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Mass loss due to dynamic changes in ice sheets is a significant contributor to sea level rise, and this contribution is expectedto increase in the future. Numerical codes simulating the evolution of ice sheets can potentially quantify this future contribution.However, the uncertainty inherent in these models propagates into projections of sea level rise, and hence is crucialto understand. Key variables of ice sheet models, such as basal drag or ice stiffness, are typically initialized using inversionmethodologies to ensure that models match present observations. Such inversions often involve tens or hundreds of thousandsof parameters, with unknown uncertainties and dependencies. The computationally intensive nature of inversions along withtheir high number of parameters mean traditional methods such as Monte Carlo are expensive for uncertainty quantification.Here we develop a framework to estimate the posterior uncertainty of inversions, and project them onto sea level change projections over the decadal timescale. The framework treats parametric uncertainty as multivariate Gaussian, and exploits theequivalence between the Hessian of the model and the inverse covariance of the parameter set. The former is computed efficientlyvia algorithmic differentiation, and the posterior covariance is propagated in time using a time-dependent model adjointto produce projection error bars. This work represents an important step in quantifying the internal uncertainty of projectionsof ice-sheet models.

There is significant uncertainty over how ice sheets and glaciers will respond to rising global temperatures. Limited knowledge of the topography and rheology of ice-bed interface is a key cause of this uncertainty, as models show that small changes in the bed can have a large influence on predicted rates of ice loss. Most of our detailed knowledge of bed topography comes from airborne and ground-penetrating radar observations. However, these direct observations are not spaced closely enough to meet the requirements of ice-sheet models, so interpolation and inversion methods are used to fill in the gaps. Here we present the results of a new inversion of surface-elevation and velocity data over Thwaites Glacier, West Antarctica, for bed topography and slipperiness (i.e. the degree of basal slip for a given level of drag). The inversion is based on a steady-state linear perturbation analysis of the shallow-ice-stream equations. The method works by identifying disturbances to surface flow which are caused by obstacles or sticky patches in the bed, and can therefore be applied wherever the shallow-ice-stream equations hold and where surface data are available, even where the ice thickness is not well known. We assess the performance of the inversion for topography with the available radar data. Although the topographic output from the inversion is less successful where the bed slopes steeply, it compares well with radar data from the central trunk of the glacier. This method could therefore be useful as either an independent test of other interpolation methods such as mass conservation and kriging, or as a complementary technique in regions where those techniques fail. We do not have data to allow us to assess the success of the slipperiness results from our inversions, but we provide maps that may guide future seismic data collection across Thwaites Glacier. The methods presented here show significant promise for using high-resolution satellite datasets, calibrated by the sparser field datasets, to generate high resolution bed topography products across the ice sheets, and therefore contribute to reduced uncertainty in predictions of future sea-level rise.

Thwaites and Pine Island glaciers as well as other ice streams in West Antarctica have been changing dramatically over the past decades. Although changes in ocean conditions are likely the primary driver of these changes, it remains unclear where other processes could cause more mass loss. By employing automatic differentiation and two independent ice sheet models, we construct maps of the sensitivity of the volume above floatation to changes in ocean-induced melt rates, ice rigidity, basal friction, and surface mass balance. We find that changes in basal melt close to the grounding lines and along shear margins have a larger impact on the glaciers' final volume. The glaciers are sensitive to changes in basal friction on regions close to the grounding lines, while changes in ice rigidity has a larger impact along the shear margins of Pine Island. The sensitivity to surface mass balance is uniform over grounded ice.

Using three independent ice-flow models and several satellite-based datasets, we assess the importance of correctly capturing ice-shelf breakup, shelf thinning, and reduction in basal traction from ungrounding in reproducing observed speed-up and thinning of Thwaites Glacier between 1995 and 2015. We run several transient numerical simulations applying these three perturbations individually. Our results show that ocean-induced ice-shelf thinning generates most of the observed grounding line retreat, inland speed-up, and mass loss, in agreement with previous work. We improve the agreement with observed inland speed-up and thinning by prescribing changes in ice-shelf geometry and a reduction in basal traction over areas that became ungrounded since 1995, suggesting that shelf breakups and thinning-induced reduction in basal traction play a critical role on Thwaites's dynamics, as pointed out by previous studies. These findings suggest that modeling Thwaites's future requires reliable ocean-induced melt estimates in models that respond accurately to downstream perturbations.

