Distinct regional patterns of MHWCI variability in the North Sea were identified using a correlation-based k-means clustering approach (Jain, 2010; Lloyd, 1982). Clustering methods have been used in climate research to identify spatially coherent regions and recurrent climate or circulation regimes (Plaut and Simonnet, 2001; Jacobeit, 2010). Unlike conventional k-means clustering, which minimizes Euclidean distance and is sensitive to absolute feature magnitude, the correlation-based version emphasizes similarity in the shape of normalized feature vectors. Similar correlation-distance-based clustering approaches have been used to classify precipitation variability regimes, identify climatically meaningful oceanic regions from subsurface temperature data, and characterize regional SST variability patterns (Santos et al., 2019; Radin et al., 2024; Radin and Nieves, 2024).

Given the pronounced seasonal variability of MHW in this region, this approach classifies grid points according to their seasonally resolved interannual variability characteristics, rather than applying the clustering separately to individual seasons. Specifically, a k-means clustering is performed using seasonal variability information derived from the full monthly record, thereby revealing spatially coherent regions with distinct seasonal responses to large-scale climate forcing.

For each grid point, MHWCI anomalies were computed for each season by subtracting the long-term seasonal climatology. The four seasons are defined as winter (December of the previous year and January-February of the current year, DJF), spring (March–May, MAM), summer (June–August, JJA), and autumn (September–November, SON), which correspond to well-established physical regimes in the North Sea (Chen and Staneva, 2024; Mohamed et al., 2023), including wintertime deep mixing and weak stratification, and summertime strong stratification with shallow mixed layers. The interannual variability during each season was quantified as the standard deviation of anomalies across the 40 years, yielding a four-component feature vector per grid point, with each component representing DJF, MAM, JJA, and SON variability. To reduce the influence of extreme values and ensure equal weighting among the four seasonal components, a logarithmic transformation followed by standardization was applied to the feature vectors. The dissimilarity between two grid points (Eq. 1) was defined as the correlation distance between their feature vectors: 1Dxi,xj=1-rxi,xj, where r(xi,xj) is the Pearson correlation coefficient between the seasonal variability patterns of MHWCI, emphasizing the similarity in their seasonal variability structures. The total within-cluster dissimilarity was computed as the sum of squared correlation distances (WCSS), which decreases as the number of clusters K increases. The number of clusters K was determined using the Elbow Method, where the reduction in WCSS begins to level off (Syakur et al., 2018). In this study, K=2 was selected as the optimal number of clusters (Fig. A1). Further validation of clustering robustness is provided in Appendix A. This number results in two well-separated and spatially coherent regions in the North Sea, broadly corresponding to the southern and northern subregions, indicating distinct temporal variability characteristics of MHWCI.

Based on the assessment, grid points were partitioned into two clusters by grouping them with similar seasonal patterns. Each cluster is characterized by its dominant season, defined as the season with the highest mean standardized variability, and the relative contributions of all four seasons. This approach identifies regions where MHWCI variability exhibits specific seasonal dependence, thereby revealing distinct spatial patterns that may be linked to different large-scale climate variations.

To characterize the upper-ocean stratification associated with MHWs, mixed layer depth (MLD) is diagnosed following a density-based criterion. Specifically, MLD is defined as the depth at which the potential density first exceeds the potential density at 10 m by 0.03 kg m⁻³ (England et al., 2025), which has been shown to be suitable for shallow and seasonally stratified shelf seas. Vertical stratification and dynamical stability are further quantified using the gradient Richardson number, Ri, defined as: 2Ri=N2S2 where N is the buoyancy frequency, 3N=-gρ∂ρ∂z1/2 and S is the vertical shear 4S=∂u∂z2+∂v∂z21/2. Here, g denotes gravitational acceleration, ρ is seawater density, and u and v are the zonal and meridional velocity components, respectively. All variables are derived from the ORAS5 reanalysis and are computed over the same temporal intervals as the temperature fields to ensure consistency among stratification and heat budget diagnostics.

