In the past few decades, glaciers in West Antarctica and the Antarctic Peninsula (AP) have experienced rapid regional atmospheric and oceanic warming, leading to significant retreat and disintegration of ice shelves and rapid acceleration of mass discharge and dynamic thinning of their feeding glaciers (Cook et al., 2016; Gardner et al., 2018; Wouters et al., 2015). Most of the West Antarctic Ice Sheet and the glaciated margins of the AP (Fig. 1a) rest on a bed below sea level sloping down towards the ice sheet interior, and the grounding lines of outlet glaciers located on such reverse bed slopes may be vulnerable to rapid retreat depending on the bedrock and ice shelf geometry (e.g. Gudmundsson, 2013; Gudmundsson et al., 2012; Schoof, 2007). Once perturbed past a critical threshold, such as grounding line retreat over a bedrock hump into a region of retrograde slope, the grounding line may continue to retreat inward until the next stable state without any additional external forcing (e.g. Mercer, 1978; Thomas and Bentley, 1978; Weertman, 1974). This marine ice sheet instability has been invoked to explain the recent widespread and rapid grounding line retreat of glaciers in the Amundsen Sea sector, likely triggered by increased basal melting reducing the buttressing influence of ice shelves (Rignot et al., 2014). Rapid grounding line retreat and accelerated flow in these unstable systems leads to significant increases in ice discharge and increased contribution from these marine ice sheets to sea-level rise.

The former Wordie Ice Shelf (WIS; Fig. 1b) on the western coast of AP started its initial recession in 1960s with a substantial break-up occurring around 1989, followed by continuous steady retreat (Cook and Vaughan, 2010; Vaughan and Doake, 1996; Wendt et al., 2010; Zhao et al., 2017). The former ice shelf is fed by three tributaries as shown in Fig. 1b. The Fleming Glacier (FG; Fig. 1b), as the main tributary glacier, splits into two branches: the main branch to the north and the southern branch (hereafter “southern FG”). The floating part in front of the main FG disappeared almost entirely sometime between 1997 and 2000 (Fig. 1b), and the ice front position in April 2008 (dark blue line in Fig. 1b and c, Wendt et al., 2010) almost coincides with the latest known grounding line position in 1996 (Rignot et al., 2011a). The main branch of the FG has thinned at a rate of -6.25±0.20 m yr-1 near the front from 2008 to 2015, more than twice the thinning rate during 2002–2008 (-2.77±0.89 m yr-1) (Zhao et al., 2017). This is consistent with the recent findings that the largest velocity changes across the whole Antarctic Ice Sheet over 2008–2015 occurred at FG (500 m yr-1 increase close to the 1996 grounding line) (Walker and Gardner, 2017). Time series of surface velocities along the centerline of the FG (extending ∼16 km upstream from the 1996 grounding line) (Friedl et al., 2018) indicate that two rapid acceleration phases occurred: in January–April 2008 and from March 2010 to early 2011, followed by a relatively stable period from 2011 to 2016. During the first acceleration phase in January–April 2008, the front of the FG retreated behind the 1996 grounding line position for the first time (Friedl et al., 2018).

As a marine-type glacier system residing on a retrograde bed with bedrock elevation as much as ∼800 m below sea level (Fig. 1c), the Fleming system is accordingly potentially vulnerable to marine ice sheet instability (Mercer, 1978; Thomas and Bentley, 1978; Weertman, 1974). The acceleration and greater dynamic thinning of the FG over 2008–2015 suggests the possible onset of unstable rapid grounding line retreat (Walker and Gardner, 2017; Zhao et al., 2017), which has been confirmed by Friedl et al. (2018). The speed-up of the FG before 2008 was originally assumed to be a continuing direct response to the collapse of the Wordie Ice Shelf (Rignot et al., 2005; Wendt et al., 2010). Recent studies (Friedl et al., 2018; Walker and Gardner, 2017) have suggested that the recent further glacier speed-up and grounding line retreat could be a direct response to oceanic forcing. The recent acceleration could also be triggered by the continued dynamic thinning passing some threshold. An alternative hypothesis is that the recent changes are reinforced by feedbacks in the dynamics of the evolving glacier, possibly involving the subglacial hydrology. The examination of changes in basal shear stress distributions between 2008 and 2015 in this modelling study provides a first step in exploring possible feedback hypotheses. We explore the potential for these hypotheses in Sect. 5.

