Glaciology - Ice Sheet Modelling

How can considerations of the forces that drive glacier and ice sheet flow help to explain the recent rapid dynamic changes in some Greenland and Antarctic outlet glaciers?

Fiona Fang, Trinity Hall

Fast-flowing outlet glaciers are the major conduits by which the interiors of the Greenland Ice Sheet (GIS) and Antarctic Ice Sheet (AIS) transfer ice to the ocean, and their recent acceleration explains much of the observed increase in ice-sheet mass loss and sea-level rise (IPCC, 2021). A force-balance perspective shows that fast flow reflects how the driving stress is partitioned among 3 resistive terms: basal traction, longitudinal stress, and lateral drag. Each term can trigger or regulate acceleration, but their relative importance differs between ice sheets. This essay examines how these forces operate, and critically evaluates why Greenland and Antarctic outlet glaciers respond differently despite sharing the same underlying physics.

Firstly, basal traction (τb) is the shear stress transmitted at the ice–bed interface that balances the gravitational driving stress, and is determined by bed properties, sliding speed, and effective pressure (Cuffey and Paterson, 2010). Weak beds with deformable till, high water pressure or low roughness offer little resistance and favour fast flow. At the land‐terminating margins of the GIS, τb is to first order controlled by subglacial hydrology. Koziol & Arnold (2018) demonstrated this by coupling a subglacial drainage model to a 2-D ice-flow model, calibrating to observed winter velocities, and forcing with observed RACMO runoff for three melt seasons. With geometry and rheology held fixed, the model reproduces the observed pattern of rapid early-summer acceleration, purely through melt-driven changes in water pressure and basal drag. In Antarctica, basal traction is more strongly controlled by bed type and large-scale substrate properties than by seasonal hydrology. Deformable marine sediments beneath major West Antarctic ice streams form low-traction corridors that permit streaming flow (Cuffey and Paterson, 2010). For example, Bindschadler Ice Stream has basal shear stress of only ~0.8–1.2 kPa while flowing faster than 300 m a⁻¹ (Joughin et al 2004). Bed topography reconstructions such as BedMachine Antarctica (Morlighem et al., 2020) reveal extensive deep marine basins with smooth beds interpreted as sedimentary substrates, contrasted with rougher bedrock highs that coincide with slower flow. Therefore, in Antarctica, low basal drag primarily sets where fast flow can exist, whereas in Greenland changes in basal stress (driven by hydrology) actively drives strong seasonal acceleration.

Secondly, longitudinal stress gradient (∂σ_xx/∂x) is the gradient of along-flow normal stress σ_xx. Where the glacier is extending, ∂σ_xx/∂x is negative and tends to accelerate flow; where it is being compressed, it adds an effective back stress that helps balance τ_d. Because ice is viscous and continuous, these longitudinal stress gradients are coupled over a length scale of several ice thicknesses. Therefore, a change in the stress state at the terminus or grounding line is transmitted tens of kilometres upstream as a change in extensional or compressional regime and therefore in surface velocity and thinning (Benn and Evans, 2010). If there is a compressive longitudinal stress at the grounding line, the glacier must respond by increasing extensional strain rates and surface speed to restore momentum balance, as seen in case studies below.

In AIS, Greene et al. (2018) document a 10–15% seasonal acceleration of Totten Ice Shelf following the breakup of rigid landfast sea ice and mélange at its front. The velocity anomaly is strongest over floating ice, and the timing of acceleration precedes surface melt, indicating that the change originates at the terminus through a reduction in frontal back stress rather than through basal hydrology. Process-based modelling studies further highlight the importance of buttressing and longitudinal stress gradient. Seroussi et al. (2014) applied increased sub-ice-shelf melt rates in a higher-order model of Pine Island Glacier: A +50% melt perturbation yields 200 m yr⁻¹ speedup within 15 years across fast tributaries, accompanied by several to tens of kilometres of grounding line retreat. Because basal traction was fixed in the model set up, the response reflects a purely buttressing-driven adjustment. Reese et al (2018) further demonstrate that highly localized ice-shelf thinning can reach across the entire shelf and accelerate ice flow in regions far from the initial perturbation. As an example, this ‘tele-buttressing’ enhances outflow from Bindschadler Ice Stream in response to thinning near Ross Island more than 900 km away. At the continental scale, Fürst et al. (2016) compute a buttressing number for all Antarctic shelves and show that roughly half of the grounded AIS flux is restrained by only 10–15 % of shelf area concentrated in narrow “safety bands”; numerically removing these bands doubles grounding-line flux in affected basins and allows speed increases to propagate tens to hundreds of kilometres inland. Together, these studies show that recent AIS accelerations can be explained by reductions in boundary resistance that reorganise the longitudinal stress field.

