Ice-Shelf Melting Around Antarctica

Major Meltdown The ice shelves and floating ice tongues that surround Antarctica cover more than 1.5 million square kilometers—approximately the size of the entire Greenland Ice Sheet. Conventional wisdom has held that ice shelves around Antarctica lose mass mostly by iceberg calving, but recently it has become increasingly clear that melting by a warming ocean may also be important. Rignot et al. (p. 266, published 13 June) present detailed glaciological estimates of ice-shelf melting around the entire continent of Antarctica, which show that basal melting accounts for as much mass loss as does calving. Basal melting of Antarctic ice shelves accounts for as much mass loss as does iceberg calving. We compare the volume flux divergence of Antarctic ice shelves in 2007 and 2008 with 1979 to 2010 surface accumulation and 2003 to 2008 thinning to determine their rates of melting and mass balance. Basal melt of 1325 ± 235 gigatons per year (Gt/year) exceeds a calving flux of 1089 ± 139 Gt/year, making ice-shelf melting the largest ablation process in Antarctica. The giant cold-cavity Ross, Filchner, and Ronne ice shelves covering two-thirds of the total ice-shelf area account for only 15% of net melting. Half of the meltwater comes from 10 small, warm-cavity Southeast Pacific ice shelves occupying 8% of the area. A similar high melt/area ratio is found for six East Antarctic ice shelves, implying undocumented strong ocean thermal forcing on their deep grounding lines.


Ice-Shelf Melting Around Antarctica
Gt/year, making ice-shelf melting the largest ablation process in Antarctica. The giant cold-cavity Ross, Filchner, and Ronne ice shelves covering two-thirds of the total ice-shelf area account for only 15% of net melting. Half of the meltwater comes from 10 small, warm-cavity Southeast Pacific ice shelves occupying 8% of the area. A similar high melt/area ratio is found for six East Antarctic ice shelves, implying undocumented strong ocean thermal forcing on their deep grounding lines.
T he Antarctic Ice Sheet and its 58-m sea level equivalent (1) is buttressed along most of its periphery by floating extensions of land ice called ice shelves and floating ice tongues (Fig. 1). Ice shelves cover an area >1.561 million km 2 , comparable in size to the Greenland Ice Sheet, and fringe 75% of Antarctica's coastline while collecting 20% of its snowfall over 11% of its area (2,3). These features are nourished by the inflow of continental ice from grounded glaciers, surface accumulation, and freezing of marine ice on their undersides. They lose mass to iceberg calving and basal melting along with topside sublimation and wind drift. Ice shelves exert considerable control on glacier stability and Antarctic Ice Sheet mass balance (4)(5)(6) and play important roles in ocean stratification and bottom water formation (7).
The traditional view of ablation from Antarctic ice shelves has been that it occurs mostly by iceberg calving, with basal melting only contributing 10 to 28% of the total mass loss (3)(4)(5)(6). Estimates of ice-shelf meltwater production derived from oceanographic data (8-10, e.g.) are impractical for synoptic circumpolar coverage. Numerical simulations of ice-ocean interactions extend from individual ice shelves to circumpolar models at various resolutions, but comparisons with observations are limited, and estimates of total ice-shelf meltwater production have varied from 357 to 1600 gigatons per year (1 Gt = 10 12 kg) (3,7,11). Glaciological estimates have focused on few ice shelves (6,12,13) or near a fraction of glacier grounding lines (14) due to incomplete velocity and thickness mapping.
Here, we present more accurate, higher-resolution glaciological estimates of ice-shelf melting around the entire continent. At any point on an ice shelf of thickness H and velocity vector v, the rate of ice-shelf thickening ∂H/∂t equals the sum of net surface mass balance SMB minus net basal melting B minus the lateral divergence in volume flux Hv (15). A negative value of B indicates the freeze-on of marine ice. The calculation of volume flux divergence on a point per point basis yields the distribution of freeze/melt (Fig. 1). The integration of the total inflow and outflow within the ice-shelf perimeters yields the areaaverage melt rate and total meltwater production ( Table 1).
For SMB, we use output products from the Regional Atmospheric and Climate Model RACMO2 (16), which is forced at the lateral boundary and sea surface by global reanalyses of the European Centre for Medium-Range Weather Forecasts. RACMO2 includes surface meltwater retention due to refreezing, evaporation, wind drift, and sublimation. The products have been validated with field data and an error propagation analysis (17) to a precision of 7 to 25%, average 10%, depending on location. We use the average SMB for the years 1979 to 2010 to represent a longerterm state.
