The numerical simulations for this study were performed using the Regional Ocean Model System (ROMS), version 3.5 , with the same configuration as the operational NorKyst-800 model along the Norwegian mainland coast that was developed in a collaboration between the Norwegian Meteorological Institute (MET Norway) and the Institute of Marine Research (IMR) . In particular, the model utilizes a bathymetry-following vertical coordinate system with 35 levels, and it was set up with a horizontal resolution of 500 m, covering the entire Svalbard region (see Fig. a). Lateral boundary conditions and tidal forcing were provided by MET Norway's operational ocean forecasting model Barents2.5 , while atmospheric forcing was obtained from MET Norway's operational AROME-Arctic numerical weather prediction model, which has a horizontal resolution of 2.5 km . The ROMS setup also incorporated daily freshwater runoff based on simulations with the CryoGrid land surface model, forced in turn by AROME-Arctic . A simple sea ice component, following , was included to account for sea ice effects. The total simulation covers the period from April 2019 to October 2024, but only the three winter (November–April) seasons in 2019–2020, 2020–2021, and 2021–2022 are considered in the present analysis, as changes in MET Norway's operational Barents2.5 forecasting system during winter 2022–2023 led to discontinuities in the hydrographic boundary conditions. Raw model output consisting of hourly hydrography and current fields was averaged to a daily resolution. A brief validation of the simulated hydrography and currents against conductivity–temperature–depth (CTD), acoustic Doppler current profiler (ADCP), and oceanographic mooring observations from the University Centre in Svalbard (UNIS) long-term ocean monitoring program is provided in Appendix . The validation shows a good agreement between the model simulations and the observed density and current structures, accurately capturing key circulation features on the West Spitsbergen Shelf. Despite some temperature and salinity biases – such as overly cold and fresh surface waters and slightly too fresh Atlantic Water – these errors largely cancel each other in density. In particular, the model realistically reproduces current variability and topographic steering on the WSS.

In a first post-processing step, the ROMS model output was horizontally re-gridded from its native curvilinear grid to a latitude–longitude coordinate system with a meridional resolution of 0.01° and a zonal resolution of 0.04°, both corresponding to approximately 1 km. The re-gridding process also ensured the proper rotation of the current components from the model grid to zonal and meridional directions. In the vertical dimension, the model output, originally defined in bathymetry-following sigma levels, was interpolated onto a regular depth grid with 10 m equidistant spacing. For the main analysis of this study, we concentrate on the WSS between Bellsund in the south and the Isfjorden Trough in the north (see the map in Fig. b). Data from 15 zonal cross-shelf sections spanning across the WSS break and slope between 77.35 and 78.05° N were extracted from the data set (see Fig. b). A local coordinate system was defined in such a way that each section is centered with x= 0 km at the shelf break, which was manually identified as the point of maximum curvature in the bathymetry (corresponding depths ranging between 240 and 450 m), and extends 30 km in each direction. The southern sections were limited to xmax < 30 km eastward to avoid influences from deeper waters in the trough that leads to Bellsund. In the following, the positive x range is referred to as the “shelf” or the WSS, while negative x values correspond to the “slope”. As the angle between the WSS break and true north is small (see Fig. b), the difference between the northward current component and the actual along-slope current speed of the WSC is small. Therefore, we choose not to define individual local coordinate systems aligned with the shelf break at each individual latitude, which substantially simplifies the analysis of the meridional propagation of warming events presented in Sect. . We also limit the study period to the winter months, spanning from 1 November through April. During this time, the impact of AW warming events on the WSS is greatest, e.g., in the context of local sea ice formation.

A brief spectral analysis (not shown) revealed that the fortnightly tide was the only remaining tidal constituent present in the daily averaged data, and this was subsequently removed using a harmonic analysis. From the potential temperature and practical salinity fields of the model, conservative temperature, absolute salinity, in situ density, potential density anomaly referenced to 0 dbar, and heat content with a reference temperature of 0 °C were calculated using the Gibbs Sea Water (GSW) TEOS-10 standard .

