The most rapid loss of ice from the Antarctic Ice Sheet is observed where ice streams flow into the ocean and begin to float, forming the great Antarctic ice shelves that surround much of the continent. Because these ice shelves are floating, their thinning does not greatly influence sea level. However, they also buttress the ice streams draining the ice sheet, and so ice shelf changes do significantly influence sea level by altering the discharge of grounded ice. Currently, the most significant loss of mass from the ice shelves is from melting at the base (although iceberg calving is a close second). Accessing the ocean beneath ice shelves is extremely difficult, so numerical models are invaluable for understanding the processes governing basal melting. This paper describes the different ways in which ice shelf/ocean interactions are modeled and discusses emerging directions that will enhance understanding of how the ice shelves are melting now and how this might change in the future.

Dinniman, M.S., X.S. Asay-Davis, B.K. Galton-Fenzi, P.R. Holland, A. Jenkins, and R. Timmermann. 2016. Modeling ice shelf/ocean interaction in Antarctica: A review. Oceanography 29(4):144–153, https://doi.org/10.5670/oceanog.2016.106.

Albrecht, T., M.A. Martin, R. Winkelmann, M. Haseloff, and A. Levermann. 2011. Parameterization for subgrid-scale motion of ice-shelf calving-fronts. The Cryosphere 5:35–44, https://doi.org/10.5194/tc-5-35-2011.
1. Arrigo, K.R., G.L. van Dijken, and A.L. Strong. 2015. Environmental controls of marine productivity hot spots around Antarctica. Journal of Geophysical Research 120:5,545–5,565, https://doi.org/10.1002/2015JC010888.
2. Årthun, M., P.R. Holland, K.W. Nicholls, and D.L. Feltham. 2013. Eddy-driven exchange between the open ocean and a sub-ice shelf cavity. Journal of Physical Oceanography 43:2,372–2,387, https://doi.org/10.1175/JPO-D-13-0137.1.
3. Arzeno, I.B., R.C. Beardsley, R. Limeburner, B. Owens, L. Padman, S.R. Springer, C.L. Stewart, and M.J.M. Williams. 2014. Ocean variability contributing to basal melt rate near the ice front of Ross Ice Shelf, Antarctica. Journal of Geophysical Research 119:4,214–4,233, https://doi.org/10.1002/2014JC009792.
4. Asay-Davis, X.S., S.L. Cornford, G. Durand, B.K. Galton-Fenzi, R.M. Gladstone, G.H. Gudmundsson, T. Hattermann, D.M. Holland, D. Holland, P.R. Holland, and others. 2016. Experimental design for three interrelated marine ice sheet and ocean model intercomparison projects: MISMIP v. 3 (MISMIP +), ISOMIP v. 2 (ISOMIP +) and MISOMIP v. 1 (MISOMIP1). Geoscientific Model Development 9:2,471–2,497, https://doi.org/​10.5194/gmd-9-2471-2016.
5. Beckmann, A., H.H. Hellmer, and R. Timmermann. 1999. A numerical model of the Weddell Sea: Large-scale circulation and water mass distribution. Journal of Geophysical Research 104:23,375–23,391, https://doi.org/​10.1029/1999JC900194.
6. Christmann, J., C. Plate, R. Müller and A. Humbert. 2016. Viscous and viscoelastic stress states at the calving front of Antarctic ice shelves. Annals of Glaciology, https://doi.org/10.1017/aog.2016.18.
7. Craven, M., I. Allison, H.A. Fricker, and R. Warner. 2009. Properties of a marine ice layer under the Amery Ice Shelf, East Antarctica. Journal of Glaciology 55(192):717–728, https://doi.org/​10.3189/002214309789470941.
8. Dansereau, V., P. Heimbach, and M. Losch. 2014. Simulation of subice shelf melt rates in a general circulation model: Velocity-dependent transfer and the role of friction. Journal of Geophysical Research 119:1,765–1,790, https://doi.org/10.1002/2013JC008846.
9. DeAngelis, H., and P. Skvarca. 2003. Glacier surge after ice shelf collapse. Science 299:1,560–1,562, https://doi.org/10.1126/science.1077987.
10. DeConto, R.M., and D. Pollard. 2016. Contribution of Antarctica to past and future sea-level rise. Nature 531:591–597, https://doi.org/10.1038/nature17145.
