The observed retreat of the grounding line of the present-day ice sheets and the simulated grounding-line retreat of ice sheets under changing climate conditions are often interpreted as indications of marine ice-sheet instability (MISI), driven by a positive feedback between the ice discharge and conditions at the grounding line. However, the arguments that support this feedback are valid only for steady-state conditions. Here, we assess how unconfined marine ice sheets may behave if atmospheric conditions and basal conditions evolve with time. We find that the behavior of grounding lines can exhibit a range from unstoppable advance and retreat to irregular oscillation irrespective of the stability of the corresponding steady-state configurations obtained with time-invariant conditions. Our results show that numerical simulations with a parameterization of the ice flux through the grounding line used in large-scale ice-sheet models produce markedly different results from simulations without the parameterization. Our analysis demonstrates that the grounding-line migration can be driven by the temporal variability in the atmospheric and basal conditions and not by MISI, which assumes unchanging conditions. Instead, the grounding-line advance or retreat is determined by interactions between ice flow, basal processes and environmental conditions throughout the length of a marine ice sheet in addition to the circumstances at its grounding line.

Ice sheet models use observations to infer basal shear stress, but the variety of methods and datasets available has resulted in a wide range of estimates. Radar-based metrics such as reflectivity and specularity content have been used to characterize subglacial hydrologic conditions that are linked to spatial variations in basal shear stress. We explore whether radar metrics can be used to inform models about basal shear stress. At Thwaites Glacier, West Antarctica, we sample basal shear stress inversions across a wide range of ice sheet models to see how the basal shear stress distribution changes in regions of varying relative reflectivity and specularity content. Our results reveal three key findings: (1) Regions of high specularity content exhibit lower mean basal shear stresses (2) Wet and bumpy regions, as characterized by high relative reflectivity and low specularity content, exhibit higher mean basal shear stresses (3) Models disagree about what basal shear stress should be at the onset of rapid ice flow and high basal melt where relative reflectivity and specularity content are low.

Subglacial lake water-volume changes produce ice-elevation anomalies that provide clues about water flow beneath glaciers and ice sheets. Significant challenges remain in the quantitative interpretation of these elevation-change anomalies because the surface expression of subglacial lake activity depends on basal conditions, rate of water-volume change, and ice rheology. To address these challenges, we introduce an inverse method that reconstructs subglacial lake activity from altimetry data while accounting for the effects of viscous ice flow. We use a linearized approximation of a Stokes ice-flow model under the assumption that subglacial lake activity only induces small perturbations relative to a reference ice-flow state. We validate this assumption by accurately reconstructing lake activity from synthetic data that are produced with a fully nonlinear model. We then apply the method to estimate the water-volume changes of several active subglacial lakes in Antarctica by inverting data from NASA's Ice, Cloud, and land Elevation Satellite 2 (ICESat-2) laser altimetry mission. The results show that there can be substantial discrepancies (20% or more) between the inversion and traditional estimation methods due to the effects of viscous ice flow. The inverse method will help refine estimates of subglacial water transport and further constrain the role of subglacial hydrology in ice-sheet evolution.

Ice-crystal fabric can induce mechanical anisotropy that significantly affects flow, but ice-flow models generally do not include fabric development or its effect upon flow. Here, we incorporate a new spectral expansion of fabric, and more complete description of its evolution, into the ice-flow model Elmer/Ice. This approach allows us to model the effect of both lattice rotation and migration recrystallization on large-scale ice flow. The fabric evolution is coupled to flow using an unapproximated non-linear orthotropic rheology that better describes deformation when the stress and fabric states are misaligned. These improvements are most relevant for simulating dynamically interesting areas, where recrystallization can be important, tuning data are scarce and rapid flow can lead to misalignment between stress and fabric. We validate the model by comparing simulated fabric to ice-core and phase-sensitive radar measurements on a transect across Dome C, East Antarctica. With appropriately tuned rates for recrystallization, the model is able to reproduce observations of fabric. However, these tuned rates differ from those previously derived from laboratory experiments, suggesting a need to better understand how recrystallization acts differently in the laboratory compared to natural settings.

