We employed the same set of ensemble climate simulations as described in , using the upper-atmosphere configuration of the ICON general circulation model (UA-ICON; ). UA-ICON is a high-top model that extends well above the stratopause and features fine vertical resolution, meeting the requirements for realistically simulating SPV behavior . The model has been shown to realistically represent stratospheric dynamics and key aspects of wave-driven troposphere–stratosphere coupling . The simulations were performed with the R2B4 grid (approximately 160 km horizontal resolution), 120 vertical levels extending up to 150 km, and were driven by annually repeating present-day (1979–2022) climatological boundary conditions. The simulations were initialized with the mean atmospheric state on 1 January, derived from the 1979–2022 ERA5 climatology, representing the present-day climatological mean.

To investigate the impact of regionally intensified orographic GW forcing, we conducted a control simulation (C) and three sensitivity experiments. The control run used the default model configuration. In the sensitivity experiments, the GW drag produced by the SSO scheme was enhanced by a factor of 10 in three GW hotspot regions – the Himalayas (HI), Northwest America (NA), and East Asia (EA) – while the low-level component of the SSO drag, associated with flow blocking and wake effects, remained unchanged. The forced regions are defined as follows: EA spans 30–60° N and 110–175° E; NA spans 30–60° N and 100–130° W; and HI spans 25–45° N and 70–100° E. Each experiment, including the control run, comprises a six-member ensemble of 30-year simulations under identical boundary conditions. The ensemble members were generated by perturbing the initial conditions. A concise summary of the exerted SSO zonal drag across hotspots is provided in Appendix  (Figs.  and ). For full details on the model configuration, ensemble design, and GW forcing strategy, see and the accompanying publicly available datasets (see Code and data availability section).

In this study, we analyzed daily model output for the extended boreal winter season (November through March, NDJFM), focusing exclusively on the Northern Hemisphere, considering data poleward of 0° latitude. Daily values were computed as the average across all model time steps within each simulation day. The first year of each simulation was considered as the model spin-up time and was therefore excluded from the analysis.

To characterize the stratospheric polar vortex, we used the geopotential height (GPH) field at the 10 hPa level. These GPH fields were interpolated onto a Lambert azimuthal equal-area projection centered on the North Pole , using a horizontal grid spacing of 1.5°, which closely matches the native resolution of the model. We also used temperature and horizontal wind fields to derive zonal-mean quantities and Eliassen–Palm (EP) flux and its divergence .

The morphology of the SPV encodes much of its dynamical state and mediates where and how PWs and GWs interact with it. Prior work has mainly followed two approaches for evaluating the SPV morphology. One uses geometric feature extraction to summarize the vortex with a few diagnostics, such as centroid latitude, aspect ratio, or equivalent area, thereby enabling split/displacement identification and basic morphology tracking . These diagnostics are transparent but necessarily coarse, and they cannot capture higher-order shape attributes such as skewness, curvature variations, or non-elliptical deformations. The other approach applies field-based clustering on wind or other dynamical fields, providing a holistic view of the flow structure . However, such gridpoint-wise similarity measures are typically blind to the spatial relationships among grid points and are sensitive to small translations and rotations of the vortex, so two vortices with nearly identical shapes but slightly different positions may appear far apart in feature space.

Here, we combine the strengths of both approaches by classifying the geometry of the SPV boundary using a representation based on Fourier descriptors. This representation encodes the boundary as a compact, physically interpretable set of coefficients. Low-order harmonics quantify global shape properties, such as circularity, elongation, and orientation, while higher orders capture finer deformations. By retaining only the leading modes, we emphasize large-scale morphology and suppress small-scale variability, yielding a low-dimensional yet expressive feature space. In this space, vortices with similar geometries (even under modest displacement or rotation) tend to cluster together, enabling a stable and physically meaningful morphology-based classification that is less sensitive to spatial shifts than gridpoint-wise approaches, yet far richer than scalar shape metrics.

We then analyzed the impact of regional GW hotspots on the SPV geometry. The workflow proceeds in three steps. First, we extracted daily SPV boundaries from 10 hPa geopotential height fields. Second, we constructed a compressed geometric feature space by computing the complex boundary signal and its Fourier descriptors, retaining only the leading modes. Third, we performed unsupervised hierarchical clustering (Ward linkage) on these descriptors to obtain discrete SPV geometry classes. In the following subsections, we provide a detailed explanation of each step in this process.

