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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

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‡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

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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

References and Notes: 125

1. Gregory JM et al. (2012) Twentieth-century global-mean sea-level rise: is the whole greater than the sum of 126

the parts? Journal of Climate:121203145300007. Available at: 127

http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-12-00319.1. 128

2. Church J ~A. et al. (2011) Revisiting the Earth’s sea-level and energy budgets from 1961 to 2008. 129

Geophysical Research Letters 38:18601. 130

3. Lorbacher K, Dengg J, Böning CW, Biastoch a. (2010) Regional Patterns of Sea Level Change Related to 131

Interannual Variability and Multidecadal Trends in the Atlantic Meridional Overturning Circulation*. 132

Journal of Climate 23:4243–4254. Available at: 133

http://journals.ametsoc.org/doi/abs/10.1175/2010JCLI3341.1 [Accessed March 28, 2012]. 134

4. Cazenave A, Llovel W (2010) Contemporary Sea Level Rise. Annual Review of Marine Science 2:145–173. 135

Available at: http://www.annualreviews.org/doi/abs/10.1146/annurev-marine-120308-081105 [Accessed 136

March 4, 2012]. 137

5. Price SF, Payne AJ, Howat IM, Smith BE (2011) Committed sea-level rise for the next century from 138

{Greenland} ice sheet dynamics during the past decade. Proceedings of the National Academy of Sciences 139

108:8978–8983. 140

6. Gladstone RM, Lee V, Vieli A, Payne AJ (2010) Grounding line migration in an adaptive mesh ice sheet 141

model. Journal of Geophysical Research 115:19 PP. 142

7. Stammer D, Cazenave A, Ponte RM, Tamisiea ME (2013) Causes for Contemporary Regional Sea Level 143

Changes. Annual Review of Marine 5:21–46. 144

8. Payne AJ et al. (2007) Numerical modeling of ocean-ice interactions under Pine Island Bay’s ice shelf. 145

Journal of Geophysical Research 112:10019. 146

9. Van den Broeke MR, Bamber J, Lenaerts J, Rignot E (2011) Ice Sheets and Sea Level: Thinking Outside the 147

Box. Surveys in Geophysics 32:495–505. Available at: http://www.springerlink.com/index/10.1007/s10712-148

011-9137-z [Accessed March 13, 2012]. 149

10. Shepherd a. et al. (2012) A Reconciled Estimate of Ice-Sheet Mass Balance. Science 338:1183–1189. 150

Available at: http://www.sciencemag.org/cgi/doi/10.1126/science.1228102 [Accessed November 29, 2012]. 151

11. Rignot E, Velicogna I, Van den Broeke MR, Monaghan A, Lenaerts J (2011) Acceleration of the contribution 152

of the Greenland and Antarctic ice sheets to sea level rise. GEOPHYSICAL RESEARCH LETTERS 38. 153

12. Rahmstorf S et al. (2007) Recent Climate Observations Compared to Projections. Science 316:709. 154

13. Rahmstorf S, Foster G, Cazenave A (2012) Comparing climate projections to observations up to 2011. 155

Environmental Research Letters 7:044035. Available at: http://stacks.iop.org/1748-156

9326/7/i=4/a=044035?key=crossref.c8d193b66d94e8b3e9454779b909f216 [Accessed November 28, 2012]. 157

14. Fettweis X, Tedesco M, Van den Broeke M, Ettema J (2011) Melting trends over the Greenland ice sheet 158

(1958–2009) from spaceborne microwave data and regional climate models. The Cryosphere 5:359–375. 159

Available at: http://www.the-cryosphere.net/5/359/2011/ [Accessed March 13, 2012]. 160

15. Fettweis X et al. (2012) Estimating Greenland ice sheet surface mass balance contribution to future sea level 161

rise using the regional atmospheric climate model MAR. The Cryosphere Discussions 6:3101–3147. 162

Available at: http://www.the-cryosphere-discuss.net/6/3101/2012/ [Accessed November 8, 2012]. 163

16. Ettema J et al. (2010) Climate of the Greenland ice sheet using a high-resolution climate model – Part 1: 164

Evaluation. The Cryosphere 4:511–527. Available at: http://www.the-cryosphere.net/4/511/2010/ [Accessed 165

March 13, 2012]. 166

17. Ligtenberg SRM, Berg WJ, Broeke MR, Rae JGL, Meijgaard E (2013) Future surface mass balance of the 167

Antarctic ice sheet and its influence on sea level change, simulated by a regional atmospheric climate model. 168

Climate Dynamics. Available at: http://link.springer.com/10.1007/s00382-013-1749-1 [Accessed May 22, 169

2013]. 170

18. Pfeffer WT, Harper JT, O’Neel S (2008) Kinematic Constraints on Glacier Contributions to 21st-Century 171

Sea-Level Rise. Science 321:1340–1343. 172

19. Solomon S et al. eds. (2007) Climate Change 2007: The Physical Science Basis. Contribution of Working 173

Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge 174

University Press, Cambridge, United Kingdom and New York, NY, USA.). 175

20. Bamber JL, Aspinall WP (2013) An expert judgement assessment of future sea level rise from the ice sheets. 176

Nature Climate Change 3:424–427. Available at: http://www.nature.com/doifinder/10.1038/nclimate1778 177

