The Editor,

Journal of Glaciology

Sir

Dr. Reference MeierMeier (1965) has made some pertinent comments on a part of my paper (Reference PatersonPaterson, 1964). I should like to make a few comments in reply, in the hope that this discussion may contribute a little to the understanding of an interesting problem. The question at issue, the travel time of subglacial run-off, appears to offer wide scope for speculative discussion, as a result of the extreme difficulty of making any direct observations on the phenomenon.

Unfortunately, I did not see Mathews’s papers (Reference Mathews1964[a], Reference Mathews[b]) on run-off from Athabasca Glacier until a few months after my paper had been submitted. The pronounced diurnal variation in stream flow during the summer months is undoubtedly the most conspicuous feature of the record. I certainly ought to have mentioned this in my paper, even though I was dealing with weekly measurements of ice velocity and therefore averaged the stream flow over the same period.

The large diurnal variation in stream flow and the occurrence of the peak in stream flow a few hours after the daily peak in the rate of ice melt are established facts. However, I fail to see that they prove that a large part, or even any, of the water flowing past the gauge on a particular day was produced by melting at the glacier surface on that same day, rather than say a few days earlier. It seems probable that melt water which does not penetrate below the glacier surface will reach the gauging station within a few hours. Examples of this arc water which drains directly off the terminus into the lake and water which drains off the surface into marginal streams at the edge of the lower part of the glacier. Meier’s dye experiments on South Cascade Glacier show that some melt water which drains into moulins also has a travel time of a few hours. I understand, however, that these experiments were conducted within about i km. of the glacier terminus. They arc perhaps not entirely representative of conditions on the glacier as a whole. In short, I agree that some melt water reaches the gauging station in a few hours. I think it is still an open question whether this constitutes a “major”, or even a large, part of the total melt water.

To deal with Meier’s other points: Reference MathewsMathews (1964[a]) showed that it was possible to relate the mean stream flow, Q, on any particular day to the mean daily air temperature, T, at the weather station nearest to Athabasca Glacier. Mathews’s formula is

Here a, b and k are constants, n = 0 refers to the day in question, n = 1 to the preceding day, and so on. The sum is taken from n = 0 to n = 11. Mathews found that, for the period to which my velocity measurements refer (July and August 1960), the best value of k was 0.7. Thus the weightings assigned to T ₀, T ₁, T ₂, … are 1, 0.7, 0.49, …. The sum of the weightings is 3.3. A larger weighting is certainly given to the current day’s temperature than is given to that of any other day, as Meier says. That weighting is however only one-third of the sum of all the weightings. This suggests to me that temperatures, and hence the amount of melting, on the preceding few days have quite an important effect on the stream flow on any given day.

As Mathews says, the discharge can fall by more than 50 per cent from 7.00 p.m. to 7.00 a.m. the following day. This refers to the difference between the maximum and minimum instantaneous discharges. It gives perhaps a slightly exaggerated impression of the difference between the stream flow over periods of a few hours around the times stated. It may be surprising that the difference between maximum and minimum discharges is as large as this. If, as Meier claims, the major part of the melt water escapes from the glacier within a few hours, it is perhaps equally surprising that discharge maintains as high a value as it does throughout the 24 hr. Melting is reduced to virtually zero during the night, except under exceptional weather conditions.

To sum up, I think it is quite possible that the travel time of a substantial part of the subglacial melt water may be an order of magnitude greater than Meier’s “few hours”. This view appears to be supported by results from the Gornergletscher (personal communication from G. R. Elliston).

The existence and size of Weertman’s hypothetical thin film of water at the glacier bed is a separate, but related, question. I felt, and still feel, that it was worthwhile to point out that my results might be relevant to this question, even though Meier thinks that this is unlikely.

I certainly support Dr. Meier’s plea that high priority be given to further investigation of the flow of water at the bed of a glacier. The whole question of the distribution and flow of water in a temperate glacier deserves further study as soon as possible.

I wish to acknowledge the kindness of Dr. G. R. Elliston in letting me see the draft of a paper of his prior to publication. This has been most helpful.

23 March 1965