Surface melting has been observed on the lower, floating half of Byrd Glacier, Antarctica, during the height of the summer ablation season, in spite of regional air temperatures consistently below 0°C. The thickness of ice in this area is about 2 500 m, but surface crevasses penetrate to a depth of about 20 m, and bottom crevasses, being water-filled, may extend all the way up to sea-level. This leaves a zone of uncrevassed ice between which is of the order of 200 m in thickness, across which lateral shear stress due to drag against fjord walls will be concentrated. Variations in the mechanical properties of ice in this zone, specifically variations in hardness due to temperature changes, will obviously have a significant effect on the dynamics of the ice stream.

A model of the rough ice surface has been constructed, in which large crevasse furrows are represented by cylindrical V-grooves. These form the upper boundary of a solid conduction region which is semiinfinite below, and whose transient temperature distribution is calculated using the finite element method. The free surface boundary condition, that of sunlight warming the rough ice surface, is calculated by the construction and solution of coupled Fredholm integral equations of the second kind; these represent the energy absorbed at a point on the V-groove surface as being due to (1) energy directly incident from the sun, if the point is not in shadow, and (2) indirect radiation reflected from the opposite wall of the V-groove. This formulation takes into account all multiple reflections of radiation between the walls of the V-groove cavity. Additionally, the reflectivity of the ice surface is not given a constant value, but is allowed to vary, increasing as the angle of incidence departs from the surface normal.

The purpose of the model is to compare temperature distributions with a rough surface to the same model with a smooth surface. Due to the many simplifications made with regard to surface heat transfer, it is imprudent to make assertions about actual temperature distributions based on the model results, but the difference between the rough and smooth model results will provide a lower bound on the actual enhancement effect of surface roughness, i.e. future, more comprehensive, modeling of energy exchange at an ice surface will be in error by at least the predicted amount if the surface is treated as if it were flat.

The major effects of the surface roughness are greater absorptive capacity and non-uniform distribution of the absorbed energy. The greater absorptive capacity of a V-groove cavity is well known from studies in radiation heat transfer. Non-uniform distribution is due to two mechanisms: (1) the cavity effect is most pronounced at the apex of the V-groove, and (2) when surface melting occurs, energy is transported in the form of latent heat of melting from wherever the melting occurs to below the apex of the V-groove where the melt water refreezes.

The possibility that lateral shear stress is concentrated in a zone only 200 m thick means that temperature perturbations due to surface roughness need only penetrate on the order of 200 m, or possibly even less, to have a significant effect on the mechanical properties of the ice, and in turn on the dynamics of the ice stream.