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Submitted Manuscript: Confidential 24 May 2013
Abrupt ice-front retreat caused by disintegration of adjacent ice shelf in Antarctica 1
Torsten Albrecht*† & Anders Levermann*†‡ 2
*Potsdam Institute for Climate Impact Research, P.O. Box 601203, 14412 Potsdam, Germany 3
†Institute of Physics, Potsdam University, Karl-Liebknecht-Strasse 24/25, 14476 Potsdam-Golm, Germany 4
5
‡Correspondence to: [email protected] 6
Abstract: Antarctic ice-discharge constitutes the largest uncertainty in future sea-level projections. Floating ice-7
shelves, fringing most of Antarctica, exert retentive forces onto the ice-flow. While abrupt ice-shelf retreat has been 8
observed, it is generally considered a localized phenomenon. Here we show that the disintegration of an ice-shelf 9
may induce the abrupt retreat of its neighbor. As an example, we reproduce the spontaneous but continuous retreat of 10
the Larsen-B ice-front as observed after the disintegration of the adjacent Larsen-A ice-shelf. We show that the 11
Larsen-A collapse yields a change in spreading rate in Larsen-B via their connecting ice-channels and thereby 12
causes a retreat of the ice-front to its observed position of the year 2000. This mechanism is particularly relevant for 13
the role of East Antarctica for future sea-level. 14
15
Keywords: Sea-level , Larsen Ice Shelf, Antarctic Peninsula, abrupt ice shelf retreat, ice shelf breakup, nonlocal 16
stress transfer 17
Short title: Communicating ice fronts (max. 50 characters)18
1 Introduction 19
Significant progress has been made in understanding past sea-level changes (1–8). When projecting future sea-level 20
rise an additional difficulty arises. While most of the observed sea-level change was due to the thermal expansion of 21
the ocean and ice loss from mountain glaciers, the contribution of the great ice-sheets on Greenland and Antarctica 22
has been increasing over the last two decades (9–11). As a consequence, physical models still underestimate the 23
observed sea-level rise of that period (12, 13) and confidence in future projections decreases with the prospect of an 24
increasing role of the ice-sheets. The part of the ice-sheet contribution that can be modeled with some accuracy 25
using process-based models is that from their surface mass balance (14–17), in contrast to the dynamic solid-ice 26
discharge. While the ice discharge from Greenland is topographically constrained (5, 18), the largest uncertainty for 27
the future resides with the ice loss from Antarctica (19, 20). 28
Along most of the Antarctic coast the grounded ice flows into floating ice shelves which exert a retentive force onto 29
the grounded ice sheet (21, 22) and thereby hinder dynamic ice discharge from the continent (23–28). The stability 30
of these ice shelves is thus crucial to understand past and future changes in ice-sheet dynamics and Antarctica´s 31
future sea-level contribution (29). While abrupt ice-shelf retreat has been observed (30–32), it is generally 32
considered to be a singular phenomenon (33–36). Along the Antarctic Peninsula and East Antarctica many ice-33
shelves are separated only partially by ice rises. Thus adjacent ice shelves are interconnected via channels of 34
currently slow-moving floating ice. A series of ice-shelf disintegration events have been observed which is generally 35
attributed to the warming environment in this most northern part of Antarctica. 36
One prominent example is the collapse of the Larsen-A ice-shelf in the year 1995 followed by a sequence of 37
small calving events at the neighboring Larsen B ice-shelf and thus a quasi-continuous retreat of its ice-front in the 38
following years (30, 31). The immediate retreat occurred through numerous iceberg calving events until also Larsen 39
B disintegrated almost completely in 2002. While the large-scale abrupt disintegration was very likely caused by 40
meltwater-enhanced fracture processes subdividing the ice shelf into an unstable melange of ice fragments, which 41
capsize and drain into the open ocean (32, 33), the retreat of the Larsen-B front between 1995 and 2000 was quasi 42
continuous and the result of a large number of small-scale calving events. Here we focus on this continuous but 43
spontaneous ice-front retreat and suggest a mechanism by which the disintegration of an ice-shelf leads to the ice-44
front retreat of an adjacent ice-shelf. 45
46
2 Methods 47
The mechanism we propose can be understood independent of numerical model results but is illustrated here using 48
simulations with the thermo-mechanically coupled Potsdam Parallel Ice Sheet Model (PISM-PIK) (37), which is 49
based on the open-source Parallel Ice Sheet Model (PISM, version “stable-0.2”) (38). Since only floating ice shelves 50
