Ice rises and ice rumples are locally grounded features found in coastal Antarctica and are surrounded by otherwise freely floating ice shelves. An ice rise has an independent flow regime, whereas the flow regime of an ice rumple conforms to that of the ice shelf and merely slows the flow of ice. In both cases, local highs in the bathymetry are in contact with the ice shelf from below, thereby regulating the large-scale ice flow, with implications for the upstream continental grounding line position. This buttressing effect, paired with the suitability of ice rises as a climate archive, necessitates a better understanding of the transition between ice rise and ice rumple, their evolution in response to a change in sea level, and their dynamic interaction with the surrounding ice shelf. We investigate this behaviour using a three-dimensional full Stokes ice flow model with idealised ice rises and ice rumples. The simulations span end-member basal friction scenarios of almost stagnant and fully sliding ice at the ice–bed interface. We analyse the coupling with the surrounding ice shelf by comparing the deviations between the non-local full Stokes surface velocities and the local shallow ice approximation (SIA). Deviations are generally high at the ice divides and small on the lee sides. On the stoss side, where ice rise and ice shelf have opposing flow directions, deviations can be significant. Differences are negligible in the absence of basal sliding where the corresponding steady-state ice rise is larger and develops a fully independent flow regime that is well described by SIA. When sea level is increased, and a transition from ice rise to ice rumple is approached, the divide migration is more abrupt the higher the basal friction. In each scenario, the transition occurs after the stoss-side grounding line has moved over the bed high and is positioned on a retrograde slope. We identify a hysteretic response of ice rises and ice rumples to changes in sea level, with grounded area being larger in a sea-level-increase scenario than in a sea-level-decrease scenario. This hysteresis shows not only irreversibility following an equal increase and subsequent decrease in sea level but also that the perturbation history is important when the ice rise or ice rumple geometry is not known. The initial grounded area needs to be carefully considered, as this will determine the formation of either an ice rise or an ice rumple, thereby causing different buttressing effects.
Great progress in ice flow modelling has improved the physical representation of dynamical processes at the margins of the Antarctic Ice Sheet, but
the transient evolution of the grounding line continues to be challenging, requiring high mesh resolution, small time steps, and advanced model physics
Ice rises and ice rumples are locally grounded features surrounded by floating ice shelves and play a dual role in this context. Firstly, ice rises
and ice rumples regulate the flow of ice towards the ocean through their buttressing effect
In adopting terminology from
To quantify non-local effects from the surrounding ice shelves, we compare the full Stokes solutions with the shallow ice approximation
Ice rises and ice rumples and their surrounding ice shelves are investigated in steady-state and transient scenarios using the three-dimensional full
Stokes numerical model Elmer/Ice
We adopt a coordinate system in which the predominant along-flow direction is aligned with the
The non-linear rheology of ice is modelled using Glen's flow law, which relates the deviatoric stress tensor,
Here,
The upper surface,
A constant flux of
Ice in contact with the bed is subject to a non-linear Weertman-type friction law,
The 60
The evolution of ice rises and ice rumples is simulated in a 60
List of parameters used in the simulations.
The centre of the bed anomaly is located at
Shown is the mesh resolution. In the horizontal, the mesh is unstructured and has a resolution of 350
The ice thickness is initialised to 300
The shallow ice approximation
We compare the velocity components only at the surface of the ice and also assume that temperature is constant, and so Eq. (
The
The Vialov profile
We compare only the lee profile of the ice rises to the Vialov profile as the bed is relatively flat in this area, and we assume that small changes in
bed topography are negligible. The profiles are compared for a central cross-section from the divide, extending in the along-flow direction into the
ice shelf (Label (3) in Fig.
The change in sea level for the transient simulations. The low and intermediate scenarios follow the green curve. A second sea level increase-and-decrease cycle is performed for the low-friction scenario (blue). Sea level is increased to 170
A cross-section of the ice rise in the along-flow direction for
To allow perturbation simulations to start from a steady-state geometry, all simulations are run for 2000 years under constant forcing. Simulations
are performed for three different basal friction coefficients,
In the low and intermediate scenarios, the ice rises transition to ice rumples at some stage during the sea level increase. In the
high-friction scenario, no such transition occurs after a sea level increase of 80
After 2000 years of spin-up time, ice rises with a characteristic local flow regime develop in all three full Stokes scenarios
(Fig.
Topographic and flow divides coincide in all three cases, and ice rise surface velocities are within tens of metres per year. There is negligible
basal sliding in the high-friction scenario (with average absolute velocities of roughly 0.5
All ice rises exhibit geometries and flow regimes which are comparable to observations. For example, the high-friction scenario is comparable
to Derwael Ice Rise, where previous studies have assumed no basal sliding a priori (e.g.
