Journal of Geophysical Research: Earth Surface

Dynamic (in)stability of Thwaites Glacier, West Antarctica

Authors


Corresponding author: B. R. Parizek, Mathematics and Geoscience, The Pennsylvania State University, DuBois, PA 15801, USA. (parizek@psu.edu)

Abstract

[1] Thwaites Glacier, West Antarctica, has the potential to directly contribute ∼1 m to sea level and currently is losing mass and thinning rapidly. Here, we report on regional results for the Sea-level Response to Ice Sheet Evolution (SeaRISE) experiments and investigate the impact of i) spatial resolution within existing data sets, ii) grounding-zone processes, and iii) till rheology on the dynamics of this outlet glacier. In addition to the SeaRISE data sets, we use detailed aerogeophysical and satellite data from Thwaites Glacier as input to a coupled ice stream/ice-shelf/ocean-plume model that includes oceanic influences across a several kilometers wide grounding zone suggested by new, high-resolution data. Our results indicate that the ice tongue provides limited stability, and that while future atmospheric warming will likely add mass to the surface of the glacier, strong ice stream stabilization on bedrock highs narrower than the length of the grounding zone may be ephemeral if circulating waters substantially reduce basal resistance and enhance melting beneath grounded ice within this zone. However, we find that stability is significantly enhanced by effectively plastic till beds. Accurate projections of future sea level change relies on correct understanding of the till rheology as well as local basal processes near the grounding line.

1 Introduction

[2] A complete collapse of the West Antarctic Ice Sheet (WAIS), including dynamic feedbacks, would lead to a eustatic sea level rise of ∼5 m, with ∼3 m from regions that can be removed rapidly through increased iceberg calving [Bamber and Riva, 2009a]. Recent modeling indicates that the major sectors act in unison, suggesting that the ∼3 m of marine-based ice are vulnerable on timescales that may be as short as one to a few centuries [Pollard and DeConto, 2009].

[3] The Amundsen Sea Embayment (ASE), fed by Thwaites Glacier (TG), Pine Island Glacier, and smaller glaciers, represents one of three principal outlet systems of WAIS [Thomas, 1979]. The submarine bed, deepening inland beneath ASE ice [Holt and Blankenship, 2006; Vaughan and Corr, 2006], allows the marine ice sheet instability that can trigger rapid deglaciation (Figure 1). Recent satellite data show that the ASE's contributions dominate the accelerating sea level rise from WAIS [Velicogna and Wahr, 2006; Shepherd and Wingham, 2007; Rignot et al., 2008; Shepherd et al., 2012]. Furthermore, warm circumpolar deep water has relatively easy access to the grounding zones in the ASE [Jenkins et al., 1997; Rignot and Jacobs, 2002; Shepherd et al., 2004; Walker et al., 2007; Pritchard et al., 2009; Jenkins et al., 2010; Arneborg et al., 2012], driving ice-shelf basal melt rates that may be sufficient (in conjunction with more modest melting beneath the larger Ross and Filchner-Ronne ice shelves) to initiate WAIS collapse [Pollard and DeConto, 2009] and that are likely to increase [Sen Gupta et al., 2009; Hattermann and Levermann, 2010; Gillett et al., 2011; Jacobs et al., 2011; Yin et al., 2011]. Given the significant potential for the ASE to impact sea level over the next few centuries, we focus on the dynamic response of TG.

Figure 1.

(a) IceBridge flight lines (gray) used in this study plotted over surface elevation. A digital elevation model [Bamber and Gomez-Dans, 2009b; Griggs and Bamber, 2009; Le Brocq and Payne, 2010] is overlain on Moderate Resolution Imaging Spectroradiometer (MODIS) mosaic of Antarctica [Haran and Bohlander, 2005]. Grounding (where the ice loses contact with the bedrock at low tide; yellow) and hydrostatic (where the ice is in hydrostatic equilibrium or freely floating; cyan) lines are from Antarctic Surface Accumulation and Ice Discharge (ASAID) [Bindschadler and Choi, 2011]. Velocities (contours) are from interferometric synthetic aperture radar [Joughin and Tulaczyk, 2009]. Flowband boundary and central flow line are depicted with white and red circles, respectively. Gray dots mark the farthest inland onset of basal hyperbolae indicative of basal crevassing. Profiles plotted in Figure A1 and A2 are plotted in solid (Figure A1a and A2a) and dashed (Figure A1b and A2b) white boxes. Projection is polar stereographic with latitude of true scale at −71°S. (b) Bed topography/bathymetry (colormap and contours) of the Amundsen Sea Embayment [Holt and Blankenship, 2006; Le Brocq and Payne, 2010]. Grounding (yellow) and hydrostatic (cyan) lines are from ASAID [Bindschadler and Choi, 2011]. IceBridge flight lines used in this study are in black [Krabill, 2009]. Flowband boundary and central flow line are depicted with white and black circles, respectively. Profiles plotted in Figure A1 and A2 are plotted in solid (Figure A1a and A2a) and dashed (Figure A1b and A2b) gray boxes. Projection is polar stereographic projection with true scale at −71°S.

[4] Mercer [1968, 1978] first warned of WAIS instability potentially causing large, rapid sea level rise. In the so-called “marine ice-sheet instability” [Weertman, 1974; Schoof, 2007], retreat of a submarine grounding line for a glacier whose bed deepens inland will result in thicker ice at the onset of flotation, leading to higher spreading stress, faster flow, thinning, and greater retreat in an unstable positive feedback cycle. Stabilizing feedbacks thus are required for a steady grounding line on an inland-deepening submarine bed such as that of TG [Parizek and Walker, 2010; Jamieson and Vieli, 2012].

[5] Stabilization can be achieved via buttressing from ice-shelf friction [Thomas, 1979; Dupont and Alley, 2005; Parizek and Alley, 2010; Parizek and Walker, 2010], enhanced drag due to narrowing of ice flow in the vertical [Anandakrishnan and Catania, 2007; Alley and Anandakrishnan, 2007; Parizek and Walker, 2010] and/or horizontal [Jamieson and Vieli, 2012] directions, or by the effects of self-gravitation on sea level [Gomez and Mitrovica, 2010]. For TG, the small, heavily fractured ice shelf likely exerts limited back-pressure on the inland ice [Rignot, 2001; MacGregor and Catania, 2012]. The deep basal topography and lack of confining fjord walls (supraglacial or subglacial) (Figure 1) are unfavorable for future formation of a large ice shelf that would supply significant back-pressure. The bedrock slopes (O(10°)) are sufficiently steep to overcome self-gravitational stabilization, the local fall in sea level caused by the reduced gravitational attraction of shrinking ice for adjacent water [Gomez and Mitrovica, 2010]. Thus, on the few-hundred-year timescales of interest here, occupation of a topographic high within a region of convergent flow appears to be the most likely stabilization mechanism to prevent retreat of TG inland along its subglacial valley.

[6] We have conducted additional model runs addressing ice flow in this setting while participating in the community-organized SeaRISE experiments [Bindschadler et al., 2013; Nowicki et al., 2013a, 2013b]. SeaRISE seeks to use existing models to provide insights into ice sheet sensitivity and guidance to future model development through a suite of simulations with moderate-to-extreme forcing scenarios over the next 100–500 years. By studying TG under a range of forcings (Figure 2), we analyze potentially destabilizing processes (some well known and some poorly parameterized) in order to i) determine if the inherent stability offered by convergent flow over topographic “bumps” is likely to prohibit dramatic dynamic changes in the coming centuries and, if not, ii) provide additional guidance on targeted data collection and process understanding to improve upper-bound estimates of the cryospheric contribution to eustatic sea level.

