Arcachon lagoon is a large low-lying area located in a semi-closed environment and mainly subject to marine overflows driven by offshore storm surge and wave forcing associated with local winds (Fig. 1A). It is a well-studied site, which benefits from a rich bibliography, covering both its general functioning (Bouchet et al., 1997a), the geological and morphosedimentary context (Saltel et al., 2014), the hydrological functioning (Bouchet et al., 1997b) and oceanographic characteristics (Castelle et al., 2007; Dupuis et al., 2006). In recent years the lagoon has been regularly affected by minor to moderate marine flooding notably during storms Klaus (2009), Xynthia (2010), and more recently Céline (2023). As illustrated on Fig. 1B, these storms generated total water levels (tide + storm surge) from annual (∼3m NGF, NGF being the official vertical reference system to measure elevations in France) to approximately 10 years (∼3.5m NGF) return periods at the Arcachon-Eyrac tide gauge but there is no historical example of event beyond. Yet, statistical and hazard studies (Mugica et al., 2014; SHOM, 2022) demonstrated that a 100 year return period event could reach up to 3.7 NGF at the same location, then affecting almost ten thousand of persons (SIBA, 2015).

Based on this bibliography and historical events, the main elements to consider when modeling coastal floods on this area are

Marine flooding by overflowing is dominant on the scale of the entire lagoon even if local sectors can also be exposed to wave overtopping (as the seafront of Andernos, see location in Fig. 1A).

The synthetic storm conditions constituting the scenarios of the pre-calculated database (used for the analysis of the physical processes and for setting up the ML-based techniques, see Sect. 3) are built on the basis of a tri-variate statistical analysis of the extremes of wind, wave and surge conditions at the Cap-Ferret wave buoy located at a depth of 50 m in front of the lagoon (Fig. 2A). The reference data are extracted at high tide from reanalyses over the period 1979–2009: CFSR (Saha et al., 2010) for wind, ANEMOC 3 (Raoult et al., 2018) for waves and MARS30 (Mugica et al., 2014) for the storm surge. After fitting probability laws for significant wave heights (Hs), skew surge (SPM, defined as the difference between the maximum simulated water level and the predicted high tide level) and wind intensity (U) using the Generalized Pareto law (Coles et al., 2001), the dependence models are adjusted for U, Hs and SPM according to the conditional extreme model of Heffernan and Tawn (2004) while managing the covariates (peak period – Tp, wave directions – Dp and winds – Du). Finally, many random combinations (here chosen at 150 000) with the same statistical characteristics as the input data are generated via Monte Carlo simulations. To constitute the learning database, 50 moderate to strong storm conditions (Hs>4m) are selected via a clustering algorithm (Camus et al., 2011) aimed at maximizing the diversity of scenarios (Fig. 2A). These 50 conditions are associated with 10 tide levels between coefficients 40 and 120 (i.e. varying from 1–2.8 m NGF at the tide gauge every 20 cm), bringing the total number of scenarios to 500. Each scenario is therefore described by 6 storm parameters at the buoy (U, Du, Hs, Tp, Dp, SPM) and a high tide level (T) at the gauge.

These synthetic events are completed with historical and pseudo-historical events for validation and demonstration purposes. Historical events (Table 1) correspond to 8 storms (Klaus, Xynthia, Emma, Fabien, Justine, Ciaran, Domingos, Céline) that occurred between 2009 and 2023 and whose forcing conditions are extracted from observed winds and waves as well as reanalysed storm surge (from Météo-France Arpège model) at the Cap-Ferret wave buoy location. Table 1 and Fig. 2A show their characteristics at high tide and Fig. 2B an example of parameters time series for storm Xynthia. Although they are well scattered in the synthetic dataset range, these events remained quite limited in terms of total water level (Fig. 1B) and marine flooding impact (as mentioned in Sect. 2.1) because the most intense storms (Fabien, Klaus and Domingos) occurred at low tide coefficients. Thus, pseudo-historical events are added by combining these 8 storms (described by parameters U, Du, Hs, Tp, Dp, SPM) with the same ten high tide levels (T) as the synthetic events, to create marine flooding events of different severity (greater or lower than historical events). This results in 80 additional events hereafter named Pseudo_StormName_TideLevel(NGF).