Class contribution quantifies the influence of different clusters – here, clusters of SPV – on anomalies in climatic parameters . The sum of class contributions across all clusters in a sensitivity simulation yields the total anomaly of a given parameter. Each cluster's class contribution consists of two main components: Within-Cluster Variability Contribution (WCVC) and Frequency-Weighted Seasonal Deviation Contribution (FSDC). The WCVC represents how changes in the mean spatial characteristics of a cluster, such as minor shifts in its geometry or location, contribute to anomalies under the applied forcing in a sensitivity simulation. In contrast, the FSDC captures how variations in the occurrence frequency of a cluster influence the overall anomaly. Together, these components help differentiate whether observed anomalies arise from internal structural changes within a cluster (WCVC) or shifts in its prevalence (FSDC) in response to external forcing. A detailed methodological formulation is provided in .

Figure a shows the climatology of GPH at 10 hPa from the control run, along with the reconstructed SPV boundary based on the mean feature space of the control simulation. The climatological SPV exhibits an elliptical shape, with its center displaced toward northern Eurasia, consistent with previous findings based on reanalysis data . Figure b–d illustrate the GPH anomalies at 10 hPa for the HI, NA, and EA sensitivity experiments, respectively, relative to the control run. The dotted regions indicate where the ensemble mean differences are consistent in sign across at least five out of six ensemble members, which we refer to as the consistency criterion throughout the manuscript. All sensitivity experiments show a displacement of the SPV toward North America, although the magnitude of this shift varies among the experiments. The HI experiment exhibits the most pronounced and consistent shift. A similar pattern is evident in the potential vorticity (PV) anomalies on the 850 K isentropic surface, as shown in Fig. .

Figure  presents the climatological structures and anomalies of PW1 (top row) and PW2 (bottom row) based on 10 hPa GPH fields. Cyan contours in panels (a)–(c) and (e)–(g) represent the climatological PW1 and PW2 patterns from the control run. PW1 is characterized by a high-pressure ridge over the North Pacific and North America and a corresponding low-pressure trough over Eurasia and the North Atlantic, whereas PW2 shows two ridge centers over the Alaska–Chukchi Sea region and Northern Europe/Scandinavia .

In all sensitivity experiments, the imposed forcings act against the climatological PW1 pattern (Fig. a–c), resulting in a reduction of PW1 amplitude across mid- to high latitudes in the Northern Hemisphere (panel d). This amplitude reduction is strongest in the HI experiment and is consistent across most mid- to high latitudes in both the HI and EA experiments. In contrast, the NA experiment shows consistent amplitude reduction only near the latitudinal edge of the forcing region. Additionally, all experiments induce an eastward (positive) phase shift in PW1, which is consistent at high latitudes in the HI and NA experiments, and at lower latitudes in the HI and EA experiments.

For PW2 (Fig. e–h), the dominant response is again a reduction in amplitude. This reduction is strongest and most spatially consistent in the EA experiment, while in NA it is only partially consistent in the southern portion of the forcing latitudinal range. The HI experiment shows consistent amplitude reductions at low and mid-latitudes, but consistent increases at higher latitudes. Across all experiments, a westward phase shift is observed at lower latitudes (consistent in HI and NA), while an eastward and more consistent shift occurs at higher latitudes.

A reference climatology of the zonal-mean zonal wind and EP flux divergence is provided in Appendix  (see Fig. ). Figure  shows anomalies in the zonal-mean zonal wind (panels a–c) and EP flux divergence (panels d–f) for each sensitivity experiment, relative to the Control run. All sensitivity experiments exhibit a deceleration of the stratospheric westerlies associated with the imposed forcing (see Fig. ), extending poleward from the forcing regions (panels a–c). This is accompanied by a general positive EP flux divergence anomaly in the stratosphere (panels d–f), meaning the divergence is reduced relative to the control run, which indicates weaker wave drag . The decomposition of the EP flux divergence anomalies into leading zonal planetary wave modes revealed that the resolved response is dominated by PW1 .

