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The first-order control of ice thickness and height above sea level is linked to the decreasing strength of ice-bed coupling alone flowlines from an interior ice divide to the calving front of an ice shelf. Uncoupling progresses as a frozen bed progressively thaws for sheet flow, as a thawed bed is progressively drowned for stream flow, and as lateral and/or local grounding vanish for shelf flow. This can reduce ice thicknesses by 90 % and ice elevations by 99 % along flowlines. Original work presented here includes (1) replacing flow and sliding laws for sheet flow with upper and lower yield stresses for creep in cold overlying ice and basal ice sliding over deforming till, respectively, (2) replacing integrating the Navier–Stokes equations for stream flow with geometrical solutions to the force balance, and (3) including resistance to shelf flow caused by lateral confinement in a fjord and local grounding at ice rumples and ice rises. A comparison is made between our approach and two approaches based on continuum mechanics. Applications are made to Byrd Glacier in Antarctica and Jakobshavn Isbrae in Greenland.

We present the detailed construction of a manufactured analytical solution to time-dependent and steady-state isothermal full-Stokes ice sheet problems. The solutions are constructed for two-dimensional flowline and three-dimensional full-Stokes ice sheet models with variable viscosity. The construction is done by choosing for the specified ice surface and bed a velocity distribution that satisfies both mass conservation and the kinematic boundary conditions. Then a compensatory stress term in the conservation of momentum equations and their boundary conditions is calculated to make the chosen velocity distributions as well as the chosen pressure field into exact solutions. By substituting different ice surface and bed geometry formulas into the derived solution formulas, analytical solutions for different geometries can be constructed. The boundary conditions can be specified as essential Dirichlet conditions or as periodic boundary conditions. By changing a parameter value, the analytical solutions allow investigation of algorithms for a different range of aspect ratios as well as for different, frozen or sliding, basal conditions. The analytical solutions can also be used to estimate the numerical error of the method in the case when the effects of the boundary conditions are eliminated, that is, when the exact solution values are specified as inflow and outflow boundary conditions.