An improved model for tidally modulated grounding-line migration

Abstract

ABSTRACT. Understanding grounding-line dynamics is necessary for predictions of long-term ice-sheet stability. However, despite growing observations of the tidal influence on grounding-line migration, this short-timescale migration is poorly understood, with most modeling attempts assuming beam theory to calculate displacements. Here we present an improved model of tidal grounding-line migration that treats migration as an elastic fracture problem, forced by the additional ocean water pressure from the tide. This new model predicts that the grounding line cannot be assumed to be in hydrostatic equilibrium and, furthermore, that migration is inherently asymmetric and nonlinear, with migration distances that are not proportional to the tidal load. Specifically, for constant surface slope, the grounding line migrates upstream approximately ten times further as the tide rises from mean sea level to high tide than it migrates downstream as the tide falls from mean sea level to low tide, and migration distances are substantially larger than simple flotation arguments suggest. Numerical tests also show that the dependence of migration distance on elastic moduli and ice-sheet thickness are inconsistent with predictions of beam theory for a range of realistic values. Finally, applying the new model to observations in Antarctica results in new estimates of bed slopes, though these estimates remain uncertain due to imperfect knowledge of the relevant rheological parameters.

On the Short‐term Grounding Zone Dynamics of Pine Island Glacier, West Antarctica, Observed With COSMO‐SkyMed Interferometric Data

“…Our examination of earlier interferograms acquired in 1992, 1994, and 2000 indicates that similar lakes were present at earlier times and hence are not the result of recent changes in grounding line position or speedup on PIG but reflect a rather sustained subglacial hydrologic system (supporting information) (Rignot et al, , FigS2S6_SOM 1992 (b), 1994 (b), 2000 (b)). We note that the elastic crack model of Tsai and Gudmundsson (, hereinafter TG15) also provides plausible results when interpreting kilometric scale tidally induced grounding line migration. The TG15 model solves a problem of elastic crack growth viewing the interface between the ice and the bed as a horizontal fracture assuming that only elastic stresses are relevant over the 12 h time scale of interest.…”

On the interpretation of ice-shelf flexure measurements

“…Clearly on shallow sloping beds where tidal migration of the grounding line is potentially as much as several kilometers (Brunt and others, 2011) the effect will be very considerable and the assumption of a fixed grounding line for either an elastic beam model or the full-Stokes model presented here would lead to an articially narrow grounding zone. Walker and others (2013) treat the GL as a fulcrum which, while it may be a suitable simplification for analysing tidal flexure, is implausible based on the known physical properties of ice and from geometrical considerations (Tsai and Gudmundsson, 2015). The limited evidence of reversed flexure upstream of the grounding line can be explained physically without this fulcrum if ice is resting on a soft till as shown in our experiments (Fig.…”

Insights into ice stream dynamics through modelling their response to tidal forcing

“…Since the distance by which the grounding line migrates is very sensitive to geometry, which is represented here by a constant shallow slope but in reality is probably much more complex, these results should not be considered as an exact study of the tidally modulated grounding line migration of an ice stream. In spite of this, the asymmetrical nature of the migration is expected, as shown in a novel study of this process (Tsai and Gudmundsson, 2014), and thus is a possible additional source of nonlinearity that could help produce the large Msf modulation observed on a number of ice streams.…”