In the HI experiment (Fig. a and d), westerlies increase consistently throughout the stratosphere at high latitudes, while EP flux divergence anomalies are consistently positive across the midlatitudes and in the high-latitude upper stratosphere, indicating a reduction in wave drag. In contrast, consistent negative EP flux divergence anomalies are observed in the lower to mid stratosphere at high latitudes, implying enhanced wave drag. In the NA experiment (panels b and e), zonal-mean zonal winds exhibit a consistent reduction of the westerlies across the midlatitudes, accompanied by the corresponding consistent positive EP flux divergence anomalies in the same region. In the EA experiment (panels c and f), westerlies increase consistently equatorward of around 40° N but show a consistent decrease north of around 45° N. EP flux divergence anomalies are consistently positive in both mid- and high-latitude regions, with weak but consistent negative anomalies in the lower stratosphere. We note that in all experiments, the zonal wind decrease related to and poleward of the GW forcing region is accompanied by a decreasing westward PW forcing, which is outweighed by the GW mean wind forcing .

Figure  displays the resulting GPH class centres, derived from all the control and sensitivity experiments, with red contours overlaid (C2–C10) showing SPV boundaries that were reconstructed from the mean feature vector of each cluster. These reconstructed boundaries closely follow the mean 10 hPa GPH field for their respective clusters, underscoring the physical consistency of the classification.

Class C1 corresponds to an unstable or dissipated vortex, characterized by elevated GPH values near the pole. C2 depicts a centered, deep vortex with slightly elevated GPH over the Pacific sector. C3 shows a moderately displaced vortex shifted toward Eurasia, stretched across the north Eurasia coasts with elevated GPH over North-Western America. C4 represents a highly displaced vortex associated with displaced SSW events, primarily shifted toward the Eurasian continent. The dendrogram in Fig.  reveals that C2, C3, and C4 are in the same branch, which reflects their similar structural characteristics and the evolution of high-GPH regions from the Pacific in C2 to North America and the central Arctic in C3 and C4 that are closely related in the dendrogram.

C5 shows a deep vortex cluster that stretches from North America to the north of Eurasia. C6 also illustrates a deep vortex cluster that extends across the north Eurasian coasts with a more circular shape. C7 and C8 are split-vortex cases, with the dominant lobe over Eurasia and a smaller one over North America; these two are also closely linked in the dendrogram. In C9, the North American lobe is dominant and extends over the Atlantic, while in C10, both lobes are of comparable size. These latter two classes also form a distinct branch in the dendrogram. Overall, the correspondence between the class centres and the hierarchical dendrogram confirms the robustness of the shape-based SPV classification. A detailed overview of the corresponding climatological PW1 and PW2 amplitudes for each SPV class is presented in Appendix  (see Fig. ).

Figure  presents the extended winter occurrence frequencies, calculated as the percentage of days each cluster occurs relative to the total days in the period across all ensembles, of SPV clusters C1–C10 (as shown in Fig. ) in the control run on top of each panel, along with the occurrence differences in the three sensitivity experiments (EA–C, NA–C, HI–C) as color bars. The occurrence frequencies are computed using all ensemble members, with standard deviations calculated across the respective six ensembles. For the control run, these standard deviations are reported as ± values, while in the sensitivity experiments, they are shown as error bars on the bars representing mean differences. Hatching indicates that the sign of the anomaly is consistent across at least five out of six ensemble members.

Among the clusters, C2 has the highest mean occurrence in the control run (35.12 % ± 0.91 %), followed by C6 (30.21 % ± 2.10 %), C3 (22.04 % ± 1.80 %), and C5 (9.39 % ± 1.41 %). While the absolute frequencies vary under different experiments, these four clusters remain the most frequent across all experiments. Among the less frequent clusters, C4 represents displaced SSW states, whereas C7-C10 correspond to split SSWs. C1, in contrast, does not exhibit a well-defined vortex structure and represents unstable vortex configurations.

The HI experiment shows a consistent increase in the frequency of C1, C2, and C5, and a consistent decrease in C6 and C9. NA shows consistent increases in C1, C4, C5, and C8. The EA experiment shows consistent increases in C2, C4, C5, and C8, and consistent decreases in C6 and C9. Cluster C3 exhibits a mean decrease in all experiments but does not show ensemble consistency in any case.

