Grounding Line Dynamics Research Articles

Seawater Intrusion in the Observed Grounding Zone of Petermann Glacier Causes Extensive Retreat

AbstractUnderstanding grounding line dynamics is critical for projecting glacier evolution and sea level rise. Observations from satellite radar interferometry reveal rapid grounding line migration forced by oceanic tides that are several kilometers larger than predicted by hydrostatic equilibrium, indicating the transition from grounded to floating ice is more complex than previously thought. Recent studies suggest seawater intrusion beneath grounded ice may play a role in driving rapid ice loss. Here, we investigate its impact on the evolution of Petermann Glacier, Greenland, using an ice sheet model. We compare model results with observed changes in grounding line position, velocity, and ice elevation between 2010 and 2022. We match the observed retreat, speed up, and thinning using 3‐km‐long seawater intrusion that drive peak ice melt rates of 50 m/yr; but we cannot obtain the same agreement without seawater intrusion. Including seawater intrusion in glacier modeling will increase the sensitivity to ocean warming.

‘Stable’ and ‘unstable’ are not useful descriptions of marine ice sheets in the Earth's climate system

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’.

Effects of calving and submarine melting on steady states and stability of buttressed marine ice sheets

AbstractMass loss from ice shelves is a strong control on grounding-line dynamics. Here we investigate how calving and submarine melt parameterizations affect steady-state grounding-line positions and their stability. Our results indicate that different calving laws with the same melt parameterization result in more diverse steady-state ice-sheet configurations than different melt parameterizations with the same calving law. We show that the backstress at the grounding line depends on the integrated ice-shelf mass flux. Consequently, ice shelves are most sensitive to high melt rates in the vicinity of their grounding lines. For the same shelf-averaged melt rates, different melt parameterizations can lead to very different ice-shelf configurations and grounding-line positions. If the melt rate depends on the slope of the ice-shelf draft, then the positive feedback between increased melting and steepening of the slope can lead to singular melt rates at the ice-shelf front, producing an apparent lower limit of the shelf front thickness as the ice thickness vanishes over a small boundary layer. Our results illustrate that the evolution of marine ice sheets is highly dependent on ice-shelf mass loss mechanisms, and that existing parameterizations can lead to a wide range of modelled grounding-line behaviours.

A new vertically integrated MOno-Layer Higher-Order (MOLHO) ice flow model

Abstract. Numerical simulations of ice sheets rely on the momentum balance to determine how ice velocities change as the geometry of the system evolves. Ice is generally assumed to follow a Stokes flow with a nonlinear viscosity. Several approximations have been proposed in order to lower the computational cost of a full-Stokes stress balance. A popular option is the Blatter–Pattyn or higher-order model (HO), which consists of a three-dimensional set of equations that solves the horizontal velocities only. However, it still remains computationally expensive for long transient simulations. Here we present a depth-integrated formulation of the HO model, which can be solved on a two-dimensional mesh in the horizontal plane. We employ a specific polynomial function to describe the vertical variation in the velocity, which allows us to integrate the vertical dimension using a semi-analytic integration. We assess the performance of this MOno-Layer Higher-Order (MOLHO) model to compute ice velocities and simulate grounding line dynamics on standard benchmarks (ISMIP-HOM and MISMIP3D). We compare MOLHO results to the ones obtained with the original three-dimensional HO model. We also compare the time performance of both models in time-dependent runs. Our results show that the ice velocities and grounding line positions obtained with MOLHO are in very good agreement with the ones from HO. In terms of computing time, MOLHO requires less than 10 % of the computational time of a typical HO model, for the same simulations. These results suggest that the MOno-Layer Higher-Order formulation provides improved computational time performance and a comparable accuracy compared to the HO formulation, which opens the door to higher-order paleo simulations.

Variational formulation of marine ice-sheet and subglacial-lake grounding-line dynamics

Abstract

The Utrecht Finite Volume Ice-Sheet Model: UFEMISM (version 1.0)

