Submesoscale Variability and Basal Melting in Ice Shelf Cavities of the Amundsen Sea

Melting of ice shelves can energize a wide range of ocean currents, from three‐dimensional turbulence to relatively large‐scale boundary currents. Here, we conduct high‐resolution simulations of the western Amundsen Sea to show that submesoscale eddies are prevalent inside ice shelf cavities. The simulations indicate energetic submesoscale eddies at the top and bottom ocean boundary layers, regions with sharp topographic slopes and strong lateral buoyancy gradients. These eddies play a substantial role in the vertical and lateral (along‐isopycnal) heat advection toward the ice shelf base, enhancing the basal melting in all simulated cavities. In turn, the meltwater provides strong buoyancy gradients that energize the submesoscale variability, forming a positive loop that could affect the overall efficiency of heat exchange between the ocean and the ice shelf cavity. Our study implies that submesoscale‐induced enhancement of basal melting may be a ubiquitous process that needs to be parameterized in coarse‐resolution climate models.


Introduction
Basal melting is one of the key processes impacting the polar ice mass loss (e.g., Adusumilli et al., 2020;Pritchard et al., 2012;Rignot et al., 2019) with consequences for accelerating global sea level rise.Ice shelf melting is locally influenced by three water masses: (a) modified Circumpolar Deep Water (mCDW) traveling from the Southern Ocean carried by large-scale off-and on-shelf ocean circulation (e.g., S. Jacobs et al., 1992;S. S. Jacobs et al., 2011;Nakayama et al., 2019), (b) high salinity shelf water produced in the coastal polynya due to intense sea ice formation (e.g., S. Jacobs et al., 1992; S. S. Jacobs & Giulivi, 2010;Janout et al., 2021), and (c) solarheated Antarctic Surface Water carried by surface ocean currents, eddies, and Ekman transport (Aoki et al., 2022;S. Jacobs et al., 1992;Silvano et al., 2016).For warm ice shelves in West Antarctica, intruding mCDW into ice shelf cavities is known to have the maximum impact near the grounding line in the inner cavity (basal melt rates ∼100 m/yr; Shean et al., 2019;Nakayama et al., 2019Nakayama et al., , 2021)).Basal melting injects buoyancy to the fresh meltwater plume that ascends along the ice shelf base, entraining heat from the surroundings to compensate for the heat loss and further enhancing melting.The relatively warm mCDW that intrudes inside ice shelf cavities sets up a strong stratification where the warm water masses, a few degrees above the freezing point, are located substantially below the ice-ocean boundary layer (Davis et al., 2023).
Building upon our understanding of ice-free ocean dynamics, we hypothesize that ice shelf cavities could provide favorable environments for the formation of submesoscale eddies because of the rough ice shelf topography and oceanic bathymetry, presence of boundary currents, and the strong ice melt that facilitates the formation of density gradients (Dutrieux, Stewart, et al., 2014;Hattermann et al., 2014;Malyarenko et al., 2019;Schmidt et al., 2023;Shean et al., 2019).Submesoscale eddies are known to be generated due to various mechanisms, including mixed layer instabilities (MLI) (Boccaletti et al., 2007;Shrestha & Manucharyan, 2022), vertical shear, mesoscale frontogenesis (Spall, 1997), and topographical wakes (Molemaker et al., 2015).Submesoscale instabilities may also occur due to bathymetric sills and rough topographical variations underneath the ice shelf associated with basal keels and apexes of channels (Gille et al., 2000).Spatial heterogeneity in melting patterns and convoluted topographic features could create mixed layer density gradients in the ice shelf cavity that trigger a set of ageostrophic instabilities (Haine & Marshall, 1998).Similarly, topographic slopes at the continental shelf can intensify vertical vorticity of inflowing bottom boundary currents leading to ageostrophic centrifugal instability (horizontal shear instability) (Gula et al., 2015(Gula et al., , 2016)), which may contribute to the generation of submesoscale vortices inside ice shelf cavities.Testing the pertinence of the eddy formation mechanisms mentioned above requires comprehensive observations in ice shelf cavities that are currently missing.Garabato et al. (2017) observed ocean dynamics at the Pine Island Ice Shelf front and explored the importance of submesoscale processes.They show that the outflow of the mCDW-meltwater mixture experiences a variety of instabilities, from gravitational to centrifugal to symmetric instabilities at the ice shelf front (Garabato et al., 2017).Nonetheless, no study has attempted to explore the presence of submesoscale dynamics within ice shelf cavities, perhaps due to the inherent difficulty in conducting field observations and associated logistics challenges, and submesoscale-permitting models are computationally expensive to resolve these small scales of oceanic motions (Graham et al., 2016;Hattermann et al., 2014;Liu et al., 2017;Nakayama et al., 2014;St-Laurent et al., 2015).
In this study, we use the Amundsen Sea configuration of the submesoscale-permitting nested Massachusetts Institute of Technology General Circulation Model (MITgcm) to elucidate the presence of submesoscale dynamics inside ice shelf cavities and explore their role in transferring heat from deep sub-surface water to the ice shelf base that may amplify basal melting.

