artificial flood defence measures on the island such as sand dunes, cliffs, sea walls, dikes, groynes, port and harbour breakwaters etc. Flood defence systems identified via a desk study (using Google Earth and flood defences identifiable in the 1 m IGN DEM, i.e. moderately augmented DEM) and the in-situ measurement campaign (see Fig. 1E, i.e. highly augmented DEM) are all included in the LFM as fixed weirs. Representing the locations and crest levels of the flood defences with adequate accuracy is crucial for detailed flood modelling. This is especially important when modelling flooding of an island as attempted in this study, because flood waters can propagate from all sides of the island. On Île de Ré, the correct representation of all flood defences is further complicated by the presence of very long and complex defence systems along the low-lying marshes in the northern, leeward part of the island. Identifying and implementing these defence structures in the model is a challenging task which here was done manually through a detailed comparison of the DEM, in situ measurements and Google Earth images. All natural (e.g. dunes) and artificial defences (e.g. dikes and revetments) around the island are included in the model as shown in Fig. 1E, with their heights ranging between 1.6 and 17 m.

Flood damage estimation

Huizinga et al.38 present a methodology and a global flood damage database which enables estimating the monetary damage from flooding (hereon referred to simply as damage), through the construction of flood depth-damage curves. These depth-damage curves are constructed at country level by multiplying normalised damage factors, that are a function of water depth, with country-specific maximum damage values (i.e. maximum damage in Euro/m2 at an upper cut-off flood depth of 6 m) per land-use class. Application of these relations in every grid cell multiplied by the cell size in a domain, gives the total damage caused by an event in that domain.

For the two land-use classes considered here (i.e. residential buildings and agricultural lands), the respective European normalised damage curves are used, as shown in Fig. 9A. These normalised damage curves are then combined with the French national maximum damage values for these two damage classes to construct the two corresponding flood depth-damage curves for Île de Ré (Fig. 9B). From Huizinga et al.‘s38 database, in which the country-specific maximum damage values are standardised at 2010 price levels, the maximum damage for residential areas in France is 155 Euro/m2, approximately 1370 times higher than that for the agricultural land, which is 0.1134 Euro/m2. It should be noted however, that these maximum damage values could be much higher now compared to these country-wise standardised 2010 prices. For example, the average real estate price in some areas like Le Bois Plage and La Flotte on Île de Ré at present is more than 8000 Euro/m2 (https://www.ft.com/content/dd2db0da-d2ee-44d5-9a9e-dd4f1c65af29), which is very much higher than the 155 Euro/m2 value obtained when using Huizinga et al.’s38 data base. However, for the main purpose of this study, which is limited to the investigation of the impacts of detailed representation of flood defences and the inclusion of waves on computed flood damage, rather than the estimation of actual absolute damage values, it is convenient to use the Huizinga approach as this enables consistent comparisons.

Fig. 9: Curves for flood damage estimation.
figure 9

A European normalised damage curves for residential and agricultural land use classes, based on Huizinga et al.38. B Flood depth-damage curves for Île de Ré for the two land use classes (with curve for agriculture multiplied by 100 for better visualisation).

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The above flood depth-damage curves are used together with modelled flooding results of the LFM simulations listed in Table 1 to estimate the flood damage values (in Euro) for each scenario. For each model simulation, the maximum modelled flood depth (in m) during the simulated duration is first identified for each grid cell in the study area. The maximum damage value (in Euro/m2) corresponding to that maximum flood depth for each grid cell is then derived from the flood depth-damage curves for each land use class. The maximum damage value is multiplied with the corresponding area (in m2) of each grid cell to arrive at the maximum flood damage (in Euro) of each grid cell. Combining these cell-damage values, the areal flood damage map for Île de Ré for each simulation is developed. The total damage value (in Euro) corresponding to each simulation is estimated by summing the cell-damages over the island.

Model validation

The Regional Tide and Surge Model (RTSM)

The Regional Tide and Surge Model (RTSM) is validated first against tides only (i.e. flow model with only tidal forcing during the summer month July in 2010) and then against TWL (i.e. flow model forced with both tide and atmospheric forcing during Xynthia). Model results were output every 10 mins and compared with the observed sea levels at La Rochelle and Les Sables d’Olonne stations.

The tide only model-data comparison (25 June 2010–01 August 2010) is shown by time series and scatter plots in Fig. 10A, C – time series; Fig. 10B, D – scatter, indicating that the model performs reasonably well at both stations with some over-prediction as shown by the root mean square errors (RMSE) of 0.257 m and 0.154 m (Fig. 10A, C) at LaRochelle and Les Sables d’Olonne respectively. Figure 10E, G – time series; Fig. 10F, H – scatter, show the model-data comparison for TWL (tide + surge) during Xynthia (27 February 2010–01 March 2010) at the same two stations, which is remarkably good (RMSE of only 0.24 m at La Rochelle and 0.23 m at Les Sables d’Olonne) considering that the maximum TWL during the storm reaches ~4.2 m at La Rochelle and ~3.6 m at Les Sables d’Olonne. However, the model predicted surge alone is slightly under-predicted compared to the observed surge. Thus, it appears that the slight over-prediction of the tidal elevations and the under-prediction of the surge cancel out each other to still provide a good predicted TWL. For the purposes of this study, what is most important is to have reasonable TWLs to drive the high resolution local flood model, and therefore the good agreement obtained between modelled and observed TWLs during Xynthia provides adequate confidence to proceed further.

