18 Mar 2024
 | 18 Mar 2024

The effect of ice rheology on shelf edge bending

W. Roger Buck

Abstract. The distribution of water pressure on the vertical front of an ice shelf has been shown to cause downward bending of the edge if the ice has vertically uniform viscosity. Satellite lidar observations show upward bending of shelf edges for some areas with cold surface temperatures. A simple analysis shows that upward bending of shelf edges can result from vertical variations in ice viscosity. Such variations are an expected consequence of the temperature dependence of ice viscosity and temperature variations through a shelf. Resultant vertical variations in horizontal stress produce an internal bending moment that can counter the bending moment due to the shelf-front water pressure. Assuming a linear profile of ice temperature with depth and an Arrhenius relation between temperature and strain rate allows derivation of an analytic expression for internal bending moments. The effect of a power-law relation between stress difference and strain rate is also included analytically. The key ice rheologic parameter affecting shelf edge bending is the ratio of the activation energy, Q, and the power-law exponent, n. For cold ice surface temperatures and large values of Q/n, upward bending is expected, while for warm surface temperatures and small values of Q/n downward bending is expected. The amplitude of bending should scale with the ice shelf thickness to the power 3/2 and this is approximately consistent with a recent analysis of shelf edge deflections for the Ross Ice Shelf.

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W. Roger Buck

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2024-557', Anonymous Referee #1, 22 Apr 2024
  • RC2: 'Comment on egusphere-2024-557', Anonymous Referee #2, 28 Apr 2024
  • AC3: 'Comment on egusphere-2024-557', W. Roger Buck, 03 Jun 2024
W. Roger Buck
W. Roger Buck


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Short summary
Standard theory predicts that the edge of an ice shelf should bend downward. Satellite observations show that the edges of many ice shelves bend upward. A new theory for ice shelf bending is developed that, for the first time, includes the kind of vertical variations in ice flow properties expected for ice shelves. Upward bending of shelf edges is predicted as long as the ice surface is very cold and the ice flow properties depend strongly on temperature.