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The Greenland Ice Sheet (GIS) is losing mass at a high rate1. Given the short-term nature of the observational record, it is difficult to assess the historical importance of this mass-loss trend. Unlike records of greenhouse gas concentrations and global temperature, in which observations have been merged with palaeoclimate datasets, there are no comparably long records for rates of GIS mass change. Here we reveal unprecedented mass loss from the GIS this century, by placing contemporary and future rates of GIS mass loss within the context of the natural variability over the past 12,000 years. We force a high-resolution ice-sheet model with an ensemble of climate histories constrained by ice-core data2. Our simulation domain covers southwestern Greenland, the mass change of which is dominated by surface mass balance. The results agree favourably with an independent chronology of the history of the GIS margin3,4. The largest pre-industrial rates of mass loss (up to 6,000 billion tonnes per century) occurred in the early Holocene, and were similar to the contemporary (ad 2000–2018) rate of around 6,100 billion tonnes per century5. Simulations of future mass loss from southwestern GIS, based on Representative Concentration Pathway (RCP) scenarios corresponding to low (RCP2.6) and high (RCP8.5) greenhouse gas concentration trajectories6, predict mass loss of between 8,800 and 35,900 billion tonnes over the twenty-first century. These rates of GIS mass loss exceed the maximum rates over the past 12,000 years. Because rates of mass loss from the southwestern GIS scale linearly5 with the GIS as a whole, our results indicate, with high confidence, that the rate of mass loss from the GIS will exceed Holocene rates this century. Rates of ice-mass loss from southwestern Greenland this century will exceed the maximum rate over the past 12,000 years, and would not be the result of natural variation.

We investigate changing precipitation patterns in the Kangerlussuaq region of western central Greenland during the Holocene thermal maximum (HTM), using a new chronology of ice sheet terminus position through the Holocene and a novel inverse modeling approach based on the unscented transform (UT). The UT is applied to estimate changes in annual precipitation in order to reduce the misfit between modeled and observed terminus positions. We demonstrate the effectiveness of the UT for time-dependent data assimilation, highlighting its low computational cost and trivial parallel implementation. Our results indicate that Holocene warming coincided with elevated precipitation, without which modeled retreat in the Kangerlussuaq region is more rapid than suggested by observations. Less conclusive is whether high temperatures during the HTM were specifically associated with a transient increase in precipitation, as the results depend on the assumed temperature history. Our results highlight the important role that changing precipitation patterns had in controlling ice sheet extent during the Holocene.

Satellite microwave brightness temperature (Tb) observations over the Greenland Ice Sheet permit determination of melted/frozen snow conditions at spatial and temporal scales that are uniquely suited for climate model validation and metrics of ice sheet change. Strong microwave sensitivity to the presence of liquid water in the snowpack is clear. Yet, a host of unique microwave-derived melt products covering the ice sheet are available, each based on different methodology, and with unknown inter-product agreement. Here, we compared five different published microwave melt products over a common 5-year (2003–2007) record to establish compatibility between products and agreement with in situ observations from a network of on-ice weather stations (AWS) spanning the ice sheet. A sixth product, leveraging both Tb seasonal trends and diurnal variability, was also introduced and included in the comparison. We found variable agreement between products and observations, with melt estimates based on microwave emissions modeling and the newly presented Adaptive Threshold (ADT) algorithm showing the best performance for AWS sites with more than 1-day average annual melt period (e.g., 68.9% of ADT melt days consistent with AWS observations; 31.1% of ADT frozen days contrasting with AWS observed melt). Spatial patterns of melting also varied between products. The different products showed substantial spread in melt occurrence even for products with the best AWS agreement. Product differences were generally larger under higher melt conditions; whereby, the fraction of the ice sheet experiencing ≥25 days of melting each year ranged from 4 to 25% for different products. While long-term satellite records have consistently shown increasing decadal trends in melt extent, our results imply that the melt frequency at any given location, particularly in the ice sheet interior where melting is less prevalent, is still subject to significant uncertainty.

Moulins permit access of surface meltwater to the glacier bed, causing basal lubrication and ice speedup in the ablation zone of western Greenland during summer. Despite the substantial impact of moulins on ice dynamics, the conditions under which they form are poorly understood. We assimilate a time-series of ice surface velocity from a network of eleven Global Positioning System receivers into an ice sheet model to estimate ice sheet stresses during winter, spring, and summer in an approx. 30 x 10 km region. Surface-parallel von Mises stress increases slightly during spring speedup and early summer, sufficient to allow formation of 16% of moulins mapped in the study area. In contrast, 63% of moulins experience stresses over the tensile strength of ice during a short (hours) supraglacial lake drainage event. Lake drainages appear to control moulin density, which is itself a control on subglacial drainage efficiency and summer ice velocities.

