Description: 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.

Description: Accurately modelling the contribution of Greenland and Antarctica to sea level rise requires solving partial differential equations at a high spatial resolution. In this paper, we discuss the scaling of the Ice-sheet and Sea-level System Model (ISSM) applied to the Greenland Ice Sheet with horizontal grid resolutions varying between 10 and 0.25 km. The model setup used as benchmark problem comprises a variety of modules with different levels of complexity and computational demands. The core builds the so-called stress balance module, which uses the higher-order approximation (or Blatter–Pattyn) of the Stokes equations, including free surface and ice-front evolution as well as thermodynamics in form of an enthalpy balance, and a mesh of linear prismatic finite elements, to compute the ice flow. We develop a detailed user-oriented, yet low-overhead, performance instrumentation tailored to the requirements of Earth system models and run scaling tests up to 6144 Message Passing Interface (MPI) processes. The results show that the computation of the Greenland model scales overall well up to 3072 MPI processes but is eventually slowed down by matrix assembly, the output handling and lower-dimensional problems that employ lower numbers of unknowns per MPI process. We also discuss improvements of the scaling and identify further improvements needed for climate research. The instrumented version of ISSM thus not only identifies potential performance bottlenecks that were not present at lower core counts but also provides the capability to continually monitor the performance of ISSM code basis. This is of long-term significance as the overall performance of ISSM model depends on the subtle interplay between algorithms, their implementation, underlying libraries, compilers, run-time systems and hardware characteristics, all of which are in a constant state of flux. We believe that future large-scale high-performance computing (HPC) systems will continue to employ the MPI-based programming paradigm on the road to exascale. Our scaling study pertains to a particular modelling setup available within ISSM and does not address accelerator techniques such as the use of vector units or GPUs. However, with 6144 MPI processes, we identified issues that need to be addressed in order to improve the ability of the ISSM code base to take advantage of upcoming systems that will require scaling to even higher numbers of MPI processes.

Description: The land ice contribution to global mean sea level rise has not yet been predicted1 using ice sheet and glacier models for the latest set of socio-economic scenarios, nor using coordinated exploration of uncertainties arising from the various computer models involved. Two recent international projects generated a large suite of projections using multiple models2,3,4,5,6,7,8, but primarily used previous-generation scenarios9 and climate models10, and could not fully explore known uncertainties. Here we estimate probability distributions for these projections under the new scenarios11,12 using statistical emulation of the ice sheet and glacier models. We find that limiting global warming to 1.5 degrees Celsius would halve the land ice contribution to twenty-first-century sea level rise, relative to current emissions pledges. The median decreases from 25 to 13 centimetres sea level equivalent (SLE) by 2100, with glaciers responsible for half the sea level contribution. The projected Antarctic contribution does not show a clear response to the emissions scenario, owing to uncertainties in the competing processes of increasing ice loss and snowfall accumulation in a warming climate. However, under risk-averse (pessimistic) assumptions, Antarctic ice loss could be five times higher, increasing the median land ice contribution to 42 centimetres SLE under current policies and pledges, with the 95th percentile projection exceeding half a metre even under 1.5 degrees Celsius warming. This would severely limit the possibility of mitigating future coastal flooding. Given this large range (between 13 centimetres SLE using the main projections under 1.5 degrees Celsius warming and 42 centimetres SLE using risk-averse projections under current pledges), adaptation planning for twenty-first-century sea level rise must account for a factor-of-three uncertainty in the land ice contribution until climate policies and the Antarctic response are further constrained.

Description: Projections of the sea level contribution from the Greenland and Antarctic ice sheets (GrIS and AIS) rely on atmospheric and oceanic drivers obtained from climate models. The Earth System Models participating in the Coupled Model Intercomparison Project phase 6 (CMIP6) generally project greater future warming compared with the previous Coupled Model Intercomparison Project phase 5 (CMIP5) effort. Here we use four CMIP6 models and a selection of CMIP5 models to force multiple ice sheet models as part of the Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6). We find that the projected sea level contribution at 2100 from the ice sheet model ensemble under the CMIP6 scenarios falls within the CMIP5 range for the Antarctic ice sheet but is significantly increased for Greenland. Warmer atmosphere in CMIP6 models results in higher Greenland mass loss due to surface melt. For Antarctica, CMIP6 forcing is similar to CMIP5 and mass gain from increased snowfall counteracts increased loss due to ocean warming.

Description: 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.

Description: Viscoelastic COMSOL COMice-ve.mph for manuscript entitled "Elastic deformation plays a non-negligible role in Greenland’s outlet glacier flow" from Christmann et al., Communications Earth & Environment, https://doi.org/10.1038/s43247-021-00296-3, 2021. You can find here the mph file and all external data used in the finite element Comsol mph file. These files are also accessible via GitLab: https://gitlab.awi.de/jchristm/viscoelastic-79ng-greenland.git.