Fig. 2.

Evolution of a 10,000-member ensemble of minimal model (Eq. 1) simulations of grounding-line retreat over idealized constant-slope bed topography and variability in ocean forcing. (A) Ensemble interquartile range (shading spans 25th percentile to 75th percentile). (B) SD derived from numerically calculated ensemble statistics (solid lines) and analytic predictions from stochastic perturbation theory (circles). (C) Skewness derived from numerically calculated ensemble statistics (solid lines) and analytic predictions from stochastic perturbation theory (circles). Negative skew indicates more retreated grounding line. There is no analytic approximation available for skewness under autocorrelated forcing (see SI Appendix for discussion of stochastic perturbation theory). Pink shading and lines are simulations on a reverse-sloping bed ($b_x=4\times 10^{-3}$) with constant ocean forcing, selected from a Gaussian distribution. Blue shading and lines are simulations on a reverse-sloping bed ($b_x=4\times 10^{-3}$) with interdecadal variability in ocean forcing (${\tau }_F=10$ y). Orange shading and lines are simulations on a reverse-sloping bed ($b_x=3.5\times 10^{-3}$) with interannual variability in ocean forcing (${\tau }_F=1$ y). Green shading and lines are simulations on a forward-sloping bed ($b_x=-10^{-3}$) with interannual variability in ocean forcing (${\tau }_F=1$ y). In all simulations, $P=0.35$ m/y, $\gamma =7.8\times 10^{-9}$ m^−2.75⋅y⁻¹, and $\beta =4.75$. In simulations with variable ocean forcing (blue, orange, green), $\overline{\eta }=0$ and ${\sigma }_F=100$ m/y. In simulations with uncertainty in constant ocean forcing (pink), ${\sigma }_P=50$ m/y.