The modelled historical ESLs are validated against GESLA3 (Global Extreme Sea Level Analysis v3) high-frequency (at least hourly) tide gauge records (Haigh et al., 2023; Woodworth et al., 2016). The validation period spans 45 years because the historical simulations cover the 1970–2014 period. Tide gauge stations with a temporal data coverage of at least 60 % over the 1970–2014 period are selected. We therefore focused the validation on the 1-in-10-year level instead of the 1-in-100-year level, as the uncertainties associated with estimates of the 1-in-10-year return period are lower for such a period. Given the horizontal resolution of the regional models (Sect. ), tide gauges located in specific locations such as estuaries, channels, and bays as in the Netherlands were discarded in this study.

Projected changes in ESLs are analysed along the north-eastern Atlantic coasts based on hourly outputs from consistent regional ocean and wave simulations. The domain covered by the regional simulations is called IBI for Iberia–Biscay–Ireland (Fig. ). It extends from 25 to 65° N and 21° W to 14° E and includes the north-eastern Atlantic Ocean, the North Sea, and the western Mediterranean Sea. This region presents a diverse range of physical processes relevant in modelling ESLs (Fig. ). The English Channel and its adjacent Atlantic area are subject to significant sea level variations, primarily driven by tidal signals of up to 10 m (Valiente et al., 2019; Stokes et al., 2021). The North Sea has a mesotidal regime and is characterized by strong winds from intense storms, leading to substantial storm surge events (Marcos and Woodworth, 2017). On the contrary, sea level variations in the western Mediterranean Sea are considerably smaller (Toomey et al., 2022), mainly due to its microtidal regime that rarely exceeds 50 cm. Regarding wave exposure, the Atlantic coast faces large swell events originating from the open ocean (Masselink et al., 2016; Bruciaferri et al., 2021), while both the North Sea and Mediterranean Sea are dominated by wind waves (wind sea) due to their protected location (Chen et al., 2002; Bergsma et al., 2022).

The regional ocean simulations are produced with a 3-D ocean circulation model at a 1/12° horizontal resolution (≈ 4–8.5 km for the latitudes of IBI) by a dynamical downscaling of a CMIP6 global climate model (GCM) at 1/4° spatial resolution for the ocean and 1/2° for the atmosphere (Saint-Martin et al., 2021; Voldoire et al., 2019). The regional wave simulations are produced at a 1/10° resolution (≈ 5.5–10 km for the latitudes of IBI) by a dynamical downscaling of a global wave model (1°), itself forced by the same GCM. Both the regional ocean simulations and wave simulations are forced by the three-hourly winds of the GCM. The particularity is that the wave model is also forced by the hourly sea level variations from the regional ocean model to include sea-level–wave interactions that are important in the IBI domain due to a large tidal range (Chaigneau et al., 2023). This consistent modelling approach provides ocean and wave simulations that are temporally phased. The simulations cover the 1970–2100 period under the high-emission, low-mitigation SSP5-8.5 and the low-emission, high-mitigation SSP1-2.6 scenarios. They are extensively described and validated in Chaigneau et al. (2022) for the ocean (mean sea level, general circulation, water masses) and Chaigneau et al. (2023) for waves (mean and extreme significant wave height and peak period). Table  summarizes the different simulations used in the study.

Hourly outputs from regional ocean and wave simulations (Sect. ) are combined to obtain the total water level (TWL) time series (Eq. ): 1ηTWL=ηSWL+ηwave.

The still water level (SWL) ηSWL (Eq. ) comes from the 3-D regional ocean simulations (Sect. , Table ). The associated extreme events are hereafter called ESWLs (extreme still water levels). The SWL includes the contribution of regionalized mean sea level, tides, storm surges, and non-linear interactions between all these processes. Here the mean sea level variations include changes (1) in the dynamic sea level due to ocean circulations and (2) in the mass variations due to the addition of water mass from the cryosphere and land to the ocean as well as to the balance between evaporation, precipitation, and river runoff. The global thermosteric SLR is added to the SWL a posteriori as the regional ocean model relies on the Boussinesq hypothesis, which does not allow the water column to expand (Griffies and Greatbatch, 2012).

