Modelling dynamics of glaciers in volcanic craters

General equations of ice dynamics are re-examined, using scale analysis, in order to derive a simplified thermomechanically coupled model for ice flow and heat transfer in ice caps filling volcanic craters. Relatively large a spect ratios between crater depths and diameters, low surface temperatures and intense volcanic heating are the principal characteristics of such crat ers. The conventional boundary-layer (shallow-ice) approximation is revised to account for these conditions and, in addition, the variable density of the snow, firn and bubbly ice. Large crater depths and intense bottom melti ng result in low longitudinal balance velocities, controlled by both shear and longitudinal stresses, and hence small surface slopes. In such situatio ns ice can be assumed to be linearly viscous. A flowline model of the glaci er dynamics is developed using this assumption. Explicit predictive formula s for ice-particle trajectories and age-depth relations, thus obtained, sug gest that the age of ice at the bottom of glaciers in volcanic craters on K amchatka Peninsula, Russia, may reach hundreds or thousands of years. Ice c ores from these glaciers represent unique climatic and volcanic archives.