Model Description
We use the ocean model setup described in Nakayama et al. (2019), which is the submesoscale-resolving nested regional configuration of the MITgcm model with hydrostatic approximation, dynamic and thermodynamic seaice (Losch et al., 2010), and thermodynamic ice shelf (Losch, 2008).The computational domain incorporates Pine Island, Thwaites, Crosson, and Dotson ice shelves in the western Antarctica region as illustrated in Figure 1, with a horizontal grid spacing of ∼200 m and equispaced vertical grid resolution of 10 m (Figure 1c).Also, a lowresolution numerical simulation with a horizontal grid spacing of ∼2 km is shown in Figure 1b.Model bathymetry is based on the International Bathymetric Chart of the Southern Ocean (IBCSO46) (Arndt et al., 2013) with a more accurate updated version for the region (Dutrieux, Rydt, et al., 2014;Millan et al., 2017), and the model ice draft is based on commercial, sub-meter satellite stereo imagery for the PIIS (Shean et al., 2019), and Antarctic Bedrock Mapping (BEDMAP-2) for the remaining ice shelves (Fretwell et al., 2013).We note that BEDMAP-2 ice shelf geometry may include significant errors for Dotson and Crosson ice shelves (Dutrieux et al., 2018), contributing to uncertainties in magnitudes of the basal melting; hence, a new simulation may be required for future study of these ice shelves.
For the atmospheric forcing, ERA-Interim (Dee et al., 2011) is used that has been adjusted using the ECCO (Estimating the Circulation and Climate of the Ocean) adjoint model-based methodology (Wunsch & Heimbach, 2013).A 30-day spin-up from the initial rest state that assumes salinity and potential temperature from the 01/2010 monthly mean fields (Nakayama et al., 2018) sets up the initial conditions for this model.Similarly, lateral boundary conditions are imposed based on Nakayama et al. (2018).The choice of the specific date for the start of the simulation is not expected to affect the basic conclusions about the presence of submesoscale variability inside the ice shelf cavities as their formation mechanisms are driven by local dynamics and are affected by external conditions only in the sense of them providing the background stratification.
This model has been duly tested in the context of exploring the water pathways toward ice shelf cavities of the Amundsen Sea (Nakayama et al., 2019), and the high-resolution simulation showed qualitative agreement with the Autosub3 AUV measurements (Jenkins et al., 2010), mooring observations (Webber et al., 2017), and CTD (conductivity-temperature-depth) observations.Satellite-based estimates of the integrated Pine Island, Thwaites, and the Dotson and Crosson ice shelf melt rates are 101 ± 8 t yr 1 , 97.5 ± 7 Gt yr 1 , and 84 ± 18 Gt yr 1 , respectively (Rignot et al., 2013).Simulated integrated ice shelf melt rates for the Pine Island, Thwaites, and the Dotson and Crosson ice shelves are 64.8Gt yr 1 , 65.1 Gt yr 1 , and 83.7 Gt yr 1 , respectively.

Numerical Experiments
Two case study experiments have been conducted -"MELT" and "NO MELT."The "NO MELT" experiment differs from the control "MELT" experiment in the model's heat and salt transfer coefficients at the ocean-ice interface that is set to zero.This turns off the melting processes in the "NO MELT" experiment.

Vertical Eddy Heat Flux
The vertical eddy heat flux, Q w , is calculated as where H is the mean mixed-layer depth, C p = 3985 J kg 1 K 1 is the specific heat capacity, ρ 0 = 1,035 kg m 3 is the reference density, w′ and T′ are vertical velocity and temperature anomalies from the temporal mean, and the overbar with a superscript indicates averaging along specified coordinates.Anomalies are computed by subtracting moving time averages from the instantaneous values.Eddy heat fluxes are horizontally averaged over regions set by green rectangular boxes (see Figure 4a), time-averaged over six inertial periods, and depthaveraged within the mixed layer.

