The weather typing method was originally developed in and later applied and validated in Hartlepool by . This statistical downscaling approach is designed to establish empirical relationships between larger-scale atmospheric conditions (predictors) and local multivariate oceanographic variables (predictands). Given a statistically robust link between the predictors and predictands, weather typing can serve as an efficient alternative to dynamical downscaling (i.e. process-based dynamical modeling) while maintaining good accuracy. This section provides a brief introduction to weather typing, outlining the datasets involved and the main procedures.

Three types of data were used to derive the WTs. Large-scale atmospheric conditions were represented by sea level pressure (SLP) from ERA5, the fifth-generation global atmospheric reanalysis produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) . The local wave climate conditions were also obtained from ERA5 at an offshore grid node near Hartlepool (55° N, 1° W; see Fig. ). The wave node is around 24 km away from the coast and at a depth of 74 m. The wave climate conditions included hourly variables characterizing both the combined wind waves and swell (including significant wave height Hs, mean wave period Tm, peak wave period Tp, and mean wave direction θm) as well as individual wind wave and swell components (including significant height Hsw and Hss, mean period Tmw and Tms, and mean direction θmw and θms, where the superscripts ^w and ^s denote wind wave and swell components, respectively). Storm surge (SS) conditions at a neighbouring location were obtained from CODEC , a global dataset for extreme sea levels and storm surges driven by wind and atmospheric pressure from ERA5. Validation of wave and storm surge was conducted in . In summary, Hs showed good agreement between ERA5 and the CEFAS wave buoy, whereas Tp displayed some discrepancies. SS from CODEC also compared well with those derived from tide gauges, although CODEC tends to slightly underestimate high surge values and overestimate low surge values. Consequently, a bias correction method was applied to SS. The weather typing analysis was conducted using data from 1979 to 2018.

The first step involved defining the atmospheric predictors in terms of variable selection, spatial domain, and temporal coverage. Here, the predictors were constructed from daily mean SLP and the squared SLP gradient (SLPG, which is closely related to the geostrophic winds) fields over a spatial domain extending from 26 to 76° N and 40° W to 30° E, with a 2° spatial resolution. The predictors were averaged over 4 d to reflect the time scale typical for extratropical storms in the North Atlantic basin , which are the main drivers of wave climate and sea level variability in this region. To facilitate the classification of WTs, a Principal Component Analysis (PCA) was performed to reduce the dimensionality of the predictors while preserving 95 % of the data variance.

Next, a regression-guided classification was implemented to categorize the predictors into a group of representative synoptic circulation patterns (i.e. weather types). This consisted of two key steps. First, a multivariate linear regression model was fitted between the predictors and a group of selected predictands (daily means of Hs, Tp, θm, and daily maximum storm surge). The estimates from the regression model captured the synoptic-scale influence on the local sea states while filtering out irrelevant signals. Second, a semi-supervised clustering was performed on a dataset composed of the predictors and the estimated predictands from the regression model, with a weighting parameter introduced to control the relative contributions of the two components. The k-means clustering was then implemented to partition the dataset into 36 clusters, minimizing the total variance within a cluster. The cluster centroids were subsequently projected back into the original high-dimensional space and plotted in a 6-by-6 lattice, where clusters with lower centroid distances (i.e. higher similarity) are positioned closer together. Figure  displays the circulation patterns for 36 WTs, represented by the anomalies of SLP, as climate variability is typically analysed in terms of deviations from the climatology .

Once the WTs were defined, the relationships between predictors and predictands were established by collecting the predictands recorded on all dates when a specific WT occurred. This allowed for the derivation of empirical distributions of wave and storm surge variables associated with each WT. Model validation confirmed the effectiveness of WTs and their empirical relationships in providing estimates of multivariate sea state variables with generally good accuracy, as well as their limitations in reproducing wave direction and extreme wave events .

Sensitivity analysis was conducted to investigate the impact of different model configurations on the performance of sea state downscaling. The analysis considered factors such as the choice of predictor variables, the spatial domain of the model, the number of days over which the predictors were averaged, the spatial resolution of the predictors, the number of WTs, and the weighting parameter used in the semi-supervised clustering. Some of the main findings are as follows: (1) using both SLP and SLPG as predictors outperforms using either one individually; (2) model performance shows low sensitivity to the spatial domain; (3) increasing the spatial resolution of the predictors does not significantly improve model performance; (4) increasing the number of WTs improves model performance, but more WTs means the associated sea state distributions for each individual WT are less representative. A detailed discussion was provided in .