The first-order regional wave contribution ηwave (Eq. ) is evaluated using the wave simulation outputs (Sect. , Table ) based on the generic parameterization of Stockdon et al. (2006) applicable for sandy beaches. The extreme events including this contribution are hereafter called ETWLs (extreme total water levels). The aim is not to represent the local behaviour of waves but to consider a regional large-scale impact of waves on ESLs: 2ηwave=0.35βHsLp, where Hs is the deep-water significant wave height, Lp is the wavelength related to the peak period Tp through the deep-water linear dispersion relationship Lp=g2πTp2, g is the acceleration of gravity, and β is the foreshore beach slope. The foreshore beach slope is constant in space and time at 4 %. This value is representative of a global spatial-mean value found in a previous broad-scale study (Melet et al., 2020). A large-scale wave contribution scaling HsLp is also presented to allow our results to be scaled with different beach slopes or other empirical formulae (e.g. Melet et al., 2020). The limitations associated with this methodology are presented in the Discussion (Sect. ).

Due to a changing climate, sea level time series are expected to be non-stationary (i.e. statistical properties such as trend and variability that vary in time), particularly due to long-term SLR. Two types of approaches are used to derive ESLs in projections: the static approach based on historical data and the dynamic approach using both past information and future information.

Different metrics are used to analyse the ESLs and their projections. We focus on the past 1-in-100-year and 1-in-10-year events defined as events that, respectively, have a 1 % and 10 % chance of exceedance in any given year. In projections, we assess the allowances and amplifications of the 1-in-100-year and 1-in-10-year past events. The allowance is defined as the change in amplitude of the ESLs (in metres) of a given extreme event probability, and the amplification is the change in frequency (in return periods) of a given extreme event threshold (Fig. b). Another metric used to analyse the projected changes in ESLs is the year in the future when the past or historical centennial event (HCE is a 1-in-100-year event over the past/historical baseline period) is expected to recur once a year on average, becoming an annual event (Fig. c). This corresponds to an amplification of 100 for the HCE.

Future evolution of the HCE including changes in all the different sea level components is assessed under both scenarios (Fig. ). A strong north–south gradient of the amplifications is observed, which is consistent with findings at a global scale (IPCC, 2019; Fox-Kemper et al., 2021; Oppenheimer et al., 2019; Vousdoukas et al., 2018b; Jevrejeva et al., 2023). This indicates that our single-forcing GCM is not an outlier compared to other GCMs. Differences of up to 40 years are observed between the two scenarios (Fig. a), regardless of the north–south gradient of the amplifications. South of 45° N, very strong amplifications are projected (Fig. ). The most impacted zone is the Balearic Islands and Canary Islands, where the HCE is expected to become an annual event within 20 years (before 2045), with a small impact of the scenario considered (Fig. a). This phenomenon occurs because these southern regions are subject to a low variability in extremes (flat curves, negative shape parameter, Fig. a). In consequence, even a slight increase in sea level leads to large amplifications (Fig. b). In the north of the domain, HCEs will become annual events later, towards the end of the century, or after, for example, in the southern North Sea. These regions are prone to intense storm surge events, resulting in a high variability of extremes (steep curves, positive shape parameter, Fig. a). This variability typically leads to lower amplifications. Results including the wave contribution are provided in the Supplement (Sects. S1 and S2), using sensitivity analyses for beach slopes (Sect. S3). As previously highlighted in Lambert et al. (2020), we found that including wave contribution delays by up to 30 years the HCE becoming annual along the European coasts. This is due to an increased variability in the extremes when accounting for waves because extreme events of waves and other sea level components do not occur at the same time.

The impact of simulating dynamic changes in extremes compared to the usually applied static approach can be assessed with our consistent modelling setup. We start by investigating changes in ESWLs from the static and dynamic approaches. Dynamic changes include changes in all the different simulated components and interactions. This encompasses (i) differences in mean SLR between the regional ocean model and the GCM; (ii) changes in storm surges and tides (mean and extreme); and (iii) changes in their interactions, including with mean SLR.

