Sir,

I read with great interest the letter from Dr. Glen concerning my recent article on mass budget concepts and terms. One of his points deserves considerable emphasis: methods (such as photogrammetry) which compare changes in surface elevation of a glacier with time at a given location cannot be used to deduce specific mass budget information. We need terms to describe the thickening or thinning of a glacier as measured from points fixed in geographical coordinates. However, these are not mass budget concepts and therefore I did not deal with them in my article.

As Glen states, my definitions are not completely clear as to whether mass budget quantities are to be measured with fixed or moving probes. The problem is whether to investigate what happens in time to an individual parcel of ice as it rides along (the Lagrangian method of description in fluid mechanics) or to investigate what is happening as the ice flows past a fixed location in space (the Eulerian method). It is obvious that my mass budget definitions are strictly correct only for the Lagrangian method of description, because on p. 253 I discussed the gain or loss from a hypothetical prism extending through a glacier from surface to bed. This prism must move and deform with the ice if we are to avoid the complication of apparent gains or losses of mass due to compressive or extending strains within the glacier.

If we restrict ourselves to surface phenomena only, however, we can see that the Eulerian method is valid for mass budget measurements. Imagine a small cloud fixed in position over a moving glacier. Snowfall from this cloud would produce accumulation on the glacier at a point fixed in geographical coordinates. An observer also fixed in these coordinates near the glacier surface (perhaps in a helicopter) could measure the amount of snow which is delivered to the glacier at this spot. This Eulerian observer would obtain jug as valid a measurement of accumulation as his Lagrangian colleague riding along on the glacier surface. Admittedly it is far easier in actual field work to adopt the Lagrangian approach. However, if the glacier is moving rapidly, and if appreciable mass budget gradients exist in space, then the Lagrangian, space-averaged data may be harder to interpet. When we assume that the geographical (vertical and horizontal) variation of mass budget has significance, we necessarily imply validity in the Eulerian approach.

My article on mass budget terms was written to stimulate discussion so that a proper conceptual framework can be evolved. I believe that Dr. Glen has definitely contributed to this aim, and I would welcome further discussion.

7 February 1963