The hypothesis that ice-sheet evolution is only controlled by the long-term non-Newtonian viscous behavior of ice has been challenged by observations indicating that effects like brittle failure, stick-slip sliding, tides and wave action may affect ice-sheet evolution on sub-daily timescales. Over these timescales, the quasi-static-creep approximation is no longer appropriate and elastic effects become important. Simulating elastic effects in ice-sheet models over relevant timescales, however, remains challenging. Here, we show that by including a visco-elastic rheology and reintroducing the oft neglected acceleration term back into the ice-sheet stress balance, we can create a visco-elastic system where the velocity is locally determined and information propagates at the elastic wave speed. Crucially, the elastic wave speed can be treated like an adjustable parameter and set to any value to reproduce a range of phenomena, provided the wave speed is large compared to the viscous velocity. We illustrate the system using three examples. The first two examples demonstrate that the system converges to the steady-state viscous and elastic limits. The third example examines ice-shelf rifting and iceberg calving. This final example hints at the utility of the visco-elastic formulation in treating both long-term evolution and short-term environmental effects.

The Greenland Ice Sheet has become an increasingly larger contributor to sea level rise in the past two decades and is projected to continue to lose mass. Climate variability is expected to increase under future warming, but the effect of climate variability on the Greenland Ice Sheet volume is poorly understood and is adding to the uncertainty of the projected mass loss. Here we quantify the influence of inter-annual temperature variability on mass loss from the Greenland Ice Sheet using the PISM model. We construct an ensemble of temperature-forcing fields that accounts for inter-annual variability in temperature using reanalysis data from NOAA-CIRES over the period 1851–2014. We investigate the steady-state and transient response of the Greenland Ice Sheet. We find that the simulated steady-state ice-sheet volume decreases by 1.9 ± 0.4 cm of sea level equivalent when forced with a varying temperature forcing compared to a constant temperature forcing, and by 11.5 ± 1.4 cm when the variability is doubled. The northern basins are particularly sensitive with a change in volume of 0.9–1.1%. Our results emphasize the importance of including temperature variability in projections of future mass loss.

Investigations of the time-dependent behavior of marine ice sheets and their sensitivity to basal conditions require numerical models because existing theoretical analyses focus only on steady-state configurations primarily with a power-law basal shear stress. Numerical results indicate that the choice of the sliding law strongly affects ice-sheet dynamic behavior. Although observed or simulated grounding-line retreat is typically interpreted as an indication of marine ice sheet instability introduced by Weertman (1974), this (in)stability is a characteristic of the ice sheet's steady states – not time-variant behavior. To bridge the gap between theoretical and numerical results, we develop a framework to investigate grounding line dynamics with generalized basal and lateral stresses (i.e. the functional dependencies are not specified). Motivated by observations of internal variability of the Southern Ocean conditions we explore the grounding-line response to stochastic variability. We find that adding stochastic variability to submarine melt rates that produced stable steady-state configurations leads to intermittently advancing and retreating grounding lines. They can also retreat in an unstoppable manner on time-scales significantly longer than the stochastic correlation time-scales. These results suggest that at any given time of their evolution, the transient behavior of marine ice sheets cannot be described in terms of ‘stable’ or ‘unstable’.

Water pressure beneath glaciers influences ice velocity. Subglacial hydrology models are helpful for gaining insight into basal conditions, but models depend on unconstrained parameters, and a current challenge is reproducing elevated water pressures in winter. We eliminate terms related to englacial storage, opening by sliding, and melt due to changes in the pressure-melting-point temperature, to create a minimalist version of the Subglacial Hydrology And Kinetic, Transient Interactions (SHAKTI) model, and apply this model to Helheim Glacier in east Greenland to explore the winter base state of the subglacial drainage system. Our results suggest that meltwater produced at the bed alone supports active winter drainage with large areas of elevated water pressure and preferential drainage pathways, using a continuum approach that allows for transitions between flow regimes. Transmissivity varies spatially over several orders of magnitude from 10−4 to 103 m2s−1, with regions of weak transmissivity representing poorly connected regions of the system. Bed topography controls the location of primary drainage pathways, and high basal melt rates occur along the steep valley walls. Frictional heat from sliding is a dominant source of basal melt; different approaches for calculating basal shear stress produce significantly different basal melt rates and subglacial discharge.

