Marine Ice Sheet Research Articles

Growth and decay of a marine terminating sector of the last British–Irish Ice Sheet: a geomorphological reconstruction

The boundary conditions that govern ice sheet dynamics can change significantly with the development of marine margins. This paper uses the glacial landscape in western Scotland to reconstruct changes in the British–Irish Ice Sheet that accompanied the growth and decay of a marine sector over the Malin Shelf. Ice advanced from a restricted mountain ice sheet with tidewater margins after ∼35 ka BP, and reached the continental shelf in ∼7 ka (average rate of ∼30 m a−1). Early ice flow had been directed through north-south, geologically controlled, over-deepened fjords that were carved during previous ‘restricted’ glaciations. This flow regime was abandoned with development of the Malin Shelf ice sheet sector; ice flow direction switched by ∼90° and was drawn westwards towards the shelf edge. The marine ice sheet phase saw episodes of west-east ice divide migration by up to 60 km over west central Scotland, possibly linked to ice streaming and calving events at the ice sheet margin. However, permanent and stationary ice divides and zones of cold-based ice, associated with subglacial topographic highs, also characterised the marine glacial stage over western Scotland. The North Channel ice divide remained a constant, though migratory feature while the BIIS occupied the Malin Shelf; it finally collapsed at the end of the Killard Point Stadial when the Irish Ice Sheet began to rapidly decay ∼16.5 ka BP. This permitted the Scottish Ice Sheet to temporarily advance over north-east Ireland (previously identified as the East Antrim Coastal Readvance) before it too retreated, at rates in the order of 102 m a−1. Although the imprint of extensive shelf-edge ice sheet glaciation exists in the coastal landscape of western Scotland, the dominant landscape features relate to a restricted, marine-proximal mountain ice sheet with markedly different flow configurations. Similar first-order geomorphological features, relating to ‘restricted’ glacial conditions, are likely to be preserved in subglacial highlands under interior parts of modern ice sheets.

Parameter and state estimation with a time-dependent adjoint marine ice sheet model

Abstract. 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.

New perspectives on paleoglaciology

Paleoglaciology deals with glaciation cycles of the Quaternary Ice Age. It combines the dynamics of present-day ice sheets deduced from glaciology with the history of former ice sheets deduced from glacial geology. Cosmogenic dating now makes a detailed chronology of a cycle possible. Radiocarbon dating has provided a detailed chronology for Termination of the last cycle, but cannot date how the cycle began. Here we identify the central challenge in applying paleoglaciology to Quaternary glaciation cycles in general, and initiation of these cycles in particular. The challenge is the role of thickening sea ice in the Arctic Ocean, possibly becoming thick ice shelves floating over deep Arctic basins and high marine ice sheets grounded on shallow Arctic continental shelves. In that case, an Arctic Ice Sheet existed that was larger and less stable than the Antarctic Ice Sheet is now or in the past. Two approaches to this problem are presented as Part 1 and Part 2. In Part 1, the height of these former ice sheets is linked primarily to the strength of ice-bed coupling, which is deduced from glacial geology. It provides “snapshots” of ice sheets that give ice elevations independent of the past history and largely independent of ice-surface conditions, temperatures and the mass balance in particular. In Part 2, heights of former ice sheets depend on both their past history, particularly initial conditions, and changing surface conditions during the glaciation cycle. This provides a “motion picture” of ice sheets during the full cycle. The challenge is to establish a “mind meld” of these two approaches. They allow new perspectives on paleoglaciology.

Why marine ice sheet model predictions may diverge in estimating future sea level rise

Despite major recent efforts, marine ice sheet models aiming at predicting future mass loss from ice sheets still suffer from uncertainties with respect to grounding line migration. A recent model intercomparison provided tools to test how models treat grounding line dynamics in a three‐dimensional setting. Here we use these tools to address to what extent differences in mass loss occur according to the approximation to the Stokes equations, describing marine ice sheet flow, used. We find that models that neglect components of vertical shearing in the force budget wrongly estimate ice sheet mass loss by ±50% over century time scales when compared to models that solve the full Stokes system of equations. Models that only include horizontal stresses also misrepresent velocities and ice shelf geometry, suggesting that interactions between the grounded ice sheet and the ocean will also be modeled incorrectly. Based on these findings, we strongly advise the use of high‐order models to compute reliable projections of ice sheet contribution to sea level rise.

