Figure  illustrates the state of the three regional models at the end of the initialization procedure. The large ice streams flowing into the Amundsen Sea, through the Filchner–Ronne Ice Shelf, and through the Ross Ice Shelf are apparent in both the flow field and the basal traction field C. The flow field itself is close to the observed speed, with the largest mismatch due to the softening in Pine Island Glacier described above, and within 200ma-1 of the observations elsewhere. Regions of fast flow are fringed by weak shear margins that are due to both the shear thinning action of Glen's flow law and localized low stiffening factor ϕ. Note that the observed velocity field cannot be matched with ϕ=1, whatever the basal traction. For example the shear margins in Pine Island Glacier and the division between the western and eastern portions of Thwaites Glacier's ice shelf require ϕ∼0.1.

The thickening rate (given a0 and M0) is between -5 and 5ma-1 except at calving fronts. Integrating this thickening rate leads to an annual loss of volume above flotation of 3 km3a-1 in the ASE, 7 km3a-1 in the Filchner–Ronne ice shelf basin and 7 km3a-1 in the Ross ice shelf basin. The synthetic accumulation a0 used to obtain this thickening rate does include some unrealistic large-amplitude short-wavelength features, with the largest values in mountainous regions with steep slopes: the ring-shaped features in the ASE surround isolated peaks, for example. Strong ablation is limited to the ice shelves, with a0 between -5 and 5ma-1: in particular there is no region of ∼100m a-1 ablation needed to counter the flux arriving at the Pine Island Glacier grounding line.

Future climate forcings were derived from the atmosphere and ocean models by computing space- and time-dependent anomalies with respect to the 1980–1989 mean, and adding them to a0(x,y) and M0(x,y,t). By combining the seven atmosphere projections with the eight ocean projections, we have fourteen experiments, as shown in Table . These are named after the anomalies: for example, the experiment named H/A/R/F combines the HadCM3/A1B/RACMO2 accumulation anomalies with the HadCM3/A1B/FESOM melt rate anomalies. Given the fourteen forcing combinations, the ice sheet model was evolved, starting from its initial state in 1980 to at least 2100 and on to 2150 or 2200 if the forcing data were available. The HadCM3/A1B/FESOM ocean data, both sets of HadCM3/A1B/BRIOS ocean data and all of the HadCM3/A1B atmosphere projections were sufficient to run the ice sheet model until 2200, the HadCM3/E1/FESOM data run to 2150, and the ECHAM5 data to 2100.

Neither ocean model produced substantial melt rate increases in the ASE or MBL domains, presumably because they are not able to resolve the small ice shelves along those coasts. We computed melt rates in those regions from projections of nearby ocean temperatures. The melt rates and consequent thinning experienced by small ice shelves, such as Pine Island Glacier, is thought to be forced by changes in the temperature of near-coast water masses . We compute a local ocean temperature anomaly ΔT(t) by averaging the projected ocean temperature over volume bounded laterally between the contemporary ice front, the sector boundaries, and the 1000 m bathymetric contour and vertically between depths of 200 and 800 m, on the grounds that water contributing to melting must be deep enough to interact with the base of an ice shelf but shallow enough to cross the continental shelf break. Finally, a melt rate anomaly ΔM(t)=16ΔT(t) ma-1K-1 was chosen to be at the upper end of the range of observational and modeling studies .

The accumulation and melt rate anomalies, plotted in Figs.  and , have a notable feature. The A1B atmosphere models project increased accumulation during the 21st century, and a further increase during the 22nd century, over and above the E1 models. Although the two atmosphere models distribute snowfall differently, with RACMO2 concentrating its increased accumulation over the Amundsen Sea Embayment and Filchner–Ronne Ice Shelf drainage basins and LMDZ4 heaping mass over Marie-Byrd Land and the Ross Ice Shelf drainage basin, both models project a threefold increase for A1B over E1. At the same time, the A1B and E1 ocean models both provide enhanced melt rates from 2100, with the most obvious difference between trends being the choice of FESOM or BRIOS. Even before carrying out any simulations, we can expect to see similar dynamic thinning in the two emissions scenarios, which, coupled with the extra accumulation in A1B, means that we expect to simulate more sea level rise for E1 (mitigation) emissions than A1B (business as usual) emissions.

