The majority of Antarctica's current net ice loss occurs along the Amundsen Coast, where warm Circumpolar Deep Water (CDW) intrudes onto the continental shelf to cause strong (tens of meters per year) melting beneath the floating ice shelves that extend seaward from the grounded ice sheet [Rignot and Jacobs, 2002; Rignot et al., 2008; Thoma et al., 2008]. Previous studies have shown that this melt produces thinning near the grounding line (the transition from ice resting on bedrock to floating), producing large speedups that propagate inland rapidly [Payne et al., 2004; Shepherd et al., 2001; Thomas et al., 2004]. How the resulting thinning on grounded ice will evolve is one of the major uncertainties in 21st century sea-level projections, as acknowledged by the Intergovernmental Panel on Climate Change .
 Arguably, nowhere on the Antarctic Ice Sheet is change more apparent than at Pine Island Glacier, which has been described as the “weak underbelly” of Antarctica [Hughes, 1981]. Earlier studies documented speedup from about 2300 m yr−1 in 1974 to just over 3800 m yr−1 in 2007, concurrent with intervals of grounding-line retreat [Joughin et al., 2003; Rignot, 2008, 1998]. Figure 1 shows subsequent speedup to nearly 4000 m yr−1 by late 2008, followed by little further change through early 2010. Using Terra-SAR-X satellite data, we also mapped the 2009 grounding-line position (Figure 1a). From 1996 to 2009, sections of the grounding line retreated by more than 20 km, substantially more than the 5-km retreat from 1992 to 1996 [Rignot, 1998]. Despite this retreat, an isolated, lightly grounded area developed forward of the main grounding line.
 While an earlier model demonstrated that change near the grounding line rapidly diffuses inland [Payne et al., 2004], it predicted a response far more moderate than is observed, likely reflecting the model's use of a fixed grounding line. We implemented a similar depth-averaged, finite-element, numerical model for the majority of the PIG catchment basin (Figure 1a), but our implementation allowed the grounding line to migrate freely and we used observations to constrain the sliding model (auxiliary material).
 To initialize our model, we used inverse methods to determine the parameterized basal shear stress, τb, from the flow velocity observed in 1996 [Joughin et al., 2009]. Unlike the Ross Ice Streams [Joughin et al., 2004], there are substantial areas beneath PIG where the bed is strong (τb > 100 kPa) [Joughin et al., 2009]. The relationship between τb and speed, u, often is parameterized such that τb ∼ u1/m. If sliding is due to till deformation, then m = 1 yields linear-viscous behavior. Measurements on subglacial till suggest plastic behavior (m → ∞) [Kamb, 1991] and similar behavior also may occur for fast flow over a hard bed [Schoof, 2007]. Alternatively, a value of m = 3 often is used for hard-bed sliding [Paterson, 1994]. We evaluated three ice-stream sliding models: 1) linear-viscous (m = 1) as used earlier for PIG [Payne et al., 2004; Schmeltz et al., 2002]; 2) a mixed model with m = 3 in hard-bedded areas (τb > 40 kPa) and plastic behavior where till likely is present (τb ≤ 40 kPa); and 3) plastic conditions over the entire ice stream. For all three sliding models, we used a value of m = 3 for slow-moving areas outside the ice stream (auxiliary material).
 We began by evaluating our model's ability to reproduce recent observations, which also served as a guide to selecting the appropriate sliding law. For our three sliding parameterizations, Figure 1b shows the model's instantaneous response to instantly setting τb = 0 in the area where the grounding line recently retreated. This represents a pseudo-ungrounding since traction is lost but the surface remains above flotation. The results from the mixed and plastic models bound the observed increase in speed at the grounding line, suggesting that the speedup resulted from a loss of basal traction, which is consistent with earlier work where the extent of ungrounding was hypothesized [Joughin et al., 2009; Payne et al., 2004; Schmeltz et al., 2002; Thomas et al., 2004]. The instantaneous ungrounding, however, cannot account for the increased speeds farther inland [e.g., Scott et al., 2009], indicating a finite time interval is required for the effect to diffuse inland [Payne et al., 2004].