The behaviour of climate modes is widely studied through climate indices, which are numerical representations of the phase and intensity of atmospheric or oceanic variability patterns. In this study, we examined six key climate indices: NAO, EA, SCAND, Arctic Oscillation (AO), East Atlantic Western Russian pattern (EA/WR), and WEPA. These are the main modes of climate variability over the North Atlantic and European regions and have been commonly considered in previous research e.g..

The first five indices were obtained from the National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center. They were calculated using Rotated Principal Component Analysis , applied to monthly mean standardized 500 mb height anomalies in the Northern Hemisphere (20–90° N). The WEPA index, available at , was developed in to explain the variability of winter wave activity along the Atlantic coast of Europe. Its definition is based on the normalized SLP difference between the stations Valentia (Ireland) and Santa Cruz de Tenerife (Canary Islands).

A correlation analysis was conducted using these six climate indices to identify climate modes relevant to wave climate and storm surge variability at Hartlepool. The analysis focuses on the extended winter months (December to March, DJFM), which aligns with previous research e.g.. This is the period when the atmospheric pressure in the Northern Hemisphere exhibits the greatest variability and perturbations reach their largest amplitudes, significantly influencing local wind fields, wave climate, and sea levels . By contrast, during summer, when westerlies and extratropical storms are weaker, mesoscale processes become more relevant in determining local wave characteristics, particularly in coastal areas .

First, we calculated the mean climate indices, the mean wave variables (including the combined wind waves and swell as well as individual wind wave and swell components), the 99th percentile of Hs (Hs99), and the 1st, 50th, and 99th percentiles of SS (SS1, SS50, and SS99) in each DJFM period. Next, Kendall's τ coefficient was calculated to measure the correlation for scalar quantities (i.e. storm surge, wave height, and wave period). We selected this measure of correlation because it does not require variables to be normally distributed (which is the assumption for the Pearson correlation) and is less sensitive to outliers than Spearman's ρ. For circular variables (wave direction), we used a circular–linear correlation method described in . The correlation coefficient ρcl between a linear variable x and a circular variable θ is defined as: 1ρcl=ρcx2+ρsx2-2ρcxρsxρsc1-ρsc2, where ρsx=corr(sin⁡θ,x), ρcx=corr(cos⁡θ,x), ρsc=corr(sin⁡θ,cos⁡θ), and corr() denotes the Pearson correlation coefficient. The range of ρcl is between 0–1, with greater values indicating stronger association between x and θ.

The synoptic circulation patterns of certain WTs have similar structures to some climate modes. For example, WT31 is characterized by strong negative pressure anomalies over Iceland and the Norwegian Sea and positive pressure anomalies across mid-latitudes (Fig. ). This pattern closely resembles the spatial structure of the positive phase of NAO, which indicates a potential link. However, not all WTs have distinct spatial patterns, and some WTs may reflect the influence of multiple overlapping climate modes.

To establish a more general and robust link between WTs and climate modes, we calculated the percentage of WT occurrence under a positive or negative climate index phase during DJFM. A WT was associated with a specific index phase if its occurrence probability under that phase exceeded a threshold (Pi), which was set to 60 %. For instance, WT1 was classified under positive NAO because 89 % of its occurrence coincided with a positive NAO index, compared to just 11 % with a negative index. The occurrence percentage naturally served as an indicator of the strength of this association. The selection of this threshold was subjective, and the choice of 60 % was intentionally conservative to ensure that each climate index phase was associated with a larger set of WTs. Additionally, WTs with a low occurrence frequency during DJFM (Pw) were excluded from the categorization to maintain statistical robustness in the association. We used a threshold of 1.5 % for Pw. The results are listed in Table  and visualized in Fig. . A sensitivity analysis was conducted on the values of Pi (i.e. 60 %, 65 %, 70 %) and Pw (i.e. 1.5 %, 2 %, 2.5 %) to examine the robustness of this approach. It should be noted that the association between WTs and climate modes is probabilistic rather than deterministic. In other words, WTs associated with a given climate index phase tend to occur more frequently during that phase, but they can also occur during the opposite phase, albeit at lower probabilities.

Climate modes influence sea states by modifying atmospheric circulation, such as wind and storm patterns. To understand the role these individual processes play in the connection between climate modes and sea state variability, we parametrized their effects on wave climate and storm surge. For each atmospheric process, we identified the key parameters that represent its intensity and related them to sea state conditions. It should be noted that the explicit physical mechanisms underlying air–sea interactions are complex and beyond the scope of this research.