11. De Rydt, J., and G.H. Gudmundsson. 2016. Coupled ice shelf-ocean modeling and complex grounding line retreat from a seabed ridge. Journal of Geophysical Research 121:865–880, https://doi.org/10.1002/2015JF003791.
12. Dinniman, M.S., J.M. Kinck, L-S Bai, D.H. Bromwich, K.M. Hines, and D.M. Holland. 2015. The effect of atmospheric forcing resolution on delivery of ocean heat to the Antarctic floating ice shelves. Journal of Climate 28:6,067–6,085, https://doi.org/10.1175/JCLI-D-14-00374.1.
13. Dutrieux, P., J. De Rydt, A. Jenkins, P.R. Holland, H.-K. Ha, S.H. Lee, E.J. Steig, Q. Ding, E.P. Abrahamsen, and M. Schröder. 2014a. Strong sensitivity of Pine Island Ice-Shelf melting to climatic variability. Science 343:174–178, https://doi.org/10.1126/science.1244341.
14. Dutrieux, P., C. Stewart, A. Jenkins, K.W. Nicholls, H.F.J. Corr, E. Rignot, and K. Steffen. 2014b. Basal terraces on melting ice shelves. Geophysical Research Letters 41:5,506–5,513, https://doi.org/10.1002/2014GL060618.
15. Galton-Fenzi, B.K., J.R. Hunter, R. Coleman, S.J. Marsland, and R. Warner. 2012. Modeling the basal melting and marine ice accretion of the Amery Ice Shelf. Journal of Geophysical Research 117, C09031, https://doi.org/​10.1029/2012JC008214.
16. Gayen, B., R.W. Griffiths, and R.C. Kerr. 2015. Melting driven convection at the ice-seawater interface. Procedia IUTAM 15:78–85, https://doi.org/10.1016/​j.piutam.2015.04.012.
17. Goldberg, D.N., C.M. Little, O.V. Sergienko, A. Gnanadesikan, R. Hallberg, and M. Oppenheimer. 2012. Investigation of land ice-ocean interaction with a fully coupled ice-ocean model: Part 1. Model description and behavior. Journal of Geophysical Research 117, F02037, https://doi.org/10.1029/2011JF002246.
18. Griffies, S.M., C. Böning, F.O. Bryan, E.P. Chassignet, R. Gerdes, H. Hasumi, A. Hirst, A.-M. Treguier, and D. Webb. 2000. Developments in ocean climate modelling. Ocean Modelling 2:123–192, https://doi.org/10.1016/S1463-5003(00)00014-7.
19. Gudmundsson, G.H. 2013. Ice-shelf buttressing and the stability of marine ice sheets. The Cryosphere 7:647–655, https://doi.org/10.5194/tc-7-647-2013.
20. Gwyther, D.E., B.K. Galton-Fenzi, M.S. Dinniman, J.L. Roberts, and J.R. Hunter. 2015. The effect of basal friction on melting and freezing in ice shelf–ocean models. Ocean Modelling 95:38–52, https://doi.org/10.1016/j.ocemod.2015.09.004.
21. Hallberg, R. 2013. Using a resolution function to regulate parameterizations of oceanic mesoscale eddy effects. Ocean Modelling 72:92–103, https://doi.org/10.1016/j.ocemod.2013.08.007.
22. Hattermann, T., L.H. Smedsrud, O.A. Nøst, J.M. Lilly, and B.K. Galton-Fenzi. 2014. Eddy-resolving simulations of the Fimbul Ice Shelf cavity circulation: Basal melting and exchange with open ocean. Ocean Modelling 82:28–44, https://doi.org/10.1016/​j.ocemod.2014.07.004.
23. Heimbach, P., and M. Losch. 2012. Adjoint sensitivities of sub-ice-shelf melt rates to ocean circulation under the Pine Island Ice Shelf, West Antarctica. Annals of Glaciology 53:59–69, https://doi.org/​10.3189/2012/AoG60A025.
24. Hellmer, H.H., F. Kauker, R. Timmermann, J. Determann, and J. Rae. 2012. Twenty-first-century warming of a large Antarctic ice shelf cavity by a redirected coastal current. Nature 485:225–228, https://doi.org/10.1038/nature11064.
25. Hellmer, H.H., and D. Olbers. 1989. A two-​dimensional model for the thermohaline circulation under an ice shelf. Antarctic Science 1:325–336, https://doi.org/10.1017/S0954102089000490.