By analysing the detailed history of surface velocities, rates of elevation change, and ice front positions from 1994 to 2016, Friedl et al. (2018) suggested that the initial ungrounding of the FG from the 1996 grounding line position (Rignot et al., 2011a) occurred during the first acceleration phase between January and April 2008 and expanded further upstream by ∼6–9 km by 2014, which explained the speed-up and thinning of the FG since 2008. They speculated this was mainly the result of unpinning caused by increased basal melting due to the greater upwelling of warm Circumpolar Deep Water (CDW). However, this study by Friedl et al. (2018) lacked direct measurements of basal melting and did not perform relevant numerical modelling of the evolution of a sub-ice ocean cavity or coupling to a cavity ocean circulation model, so it is still uncertain whether the enhanced basal melting driven by ocean warming is the dominant reason for the recent changes in the FG. A positive feedback between basal sliding and basal water pressure (through friction heating) upstream of the grounding line could be another possible factor in the glacier acceleration and grounding line retreat (Bartholomaus et al., 2008; Iken and Bindschadler, 1986; Schoof, 2010). The possibility of such a feedback is not ruled out by Friedl et al. (2018) and is discussed further in Sects. 4.2 and 5.

In this study, we employ the Elmer/Ice code (Gagliardini et al., 2013), a three-dimensional (3-D) full-Stokes ice sheet model, to solve the Stokes equations over the whole WIS–FG catchment. Our implementation of the model solves the ice flow equations and the steady-state heat equation (Gagliardini et al., 2013; Gladstone et al., 2014). We also infer the basal shear stress using an inverse method (e.g. Gillet-Chaulet et al., 2016; Gong et al., 2017).

In the first part of this study (Zhao et al., 2018), we explored the sensitivity of the inversion for basal shear stress to the following: enhancement of ice deformation rates, bedrock elevation data, the ice front boundary condition, and initial model assumptions about englacial temperatures. In the current paper, we adopt the three-cycle spin-up scheme of Zhao et al. (2018) to derive the distributions of basal shear stress in 2008 and 2015. We present the observational data in Sect. 2 and our methods in Sect. 3. We compare the resulting basal shear distributions for 2008 and 2015 and their connections with driving stress and basal friction heating in Sect. 4.1 and 4.2. The height above buoyancy for the two epochs is computed in Sect. 4.3 as an independent guide to grounding line changes. Through comparison of basal shear stress and height above buoyancy between 2008 and 2015, we analyse the stability of the grounding line in this period and discuss ongoing marine ice sheet instability and direct oceanic forcing as possible reasons for the speed-up of the FG in Sect. 5.

The modelling method using Elmer/Ice presented in Part 1 of this study (Zhao et al., 2018) is adopted here, including the mesh generation, mesh refinement, model parameter choices and boundary conditions. The simulations for both 2008 and 2015 retain the same assumptions about the ice-covered domain, namely a common spatial extent with fixed ice front location, and the assumption that all the ice is grounded. The ice front position is assumed to coincide with the 1996 grounding line position (Rignot et al., 2011a). This assumption might be incorrect for the main branch of the FG, and we evaluate it based on the deduced floating area where the inferred basal shear stress is lower than a threshold, which is discussed in Sect. 4.1. It is very clear from satellite imagery that in 2008 a small ice shelf is still present in front of the southern FG and the Prospect Glacier (hereafter PG) (Fig. 1c). In 2015 the ice shelf in front of the southern FG disappeared, while the floating part of the PG retreated in the east and re-advanced in the west (Fig. 1c). However, we do not include the floating parts of the southern FG and PG in either epoch in this study, owing to the lack of ice shelf thickness data.