With a temporal resolution of 1 d, the ROMS model data time series constitute variability over a wide frequency range, from short-term inertial oscillations to the annual cycle. Because the major warming events of interest in this study occur over characteristic timescales of several days to weeks (see Sect. ), it is necessary to separate the corresponding low-frequency variability from higher-frequency fluctuations, particularly those caused by transient eddies and internal waves. To achieve this, we applied a fourth-order Butterworth low-pass filter with a cutoff frequency of 20 d to the ROMS hydrographic and current time series. Due to its flat frequency response in the passband, this filter ensures minimal distortion of the retained signal. Figure  illustrates the effects of this filtering on example time series of conservative temperature, absolute salinity, and current speed.

Afterward, warming events were identified based on the frequency-filtered conservative temperature data set. We used a pseudo-Lagrangian approach, which, in contrast to the classic Eulerian view on the data (analyzing, e.g., the temperature time series at a fixed point in time, such as a mooring location), allows for a wide range of initial and boundary conditions during periods identified as warming events. At each time step and latitude section, a series of temperature contour elements were defined by 0.2 °C increment isotherms covering the whole temperature range of the data set (-1.6 to 8.2°C; see Fig. a). In case of multiple, separate contour elements corresponding to the same isotherm present at the same section at the same time step, the largest one originating over the slope (westernmost point of the contour at negative x) and penetrating onto the shelf (easternmost point of the contour at positive x) was chosen for the further processing steps. For all contour elements, the position of their easternmost point was tracked independently at each latitude section throughout the study period. A warming event could then be identified as an increase in the x locations of the tracked positions (see Fig. b) of more than 10 isotherms at all 15 zonal cross-shelf sections. Smaller events (based on only a few contour levels, not detected at an extended latitude range etc.) were manually discarded for further analysis. In the end, the heat content increase at any position on the shelf was calculated as the temperature difference between the isotherms located at that position before and at the end of the warming, multiplied by the mean density (1028 kgm-3) and the specific heat capacity of seawater (3985 Jkg-1K-1). The resulting data set, which serves as the basis for all further analyses presented in this study, can be found at 10.5281/zenodo.15188605 .

For the analysis of the role of the regional current systems in forcing WSS warming events, core positions of individual current branches were identified as local maxima in the northward current cross section at each latitude and time step. An example cross section is given in Fig. . Minor peaks with a maximum northward speed of less than 0.05 ms-1 or a prominence of less than 20 % of their maximum speed were discarded (gray markers in Fig. ). Based on contour lines with a spacing of 0.02 ms-1, the lowest contour solely contributing to each of the remaining peaks was identified (the color-coded contours in Fig. a). The water column spanning over the same x range as this contour was chosen as the corresponding current branch cross section for each branch (indicated by the dashed lines in Fig. a), and the average position of all contours at levels higher than this contour (colored in Fig. b) was chosen as the respective branch position.

Regional wind forcing was quantified as the spatially averaged surface wind stress over an area spanning from 77.3 to 78.1° N (see the light-green shading in Fig. b), calculated from the same AROME-Arctic wind data used to force the ROMS simulations. In the first place, the wind stress was calculated according to 1τ=ρaCDWS102, where ρa is the air density (1.3 gkg-1); WS₁₀ is the wind speed at 10 m height; and CD is the drag coefficient, which was parameterized in a nonlinear form based on and adapted for low wind speeds according to (see also ): 2CD=0.001⋅2.18for WS10≤1ms-10.62+1.56WS10for 1ms-1<WS10≤3ms-11.14for 3ms-1<WS10≤10ms-10.49+0.065WS10for WS10>10ms-1. The total wind stress was decomposed into its zonal and meridional components (τx and τy, respectively), and subsequent Ekman transport was calculated from the individual components according to 3Mx=τyρwf;My=-τxρwf. Here, ρw is the water density (1027 gkg-1) and f is the Coriolis parameter that depends on the Earth's angular velocity Ω and the latitude φ according to f=2Ωsin⁡(φ). In the following analysis, Ekman transport accumulated over 20 d (matching the threshold in the frequency filtering of the ocean data) is presented in order to account for time lags between wind forcing and Ekman transport as well as inertial impacts.

It should be noted that, in this paper, we use the term AW for any water mass originating in the WSC over the slope that is warm and saline relative to the water masses present on the WSS. In particular, we do not define threshold values for temperature and salinity, as generally done in other studies.