26. Holland, P.R. 2008. A model of tidally dominated ocean processes near ice shelf grounding lines. Journal of Geophysical Research 113, C11002, https://doi.org/10.1029/2007JC004576.
27. Holland, P.R., H.F.J. Corr, D.G. Vaughan, A. Jenkins, and P. Skvarca. 2009. Marine ice in Larsen Ice Shelf. Geophysical Research Letters 36, L11604, https://doi.org/10.1029/2009GL038162.
28. Holland, P.R., and D.L. Feltham. 2006. The effects of rotation and ice shelf topography on frazil-laden ice shelf water plumes. Journal of Physical Oceanography 36:2,312–2,327, https://doi.org/​10.1175/JPO2970.1.
29. Holland, D.M., and A. Jenkins. 1999. Modeling thermodynamic ice-ocean interactions at the base of an ice shelf. Journal of Physical Oceanography 29:1,787–1,800, https://doi.org/​10.1175/1520-0485(1999)029<1787:MTIOIA>​2.0.CO;2.
30. Holland, D.M., and A. Jenkins. 2001. Adaptation of an isopycnic coordinate ocean model for the study of circulation beneath ice shelves. Monthly Weather Review 129:1,905–1,927, https://doi.org/10.1175/​1520-0493(2001)129<1905:AOAICO>2.0.CO;2.
31. Jacobs, S.S., and C.F. Giulivi. 2010. Large multidecadal salinity trends near the Pacific-Antarctic continental margin. Journal of Climate 23:4,508–4,524, https://doi.org/​10.1175/2010JCLI3284.1.
32. Jacobs, S.S., H.H. Helmer, C.S.M. Doake, A. Jenkins, and R.M. Frolich. 1992. Melting of ice shelves and the mass balance of Antarctica. Journal of Glaciology 38:375–387.
33. Jenkins, A. 1991. A one-dimensional model of ice shelf-ocean interaction. Journal of Geophysical Research 96:20,671–20,677, https://doi.org/​10.1029/91JC01842.
34. Jenkins, A. 2016. A simple model of the ice shelf–ocean boundary layer and current. Journal of Physical Oceanography 46:1,785–1,803, https://doi.org/10.1175/JPO-D-15-0194.1.
35. Jenkins, A., and A. Bombosch. 1995. Modeling the effects of frazil ice crystals on the dynamics and thermodynamics of ice shelf water plumes. Journal of Geophysical Research 100:6,967–6,981, https://doi.org/10.1029/94JC03227.
36. Jenkins, A., K.W. Nicholls, and H.F. Corr. 2010. Observation and parameterization of ablation at the base of Ronne Ice Shelf, Antarctica. Journal of Physical Oceanography 40:2,298–2,312, https://doi.org/10.1175/2010JPO4317.1.
37. Jordan, J.R., P.R. Holland, A. Jenkins, M.D. Piggott, and S. Kimura. 2014. Modeling ice-ocean interaction in ice shelf crevasses. Journal of Geophysical Research, 119:995–1,008, https://doi.org/10.1002/2013JC009208.
38. Joughin, I., B.E. Smith, and B. Medley. 2014. Marine ice sheet collapse potentially under way for the Thwaites Glacier Basin, West Antarctica. Science 344:735–738, https://doi.org/10.1126/science.1249055.
39. Kimura, S., A.S. Candy, P.R. Holland, M.D. Piggott, and A. Jenkins. 2013. Adaptation of an unstructured-mesh, finite-element ocean model to the simulation of ocean circulation beneath ice shelves. Ocean Modelling 67:39–51, https://doi.org/10.1016/​j.ocemod.2013.03.004.
40. Kusahara, K., and H. Hasumi. 2013. Modeling Antarctic ice shelf responses to future climate changes and impacts on the ocean. Journal of Geophysical Research 118:2,454–2,475, https://doi.org/10.1002/jgrc.20166.
41. Little, C.M., A. Gnanadesikan, and R. Hallberg. 2008. Large-scale oceanographic constraints on the distribution of melting and freezing under ice shelves. Journal of Physical Oceanography 38:2,242–2,255, https://doi.org/10.1175/2008JPO3928.1.