A bird's eye view of the grounded area corresponding to the steady states at
The full Stokes and SIA surface velocities at
Cross-sections of the full Stokes simulations at
The comparison of full Stokes surface velocities to SIA surface velocities on ice rises illustrates where the local flow assumptions are
violated. Figure
The response of grounded area and upstream ice shelf velocity to sea level perturbation in the case of low basal friction. Panels
The response of grounded area and upstream ice shelf velocity to sea level perturbation in the case of high basal friction. In
The response of the dome position to a raising and lowering of sea level in the case of
To understand the response of ice rises and ice rumples with differing basal friction to sea level perturbation, we analyse the grounded area
(Figs.
Before transitioning to an ice rumple, the dome position in the low-friction scenario migrates linearly at a rate of 1.7
After a sea level increase of 20
A steady acceleration of the upstream ice shelf is seen in both the low- and intermediate-basal-friction scenarios, and there is no
abrupt change once a transition from ice rise to ice rumple has occurred (Fig.
The figures show a cross-section of the ice rises in the along-flow direction for
An along-flow cross-section of the ice rumple at
After keeping the sea level constant for 2000 years at a sea level perturbation of 80
When sea level rise is halted in the high-basal-friction scenario prior to the unstable grounding line retreat (here at a sea level
perturbation of 155 m), the ice rise volume and grounded area also recover asymmetrically, resulting in two differing states for a given sea level
displacement (Fig.
We investigate the migration of the stoss- and lee-side grounding lines of the ice rise and make a comparison with the grounding line position in the
case of hydrostatic equilibrium (video in the Supplement). The maximum differences in position are 0.5
A number of previous studies have argued that basal sliding near ice rise divides is negligible because thermomechanically coupled models often
predict ice significantly below the freezing point at the ice–bed interface near the summits
The simulations show that ice rises can form in scenarios where basal sliding is significant. Surface velocities in the low and intermediate scenarios are within a few metres per years near the crests, similar to the predictions in the high-friction scenario (Fig. 5). In this regard, surface velocities alone are a poor indicator for the presence or absence of basal sliding on ice rises. However, the geometries between the three scenarios differ significantly, and only the high-friction scenario can be adequately approximated with the Vialov profile, whereas the low and intermediate scenarios exhibit significant misfits (Fig. 8). This means that a simple fit with a Vialov profile can serve as a first-order metric for the absence or existence of basal sliding for specific ice rises. This is important, as the degree of basal sliding in the vicinity of the grounding line determines the local ice flow and the ice rise's transient behaviour in response to sea level perturbation. When comparing the grounding line positions of the full Stokes model and the hydrostatic grounding line position, we find that differences are small. However, over the millennial timescales considered here, together with the compounding effect of the small errors in grounding line position at each time step, it is possible that a hydrostatic assumption may result in differing ice rise and ice rumple geometries as well as a differing transition point.
Many ice rises are fully surrounded by ice shelves, and the extent to which isle-type ice rise velocities are affected by longitudinal and shear
stresses transferred from the upstream ice shelf is not fully clear. This effect is analysed here using the differences between the non-local full
Stokes simulations and the fully local SIA. The flow regime in the high-friction scenario is, to a large extent, independent of the
surrounding ice shelf. In the low- and intermediate-basal-friction scenarios, however, the differences between full Stokes and SIA
are greater and are especially evident on the stoss side of the ice rise. The greater velocity differences in the lower-friction scenarios show that
these ice rises are influenced more by the stresses in the surrounding ice shelf. Implications for the presence or absence of a fully local flow
regime are twofold: (1) if basal sliding is negligible even in areas close to the grounding zone, then SIA is an appropriate modelling framework, for
example, when investigating the surface accumulation history using inverse methods
An along-flow ground-based radargram
The low- and intermediate-friction scenarios respond immediately to a rising sea level, with a retreat of the leeward grounding line
accompanied by a stossward migration of the dome position. The ice rises progressively thin and eventually transition into ice rumples. There is no
significant threshold behaviour between these two states, and once the sea level increase is halted, the system converges to a steady-state ice rumple
with the lee-side grounding line located on the retrograde slope at the edge of the basal plateau. The summits are a few tens of metres above the ice
shelf surface, and the overall geometry is consistent with, for example, the ice rumple located in the Roi Baudouin Ice Shelf
(Fig.
Conversely, the high-friction case only transitions to an ice rumple for sea level perturbations that are greater than what is expected in a
glacial–interglacial cycle. In fact, there is no noticeable change in grounded area even for a sea level displacement of 50
Interestingly, the low-friction ice rumple exhibits lower minimum velocities than the intermediate-friction ice rumple, most likely
due to a greater grounded area (Fig.
The required sea level perturbation for ungrounding clearly depends on the elevation below sea level of the bed protrusion, but the scenarios shown
here with a maximum bed elevation of 80 m below sea level have many real-world counterparts (e.g. Kupol Moskovskij, Kupol Coilkovskogo, Leningrad Ice
Rise, Djupranen Ice Rise –
In all basal friction scenarios, there are two differing ice rises for a given sea level (Figs.
There is a difference in the individual pairs, with the grounded area being larger in the sea-level-increase scenario than in the sea-level-decrease
scenario. In all cases, the pairs occupy virtually the same region on the obstacle's stoss side, but the extent of grounding on the plateau differs
(Fig.