The physical processes driving MHWCI variations in the subregions identified by the k-means clustering were quantitatively examined through an upper-ocean heat budget analysis. After linearizing the variables, the perturbation equation of upper ocean heat anomalies (Eq. 3) can be described as (Liu et al., 2014; Tan et al., 2016): 5∂Tm′∂t=Qnet′ρCphm-ug⋅∇Tm′+ug′⋅∇T‾m-ue⋅∇Tm′+ue′⋅∇T‾m-w‾eTm-Td′hm-we′Tm-Td‾hm+RES where the overbar and prime denote the monthly mean and anomaly, respectively. The left-hand side represents the sea surface temperature anomaly tendency. We calculated this tendency as the temperature difference between February and December for winter and between August and June for summer, respectively. The right-hand side comprises four main terms, namely the net heat flux, geostrophic heat advection, Ekman heat advection, and entrainment heat flux, respectively. The last term denotes the residual term (RES), which includes nonlinear heat advection and diffusion, etc. These terms are averaged over the respective seasonal periods. Qnet′ refers to the sea surface net heat flux anomaly, comprising the net shortwave and longwave radiative components, as well as the net latent and sensible heat fluxes. Positive values of Qnet′ indicate ocean gaining heat from the atmosphere. ρ is the seawater density (1025 kg m⁻³), Cp is the specific heat capacity (3890 J kg⁻¹ K⁻¹), and hm is the MLD. ORAS5 provides ocean variables on 75 vertical levels, with vertical spacing increasing from approximately 1 m near the surface, allowing a physically consistent estimation of MLD and mixed-layer heat budget terms at seasonal to interannual timescales. The horizontal circulation in the surface layer can be divided into the Ekman current component ue and the geostrophic current component ug. we is the Ekman pumping (entrainment) velocity, with positive values indicating Ekman upwelling, pumping or divergence and negative values for Ekman downwelling or convergence, respectively. Tm is the mixed-layer temperature, and is set to SST in this study for simplicity. Td is the temperature below the base of the mixed layer. This heat tendency equation (Eq. 6) follows the standard formulation commonly used in upper-ocean heat budget studies. All terms are computed using monthly mean fields.

Large-scale atmospheric teleconnections influence the formation and persistence of MHWs by modulating atmospheric circulation and surface heat fluxes. The Pacific–Atlantic teleconnection is closely linked to Rossby wave propagation (Hou et al., 2023). The propagation of these teleconnection signals was diagnosed using the wave activity flux (WAF, Eq. 7), which quantifies the direction and intensity of stationary Rossby wave energy propagation (Takaya and Nakamura, 2001). Hence, the horizontal WAF (unit: m²s⁻²) was calculated as follows: 6WAF=pcos⁡φ2|U|Ua2cos⁡2φ∂ψ′∂λ2-ψ′∂2ψ′∂λ2+Va2cos⁡ϕ∂ψ′∂λ∂ψ′∂φ-ψ′∂2ψ′∂λ∂φUa2cos⁡φ∂ψ′∂λ∂ψ′∂φ-ψ′∂2ψ′∂λ∂φ+Va2∂ψ′∂φ2-ψ′∂2ψ′∂φ2, where p is the pressure normalized to 1000 hPa, φ is the latitude, λ is the longitude, a is the radius of the Earth, ψ(=z/f) is the geostrophic stream function, z (m) is the geopotential height, f is the Coriolis parameter and ψ′ is the perturbed stream function, calculated as the deviation of the geostrophic stream function from its climatological mean state. |U|, U and V represent the averaged wind speed, zonal, and meridional wind velocity, respectively.

To link regional MHW variability with its large-scale drivers, we first identify the dominant spatial-seasonal patterns of MHWCI and their associated climate indices, and then examine the corresponding atmospheric and oceanic anomalies. Power spectrum analysis of the detrended monthly MHWCI (Fig. 1b), constructed as a continuous time series by summing the cumulative intensity of all MHW events occurring within each month (and set to zero when no events occur), shows that, after removing the dominant seasonal pattern, substantial variability remains at interannual timescales. Several spectral peaks exceed the 90 % confidence level, suggesting that MHWCI variability in the North Sea is organized on multi-year timescales. This provides a basis for exploring whether such variability exhibits coherent spatial and seasonal structures across the region.

Based on the seasonal patterns of interannual MHWCI variability, the correlation-based k-means clustering identifies two spatially coherent subregions (named as Cluster 1 and 2, respectively) in the North Sea (Fig. 2a). Cluster 1 mainly covers the central and southern parts of the North Sea, while Cluster 2 includes the deeper northern region. The two clusters are geographically contiguous and broadly aligned with the contrast between the shallow southern shelf and the deeper northern basin.

