Large-scale Ice Sheet Models Research Articles

Diverse behaviors of marine ice sheets in response to temporal variability of the atmospheric and basal conditions

Abstract 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.

Local forcing mechanisms challenge parameterizations of ocean thermal forcing for Greenland tidewater glaciers

Abstract. Frontal ablation has caused 32 %–66 % of Greenland Ice Sheet mass loss since 1972, and despite its importance in driving terminus change, ocean thermal forcing remains crudely incorporated into large-scale ice sheet models. In Greenland, local fjord-scale processes modify the magnitude of thermal forcing at the ice–ocean boundary but are too small scale to be resolved in current global climate models. For example, simulations used in the Ice Sheet Intercomparison Project for CMIP6 (ISMIP6) to predict future ice sheet change rely on the extrapolation of regional ocean water properties into fjords to drive terminus ablation. However, the accuracy of this approach has not previously been tested due to the scarcity of observations in Greenland fjords, as well as the inability of fjord-scale models to realistically incorporate icebergs. By employing the recently developed IceBerg package within the Massachusetts Institute of Technology general circulation model (MITgcm), we here evaluate the ability of ocean thermal forcing parameterizations to predict thermal forcing at tidewater glacier termini. This is accomplished through sensitivity experiments using a set of idealized Greenland fjords, each forced with equivalent ocean boundary conditions but with varying tidal amplitudes, subglacial discharge, iceberg coverage, and bathymetry. Our results indicate that the bathymetric obstruction of external water is the primary control on near-glacier thermal forcing, followed by iceberg submarine melting. Despite identical ocean boundary conditions, we find that the simulated fjord processes can modify grounding line thermal forcing by as much as 3 °C, the magnitude of which is largely controlled by the relative depth of bathymetric sills to the Polar Water–Atlantic Water thermocline. However, using a common adjustment for fjord bathymetry we can still predict grounding line thermal forcing within 0.2 °C in our simulations. Finally, we introduce new parameterizations that additionally account for iceberg-driven cooling that can accurately predict interior fjord thermal forcing profiles both in iceberg-laden simulations and in observations from Kangiata Sullua (Ilulissat Icefjord).

Persistent, extensive channelized drainage modeled beneath Thwaites Glacier, West Antarctica

Abstract. Subglacial hydrology is a leading control on basal friction and the dynamics of glaciers and ice sheets. At low discharge, subglacial water flows through high-pressure, sheet-like systems that lead to low effective pressures. However, at high discharge, subglacial water melts the overlying ice into localized channels that efficiently remove water from the bed, thereby increasing effective pressure and basal friction. Recent observations suggest channelized subglacial flow exists beneath Thwaites Glacier, yet it remains unclear if stable channelization is feasible in West Antarctica, where surface melting is nonexistent and water at the bed is limited. Here, we use the MPAS-Albany Land Ice model to run a suite of over 130 subglacial hydrology simulations of Thwaites Glacier across a wide range of physical parameter choices to assess the likelihood of channelization. We then narrow our range of viable simulations by comparing modeled water thicknesses to previously observed radar specularity content, which indicates flat, spatially extensive water bodies at the bed. In all of our data-compatible simulations, stable channels reliably form within 100–200 km of the grounding line and reach individual discharge rates of 35–110 m3 s−1 at the ice–ocean boundary. While only one to two channels typically form across the 200 km width of the glacier in our simulations, their high efficiency drains water across the entire lateral extent of the glacier. We posit the large catchment size of Thwaites Glacier, its funnel-like geometry, and high basal melt rates together accumulate enough water to form stable channels. No simulations resembled observed specularity content when channelization was disabled. Our results suggest channelized subglacial hydrology has two consequences for Thwaites Glacier dynamics: (i) amplifying submarine melting of the terminus and ice shelf while (ii) simultaneously raising effective pressure within 100 km of the grounding line and increasing basal friction. The distribution of effective pressure implied from our modeling differs from parameterizations typically used in large-scale ice sheet models, suggesting the development of more process-based parameterizations may be necessary.