Persistent and strong southerly winds generate surface wind stress that drives an eastward Ekman transport. demonstrated how such conditions can facilitate the on-shelf transport of AW from the WSC at the surface, leading to a warming of the WSS. Examining the onset timing of all 17 warming events in relation to time series of surface wind stress, we identify four cases, 2019/20-A, 2020/21-A, 2020/21-C, and 2021/22-F, where this direct wind-driven forcing plays a substantial role. We present 2020/21-A as a case study. Figure a illustrates the temporal and meridional development of the increase in heat content on the shelf during the warming event, revealing that the largest changes occur in the southern part of the study area. It can, furthermore, be seen that the strongest warming occurs approximately 1 week to 10 d after the onset consistently across all latitudes.

Comparing this evolution to the atmospheric wind forcing in Fig. b shows that the warming event coincides with a pronounced southerly wind episode toward the end of December 2020. The resulting eastward Ekman transport accumulates to values of approximately 20 m2s-1, the highest seen during the study period. The strong correspondence in timing underlines the role of Ekman transport as a key driver of cross-shelf exchange and subsequent shelf warming, with similar patterns evident in events 2019/20-A, 2020/21-C, and 2021/22-F (not shown).

Figure c provides insight into the day-to-day progression of the AW intrusion onto the shelf, exemplified by the 3 °C isotherm at the 77.75° N section. Comparison of the density of the intruding water at its initial entry point (locked into the circle on the easternmost extent in each isotherm) with the density profiles of the shelf water en route shows how the shelf stratification determines the intrusion depth. While originally pushed toward the shelf at the surface due to wind-driven Ekman transport, the intruding AW encounters a much fresher and, thus, lighter shelf water mass, causing it to subduct and spread along the bottom as it moves eastward. The idealized comparison of the ambient shelf water density with only the initial intrusion density of course neglects the effects of mixing of the two water masses. However, the fact that such a simplified comparison fits the actual intrusion depth development so well suggests that the effects of mixing processes between intrusion and ambient shelf water are small over the course of the intrusion. In their work on the effect of a residual eddy overturning circulation, linked the depth of resulting AW intrusions to the tilt of the initial density front separating the Arctic-type shelf water from the AW carried northward by the WSC over the slope. The negative tilt of the black example contour (1027.6–1000 kgm-3) in Fig. c, which deepens by approximately 90 m over a horizontal distance of 20 km, and the intrusion along the bottom align precisely with this relationship. This suggests that the connection can be generalized to intrusions driven by other cross-shelf exchange mechanisms, such as surface Ekman transport. In the end, Fig. d shows the total increase in heat content on the shelf at the same section due to the warming event. While the strongest warming eventually takes place along the bottom of the inner shelf areas, the path of the intruding AW can clearly be seen, originating from the surface at the shelf break, where it met the lighter shelf water and was forced to subduct.

The opposite process, when northerly winds drive offshore Ekman transport and induce upwelling at the shelf break, has been described by based on data from the winter of 2005–2006. In that case, persistent northerly winds led to westward surface Ekman transport, which in turn triggered upwelling of AW from depth across the shelf break and onto the WSS. While this mechanism is also present in our data set, its signature appears less pronounced compared to the onshore Ekman transport by southerly winds described above. While different warming events in all three winter seasons can be attributed to onshore Ekman transport, shelf warming due to upwelling induced by surface offshore Ekman transport is only seen in spring 2020. The most illustrative example is warming event 2019/20-F, shown in Fig. . Even though other wind events with similar meridional negative wind stress forcing and magnitudes of offshore Ekman transport are present in the data set, they do not lead to corresponding warming events. This suggests that upwelling-driven intrusions are less dominant and more susceptible to being masked by other concurrent processes. The interplay between different forcing mechanisms, including their potential synergistic or compensating effects on the warming of the WSS, is further examined in Sect. . Figure a shows how warming event 2019/2020-F closely resembles the previous example 2020/21-A in terms of duration, magnitude, and temporal evolution. However, in contrast to 2020/21-A, the onset of 2019/20-F coincides with a particularly strong northerly wind event, further intensifying the already negative zonal (westward) accumulated surface Ekman transport (Fig. b). During this period, accumulated zonal Ekman transport reaches values of almost -40 m2s-1. Unlike the previous case, in which the stratification forced AW to intrude at depth, the density of the water mass residing on the shelf prior to the warming event is higher than the density of the AW being lifted over the shelf break (Fig. c). This allows an intrusion further onto the shelf only at the surface, where the strongest increase in heat content can ultimately be found (Fig. d).