 In order to examine the response to the recent ungrounding with a time-dependent model, first we adjusted the basal-melt rate to force a steady state with the 1996 grounding line (auxiliary material). Next, we perturbed the model by steadily reducing τb to zero over several-year periods in the region that recently ungrounded (Figure 1), during which time the model thickness, speed, and grounding line could evolve freely. We compared these results with thinning rates determined using ICESat data (2003-to-2008). The mixed model provided a remarkably close match to the ICESat thinning rates for a simulated 8-year ungrounding period and a 50% melt-rate increase (Figure 2a). Figure 2b indicates that the viscous model underpredicts the inland thinning, while the plastic model cannot reproduce the strong near-grounding-line thinning. The simulated 8-year ungrounding is the same duration as the 2000-to-2008 interval when much of the observed change occurred (Figure 1).
 Based on extrapolation of observed thinning rates near the grounding line, it was suggested that the entire main trunk of PIG may go afloat within 100 years [Wingham et al., 2009]. Our model, however, indicates that such large thinning rates near the grounding line are not sustained, indicating a far longer period may be required to unground the entire trunk. This effect is clear in Figure 2b (mixed and viscous models) where the near-grounding-line thinning exceeded 5 m yr−1 at year 8, but decreased to less than 1 m yr−1 by year 15 as flow upstream of the strong thinning increased while downstream speeds stabilized. While we have not measured thinning from 2009 to 2010, Figure 1b indicates negligible speedup near the grounding line for this period, but ∼4% speedup upstream of the rapidly thinning area, suggesting that the strong near-grounding-line thinning is diminishing as the model predicts. This should moderate the rate of grounding-line retreat even though the net basin-wide loss should not diminish substantially.
 The fixed spatial pattern of oceanic melt that we used to model recent behavior is not suitable for longer-term experiments with large grounding-line migrations. To examine century-scale behavior, we used a depth-parameterized melt rate and let the model evolve for 500 years to achieve a steady-state with the grounding line near its 2009 position (auxiliary material). This steady-state configuration served as the starting point for our century-long experiments, all of which involved applying some step change in melt rate or shelf geometry. Since the mixed-bed model provided the best agreement with observations, all of our longer simulations used this model.
 In our first 100-year simulation, we scaled the melt rate by a factor of 4, which produces grounding-line melt well in excess of modeled [Payne et al., 2007] and estimated [Rignot and Jacobs, 2002] rates for Antarctic ice shelves. The increased melt thinned the shelf, exposing less area to the stronger melt at depth, so the total melt was about 75% greater than steady state through much of the simulation. After 5 years of speedup in response to this enhanced melt, the speed leveled off and the ice stream lost mass at about 25 Gtons yr−1 for the remaining 95 years (Figure 3a). In a second experiment, we increased the melt rate for the first 50 years and returned it to the steady-state value for the last 50 years. Once melting was reduced, the losses rapidly declined to 10 Gtons yr−1 and might have declined further if we had the necessary data (e.g., bed elevation) available to adequately model the grounding line forward of its initial position.
 Despite extreme melt rates at the grounding line (>600 m yr−1), simulated losses (25 Gtons yr−1) driven purely by melt represent about half the present rate of loss (46 Gtons yr−1) [Rignot, 2008]. Our simulations, however, commence from a steady state with a grounding-line position and surface geometry (near the 2009 location). Prior to the recent acceleration, an ice plain (area grounded just above flotation) existed in the recently ungrounded area [Corr et al., 2001]. Figure 3c (inset) shows the surface evolving over 80 years to form a similar ice plain, almost immediately after which the grounding line retreated rapidly (<10 years) over a reverse bedrock slope in a manner similar to the recent retreat. We observe similar progressions in numerous simulations (e.g., other rapid increases in loss visible in Figure 3c), suggesting that such an ice plain represents a transient geometry, poised to retreat rapidly down a reverse bed slope until a new position is reached upstream near the next bedrock high. With the former ice plain now afloat, the surface rises steeply inland of the grounding line, suggesting the grounding line may stabilize, at least for several decades, near its current position. The model also suggests that while CDW moving under the ice shelf may have brought on the recent retreat, the surface may have evolved over decades to centuries to form the ice plain that was predisposed toward the recent large response [Jenkins et al., 2010]. Thus, PIG's dramatic retreat and speedup may not indicate a trend of continued acceleration, and speeds may stabilize at their current elevated levels as thinning continues.
