Sir,

Dye tracing through glaciers provides one means of studying the inaccessible glacial drainage system. Unfortunately, the complex, unstable character of the drainage system, rapid variations of discharge, and high sediment concentrations make the tracing in the glacial environment challenging. The recent paper by Reference Seaberg, Seaberg, Hooke and WibergSeaberg and others (1988) constitutes perhaps the best work to date on glacier tracing by virtue of high-quality data, replicate tracing, and systematic analysis. However, there may be alternative explanations for some of their data.

The tracer break-through curve obtained at the glacier snout results from dispersion, dilution, and flow routing. Seaberg and others considered the englacial flow route to be a homogeneously braided open channel with dramatic increases in sinuosity with stage accounting for the proportional relationship between travel time and discharge. They attributed occasional multiple-peaked break-through curves to temporary development of a few dominant flow routes from the homogeneously braided channel.

In contrast, the velocity-discharge plot of Reference Seaberg, Seaberg, Hooke and WibergSeaberg and others (1988, fig. 5) suggests closed-conduit flow (Reference Smart and BeckSmart, 1981), an inference they disproved by considering hydraulic gradient changes from a minimum (S ₀) to maximum (S) and corresponding discharge (Seaberg and others, 1988, p. 225). Figure I shows that lower minimum hydraulic gradients (e.g. S ₂) are possible, and can account for observed variations in discharge. For example, ifS ₂ were 0.0045, it would account precisely for a six-fold increase in discharge when the drainage system filled to the surface. The implied system is largely water-filled, but with a variable free-surface component.

Fig. 1.

Sketch cross-section through Storglaciären along the straight-line tracer route (from Seaherg and others 1988 fig- 1).

Travel time in such a hybrid system is a combination of closed-conduit and free-surface components. Tracer travel times in open-channel systems are more rapid on rising stage than falling stage (e.g. Reference CollinsCollins, 1982), giving a wide hysteretic scatter to velocity-discharge plots reflecting the changing storage in the conduit. This does not appear to be the case for the Storglaciären traces, suggesting a predominantly closed conduit. (Although most glacier traces are made in late morning-afternoon by force of circumstances, they may not demonstrate diurnal hysteresis.) This inference may be tested by plotting “system volume” against discharge. System volume is a measure of the volume of water passing through a drainage system in the travel time of a tracer. In a simple conduit, it is the volume of water which must be emptied as a tracer passes from one end to another. It is calculated using the integral of output discharge over the travel time (e.g. Reference SmartSmart, 1988b), but can be loosely approximated by multiplying mean discharge (Q _p; Reference Seaberg, Seaberg, Hooke and WibergSeaberg and others, 1988) by the travel time as shown in Table I. Figure 2 indicates that volume changes surprisingly little with discharge, confirming the predominantly closed conduit. The intercept of a line drawn through these points indicates static storage of 3700 m³. (The linear regression used is arbitrary, a simple function is not necessarily appropriate.) The high static storage may indicate that the conduit follows the bed and is ponded behind the lower riegel (Fig. 1). In contrast, the maximum dynamic storage implied by the line is only 640 m³. This shows that discharge variation is accomplished with relatively small volume changes.

TABLE. 1.

Summary of tracer results of Reference Seaberg, Seaberg, Hooke and WibergSeaberg and others (1988) with implicit travel times and system volumes

Fig. 2.

Volume of subglacial drainage system beneath Storglaciären based on data of Reference Seaberg, Seaberg, Hooke and WibergSeaberg and others (1988).

The estimated volume is very approximate, in part due to the use of an estimated mean discharge, but also because applying a single travel time for the traced route to all tributaries of a dendritic or anabranching network is inaccurate. Some volume variability may also result from changing proportions of open and closed channels. However, the consistently high volume indicates that the drainage system is largely closed. Any stage-dependent morphological changes must occur in restricted parts of the channel, probably “paraphreatic” parts experiencing frequent inundation and drainage. The balance of changes results from other processes such as erosional and tectonic processes (e.g. Reference Seaberg, Seaberg, Hooke and WibergSeaberg and others, 1988, p. 224) which will be especially active in glaciers. However, karst systems recharged by glacial melt also show irreproducible break-through curves, and erosional and tectonic explanations are not reasonable in such cases. Hydraulic effects associated with varying flow are inferred (Reference SmartSmart, 1988a). It is possible that these processes may also be active' in glaciers, and some examples are described below.

Under rising stage, an unknown part of run-off is routed under high hydraulic potential away from subglacial conduits into “off-line” stores such as the subglacial film or cavities. The water subsequently returns to the conduit as discharge and conduit potential decline. Any dye labelling this component will exhibit secondary peaks during falling stage.

“Hydraulic damming” results when variations in flow through the traced route and a diluting tributary interact to alter the proportion of tracer entering their junction. “Hydraulic switching” occurs when tracer routing at a distributary junction is controlled by an independent tributary to one of the branches down-stream of the junction. The exact effect depends upon the discharge of each element and the change in volume required to produce a matching hydraulic potential. The result can be highly irregular, non-reproducible break-through curves, with little apparent change in discharge.

Unfortunately, it is not yet possible to obtain the data necessary to establish firmly complete explanations of complex break-through curves. It is essential that alternative hypotheses be evaluated before undertaking modelling based on such data.

A final comment addresses the early season trace 85–1 which is the outlier on Figure 2. It indicates anomalously large system volume despite modest discharge. Assuming no radical alteration in system topology, this indicates substantial springtime storage of water within the glacier without highly efficient drainage, an effect already inferred from other data (e.g. Reference Iken and BindschadlerIken and Bindschadler, 1986).

The paper by Seaberg and others constitutes a valuable example of the contemporary approach to studying glacier hydrology. Yet we are still unable to monitor adequately the complex, erosionally and tectonically active subglacial system with typically unsteady flows and corresponding complications in tracer dilution, routing, and storage. This makes strict structural interpretation of tracer break-through curves difficult. However, there is some evidence that the system beneath Storglaciaren might be a simple, largely water-filled conduit with distributaries rather than the complex braided free-surface stream described.