The climate-forced experiments outlined above present a rather limited view of future change. Since both the ocean and atmosphere models project similar futures, they cannot provide much information about the response to earlier or more widely distributed ice shelf thinning. At the same time, the assumption that the ice sheet was in steady state at the end of the 20th century does not allow us to examine changes that may already be under way. A number of experiments with melt rate anomalies but no accumulation anomalies were carried out to address these limitations.

Parts of the ice sheet model might be on the brink of dramatic change in 2200, so we ran a longer set of calculations, starting in 1980 and running until 2300, based on the HadCM3/A1B/FESOM melt rates. This experiment has only the synthetic accumulation field, so we label it H/A/0/F. The HadCM3/A1B/FESOM melt rates were chosen because they run up to 2200, produce enhanced melting in all of the basins, and rise constantly from 2050 onward to give the largest melt rates at the end of the 22nd century. From 1980 to 2200 we applied the melt rate anomalies as before, and applied the 2200 melt rate anomaly for the remainder of the simulation.

Imposing a synthetic accumulation field to hold the ice sheets close to steady state given the present-day geometry and velocity is a questionable choice in the Amundsen Sea Embayment, where observations over the last decades show extensive thinning. Furthermore, the synthetic mass balance field a0(x,y), which we constructed to hold Thwaites Glacier in steady state during the control experiment, includes a spot of unrealistic – 5 ma-1 – accumulation close to the Thwaites Glacier grounding line (see Fig. ). In light of these issues, we carried out three additional simulations. None of these experience accumulation anomalies but the first, H/A/0′/F, has a synthetic accumulation field a0′(x,y) with the 5 ma-1 accumulation spot removed, and the second and third, H/A/0′′/F and control′′ do not make use of a synthetic accumulation field at all, but employ the HadCM3/E1/RACMO2 1990–1999 temporal mean, which we will call a0′′(x,y), from 1980 onward. H/A/0′/F and H/A/0′′/F are subject (like H/A/0/F) to the HadCM3/A1B/FESOM melt rate anomaly data, while the control′′ experiment maintains the same melt rate parametrization as the control experiment, that is M0(x,y,t).

As none of the melt rate anomalies in the ASE exceed 10 ma-1 until after 2050, we also examined the model's response to earlier ocean warming. Two simulations, 0/U16 and 0′′/U16, were performed, with melt rate anomalies of 16 ma-1 applied across all floating ice from 1980 onward. 0/U16 used the synthetic accumulation field a0(x,y), while 0′′/U16 used the HadCM3/E1/RACMO2 1990–2000 mean accumulation field a0′′(x,y).

Both FESOM and BRIOS ocean models produce similar melt rate anomalies, with enhanced melt rates concentrated around Berkner Island in the Filchner–Ronne ice shelf, and around Roosevelt Island in the Ross Ice Shelf. Those similar patterns are due to the physics of ocean circulation in the two models, but it makes sense to consider ice sheet sensitivity to melt rates that cover a greater extent. At the same time, as in the ASE, melt rates begin to grow around 2100 in all of the drainage basins, so we need to consider our sensitivity to earlier warming. With those aims in mind, we carried out a pair of uniform melt rate experiments (0/U8,0/U16) in the RISFRIS domain, applying melt rate anomalies of 8 and 16 ma-1 across the entire extent of floating ice starting from 1980.

The Amundsen Sea Embayment thins throughout the melt rate anomaly simulations, losing 5–14×103km3 (15–40 mm SLE) volume above flotation between 2000 and 2100 and 20–70×103km3 (50–190 mm SLE) by 2200 (Fig. ). Pine Island Glacier and the ice streams feeding the Crosson and Dotson Ice Shelves experience ∼1kma-1 grounding line retreat from the present day onward in all of the experiments apart from control and control′′, while Thwaites Glacier sees its retreat delayed in some simulations. The major distinction between simulations is the onset of retreat in Thwaites Glacier: experiments in which its grounding line begins to retreat around 2000 lose volume at more than twice the rate of those in which retreat begins around 2200.

