Future wave climate in the NW Mediterranean from multi-model CMIP6 wind projections

Abstract

Coastal areas play a critical role in the well-being of communities worldwide. The Mediterranean basin is a climate change hotspot and contains several vulnerable, low-lying areas such as the Ebro Delta (Northeast Spain). In this study, CMIP6 wind projections from 19 GCMs are used to obtain medium-to-high resolution wave conditions for 2070–2100 in the North-Western Mediterranean, and very-high resolution wave data near the Ebro Delta. The SWAN wave model included in the COAWST modeling suite is used to simulate wave conditions following a nesting approach with three domains (Western Mediterranean, Balearic Sea, Ebro Delta). The model is first validated in the Western Mediterranean by forcing it with ERA5 winds and comparing the results with measurements from seven wave buoys. SWAN model outputs forced with historical GCMs are then evaluated and compared to results from the validation model. Finally, wave conditions are projected under two climate change scenarios, SSP2-4.5 and SSP5-8.5. Evaluation of historical models shows a clear relation between GCM resolution and historical model performance, highlighting the importance of high-resolution wind projections. Wave projections show future decreases in mean and extreme significant wave height, the strongest and most consistent in the Balearic Sea. A general end-of-century reduction in mean significant wave height is detected, with the best-performing models projecting 5-10% reductions at Tarragona buoy, closest to the Ebro Delta. Changes in extremes are more uncertain and heterogeneous, between 10-20%. Overall, this study is novel in its generation of a multi-model wave ensemble using CMIP6 wind projections, sensitivity analysis to domain and wind resolution, and use of model ranking procedures.

1 Introduction

Coastal areas play a crucial role in the environmental, economic, and social well-being of communities worldwide. According to the IPCC (Glavovic et al., 2022), in 2020, almost 900 million people lived in Low Elevation Coastal Areas (i.e., areas within 10 m of the mean sea level and hydrologically connected to the sea) - a number that is expected to increase in coming decades (e.g., Oppenheimer et al., 2019). In addition, the economic value of infrastructural and economic assets developed on the 1-in-100-year floodplain amounts to between 6,500 and 11,000 billion USD (Glavovic et al., 2022). Coastal ecosystems are also biodiversity hotspots, providing key ecosystem services such as coastal protection and carbon sequestration (Bonaldo et al., 2023).

At the same time, coastal zones are among the most vulnerable systems to climate change threats, compounded with overpopulation and intensive exploitation activities (Kombiadou et al., 2019). Two of the most relevant coastal risks from an anthropocentric standpoint, flooding and erosion, are foreseen to increase under future climate scenarios, primarily due to rising sea levels and altered patterns of storm frequency and/or magnitude. Understanding how these processes influence coastal hazards is critical to building resilience and developing long-term risk mitigation strategies in coastal environments.

In this climate change context, the Mediterranean basin is widely accepted to be a hotspot (Giorgi, 2006; Tuel and Eltahir, 2020; Campos et al., 2025). Projected effects related to climate change include modified wind patterns (Martinez and Iglesias, 2023), higher temperatures and more intense droughts (Lereboullet et al., 2014; Olmo et al., 2025), mean sea surface temperature increases that more than double the global trend (Darmaraki et al., 2024), more frequent, long and intense marine heat waves (Oliver et al., 2018), rising sea levels (Gualdi et al., 2013), changes in storm surge patterns (Makris et al., 2023), or wave behavior (De Leo et al., 2021), amongst others.

Thus, with almost half the world’s coastlines susceptible to future changes in wave climate, analysis of wave climate change has drawn significant attention from researchers (Morim et al., 2019), highlighting its large spatial variability at all scales. As an example, mean wave height is expected to grow by 5-10% in the Southern Ocean but decrease by up to 10% in parts of the Atlantic and Pacific Oceans (Casas-Prat et al., 2024), whereas specific localized areas in the Mediterranean are projected to experience increases in wave height in contrast with the general decrease forecasted in this sea (Casas-Prat and Sierra, 2013).

The Ebro Delta in NE Spain is especially vulnerable to wave action, as proved recurrently by the impact of storms (Jiménez et al., 2012), including Storms Gloria (January 2020; Amores et al., 2020) or Filomena (January 2021; Sánchez-Artús et al., 2024). Originally sustained by a balance between the deposition of river-borne sediment and wave-induced erosion along its coast, the dramatic decrease in sediment supply during the last century due to dam construction (estimated at 99%; Rovira et al., 2015) has left wave action as the dominant driver of the delta’s morphodynamic processes (Sánchez-Arcilla et al., 2008a). This, together with its low-lying profile, with 60% of its surface less than 0.5 m above mean sea level (Romero-Martín et al., 2025), makes it extremely fragile in the face of energetic wave storms, resulting in severe erosion, barrier beach destruction, and intense flooding (Amores et al., 2020; Caballero et al., 2024; Cabezas-Rabadán et al., 2024).