Ice-shelf thickness is from Operation IceBridge (OIB) (18,19) and BEDMAP-2 (1) (fig. S1, supplementary materials). It combines direct measurements from radio-echo sounding, with indirect estimates from altimetry-derived ice-shelf surface elevation assuming hydrostatic equilibrium with a nominal precision of 15 to 50 m (20). Flux gates are selected at the location of Interferometric Synthetic Aperture Radar (InSAR)derived grounding lines, which are more precise than those derived from photogrammetric techniques or visible imagery (21), with accompanying impacts on estimates of volume fluxes. Ice-front flux gates are at the seaward limit of the volume flux data, within 1 to 3 km of ice-front positions digitized from a 150-m spacing mosaic of Ad-  S2). In the absence of vertical shear on floating ice, the surface-derived velocity is equivalent to a depth-averaged velocity. We surveyed 99.5% of Antarctic ice-shelf area in 2007 and 2008 (Table 1), or 1.554 million km 2 , excluding a few smaller ice shelves where ice thickness is not well known (table S1). Drainage boundaries between ice shelves, including the eastern and western Ross, are defined by flow vector direction. Ice rises and islands are excluded from the ice-shelf area estimates but included in the SMB calculation.
Ice-shelf thickening ∂H/∂t for the period 2003 to 2008 is calculated using the procedure in (23), with an error dependent on firn depth corrections ( fig. S3). The results are combined with SMB and the flux divergence to calculate B, with a precision dominated by uncertainties in ice-front thickness and firn depth corrections (table S1). We also calculate the results for ∂H/∂t = 0, i.e., no ice-shelf thickness change, to obtain a reference rate B ss corresponding to the amount of freezing or melting that would be required to maintain an ice shelf in "steady state" for 2007 and 2008 ( fig. S4).
The freeze/melt distribution confirms that basal melting is strongest near the grounding zones of major glaciers and along the ice fronts of some of the largest ice shelves, especially Ronne ( Fig. 1). Ice-shelf melting decreases away from grounding lines and becomes negative (accretion of marine ice) on all large ice shelves and some smaller ice shelves. This general pattern of melting and freezing beneath ice shelves is well understood (4-6, 15) and is governed by the Coriolis-influenced transport and vertical mixing of ocean heat, the pressure dependence of the freezing point of seawater, and the sea floor and cavity morphology. On some large ice shelves, freezing is concentrated on the western sides, consistent with an oceanic circulation during which seawater is first cooled, freshened, and made more buoyant by melting.
The highest melt rates are detected in the Southeast Pacific sector of the Antarctic Peninsula and West Antarctica, from the northern end of George VI to the western end of Getz Ice Shelf. On slow-moving to nearly stationary ice shelves like the Wilkins, George VI, Abbot, and Sulzberger, basal melting entirely consumes the inflow of individual glaciers within a few km of their grounding zones. High melt rates are also revealed in the grounding zones of the Amery, Moscow University, Shackleton, and Totten in East Antarctica.
In contrast, low melt rates are found under the largest ice shelves-for example, the Ross West-except near deep grounding lines. Maximum grounding-line depth is only 0.9 km under the Ross West but 2.1 km under the Filchner and Ronne, 1.8 km under the Ross East, and 2.4 km under the Amery (1). Each additional 100 m adds 0.076°C to the thermal driving of seawater that may have started out near the sea-surface freezing point. Differences in observed melt rate may also be accentuated by variations in flushing time and tidal activity (24).
Total ice inflow and outflow for each ice shelf is summarized in Fig. 1 and Table 1. Icefront flux is a proxy for, but not identical to, iceberg calving, which occurs at irregular time intervals ranging from days to decades. The higher basal melting near some ice-shelf fronts (12,25) results from stronger tidal currents and mixing, especially in combination with a shallow water column (24), as along the eastern front of Ronne [150 T 50 m in (1)

REPORTS
The total ice-shelf grounding-line inflow of 1696 T 146 Gt/year combined with an SMB input of 430 T 81 Gt/year is partitioned into an ice-front flux of 1,089 T 139 Gt/year and a basal meltwater production of 1,325 T 235 Gt/year. Basal melting thus accounts for 55 T 10% of ice-shelf mass ablation. The corresponding area-average melt rate of 85 T 15 cm/year is three times as large as the average SMB on ice shelves (28 T 5 cm) and five times the average SMB on grounded ice sheet (16 T 1 cm) (16), illustrating the considerable importance of ocean interactions in freshwater transfers between the ice and ocean.
The grounding-line flux of all surveyed ice shelves accounts for 83 T 7% of the total ice discharge into the Southern Ocean (Table 1). Total Antarctic grounded ice discharge (26) is 352 T 30 Gt/year higher than our grounding-line flux because of additional discharge from smaller ice shelves and ice walls that terminate in the ocean (27). An equal partitioning of these missing areas between calving and basal melting (see supplementary materials) would increase in situ meltwater production to 1500 T 237 Gt/year and ice-front flux to 1265 T 139 Gt/year.