Figure 2.

Schematic diagram of the model domain (based on Figure 2 in Parizek and Alley [2010]). Ice: 2-D flow line with longitudinal and vertical shear stresses, parameterized side shear, and flowband width. Ocean: Either prescribed SeaRISE melt rates or steady state plume model with equations for continuity, momentum, heat, and salt conservation (modified [Jenkins, 1991]) with entrainment rate from Stigebrandt [1987] and calculated water properties and exchange coefficients as in Holland and Jenkins [1999]).

2 Model

[7] To assess the sensitivity of TG dynamics to the SeaRISE forcings, data set resolution, physical processes within a grounding zone, and till rheology, we use the coupled ice stream/ice-shelf/ocean-plume finite element model of Parizek and Walker [2010]. (For brevity, here we report on the basic components of the coupled model and specific details that are unique to this study; the reader is referred to Parizek and Alley[2010] and Parizek and Walker [2010] for more complete presentations of the standard assumptions and equations.)

2.1 Ice Flow

[8] The two-dimensional (in x and z Cartesian coordinates) ice-flow model assumes a power law, n=3, rheology for ice [Glen, 1955; Budd and Jacka, 1989] as follows:

display math(1)
display math(2)

where inline image and inline image are the deviatoric-stress and strain-rate components, νis the effective viscosity, B is the ice-hardness parameter, and inline image is the effective strain rate. In all simulations, B is variable in position, but static in time. Its value is determined using Table 5.2 in Paterson [1994] after interpolating modern ice temperatures from 3-D model output (Pollard, pers. comm., 2011) onto our flow line domain (Figure 3).

Figure 3.

(top row) Synthetic borehole temperatures spaced every 50 km along the flow line. (bottom row) Ice temperatures interpolated from 3-D model output (Pollard, pers. comm., 2011) and used for ice-softness parameterization and melt rates beneath grounded ice. Basal temperatures are the minimum of model values and the local pressure melting point. Internal temperatures are then taken as the minimum of model output and a linear trend between surface and bed temperatures. Both corrections are to account for a slightly thinner-than-observed model reconstruction.

[9] Using the Petrov-Galerkin method of weighted residuals with linear basis functions and fully implicit time stepping (e.g., Dupont [2004]), we solve the width- and depth-averaged flux form of the continuity equation that includes experiment-specific terms for mass balance at the surface, inline image, and base of the ice, inline image:

display math(3)

where h, inline image, and β are the ice thickness, depth-averaged horizontal velocity, and flowband width, respectively. Beneath grounded ice, spatially variable inline imageare interpolated from 3-D modern reconstructions of TG (Pollard, pers. comm., 2011) and held constant throughout the simulations. A constant width-averaged upstream flux, qo, calculated from velocity [Rignot et al., 2005] and ice-thickness [Bamber and Gomez-Dans, 2009b; Griggs and Bamber, 2009; Le Brocq and Payne, 2010] data sets, serves as the boundary condition. The upstream limit of the flowband is located at the confluence of the TG tributaries (Figure 1). We are therefore simulating the ice flux through the main trunk. When not constrained by satellite data (section 3), the ice-front position evolves based on the mass balance, with a minimum thickness of 10 m, and a free radiation condition applied at the downstream end of the domain [Parizek and Alley, 2010; Parizek and Walker, 2010]. With our parameterization of convergent/divergent flow, (3) becomes a 1.5-dimensional treatment of mass continuity, and (4) serves as a 2.5-dimensional treatment of momentum balance.

[10] The width-averaged horizontal momentum balance is the following:

display math

and includes longitudinal and vertical shear stresses (σxand τxz, respectively) as well as lateral drag, τs. Here, the longitudinal stress is written in terms of deviatoric stresses in the horizontal and transverse direction as well as the full vertical normal stress (inline image). Combining the flow law (1) with the definition of strain rates in terms of velocities and assuming σz=−ρg(sz) for the depth-dependent glaciostatic pressure, the above momentum equation becomes [MacAyeal, 1989; Pattyn, 2002; Parizek and Alley, 2010; Parizek and Walker, 2010] the following:

display math(4)

and is solved using the Galerkin method of weighted residuals with bilinear basis functions. Lateral drag is treated within the momentum balance as a horizontal body force (i.e., side drag is assumed to act within a narrow shear zone and can therefore be parameterized as a boundary-layer phenomenon [Dupont and Alley, 2005; Dupont, 2009; Goldberg et al., 2009; Parizek et al., 2010; Parizek and Walker, 2010]). Any portion of the ice shelf that is beyond the model domain, x>L (where L=265 km is the length of the flowband that ends near the mouth of the embayment), or is thinner than 300 m is assumed to be freely floating and therefore provides no buttressing to the outlet glacier. Due to the dominance of basal drag over lateral drag in this study area (section 3.2), selecting other realistic threshold values somewhat lower than 300 m has minimal impact on ice flow speeds over grounded regions; yet, in some cases, the lower threshold requires slightly stronger forcing to initiate comparable retreat.

[11] While the surface boundary condition is assumed to be stress-free, both drag and normal stress conditions are applied at the base of grounded ice. In floating regions, basal drag is assumed negligible. At the vertical ice front (x=xifL), stress-free and hydrostatic conditions are included above and below the water line, respectively; whereas, at the upstream end (x=0), a time-dependent Dirichlet boundary condition is applied, u(0,t)=qo/h(0,t).

[12] Basal drag of grounded ice, τb=Bbu(b)1/m, is calculated assuming deformation of either a linear viscous (m=1) or effectively plastic (m=8; e.g., Rathbun and Marone [2008]) substrate, with partial-element scaling across the first floating element [Parizek and Alley, 2010]. The spatially variable, yet temporally constant, basal friction coefficient, Bb, is calculated using the basal shear stress distribution from Joughin and Tulaczyk [2009], velocities measured by interferometric synthetic aperture radar [Rignot et al., 2005; Joughin et al., 2009] and the chosen rheology of the till. The resulting Bbfield is then hand-tuned using our ice flow model to arrive at a diagnostic fit to velocities (Figure 4) [Rignot et al., 2005; Joughin et al., 2009] from 1996 and ice and bedrock geometry along our flow line (5 km resolution) from 2003–2008 for the SeaRISE simulations as well as higher resolution 2009 data for our additional experiments [Griggs and Bamber, 2009; Krabill, 2009; Allen, 2009]. As illustrated in Figure 1, the bedrock geometry is variable across our flowband. Width-averaging removes prominent features, with basal highs and lows replaced by increased and decreased Bb, respectively, in this tuning process. Here, we opt to balance the resistance to flow across both of these variables by using the geometry that follows our central flow line, which does not cross the most prominent ridges or the deepest troughs yet includes the character of both.

Figure 4.

Basal friction coefficients are tuned for a model (gray circles) match to interferometric synthetic aperture radar-derived velocities from 1996 (black line) [Rignot et al., 2005; Joughin et al., 2009].

2.2 Ocean Plume

[13] The steady state ocean-plume model includes diagnostic equations for continuity, momentum, and heat and salt conservation based on Jenkins [1991]; Stigebrandt [1987]; Holland and Jenkins [1999]. The sub-ice-shelf cavity is physically and thermodynamically interactive, such that feedbacks between the slope of the ice shelf base and the ocean-plume flow yield temporally and spatially variable melt profiles that can impact grounding line evolution [Walker and Holland, 2007; Little and Gnanadesikan, 2009; Parizek and Walker, 2010].

