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Recent observations of dynamic water systems beneath the Greenland and Antarctic ice sheets have sparked renewed interest in modelling subglacial drainage. The foundations of today's models were laid decades ago, inspired by measurements from mountain glaciers, discovery of the modern ice streams and the study of landscapes evacuated by former ice sheets. Models have progressed from strict adherence to the principles of groundwater flow, to the incorporation of flow 'elements' specific to the subglacial environment, to sophisticated two-dimensional representations of interacting distributed and channelized drainage. Although presently in a state of rapid development, subglacial drainage models, when coupled to models of ice flow, are now able to reproduce many of the canonical phenomena that characterize this coupled system. Model calibration remains generally out of reach, whereas widespread application of these models to large problems and real geometries awaits the next level of development.

The Greenland Ice Sheet has been a major contributor to global sea-level rise in recent decades 1 , 2 , and it is expected to continue to be so 3 . Although increases in glacier flow 4 – 6 and surface melting 7 – 9 have been driven by oceanic 10 – 12 and atmospheric 13 , 14 warming, the magnitude and trajectory of the ice sheet’s mass imbalance remain uncertain. Here we compare and combine 26 individual satellite measurements of changes in the ice sheet’s volume, flow and gravitational potential to produce a reconciled estimate of its mass balance. The ice sheet was close to a state of balance in the 1990s, but annual losses have risen since then, peaking at 345 ± 66 billion tonnes per year in 2011. In all, Greenland lost 3,902 ± 342 billion tonnes of ice between 1992 and 2018, causing the mean sea level to rise by 10.8 ± 0.9 millimetres. Using three regional climate models, we show that the reduced surface mass balance has driven 1,964 ± 565 billion tonnes (50.3 per cent) of the ice loss owing to increased meltwater runoff. The remaining 1,938 ± 541 billion tonnes (49.7 per cent) of ice loss was due to increased glacier dynamical imbalance, which rose from 46 ± 37 billion tonnes per year in the 1990s to 87 ± 25 billion tonnes per year since then. The total rate of ice loss slowed to 222 ± 30 billion tonnes per year between 2013 and 2017, on average, as atmospheric circulation favoured cooler conditions 15 and ocean temperatures fell at the terminus of Jakobshavn Isbræ 16 . Cumulative ice losses from Greenland as a whole have been close to the rates predicted by the Intergovernmental Panel on Climate Change for their high-end climate warming scenario 17 , which forecast an additional 70 to 130 millimetres of global sea-level rise by 2100 compared with their central estimate. Three techniques for estimating mass losses from the Greenland Ice Sheet produce comparable results for the period 1992–2018 that approach the trajectory of the highest rates of sea-level rise projected by the IPCC.

Knowledge of the ice thickness distribution of the world’s glaciers is a fundamental prerequisite for a range of studies. Projections of future glacier change, estimates of the available freshwater resources or assessments of potential sea-level rise all need glacier ice thickness to be accurately constrained. Previous estimates of global glacier volumes are mostly based on scaling relations between glacier area and volume, and only one study provides global-scale information on the ice thickness distribution of individual glaciers. Here we use an ensemble of up to five models to provide a consensus estimate for the ice thickness distribution of all the about 215,000 glaciers outside the Greenland and Antarctic ice sheets. The models use principles of ice flow dynamics to invert for ice thickness from surface characteristics. We find a total volume of 158 ± 41 × 103 km3, which is equivalent to 0.32 ± 0.08 m of sea-level change when the fraction of ice located below present-day sea level (roughly 15%) is subtracted. Our results indicate that High Mountain Asia hosts about 27% less glacier ice than previously suggested, and imply that the timing by which the region is expected to lose half of its present-day glacier area has to be moved forward by about one decade.The ice volume of glaciers outside the Greenland and Antarctic ice sheets totals about 158,000 km3, with about 27% less ice in High Mountain Asia than thought, according to multiple models that estimate ice thickness from surface characteristics.