Sediment deposition at the modern grounding zone of Whillans Ice Stream, West Antarctica

Much of the threshold behavior of marine ice sheets is thought to result from processes occurring at the grounding zone, where the ice sheet transitions into the ice shelf. At short timescales (decades to centuries), grounding zone behavior is likely to be influenced by ongoing sediment deposition, which can stabilize the grounding zone position. We present a ground‐based geophysical study across the modern grounding zone of Whillans Ice Stream. Within an embayment setting, where subglacial meltwater drains, we image sedimentary deposits; however, we do not observe the classic asymmetric grounding zone wedge deposits, which are found in the paleorecord and are thought to stabilize the grounding zone position. At an adjacent peninsula, we image the grounding zone and an ice‐shelf pinning point and again observe no wedge deposits.

Evidence for a water system transition beneath Thwaites Glacier, West Antarctica

Thwaites Glacier is one of the largest, most rapidly changing glaciers on Earth, and its landward-sloping bed reaches the interior of the marine West Antarctic Ice Sheet, which impounds enough ice to yield meters of sea-level rise. Marine ice sheets with landward-sloping beds have a potentially unstable configuration in which acceleration can initiate or modulate grounding-line retreat and ice loss. Subglacial water has been observed and theorized to accelerate the flow of overlying ice dependent on whether it is hydrologically distributed or concentrated. However, the subglacial water systems of Thwaites Glacier and their control on ice flow have not been characterized by geophysical analysis. The only practical means of observing these water systems is airborne ice-penetrating radar, but existing radar analysis approaches cannot discriminate between their dynamically critical states. We use the angular distribution of energy in radar bed echoes to characterize both the extent and hydrologic state of subglacial water systems across Thwaites Glacier. We validate this approach with radar imaging, showing that substantial water volumes are ponding in a system of distributed canals upstream of a bedrock ridge that is breached and bordered by a system of concentrated channels. The transition between these systems occurs with increasing surface slope, melt-water flux, and basal shear stress. This indicates a feedback between the subglacial water system and overlying ice dynamics, which raises the possibility that subglacial water could trigger or facilitate a grounding-line retreat in Thwaites Glacier capable of spreading into the interior of the West Antarctic Ice Sheet.

An adaptive Newton multigrid method for a model of marine ice sheets

In this paper, we consider a model for the time evolution of three-dimensional marine ice sheets. This model combines the Shallow Ice Approximation (SIA) for the ice deformation, the Shallow Shelf Approximation (SSA) for the basal sliding, and the mass conservation principle. At each time step, we solve a scalar p-Laplace minimization-type problem with obstacle (SIA), a vectorial p-Laplace minimization-type problem (SSA) and a transport equation (mass conservation). The two minimization problems are solved using a truncated nonsmooth Newton multigrid method while the transport equation is solved using a vertex-centred finite volume method. Our approach is combined to an heuristic mesh adaptive refinement procedure to face the large gradients of the solution that are expected between the ice sheet and the ice shelf. As applications, we present some simulations of the Marine Ice Sheet Model Intercomparison Project MISMIP (2D and 3D) and validate our results against an analytic solution (2D) and other participant model results (3D). Further numerical results show that the convergence of our Newton multigrid method is insensitive to local refinements making our overall adaptive strategy fully efficient.