Figure  shows the contributions of individual SPV clusters to the 10 hPa GPH anomaly in the HI experiment (see Fig. b). Each cluster contributes through WCVC (changes in mean structure) and FSDC (changes in occurrence frequency). The clusters do not contribute equally; their impacts vary in spatial pattern, magnitude, and consistency. Dominant contributions come from frequent clusters C2, C3, C5, and C6. The WCVC of C6 deepens the vortex over the central Arctic (panel C6a), indicating that when C6 occurs in the HI experiment, it consistently exhibits a stronger vortex than in the control run. In contrast, the FSDC of C5 weakens the PW1 structure (panel C5b), reflecting the impact of its consistently increased frequency in HI (see Fig. ). The WCVC components of C2 and C3 contribute with patterns opposing the PW1 climatology, thereby reducing PW1 amplitude (panels C2a and C3a); C2, in particular, consistently lowers GPH over the Pacific sector. Other clusters play smaller roles, for example, the reduced frequency of C9 yields modest but consistent negative GPH anomalies at high latitudes via its FSDC component (panel C9b).

Figure  shows the class contributions to the zonal-mean zonal wind anomaly, as shown in Fig. a. The WCVC components of C2, C3, C5, and C6 weaken the midlatitude westerlies from the upper troposphere into the middle stratosphere, reflecting direct forcing effects. C6 primarily strengthens the high-latitude westerlies through its WCVC component (panel C6a). The increased frequency of C5 and the decreased frequency of C9 (see Fig. ) lead to modest but consistent high-latitude westerly enhancements via their FSDC components (panels C5b and C9b). C3’s FSDC also contributes to upper-stratospheric westerly enhancement, though inconsistently, reflecting the similarly inconsistent reduction in its occurrence change. The WCVC components of C2 and C3 resemble the overall HI wind anomaly pattern.

Figure  shows the class contributions to EP flux divergence anomalies, as presented in Fig. d. The WCVC component of C2 produces positive anomalies in the midlatitude middle and upper stratosphere, indicating reduced wave drag (panel C2a). C3 and C6 contribute modestly to similar positive anomalies through their WCVC components, while also enhancing wave drag in the high-latitude lower and middle stratosphere (panels C3a and C6a). The increased frequency of C5 (see Fig. ) yields a consistent positive contribution in the high-latitude upper stratosphere via its FSDC component (panel C5b). C3's FSDC also contributes positively in this region, although inconsistently across ensemble members.

Figure  shows the class contributions to the 10 hPa GPH anomaly in the NA experiment (see Fig. c). In general, both the class contributions and the resulting anomaly patterns are less consistent than in the HI and EA (see below) experiments. The consistent increase in the frequency of C5 in the NA experiment (see Fig. ) results in a consistent contribution through its FSDC component, which resembles a weakening of the climatological PW1 structure (panel C5b). The WCVC of C2 consistently lowers GPH over the Pacific sector (panel C2a) but also produces an inconsistent positive anomaly over the Arctic. C6 contributes a consistent positive anomaly over northeastern Asia through its WCVC component (panel C6a). C4 and C8, whose frequencies increase consistently in the NA experiment, provide modest but consistent positive contributions over the Arctic via their FSDC components (panels C4b and C8b).

Figure  shows the class contributions to the zonal-mean zonal wind anomaly in the NA experiment (see Fig. b). The direct weakening effects of zonal-mean zonal wind westerlies associated with the imposed forcing are evident in the WCVC components of C2, C3, C5, and C6. The increased frequency of C5 (see Fig. ) produces a consistent strengthening of the high-latitude upper-stratospheric westerlies via its FSDC component (panel C5b). Similarly, the increased frequencies of C4 and C8 yield a modest but consistent weakening of the high-latitude stratospheric westerlies through their FSDC components (panels C4b and C8b). The WCVC of C2 produces a strong but largely inconsistent weakening across the mid- and high-latitude stratosphere (panel C2a), while C6’s WCVC strengthens the upper-stratospheric flow at high latitudes, also inconsistently (panel C6a).

Figure  shows the class contributions to the EP flux divergence anomaly in the NA experiment (see Fig. e). The increased frequencies of C4, C5, and C8 (see Fig. ) provide modest but consistent positive contributions in the high-latitude upper stratosphere via their FSDC components (panels C4b, C5b, and C8b). The WCVC component of C2 contributes consistently to positive EP flux divergence anomalies from the high-latitude lower stratosphere into the midlatitude upper stratosphere (panel C2a). Contributions from the other clusters are generally not consistent across ensemble members.

