Comparison of ice dynamics using full-Stokes and Blatter–Pattyn approximation: application to the Northeast Greenland Ice Stream

Full-Stokes (FS) ice sheet models provide the most sophisticated formulation of ice sheet flow. However, their applicability is often limited due to the high computational demand and numerical challenges. To balance computational demand and accuracy, the so-called Blatter–Pattyn (BP) stress regime is frequently used. Here, we explore the dynamic consequences of using simplified approaches by solving FS and the BP stress regime applied to the Northeast Greenland Ice Stream. To ensure a consistent comparison, we use one single ice sheet model to run the simulations under identical numerical conditions. A sensitivity study to the horizontal grid resolution (from 12.8 to a resolution of 0.1 km) reveals that velocity differences between the FS and BP solution emerge below ∼ 1 km horizontal resolution and continuously increase with resolution. Over the majority of the modelling domain both models reveal similar surface velocity patterns. At the grounding line of the 79∘ North Glacier the simulations show considerable differences whereby the BP model overestimates ice discharge of up to 50 % compared to FS. A sensitivity study to the friction type reveals that differences are stronger for a power-law friction than a linear friction law. Model differences are attributed to topographic variability and the basal drag, in which neglected stress terms in BP become important

Discussion of Different Model Approaches for the Flow Behavior of Ice

Ice of Antarctic ice shelves is assumed to behave on long-term as an incompressible viscous fluid, which is dominated on short time scales by the elastic response. Hence, a viscoelastic material model is required. The thermodynamic pressure is treated differently in elastic and viscous models. For small deformations, the elastic isometric stress for ν → 0.5 gives similar results to those solving for pressure in an incompressible laminar flow model. A viscous model, in which the thermodynamic pressure is approximated by an elastic isometric stress, can be easily extended to viscoelasticity

Extended enthalpy formulations in the Ice-sheet and Sea-level System Model (ISSM) version 4.17: discontinuous conductivity and anisotropic streamline upwind Petrov--Galerkin (SUPG) method

The thermal state of an ice sheet is an important control on its past and future evolution. Some parts of the ice sheet may be polythermal, leading to discontinuous properties at the cold–temperate transition surface (CTS). These discontinuities require a careful treatment in ice sheet models (ISMs). Additionally, the highly anisotropic geometry of the 3D elements in ice sheet modelling poses a problem for stabilization approaches in advection-dominated problems. Here, we present extended enthalpy formulations within the finite-element Ice-Sheet and Sea-Level System model (ISSM) that show a better performance than earlier implementations. In a first polythermal-slab experiment, we found that the treatment of the discontinuous conductivities at the CTS with a geometric mean produces more accurate results compared to the arithmetic or harmonic mean. This improvement is particularly efficient when applied to coarse vertical resolutions. In a second ice dome experiment, we find that the numerical solution is sensitive to the choice of stabilization parameters in the well-established streamline upwind Petrov–Galerkin (SUPG) method. As standard literature values for the SUPG stabilization parameter do not account for the highly anisotropic geometry of the 3D elements in ice sheet modelling, we propose a novel anisotropic SUPG (ASUPG) formulation. This formulation circumvents the problem of high aspect ratio by treating the horizontal and vertical directions separately in the stabilization coefficients. The ASUPG method provides accurate results for the thermodynamic equation on geometries with very small aspect ratios like ice sheets

A confined–unconfined aquifer model for subglacial hydrology and its application to the Northeast Greenland Ice Stream

Subglacial hydrology plays an important role in ice sheet dynamics as it determines the sliding velocity. It also drives freshwater into the ocean, leading to undercutting of calving fronts by plumes. Modeling subglacial water has been a challenge for decades. Only recently have new approaches been developed such as representing subglacial channels and thin water sheets by separate layers of variable hydraulic conductivity. We extend this concept by modeling a confined–unconfined aquifer system (CUAS) in a single layer of an equivalent porous medium (EPM). The advantage of this formulation is that it prevents unphysical values of pressure at reasonable computational cost. We performed sensitivity tests to investigate the effect of different model parameters. The strongest influence of model parameters was detected in terms of governing the opening and closure of the system. Furthermore, we applied the model to the Northeast Greenland Ice Stream, where an efficient system independent of seasonal input was identified about 500km downstream from the ice divide. Using the effective pressure from the hydrology model, the Ice Sheet System Model (ISSM) showed considerable improvements in modeled velocities in the coastal region

Dynamics of the ice cap on King George Island, Antarctica: field measurements and numerical simulations

ABSTRACT. King George Island is located at the northern tip of the Antarctic Peninsula, which is influenced by maritime climate conditions. The observed mean annual air temperature at sea level is -2.

Calving Induced Speedup of Petermann Glacier

This study assesses the response on ice dynamics of Petermann Glacier, a major outlet glacier in northern Greenland, to the 2012 and a possible future calving event. So far Petermann Glacier has been believed to be dynamically stable as another large calving event in 2010 had no significant impact on flow velocity or grounding line retreat. By analyzing a time series of remotely sensed surface velocities, we find an average acceleration of 10% between winter 2011/2012 and winter 2016/2017. This increase in surface velocity is not linear but can be separated into two parts, starting in 2012 and 2016 respectively. By conducting modeling experiments, we show that the first speedup can be directly connected to the 2012 calving event, while the second speedup is not captured. However, on recent remote sensing imagery newly developing fractures are clearly visible ∼12 km upstream from the terminus, propagating from the eastern fjord wall to the center of the ice tongue, indicating a possible future calving event. By including these fracture zones as a new terminus position in the modeling domain, we are able to reproduce the second speedup, suggesting that surface velocities remain on the 2016/2017 level after the anticipated calving event. This indicates that, from a dynamical point of view, the terminus region has already detached from the main ice tongue