An experimental and theoretical study of the dynamics of grounding lines

AbstractWe present an experimental and theoretical study of a thin, viscous fluid layer that flows radially under gravity from a point source into a denser inviscid fluid layer of uniform depth above a rigid horizontal surface. Near the source, the viscous layer lies in full contact with the surface, forming a vertical-shear-dominated viscous gravity current. At a certain distance from the source, the layer detaches from the surface to form a floating current whose dynamics are controlled by the viscous stresses due to longitudinal extension. We describe the dynamics of the grounded and floating components using distinct thin-layer theories. Separating the grounded and floating regions is the freely moving line of detachment, or grounding line, whose evolution we model by balancing the horizontal forces between the two regions. Using numerical and asymptotic analysis, we calculate the evolution of the system from a self-similar form at early times towards a steady state at late times. We use our solutions to illustrate how three-dimensional stresses within marine ice sheets, such as that of West Antarctica, can lead to stabilization of the grounding line. To assess the validity of the assumptions underlying our model, we compare its predictions with data from a series of laboratory experiments.

Ice-shelf buttressing and the stability of marine ice sheets

Abstract. Ice-shelf buttressing and the stability of marine-type ice sheets are investigated numerically. Buttressing effects are analysed for a situation where a stable grounding line is located on a bed sloping upwards in the direction of flow. Such grounding-line positions are known to be unconditionally unstable in the absence of transverse flow variations. It is shown that ice-shelf buttressing can restore stability under these conditions. Ice flux at the grounding line is, in general, not a monotonically increasing function of ice thickness. This, possibly at first somewhat counterintuitive result, is found to be fully consistent with recent theoretical work. Grounding lines on retrograde slopes are conditionally stable, and the stability regime is a non-trivial function of bed and ice-shelf geometry. The stability of grounding lines cannot be assessed from considerations of local bed slope only.

Grounding line transient response in marine ice sheet models

Abstract. Marine ice-sheet stability is mostly controlled by the dynamics of the grounding line, i.e. the junction between the grounded ice sheet and the floating ice shelf. Grounding line migration has been investigated within the framework of MISMIP (Marine Ice Sheet Model Intercomparison Project), which mainly aimed at investigating steady state solutions. Here we focus on transient behaviour, executing short-term simulations (200 yr) of a steady ice sheet perturbed by the release of the buttressing restraint exerted by the ice shelf on the grounded ice upstream. The transient grounding line behaviour of four different flowline ice-sheet models has been compared. The models differ in the physics implemented (full Stokes and shallow shelf approximation), the numerical approach, as well as the grounding line treatment. Their overall response to the loss of buttressing is found to be broadly consistent in terms of grounding line position, rate of surface elevation change and surface velocity. However, still small differences appear for these latter variables, and they can lead to large discrepancies (> 100%) observed in terms of ice sheet contribution to sea level when cumulated over time. Despite the recent important improvements of marine ice-sheet models in their ability to compute steady state configurations, our results question the capacity of these models to compute short-term reliable sea-level rise projections.

Ice-Sheet Dynamics

We describe the development of mathematical models of ice sheets, focusing on underlying physics and the minimal components that successful models must contain. Our review describes the basic fluid dynamical ice-flow models currently in use; points out numerous poorly understood thermomechanical feedbacks in ice flow; and describes the current, often poorly constrained, state of models for ice-sheet sliding and subglacial drainage, as well as their role in ice-stream dynamics. We conclude with a survey of marine ice-sheet models, outlining recent developments of self-consistent free-boundary models and ongoing research into three-dimensional marine ice sheets.

Orbitally paced shifts in the particle size of Antarctic continental shelf sediments in response to ice dynamics during the Miocene climatic optimum

The AND-2A drill hole (ANDRILL [Antarctic Geological Drilling Program] Southern McMurdo Sound Project), ∼10 km from the East Antarctica coastline, records nearly 6 m.y. of sedimentation across the Miocene climatic optimum at a high-latitude site. Sedimentological studies of bedforms and particle size distributions indicate that the paleoenvironment was strongly affected by waves and currents, consistent with deposition in a glacially influenced neritic environment. We document abrupt shifts in mud percent within glacial-interglacial cycles ca. 17.8 Ma and between ca. 16.7 and 15.7 Ma that we attribute to the hydrodynamic effects of wave stirring tied to episodes of ice growth and decay. Although wave climate and geodynamic forcing of the paleobathymetry simultaneously affect wave stirring on a high-latitude shelf, both are ultimately controlled by the size of the ice sheet. The mud percent record displays cyclicity at short-eccentricity time scales (94–99 k.y.) and, unexpectedly, ice retreat phases interpreted from the particle size record coincide with eccentricity minima. We attribute the eccentricity-paced ice retreat phases during the late Early Miocene polythermal glacial conditions and the cool orbital parameters to marine ice sheet instability in response to changes in ocean circulation and heat transport. The particle size record of the AND-2A core provides unique near-field evidence for orbitally paced changes in high-latitude climate and ice volume during the Miocene climatic optimum and important insights into the mechanisms of ice sheet growth and decay in a period of global warmth.

