In climate modelling, Ice-sheet models use numerical methods to simulate the evolution, dynamics and thermodynamics of ice sheets, such as the Greenland ice sheet, the Antarctic 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.[1] Since the Journal of Glaciology's founding, physicists have been publishing glacial mechanics.[1]

Barnes Ice Cap

The first 3-D model was applied to the Barnes Ice Cap.[1] 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.[1] This model had a resolution of 40 km and 10 vertical layers.[1]

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.[2] When the second IPCC assessment report came out in 1996, the beginning of both 2D and 3D modelling was shown with ice sheets.[2] The 1990s heralded several more computational models, bringing with it the European Ice Sheet Modelling Initiative (EISMINT).[1][3] The EISMINT produced several workshops throughout the 1990s of an international collaboration, comparing most models of Greenland, Antarctic, ice-shelf, thermomechanical and grounding-line.[3]

The 2000s included integrating first-order approximation of full Stokes Dynamics into an ice-sheet model.[1] 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.[2]

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.[4] The project allowed for both improvement in numerical and physical approaches to ice sheets.[5]

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.[6] The approximation is best applied to ice sheet with a small depth-to-width ratio, without many sliding dynamics and a simple bed topography.[7] SIA does not include many forces on an ice sheet, and can be considered a 'zero-order' model.[7] The model assumes that ice sheets are mostly split up by basal sheer stress, and it is not necessary to consider the other forces.[8] It also assumes that the basal shear stress and the gravitational driving stress of the grounded ice balance one another out.[7] The method is computationally inexpensive.[8]

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.[9] Also known as a membrane model, they are similar to free-film models in fluid dynamics.[10] As opposed to Shallow Ice Approximation, Shallow Shelf Approximation models ice flow when longitudinal forces are strong; sliding and vertical forces.[7] SSA can also be considered a 'zero-order' model.[7]

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.[6] As these equations are computationally expensive, it is important to include many approximations to reduce running time.[6] 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.[11]

A diagram of some of the aspects of an ice-sheet model

Interactions with other climatic components

Ice sheets interact with the surrounding atmosphere, ocean and sub-glacial earth.[12] All of these interactive components need to be included to be able to have a comprehensive ice-sheet model.[12]

Basal Conditions play an important role in determining the behavior of ice sheets. The basal thermal state (if the ice is thawed or frozen) and the basal topography are difficult to map.[12] The most favored method is to apply mass conservation constraints.[12] For long-term projections, it is important to project the topography onto the continental shelf or into the fjords, and this can be difficult when the sub-glacial topography is not well-known.[12]

Summer Insolation drive temperature responses that have an effect on the rate of melting and mass balance of the ice sheet.[13] For example, the dependence of ice volume on summer insolation can be represented with , where I is ice volume, is the rate of change of ice volume per unit of time, T is the response time of the ice sheet and S is the insolation signal.[13]

Air Temperature is needed in a model as it informs surface melt and runoff rates.[14] For example, surface air temperature can be expressed with latitude 'lat', surface elevation h and mean temperature to provide an estimate of annual mean temperatures:[14] . This example assumes the ice shelf 's surface is as cold as at 1000m altitude.[14]

Precipitation is directly tied to air temperature, and also depends on moisture above and around the ice sheet.[14] Precipitation plays an important part in ice-sheet melting and accumulation.[14]

Calving

Calving is still an active area of investigation in ice-sheet modelling.[12] A total picture of calving will include many different aspects, including but not limited to tides, basal crevasses, collisions with ice bergs, thickness and temperature.[15] The recent development of the concepts of Marine Ice Sheet Instability and Marine Ice Cliff Instability have contributed to more accurate results of ice-sheet calving processes.[16]

Examples

CISM

The Community Ice Sheet Model is part of the Community Earth Systems Model funded by the National Science Foundation and models ice dynamics.[17][18] It is written in Fortran 90 and is open-source.[17] The US Department of Energy has begun to contribute to CISM.[18] The CISM project works on other adjacent projects in developing a cirriculum to expand knowledge on ice sheets, and engaging a broader community in ice-sheet modelling.[18] Many ice-sheet modelling softwares have influenced CISM, including the Parallel Ice Sheet Model (PSIM) and Glimmer.[19][20]

seaRISE

Sea-level Response to Ice Sheet Evolution (SeaRISE) is a subcommunity of CISM that sets out to estimate the upper limit of sea level rise from ice sheets.[21] The project sets out to develop a set of experiments and assessments for ice sheet and sea level rise modelling, as well as make a unified input dataset for ice sheet models.[21]

