Sir
Geo-information systems (GIS): provide “triangulation irregular network digital terrain models” (TIN DTMs) as routines for many purposes. These include the determination of “true” rough surface areas in order to improve the results one obtains from the traditional glaciological mass-balance method (Hoinkes, 1970), where mass and volume changes are obtained from point measurements which are extrapolated to areal values. (1) These “true” surface areas are not at all true, and (2) even if they were true, their use for the calculation of mass balance and related topics (e.g. energy balance) would be wrong by definition.
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(1) The value of a rough surface area is mainly a function of scale, similar to the determination of the perimeter of an island. Zooming continuously into larger scales, it becomes longer and longer, even up to orders of magnitude (e.g. Penck, 1894). If Reference Östrem, and Brugman.Jacobsen and Theakstone (1995) went to even larger scales than 1:2000 they would obtain “true” areas which become larger than the projected area not only by 10-20%, but finally by orders of magnitude if the scale is chosen large enough. These rough surface areas are neither wrong nor true. However, it is impossible to define them exactly.
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(2) If one looks at the calculation of the mass balance of a glacier along a longitudinal cross-section, one has to deal with the surface area of a rhombus which has two vertical and two inclined sides. The surface area of such a rhombus, corresponding to changes in the volume of a glacier, is calculated by multiplying the arithmetic mean of the vertical sides by the arithmetic mean of the horizontal projections of the inclined sides. Therefore, as long as specific mass- as well as energy-balance terms are measured vertically, they must be related to the horizontal projection of the Corresponding surface area which is, moreover, well defined. Using mass-balance values and energy fluxes which are directed normal to the surface would again lead to a scale problem (normal to which surface with which inclination?), in addition to measuring problems, and would not improve the results objectively.
The problem of serac areas is well known but there is no realistic way to solve it. Not only for this reason it has in be noted that not every glacier is suitable for mass-balance studies, and “mass-balance glaciers” should be chosen very carefully (e.g. Østrem and Brugman, 1991, p. 9).
6 February 1996