Figure  shows the class contributions to the 10 hPa GPH anomaly in the EA experiment (see Fig. d). Overall, the cluster contributions in EA are similar to those in NA, but they are more consistent across ensemble members. The increased frequency of C5 in the EA experiment (see Fig. ) produces an FSDC contribution that weakens the climatological PW1 pattern (panel C5b). The reduced frequency of C6 yields a wave-1-like response that is slightly shifted relative to the climatology (panel C6b). The increased occurrence of C4 and C8, clusters associated with SSWs, leads to consistent positive GPH anomalies at high latitudes through their FSDC components (panels C4b and C8b). The decreased frequency of C9 and increased frequency of C2 both contribute to a moderate but consistent negative high-latitude GPH anomaly (panels C9b and C2b). The WCVC components of C2, C3, C5, and C6 also contribute notably. C2 exhibits a dipole pattern, with a negative anomaly over the Pacific sector and a positive anomaly at high latitudes (panel C2a). C3 shows a moderate weakening of the PW1 structure (panel C3a). C6 is mostly negative overall, with a localized positive anomaly over northeastern Asia (panel C6a).

Figure  shows the class contributions to the zonal-mean zonal wind anomaly in the EA experiment (see Fig. c). The WCVC component of C2 is the primary and most consistent contributor, weakening the high-latitude westerlies and strengthening the midlatitude westerlies (panel C2a). C5 and C6 show similar patterns through their WCVC components, but with more moderate amplitude and less consistency (panels C5a and C6a). The increased occurrence of C4 and C8 in EA (see Fig. ) leads to a modest but consistent weakening of the high-latitude westerlies via their FSDC components (panels C4b and C8b). By contrast, the increased occurrence of C2 and C5, together with the decreased occurrence of C9, enhances the high-latitude westerlies through their FSDC components (panels C2b, C5b, and C9b), partially compensating the net high-latitude weakening seen in the total anomaly.

Figure  shows the class contributions to the EP flux divergence anomaly in the EA experiment (see Fig. f). The increased occurrence frequencies of C2, C4, C5, and C8 in EA (see Fig. ) produce modest but consistent positive anomalies in the high-latitude upper stratosphere via their FSDC components (panels C2b, C4b, C5b, and C8b), whereas the decreased occurrence of C9 contributes a modest negative anomaly through FSDC (panel C9b). The WCVC component of C5 is the primary contributor to the positive EP flux divergence anomalies in the high-latitude upper stratosphere (panel C5a). In addition, the WCVC components of C6, C3, and C2, listed in order of decreasing strength, also contribute consistently to positive anomalies in the middle and upper stratosphere (panels C6a, C3a, and C2a).

This study provides new insights into the response of the SPV to GW forcing in Northern Hemisphere stratospheric hotspots using a novel shape-based clustering approach. The SPV does not respond in a zonally symmetric manner to localized GW forcing in the defined hotspot regions. Across all experiments, regardless of the specific hotspot location, the response consistently features a PW1-like displacement of the vortex core (Fig. ). This involves a more irregular, ragged edge over northern Eurasia, although the detailed anomaly pattern remains distinct for each case. The dominant dynamical feature underlying these anomalies is the consistent reduction in the amplitude of PW1 across all experiments. This is also evident in the EP flux divergence anomalies (Fig. ), which show positive EP flux divergence anomalies associated with the PW1 structure in the midlatitude stratosphere .

Our results differ in some aspects for the hotspot regions compared with and . They analyse short-timescale event composites of strong SSO GW drag peaks in a specified-dynamics Canadian Middle Atmosphere Model (CMAM) framework in the lower stratosphere. By contrast, we impose localized enhancements of SSO drag in a free-running UA-ICON ensemble and evaluate NDJFM season-mean responses across 180 simulated years. In this climate-mean framework, the time-integrated effect of many intermittent events, together with the background-state adjustments induced by the forcing, yields a hemispheric reduction of PW1 amplitude and weaker resolved wave drag. Differences thus arise from (i) timescale and averaging (event composites vs. season-mean) and (ii) model configuration and the associated background-state evolution.