Increases in ocean temperatures in the Filchner Ronne region of Antarctica are likely to result in increased ice mass loss and sea level rise. We constrain projections of the 21st century sea level contribution of this region using process-based ice-sheet modeling, with model parameters controlling ice dynamics calibrated using observed surface speeds and Markov-chain Monte Carlo sampling. We use climate forcing from Representative Concentration Pathway (RCP) scenarios as well as a set of hypothetical scenarios of deep ocean warming to evaluate the sensitivity of this region to ocean temperatures. Projected changes in regional ice mass correspond to a decrease in global mean sea level of 24±7 mm over 2015–2100 under RCP 2.6 and 28±9 mm under RCP 8.5. Increased regional inland surface accumulation related to higher warming levels in RCP 8.5 leads to more ice above flotation, offsetting increased ice shelf basal melt. The tests involving step changes in ocean temperatures with constant surface forcing show that one degree of ocean warming from present results in an additional +11 mm contribution to sea level by 2100 and 1% of the ice-covered area in the domain becomes ungrounded (23 200 km2). The rate of mass loss with temperature increases at higher temperatures.

Spatially variable basal conditions are thought to govern how ice sheets behave at glacial time scales (>1000 years) and responsible for changes in dynamics between the core and peripheral regions of the Laurentide and Fennoscandian ice sheets. Basal motion is accomplished via the deformation of unconsolidated sediments, or via sliding of the ice over an undeformable bed. We present an ice sheet sliding module for the Parallel Ice Sheet Model (PISM) that takes into account changes in sediment cover and incorporates surface meltwater. This model routes meltwater, produced at the surface and base of the ice sheet, toward the margin of the ice sheet. Basal sliding is accomplished through the deformation of water saturated sediments, or sliding at the ice-bed interface. In areas with continuous, water saturated sediments, sliding is almost always accomplished through sediment deformation. In areas with incomplete cover, sliding has a stronger dependence on the supply of water. We find that the addition of surface meltwater to the base is a more important factor for ice sheet evolution than the style of sliding. In a glacial cycle simulation, our model causes a more rapid buildup of the Laurentide Ice Sheet.

Numerical glacier and ice-sheet models compute evolving ice geometry and velocity fields using various stress-balance approximations and boundary conditions. At high spatial resolution, with horizontal mesh/grid resolutions of a few kilometers or smaller, these models usually require time steps shorter than climate-coupling time scales because they update ice thickness after each velocity solution. High-resolution performance is degraded by the stability restrictions of such explicit time-stepping. This short note, which considers the shallow ice approximation and Stokes models as stress-balance end members, clarifies the scaling of numerical model performance by quantifying simulation cost per model year in terms of mesh resolution and the number of degrees of freedom. The performance of current-generation explicit time-stepping models is assessed, and then compared to the prospective performance of implicit schemes. The main results highlight the key roles played by the algorithmic scaling of stress-balance solvers and coupled, implicit-step solvers.

Using data from three automatic weather stations (LGB69, Eagle and Dome A) from distinctly different climatological zones along the CHINARE (Chinese National Antarctic Research Expedition) traverse route from Zhongshan Station to Dome A, we investigated the characteristics of meteorological conditions and subsurface heat conduction. Spatial analysis indicated decreasing trends in air temperature, relative humidity and wind speed from the coastal katabatic wind zone to the inland plateau region, and air temperatures clearly showed a strong daily variability in winter, suggesting the effect from the fluctuation in the Antarctic atmospheric system. We also analyzed the optimal response time of the 1 and 3 m depth snow temperatures to the 0.1 m depth snow temperature for each site under clear/overcast and day/night situations. This showed an important enhancement to the heat transfer from shortwave radiation penetration. Using an iterative optimization method, we estimated the subsurface heat conduction variations along the transect. This was ~3–5 W m–2. Multiple maxima in daily mean subsurface fluxes were found in winter, with a typical value above 2 W m–2, while a single minimum value under –2 W m–2 was found in summer. On an annual scale, a larger mean loss of subsurface heat conduction was observed in the inland plateau compared to in the coastal katabatic area. Finally, we discussed the possible influences of turbulent and radiant transport on the vertical heat response and confirmed the wind enhancement on the growth of thermal conductivity. This preliminary study provides a brief perspective and an important reference for studying subsurface heat conduction in inland areas of Antarctica.