Many studies have focused on the future wave climate in the Mediterranean Sea or its sub-basins. Lira-Loarca et al. (2021), for instance, estimated future wave energy resources in the Mediterranean under an extreme scenario (RCP8.5) using an ensemble of 9 Global Climate Model (GCM) – Regional Climate Model (RCM) combinations from CMIP5 EURO-CORDEX (Jacob et al., 2014), and found a general decrease of up to 20% in the mean annual wave flux in most of the domain, although some areas showed a robust increase of up to 45%. This projected reduction in mean wave energy is compatible with the predicted decrease in wind speed and power in the Mediterranean area (Martinez and Iglesias, 2023; Gonçalves-Ageitos et al., 2015), with some notable exceptions (e.g., the Gulf of Lyon -Alvarez and Lorenzo, 2019; Koletsis et al., 2016). In a later paper, Lira-Loarca and Besio (2022) employed an extended ensemble of 17 model combinations to assess the expected changes and seasonal variability of the directional wave spectra in eleven locations across the Mediterranean, finding changes in the significant wave heights consistent with their previous work, while also revealing behavioral changes in the wave climate at many of the locations, going from unimodal to bimodal/multimodal distributions. Toomey et al. (2025) used an expanded ensemble of 31 CMIP5 EURO-CORDEX models to project changes in wave climate and found notable decreases in future mean significant wave height in much of the Mediterranean during the Autumn and Winter seasons with less notable changes during the Summer and Spring. Extreme wave heights were higher for many locations in the Mediterranean in Toomey et al. (2025) but either decreased or showed changes that were not statistically significant in the Balearic Sea. Rusu (2024) forced a SWAN model of the Mediterranean with two RCMs (one developed under CMIP5 and the other under CMIP6, Eyring et al., 2016) and found that their CMIP6-forced wave hindcasts showed a better agreement when compared with the results of a model forced with ERA5 reanalysis data. This suggests that more recent wave estimations derived from CMIP6 climate projections might be more reliable than previous ones, as pointed out also by Meucci et al. (2023).

Regarding sub-basin projections, works in the Black Sea (Rusu, 2019), Adriatic Sea (Benetazzo et al., 2012; Denamiel et al., 2021), Western Mediterranean (Casas-Prat and Sierra, 2013) or Southern Mediterranean (Sierra et al., 2016) all show future wave climates compatible with the overall spatial variability resulting from basin-scale analyses.

In the Ebro Delta region, studies on the future wave climate are very scarce. Casas-Prat and Sierra (2013) assessed the wave conditions along the entire Balearic Sea using SWAN forced by a combination of five GCMs and RCMs developed within the EU-funded ENSEMBLES project (2004-2009) and based on the CMIP3 A1B scenario. Their results showed a general decrease in median significant wave height (HS) and mean period (Tm) in the area, with significant seasonal variability, and higher uncertainty regarding extreme wave conditions in the winter. More recently, and prompted by Storm Gloria, the Catalan Meteorological Agency (SMC) tried to assess wave climate change in the Delta by investigating past storms along the Balearic Sea, recorded at several buoys over the past three decades, but found no statistically significant trend in extreme wave heights [Servei Meteorològic de Catalunya (SMC), 2020].

In this paper we use a set of 19 GCMs based on CMIP6 to estimate the future wave conditions in the Western Mediterranean, with emphasis placed on the Ebro Delta area, under two different climate scenarios, SSP2-4.5 and SSP5-8.5. Although likely failing to account for complex wind patterns close to the coast due to their coarse resolution (Obermann et al., 2018), the use of raw GCM data allows for a larger ensemble of wave projections to be considered, since downscaled wind projections are currently unavailable for most of the GCMs developed under CMIP6. While providing a general view of end-of-the-century wave conditions in the Western Mediterranean, it is expected that the high-resolution projections in the Ebro Delta will deliver key information to assess future hazards in this vulnerable area and contribute to the medium to long-term planning of climate adaptation and mitigation measures.

The nested SWAN model presented in this work is a first step towards analyzing the effects of climate change on the Ebro Delta area using the latest climate projections from CMIP6. The nested SWAN model was developed within the Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) modeling system which allows for nesting of multiple SWAN domains as well as integration of SWAN with the Regional Ocean Modelling System (ROMS) and the Weather Research Forecasting (WRF) model. In future work, SWAN will be coupled with ROMS within the COAWST system to analyze the combined effects of changes in wind-wave climates, ocean currents, and variations in sea level during storm surges. In addition, as higher-resolution CMIP6 wind data from the EURO-CORDEX project becomes available, these wind datasets can be used in place of the current raw CMIP6 GCM data. WRF could be used for further dynamic downscaling of wind data to generate even higher- resolution wind projections near the Ebro Delta domain within the COAWST modeling system.

The structure of the paper is as follows. Section 2 describes the methodology that has been followed, together with the numerical approach and the data used. The results are presented in Section 3 and discussed in Section 4. Finally, Section 5 summarizes the findings of the paper and presents our conclusions.