Seasonal differences between the two clusters were quantified by calculating the relative contribution of each season, expressed as the percentage of its spatially averaged interannual variability intensity (VI) relative to all four seasons within each cluster. Positive values of VI indicate seasons that contribute more strongly to the total variability of that cluster, while negative values indicate weaker contributions. In Cluster 1, variability is dominated by winter (VI = 0.66) and autumn (VI = 0.41), with substantially weaker variability in summer (VI = -0.28) and spring (VI = 0.07) (Fig. 2b). Cluster 2, by contrast, shows its strongest variability in summer (VI = 0.57) and moderate variability in spring (VI = 0.24), while variability in autumn (VI = -0.08) and winter (VI = -0.30) is relatively weak. These results indicate a clear seasonal asymmetry between the central-southern and northern North Sea, implying that seasons with the most active MHW-related variability differ between the two regions.

In the central-southern North Sea (Cluster 1), variability is dominated by winter, whereas in the northern deeper region (Cluster 2) it is primarily expressed in summer. These seasonal contrasts are derived from the relative contributions of each season to the standardized interannual variability of MHWCI and therefore reflect when MHW-related variability is most active in each region. Based on this diagnosis, the subsequent analyses focus on winter MHWCI for Cluster 1 and summer MHWCI for Cluster 2 in order to examine large-scale climate influences during the season of maximum variability for each region. The relationship between regional differences and large-scale climate modes was examined using the time series of domain-average MHWCI extracted for each cluster. Consistent with the identified seasonal dominance, the winter series was analyzed for Cluster 1 and the summer series for Cluster 2.

While the clustering analysis identifies when MHWCI variability is most pronounced in each region, it does not indicate which MHW characteristics primarily contribute to the enhanced cumulative intensity. To address this, composite analysis of MHW frequency, intensity, and duration anomalies was examined during positive phases of the cluster-specific MHWCI time series (Fig. 3). In Cluster 1, enhanced winter MHWCI is associated with concurrent increases in MHW frequency, intensity, and duration (Fig. 3a–c), indicating that winter MHWs in the central and southern North Sea become more frequent, persistent, and intense. In contrast, enhanced summer MHWCI in Cluster 2 is mainly associated with increases in MHW frequency and duration, while mean intensity shows a slight reduction (Fig. 3d–f). This suggests that summer MHWs in the northern North Sea tend to be more persistent but less intense.

Based on the seasonal dominance and the contributing MHW characteristics identified above, the temporal evolution of the cluster-mean MHWCI and its relationship with large-scale climate indices is examined (Fig. 2c and d). In Cluster 1, the winter-averaged MHWCI exhibits pronounced interannual variability, with enhanced values tending to coincide with positive phases of EAP (r=0.64, 95 % confidence interval). In addition, negative phases of the NAO in the preceding October frequently precede winters with elevated MHWCI.

In Cluster 2, the summer-averaged MHWCI displays pronounced decadal modulation (Fig. 2d). During the negative AMV phase (1982–1994, blue shading in Fig. 2d), MHWCI exhibits relatively weak intensity. In contrast, during the positive AMV phase (1994–2013, red shading in Fig. 2d), MHWCI shows notable enhancement, with its interannual variability strongly correlated with both ENSO and the Interdecadal Pacific Oscillation (IPO) (r=0.69 and 0.70, respectively). However, this teleconnection substantially weakens after 2013 (Fig. S2), and the correlations are no longer statistically significant (p>0.1), indicating a substantial reduction in Pacific influence on North Sea MHWs.

These results demonstrate that MHWCI variability in the North Sea is organized into two spatially distinct regions with contrasting seasonal dominance, MHW characteristics, and temporal behaviour. Based on these differences, subsequent analyses focus on winter MHWs in Cluster 1 and summer MHWs in Cluster 2 to investigate the associated atmospheric and oceanic processes.

The winter EAP-related pathway in Cluster 1 is examined through the evolution of large-scale atmospheric circulation, surface forcing, regional circulation, stratification, and heat transport. Composite anomalies are calculated for winters when the standardized cluster-mean MHWCI exceeds +1 SD (standard deviation) (black line in Fig. 2c), providing the background physical conditions associated with enhanced winter MHWCI.