Simulating ice-shelf extent using damage mechanics

Abstract 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 role of subtemperate slip in thermally driven ice stream margin migration

Abstract. The amount of ice discharged by an ice stream depends on its width, and the widths of unconfined ice streams such as the Siple Coast ice streams in West Antarctica have been observed to evolve on decadal to centennial timescales. Thermally driven widening of ice streams provides a mechanism for this observed variability through melting of the frozen beds of adjacent ice ridges. This widening is driven by the heat dissipation in the ice stream margin, where strain rates are high, and at the bed of the ice ridge, where subtemperate sliding is possible. The inflow of cold ice from the neighboring ice ridges impedes ice stream widening. Determining the migration rate of the margin requires resolving conductive and advective heat transfer processes on very small scales in the ice stream margin, and these processes cannot be resolved by large-scale ice sheet models. Here, we exploit the thermal boundary layer structure in the ice stream margin to investigate how the migration rate depends on these different processes. We derive a parameterization of the migration rate in terms of parameters that can be estimated from observations or large-scale model outputs, including the lateral shear stress in the ice stream margin, the ice thickness of the stream, the influx of ice from the ridge, and the bed temperature of the ice ridge. This parameterization will allow the incorporation of ice stream margin migration into large-scale ice sheet models.

Implementing an empirical scalar constitutive relation for ice with flow-induced polycrystalline anisotropy in large-scale ice sheet models

Abstract. The microstructure of polycrystalline ice evolves under prolonged deformation, leading to anisotropic patterns of crystal orientations. The response of this material to applied stresses is not adequately described by the ice flow relation most commonly used in large-scale ice sheet models – the Glen flow relation. We present a preliminary assessment of the implementation in the Ice Sheet System Model (ISSM) of a computationally efficient, empirical, scalar, constitutive relation which addresses the influence of the dynamically steady-state flow-compatible induced anisotropic crystal orientation patterns that develop when ice is subjected to the same stress regime for a prolonged period – sometimes termed tertiary flow. We call this the ESTAR flow relation. The effect on ice flow dynamics is investigated by comparing idealised simulations using ESTAR and Glen flow relations, where we include in the latter an overall flow enhancement factor. For an idealised embayed ice shelf, the Glen flow relation overestimates velocities by up to 17 % when using an enhancement factor equivalent to the maximum value prescribed in the ESTAR relation. Importantly, no single Glen enhancement factor can accurately capture the spatial variations in flow across the ice shelf generated by the ESTAR flow relation. For flow line studies of idealised grounded flow over varying topography or variable basal friction – both scenarios dominated at depth by bed-parallel shear – the differences between simulated velocities using ESTAR and Glen flow relations depend on the value of the enhancement factor used to calibrate the Glen flow relation. These results demonstrate the importance of describing the deformation of anisotropic ice in a physically realistic manner, and have implications for simulations of ice sheet evolution used to reconstruct paleo-ice sheet extent and predict future ice sheet contributions to sea level.

Role of model initialization for projections of 21st-century Greenland ice sheet mass loss

AbstractModel simulations of the Greenland ice sheet contribution to 21st-century sea-level rise are performed with a state-of-the-art ice-sheet model (Parallel Ice Sheet Model (PISM)). The climate-forcing fields are obtained from the European Union’s Seventh Framework Programme project ice2sea, in which three regional climate models are used to dynamically downscale two scenarios (A1B and E1) from two general circulation models (ECHAM5 and HadCM3). To assess the sensitivity of the projections to the model initial state, four initialization methods are applied. In these experiments, the simulated contribution to sea-level rise by 2100 ranges from an equivalent of 0.2 to 6.8 cm. The largest uncertainties arise from different formulations of the regional climate models (0.8–3.9 cm) and applied scenarios (0.65–1.9 cm), but an important source of uncertainty is the initialization method (0.1–0.8 cm). These model simulations do not account for the recently observed acceleration of ice streams and consequent thinning rates, the changing ice discharge that may result from the spatial and temporal variability of ocean forcing, or the feedback occurring between ice-sheet elevation changes and climate forcing. Thus the results should be considered the lower limit of Greenland ice sheet contributions to sea-level rise, until such processes have been integrated into large-scale ice-sheet models.

