In order to understand how inter-model differences in wind extremes at 100 m relate to surface characteristics and provide a spatial comparison context for subsequent analyses, we develop a spatial categorisation based on climate patterns, roughness, and topography.

On the one hand, climate classification systems capture this heterogeneity, as different Köppen–Geiger climate zones exhibit different surface wind characteristics due to contrasting thermal regimes, land–ocean distributions, and seasonal circulation patterns that modify boundary layer processes across spatial scales . On the other hand, showed that wind power meteorology needs to consider other surface–atmosphere interactions that influence superficial wind flows, such as surface roughness effects and orographic acceleration. Orographic lifting and thermal circulation modify local wind patterns , while surface roughness controls boundary layer dynamics and turbulent mixing , including the modulation of convective processes . An analogous categorisation was implemented in the European Wind Atlas methodology and further developed with modern multivariate categorisation schemes in the New European Wind Atlas .

Principal component analysis (PCA) offers a framework for multi-model agreement evaluation by decomposing the temporal co-variability of multiple model time series into orthogonal components that distinguish common signals from model-specific divergences . Similarly, inter-model correlations of the seasonal variations provide insights into when and why CPM members differ throughout the year.

The simplified metastatistical extreme value (SMEV) approach, proposed by , relies on a different set of assumptions with respect to classical extreme value theory, which enables one to use the entire set of independent events (temporally uncorrelated local maxima termed “ordinary events”, see Sect. 3.3.1), instead of annual maxima or peaks over threshold only.

Namely, SMEV assumes that the class of the parent distribution describing the ordinary events is known. It then estimates the parameters of this distribution from all the available independent realisations and explicitly accounts for their finite annual occurrence frequency, avoiding the asymptotic assumptions of classical extreme value theory . Therefore, SMEV accounts for both the distribution of wind speed magnitudes (through shape and scale parameters) and the annual frequency of occurrence of the events, thereby providing a more direct physical interpretation of the atmospheric processes generating extreme winds . For the case of wind speed, the Weibull distribution represents a natural choice for the parent distribution, as supported by numerous previous studies and has been shown to effectively approximate distributions with theoretical foundations in atmospheric physics .

Figure  shows that CPMs with different bulk statistics (panel a) can produce similar extreme wind behaviour (panel b, winds > 25 m s⁻¹), confirming the need for dedicated extreme value analysis in wind engineering. Given this, we first quantify baseline differences in extreme wind representation among CPMs by analysing the spatial distribution of mean and coefficient of variation (CV, standard deviation divided by the mean) of annual maximum wind speed. These results are shown in Fig. , which reveals preliminary differences among the three CPMs. ETH exhibits systematically higher wind speeds across the inland domain, with average annual maxima ranging from 15 to 20 m s⁻¹ in low-lying areas to over 35 m s⁻¹ in mountainous regions and coastal zones. CNRM produces intermediate values with a more moderate spatial gradient, while CMCC consistently generates the lowest annual maxima, particularly in complex terrain where values remain below 20 m s⁻¹. All models seem to reproduce a clear orographic enhancement and land–sea contrast effects on the extreme wind speeds. However, the CV reveals generally low inter-annual variability across all models (CV < 0.45), with CNRM showing higher variability than ETH and CMCC, particularly in mountainous regions. These spatial patterns remain consistent when disaggregated by individual surface categories (Fig. ), persisting across all spatial category levels.

The differences in magnitude and patterns across models reveal the systematic inter-model uncertainty in extreme wind representation, particularly in regions with complex topography where surface–atmosphere interactions are most challenging to simulate accurately.

Figure  presents the distribution of 50-year wind return level (U50) estimates. Figure a–c illustrates the inherent intra-model variability across disaggregated spatial categories. In d–f, the ensemble return levels (boxplot, average extreme wind estimates of each single CPM member) are compared with the sampling uncertainty (bootstrap 95 % confidence interval shown as grey bands). Sample sizes vary substantially across categories (Fig. g–i), with temperate and cold climates providing the largest samples (700 and 600 points, respectively), while arid and polar climates contribute smaller samples (100 and 200 points). Roughness category R5 dominates the domain with 900 points, while water surfaces (R1) and R2 provide limited and null representation. The topographic distribution is more balanced, although T1 contributes the largest sample (700 points) compared to T2–T4 (200–400 points each).