The marine flooding model set up for the project includes a chaining of WW3 spectral wave model (Tolman, 2014) and UHAINA hydrodynamic models (Filippini et al., 2024) that resolves Saint-Venant equations. The grid is an unstructured mesh with a resolution from kilometric offshore to decametric inside the lagoon (from 20–50 m) and on land (∼10m) (Fig. 3). This chain of models is forced by tidal harmonics, atmospheric surge and waves at the western boundary (that passes through the Cap-Ferret buoy) and by the wind on the entire domain. It can simulate (1) the propagation of tide, atmospheric surge and waves inside the lagoon; (2) the generation and propagation of the additional surge induced by local winds and the breaking of waves and (3) the marine flooding by overflowing. Despite the resolution of the mesh remains limited on land, the model represents the main obstacles for water flows thanks to the line constraints that represent the protection structures (dikes), the little walls, the embankments and the roads. For each point of the grid, an altitude is extracted from a digital terrain model (DTM) built with a combination of bathymetric surveys with resolutions of 100 m offshore and 10 m inside the lagoon as well as LIDAR data from 2016 survey on land. Finally, the land cover is represented by a manning coefficient extracted from friction maps (Mugica et al., 2014).

For historical and pseudo-historical events, forcing conditions come from time-varying observations at the Cap-Ferret buoy (for waves and wind) and reanalysed data of Météo-France Arpège model (for storm surge). For synthetic events, it corresponds to the set of parameters at high tide determined with the statistical analysis (U, Du, Hs, Tp, Dp, SPM) that are applied as stationary conditions during the tidal cycle. Thus, a fundamental difference between synthetic cases (for learning of metamodels) and historical or pseudo-historical cases (for validation of metamodels) is the consideration of temporality.

To evaluate the influence of the temporal variations of these conditions before and after high tide, sensitivity tests are carried out by simulating the 8 historical storms of the validation set on a tidal cycle with both dynamic conditions (i.e. with time varying time series) and stationary conditions (i.e. with the conditions extracted at high tide ±1h). For the maximum total water level over time (TWLmax), the comparisons between the 8 storm simulations (dynamic and stationary) and tide gauge observations show errors less than 10 cm (Table 2). More generally, Table 3 shows that differences between dynamic and stationary simulations is less than 10 cm from Arcachon to Biganos (on the southwest part of the lagoon) and less than 14 cm from Audenge to Lège (on the northeast part of the lagoon) where the effect of strong winds on the amplification of storm surge is the most important (like for Domingos). Regarding flooded surfaces and maximum water height on land over time (Hmax), the flooded sectors are generally well reproduced and very similar for dynamic and stationary simulations. Figure 4 presents an example for Xynthia (in Gujan-Mestras and Le Teich) and shows that dynamic and stationary simulations result in very similar patterns as observations despite TWLmax differences of 8 cm. The interested reader will find further information about simulations sensitivity tests in Lecacheux et al. (2023). They corroborate that (1) the modeling chain reproduces correctly TWLmax and Hmax on the ten municipalities (2) TWLmax and Hmax are mainly controlled by conditions at high tide, which justifies the use of storm parameters at high tide (U, Du, Hs, Tp, Dp, SPM) in the simulations.

Scenarios of the learning and validation datasets are thus simulated on a tidal cycle by applying stationary conditions of surge, wind and waves on the entire tidal cycle. For each event, simulations are carried out sequentially, starting from the highest high tide level to the lowest, and stopping at the last overflowing level (corresponding approximately to TWLmax of 3 m NGF inside the lagoon). It induces that strong storm events are simulated with more tide levels than moderate storm events (because moderate events generate marine flooding only for the highest tidal coefficients). To sum up, the learning dataset is composed of 220 simulated scenarios and the validation dataset of 32 simulated scenarios (corresponding to the subset of the initial scenarios that generated marine flooding). They are all described by (1) forcing conditions of 6 storm parameters at the buoy (U, Du, Hs, Tp, Dp, SPM) and a high tide level (T) at the gauge (2) maps of maximum total water level in the lagoon (TWLmax) and water height on land (Hmax).