A balanced water layer concept for subglacial hydrology in large-scale ice sheet models

Abstract. There is currently no doubt about the existence of a widespread hydrological network under the Antarctic Ice Sheet, which lubricates the ice base and thus leads to increased ice velocities. Consequently, ice models should incorporate basal hydrology to obtain meaningful results for future ice dynamics and their contribution to global sea level rise. Here, we introduce the balanced water layer concept, covering two prominent subglacial hydrological features for ice sheet modeling on a continental scale: the evolution of subglacial lakes and balance water fluxes. We couple it to the thermomechanical ice-flow model RIMBAY and apply it to a synthetic model domain. In our experiments we demonstrate the dynamic generation of subglacial lakes and their impact on the velocity field of the overlaying ice sheet, resulting in a negative ice mass balance. Furthermore, we introduce an elementary parametrization of the water flux–basal sliding coupling and reveal the predominance of the ice loss through the resulting ice streams against the stabilizing influence of less hydrologically active areas. We point out that established balance flux schemes quantify these effects only partially as their ability to store subglacial water is lacking.

A simple inverse method for the distribution of basal sliding coefficients under ice sheets, applied to Antarctica

Abstract. Variations in intrinsic bed conditions that affect basal sliding, such as the distribution of deformable sediment versus hard bedrock, are important boundary conditions for large-scale ice-sheet models, but are hard to observe and remain largely uncertain below the modern Greenland and Antarctic ice sheets. Here a very simple model-based method is described for deducing the modern spatial distribution of basal sliding coefficients. The model is run forward in time, and the basal sliding coefficient at each grid point is periodically increased or decreased depending on whether the local ice surface elevation is too high or too low compared to observed in areas of unfrozen bed. The method considerably reduces large-scale errors in Antarctic ice elevation, from several 100s to several 10s of meters in most regions. Remaining ice elevation errors over mountain ranges such as the Transantarctics are further improved by parameterizing the possible effect of sub-grid topography in the basal sliding law, representing sliding in deep valleys. Results are compared with modern velocity data, and various sensitivity tests are described in Appendices.

Representing Grounding Line Dynamics in Numerical Ice Sheet Models: Recent Advances and Outlook

Recent satellite observations of the Antarctic and Greenland ice sheets show accelerated ice flow and associated ice sheet thinning along coastal outlet glaciers in contact with the ocean. Both processes are the result of grounding line retreat due to melting at the grounding line (the grounding line is the contact of the ice sheet with the ocean, where it starts to float and forms an ice shelf or ice tongue). Such rapid ice loss is not yet included in large-scale ice sheet models used for IPCC projections, as most of the complex processes are poorly understood. Here we report on the state-of-the art of grounding line migration in marine ice sheets and address different ways in which grounding line migration can be attributed and represented in ice sheet models. Using one-dimensional ice flow models of the ice sheet/ice shelf system we carried out a number of sensitivity experiments with different spatial resolutions and stress approximations. These are verified with semi-analytical steady state solutions. Results show that, in large-scale finite-difference models, grounding line migration is dependent on the numerical treatment (e.g. staggered/non-staggered grid) and the level of physics involved (e.g. shallow-ice/shallow-shelf approximation).