The stability of grounding lines on retrograde slopes

Abstract. The stability of marine ice sheets grounded on beds that slope upwards in the overall direction of flow is investigated numerically in two horizontal dimensions. We give examples of stable grounding lines on such retrograde slopes illustrating that marine ice sheets are not unconditionally unstable in two horizontal dimensions. Retrograde bed slopes at the grounding lines of marine ice sheets, such as the West Antarctic Ice Sheet (WAIS), do not per se imply an instability, nor do they imply that these regions are close to a threshold of instability. We therefore question those estimates of the potential near-future contribution of WAIS to global sea level change based solely on the notion that WAIS, resting on a retrograde slope, must be inherently unstable.

Adaptive mesh, finite volume modeling of marine ice sheets

Continental scale marine ice sheets such as the present day West Antarctic Ice Sheet are strongly affected by highly localized features, presenting a challenge to numerical models. Perhaps the best known phenomenon of this kind is the migration of the grounding line — the division between ice in contact with bedrock and floating ice shelves — which needs to be treated at sub-kilometer resolution. We implement a block-structured finite volume method with adaptive mesh refinement (AMR) for three dimensional ice sheets, which allows us to discretize a narrow region around the grounding line at high resolution and the remainder of the ice sheet at low resolution. We demonstrate AMR simulations that are in agreement with uniform mesh simulations, but are computationally far cheaper, appropriately and efficiently evolving the mesh as the grounding line moves over significant distances. As an example application, we model rapid deglaciation of Pine Island Glacier in West Antarctica caused by melting beneath its ice shelf.

Results of the Marine Ice Sheet Model Intercomparison Project, MISMIP

Abstract. 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.

Marine ice sheet stability

AbstractWe examine the stability of two-dimensional marine ice sheets in steady state. The dynamics of marine ice sheets is described by a viscous thin-film model with two Stefan-type boundary conditions at the moving boundary or ‘grounding line’ that marks the transition from grounded to floating ice. One of these boundary conditions constrains ice thickness to be at a local critical value for flotation, which depends on depth to bedrock at the grounding line. The other condition sets ice flux as a function of ice thickness at the grounding line. Depending on the shape of the bedrock, multiple equilibria may be possible. Using a linear stability analysis, we confirm a long-standing heuristic argument that asserts that the stability of these equilibria is determined by a simple mass balance consideration. If an advance in the grounding line away from its steady-state position leads to a net mass gain, the steady state is unstable, and stable otherwise. This also confirms that grounding lines can only be stable in positions where bedrock slopes downwards sufficiently steeply.

Evolution of a coupled marine ice sheet–sea level model

We investigate the stability of marine ice sheets by coupling a gravitationally self‐consistent sea level model valid for a self‐gravitating, viscoelastically deforming Earth to a 1‐D marine ice sheet‐shelf model. The evolution of the coupled model is explored for a suite of simulations in which we vary the bed slope and the forcing that initiates retreat. We find that the sea level fall at the grounding line associated with a retreating ice sheet acts to slow the retreat; in simulations with shallow reversed bed slopes and/or small external forcing, the drop in sea level can be sufficient to halt the retreat. The rate of sea level change at the grounding line has an elastic component due to ongoing changes in ice sheet geometry, and a viscous component due to past ice and ocean load changes. When the ice sheet model is forced from steady state, on short timescales (<∼500 years), viscous effects may be ignored and grounding‐line migration at a given time will depend on the local bedrock topography and on contemporaneous sea level changes driven by ongoing ice sheet mass flux. On longer timescales, an accurate assessment of the present stability of a marine ice sheet requires knowledge of its past evolution.