Abstract. Improving our confidence in future projections of sea-level rise requires models that can simulate ice-sheet evolution both in the future and in the geological past. A physically accurate treatment of large changes in ice-sheet geometry requires a proper treatment of processes near the margin, like grounding line dynamics, which in turn requires a high spatial resolution in that specific region, so that small-scale topographical features are resolved. This leads to a demand for computationally efficient models, where such a high resolution can be feasibly applied in simulations of 105–107 years in duration. Here, we present and evaluate a new ice-sheet model that solves the hybrid SIA–SSA approximation of the stress balance, including a heuristic rule for the grounding-line flux. This is done on a dynamic adaptive mesh which is adapted to the modelled ice-sheet geometry during a simulation. Mesh resolution can be configured to be fine only at specified areas, such as the calving front or the grounding line, as well as specified point locations such as ice-core drill sites. This strongly reduces the number of grid points where the equations need to be solved, increasing the computational efficiency. A high resolution allows the model to resolve small geometrical features, such as outlet glaciers and sub-shelf pinning points, which can significantly affect large-scale ice-sheet dynamics. We show that the model reproduces the analytical solutions or model intercomparison benchmarks for a number of schematic ice-sheet configurations, indicating that the numerical approach is valid. Because of the unstructured triangular mesh, the number of vertices increases less rapidly with resolution than in a square-grid model, greatly reducing the required computation time for high resolutions. A simulation of all four continental ice sheets during an entire 120 kyr glacial cycle, with a 4 km resolution near the grounding line, is expected to take 100–200 wall clock hours on a 16-core system (1600–3200 core hours), implying that this model can be feasibly used for high-resolution palaeo-ice-sheet simulations.

Deglacial Ice Sheet Instabilities Induced by Proglacial Lakes

AbstractDuring the last deglaciation (21–7 kaBP), the gradual retreat of Northern Hemisphere ice sheet margins produced large proglacial lakes. While the climatic impacts of these lakes have been widely acknowledged, their role on ice sheet grounding line dynamics has received very little attention so far. Here, we show that proglacial lakes had dramatic implications for the North American ice sheet dynamics through a self‐sustained mechanical instability which has similarities with the known marine ice sheet instability consequently providing fast retreat of large portions of the ice sheet over the continent. This instability mechanism is likely important in contributing to deglaciation of terrestrial glaciers and ice sheets with proglacial lakes at their margins as it can substantially accelerate the mass loss. Echoing our knowledge of Antarctic ice sheet dynamics, proglacial lakes are another manifestation of the importance of grounding line dynamics for ice sheet evolution.

Implementation and performance of adaptive mesh refinement in the Ice Sheet System Model (ISSM v4.14)

Abstract. Accurate projections of the evolution of ice sheets in a changing climate require a fine mesh/grid resolution in ice sheet models to correctly capture fundamental physical processes, such as the evolution of the grounding line, the region where grounded ice starts to float. The evolution of the grounding line indeed plays a major role in ice sheet dynamics, as it is a fundamental control on marine ice sheet stability. Numerical modeling of a grounding line requires significant computational resources since the accuracy of its position depends on grid or mesh resolution. A technique that improves accuracy with reduced computational cost is the adaptive mesh refinement (AMR) approach. We present here the implementation of the AMR technique in the finite element Ice Sheet System Model (ISSM) to simulate grounding line dynamics under two different benchmarks: MISMIP3d and MISMIP+. We test different refinement criteria: (a) distance around the grounding line, (b) a posteriori error estimator, the Zienkiewicz–Zhu (ZZ) error estimator, and (c) different combinations of (a) and (b). In both benchmarks, the ZZ error estimator presents high values around the grounding line. In the MISMIP+ setup, this estimator also presents high values in the grounded part of the ice sheet, following the complex shape of the bedrock geometry. The ZZ estimator helps guide the refinement procedure such that AMR performance is improved. Our results show that computational time with AMR depends on the required accuracy, but in all cases, it is significantly shorter than for uniformly refined meshes. We conclude that AMR without an associated error estimator should be avoided, especially for real glaciers that have a complex bed geometry.

The GRISLI ice sheet model (version 2.0): calibration and validation for multi-millennial changes of the Antarctic ice sheet

Abstract. In this paper, we present the GRISLI (Grenoble ice sheet and land ice) model in its newest revision (version 2.0). Whilst GRISLI is applicable to any given ice sheet, we focus here on the Antarctic ice sheet because it highlights the importance of grounding line dynamics. Important improvements have been implemented in the model since its original version (Ritz et al., 2001). Notably, GRISLI now includes a basal hydrology model and an explicit flux computation at the grounding line based on the analytical formulations of Schoof (2007) or Tsai et al. (2015). We perform a full calibration of the model based on an ensemble of 300 simulations sampling mechanical parameter space using a Latin hypercube method. Performance of individual members is assessed relative to the deviation from present-day observed Antarctic ice thickness. To assess the ability of the model to simulate grounding line migration, we also present glacial–interglacial ice sheet changes throughout the last 400 kyr using the best ensemble members taking advantage of the capacity of the model to perform multi-millennial long-term integrations. To achieve this goal, we construct a simple climatic perturbation of present-day climate forcing fields based on two climate proxies: atmospheric and oceanic. The model is able to reproduce expected grounding line advances during glacial periods and subsequent retreats during terminations with reasonable glacial–interglacial ice volume changes.

