Transition to marine ice cliff instability controlled by ice thickness gradients and velocity

The Antarctic and Greenland ice sheets are drained by glaciers and ice shelves that terminate in near vertical ice cliffs submerged in the ocean. The portions of these ice sheets grounded beneath sea level have the potential to catastrophically collapse through a spectrum of instabilities, including the marine ice sheet instability and the marine ice cliff instability (MICI) (1–4). MICI was only recently proposed and occurs because the height of ice cliffs is limited by the strength of ice (4). When glaciers retreat into an overdeepening basin—or ice shelf collapse exposes a tall ice cliff—cliffs become structurally unstable at a threshold cliff height, leading to runaway cliff failure and ice sheet disintegration (3, 4).

Because MICI proceeds through brittle failure, it could lead to rapid ice sheet mass loss, with serious implications for sea level rise in the 21st century and beyond (3). Although there is evidence supporting the MICI in the paleo-record (5), MICI remains controversial because it has yet to be observed in modern-day glaciers. Moreover, current models of MICI rely on quasi-empirical parameterizations extrapolated from limited observations to simulate retreat (3, 6, 7). Without understanding the processes that limit rates of collapse, projections of sea level rise remain uncertain.

Here we show that, contrary to the MICI hypothesis, ice cliffs perched just above the maximum cliff height will not always catastrophically collapse, even when grounded on retrograde bed slopes with ice thickness increasing upstream. Instead, we find that catastrophic collapse is triggered when the ice thickness gradient exceeds a critical threshold. To probe ice cliff stability, we use the m-ice model (8), which treats ice like a power-law viscous material only until a yield strength is reached (9, 10). Once the yield strength is reached, the ice deforms rapidly and accumulation of plastic strain in failed portions of the ice reduces the strength of ice, resulting in failure localization. Our m-ice simulations neglect transient elastic stresses. The starting point of our simulations thus roughly corresponds to the end point of the viscoelastic simulations in (11). Our simulations, however, use a representation of the strength of ice that is more appropriate for modern-day Greenland calving glaciers and Antarctic ice shelves (8).

In our experiments, we first examined idealized slabs of ice on a flat bed with varying ice cliff thickness (H) and water depth (D), with ice thickness increasing upstream. For each simulation, the ice thickness or water depth was chosen empirically so that the stress at the ice cliff was initially perched slightly above the failure threshold. This resulted in simulations with an initially 135-m-thick dry ice cliff, a 400-m-thick glacier grounded in 290 m of water, and an 800-m-thick glacier grounded in 690 m of water.

In the dry case (D = 0, H ~135 m; Fig. 1, A to C), failure occurs as a slump. Calved debris accumulates ahead of the ice cliff, but the cliff is stable. After the initial slump, the glacier slowly thins and advances, with cascades of smaller calving events avalanching from the cliff top (movie S1 and Fig. 2A). The slope of the cliff is ~55°, similar to observations of Eqip Sermia, Greenland, which has a ~100-m-tall cliff that terminates in tens of meters of water (12). Moreover, additional simulations using a discrete element model to simulate brittle failure reveal similar patterns of failure, with a stable slumped cliff (movies S4 and S5), supporting the simplified continuum representation of failure used here.

We next simulated cliff collapse from a 400-m-thick glacier terminating in ~290 m of water (Fig. 1, D to F, and movie S2), comparable to typical Greenland outlet glaciers. An initial full-thickness fracture results in an iceberg that detaches. The berg is buoyant, drifts away and, unlike the dry case, does not provide a stabilizing compressive stress. The new calving face has a slight slope, resulting in buoyancy forces that trigger a second calving event. This exposes thicker ice upstream and causes another full-thickness fracture, leading to a cycle of catastrophic cliff collapse (Fig. 2B and movie S2). However, the addition of a small ~25-kPa back-stress at the ice cliff, similar to or smaller than the back-stress inferred in iceberg-choked Greenlandic fjords (13), slows retreat and prevents complete collapse (Fig. 2B). Retreat continues once the back-stress or “buttressing” is removed. This is consistent with observations of Greenland glaciers that show that the seasonal presence of sea-ice and icebergs clogging fjords stabilizes glacier retreat (13–16).

Finally, we examined an 800-m-tall cliff terminating in 690 m of water (~25 m height-above-buoyancy (Fig. 1, G to I), comparable to Greenland’s largest outlet glaciers and to the current grounding line thickness of Thwaites and Pine Island glaciers. Here, calving initiates with a subaerial slump, which triggers a buoyant calving event (Fig. 1G and movie S3). This is similar to the “footloose” theory of buoyant calving and observations of large Greenland glaciers (17–19). Thicker ice upstream is exposed as icebergs are quickly evacuated. However, episodic “serac” failure from the ice cliff results in a sequence of repeated events where wasting from the top of the ice cliff exposes a buoyant foot that episodically detaches (Fig. 1I). A small 25-kPa back-stress again stabilizes the ice cliff, this time resulting in cliff advance (Fig. 2C).