2 Materials and methods

This study uses wind projections from 19 GCMs to obtain medium-to-high resolution wave conditions for the 2070–2100 period in the Western Mediterranean, and very high-resolution wave data around the Ebro Delta for the same period. The general data requirements and workflow are presented in Figure 1 and described below. The study consists of three main phases: i) validation of the wave model using ERA5 reanalysis wind data; ii) evaluation of CMIP6 wind models using historical data; iii) long- term wave forecasting using CMIP6 wind projections for two climate change scenarios (SSP2-4.5 and SSP5-8.5, Eyring et al., 2016).

Figure 1

2.1 Numerical model and configuration

The study area encompasses the Western Mediterranean basin, which is discretized into three nested domains, as shown in Figure 2. The largest of the domains (Domain A) covers the entire Western Mediterranean, while the two smaller nested domains cover the Balearic Sea (Domain B) and Ebro Delta (Domain C), with resolutions of 0.180°, 0.0361°, and 0.0111°, respectively. With model nesting, a very detailed description of wave parameters around the Ebro Delta is obtained within acceptable computational times. The boundaries of the largest domain are set near the Gibraltar Strait, in the West, and the Boniface-Sardinia straits in the East, taking advantage of the fact that they lie away from the area of interest and that energetic waves generated outside these limits seldom propagate across them into the Western Mediterranean (Cavaleri and Sclavo, 2006; Sánchez-Arcilla et al., 2008b), thus removing the need to specify boundary conditions for the wave model. This assumption is supported by analyses of both measured and reanalysis wave data at these sections, which show that only a small proportion of incoming waves have significant heights exceeding 2 m (see Supporting Information S0). The bathymetry is derived from EMODNet high-resolution digital terrain maps (EMODnet Bathymetry Consortium, 2022; https://emodnet.ec.europa.eu) covering all three domains with a spatial resolution of 0.001° and interpolated onto the respective computational grids.

Figure 2

The model used in this study is the third-generation spectral wave model, SWAN (SWAN Team, 2024b). SWAN offers several options for modeling physical processes associated with wave generation and dissipation. The model simulates random short-crested, wind-generated waves in coastal regions and inland waters, and is governed by the wave action balance equation which distributes wave energy over a directional spectrum:

Equation 1:

where θ and σ denote direction and frequency respectively, N is the action density defined as N=E/σ (where E is energy density and σ is frequency in radians), and cx, cy, and c𝜃 are wave energy propagation speeds. The energy source/sink term, Stot can be expressed as:

Equation 2:

Energy input by wind (Sin) is a source term while whitecapping (Sds,w), bottom friction (Sds,b), and depth-induced breaking (Sds.br) are sink terms. Sn,13 and Sn,14 represent triplet and quadruplet nonlinear wave-wave interactions. Further details are available in the SWAN Scientific and Technical Documentation (SWAN Team, 2024a).

The SWAN model used herein is version 41.51, included within the 3.7 version of the Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) modeling system (Warner et al., 2010), which allows running the three domains simultaneously, ensuring the continuous transfer of boundary information between the three grids. The model configuration and process parameter choices are those defined by default in this version of SWAN (see Supporting Information), which has been successfully tested and validated in the Catalan coast and the Balearic Sea using high-resolution wind data by Pallares et al. (2014). The only meaningful difference is an increase in the wave frequency range, which is here set from 0.03 to 1 Hz to better match the frequency of measuring instruments and avoid the generation of lower mean wave periods, as shown in Pallares et al. (2014).

2.2 Data

The wind forcing used for wave generation is taken from different sources. For the initial SWAN model validation, surface wind data from the European Center for Medium-Range Weather Forecasting (ECMWF) ERA5 weather and climate reanalysis project (Hersbach et al, 2020; https://cds.climate.copernicus.eu) was used. This dataset provides three-hourly wind speed components with a 0.25° spatial resolution. For the validation exercise, data for 1999–2014 was collected for model input; prior to 1999, the availability of wave buoy data was scarce, making model evaluation difficult, whereas CMIP6 historical experiments only run through 2014, so the evaluation model cannot be compared with SWAN models forced with historical GCM data past 2014.

For the wave projections, near-surface (10 m) wind data from a set of GCMs is used. The selection of GCMs was based on a) the availability of simulations corresponding to the two climate scenarios chosen - SSP2-4.5 and SSP5-8.5- and b) the temporal resolution of the data (3 hr). A total of 19 GCMs fulfilled both conditions, whereas one (HadGEM3-GC31-MM) included only the SSP5-8.5 scenario (Table 1). For each GCM, data for the 1985–2014 period was used to assess the historical performance of the GCM as compared to ERA5. Data between 2070 and 2100 was used to simulate future wave scenarios under SSP2-4.5 and SSP5-8.5.

Numerical model validation and evaluation was performed using data measured at seven wave buoy stations in the Western Mediterranean (Figure 2). The buoys at Nice and Alghero are operated by the French Centre for Studies and Expertise on Risks, the Environment, Mobility, and Urban Planning (https://candhis.cerema.fr/) and the Italian Institute for Environmental Protection and Research (www.isprambiente.gov.it/it) respectively, while the five remaining buoys are operated by the Spanish National Harbor Administration (www.puertos.es/en-us).