Among the most important challenges faced by ice flow models is how to represent basal and rheological conditions, which are challenging to obtain from direct observations. A common practice is to use numerical inversions to calculate estimates for the unknown properties, but there are many possible methods and not one standardised approach. As such, every ice flow model has a unique initialisation procedure. Here we compare the outputs of inversions from three different ice flow models, each employing a variant of adjoint-based optimisation to calculate basal sliding coefficients and flow rate factors using the same observed surface velocities and ice thickness distribution. The region we focus on is the Amundsen Sea Embayment in West Antarctica, the subject of much investigation due to rapid changes in the area over recent decades. We find that our inversions produce similar distributions of basal sliding across all models, despite using different techniques, implying that the methods used are highly robust and represent the physical equations without much influence by individual model behaviours. Transferring the products of inversions between models results in time-dependent simulations displaying variability on the order of or lower than existing model intercomparisons. Focusing on contributions to sea level, the highest variability we find in simulations run in the same model with different inversion products is 32 %, over a 40-year period, a difference of 3.67 mm. There is potential for this to be improved with further standardisation of modelling processes, and the lowest variability within a single model is 13 %, or 1.82 mm over 40 years. While the successful transfer of inversion outputs from one model to another requires some extra effort and technical knowledge of the particular models involved, it is certainly possible and could indeed be useful for future intercomparison projects.

The Marine Ice Sheet-Ocean Model Intercomparison Project (MISOMIP) is a community effort sponsored by the Climate and Cryosphere (CliC) project. MISOMIP aims to design and coordinate a series of MIPs—some idealized and realistic—for model evaluation, verification with observations, and future projections for key regions of the West Antarctic Ice Sheet (WAIS). The first phase of the project, MISOMIP1, was an idealized, coupled set of experiments that combined elements from the MISMIP+ and ISOMIP+ standalone experiments for ice-sheet and ocean models, respectively. These MIPs had 3 main goals: 1) to provide simplified experiments that allow model developers to compare their results with those from other models; 2) to suggest a path for testing components in the process of developing a coupled ice sheet-ocean model; and 3) to enable a large variety of parameter and process studies that branch off from these basic experiments.Here, we describe preliminary analysis of the MISOMIP1 results. Eight models in 14 configurations participated in the MIP. In keeping with analysis of the MISMIP+ experiment, we find that the choice of basal friction parameterizations in the ice-sheet component (Weertman vs. Coulomb limited) has a particularly significant impact on the rate of ice-sheet retreat but the choice of stress approximation (SSA, SSA* or L1Lx) seems to have little impact. Models with Coulomb-limited basal friction also tend to be those with the highest melt rates, confirming a positive feedback between melt and retreat in the MISOMIP1 configuration seen in previous work. The ocean component’s treatment of the boundary layer below the ice shelf also has a significant impact on melt rates and resulting retreat, consistent with findings based on ISOMIP+. Feedbacks between the components lead to localized features in the melt rates and the ice geometry not seen in standalone simulations, though the ~2-km horizontal and ~20-m vertical resolution of these simulations appears to be too coarse to produce long-lived, sub-ice-shelf channels seen at higher resolution.

Active subglacial lakes have been identified throughout Antarctica, offering a window into subglacial environments and their impact on ice sheet mass balance. We use high-resolution altimetry measurements over the Thwaites Glacier to show that a lake system underwent a second episode of drainage activity in 2017, only four years after another substantial drainage event. Our observations suggest significant modifications of the drainage system between the two events, with 2017 experiencing greater upstream discharge, faster lake-to-lake connectivity, and the transfer of water within a closed system. Measured rates of lake recharge during the inter-drainage period are significantly larger than modelled estimates, suggesting processes which drive subglacial melt production are currently underestimated. Our study highlights new methods of exploring subglacial environments through the application of altimetry, with potential applications for studying subglacial lakes across Antarctica

