[1] The reaction of alpine glaciers to shifts in the equilibrium line altitude (ELA) is calculated by using a two-dimensional numerical model to solve the full equations for the velocity and stress fields (full-system model) in the absence of basal motion. Rates of advance and retreat of the snout of typically sized alpine glaciers are found to be insensitive to the details of the flow at the snout, even when the glaciers are far from steady state. A comparison of results obtained with a full-system model and a shallow ice approximation (SIA) model yields no significant differences in advance or retreat rates. This assumption has been implicitly made in numerous previous climatic studies and is here shown to be well justified. Using a realistic mass balance altitude feedback, only slight model-dependent changes in steady state lengths are found. The relative importance of mass balance and glacier dynamics for the transient response of alpine glaciers to changes in the ELA is given a precise meaning by determining the model-dependent additional shifts in ELA needed for the SIA and the full-system models to produce identical changes in length. For alpine glaciers, these additional shifts in ELA are on the order of 10 m, which is within the error range of ELA estimates. It follows that at least in the absence of significant basal motion, there is no need to include the effects of horizontal stresses when calculating the reaction of alpine glaciers to climatic changes. Attention should focus on accurate determination of the mass balance distribution and model tuning to give realistic ice thickness distributions.

[1] Internal isochronic layers in ice sheets sensed by radar show two characteristic relationships to the basal topography: Either they override it, with layers above the crests of rises lying essentially flat, or they drape over it, with the layers following rises and falls in basal topography. A mechanical theory is presented which shows that overriding is the expected behavior when topographic wavelengths are comparable with or less than the ice thickness, while draping occurs at longer wavelengths. This is shown with analytical perturbation solutions for Newtonian fluids, numerical perturbation solutions for nonlinear fluids, and finite element solutions for nonlinear fluids and large-amplitude variations. Bed variation from topography and changes in the basal boundary condition are considered, for fixed bed and sliding beds, as well as three-dimensional flows and thermomechanically coupled flows. In all cases, the dominant effect on draping/overriding is the wavelength of the topography or variation in basal boundary conditions. Results of these full mechanical system calculations are compared with those from the shallow ice approximation and the longitudinal stress approximation. Some calculations are carried out for zero accumulation, where the age of the ice and therefore isochrone geometry is not defined. It is shown that there is a close relationship between isochrones and streamlines, and that they behave similarly when bed wavelength divided by the ice thickness is small compared with the ratio of ice velocity and accumulation rate, which is a useful approximation. Numerical comparisons of isochrones and streamlines show them to be virtually coincident. The effect of horizontal stress gradients on internal layer architecture in ice sheets,

[1] In East Antarctica surface mass balance data can only be obtained from the sparsely distributed ice cores when considering time periods greater than a few decades. Observations of internal layers measured by airborne ice penetrating radar, in principle, permit extrapolation of mass balance information from these ice cores. We use radar survey lines gathered in the 1970s, and a three-dimensional numerical model, to investigate the feasibility of such extrapolation, seeking to match the calculations of englacial layer geometry with observations. First, we justify the use of a three-dimensional model by showing that simple vertical flow models cannot explain all the observations and that horizontal advection is a significant glacial process. Then we examine processes that affect calculations of layer geometry, finding that spatial accumulation-rate patterns are extremely important while geothermal heat flux and flow mode (sliding or internal deformation) are of substantially less importance. Where the layer is from the Last Glacial Maximum (17.5 ka), we find a very good match between the spatial pattern of accumulation rates inferred from this layer and the modern spatial pattern of accumulation rates. When considering deeper layers from beyond the current interglacial, we find that a different spatial accumulation-rate pattern must have existed, in addition to the known change in accumulation rate from ice cores. The glacial spatial accumulation-rate pattern would have had proportionally greater accumulation at the South Pole than now, compared with the Vostok and Dome C ice cores.