TWLmax obtained with the simulations of learning scenarios vary from 2.6–4.4 m NGF at the tide gauge. For comparison, the annual and centennial levels at the same location are respectively 3 and 3.7 m NGF (Fig. 1). The learning dataset thus enables to describe a wide range of events from annual to exceptional.

The exposure of the municipalities surrounding the lagoon is quite variable. Figure 5 presents two maps showing the percentage of scenarios generating marine flooding (A) as well as TWLmax and Hmax induced by the most intense one (B). They highlight that:

Municipalities with wetlands, either limited (La-Teste-de-Buch, Lanton and Ares) or quite extended (Le Teich, Biganos, Audenge) present a greater general exposure with a higher rate of flooding and higher potential Hmax (although it concerns non-urbanized areas).

But being exposed does not necessarily mean being vulnerable. The impact of a flooding event depends not only on its severity, but also on the stakes involved and the challenges faced by crisis managers. Crisis managers need aggregated indicators to strengthen their capacity to understand the information and take actions. To address this issue on the Arcachon lagoon, collaborative work was realized with the municipalities to classify the scenarios into 3 categories (CAT) representing graduated levels of impact and related to specific action plans:

CAT 1 corresponds to limited flooding events concerning only seafronts, port docks or oyster farming districts that are regularly subject to marine flooding and for which the municipalities are well prepared and autonomous to manage the events.

This preliminary work highlighted the need to forecast water levels (TWLmax) and the associated categories of impact (CAT) for each municipality first, so that crisis managers can rely on predefined action plan typologies. Forecasting marine flood maps (Hmax) should then be undertaken as a second step, in order to complement and refine the characterization of the event within each impact category. In the following, we thus propose different methods enabling to articulate the prediction of both TWLmax and Hmax with different levels of accuracy.

The objective is to measure to which extent the different approaches are respectively able to correctly predict TWLmax on the reference points and whole maps of Hmax given “yet-unseen” offshore metocean conditions. Two approaches are used:

The first approach relies on the available learning scenarios using a 10-fold cross-validation procedure (e.g., Hastie et al., 2009). This holds as follows: (1) the initial training dataset of input forcing conditions is randomly split into 10 equal sub-sets; (2) a sub-set is removed from the initial set, and a new Random Forest model is constructed using the remaining set; (3) the sub-set removed from the initial set constitutes the verification set and the differences between the true and the estimated value can then be estimated. In this procedure, the initial random split at step (1) may have some influence on the results. This can be minimized by repeating the procedure given number of times (typically 10 times).

Figure 8 presents the results of the 10-fold cross validation on TWLmax and Hmax for the three methods presented in Sect. 3. For TWLmax, the error corresponds to the difference between numerical simulations and metamodel-based predictions for each event on the reference points of each municipality (see Fig. 5). For Hmax, the error corresponds to the Mean Absolute Error (or MAE, see Sect. 3.2 and Eq. 2) calculated for each municipality for the flooded nodes where Hmax>0 in the numerical simulation (results of MAE for Hmax=0 in the simulation are also provided in Appendix C to compare the performances of prediction of the flood extent).

Concerning TWLmax, the analog-based approach (M1) enables to estimate the simulation results with a MAE of 10 cm in average, but for some cases it can reach up to 30 cm. On the other hand, using metamodels (in M2 and thus M3) enables to get closer to the target value within 5 cm most of the time and within 10 cm in all cases. On average, the uncertainty of M2/M3 predictions provided by the Gp model (via the kriging variance see Appendix A) is less than 4 cm which remains far below the ranges between categories of flooding presented in Sect. 2.4 (around 30 cm). When looking at Hmax, we notice that the MAE decreases by introducing successively metamodel-based approaches to estimate TWLmax and Hmax (from M1 to M3). With M3, the median of the MAE is below 20 cm whereas its ranges between 15 and 40 cm depending on the municipality for M1 and M2.