The wave climate is dependent on the effects of local wind and distant storms. performed a Canonical Correlation Analysis over the North Atlantic and North Pacific and found that wind wave variability is closely linked to local wind speed, whereas swell is more strongly associated with the frequency of deep (<980 hPa) cyclones. To parametrize the impact of local wind, we obtained the surface wind speed W from ERA5 using the eastward and northward 10 m wind components (U and V, respectively). The wind speed was averaged over a 0.5°×0.5° grid box centred on the study location to represent regional wind conditions. For the impact of extratropical storms on waves, we used the storm track dataset derived in . The dataset was generated by applying a storm tracking algorithm to sea level pressure and 10 m wind speed fields at 0.25° resolution from ERA5. The algorithm calculated the vortex strength based on the U and V wind components and identified potentially significant storms by applying both a vortex strength threshold (0.5) and a sea level pressure threshold (1010 hPa) on an hourly basis. Once a storm was detected, it was tracked over consecutive time steps using a nearest neighbour detection approach within a maximum distance of 5°. The storm frequency was parametrized by the number of hours with storms detected in each 1°×1° grid box divided by the total number of hours.

Storm surges are mainly driven by changes in the atmospheric pressure and the force of wind stress . The impact of atmospheric pressure is commonly known as the inverse barometer effect, which is expressed as: 2Δη=-ΔPA/ρg, where Δη is the change in sea level, ΔPA is the local pressure anomaly relative to the global mean sea level pressure over the entire ocean (assumed to be constant at 1013.3 hPa in most applications), ρ is water density, and g is the gravitational acceleration . Hence, the impact of atmospheric pressure on storm surge was parametrized by ΔPA. Since each WT is represented by a spatial pattern of SLP, the ΔPA at our study location (55° N, 1° W) was estimated by SLP values on the four nearest grid points. These values were averaged with a weight of the cosine of the corresponding latitude to account for the convergence of meridians at higher latitudes. Storm surge generated by wind occurs through the shear stress exerted by wind on the sea surface, which pushes water toward certain directions. In shallow waters, the storm surge caused by wind stress can be expressed in the following form: 3∂η∂x=ρairCdW2ρgD, where ∂η∂x is the gradient of sea level, ρair is air density, Cd is the drag coefficient (related to wind speed due to increasing roughness of sea surface with a stronger wind), W is wind speed, and D is water depth . Since our focus is on representing the effect of wind stress on storm surge rather than quantifying wind-generated surge itself, we parametrized this effect using W only.

The first objective of the study is to identify climate modes contributing to the sea state variability at Hartlepool. This was achieved through a correlation analysis between six climate indices and local wave and storm surge variables, with the results given in Table . Significant correlations (at the 95 % confidence level) are found for NAO, AO, SCAND, and WEPA, with moderate to strong associations. NAO and AO show similar correlation patterns, particularly for storm surge and wave directions. This is not surprising considering the strong correlation between these two indices, with a Pearson coefficient of 0.80 between their winter means. Indeed, there has been ongoing debate about whether they represent distinct phenomena or different manifestations of the same underlying climate variability e.g.. SCAND seems to have the opposite correlation compared to NAO. No significant correlation is found for either EA or EA/WR.

Although four indices were identified as relevant to local sea state variability, we focus on NAO and SCAND for further analysis based on the following considerations. The subtle differences between NAO and AO are unlikely to be distinguished by our WTs which only account for the Atlantic region. NAO is chosen as it has been extensively examined in previous studies and may provide a more physically meaningful interpretation of climate dynamics than AO . WEPA is not considered because it is more relevant in regions south of 52° N .

The second objective of the study is to characterize the response patterns of wave and storm surge to the selected climate indices. The 36 WTs, along with their empirical distributions of wave climate and storm surge, were associated with the positive or negative phases of NAO (NAO+, NAO-) and SCAND (SCAND+, SCAND-) indices. The categorization of each WT is shown in Fig. . WTs that occur more frequently during NAO+ and NAO- are found at the top and bottom of the lattice, while those that occur more frequently during SCAND+ and SCAND- are mainly positioned on the left and right sides, respectively. It should be noted that the positioning of each WT is purely based on the centroid distances (i.e. similarity of their spatial patterns) between its neighbouring WTs and does not consider which climate index phases they are associated with. The reason that most WTs associated with the same index phase are placed together is that they share more or less the same broad-scale atmospheric circulation structure. This section focuses on identifying common response patterns linked to the same index phase and comparing the differences between the positive and negative phases.