[14] We use a combination of observations and models to constrain our treatment of the circumpolar deep water (CDW) in the ice shelf cavity. Vertical temperature and salinity profiles collected in the mid-1990s indicate that CDW occupies depths below ∼700 m in Pine Island Bay, forming a layer there that is typically ∼300 m thick [Jacobs and Helmer, 1996; Jenkins and Vaughan, 1997; Walker and Brandon, 2007; Jenkins and Dutrieux, 2010; Arneborg and Wåhlin, 2012]. Additionally, isopycnic-coordinate modeling results suggest that, due to deep bathymetric troughs, the CDW column can reach thicknesses of well over 300 m [Thoma and Jenkins, 2008] in the immediate vicinity of Thwaites Glacier Tongue. However, we limit the thickness of the CDW layer in our model runs to ∼200 m because a bathymetric ridge that lies 40 km seaward of the present grounding line [Tinto and Bell, 2011] can restrict inflow and prevent CDW from filling the entire deep sub-ice-shelf cavity. Situations can be envisioned with either more or less CDW reaching the grounding line, and thus either more or less sub-ice-shelf melting, and might be better constrained given additional data and targeted three-dimensional ocean modeling.

[15] The surface ocean (0–100 m depth) temperature is set at the surface freezing point (−1.8°C), and the bottom layer of CDW is set to a temperature of 1.0°C, with a linear interpolation between these two layers. We assume the same structure for salinity, with values of 33.9 and 34.7 practical salinity unit for the surface and CDW water layers, respectively. We further decrease CDW thickness coming into the ice-shelf cavity by assuming that the column cannot infiltrate beyond ridges that are shallower than the shallowest point of the CDW column, such that the initial ∼200 m thickness of CDW is reduced by the height of any topographic ridges crossed, until no CDW penetrates landward after ridges with a cumulative height of ∼200 m have been crossed. We note that recent observations by Jacobs and Jenkins [2011] indicate that in some regions near Pine Island Glacier, the CDW layer has since warmed and thickened by as much as 0.2°C and 100 m, respectively. With variability likely to continue in this deepwater mass, our ocean settings might alternate between being somewhat conservative and slightly aggressive going into the future.

3 Simulations and Results

[16] The models are run for a configuration approximating TG and the bathymetry in Pine Island Bay (Figure 1). Simulations begin in 1973 (Figure 3 with an additional 10 m ice thickness to account for thinning in subsequent years) and extend to the “present” (year 2004, as designated by SeaRISE) using 2004 atmospheric conditions [Bindschadler et al., 2013; Nowicki et al., 2013a, 2013b], with ice-front position forced by available satellite data through 2011 [MacGregor and Catania, 2012]. In the SeaRISE experiments, the prescribed forcings are initiated in 2004 and continue through 2500 as described in section 3.1. The three decades of spin-up allow early changes in the system, arising from choice of model physics, to relax prior to the 2004 start date, while also including the transient effects of known changes in ice-front position in the century-scale evolution. We note that unless there are nonlinear feedbacks associated with the different forcings, much of this variability will ultimately be removed from the SeaRISE results by the differencing strategy discussed in section 3.1.

[17] In all experiments, along-flow nodal spacing is 1000 m for continuity (3) and adaptive in the ice when solving for momentum (4), ranging from 100 to 1000 m in order to minimize numerical artifacts that affect grounding line migration [Vieli and Payne, 2005; Durand and Gagliardini, 2009; Goldberg and Holland, 2009; Parizek and Alley, 2010]. See Table 1 for a list of the simulations discussed below.

3.1 Simulations: SeaRISE

[18] The SeaRISE experiments [Bindschadler et al., 2013; Nowicki et al., 2013a, 2013b] were designed to assess the sensitivity of ice sheets to forcings at the various exterior boundaries: the i) surface, ii) bed, and iii) floating margin (ice tongue or ice shelf) through changes in climate, basal sliding (lubrication), and ocean dynamics, respectively (Figure 2). Following the experimental guidelines, we initially subject TG to a constant climate (CC) control run (spatially variable inline image are held at 2004 values) that is then compared to the various forcing runs to account for the impact of model transients associated with our choice of initial conditions as well as the brief spin-up to “present.” Furthermore, across all SeaRISE experiments, we assume ice flows over a linear viscous (m=1) substrate.

3.1.1 Surface

[19] During the climate-forcing simulations, 2004 local mean annual surface temperatures and precipitation rates are perturbed with 1 ×, 1.5 ×, and 2 × the monthly anomalies from the ensemble mean of 18 Intergovernmental Panel on Climate Change AR4 climate models for the relatively moderate emissions scenario A1B through year 2097 [T. Bracegirdle, pers. comm., 2009; Solomon et al., 2007] and held constant thereafter (experiments C1, C2, and C3, respectively).

3.1.2 Bed

[20] To test system sensitivity to potential changes in the subglacial hydrologic system, 2 ×, 2.5 ×, and 3 × amplification factors were applied to the spatially variable sliding velocities (forcing experiments S1, S2, and S3, respectively). The perturbations were implemented by altering our basal friction coefficient field to Bb/(21/m), Bb/(2.51/m), and Bb/(31/m), respectively. We note that local reduction of basal resistance is compensated regionally in our higher order model due to the inclusion of longitudinal stresses (cf. models based on the shallow ice approximation). Furthermore, subsequent changes in the ice profile lead to changes in the driving stress. Therefore, the amplification factors do not result in speedups at all times and places, and local speed increases are not necessarily sustained.

3.1.3 Ocean

[21] SeaRISE perturbations at the floating margin are meant to account for changes in regional ocean properties and are simulated by assigning 2 m/yr, 20 m/yr, and 200 m/yr basal melting rates at the last grounded node and all floating nodes downglacier (M1, M2, and M3, respectively). Here, we add an additional simulation (M4) using the coupled ocean-ice models under 1994 [Jacobs and Helmer, 1996] ocean conditions to account for geometric changes in the ice-shelf cavity and spatially variable melt rates.

3.1.4 Multiple Forcings

[22] The last set of SeaRISE experiments includes combination runs to assess potential nonlinear feedbacks in TG dynamics triggered by simultaneous forcings at multiple boundaries. These four simulations test the combination of a) 1 ×AR4 at the surface, 2 × sliding beneath grounded ice, and the coupled ocean-ice model (C1S1M4); b) 1 ×AR4 and double sliding (C1S1); c) 1 ×AR4 and 2 m/yr subshelf melt rates (C1M1); and d) 1 ×AR4 and coupled ocean- ice (C1M4).

3.2 Results: SeaRISE

[23] The prescribed ice-front forcing through 2011 leads to ∼80 years of variability in total ice volume (solid black line in Figure 5a) as well as grounding line migration within an ∼8 km region of the prominent basal high centered at x=145 km (Figure 6a) for the CC control run. Because SeaRISE is interested in the cryospheric impact on eustatic sea level, all remaining ice volume histories in Figure 5 are reported in terms of volume above flotation (VAF). Initially, the VAF within our flowband domain is ∼22.7 mm sea level equivalent (SLE). While there is a mass loss trend for the CC simulation over the first century as the inland ice thins to a steady state configuration (Figure 6a), TG stabilizes thereafter with the grounding line resting on the leeward side of the basal high and an overall ∼18% reduction in VAF from the initial conditions. As previously mentioned, because we are interested in isolating the response of TG to the various SeaRISE forcings (Table 1), VAF for each forcing run in Figures 5b–5e) is the result of the sensitivity simulation minus this CC trend.

