CR3.2

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. This leads to a demand for computationally efficient models, where such a high resolution can be feasibly applied in simulations of 10⁵ – 10⁷ yr in duration. To solve this, we developed UFEMISM, a new ice-sheet model that solves the hybrid SIA/SSA approximation of the stress balance on a fully adaptive, unstructured triangular mesh. This strongly reduces the number of grid points where the equations need to be solved, making the model much faster than the square-grid models that are typically used in paleo-ice-sheet research. We will discuss some of the difficulties in developing such a model, and the solutions we came up with. We will show that the model successfully performs several common schematic benchmark experiments for ice-sheet models, and we will take a look at some preliminary results of realistic experiments.

How to cite: Berends, T., van de Wal, R., and Goelzer, H.: The Utrecht Finite Volume Ice-Sheet Model: UFEMISM, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14778, https://doi.org/10.5194/egusphere-egu21-14778, 2021.

Ice sheet models differ in their numerical treatment of dynamical processes. Simulations of marine-based ice are sensitive to the choice of Stokes flow approximation and basal friction law, and to the treatment of stresses and melt rates near the grounding line. We present the effects of these numerical choices on marine ice-sheet dynamics in the Community Ice Sheet Model (CISM). In the experimental framework of the Marine Ice Sheet Model Intercomparison Project (MISMIP+), we compare different treatments of sub-shelf melting near the grounding line. In contrast to recent studies arguing that melting should not be applied in partly grounded cells, it is usually beneficial in CISM simulations to apply some melting in these cells. This suggests that the optimal treatment of melting near the grounding line can depend on ice-sheet geometry, forcing, or model numerics. In the MISMIP+ framework, the ice flow is also sensitive to the choice of basal friction law. To study this sensitivity, we evaluate friction laws that vary the connectivity between the basal hydrological system and the ocean near the grounding line. CISM yields accurate results in steady-state and perturbation experiments at a resolution of ∼2 km (arguably 4 km) when the connectivity is low or moderate, and ∼1 km (arguably 2 km) when the connectivity is strong.

How to cite: Leguy, G., Lipscomb, W., and Asay-Davis, X.: Marine ice-sheet experiments with the Community Ice Sheet Model using the MISMIP+ experimental framework., EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6608, https://doi.org/10.5194/egusphere-egu21-6608, 2021.

Computation of temperature and age fields by numerical ice-sheet models is an important issue for ice-core related studies.  Generally the evolution of temperature and/or age in an ice-sheet model is formulated using an advection equation.  There are many variation of the formulation, which differ in numerical aspects such as stability, accuracy, numerical diffusivity, conservation and/or computational costs.  Saito et al (2020, GMD) implement Rational Constrained Interpolation Profile (RCIP) scheme on vertical 1-d age computation of ice sheet, and demonstrate its efficiency, in particular, to preserve surface mass balance properties recorded at the deposit in terms of annual layer thickness.  Successively, we have been extending the development using RCIP or similar higher-order advection schemes on 3-d age or temperature computation.  In this study, we demonstrate 1-d temperature computation by various numerical schemes including classical upwind schemes and compare the accuracy of those schemes.

How to cite: Saito, F., Abe-Ouchi, A., and Obase, T.: Implementation of higher-order advection schemes in a numerical ice-sheet model for ice-core studies, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-6854, https://doi.org/10.5194/egusphere-egu21-6854, 2021.

The Stokes solution to ice dynamics is computationally expensive, and in many cases unnecessary. Many approximations have been developed that reduce the complexity of the problem and thus reduce computational cost. Most approximations can generally be tuned to give reasonable solutions to ice-dynamics problems, depending on the domain and scale being simulated. However, the inherent numerical stability of time-stepping with different solvers has not been studied in detail. Here we investigate how different approximations lead to limits on the maximum timestep in mass conservation calculations for both idealized and realistic geometries. The ice-sheet models Yelmo and CISM are used to compare the following approximations: the shallow-ice approximation (SIA), the shallow-shelf approximation (SSA), the SIA+SSA approximation (Hybrid) and two variants of the L1L2 solver, namely one that reduces to SIA in the case of no-sliding (dubbed L1L2-SIA here) and the so-called depth-integrated viscosity approximation (DIVA). We find that these approaches vary significantly with respect to numerical stability. The extreme dependence on the local surface gradient of the SIA-based approximations (SIA, Hybrid, L1L2-SIA) leads to an amplified local velocity response and greater potential for instability, especially as grid resolution increases. In contrast, the SSA and DIVA approximations allow for longer time steps, because numerical oscillations in ice thickness are damped with increasing resolution. Given its high fidelity to the Stokes solution and its favorable stability properties, we demonstrate the strong case for using the DIVA approximation in many contexts.