In the context of discussing the impact of shelf stratification, we present two more examples, highlighting further variations in the intrusion depths. Figure a shows the day-to-day propagation of the 0.4 °C isotherm at 77.9° N during warming event 2021/22-D. The background color reveals that during the warming period, the shelf stratification is weak and zonally uniform (indicated by the two example isopycnals in Fig. a). Furthermore, there is no density front separating the shelf from the slope. This means that water masses from the shelf and the slope can readily exchange places in a so-called interleaving layer. This layer is not necessarily found at the surface or the bottom of the water column but, rather, at the depth where the density of the intruding water exactly matches that of the ambient shelf water. In the presented example, this is the case at an intermediate depth of 100 m, where the intrusion propagates eastward.

Furthermore, Fig. b illustrates how the intrusion depth may also change en route if the intrusion encounters different and/or changing stratification regimes further east on the shelf. The initial horizontal density gradient between the slope and shelf at the beginning of the presented warming event 2019/20-C is weak, and the intrusion first penetrates the shelf at an intermediate depth range of 50–100 m (similar to the previous example 2021/22-D). However, the inner shelf area is occupied by a denser water mass. When the intrusion meets the corresponding front, it has to adjust its depth in order to match the ambient stratification and moves to the top of the water column in an isopycnal manner, from there on penetrating the shelf further east at the surface.

Taking all presented examples together, we conclude that the intrusion depth is governed solely by the relative density difference between the intruding water and the ambient shelf water, independent of the cross-shelf exchange mechanism responsible for triggering the intrusion in the first place. This underscores the crucial role of shelf stratification in determining the final intrusion depth.

In the previously discussed examples, cross-shelf water mass exchange and subsequent shelf warming has been examined primarily as a zonal process. However, it is clear from Figs.  and a that the resulting shelf warming events also exhibit a pronounced meridional component, with warming initiating in the south and propagating northward over time. This northward progression is particularly evident in warming event 2019/20-B, shown in Fig. , where a distinct lag in warming onset can be observed along the shelf. While 2019/20-B provides the clearest example of this pattern, similar behavior is present, to varying degrees, in most of the 17 winter warming events identified throughout the study period. The detailed examination of the horizontal structure of warming event 2019/20-B in Fig.  further reveals that the strongest increase in depth-averaged heat content on the shelf does not occur near the shelf break but, rather, along the secondary shelf slope further onto the shelf, which separates Eggbukta from the shallower inner shelf regions (see Fig. ). This pattern of warming propagation strongly suggests that a topographically steered current serves as the primary mechanism for heat transport during this event. In the following, we investigate the connections between WSS warming events and the regional current systems in more detail.

Due to the diverging isobaths extending from the continental shelf break into Eggbukta (Fig. b), the WSC connects most strongly to the WSS in the southern part of the study area. As shown in Fig. a, the WSC core composite maps of the three winter seasons illustrate how the WSC splits into two branches: a main northward-flowing branch along the steepest continental slope and a sub-branch that veers onto the WSS, following the secondary slope around Eggbukta as the STC.

To quantify the role of this topographic steering in the warming events, we analyze the relative strength of the STC compared to the WSC using the volume and heat transport ratios across the respective current branch sections (for our definition of the current branch, see Sect. ) at 77.6° N, shown in Fig. b and c. Although differences in cross-sectional area and water mass characteristics complicate direct comparisons, the relative fluctuations in these transport ratios provide valuable insight. Many warming events coincide with increased STC volume and heat transport (2019/20-B, 2020/21-A, 2020/21-B, 2020/21-C, 2020/21-D, 2021/22-C, 2021/22-E, and 2021/22-G), emphasizing the role of topographic steering in directing warm water from the continental shelf break onto the WSS.