Table 1. Simulation Definitions
SimulationsDescription of Forcing
SeaRISE 
CCConstant-climate control run; fixed at 2004 values
C1, C2, C3Climate forcing of 1 ×, 1.5 ×, and 2 × the anomalies
 from ensemble mean of 18 AR4 climate models
 for the A1B emissions scenario
S1, S2, S3Sliding forcing with 2 ×, 2.5 ×, and 3 × amplification
 factors on u(b)
M1, M2, M3, M4Ocean forcing with subshelf melt rates of
 2 m/yr, 20 m/yr, 200 m/yr, and coupled ocean-ice
 models
C1S1M4, C1S1, C1M1, C1M4Combination forcings. See above for the surface,
 bed, and ocean components included here.
Data Resolution and Grounding Zone 
T1C1M4 above with higher resolution topographic
 data around the grounding zone and activation of
 ocean coupling for entire simulation
GZ1, GZ2, GZ3, GZ4, GZ5T1 with enhanced basal melting and reduced friction
 within 5 km, 6 km, 7 km, and 10 km grounding zones.
 GZ5 includes a 6 km grounding zone and the lower
 resolution SeaRISE basal topography.
GZ3PEffectively plastic (m=8) substrate across entire
 domain following forcing of linear viscous (m=1)
 GZ3 run
Figure 5.

Evolution of ice volume in millimeters of sea level equivalent (SLE). (a) CC control run. Over the first several decades, variability in total ice volume (solid black) is due to prescribed ice-front forcing through 2011. Results of the SeaRISE sensitivity simulations are reported as (a) VAF in SLE after subtracting the control run (dashed VAF line) from: (b) climate; (c) sliding and C1S1M4-combination; (d) ice shelf melting; and (e) combination and GZ4 runs, respectively. Positive (negative) values indicate mass gain (loss) for TG relative to the standard run, and therefore a drop (rise) in sea level. See text and Table 1 for simulation descriptions (based on Figures 912 in Bindschadler et al. [2013]; Norwicki et al., [2013a, 2013b]).

Figure 6.

Simulated SeaRISE profiles. Output is displayed every 20 years from model year 1973 to 2500 for the (a) CC control run; (b) C1 (1 ×AR4) climate forcing; (c) S1 (2 ×) sliding; (d) M2 (inline image m/yr) ice shelf basal melting; (e) M4 (coupled ocean-ice); and (f) C1S1M4 combination forcing. The flotation surface is denoted by the dashed line. Initial and final profiles are labeled with their model year and displayed in green and red, respectively.

3.2.1 Surface

[24] In the climate experiments, because surface temperatures are so low in the ASE, warming causes increases in ice accumulation which outpace increases in seasonal surface ablation. With the control run trend removed, the VAF not only increases through the century of AR4 anomalies but continues to rise for an additional ∼150 years under the larger-than-present “year 2097” precipitation forcing before leveling off at a new steady state as the dynamic response balances the additional precipitation (Figure 5b; profiles in Figure 6b are slightly larger than in 6a). Furthermore, as time progresses from 100, 200, to 500 years into the future, the trend between amplification factor and VAF change becomes increasingly linear (Figure 7a), in agreement with results from whole ice sheet models [Bindschadler et al., 2013; Nowicki et al., 2013a, 2013b].

Figure 7.

Sensitivity to SeaRISE forcing magnitude at 100, 200, and 500 years after present (2004) for (a) climate, (b) sliding, and (c) melting experiments. The lower-left and right vertices (open circles) of the shaded triangles in Figure 7c represent the average and maximum inline image, respectively, for the ice shelf at the end of the ME4 simulation. Assuming a linear trend between amplification factor and VAF changes, the vertical arrows illustrate the difference between the predicted and simulated VAF change for a spatially constant 15 m/yr melt rate and spatially variable melt rates with a shelf average of ∼15 m/yr. Similarly, reaching the simulated VAF change with a spatially constant melt rate would require an ∼67% increase to ∼25 m/yr (based on Figures 911 in Bindschadler et al. [2013]; Norwicki et al., [2013a, 2013b]).

3.2.2 Bed

[25] If some perturbation were to occur causing basal lubrication to increase across the domain, then we would expect sliding rates to initially increase until geometric changes sufficiently reduce the regional driving stress. With ice velocities largely controlled by basal motion, the SeaRISE sliding forcings dominate system response. Depending on the amplification factor, there is an ∼18–40% reduction in VAF within the first two centuries (Figure 5c) as surface elevations within the main trunk drop (∼400 m for S1; Figure 6c). Because there is no melt beneath the ice shelf in these sliding simulations, after ∼30, 35, or 45 years beyond 2004 (S1, S2, and S3, respectively), the enhanced flux across the grounding line leads to a thickening ice shelf that grounds on the broad basal high centered at x=200 km. This slows (S3), stops (S2), or even reverses (S1) VAF loss as enhanced buttressing leads to thickening in the grounding zone and a subsequent ∼50 km grounding line advance. The trend between amplification factor and VAF change remains linear at 100, 200, and 500 years (Figure 7b; by 500 years, some of the continent-scale models produce essentially the same VAF change for the S1 and S2 simulations [Bindschadler et al., 2013; Nowicki et al., 2013a, 2013b]).

3.2.3 Ocean

[26] In the experiments in which melting is increased beneath the ice shelf, ice volume changes are of similar magnitude but opposite sign to the climate-forcing runs. As melt rates increase, ice-shelf buttressing decreases and mass loss near the grounding line increases (e.g., Figure 6d and 6e), resulting in a reduction in VAF (Figure 5d). Under the extreme forcing of inline image m/yr (M3), the entire domain deglaciates in less than four decades (Figure 5d). It is important to note that this catastrophic retreat results from applying ice-shelf melting rates at the grounding line as well as beneath the floating shelf. (Total buttressing provided by side shear along the shelf is presently so minimal that a simulation with complete shelf removal, equivalent to rapid melting not reaching the most downglacier grounded point, did not lead to deglaciation past the bedrock high centered at x=145 km.) We consider this to be an important result for achieving the SeaRISE goal of providing limiting estimates of sea level rise and return to it below.

[27] Short of the M3-magnitude forcing, VAF changes increase linearly with spatially constant prescribed melt rates (Figure 7c). However, with the coupled ice-ocean simulation (M4), this linearity breaks down. The lower left vertices of the shaded triangles in Figure 7c represent the volume loss referenced to the average melt rate for the ice shelf (∼15 m/yr). As peak melt rates (∼40 m/yr, lower right vertices) are concentrated near the grounding line, spatially variable melt leads to efficient removal of the ice shelf (cf. Figure 6d and 6e) [Little et al., 2009; Walker and Holland, 2007; Parizek and Walker, 2010] and a nonlinear response to the average melt magnitude (roughly 50–70% more volume loss than a linear trend would predict for a spatially constant 15 m/yr melt rate; see arrows in Figure 7c).

3.2.4 Multiple Forcings

[28] Forcings are rarely isolated in nature, with dynamic feedbacks either amplifying or diminishing system response to multiple forcing fields. Figure 5e displays VAF results from our combination experiments. The relative insensitivity and opposing response of the system to surface climate and ocean forcings are evident by the nearly flat-lined responses to the C1M4 and C1M1 experiments. When comparing the ratio of VAF for these combination runs to the sum of the VAF histories for the isolated experiments (e.g., Figure 8c), the ratios are within 10% of unity for nearly the entire simulation. The largest excursions occur during the earliest part of the simulations when the values in the ratio are nearly equal and close to zero. Therefore, small changes in either value lead to large deviations in the ratio. Furthermore, early in the simulations, variations in VAF are dominated by system response to the ice-front forcing and are doubly counted in the sum of the single-forcing runs.

