Extended Data Fig. 4: Physical regimes of surface and basal fractures.

a, b, The schematics of a surface (a) and basal crevasse (b) with depth varying resistive stress R_xx(z) due to the vertical temperature gradient (assumed to be linear). c, The fracture stability diagram for surface and basal crevasses with and without temperature effects (assuming the surface and the base of ice shelf are −30 and 0 °C, respectively). Dashed and solid lines represent the transition boundaries of stable-to-unstable and no fracture-to-stable fracture regions, respectively. Warmer ice at the base reduces the ice viscosity (and thus stress), which impacts the locations of the stability boundaries of basal crevasse. d, The five physical regimes (I–V) defined by the transition boundaries for surface crevasse (black curves in c) and basal crevasse with temperature effects (light blue curves in c). e–h, The locations corresponding to regimes I–V on ice shelves are determined by different estimates of stress. The percentage values denote the portion of ice-shelf area containing the physical condition in each regime. The green, pink, blue, red, yellow and white areas correspond to regimes I, II, III, IV, V and the U-Net-detected fracture locations, respectively. e, f, The stress field determined by the temperature dependent viscosity factor B(T) (equation (6) in ref. ⁵⁷) combined with along-flow strain rates obtained by Fürst et al.¹³ (e) and Wearing⁶¹ (f). g, h, The stress fields in the along-flow (g) and 1st principal (h) stress directions calculated by ref. ¹³ include the effects of damage-induced ice softening through the data assimilation and model inversion process. The second row of e–h is the close-up view of the white box in the first row. Note that the spatial areas of regimes I—V were calculated solely on the basis of the dimensionless stress and toughness, and are independent of the U-Net result. The spatial resolution is 1 km, the same as the stress field resolution used in ref. ¹³.