Dynamically coupling full Stokes and shallow shelf approximation for marine ice sheet flow using Elmer/Ice (v8.3)

Abstract. Ice flow forced by gravity is governed by the full Stokes (FS) equations, which are computationally expensive to solve due to the nonlinearity introduced by the rheology. Therefore, approximations to the FS equations are commonly used, especially when modeling a marine ice sheet (ice sheet, ice shelf, and/or ice stream) for 103 years or longer. The shallow ice approximation (SIA) and shallow shelf approximation (SSA) are commonly used but are accurate only for certain parts of an ice sheet. Here, we report a novel way of iteratively coupling FS and SSA that has been implemented in Elmer/Ice and applied to conceptual marine ice sheets. The FS–SSA coupling appears to be very accurate; the relative error in velocity compared to FS is below 0.5 % for diagnostic runs and below 5 % for prognostic runs. Results for grounding line dynamics obtained with the FS–SSA coupling are similar to those obtained from an FS model in an experiment with a periodical temperature forcing over 3000 years that induces grounding line advance and retreat. The rapid convergence of the FS–SSA coupling shows a large potential for reducing computation time, such that modeling a marine ice sheet for thousands of years should become feasible in the near future. Despite inefficient matrix assembly in the current implementation, computation time is reduced by 32 %, when the coupling is applied to a 3-D ice shelf.

Suppression of marine ice sheet instability

A long-standing open question in glaciology concerns the propensity for ice sheets that lie predominantly submerged in the ocean (marine ice sheets) to destabilise under buoyancy. This paper addresses the processes by which a buoyancy-driven mechanism for the retreat and ultimate collapse of such ice sheets – the marine ice sheet instability – is suppressed by lateral stresses acting on its floating component (the ice shelf). The key results are to demonstrate the transition between a mode of stable (easily reversible) retreat along a stable steady-state branch created by ice-shelf buttressing to tipped (almost irreversible) retreat across a critical parametric threshold. The conditions for triggering tipped retreat can be controlled by the calving position and other properties of the ice-shelf profile and can be largely independent of basal stress, in contrast to principles established from studies of unbuttressed grounding-line dynamics. The stability and recovery conditions introduced by lateral stresses are analysed by developing a method of constructing grounding-line stability (bifurcation) diagrams, which provide a rapid assessment of the steady-state positions, their natures and the conditions for secondary grounding, giving clear visualisations of global stabilisation conditions. A further result is to reveal the possibility of a third structural component of a marine ice sheet that lies intermediate to the fully grounded and floating components. The region forms an extended grounding area in which the ice sheet lies very close to flotation, and there is no clearly distinguished grounding line. The formation of this region generates an upsurge in buttressing that provides the most feasible mechanism for reversal of a tipped grounding line. The results of this paper provide conceptual insight into the phenomena controlling the stability of the West Antarctic Ice Sheet, the collapse of which has the potential to dominate future contributions to global sea-level rise.

Atmosphere-driven ice sheet mass loss paced by topography: Insights from modelling the south-western Scandinavian Ice Sheet

Marine-terminating glaciers and ice streams are important controls of ice sheet mass balance. However, understanding of their long-term response to external forcing is limited by relatively short observational records of present-day glaciers and sparse geologic evidence for paleo-glaciers. Here we use a high-resolution ice sheet model with an accurate representation of grounding line dynamics to study the deglaciation of the marine-based south-western Norwegian sector of the Scandinavian Ice Sheet and its sensitivity to ocean and atmosphere forcing. We find that the regional response to a uniform climate change is highly dependent on the local bedrock topography, consistent with ice sheet reconstructions. Our simulations suggest that ocean warming is able to trigger initial retreat in several fjords, but is not sufficient to explain retreat everywhere. Widespread retreat requires additional ice thinning driven by surface melt. Once retreat is triggered, the underlying bedrock topography and fjord width control the rate and extent of retreat, while multi-millennial changes over the course of deglaciation are modulated by surface melt. We suggest that fjord geometry, ice-ocean interactions and grounding line dynamics are vital controls of decadal-to centennial scale ice sheet mass loss. However, we postulate that atmospheric changes are the most important drivers of widespread ice sheet demise, and will likely trump oceanic influence on future ice sheet mass loss and resulting sea level rise over centennial and longer time scales.

