Ice Sheet Grounding Line Dynamics: Steady States, Stability, and Hysteresis

Abstract

The ice sheet-ice shelf transition zone plays an important role in controlling marine ice sheet dynamics, as it determines the rate at which ice flows out of the grounded part of the ice sheet. Together with accumulation, this outflow is the main control on the mass balance of the grounded sheet. In this paper, we verify the results of a boundary layer theory for ice flux in the transition zone against numerical solutions that are able to resolve the transition zone. Very close agreement is obtained, and grid refinement in the transition zone is identified as a critical component in obtaining reliable numerical results. The boundary layer theory confirms that ice flux through the grounding line in a two-dimensional sheet-shelf system increases sharply with ice thickness at the grounding line. This result is then applied to the large-scale dynamics of a marine ice sheet. Our principal results are that (1) marine ice sheets do not exhibit neutral equilibrium but have well-defined, discrete equilibrium profiles; (2) steady grounding lines cannot be stable on reverse bed slopes; and (3) marine ice sheets with overdeepened beds can undergo hysteresis under variations in sea level, accumulation rate, basal slipperiness, and ice viscosity. This hysteretic behavior can in principle explain the retreat of the West Antarctic ice sheet following the Last Glacial Maximum and may play a role in the dynamics of Heinrich events.

Potential Antarctic Ice Sheet retreat driven by hydrofracturing and ice cliff failure

“…5a), the model functions much as in earlier work (Pollard and DeConto, 2009). As expected, West Antarctica undergoes major collapse driven primarily by increased sub-ice melt from the +2 • C ocean warming, causing reduced buttressing at the major WAIS grounding lines, and leading to classic marine instability (MISI) into the deepening interior beds (Weertman, 1974;Schoof, 2007). The time scale of this retreat is several hundred to a thousand years (Pollard and DeConto, 2009, and Fig.…”

“…ρ i and ρ w are densities of ice and ocean water respectively, g is gravitational acceleration, and θ is 1 minus the fractional reduction in the hydrostatic imbalance at the grounding line due to back stress on an ice shelf (Schoof, 2007;Pollard and DeConto, 2012). For completely freely floating shelf ice, or no shelf at all, θ = 1, and the right-hand side of Eq.…”

“…Floating ice shelves and grounding-line migration are included. It uses hybrid ice dynamics and an internal condition on ice velocity at the grounding line (Schoof, 2007). Bedrock deformation is modeled as an elastic lithospheric plate above local isostatic relaxation.…”

Evaluating Marie Byrd Land stability using an improved basal topography

“…As a result, we chose to use the model of Pollard and DeConto (2012b), which has demonstrated its ability to make long-term paleoclimatic runs for Antarctica (Mackintosh et al, 2011;DeConto et al, 2012;Gomez et al, 2013), and can provide direct comparison to the previous studies of WAIS referenced above (Pollard and DeConto, 2009;Deconto et al, 2008). The ice dynamics in this model are a combination of (i) internal shearing flow (Shallow Ice Approximation, SIA) for grounded ice, and (ii) stretching flow (Shallow Shelf Approximation, SSA) for ice shelves, coupled using a boundary-layer treatment of ice flux across grounding lines after Schoof (2007) that captures grounding-line migration reasonably accurately without very fine resolution in the grounding zone (e.g., Gladstone et al, 2010Gladstone et al, , 2012. The model for bedrock deformation beneath grounded ice follows Huybrechts and de Wolde (1999) and Ritz et al (2001), with local asthenospheric relaxation towards isostasy below an elastic plate representing non-local lithospheric deformation.…”

“…Geologic and glaciological features discussed by name are labeled. thought to precipitate unstable retreat of the ice (Weertman, 1974;Schoof, 2007). As a result, comprehensive seismic and radar surveys of the ice sheet are essential to both our geologic and glaciological understanding.…”