We follow the three-cycle spin-up scheme (Zhao et al., 2018) and simulate the basal shear stress τb in 2008 and 2015 with the linear sliding law: τb=-Cub. Here C is the basal friction coefficient, a variational parameter in the inversion procedure, and ub is the basal sliding velocity.

There are two key differences between the data used for the 2008 and 2015 inversions: increased surface velocity and changed ice geometry, namely a thinner glacier in 2015 compared to 2008 due to dynamic thinning. To explore their relative impacts, we carry out an additional inversion with the geometry from 2008 but the surface velocity from 2015 (see Sect. S1 in the Supplement). We find that both geometry variations and velocity changes are important to the inverted basal stress condition.

To explore the relationship between the basal shear stress and local gravitational driving stress τd, the gravitational driving stress is also computed for both epochs: τd=ρigH∇zs, where ρi is the ice density, g is the gravitational constant, H is the ice thickness, and ∇zs is the gradient of the ice surface elevation. Considering the snow and firn on the ice surface, we apply a relatively low ice density of 900 kg m-3 following Berthier et al. (2012).

Hoffman and Price (2014) found a positive feedback between the basal melt and basal sliding through the frictional heating for an idealized mountain glacier using coupled subglacial hydrology and ice dynamics models. To explore possible effects of changes of basal frictional heating between 2008 and 2015, we compute the friction heating (qf) generated at the bed: qf=τbub. To explore the possible flow path of subglacial water beneath the FG, we calculate hydraulic potential at the bed, since its negative gradient determines subglacial flow direction. The hydraulic potential, Φ, expressed in equivalent metres of water, is given by Φ=zs-zbρiρfw+zb, where ρfw is the fresh water density (1000 kg m-3), and zs and zb are the surface and bed elevations, respectively. Here we assume that the water pressure in the subglacial hydrologic system is given by the ice overburden pressure, which is equivalent to assuming that the effective pressure at the bed, N, is zero (Shreve, 1972).

Height above buoyancy (Z*) is an indicator of how close to floatation a marine-based glacier is, which is relevant to the glacier's evolution and additionally helps identify likely floating regions. Z* is related to the effective pressure N at the bed by the following relationship: N=ρigZ*. In this study, we use a simpler hydrostatic balance based on sea level with the following relationship: Z*=H,ifzb>=zslH+zb-zslρwρi,ifzb<zsl, where ρw is the density of ocean water and zsl is the sea level. This expression for Z* assumes a perfect connectivity of the basal hydrology system with the ocean. This is appropriate for the present study where we are exploring the degree of grounding of the fast-flowing regions of the FG over the downstream basin.

The sticky spots of high basal shear stress near the terminus of the FG in 2008 might be artefacts, but the possibility that this high friction area is a real feature due to some pinning points is not excluded. If the high basal resistance spots are artefacts, ungrounding of this region in early 2008 is less viable as an explanation for an abrupt increase in ice flow speed, since the loss of backstress would be more gradual. In this case, positive feedbacks, such as the marine ice sheet instability or the subglacial hydrology feedback, are even more likely to explain the FG's recent behaviour. If the sticky spots are real features, the implication is that the ice front was at least partly grounded in early 2008. This interpretation is consistent with the relatively high bedrock topography near the ice front compared to upstream (Fig. 1c). Friedl et al. (2018) proposed that the grounding line of the FG after January–April 2008 must have been located upstream of the 1996 grounding line from their interpretation of abrupt surface acceleration detected around the same period. This is also confirmed by the fact that the glacier front had retreated behind the 1996 grounding line during the acceleration phase (Friedl et al., 2018). However, it is possible that this grounding line retreat occurred after January 2008, when our DEM2008 was acquired. The analysis of height above buoyancy for DEM2008 and inferred basal shear stress in 2008 support the main FG being grounded close to the ice front and hence near the 1996 grounding line location. Given the uncertainties of grounding line position in 1996 (several kilometres) (Rignot et al., 2011a) and uncertainty about interpreting the frontal high basal friction area in this study, the exact grounding line position in January 2008 is somewhat uncertain. Improved bed topography–ice thickness data and accurate historic ice front position are necessary to interpret the precise grounding line position in 2008. Detailed bathymetry of the relevant location might become available if the ice front of the FG retreats in future.

