Background

A glacier transports heat both through diffusion and also through its flow. That portion transported through flow is so substantial that no accurate analysis of internal temperature in a glacier is possible without considering it. A highly simplified model of flow, but one that captures the essence of heat transport nevertheless, is as follows. Snow accumulates at the surface of the glacier. Its weight bears upon the snow below it, and causes a vertical compression or strain of the glacier. At the same time the glacier moves laterally. At the base of the glacier all vertical strain ceases and the motion is entirely lateral. A model that describes this motion is the complex velocity potential ƒ(w) = εw2; where ε is the vertical strain rate of the glacier and w is the complex variable x+jz. At any location the vertical velocity of material is –z where z is the height above the bedrock. Using this flow model, the 1-D equation for heat transfer is 1. α∂2T/∂z2+εz∂T/∂z =∂T/∂t The first term describes conductive heat transfer, in which α is the thermal diffusivity of the ice. The second term describes convective heat transport. If strain rate, ε, is large enough, temperatures in the glacier will reach a steady state very quickly. In this case th