Our model predicts a distinct pattern of uplift near the ice cliff associated with progressive “serac” failure that precedes calving. This pattern of uplift is markedly similar to observed patterns of uplift observed near the cliffs of thick Greenland glaciers (Fig. 3), although additional processes, like submarine melt and formation of a super-buoyant tongue, may also play a role in Greenland calving cliff evolution. Nonetheless, the agreement between observations and simulations hint that cliff failure may already be underway in sections of Greenland.

To determine if stable cliff positions are possible in the absence of buttressing, we varied upstream velocity and bed slope to assess stability of the 800-m cliff. We ran simulations for at least 1 year or until the glacier completely collapsed to determine mean rates of cliff advance (Fig. 4). Simulations were initialized with identical surface slopes. To examine the role of bed slope and ice thickness gradients in controlling cliff stability, we also performed a few simulations with half the initial surface slope but equivalent ice thickness gradient (Fig. 4, filled squares).

For modest ice thickness gradients, we see patterns of retreat and advance largely controlled by the upstream velocity rather than the bed slope. Experiments performed with identical initial thickness gradients, but different bed slopes, result in comparable rates of terminus advance and retreat. For modest ice thickness gradients, larger upstream velocities result in advancing cliffs, whereas smaller upstream velocities result in retreating cliffs. Glacier advance and retreat is separated by a transition region, where rates of terminus advance are small (<100 m/annum) and quasi-stable over our 1- to 2-year simulation period (fig. S1).

As the ice thickness gradient becomes increasingly negative—ice thickness increases upstream faster—there is an abrupt transition at a critical thickness gradient to catastrophic collapse for all inflow velocities (Fig. 4). This “marine ice cliff collapse” regime is a consequence of retreat (by calving) exposing thicker ice upstream much faster than dynamic thinning can reduce the thickness of the upstream ice exposed. Glacier advance on a steeply sloping bed also increases cliff height, leading to runaway cliff failure and retreat rates exceeding tens of kilometers per year. This mechanism suggests that cliff stability is a strong function of dynamic thinning and hence, ice temperature. We confirmed this hypothesis with an additional set of simulations showing that warmer ice stabilizes retreat and results in a larger-magnitude (and flux dependent) critical thickness gradient (figs. S2 and S3).

Crucially, our results highlight the key role that dynamic thinning of the ice plays in controlling cliff failure. Resistance to collapse is controlled by a balance between upstream flux, dynamic thinning, and advection of thicker ice from upstream (supplementary text). This results in two regimes of cliff collapse. In the first regime, dynamic thinning keeps pace with calving, preventing runaway collapse by restricting growth of the cliff height during retreat. This regime is characterized by uplift near the cliff that precedes calving and strongly resembles observed patterns of uplift in thick Greenland outlet glaciers (Fig. 3). The second regime, marine ice cliff collapse, occurs when ice thickness increases rapidly upstream. However, even if a glacier enters into a regime where marine ice cliff collapse is imminent, a relatively small back-stress on the ice cliff of a few tens of kilopascals can slow or even stabilize retreat, making sustained ice sheet collapse less likely. This back-stress can be provided by the mixture of icebergs, sea-ice, and land-fast ice that abuts pinning points or ice margins. We also examined the possibility that gradual removal or weakening of an ice shelf could stabilize and prevent runaway retreat (11). Initializing simulations with 25 to 50 kPa of buttressing and then ramping the buttressing down over 1 to 50 days (fig. S4) shows that, consistent with our previous experiments, retreat and collapse can be postponed by a modest back-stress. The ice-cliff, however, remains precarious and retreat eventually accelerates, leading to collapse. These results support our previous interpretation but further emphasize that glacier geometry plays a dominant role in controlling rates of retreat associated with the marine ice cliff instability.

Thwaites Glacier, located in the Amundsen Sea Embayment of West Antarctica, is hypothesized to be one of the glaciers most vulnerable to cliff collapse (3). Our results suggest that disintegration or weakening of the floating ice shelf that currently buttresses Thwaites Glacier will expose a grounding line thickness large enough to initiate cliff retreat. At present grounding line conditions, Thwaites is unlikely to initially collapse. However, exposing the grounding line could trigger glacier retreat of a few kilometers per year (Fig. 3), comparable to the current retreat rate of large Greenland outlet glaciers like Jakobshavn Isbræ (Greenlandic: Sermeq Kujalleq) (20). Thwaites, however, is more than an order-of-magnitude wider than Jakobshavn and, even if Thwaites does not transition to catastrophic cliff collapse, initiating retreat would result in a substantial increase in the contribution of Thwaites Glacier to sea level rise.