How to cite: Robinson, A., Lipscomb, W., Goldberg, D., and Alvarez-Solas, J.: On the speed and numerical stability of ice-dynamics approximations, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2549, https://doi.org/10.5194/egusphere-egu21-2549, 2021.

Modelling ice sheet flow is at best modelled using the full-Stokes (FS) equations. However, it rarely sees application even in recent years due to its high computational demand and problems in numerical convergence due to the thin aspect ratio of ice sheets. For this reason, the modelling community has relied on simplified mathematical models, such as the three-dimensional Higher-Order (HO) approximation which neglects horizontal gradients of vertical velocities and bridging effects. Here, we conduct an analysis of the difference in stresses and velocity fields solving the FS system of equation and using two different types of HO approximations equivalent to LMLa (known as Blatter-Pattyn type) and LTSML according to Hindmarsh (2004). Our intention was to avoid any bias from a difference in discretization or implementation, therefore we implemented it in a single ice sheet model to avoid effects arising from discretization and implementation. We selected a subset of the North East Greenland Ice Stream (NEGIS) as investigation area. As differences between FS and HO emerge in regions with steep bedrock gradients or high aspect ratios, we step-wise increase spatial resolution from 12.8 km down to 0.1 km. Our analysis reveals that surface velocity differences between the FS and HO solution emerge below 1km horizontal resolution and increase with resolution. Compared to the absolute ice flow velocity, the relative error between FS and HO remains small. We present an in-depth analysis, that reveals that different factors are affected by the approximation, such as basal drag and rheology

References:
Hindmarsh, R. C. A.: A numerical comparison of approximations to the Stokes equations used in ice sheet and glacier modeling, Journal of Geophysical Research: Earth Surface, 109, https://doi.org/10.1029/2003JF000065, 2004

How to cite: Rückamp, M., Kleiner, T., and Humbert, A.: Consistent comparison of full-Stokes and higher-order approximation in the central North East Greenland Ice Stream, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-2568, https://doi.org/10.5194/egusphere-egu21-2568, 2021.

Subglacial cavitation is a phenomenon that occurs at the base of an ice sheet or a glacier where the ice detaches from the bedrock at high water pressures. The process is recognised as an essential mechanism in glacial sliding. A mathematical description of subglacial cavitation involves a free boundary equation and a Stokes equation with contact boundary conditions. These contact boundary conditions model the process of detachment from the bed at each instant in time. 

In this talk we show that the problem can be written as a variational inequality and present a novel approach to solving the equations with finite element methods that exploit the structure of the variational inequality. In particular, we present a formulation involving Lagrange multipliers, which allows us to solve the discrete contact conditions exactly. Thanks to this latter property, the Stokes equations can be solved together with the free boundary equations in a robust and stable manner. A similar method should also prove useful for improving grounding-line calculations.

With this numerical method, we compute a friction law (the relation between sliding velocity and shear stress) for ice flowing over a periodic bed.  We recover existing results for the case when the cavities are in a steady state for a given effective pressure. We extend these results to consider time-varying cavitation driven by changes in subglacial water pressure.

How to cite: Gonzalez de Diego, G., Farrell, P., and Hewitt, I.: A numerical method for subglacial cavitation posed as a variational inequality, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-5796, https://doi.org/10.5194/egusphere-egu21-5796, 2021.

How to cite: Schoof, C. and Mantelli, E.: Ice stream formation, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14043, https://doi.org/10.5194/egusphere-egu21-14043, 2021.

Pine Island Glacier in West Antarctica is among the fastest changing glaciers worldwide. Much of its fast-flowing central trunk is thinning and accelerating, a process thought to have been triggered by ocean-induced changes in ice-shelf buttressing. The measured acceleration in response to perturbations in ice thickness is a non-trivial manifestation of several poorly-understood physical processes, including the transmission of stresses between the ice and underlying bed. To enable robust projections of future ice flow, it is imperative that numerical models include an accurate representation of these processes. Here we combine the latest data with analytical and numerical solutions of SSA ice flow to show that the recent increase in flow speed of Pine Island Glacier is only compatible with observed patterns of thinning if a spatially distributed, predominantly plastic bed underlies large parts of the central glacier and its upstream tributaries.