[Accessed May 22, 2013]. 178

21. Dupont TK, Alley RB (2005) Assessment of the importance of ice-shelf buttressing to ice-sheet flow. 179

Geophysical Research Letters 32:4503. 180

22. Dupont TK, Alley RB (2006) Role of small ice shelves in sea-level rise. Geophysical Research Letters 181

33:9503. 182

23. Rott H, Rack W, Nagler T (2007) Increased export of grounded ice after the collapse of northern Larsen ice 183

shelf, Antarctic Peninsula, observed by Envisat ASAR. Geoscience and Remote Sensing Symposium, IEEE 184

International:1174–1176. 185

24. Rott H, Müller F, Nagler T, Floricioiu D (2011) The imbalance of glaciers after disintegration of Larsen-B 186

ice shelf, Antarctic Peninsula. The Cryosphere 5:125–134. 187

25. De Angelis H, Skvarca P (2003) Glacier surge after ice shelf collapse. Science (New York, NY) 299:1560–2. 188

Available at: http://www.ncbi.nlm.nih.gov/pubmed/12624263 [Accessed March 1, 2012]. 189

26. Rignot E et al. (2004) Accelerated ice discharge from the Antarctic Peninsula following the collapse of 190

Larsen B ice shelf. Geophysical Research Letters 31:2–5. Available at: 191

http://www.agu.org/pubs/crossref/2004/2004GL020697.shtml. 192

27. Scambos TA, Bohlander J, Shuman JA, Skvarca P (2004) Glacier acceleration and thinning after ice shelf 193

collapse in the Larsen B embayment, Antarctica. Geophysical Research Letters 31:L18402. 194

28. Hulbe CL, Scambos T a., Youngberg T, Lamb AK (2008) Patterns of glacier response to disintegration of the 195

Larsen B ice shelf, Antarctic Peninsula. Global and Planetary Change 63:1–8. Available at: 196

http://linkinghub.elsevier.com/retrieve/pii/S0921818108000404 [Accessed April 17, 2012]. 197

29. Joughin I, Alley RB (2011) Stability of the West Antarctic ice sheet in a warming world. Nature Geoscience 198

4:506–513. Available at: http://www.nature.com/doifinder/10.1038/ngeo1194 [Accessed July 29, 2011]. 199

30. Rack W, Rott H (2004) Pattern of retreat and disintegration of Larsen B Ice Shelf, Antarctic Peninsula. 200

Annals of Glaciology 39:505–510. 201

31. Cook a. J, Vaughan DG (2010) Overview of areal changes of the ice shelves on the Antarctic Peninsula over 202

the past 50 years. The Cryosphere 4:77–98. Available at: http://www.the-cryosphere.net/4/77/2010/. 203

32. Glasser NF, Scambos TA (2008) A structural glaciological analysis of the 2002 Larsen B Ice Shelf collapse. 204

Journal of Glaciology 54:3–16. 205

33. MacAyeal DR, Scambos TA, Hulbe CL, Fahnestock MA (2003) Catastrophic ice-shelf break-up by an ice-206

shelf-fragment-capsize mechanism. Journal of Glaciology 49:22–36. 207

34. Doake CSM, Corr HFJ, Skvarca P, Young NW (1998) Breakup and conditions for stability of the northern 208

Larsen Ice Shelf, Antarctica. Nature 391:778–780. 209

35. Doake CSM (2001) Ice Shelf Stability. British Antarctic Survey:1282–1290. 210

36. Vieli A, Payne AJ, Du Z, Shepherd A (2006) Numerical modelling and data assimilation of the Larsen B ice 211

shelf, Antarctic Peninsula. Philosophical transactions Series A, Mathematical, physical, and engineering 212

sciences 364:1815–39. Available at: http://www.ncbi.nlm.nih.gov/pubmed/16782611 [Accessed May 14, 213

2012]. 214

37. Winkelmann R et al. (2011) The Potsdam Parallel Ice Sheet Model (PISM-PIK) Part 1: Model description. 215

The Cryosphere 5:715–726. 216

38. Bueler E, Brown J (2009) The shallow shelf approximation as a sliding law in a thermomechanically 217

coupled ice sheet model. Journal of Geophysical Research 114:F03008. 218

39. Le Brocq a. M, Payne a. J, Vieli a. (2010) An improved Antarctic dataset for high resolution numerical ice 219

sheet models (ALBMAP v1). Earth System Science Data 2:247–260. Available at: http://www.earth-syst-sci-220

data.net/2/247/2010/ [Accessed March 30, 2012]. 221

40. Levermann A et al. (2012) Kinematic first-order calving law implies potential for abrupt ice-shelf retreat. 222

The Cryosphere 6:273–286. 223

41. Alley RB et al. (2008) A simple law for ice-shelf calving. Science (New York, NY) 322:1344. Available at: 224

http://www.ncbi.nlm.nih.gov/pubmed/19039129 [Accessed March 29, 2012]. 225

42. Winkelmann R, Levermann a., Martin M a., Frieler K (2012) Increased future ice discharge from Antarctica 226

owing to higher snowfall. Nature 492:239–242. Available at: 227

http://www.nature.com/doifinder/10.1038/nature11616 [Accessed December 12, 2012]. 228

43. Albrecht T, Martin MA, Winkelmann R, Haseloff M, Levermann A (2011) Parameterization for subgrid-229

scale motion of ice-shelf calving fronts. The Cryosphere 5:35–44. 230

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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

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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