The disappearance of the inferred high basal shear region (possible physical pinning points) near the FG front between 2008 and 2015 is a possible trigger for the sudden acceleration and increased surface lowering of the FG during this period. The increased flux of ice, combined with the changed glacier geometry, suggests the substantial grounding line retreat, which agrees with two recent studies (Friedl et al., 2018; Walker and Gardner, 2017). The timing of the acceleration, which occurred in January–April 2008 (Friedl et al., 2018), suggests that the loss of this basal resistance occurred shortly after the first epoch we analysed (January 2008). Given the low basal friction already present over most of the downstream basin (a possible cavity proposed by Friedl et al., 2018), one would expect the loss of the localized friction near the ice front to promptly result in an increase in velocity over the entire low-friction region. This is consistent with the near-uniform increase in velocity in April 2008 for a region 4–10 km upstream of the 1996 grounding line reported by Friedl et al. (2018).

For a glacier lying on a retrograde slope in a deep trough, the grounding line may be vulnerable to rapid retreat without any further change in external forcing, once its geometry crosses a critical threshold, which is the marine ice sheet instability hypothesis (e.g. Mercer, 1978; Thomas and Bentley, 1978; Weertman, 1974). A similar theory has been proposed on the prospective rapid retreat of Jakobshavn Isbræ in West Greenland without any trigger after detaching from a pinning point (Steiger et al., 2017). The FG grounding line in early 2008 may have experienced a retreat after moving across the geometric pinning points near the front, and then retreated further to the position about 9 km upstream in the FG downstream basin by 2015. This has been proven by Friedl et al. (2018), and they also suggested that a further stage of grounding line retreat of the FG may have happened between March 2010 and early 2011. A similar ungrounding process has been detected in the Thwaites, Smith and Pine Island glaciers from 1996 to 2011 (Rignot et al., 2014).

The current grounding line of the FG (Friedl et al., 2018) appears to be on the prograde slope of the bedrock high between the FG downstream and upstream basins. With the establishment of an ocean cavity under the new ice shelf we can expect that ocean-warming-driven basal melting will further modify the thickness of the recently ungrounded ice. If the system remains out of balance and continues to thin, the grounding line could eventually move across this bed obstacle. If this occurs, the grounding line is then likely to retreat rapidly down the retrograde face of the FG upstream basin, likely to be accompanied by further glacier speed-up and dynamic thinning.

Walker and Gardner (2017) attribute the significant increase in observed ice velocity and drop in surface elevation from 2008 to 2015 to increased calving front melting caused by incursion of relatively warm Circumpolar Deep Water (CDW). The CDW flows onto the continental shelf within the Bellingshausen Sea, penetrating into Marguerite Bay, driven by changes in regional wind patterns resulting from global atmospheric circulation changes (Walker and Gardner, 2017). Friedl et al. (2018) also explain both the unpinning from the 1996 grounding line position in 2008 and further landward migration of the grounding line in 2010–2011 with the same mechanism, namely the increased basal melting due to ocean warming. This explanation appears consistent with the finding that the acceleration, retreat, and thinning of outlet glaciers in the Amundsen Sea embayment (ASE) are triggered by the inflow of warm CDW onto its continental shelf and into sub-ice-shelf cavities (Turner et al., 2017). However, the floating parts of the FG remained negligible in 2008 as indicated in Sect. 4.3 (Fig. 6a). The speed-up and ungrounding occurring in the ASE glaciers was a direct response to significant loss of buttressing caused by ice shelf thinning and grounding-line retreat (Turner et al., 2017). When the CDW incursions started in the ASE, the floating parts of ASE glacier systems were much larger than the residual ice shelf of the Fleming system in 2008. After the recent changes the newly floating region of the FG had an area of ∼60 km2, based on the estimated 2014 grounding line from Friedl et al. (2018) and the 2016 ice front position in this study, which is consistent with our height above buoyancy analysis for 2015 (Fig. 6b). So, significant buttressing reduction is not likely to have occurred on the FG during the rapid acceleration of 2008, but further changes to the FG after 2015 may resemble ASE glacier and ice shelf systems more closely. No direct measurements are available to confirm the direct effect of the frontal or basal melting on the FG grounding zone over this period, nor have previous studies attempted to quantify the amount of melting required to drive significant FG grounding line retreat. The ocean-driven basal melting at the ice shelf front or base may have contributed to grounding line retreat, or the reduction of the frontal high basal shear zone, but establishing this as the main cause would require further quantification of the cause–effect link.