Figure 8.

Ratio of VAF histories as an indicator of dynamic feedbacks. Results from the combination forcings (Figure 5e) are divided by the sum of the individual component runs (Figures 5b, 5c, and 5d): (a) C1S1M4/(C1+S1+M4); (b) C1S1/(C1+S1); and (c) C1M4/(C1+M4). Because of the sign convention in Figures 5b–5e, ratios greater (less) than unity indicate feedbacks lead to additional (reduced) sea level rise. See text and Table 1 for simulation descriptions (based on Figure 12 in Bindschadler et al. [2013]; Norwicki et al., [2013a, 2013b]).

[29] Feedbacks become evident once enhanced sliding is included. When 2 × sliding and 1 ×AR4 warming are simultaneously introduced (C1S1), the result is initially dominated by the mass loss due to enhanced sliding. However, as the ice surface is lowered into a warmer level of the atmosphere amidst a warming climate, accumulation rates increase beyond those in the C1 experiment. The additional ice leads to a dynamic response as the grounding line advances. The increased basal drag results in additional thickening and ultimately an ∼11 km advance on the local bedrock high. The final VAF contributes roughly 1 mm SLE less ice to the ocean than the S1 experiment (which is ∼16× the SLE gained by C1 alone; Figure 5a, 5b, and 5e). The feedback is also evident in Figure 8b, where the VAF loss in the combination run is nearly 23% lower than the VAF loss in S1 combined with the minor gain in C1.

[30] The significant role dynamic feedbacks can play becomes especially evident when analyzing our C1S1M4 results (Figures 5c and 5e). Here, VAF loss for TG nearly doubles the S1 loss and approaches the S3 magnitude, even though the response to the combination of C1 and M4 essentially canceled each other (recall C1M4 near-zero VAF results). The more than 76% increase in VAF lost by C1S1M4 compared with the sum of the C1, S1, and M4 simulations (Figure 8a) arises because the coupled ice-ocean forcing leads to a much smaller ice shelf that never grounds on the basal high centered at 200 km along flow (cf., Figures 6c and 6f).

3.3 Simulations: Sensitivities to Data Resolution and Properties in the Grounding Zone

[31] TG is now grounded on a prominent bedrock sill. In the SeaRISE experiments described above, whether or not this sill provides stability against rapid oceanic warming depends on the details of the model treatment of the grounding zone. Removing the ice shelf, equivalent to greatly increased melting beneath floating ice but no change in melting beneath grounded ice across a discrete grounding line, has little influence on TG. However, the entire domain deglaciates in only 40 years if a smaller but still substantial increase in melting is applied not only to the floating ice but also to the node at the grounding line. Numerically, this is equivalent to a grounding zone of the same length as the last grounded finite element (typically 1 km), with the melt rate increasing from near zero at the upglacier end to the ice-shelf value (200 m/yr) at the downglacier end.

[32] As discussed in the appendix, physical understanding plus the limited available data show that a grounding zone is physically more accurate than a grounding line. This motivates an additional suite of experiments, exploring how the effects of moderate oceanic warming depend on extent and other characteristics of the grounding zone. Within a range of behaviors that we do not believe are excluded by available data, we find both near-stability and notable instability. This indicates that improved data, physical understanding, and modeling of grounding zones will be required to provide accurate projections of sea level rise.

3.3.1 Data Resolution

[33] With 5 km spatial resolution, the gridded Antarctic data sets used in SeaRISE are significantly refined compared to the ∼20–80 km nodal spacing that was historically used by whole ice sheet models when simulating the Antarctic ice sheets. In most regions of Antarctica, however, this resolution is only made possible through interpolation. Even with the ∼15 km Airborne Geophysical Survey of the Amundsen Sea Embayment, coverage over TG [Holt and Blankenship, 2006], the data are still likely too coarse to resolve important basal features and to accurately simulate grounding line migration [Vieli and Payne, 2005; Durand and Gagliardini, 2009; Goldberg and Holland, 2009; Parizek and Alley, 2010]. To test this assertion, within an ∼35 km region upstream of the grounding line, our 1 km grid captures significant variations in basal topography that are observed in the Operation IceBridge data sets that were collected in November 2009 (Figure 9) [Krabill, 2009; Allen, 2009; Leuschen, 2010]. Where Operation IceBridge data were unavailable, we substituted the coarser SeaRISE data set [Bamber et al., 2009b; Griggs and Bamber, 2009; Le Brocq et al., 2010; Bindschadler et al., 2013; Nowicki et al., 2013a, 2013b].

Figure 9.

TG initial profile. The resulting geometry is a combination of 5 km resolution SeaRISE data sets (bedrock in dashed red) [Bamber et al., 2009b; Griggs and Bamber, 2009; Le Brocq et al., 2010; Bindschadler et al., 2013; Nowicki et al., 2013a, 2013b] outside of an ∼35 km region upglacier of the modern grounding line and 11.7 m resolution surface elevation from swath laser altimetry [Krabill, 2009] and bed elevation from ice-penetrating radar (solid cyan lines) [Allen, 2009; Leuschen, 2010]. These data sets are interpolated onto our 1 km mesh (solid black). Notice that all major features in bedrock topography within the ∼35 km region are captured on the 1 km grid. The ice-shelf profile represents a smoothed version of the IceBridge data sets (Figures A1a and A2a) following equation 1 in Holland and Jenkins [2008].

[34] As a standard run for our remaining experiments and to facilitate comparisons to our SeaRISE results, a second control run from 1973 to 2500 was established using the C1M4 setup with this higher resolution topographic data (experiment T1). In this and all remaining runs, the ocean coupling is activated from the beginning of the simulation.

3.3.2 Grounding Zone

[35] Special attention to the grounding zone is motivated by the known importance of the detailed grounding zone geometry for ice sheet stability and the improving ability to observe transitions in boundary conditions and to model the associated processes there. Physical understanding, process modeling, and data (Appendix A) show that at least some oceanic influence extends inland of the most commonly mapped grounding line. It is difficult to define a tidally modulated grounding line across a complex bathymetric region containing neighboring highs and lows without the reasonable conclusion that we must consider numerous subglacial lubrication pathways [Domack and Amblas, 2006; Joughin and Howat, 2008]. Our data analysis indicates that this zone of marine influence might be up to several kilometers wide. Here, we test the implications of an active grounding zone for TG response to future warming.

[36] While additional data and analyses are needed before we can conclusively map out grounding zones and simulate their poorly constrained thermomechanical processes (necessary to account for englacial attenuation), we consider the possibility that a thin layer of either ocean or brackish water extends as much as 5–10 km inland of the grounding line in many places (Appendix A). As discussed above, the strong variations in basal topography transverse to flow suggest that seawater may penetrate inland in some regions and then spread laterally. Melting of ice above such a layer would be less than in the ice-shelf cavity, where ocean circulation is vigorous. However, under some conditions, it is likely to be notably larger than beneath fully grounded ice where the enhanced melting from transport of warmed ocean waters exceeds the reduced melting from lubrication suppressing basal friction.