The comparison of basal melting B (Fig. 1) with steady state melting B ss (fig. S4, Table 1, and table S1) shows that many ice shelves are near equilibrium (B~B ss ), whereas some are thickening (B < B ss ) and others are thinning (B > B ss ). High basal melting is therefore not synonymous with thinning. Ice shelves with high melt rates can be in a state of mass balance, but meltwater production is 28 T 9% higher than required to maintain the ice shelves in overall steady state (1037 T 218 Gt/year). Ice shelves in the Amundsen Sea sector (Pine Island to Getz) contribute 59% of the 287 T 89 Gt/year imbalance, an attrition rate twice that of their glacier source regions over the same time period (26). Similarly, the total imbalance of all Antarctic ice shelves combined is more than twice that of the grounded ice (26).
The ratio of calving to melting averages 0.45 T 0.3, but exhibits considerable regional variability (Table 1), with area-average melt rates varying from negative to > 40 m/year. This wide range reflects diverse ocean environments, which include seawater temperature, the depths of troughs and sills that influence the access of oceanic heat to ice-shelf cavities, and the sea-ice formation and drifts resulting from atmospheric forcing.
Large ice shelves generate a disproportionally small portion of the total ice-shelf meltwater despite high production rates in their deep grounding zones and along lengthy ice fronts. The four giants with areas >100,000 km 2 (Ross East, Ross West, Filchner, and Ronne) cover 61% of the total ice-shelf area but contribute only 15% of the meltwater at an average rate of 13 cm/year. The low melt rates result from the relatively weak ocean heat source provided by cold shelf waters, in turn leading to substantial marine ice accretion (28). Despite areas 3 to 10 times as large as the Getz, none of the big four ice shelves produce as much meltwater, with the Ross West contributing no net melt. Meltwater from the Southeast Pacific-Antarctic sector (George VI through Getz) accounts for 48% of the total meltwater over only 8% of the area, with the Getz being the largest meltwater source in Antarctica during the study period. B averages 5.1 m/year in this region, from a maximum of 43 m/year under the short Ferrigno Glacier tongue to a minimum of 1.8 m/year beneath the Abbot. That area-average rate may seem low for a warm-cavity Southeast Pacific ice shelf, but the moderate-sized, shallow-draft Abbot (29) ranks eighth overall in meltwater production, while maintaining a positive mass balance (B < B ss ).
Meltwater production from several small East Antarctic ice shelves in the Wilkes Land sector is larger than expected. Area-average melt rates from Dibble through Vincennes (4 to 11 m/year) are comparable to Amundsen Sea ice-shelf rates from Crosson through Land (4 to 11 m/year), whereas meltwater produced by Shackleton and West (73 and 27 Gt/year, respectively) rivals that from Thwaites and Sulzberger (98 and 18 Gt/year, respectively). Except for the region from 140°to 150°W where Mertz and Ninnis melting is dominated by shelf waters, oceanographic data are sparse along the Wilkes Land coastline. "Modified" warm deep water at a temperature near 0°C has been reported 40 km south of the continental shelf break northeast of Totten (30). By analogy with observations in the Amundsen Sea, our results suggest the presence of seawater at similar temperatures under several East Antarctic ice shelves. Even 0°seawater at outer continental shelf depths could expose ice shelves with deep grounding lines like the Totten (2.2 km), Moscow (2.0 km), and Shackleton (1.8 km) to temperatures more than 3°C above their melting points. To evaluate the impact of these warm deep waters on ice-shelf melting, more information is needed about their spatial and temporal variability on the outer shelf and links through glacially scoured troughs to the vulnerable glacier grounding lines.
Our glaciological estimates are generally consistent with recent results from high-resolution ocean models in the Amundsen, Bellingshausen, and Weddell Seas (29, 31-33) (see supplementary materials), but total melting of 10 of the larger ice shelves is notably less here than in circumpolar models (7,11). Discrepancies between model results and observations have been attributed to deficiencies in atmospheric forcing, the representation of sea-ice cover, the smoothing of bottom topography, and assumptions regarding cavity shape. Some models yield annual cycles and decadal variability (29) that can now be compared for specific periods with glaciological measurements, which need to be extended in time.
Our results indicate that basal melting accounts for a larger fraction of Antarctic ice-shelf attrition than previously estimated. These improved glaciological estimates provide not only more accurate and detailed reference values for modeling but also a baseline for similar future studies. Ice-shelf meltwater production exhibits a complex spatial pattern around the continent, with an outsized contribution of smaller, fast-melting ice shelves in both West and East Antarctica. Warm-cavity ice shelves along the Southeast Pacific coastline, predicted and observed to be sensitive to ocean warming and circulation strength (9,34), were thinning rapidly in 2003 to 2008 (23). Nearly half of the East Antarctic ice shelves were also thinning, some due to probable exposure to "warm" seawater, with connections to ice drainage basins grounded below sea level.
Continued observations of ice-shelf velocity and thickness change, along with more detailed information on cavity shape, seafloor topography, and atmospheric and oceanic forcing variability are critical to understand the temporal variability and evolution of Antarctic ice shelves. Continued warming of the ocean will slowly increase ice-shelf thinning, but if major shifts in sea ice cover and ocean circulation tip even large ice-shelf cavities from cold to warm (35), there could be major changes in ice shelf and thus ice-sheet mass balance.