A Thin-Plate (Shallow Shelf) Treatment of Viscoelastic Ice-Shelf Flexure with Applications

Abstract:

We derive a Shallow Shelf style treatment of the viscoelastic flexural deformation of a floating ice shelf and apply it to various problems relevant to ice-shelf response to sudden changes of loads (e.g., draining supra glacial lakes, iceberg calving, basal crevassing). Our analysis is based on the assumption that total deformation is the simple sum of elastic and viscous (or power-law creep) deformations (i.e., akin to a Maxwell model having a spring and dashpot in series). The key simplification in our analysis is the assumption that strain and its time derivative vary linearly as a function of depth through the thin ice shelf, and are zero at the neutral plane half the distance between the surface and base. We develop an analytic solution for idealized geometry and loading functions, and compare to a hierarchy of numerical treatments, including comparisons with full-Stokes solutions of viscoelastic flexure using an advanced finite-element package. Our work is applicable to numerous problems in ice-shelf and ice-tongue glaciology where impulsive loads or impulsive changes in geometry are involved. Examples of application include hydrostatic rebound in the aftermath of sudden surface lake drainage on Larsen B Ice Shelf immediately prior to its disintegration, ice-shelf and iceberg margin response to sudden edge-on-edge collisions between the two (push-mound formation), impulsive changes to geometry associated with ice-shelf calving, ice-front geometry modification by melting, necking phenomena, and basal crevassing.