[37] Existing basin- or continental-scale ice-flow models generally do not explicitly treat a “grounding zone” and the processes acting therein; adjacent nodes are fully grounded and fully floating, perhaps with partial element scaling of basal drag between. Here we assess the impact of a laterally extensive grounding zone on ice dynamics. For basal melting in the grounding zone, we extend our SeaRISE implementation by applying a linear ramp from the melt rates calculated by the ocean model on the freely floating shelf (∼20 m/yr near the grounding line) to the much lower melt rates typically generated by basal sliding and the geothermal heat flux at the inland limit of the grounding zone (inline image(1–100) mm/yr). To simulate the enhanced basal lubrication from this extra melting, the basal drag coefficient in the grounding zone is weakened to 25% of its local, tuned value (T1 control run with grounding zone lengths of Δxgz=5,6,7, and 10 km, leading to experiments GZ1, GZ2, GZ3, and GZ4, respectively). To further test the importance of the high-resolution basal topography, we apply the 6 km grounding zone to the SeaRISE topography (e.g., C1M4 with a more extensive grounding zone and ocean forcing from the start of the simulation; GZ5). As with several of the SeaRISE forcings, we acknowledge that these are crude, end-member treatments and that an infinite number of other less aggressive parameterizations could be considered.

3.3.3 Basal Rheology

[38] Recent studies indicate different till rheologies likely exist beneath Rutford and Bindschadler Ice Streams in West Antarctica [Gudmundsson, 2011; Walker and Christianson, 2012]. Without data constraint on TG, we test the differences in ice-flow behavior when specifying linear viscous (m=1 exponent in basal flow law) and effectively plastic (m=8) till beneath the outlet glacier for the duration of the simulations. Because all previous simulations included a linear viscous substrate, we simply repeated GZ3 with an effectively plastic bed (GZ3P).

3.4 Results: Sensitivities in the Grounding Zone

3.4.1 Data Resolution and Grounding Zone

[39] After numerous runs for different bed conditions, geometries, and ice-shelf buttressing treatments, we found that the most important factor affecting TG stability is the ratio of grounding zone to bedrock ridge length. For the geometry in Figures 1 and 9, significant stability is provided by a bedrock ridge located ∼10 km inland from the current grounding line position (Figures 10a, 11a, and 11b). However, including a 6 km-long grounding zone with enhanced basal melt and reduced basal friction (GZ2) leads to retreat of TG (Figures 11c and 11d). If the grounding zone is narrower than 6 km (GZ1), then the grounding line retreats to the next inland bedrock bump (∼136 km along-flow distance) and stabilizes for at least the next 600 years. Increasing the length of the grounding zone (GZ3 and GZ4) leads to earlier retreat (cf. Figures 11c, 11d, 12a, and 12b). In addition, sensitivity runs with a 10 km wide grounding zone (GZ4) indicate that basal resistance has a greater impact than basal melt there, but that it takes both to destabilize TG.

Figure 10.

Simulated profiles for processes in the grounding zone. Output is displayed every 20 years from model year 1973 to 2500 for (a) the T1 control run with high-resolution topography in the grounding zone, (b) GZ2 (m =1 and Δxgz=6 km; last profile at model year 2413), (c) GZ5 (m =1 and Δxgz=6 km on SeaRISE basal topography; last profile at model year 2173), (d) GZ3 (m =1 and Δxgz=7 km; last profile at model year 2333), (e) GZ3P (effectively plastic rheology for substrate (m =8) with Δxgz=7 km), and (f) GZ3P with an ∼11% reduction in upstream flux (last profile at model year 2213). The flotation surface is denoted by the dashed line. Initial and final profiles are labeled with their model year and displayed in green and red, respectively.

Figure 11.

Histories of the rates of ice-thickness change and basal melting over a high-resolution bed. Output is displayed weekly along the model domain for (a and b) T1, (c and d) GZ2, and (e and f) GZ5 with SeaRISE basal topography. The history of grounding line position is represented by the black line in each panel. During retreat, the grounding line often oscillates (Figure 12) as its position is controlled by dynamic changes in ice flux over variable basal topography. See text and Table 1for simulation descriptions.

Figure 12.

Histories of the rates of ice-thickness change and basal melting over linear viscous and effectively plastic beds. Output is displayed weekly along the model domain for (a and b) GZ3, (c and d) GZ3P, and (e and f) GZ3P with an ∼11% reduction in upstream flux. The grounding line position is represented by the black line in each panel. See text and Table 1for simulation descriptions.

[40] Furthermore, comparing our GZ2 and GZ5 results (Δxgz=6 km for both, but with IceBridge and SeaRISE data, respectively, in the grounding zone) indicates that the additional bedrock bumps detected by the IceBridge mission inland of the current grounding line provide roughly two additional centuries of stability to TG (cf. Figures 10b, 10c as well as 11c, 11d, 11e, and 11f), yet whole ice sheet models are typically relying on the coarser data resolution [Bindschadler et al., 2013; Nowicki et al., 2013a, 2013b]. Improved knowledge of bedrock topography is also necessary to help predict when an ongoing TG retreat is likely to continue, versus having increased ice flux lead to shelf thickening (e.g., Figure 11e), regrounding, and a readvance.

[41] The critical grounding zone length that initiates catastrophic retreat is highly dependent on bedrock bump size. In GZ2, a subglacial lake (loosely defined here due to the 2-D nature of the bed) begins to form between 127 and 130 km along-flow distance (Figure 10b). The length between the top of the bedrock sill (at 136 km) and the downstream end of the subglacial lake is 6 km. The lake gradually expands and a second forms in the hollow (∼114–125 km along-flow distance) behind a prominent bedrock sill (at 126 km along-flow distance). The loss of basal contact leads to enhanced flow over the lake(s), thinning upstream, and thickening over grounded points downglacier, further stabilizing the grounding line on the ridge (similar dynamic patterns can be seen in Figures 11a, 11c, 11e, 12a, 12c, and 12e). Similarly, basal melt rates are relatively stable (with a peak value of ∼40 m/a out under the shelf, ∼11 km from the grounding line; e.g., Figure 11d). As thinning resumes near the grounding line, the ice reaches flotation farther inland and the lakes enlarge, eventually submerging the prominent bedrock ridge (model year ∼2175). Because there is essentially no basal drag at the subglacial lake/ice boundary, and the ice over the lake is already in hydrostatic equilibrium, only the bedrock ridge at 136 km prevents grounding line retreat. However, eventually the ice thins to flotation over the bedrock ridge, leading to retreat across the domain by model year 2413. Thus, if the grounding zone is narrower than the distance between the peak of the bedrock ridge and the downstream edge of the subglacial lake, then grounding line stabilization occurs; otherwise, catastrophic retreat begins (136 km in ∼55 years), with no other points of stabilization in our model domain.

3.4.2 Basal Rheology

[42] Finally, we also find significant differences in TG response that depend on the assumed basal rheology. Thus far, all simulations included a linear viscous substrate beneath TG. Results from these runs indicate that thinning waves initiated near the grounding line propagate ∼140 km upglacier over a period of several decades (Figures 11a, 11c, 11e, and 12a). As previously stated, with a 1 km wider grounding zone, the GZ3 simulation leads to earlier retreat than GZ2 (Figures 10d, 12a, and 12b). However, with a nearly plastic basal rheology and Δxgz=7 km, the GZ3P simulation forms two subglacial lakes in the grounding zone but ultimately stabilizes (Figures 10e, 12c, and 12d) as basal stresses are spread across a larger length scale. Furthermore, thinning waves propagate rapidly across the entire glacier (cf., m=1 bed), and only minor geometric adjustments are required to deliver the ice flux necessary to maintain grounding on the bedrock ridge. Because little change in driving stress is required to compensate large marginal forcings arising from the 7 km grounding zone, only the last ∼45 km of grounded ice has a significantly different profile (|Δs|>∼20 m) when compared to the end of the T1 standard simulation. Therefore, given the high-resolution basal topography in the grounding zone, higher bed exponents tend to stabilize the TG system. This novel result further highlights the need for additional data and analyses to determine bed type [Anandakrishnan et al., 2003; Joughin et al., 2004, 2009; Walker et al., 2012]. This significant stability can be overcome, however, if we reduce the upstream flux by ∼11%. Even though episodic advances persist late into the deglaciation, this additional forcing leads to rapid retreat (Figures 10f, 12e, and 12f).

