ON THE THEORY OF GLACIER VARIATIONS

Abstract

Summary A glacier remains in a steady state only when a strict relation exists between the rate of external mass exchange, the ice velocity and the thickness at every point. The shape of the glacier and its velocity distribution is determined by a system of equations which take into account is determined by a system of equations which take into account the distribution of the external mass exchange, the temperature, the form and the properties of the bed. Stability of motion and steadiness of external conditions are necessary to maintain the steady state. Glacier variations are caused by changes in the conditions at the glacier boundaries (the rate of mass exchange, temperature, stress tensor and inclination ot the bed). From the equation of continuity of an unsteady glacier, the equation of flow, and the rheological equation for ice a set of equations for the unsteady state of a glacier is deduced. From these equations it follows necessarily that the whole glacier reacts to changes in any part, including its snout. This is in contrast to the theory of kinematic waves, according to which the changes can spread only downstream along the glacier. The equations are a set of linear differential equations of the second order; they can be solved by numerical and other approximate methods. By applying these methods to the retreating ice cap on Drygalsky Island, Antarctica, it was possible to determine time derivatives of the velocity, thickness and the position of the edge of the cap, the size of the cap and the velocity distribution in the steady state. The causes for the observed changes can be deduced from the equations by calculating the distbution of the changes in the rate of external mass exchange and ice temperature along the length of a glacier. An increase in the temperature of cold glaciers causes an acceleration of motion and a decrease in thickness; the snouts of glaciers, as a rule, retreat, including the snouts of the glaciers which descend to water to a line of hydrostatic balance. During the warming and moistening of the Antarctic climate an increase of ice temperature causes a decrease in thickness of the Antarctic Ice Cap in spite of an increase in precipitation. Warming must cause thinning and retreat of the edge of the Antarctic Ice Cap. With simultaneous changes of climate the glacial epochs of the Antarctic and continents of the Northern Hemisphere cannot be metachronous.