Pine Island Glacier (PIG), a part of the West Antarctic marine ice sheet, has recently undergone substantial changes including acceleration, grounding-line retreat and thinning. Theoretical arguments suggest that marine ice sheets can become unstable, entering phases of irreversible retreat. Modelling work indicates this as a possible future scenario for PIG. However, to date, no firm evidence is available of an unstable retreat phase having occurred. Here we present a modelling study, validated by observational data, of a rapid PIG retreat in the 1970s, and demonstrate that it was self-enhancing and irreversible. Results show PIG had crossed a tipping point by the early 1970s whereby further grounding-line retreat was inevitable despite temporal reversal in climatic conditions. The irreversible phase had ended by the early 1990s after almost 40 km of retreat and 0.34 mm added to global sea level, causing PIG to become the main contributor from the Antarctic Ice Sheet.
Article
Recent irreversible retreat of Pine Island Glacier
https://doi.org/10.21203/rs.3.rs-2241776/v1
This work is licensed under a CC BY 4.0 License
Journal Publication
published 04 Dec, 2023
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The West Antarctic Ice Sheet (WAIS) has been losing mass since at least the start of the satellite era1, resulting in half of the overall sea level rise contribution from the entire continent2. In the Amundsen Sea sector there has been widespread thinning3, accelerated ice flow1 and grounding-line retreat4, which has prompted questions about the future stability of the region5,6. Modelling studies have predicted further retreat under current and future climate conditions7–10, and there is a possibility of a complete collapse of the WAIS if a local destabilisation occurs11. Due to the retrograde bed (sloping downwards in the inland direction) beneath its largest glaciers, the Amundsen Sea sector is vulnerable to the marine ice sheet instability, MISI,12,13 where a small perturbation in grounding-line position could result in irreversible mass loss and grounding-line retreat beyond a tipping point14,15. The floating extensions of glaciers, known as ice shelves, provide buttressing of upstream grounded ice and can be sufficient to restore stability to an unstable grounding-line retreat16,17, particularly through the aid of pinning points such as ice rises and ice rumples18,19. However, ice shelves are susceptible to ocean-induced melting from below20, which can lead to thinning, weakened buttressing and accelerated ice flow21.
One of the largest glaciers in the Amundsen Sea sector is Pine Island Glacier (PIG), which has contributed more to global sea level rise in recent decades than any other glacier in Antarctica2. Thinning of the present-day ice shelf and the subsequent grounding-line retreat can be traced back to the 1940s when an ocean cavity first started to form upstream of a subglacial bedrock ridge22. There was further grounding-line retreat and increased ice discharge in the 1970s with the ungrounding of an ice rumple over the highest part of the ridge1,23. These events in the 1940s and 1970s coincide with notable climate anomalies in the central tropical Pacific, which has been shown to have a teleconnection with the Amundsen Sea24. It’s possible that tropically forced wind anomalies over the continental shelf caused a shallowing of the thermocline, allowing more warm Circumpolar Deep Water to access the underneath of the ice shelf, leading to higher melt and enhanced thinning25–28. Previous ice flow modelling studies have shown that a shallower thermocline can cause irreversible retreat on an idealised representation of PIG, and this happens once there is a sufficient gap between the bedrock ridge and ice shelf29,30.
Here, we investigate the retreat of PIG from the subglacial ridge and whether MISI played a role in that retreat. To do this, we use the finite-element, vertically integrated ice-flow model Úa31 to solve the ice dynamics equations in the shallow ice-stream approximation. We first advance a present-day PIG configuration to a steady state position on the subglacial ridge. This is then perturbed under two different scenarios: cold forcing to represent conditions prior to 1940s; and warm forcing, with a shallower thermocline, to represent conditions during a tropically forced warm period. The final experiment explores the stability regime of the glacier by incrementally changing the thermocline depth in retreat and advance steady state simulations.
