## Three representative profiles

The GIS profile used here leads westward down-gradient. from the ice divide at Summit (Ohmura & Reeh, 1991). The b used in Equation (16) is 0.23 myr-1 at the divide, increases to a pronounced orographic high on the flank, and then decreases sharply to ca. -6.5myr-1 at the terminus. This melt rate was chosen to ensure zero net balance along the profile. Given an n value, adjustment of one parameter (S(G)) optimizes the model.

The EAIS profile used here is that directly inland from Mirny Station, as used originally by Vialov (also see Hamley et al., 1985). This profile is unusually simple for EAIS, where most gradient lines either cross margin-region mountain ranges or are affected by the Lambert basin. The b is 0.03 myr-1 at its head (chosen to be exactly 1000 km inland), and increases sharply near the margin to more than 0.2myr-1. Much of the ice in this area terminates in ice shelves, so I specify a nominal 200 m grounding line thickness, and this initial thickness is included in the integration giving Equation (16). Given an n value, adjustment of one parameter (S(EA)) optimizes the model.

The WAIS profile is an approximate Siple Coast transect from the grounding line up Ice Stream C and to the divide (Alley & Whillans, 1991; Fahnestock & Bamber, 2001). To model this profile, a transition point (x = 500 km) is chosen that separates the ice-stream section from the inner core. Below this point, Equation (27) is solved, starting with 1km-thick ice at the grounding line, and using a uniform ice-stream width of 40km (w = 20 km). Above the transition point, the version of Equation (16) accounting for a non-zero initial thickness is solved. The b is maximum at the ice divide (0.25 myr-1) and decreases linearly to 0.10 myr-1 at the grounding line. The plan-view curvature of the ice streams, the differences between ice streams, the interstream ridges and the mountainous topography in the southern region of the divide all add complexity and variability to Siple Coast transects. Here I am only interested in the most general features of the topography (the gently sloped ice-stream section and the steeper inner core) and ignore these complexities; similar results are obtained for other profiles, given that parameters such as the ice-stream width and the location of transition from streaming flow to creeping flow are here specified, not modelled. Given an n value, two parameters are adjusted to optimize the model: the shear-zone A*®' for the ice stream section, and S(WA) for the inland section.

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