Marine Ice Sheet Instability

Marine Ice Sheet Instability (abbreviated MISI) is a nonlinear dynamical positive feedback and cryospheric tipping point that governs the stability and irreversible retreat of marine ice sheets—continental ice sheets whose bedrock base lies below sea level and whose margins terminate in the ocean as floating ice shelves. First hypothesized in 1974 by glaciologist Johannes Weertman (and applied to the West Antarctic Ice Sheet by John H. Mercer in 1978 and Terry Hughes in 1981), and proven mathematically via asymptotic boundary-layer theory by Christian Schoof in 2007, Marine Ice Sheet Instability occurs whenever an unbuttressed marine ice sheet's grounding line (the transition boundary where grounded continental ice becomes buoyant and begins to float as an ice shelf) rests on a retrograde bedrock slope—a submarine bed that deepens inland toward the interior of the ice sheet. Because ice discharge flux across the grounding line scales as a high power of ice thickness (q_g ∝ h_g³ to h_g⁵), any initial retreat of the grounding line into deeper water increases the local ice thickness at the grounding line, accelerating ice outflow, thinning the upstream ice, and driving self-sustaining retreat until the grounding line reaches a shallow, prograde (upward-sloping) bedrock ridge.

Consider a marine ice sheet resting on a submarine bedrock elevation b(x) below sea level (b(x) < 0, where x increases seaward). At the grounding line (x = x_g), the grounded ice of thickness h_g transitions from resting on the bed to floating hydrostatically in seawater of density ρ_w ≈ 1,028 kg m⁻³. By Archimedes' hydrostatic flotation criterion, the ice thickness h_g at the grounding line is directly fixed by the water depth −b(x_g):

ρ_i h_g = − ρ_w b(x_g)   ⟹   h_g(x_g) = − (ρ_w / ρ_i) b(x_g) ≈ −1.12 b(x_g)

where ρ_i ≈ 917 kg m⁻³ is the density of glacial ice.

In 2007, mathematician Christian Schoof used matched asymptotic expansions of the Shallow Shelf / Shallow Stream Approximation (SSA) coupled with Glen's flow law (strain rate ε̇_xx = A τ_xxⁿ, with creep exponent n ≈ 3) and Weertman's basal sliding law (τ_b = C u_b^m, with m ≈ 1/3) across the narrow membrane-stress transition zone around the grounding line. Schoof proved that for an unbuttressed two-dimensional marine ice sheet, the ice volume flux per unit width across the grounding line (q_g = h_g u_g) is an increasing, superlinear power-law function of grounding-line thickness h_g:

q_g(x_g) = [ A (ρ_i g)ⁿ⁺¹ (1 − ρ_i / ρ_w)ⁿ / (4ⁿ C) ]^1/(m+1) · h_g^{(m+n+3)/(m+1)}   ∝   h_g^β

For standard glaciological parameters (n = 3 and m = 1/3), the flux exponent is:

β = (m + n + 3) / (m + 1) = (19/3) / (4/3) = 19/4 = 4.75   (typically β ≈ 3 to 5 across sliding laws).

Conservation of ice mass requires that the grounding line advance or retreat at rate dx_g/dt determined by the imbalance between total upstream catchment snow accumulation Q_in(x_g) = ∫₀^x_g a(x) dx and grounding-line discharge q_g(x_g). Linear stability perturbation around a steady-state grounding-line position (Q_in(x_g) = q_g(x_g)) yields two opposite regimes depending on the sign of the bedrock slope db/dx at x = x_g:

In real three-dimensional Antarctic fjords and embayments, two physical processes can stabilize a grounding line even when it rests on a retrograde bed (db/dx > 0):

1. Ice-Shelf Buttressing (Gudmundsson et al., 2012; Pegler, 2018): Most Antarctic marine ice streams do not calve directly at the grounding line; instead, they flow out into floating ice shelves confined within narrow coastal embayments or pinned against submarine seabed highs (ice rises and pinning points). Lateral shear stress along the embayment sidewalls and drag over pinning points exert a compressive back-stress (σ_butt) on the grounding line, modifying Schoof's flux formula by a dimensionless buttressing factor Θ ∈ (0, 1]:

q_g ∝ Θ^{n / (m+1)} h_g^β

As Hilmar Gudmundsson (2012, 2013) demonstrated in three-dimensional modeling, if grounding-line retreat into a confined embayment increases the length and lateral drag of the floating ice shelf fast enough that Θ decreases more rapidly than h_g increases, ice-shelf buttressing can stabilize a grounding line on a retrograde bed. Conversely, when warm Southern Annular Mode–driven Circumpolar Deep Water (CDW) intrudes beneath the ice shelf and thins it from below (or unpins it from a seabed ridge), Θ → 1, removing the buttressing brake and triggering MISI.