Pre 1940s Pine Island Glacier
The model starts from a present-day representation of PIG, with the grounding line of the main central trunk sitting on a 1200 m deep section of bedrock, 45 km upstream of the subglacial ridge crest (Fig. 1). It is then run for 500 years, with no basal melting applied, allowing a new steady state to be reached. During this period, the ice stream thickens and advances forward, reduces in speed, and grounds at the ridge crest front. The final grounding-line ice flux is 68 Gt yr− 1, which is almost within the error range of the earliest observed grounding-line flux, when PIG was still grounded on the ridge1. This final configuration is the starting point for the following cold and warm perturbations.
For the following experiments, we apply a simple depth-dependent melt-rate parameterisation, following a similar approach in a previous PIG study7. The parameterisation represents a two-layer ocean, typically used for conditions in Pine Island Bay30,32, with zero melting at shallow depths and maximum melting in the deep (Supplementary Fig. 4). Between the two layers is a linearly changing melt rate which represents the thermocline. We first run a control simulation, which represents cold conditions. This has a maximum melt rate of 100 m yr− 1 below a depth of 800 m, decreasing to zero melt at 400 m. We refer to this as having a thermocline depth of 800 m to be consistent with other studies. Crucially, the highest melt rate is below the depth of the ridge crest, and hence, most of the ice shelf is exposed to lower melt rates (Supplementary Fig. 5). At the start of the run, the integrated melt rate across the ice shelf is 98 Gt yr− 1, the mean melt rate is 40 m yr− 1 and ice flux across the grounding line is 67 Gt yr− 1. After 50 years of control forcing, the ice stream reaches a new steady state and has thinned a little, sped up by 8–10% and retreated 2–3 km. However, importantly, it remains grounded along the middle of the ridge crest (Fig. 1). The mean melt rate decreases to 15 m yr− 1 and the integrated melt rate decreases to 32 Gt yr− 1, as the ice shelf lower surface becomes shallower, which agrees well with observations for a typical cold year32. Due to faster flowing ice, the grounding-line ice flux increases to 73 Gt yr− 1, which is close to the earliest recorded observation1. The final configuration of the control case is an estimation of how PIG was situated prior to the 1940s.
Rapid retreat from a subglacial ridge
To simulate the response of PIG to warmer ocean conditions when grounded at the ridge, we raise the melt-rate profile by 200 m so that the maximum melt rate is below a depth of 600 m and decreases to zero at 200 m, similar to other studies30,33. In this experiment the highest melt rate is above the depth of the ridge crest, which compared to the control case results in an almost doubling of the starting mean melt rate (77 m yr− 1) and integrated melt rate (180 Gt yr− 1) across the ice shelf (Supplementary Fig. 5). After 50 years of warm forcing, there is extensive thinning of grounded and floating ice, the ice stream accelerates by 50%, and there is a 30 km grounding-line retreat from the ridge crest to the next raised section of bedrock (Fig. 1). After the main period of retreat, the mean melt rate decreases to 20–30 m yr− 1 and the integrated melt rate decreases below 100 Gt yr− 1, which is in agreement with observations for recent warm years32. The ice flux across the grounding line at the end of the warm forcing simulation is 92 Gt yr− 1, which is comparable to the 1996 observation, when PIG was grounded in a similar position.