The differences among models remain uniform across spatial categories (Fig. a–c). ETH consistently produces the highest extreme winds across all spatial categories, showing the most consistent estimates within categories. Conversely, CMCC generates the lowest estimates, with differences of approximately 10–15 m s⁻¹ in the central distribution among the models and has greater internal variability. CNRM has intermediate behaviour with moderate dispersion within categories, which is closer to ETH patterns.

The ensemble mean U50 return levels within their bootstrap confidence intervals (Fig. d–f) reveal differences in extreme wind speed across spatial categories. A clear progression can be noticed, with tundra (Td) and cold (Co) climates having higher ensemble means (∼ 28 m s⁻¹) compared to arid (Ar) climates (∼ 23 m s⁻¹). Water surfaces (R1) show the highest inter-model consistency, while terrestrial roughness categories (R3–R5) exhibit greater model disagreement despite similar ensemble means. Topographic categories demonstrate both similar ensemble means and comparable inter-model variability, with all terrestrial categories (T1–T4) yielding consistent extreme wind estimates of 25–27 m s⁻¹.

The ensemble approach captures the central tendency across the three CPMs, providing more balanced extreme wind estimates than using individual models. The bootstrap confidence intervals confirm the statistical robustness of the ensemble means across all spatial categories. Moreover, it shows consistent inter-model differences for all surface types. This indicates that the estimation uncertainty comes mainly from model formulation rather than surface-dependent processes.

To complement the U50 estimations in Fig. , we have analysed the distribution of the Weibull parameters across the disaggregated spatial categories (Fig. ). The lower U50 estimates in R1 primarily reflect an 18 % lower scale parameter λ (median: 9.1 m s⁻¹ vs 10.4–11.1 m s⁻¹ in R3–R5), while shape parameter k shows minimal variation (3 %–5 %; Fig. ).

CPMs explicitly resolve convective processes, allowing each model to develop its own mesoscale meteorology, including convective systems, localised circulations, and fine-scale momentum transport processes . One of the first findings is the systematic hierarchy in the annual maxima magnitudes observed in Fig. , with ETH > CNRM > CMCC, suggesting that each model's treatment of these explicitly resolved processes leads to systematically different extreme wind speeds at 100 m height.

Figure  provides information on the physical processes driving this model hierarchy. On the one hand, continental areas, particularly those with mountainous terrain, exhibit the largest inter-model spreads in annual maxima, reflecting the complexity of representing orographic flows, channelisation effects, and topographically induced turbulence, where small-scale processes strongly influence wind field development. These differences in Fig. a–c can exceed 15–20 m s⁻¹ over mountainous terrain and are important because they could significantly alter turbine design loads and compromise structural safety analyses, making the selection of a single CPM a critical source of uncertainty. On the other hand, marine environments show reduced inter-model variability, in line with more spatially uniform surface characteristics that reduce sensitivity to differences in surface–atmosphere coupling approaches. Moreover, the coefficient of variation patterns in Fig. d–f reveal that CNRM exhibits greater inter-annual variability in extreme wind speed, particularly in complex terrain, indicating higher sensitivity to meteorological forcing variations compared to ETH and CMCC. These findings challenge the reliability of isolated CPM applications for extreme wind estimation and demonstrate that inter-model differences require an evaluation to distinguish robust physical signals from model-specific artefacts. Without an assessment of inter-model divergences, extreme wind estimates lack the statistical foundation necessary for engineering applications where structural integrity depends on accurate load projections.

The PCA (Fig. ) reveals insights into the CPM representation of extreme wind processes across different surface characteristics, preserving the systematic hierarchy ETH > CNRM > CMCC detected in the previous analysis. The dominant mode (PC1, accounting for 74.2 % of variance) represents a common climatological signal, with consistent loading patterns across spatial categories, suggesting that this fundamental signal is robust regardless of surface characteristics. This likely reflects their shared response to large-scale synoptic forcing from ERA-Interim boundary conditions, such as the passage of extratropical cyclones and frontal systems that dominate extreme wind generation across central Europe.