The third objective of this study is to investigate the atmospheric processes linking climate modes to the corresponding sea state responses. At this stage, WTs become particularly relevant, as they provide an intermediate, physically interpretable layer for identifying the synoptic-scale atmospheric conditions through which climate modes influence local sea-state variability. These conditions are examined in terms of wind forcing, storm activity, and atmospheric pressure anomalies.

The relationship between ocean waves and climate modes has been widely discussed in previous studies, with a focus on Hs. A commonly observed pattern in the North Atlantic basin is that Hs tends to be positively correlated with the NAO index at higher latitudes, while showing a negative correlation at mid-latitudes . However, in the North Sea where the basin is more sheltered from the open ocean, the association between Hs and NAO is notably weaker, with the correlation in winter generally below 0.5 . In our study, no significant link was found between Hs and NAO or SCAND through either correlation analysis (Table ) or comparing the Hs distributions associated with each climate index phase. This does not imply that local wave climate is insensitive to these climate modes. Rather, the response is expressed more clearly through other wave characteristics.

First, we observed that local Tp distributions are bimodal during NAO+/SCAND- and near-unimodal shapes during NAO-/SCAND+. This pattern is likely attributable to the frequency of observing wind wave-dominated or swell-dominated wave spectra. During NAO+/SCAND-, the chance of the wave spectra at Hartlepool being dominated by either wind waves or swell is relatively comparable (around 56 % and 44 %, respectively), which leads to the formation of two distinct peaks in Tp distributions. On the other hand, during NAO-/SCAND+, the wave spectra are largely dominated by swell, resulting in a low probability of Tp falling in the wind wave range, which is insufficient to form a distinct secondary peak. This wave climate characteristic is different from the general pattern in the global open ocean, where the prevalence of swell is observed almost everywhere, even in mid to high latitudes along the extratropical storm tracks . Our results suggest that the likelihood of wind wave dominance can exceed that of swell waves in more sheltered areas under NAO+/SCAND-. also reported a lower frequency of swell-dominated wave fields in this region under NAO+, consistent with our findings.

Second, the wave directions vary between NAO/SCAND phases. The prevailing wind conditions under NAO+/SCAND- closely align with the primary wind wave directions, and this relationship remains robust throughout our sensitivity analyses. In contrast, during NAO-/SCAND+, local wind directions show greater variability and do not fully align with the corresponding wind wave directions. For swell waves, the dominant directions generally correspond to the regions with higher storm frequency in each climate index phase.

The WT analysis helps interpret why these phase-dependent wave responses arise, by showing how climate modes alter the occurrence probabilities of synoptic circulation patterns that favour different combinations of remote swell generation and local wind forcing. During NAO+/SCAND-, it is more likely to observe WTs characterized by intense low pressure systems centred near Iceland, the Norwegian Sea, or the Scandinavian Peninsula. These regions also correspond to areas of enhanced storm activity and are relatively distant from Hartlepool, allowing remotely generated waves to develop longer periods before reaching the site. Meanwhile, most of these WTs are also characterized by strong local south-westerly wind forcing across the UK, contributing to more energetic wind wave conditions. In comparison, WTs that occur more frequently during NAO-/SCAND+ are characterized by low pressure systems located at lower latitudes, mainly around the British Isles. Under these conditions, the North Sea becomes a more important source region for swell generation. Because this source region is closer to Hartlepool, the resulting swell is likely to have shorter propagation distances and therefore less time to develop into distinctly long-period waves. At the same time, the distribution of low pressure systems of these WTs is less spatially concentrated. This leads to larger variability in the orientation of pressure gradient, which favours less consistent wind wave directions.

Storm surge characteristics in the North Sea generally display a positive correlation with the NAO index, with this association being stronger in the northeastern part of the basin, as revealed by previous research e.g.. further showed that the sensitivity to NAO differs between median and extreme storm surge conditions: SS99 increases more than SS50 for each unit increase in the NAO index. This difference in sensitivity can be explained by the change in the shape of storm surge distributions. Given that the storm surge associated with each WT approximately follows a normal distribution, SS50 can be represented by μSS, whereas SS99 is affected by both μSS and σSS. Since both μSS and σSS are positively correlated with NAO, a higher NAO index typically favours both a positive shift and widening of the distribution, thereby increasing SS99 more significantly than SS50. This may also explain the lack of significant correlation with SS1, which is positively related to μSS but negatively to σSS. As such, the effects of μSS and σSS counteract each other, resulting in no significant change in SS1 in response to NAO.