Fractures in glaciers - Crack tips and their stress fields by observation and modeling

High-resolution optical camera systems are opening new opportunities to studyfractures in ice. Here, we present data obtained from the Modular Aerial CameraSystem camera system operated onboard of Alfred Wegener Institute HelmholtzCentre for Polar and Marine Research (AWI) polar aircraft in northeast Green-land in 2022. In addition, we are using optical and radar satellite imagery. Thestudy area is the 79N Glacier (Nioghalvfjerdsbræ, 79NG), an outlet glacier of theNortheast Greenland Ice Stream. We found that crack tips are exhibiting addi-tional isolated cracks ahead of the main crack. Subsequent crack propagationis starting from those isolated cracks, leading to an advance of the crack, withbridges between crack faces. The bridges provide information of the episodiccrack propagation. Fractures have typically a length scale of kilometers andthe distance of crack faces is in the order of meters to tenths of meters. Frac-ture modes will be inferred from stress fields computed by an inverse modelingapproach using the Ice Sheet and Sea Level System Model. To this end, a surfacevelocity field derived from satellite remote sensing is used for the optimal controlmethod that constrains model parameters, for example, basal friction coefficientor rheology

Simulation of the future sea level contribution of Greenland with a new glacial system model

We introduce the coupled model of the Green- land glacial system IGLOO 1.0, including the polythermal ice sheet model SICOPOLIS (version 3.3) with hybrid dy- namics, the model of basal hydrology HYDRO and a param- eterization of submarine melt for marine-terminated outlet glaciers. The aim of this glacial system model is to gain a better understanding of the processes important for the future contribution of the Greenland ice sheet to sea level rise under future climate change scenarios. The ice sheet is initialized via a relaxation towards observed surface elevation, impos- ing the palaeo-surface temperature over the last glacial cycle. As a present-day reference, we use the 1961–1990 standard climatology derived from simulations of the regional atmo- sphere model MAR with ERA reanalysis boundary condi- tions. For the palaeo-part of the spin-up, we add the temper- ature anomaly derived from the GRIP ice core to the years 1961–1990 average surface temperature field. For our pro- jections, we apply surface temperature and surface mass bal- ance anomalies derived from RCP 4.5 and RCP 8.5 scenar- ios created by MAR with boundary conditions from simula- tions with three CMIP5 models. The hybrid ice sheet model is fully coupled with the model of basal hydrology. With this model and the MAR scenarios, we perform simulations to estimate the contribution of the Greenland ice sheet to future sea level rise until the end of the 21st and 23rd centuries. Fur- ther on, the impact of elevation–surface mass balance feed- back, introduced via the MAR data, on future sea level rise is inspected. In our projections, we found the Greenland ice sheet to contribute between 1.9 and 13.0 cm to global sea level rise until the year 2100 and between 3.5 and 76.4 cm until the year 2300, including our simulated additional sea level rise due to elevation–surface mass balance feedback. Translated into additional sea level rise, the strength of this feedback in the year 2100 varies from 0.4 to 1.7 cm, and in the year 2300 it ranges from 1.7 to 21.8 cm. Additionally, taking the Helheim and Store glaciers as examples, we inves- tigate the role of ocean warming and surface runoff change for the melting of outlet glaciers. It shows that ocean temper- ature and subglacial discharge are about equally important for the melting of the examined outlet glaciers

Results of the third Marine Ice Sheet Model Intercomparison Project (MISMIP+)

We present the result of the third Marine Ice Sheet Model Intercomparison Project, MISMIP+. MISMIP+ is intended to be a benchmark for ice-flow models which include fast sliding marine ice streams and floating ice shelves and in particular a treatment of viscous stress that is sufficient to model buttressing, where upstream ice flow is restrained by a downstream ice shelf. A set of idealized experiments first tests that models are able to maintain a steady state with the grounding line located on a retrograde slope due to buttressing and then explore scenarios where a reduction in that buttressing causes ice stream acceleration, thinning, and grounding line retreat. The majority of participating models passed the first test and then produced similar responses to the loss of buttressing. We find that the most important distinction between models in this particular type of simulation is in the treatment of sliding at the bed, with other distinctions - notably the difference between the simpler and more complete treatments of englacial stress but also the differences between numerical methods - taking a secondary role. © 2020 Wolters Kluwer Medknow Publications. All rights reserved

Results of the third Marine Ice Sheet Model Intercomparison Project (MISMIP+)

We present the result of the third Marine Ice Sheet Model Intercomparison Project, MISMIP+. MISMIP+ is intended to be a benchmark for ice-flow models which include fast sliding marine ice streams and floating ice shelves and in particular a treatment of viscous stress that is sufficient to model buttressing, where upstream ice flow is restrained by a downstream ice shelf. A set of idealized experiments first tests that models are able to maintain a steady state with the grounding line located on a retrograde slope due to buttressing and then explore scenarios where a reduction in that buttressing causes ice stream acceleration, thinning, and grounding line retreat. The majority of participating models passed the first test and then produced similar responses to the loss of buttressing. We find that the most important distinction between models in this particular type of simulation is in the treatment of sliding at the bed, with other distinctions – notably the difference between the simpler and more complete treatments of englacial stress but also the differences between numerical methods – taking a secondary role