The disparities shown by PC2 and PC3 demonstrate how the models vary in their extreme wind simulations. PC2 identifies the main axis of disagreement among models, showing how CNRM and CMCC diverge in opposite directions while ETH stays close to the overall consensus. Meanwhile, PC3 reveals a secondary divergence in which ETH separates from the CNRM-CMCC duo, as evidenced by persistent sign patterns in the loading distributions across all spatial categories (Fig. c). Because PC2 and PC3 are orthogonal, these divergences are statistically independent. This implies that the systematic differences among models originate from various uncorrelated sources within the CPM formulations, rather than being driven by a single dominant factor. These independent divergence patterns indicate that systematic differences originate from various uncorrelated aspects of model formulation. While we cannot definitively attribute these to specific parameterisations without sensitivity experiments, as illustrative examples, PC2 could potentially relate to subgrid schemes and vertical momentum transport, while PC3 might involve boundary layer mixing and surface flux calculations – both crucial areas where CPM settings can differ significantly .

Furthermore, the consistent loadings across diverse surface types suggest that each CPM maintains its characteristic behaviour independent of local surface conditions, pointing to systematic (not random or specific) differences in model physics as the primary drivers of inter-model uncertainty. These results establish that ensemble approaches are necessary because single-model representations of wind fields could provide complementary information.

A pronounced seasonal cycle in inter-model correlations of the monthly 99th percentile is observed (Fig. ), providing clear evidence for the physical mechanisms controlling extreme wind generation and revealing fundamental differences in how CPMs represent diverse meteorological regimes. Winter months exhibit consistently higher correlations across most spatial categories, reflecting the dominance of extratropical cyclones and large-scale synoptic systems in generating extreme winds. This synoptic-scale inter-model agreement is the result of the ERA-Interim boundary forcing, which provides the common meteorological boundaries that all three models represent similarly. In contrast, correlations are lower during summer months, especially July, reflecting a shift in the physical processes generating extreme winds. During summer, large-scale synoptic systems are weakened, and extreme wind events become increasingly driven by localised convective processes, thermal circulations, and mesoscale phenomena. In the summer, in the absence of strong, large-scale synoptic forcing, each CPM internally develops its own mesoscale meteorology, including convective systems, land–sea breezes, and orographically influenced flows. The reduced summer correlations reflect both differences in convective physics representation and potential spatial displacement of similar events. This independent representation of subgrid phenomena explains why model agreement decreases when these internally driven processes dominate the generation of extreme winds.

The spatial behaviour of seasonal correlation patterns reveals that CNRM-CMCC consistently exhibits the lowest correlations across all months and surface categories. At the same time, ETH-CMCC and ETH-CNRM show comparable and alternating correlation levels throughout the seasonal cycle (Fig. ). This pattern is consistent with the PC2 results, where CNRM and CMCC systematically diverged in opposite directions, while ETH remained near the consensus. Rather than surface-specific variations driving inter-model agreement, the almost consistent correlation patterns across diverse surface types reinforce that systematic model differences dominate over surface–atmosphere interaction effects. However, while spatial variations in correlations are typically modest (∼ 0.2 range), certain months, such as September and February, show substantially larger spatial dependency (∼ 0.4 range), suggesting that specific seasonal conditions may amplify surface-related effects on inter-model agreement. Lower winter correlations in cold and tundra categories likely arise from model contrasting treatments of stable boundary layer dynamics and/or orographic flow interactions under temperature inversions and systematic model biases in high-elevation regions where terrain-induced processes amplify inter-model uncertainties .

Future climate projections of extreme winds in convectively active regimes will likely carry greater uncertainty and would benefit significantly from multi-model ensemble approaches to capture the range of possible mesoscale responses to changing thermodynamic conditions. In addition, particular care should be taken regarding the possible changes in the seasonality of large-scale systems, such as extra-tropical cyclones.

The application of SMEV to estimate extreme wind return levels from CPMs is a novel contribution of this study. The systematic differences among individual models and the ensemble's central tendency provide a benchmark for future CPM evaluation studies, while the spatial category approach enables the targeted assessment of model performance across different surface types relevant to wind energy development.