are considered in this study, the full dynamics captured by PISM is not applied, but the velocity field is simply 51
computed according to the Shallow Shelf Approximation (SSA) fed by prescribed inflow at the observed grounding 52
line (39). Central to this study is the application of the first-order kinematic calving law (40) (denoted eigencalving 53
hereafter), which tries to comprise large-scale observational constraints (34, 35, 41) into a simple relation and is 54
regularly applied in dynamic simulations with PISM (42) using a sub-grid scheme for ice-front motion (43). In order 55
to improve the temporal representation of calving we adapt the time-step within PISM-PIK with a CFL-criterion, 56
which is based on the maximum of the computed calving rate in each time step; thereby restricting the calving flux 57
to at most one grid-cell at the ice shelf margin in each time step. Simulations use a horizontal resolution of 1 km. 58
59
3 Results 60
3.1. Basic mechanism of communicating ice shelves 61
The mechanism of the communication of adjacent ice fronts is illustrated in a simplified geometry of two ice shelves 62
confined in rectangular embayments that are connected by an ice channel (Fig. 1) before applying it to more realistic 63
topography. The ice shelves are fed by a constant inflow at the upstream boundary. The mechanism does not depend 64
on the specific distribution of the inflow. We chose a homogenous inflow along the entire upper boundary of the 65
basins. The position of the freely moving calving front is generally determined by the inflow of ice, the basin 66
geometry and the calving rate. Here, the ice-shelf system is integrated into dynamical equilibrium for constant 67
boundary conditions with a calving rate, C, that is proportional to the determinant of the horizontal spreading rate 68
tensor (eigencalving) 69
C=K2±∙ε+∙ε- for ε±>0 70
where ε+ and ε- are the eigenvalues of the horizontal spreading rate tensor and K2±=108ma is a proportionality 71
constant that incorporates all material properties that are relevant for the calving rate. For simplicity and in order to 72
demonstrate the mechanism, it is chosen to be constant in this study, but will generally depend on ice properties such 73
as the fracture density and ice rheology which might change the results quantitatively but not qualitatively. 74
In order to mimic the rapid disintegration of an ice-shelf as observed for example for Larsen-A, we eliminate the 75
entire ice-shelf on the right hand-side within one time step. This somewhat unrealistic instantaneous collapse allows 76
for investigating the immediate effect on the far-field strain-rate distribution within the remaining ice shelf and best 77
reveals the mechanism: While the flow between the two basins was very small when both ice-shelves were intact 78
(Fig. 1b), the void left by the collapsed ice-shelf allows for an ice-flow between the two basins (Fig 1d). Due to the 79
non-local nature of the membrane stresses computed within the ice shelf this changes the spreading rate in the entire 80
ice-shelf that remains (Fig. 1a, c). In particular the spreading perpendicular to the main flow direction, as 81
represented by the minor eigenvalue ε-, becomes positive in a large region along the ice-front which results in 82
enhanced calving and a spontaneous retreat of the ice-front. This effect is robust against changes in boundary 83
condition, lateral friction, calving constant K2± and other ice-properties. 84
3.2 Application to the Larsen Ice Shelf 85
Analogous to these conceptual computations, we conduct simulations for a realistic geometry and inflow of the 86
Larsen A and B Ice Shelf system (Fig. 2 and animation in SI). Mimicking the observed spontaneous disintegration in 87
1995, we eliminate the smaller Larsen-A ice-shelf by introducing rifts along the side margins. While we do not 88
advocate that the actual event occurred like this, we hereby merely use the property of the eigencalving equation that 89
allows for multiple stable ice-fronts to induce a collapse of Larsen A by these rifts. As a consequence, the 90
destabilized ice tongue of Larsen A retreats abruptly (a few model months) under the calving law leading to a 91
practically ice-free Larsen-A embayment. The consecutive events are independent of the way in which the Larsen-A 92
disintegration is triggered: The integration of the model after initialization with realistic boundary conditions yields 93
dynamically stable ice-fronts similar to the observed situation up to 1993 (Fig. 2a,b). The perturbation of Larsen A 94
leads to its disintegration. Since Larsen A and B were connected by a channel of slowly moving ice in the region of 95