Constraining past West Antarctic Ice Sheet (WAIS) change helps validate numerical models simulating future ice sheet dynamics. Following rapid deglaciation during the mid‐Holocene, ice near Thwaites Glacier was ∼35 m thinner than present; however, the timing of ice regrowth to its present configuration remains unknown. To fill this knowledge gap, we present cosmogenic nuclide exposure ages of cobbles from the surface of a moraine situated between Thwaites and Pope glaciers. We infer that the moraine formed and stabilized in the Late Holocene (∼1.4 ka) when a small glacier thickened. We also present a novel reconstruction of WAIS volume constrained by sea‐level data, which demonstrates that moraine formation coincided with a large‐scale WAIS readvance. Our new geologic constraints will help inform models of the solid Earth response to surface mass loading, improving our understanding of ice sheet dynamics in a vulnerable part of WAIS. Plain Language Summary The Antarctic ice sheets are melting and adding to sea‐level rise, with the rate at which they lose mass expected to increase in the coming decades to centuries. However, recent studies have shown that, only a few thousand years ago, the Antarctic ice sheets were smaller than they are now, and subsequently regrew to their present size. Understanding how the Antarctic ice sheets regrew to their present size, as well as the rate it happened, helps us understand whether ongoing loss of ice sheet mass is reversible. In this study, we identify a glacial landform (a moraine) that was deposited as an Antarctic glacier grew in size after the Antarctic ice sheets were smaller than they are today. We collected rocks from the surface of the glacial landform and measured isotopes in them. These isotopes tell us the landform was created by the glacier about 1,400 years ago. The new information from this study on the past of the Antarctic ice sheets can be used to improve our understanding of how the Antarctic ice sheets will change, and add to sea‐level rise, in the future. Key Points Direct evidence is found for a Late Holocene episode of glacier thickening in the Amundsen Sea Embayment, West Antarctica Ice thickening is evidenced by a moraine between Thwaites and Pope glaciers and is dated with surface exposure dating of erratic cobbles The moraine may help to constrain the end of a mid‐Holocene contracted ice sheet configuration in the Amundsen Sea sector

The stability and dynamics of Thwaites Glacier depend on the structural properties of its marine terminus; however, the relationship between these variables on the floating ice tongue is poorly understood. Here we present a six-year record of ice speed, derived from satellite observations starting in 2015, showing two large-magnitude (approximately 30–45%) and prolonged (approximately one to two years) cycles of speed variation across the ice tongue. Using an automated, deep learning-based method of extracting high-resolution fracture maps from satellite imagery, we detail periods of increasing fracture development and subsequent reconsolidation in the ice tongue shear margin that coincide with the observed speed changes. Inverse modelling using the BISICLES ice-sheet model indicates that the variation in ice speed can be accounted for by these observed changes to the spatial pattern of fracturing. This study provides further evidence of direct coupling between fracturing and dynamic variability in West Antarctica but indicates that increased fracturing and associated speed changes are reversible on one- to two-year timescales. We suggest that fracturing does not necessarily lead to positive feedback with glacier acceleration on these timescales and that damage process modelling is important for accurately predicting the evolution of the Antarctic Ice Sheet.Observations and modelling of the Thwaites Glacier Ice Tongue link episodic changes in ice speed to fracturing between 2015 and 2021 and show these changes to be reversible over one- to two-year timescales.

Subglacial hydrology is an important component of the ice dynamic system in Antarctica but is challenging to investigate due to the large spatial scales of the catchment systems, the ice thickness, and remote location. Here I discuss key discoveries about Antarctic subglacial hydrology from the Glacier Drainage System (GlaDS) model, including the presence of long, often high-pressure, subglacial channels. These channels pump tens of cubic metres per second of freshwater into ice-shelf cavities and directly affect melt rates at the critical grounding zone regions. Future ice dynamics and ice-shelf cavity models should take subglacial hydrology into account if they are to accurately predict future behaviour of the Antarctic Ice Sheet.

Petermann Glacier is a major outlet glacier of northern Greenland that drains a marine‐based basin vulnerable to destabilization from enhanced oceanic and atmospheric forcings. Using satellite radar interferometry data from the Sentinel‐1a/b missions, we observe a seasonal glacier acceleration of 15% in the summer, from 1,250 to 1,500 m/yr near the grounding line, but the physical drivers of this seasonality have not been elucidated. Here, we use a subglacial hydrology model coupled one‐way to an ice sheet model to evaluate the role of subglacial hydrology as a physical mechanism explaining the seasonal acceleration. We find excellent agreement between the observed and predicted velocity in terms of timing and magnitude with the addition of an applied lower limit on effective pressure of 6% of ice overburden pressure. We conclude that seasonal changes in subglacial hydrology are sufficient to explain the observed seasonal speed up of Petermann Glacier. Plain Language Summary Petermann Glacier is one of the largest glaciers in northern Greenland with a sea‐level rise potential of about half a meter. In recent years, extensive satellite data have become available which provide frequent and widespread observations over much of the Greenland ice sheet, including Petermann. Access to such records provides the opportunity to investigate changes in glacier dynamics taking place over much smaller time periods. We see that in the summer Petermann's speed increases by about 15% from 1,250 to 1,500 m/year near the grounding line. We are able to reproduce this observed pattern in speed by predicting how friction at the base of the glacier will change with the addition of summer surface melt to the bed, and using those changes in friction to calculate seasonal speedup of the ice. Key Points Petermann Glacier in northern Greenland accelerates by 15% from 1,250 to 1,500 m/yr during the summer months near the grounding line A subglacial hydrology model quantifies seasonal changes in effective pressure at the bed in response to meltwater runoff input Simulated effective pressure drives velocity behavior that matches observations in magnitude and timing over three consecutive years