Thwaites Glacier in West Antarctica is one of the regions of the fastest accelerating ice thinning and highest observed ice loss. The topography of the bed beneath the glacier is a key control of future ice loss, but is not currently well enough known to satisfy the requirements of ice sheet models predicting glacier behaviour. It has previously been suggested that in fast flowing ice streams the shapes of landforms at the bed should be reflected in the ice surface morphology, which is known to a much higher resolution. Indeed, recently published radar grids from Pine Island Glacier reveal bed landforms with a definite resemblance to the ice surface above them. Here, we present a new high resolution bed topography map of Thwaites Glacier, inverted from REMA and ITSLIVE data using linear perturbation theory, a mathematical formulation of this resemblance between bed and surface. As it is based on linear physics, this method is faster than mass conservation and streamline diffusion interpolation, the two main techniques utilised by existing bed topography products in this region. Furthermore, as the theory is based on both mass and momentum balance, it provides a physically consistent estimate of elevation and basal slipperiness, in contrast to these more widely used methods. The resulting bed matches well with existing airborne and swath radar surveys, with significant detail between these radar lines. Variation in the results obtained using different reference models provides a measure of validity of the linear perturbation theory. Due to the importance of form drag in patterns of ice retreat, the inverted topographic features are potentially important for the future behaviour of Thwaites Glacier.

Dotson Ice Shelf (DIS) in West Antarctica is undergoing rapid basal melting driven by intrusions of warm, saline Circumpolar Deep Water (CDW) onto the continental shelf. Meltwater from DIS is thought to influence biology in the adjacent Amundsen Sea Polynya (ASP), which exhibits the highest Net Primary Productivity (NPP) per unit area of any coastal polynya in the Southern Ocean. However, the relative importance of iron and light in colimiting the spring phytoplankton bloom in the ASP remains poorly understood. In this modelling study we first investigate the mechanisms by which ice shelves impact NPP, then map spatio‐temporal patterns in iron‐light colimitation, and finally examine the environmental drivers of iron and light supply. We find that ice shelf melting leads to greater upper ocean iron concentrations, both directly due to release of iron from sediments entrained at the glacier bed, and indirectly via a buoyancy‐driven overturning circulation which pulls iron from CDW to the surface. Both of these mechanisms increase NPP compared to experiments where ice shelf melt is suppressed. We then show that the phytoplankton self‐shading feedback delays the bloom and reduces peak NPP by 80% compared to experiments where light penetration is independent of chlorophyll. Compared to light limitation, iron limitation due to phytoplankton uptake is more important a) later in the season, b) higher in the water column and c) further from the ice shelf. Finally, sensitivity experiments show that variability in CDW intrusion influences NPP by controlling the horizontal spreading of iron‐rich meltwater.

Ocean bathymetry exerts a strong control on ice sheet-ocean interactions within Antarctic ice-shelf cavities, where it can limit the access of warm, dense water at depth to the underside of floatin...

Active subglacial lakes have been identified throughout Antarctica, offering a window into subglacial environments and into controls on ice dynamics. Between June 2013 and January 2014 a system of connected subglacial lakes drained in unison under the Thwaites glacier in the West Antarctic ice sheet, the first time that such a system has been observed in the Amundsen Sea Sector. Estimates based on catchment scale melt production suggested that lake drainages of this type should occur every 20 to 80 years. We collected elevations from January 2011 to December 2019 over the Thwaites lake region using the CryoSat-2 swath interferometric mode and ICEsat-2 land ice elevations, as well as ice velocity from the Sentinel-1 SAR mission since 2014. Using various elevation time series approaches, we obtain time dependent elevations over each lake. Results indicate that the upstream lakes undertake a second episode of drainage during mid-2017, only 3 years after the previous event, and that a new lake drained. Unlike the 2013-2014 episode, this new drainage episode contributed to filling one of the downstream lake with no evidence of further downstream activity. This new sub-glacial lake activity under Thwaites offer the possibility to explore lake connectivity, subglacial melt production and the interaction with ice dynamics.