In this study, we investigate the differences between two transient, three-dimensional, thermomechanically coupled ice-sheet models, namely, a first-order approximation model (FOM) and a ‘full’ Stokes ice-sheet model (FSM) under the same numerical framework. For all numerical experiments, we take the FSM outputs as the reference values and calculate the mean relative errors in the velocity and temperature fields for the FOM over 100 years. Four different boundary conditions (ice slope, geothermal heat flux, basal topography and basal sliding) are tested, and by changing these parameters, we verify the thermomechanical behavior of the FOM and discover that the velocity and temperature biases of the FOM generally increase with increases in the ice slope, geothermal heat flux, undulation amplitude of the ice base, and with the existence of basal sliding. In addition, the model difference between the FOM and FSM may accumulate over time, and the spatial distribution patterns of the relative velocity and temperature errors are in good agreement.

The interior of an ice sheet consists of layers of accumulated snow, which contain important information on accumulation and ice dynamics that are imprinted on layer shapes over time. This work describes how changes in accumulation influence the stratigraphy of an ice sheet. The thickness of each layer at present day depends both on accumulation and on the effect of dynamic thinning after its deposition. An isochronal numerical model is used to simulate the evolution of a 2-D, idealized ice sheet while explicitly representing the layers. A series of simulations was carried out to quantify the changes that anomalous accumulation at different locations and times has on the stratigraphy. These simulations form the basis of a linear response function. A second set of simulations with more sustained changes in accumulation is then used to describe large-scale and long-term impacts on the layering of the ice sheet as well as to test the quality of the linear approximation. The aim is to examine whether long-term effects can be extrapolated from small differential changes. The result confirms a certain degree of linearity between changes in accumulation and layer thickness that may be exploited for future inverse modeling applications.

Increasing ice flux from glaciers retreating over deepening (retrograde) bed topography has been implicated in the recent acceleration of mass loss from the Greenland and Antarctic ice sheets. We show in observations that some glaciers have remained at peaks in bed topography without retreating despite enduring significant changes in climate. Observations also indicate that some glaciers which persist at bed peaks undergo sudden retreat years or decades after the onset of local ocean or atmospheric warming. Using model simulations, we show that persistence of a glacier at a bed peak is caused by ice slowing as it flows up a reverse-sloping bed to the peak. Persistence at bed peaks may lead to two very different future behaviors for a glacier: one where it persists at a bed peak indefinitely, and another where it retreats from the bed peak after potentially long delays following climate forcing. However, it is nearly impossible to distinguish which of these two future behaviors will occur from current observations. We conclude that inferring glacier stability from observations of persistence obscures our true commitment to future sea-level rise under climate change. We recommend that further research is needed on seemingly stable glaciers to determine their likely future.

Upernavik Isstrøm, a marine glacier undergoing rapid retreat, is simulated by forcing a numerical model with ocean-driven melt. A review of processes driving retreat led us to hypothesize that a glacier undergoing rapid retreat may be less sensitive to perturbations in the balance of forces than a glacier that is undergoing moderate changes or a glacier in steady state. Numerical experiments suggest this is not the case, and that a system in rapid retreat is as sensitive to basal traction perturbations as a system that is near to steady state. This result is important when considering other glacier systems experiencing marine-forced retreat. While the ice–ocean interface is of primary importance, additional perturbations from meltwater-forced decoupling of the glacier from its bed continue to feature in glacier dynamics.