Abstract Surface melt forces summertime ice‐flow accelerations on glaciers and ice sheets. Here, we show that large meltwater‐forced accelerations also occur during wintertime in Greenland. We document supraglacial lakes (SGLs) draining in cascades at unusually high elevation, causing an expansive flow acceleration over a ∼5,200 km 2 region during winter. The three‐component interferometric surface velocity field and decomposition modeling reveal the underlying flood propagation with unprecedented detail as it traveled over 160 km from the drainage site to the margin, providing novel constraints on subglacial water pathways, drainage morphology, and links with basal sliding. The triggering SGLs continuously grew over 40 years and suddenly released decades of stored meltwater, demonstrating surface melting can impact dynamics well beyond melt production. We show these events are likely common and thus their cumulative impact on dynamics should be further evaluated.

Two outstanding questions for the future of the Greenland Ice Sheet are (a) how enhanced meltwater draining beneath the ice will impact the behavior of large tidewater glaciers, and (b) to what extent tidewater glacier velocity is driven by changes at the terminus versus changes in sliding velocity due to meltwater. We present a two‐way coupled framework to simulate the nonlinear feedbacks of evolving subglacial hydrology and ice dynamics using the Subglacial Hydrology And Kinetic, Transient Interactions (SHAKTI) model within the Ice‐sheet and Sea‐level System Model (ISSM). Through coupled simulations of Helheim Glacier, we find that terminus effects dominate the seasonal velocity pattern up to 15 km from the terminus, while hydrology drives the velocity response upstream. With increased melt, the hydrology influence yields seasonal acceleration of several hundred meters per year in the interior, suggesting that hydrology will play an important role in future mass balance of tidewater glaciers. Plain Language Summary Water draining under glaciers and ice sheets affects the friction between the ice and the bed, and controls how fast the ice can slide into the ocean, contributing to sea‐level rise. We present a framework for simulating the feedbacks between hydrology and ice flow. We investigate the relative influence of changes at the terminus of the glacier where it meets the ocean, versus changes in meltwater drainage, in determining how fast the glacier moves. Our modeling of Helheim Glacier in southeast Greenland highlights the importance of terminus effects up to 15 km from the terminus, and hydrology farther upstream, with increased melt yielding higher inland acceleration. These results suggest that meltwater will play an increasingly important role in the future behavior of glaciers. Key Points We couple a subglacial hydrology model with an ice flow model to simulate the relationship between sliding velocity and effective pressure Terminus effects at Helheim Glacier drive velocity up to 15 km upstream, but seasonal hydrology controls velocity patterns further inland Increased melt accelerates ice inland of the main trunk, implying importance of hydrology in tidewater glacier future mass balance

In recent decades, the Greenland ice sheet has been losing mass through glacier retreat and ice flow acceleration. This mass loss is linked with variations in submarine melt, yet existing ocean models are either coarse global simulations focused on decadal‐scale variability or fine‐scale simulations for process‐based investigations. Here, we unite these scales with a framework to downscale from a global state estimate (15 km) into a regional model (3 km) that resolves circulation on the continental shelf. We further downscale into a fjord‐scale model (500 m) that resolves circulation inside fjords and quantifies melt. We demonstrate this approach in Scoresby Sund, East Greenland, and find that interannual variations in submarine melt at Daugaard‐Jensen glacier induced by ocean temperature variability are consistent with the decadal changes in glacier ice dynamics. This study provides a framework by which coarse‐resolution models can be refined to quantify glacier submarine melt for future ice sheet projections. Plain Language Summary Over the past several decades, the Greenland ice sheet has been losing ice and contributing to sea‐level rise. About half of this ice loss is induced by melt that occurs where glaciers meet the ocean. Using coarse‐scale ocean models that simulate circulation around the globe, previous studies have noted a strong link between ocean temperature and enhanced glacier ice loss. However, due to the small scale of Greenland's fjords, coarse models are unable to directly quantify circulation in these fjords and melt on submerged glaciers. In this study, we develop a new framework to “zoom in” on a fjord, using high‐resolution models driven by larger coarse‐resolution models. In this approach, we simulate melt on one of Greenland's biggest glaciers and find that periods of higher melt coincide with more ice loss as observed from satellites. Since this framework is adaptable to other regions, it could also be used to simulate melt on other glaciers and support estimates of future sea‐level rise. Key Points Subsurface temperature variability is simulated in a narrow fjord network using regional models downscaled from a global state estimate Modeled increases in ocean melt at Daugaard‐Jensen glacier coincide with the onset of acceleration in 2005 and retreat and thinning in 2011 Model variations in shelf‐to‐fjord ocean properties match with observations, providing a basis to estimate ocean forcing in ice projections