As the uncertainties are larger for the 1-in-100-year event, results are provided here for the 1-in-10-year event. In addition, results for the 1-in-5-year event are included in the Supplement (Sect. S4), together with results for the 1-in-100-year event. Under the SSP5-8.5 scenario, the largest significant differences between the static and dynamic approaches are in the Mediterranean Sea, where the differences in the decennial return level are up to +20 %, as well as along the Iberian coast, the Canary Islands, and the English Channel (Fig. c). Except in the English Channel, these significant differences are mainly due to the differences in the regionalized mean sea level projections (dynamic sea level due to ocean circulations) compared to those of the GCM. For the Mediterranean, the Canary Islands, and the southern Iberian coasts, the differences in mean sea level projections between the regional model and the GCM are especially due to bias corrections applied in the regional simulations (Fig. 5a from Chaigneau et al., 2022). Along the northern Iberian coast, the differences are rather attributed to the increased horizontal resolution of the regional model (Fig. 14a from Chaigneau et al., 2022). On the other hand, large negative differences of up to 10 % are found in the English Channel and Bristol Channel and are associated with a projected decrease in the mean amplitude of the M2 tidal constituent (Fig. 18 in Chaigneau et al., 2022). Under the SSP1-2.6 scenario, future changes in the different drivers are expected to be of smaller amplitude but so is the increase in mean sea level. In the end, the impact of the dynamic approach (Fig. d) is of similar magnitude under the SSP1-2.6 than under the SSP5-8.5 scenario. However, coastal locations exhibiting significant differences are fewer under the SSP1-2.6 scenario (Fig. d) owing to the larger confidence intervals (Fig. c). Therefore, the use of a dynamic approach should be applied for all scenarios and not only when high emissions are considered.

When including the wave contribution, differences between the static and dynamic approaches additionally reflect changes in wave climate and associated interactions (Fig. a). We found less significant impact of dynamic changes in ETWLs than in ESWLs. In fact, over the whole domain, 19 % of the coastal points show significant differences for ESWLs (Fig. c) and only 5 % when waves are included, almost only located in the Mediterranean Sea (Fig. a). The isolated effect of dynamic changes in waves on future ESLs is shown in Fig. b. This effect is generally small over the region, but it tends to reduce future ESLs and therefore to compensate for the increase in ESWL amplitude resulting from changes in regionalized mean sea level, storm surges, tides, and interactions (Fig. c). This pattern matches the pattern of projected changes in extreme waves from our wave model (Fig. b). However, the effect of projected changes in waves on total ESLs remains small compared to the robust decrease in mean and extreme significant wave height and peak period that have been highlighted in several studies along the Atlantic coasts (e.g. Aarnes et al., 2017; Lobeto et al., 2021; Morim et al., 2021, 2023; Chaigneau et al., 2023; Melet et al., 2020) and in Fig. b.

To provide projections of ESLs at a large scale considering coastal drivers, some large-scale studies have combined the distribution of the different drivers (e.g. considering their 95th percentile separately in Jevrejeva et al., 2023). Compared to these approaches, our modelling setup with a consistent forcing for all drivers of ESLs allows us to investigate the co-occurrence of the different contributions to ESLs. For instance, it cannot be inferred that a large reduction in the future wave contribution (HsLp) will lead in a reduction in the future amplitude of the ESLs. This is because ESLs are reached due to a combination of different drivers that do or do not necessarily occur at the same time. For instance, local wind forcing can lead to both significant storm surges and extreme waves associated with the wind sea, such as in the Mediterranean Sea and North Sea (Fig. ). The percentage of the time when extreme events of SWL co-occur with extreme events of waves defined by the wave contribution scaling (Sect. ) is displayed in Fig. c. Employing wave contribution scaling to explore the timing between the different contributors enables independence from the selected beach slope (Sect. ). Except in the Mediterranean Sea and southern North Sea dominated by wind sea (Fig. ), SWL and wave extreme events do not often co-occur. In our domain in general, ESLs are dominated by tides and storm surges. Therefore, the extreme events are selected because of the SWL contribution rather than because of the wave contribution. As extremes in SWL and waves do not often co-occur in the region (apart in the Mediterranean Sea and southern North Sea), the added contribution of waves to ESLs is small. For example, along the Atlantic coasts except the French part, both energetic swells are found (Fig. a) and a robust decrease in mean and extreme waves is projected (Fig. b), but extremes in SWL and waves rarely co-occur (Fig. a). In the southern North Sea, SWL and wave extreme events seem to co-occur frequently (Fig. b), but this region is not subject to large projected changes in significant wave height or peak period (Fig. b). The only regions where dynamic changes in waves significantly impact changes in ESLs are the Mediterranean Sea, the Norwegian coasts, and the Scottish Sea, where both a quite large co-occurrence and future changes in wave characteristics occur. This shows that wave future contribution could be neglected in regions where they do not occur at the same time as the dominant contributors, here tides and storm surges. It would probably be different in regions where the amplitudes of tides and storm surges are smaller and where waves (swell and/or wind sea) dominate the ESLs, as for some tropical coastlines.