Seal Nunataks, the flow across this channel enhances and (following the momentum balance) longitudinal stresses 96
are transferred into Larsen B (Fig 2c,d). In the following years the Larsen-B ice-front retreats according to the same 97
mechanism described for the conceptual geometry (Fig. 2e, f). 98
This retreat of the calving front in the aftermath of a collapse of the neighboring ice shelf is robust against changes 99
in parameters also in the observation-based geometry and velocity distribution of the Larsen A and B ice-shelf 100
system. As reported in earlier studies (30–32), the observed disintegration of the remaining Larsen-B ice-shelf in 101
2002 was caused by meltwater-enhanced fracture and was not following the spontaneous but continuous mechanism 102
described here. 103
104
4 Discussion and Conclusion 105
The mechanism described here is qualitatively robust against changes in parameter and geometry and can indeed be 106
clearly understood on physical grounds. The timing and exact position of the ice-fronts in different stages, depends 107
on the ice-softness, the inflow speed, the calving parameter K2± and also on the resolution of the integration. 108
Especially the fact that in our simulation the retreat of the calving front though spontaneous takes longer than 109
observed is likely due to computational limitation associated with the spatial resolution and time-step. Friction along 110
the side margins generally stabilizes the ice-shelf flow by restraining the shear stresses within the ice. For the 111
mechanism to be effective, the connecting channel between the ice shelves has to be wide enough to allow for the 112
transfer of longitudinal stresses. The geometry of the embayment and hence the degree of confinement determines 113
the flow pattern in the interior ice shelf and hence the curvature of the steady state calving front position. The 114
distribution of the inlet boundary velocity affects the occurrence and extent of divergent regions (ε->0) in the interior 115
ice shelf, which imply the possibility of a complete calving front retreat. 116
Our hypothesis that the Larsen-B retreat between the years 1995 and 2000 was caused by the disintegration of 117
Larsen-A and successive gradual calving is supported by various simulations in simplified geometric situations and 118
finds its realistic counterpart in the observed behavior of the Larsen A and B ice-shelf system prior to the complete 119
disintegration in the year 2002. The mechanism could become relevant for a number of ice-shelf systems fringing 120
the Antarctic Peninsula and East Antarctica which might become more exposed to future warming than the more 121
southern ice-shelves Ross- and Filchner Ronne. In combination with a possible acceleration of ice flow across the 122
grounding line due to reduced buttressing of a reduced ice-shelf, it might be relevant for future sea-level rise. 123
124
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231
Figure 1. Mechanism of ice-front retreat (left bay) caused by disintegration of adjacent ice shelf (right bay). The 232
figures show the ice-geometry at different stages of the simulation. The black line delineates the current calving 233
fronts in panels e and f; the initial front of panels a and b is provided as a brown line for reference. Left panels show 234
the minor strain-rate eigenvalue ε- (in units s-1) which generally corresponds to the flow perpendicular to the main 235
flow direction. Right panels provide the ice velocity as arrows on top of colour-coded ice speed in different states of 236
simulation (in panels d and f, anomalies to panel b are shown): Starting from an dynamically equilibrated geometry 237
(top), the left ice-shelf is eliminated (centre). The bottom panels show a transient state 40 years after the event. 238
239
Figure 2. Three states of the Larsen A and B Ice Shelf system chronologically from top to down as described in the 240
text. As in Fig. 1 the minor spreading-rate eigenvalue ε- is shown on the left and ice shelf velocities (panel b) and 241
their anomalies to the right. The steady state calving front position in the top panels as well as minimal front position 242
years after the disintegration of Larsen A in the bottom panel agree well with observed shapes of different dates of 243
the late 1990s (coloured contour lines are based on satellite data kindly provided by H. Rott). 244
245
Acknowledgments: 246
TA was funded by the German National Merit Foundation. 247
248
Supplementary Materials 249
Movie S1 Animation of retreat of Larsen-B ice shelf after the observed disintegration of Larsen-A ice shelf. The 250
experiment is described in the text and shown in figure 2. 251
252
253 Figure 1. 254
255 Figure 2 256