Interplay of grounding-line dynamics and sub-shelf melting during retreat of the Bj\xf8rn\xf8yrenna Ice Stream

The Barents Sea Ice Sheet was a marine-based ice sheet, i.e., it rested on the Barents Sea floor during the Last Glacial Maximum (21 ky BP). The Bjørnøyrenna Ice Stream was the largest ice stream draining the Barents Sea Ice Sheet and is regarded as an analogue for contemporary ice streams in West Antarctica. Here, the retreat of the Bjørnøyrenna Ice Stream is simulated by means of two numerical ice sheet models and results assessed against geological data. We investigate the sensitivity of the ice stream to changes in ocean temperature and the impact of grounding-line physics on ice stream retreat. Our results suggest that the role played by sub-shelf melting depends on how the grounding-line physics is represented in the models. When an analytic constraint on the ice flux across the grounding line is applied, the retreat of Bjørnøyrenna Ice Stream is primarily driven by internal ice dynamics rather than by oceanic forcing. This suggests that implementations of grounding-line physics need to be carefully assessed when evaluating and predicting the response of contemporary marine-based ice sheets and individual ice streams to ongoing and future ocean warming.

The effect of buttressing on grounding line dynamics

ABSTRACTDetermining the position and stability of the grounding line of a marine ice sheet is a major challenge for ice-sheet models. Here, we investigate the role of lateral shear and ice-shelf buttressing in grounding line dynamics by extending an existing boundary layer theory to laterally confined marine ice sheets. We derive an analytic expression for the ice flux at the grounding line of confined marine ice sheets that depends on both local bed properties and non-local ice-shelf properties. Application of these results to a laterally confined version of the MISMIP 1a experiment shows that the boundary condition at the ice-shelf front (i.e. the calving law) is a major control on the location and stability of the grounding line in the presence of buttressing, allowing for both stable and unstable grounding line positions on downwards sloping beds. These results corroborate the findings of existing numerical studies that the stability of confined marine ice sheets is influenced by ice-shelf properties, in contrast to unconfined configurations where grounding line stability is solely determined by the local slope of the bed. Consequently, the marine ice-sheet instability hypothesis may not apply to buttressed marine ice sheets.

On the Short‐term Grounding Zone Dynamics of Pine Island Glacier, West Antarctica, Observed With COSMO‐SkyMed Interferometric Data

AbstractUsing radar satellite data from the Italian COSMO‐SkyMed (CSK) constellation and the German TanDEM‐X formation, we present comprehensive measurements of the biweekly grounding line dynamics of Pine Island Glacier, West Antarctica, from August to December 2015. The 1 day repeat cycle of CSK reveals tidally induced, grounding line migration on the scale of kilometers and extensive seawater intrusion within the grounding zone, which significantly exceeds that predicted for a stiff bed but are consistent with that calculated for a deformable bed. The deformable bed also explains the continuous draining/filling of subglacial lakes proximal to the grounding line. After correction for oceanic tides, we estimate a retreat rate for 2011–2015 of 0.3 km/yr at the glacier center and 0.5 km/yr on the sides, which is 3 times slower than for 1994–2011 (1.2 km/yr at the center). We attribute the decrease in retreat rate to colder ocean conditions in 2012–2013 relative to 2000–2011.

Sensitivity of grounding line dynamics to the choice of the friction law

ABSTRACTBasal slip accounts for a large part of the flow of ice streams draining ice from Antarctica and Greenland into the ocean. Therefore, an appropriate representation of basal slip in ice flow models is a prerequisite for accurate sea level rise projections. Various friction laws have been proposed to describe basal slip in models. Here, we compare the influence on grounding line (GL) dynamics of four friction laws: the traditional Weertman law and three effective pressure-dependent laws, namely the Schoof, Tsai and Budd laws. It turns out that, even when they are tuned to a common initial reference state, the Weertman, Budd and Schoof laws lead to thoroughly different steady-state positions, although the Schoof and Tsai laws lead to much the same result. In particular, under certain circumstances, it is possible to obtain a steady GL located on a reverse slope area using the Weertman law. Furthermore, the predicted transient evolution of the GL as well as the projected contributions to sea level rise over a 100-year time horizon vary significantly depending on the friction law. We conclude on the importance of choosing an appropriate law for reliable sea level rise projections and emphasise the need for a coupling between ice flow models and physically based subglacial hydrological models.