These anomalies manifest as negative GPH anomalies within the forced region and positive anomalies northward of it (Fig. ). A plausible explanation is that enhanced GW drag near the forced region disrupts the SPV edge through increased small-scale wave breaking and secondary instabilities, thereby promoting geometry-specific PV redistribution rather than a uniform vortex response . This mixing across the vortex boundary locally blurs the typically sharp SPV edge, resulting in the observed pattern of anomalies. Specifically, positive GPH anomalies at the SPV periphery often indicate incursions of low-PV, warm high-pressure ridges, while negative anomalies reflect high-PV polar air being displaced equatorward, forming cold low-pressure troughs (Fig. ). Such patterns are characteristic of surf zone wave activity impinging on the SPV . The HI experiment, which represents the southernmost hotspot region, shows the strongest response, with the positive anomaly band north of the forcing extending only to the northern Eurasian coastline. The latitudinal position of the positive anomaly band in the HI experiment, located well south of the vortex edge over northern Eurasia, effectively sharpens the vortex edge in that sector and further deepens the polar vortex core toward higher latitudes.

Examining the forcing effect on the occurrence frequency of the preferred SPV geometry clusters (as detailed in Sect. ; see also Fig. ) reveals a consistent increase in the occurrence of C5 across all experiments (Fig. ). Among the single vortex clusters (C2–C6), C5 has the weakest PW1 amplitude except for C4, which represents displaced SSW events (Fig. , left panel). The PW1 amplitude associated with C5 remains well below the climatological mean, suggesting that its increased occurrence frequency contributes to or favors the reduction in PW1 amplitude observed across all three experiments. This effect is clearly evident in the FSDC components of C5’s contributions to the 10 hPa GPH anomalies, which exhibit a pattern opposite to the PW1 climatology (panel C5b in Figs. , , and ). A similar signal is apparent in the EP flux divergence anomalies, with positive anomalies consistent with a weakened PW1 structure (panel C5b in Figs. , , and ) . Although the amplitude of this contribution varies among experiments, it remains a consistent feature. However, it does not represent the dominant driver of the anomalies in any individual case.

C5 is the only cluster that shows a consistent and similar sign change in occurrence frequency across all experiments. There were other clusters where the occurrence frequency change is only consistent in one or two experiments, such as C4 and C8, displaying consistent increases in occurrence frequency only in the EA and NA experiments. These clusters are associated with SSW events, and their increased occurrence contributes to the anomalies by weakening the SPV (see panels C4b and C8b in Figs.  and  for EA, as well as Figs.  and  for NA). However, because these clusters have relatively low occurrence frequencies in the climatology, their contributions, though consistent, remains comparatively weak. The robust increased occurrence of these SSW clusters in the EA experiment is consistent with the higher number of SSW events per decade diagnosed for this case .

The WCVC component of the class contribution quantifies how the forcing influences the general structure and geometry of a given cluster, but these structural changes are typically small enough that they do not lead to reassignment to a different cluster . The WCVC contribution is generally stronger in the most frequent clusters (C2, C3, C5, and C6) and often represents the dominant pathway shaping the observed anomalies. However, these structural responses do not always occur consistently across ensemble members, underscoring the role of internal variability, a feature particularly evident in the NA experiment. When consistent, however, the WCVC patterns can be useful for revealing the underlying mechanisms and physically meaningful signals by which localized forcing modifies the SPV.

The consistently increased frequency of C5 across all experiments is not the only factor associated with the reduction in PW1 amplitude observed in all the sensitivity experiments. The WCVC components of the most frequent clusters, such as C2 and C3, also generally exhibit patterns opposing the PW1 climatology, indicating that the forcing tends to modify the prevailing clusters toward configurations with weaker PW1 amplitudes. For example, in the HI experiment, the WCVC component of C3 contributes with a PW1-like pattern; together with C2, these two clusters, both characterized by strong PW1 amplitudes (left panel of Fig. ), contribute to the anomaly with a pattern opposite to the PW1 climatology. This suggests that the forcing acts to weaken the PW1 amplitude even in clusters that typically exhibit strong PW1 activity.

The WCVC components of C2, C3, and C6 consistently generate positive GPH anomalies north of the forced region and negative anomalies within it. This pattern aligns zonally along the SPV boundaries, which correspond to the GPH isolines representing each cluster’s mean circulation, highlighting how the forcing interacts with the geometry of the SPV. The resulting positive anomaly patches reflect localized SPV edge mixing driven by the forcing and tend to follow the mean circulation (i.e., along the geostrophic wind direction implied by the mean GPH isolines) associated with each cluster, consistent with edge-focused wave breaking and secondary instabilities acting along the vortex boundary . Notably, for C6, this interaction strengthens the SPV edge by producing a narrow band of higher GPH north of the forced region. This demonstrates how the relative position and geometry of the SPV relative to the hotspot can determine whether the hotspot forcing leads to mixing and weakening or, conversely, to intensification of the vortex structure, indicating a shape-related, geometry-dependent stratospheric adjustment.

