The Editor,

The Journal of Glaciology

Sir,

Finsterwalder’s and Ahlmann’s rules are often used in calculations of the accumulation and ablation balance of glaciers. I doubt whether they are in fact valid for an alpine glacier in equilibrium. They are based on the shape of the curves of precipitation p and ablation a as a function of altitude z (the slight modification introduced by movement of the glacier is here neglected). These curves were obtained by Ahlmann for sub-polar glaciers (Fig. 1, below). The precipitation curve p increases slowly with z, and is concave downwards, reaching a maximum a little after the firn line z ₀. However, Mörikofer in the Oberland and Péguy in the eastern Oisans have found that the precipitation increases rapidly with altitude (see, for example, Péguy, C.-P., La neige, Paris, Presses Universitaires de France, 1952, p. 51); the curve for p is concave upwards until very near to the maximum which is appreciably higher than the firn line, at about 4000 m. (Fig. 2). In the Andes of central Chile the same seems to be true.

Fig. 1

Fig. 2

In this case, the curve of p − a = f(z), instead of being a parabola reaching its maximum at the highest altitude of the glacier as Finsterwalder supposes, will be approximately a straight line.

We can write Ahlmann’s rule as follows: if S is the surface area of the glacier in horizontal projection and p ₀ = a ₀ the precipitation at the firn line, then

the integral being extended over the whole area of the glacier. p ₀ must be equal to the weighted mean of

if the glacier is in equilibrium. This is possible in the case shown in Fig. 1, for the curve is roughly a straight line except at its ends, where the weight is negligible, but in the case shown in Fig. 2 (p. 510), p ₀ = a ₀ is certainly less than the weighted mean of ,even if the glacier is in equilibrium.

That the glacier is in balance can only be seen on curves of

and as functions of z (Fig. 3, p. 510). The areas between the curves and the z-axis represent the total ablation and accumulation of the glacier. If the glacier is in equilibrium the two shaded areas in Fig. 3 must be equal, and will both be equal to the amount of snow and ice crossing a vertical surface through the firn line in one year.

Fig. 3

It would be of great interest to have further data on the accumulation and ablation at different heights.