42. Liu, Y., J.C. Moore, X. Cheng, R.M. Gladstone, J.N. Bassis, H. Liu, J. Wen, and F. Hui. 2015. Ocean-driven thinning enhances iceberg calving and retreat of Antarctic ice shelves. Proceedings of the National Academy of Sciences of the United States of America 112(11):3,263–3,268, https://doi.org/10.1073/pnas.1415137112.
43. Losch, M. 2008. Modeling ice shelf cavities in a z coordinate ocean general circulation model. Journal of Geophysical Research 113, C08043, https://doi.org/10.1029/2007JC004368.
44. MacAyeal, D.R. 1985. Evolution of tidally triggered meltwater plumes below ice shelves. Pp. 133–143 in Oceanology of the Antarctic Continental Shelf. S.S. Jacobs, ed., American Geophysical Union Antarctic Research Series, Vol. 43, Washington, DC.
45. Makinson, K., P.R. Holland, A. Jenkins, K.W. Nicholls, and D.M. Holland. 2011. Influence of tides on melting and freezing beneath Filchner-Ronne Ice Shelf, Antarctica. Geophysical Research Letters 38, L06601, https://doi.org/10.1029/2010GL046462.
46. Martin, D., X. Asay-Davis, S. Cornford, S. Price, E. Ng, and W. Collins. 2015. A tale of two forcings: Present-day coupled Antarctic Ice-sheet/Southern Ocean dynamics using the POPSICLES model. Paper presented at the European Geosciences Union General Assembly, Vienna, Austria, April 12–17, 2015, no. 7564.
47. Martinson, D.G., and D.C. McKee. 2012. Transport of warm Upper Circumpolar Deep Water onto the western Antarctic Peninsula continental shelf. Ocean Science 8:433–442, https://doi.org/10.5194/os-8-433-2012.
48. McMillan, M., A. Shepherd, A. Sundal, K. Briggs, A. Muir, A. Ridout, A. Hogg, and D. Wingham. 2014. Increased ice losses from Antarctica detected by CryoSat-2. Geophysical Research Letters 41:3,899–3,905, https://doi.org/​10.1002/2014GL060111.
49. Merino, N., J. Le Sommer, G. Durand, N.C. Jourdain, G. Madec, P. Mathiot, and J. Tournadre. 2016. Antarctic icebergs melt over the Southern Ocean: Climatology and impact on sea ice. Ocean Modelling 104:99–110, https://doi.org/10.1016/​j.ocemod.2016.05.001.
50. Mueller, R.D., L. Padman, M.S. Dinniman, S.Y. Erofeeva, H.A. Fricker, and M.A. King. 2012. Impact of tide-topography interactions on basal melting of Larsen C Ice Shelf, Antarctica. Journal of Geophysical Research 117, C05005, https://doi.org/10.1029/2011JC007263.
51. Nakayama, Y., R. Timmermann, M. Schröder, and H.H. Hellmer. 2014. On the difficulty of modeling Circumpolar Deep Water intrusions onto the Amundsen Sea continental shelf. Ocean Modelling 84:26–34, https://doi.org/10.1016/​j.ocemod.2014.09.007.
52. Nicholls, K.W., E.P. Abrahamsen, J.J.H. Buck, P.A. Dodd, C. Goldblatt, G. Griffiths, K.J. Heywood, N.E. Hughes, A. Kaletzky, G.F. Lane-Serff, and others. 2006. Measurements beneath an Antarctic ice shelf using an autonomous underwater vehicle. Geophysical Research Letters 33, L08612, https://doi.org/10.1029/2006GL025998.
53. Nicholls, K.W., and K. Makinson. 1998. Ocean circulation beneath the western Ronne Ice Shelf, as derived from in situ measurements of water currents and properties. Pp. 301–318 in Ocean, Ice, and Atmosphere: Interactions at the Antarctic Continental Margin. S.S. Jacobs and R.F. Weiss, eds, American Geophysical Union Antarctic Research Series, Vol. 75, Washington, DC.
54. Petersen, M.R., X. Asay-Davis, T.D. Ringler, D. Jacobsen, S.F Price, and J.G. Fyke. 2016. Ocean-ice shelf interactions in the Accelerated Climate Model for Energy (ACME). Paper A14A-2524 presented at the Ocean Sciences Meeting, New Orleans, LA, February 21–26, 2016.
