E l e c t r o n i c   r e p r i n t


HYDRAULIC GEOMETRY
OF A SUPRAGLACIAL STREAM,

RAGNARBREEN, SPITSBERGEN

Andrzej Kostrzewski and Zbigniew Zwolinski

A MODEL OF THE EVOLUTION OF A SUPRAGLACIAL CHANNEL

Supraglacial streams are assumed to develop when the rate of incision of surface meltwater exceeds the rate of glacier surface ablation (Marston 1983). This situation arises when the glacier surface has a snow cover. Having low thermal conductivity, the snow cover performs a conserving function and prevents glacier ice from melting. The meltwater from the snow cover infiltrates into it, reaches the ice surface and accumulates in its cracks and crevasses, or adjusts to the ice microrelief (Marston 1983). Warm meltwater causes the ice surface to thaw in the contact zone, and that is how an outline of a supraglacial channel is formed. With the snow cover around, the ice tends to melt quicker where the meltwater flows. In other words, the bed of a supraglacial channel incises into the glacier surface by way of thermal erosion (Fig. 5.1). In terms of hydraulic geometry, this process involves a faster change in the channel depth than width, or f > b. Such relations have been recorded in the literature (Table 5). We can assume, therefore, that such is the first stage in the development of an emerging supraglacial channel.


Fig. 5. A model of development of a newly created supraglacial channel


Table 5. Exponents of downstream hydraulic geometries of supraglacial streams


Glacier Region b f m Source
Lower Arolla Alps 0.28 0.41 0.31 Park (1981)
Austre Okstind Northern Norway 0.26 0.29 0.45 Knighton (1981)
Austre Okstind Northern Norway 0.30 0.53 0.13 Knighton (1981)
Austre Okstind Northern Norway 0.30 0.32 0.38 Knighton (1981)
Ragnar Spitsbergen 0.45 0.21 0.34 this paper

After a time, usually around the middle of the ablation season, when the snow cover has melted away, a second stage begins. Solar radiation reaches the glacier surface directly causing it to thaw and melt. Ablation processes start to prevail on the glacier surface. This makes the superficial ice layer more permeable than the sub-surface layer, the one that usually supports the supraglacial channel bed. The superficial layer has higher thermal conductivity, as a result of which ablation water flowing down the channel melts its "warmer" banks (sides) faster than the "cooler" bottom. This means that thermal bank erosion exceeds thermal incision (Fig. 5.2). In terms of hydraulic geometry, differences between these two directions of thermal erosion are reflected in a faster rate of change in channel width than in depth. Thus b > f. The Ragnarbreen supraglacial stream under study seems to be going through this stage (Table 5).

As the time passes, widespread ablation processes lead to the formation of a thick permeable layer, and thermal erosion intensifies in its tendencies which have formed in the second stage. Water flow is characterised by increasing values of the Reynolds number Re and sometimes by decreasing values of the Froude number Fr. After the combined operation of thermal bank erosion and thermal incision has crossed a threshold value, the process of meandering is set in motion, locally at first, to become ever more widespread (Fig. 5.3). This observation confirms the studies of Ferguson (1973), Knighton (1981) and Parker (1975). Meandering processes mark the third stage in the development of a supraglacial channel. In terms of hydraulic geometry, it manifests itself in low values of the velocity exponent m (Table 5). The slower rate of change in velocity results from the growing resistance of the flowing water caused by disturbances in the free gravitational flow of water in the channel, which has by now developed an intricate relief of the bed and banks as well as meander bends.