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The sea level contribution of the Antarctic ice sheet constitutes a large uncertainty in future sea level projections. Here we apply a linear response theory approach to 16 state-of-the-art ice sheet models to estimate the Antarctic ice sheet contribution from basal ice shelf melting within the 21st century. The purpose of this computation is to estimate the uncertainty of Antarctica's future contribution to global sea level rise that arises from large uncertainty in the oceanic forcing and the associated ice shelf melting. Ice shelf melting is considered to be a major if not the largest perturbation of the ice sheet's flow into the ocean. However, by computing only the sea level contribution in response to ice shelf melting, our study is neglecting a number of processes such as surface-mass-balance-related contributions. In assuming linear response theory, we are able to capture complex temporal responses of the ice sheets, but we neglect any self-dampening or self-amplifying processes. This is particularly relevant in situations in which an instability is dominating the ice loss. The results obtained here are thus relevant, in particular wherever the ice loss is dominated by the forcing as opposed to an internal instability, for example in strong ocean warming scenarios. In order to allow for comparison the methodology was chosen to be exactly the same as in an earlier study (Levermann et al., 2014) but with 16 instead of 5 ice sheet models. We include uncertainty in the atmospheric warming response to carbon emissions (full range of CMIP5 climate model sensitivities), uncertainty in the oceanic transport to the Southern Ocean (obtained from the time-delayed and scaled oceanic subsurface warming in CMIP5 models in relation to the global mean surface warming), and the observed range of responses of basal ice shelf melting to oceanic warming outside the ice shelf cavity. This uncertainty in basal ice shelf melting is then convoluted with the linear response functions of each of the 16 ice sheet models to obtain the ice flow response to the individual global warming path. The model median for the observational period from 1992 to 2017 of the ice loss due to basal ice shelf melting is 10.2 mm, with a likely range between 5.2 and 21.3 mm. For the same period the Antarctic ice sheet lost mass equivalent to 7.4mm of global sea level rise, with a standard deviation of 3.7mm (Shepherd et al., 2018) including all processes, especially surface-mass-balance changes. For the unabated warming path, Representative Concentration Pathway 8.5 (RCP8.5), we obtain a median contribution of the Antarctic ice sheet to global mean sea level rise from basal ice shelf melting within the 21st century of 17 cm, with a likely range (66th percentile around the mean) between 9 and 36 cm and a very likely range (90th percentile around the mean) between 6 and 58 cm. For the RCP2.6 warming path, which will keep the global mean temperature below 2 °C of global warming and is thus consistent with the Paris Climate Agreement, the procedure yields a median of 13 cm of global mean sea level contribution. The likely range for the RCP2.6 scenario is between 7 and 24 cm, and the very likely range is between 4 and 37 cm. The structural uncertainties in the method do not allow for an interpretation of any higher uncertainty percentiles.We provide projections for the five Antarctic regions and for each model and each scenario separately. The rate of sea level contribution is highest under the RCP8.5 scenario. The maximum within the 21st century of the median value is 4 cm per decade, with a likely range between 2 and 9 cm per decade and a very likely range between 1 and 14 cm per decade.

In the Amundsen Sea, modified Circumpolar Deep Water (mCDW) intrudes into ice shelf cavities, causing high ice shelf melting near the ice sheet grounding lines, accelerating ice flow, and controlling the pace of future Antarctic contributions to global sea level. The pathways of mCDW towards grounding lines are crucial as they directly control the heat reaching the ice. A realistic representation of mCDW circulation, however, remains challenging due to the sparsity of in-situ observations and the difficulty of ocean models to reproduce the available observations. In this study, we use an unprecedentedly high-resolution (200 m horizontal and 10 m vertical grid spacing) ocean model that resolves shelf-sea and sub-ice-shelf environments in qualitative agreement with existing observations during austral summer conditions. We demonstrate that the waters reaching the Pine Island and Thwaites grounding lines follow specific, topographically-constrained routes, all passing through a relatively small area located around 104°W and 74.3°S. The temporal and spatial variabilities of ice shelf melt rates are dominantly controlled by the sub-ice shelf ocean current. Our findings highlight the importance of accurate and high-resolution ocean bathymetry and subglacial topography for determining mCDW pathways and ice shelf melt rates.

