full-Stokes Models Research Articles

ISMIP-HOM benchmark experiments using Underworld

Abstract. Numerical models have become an indispensable tool for understanding and predicting the flow of ice sheets and glaciers. Here we present the full-Stokes software package Underworld to the glaciological community. The code is already well established in simulating complex geodynamic systems. Advantages for glaciology are that it provides a full-Stokes solution for elastic–viscous–plastic materials and includes mechanical anisotropy. Underworld uses a material point method to track the full history information of Lagrangian material points, of stratigraphic layers and of free surfaces. We show that Underworld successfully reproduces the results of other full-Stokes models for the benchmark experiments of the Ice Sheet Model Intercomparison Project for Higher-Order Models (ISMIP-HOM). Furthermore, we test finite-element meshes with different geometries and highlight the need to be able to adapt the finite-element grid to discontinuous interfaces between materials with strongly different properties, such as the ice–bedrock boundary.

Quantifying the effect of ocean bed properties on ice sheet geometry over 40 000 years with a full-Stokes model

Abstract. Simulations of ice sheet evolution over glacial cycles require integration of observational constraints using ensemble studies with fast ice sheet models. These include physical parameterisations with uncertainties, for example, relating to grounding-line migration. More complete ice dynamic models are slow and have thus far only be applied for < 1000 years, leaving many model parameters unconstrained. Here we apply a 3D thermomechanically coupled full-Stokes ice sheet model to the Ekström Ice Shelf embayment, East Antarctica, over a full glacial cycle (40 000 years). We test the model response to differing ocean bed properties that provide an envelope of potential ocean substrates seawards of today's grounding line. The end-member scenarios include a hard, high-friction ocean bed and a soft, low-friction ocean bed. We find that predicted ice volumes differ by > 50 % under almost equal forcing. Grounding-line positions differ by up to 49 km, show significant hysteresis, and migrate non-steadily in both scenarios with long quiescent phases disrupted by leaps of rapid migration. The simulations quantify the evolution of two different ice sheet geometries (namely thick and slow vs. thin and fast), triggered by the variable grounding-line migration over the differing ocean beds. Our study extends the timescales of 3D full-Stokes by an order of magnitude compared to previous studies with the help of parallelisation. The extended time frame for full-Stokes models is a first step towards better understanding other processes such as erosion and sediment redistribution in the ice shelf cavity impacting the entire catchment geometry.

Shallow ice approximation, second order shallow ice approximation, and full Stokes models: A discussion of their roles in palaeo-ice sheet modelling and development

Shallow ice approximation, second order shallow ice approximation, and full Stokes models: A discussion of their roles in palaeo-ice sheet modelling and development

Shallow ice approximation, second order shallow ice approximation, and full Stokes models: A discussion of their roles in palaeo-ice sheet modelling and development

Full Stokes ice sheet models provide the most accurate description of ice sheet flow, and can therefore be used to reduce existing uncertainties in predicting the contribution of ice sheets to future sea level rise on centennial time-scales. The level of accuracy at which millennial time-scale palaeo-ice sheet simulations resolve ice sheet flow lags the standards set by Full Stokes models, especially, when Shallow Ice Approximation (SIA) models are used. Most models used in paleo-ice sheet modeling were developed at a time when computer power was very limited, and rely on several assumptions. At the time there was no means of verifying the assumptions by other than mathematical arguments. However, with the computer power and refined Full Stokes models available today, it is possible to test these assumptions numerically. In this paper, we review (Ahlkrona et al., 2013a) where such tests were performed and inaccuracies in commonly used arguments were found. We also summarize (Ahlkrona et al., 2013b) where the implications of the inaccurate assumptions are analyzed for two paleo-models – the SIA and the SOSIA. We review these works without resorting to mathematical detail, in order to make them accessible to a wider audience with a general interest in palaeo-ice sheet modelling. Specifically, we discuss two implications of relevance for palaeo-ice sheet modelling. First, classical SIA models are less accurate than assumed in their original derivation. Secondly, and contrary to previous recommendations, the SOSIA model is ruled out as a practicable tool for palaeo-ice sheet simulations. We conclude with an outlook concerning the new Ice Sheet Coupled Approximation Level (ISCAL) method presented in Ahlkrona et al. (2016), that has the potential to match the accuracy standards of full Stokes model on palaeo-timescales of tens of thousands of years, and to become an alternative to hybrid models currently used in palaeo-ice sheet modelling. The method is applied to an ice sheet covering Svalbard.

Capabilities and performance of Elmer/Ice, a new-generation ice sheet model

Abstract. The Fourth IPCC Assessment Report concluded that ice sheet flow models, in their current state, were unable to provide accurate forecast for the increase of polar ice sheet discharge and the associated contribution to sea level rise. Since then, the glaciological community has undertaken a huge effort to develop and improve a new generation of ice flow models, and as a result a significant number of new ice sheet models have emerged. Among them is the parallel finite-element model Elmer/Ice, based on the open-source multi-physics code Elmer. It was one of the first full-Stokes models used to make projections for the evolution of the whole Greenland ice sheet for the coming two centuries. Originally developed to solve local ice flow problems of high mechanical and physical complexity, Elmer/Ice has today reached the maturity to solve larger-scale problems, earning the status of an ice sheet model. Here, we summarise almost 10 yr of development performed by different groups. Elmer/Ice solves the full-Stokes equations, for isotropic but also anisotropic ice rheology, resolves the grounding line dynamics as a contact problem, and contains various basal friction laws. Derived fields, like the age of the ice, the strain rate or stress, can also be computed. Elmer/Ice includes two recently proposed inverse methods to infer badly known parameters. Elmer is a highly parallelised code thanks to recent developments and the implementation of a block preconditioned solver for the Stokes system. In this paper, all these components are presented in detail, as well as the numerical performance of the Stokes solver and developments planned for the future.

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.

Imaging Stars by Performing Full-Stokes Optical Interferometric Polarimetry

Optical interferometry and polarimetry have separately provided new insights into stellar astronomy, especially in the fields of fundamental parameters and atmospheric models. We present: scientific justifications for "full-Stokes" optical interferometric polarimetry (OIP); updated instrument requirements; preliminary beam combiner designs; polarimeter design; end-to-end OIP data reduction; and realistic reimaged full-Stokes models of Be stars with a suitable number of telescopes plus noise sources. All of this work represents preliminary research to construct an OIP beam combiner.

Benchmark experiments for higher-order and full-Stokes ice sheet models (ISMIP–HOM)

Abstract. We present the results of the first ice sheet model intercomparison project for higher-order and full-Stokes ice sheet models. These models are compared and verified in a series of six experiments of which one has an analytical solution obtained from a perturbation analysis. The experiments are applied to both 2-D and 3-D geometries; five experiments are steady-state diagnostic, and one has a time-dependent prognostic solution. All participating models give results that are in close agreement. A clear distinction can be made between higher-order models and those that solve the full system of equations. The full-Stokes models show a much smaller spread, hence are in better agreement with one another and with the analytical solution.