Understanding and Modelling Rapid Dynamic Changes of Tidewater Outlet Glaciers: Issues and Implications

Recent dramatic acceleration, thinning and retreat of tidewater outlet glaciers in Greenland raises concern regarding their contribution to future sea-level rise. These dynamic changes seem to be parallel to oceanic and climatic warming but the linking mechanisms and forcings are poorly understood and, furthermore, large-scale ice sheet models are currently unable to realistically simulate such changes which provides a major limitation in our ability to predict dynamic mass losses. In this paper we apply a specifically designed numerical flowband model to Jakobshavn Isbrae (JIB), a major marine outlet glacier of the Greenland ice sheet, and we explore and discuss the basic concepts and emerging issues in our understanding and modelling ability of the dynamics of tidewater outlet glaciers. The modelling demonstrates that enhanced ocean melt is able to trigger the observed dynamic changes of JIB but it heavily relies on the feedback between calving and terminus retreat and therefore the loss of buttressing. Through the same feedback, other forcings such as reduced winter sea-ice duration can produce similar rapid retreat. This highlights the need for a robust representation of the calving process and for improvements in the understanding and implementation of forcings at the marine boundary in predictive ice sheet models. Furthermore, the modelling uncovers high sensitivity and rapid adjustment of marine outlet glaciers to perturbations at their marine boundary implying that care should be taken in interpreting or extrapolating such rapid dynamic changes as recently observed in Greenland.

Modeling 5 years of subglacial lake activity in the MacAyeal Ice Stream (Antarctica) catchment through assimilation of ICESat laser altimetry

AbstractSubglacial lakes beneath Antarctica’s fast-moving ice streams are known to undergo ∼1 km3volume 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.

Investigating the sensitivity of numerical model simulations of the modern state of the Greenland ice-sheet and its future response to climate change

Abstract. Ice thickness and bedrock topography are essential boundary conditions for numerical modelling of the evolution of the Greenland ice-sheet (GrIS). The datasets currently in use by the majority of GrIS modelling studies are over two decades old and based on data collected from the 1970s and 80s. We use a newer, high-resolution Digital Elevation Model of the GrIS and new temperature and precipitation forcings to drive the Glimmer ice-sheet model offline under steady state, present day climatic conditions. Comparisons are made of ice-sheet geometry between these new datasets and older ones used in the EISMINT-3 exercise. We find that changing to the newer bedrock and ice thickness makes the greatest difference to Greenland ice volume and ice surface extent. When all boundary conditions and forcings are simultaneously changed to the newer datasets the ice-sheet is 33% larger in volume compared with observation and 17% larger than that modelled by EISMINT-3. We performed a tuning exercise to improve the modelled present day ice-sheet. Several solutions were chosen in order to represent improvement in different aspects of the GrIS geometry: ice thickness, ice volume and ice surface extent. We applied these new parameter sets for Glimmer to several future climate scenarios where atmospheric CO2 concentration was elevated to 400, 560 and 1120 ppmv (compared with 280 ppmv in the control) using a fully coupled General Circulation Model. Collapse of the ice-sheet was found to occur between 400 and 560 ppmv, a threshold substantially lower than previously modelled using the standard EISMINT-3 setup. This work highlights the need to assess carefully boundary conditions and forcings required by ice-sheet models, particularly in terms of the abstractions required for large-scale ice-sheet models, and the implications that these can have on predictions of ice-sheet geometry under past and future climate scenarios.

Improving surface boundary conditions with focus on coupling snow densification and meltwater retention in large-scale ice-sheet models of Greenland

AbstractSnowpack changes during the melt season are often not incorporated in modelling studies of the surface mass balance of the Greenland ice sheet. Densification of snow accelerates when meltwater is present, due to percolation and subsequent refreezing, and needs to be incorporated in ice-sheet models for ablation calculations. In this study, simple parameterizations to calculate surface melt, snow densification and meltwater retention are included as surface boundary conditions in a large-scale ice-sheet model of Greenland. Coupling the snow densification and meltwater-retention processes achieves a separation of volume and mass changes of the surface layer, in order to determine the surface melt contribution to runoff. Experiments for present-day conditions show that snow depth at the onset of melt, mean annual near-surface air temperature and the mean density of the annual snow layer are key factors controlling the quantity and spatial distribution of meltwater runoff above the equilibrium line on the Greenland ice sheet.

Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation

Abstract. New analytical solutions describing the effects of small-amplitude perturbations in boundary data on flow in the shallow-ice-stream approximation are presented. These solutions are valid for a non-linear Weertman-type sliding law and for Newtonian ice rheology. Comparison is made with corresponding solutions of the shallow-ice-sheet approximation, and with solutions of the full Stokes equations. The shallow-ice-stream approximation is commonly used to describe large-scale ice stream flow over a weak bed, while the shallow-ice-sheet approximation forms the basis of most current large-scale ice sheet models. It is found that the shallow-ice-stream approximation overestimates the effects of bed topography perturbations on surface profile for wavelengths less than about 5 to 10 ice thicknesses, the exact number depending on values of surface slope and slip ratio. For high slip ratios, the shallow-ice-stream approximation gives a very simple description of the relationship between bed and surface topography, with the corresponding transfer amplitudes being close to unity for any given wavelength. The shallow-ice-stream estimates for the timescales that govern the transient response of ice streams to external perturbations are considerably more accurate than those based on the shallow-ice-sheet approximation. In particular, in contrast to the shallow-ice-sheet approximation, the shallow-ice-stream approximation correctly reproduces the short-wavelength limit of the kinematic phase speed given by solving a linearised version of the full Stokes system. In accordance with the full Stokes solutions, the shallow-ice-sheet approximation predicts surface fields to react weakly to spatial variations in basal slipperiness with wavelengths less than about 10 to 20 ice thicknesses.

A comparison of Eulerian and Lagrangian methods for dating in numerical ice-sheet models

AbstractAccurate dating in ice sheets is required for a correct interpretation of palaeoclimatic records and for incorporation of material characteristics in the flow law which depend on ice age. In this paper, we make a comparison between a Lagrangian and Eulerian approach to the ice advection problem in numerical ice-sheet models. This comparison is first performed for a schematic two-dimensional ice sheet of Nye–Vialov type with a prescribed stationary velocity field. Severalcases are examined which incorporate basal melting, basal sliding and an undulating bed. A further comparison is made with an analytical solution for the ice divide. Both methods are also applied in a thermomechanical model of the Antarctic ice sheet for steady-state present-day conditions. Our main conclusion is that, for similar discretization parameters, the Lagrangian method produces less error than an Eulerian approach using a second-order upwinding finite-difference scheme, though the difference is small (<1%) for the largest part of the model domain. However, problems with the Lagrangian approach are introduced by the dispersion of tracers, necessitating the use of interpolation procedures that are a main source of additional error. It is also shown that a cubic-spline approximation of Lagrangian trajectories improves accuracy, but such a method is computationally hardly applicable in large-scale ice-sheet models.

The EISMINT benchmarks for testing ice-sheet models

We present a series of benchmark experiments designed for testing and comparing numerical ice-sheet models. Following the outcome of two EISMINT workshops organized to intercompare large-scale ice-sheet models currently in operation, model benchmark experiments ate described for ice sheets under fixed and moving margin conditions. These address both steady-state and time-dependent behaviour under schematic boundary conditions and with prescribed physics. A comparison was made of each model’s prediction of basic geophysical variables such as ice thickness, velocity and temperature. Consensus achieved in the model inter-comparison provides reference solutions against which the accuracy and consistency of ice-sheet modelling codes can be assessed.

The EISMINT benchmarks for testing ice-sheet models

We present a series of benchmark experiments designed for testing and comparing numerical ice-sheet models. Following the outcome of two EISMINT workshops organized to intercompare large-scale ice-sheet models currently in operation, model benchmark experiments ate described for ice sheets under fixed and moving margin conditions. These address both steady-state and time-dependent behaviour under schematic boundary conditions and with prescribed physics. A comparison was made of each model’s prediction of basic geophysical variables such as ice thickness, velocity and temperature. Consensus achieved in the model inter-comparison provides reference solutions against which the accuracy and consistency of ice-sheet modelling codes can be assessed.