Ongoing thinning as a result of backstress reduction following the collapse of the WIS is another possible cause of the recent ungrounding. The WIS evolved from an embayment-wide ice shelf in 1966 to smaller individual remnant ice shelves in 1997 (Fig. 1b) (Cook and Vaughan, 2010; Wendt et al., 2010). The floating part of the FG in particular was in the form of an ice tongue in 1997 (Cook and Vaughan, 2010) and as such would likely have imposed much lower backstress on the grounded part. Point measurements indicate that the FG accelerated by 40 %–50 % between 1974 and 1996 (Doake, 1975; Rignot et al., 2005). If this acceleration was a response to loss of buttressing, the FG system may have been out of equilibrium and losing mass since before 1996. If the increased velocity in response to shelf collapse was maintained over time, maintaining persistent thinning, eventual ungrounding of the bedrock high where the 1996 grounding line was located, would occur independently of ocean-induced increased shelf melt. The recent accelerations and enhanced thinning (Friedl et al., 2018; Gardner et al., 2018; Walker and Gardner, 2017) may indicate an ongoing response to the WIS collapse, amplified by positive feedbacks within the FG system.

Rapid sliding at the base is dependent on the presence of a sub-glacial hydrologic system. Evidence suggests that increased basal water supply could accelerate basal motion of both mountain glaciers (Bartholomaus et al., 2008) and ice sheets (Hoffman et al., 2011), presumably by changing the subglacial water pressure or bed contact, and further contribute to grounding line retreat of marine-based glaciers. Jenkins (2011) has also suggested that subglacial water emerging at the grounding line can enhance local ice shelf basal melt rates by initiating buoyancy-driven plumes in the ocean cavity. The rapid sliding and high friction heating in the upstream FG (Fig. 4a and b), together with the direction of the hydraulic potential gradient (Fig. 5), provide evidence for an extensive active hydrologic system beneath the FG, which might already have been enhanced by the previous significant WIS collapse that occurred before 2008.

High basal friction heating in the fast-flowing regions of the FG is the main source of meltwater flowing into the FG downstream basin. It is also clear that the friction heating in 2015 was greater than in 2008 in the upstream basin (Fig. 4c), with the increase in basal meltwater production peaking over the bedrock rise between the downstream and upstream basins (see Sect. S2 and Fig. S4). The plateaus in hydraulic potential in both downstream and upstream basins of the FG (Fig. 5b) suggest the possibility that basal water may accumulate in those regions, or at least show a low throughput. The downstream plateau appears to be fed by a large frictional heat source over the ridge between the downstream and upstream basins in addition to flow from further inland, while the upstream plateau appears to be fed by an extensive upstream region of basal melting. There might have been some pooling of water in those plateaus in 2008, but the inferred basal shear stress (Fig. 3a) and the height above buoyancy (Fig. 6a) indicate that those regions should still remain grounded. According to our hydraulic potential calculations (Fig. 5b), outflow from the upstream plateau region is likely to be predominantly in the direction of the downstream basin, but future outflow across the shallow saddle in hydraulic potential towards the southern branch of the FG cannot be ruled out, since the evolution of the potential responds to the changing elevation (Fig. 2a) as discussed above.