 Although its grounding line may now have reached a position of at least multi-decade stability, PIG is well out of balance and continues to thin [Pritchard et al., 2009; Rignot, 2008]. Our long-term simulations start from a steady-state geometry with no ice plain. Because it can take decades to form such a feature (Figure 3c), even with strong melt, our simulation does not reproduce the present, non-steady conditions that resulted from the ice-plain ungrounding.
 We also simulated an ice-shelf breakup by removing the thinner parts of the shelf (approximately two thirds of the 1996 ice-shelf area). This produces an initial speedup similar to that currently observed following the loss of the ice plain (Figure 1). For regions inland of the present grounding line, the actual ice-plain ungrounding and the simulated shelf loss represent nearly equivalent effects. This is because each event produces a loss of resistive stress downstream of the present grounding line that must be compensated for in each case by a similar degree of speedup upstream. Thus, by starting from a state similar to present in terms of speed, thinning, and lack of an ice plain, the missing shelf simulation should provide a reasonable representation of how PIG will evolve over the next century. While not a perfect analog, even without enhanced melt, this simulation indicates that losses similar to present could be sustained throughout this century, with larger losses if warm CDW maintains high melt rates (Figure 3).
 Since our glaciological model is not coupled to an ocean-atmosphere climate model, it is more useful in revealing sensitivity to climate than in projecting sea level. Nonetheless, our results establish some reasonable bounds on the PIG 21st century contribution to sea level. At one extreme, our simulated removal of much of the shelf and application of a four-fold increase in melt at depth increases sea level by 2.7 cm over a century, comparable to an extrapolation of 3 cm in 130-140 years [Wingham et al., 2009]. A melt rate greatly in excess of the present-day inferred rate may be unlikely for PIG. This principally is because already this region is already experiencing a strong, direct influx of CDW [Thoma et al., 2008], and a further increase in melt rate might only be possible with a warming of the inflowing CDW, an unlikely scenario given the present-day arrangement of warm water masses in this region of the Southern Ocean. Thus, more likely 21st century sea-level contributions from PIG are in the 1.1-to-1.8 cm range for the reduced shelf with the melt rate scaled by a factor of one to two. At the other extreme, our model does show that a melt reduction can curtail losses, a possibility if there is a decrease in warm CDW flow onto the Amundsen continental shelf. Too little is currently known about the process controlling the amount of CDW flowing onto the continental shelf to draw further conclusions at this juncture.
 Estimates of present mass loss for the Amundsen Coast (Pine Island, Thwaites, Smith, Pope, and Kohler glaciers) range from 1.4-to-2.9 cm/century [Pritchard et al., 2009; Rignot et al., 2008], of which more than 40% is attributable to PIG (0.6-to-1.2 cm/century). Upper bounds on the 21st century contributions are provided by a heuristic scaling that indicates a maximum range of 4-to-15 cm of sea level increase from PIG and a maximum of 11-to-39 cm for the entire Amundsen Coast [Pfeffer et al., 2008]. Our model-derived upper bound (2.7 cm/century) and more-likely estimates (<1.8 cm/century) are substantially smaller. While we have not modeled the other glaciers, PIG is the most rapidly changing and largest contributor to the current imbalance, indicating future model-derived upper bounds on 21st century sea level for the entire region are likely to fall well below the heuristically derived 11-to-39 cm upper bound [Pfeffer et al., 2008].
 Our model simulations suggest that the present position of the PIG grounding line is likely near a point of multi-decadal stability. Strong thinning near the grounding line likely will moderate as the rate of speedup declines, which represents a hypothesis that is testable through observation over the next decade. Widespread thinning and mass loss may continue, however, at roughly the present rate through much of the century with ice-surface drawdown by tens of meters extending well inland. While we have limited our model to century-scale runs, many of the simulations suggest no abatement at the end of the century. Thus, it is possible that drawdown will continue at similar rates indefinitely.