In conclusion, our modelling chain methodology enables the simulation of dynamic changes in ESL drivers. Significant projected changes in the coastal drivers occur, such as for the wave contribution, underscoring the necessity of employing a dynamic approach to generate ESL projections. We found the dynamic approach to be significantly important in the Mediterranean Sea due to the influence of the refined future mean SLR from the regional ocean circulation model. Since mean sea level directly influences changes in ESLs, this emphasizes the importance of downscaling dynamically GCMs, along with potentially bias-correcting their forcings, to resolve ocean circulations and associated mean sea level as accurately as possible. Elsewhere in our region, the relatively small impact of the dynamic approach is attributed to compensating changes between drivers of ESLs (storm surges, tides, waves, regional mean sea level), which are specific to our region (e.g. decrease in waves and increase in regionalized mean sea level on the Atlantic coast and in the Mediterranean Sea) and driven by a single GCM. For the north-eastern Atlantic coasts, it is also due to differences in timing between extreme coastal sea level contributions. For instance, the robust projected decrease in extreme waves along the eastern Atlantic facade does not significantly impact projected changes in ESLs due to a rare co-occurrence between extreme waves and the dominant processes (i.e. storm surges and tides). In the end, for all these reasons, our findings are in agreement with previous modelling studies using barotropic dynamic approaches (Vousdoukas et al., 2018b; Muis et al., 2020; Jevrejeva et al., 2023) showing that changes in ESLs primarily depend on mean SLR.

The primary focus of our study is on understanding the overall added value of the dynamic approach for ESL projections. Additionally, it would be valuable to explore the relative significance of changes in each contributor to ESLs. Doing so would require conducting dedicated simulations deactivating only one component at a time (tides, storm surges, mean sea level from higher resolution and from corrections of the GCM forcings), which would be computationally very expensive and was unaffordable for this study.

The results obtained for the dynamic changes in extremes are dependent on the modelling chain that is implemented. For the ocean and wave models, the representation of the different coastal processes and their interactions is limited by the model horizontal resolution (5–10 km), by the corresponding bathymetry and coastline resolution, and by the fact that dry areas are not allowed in the current version of the ocean model. The new version of the NEMO ocean model (v4.2) should improve this limitation by incorporating wetting and drying processes (O'Dea et al., 2020). Additionally, the global mean thermosteric SLR is not included as an input in the ocean model and is instead added a posteriori (Sect. ). Therefore, its impact (with global mean thermosteric SLR projected to be +30 cm by the end of the century under the SSP5-8.5 scenario) on the different components is not accounted for. The impact of waves in the ocean model is also neglected, whereas Bonaduce et al. (2020) highlights a non-negligible contribution of wave-induced processes to sea level, particularly for the extremes. Due to the assumptions made in the ocean model (fixed geoid in particular), some contributions from regional to local sea level variations are also not considered in the projections of extremes, in particular those inducing vertical land motion (such as contemporary gravitational, rotational, and deformational effects; glacial isostatic adjustment; sediment deposition or compaction; plate tectonics; local pumping of groundwater and hydrocarbons; and the weight of infrastructure in coastal cities). In some areas it could be interesting to add this contribution a posteriori, for example, for the Baltic Sea and the northern North Sea, which are subject to a significant land elevation due to the glacial isostatic adjustment (Piña-Valdés et al., 2022). Furthermore, considering coupling effects between the ocean, the atmosphere, and wind waves (Lewis et al., 2019) could allow us to better resolve coastal processes, notably storm surges that depend on the wind stress. An alternative at a lower computational cost could be the use of a simplified atmosphere such as the atmospheric boundary layer model (ABL, Lemarié et al., 2021) that would allow the ocean feedback on the atmosphere, therefore better resolving the winds at the coast.