2.3 Methodology

The performance of each wave model forced with GCM wind projections has been assessed and ranked based on its ability to simulate past wave conditions. Significant wave height (H_S) and mean period (T_m) for models forced with historical GCM data have been compared with an ERA5-forced validation model using the Distance between Indices of Simulation and Observation (DISO) Index (Hu et al., 2019), a comprehensive metric combining three error metrics: normalized mean bias (NMB), root mean squared error (NRMSE), and the Spearman’s rank correlation coefficient (R) – see Equations S1–S3 in Supporting Information (Dodge, 2008). The three error metrics were computed from daily mean values calculated across all the simulation years after applying a 14-day moving average. The study does not evaluate how temporal autocorrelation affects uncertainty estimates or model ranking. Although this omission may result in underestimated uncertainty and increased confidence in the ranking, the primary source of uncertainty arises from the different representations by the GCMs.

Equation 3:

The DISO index is an effective tool for assessing historical model performance and has been used in previous studies to analyze the historical performance of GCMs (Liu et al., 2023) and, specifically, on the Mediterranean climate (Olmo et al., 2025, Olmo et al., 2026). However, given the non-normal characteristics of wave data, we also explore the Perkins Skill Score (PSS) as a non-parametric approach to evaluate model performance (Perkins et al., 2007). PSS is used to quantify the agreement between two probability distributions by measuring the overlap between their normalised histograms, ranging from 0 (no overlap) to 1 (perfect agreement). Ensembles of the best-performing GCMs (top 4) are generated using DISO and PSS metrics with equal and skill weights (see Equation S5 in the Supporting Information). Results from this sensitivity assessment are available in the Supporting Information (see Supplementary Table 4; Supplementary Figures 76–S78 in the Supporting Information).

On the other hand, the wave mean direction θ_m has been assessed using the Kuiper test, a metric best suited for circular variables that measures the degree of similarity between overall distributions of measured and modeled θ_m. This test (Equation 4) is similar to other statistical methods like the Kolmogorov-Smirnov test, which is commonly used to assess whether two datasets come from the same population. However, the Kuiper test is independent of origin making it suitable for circular or cyclical data (Kuiper, 1960).

Equation 4.

Where V_ij is the Kuiper statistic for model i at buoy j, F_S,ij(θ_m) is the empirical cumulative distribution function (CDF) of simulated θ_m, F_M,ij(θ_m) is the empirical CDF of measured θ_m, and the supremum function denoted by sup determines the upper boundary of a set of numbers (Jammalamadaka and Sengupta, 2001). In other words, the Kuiper statistic finds the sum of the largest deviations between the empirical CDFs of observed and modeled θ_m in both the positive and negative directions (no bins in wind direction were considered for this test).

Furthermore, a statistical evaluation of the GCMs performance has been done by comparing individual wave roses at each buoy location, as presented in the Supporting Information.

A ranking system based on these error metrics was developed to identify which GCMs are the most reliable to deliver wave projections. For each wave parameter, the 19 GCMs are ordered and ranked at every buoy according to the DISO and Kuiper statistics, and a Mean Rank (MR) across buoys is computed per model and wave variable. Then, each model is assigned a Cumulative Mean Rank by averaging the Mean Rank for H_S, T_m, and θ_m, as described in the following equations:

Equation 5:

Equation 6:

Where MR_WP,i is the mean rank of CGM i for the wave parameter WP, averaged over the N = 7 validation buoys.

Note that directional skill, using the Kuiper test (significant results at the 99% confidence level, is considered independently from magnitude-based metrics (DISO for H_S and T_m), assuming that the ability of a model to reproduce wave direction provides complementary information to magnitude-based performance, particularly given that direction in deep waters is primarily controlled by large-scale wind patterns. However, this also implies that models with strong directional agreement but large biases in wave height may still achieve favorable rankings since metrics are equally weighted. As a result, the combined ranking should be interpreted with caution, and projections are discussed in terms of relative changes rather than absolute values to reduce the influence of systematic biases.

Assessment of future wave conditions also includes an analysis of extreme waves. Return periods can be determined by fitting probability distributions to a record of wave extremes. Two approaches based on either block maxima (BM) or peaks above a threshold (POT) are commonly used for extreme wave frequency analysis (Caires, 2011). In the BM approach, extremes corresponding to a given block length (normally one year) are identified, and a probability distribution such as the generalized extreme value (GEV) distribution is fitted to the record of extremes. In the POT approach, a storm threshold unique to the study area is first identified, and storm peaks above this threshold are fitted to a generalized Pareto distribution (GPD). Oftentimes, a single storm event generates multiple peaks. To ensure independence of peaks, a maximum storm duration must also be chosen. If multiple peaks occur within the maximum storm duration, they are not considered independent, and only the highest of the peaks is used when fitting the GPD. While the implementation of the BM approach is often simpler, the POT method enables consideration of multiple peaks within a single year, resulting in an increased dataset size. The POT method is, therefore, recommended for extreme wave analysis in which records of annual maxima may be limited (Mathiesen et al., 1994). The CDF of the GPD can be represented as Equation 7:

where ξ is a shape parameter, σ is a scale parameter, and u is the sample mean (Wilks, 2019). Use of the POT method in this study required identification of both a maximum storm duration and a threshold value. A maximum storm duration of 96 hr was chosen as large storms in the Western Mediterranean can generate extreme waves that affect coastal zones for up to four days. Previous research involving extreme wave storms along the Catalan Coast has used a threshold value of 2.7 m for significant wave height (Sánchez-Arcilla et al., 2008c, Sánchez-Arcilla et al., 2021). However, as discussed in the Results section, SWAN models forced by many of the GCMs exhibited large negative biases when compared with measured values. For instance, at the Tarragona buoy, several models generated no wave storms when considering a storm threshold of 2.7 m. Although bias correction is often applied to modeled H_S values when projecting changes in extreme H_S to account for large climate model-derived biases (Toomey et al., 2025), this methodology is not followed here since we are focusing not on absolute wave changes, but on relative variations in the wave parameters.

Alternatively, to address the aforementioned lack of storms, a percentile-based approach is adopted. In this method, the storm threshold is defined not by a fixed value of significant wave height (Hs), but by a percentile derived from a reference time series. This approach has been previously applied to estimate critical thresholds across multi-model ensembles of wave projections using a POT method without prior bias correction (Grabemann and Weisse, 2008; Erikson et al., 2015; Casas-Prat and Sierra, 2013; Liu et al., 2023). Using the historical time series from the Tarragona buoy as a reference, a significant wave height of 2.7 m corresponds to the 98.75th percentile. This percentile is therefore used to define wave storms in the output of each model.

Based on CDFs of extreme wave height, return periods corresponding to H_S values can be found using Equations 8, 9. Analysis of changes in extreme wave height focused on differences between H_S from historical scenarios and SSP2-4.5 and SSP5-8.5 scenarios.

Equation 8:

Equation 9:

Where P(x) is the probability of exceedance corresponding to a given value x, t is the data record length in years, and R(x) is the return period corresponding to a given value x. The Python package pyextremes (https://pypi.org/project/pyextremes/) was used for the identification of extremes based on the POT approach and to fit the GPD to each dataset using the maximum-likelihood estimates (MLE) method.

3 Results

3.1 SWAN model validation

The SWAN model run with ERA5 forcing and the configuration used in Pallares et al. (2014), simulated the patterns of integral wave parameters measured at the buoys with acceptable accuracy. Throughout the full simulation length, the model reproduced the general pattern of H_S, including periods of high and low wave heights, but often underestimated its magnitude, especially at peaks. Model behavior was similar for T_m, capturing periods of high and low T_mbut underestimating its magnitude. The results from the three domains were very similar, with increased computational grid resolution alone failing to improve model accuracy, as expected since all the buoys are located relatively far from the coast. Figure 3, for instance, shows the comparison between the measured and modeled wave data at the Tarragona buoy over a sample period of three months, together with the wave roses for the same period. The Tarragona buoy is especially important for model evaluation as it is the buoy closest to the Ebro Delta, and the only one located in all three domains. The same analysis was performed for the other six buoys, as shown in the Supporting Information (Supplementary Figures 4–S9).

Figure 3

Model performance was similar at other buoy stations, with high R values ranging from 0.84 to 0.96 for H_S, but consistent negative NMB of -5 to -45% and significant NRMSE ranging from 31% to 54% (Table 2). The validation model also yielded persistent negative NMB for T_m ranging from -2.3% to -9.9%, but high R values between 0.80 and 0.90, with the exception of the Nice buoy. NRMSE values for θ_m were small, ranging from 8.5% to 11.7%. Despite high NMB and NRMSE values, the error levels observed in the validation model were comparable to previous studies using SWAN in similar domains (Pallares et al., 2014).

3.2 Evaluation of historical models

Mean annual cycles in H_S and T_m from the ERA5 validation model and the historical models forced with GCM data were first compared. Figure 4 shows the mean daily H_Sand T_mfrom all 19 historical models, the validation model, and measured data at the Tarragona buoy for Domain C. A 14-day moving average is applied to daily means to reduce noise. Historical models generally show lower H_S and T_m when compared with both measured data and the validation model. Underestimation of H_S and T_m in the historical models is likely explained by the low resolution of GCM data when compared with ERA5 data. While significantly underestimating wave height and period, most historical models simulate the seasonal trends well, showing increased H_S and T_m in the winter and reduced H_S and T_m in the summer. Results at the remaining six buoys (S10-S15) resemble those at Tarragona, with general underestimation of H_S and T_m, but accurate simulation of seasonal cycles.

Figure 4

Overall model rankings based on the DISO index for H_S and T_m and the Kuiper test for θ_m indicate a clear relation between GCM data resolution and model performance (Table 3). The SWAN model forced with wind data from CNRM-CM6-1-HR, the highest resolution GCM, performed best when compared with the remaining models, and the four top-performing models were all forced with GCM wind data with resolutions finer than 1°. It is worth noting that models which perform well when considering one integral wave parameter do not necessarily simulate other wave parameters well. The model forced with BCC-CSM2-MR, for example, simulated past H_S and T_m acceptably but was one of the worst-performing models when reproducing θ_m. Detailed error metrics used for the model ranking are available in the Supporting Information (Supplementary Tables 16–S20, S27–S31, S38, S39).