Projections of retreat in Thwaites Glacier are strongly affected by initial conditions, with some simulations showing little retreat and others shedding between 100 and 210 km3a-1 volume above flotation over the 21st and 22nd centuries. In calculations with the synthetic mass balance a0: H/A/0/F, 0/U16, and the control experiment 0/U0), the grounding line remains close to the present-day position until after 2200, despite the near complete removal of its ice shelf by that time in H/A/0/F and 0/U16. It seems that even with the isolated promontory in the slowly flowing eastern section, the ice shelf exerts little back-pressure on the ice stream and so its loss is not felt strongly. The majority of the grounding line retreat only begins after 2200, triggered by the retreat of the small stream which diverts from Thwaites glacier to flow into the south-western corner of Pine Island Glacier and from then on the grounding line retreats at a rate of 1 kma-1 until 2300. In contrast, the glacier begins to retreat around 2100 in the H/A/0′/F experiment, and around 2000 in the H/A/0′′/F, 0′′/U16 and even the control′′ experiments. In these last three simulations, marine ice sheet instability is already acting at the beginning of the simulation, and at no point does the ice shelf provide enough buttressing to prevent it. Provided that retreat is initiated, the higher melt rates applied in H/A/0′′/F, 0′′/U16 do result in faster retreat (∼ 200km3a-1) than in the control′′ (∼ 100km3a-1).

Both mass loss and grounding line migration in Thwaites Glacier accelerate during the second century of retreat. For the H/A/0′′/F simulation, volume above flotation decreases at a mean rate of 75km3a-1 (0.2mma-1SLE) between 2000 and 2100, while the grounding line retreats at a rate ∼1kma-1 across a region featuring a broad area less than 800 m below sea level and a narrow trough between 800 and 1200 m below sea level. Over the following century, the grounding line crosses a widening region of deeper bedrock (>1200 m below sea level), so that the greater rate of flow associated with thicker ice at the grounding line is integrated over a broadening front. The average rate of grounding line retreat grows to ∼2kma-1, and the rate of loss of volume above flotation to 320km3a-1 (0.9mma-1SLE). A similar calculation of accelerating mass loss, with losses of less than 0.25mma-1SLE during the 21st century and up to 1mma-1SLE thereafter was reported by .

Variation between the remaining ASE projections, dominated by Pine Island Glacier, is due to both ocean forcing and initial conditions. Neither the control nor the control′′ simulations exhibit as much grounding line retreat in Pine Island Glacier as those with enhanced melt rates, with the control grounding line holding its initial position and the control′′ grounding line retreating by around 50 km over 200 years. In contrast, the FESOM-forced simulations all see the grounding line retreat by 60 km in the 21st century and a further 160 km in the 22nd century. The H/A/0′′F simulation, which employs the RACMO2 surface mass balance rather than a synthetic mass balance, loses volume above flotation at a rate rising from 70 km3a-1 over the 21st century, comparable to rates computed in other modeling studies , and present-day observations . Grounding line retreat slows toward the end of the 21st century around a bedrock rise and stronger bed 60 km upstream from the present-day position , after which increase in melt rates from around 2100 drives the grounding line over this stabilizing region and into the deeper beds upstream. From then on, volume above flotation losses increase to 150 km3a-1. Applying uniform melt rates of 16ma-1 pushes the glacier over this region earlier, but the mean rate of volume loss still increases, from 110 to 170 km3a-1 in the 0′′/U16 experiment.

The Weddell Sea ice streams feeding the Filchner–Ronne Ice Shelf speed up and lose mass in response to the FESOM melt rates from the mid 21st century, thinning faster in the 22nd century and faster still in the 23rd. The H/A/0/F experiment sees 22nd-century grounding line retreat in the Evans, Möller, Institute and Foundation Ice Streams, with the remaining ice streams starting to retreat only after 2200. Figure  shows the corresponding loss of volume above flotation, increasing from 20km3a-1 (5 mm SLE per century) over the 21st century through 60km3a-1 (15 mm SLE per century) over the 22nd – a rate comparable to Pine Island Glacier in the 21st century. Although the melt rate anomaly is held at its late-22nd century values over the 23rd century, the rate of retreat continues to increase, reaching 210km3a-1 (50 mm SLE per century).