Figure 4 shows the composite anomalies of 500 hPa geopotential and WAF (Eq. 7) from October of the preceding year to January of the MHW winter. The anomalous WAF flux is shown only when its magnitude is larger than 0.1 m² s⁻² (Hou et al., 2023). In October, during enhanced MHWCI periods, the geopotential anomalies, defined relative to the long-term monthly climatology, exhibit pronounced negative anomalies over the subpolar North Atlantic, with positive anomalies observed over the subtropical and polar regions (Fig. 4a). This atmospheric configuration corresponds to a negative NAO phase, characterized by a weakened Azores High and intensified Icelandic Low. Additionally, the WAF vectors indicate relatively weak wave activity over the eastern Atlantic.

In November, the system enters a transition phase. The negative geopotential anomalies over the subpolar Atlantic intensify and extend eastward, while positive anomalies expand toward northern Europe (Fig. 4b). During this period, an eastward-propagating Rossby wave train becomes apparent, with WAF vectors indicating energy propagation from the North American sector toward the eastern North Atlantic.

By December, the wave train includes both eastward and westward-propagating components across the North Atlantic. This WAF configuration generates strong convergence over the subpolar region, significantly reinforcing the negative geopotential anomalies there. Consequently, the atmospheric transitions to a positive EAP phase. The geopotential field displays a distinct tripole structure, reflecting intensified Azores High and Icelandic Low systems, accompanied by a strengthened high-pressure system over western Europe (Fig. 4c). This configuration persists into January (Fig. 4d).

The sea surface temperature (SST) and wind stress anomalies from October to January are illustrated in Fig. 5. In October, anomalous cyclonic wind stress is observed over the central North Atlantic, accompanied by negative SST anomalies in the same region (Fig. 5a). In November, the region of SST cooling expands northward and eastward, accompanied by a weakening of cyclonic wind anomalies over the mid-latitude North Atlantic (Fig. 5b). By December and January, strengthened southwesterly wind anomalies are evident over the northeastern North Atlantic and the North Sea region (Fig. 5c and d). During these months, SST anomalies over the southern North Sea become positive, in contrast to the persistent negative SST anomalies over the subpolar Atlantic. These patterns indicate a clear spatial contrast in surface thermal patterns between the open North Atlantic and the shelf region during winters with enhanced MHWCI in Cluster 1.

Figure 6 presents composite anomalies of the net surface heat flux and its individual components averaged over the Cluster 1 region during winters with enhanced MHWCI. The net surface heat flux anomaly is negative, indicating a net loss of heat from the ocean to the atmosphere. Among the individual components, the sensible heat flux exhibits the largest negative anomalies, while latent heat flux, shortwave radiation, and longwave radiation anomalies are weaker in magnitude. The dominance of the sensible heat flux anomaly is consistent with the strengthened near-surface winds observed during these winters. The surface heat flux anomalies indicate that atmospheric forcing acts to cool the ocean surface over the Cluster 1 region during periods of enhanced MHWCI.

Figure 7 shows composite anomalies of oceanic circulation and stratification-related variables during enhanced MHWCI winters. The surface current anomalies (Fig. 7a) reveal enhanced northward and eastward flow at the southern entrance of the North Sea, indicating increased inflow from the adjacent North Atlantic. Within the southern and central North Sea, the current anomalies exhibit convergence, as reflected by the spatial arrangement of the velocity vectors. Additionally, the warm water inflow reduces cold outflow from the Baltic Sea.

In winter, the Cluster 1 region is predominantly well mixed due to strong wind forcing and shallow bathymetry, as reflected by weak climatological stratification (Fig. S4a) with low Ri (Fig. S3). Consistent with this background state, composite MLD anomalies (Fig. 7b) are negligible across most of the Cluster 1 region, with positive anomalies confined to very shallow shelf regions.

The Richardson number anomalies displayed in Fig. 7c exhibit a similar spatial structure. While Ri anomalies are weak or near zero over the well-mixed central basin, pronounced negative anomalies appear in the same shallow shelf regions where MLD shoaling is observed. This spatial correspondence indicates that changes in stratification and velocity shear are spatially collocated over shallow shelf areas during enhanced MHWCI winters.

These localized structural changes occur together with coherent atmospheric and oceanic anomalies. Enhanced Atlantic inflow provides a positive contribution to the mixed-layer heat budget, while strengthened southwesterly winds are associated with increased surface heat loss. Additionally, positive MLD anomalies are confined to very shallow shelf regions and are negligible across most of the Cluster 1 area, suggesting that changes in MLD play only a limited role in the basin-scale evolution of winter MHWs. Meanwhile, reduced Ri indicates enhanced shear relative to stratification, which modulates vertical mixing without promoting deep redistribution of heat. Consequently, heat transported by horizontal advection can be preferentially retained in the near-surface layer, favoring the development and persistence of winter MHWs despite concurrent surface heat loss.