Fig. 10: RTSM modelled and observed water levels (WL, m) and associated error metrics at La Rochelle and Les Sables d’Olonne stations.
figure 10

A–D tide only – during July 2010, and E–H tide + surge – during Xynthia (27 February 2010–01 March 2010).

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The Regional Wave Model (RWM)

The Regional Wave Model (RWM) was run for the period 22 February 2010–03 March 2010, encapsulating the Xynthia event (27 February 2010–01 March 2010). Modelled wave conditions were output every 1 h and compared against measured wave data available during Xynthia at three stations; Île d’Yeu Nord, Plateau Du Four and Gascogne (Fig. 11). The time series comparisons at three stations show that modelled wave characteristics are in the right order of magnitude and captures the peak wave height during the storm. The outputs of the RWM are used as boundary wave forcing for the high resolution local flooding model (LFM).

Fig. 11: Regional wave model validation.
figure 11

RWM modelled and observed wave heights (left column) and periods (right column) at Île d’Yeu Nord, Plateau Du Four and Gascogne stations during Xynthia (27 February 2010–01 March 2010).

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Local Flooding Model (LFM)

The maximum flood depths and flood extents simulated by the LFM during Xynthia for the 6 scenarios listed in Table 1 are shown in Fig. 12 (also see Table 2, 1st row). Among the 6 scenarios, the modelled flood depths and extents of the two simulations with the base case DEM (F01 and FW01 – Fig. 12A, B) are the greatest; and the resulting inundation extents are larger than the observed flood extent on Île de Ré during Xynthia (i.e. the blue line). When using the moderately and highly augmented DEMs (F02, F03, FW02, FW03 – Fig. 12C–F), the flood extents reduce. Compared to the simulations with the moderately augmented DEM (F02 and FW02), there is no significant difference in modelled flood depths and extents in the simulations with the highly augmented DEM (F03 and FW03). However, there are notable differences in simulated flood depths and extents between comparable simulations with (FW02 and FW03) and without waves (F02 and F03). Inclusion of waves leads to larger flood depths and extents, especially in the western part of the island.

Fig. 12: Computed maximum flood depths (m) on Île de Ré for the six considered scenarios and observed flood extent (blue lines).
figure 12

A, B Maximum flood depths of Base case DEM simulations, without and with waves (F01 and FW01). C, D Maximum flood depths of Moderately augmented DEM simulations, without and with waves (F02 and FW02). E, F Maximum flood depths of Highly augmented DEM simulations, without and with waves (F03 and FW03).

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The maximum modelled flood depths during Xynthia differ among the LFM scenarios. The highest flood depths are in simulations F01 and FW01 (i.e. base case DEM (Fig. 12A, B) with depths of 4–5 m in a large part of the flooded area, and even higher flood depths of 5–6 m in a few locations, especially in the marsh areas in the western part of the island. With the augmented representation of flood defences (Fig. 12C–F), the maximum flood depths decrease throughout the whole island, with maximum values of about 3 m, with locally higher values in the marsh areas. However, the differences between the simulations with the moderately augmented DEM (F02 and FW02) and the highly augmented DEM (F03 and FW03) are minimal. The maximum flood depth results simulated with the augmented DEMs are comparable with the modelled maximum water depths in Bertin et al.33.

To compare the modelled and observed flood extents for each LFM scenario in a more insightful way, here we use the fit measurement (F)33,45 given by: F = A/(A + B + C); where: A is the agreed flooded area in both data and model; B is the area that is flooded in model, but dry in observations; C is the area that is dry in model, but flooded in observations. F is in the range[0-1], with 0 corresponding to no agreement between model and observations and 1 indicating a perfect agreement. The detailed values of the components of the fit measurement calculation are shown in Table 3.

Table 3 Values of fit measurement calculation
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The fit measurements calculated for the 6 LFM scenarios lie between 0.52 and 0.61. These fit values are very similar to those obtained in33 for Xynthia induced flood modelling in Île de Ré. The A values (the agreed flooded area) and B values (the modelled flooded area) in Table 3 indicate the expected result that the modelled flood extent reduces (i.e. smaller A and B) when flood defences are inserted manually into the 5 m DEM. The B values however also show that in all modelled scenarios, about 33–47% of the total modelled flood extent is identified as dry area in the observations. This is a substantial mismatch. However, there is uncertainty regarding the level of precision in the observed flood extent as it was compiled from observations after Xynthia, combining information from several different sources (e.g. satellite images, storm deposits etc)33. Qualitatively however, the modelled flood extent follows the general shape of the observed flood extent. It is noteworthy that the C values in Table 3 are very small compared to the values of A and B, which implies that the model does not miss much of the flooding that occurred on the island. While noting these complexities and uncertainties, we conclude that the level of agreement of our model results with observations and previous modelling of the same event is sufficient to cautiously proceed with the scenario testing required to achieve the goals of this study.