In recent years, there have been great advances in coupled ice sheet-ocean modelling, to the point where ice-ocean interactions can be represented in global climate models — with potential to greatly improve forecasting of marine ice-sheet loss and sea level rise in the coming century and beyond. However, initialisation of coupled ice sheet-ocean models has not yet been properly examined; and initialisation approaches applied to ocean and coupled atmosphere-ocean models may not be appropriate due to the long time scales inherent in dynamic ice sheets. Moreover, as ocean melt rates and ice-shelf geometry strongly influence each other, nonphysical transients in incorrectly initialised coupled ice-ocean models may persist for longer than in ice-sheet models alone.In this work, two approaches to coupled initialisation are considered using a synchronously coupled ice-ocean model. The two approaches are based on two commonly used approaches to ice sheet model initialisation: “snapshot” calibration, where ice-sheet basal and internal parameters are configured to optimise fit with observed surface velocity; and “transient” calibration, where these parameters are configured to jointly optimise fit with velocity and geometry change; however, the transient calibration makes use of the ocean component to ensure the ice model is not subject to “initialisation shock” from ocean melting. The approaches are applied to Smith Glacier, a small but fast-thinning glacier in West Antarctica, and the model is forced under ocean warming scenarios in multidecadal runs. Initially there is much faster retreat seen in the Snapshot-calibrated simulation, but this difference decays over several decades, and ultimately the Transiently-calibrated model sees more retreat.The experiments further suggest that Smith Glacier is not likely to exhibit Marine Ice Sheet instability in the next century. But the methods discrepancy has strong implications for glaciers which are susceptible to this instability.

The first fully synchronous, coupled ice shelf-ocean model with a fixed grounding line and imposed upstream ice velocity has been developed using the MITgcm (Massachusetts Institute of Technology general circulation model). Unlike previous, asynchronous, approaches to coupled modeling our approach is fully conservative of heat, salt, and mass. Synchronous coupling is achieved by continuously updating the ice-shelf thickness on the ocean time step. By simulating an idealized, warm-water ice shelf we show how raising the pycnocline leads to a reduction in both ice-shelf mass and back stress, and hence buttressing. Coupled runs show the formation of a western boundary channel in the ice-shelf base due to increased melting on the western boundary due to Coriolis enhanced flow. Eastern boundary ice thickening is also observed. This is not the case when using a simple depth-dependent parameterized melt, as the ice shelf has relatively thinner sides and a thicker central “bulge” for a given ice-shelf mass. Ice-shelf geometry arising from the parameterized melt rate tends to underestimate backstress (and therefore buttressing) for a given ice-shelf mass due to a thinner ice shelf at the boundaries when compared to coupled model simulations.

Meltwater from the glaciers in High Mountain Asia plays a critical role in water availability and food security in central and southern Asia. However, observations of glacier ablation and accumulation rates are limited in spatial and temporal scale due to the challenges that are associated with fieldwork at the remote, high-altitude settings of these glaciers. Here, using a remote-sensing-based mass-continuity approach, we compute regional-scale surface mass balance of glaciers in five key regions across High Mountain Asia. After accounting for the role of ice flow, we find distinctively different altitudinal surface-mass-balance gradients between heavily debris-covered and relatively debris-free areas. In the region surrounding Mount Everest, where debris coverage is the most extensive, our results show a reversed mean surface-mass-balance gradient of −0.21 ± 0.18 m w.e. a−1 (100 m)−1 on the low-elevation portions of glaciers, switching to a positive mean gradient of 1.21 ± 0.41 m w.e. a−1 (100 m)−1 above an average elevation of 5520 ± 50 m. Meanwhile, in West Nepal, where the debris coverage is minimal, we find a continuously positive mean gradient of 1.18 ± 0.40 m w.e. a−1 (100 m)−1. Equilibrium line altitude estimates, which are derived from our surface-mass-balance gradients, display a strong regional gradient, increasing from northwest (4490 ± 140 m) to southeast (5690 ± 130 m). Overall, our findings emphasise the importance of separating signals of surface mass balance and ice dynamics, in order to constrain better their contribution towards the ice thinning that is being observed across High Mountain Asia., Remote Sensing, 12 (10), ISSN:2072-4292