Earlier large-scale Greenland ice sheet sea-level projections (e.g., those run during the ice2sea and SeaRISE initiatives) have shown that ice sheet initial conditions have a large effect on the projections and give rise to important uncertainties. The goal of the initMIP-Greenland intercomparison exercise is to compare, evaluate and improve the initialisation techniques used in the ice sheet modelling community and to estimate the associated uncertainties in modelled mass changes. initMIP-Greenland is the first in a series of ice sheet model intercomparison activities within ISMIP6 (the Ice Sheet Model Intercomparison Project for CMIP6), which is the primary activity within the Coupled Model Intercomparison Project - phase 6 (CMIP6) focusing on the ice sheets. Two experiments for the large-scale Greenland ice sheet have been designed to allow intercomparison between participating models of 1) the initial present-day state of the ice sheet and 2) the response in two idealised forward experiments. The forward experiments serve to evaluate the initialisation in terms of model drift (forward run without additional forcing) and in response to a large perturbation (prescribed surface mass balance anomaly), and should not be interpreted as sea-level projections. We present and discuss results that highlight the diversity of data sets, boundary conditions and initialisation techniques used in the community to generate initial states of the Greenland ice sheet. We find good agreement across the ensemble for the dynamic response to surface mass balance changes in areas where the simulated ice sheets overlap, but differences arising from the initial size of the ice sheet. The model drift in the control experiment is reduced for models that participated in earlier intercomparison exercises.

Estimating the future evolution of the Antarctic Ice Sheet (AIS) is critical for improving future sea level rise (SLR) projections. Numerical ice sheet models are invaluable tools for bounding Antarctic vulnerability; yet, few continental-scale projections of century-scale AIS SLR contribution exist, and those that do vary by up to an order of magnitude. This is partly because model projections of future sea level are inherently uncertain and depend largely on the model's boundary conditions and climate forcing, which themselves are unknown due to the uncertainty in the projections of future anthropogenic emissions and subsequent climate response. Here, we aim to improve the understanding of how uncertainties in model forcing and boundary conditions affect ice sheet model simulations. With use of sampling techniques embedded within the Ice Sheet System Model (ISSM) framework, we assess how uncertainties in snow accumulation, ocean-induced melting, ice viscosity, basal friction, bedrock elevation, and the presence of ice shelves impact continental-scale 100-year model simulations of AIS future sea level contribution. Overall, we find that AIS sea level contribution is strongly affected by grounding line retreat, which is driven by the magnitude of ice shelf basal melt rates and by variations in bedrock topography. In addition, we find that over 1.2 m of AIS global mean sea level contribution over the next century is achievable, but not likely, as it is tenable only in response to unrealistically large melt rates and continental ice shelf collapse. Regionally, we find that under our most extreme 100-year warming experiment generalized for the entire ice sheet, the Amundsen Sea sector is the most significant source of model uncertainty (1032 mm 6σ spread) and the region with the largest potential for future sea level contribution (297 mm). In contrast, under a more plausible forcing informed regionally by literature and model sensitivity studies, the Ronne basin has a greater potential for local increases in ice shelf basal melt rates. As a result, under this more likely realization, where warm waters reach the continental shelf under the Ronne ice shelf, it is the Ronne basin, particularly the Evans and Rutford ice streams, that are the greatest contributors to potential SLR (161 mm) and to simulation uncertainty (420 mm 6spread).