The further abrupt speed-up events that occurred in 2010–2011 reported by Friedl et al. (2018) could have several potential causes in addition to the previously proposed mechanism of a direct response to ocean-induced melting (Walker and Gardner, 2017). One possibility is an outburst of subglacial water from the upstream basin after building up over years to decades in response to increased sliding and friction heating and progressive lowering of the ice surface. Another possibility is local unpinning near the retreating grounding line: ungrounding from pinning points may cause a step reduction in basal resistance. This unpinning could be a feature of ongoing thinning in response to WIS collapse, as discussed above. Another possible cause could be a positive feedback in the subglacial hydrologic system – rapid change may result from the direct feedback between changes in sliding speed, friction heat and basal water production, as discussed in Sect. 4.2.

The height above buoyancy is an indicator of the vulnerability of marine-based grounded ice to dynamic thinning and acceleration. The area with Z*<20 m in 2015 has shown that the downstream basin is currently ungrounding, and this may continue until the grounding line finds a stable position on the prograde slope separating the two major basins. More thinning would be needed to destabilize the upstream basin, and it is hard to estimate how much forcing would be needed to push the grounding line into the upstream basin boundary. If the retrograde slope of the upstream basin is reached, further rapid and extensive grounding line retreat would be expected. A clear decrease can be seen in Z* from 2008 (red in Fig. 6a) to 2015 (dark red in Fig. 6b) in the upstream basin (around the 2008 velocity contour of 1000 m yr-1), indicating the potential vulnerability of the FG to continued ice mass loss. The surface lowering rate between 2008 and 2015 in this region is ∼4.6 m yr-1 (Zhao et al., 2017). If this thinning rate continues, the ice in regions with Z*  of 200–300 m would be expected to unground in ∼45–65 years. This could take a longer or shorter period since the future thinning rate cannot be expected to remain constant.

In the absence of precise and accurate knowledge of bed topography and ice shelf/stream basal processes, the cause of the recent FG ungrounding cannot be determined. Further research is necessary to better understand the interplay of a range of possible mechanisms.

We used a full-Stokes ice dynamics model (Elmer/Ice) at high spatial resolution to estimate the basal shear stress, temperature and friction heating of the Wordie Ice Shelf–Fleming Glacier system in 2008 and 2015. Both increased surface velocity and surface lowering during this period are important for the calculation of basal shear stress.

Decreased basal friction from 2008 to 2015 in the Fleming Glacier downstream basin indicates significant grounding line retreat, consistent with change in the suggested floating area based on the geometry in 2015 and the deduced grounding line in 2014 from Friedl et al. (2018). Grounding line retreat also occurred on the southern branch of the FG. Our height above buoyancy calculations also indicate the FG downstream basin was close to flotation in 2015 and is vulnerable to continued ice thinning and acceleration.

Pronounced basal melting driven by oceanic warming in Marguerite Bay may have triggered the ungrounding of the Fleming Glacier front in early 2008, as previously suggested by Walker and Gardner (2017) and Friedl et al. (2018), but ongoing thinning following the collapse of Wordie Ice Shelf may also provide an explanation. In either case, feedbacks in the subglacial hydrologic system may be a significant factor in reducing basal shear stress, leading to rapid increases in basal sliding and ongoing ungrounding. The derived basal shear stress distributions suggest a major influence could have been the ungrounding of some sticky spots of higher basal shear near the ice front of the main Fleming Glacier, as basal friction under most of the region considered afloat by 2015 was already low in 2008 (a possible subglacial cavity).

The marine-based portion of the Fleming Glacier extends far inland. It is not clear whether grounding line retreat into the Fleming Glacier upstream basin will occur without further forcing. Transient simulations with improved knowledge of bed topography are necessary to predict the movement of the grounding line and how long it will take to achieve a new stable state. Coupled ice sheet ocean modelling will be required to explore the evolution of the ice shelf melting and impact of buttressing from the remaining and new ice shelf on the grounded glacier. Future studies of the dynamic evolution of the Fleming Glacier system will enhance our understanding of its vulnerability to marine ice sheet instability and provide projections of its future behaviour.