Freezing Temperature
Computation of freezing temperature, T f = (0.0901 0.0575 S b ) 0.000761 p b assumes a linear equation of state, where S b and p b are salinity and pressure at ocean-ice shelf interface (Losch et al., 2010;Marshall et al., 1997).
The freezing temperature is used in the bulk formula for computing the heat fluxes at the base of an ice sheet.

Ertel Potential Vorticity and Rossby Number
Ertel potential vorticity (PV) is defined as,

Prevalence of Submesoscale Variability in Ice Shelf Cavities
The prevalence of submesoscale flow in all ice shelf cavities can be clearly identified in the model simulation using diagnostic quantities such as Rossby number and PV.Rossby number contours in Figures 2a,2c and 2e Another crucial diagnostic pointing to submesoscale instabilities is the Ertel PV.When PV takes an opposite sign of the Coriolis parameter, various instabilities develop that lead to submesoscale eddies (Hoskins, 1974).Thus, positive PV inside ice shelf cavities in the Antarctic region indicates the triggering of submesoscale instabilities that are only partially represented in the model.In our simulations, positive PV regions are often co-located with the patches of high Rossby number flows, particularly in regions with strong density gradients, behind bathymetric sills, and the base of the ice shelves (Figures 2b, 2d, and 2f).There are multiple factors contributing to the formation of negative PV water masses.At the ice shelf base, local lateral temperature gradients are created due to the entrainment of blobs of warm dense water from below as the buoyant plume ascends (Malyarenko et al., 2019) (as seen inside Thwaites cavity in Figure 2d) or due to spatial heterogeneity in the melting pattern as a result of complex basal topographical variations (Dutrieux, Stewart, et al., 2014) (as seen inside Pine Island cavity in Figure 2f).The substantial temperature deviations from the freezing point in ice shelf cavities, particularly near the bases of the ice shelves, highlight the presence of stirring of the background stratification that leads to intermittent frontal formation.Since the ice shelf provides a frictional boundary condition for the ocean, the PV injections at strong baroclinic fronts may also contribute to submesoscale eddy formation and associated mixed layer restratification.
Regions near the Thwaites ice front have particularly energetic eddies (Figure 3) that can modify the properties of water masses propagating into the cavity.Recent observations reveal additional warm water pathways entering the cavity from the eastern Pine Island Bay (Dotto et al., 2022;Wahlin et al., 2021) in addition to previously known pathways at the northern side along the deep troughs (Nakayama et al., 2019;Seroussi et al., 2017).The deep water originating from Pine Island Bay was found to be fresher, lighter, and deeper than the saltier water in Thwaites Trough, leading to possibilities of strong horizontal density gradients and enhanced submesoscale turbulence near the ice front.
In addition, bathymetric sills may also contribute to the negative PV formation in Crosson, Thwaites, and Pine Island (Figures 2b,2d,and 2f).Bathymetric ridges induce bottom drag along their slopes, intensifying positive vertical vorticity and PV of the inflow on the cyclonic side; downstream, thin vorticity filaments may become unstable to horizontal shear instability, forming a street of submesoscale vortices as observed in open ocean simulations (Gula et al., 2015).As was shown in Gula et al. (2016), the topographic slope amplifies the vertical vorticity of the inflow such that its PV sign changes and triggers ageostrophic centrifugal instability; this process may occur in ice shelf cavities as well.Furthermore, the presence of bathymetric sill in the Pine Island cavity (Jenkins et al., 2010;Nakayama et al., 2019), as seen in Figure 2f, can modulate the temperature and salinity characteristics of saline, warm mCDW entering into the ice shelf cavity to a cooler and diluted state.This can cause salinity gradients across the bathymetry sill, triggering frontal instabilities leading to submesoscale activity.Due to the complexity of bathymetry in individual ice shelf cavities and highly heterogeneous buoyancy fluxes at the base of ice shelves, there is a wide range of possible mechanisms simultaneously driving eddy production at any given location in the model.Hence, we emphasize that numerical simulations demonstrate a strong presence of submesoscale flows in all ice shelf cavities and proceed with quantifying their cumulative effect on basal melting.