Englacial radar reflectors in the ablation zone of the Greenland Ice Sheet are derived from layering deposited in the accumulation zone over past millennia. The original layer structure is distorted by ice flow toward the margin. In a simplified case, shear and normal strain incurred between the ice divide and terminus should align depositional layers such that they closely approximate particle paths through the ablation zone where horizontal motion dominates. It is unclear, however, if this relationship holds in western Greenland where complex bed topography, three dimensional ice flow, and historical changes to ice sheet mass and geometry since layer deposition may promote a misalignment between present-day layer orientation and the modern ice flow field. We investigate this problem using a suite of analyses that leverage ice sheet models and observational datasets. Our findings suggest that across a study sector of western Greenland, the radiostratigraphy of the ablation zone is closely aligned with englacial particle paths, and is not far departed from a state of balance. The englacial radiostratigraphy thus provides insight into the modern, local, internal flow field, and may serve to further constrain ice sheet models that simulate ice dynamics in this region.

Force-balance calculations on Byrd Glacier, East Antarctica, reveal large spatial variations in the along-flow component of driving stress with corresponding sticky spots that are stationary over time. On the large scale, flow resistance is partitioned between basal (~80%) and lateral (~20%) drag. Ice flow is due mostly to basal sliding and concentrated vertical shear in the basal ice layers, indicating the bed is at or close to the pressure-melting temperature. There is a significant component of driving stress in the across-flow direction resulting in nonzero basal drag in that direction. This is an unrealistic result and we propose that there are spatial variations of bed features resulting in small-scale flow disturbances. The grounding line of Byrd Glacier is located in a region where the bed slopes upward. Nevertheless, despite a 10% increase in ice discharge between December 2005 and February 2007, following drainage of two subglacial lakes in the catchment area, the position of the grounding line has not retreated significantly and the glacier has decelerated since then. During the speed-up event, partitioning of flow resistance did not change, suggesting the increase in velocity was caused by a temporary decrease in basal effective pressure.

We introduce a novel, higher order, finite element ice sheet model called VarGlaS (Variational Glacier Simulator), which is built on the finite element framework FEniCS. Contrary to standard procedure in ice sheet modelling, VarGlaS formulates ice sheet motion as the minimization of an energy functional, conferring advantages such as a consistent platform for making numerical approximations, a coherent relationship between motion and heat generation, and implicit boundary treatment. VarGlaS also solves the equations of enthalpy rather than temperature, avoiding the solution of a contact problem. Rather than include a lengthy model spin-up procedure, VarGlaS possesses an automated framework for model inversion. These capabilities are brought to bear on several benchmark problems in ice sheet modelling, as well as a 500 yr simulation of the Greenland ice sheet at high resolution. VarGlaS performs well in benchmarking experiments and, given a constant climate and a 100 yr relaxation period, predicts a mass evolution of the Greenland ice sheet that matches present-day observations of mass loss. VarGlaS predicts a thinning in the interior and thickening of the margins of the ice sheet.

Atmospheric, oceanic, and subglacial forcing scenarios from the Sea-level Response to Ice Sheet Evolution (SeaRISE) project are applied to six three-dimensional thermomechanical ice-sheet models to assess Antarctic ice sheet sensitivity over a 500 year timescale and to inform future modeling and field studies. Results indicate (i) growth with warming, except within low-latitude basins (where inland thickening is outpaced by marginal thinning); (ii) mass loss with enhanced sliding (with basins dominated by high driving stresses affected more than basins with low-surface-slope streaming ice); and (iii) mass loss with enhanced ice shelf melting (with changes in West Antarctica dominating the signal due to its marine setting and extensive ice shelves; cf. minimal impact in the Terre Adelie, George V, Oates, and Victoria Land region of East Antarctica). Ice loss due to dynamic changes associated with enhanced sliding and/or sub-shelf melting exceeds the gain due to increased precipitation. Furthermore, differences in results between and within basins as well as the controlling impact of sub-shelf melting on ice dynamics highlight the need for improved understanding of basal conditions, grounding-zone processes, ocean-ice interactions, and the numerical representation of all three.

