Description: [1]  We use a finite-element model to solve for the response of Ganymede and Europa to tidal forcing from Jupiter, using various icy shell models with laterally variable (3-D) structure. In all cases, the shell is assumed to be underlain by a liquid water ocean. Icy shells with laterally varying thickness are derived from a thermal conduction model. 3-D shear modulus profiles for the shell are built either from a conduction model or, for Europa, by assuming a hemispherical difference in composition. Icy shell structures with a non-global ocean are built for Ganymede. Using these shell structures to calculate the tidal response of Ganymede and Europa, we conclude: (1) the presence of lateral variations in thickness or in shear modulus would not degrade future attempts to use tidal observations to decide on the existence or absence of a liquid ocean, and to determine the mean icy shell thickness. (2) Given accurate enough observations, the presence of lateral variations in thickness or in shear modulus could be determined by searching for non-degree-2 components in the tidal response. (3) In the absence of significant viscous convective flow in the shell, the effects of a laterally varying shear modulus on the tidal response would be smaller than those of a laterally varying shell thickness. (4) If the shell is partially grounded, tidal observations of either gravity or uplift would be able to roughly differentiate regions where the ice is grounded from those where it is floating.

Description: The Antarctic Ice Sheet is an important indicator of climate change and driver of sea-level rise. Here we combine satellite observations of its changing volume, flow and gravitational attraction with modelling of its surface mass balance to show that it lost 2,720 ± 1,390 billion tonnes of ice between 1992 and 2017, which corresponds to an increase in mean sea level of 7.6 ± 3.9 millimetres (errors are one standard deviation). Over this period, ocean-driven melting has caused rates of ice loss from West Antarctica to increase from 53 ± 29 billion to 159 ± 26 billion tonnes per year; ice-shelf collapse has increased the rate of ice loss from the Antarctic Peninsula from 7 ± 13 billion to 33 ± 16 billion tonnes per year. We find large variations in and among model estimates of surface mass balance and glacial isostatic adjustment for East Antarctica, with its average rate of mass gain over the period 1992–2017 (5 ± 46 billion tonnes per year) being the least certain.

Description: The Greenland Ice Sheet has been a major contributor to global sea-level rise in recent decades1,2, and it is expected to continue to be so3. Although increases in glacier flow4–6 and surface melting7–9 have been driven by oceanic10–12 and atmospheric13,14 warming, the magnitude and trajectory of the ice sheet’s mass imbalance remain uncertain. Here we compare and combine 26 individual satellite measurements of changes in the ice sheet’s volume, flow and gravitational potential to produce a reconciled estimate of its mass balance. The ice sheet was close to a state of balance in the 1990s, but annual losses have risen since then, peaking at 345 ± 66 billion tonnes per year in 2011. In all, Greenland lost 3,902 ± 342 billion tonnes of ice between 1992 and 2018, causing the mean sea level to rise by 10.8 ± 0.9 millimetres. Using three regional climate models, we show that the reduced surface mass balance has driven 1,964 ± 565 billion tonnes (50.3 per cent) of the ice loss owing to increased meltwater runoff. The remaining 1,938 ± 541 billion tonnes (49.7 per cent) of ice loss was due to increased glacier dynamical imbalance, which rose from 46 ± 37 billion tonnes per year in the 1990s to 87 ± 25 billion tonnes per year since then. The total rate of ice loss slowed to 222 ± 30 billion tonnes per year between 2013 and 2017, on average, as atmospheric circulation favoured cooler conditions15 and ocean temperatures fell at the terminus of Jakobshavn Isbræ16. Cumulative ice losses from Greenland as a whole have been close to the rates predicted by the Intergovernmental Panel on Climate Change for their high-end climate warming scenario17, which forecast an additional 70 to 130 millimetres of global sea-level rise by 2100 compared with their central estimate.