In climate modelling, ice-sheet models use numerical methods to simulate the evolution, dynamics and thermodynamics of ice sheets, such as the Antarctic ice sheet, the Greenland ice sheet or the large ice sheets on the Northern Hemisphere during the Last Glacial Period. They are used for a variety of purposes, from studies of the glaciation of Earth over glacial–interglacial cycles in the past to projections of ice-sheet decay under future global warming conditions.
History Beginning in the mid-18th Century, investigation into ice sheet behavior began. Since the Journal of Glaciology's founding, physicists have been publishing glacial mechanics.
The first 3-D model was applied to the Barnes Ice Cap. In 1988, the first thermodynamically coupled model incorporating ice-shelves, sheet/shelf transition, membrane stress gradients, isostatic bed adjustment and basal sliding using more advanced numerical techniques was developed and applied to the Antarctic ice sheet. This model had a resolution of 40 km and 10 vertical layers. When the first IPCC assessment report came out in 1990, ice sheets were not an active part of the climate system model, their evolution was based on a correlation between global temperature and surface mass balance. When the second IPCC assessment report came out in 1996, the beginning of both 2D and 3D modelling was shown with ice sheets. The 1990s heralded several more computational models, bringing with it the European Ice Sheet Modelling Initiative (EISMINT). The EISMINT produced several workshops throughout the 1990s of an international collaboration, comparing most models of Greenland, Antarctic, ice-shelf, thermomechanical and grounding-line. The 2000s included integrating first-order approximation of full Stokes Dynamics into an ice-sheet model. The fourth IPCC assessment report showed ice-sheet models with projections of rapid dynamical responses in the ice, which led to evidence of significant ice loss. In 2016, part of the Coupled Model Intercomparison Project Phase 6 (CMIP Phase 6) was the Ice Sheet Model Intercomparison Project, which defined a protocol for all variables related to ice sheet modelling. The project allowed for both improvement in numerical and physical approaches to ice sheets.
Modelling
Ice-Flow
Shallow Ice Approximation Shallow Ice Approximation (SIA) is a simple method to model ice flow without having to solve full-Stokes equations. The approximation is best applied to ice sheet with a small depth-to-width ratio, without many sliding dynamics and a simple bed topography. SIA does not include many forces on an ice sheet, and can be considered a 'zero-order' model. The model assumes that ice sheets are mostly split up by basal sheer stress, and it is not necessary to consider the other forces. It also assumes that the basal shear stress and the gravitational driving stress of the grounded ice balance one another out. The method is computationally inexpensive.
Shallow Shelf Approximation Shallow Shelf Approximation is another method to model ice flow, in particular a membrane-type flow of floating ice, or of sliding grounded ice over a base. Also known as a membrane model, they are similar to free-film models in fluid dynamics. As opposed to Shallow Ice Approximation, Shallow Shelf Approximation models ice flow when longitudinal forces are strong; sliding and vertical forces. SSA can also be considered a 'zero-order' model.
Full Stokes Equations It is considered advantageous to model ice using Navier-Stokes equations as ice is a viscous fluid and these capture all forces exerted on the ice. As these equations are computationally expensive, it is important to include many approximations to reduce running time. Because of their computational expense, they are not easily used at a large scale and can be used in specific sections or scenarios, such as at grounding lines.
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