A reply to ‘a discussion of hirano and Aniya's (1988, 1989) explanation of glacial valley cross profile development’ by Jonathan M. Harbor

Abstract

Abstract The extremum principle is again justified as a valid and relevant approach to cross sectional form of the glacial valley. It is accepted that the extremum previously obtained was a maximum, and not a minimum for friction, but this still appears to be a valid application of the principle. Harbor's more detailed discussion is recognized as valid assuming the presence of appreciable water pressures, and that Hallet's theory is to be preferred over Boulton's, but these assumptions do not always seem appropriate. While the importance of time for valley evolution is fully accepted, the extremum approach is still thought to be useful, for example in maximizing cross section for a given resistance.