Glaciers in High Mountain Asia have experienced heterogeneous rates of loss since the 1970s. Yet, the associated changes in ice flow that lead to mass redistribution and modify the glacier sensitivity to climate are poorly constrained. Here we present observations of changes in ice flow for all glaciers in High Mountain Asia over the period 2000–2017, based on one million pairs of optical satellite images. Trend analysis reveals that in 9 of the 11 surveyed regions, glaciers show sustained slowdown concomitant with ice thinning. In contrast, the stable or thickening glaciers of the Karakoram and West Kunlun regions experience slightly accelerated glacier flow. Up to 94% of the variability in velocity change between regions can be explained by changes in gravitational driving stress, which in turn is largely controlled by changes in ice thickness. We conclude that, despite the complexities of individual glacier behaviour, decadal and regional changes in ice flow are largely insensitive to changes in conditions at the bed of the glacier and can be well estimated from ice thickness change and slope alone. Changes in glacier speed in High Mountain Asia are closely linked to mass balance through gravitational driving stress, and largely insensitive to basal conditions, according to satellite-derived ice-flow observations.

To date, assimilation of observations into large-scale ice models has consisted predominantly of time-independent inversions of surface velocities for basal traction, bed elevation, or ice stiffness, and has relied primarily on analytically derived adjoints of glaciological stress balance models. To overcome limitations of such "snapshot" inversions – i.e., their inability to assimilate time-dependent data for the purpose of constraining transient flow states, or to produce initial states with minimum artificial drift and suitable for time-dependent simulations – we have developed an adjoint of a time-dependent parallel glaciological flow model. The model implements a hybrid shallow shelf–shallow ice stress balance, solves the continuity equation for ice thickness evolution, and can represent the floating, fast-sliding, and frozen bed regimes of a marine ice sheet. The adjoint is generated by a combination of analytic methods and the use of algorithmic differentiation (AD) software. Several experiments are carried out with idealized geometries and synthetic observations, including inversion of time-dependent surface elevations for past thicknesses, and simultaneous retrieval of basal traction and topography from surface data. Flexible generation of the adjoint for a range of independent uncertain variables is exemplified through sensitivity calculations of grounded ice volume to changes in basal melting of floating and basal sliding of grounded ice. The results are encouraging and suggest the feasibility, using real observations, of improved ice sheet state estimation and comprehensive transient sensitivity assessments.

A glacial flow model of Smith, Pope and Kohler Glaciers is calibrated by means of control methods against time varying, annually resolved observations of ice height and velocities, covering the period 2002 to 2011. The inversion – termed "transient calibration" – produces an optimal set of time-mean, spatially varying parameters together with a time-evolving state that accounts for the transient nature of observations and the model dynamics. Serving as an optimal initial condition, the estimated state for 2011 is used, with no additional forcing, for predicting grounded ice volume loss and grounding line retreat over the ensuing 30 years. The transiently calibrated model predicts a near-steady loss of grounded ice volume of approximately 21 km3 a−1 over this period, as well as loss of 33 km2 a−1 grounded area. We contrast this prediction with one obtained following a commonly used "snapshot" or steady-state inversion, which does not consider time dependence and assumes all observations to be contemporaneous. Transient calibration is shown to achieve a better fit with observations of thinning and grounding line retreat histories, and yields a quantitatively different projection with respect to ice volume loss and ungrounding. Sensitivity studies suggest large near-future levels of unforced, i.e., committed sea level contribution from these ice streams under reasonable assumptions regarding uncertainties of the unknown parameters.

Stick-slip behavior is a distinguishing characteristic of the flow of Whillans Ice Stream (Siple Coast, Antarctica). Distinct from stick slip on Northern Hemisphere glaciers, which is generally attributed to supraglacial melt, the behavior is thought be controlled by basal processes and by tidally induced stress. However, the connection between stick-slip behavior and flow of the ice stream on long time scales, if any, is not clear. To address this question we develop a new ice flow model capable of reproducing stick-slip cycles similar to ones observed on the Whillans Ice Plain. The model treats ice as a viscoelastic material and emulates the weakening and healing that are suggested to take place at the ice-till interface. The model results suggest the long-term ice stream flow that controls ice discharge to surrounding oceans is somewhat insensitive to certain aspects of stick-slip behavior, such as velocity magnitude during the slip phase and factors that regulate it (e.g., elastic modulus). Furthermore, it is found that factors controlling purely viscous flow, such as temperature, influence stick-slip contribution to long-term flow in much the same way. Additionally, we show that viscous ice deformation, traditionally disregarded in analysis of stick-slip behavior, has a strong effect on the timing of slip events and therefore should not be ignored in efforts to deduce bed properties from stick-slip observations.