GIS outlet glaciers show similar longitudinal transmission of frontal perturbations, but it sits more clearly alongside basal traction changes. At Jakobshavn Isbræ, Joughin et al. (2012) showed that seasonal advance and retreat of the front can explain most of the near-terminus summer-winter speedup. As the winter tongue collapses and the terminus retreats, the frontal force drops, extensional stresses near the front rise, and speeds increase in phase along the lower 10–20 km. However, the same study shows that this cannot explain the full long-term acceleration: loss of the 15 km ice tongue and associated change in frontal force accounts for only ~20–40 % of the doubling in speed. The remainder arises changes in driving stress and effective pressure induced by thinning: steeper surface gradient increases the driving stress, while thinner ice lowers the effective pressure and therefore weakens basal traction, both contribute to acceleration. To sum up, longitudinal stress transmission clearly matters in Greenland, but its effect is superimposed on a background set by basal and hydrological evolution, whereas in many West Antarctic outlets, particularly those with extensive floating ice shelves, the trunk is more directly sensitive to changes in buttressing and longitudinal stress.

While longitudinal stress transmission explains how boundary perturbations reorganise flow over tens of kilometres, the magnitude and stability of that response ultimately depend on how much resistance is supplied by the bed and by lateral confinement. Lateral drag is the shear stress exerted along the glacier’s side-walls and shear margins, where fast trunk ice deforms against slower or stagnant ice and valley walls. In narrow, well-confined outlets, this side drag supports a substantial fraction of the driving stress and therefore limits further acceleration. For instance, van der Veen et al. (2011) used a force-balance analysis of Jakobshavn Isbræ and showed that as the glacier accelerated after 1998, increases in driving stress were largely offset by rising lateral drag along the fjord walls and shear margins. Idealised experiments by Åkesson et al. (2018) show that under identical climate forcing, changing only fjord width can alter grounding-line retreat by tens of kilometres. When confinement weakens, such as through fjord widening, shear-margin weakening, or loss of pinning points, lateral resistance drops and velocities increase under the same driving stress. For example, Wehrlé et al. (2025) analyze a large calving event at Jakobshavn Isbræ and argue that loss of lateral drag due to calving lead to a 3.3% speedup in the main trunk, affecting flow up to 11 km upstream. Together, these studies show that lateral drag, as controlled by geometry, is a first-order regulator of outlet-glacier flow.

Where grounding lines sit on retrograde beds, geometry alters the force balance in a fundamentally different way: any perturbation that drives grounding-line retreat pushes it inland into deeper water, so the ice must be thicker to float. This increases the driving stress and increases grounding-line flux non-linearly with thickness (Benn and Evans, 2010). Once boundary resistance (shelf buttressing and lateral drag) is weakened, this geometric feedback becomes the main control on whether retreat self-limits or accelerates into a marine ice sheet instability regime (Schoof, 2012). Pine Island Glacier (PIG) is a clear example. Favier et al (2014) forced three models (Elmer/Ice, BISICLES L1L2, and Úa with several sub-ice-shelf melt perturbations (m1–m4). For realistic “strong” perturbations (m2, m3), Elmer/Ice and BISICLES both show a ~40 km grounding-line retreat across the steep reverse slope within a few years, with peak dynamic imbalance 130 Gt yr⁻¹. Crucially, once retreat is triggered, the details of the melt pattern matter less than the bed geometry: different perturbations produce very similar retreat across the retrograde trench. In “reverse” experiments, where melt is reduced back towards present-day values after retreat starts, the grounding line does not stabilise on the reverse slope but continues to retreat to the bottom of the trench; only very strong melt reductions (<10–25 % of present rates) cause re-advance. Joughin et al (2014) reach a similar conclusion for Thwaites glacier, whose grounding line currently sits on a coastal sill ~600 m b.s.l., with a deep (>1200 m) inland basin 60–80 km upstream. A basin-scale SSA model is used, forced with different melt scenarios. For all but the lowest melt case (m = 0.5), grounding line eventually retreats into the deep basin and crosses a “threshold” where basin-wide mass loss exceeds 1 mm yr⁻¹ sle, which they interpret as onset of rapid collapse. It takes ~200–900 yr to reach the threshold depending on melt and margin strength. Together with PIG, this shows that, for glaciers with reverse-slope beds, geometry and longitudinal coupling set the long-term fate once buttressing is reduced; ocean forcing mainly sets how quickly the threshold is crossed, not whether the system is fundamentally stable.

Viewed through a force-balance lens, recent accelerations of Greenland and Antarctic outlet glaciers occur when gravitational driving stress is redistributed among basal traction, longitudinal stresses, and lateral drag. In Greenland, melt-driven weakening of the bed interacts with seasonal and secular changes in frontal back-stress to produce strong but relatively localised speed-ups. In West Antarctica, by contrast, weak marine sediments, extensive ice shelves, and retrograde beds create a system in which even modest reductions in buttressing reorganise the longitudinal stress field and can potentially trigger non-linear grounding-line retreat. A force-balance perspective therefore shows that fast flow of the outlet glacier is not the product of a single external forcing, but of how these forcings interact with each glacier’s internal stress hierarchy – a distinction is essential for anticipating their future instability.

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