The ice stability depth is defined as the depth at which water ice will sublimate at a rate of 1 mm Gyr⁻¹). a–f, Full-resolution maps of ice stability depth for areas where water ice is stable at the current orientation (a, b), in the palaeopole orientation (c, d) and in an ‘overlapping’ orientation (e, f); left panels shown the north polar region, right panels show the south. These models define the locations at which isotropically supplied water ice would be stable over geologic time; depth is given as an average of the two models in those locations. Panels a–d are the bases for Fig. 1c, d. Models are constrained to ± 300 km in stereographic x, y coordinates. Latitude lines are every 2° poleward of 80°. All other symbols are defined in Fig. 1. Panel b adapted from ref. 5, American Association for the Advancement of Science.