1. Tracer travel times and system implications

Smart argues that, under low flow conditions, the hydraulic head driving the flow may have been lower than we originally thought was reasonable, and that the slope of unity in the velocity-discharge relation (Reference Seaberg, Seaberg, Hooke and WibergSeaberg and others. 1988, fig. 5) can thus be attributed solely to variations in head in a closed-conduit system. We agree, and had come to the same conclusion independently on the basis of additional tracer studies.

Smart’s system-volume calculations provide another interesting way of elucidating drainage systems from relatively few tracer experiments. However, caution is required in interpreting these calculations in the present case because dye was injected at only one input point, whereas the discharge used in the calculation is that at the terminus, which is the sum of discharges entering the glacier at several different input points. If the ratios of the discharges among the various tributaries changed between tests, the amount of water discharged at S-1 during the time required for the dye to pass from the injection point to S-1 would change, even if there were no change in the geometry of the system.

Smart suggests that the large system-volume calculated for test 85–1 may be a consequence of spring-time storage within the glacier. This would require that storage decrease between 28 June (test 85–1) and 10 July (test 85–2). However, Reference Østling and HookeÖstling and Hooke (1986) found that, after increasing in May and early June 1984, storage was roughly constant until early August. There is no reason to suspect that conditions were substantially different in 1985. It is possible that there is extensive drainage through the snow cover in late June. Such drainage would contribute to the discharge used in the system-volume calculation without having to pass through the glacier.

Incidentally, Östling and Hooke suggested that storage during the middle of the melt season might be in subglacial cavities. Reference Hooke, Calla, Holmlund, Nilsson and StroevenHooke and others (1989), however, showed that the reasoning leading to the conclusion that such subglacial cavities existed was faulty. We presently infer that the storage is principally in snow and firn.

2. Multiple peaks in dye-return curves

Smart suggests that the multiple peaks in the dye-return curves might be the result of dye being routed into blind storage locations on a rising stage and subsequently released back into the flow on a falling stage. In test 84–2, the peak discharge, 625 1/s, occurred at about the time of the second peak in dye concentration, and by the time of the third peak the discharge had fallen to c. 460 1/s. In test 84–6, the peak discharge, 380 l/s, again occurred at about the time of the second peak in dye concentration, and by the time of the third peak it had fallen only 10 1/s, to c. 370 1/s. Thus, this mechanism probably cannot explain three of the four secondary peaks.

Furthermore, to drive significant quantities of dye into blind passages, the passages must either be only partially full of water or the hydraulic gradient away from the conduit must be substantial. The former is possible, though, owing to closure, such storage locations would not be large, and the probability of their filling at precisely the time of passage of the dye cloud is, perhaps, remote. The latter is contradicted by bore-hole water-pressure measurements.

Smart’s alternative mechanism for producing multiple peaks, involving variations in discharge in a tributary, also seems unlikely in this case, as the discharge curves did not have multiple peaks.

Conclusions

We are in agreement with Smart’s explanation for the linear velocity-discharge relation, and had come to the same conclusion ourselves. We also like the system-volume calculation, but feel that caution is required in its interpretation. We thank C.C. Smart for his interest in our work, and for pointing out these alternative interpretations.

Acknowledgement

We thank J.Z. and S.Z. Seaberg for providing unpublished data.