Figure 2 shows the transient behaviour of the glacier during the warm forcing experiment and reveals four different stages of the retreat, similar to a previous idealised study of PIG30. During the first stage, for approximately 5 to 10 years, there is a gradual retreat from the front of the ridge crest, as the ice shelf rapidly thins in response to the high melt rate, transforming the profile of the ice shelf lower surface from convex to concave. The slowest rate of retreat occurs from the north end of the ridge, where the bedrock is shallow and wide, whilst the fastest retreat occurs from the south, along the deep bedrock channel (Fig. 2a). There is a sharp decrease in integrated melt rate, from 180 Gt yr− 1 down to 84 Gt yr− 1, as the ice shelf thins and becomes shallower, experiencing lower melting. During the second stage, from 10 to approximately 32 years, the grounding-line retreats gradually across the ridge crest, with occasional jumps across small retrograde slopes (See Supplementary Figs. 6–8), before slowing down towards the back of the ridge crest. There is a little ice shelf thinning, a gradual decrease in integrated melt rate, and a slowdown in retreat. During this period, two isolated subglacial lakes start to form upstream of the ridge beneath the gradually thinning ice shelf, but they remain disconnected from the main outer ice shelf cavity, so they do not experience any melting. Between 32 and 40 years, the third stage is illustrated by rapid grounding-line retreat across several areas of retrograde bed on the landward side of the ridge, and the upstream lakes merge with the main cavity via the deep southern channel. An ice rumple forms over the highest part of the ridge in the North, and then the ice shelf ungrounds completely around 40 years. This stage of retreat shows a sharp increase in integrated melt rate as the grounding line enters a deeper section of the bedrock and experiences higher melting. For the fourth and final stage, from 40 years until the end of the simulation, there is a gradual retreat of the grounding line onto the next prominent section of prograde bedrock, and the ice stream begins to approach a new steady state. There is a gradual decrease in integrated melt rate as the ice shelf continues to slowly thin.
Marine Ice Sheet Instability
The warm forcing experiment showed several instances of rapid grounding-line retreat across retrograde sloping bedrock in response to increased melting, but to assess whether the retreat crossed a tipping point we perform a stability analysis, where additional model simulations show the impact of incremental changes in thermocline depth (Fig. 3). The experiment consists of 38 separate simulations, with 19 comprising a retreat group and 19 in a subsequent advance group. The retreat simulations all start from the no-melt steady state solution at the ridge, approximately 45 km downstream of the present-day grounding line (Fig. 1). The advance simulations all start from the final steady state solution of the last model run in the retreat group, which is approximately 10 km from the present-day grounding line. All model simulations in the two groups have a different thermocline depth, which ranges from 1300 m to 400 m (Fig. 3e), and each is run to a steady state, indicating how far the grounding line can move under each forcing.
The first six retreat simulations, with thermocline depths between 1300 m and 1050 m, do not cause any thinning of the ice shelf because the highest melt rates are deeper than the ridge crest and lower ice surface. The maximum melt rate from the warmest of these runs is 34 m yr− 1, whilst the mean is 2 m yr− 1 and the median is 0 m yr− 1. As the thermocline is raised above 1050 m, the steady state solutions show a gradual, continual thinning of the ice shelf and retreat of the grounding line from the front of the ridge crest to the back (Fig. 3a,b,e). Once the thermocline is raised above 700 m, the steady state grounding-line retreats a further 20 km from the ridge crest down the retrograde slope to the next prominent high point in the bed. For thermocline depths above 650 m there is only a further 5 km of retreat, with the final steady state grounding line resting on an upstream prograde section of bedrock.
The large transition in grounding-line position in response to the small change in thermocline depth above 700 m doesn’t necessarily mean a tipping point has been crossed. To examine whether this retreat has become irreversible we perform an opposite set of simulations, in the advance direction, and incrementally lower the thermocline, creating progressively colder conditions with lower melt rates. As the thermocline is lowered from a depth of 400 m to 1000 m, there is a gradual thickening of the ice shelf and a total grounding-line advance of 8 km from the upstream prograde slope of the bed rise. The thermocline must be lowered below 1000 m for the melt rates to become small enough to allow for sufficient thickening of the ice shelf and regrounding on the subglacial ridge. There is no change in ice shelf thickness or grounding line once the thermocline is lowered beneath a depth of 1050 m and the steady state position coincides with the original starting position, 45 km from the present-day grounding line.
It's evident from this experiment that a hysteresis behaviour exists when PIG is forced with a changing thermocline depth. The final position of the steady state grounding line depends on the history of forcing applied, whether the glacier has been retreating or advancing. There are two threshold thermocline depths at 700 m and 1000 m, that when crossed, lead to irreversible grounding-line motion. These are irreversible transitions because the thermocline depth must be changed more than the forcing in the opposite direction to achieve the same grounding-line position. Furthermore, there are no steady state grounding lines on the steep retrograde slope behind the central section of bedrock ridge, except for two isolated lakes where there is no melting. These results suggest that PIG has likely been subject to the MISI in its past as it started to retreat from the subglacial bedrock ridge. Figure 3e shows the main region of instability along one of the central flowlines as the steep, landward (retrograde) slope of the ridge, which is also seen in other flowlines across the shelf (Supplementary Figs. 9–11).