The mechanisms controlling periodic STC intensification and associated warming events have been explored in previous studies. proposed that a strengthened WSC core leads to a widening of the current, enabling warm water masses from its eastern flank to reach shallower isobaths and be topographically guided onto the WSS. To investigate this connection in our data, Fig. d presents the WSC core speed further upstream at 77.35° N, revealing substantial variability with peak velocities ranging from 0.2 to 0.7 ms-1. linked increased WSC velocities and subsequent WSS warming to periods of strong southerly winds over the WSS and adjacent shelf break. These winds induce a positive meridional wind stress, a negative wind stress curl, and a subsequently converging eastward surface Ekman transport across the WSS (as discussed in Sect. ). This leads to a pileup of water along both the WSS break and the Spitsbergen coastline, with corresponding increases in the sea surface tilt, which in turn strengthens the northward currents underneath to maintain geostrophic balance. However, a direct correlation between individual peaks in the WSC core speed and the cumulative zonal Ekman transport, shown in Fig. d and e, is not immediately apparent. Instead, we observe that current speed variations tend to be less pronounced during periods of weak or negative zonal Ekman transport. This aligns with the general seasonal cycle, where WSC velocities are typically higher in winter due to the frequent passage of atmospheric storm systems, a pattern well documented in previous studies e.g., but not analyzed in detail here.

Comparing the timing of the warming onsets with the time series of the WSC core speed shows that some warming events, such as event B in 2019–2020, events A and B in 2020–2021, and event B in 2021-2022, coincide with WSC velocity peaks. However, other velocity peaks, such as those in January 2020 and November 2021, do not result in warming events, indicating that an increase in WSC speed alone does not necessarily trigger STC intensification and warming of the WSS.

Another factor influencing the intensification of the STC, which was not considered by , is the variability in the exact position of the WSC. The spread of current core positions in the composites shown in Fig. a highlights a wide range of core locations, which translates into temporal variations in the WSC position at 77.35° N, as illustrated in Fig. f. Parts of this variability can be attributed to higher-frequency processes such as eddy activity and baroclinic geostrophic adjustments to hydrographic changes, which were filtered from the data set using a 20 d low-pass filter (see Sect. ). However, the gray markers in Fig. f show that even the more stable current branch position (for details on the definition of branch and core position in this study, see also Sect. ) exhibits substantial fluctuations. In particular, during nine periods within the three investigated winter seasons, the WSC branch position shifts closely toward or even crosses the shelf break. Eight of these occurrences coincide with increased volume and/or heat transport in the STC and the onset of warming events. This suggests that the lateral displacement of the WSC represents an additional mechanism to strengthen the STC, making it follow shallower isobaths and, in that way, drive the warming of the WSS. Similar to the reduced variability in the WSC peak speed, the position tends to shift toward deeper bathymetry during prolonged periods of negative zonal Ekman transport. In contrast, a connection between the WSC and shallower bathymetry feeding into the STC is more likely during episodes of weak or even southerly wind forcing. This also contradicts offshore surface Ekman transport due to northerly winds and subsequent upwelling of AW onto the WSS at depth as a shelf warming mechanism and could explain the corresponding weak connection discussed in Sect. .

The findings presented so far have focused primarily on the individual effects of different processes driving cross-shelf exchange and subsequent shelf warming. However, it has also become evident that multiple forcing mechanisms can interact and that a given warming event may result from a combination of these processes. For instance, as discussed in Sect. , the intensification of the STC and a subsequent warming event on the WSS can be triggered by (1) an increase in the WSC core speed, (2) an eastward displacement of the WSC core over shallower bathymetry, or (3) a combination of both. This interplay is particularly evident in winter 2020–2021, where a certain co-variability between these two current properties can be observed (see Fig. d and f).

Similarly, atmospheric wind forcing can contribute to WSS warming events in both direct and indirect ways. Directly, strong southerly winds induce on-shelf Ekman transport, while indirectly, they modify the sea surface tilt, which can subsequently accelerate the WSC. To illustrate how different processes can interact, Fig.  presents the warming event 2020/21-C as an example of a shelf warming event likely driven by multiple mechanisms. Comparison of Fig. a and b reveals that the warming starts at a time when the WSC core is located on the shelf (positive x), indicating a direct input of warm AW into the STC. Even though the core position moves westward during the following days, the branch as a whole shifts toward shallower bathymetry. At the same time, the WSC core speeds up to almost 0.6 ms-1, with the peak speed coinciding with the largest daily increase in heat content on the shelf across all latitudes (Fig. c). Furthermore, while wind forcing is relatively weak at the beginning of the warming event, a strong wind event occurs at the same time (Fig. d). Although this wind event cannot have caused the initial WSC speedup, the associated Ekman transport, reaching up to 10 m2s-1, likely contributes to the overall warming by facilitating an additional cross-shelf advection of warm water already present near the shelf break. This example underscores how different forcing mechanisms may not only act independently but also amplify one another, emphasizing the complexity of cross-shelf exchange and shelf heat variability in this region.