Additionally, we explored the relative ranking of models using the non-parametric Perkins Skill Score (PSS). The top six models are broadly consistent across the evaluation methods, including CNRM-CM6-1-HR, MPI-ESM1-2-HR, EC-Earth3, MRI-ESM2-0, AWI-CM1-1-MR and BSCC-CSM2-MR (more details are provided in the Supporting Information (Equation; Supplementary Table 4).

3.3 Wave climate projections

The ensemble of GCM-forced models indicates reductions in mean H_S and T_m for the SSP2-4.5 scenario, with even greater decreases in both parameters for the SSP5-8.5 scenario at all seven buoy locations. Reductions in mean H_S and T_m are larger along the Balearic Sea (i.e. at the Tarragona and Barcelona II buoys) when compared with the buoys at Nice and Cabo de Gata (Figure 5a). At the Tarragona buoy, a few models - including those forced with IITM-ESM and GISS-E2-1-G - point to future increases in H_S and T_m. However, these models performed poorly in historical scenarios and are likely less reliable than the top-performing models. While the results generally show decreases in H_S and T_m, the magnitudes of the relative changes vary significantly, as do seasonal trends. For example, the projected decrease in H_S from the model forced with CNRM6-CM6-1-HR was almost three times lower than the projected decrease in H_S from the EC-Earth3 model under the SSP2-4.5 scenario. The CNRM6-CM6-1-HR model also projects increases in H_S and T_m during the months of November and December while the EC-Earth3 model projects large reductions in H_S and T_m in the same months (Figures 5b, c).

Figure 5

Results also suggest an overall decline in extreme H_S magnitude in the Balearic Sea. However, other locations in the Western Mediterranean, including Cabo de Gata and Alghero, experience smaller reductions or even increases in H_S for some return periods (Figure 6a). More insights on wave projections over the different buoys are available in the Supporting Information (Supplementary Figures 40–S75). Furthermore, at the Tarragona buoy, the dispersion in extreme H_S projections across the 19 models is much greater when compared with variation in mean H_S (Figure 6b). For example, the model forced with CNRM-CM6-1-HR shows increases in extreme H_S for the SSP2-4.5 scenario and all return periods, while the next three top-performing models indicate reductions in this variable.

Figure 6

Interestingly, changes coming from the PSS-based (H_Sand Tm) top 4 models (identical for SSP2-4.5 and including HadGEM-GC31-MM for the SSP5-8.5 scenario, figures available in the Supporting Information) are broadly consistent with results coming from DISO (Figures 5, 6). Results coming from skill-weighted ensembles (see Methodology for more details) also depict similar changes, indicating robustness in the best-performing GCMs ensemble changes.

4 Discussion

4.1 Impact of wind data resolution

The nested approach used in this study is important for simulating wave processes along the complex coastline near the Ebro Delta while limiting computational requirements for wave modeling on a high-resolution grid. In addition, when wind data with improved resolution becomes available for the region (i.e. EURO-CORDEX), the nested approach in this study can be used to take advantage of high-resolution wind projections near the Ebro Delta. However, increased computational grid resolution in the validation model forced with ERA5 reanalysis data produced no notable improvement in model accuracy (Figure 3) at the Tarragona buoy which is located several kilometers offshore. The ERA5 reanalysis data resolution (0.25°) is even coarser than the computational grid resolution of the largest domain (i.e. Domain A) suggesting that, without improved wind data resolution, increased computational grid resolution may not have a significant impact on model accuracy except in areas closest to the coast.

To assess the impact of increased wind data resolution, an additional SWAN model was run using data from the Spanish Meteorological Agency (AEMET) with a higher resolution of 0.025° for a single year, 2018 (available period for the comparison). The AEMET data was only available over Domain C, so Domains A and B were forced with the ERA5 reanalysis wind data, while Domain C was forced with the AEMET high-resolution data. Results indicate reductions in negative mean biases of about 50% and 40% in Domain C for HS and Tm respectively (Figure 7; Supplementary Tables 40–S42 in the Supporting Information). The use of high-resolution wind data in Domain C significantly improves model results, considering that large negative mean biases in HS and Tm were the main deficiency of the validation model.

Figure 7

In addition, results from the assessment of historical wave models indicate a clear correlation between wind data resolution and model performance. The top performing model was forced with the highest resolution wind data (i.e. CNRM-CM6-1-HR), and the four top-performing models all had resolutions finer than 1°. The improved accuracy of the wave model forced with high-resolution AEMET data and the strong performance of historical models with higher-resolution wind data highlight the large influence of wind data resolution on the quality of the wave predictions. While relatively low-resolution wind projections are used in this preliminary study, the nested SWAN model can incorporate high-resolution wind data as it becomes available to improve model accuracy. Future work should incorporate more years of high-resolution data to demonstrate the robustness of the inferred resolution benefit.