To further assess the dynamical response associated with these coupled structural and heat transport anomalies, the corresponding overturning circulation anomalies are investigated. Figure 7d presents composite anomalies of the meridional overturning circulation (MOC) during enhanced MHWCI winters. The MOC is strengthened, with increased northward and downward transport in the southern and central North Sea, respectively. These overturning features align with regions of enhanced Atlantic inflow and current convergence. The enhanced downward transport in the central North Sea occurs within a water column that is already well mixed during winter. As a result, the intensified overturning circulation does not produce a discernible mixed-layer deepening, consistent with the absent MLD and Ri anomalies observed in the central basin. Instead, the enhanced overturning facilitates the redistribution and retention of advected heat within the water column, contributing to elevated winter temperatures and enhanced MHWCI in the central North Sea.

The relative contributions of different processes to the upper-ocean temperature tendency during winter are quantified using a mixed-layer heat budget analysis (Eq. 6, Fig. 8). The total temperature tendency is positive, indicating net warming over the winter season in Cluster 1. Among the individual terms, geostrophic heat advection provides the largest positive contribution to the temperature tendency, while the contribution from surface heat flux is negative. Ekman advection and entrainment terms are comparatively small, and the residual term contributes weakly. The relative magnitudes of the heat budget terms indicate that horizontal ocean heat transport supplies a substantial positive contribution to wintertime warming, partially offsetting the cooling effect associated with surface heat loss.

The summer MHWCI variability in Cluster 2 exhibits a distinct dependence on the background state of the AMV. As shown in Fig. 2d, the Cluster 2 MHWCI remains relatively weak during the negative AMV phase but is substantially enhanced during the positive AMV phase before 2013. During this strong positive AMV period, the summer MHWCI is strongly correlated with the IPO index. However, this relationship weakens after 2013, when the correlation with Pacific indices becomes statistically insignificant. These results suggest that the Pacific influence on summer MHW variability in the northern North Sea is not stationary but is modulated by the background state of the North Atlantic.

To examine this phase dependence, we regressed atmospheric and oceanic variables onto the IPO index during three periods: the negative AMV phase, the strong positive AMV phase before 2013, and the post-2013 positive AMV period. The large-scale atmospheric circulation and horizontal WAF are shown in Fig. 9, while the corresponding wind stress, SST, precipitation, and cloud-cover anomalies are shown in Fig. 10. This comparison allows us to assess whether the IPO-related signal is transmitted from the Pacific to the North Atlantic-European sector and whether it produces a local response over the northern North Sea.

During the strong positive AMV phase, the warm North Atlantic background may have provided favorable large-scale conditions for the development and downstream transmission of IPO-related atmospheric anomalies. Previous studies have shown that North Atlantic SST anomalies can influence tropical Pacific variability by modifying the Walker circulation and Pacific trade winds, thereby affecting Pacific-related variability on multidecadal timescales (McGregor et al., 2014; Levine et al., 2017). In addition, ENSO-related teleconnections to the North Atlantic-European sector are known to be sensitive to the SST background state and upper-level flow, which regulate Rossby-wave excitation and propagation pathways (Fernández-Castillo et al., 2025). Consistent with this background-state modulation, the IPO-related atmospheric response is well developed over the North Pacific during the strong positive AMV phase. The regression pattern of 500 hPa geopotential height exhibits a clear dipole-like structure between the subpolar and subtropical North Pacific. This circulation pattern is accompanied by enhanced WAF extending eastward from the Pacific sector toward North America and the North Atlantic (Fig. 9a), indicating that IPO-related stationary wave activity is more effectively transmitted downstream under the strong positive AMV background. The tropical Atlantic and Caribbean region also forms part of this broader Pacific-Atlantic teleconnection pattern. During the strong positive AMV phase, negative SST anomalies and reduced precipitation develop over the Caribbean Sea (Fig. 10a and b), suggesting a coherent tropical Atlantic response associated with the downstream atmospheric adjustment. In contrast, the downstream WAF propagation and the convection anomalies are much weaker during the negative AMV phase and after 2013, suggesting that the AMV background modulates the efficiency with which IPO-related atmospheric variability is transmitted from the Pacific into the Atlantic sector.