A self-stabilising feedback occurs, with divide migration opposing grounding line retreat in a sea-level-increase scenario. The ice rise height
reduces, and the divide migrates stossward during lee-side grounding line retreat. Because the divide moves stossward, the area of accumulation
adjacent to the divide on the lee side of the ice rise increases. The increased accumulation area promotes an increased flux across the grounding
line, opposing grounding line retreat. Analogously, sea level decrease results in leeward divide migration. The resulting reduction in accumulation
area adjacent to the divide on the lee side of the ice rise opposes grounding line advance. The existence of negative feedback mechanisms in both the
sea-level-increase and sea-level-decrease scenario results in hysteretic behaviour (Figs.
Another mechanism that plays a role is the sensitivity of the grounding line to bed shape, with hysteretic behaviour occurring due to the positioning
of retrograde and prograde slope segments
Although in our study, we have used a constant surface accumulation, we would expect orographic precipitation to enhance the hysteretic behaviour. In
future work it is worth investigating whether effects such as an increased melt rate also produce a hysteretic response in ice rises and ice
rumples. Given that the grounded area and basal sliding determine the ice rise evolution, future simulations should include a more informative guess
of the basal friction coefficients guided by, for example, seismic studies determining the bed properties
The existence of multiple steady states means that the grounding lines of ice rises and ice rumples observed today are dependent on the local ice flow
history during the last glacial cycle. Inversely, the dynamics and buttressing effect of ice rises and ice rumples are dependent on the initial
geometry prescribed, which is typically unknown. The degree of buttressing is of importance for determining the stability and evolution of the
continental grounding line
We have shown that the difference between the simulated grounding line and the hydrostatic equilibrium grounding line is small at each time step. This small error may, however, lead to an error propagation during transient simulation, leading to inaccurate grounding line migration if a hydrostatic equilibrium assumption is used.
We examined the effect of basal friction and sea level variation on the evolution of ice rises and ice rumples using idealised simulations including the surrounding ice shelves. In a high-basal-friction scenario, there is negligible mismatch when comparing simulated steady-state full Stokes velocities with steady-state SIA velocities, whereas in a low-basal-friction scenario the mismatch is larger due to stronger mechanical coupling to the surrounding ice shelf. The locality of the ice flow and the degree of basal sliding can be diagnosed by examining the (mis-)fit of a Vialov profile to the observed thickness profile. In response to an increasing sea level, a transition from ice rise to ice rumple occurs. Steady-state ice rumples form in the low-basal-friction scenarios, whereas the ice rumple in the high-friction scenario is ephemeral and ungrounds rapidly. The higher-friction ice rise, on the other hand, is largely unresponsive to sea level variations, requiring more than double the sea level rise to trigger the transition compared to the lower-friction scenarios.
All basal friction scenarios show self-stabilising, hysteretic behaviour, with grounded area and upstream ice shelf buttressing dependent on the evolution history. As a consequence of this behaviour, we identify the importance of perturbation history for the formation of the correct feature. Although in our study, we have concentrated only on the response of ice rises to sea level perturbation, further processes such as an increase in basal melt are also likely to result in hysteretic and potentially irreversible behaviour in ice shelf buttressing upstream of ice rises.
Presented in Fig.
The response of the grounded area and ice shelf velocity to sea level perturbation in the intermediate-friction scenario. In
In the case of the low-basal-friction scenario, we have run equivalent simulations using a differing grounding line numerical implementation,
namely the
Shown is the response of the grounded area in the low-friction case of the first floating (red) and discontinuous (blue) Elmer/Ice numerical grounding line implementations.
The code used to run the simulations and the post-processing code can be found at
The model output data are available for download (
A supplementary video is provided, showing the evolution of an ice rise in response to sea level perturbation as well as the position of the grounding line if the system were in hydrostatic equilibrium (DOI:
The supplement related to this article is available online at:
ACJH, CS, and RD conceived the idea for the study and designed the experiments. ACJH performed the simulations and analysis with support from all authors. The manuscript was written by ACJH with contributions from all authors.
At least one of the (co-)authors is a member of the editorial board of
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This work used resources of the Deutsches Klimarechenzentrum (DKRZ) granted by its Scientific Steering Committee (WLA) under project ID bm1164. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (
A. Clara J. Henry was supported by the Deutsche Forschungsgemeinschaft (DFG) in the framework of the priority programme 1158 “Antarctic Research with Comparative Investigations in Arctic Ice Areas” by grant SCHA 2139/1-1. Clemens Schannwell was supported by the German Federal Ministry of Education and Research (BMBF) as a Research for Sustainability initiative (FONA) through the PalMod project under the grant number 01LP1915C. Reinhard Drews and Vjeran Višnjević were supported by an Emmy Noether grant of the Deutsche Forschungsgemeinschaft (DR 822/3-1). The article processing charges for this open-access publication were covered by the Max Planck Society.
This paper was edited by Nicolas Jourdain and reviewed by two anonymous referees.