Table 1.
Magnitude and rate of ice-cliff failure resulting from viscous deformation and brittle failure.
| H/Hc (m) | Tice = −20 °C |
Tice = −10 °C Bn |
Tice = −5 °C Bn |
Back force (N m−1) | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Bf | Bn | Bh | ||||||||||||||
| TtF | R | Ĉ | TtF | R | Ĉ | TtF | R | Ĉ | TtF | R | Ĉ | TtF | R | Ĉ | ||
| 800/136 | 33.50 | 45 | 1 | 4.2e6 | ||||||||||||
| 850/144 | 32.50 | 20 | 1 | – | ||||||||||||
| 900/153 | 26.75 | 20 | 1 | – | ||||||||||||
| 950/161 | 41.00 | 30 | 1 | 47.25 | 80 | 2 | 40.00 | 40 | 1 | 16.25 | 20 | 1 | – | |||
| 1000/169 | 33.25 | 40 | 1 | 37.25 | 55 | 2 | 36.25 | 60 | 2 | 9.75 | 50 | 5 | 6.6e6 | |||
| 1500/255 | 10.00 | 90 | 9 | 12.00 | 90 | 8 | 29.00 | 190 | 7 | 4.50 | 120 | 27 | 1.75 | 50 | 92 | 1.0e7 |
| 2000/339 | 1.50 | 180 | 120 | 1.50 | 240 | 160 | 8.75 | 230 | 26 | 1.00 | 220 | 220 | 0.50 | 320 | 640 | 5.7e7 |
| 2500/424 | 0.50 | 350 | 700 | 1.00 | 440 | 440 | 1.75 | 460 | 260 | 0.25 | 360 | 1440 | 0.25 | 370 | 1480 | 2.1e7 |
The time to failure (TtF; d), retreat magnitude (R; m) and calving retreat rate (Ĉ; m d−1) found with the Elmer/Ice–HiDEMbe (the brittle-elastic version of the Helsinki Discrete Element Model) workflow over the range of susceptible ice thicknesses with varying ice temperature (Tice) and basal slip conditions. Bn, Bf and Bh represent normal, approaching frozen and high basal-slip conditions. The magnitude of mélange back force required to halt failure for the associated Bn, Tice = −5 °C scenario is provided. Blank spaces denote simulations in which failure did not occur within our 50 d viscous deformation window (Supplementary Note 3). Hash marks note simulations that were not conducted for this study.