Enhanced Basal Melting and Submesoscale Variability
The preceding section established the prevalence of submesoscale variability inside ice shelf cavities.Eddies of these scales are known to dramatically enhance vertical velocities and tracer transport compared to large-scale mesoscale processes (Bachman et al., 2017;Klein & Lapeyre, 2009;Su et al., 2018), and thus, can contribute to vertical advection of deeper warmer waters toward the ice-ocean interface.Since ice shelf cavities are in a dynamic equilibrium in which the intensity of basal melting is affecting, and at the same time affected by, submesoscale variability and large-scale circulations, it is not straightforward to discern causality here.However, we can explore the sensitivity of the eddy field to melt water release by conducting a hypothetical case-study experiment "NO MELT."By comparing vertical eddy heat fluxes in different cavities between the two experiments, we can assess the robustness of the relation between submesoscale-driven heat fluxes and basal melting.
In the control experiment, regions of relatively low basal melt rates are generally collocated with the regions where Rossby numbers of flows are significantly reduced, and regions of pronounced submesoscale variability are often co-located with the regions of high basal melt (Figure 3).The control experiment shows significantly higher Rossby number dynamics compared to the "NO MELT" experiment in each of the simulated ice shelf cavities (Figure 4), demonstrating that the presence of melt-driven surface buoyancy fluxes is indeed crucial for the generation of energetic submesoscale eddies.Notably, the Rossby numbers in all cavities are dramatically stronger than in the open ocean in the control experiment (Figure 5a).Thus, basal melting is a key driver of submesoscale variability in oceanic mixed layers.However, basal melting, in turn, can be enhanced by the vertical advection of heat by submesoscale eddies.Indeed, the "NO MELT" experiment demonstrates that the Rossby number variance and the vertical eddy heat fluxes are significantly reduced, consistent with the notion that the vertical advection of heat is associated with submesoscale eddies (Figure 4).
A more detailed understanding of the vertical penetration of submesoscale activity near the ice shelf base can be attained by assessing the vertical structure of eddy vorticity variance and vertical heat fluxes (Figures 5a-5d).Submesoscale eddies are generally amplified toward the ocean's surface, where they are in contact with the ice shelf base, and extend substantially beyond the mixed-layer depth, about 45 m below the ice shelf base.The associated vertical eddy heat fluxes peak around 50 m below the base in the "NO MELT" experiment and extend to about 100 m in the control experiment.The Thwaites and Dotson cavities have well-pronounced maxima in the vertical heat fluxes at about 30-50 m, while others have less pronounced peaks with significant fluxes extending to below 100 m.The surface intensification of eddies and the fluxes are again consistent with the notion that strong lateral buoyancy gradients in the local mixed layer are crucial to their formation.The gradual decay of vertical eddy heat fluxes with depth suggests that eddy vertical velocities extend beyond the local mixed-layer base (Erickson & Thompson, 2018;Yu et al., 2019).One exception is the Crosson ice shelf cavity in which strong Rossby number flows are maintained even beyond 100 m depth because of its narrow cavity geometry (see Figures 2a and 2b), where submesoscale dynamics is also generated at the bottom boundary layer.
In the Thwaites cavity, the mixed layer vertical eddy heat fluxes are about ten times more intense than for other nearby glaciers (Figure 5c), even though the Rossby numbers are relatively similar (Figure 5a).The vertical eddy heat flux of about 50 W/m 2 in the Thwaites cavity translates to 5.1 m/yr or 26 Gt/yr of basal melt (considering its area of about 5,500 km 2 ).This eddy-driven melt is significant given that the total basal melt rate for the Thwaites cavity is estimated to be 17.7 m/yr or 97.5 Gt/yr (Rignot et al., 2013).While submesoscale eddies are prominent in all simulated cavities, the vertical eddy heat fluxes for Pine Island, Dotson, and Crosson ice shelves are of the order of 5 W/m 2 , contributing about 0.5 m/yr of basal melt, which is significantly lower than in Thwaites.This suggests that MLIs appear to amplify the vertical eddy heat fluxes in Thwaites, and other eddy formation processes may be dominant in the other simulated cavities.
The linkage between submesoscale activity represented by the variance of the Rossby number and the upward eddy heat flux is summarized in Figure 5e.In the ice shelf cavities of the Amundsen Sea, the "MELT" scenarios show a comparatively higher amount of submesoscale activity and eddy heat flux.The Ro 2 and Q w are around 5-7 times more intense in melting-activated experiments than when the heat and salt transfer coefficients at the oceanice interface are set to zero.The strong decrease of the eddy fluxes (to ≈ 5 W/m 2 ) in the Thwaites cavity when the melting is turned off brings it more in line with other cavities (Figure 5d).This points to the particular importance of submesoscale dynamics in it.
The dramatic differences in submesoscale variability between the "MELT" and "NO MELT" experiments should not be explicitly interpreted as a difference between the resolved and non-resolved submesoscale variability because of the nonlinear coupling between the eddy dynamics and basal melting.Instead, the comparison with the extreme "NO MELT" experiment highlights the buoyancy fluxes from basal melting as a key driving factor of submesoscale dynamics inside ice shelf cavities.Hence, further studies are needed to develop submesoscale eddy parameterizations for coarse ocean models of ice shelf cavities.