How to cite: De Rydt, J., Reese, R., Paolo, F., and Gudmundsson, G. H.: On the relation between ice thickness changes and glacier speed-up, with application to Pine Island Glacier in West Antarctica, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7758, https://doi.org/10.5194/egusphere-egu21-7758, 2021.

The "marine ice-sheet instability hypothesis", which states that unconfined marine ice sheets are unconditionally unstable on retrograde slopes, was developed under assumptions of negligible bed slopes. Realistic ice sheets, however, flow over beds which topographies have a wide range of bed slopes (for example, Thwaites Glacier in the Amundsen Sea sector, West Antarctica). Reexamining the original model of marine ice sheets proposed by Schoof (2007), and relaxing an assumption of negligible bed slopes, we find that a steady-state ice flux at the grounding line is an implicit function of the grounding-line ice thickness, bed slope and accumulation rate. Depending on the sliding conditions, the magnitudes of the ice flux at the grounding line differ by one-to-three orders of magnitudes from that computed with a power-law expression derived by Schoof (2007) under assumptions of the negligible bed slopes. Non-negligible bed slopes also result in conditions of stability of the grounding line that are significantly more complex than those associated with the "marine ice sheet instability hypothesis". Bed slopes are no longer the sole determinant of whether the grounding line is stable or unstable. We find that the grounding line can be stable on beds with retrograde slopes and unstable on beds with prograde slopes. 

How to cite: Sergienko, O. and Wingham, D.: The effects of bed topography and strength on stability of marine ice sheets, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-1413, https://doi.org/10.5194/egusphere-egu21-1413, 2021.

The dynamics of soft-bedded glacial sliding over saturated till are poorly constrained and difficult to realistically capture in large scale models. While experiments characterise till as a plastic material with a pressure dependent yield stress, large scale models rely on a viscous or power-law description of the subglacial environment to efficiently constrain the basal sliding rate of the ice. Further, the subglacial water pressure may fluctuate on timescales from annual to daily, leading to transient adjustment of the till.

We construct a continuum two-phase model of coupled fluid and solid flows, using Darcy flow for the fluid phase and a recently described saturated granular model for the solid. After verifying our model against the steady-state experiments, we force the model with a fluctuating effective pressure at the ice-till interface and infer the resulting relationships between basal traction, porosity, rate of deformation, and till flux. Shear dilation introduces internal pressure variations, leading to hysteretic behaviour in low-permeability materials, resulting in a time-dependent effective sliding law.

How to cite: Warburton, K., Hewitt, D., and Neufeld, J.: Time-dependent soft-bedded sliding laws, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8766, https://doi.org/10.5194/egusphere-egu21-8766, 2021.

Ice’s predominantly viscous rheology exhibits a significant temperature and strain-rate dependence, commonly captured as a single deformation mechanism by Glen's flow law. However, Glen’s power-law relationship may fail to capture accurate stress levels at low and elevated strain-rates ultimately leading to velocity over- and under-estimates, respectively. Alternative more complex flow laws such as Goldsby rheology combine various creep mechanisms better accounting for micro-scale observations resulting in enhanced localisation of ice flow at glacier scales and internal sliding.

The challenge in implementing Goldsby rheology arises with the need of computing an accurate partitioning of the total strain-rate among the active creep mechanisms. Some of these mechanisms exhibit grain-size evolution sensitivity potentially impacting the larger scale ice dynamics.

We here present a consistent way to compute the effective viscosity of the ice using Goldsby rheology for temperature and strain-rate ranges relevant to ice flow. We implement a local iteration procedure to ensure accurate implicit partitioning of the total strain-rate among the active creep mechanisms including grain-size evolution. We discuss the composite deformation maps and compare the results against Glen's flow law. We incorporate our implicit rheology solver into an implicit 2D thermo-mechanical ice flow solver to investigate localisation of ice flow over variable topography and in shear margin configurations. We quantify discrepancies  in surface velocity patterns when using Goldsby rheology instead of Glen's flow law.

How to cite: Räss, L. and Duretz, T.: Ice flow localisation enhanced by composite ice rheology, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-4964, https://doi.org/10.5194/egusphere-egu21-4964, 2021.

