A marine-terminating ice sheet sits on bedrock that dips below sea level. Whether ice is grounded (resting on the bed) or floating (an ice shelf) is set by Archimedes' flotation criterion applied to the ice column:
H_f(x) = (ρ_w / ρ_i) · (sea level − bed(x))
grounded if H(x) ≥ H_f(x), floating otherwise
The boundary between the two — the grounding line — is not fixed. Grounded ice obeys a nonlinear diffusion from the shallow-ice approximation, H evolving under mass conservation ∂H/∂t = a − ∂Q/∂x with Glen's-law flux Q ∝ H^(n+2)·|∂S/∂x|^(n−1)·∂S/∂x (n≈3). At the grounding line itself, ice discharges into the ocean at a rate that rises steeply with the local ice thickness — the scaling from Schoof (2007), Q_gl ∝ H_gl^α with α > 4 for realistic sliding laws.
That steep dependence is what makes Marine Ice Sheet Instability (MISI) possible: on a retrograde (reverse-sloping) bed that deepens inland, any small retreat puts the grounding line in deeper water, which demands a thicker ice column to stay grounded, which pushes discharge — and therefore retreat — even further, with no stabilizing feedback until the bed slope reverses. A prograde bed that shallows inland does the opposite: retreat moves the grounding line into shallower water, discharge falls, and the position self-stabilizes. This mechanism (Weertman 1974; Schoof 2007) is the leading explanation for the ongoing, hard-to-reverse retreat of West Antarctic outlet glaciers such as Thwaites and Pine Island.
Beyond the grounding line, the floating ice shelf thins from sub-shelf ocean melting (warmer intruding water) and viscous spreading as it flows toward the open ocean. When its thickness at the front drops below a threshold, it can no longer support the along-flow stress and a slab breaks free — a simplified thickness-threshold stand-in for the crevasse-penetration calving laws (Benn et al. 2007) used in real ice-sheet models. Each event here spawns a drifting tabular iceberg and the calving front retreats one grid cell.
- Bed profile — switch between the unstable (retrograde) and stable (prograde) bedrock geometry and watch the grounding line's long-term behaviour change qualitatively.
- Basal slipperiness / ice softness — scales how easily grounded ice deforms and slides, and how much flux it can push through the grounding line.
- Sub-shelf ocean melt — the real-world lever: warmer ocean water thins the shelf and can single-handedly trigger runaway retreat on a retrograde bed, mirroring observed Antarctic "ice-shelf ocean forcing".
- Sea-level offset — raising sea level directly raises the flotation threshold everywhere, an independent way to destabilize the grounding line.