Many of the outlet glaciers in Greenland overlie deep and narrow trenches cut into the bedrock. It is well known that pronounced topography intensifies the geothermal heat flux in deep valleys and attenuates this flux on mountains. Here we investigate the magnitude of this effect for two subglacial trenches in Greenland. Heat flux variations are estimated for idealized geometries using solutions for plane slopes derived by Lachenbruch (1968). It is found that for channels such as the one under Jakobshavn Isbræ, topographic effects may increase the local geothermal heat flux by as much as 100%.

[1] Ice discharge from the fastest glaciers draining the Greenland and Antarctic ice sheets -Jakobshavn Isbrae (JI) and Pine Island Glacier (PIG)-continues to increase, and is now more than double that needed to balance snowfall in their catchment basins. Velocity increase probably resulted from decreased buttressing from thinning (and, for JI, breakup) of their floating ice tongues, and from reduced basal drag as grounding lines on both glaciers retreat. JI flows directly into the ocean as it becomes afloat, and here creep rates are proportional to the cube of bed depth. Rapid thinning of the PIG ice shelf increases the likelihood of its breakup, and subsequent rapid increase in discharge velocity. Results from a simple model indicate that JI velocities should almost double to >20 km a −1 by 2015, with velocities on PIG increasing to >10 km a −1 after breakup of its ice shelf. These high velocities would probably be sustained over many decades as the glaciers retreat within their long, very deep troughs. Resulting sea-level rise would average about 1.5 mm a −1 .

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.