In this study, the wave contribution is evaluated based on a generic parameterization (Stockdon et al., 2006), as seen in other climate studies (Melet et al., 2018, 2020; Lambert et al., 2020). This approach appears pragmatic given the wave model resolution of 10 km and the coastal processes that are poorly resolved in the wave model. However, this parameterization comes with notable limitations. It assumes sandy beach conditions, which may not accurately reflect the diverse sediment types found along many European coastlines, such as rocky shores or mixed sediments. Additionally, the parameterization is designed for deep-water conditions, which may not be representative of all coastal points of the domain, as they are not all purely deep water. The model also relies on a prescribed beach slope β, which varies across different coastal areas. Regional estimates of β are being developed (Vos et al., 2020), but public estimates of this environmental parameter applicable in empirical formulations are not yet available for the European region. While other studies offer global-scale beach slope information, they typically provide either the nearshore slope (Athanasiou et al., 2019) or the sub-aerial coastal slope (Almar et al., 2021), rather than the foreshore beach slope required in Eq. (). Incorporating these values would introduce regional spatial information that may not be accurate, leading to other types of uncertainties – resulting in either underestimations or overestimations of the wave contribution. Therefore, we opted to maintain a constant representative value of 4 % from Melet et al. (2020). Sensitivity analyses were conducted using slopes of 2 % and 10 % in the Supplement (Sect. S3). Amplification factors and allowances of ESLs are found to be strongly sensitive to the value of the beach slope. For these reasons, we used here the wave contribution only to derive future changes in the large-scale wave contribution (in %) or to investigate the timing between different contributions, with both being independent of the choice of the beach slope. To obtain precise and reliable estimates of coastal wave processes such as wave setup, runup, and total water level for adaptation measures, localized studies are needed (e.g. Serafin et al., 2019). However, our study does not aim to provide such localized estimates.

The results are also dependent on the choice of the extreme value analysis method (e.g. Wahl et al., 2017) and can be sensitive to the choice of confidence interval calculation method, particularly in unbounded cases such as those found in the northern domain (Scottish coasts, North Sea) and in the Mediterranean Sea when wave contributions are included. However, such cases are not prevalent in our study area. In this study, the shape parameter remains constant over time, which is probably not valid for all coastal points of the domain as shown in the Supplement (Sect. S5). Moreover, changes in seasonality and natural variability are not taken into account in the method, whereas Hermans et al. (2022) and Roustan et al. (2022) have reported changes in the seasonal cycle of sea level in the same domain. It would be interesting to compare the results obtained with our (relatively) simplified extreme value analysis method with a more sophisticated method such as a multivariate approach (Arns et al., 2017; Lambert et al., 2020; Marcos et al., 2019; Sayol and Marcos, 2018; Serafin et al., 2017) like the skew surge joint probability method, where the stochastic surge or wave part is analysed with extreme value models and then combined with the deterministic tidal signal. This would require an estimation of the dependence structure between the different processes and variables to account for the interactions between the different components. Here, the aim was to preserve the simulated dependence between all the extremes by using the direct method. For instance, by applying the direct method based on the whole time series, the extreme value analyses can account for the projected future decrease in tidal amplitude in the English Channel (Fig. c).

Our findings align with previous modelling studies using barotropic dynamic approaches (Jevrejeva et al., 2023; Muis et al., 2020; Vousdoukas et al., 2018b), indicating that changes in ESLs primarily depend on mean SLR. This challenges recent research showing that historical trends in storm surges (Reinert et al., 2021; Calafat et al., 2022; Tadesse et al., 2022; Roustan et al., 2022) and tides (Pineau-Guillou et al., 2021) have been comparable in magnitude to historical mean sea level rise trends. However, the conclusions these authors draw from historical trends do not necessarily apply to future trends, which is the main focus of this article. Further research is needed to better understand and quantify dynamic projected changes in all the extreme components, their interactions, and timing (e.g. Melet et al., 2024). Currently, dynamic approaches typically do not account for projected changes in all coastal sea level components (mean sea level, tides, storm surges, waves, freshwater discharge) or their nonlinear interactions. These approaches often lack the resolution to accurately capture the various contributions and their nonlinear interactions, as previously discussed. This can result in a misrepresentation of ESLs and their changes, potentially underestimating the significance of dynamic changes in extremes. Additionally, most studies projecting dynamic changes in extremes rely on small ensembles of model simulations or emission scenarios, similar to our study, due to the high computational cost of simulating all the different components and the limited availability of forcing data (Vousdoukas et al., 2017, 2018b; Muis et al., 2020, 2023; Jevrejeva et al., 2023). For instance, global climate models used for driving projections often have relatively low atmospheric resolution, typically around 1° (0.5° in this study), with only a few models being part of the HighResMIP project (0.25°), which better simulates extreme winds responsible for storm surges. Even with a 0.25° resolution, it may still be insufficient to accurately resolve historical and future atmospherically driven contributions, including for instance extra-tropical cyclones in our region. The use of dedicated products such as downscaled atmospheric forcing (e.g. Euro-CORDEX, Outten and Sobolowski, 2021) may offer a promising alternative. Finally, as suggested by Calafat et al. (2022), differences between driving climate models and internal climate variability may also lead to robustness challenges in projecting ESLs. For example, Muis et al. (2023) found little agreement between projected changes in storm surges using different HighResMIP models.