Sir,
I appreciate the opportunity to comment on Mr. Fisher’s interesting suggestions.
In my calculations I assumed the ice to be contained and motionless within the Marie Byrd Land basin—a non-steady state condition both with respect to temperature and mass. If a layer of ice is moving then certainly friction will introduce another heat source; but whereas geothermal heat is supplied at the bottom of the ice, this is not true for frictional heating released by sinking ice layers. It is difficult to see how surface layers could make their way to the bottom of the ice as Mr. Fisher postulates. An ice mass moving horizontally would have to be of infinite extent to enable layers deposited on the surface eventually to move close to the bottom. For an ice mass moving down a slope, the ice trajectories within the glacier would dip down in the accumulation zone, but move up again to the surface in the ablation zone. Thus it is likely that the heat of friction released by vertical motion of the ice layers is not concentrated at the bottom of the ice.
With regard to the thermal conductivity of glacier ice, I found Mr. Fisher’s description of thermal conductivity experiments on “normal” and “bubbly” glacier ice to be of considerable interest. If the thermal conductivity of the bubbly ice is only half the normal value of 5.3 × 10−3 c.g.s. units, and if this ice is the same as that resting on bedrock under 3,000 m. of ice in Marie Byrd Land, then after 10,000 years the bottom temperature would become −13.0° C. instead of −18.5° C. as originally computed for the case of no loss of geothermal heat through the ice. This new value is based on an ice density of 0.87, as given by Mr. Fisher. Using the density of pure ice, 0.92, the temperature would be −13.4° C
If the ice is 20.000 years old. then the bottom temperatures in these three different cases would be. respectively, −4.9° C., −12.7° C. and −5.5° C. However because of the loss of geothermal heat through the ice, especially in the early stages, the actual temperatures would be several degrees lower.
There is, however, considerable doubt whether Mr. Fisher’s “bubbly” ice would be similar to that found at the great pressure existing under 3,000 m. of ice. At the bottom of the Maudheim hole at 100 m., Schytt4 found ice of density 0.885 containing air bubbles, mostly round, with a mean diameter of about 0.5 mm. At a pressure 30 times greater, the air bubbles would be even smaller and hence the effect on thermal conductivity probably negligible. It is hoped that further light on this problem can be cast by measurements of thermal conductivity on the ice recovered from 300 m. in the Byrd hole.
28 September 1959