Physical processes within ice sheet models are sometimes described by simplified schemes known as parameterisations. The values of the parameters within these schemes can be poorly constrained by theory or observation. Uncertainty in the parameter values translates into uncertainty in the outputs of the models. Proper quantification of the uncertainty in model predictions therefore requires a systematic approach for sampling parameter space. We demonstrate a simple and efficient approach to identify regions of multi-dimensional parameter space that are consistent with observations. Using the Parallel Ice Sheet Model to simulate the present-day state of the Antarctic Ice Sheet, we find that co-dependencies between parameters preclude the identification of a single optimal set of parameter values. Approaches such as large ensemble modelling are therefore required in order to generate model predictions, such as projections of future global sea level rise, that incorporate proper quantification of the uncertainty arising from the parameterisation of physical processes.

How to cite: Phipps, S., Roberts, J., and King, M.: Exploring parameter uncertainty in a model of the Antarctic Ice Sheet, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15304, https://doi.org/10.5194/egusphere-egu21-15304, 2021.

One current concern in Climate Sciences is the estimation of the annual amount of ice lost by glaciers and the corresponding rate of sea level rise. Greenland ice sheet contribution is significant with about 30% to the global ice mass losses. Ice loss in Greenland is distributed approximately equally between loss in land by surface melting and loss at the front of marine-terminating glaciers that is modulated by dynamic processes. Dynamic mass loss includes both submarine melting and iceberg calving. The processes that control ablation at tidewater glacier termini, glacier retreat and calving are complex, setting the limits to the estimation of dynamic mass loss and the relation to glacier dynamics. It involves interactions between bedrock – glacier – icebergs – ice-mélange – water – atmosphere. Moreover, the capsize of cubic kilometer scale icebergs close to a glacier front can destabilize the glacier, generate tsunami waves, and induce mixing of the water column which can impact both the local fauna and flora.

We aim to improve the physical understanding of the response of glacier front to the force of a capsizing iceberg against the terminus. For this, we use a mechanical model of iceberg capsize against the mobile glacier interacting with the solid earth through a frictional contact and we constrain it with measured surface displacements and seismic waves that are recorded at teleseismic distances. Our strategy is to construct a solid dynamics model, using a finite element solver, involving a deformable glacier, basal contact and friction, and simplified iceberg-water interactions. We fine-tune the parameters of these hydrodynamic effects on an iceberg capsizing in free ocean with the help of reference direct numerical simulations of fluid-structure interactions involving full resolution of Navier-Stokes equations. We simulate the response of a visco-elastic near-grounded glacier to the capsize of an iceberg close to the terminus. We assess the influence of the glacier geometry, the type of capsize, the ice properties and the basal friction on the glacier dynamic and the observed surface displacements. The surface displacements simulated with our model are then compared with measured displacements for well documented events. 

How to cite: Bonnet, P., Yastrebov, V., Mangeney, A., Castelnau, O., Leroyer, A., Queutey, P., Rueckamp, M., Stutzmann, E., Montagner, J.-P., and Sergeant, A.: Modelling the source of glacial earthquakes, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8915, https://doi.org/10.5194/egusphere-egu21-8915, 2021.

The formation of surface meltwater has been linked with the disintegration of many ice shelves in the Antarctic Peninsula over the last several decades. Despite the importance of surface meltwater production and transport to ice shelf stability, knowledge of these processes is still lacking. Understanding the surface hydrology of ice shelves is an essential first step to reliably project future sea level rise from ice sheet melt.

In order to better understand the processes driving meltwater distribution on ice shelves, we present results from case studies using a new 3-D model of surface hydrology for Antarctic ice shelves. It is the first comprehensive model of surface hydrology to be developed for Antarctic ice shelves, enabling us to incorporate key processes such as the lateral transport of surface meltwater. Recent observations suggest that surface hydrology processes on ice shelves are more complex than previously thought, and that processes such as lateral routing of meltwater across ice shelves, ice shelf flexure and surface debris all play a role in the location and influence of meltwater. Our model allows us to account for these and is calibrated and validated through both remote sensing and field observations. Here we present results from in depth studies from selected ice shelves with significant surface melt features.

This community-driven, open-access model has been developed with input from observations, and allows us to provide new insights into surface meltwater distribution on Antarctica’s ice shelves. This enables us to answer key questions about their past and future evolution under changing atmospheric conditions and vulnerability to meltwater driven hydrofracture and collapse.

How to cite: Buzzard, S. and Robel, A.: A 3-D Model of Antarctic Ice Shelf Surface Hydrology, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15890, https://doi.org/10.5194/egusphere-egu21-15890, 2021.