No abstract

ICESat elevation profiles of tabular iceberg margins and the Ronne Ice Shelf edge reveal shapes indicative of two types of bending forces. Icebergs and shelf fronts in sea‐ice‐covered areas have broad (∼1000 m wide), rounded, ∼0.6 m high ‘berms’ and outer edges that slope down several meters toward the water. Bergs in warmer water have 2 to 5m ‘ramparts’ with ∼1500 m wide edge‐parallel ‘moats’ inboard of the edge. This latter pattern was first revealed in images from International Space Station (ISS) showing edge‐parallel melt ponds on one iceberg just prior to its disintegration. Model results indicate the patterns are caused by hydrostatic and lithostatic forces acting on the ice face. ‘Berm’ profiles arise from differences between ice and water pressure along the face. ‘Rampart‐moat’ profiles result from waterline erosion, creating a submerged bench of ice that lifts the ice edge. We use the results to discuss iceberg breakup at low latitudes.

[1] Ice sheet thickness is determined mainly by the strength of ice-bed coupling that controls holistic transitions from slow sheet flow to fast streamflow to buttressing shelf flow. Byrd Glacier has the largest ice drainage system in Antarctica and is the fastest ice stream entering Ross Ice Shelf. In 2004 two large subglacial lakes at the head of Byrd Glacier suddenly drained and increased the terminal ice velocity of Byrd Glacier from 820 m yr −1 to 900 m yr −1 . This resulted in partial ice-bed recoupling above the lakes and partial decoupling along Byrd Glacier. An attempt to quantify this behavior is made using flowband and flowline models in which the controlling variable for ice height above the bed is the floating fraction of ice along the flowband and flowline. Changes in before and after drainage are obtained from available data, but more reliable data in the map plane are required before Byrd Glacier can be modeled adequately. A holistic sliding velocity is derived that depends on , with contributions from ice shearing over coupled beds and ice stretching over uncoupled beds, as is done in state-of-the-art sliding theories.

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. <br><br> 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

Abstract. The first-order control of ice thickness and height above sea level is linked to the decreasing strength of icebed coupling along 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.