All of the ice streams respond immediately to the higher melt rates imposed in the uniform melt rate experiments. Grounding line retreat is most apparent in the Evans, Möller and Institute Ice Streams, but even the narrow Rutford Ice Stream and Carlson Inlet see grounding line migration over 50 km or more by 2200. Rates of retreat in the Evans, Möller and Institute Ice streams are comparable to rates of retreat, given the same forcing, in Thwaites and Pine Island Glacier, while volume loss in the two regions is similar over the 21st century: 220 vs. 180km3a-1 and somewhat lower in the 22nd century: 340 vs. 500km3a-1.

The Möller and Institute Ice Streams exhibit a century-long period of accelerated retreat in all of our simulations, though its onset varies considerably. The H/A/0/F experiment shows some retreat from 2100–2200 in response to the FESOM projection of increased melt rates under the Filchner–Ronne ice shelf, but from 2200 onward the grounding lines of the two ice streams merge and then migrate across the bulk of the deep-bedded Robin Sub-glacial Basin in a single century to reach down-sloping beds by 2300 CE (Fig. ). At the same time, the Bungenstock ice rise is isolated and then floats. Compared to that, retreat begins right away in the 0/U16 experiment, reaches the down-sloping bed by 2100 CE, and retreats little more after that, while the 0/U8 calculation produces a similar period of retreat starting in 2050. Figure  shows the change in volume above flotation for each of these simulations: all three sustain a maximum rate of volume loss, approximately 210km3a-1, for the hundred-year period corresponding to this retreat. These streams, it would seem, are close to marine ice sheet instability as seen in and can be forced into unstable retreat by physically plausible (FESOM) melt rates. We compute faster retreat here than simply because the melt rates are greater.

The Siple coast ice streams feeding the Ross Ice Shelf lose up to 50 mm SLE by 2100 and 150 mm SLE by 2200 in response to increased melt rates, but respond less to melt rates derived from FESOM. Figure  shows the mass loss trend for the control, H/A/0/F, 0/U16 and U/08 experiments, and grounding lines are shown for the first three in Fig. . The MacAyeal, Bindschadler, Mercer and Whillans ice streams all flow over retrograde beds and exhibit ∼1kma-1 grounding line retreat in the 0/U16 and U/08 experiments and lose volume above flotation at a rate of around ∼200km3a-1. Although the Mercer and Whillans ice streams do retreat in response to the H/A/0/F experiment, they retreat in a similar fashion in the control experiment. Both the H/A/0/F and control grounding lines sweep across an area which is lightly grounded in the model's initial state but just floating in (for example) Bedmap2 . The MacAyeal and Bindschadler ice streams do start to retreat around 2150, when the FESOM melt rates grow to 10ma-1 in the region of Roosevelt Island; that retreat is sustained, and accelerates, until the end of the experiment in 2300. The accompanying loss of volume above flotation amounts to about 60km3a-1. There is little retreat apparent in the inactive Kamb ice stream in any of the experiments.

Marie-Byrd Land shows little sign of retreat in the H/A/0/F experiments, amounting to around 0.5×103km3 (1.5 mm SLE), despite the elevated melt rates imposed from 2100 onward. Even when uniform 16ma-1 melt rates are imposed across the ice shelves, the grounding line retreats by only a few kilometers over the 200 years, with an accompanying loss of volume above flotation of 1.6×103km3 (5 mm SLE). It is apparent in Fig.  that the present-day grounding line in this region runs perpendicular to a down-sloping bed, with much of the bed above sea level, so there is no possibility of marine ice sheet instability. As a result, we might not expect to see century-scale retreat. On the other hand, all of the glaciers in this region are rather narrow, which leaves the possibility that they are under-resolved even at Δxmin=625m, and their beds are inevitably under-resolved by the sparse bedrock data in this region .