Ten ice-sheet models are used to study sensitivity of the Greenland and Antarctic ice sheets to prescribed changes of surface mass balance, sub-ice-shelf melting and basal sliding. Results exhibit a large range in projected contributions to sea-level change. In most cases, the ice volume above flotation lost is linearly dependent on the strength of the forcing. Combinations of forcings can be closely approximated by linearly summing the contributions from single forcing experiments, suggesting that nonlinear feedbacks are modest. Our models indicate that Greenland is more sensitive than Antarctica to likely atmospheric changes in temperature and precipitation, while Antarctica is more sensitive to increased ice-shelf basal melting. An experiment approximating the Intergovernmental Panel on Climate Change’s RCP8.5 scenario produces additional first-century contributions to sea level of 22.3 and 8.1 cm from Greenland and Antarctica, respectively, with a range among models of 62 and 14 cm, respectively. By 200 years, projections increase to 53.2 and 26.7 cm, respectively, with ranges of 79 and 43 cm. Linear interpolation of the sensitivity results closely approximates these projections, revealing the relative contributions of the individual forcings on the combined volume change and suggesting that total ice-sheet response to complicated forcings over 200 years can be linearized.

Ice flows when gravity acts on gradients in surface elevation, producing driving stresses. In the Isunnguata Sermia and Russell Glacier catchments of western Greenland, a 50% decline in driving stress along a flow line is juxtaposed with increasing surface flow speed. Here, these circumstances are investigated using modern observational data sources and an analysis of the balance of forces. Stress gradients in the ice mass and basal drag which resist the local driving stress are computed in order to investigate the underlying processes influencing the velocity and stress regimes. Our results show that the largest resistive stress gradients along the flowline result from increasing surface velocity. However, the longitudinal coupling stresses fail to exceed 15 kPa, or 20% of the local driving stress. Consequently, computed basal drag declines in proportion to the driving stress. In the absence of significant resistive stress gradients, other mechanisms are therefore necessary to explain the observed velocity increase despite declining driving stress. In the study area, the observed velocity—driving stress feature occurs at the long-term mean position of the equilibrium line of surface mass balance. We hypothesize that this position approximates the inland limit where seasonal surface meltwater penetrates the bed, and that the increased surface velocity reflects enhanced basal motion associated with these meltwater perturbations.

Ice-penetrating radar and ice core drilling4 have shown that large parts of the north-central Greenland ice sheet are melting from below. It has been argued that basal ice melt is due to the anomalously high geothermal flux, that has also influenced the development of the longest ice stream in Greenland. Here we estimate the geothermal flux beneath the Greenland ice sheet and identify a 1,200-km-long and 400-km-wide geothermal anomaly beneath the thick ice cover. We suggest that this anomaly explains the observed melting of the ice sheet’s base, which drives the vigorous subglacial hydrology and controls the position of the head of the enigmatic 750-km-long northeastern Greenland ice stream5. Our combined analysis of independent seismic, gravity and tectonic data implies that the geothermal anomaly, which crosses Greenland from west to east, was formed by Greenland’s passage over the Iceland mantle plume between roughly 80 and 35 million years ago. We conclude that the complexity of the present-day subglacial hydrology and dynamic features of the north-central Greenland ice sheet originated in tectonic events that pre-date the onset of glaciation in Greenland by many tens of millions of years.

Subglacial lakes beneath Antarctica’s fast-moving ice streams are known to undergo ∼1 km3 volume changes on annual timescales. Focusing on the MacAyeal Ice Stream (MacIS) lake system, we create a simple model for the response of subglacial water distribution to lake discharge events through assimilation of lake volume changes estimated from Ice, Cloud and land Elevation Satellite (ICESat) laser altimetry. We construct a steady-state water transport model in which known subglacial lakes are treated as either sinks or sources depending on the ICESat-derived filling or draining rates. The modeled volume change rates of five large subglacial lakes in the downstream portion of MacIS are shown to be consistent with observed filling rates if the dynamics of all upstream lakes are considered. However, the variable filling rate of the northernmost lake suggests the presence of an undetected lake of similar size upstream. Overall, we show that, for this fast-flowing ice stream, most subglacial lakes receive >90% of their water from distant distributed sources throughout the catchment, and we confirm that water is transported from regions of net basal melt to regions of net basal freezing. Our study provides a geophysically based means of validating subglacial water models in Antarctica and is a potential way to parameterize subglacial lake discharge events in large-scale ice-sheet models where adequate data are available.

A full-stress, thermomechanically coupled, numerical model is used to explore the interaction between basal thermal conditions and motion of a terrestrially terminating section of the west Greenland ice sheet. The model domain is a two-dimensional flowline profile extending from the ice divide to the margin. We use data-assimilation techniques based on the adjoint model in order to optimize the basal traction field, minimizing the difference between modeled and observed surface velocities. We monitor the sensitivity of the frozen/melted boundary (FMB) to changes in prescribed geothermal heat flux and sliding speed by applying perturbations to each of these parameters. The FMB shows sensitivity to the prescribed geothermal heat flux below an upper threshold where a maximum portion of the bed is already melted. The position of the FMB is insensitive to perturbations applied to the basal traction field. This insensitivity is due to the short distances over which longitudinal stresses act in an ice sheet.