4.2 Key insights into future wave climate

The results from this study indicate reductions in mean HS as well as extreme wave (storm) at all seven buoys in the Western Mediterranean. However, changes in extreme HS magnitude are less uniform, with the Balearic Sea showing clear reductions in extreme HS values, but the other five buoys experiencing smaller changes or even increases in extreme wave heights. While this study is the first to project wave conditions in the Western Mediterranean using a multi-model ensemble of the most recent CMIP6-based wind projections, several previous studies have projected wave conditions in similar domains using either older generations of GCMs and/or smaller ensembles of wind projections. Casas-Prat and Sierra (2013), for instance, modeled future wave climate along the Balearic Sea using SWAN forced with downscaled CMIP3-based wind projections. Other studies have generated wave projections in the Western Mediterranean using CMIP3 (Aznar Lecocq et al., 2016) and CMIP5-based (Ramírez Pérez et al., 2019; Toomey et al., 2025) models. More recently, Rusu (2024) projected wave conditions in the entire Mediterranean Sea using a single CMIP6-based model. The wave projections from this study are largely in line with the findings from previous research and, in many ways, confirm them by using a larger ensemble of the latest generation of GCMs.

Projected mean HS in this study generally resemble the results from Casas-Prat and Sierra (2013); Aznar Lecocq et al. (2016); Ramírez Pérez et al. (2019); Rusu (2024), and Toomey et al. (2025), all showing decreasing HS in the Western Mediterranean. Earlier studies have also found lower reductions in HS along the southern Spanish coast near Cabo de Gata relative to the rest of the Western Mediterranean, in agreement with results from this study. Fewer works include extreme wave analysis in wave climate projections but, in general, the results from this study are in line with the extreme wave projections from Ramírez Pérez et al. (2019) who found large reductions in the 99th percentile of HS in the Balearic Sea (i.e. near the Tarragona and Barcelona II buoys) but smaller reductions near Cabo de Gata, Cabo Begur, Alghero, and Mahon. Around Nice, Ramírez Pérez et al. (2019) found a slight reduction in extreme HS for the SSP2-4.5 scenario and no change in extreme HS for the SSP5-8.5 scenario. Aznar Lecocq et al. (2016) found decreases in HS for 50-yr return periods from 2060–2099 averaged over the entire Western Mediterranean. Spatial distribution of changes in Aznar Lecocq et al. (2016) varied depending on the climate model used for forcing, however. Projected changes in 100-yr HS in Toomey et al. (2025) resemble those observed in this study with reductions in extreme HS along the Catalan Coast but increases in other areas of the Western Mediterranean including the Strait of Gibraltar (near Cabo de Gata), the Gulf of Lyon (near Cabo Begur), and the western coast of Sardinia (near Alghero).

The reductions in HS observed in this study and previous research can be explained in the context of projected changes in wind patterns in the study area, which generally indicate a future decrease in wind speeds and wind power in the Mediterranean and Western Mediterranean (Gonçalves-Ageitos et al., 2015; Martinez and Iglesias, 2023) with the possible exception of the Gulf of Lyon (Koletsis et al., 2016; Alvarez and Lorenzo, 2019).

4.3 Implications for the Ebro Delta

Wave climate change near the Ebro Delta carries important implications for long-term morphological trends in the delta as well as future flood hazard. The real repercussions on the Ebro Delta of climate-induced wave changes should be assessed in combination with other relevant processes, such as deltaic subsidence, sea level rise (SLR) and wave-induced bathymetric and coastline changes, which are not accounted for in this study since the model assumes a fixed bathymetry. Average subsidence in the delta currently reaches 2.3 mm/yr in some areas (Rodriguez-Lloveras et al., 2020) and global SLR by 2100 is expected to be between 0.43 m and 0.84 m for RCP2.6 and RCP8.5 scenarios respectively (Fox-Kemper et al., 2021). While dynamic deltas can respond to SLR through sediment accretion, sediment supply to the Ebro Delta has been greatly depleted. Only a few areas near the river mouth will experience sufficient sediment accretion (Ibàñez et al., 1997) to balance SLR, resulting in large relative sea level rise (RSLR). Under a constant wave climate, RSLR would reduce return periods for wave overtopping and wave-induced flooding, increasing inundation of low-lying areas and promoting coastal retreat.

Projected reductions in mean HS in this study suggest a potential decrease in incident wave energy, however, their implications for coastal response should be interpreted cautiously. Wave projections are driven by relatively coarse-resolution wind fields and exhibit systematic biases. Furthermore, the modeling framework does not account for dynamic coupling with storm surge, currents, or evolving bathymetry. Under these limitations, reductions in mean Hs may conditionally contribute slower rates of wave-driven coastal evolution, consistent with previous findings (Sánchez-Arcilla et al., 2008c).

Therefore, the combined signal should be framed as indicative rather than predictive: lower projected Hs may reduce wave-energy contribution to overtopping frequency, but plausible sea-level-rise scenarios are likely to shift the baseline water level upward enough that overtopping thresholds are crossed more often. This is especially relevant for the low-lying Ebro Delta, where Storm Gloria demonstrated the sensitivity of the systems to extreme events (Sierra et al., 2016; Amores et al., 2020).

