Modeling Alpine Glaciers

Modeling Alpine Glaciers

The model developed here is based on a paper by Gerard Roe, from the University of Washington, and the basics of the model are illustrated below. The glacier is treated as a slab of ice with width W, thickness H, and length L; multiplied together these give the volume of the glacier, and W*L gives the surface area A.

The change in volume of the glacier is given by the difference between the accumulation and the ablation. The accumulation is the total area times the rate of snowfall, while the ablation is the product of the melt area, the melting factor (whose units are in m/yr per °C) and half the temperature at the terminus of the glacier. Why one half this temperature at the terminus? It is because that gives an average temperature for the melt zone, since the upper limit of the melt zone is defined by the place where the temperature is 0°C. The melt area is the width times the length of the melt area, which is given by the temperature at the terminus divided by the lapse rate (Γ) times the slope (α). The lapse rate is simply the rate at which temperature decreases with increasing elevation.

The temperature at the terminus of the glacier is given by the initial temperature (which we must assign) plus the change in length since the beginning times the slope times the lapse rate plus any climate-related temperature change (Tf below)

Let’s think about how this system might work. If you start out with a relatively cold temperature at the terminus of the glacier, then your ablation area might be quite small and so accumulation might dominate the ablation. In this case, the volume of the glacier will increase, and so will its length. This increase in length will force the temperature at the terminus to be higher (it gets warmer as you move to lower elevations); this will make a small increase in the area of ablation, and so in the next increment of time, the glacier might not advance as much. Eventually, its advance will mean that the ablation matches the accumulation, and at that point, the length of the glacier will remain the same — it will be in a steady state. Then, if we were to increase the snowfall, it would advance again until a new steady state was achieved; if we raised the temperature, the glacier would retreat until the ablation area shrank enough to get to a new steady state.

Basically, this system is one that will naturally try to find a steady state and it gets pushed and pulled by temperature changes and precipitation changes. But, as we will see, it is sluggish to respond, which means that short-term temperature and precipitation changes do not have a big influence, the the longer-term changes do have a big influence. You could even think of the glacier as a sort of filter that removes the effects of these short-term changes (many of which are essentially random noise in the climate system) and instead highlights the longer term changes.