1. Rapid Glacial Isostatic Adjustment (GIA) and Gravitational Sea-Level Fingerprints (Gomez et al., 2010, 2015): As a marine ice stream thins and loses mass during retreat, two rapid solid-Earth and gravitational feedbacks reduce the local water depth at the grounding line:
   • Diminished gravitational attraction of the shrinking ice sheet causes the local ocean surface (the geoid) immediately adjacent to the grounding line to fall, lowering local relative sea level.
   • Because the upper mantle beneath the West Antarctic Rift System has an unusually low viscosity (η ≈ 10¹⁸–10¹⁹ Pa s, 100 to 1,000 times less viscous than cratonic East Antarctica), crustal elastic and viscoelastic isostatic uplift rebounds upward on decadal-to-centennial timescales (at rates up to 40–50 mm yr⁻¹ observed by GPS in the Amundsen Sea sector, Barletta et al., 2018), shallowing the bedrock beneath the grounding line and slowing MISI retreat.

Airborne ice-penetrating radar surveys (compiled in the BedMachine Antarctica high-resolution subglacial topography dataset by Mathieu Morlighem et al., 2020) reveal that marine-based ice grounded on retrograde beds below sea level holds a total global sea-level equivalent (SLE) of ~22.5 meters:

In 2015 and 2016, David Pollard, Robert M. DeConto, and Richard B. Alley proposed a distinct, structurally driven mechanical instability that could compound MISI under high-emission warming scenarios—termed Marine Ice Cliff Instability (MICI):

• Hydrofracturing of Buttressing Ice Shelves: If intense surface atmospheric warming generates meltwater ponds on top of a floating ice shelf, dense liquid water percolating into crevasses drives rapid hydrofracture that disintegrates the floating ice shelf within weeks (as observed during the March 2002 collapse of the Larsen B Ice Shelf on the Antarctic Peninsula).
• Subaerial Ice-Cliff Structural Failure (>90–100 m Cliff Height): If an ice shelf collapses over a deep marine grounding line (h_g > 800–1,000 m), it exposes an unbuttressed vertical ice cliff rising >90 to 100 meters above the sea surface. Because the longitudinal tensile and shear stresses at the base of a subaerial cliff taller than ~90–100 m exceed the yield tensile/shear strength of glacial ice (~1 MPa), the cliff face fails mechanically by brittle slumping and calving (Bassis & Walker, 2012), exposing an even taller cliff further inland along the retrograde bed. Subsequent laboratory and viscoelastic damage-mechanics studies (Bassis et al., 2021; Crawford et al., 2021) demonstrated that whether MICI triggers runaway collapse depends on the rate of ice-shelf removal versus viscous creep relaxation and mélange back-stress inside the fjord.

In 2020, compilation of the high-resolution BedMachine Antarctica mass-conservation subglacial topography dataset mapped deep retrograde submarine troughs exceeding 2,000 meters below sea level beneath Thwaites, Pine Island, Denman, and Totten glaciers, refining spatial vulnerability assessments for Marine Ice Sheet Instability across both West and East Antarctica (Morlighem et al., 2020).

In 2022, autonomous underwater vehicle multibeam sonar surveys of the deglaciated seafloor in front of Thwaites Glacier documented rib-like tidal grounding-line corrugations showing that during a prior warm pulse the glacier retreated down its retrograde bed slope at rates exceeding 2.1 kilometers per year—more than double its satellite-observed retreat rate between 2011 and 2019 (Graham et al., 2022).

In 2024, high-resolution synthetic aperture radar interferometry from the commercial ICEYE satellite constellation demonstrated that warm, high-pressure seawater intrudes 2 to 6 kilometers upstream of the nominal grounding line beneath Thwaites Glacier during spring tides, creating a dynamic grounding-zone boundary layer that amplifies basal melt on retrograde bedrock slopes (Rignot et al., 2024).

1. Weertman, J. (1974). Stability of the junction of an ice sheet and an ice shelf. Journal of Glaciology, 13(67), 3–11.
2. Schoof, C. (2007). Ice sheet grounding line dynamics: Steady states, stability, and hysteresis. Journal of Geophysical Research: Earth Surface, 112(F4), F04028.
3. Joughin, I., Smith, B. E., & Medley, B. (2014). Marine ice sheet collapse potentially under way for the Thwaites Glacier Basin, West Antarctica. Science, 344(6185), 735–738.
4. Rignot, E., Mouginot, J., Morlighem, M., Seroussi, H., & Scheuchl, B. (2014). Widespread, rapid grounding line retreat of Pine Island, Thwaites, Smith, and Kohler glaciers, West Antarctica, from 1992 to 2011. Geophysical Research Letters, 41(10), 3502–3509.
5. Morlighem, M., Rignot, E., Binder, T., Blankenship, D., Drews, R., Eagles, G., et al. (2020). Deep glacial troughs and stabilizing ridges unveiled beneath the margins of the Antarctic ice sheet. Nature Geoscience, 13(2), 132–137.
6. Graham, A. G. C., Wåhlin, A., Hogan, K. A., Nitsche, F. O., Heywood, K. J., Totten, R. L., et al. (2022). Rapid retreat of Thwaites Glacier in the pre-satellite era. Nature Geoscience, 15(9), 706–713.
7. Rignot, E., Ciracì, E., Scheuchl, B., Tolpekin, V., Wollersheim, M., & Dow, C. (2024). Widespread seawater intrusions beneath the grounded ice of Thwaites Glacier, West Antarctica. Proceedings of the National Academy of Sciences, 121(22), e2404766121.