Thwaites Glacier (TG), West Antarctica, has been losing mass and retreating rapidly in the past few decades. Here, we present a study of its calving dynamics combining a two-dimensional flow-band full-Stokes (FS) model of its viscous flow with linear elastic fracture mechanics (LEFM) theory to model crevasse propagation and ice fracturing. We compare the results with those obtained with the higher-order (HO) and the shallow-shelf approximation (SSA) models coupled with LEFM. We find that FS/LEFM produces surface and bottom crevasses that are consistent with the distribution of depth and width of surface and bottom crevasses observed by NASA's Operation IceBridge radar depth sounder and laser altimeter, whereas HO/LEFM and SSA/LEFM do not generate crevasses that are consistent with observations. We attribute the difference to the nonhydrostatic condition of ice near the grounding line, which facilitates crevasse formation and is accounted for by the FS model but not by the HO or SSA models. We find that calving is enhanced when pre-existing surface crevasses are present, when the ice shelf is shortened or when the ice shelf front is undercut. The role of undercutting depends on the timescale of calving events. It is more prominent for glaciers with rapid calving rates than for glaciers with slow calving rates. Glaciers extending into a shorter ice shelf are more vulnerable to calving than glaciers developing a long ice shelf, especially as the ice front retreats close to the grounding line region, which leads to a positive feedback to calving events. We conclude that the FS/LEFM combination yields substantial improvements in capturing the stress field near the grounding line of a glacier for constraining crevasse formation and iceberg calving.

Identifying fast and robust numerical solvers is a critical issue that needs to be addressed in order to improve projections of polar ice sheets evolving in a changing climate. This work evaluates the impact of using advanced numerical solvers for transient ice-flow simulations conducted with the JPL-UCI Ice Sheet System Model (ISSM). We identify optimal numerical solvers by testing a broad suite of readily available solvers, ranging from direct sparse solvers to preconditioned iterative methods, on the commonly used Ice Sheet Model Intercomparison Project for Higher-Order ice sheet Models benchmark tests. Three types of analyses are considered: mass transport, horizontal stress balance, and incompressibility. The results of the fastest solvers for each analysis type are ranked based on their scalability across mesh size and basal boundary conditions. We find that the fastest iterative solvers are ĝ1/4ĝ€1.5-100 times faster than the default direct solver used in ISSM, with speed-ups improving rapidly with increased mesh resolution. We provide a set of recommendations for users in search of efficient solvers to use for transient ice-flow simulations, enabling higher-resolution meshes and faster turnaround time. The end result will be improved transient simulations for short-term, highly resolved forward projections (10-100 year time scale) and also improved long-term paleo-reconstructions using higher-order representations of stresses in the ice. This analysis will also enable a new generation of comprehensive uncertainty quantification assessments of forward sea-level rise projections, which rely heavily on ensemble or sampling approaches that are inherently expensive.

Abstract. Thwaites Glacier (TG), West Antarctica, has been losing mass and retreating rapidly in the past few decades. Here, we present a study of its calving dynamics combining a two-dimensional flowband Full Stokes (FS) model of its viscous flow with linear elastic fracture mechanics (LEFM) theory to model crevasse propagation and ice fracturing. We compare the results with those obtained with the higher-order (HO) and the shallow-shelf approximation (SSA) models coupled with LEFM. We find that FS/LEFM produces surface and bottom crevasses that match the distribution of crevasse depth and width observed from NASA's Operation IceBridge radar depth sounders, whereas HO/LEFM and SSA/LEFM do not generate crevasses that match observations. We attribute the difference to the non-hydrostatic condition of ice near the grounding line, which facilitates crevasse formation, and is accounted for by the FS model but not by the HO or SSA model. We also find that calving is enhanced when pre-existing surface crevasses are present, when the ice shelf is shortened or when the ice shelf front is undercut. The role of undercutting depends on the time scale of calving events. It is more prominent for glaciers with rapid calving rates than glaciers with slow calving rates. Glaciers extending into a shorter ice shelf are more vulnerable to calving than glaciers developing a long ice shelf, especially as the ice front retreats close to the grounding line region, which leads to a positive feedback. We conclude that the FS/LEFM combination yields substantial improvements in capturing the stress field near the grounding line for constraining crevasse formation and iceberg calving.

