Figure S1. Predicted minus observed ice thicknesses for the present-day ice-sheet reconstruction of Whitehouse et al. (2012).

Figure S2. (a) Plan view of grounding line retreat superimposed upon the 20 km grid. The three grounding line regions are labelled in red (see text). The blue arrow indicates the direction of grounding line retreat between time t ka BP and time (t – 5) ka BP. The red dot indicates node j, the green dots indicate the closest nodes in regions ϕ = 2 and ϕ = 0. d2j and d0j are the distances between these nodes and node j, respectively. (b) Side view of ice surfaces during grounding line retreat between time t ka BP and time (t – 5) ka BP. The three grounding line regions are labelled in red. The darkest and lightest solid blue lines indicate the ice surface derived from the numerical ice sheet model at times t and (t – 5) ka BP, respectively. The mid-blue solid line indicates the position of the intermediate ice surface at (t – 2.5) ka BP. The dashed lines indicate the ‘target’ ice thickness (see text) at the intermediate time (mid-blue) and (t – 5) ka BP (light blue). d2GL and d0GL are the distances used to define the ratio (d2/d0)GL, which is used to test whether a node lies inside or outside the grounding line. (c) Side view of the ice surfaces during grounding line retreat if the ‘target’ ice thickness at the intermediate time is assumed to be zero rather than the thickness of ice at flotation.

Table S1. Details of the 16 ice-sheet reconstructions used in Experiment 3 (see main text). The values in italics define the ‘best’ deglaciation history of Whitehouse et al. (2012); this is the model that we call W12. D is lithospheric rigidity and τ is asthenospheric relaxation time, as described in the Glimmer ice-sheet model (Rutt et al. 2009). The spatially variable sea surface height is derived using the ICE-5G global deglaciation model (see Whitehouse et al. (2012) for further details).

Table S2. Details of the GPS sites used in this study together with the observed, modelled elastic, and elastic-adjusted vertical GPS rates, modelled vertical GIA rates, and the misfit between modelled and observed (elastic-adjusted) vertical rates (positive denotes uplift). One sigma uncertainties are given (see Thomas et al. 2011), and the method used to model the elastic rates is described in Thomas et al. (2011). At nine locations with co-located receivers, individual site rates are not used (grey); rather, weighted average rates are derived to give the ‘_AV’ rates (bold). At the Northern Antarctic Peninsula sites, the starred (*) records are the rates used in the analysis as the best estimate of the viscous GIA signal. These are derived from pre-March 2002 data: the elastic signal prior to the breakup of Larsen-B Ice shelf is assumed to be close to zero at these locations. The subsequent entries for these sites are given the suffix ‘_EL’ where the GPS rates are derived from the post-March 2002 data and are dominated by the elastic signal associated with the glacier speedup after the Larsen-B break up. The modelled GIA rates are generated using the W12 and W12a deglaciation models with the optimum earth model (see main text), as plotted in Figs 10(b) and (d) of the main text.

Supplement. Material that is critical to understanding the development of the new glacial isostatic adjustment (GIA) model is included in the main text. Here we present highly specialized details, which are only likely to be of interest to those seeking to perform a similar study.

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