The response patterns of μSS and σSS are related to the effects of local atmospheric pressure and wind stress, both of which are modulated by large-scale climate modes. During NAO+/SCAND-, WTs characterized by negative pressure anomalies over Hartlepool and stronger winds occur more frequently. Similar synoptic conditions have been reported in previous studies e.g.. These conditions contribute to the increase in μSS and σSS, producing SS distributions that are more widely spread and shifted toward positive values. In comparison, WTs occurring more frequently during NAO-/SCAND+ are generally associated with positive pressure anomalies and weaker winds over the study region. These conditions favour lower μSS and reduced σSS, resulting in SS distributions that are more narrowly centred around zero.

The added value of this study arises from combining weather typing with a multivariate characterization of sea state conditions, including the partitioning of the wave field into wind wave and swell components. The WT framework provides a probabilistic link between climate modes, synoptic circulation patterns, and local sea state distributions, while the partitioned wave analysis reveals response features that would not be evident from the combined wave fields. A further advantage of this approach is its ability to capture response patterns through full distributions rather than correlation coefficients alone, thereby offering a complementary perspective to conventional statistical analyses. For example, the modality of Tp distribution is linked with NAO and SCAND phases, a feature that cannot be captured by a simple correlation coefficient. The sensitivity of the mean and extreme storm surge to climate indices can be interpreted through the variations of mean and standard deviation of the storm surge distributions.

The WT-based approach also allows the investigation of the joint response of multiple sea state variables to climate modes using two-dimensional distributions. In this work, we demonstrated the joint response pattern of wave height and wave direction through wave rose diagrams (Fig. ). It would also be interesting to examine whether climate indices modulate the probability of compound wave–surge events. In addition, the local tidal range varies from around 1–5 m. Incorporating tidal variability into such an analysis might further clarify whether extreme coastal water levels during particular climate index phases arise from the concurrence of multiple drivers or from the dominance of a single component. A comprehensive compound analysis of waves, surge, and tide is, however, beyond the scope of the present study.

Our findings show that weather types, despite representing synoptic conditions over relatively short time scales (4 d in our case), can effectively link interannual climate modes with local sea states. This provides a strong rationale for the construction of WT-based stochastic emulators of sea state conditions e.g.. In these emulators, the impact of climate modes is reproduced through modelling the occurrence frequencies of WTs at different climate index phases, which in turn produce sea state variations at the corresponding time scales. Such emulators are designed to generate infinitely long time series of sea state conditions for coastal risk assessments (e.g. extrapolation of extreme conditions and evaluation of long-term risk evolution). Given the role of climate modes in modulating coastal hazards, it is important to incorporate their influence into the emulator to reproduce realistic time series of sea states.

Investigating the influence of climate modes through weather types is also relevant from a predictability perspective. Individual synoptic weather systems have limited predictability beyond weather-forecast timescales, whereas slowly varying climate modes may contain predictable components on seasonal to decadal timescales , although the level of skill varies among prediction systems and remains sensitive to the representation of North Atlantic ocean–atmosphere interactions . Establishing how such climate modes alter the occurrence probabilities of synoptic circulation patterns and associated local sea states could therefore provide a basis for translating large-scale climate predictions into probabilistic information on coastal wave and storm surge conditions.

The weather types developed in this study are tailored to the specific location using regression-guided classification to enhance downscaling performance. However, this also implies that caution should be exercised when transferring the results to other regions, particularly those with distinct geographic or oceanographic characteristics. To assess the broader applicability of our results, we calculated spatial correlations of sea state parameters across the North Sea relative to our study location (Fig. ). The offshore wave and storm surge conditions along the north-east coast of England exhibit very high correlations (>0.9), which indicates similar response patterns associated with climate modes. This regional coherence in sea state variations was also reported in . The correlations decrease with increasing distance from the study location, but the rate of decline varies among sea state parameters. Storm surge correlations remain relatively high (>0.8) across the south of the North Sea, whereas wave parameters exhibit a more rapid spatial decay. This suggests the response patterns of storm surge are transferable over a larger region than those of the wave climate.

Although the design of this research is inherently site-specific, the weather typing method itself is applicable to any location. To extend the analysis to multiple sites in a region, a single set of weather types can be developed using unsupervised classification (i.e. without tailoring to specific sites) to ensure consistency and comparability across locations. Alternatively, the weather types can be tailored to represent sea states over a larger region using the approach described by , which allows the investigation of the spatial variations in the impacts of climate modes.