The advantage of using SMEV instead of a traditional extreme value approach comes from the short duration of CPM simulations. While traditional extreme value analysis depends on annual maximum values, which are just 10 values from the length of the simulations, or a still limited number of peak values above a very high threshold, SMEV uses the complete set of independent events. This provides abundant information for estimating extremes from the available short time series, thereby addressing this critical limitation of CPM simulations. This is particularly important for wind energy, where design standards require estimates for 50-year return periods that typically need to be based on limited simulation periods.

The assumption of Weibull tails for the distribution of the wind ordinary events, while well supported for wind data , may not fully capture wind field complexity in heterogeneous terrain where multiple meteorological mechanisms contribute to extreme generation . However, this potential limitation is mitigated in the present study through the use of left censoring, by which the potential impact of heterogeneous wind processes with different typical magnitudes is reduced.

Using ensemble approaches offers clear benefits over relying on single-model assessments for extreme wind evaluations. The individual models in Fig. a–c follow the same consistent hierarchy (ETH > CNRM > CMCC) across all spatial categories, as evidenced in previous results. This reinforces the idea that the way models are formulated leads to differences between them, rather than specific surface effects. In this context, CMCC shows greater internal variability, as indicated by its wider interquartile ranges, compared to ETH and CNRM. This suggests varying levels of dispersion within categories that warrant further investigation.

The CPM ensemble analysed here differs in multiple aspects of model configuration: dynamical cores (COSMO vs AROME), PBL parameterisations (TKE vs CBR), vertical discretisation (50–60 levels), horizontal diffusion approaches (fourth-order Smagorinsky vs none vs SLHD), and horizontal grid spacing (2.2–3.0 km), as explained in Sect. 2. A key finding from our inter-model comparison is that CMCC and ETH show U50 differences that are similar in size to those between models using different PBL schemes, even though they have the same PBL parameterisations. For instance, the U50 spread between CMCC or ETH (both using TKE-based PBL) is similar to the spread between CMCC and CNRM (TKE vs CBR). This pattern suggests that uncertainty in extreme wind estimates among models arises from the combined effects of various configuration choices, including but not limited to, PBL parameterisation and fine-scale heterogeneity. These inter-model differences highlight the importance of using ensemble-based approaches for reliable extreme wind assessment in wind energy applications.

Some spatial categories, like Ar (arid climates) and R1 (water surfaces), show less variability among the models. This probably reflects the more stable and limited range of meteorological conditions typical of these environments. Additionally, the ensemble approach in Fig. d–f gives more balanced estimates by averaging these systematic model differences and varying internal sensitivities. This helps to avoid the potential bias that could arise from using a single model. These patterns confirm that while the model hierarchy is consistent, individual models respond differently to subgrid processes, highlighting the importance of ensemble approaches in capturing the full spectrum of physical process representations. While previous validation confirms that these models are physically sound and multi-model ensembles quantify structural uncertainty, observational validation remains essential to establishing absolute accuracy and to detecting potential shared systematic biases beyond the structural uncertainty quantified by multi-model ensembles.

The bootstrap confidence intervals in Fig. d–f provide strong statistical uncertainty bounds that are much narrower than the spatial variability seen within ensemble estimates across each category. This offers wind energy practitioners a more reliable range for design purposes, compared to the broader variability found in the full ensemble data.

The intra-category variability in U50 estimates shows the combined effects of meteorological sampling over the 10-year period and fine-scale spatial heterogeneity. During these temporal windows, different sites may have varying extreme meteorological conditions, with some experiencing more severe convective storms or synoptic extremes randomly, leading to different sets of ordinary events and consequently varying U50 estimates. Additionally, local surface characteristics (fine-scale roughness, microtopography) vary within categories; although this heterogeneity is less than the heterogeneity among categories, it is physically reasonable because categories inevitably capture dominant patterns but not absolute uniformity. In this sense, both factors represent features of high-resolution climate data rather than methodological limitations.