This large-scale circulation response is accompanied by a positive geopotential anomaly over the northern North Sea, where the regression patterns show reduced cloud cover within Cluster 2 (black box in Fig. 10c). Reduced cloud cover favors increased downward shortwave radiation at the sea surface and therefore enhances the surface radiative contribution to the upper-ocean heat budget. Consistently, the summer heat-budget analysis shows a positive net surface heat-flux contribution over Cluster 2 (Fig. 6), indicating that atmospheric surface forcing provides an important pathway linking the large-scale circulation response to regional MHW.

The heat-budget analysis further supports this interpretation. In contrast to the winter mechanism in Cluster 1, where geostrophic heat advection associated with enhanced Atlantic inflow provides the dominant warming contribution, the summer temperature tendency in Cluster 2 is mainly associated with surface heat flux and the RES term (Fig. 8). The contributions from geostrophic and Ekman heat advection are comparatively weak. This indicates that the summer MHW response in the northern North Sea is primarily mediated by atmospheric surface forcing rather than by horizontal oceanic heat transport.

The regional upper-ocean structure further determines how this atmospheric forcing influences MHW characteristics. During summer, the northern North Sea is characterized by a shallow MLD and strong stratification (Fig. S4b). During enhanced MHWCI summers, the mixed layer becomes shallower over much of Cluster 2 (Fig. 7f), reducing the effective heat capacity of the surface layer. Figure 7g also shows predominantly positive Ri anomalies over the same region, indicating enhanced stratification stability and a reduced susceptibility to shear-driven instabilities. The spatial co-location of MLD shoaling and increased Ri suggests that buoyancy-driven stratification strengthens sufficiently to offset any increase in velocity shear, resulting in a more stably stratified upper ocean during these summers. Together, these changes imply that radiative and surface heat flux anomalies are confined to a thin surface layer, allowing relatively short-lived atmospheric forcing anomalies to produce a pronounced near-surface thermal response. In addition to surface forcing, the regression patterns indicate a dynamical response in the regional circulation. The reduced Atlantic flow leads to weakened surface winds over the northern North Sea. These wind anomalies are accompanied by negative MOC anomalies (Fig. 7h), indicating an anomalous anticlockwise overturning circulation with enhanced upwelling over the northern North Sea.

This mechanism is consistent with the observed changes in MHW characteristics. Enhanced summer MHWCI in Cluster 2 is mainly associated with increased MHW frequency and duration, whereas mean intensity slightly decreases. The teleconnection-related radiative anomaly provides a relatively persistent but moderate surface heating tendency. However, the northern North Sea remains dynamically active in summer, and local circulation, vertical exchange, and residual processes can limit the development of strong peak warming. Therefore, the remote atmospheric forcing preferentially increases the persistence and occurrence of MHWs rather than their mean intensity (Fig. 3d–f).

After 2013, previous studies have documented an abrupt cooling in the subpolar North Atlantic (Mooney, 2015), often referred to as the development of the “cold anomaly” or “cold blob,” which coincides with a weakening of the AMV signal during the early 2010s (Moat et al., 2020; Josey and Sinha, 2022; Frajka-Williams et al., 2017). During this period, the IPO-related atmospheric and oceanic responses are much weaker. The geopotential dipole over the North Pacific is less coherent, and the WAF pattern no longer shows a clear downstream pathway from the Pacific to the North Atlantic-European sector (Fig. 9b). The Caribbean wind, precipitation, and SST anomalies are also weaker and less spatially organized, indicating a reduced tropical Atlantic response (Fig. 10d–f). As a result, the IPO-related response over the northern North Sea becomes weak and spatially less coherent.

This Pacific-Atlantic teleconnection weakens even further during the negative AMV phase. The IPO-regressed geopotential dipole in the Pacific is much less pronounced (Fig. 9c), further diminishing the dipole circulation and reducing zonal wind anomalies between these regions. The SST anomaly distribution remains inconsistent with the IPO spatial pattern, with the North American coastal warming signature nearly absent (Fig. 10g). Correspondingly, the westerly wind anomalies over the tropical Pacific are substantially more suppressed. This also suppresses the Rossby wave source, leading to a marked reduction of eastward Rossby wave energy flux into the Atlantic region (Fig. 9c). The diminished atmospheric response produces minimal impacts on North Atlantic circulation and limited modification of the North Sea (Fig. 10h and i).