Adaptive mesh refinement versus subgrid friction interpolation in simulations of Antarctic ice dynamics

ABSTRACTAt least in conventional hydrostatic ice-sheet models, the numerical error associated with grounding line dynamics can be reduced by modifications to the discretization scheme. These involve altering the integration formulae for the basal traction and/or driving stress close to the grounding line and exhibit lower – if still first-order – error in the MISMIP3d experiments. MISMIP3d may not represent the variety of real ice streams, in that it lacks strong lateral stresses, and imposes a large basal traction at the grounding line. We study resolution sensitivity in the context of extreme forcing simulations of the entire Antarctic ice sheet, using the BISICLES adaptive mesh ice-sheet model with two schemes: the original treatment, and a scheme, which modifies the discretization of the basal traction. The second scheme does indeed improve accuracy – by around a factor of two – for a given mesh spacing, but $\lesssim 1$ km resolution is still necessary. For example, in coarser resolution simulations Thwaites Glacier retreats so slowly that other ice streams divert its trunk. In contrast, with $\lesssim 1$ km meshes, the same glacier retreats far more quickly and triggers the final phase of West Antarctic collapse a century before any such diversion can take place.

Contrasting the modelled sensitivity of the Amundsen Sea Embayment ice streams

AbstractPresent-day mass loss from the West Antarctic ice sheet is centred on the Amundsen Sea Embayment (ASE), primarily through ice streams, including Pine Island, Thwaites and Smith glaciers. To understand the differences in response of these ice streams, we ran a perturbed parameter ensemble, using a vertically-integrated ice flow model with adaptive mesh refinement. We generated 71 sets of three physical parameters (basal traction coefficient, ice viscosity stiffening factor and sub-shelf melt rate), which we used to simulate the ASE for 50 years. We also explored the effects of different bed geometries and basal sliding laws. The mean rate of sea-level rise across the ensemble of simulations is comparable with current observed rates for the ASE. We found evidence that grounding line dynamics are sensitive to features in the bed geometry: simulations using BedMap2 geometry resulted in a higher rate of sea-level rise than simulations using a rougher geometry, created using mass conservation. Modelled grounding-line retreat of all the three ice streams was sensitive to viscosity and basal traction, while the melt rate was more important in Pine Island and Smith glaciers, which flow through more confined ice shelves than Thwaites, which has a relatively unconfined shelf.

Reducing uncertainties in projections of Antarctic ice mass loss

Abstract. Climate model projections are often aggregated into multi-model averages of all models participating in an intercomparison project, such as the Coupled Model Intercomparison Project (CMIP). The "multi-model" approach provides a sensitivity test to the models' structural choices and implicitly assumes that multiple models provide additional and more reliable information than a single model, with higher confidence being placed on results that are common to an ensemble. A first initiative of the ice sheet modeling community, SeaRISE, provided such multi-model average projections of polar ice sheets' contribution to sea-level rise. The SeaRISE Antarctic numerical experiments aggregated results from all models devoid of a priori selection, based on the capacity of such models to represent key ice-dynamical processes. Here, using the experimental setup proposed in SeaRISE, we demonstrate that correctly representing grounding line dynamics is essential to infer future Antarctic mass change. We further illustrate the significant impact on the ensemble mean and deviation of adding one model with a known bias in its ability of modeling grounding line dynamics. We show that this biased model can hardly be identified from the ensemble only based on its estimation of volume change, as ad hoc and untrustworthy parametrizations can force any modeled grounding line to retreat. However, tools are available to test parts of the response of marine ice sheet models to perturbations of climatic and/or oceanic origin (MISMIP, MISMIP3d). Based on recent projections of Pine Island Glacier mass loss, we further show that excluding ice sheet models that do not pass the MISMIP benchmarks decreases the mean contribution and standard deviation of the multi-model ensemble projection by an order of magnitude for that particular drainage basin.

An improved model for tidally modulated grounding-line migration

AbstractUnderstanding grounding-line dynamics is necessary for predictions of long-term ice-sheet stability. However, despite growing observations of the tidal influence on grounding-line migration, this short-timescale migration is poorly understood, with most modeling attempts assuming beam theory to calculate displacements. Here we present an improved model of tidal grounding-line migration that treats migration as an elastic fracture problem, forced by the additional ocean water pressure from the tide. This new model predicts that the grounding line cannot be assumed to be in hydrostatic equilibrium and, furthermore, that migration is inherently asymmetric and nonlinear, with migration distances that are not proportional to the tidal load. Specifically, for constant surface slope, the grounding line migrates upstream approximately ten times further as the tide rises from mean sea level to high tide than it migrates downstream as the tide falls from mean sea level to low tide, and migration distances are substantially larger than simple flotation arguments suggest. Numerical tests also show that the dependence of migration distance on elastic moduli and ice-sheet thickness are inconsistent with predictions of beam theory for a range of realistic values. Finally, applying the new model to observations in Antarctica results in new estimates of bed slopes, though these estimates remain uncertain due to imperfect knowledge of the relevant rheological parameters.