4 Discussion

[43] In order to match observed surface velocities in its present configuration, our simulations indicate that the ice tongue on TG is providing insignificant buttressing of the grounded ice. Furthermore, results suggest that velocities in the main channel are dominated by basal motion. Without much buttressing or grounding zone effects, ocean forcings are limited in their ability to drive significant grounding line motion. Under the SeaRISE experiments, mass loss due to ocean forcings is nearly balanced by additional accumulation in a warming world, with enhanced sliding dominating dynamic changes in TG (cf., on a continent-wide basis, whole ice sheet models predict that ice-shelf melting will dominate Antarctic mass loss) [Bindschadler et al., 2013; Nowicki et al., 2013a, 2013b]. Except under the most severe ocean-forcing scenario, strong ice stream stabilization occurs in the SeaRISE experiments on the bedrock high that is a few kilometers upstream of the current grounding line location.

[44] Furthermore, while geophysical evidence from NASA's IceBridge Mission reveals stabilizing topographic features that are absent in older data sets with spatial resolutions ≥15 km, it also suggests the existence of an extensive (several kilometers wide) grounding zone that can lead to significant instability, as discussed above. Our modeling indicates that improved knowledge of both is critical to accurate projections of future sea level rise from TG. Given the topographic setting, the eventual formation of subglacial lakes proximal to the grounding zone is predicted, with an associated evolution of surface morphology, basal conditions, and ice dynamics forewarning dramatic change [Siegert et al., 2005; Domack et al., 2006; Carter et al., 2007; Joughin et al., 2008; Stearns et al., 2008; Wright et al., 2008; Smith et al., 2009; Scambos et al., 2011]. Because of our reduced dimensional modeling, we note that these cavities are potentially interconnected with the ocean in the transverse dimension. We also find that retreat is unlikely to be a monotonic process. On a background trend towards mass loss, the grounding line oscillates between neighboring bedrock highs, with ephemeral grounding providing buttressing during times of readvance.

[45] Basal rheology can also have a controlling influence on TG dynamics. While plastic substrates quickly propagate changes far upglacier, only minor geometric adjustments are required to effectively stabilize migrating grounding lines on basal highs. The resulting stability persists even with an extensive 7 km grounding zone.

[46] We note that the mismatch in data acquisition times leads to an unavoidable bias in our Bbfield. Over recent decades, TG has lost a majority of its ice tongue, thinned, and sped up [Rignot, 2001; Velicogna and Wahr, 2006; Shepherd and Wingham, 2007; Rignot et al., 2008, 2011; MacGregor et al., 2012]. In all likelihood, an extensive ice tongue in 1996 provided more drag than in 2008 [MacGregor et al., 2012]. Assuming, prior to drawdown, the surface just inland of the grounding line was relatively flat, driving stress would have been lower there. With ice-tongue rifting, shortening, and thinning, drag has since reduced. Furthermore, thinning near the grounding line has likely increased the surface slope and thus the driving stress on the grounded ice. Therefore, using old velocities and a recent geometry to calculate Bbnumerically stabilizes the modern TG to some extent by assigning basal drag sufficient to arrive at the formerly low velocities with relatively weak buttressing and high-basal shear stress. In addition, as the subglacial system evolves, there is little reason to expect that the background basal friction coefficient field will remain temporally constant as is assumed here. Finally, the temperature and volume of CDW entering Pine Island Bay have recently increased in some regions [Jacobs and Jenkins, 2011], and both could experience interannual or decadal variability over time; yet we assumed they are constant. Also, we have not included a mechanism to allow ocean water infiltration through gaps in bedrock ridges or switches in hydraulic pathways, which might connect to newly formed subglacial lakes and drive additional melting. When compared to the uncertainties in our parameterizations, we suspect that these data-related biases are not huge, and have chosen to use the available data rather than to try to modify them.

[47] In summary, due to remaining uncertainties in important system components, such as the present and future forcings, basal topography/bathymetry, basal properties, physical processes operating within the grounding zone, and the model implementation of each, our results do not yet provide reliable projections of best estimate or upper limit sea level rise from TG. While our assumptions of a linear decrease in basal melt and weakening of the basal drag coefficient in the grounding zone are aggressive, they are not worst case scenarios.

5 Conclusions

[48] Simulations incorporating the combined SeaRISE and IceBridge-derived configuration show that although its ice tongue provides limited stability, under some possible parameter sets, the topographic high ∼10 km upglacier of the current TG grounding line (Figure 9) may stabilize the future grounding line position for centuries or longer. However, if we reduce basal friction and allow warm ocean water to penetrate into a grounding zone with length chosen to match available data, then the stabilizing feedbacks due to this ridge are insufficient to halt the retreat of TG unless the bed is effectively plastic. Yet, the till rheology beneath TG is unknown, with a wide range of possible behaviors remaining viable. It is noteworthy that the distinction can be made remotely by assimilating high temporal resolution data into a viscoelastic model. For example, Walker and Christianson [2012] determined that Bindschadler Ice Stream, which flows along the Siple Coast of West Antarctica, exhibits tidally forced behavior that is only consistent with an effectively plastic substrate.

[49] Therefore, we need detailed knowledge of the topography, basal rheology, and the character of the grounding zone to learn whether, amidst ongoing thinning and speedup of TG [Rignot and Mouginot, 2011], the grounding line will indeed stabilize on the bedrock bump or retreat catastrophically. Recent studies using higher order models have not included a wide grounding zone and often were insensitive to local topography due to the relatively large grid size in both the data sets (at least 15 km for lines flown; interpolated more densely to 5 km) and models (typically at least 5 km for whole ice sheet simulations across century timescales). Although we omit a full treatment of the lateral dimension, bridging stresses, and energy conservation within our model physics, our targeted simulations indicate that even three-dimensional thermomechanical models with full-momentum solvers will have difficulty assessing ice sheet stability if they smooth existing topographic variability, assume an incorrect basal rheology, inadequately couple ice-ocean interactions, and do not parameterize the impact of important processes operating within a zone of marine influence. Thus, additional field and remote-sensing studies are required to provide the most accurate data on TG, to drive both two-dimensional and state-of-the-art whole ice sheet models incorporating the effects of a grounding zone towards reliable cryospheric projections.

Appendix A

[50] Models typically assume that ice switches from grounded to floating across a discrete, zero-width grounding line. The models may take the initial position of this grounding line from a data set such as the Antarctic Surface Accumulation and Ice Discharge (ASAID) project [Bindschadler and Choi, 2011]. ASAID identified the grounding line “primarily by interpreting the seaward limit of the region of grounded ice features in optical imagery,” which they argued gave a close approximation of the point where the ice loses contact with the bed at low tide. However, the high tide raises the ice, causing flexure that is observed farther inland [Bindschadler and Choi, 2011] and thus extending the marine influence [Walker and Parizek, 2013].

[51] Because the grounding line often occupies the lee of a stabilizing basal high [Alley and Anandakrishnan, 2007], starting with a grounding line shifted seaward of its mean position, and omitting ocean-driven melting and increased lubrication in the grounding zone during high tide, tend to provide anomalous stability to a modeled ice stream. However, this may be offset by the tendency of relatively coarsely sampled data to miss the full height of the stabilizing basal high.

