Ice sheet grounding line dynamics: Steady states, stability, and hysteresis

Abstract

[1] 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.

Similitude of ice dynamics against scaling of geometry and physical parameters

“…Here we show that the scaling conditions derived above by dimensional analysis under the concept of similitude are consistent with the boundary-layer theory which was introduced by Schoof (2007b) for a steady-state, unbuttressed, isothermal, flow-line ice sheet in SSA. Neglecting membrane stresses in the SSA stress balance, matched asymptotics are applied to solve a boundary-layer problem for the transition zone between grounded and floating ice.…”

“…The scaling behavior of ice sheets, which here is analyzed in a conceptual way, might be of use to better understand the large-scale evolution of the polar ice sheets. Of particular interest is the scaling of the ice-sheet response time (Levermann et al, 2013 against the background of Antarctic instabilities (Weertman, 1974;Schoof, 2007b;Rignot et al, 2014;Fogwill et al, 2014;Mengel and Levermann, 2014). The timescales of possible rapid ice discharge due to instability in the past (Pollard and DeConto, 2009;Pollard et al, 2015) and future (Favier et al, 2014;Joughin et al, 2014;Feldmann and Levermann, 2015b) are highly uncertain.…”

Dynamically and Observationally Constrained Estimates of Water-Mass Distributions and Ages in the Global Ocean

“…[28] Grounding line migration is a key control on ice flow dynamics [Schoof, 2007a[Schoof, , 2007bNowicki, 2007;Durand et al, 2009bDurand et al, , 2009a, which is important to capture in order for transient ice flow models to be realistic. In ISSM, we use a simple 3D grounding line migration criterion based on the hydrostatic equilibrium (see Figure 1).…”

On the reconstruction of palaeo-ice sheets: Recent advances and future challenges

“…MacAyeal, 1989;Weis et al, 1999). However, simple coupling of SIA and SSA models across the grounding line was difficult and so alternative approaches explored how ice dynamics in the transition zone could be modelled without having to employ the more computationally intense 'Stokes' equations (Chugunov and Wilchinski 1996;Hulbe and MacAyeal 1999;Schoof, 2007;Schoof and Hewitt, 2013).…”