Extended Data Table 1 Overview of the parameters used in the idealized model experiment

s_T

Stability parameter that isolates dependence of ice-sheet response on ‘static’ features of conveying ice-stream.

\(1+\frac{\frac{{\rho }_{w}}{{\rho }_{i}}\left(\beta \bar{{b}_{x}}\bar{L}\right)}{{h}_{g}}\)

α

Parameter that describes partition of stress accommodated by internal deformation and basal slip.

\(2\left(\frac{1}{m}\right)+1\)

h_g

Grounding zone thickness.

\(\frac{{\rho }_{w}}{{\rho }_{i}}(\bar{{b}_{x}}\bar{L}+{b}_{0})\)

β

Grounding zone outflow sensitivity to ice thickness derived from boundary-layer analysis of ref. ⁴⁸

\(\frac{m+n+3}{m+1}\)

m

Bed exponent in Weertman basal-sliding relation.

\(\frac{1}{3},\frac{1}{4},\frac{1}{5}\)

C

Friction coefficient

1e⁶, 2e⁶, . . . 10e⁶

b₀

Interior bed elevation (m)

400, 600, 800, 1000

b_x

Bed slope

− 2e⁻³, − 3e⁻³, − 4e⁻³, − 5e⁻³

\(\bar{L}\)

Equilibrium glacier length (m)

200e³ − 400e³

n

Ice flow exponent

3

ρ_i

Density of ice (kg/m³)

917

ρ_w

Density of water (kg/m³)

1028