Conclusions
We show that submesoscale eddies are abundant inside the ice shelf cavities of the Amundsen Sea that can efficiently advect warm water vertically toward the ice shelf base, enhancing the ocean-ice shelf heat fluxes.This induces ice shelf basal melting.Spatially heterogeneous melting patterns due to convoluted under-ice-shelf basal topography and topographical features drive strong lateral buoyancy gradients in sub-ice-shelf cavities that facilitate the development of submesoscale instabilities.Thus, this study highlights an additional heat pathway to the ocean-ice boundary layer driven by submesoscale eddies.The coupling between the eddy-driven heat fluxes and meltwater fluxes that energize them forms a positive feedback loop, the strength of which needs to be quantified in future studies.This feedback may affect the net basal melt rates inside ice shelf cavities and contribute to establishing mean conditions in ice shelf cavities.Our results emphasize the need to quantify and parameterize submesoscale-induced basal melt rates to improve the representation of ice shelves in coarseresolution climate models.

Figure 1 .
Figure 1.Regions used for nested high-resolution numerical simulations of the ocean dynamics in ice shelf cavities of the Amundsen Sea region.(a) Antarctica map with an indication of the Amundsen and Bellingshausen Sea region.(b) Instantaneous Rossby number contours in a low-resolution (horizontal grid size = 2 km) simulation, with an indication of the subdomain used for high-resolution simulations.(c) Instantaneous Rossby number contours in a submesoscale-resolving, high-resolution (horizontal grid size = 0.2 km) simulation.Note that the Rossby number color scales are different for (b) and (c).
where f is the Coriolis parameter, u is the velocity vector, b = −gρ/ρ 0 is the buoyancy, and g is the acceleration due to gravity.Rossby number is defined here as the vorticity normalized by the Coriolis parameter: Ro = |ζ|/f, where ζ = v x − u y is the vertical component of the relative vorticity of the ocean.

Figure 2 .
Figure 2. Vertical transects of simulated ocean properties inside Crosson, Thwaites, and Pine Island ice shelf cavities, measured along the yellow lines shown in Figure 4a.(a, c, e) Rossby number colormap with isopycnals indicated by black lines.(b, d, f) Ertel Potential vorticity colormap with contour lines of temperature above freezing point, T T f , indicated by gray lines, where T is temperature and T f is the freezing point temperature.

Figure 3 .
Figure 3. Submesoscale variability and basal melt rates inside (a, d) Pine Island (b, e) Thwaites (c, f) Dotson and Crosson ice shelves.The top row panels show the Rossby number at the first level below the ice shelf base.In the bottom row, the basal melting rate colormap (m yr 1 ) shows the highest melting near the grounding line.

Figure 4 .
Figure 4. Rossby number comparisons between (a) MELT (b) NO MELT experiments for different ice shelf cavities in the Amundsen Sea region, with an indication of areas used for estimating the variance of the Ro and eddy heat flux (green rectangles).Panel (a) also shows yellow lines along which vertical sections of simulated ocean properties have been made in Figure 2.

Figure 5 .
Figure 5. Vertical profiles of variance of Rossby number for (a) "MELT" (b) "NO MELT" experiments.Likewise, vertical profiles of eddy heat flux for (c) "MELT" (d) "NO MELT."Diagnostic quantities are horizontally averaged over the gray rectangular boxes inside Dotson, Crosson, Thwaites, and Pine Island cavities, including open ocean for reference (see Figure 4a) and then time-averaged over six inertial periods (6T 1 ) to eliminate inertial oscillations (from the statistics).For the given f = 1.4 * 10 4 s 1 , 1T 1 ≈ 0.5 days.(e) Bar chart comparing the variance of the Ro and vertical eddy heat flux over the open ocean and ice shelf regions denoted with rectangles in Figure 4a.〈Ro 2 〉 bars plot values at the second level below the ice shelf base where the magnitude of 〈Ro 2 〉 is maximum (∼15 m below the base), while eddy heat fluxes are depth-averaged from the ice shelf base to the mean mixed layer depth for the region (∼45 m beneath the ice shelf base).