The floating terminal of Jakobshavn Isbræ, the fastest Greenland ice stream, has disintegrated since 2002, resulting in a doubling of ice velocity and rapidly lowering inland ice elevations. Conditions prior to disintegration were modeled using control theory in a plane-stress solution, and the Missoula model of ice-shelf flow. Both approaches pointed to a mechanism that inhibits ice flow and that is not captured by either approach. Jamming of flow, an inherent property of granular materials passing through a constriction (Jakobshavn Isfjord), is postulated as the mechanism. Rapid disintegration of heavily crevassed floating ice accompanies break-up of the ice jam.

The Sea-level Response to Ice Sheet Evolution (SeaRISE) effort explores the sensitivity of the current generation of ice sheet models to external forcing to gain insight into the potential future contribution to sea level from the Greenland and Antarctic ice sheets. All participating models simulated the ice sheet response to three types of external forcings: a change in oceanic condition, a warmer atmospheric environment, and enhanced basal lubrication. Here an analysis of the spatial response of the Greenland ice sheet is presented, and the impact of model physics and spin-up on the projections is explored. Although the modeled responses are not always homogeneous, consistent spatial trends emerge from the ensemble analysis, indicating distinct vulnerabilities of the Greenland ice sheet. There are clear response patterns associated with each forcing, and a similar mass loss at the full ice sheet scale will result in different mass losses at the regional scale, as well as distinct thickness changes over the ice sheet. All forcings lead to an increased mass loss for the coming centuries, with increased basal lubrication and warmer ocean conditions affecting mainly outlet glaciers, while the impacts of atmospheric forcings affect the whole ice sheet. Key Points Sensitivity study of Greenland to atmospheric, oceanic and subglacial forcings Each forcing result in a different regional thickness response All forcings lead to an increased mass loss for the coming centuries ©2013. American Geophysical Union. All Rights Reserved.

Results from the Heinrich Event Intercomparison (HEINO) topic of the Ice-Sheet Model Intercomparison Project (ISMIP) are presented. ISMIP HEINO was designed to explore internal large-scale ice-sheet instabilities in different contemporary ice-sheet models. These instabilities are of interest because they are a possible cause of Heinrich events. A simplified geometry experiment reproduces the main characteristics of the Laurentide ice sheet, including the sedimented region over Hudson Bay and Hudson Strait. The model experiments include a standard run plus seven variations. Nine dynamic/thermodynamic ice-sheet models were investigated; one of these models contains a combination of the shallow-shelf (SSA) and shallow-ice approximation (SIA), while the remaining eight models are of SIA type only. Seven models, including the SIA–SSA model, exhibit oscillatory surges with a period of ∼1000 years for a broad range of parameters, while two models remain in a permanent state of streaming for most parameter settings. In a number of models, the oscillations disappear for high surface temperatures, strong snowfall and small sediment sliding parameters. In turn, low surface temperatures and low snowfall are favourable for the ice-surge cycles. We conclude that further improvement of ice-sheet models is crucial for adequate, robust simulations of cyclic large-scale instabilities.

We present the results of the first ice sheet model intercomparison project for higher-order and full-Stokes ice sheet models. These models are compared and verified in a series of six experiments of which one has an analytical solution obtained from a perturbation analysis. The experiments are applied to both 2-D and 3-D geometries; five experiments are steady-state diagnostic, and one has a time-dependent prognostic solution. All participating models give results that are in close agreement. A clear distinction can be made between higher-order models and those that solve the full system of equations. The full-Stokes models show a much smaller spread, hence are in better agreement with one another and with the analytical solution.

Large ice sheets, such as those presently covering Greenland and Antarctica, are important in driving changes of global climate and sea level. Yet numerical models developed to predict climate change and ice sheet-driven sea level fluctuations have substantial limitations: Poorly represented physical processes in the ice sheet component likely lead to an underestimation of sea level rise forced by a warming climate. The resultant uncertainty in sea level projections, and the implications for climate policy, have been widely discussed since the publication of the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) [IPCC, 2007]. The assessment report notes that current models do not include “the full effects of changes in ice sheet flow, because a basis in published literature is lacking.” The report also notes that the understanding of rapid dynamical changes in ice flow “is too limited to assess their likelihood or provide a best estimate or an upper bound for sea level rise.”