[52] Other physical processes may extend the marine influence inland of the high-tide grounding position. For example, drainage of meltwater beneath grounded ice typically occurs at a pressure slightly less than the ice-overburden pressure, offering a potential pathway for inland penetration of ocean water at high tide, in some ways analogous to subaerial estuarine tidal flows.

[53] Such flows may be amplified, modified, or even reversed by tidal pumping. As described by Walker and Parizek [2013], data and models show that resistance of ice to bending causes slight uplift of grounded ice at low tide over a flexural wavelength of a few times the ice thickness (hence, typically a few kilometers for Antarctic ice streams). Model estimates for likely subglacial materials yield a low-tide pressure drop beneath this flexural uplift that is larger in magnitude than the oceanic pressure drop from the tide. This may cause tidal pumping of seawater upglacier. This ocean water then may be spread farther inland by strong water pressure variations associated with ice flexure [Murray and Clarke, 1995; Walker and Parizek, 2013]. Such pumping may explain why radar data collected across grounding lines typically show a bright reflection typical of ice over seawater extending inland and only gradually fading to a weaker reflector more consistent with a thin layer of freshwater [Walker and Parizek, 2013].

[54] Observations [Domack and Amblas, 2006; Joughin and Howat, 2008] and modeling including ours here show that thinning of ice grounded on a local ridge can lead to lake formation upglacier. For a flow line model such as ours, it is very unlikely that the chosen flow line will correspond to the point at which seawater will first access the lake in response to continuing thinning; instead, it is likely that the lake will begin to interact with the ocean through a low spot in the ridge away from the flow line, contributing to basal melting upglacier of the ridge before such melting would be simulated in the model.

[55] Looking at the particular case of TG, new airborne geophysical observations show that it currently is grounded near the top of a local topographic high that is likely a source of recent stability. Furthermore, the data indicate that there is a variable length zone over which there is likely reduced basal resistance and enhanced melt, both of which would somewhat decrease the stability. The data also show a broad high (wavelength ∼8 km, amplitude ∼200 m) ∼10–20 km farther inland that may prevent a drastic grounding line retreat in the coming centuries should thinning continue. Based on current geophysical data sets, in the event that stabilizing feedbacks are insufficient to halt the retreat of TG at this second ridge, no similar topographic feature exists farther inland along our 265 km model domain.

[56] These data also allow the possibility that in some places near the front of TG seawater is penetrating as much as 10 km or more inland of the grounding line position as determined by ASAID and the MODIS Mosaic of Antarctica [Bindschadler and Choi, 2011; Haran and Bohlander, 2005], although much less penetration seems likely in other places.

[57] Basal crevassing may have many causes, but is especially associated with flexure of ice shelves and is often taken as marking the grounding line. For TG (Figure 1), we identify the inland limit of flexure with the most landward basal crevasses, as shown by basal hyperbolae in the radar profiles (Figure A1). This is just downglacier of the steepest surface slopes (excluding the disturbed region from heavy crevassing on the ice tongue); these slopes are more than 10× those seen on the Siple Coast of Antarctica [Horgan and Anandakrishnan, 2006], indicating an important dynamical boundary. Along some radar lines basal crevassing extends more than 10 km inland of the ASAID grounding line, although the ASAID grounding line and the farthest inland crevasse are nearly coincident for the central trunk of TG (cf. Figure A1a and A1b) and for the ice feeding the grid northern section of the ice shelf, which may have local ice rises.

Figure A1.

Radar profiles highlighted in the (a) solid (also the high-resolution data from ∼110–145 km along the flow line in Figure 9) and (b) dashed boxes of Figure 1. Returned basal reflector power is plotted in the colorbar above each radargram. Consistently bright returns extending at least ∼5 km inland from the grounding line imply seawater lubrication within a grounding zone in both profiles. The inland limit of basal crevassing is nearly coincident with the surface slope break calculated from airborne laser altimetry [Krabill, 2009] for both profiles. While it is also coincident with the ASAID grounding line [Bindschadler and Choi, 2011] in Figure A1a, it extends ∼10 km inland of the ASAID grounding line in Figure A1b.

[58] Additional lines of evidence support the inference from basal crevassing that ocean water likely penetrates well inland of the low-tide ASAID grounding line in many places. Where crevasses are found significantly inland of the ASAID grounding line, profiles are in or near hydrostatic equilibrium with the ocean from the ASAID grounding line to the inland-most crevasse (Figure A1b and A2b) [Joughin et al., 2008], suggesting that ocean water can penetrate there via tidal pumping.

Figure A2.

Surface elevation, basal elevation, and hydrostatic profiles highlighted in the (a) solid (also the high-resolution data from ∼110–145 km along the flow line in Figure 9) and (b) dashed boxes in Figure 1. Surface elevation is from swath laser altimetry (solid line) [Allen, 2009], bed elevation is from ice-penetrating radar (solid line) [Allen, 2009], hydrostatic profiles (dashed) are calculated following Horgan and Walker [2011], and current grounding line position is from ASAID [Bindschadler and Choi, 2011]. The inland limit of basal crevassing observed in ice-penetrating radar data is also shown [Leuschen, 2010].

[59] Past airborne and recent ground-based (2011–2012 field season) observations on the Siple Coast have shown a broad transition zone from high-radar reflectivity of the floating ice base over seawater, to lower reflectivity over freshwater and rock, with high reflectivity extending several kilometers inland [Peters et al., 2005; Christianson, pers. comm.]. If estuarine-type mixing is occurring, enhanced by ice flexure, then we would expect that the high-basal reflectivity of the ice shelf would extend inland on TG to or toward the inland limit of basal crevassing. In airborne radar data from TG [Allen, 2009; Leuschen, 2010], we find basal reflectivity of floating and adjacent grounded ice over inline image5 km are indeed similar (within 6 dB; Figure A1).

[60] We measure relative return power from the bed and assume that the radar system is stable over the course of a flight-line so that we can compare bed properties along a transect. Bed reflection strength does not change abruptly across the grounding line, suggesting that some seawater (possibly only a thin layer, but sufficient to affect the reflection) is present inland of the grounding line. Furthermore, recent joint ground-based radar (where the presence of a long-path multiple allowed direct calculation of englacial attenuation rate) and active source seismic observations over the grounding zone of Whillans Ice Stream indicate a gradual transition from a seawater column to fully grounded ice over a several kilometers-wide grounding zone which is well imaged in both data sets and consistent with the existence of a water-mixing zone inland of the grounding line [Horgan, pers. comm.; Christianson, pers. comm.]. Thus, this observation is likely not unique to the grounding zone of TG.

[61] For these reasons, we believe that it is appropriate to explore the impact of a grounding zone rather than a grounding line on model stability. We have chosen to use a linear transition from fully grounded to fully floating marine behavior for simplicity to match the SeaRISE runs and because we lack strong reasons to choose any other particular form; however, we are confident that different grounding zones will have quite different character and that none of them will be exactly linear.

Acknowledgments

[62] This work was supported by NSF grants 0531211, 0632198, 0732844, 0758274, 0909335, the Center for Remote Sensing of Ice Sheets (CReSIS) 0424589, by NASA under grants NRA-04-OES-02, NNX-09-AV94G, NNX-10-AI04G, 10-CRYO10-0025, and the NASA Cryospheric Science program (Grant 281945.02.53.02.19), as well as an NSF graduate research fellowship (K.C.). We thank Operation IceBridge and the National Snow and Ice Data Center for access to aerogeophysical data and the SeaRISE community of scientists for all of the collaborative work over the past several years. Finally, we would like to recognize the efforts of the Scientific Editor, Bryn Hubbard, the Associate Editor, and two anonymous referees. Their critical reviews were invaluable.

Ancillary