The effect of ice shelf rheology on shelf edge bending

• Published in: The Cryosphere
• Main Author: W. R. Buck
• Format: Article in Journal/Newspaper
• Language: English
• Published: Copernicus Publications 2024
• Subjects: Environmental sciences; GE1-350; Geology; QE1-996.5; Ice Shelf; The Cryosphere
• Online Access: https://doi.org/10.5194/tc-18-4165-2024; https://doaj.org/article/e6f77c8faf284d849d7ac44bb5e60491

The distribution of pressure on the vertical seaward front of an ice shelf has been shown to cause downward bending of the shelf if the ice is assumed to have vertically uniform viscosity. Satellite lidar observations show that many shelf edges bend upward and that the amplitude of upward deflections depends systematically on ice shelf thickness. A simple analysis is presented showing that upward bending of shelf edges can result from vertical variations in ice viscosity that are consistent with field observations and laboratory measurements. 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 as a function of shelf surface temperatures, shelf thickness and ice rheologic parameters. The effect of a power-law relation between stress difference and strain rate can also be 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 <svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="23pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="69f9d0e5393dfb4758e625fb9659e665"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tc-18-4165-2024-ie00001.svg" width="23pt" height="14pt" src="tc-18-4165-2024-ie00001.png"/></svg:svg> , upward bending is expected, while for warm surface temperatures and small values of Q / n <svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="23pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="c436b54090b67d02ff51684a841eda67"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tc-18-4165-2024-ie00002.svg" width="23pt" height="14pt" ...