This first performance analysis based on cross validation shows that the two metamodels are correctly trained and improve the accuracy of TWLmax and Hmax predictions. However, we can observe differences between the municipalities, with potentially higher MAE (up to 60 cm) on whose comprising wetlands (Le Teich, Biganos, Audenge, Ares). A first explanation is the deeper Hmax expected on wetlands. To better understand the sources of errors, a deeper analysis is carried out in the next section with the validation dataset.

The analysis of the predictive performance with validation cases presented on Fig. 9 reveals the same ranges of errors than the cross validation with a global improvement of the prediction of TWLmax and Hmax from M1 to M3. However, some differences appear as predictions of TWLmax tend to be slightly overestimated for all the municipalities and M3 seems to perform better than in cross validation for municipalities with wetlands. These differences, due to the limited validation sample available, do not change the conclusions of Sect. 4.1.

If the MAE on Hmax enables to compare the prediction accuracy between the methods, it also aggregates different sources of errors depending on (1) the accuracy of TWLmax prediction (2) the marine flooding category (3) the exposure of the municipalities. To deepen this analysis, Fig. 10 provides the correlation between errors on TWLmax and Hmax for each method (one point corresponds to the MAE of one municipality for one event). These plots show that:

Higher errors on TWLmax logically lead to higher errors on Hmax but some scenarios among the most important errors on Hmax also present small errors on TWLmax.

To investigate further, we focus the analysis on two examples that illustrate different situations in Gujan Mestras and Audenge, namely Pseudo_Klaus_2.0, that is characterised by a low-level category CAT 1, and Pseudo_Klaus_2.6, that is characterised by a high-level category CAT2-3. For these events, MAE on Hmax for M2 and M3 remain quite high (between 20 and 50 cm) although TWLmax errors do not exceed 5 cm. The flooding and error maps plotted in Fig. 11 (for Pseudo_Klaus_2.0) and Fig. 12 (for Pseudo_Klaus_2.6) illustrate that, whatever the category of events, the maximum Hmax errors are localized in the seafront quarters (like in Gujan-Mestras) or inside wetlands (like in Audenge). These sectors both present (1) a higher sensitivity to threshold effects on TWLmax which has a direct effect on seafront flooding and controls the quantity of water discharged into low lying areas and (2) greater water heights on land and then potential Hmax prediction errors. Figures 10–12 also illustrate the improvement of marine flooding maps prediction from M1 to M3 both in terms of flooding extent and water height on land. Even for these cases with MAE of Hmax above the median, the flooding maps reproduced with M2 and more particularly M3 are similar to the flooding maps obtained with the simulation of the numerical model. The scatter plots available in Appendix D (Figs. D1 and D2) confirm these results notably at the scale of the Arcachon lagoon with a significant improvement from M1 to M2 and similar patterns centred on the diagonal between M2 and M3.

To complete the comparison of the performance between the three methods, we analyse the confusion matrix on TWLmax and Hmax (Fig. 13) to check how often (all municipalities, mesh nodes and validation scenarios combined) the right category of impact (through TWLmax) and the right Hmax range (with classes of 50 cm commonly used for flood mapping) are predicted. This shows that the categories of impact (CAT) are quite well predicted by M1 (more than 70 % of the test cases) but globally better predicted by M2 and M3 (more than 90 % of the tests cases). This result agrees with the errors on TWLmax presented in Fig. 9 (potentially up to 20–30 cm for M1 and 10 cm for M2 and M3). The representation of the flood extent improves from M1 to M3 as evidenced by F1 score (that can be interpreted as a harmonic mean of the precision and recall, reaching its best value at 1 and worst value at 0) which reaches 0.94 for M1, 0.96 for M2 and 0.97 for M3. More precisely, the confusion matrix shows thatM1 allows to predict the correct order of magnitude only half of the time while M2 and M3 perform better with satisfactory predictions respectively around 65 % and 75 % of the time. More generally, M2 and M3 has a tendency of overestimation, but it should be underlined that the incorrect class is almost always the closest, i.e. when misclassifying the “0.5–1” class, the predicted one is often the “1–1.5”. From a risk perspective, this means that the approach minimises the false positives but tend to over-predict with more false positives.