The consistent differences in how extreme winds are represented among CPMs and their spatial patterns offer insights for wind energy applications that go beyond traditional meteorological analysis. The variability of seasonal agreement among models provides a framework for assessing uncertainty and enables wind industry experts to adjust the confidence levels based on the season. For example, one could consider applying higher uncertainty margins during the summer months, when convective processes are more prevalent and inter-model correlations tend to decrease. In contrast, higher confidence can be placed in model consensus during winter periods, when synoptic processes dominate and correlations increase. The uniformity of model differences across all surface types indicates that ensemble approaches are essential, regardless of the project's location.

In terms of wind resource assessment, this systematic model hierarchy allows for risk-based approaches. For critical infrastructure design, conservative estimates using ETH can be employed, while ensemble estimates offer balanced projections for general applications. Given the consistent differences among models across all spatial categories, adopting ensemble approaches should be standard practice for evaluating extreme winds, irrespective of the type of surface or geographic location. Insights into the systematic behaviours of the models identified in this study can assist wind energy professionals in understanding the inherent uncertainties in CPM-based projections and in implementing appropriate ensemble strategies that align with their risk tolerance and application needs.

The intra-category variability of U50 has practical implications for multi-scale wind resource assessment and long-term planning. Our CPM ensemble approach provides robust climatological information at the regional and categorical scales (3 km horizontal grid spacing), as evidenced by the strong common signal (74.2 % of variance), which is valuable for regional resource mapping and preliminary site identification. However, when transitioning to site-specific turbine design, wind energy specialists require micrositing assessments at subgrid scales (1–100 m) to capture fine-scale terrain features, local obstacles, and surface roughness variations not resolved by CPMs. This site-specific refinement follows established industry protocols and is necessary regardless of the regional climate data source employed.

Our U50 estimates over R1 should be interpreted cautiously for offshore wind energy applications. First, considering our study area, the R1 sample represents semi-enclosed Mediterranean/Adriatic waters rather than the unlimited-fetch open-ocean conditions characteristic of major offshore wind farms in other open-basin seas, such as the North Sea, where persistent westerly flow and unrestricted fetch typically generate systematically higher extreme wind speeds. Second, CORDEX-FPS CPMs employ coarse-resolution SST forcing (∼ 80 km monthly means), creating scale mismatches with the fine-resolution (2–3 km) atmospheric grid , which may contribute to conservative marine wind estimates. These geographic and technical factors, combined with the physical process whereby water surfaces experience occasional intense synoptic events but lack the high-frequency convective events enriching terrestrial tail distributions, result in 18 % lower scale parameter λ in R1 compared to land categories R3–R5 (Fig. ), translating approximately linearly to lower U50 estimates.

A fundamental limitation of this study is the lack of observational datasets with sufficient spatial coverage, temporal extent, open accessibility, and consistent measurement heights to enable direct validation of CPM simulations. This observational gap limits our ability to validate the physical realism of the observed model hierarchy and to assess whether the U50 estimates align with real-world extremes across spatial categories. Additionally, the relatively short 10-year simulation period, while sufficient for obtaining reasonable estimates with SMEV, represents a limitation for characterising long-term climate variability. Nevertheless, since identical forcing isolates systematic model differences from climatic variations, 10 years is sufficient as well for inter-model comparison purposes. Also, an increased number of ensemble members is needed for a more robust assessment of model uncertainty.

Future validation efforts would greatly benefit from extensive observational networks that provide long-term wind measurements at hub height across diverse surface types. Specific validation campaigns in representative spatial categories could be helpful in assessing absolute model performance and bias characteristics on the typical wind conditions but would hardly provide actionable information about the extreme return levels needed for turbine design. To this end, priority should be given to the already available observational datasets, which should be made available to the community as open data. Until such validation becomes possible, the framework presented here serves as a methodological baseline for understanding CPM capabilities and inter-model uncertainties in extreme wind assessment.

The 10-year simulation period provides enough temporal coverage for SMEV application, as demonstrated by the strong inter-model consensus. However, this simulation period captures a finite sample of possible meteorological events, and some intra-category spread in U50 estimates reflects this meteorological sampling variability. Future studies with longer simulation periods (20–30 years) would further refine the separation between systematic spatial patterns and temporal sampling effects.