A three-dimensional full Stokes model of the grounding line dynamics: effect of a pinning point beneath the ice shelf

Abstract. The West Antarctic ice sheet is confined by a large area of ice shelves, fed by inland ice through fast flowing ice streams. The dynamics of the grounding line, which is the line-boundary between grounded ice and the downstream ice shelf, has a major influence on the dynamics of the whole ice sheet. However, most ice sheet models use simplifications of the flow equations, as they do not include all the stress components, and are known to fail in their representation of the grounding line dynamics. Here, we present a 3-D full Stokes model of a marine ice sheet, in which the flow problem is coupled with the evolution of the upper and lower free surfaces, and the position of the grounding line is determined by solving a contact problem between the shelf/sheet lower surface and the bedrock. Simulations are performed using the open-source finite-element code Elmer/Ice within a parallel environment. The model's ability to cope with a curved grounding line and the effect of a pinning point beneath the ice shelf are investigated through prognostic simulations. Starting from a steady state, the sea level is slightly decreased to create a contact point between a seamount and the ice shelf. The model predicts a dramatic decrease of the shelf velocities, leading to an advance of the grounding line until both grounded zones merge together, during which an ice rumple forms above the contact area at the pinning point. Finally, we show that once the contact is created, increasing the sea level to its initial value does not release the pinning point and has no effect on the ice dynamics, indicating a stabilising effect of pinning points.

The Potsdam Parallel Ice Sheet Model (PISM-PIK) – Part 2: Dynamic equilibrium simulation of the Antarctic ice sheet

Abstract. We present a dynamic equilibrium simulation of the ice sheet-shelf system on Antarctica with the Potsdam Parallel Ice Sheet Model (PISM-PIK). The simulation is initialized with present-day conditions for bed topography and ice thickness and then run to steady state with constant present-day surface mass balance. Surface temperature and sub-shelf basal melt distribution are parameterized. Grounding lines and calving fronts are free to evolve, and their modeled equilibrium state is compared to observational data. A physically-motivated calving law based on horizontal spreading rates allows for realistic calving fronts for various types of shelves. Steady-state dynamics including surface velocity and ice flux are analyzed for whole Antarctica and the Ronne-Filchner and Ross ice shelf areas in particular. The results show that the different flow regimes in sheet and shelves, and the transition zone between them, are captured reasonably well, supporting the approach of superposition of SIA and SSA for the representation of fast motion of grounded ice. This approach also leads to a natural emergence of sliding-dominated flow in stream-like features in this new 3-D marine ice sheet model.

The Potsdam Parallel Ice Sheet Model (PISM-PIK) – Part 1: Model description

Abstract. We present the Potsdam Parallel Ice Sheet Model (PISM-PIK), developed at the Potsdam Institute for Climate Impact Research to be used for simulations of large-scale ice sheet-shelf systems. It is derived from the Parallel Ice Sheet Model (Bueler and Brown, 2009). Velocities are calculated by superposition of two shallow stress balance approximations within the entire ice covered region: the shallow ice approximation (SIA) is dominant in grounded regions and accounts for shear deformation parallel to the geoid. The plug-flow type shallow shelf approximation (SSA) dominates the velocity field in ice shelf regions and serves as a basal sliding velocity in grounded regions. Ice streams can be identified diagnostically as regions with a significant contribution of membrane stresses to the local momentum balance. All lateral boundaries in PISM-PIK are free to evolve, including the grounding line and ice fronts. Ice shelf margins in particular are modeled using Neumann boundary conditions for the SSA equations, reflecting a hydrostatic stress imbalance along the vertical calving face. The ice front position is modeled using a subgrid-scale representation of calving front motion (Albrecht et al., 2011) and a physically-motivated calving law based on horizontal spreading rates. The model is tested in experiments from the Marine Ice Sheet Model Intercomparison Project (MISMIP). A dynamic equilibrium simulation of Antarctica under present-day conditions is presented in Martin et al. (2011).