Beyond the individual forcing mechanisms discussed so far, warming event 2020/21-C highlights yet another important factor influencing the WSS warming: the variability in the temperature of the AW transported northward by the WSC. As the primary heat source for all cross-shelf warming events, fluctuations in the temperature of the WSC can substantially impact the magnitude of warming events on the WSS. Although this variability has been extensively studied in the context of northward heat transport toward the central Arctic Ocean e.g., and the warming of west Spitsbergen fjords e.g.,, its role in driving the intensity of the WSS warming has, to the authors’ knowledge, not been explored before.

Figure e shows the average conservative temperature of the upper 300 m of the water column over the slope (x< 0 km) during the warming event. A notable increase of more than 0.5 °C is observed, coinciding with the increase in heat content on the shelf. The northward propagation speed of this temperature anomaly (0.2–0.4 ms-1) approximately matches the WSC speed. A broader analysis of this relationship is provided in Fig. , which presents the time series of the upper 300 m average conservative temperature, absolute salinity, and potential density anomaly over the slope at 77.6° N (solid color-coded curves) throughout the study period. Figure a reveals that several warming events (2019/20-C, 2019/20D, and 2019/20F; 2020/21-A and 2020/21-C; and 2021/22-D, 2021/22-E, and 2021/22-G) coincide with rising temperatures or peaks in the temperature time series, further supporting the role of upstream hydrographic variability in the WSC in modulating WSS warming events.

A particularly striking example is warming event 2019/20-C, which stands out as the longest and by far strongest warming event identified in this study period (see Table ). From Fig. a and b, it becomes evident that this event closely coincides with a pronounced temperature and salinity increase in the WSC region over the slope. Unlike other warming events, there is no substantial increase in the STC/WSC heat and volume transport ratios, no eastward displacement of the WSC (Fig. ), and no substantial zonal Ekman transport anomalies observed. Instead, the increase in temperature over the slope leads to a density decrease (the salinity increase does not compensate for the temperature increase) and a subsequent degeneration of the density front separating the shelf from the slope. This allows warm AW from the WSC to penetrate the WSS in an interleaving layer at intermediate depth (see Fig. b). As a consequence of the reduced zonal density gradient between the shelf and slope, the baroclinic component of the WSC also weakens. As the slope region warms further and ultimately becomes lighter than the shelf (Fig. c), the baroclinic current structure also reverses, resulting in a downward intensification of the northward flow in the WSC. As a consequence, the core not only accelerates (Fig. d) but also shifts to a depth of approx. 400 m in the water column during this period (Fig. f). Thus, in this case, the increased core speed of the WSC during the warming is not a driver (as described in Sect. ) but, rather, a consequence of the altered zonal density gradient.

The impact of warming event 2019/20-C on the WSS extends well beyond its immediate duration. As seen in Fig. a and b, the shelf not only experiences a temperature increase of approximately 2 °C but also becomes flooded with saline water (salinity up to 35 g kg⁻¹) that persists throughout the remainder of the winter season and leads to an increase in shelf water density. In fact, over the course of a winter, the shelf becomes progressively denser not only due to saline AW intrusions but also due to surface heat loss and cooling of the shelf water column and, if freezing temperatures are reached, an increase in salinity owing to brine release from local or upstream sea ice formation. This seasonal evolution of the shelf hydrography plays a crucial role in determining the depth of warm-water intrusions. Early in the season, when the shelf is still relatively warm and fresh, warm intrusions are more likely to occur at depth, whereas later in the season, when the shelf has cooled and become more saline, warm AW intrusions reach the surface more frequently. In the case of warming event 2019/20-C, the corresponding AW intrusion resulted in a substantially warmer and more saline shelf during the second half of winter 2019–2020. This marks a regime shift, from all warming events occurring along the bottom earlier in the season, while those later in the season penetrate the shelf at the surface rather than at depth. These findings underscore how cross-shelf intrusions shape the seasonal and interannual variability in the shelf hydrography.