It is generally assumed that the mass-balance gradient on glaciers is more or less conserved under climatic change. In studies of the dynamic response of glaciers to climatic change, one of the following assumptions is normally made: (i) the mass-balance perturbation is independent of altitude or (ii) the mass-balance profile does not change — it simply shifts up and down. Observational evidence for such an approach is not convincing; on some glaciers the inter-annual changes in mass balance seem to be independent of altitude, on others not at all. Moreover, it is questionable whether inter-annual variation can be “projected“ on different climatic states.
To see what a physical approach might contribute, we developed an altitude-dependent mass-balance model. It is based on the energy balance of the ice/snow surface, where precipitation is included in a parameterized form and numerical integrations are done through an entire balance year (with a 30 min time step). Atmospheric temperature, snowfall, and atmospheric transmissivity for solar radiation are all dependent on altitude, so a mass-balance profile can be calculated. Slope and exposure of the ice/snow surface are taken into account (and the effects of these parameters studied). In general, the calculations were done for 100m elevation intervals.
Climatological data from the Sonnblick Observatory (Austria; 3106 m a.s.l.) and from Vent (2000 m a.s.l.; Oetztal Alps, Austria) served as input for a number of runs. Simulation of the mass-balance profiles for Hinterseisferner (north-easterly exposure) and Kesselwandferner (south-easterly exposure) yields reasonable results. The larger balance gradient on Kesselwandferner is produced by the model, so exposure appears to be an important factor here.
Sensitivity of mass-balance profiles to shading effects, different slope, and exposure are systematically studied. Another section deals with the sensitivity to climatic change. Perturbations of air temperature, cloudiness, albedo, and precipitation are imposed to see their effects on the mass-balance profiles. The results clearly show that, in general, mass-balance perturbations depend strongly on altitude. They generally increase down-glacier, and are not always symmetric about the reference state.
For typical climatic conditions in the Alps, we found that a 1 K temperature change leads to a change in equilibrium-line altitude of 130 m. Three factors contribute to this large value; turbulent heat flux, longwave radiation from the atmosphere, and fraction of precipitation falling as snow. Here, the albedo feed-back increases the sensitivity in a significant way.