Prior to the 1940s, it’s likely that PIG had been grounded in a stable position on a subglacial ridge 45 km downstream from its present-day position22. Then, following notable climate anomalies, and possibly warmer basal conditions, in the 1940s and 1970s27, an ocean cavity formed beneath the ice shelf and the glacier started to retreat from the ridge crest22,23. By the early 1990s, the grounding-line had completely retreated off the ridge, across the retrograde bed, settling at an ice plain 30 km upstream34 (Supplementary Fig. 12). This raises the question of whether its retreat from the ridge was unstable in response to the initial perturbation, which could explain why the glacier didn’t advance back to the ridge during the intermediary cooler years27.
Using a vertically integrated ice-flow model and a depth-dependent melt rate parameterisation, we investigated the aspect of the retreat from the subglacial ridge that was due to internal dynamics of the system rather than changes in external forcing. The ocean forcing in this experiment is therefore simplified as we focus solely on whether MISI played a role in the retreat of PIG from the ridge. At the beginning of a warm simulation, the grounding line is in a stable position at the ridge crest. After a step change in forcing, the grounding line retreats initially slowly across the ridge, before undergoing a rapid retreat down the retrograde slope with the merging of upstream lakes. Although we used a simple melt rate parameterisation, the initial behaviour of retreat, the speed at which it progresses and the final ungrounding of a pinning point above the ridge are all comparable with satellite observations and sediment records from the 1940s and 1970s22,23. The same key features of retreat also occurred when we used a more realistic parameterisation which tapered the melt rate down to zero at the grounding line (Supplementary Figs. 13–14).
Our stability analysis suggests that by the early 1970s, when PIG had already started retreating from the ridge23, a tipping point had been crossed, whereby further retreat was inevitable despite a return to cooler conditions27. This irreversible phase comes to a halt as the grounding line reaches a new steady state on the next bed high point. This location coincides with its early 1990s position, when PIG was grounded at an ice plain34. During the suspected period of rapid retreat from the 1970s to the early 1990s, PIG was responsible for a third of the mass loss from West Antarctica, and almost 13% of the overall Antarctic Ice Sheet mass loss2. Despite its basin comprising of only 1.5% of the entire ice sheet area, PIG was the largest contributor to sea level rise during those years, adding 0.34 mm in total2. We have shown for the first time an example of MISI occurring which is validated by observations. We show that although prominent highs in the seafloor may provide a period of temporary stability to a glacier, once the grounding line starts to retreat down the retrograde landward side, the retreat can be quick and irreversible despite changes in climatic conditions.
In this study we used the finite-element, vertically integrated ice-flow model Úa31 to solve the ice dynamics equations in the shallow ice-stream approximation (SSTREAM or SSA)35. The model has previously been used to study tipping points and drivers of retreat of Pine Island Glacier15,36, grounding-line stability and ice shelf buttressing31,37,38 and in a number of intercomparison projects39–41.