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 (

West Antarctic Ice Sheet loss is a significant contributor to sea level rise. While the ice loss is thought to be triggered by fluctuations in oceanic heat at the ice shelf bases, ice sheet response to ocean variability remains poorly understood. Using a synchronously coupled ice-ocean model permitting grounding line migration, this study evaluates the response of an ice sheet to periodic variations in ocean forcing. Resulting oscillations in grounded ice volume amplitude is shown to grow as a nonlinear function of ocean forcing period. This implies that slower oscillations in climatic forcing are disproportionately important to ice sheets. The ice shelf residence time offers a critical time scale, above which the ice response amplitude is a linear function of ocean forcing period and below which it is quadratic. These results highlight the sensitivity of West Antarctic ice streams to perturbations in heat fluxes occurring at decadal time scales.

International audience; Ice flow along land-terminating margins of the Greenland Ice Sheet (GIS) varies considerably in response to fluctuating inputs of surface meltwater to the bed of the ice sheet. Such inputs lubricate the ice–bed interface, transiently speeding up the flow of ice1, 2. Greater melting results in faster ice motion during summer, but slower motion over the subsequent winter, owing to the evolution of an efficient drainage system that enables water to drain from regions of the ice-sheet bed that have a high basal water pressure2, 3. However, the impact of hydrodynamic coupling on ice motion over decadal timescales remains poorly constrained. Here we show that annual ice motion across an 8,000-km2 land-terminating region of the west GIS margin, extending to 1,100 m above sea level, was 12% slower in 2007–14 compared with 1985–94, despite a 50% increase in surface meltwater production. Our findings suggest that, over these three decades, hydrodynamic coupling in this section of the ablation zone resulted in a net slowdown of ice motion (not a speed-up, as previously postulated1). Increases in meltwater production from projected climate warming may therefore further reduce the motion of land-terminating margins of the GIS. Our findings suggest that these sectors of the ice sheet are more resilient to the dynamic impacts of enhanced meltwater production than previously thought.

Dynamic and thermodynamic regimes of ice shelves experiencing weak (inline image1 m year−1) to strong (~10 m year−1) basal melting in cold (bottom temperature close to the in situ freezing point) and warm oceans (bottom temperature more than half of a degree warmer than the in situ freezing point) are investigated using a 1-D coupled ice/ocean model complemented with a newly derived analytic expression for the steady state temperature distribution in ice shelves. This expression suggests the existence of a basal thermal boundary layer with thickness inversely proportional to the basal melt rate. Model simulations show that ice shelves afloat in warm ocean waters have significantly colder internal ice temperatures than those that float in cold waters. Our results indicate that in steady states, the mass balance of ice shelves experiencing strong and weak melting is controlled by different processes: in ice shelves with strong melting, it is a balance between ice advection and basal melting, and in ice shelves with weak melting, it is a balance between ice advection and deformation. Sensitivity simulations show that ice shelves in cold and warm oceans respond differently to increase of the ocean heat content. Ice shelves in cold waters are more sensitive to warming of the ocean bottom waters, while ice shelves in warm waters are more sensitive to shallowing of the depth of the thermocline.

