Background
The authors write that several studies (Oppenheimer, 1998; Meehl et al., 2007; Vaughan, 2008; Smith et al., 2009) have suggested that "climate change could potentially destabilize marine ice sheets, which would affect projections of future sea-level rise," specifically highlighting "an instability mechanism (Weertman, 1974; Thomas and Bentley, 1978; Schoof, 2007; Katz and Worster, 2010)," which they say "has been predicted for marine ice sheets such as the West Antarctic ice sheet that rest on reversed bed slopes, whereby ice-sheet thinning or rising sea levels leads to irreversible retreat of the grounding line."

What was done
Noting that existing analyses of this particular instability mechanism "have not accounted for deformational and gravitational effects that lead to a sea-level fall at the margin of a rapidly shrinking ice sheet," Gomez et al. go on to present "a suite of predictions of gravitationally self-consistent sea-level change following grounding-line migration," wherein they "vary the initial ice-sheet size and also consider the contribution to sea-level change from various sub-regions of the simulated ice sheet."

What was learned
The four researchers report that their new results "demonstrate that gravity and deformation-induced sea-level changes local to the grounding line contribute a stabilizing influence on ice sheets grounded on reversed bed slopes," contrary to previously prevailing assumptions based on earlier analyses of the subject. In fact, they conclude that "local sea-level change following rapid grounding-line migration will contribute a stabilizing influence on marine ice sheets, even when grounded on beds of non-negligible reversed slopes [italics added]."

What it means
In a terse statement describing the implications of their work, Gomez et al. write that their new and more "accurate" treatment of sea-level change "should be incorporated into analyses of past and future marine-ice-sheet dynamics."

References
Katz, R.F. and Worster, M.G. 2010. Stability of ice-sheet grounding lines. Proceedings of the Royal Society A 466: 1597-1620.

Meehl, G.A. et al. in IPCC Climate Change 2007: The Physical Science Basis: Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K.B., Tignor, M. and Miller, H.L., Eds.), Cambridge University Press, Cambridge, UK, pp. 748-845.

Oppenheimer, M. 1998. Global warming and the stability of the West Antarctic Ice Sheet. Nature 393: 325-332.

Schoof, C. 2007. Ice sheet grounding line dynamics: Steady states, stability and hysteresis. Journal of Geophysical Research 112: 10.1029/2006JF000664.

Smith, J.B., Schneider, S.H., Oppenheimer, M., Yohe, G.W., Hare, W., Mastrandrea, M.D., Patwardhan, A., Burton, I., Corfee-Morlot, J., Magadza, C.H.D., Fussel, H.-M., Pittock, A.B., Rahman, A., Suarez, A. and van Ypersele, J.-P. 2009. Assessing dangerous climate change through an update of the Intergovernmental Panel on Climate Change (IPCC), 'reasons for concern'. Proceedings of the National Academy of Sciences, USA 106: 4133-4137.

Thomas, R.H. and Bentley, C.R. 1978. A model for Holocene retreat of the West Antarctic Ice Sheet. Quaternary Research 10: 150-170.

Vaughan, D.G. 2008. West Antarctic Ice Sheet collapse -- the fall and rise of a paradigm. Climatic Change 91: 65-79.

Weertman, J. 1974. Stability of the junction of an ice sheet and an ice shelf. Journal of Glaciology 13: 3-11.