Boulton & Dobbie (1993) suggested that areas in Holland, during the Saalian glaciation, had sufficient transmissivity to drain all meltwater from the ice sheet base. This inference was based on calculations with very low basal melting rates of 2-3mmyr-1, but claimed valid also in subsequent simulations with melting rates of 20mmyr-1 (Boulton et al., 1993). In a numerical model of groundwater flow under ice sheets of the last two glaciations along a transect from the ice divide in Scandinavia to the ice periphery in Holland, Boulton et al. (1995) used a melting rate of 25 mmyr-1 with a similar conclusion. In their model, however, the entire Quaternary sequence was lumped together into one aquifer with conductivity of 3 x 10-4ms-1, corresponding to the conductivity of sand. This value is clearly too high, neglecting the true nature of Quaternary strata characterized by interlayered sediments of much lower bulk transmissivity. The hypothesis of basal water drainage entirely through the bed is also inconsistent with widespread sediment deformation postulated by Boulton (1996a), because such deformation will occur only if porewater pressure is at least 90-95% of the overburden pressure (Paterson, 1994, p. 169), that is when the bed capacity to absorb meltwater is reached. As pointed out by Arnold & Sharp (2002), the modelling of Boulton and co-workers is seemingly contrary to most geological evidence. More recently, Boulton et al. (2001b) proposed a revised model of basal hydraulic regimes that considers a zone where the meltwater flux is too large to be discharged by groundwater flow alone, and in which tunnels form.
In a three-dimensional model of groundwater flow under the Weichselian ice sheet in northwestern Germany that accounts for the heterogeneity of Quaternary sediments, located close to Boulton's transect, Piotrowski (1997a) showed that only about 25% of meltwater could have been evacuated through the bed, and the rest was drained in spontaneous outburst episodes through subglacial channels. This is supported by the occurrence of tunnel valleys, some up to ca. 80m deep (Piotrowski, 1994), abundantly found in this area. Modelling the adjacent area around the Eckernforde Bay showed that about 30% of basal meltwater drained as groundwater flow, and the rest through channels (Marczinek, 2002; Marczinek & Piotrowski, this volume,
Chapter 10). It should be noted that these simulations were made with conservative basal melting rates of 36 mmyr-1 not considering surface ablation water, which probably recharged the bed close to the ice margin. Accounting for this additional water source would further substantiate the conclusion about the insufficient drainage capacity of the bed, consistent with the formation of tunnel valleys as high-discharge drainage pathways. It also should be stressed that if a permafrost wedge under the ice-sheet margin is considered, the bed conductivity will be yet lower (Fig. 9.3), further increasing the likelihood of tunnel valley formation.
It is tempting to suggest that similar hydraulic deficiency of the bed could have initiated tunnel valleys elsewhere across the Central European Lowland and at the bottom of the North Sea, where they represent the largest glacial features of the Elsterian and Weichselian glaciations, some over 500 m deep and hundreds of kilometres long (e.g. Huuse & Lykke-Andersen, 2000). Iftunnel drainage is predicted to have extended up to 150 km from the ice sheet margin (Arnold & Sharp, 2002), then some of these tunnel valleys possibly formed time-transgressively during deglaciation.
Because subglacial channels form in response to the excess of water at the ice sole, a succession of drainage mechanisms operating in cycles can be envisaged. Each cycle starts with low water pressure in the bed and groundwater recharge, followed by gradual increase of water pressure, formation of a basal water layer or a lake at the ice flotation pressure, succeeded by spontaneous drainage through channels, lowering the water pressure and ending with basal recoupling (Piotrowski, 1997a). Formation of the channels would thus act as a stabilizing feedback preventing widespread basal decoupling and catastrophic collapse of an ice lobe. Origin of subglacial lakes owing to meltwater ponding in low-transmissivity areas of northern Germany was also considered by van Weert et al. (1997), and in marginal zones of the Laurentide Ice Sheet by Cutler et al. (2000), in accordance with the considerations of Shoemaker (1991) who gave a physical framework for the formation of such lakes.
Most reconstructions of groundwater flow under past ice sheets in North America and Europe indicate a deficiency of bed materials to evacuate all the incoming meltwater, which is interesting, bearing in mind the diversity of beds overridden by ice sheets on the two continents. Brown et al. (1987) showed that only a fraction of basal meltwater could have been evacuated through a soft substratum under the last glacial Puget Lobe of the Cordilleran Ice Sheet. They envisage a widespread basal decoupling by water pressurized to the ice flotation level, indicated among other things by lenses and layers of sand in till, and low overconsolidation of subglacial clays. The same line of sedimentological and geotech-nical evidence was used by Piotrowski & Kraus (1997) and Piotrowski & Tulaczyk (1999) to suggest bed drainage deficiency in northern Germany. Shoemaker (1986) demonstrated that even under an ice sheet resting on a metre-thick gravel bed, channels must develop to keep porewater pressures below the ice overburden pressure, which was later confirmed by Ng (2000a). Two recent studies along transects from the Hudson Bay to the southern margin of the Wisconsinan ice sheet independently show that subglacial aquifers were not capable of evacuating the basal meltwater, possibly due to a combination of low bed-permeability and permafrost, compensated by channelized drainage (Breemer et al., 2002) or subglacial water storage (Cutler et al., 2000). Under
Figure 9.3 Numerical model of groundwater flow under the maximum extent of the Weichselian ice sheet in northwestern Germany along an ice-flow parallel transect between the ice margin (0km) and the present Baltic Sea coast (30 km). Geology (a) is generalized into two aquifers (dark grey) and two aquitards (light grey) resting on impermeable Tertiary sediments. Groundwater flow lines are shown with time markers and direction arrows. Scenario in (b) assumes non-permafrost conditions, and scenario in (c) considers a permafrost wedge under the ice margin. Note that in (c) the whole upper aquifer is frozen, so that (i) more groundwater drains through the lower aquifer, (ii) less water recharges the bed from the ice sole, and (iii) more water is forced upward toward the ice sole from the bed. (From Piotrowski, 1997b.)
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