[1] Antarctic ice shelves interact closely with the ocean cavities beneath them, with ice shelf geometry influencing ocean cavity circulation, and heat from the ocean driving changes in the ice shelves, as well as the grounded ice streams that feed them. We present a new coupled model of an ice stream-ice shelf-ocean system that is used to study this interaction. The model is capable of representing a moving grounding line and dynamically responding ocean circulation within the ice shelf cavity. Idealized experiments designed to investigate the response of the coupled system to instantaneous increases in ocean temperature show ice-ocean system responses on multiple timescales. Melt rates and ice shelf basal slopes near the grounding line adjust in 1–2 years, and downstream advection of the resulting ice shelf thinning takes place on decadal timescales. Retreat of the grounding line and adjustment of grounded ice takes place on a much longer timescale, and the system takes several centuries to reach a new steady state. During this slow retreat, and in the absence of either an upward-or downward-sloping bed or long-term trends in ocean heat content, the ice shelf and melt rates maintain a characteristic pattern relative to the grounding line.

Ice-shelf basal melting is tightly coupled to ice-shelf morphology. Ice shelves, in turn, are coupled to grounded ice via their influence on compressive stress at the grounding line (‘ice-shelf buttressing’). Here, we examine this interaction using a local parameterization that relates the basal melt rate to the ice-shelf thickness gradient. This formulation permits a closed-form solution for a steady-state ice tongue. Time-dependent numerical simulations reveal the spatial and temporal evolution of ice-shelf/ice-stream systems in response to changes in ocean temperature, and the influence of morphology-dependent melting on grounding-line retreat. We find that a rapid (

Predictions of marine ice-sheet behaviour require models that are able to robustly simulate grounding line migration. We present results of an intercomparison exercise for 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 effects of lateral buttressing). Unique steady state grounding line positions exist for ice sheets on a downward sloping bed, while hysteresis occurs across an overdeepened bed, and stable steady state grounding line positions only occur on the downward-sloping sections. Models based on the shallow ice approximation, which does not resolve extensional stresses, do not reproduce the approximate analytical results unless appropriate parameterizations for ice flux are imposed at the grounding line. For extensional-stress resolving "shelfy stream" models, differences between model results were mainly due to the choice of spatial discretization. Moving grid methods were found to be the most accurate at capturing grounding line evolution, since they track the grounding line explicitly. Adaptive mesh refinement can further improve accuracy, including fixed grid models that generally perform poorly at coarse resolution. Fixed grid models, with nested grid representations of the grounding line, are able to generate accurate steady state positions, but can be inaccurate over transients. Only one full-Stokes model was included in the intercomparison, and consequently the accuracy of shelfy stream models as approximations of full-Stokes models remains to be determined in detail, especially during transients. © 2012 Author(s)., SCOPUS: ar.j, info:eu-repo/semantics/published

An approximation to the first-order momentum balance with consistent boundary conditions is derived using variational methods. Longitudinal and lateral stresses are treated as depth-independent, but vertical velocity gradients are accounted for both in the nonlinear viscosity and in the treatment of basal stress, allowing for flow over a frozen bed. A numerical scheme is presented that is significantly less computationally expensive than that of a fully three-dimensional (3-D) solver. The numerical solver is subjected to the ISMIP-HOM experiments and experiments involving nonlinear sliding laws, and results are compared with those of 3-D models. The agreement with first-order surface velocities is favorable down to length scales of 10 km for flow over a flat bed with periodic basal traction, and ∼40 km for flow over periodic basal topography.

[1] Understanding the dynamics of marine ice sheets is integral to studying the evolution of the Antarctic ice sheet in both the short and long terms. An important component of the dynamics, grounding line migration, has proved difficult to represent in numerical models, and most successful attempts have made use of techniques that are only readily applicable to flow line models. However, to capture the stress transmission involved in another important component, the buttressing of a marine ice sheet by its ice shelf, the transverse direction must also be resolved. We introduce a model that solves the time-dependent shelfy stream equations and makes use of mesh adaption techniques to overcome the difficulties typically associated with the numerics of grounding line migration. We compare the model output with a recent benchmark for flow line models and show that our model yields an accurate solution while using far less resources than would be required without mesh adaption. We also show that the mesh adapting techniques extend to two horizontal dimensions. Experiments are carried out to determine how both ice shelf buttressing and ice rises affect the marine instability predicted for an ice sheet on a foredeepened bed. We find that buttressing is not always sufficient to stabilize such a sheet but collapse of the grounded portion is still greatly delayed. We also find that the effect of an ice rise is similar to that of narrowing the ice shelf.