Time series of surface elevation, h, allowed us to calculate ice shelf melt rates, m. We calculated the height of the ice above floatation, hf. We identified when the glacier reaches hf = 0 m (Fig. 2A) in the time series and calculated the slope of the change in elevation before that transition, dh/dtPRE, and after that transition, dh/dtPOST, i.e., the date of ungrounding of ice. dh/dtPRE is the average thinning rate on grounded ice, which is caused principally by dynamic thinning, and reflects a total change in thickness (because the bed elevation is not changing with time during that time period). dh/dtPOST is the average thinning rate on floating ice, which includes dynamic thinning and also ice shelf melt. The ice shelf melt rate, mb, was deduced fromEmbedded Image(2)Embedded Image(3)Embedded Image(4)where ms and mb are the melt rates (positive is melt, and negative is accretion) at the surface and base of the ice, respectively; h is the ice surface elevation above mean sea level; u is the depth-averaged velocity; and f = 9.61 is a flotation factor deduced from densities of ice and seawater. We assumed that the rate of dynamic thinning, Embedded Image, varies smoothly along the flow; hence, it is nearly the same above and below the grounding line, which is justified a priori because changes in ice velocity take place over spatial scales of 10 to 100 km. We also assumed that ice shelf melt is smoothly varying near the grounding line, which is an approximation, so the change in surface elevation may be assumed to be varying almost linearly with time (Fig. 2, A to F). This Eulerian framework, based on the change in elevation with time at a fixed point in space, identifies the temporal change in ice melt at a given location; hence, it reveals how rapidly a piece of ice melts as the grounding line retreats and ice ungrounds and is exposed to warm ocean waters. One drawback of this method is that it produces noisy results, where heterogeneities in ice thickness are advected downstream, for instance, seaward of the grounding line due to the presence of deep bottom crevasses traveling with the main flow.

In a Lagrangian framework (see below), we tracked a piece of ice with time and calculated its rate of ice melt after correction for flow divergence. The heterogeneities in ice shelf melt were removed, but the method did not apply on grounded ice; hence, we could not use the Lagrangian framework to calculate how ice melt changes with time as ice ungrounds. In our analysis, we only used a Eulerian framework for that reason and we noted that caution must be exercised when interpreting the results within a few kilometers seaward of the grounding line due to the rebound of ice to hydrostatic equilibrium as the bending zone migrates.

Using ATM surface elevation and MCoRDS depth-sounding radar-derived thickness, we obtained direct information about changes in ice thickness along profiles T1-T2 and T3-T4 from years 2011, 2014, and 2016. We compared ATM versus TDX surface elevation acquired closest in time. We found a difference with an SD of 4 m (fig. S4). We compared MCoRDS direct thickness changes with thickness changes inferred using TDX DEMs closest in time to the MCoRDS data. We found an agreement at the 4-m level along the grounded part of T3-T4 in 2014–2016 (fig. S5). Near the grounding line of T1-T2 for the 2014–2016 data and along T3-T4 for the 2011–2014 data, ATM/MCoRDS showed peak changes of 150 and 20 m, respectively, whereas TDX DEMs indicated 50- and 300-m thickening, respectively (fig. S5). As explained in the main text, we attributed this discrepancy to the rebound of ice from below floatation to at floatation as the grounding line retreats, i.e., the bending zone retreats, and ice exits the bending zone to become freely floating. Direct measurements of ice thickness confirmed that ice melted from the bottom despite the observed uplift in surface elevation.

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