The deceleration of the zonal-mean zonal wind near the forcing region in HI is evident in the WCVC components of the most frequent clusters (Fig. ), indicating the direct and consistent role of the imposed forcing in shaping these contributions. The WCVC component of C6 emerges as the main contributor to the zonal wind acceleration over the polar regions, consistent with its role in deepening the SPV core. Comparing the class contribution to the EP flux divergence (Fig. ) and zonal-mean zonal wind reveals that they do not always align straightforwardly across clusters. For example, in the midlatitude lower and mid-stratosphere, the deceleration of the mean flow is not accompanied by corresponding negative anomalies in EP flux divergence as would typically be expected. This discrepancy suggests that other momentum sources, such as GW drag imposed in the experiment , play a dominant role in this region (see Fig. ). Similar inconsistencies are apparent in the C6 WCVC component, where positive anomalies in EP flux divergence do not coincide with stronger westerlies (see panel C6a in Figs.  and ). Overall, such differences arise because the class contribution framework captures the simultaneous response but does not account for the delayed adjustments that are typical of wave–mean flow interactions.

For the NA experiment, the most consistent contributions arise from the FSDC components of clusters C4, C5, and C8, which reflect the consistent increase in their occurrence frequencies. In contrast, other class contributions, while locally strong, tend to be less consistent. The WCVC components of C2, C3, and C6, for example, display localized patches of positive GPH anomalies in a higher-latitude band north of the forced region, extending along the SPV boundary in a manner similar to the HI experiment (Fig. ), but with only partial consistency. Notably, the WCVC contribution of C2 is particularly strong and extends into the polar region, but it is consistent only in a relatively small area northeast of North America. This pattern is linked to the C2 WCVC’s associated deceleration of the zonal-mean zonal wind in the mid- and high-latitude stratosphere (panel C2a in Fig. ), which also shows patchy consistency, especially at higher latitudes. Overall, this highlights how internal variability in the NA experiment tends to obscure clear, spatially coherent responses to the imposed forcing, in contrast to the more robust signals evident in the HI experiment.

In the EA experiment, the class contributions are generally similar to those in the NA experiment but exhibit more spatially consistent signals. This similarity likely stems from the more northward placement of the NA and EA hotspots compared to the HI hotspot, which might influence the location and magnitude of the SPV response. The greater consistency observed in the EA experiment compared to NA can also be related to the relative phase alignment of the hotspot region with the stationary PW1 pattern . Across all experiments, a common feature is the presence of a positive GPH anomaly north of the forced region, indicative of PV mixing along the SPV edge. Notably, the responses in NA and EA, the two more poleward hotspots, show deeper intrusions of this anomaly into the polar vortex core compared to the HI experiment.

Like in any sensitivity study, the results may be influenced by inherent biases in the underlying model. In this study, UA-ICON, in its default configuration, exhibits a SSO-induced GW drag maximum in the mid-latitude lower stratosphere (see Fig. ), corresponding to the so-called valve layer . This maximum occurs slightly lower than the multi-model mean in the Coupled Model Intercomparison Project Phase 6 (CMIP6) Atmospheric Model Intercomparison Project (AMIP) simulations . A lower placement of this SSO-induced drag peak may influence the interaction between parameterized and resolved waves and, consequently, aspects of the simulated stratospheric dynamics. A quantitative assessment of the sensitivity of these interactions to the vertical placement of the valve-layer maximum would require dedicated experiments, which lie beyond the scope of this work.

Overall, localized GW drag exerts a decisive yet geometry-sensitive influence on SPV variability. The shape-based clustering and class contribution framework developed in this study help reveal robust and spatially coherent responses to localized forcing that might otherwise be obscured by internal variability within the full ensemble. While the current analysis is limited to present-day climatological conditions, extending this morphology-based approach to transient climate scenarios and observational reanalyses would further test its utility. Such applications could improve our understanding of the mechanisms governing SPV variability and offer new opportunities for enhancing subseasonal prediction.