The vertically integrated, or two horizontal dimension, momentum equations can be written in compact form as
where h is the ice thickness, tbh is the horizontal component of the bed-tangential basal traction tb, \({{\rho }}_{i}\) is the vertically averaged ice density, g is gravitational acceleration, s is the ice upper surface elevation, and R is the resistive stress tensor defined as
$${R}\text{=}\left( \begin{array}{cc}\text{2}{\tau }_{xx}\text{+}{\tau }_{yy}& {\tau }_{xy}\\ {\tau }_{xy}& {\tau }_{yy}+{\tau }_{xx}\end{array} \right)$$
2
and
$${\nabla }_{xy}={\left({\partial }_{x},{\partial }_{y}\right)}^{T}.$$
3
Here, \({\tau }_{ij}\) are the components of the deviatoric stress tensor. The relationship between deviatoric stresses \({\tau }_{ij}\) and strain-rates \(\dot{{\text{ϵ}}_{ij}}\) is given by Glen's flow law
$$\dot{{ϵ}_{ij}}=A{\tau }^{n-1}{\tau }_{ij}$$
4
where \(\tau\) is the second invariant of the deviatoric stress tensor
$${\tau }=\sqrt{{{\tau }}_{ij}{{\tau }}_{ij}/2}$$
5
A is a spatially varying ice rate factor determined using inverse methods and \(n=3\) is a creep exponent. For grounded ice, the basal traction is given by Weertman's sliding law
where vb is the horizontal component of the bed-tangential ice-velocity, C is a spatially varying slipperiness parameter, determined using inverse methods, and \(m=3\)which gives a non-linear viscous relationship. Downstream of the grounding line the slipperiness parameter is set to a constant of 0.03, which allows the ice stream to advance forward. This constant is representative of upstream slipperiness values along the fast-flowing tributaries.
Model domain and mesh
The model domain includes the grounded catchment of PIG (182,000 km2) and its floating ice shelf42 (Supplementary Fig. 1). The calving front position is fixed throughout the study and corresponds approximately to the 2008/09 ice front. For all experiments in this study, a Dirichlet boundary condition is imposed on the grounded portion of the boundary to set the velocity to zero along the ice divides, and a Neumann boundary condition arising from ocean pressure is imposed along the ice front.
An irregular, triangular mesh was generated using MESH2D43 for the entire domain, and consisted of 58777 linear elements and 29797 nodes. The mesh was refined for ice shelf elements (1 km) and in areas of high strain rate and high strain rate gradients (700–1.5 km), whereas larger elements (10 km) were used for the slowest moving ice inland away from the main tributaries (Supplementary Fig. 2). This gave a mesh with minimum, median, and maximum element sizes of 563 m, 1311 m and 11330 m respectively. For the control and warm experiments, a further grounding line mesh adaption was applied to ensure fine element sizes were used in a crucial transition area. Due to computational and time limitations, no mesh adaption was used for the reversibility experiments.
Input data
This study aims to simulate the response of a 1940s PIG to a change in external forcing, however, with very little data available for that period we set up our model using present day observations and then let the model evolve in time to get an approximate configuration for 1940. The bedrock topography, ice thickness, surface elevation and ice density were taken from BedMachine Antarctica, v244. These datasets have a resolution of 500 m and nominal data of 2015. Some local adjustments were made to the ice shelf thickness near the grounding line to ensure the hydrostatic floating condition was met. Upper surface accumulation was from RACMO2.3p245 and averaged between 1979 to 2016.
Inversion
To initialise the model, we used present day velocities from the MEaSUREs Annual Antarctic Ice Velocity Maps46,47 dataset to invert for the slipperiness parameter and the ice rate factor. For the inversion process, Úa minimises a cost function containing a misfit and a regularisation term, using the adjoint method and Tikhonov regularisation, as has been done in previous studies48–50. The inversion results are shown in Supplement Fig. 3.
Melt rate parameterisation
The basal melt rate is given by a depth dependent parameterisation (see Supplement Figs. 4 and 5), similar to previous study on Pine Island Glacier retreat7. Although this is a simple parameterisation, it allows for conclusions to be made about the direct effect of basal melting. To ensure the grounding line retreat was not overestimated, we applied basal melting on mesh elements that are strictly downstream of the grounding line51. For the stability analysis, model simulations were run for 100s of years until a steady state was reached. During these runs, to avoid unrealistic retreat along the southwest tributary, close to the model domain boundary, the basal melting was set to zero for elements in this region.
Acknowledgments
We would like to acknowledge the support and resources of the Supercomputing Wales (SCW) project, without which these simulations and results would not have been possible. B. C. Reed is supported by the ENVISION Doctoral Training Partnership studentship from the Natural Environment Research Council.
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