Inaccurate representations of iceberg calving from ice shelves are a large source of uncertainty in mass-loss projections from the Antarctic ice sheet. Here, we address this limitation by implementing and testing a continuum damage-mechanics model in a continental scale ice-sheet model. The damage-mechanics formulation, based on a linear stability analysis and subsequent long-wavelength approximation of crevasses that evolve in a viscous medium, links damage evolution to climate forcing and the large-scale stresses within an ice shelf. We incorporate this model into the BISICLES ice-sheet model and test it by applying it to idealized (1) ice tongues, for which we present analytical solutions and (2) buttressed ice-shelf geometries. Our simulations show that the model reproduces the large disparity in lengths of ice shelves with geometries and melt rates broadly similar to those of four Antarctic ice shelves: Erebus Glacier Tongue (length ~ 13 km), the unembayed portion of Drygalski Ice Tongue (~ 65 km), the Amery Ice Shelf (~ 350 km) and the Ross Ice Shelf (~ 500 km). These results demonstrate that our simple continuum model holds promise for constraining realistic ice-shelf extents in large-scale ice-sheet models in a computationally tractable manner.

The geometry and thermal structure of western Greenland ice sheet are known to have undergone relatively substantial change over the Holocene. Evolution of the frozen and melted fractions of the bed associated with the ice-sheet retreat over this time frame remains unclear. We address this question using a thermo-mechanically coupled flowline model to simulate a 11 ka period of ice-sheet retreat in west central Greenland. Results indicate an episode of ~100 km of terminus retreat corresponded to ~16 km of upstream frozen/melted basal boundary migration. The majority of migration of the frozen area is associated with the enhancement of the frictional and strain heating fields, which are accentuated toward the retreating ice margin. The thermally active bedrock layer acts as a heat sink, tending to slow contraction of frozen-bed conditions. Since the bedrock heat flux in our region is relatively low compared to other regions of the ice sheet, the frozen region is relatively greater and therefore more susceptible to marginward changes in the frictional and strain heating fields. Migration of melted regions thus depends on both geometric changes and the antecedent thermal state of the bedrock and ice, both of which vary considerably around the ice sheet.

In this study, we explore small-scale (~1 to 20 km) thermal-refractive effects on basal geothermal heat flux (BGHF) at subglacial boundaries resulting from lateral thermal conductivity contrasts associated with subglacial topography and geologic contacts. We construct a series of two-dimensional, conductive, steady-state models that exclude many of the complexities of ice sheets in order to demonstrate the effect of thermal refraction. We show that heat can preferentially flow into or around a subglacial valley depending on the thermal conductivity contrast with underlying bedrock, with anomalies of local BGHF at the ice–bedrock interface between 80 and 120% of regional BGHF and temperature anomalies on the order of ±15% for the typical range of bedrock conductivities. In the absence of bed topography, subglacial contacts can produce significant heat flux and temperature anomalies that are locally extensive (>10 km). Thermal refraction can result in either an increase or decrease in the likelihood of melting and ice-sheet stability depending on the conductivity contrast and bed topography. While our models exclude many of the physical complexities of ice behavior, they illustrate the need to include refractive effects created by realistic geology into future glacial models to improve the prediction of subglacial melting and ice viscosity.

Basal motion is the primary mechanism for ice flux in Greenland, yet a widely applicable model for predicting it remains elusive. This is due to the difficulty in both observing small-scale bed properties and predicting a time-varying water pressure on which basal motion putatively depends. We take a Bayesian approach to these problems by coupling models of ice dynamics and subglacial hydrology and conditioning on observations of surface velocity in southwestern Greenland to infer the posterior probability distributions for eight spatially and temporally constant parameters governing the behavior of both the sliding law and hydrologic model. Because the model is computationally expensive, characterization of these distributions using classical Markov Chain Monte Carlo sampling is intractable. We skirt this issue by training a neural network as a surrogate that approximates the model at a sliver of the computational cost. We find that surface velocity observations establish strong constraints on model parameters relative to a prior distribution and also elucidate correlations, while the model explains 60% of observed variance. However, we also find that several distinct configurations of the hydrologic system and stress regime are consistent with observations, underscoring the need for continued data collection and model development.