In addition, extreme wave events have the potential to cause major erosion, breaching of barrier beaches, and flooding. Storm Gloria in 2020, for example, caused an average shoreline retreat of 47 m in the Ebro Delta, and recovery following such events may be incomplete if storm frequency or water levels increase. While the present results indicate possible reductions in the frequency and magnitude of extreme waves in parts of the NW Mediterranean, these projections are subject to substantial uncertainty. Consequently, any potential reduction in extreme-wave-driven impacts should be interpreted as conditional and does not imply a reduction in overall coastal risk. A quantitative assessment of future hazards requires fully coupled modeling of wave surge, and morphodynamics, which is beyond the scope of this study.

5 Conclusions

Wave climate change driven by altered wind patterns will significantly impact morphology and flood hazard in vulnerable low-lying areas around the world including the Ebro Delta in Northeast Spain. Currently, research on wave climate change in the Western Mediterranean utilizes wind projections from previous generations of climate models or wind projections from single GCMs developed under CMIP6. Updated wave projections for this region using a multi-model ensemble of the most recent CMIP6 wind projections may provide improved understanding of future wave climate change and associated GCM-based uncertainty. This study provides a multi-model ensemble of wave projections for the Western Mediterranean, Balearic Sea, and Ebro Delta for the end of the century using 19 GCMs from CMIP6 under two climate change scenarios. A nested SWAN wave model was used to generate high-resolution projections near the Ebro Delta. The wave model was validated using measured data from seven wave buoys, and models forced with historical GCM wind data were evaluated and ranked through comparison with an ERA5-forced wave model. The main findings of the study include:

• The validation model forced with ERA5 reanalysis data was able to simulate past wave conditions with acceptable levels of error compared to a previous study in a similar domain (Pallares et al., 2014). The model produced significant negative NMB at most buoys for both H_S and T_m but high R values reflecting strong simulation of patterns in wave conditions. The validation model was also able to simulate general distribution of θm although quantities of waves from several directions were under or overestimated. Use of high-resolution AEMET data led to reductions in NMB for HS of over 50%, demonstrating the importance of wind data resolution.

• SWAN models forced with higher-resolution GCM wind data generally performed better. The model forced with the highest resolution GCM, CNRM-CM6-1-HR, performed best and all of the four top-performing models had resolutions finer than 1°.

• All but two models showed reductions in mean H_S and T_m at the Tarragona buoy for the SSP2-4.5 and SSP5-8.5 scenarios. The only two models which indicated increases in wave height and wave period performed poorly in historical scenarios. At the other six buoys, mean H_S and T_m also decreased for the SSP2-4.5 and SSP5-8.5 scenarios. Projections showed significant reductions in extreme H_S in some buoys. Projections also showed decreases in extreme HS magnitude along the Balearic Sea for all return periods considered. However, for some return periods, model results showed increases in extreme HS magnitude at other buoys, including Mahon and Alghero.

This study serves as an initial analysis of future wave conditions based on the most recent CMIP6 wind projections. Projections generated in this work include several limitations, the most obvious of which being the use of relatively low-resolution wind projections. However, model filtering and ranking approaches, as employed here, can be useful to identify common features in different simulations, although this is sensitive to the weighted metrics and criteria. Here, we followed a weighting scheme developed in previous studies in the Mediterranean (Olmo et al., 2025, Olmo et al., 2026) with results from a non-parametric approach based on the Perkins Skill Score and skill-weighted ensembles, indicating a good general agreement in model performance ranking. In addition, this work limits the analysis to relative changes using percentile-based thresholds for each GCM to reduce the influence of systematic biases and avoid the need for bias-correction. Follow-up studies will address this issue and explore the sensitivity of applying different methods (e.g. univariate vs. multi-variate techniques) and approaches (e.g. correcting the wind inputs vs. correcting the wave projections) (Solari and Alonso, 2025). To this purpose, the availability of long-term and high-quality observations becomes essential.

Currently, downscaled regional climate model datasets for Europe are only available through the EURO-CORDEX project (Jacob et al., 2014) based on the previous generation of CMIP5 GCMs. CMIP6-based CORDEX projections are expected to become available in the near future. Follow-up work should incorporate downscaled CMIP6 datasets to assess sensitivity to input wind fields with the aim to avoid inaccuracies stemming from poor wind data resolution, while including improvements provided in the newest CMIP6 GCMs.

The present work also includes a qualitative and preliminary analysis of the implications of the expected relative changes in wave climate for the climate-fragile Ebro Delta, based on the hypothetical scenarios considered in Sánchez-Arcilla et al. (2008c). The results obtained in this study can be used as boundary conditions for morphodynamic models (e.g., XBeach), allowing for a quantitative, model-based analysis of the impacts of wave climate change on beach morphology and wave-induced flooding.

Furthermore, the combined effects of sea level rise, storm surges and waves on the Ebro Delta can be accounted for through the coupling of the SWAN approach developed herein with the ROMS (Regional Ocean Modelling System) hydrodynamic model via the COAWST suite. This is part of an ongoing research plan that aims to provide a more comprehensive description of the fate of the Ebro Delta in the face of climate change effects.

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