Enhanced submarine ice-shelf melting strongly controls ice loss in the Amundsen Sea embayment (ASE) of West Antarctica, but its magnitude is not well known in the critical grounding zones of the ASE's major glaciers. Here we directly quantify bottom ice losses along tens of kilometres with airborne radar sounding of the Dotson and Crosson ice shelves, which buttress the rapidly changing Smith, Pope and Kohler glaciers. Melting in the grounding zones is found to be much higher than steady-state levels, removing 300-490 m of solid ice between 2002 and 2009 beneath the retreating Smith Glacier. The vigorous, unbalanced melting supports the hypothesis that a significant increase in ocean heat influx into ASE sub-ice-shelf cavities took place in the mid-2000s. The synchronous but diverse evolutions of these glaciers illustrate how combinations of oceanography and topography modulate rapid submarine melting to hasten mass loss and glacier retreat from West Antarctica.

Basal sliding is a main control on glacier flow primarily driven by water pressure at the glacier base. The ongoing increase in surface melting of the Greenland Ice Sheet warrants an examination of its impact on basal water pressure and in turn on basal sliding. Here we examine the case of Russell Glacier, in West Greenland, where an extensive set of observations has been collected. These observations suggest that the recent increase in melt has had an equivocal impact on the annual velocity, with stable flow on the lower part of the drainage basin but accelerated flow above the Equilibrium Line Altitude (ELA). These distinct behaviors have been attributed to different evolutions of the subglacial draining system during and after the melt season. Here we use a high-resolution subglacial hydrological model forced by reconstructed surface runoff for the period 2008 to 2012 to investigate the cause of these distinct behaviors. We find that the increase in meltwater production at low elevation yields a more efficient drainage system compatible with the observed stagnation of the mean annual flow below the ELA. At higher elevation, the model indicates that the drainage system is mostly inefficient and is therefore strongly sensitive to an increase in meltwater availability, which is consistent with the observed increase in ice velocity.

The mechanical properties of glacier beds play a fundamental role in regulating the sensitivity of glaciers to environmental forcing across a wide range of timescales. Glaciers are commonly underlain by deformable till whose mechanical properties and influence on ice flow are not well understood but are critical for reliable projections of future glacier states. Using synoptic-scale observations of glacier motion in different seasons to constrain numerical ice flow models, we study the mechanics of the bed beneath Hofsjökull, a land-terminating ice cap in central Iceland. Our results indicate that the bed deforms plastically and weakens following incipient summertime surface melt. Combining the inferred basal shear traction fields with a Coulomb-plastic bed model, we estimate the spatially distributed effective basal water pressure and show that changes in basal water pressure and glacier accelerations are non-local and non-linear. These results motivate an idealized physical model relating mean basal water pressure and basal slip rate wherein the sensitivity of glacier flow to changes in basal water pressure is inversely related to the ice surface slope.