Our analysis of observed SST data demonstrates how multiple climate modes interact to influence MHWs at a regional scale through seasonally distinct mechanisms. Different from previous studies that mainly applied clustering analysis to group heatwaves based on common characteristics (Chauhan et al., 2023; Artana et al., 2024), location (Hansen et al., 2024), and underlying dynamic drivers (Vogt et al., 2022), this study employed a correlation-based k-means clustering approach to further explore their spatial and temporal coherence. Our analysis identified two distinct regions in the North Sea, a southern shallow region and a northern deep region, each dominated by different climate variations and seasonal dynamics. Similar north–south spatial contrasts in MHW-induced stratification associated with water depth have also been reported in the North Sea (Chen et al., 2022).

In the central-southern shallow North Sea (Cluster 1), enhanced MHWCI is closely linked to positive winter EAP conditions, typically following a negative late-autumn NAO. Previous studies have shown that MHW frequency in the southern North Sea increases during positive phases of either NAO or EAP (Mohamed et al., 2023). Similar NAO-related influences have also been reported in the adjacent Baltic Sea (Gröger et al., 2024). Our results refine this understanding by identifying the positive winter EAP as the primary driver, enhancing not only the frequency but also the intensity and duration.

Recent research also indicates that AMV plays a more important role than the NAO in influencing the frequency of summer MHWs in the southern North Sea (Mohamed et al., 2023). However, its role in the northern North Sea has received little attention. Our results show that in Cluster 2, representing the deeper northern North Sea, the enhanced MHW frequency and duration in summer is linked to the synergistic influence of the AMV and Pacific climate modes. These teleconnections propagated from the Pacific to the North Sea through Rossby wave energy propagation, which is consistent with studies emphasizing the role of Pacific teleconnections in shaping the North Atlantic atmospheric pattern (Hou et al., 2023).

The detrended results show that Cluster 2 exhibits increased MHW frequency and duration, accompanied by a slight decrease in intensity during positive MHWCI periods. This pattern suggests that the summer response in the northern North Sea cannot be attributed solely to the long-term warming trend. This result is consistent with basin-wide observations from 1993 to 2022, which show a declining trend of MHW intensity but increasing frequency and duration (Chen and Staneva, 2024). Such a change is attributed to large-scale atmospheric circulation changes and regional oceanic processes rather than global warming. The reduction in intensity has been proposed to be related to the weakening of the North Atlantic Jet Stream and more frequent atmospheric blocking events (Woollings et al., 2018), which promote stagnant atmospheric conditions and persistent but less intense warm anomalies over the North Sea, while freshwater-salt exchange, stratification changes, and Baltic Sea inflow also modulate regional SST responses (Mathis and Pohlmann, 2014). As an additional possible mechanism, the interannual-decadal variability linked to the AMV and Pacific teleconnections could modulate the summer North Atlantic atmospheric pattern, which then changes MHW intensity in the northern North Sea.

Current MHW forecast systems exhibit the highest skill in the El Niño region, the Caribbean, the wider tropics, the north-eastern extra-tropical Pacific, and southwest of the extra-tropical basins. However, the skill is much lower in the North Sea, whatever the forecast range (de Boisséson and Balmaseda, 2024; Jacox et al., 2022). This is likely due to the impact of unresolved atmospheric variability, limited representation of teleconnections and climate modes (Ardilouze et al., 2017; Patterson et al., 2022). Since climate indices serve as important forecasting factors influencing these events (Jacox et al., 2022; Mi et al., 2025), incorporating synergistic climate interactions into forecasting frameworks could enhance predictive skill for MHWs.

Similar teleconnection mechanisms have been documented in other shelf seas and marginal seas, including the Baltic Sea (Gröger et al., 2024) and South China Sea (Deng et al., 2022). For instance, the Indian Ocean Basin-Wide index has been identified as a key predictor of long-term MHWs occurrence in the South China Sea (Mi et al., 2025), while including ENSO-related variability in the tropical Pacific may extend the duration of skilful forecasts of atmospheric patterns over the North Atlantic (Shackelford et al., 2025). Our results reveal clear regional and seasonal contrasts in how large-scale climate variations influence MHW variability across the North Sea. These contrasts highlight that MHW predictability in shelf seas depends on the timing, location, and combined effects of multiple climate drivers rather than their individual strengths alone. Realistic simulation of these spatially and seasonally varying relationships in forecast systems would improve the ability to predict when and where MHWs are most likely to occur.