Glimmer

Glimmer (GENIE Land Ice Model with Multiply-Enabled Regions) is an ice-sheet model initially made to contribute to a more comprehensive earth system model, GENIE.[22]

PISM

The Parallel Ice Sheet Model is an open-sourced 3D ice sheet model capable of high resolution.[23] PISM is written in C++ and Python, and takes NetCDF files as input for the model.[24] PISM uses a "SIA+SSA hybrid" model, using both the shallow shelf approximation and shallow ice approximation models as stress balance models and does not solve full Stokes equations.[23] The model gets climatic information from an external General Circulation Model, and needs information like boundary temperature, mass flux into the ice, precipitation and air temperature.[25]

A horizontal grid of equal distance is used, with a variable vertical axis, and runs on a year timescale.[26][27]

See also

Ice-sheet models on the web

  • CISM – Community Ice Sheet Model, under development as a land-ice component of the Community Earth System Model (CESM)
  • Elmer/Ice, a multi-physics finite element code with special modules for full-stress ice dynamics analysis
  • ISSM – Ice Sheet System Model, a multi-purpose massively parallelized finite element framework dedicated to ice sheet systems modeling (thermomechanical coupling, data assimilation, sensitivity analysis,...)
  • PISM – Parallel Ice Sheet Model, which includes ice shelves and ice streams
  • SICOPOLIS – SImulation COde for POLythermal Ice Sheets, a 3D ice-sheet model which accounts for polythermal conditions (coexistence of ice at and below the melting point in different parts of an ice sheet)