55. Petty, A.A., D.L. Feltham, and P.R. Holland. 2013. Impact of atmospheric forcing on Antarctic continental shelf water masses. Journal of Physical Oceanography 43:920–940, https://doi.org/10.1175/jpo-d-12-0172.1.
56. Potter, J.R., and J.G. Paren. 1985. Interaction between ice shelf and ocean in George VI Sound, Antarctica. Pp. 35–58 in Oceanology of the Antarctic Continental Shelf. S.S. Jacobs, ed., American Geophysical Union Antarctic Research Series, Vol. 43, Washington, DC.
57. Pritchard, H.D., S.R.M. Ligtenberg, H.A. Fricker, D.G. Vaughan, M.R. van den Broeke, and L. Padman. 2012. Antarctic ice-sheet loss driven by basal melting of ice shelves. Nature 484:502–505, https://doi.org/10.1038/nature10968.
58. Rignot, E., S. Jacobs, J. Mouginot, and B. Scheuchl. 2013. Ice shelf melting around Antarctica. Science 341:266–270, https://doi.org/10.1126/science.1235798.
59. Robinson, R., A. Beckmann, and H. Hellmer. 2003. M2 tidal dynamics in the Ross Sea. Antarctic Science 15:41–46, https://doi.org/10.1017/S0954102003001044.
60. Robertson, R. 2013. Tidally induced increases in melting of Amundsen Sea ice shelves. Journal of Geophysical Research 118:3,138–3,145, https://doi.org/10.1002/jgrc.20236.
61. Schaffer, J., R. Timmermann, J.E. Arndt, S. Savstrup Kristensen, C. Mayer, M. Morlighem, and D. Steinhage. 2016. A global high-resolution data set of ice sheet topography, cavity geometry and ocean bathymetry. Earth Systems Science Data Discussions, https://doi.org/10.5194/essd-2016-3.
62. Schodlok, M.P., D. Menemenlis, and E.J. Rignot. 2016. Ice shelf basal melt rates around Antarctica from simulations and observations. Journal of Geophysical Research 121:1,085–1,109, https://doi.org/​10.1002/2015JC011117.
63. Sergienko, O.V. 2013. Basal channels on ice shelves. Journal of Geophysical Research 118:1,342–1,355, https://doi.org/10.1002/jgrf.20105.
64. Stewart, A.L., and A.F. Thompson. 2015. Eddy-mediated transport of warm Circumpolar Deep Water across the Antarctic shelf break. Geophysical Research Letters 42:432–440, https://doi.org/10.1002/2014GL062281.
65. St-Laurent, P., J.M. Klinck, and M.S. Dinniman. 2015. Impact of local winter cooling on the melt of Pine Island Glacier, Antarctica. Journal of Geophysical Research 120:6,718–6,732, https://doi.org/10.1002/2015JC010709.
66. Thoma, M., K. Grosfeld, C. Mayer, and F. Pattyn. 2010. Interaction between ice sheet dynamics and subglacial lake circulation: A coupled modelling approach. The Cryosphere 4(1):1–12, https://doi.org/10.5194/tc-4-1-2010.
67. Timmermann, R., and H.H. Hellmer. 2013. Southern Ocean warming and increased ice shelf basal melting in the 21st and 22nd centuries based on coupled ice-ocean finite-element modelling. Ocean Dynamics 63:1011, https://doi.org/10.1007/s10236-013-0642-0. 
68. Timmermann, R., Q. Wang, and H.H. Hellmer. 2012. Ice-shelf basal melting in a global finite-​element sea-ice/ice-shelf/ocean model. Annals of Glaciology 53:303–314, https://doi.org/10.3189/2012AoG60A156.
69. Williams, M.J.M., A. Jenkins, and J. Determan. 1998. Physical controls on ocean circulation beneath ice shelves revealed by numerical models. Pp. 285–299 in Ocean, Ice, and Atmosphere: Interactions at the Antarctic Continental Margin. S.S. Jacobs and R.F. Weiss, eds, American Geophysical Union Antarctic Research Series, Vol. 75, Washington, DC.

This is an open access article made available under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution, and reproduction in any medium or format as long as users cite the materials appropriately, provide a link to the Creative Commons license, and indicate the changes that were made to the original content. Images, animations, videos, or other third-party material used in articles are included in the Creative Commons license unless indicated otherwise in a credit line to the material. If the material is not included in the article’s Creative Commons license, users will need to obtain permission directly from the license holder to reproduce the material.