© 2015 Elsevier B.V. Following the 2002 disintegration of the northern and central parts of the Larsen B Ice Shelf, the tributary glaciers of the southern surviving part initially appeared relatively unchanged and hence assumed to be buttressed sufficiently by the remnant ice shelf. Here, we modify this perception with observations from IceBridge altimetry and InSAR-inferred ice flow speeds. Our analyses show that the surfaces of Leppard and Flask glaciers directly upstream from their grounding lines lowered by 15 to 20 m in the period 2002-2011. The thinning appears to be dynamic as the flow of both glaciers and the remnant ice shelf accelerated in the same period. Flask Glacier started accelerating even before the 2002 disintegration, increasing its flow speed by ~55% between 1997 and 2012. Starbuck Glacier meanwhile did not change much. We hypothesize that the different evolutions of the three glaciers are related to their dissimilar bed topographies and degrees of grounding. We apply numerical modeling and data assimilation that show these changes to be accompanied by a reduction in the buttressing afforded by the remnant ice shelf, a weakening of the shear zones between its flow units and an increase in its fracture. The fast flowing northwestern part of the remnant ice shelf exhibits increasing fragmentation, while the stagnant southeastern part seems to be prone to the formation of large rifts, some of which we show have delimited successive calving events. A large rift only 12 km downstream from the grounding line is currently traversing the stagnant part of the ice shelf, defining the likely front of the next large calving event. We propose that the flow acceleration, ice front retreat and enhanced fracture of the remnant Larsen B Ice Shelf presage its approaching demise.

The contribution of the Antarctic ice sheet is one of the most uncertain components of sea level rise to 2100. Ice sheet models are the primary tool for projecting future sea level contribution from continental ice sheets. The Ice Sheet Model Intercomparison for the Coupled Model Intercomparison Phase 6 (ISMIP6) provided projections of the ice sheets contribution to sea level over the 21st century. It quantified uncertainty due to ice sheet model, climate scenario, forcing climate model and uncertain model parameters. We present simulations following the ISMIP6 framework with the BISICLES ice sheet model, alongside new experiments extending the ISMIP6 protocol to more comprehensively explore uncertain ice sheet processes. These results contributed to Antarctic projections of Edwards et al. (2021), which formed the basis of sea level projections for the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (AR6). The BISICLES experiments presented here show the important interplay between surface mass balance forcing and ocean driven melt, with high warming, high accumulation forcing conditions leading to mass gain (negative sea level contribution) under low sensitivity to ocean driven melt. Conversely, we show that when sensitivity to ocean warming is high, ocean melting drives increased mass loss despite high accumulation. Finally, we show that collapse of ice shelves due to surface warming increases sea level contribution by 25 mm for both moderate and high sensitivity of ice shelf melting to ocean forcing tested. [ABSTRACT FROM AUTHOR]

Predictions of marine ice-sheet behaviour require models able to simulate grounding-line migration. We present results of an intercomparison experiment for plan-view marine ice-sheet models. Verification is effected by comparison with approximate analytical solutions for flux across the grounding line using simplified geometrical configurations (no lateral variations, no buttressing effects from lateral drag). Perturbation experiments specifying spatial variation in basal sliding parameters permitted the evolution of curved grounding lines, generating buttressing effects. The experiments showed regions of compression and extensional flow across the grounding line, thereby invalidating the boundary layer theory. Steady-state grounding-line positions were found to be dependent on the level of physical model approximation. Resolving grounding lines requires inclusion of membrane stresses, a sufficiently small grid size (

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.

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. Key Points Sensitivity study of Antarctica to atmospheric, oceanic and subglacial forcings Different sectors of Antarctica are vulnerable to the forcings Atmospheric forcing lead to a growth, but dynamic forcing lead to a mass loss ©2013. American Geophysical Union. All Rights Reserved.

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 flow numerical models are essential for predicting the evolution of ice sheets in a warming climate. Recent research emphasizes the need for higher-order and even full-Stokes flow models, instead of the traditional shallow-ice approximation, whose assumptions are not valid in certain critical areas. These higher-order models are, however, computationally intensive and difficult to use at the continental scale. Here we present a new technique, the Tiling method, to couple ice flow models of varying orders of complexity. The goal of the method is to limit the spatial extent of where higherorder models are applied to reduce the computational cost, while maintaining the model precision. We apply this method on synthetic geometries to demonstrate its practical use. We first use a geometry for which all models yield the same results to check the consistency of the method. Then we apply our method to a geometry for which a full-Stokes model is required in the vicinity of the ice front. Our results show that the hybrid models present significant improvements over mono-model approaches and reduce computational times.