References

  1. 1 2 3 4 5 6 7 Blatter, Heinz; Greve, Ralf; Abe-Ouchi, Ayako (2010). "A short history of the thermomechanical theory and modeling of glaciers and ice sheets". Journal of Glaciology. 56 (200): 1087–1094. Bibcode:2010JGlac..56.1087B. doi:10.3189/002214311796406059. hdl:2115/46879. ISSN 0022-1430.
  2. 1 2 3 Shepherd, Andrew; Nowicki, Sophie (October 2017). "Improvements in ice-sheet sea-level projections". Nature Climate Change. 7 (10): 672–674. Bibcode:2017NatCC...7..672S. doi:10.1038/nclimate3400. ISSN 1758-678X.
  3. 1 2 Philippe, Huybrechts (1997). Report of the Third EISMINT Workshop on Model Intercomparison (PDF).
  4. ↑ Nowicki, Sophie M. J.; Payne, Anthony; Larour, Eric; Seroussi, Helene; Goelzer, Heiko; Lipscomb, William; Gregory, Jonathan; Abe-Ouchi, Ayako; Shepherd, Andrew (21 December 2016). "Ice Sheet Model Intercomparison Project (ISMIP6) contribution to CMIP6". Geoscientific Model Development. 9 (12): 4521–4545. Bibcode:2016GMD.....9.4521N. doi:10.5194/gmd-9-4521-2016. ISSN 1991-9603. PMC 5911933. PMID 29697697.
  5. ↑ Pattyn, Frank (December 2018). "The paradigm shift in Antarctic ice sheet modelling". Nature Communications. 9 (1): 2728. Bibcode:2018NatCo...9.2728P. doi:10.1038/s41467-018-05003-z. ISSN 2041-1723. PMC 6048022. PMID 30013142.
  6. 1 2 3 Oerlemans, J. (December 1982). "Glacial cycles and ice-sheet modelling". Climatic Change. 4 (4): 353–374. Bibcode:1982ClCh....4..353O. doi:10.1007/BF02423468. hdl:1874/21024. ISSN 0165-0009. S2CID 189889177.
  7. 1 2 3 4 5 Davies, Bethan (22 June 2020). "A hierarchy of ice-sheet models". AntarcticGlaciers.org. Retrieved 18 October 2021.
  8. 1 2 Van Den Berg, J.; Van De Wal, R. S. W.; Oerlemans, J. (2006). "Effects of spatial discretization in ice-sheet modelling using the shallow-ice approximation". Journal of Glaciology. 52 (176): 89–98. Bibcode:2006JGlac..52...89V. doi:10.3189/172756506781828935. ISSN 0022-1430.
  9. ↑ "Two stress balance models: SIA and SSA – PISM, a Parallel Ice Sheet Model 1.2.1 documentation". pism-docs.org. Retrieved 19 October 2021.
  10. ↑ Schoof, Christian; Hewitt, Ian (3 January 2013). "Ice-Sheet Dynamics". Annual Review of Fluid Mechanics. 45 (1): 217–239. Bibcode:2013AnRFM..45..217S. doi:10.1146/annurev-fluid-011212-140632. ISSN 0066-4189.
  11. ↑ Davies, Bethan (22 June 2020). "A hierarchy of ice-sheet models". AntarcticGlaciers.org. Retrieved 18 October 2021.
  12. 1 2 3 4 5 6 Goelzer, Heiko; Robinson, Alexander; Seroussi, Helene; van de Wal, Roderik S. W. (December 2017). "Recent Progress in Greenland Ice Sheet Modelling". Current Climate Change Reports. 3 (4): 291–302. Bibcode:2017CCCR....3..291G. doi:10.1007/s40641-017-0073-y. ISSN 2198-6061. PMC 6959375. PMID 32010550.
  13. 1 2 Ruddiman, William (2014). Earth's Climate: Past and Future. New York: W.H. Freeman and Company. ISBN 978-1-4292-5525-7.
  14. 1 2 3 4 5 Albrecht, Torsten; Winkelmann, Ricarda; Levermann, Anders (14 February 2020). "Glacial-cycle simulations of the Antarctic Ice Sheet with the Parallel Ice Sheet Model (PISM) – Part 1: Boundary conditions and climatic forcing". The Cryosphere. 14 (2): 599–632. Bibcode:2020TCry...14..599A. doi:10.5194/tc-14-599-2020. ISSN 1994-0424.
  15. ↑ Alley, Richard B.; Horgan, Huw J.; Joughin, Ian; Cuffey, Kurt M.; Dupont, Todd K.; Parizek, Byron R.; Anandakrishnan, Sridhar; Bassis, Jeremy (28 November 2008). "A Simple Law for Ice-Shelf Calving". Science. 322 (5906): 1344. Bibcode:2008Sci...322.1344A. doi:10.1126/science.1162543. PMID 19039129. S2CID 206514828.
  16. ↑ Pattyn, Frank; Favier, Lionel; Sun, Sainan; Durand, Gaël (1 September 2017). "Progress in Numerical Modeling of Antarctic Ice-Sheet Dynamics". Current Climate Change Reports. 3 (3): 174–184. Bibcode:2017CCCR....3..174P. doi:10.1007/s40641-017-0069-7. ISSN 2198-6061. S2CID 134517464.
  17. 1 2 "CISM / The Community Ice Sheet Model". cism.github.io. Retrieved 14 October 2021.
  18. 1 2 3 "Development of a Community Ice Sheet Model - Interactive System for Ice sheet Simulation". websrv.cs.umt.edu. Retrieved 28 October 2021.
  19. ↑ "Software – Interactive System for Ice sheet Simulation". websrv.cs.umt.edu. Retrieved 28 October 2021.
  20. ↑ "Documentation for PISM, the Parallel Ice Sheet Model". pism-docs.org. Retrieved 28 October 2021.
  21. 1 2 "SeaRISE Assessment – Interactive System for Ice sheet Simulation". websrv.cs.umt.edu. Retrieved 28 October 2021.
  22. ↑ Rutt, I. C.; Hagdorn, M.; Hulton, N. R. J.; Payne, A. J. (2009). "The Glimmer community ice sheet model". Journal of Geophysical Research: Earth Surface. 114 (F2). Bibcode:2009JGRF..114.2004R. doi:10.1029/2008JF001015. hdl:20.500.11820/fd14bca6-3e08-4c40-a099-6cb4ced05157. ISSN 2156-2202.
  23. 1 2 "Documentation for PISM, the Parallel Ice Sheet Model". pism-docs.org. Retrieved 17 October 2021.
  24. ↑ PISM, a Parallel Ice Sheet Model, Parallel Ice Sheet Model, 11 October 2021, retrieved 17 October 2021
  25. ↑ "Climate inputs, and their interface with ice dynamics – PISM, a Parallel Ice Sheet Model 1.2.1 documentation". pism-docs.org. Retrieved 17 October 2021.
  26. ↑ "Spatial grid – PISM, a Parallel Ice Sheet Model 1.2.1 documentation". pism-docs.org. Retrieved 18 October 2021.
  27. ↑ "Model time – PISM, a Parallel Ice Sheet Model 1.2.1 documentation". pism-docs.org. Retrieved 18 October 2021.
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