Modelling distributed and channelized subglacial drainage: the spacing of channels

Abstract

Models are proposed for channelized and distributed flow of meltwater at the base of an ice sheet. The volumes of both channel and distributed systems evolve according to a competition between processes that open drainage space (e.g. sliding over bedrock, melting of the ice) and processes that close it (e.g. viscous creep of the ice due to a positive effective pressure). Channels are generally predicted to have lower water pressure and therefore capture water from the surrounding regions of distributed flow. There is a natural length scale associated with the distributed system that determines the width of the bed from which water can be drawn into a channel. It is suggested that this determines the spacing between major channels and that this may be reflected in the spacing of eskers. A more permeable distributed system results in more widely spaced, and therefore larger, channels. Calculations of the flow into the head of a channel reveal that there is a critical discharge necessary for it to form, and provide a criterion for where channels can exist.

A map of large Canadian eskers from Landsat satellite imagery

“…similar to that recently undertaken for drumlins Hillier et al, 2013;Spagnolo et al, 2010Spagnolo et al, , 2011Spagnolo et al, , 2012 These data could then be used to test numerical models that predict the configuration of meltwater drainage beneath ice sheets (e.g. Boulton et al, 2009;Hewitt, 2011) and quantitatively test various hypotheses that seek to explain where and why eskers form (e.g. subglacial geology, groundwater characteristics, ice surface slope).…”

“…For example, large sample sizes of ribbed moraine measurements have been used to test numerical models of their formation (Dunlop, Clark, & Hindmarsh, 2008). As noted above, such data have hitherto not been available for eskers and the data presented in this map can be used to test numerical models that, for example, predict esker spacing (Boulton, Lunn, Vidstrand, & Zatsepin, 2007a, 2007bBoulton et al, 2009;Hewitt, 2011) or make assumptions about, and parameterise, channel sinuosity (Schuler & Fischer, 2009). A key advantage of our dataset is that these numerical models can be tested against representative data from over 20,000 eskers, rather than being subject to the vagaries of smaller sample sizes.…”

“…The map presented here could therefore be used as the foundation for a more in-depth analysis of esker patterns (and morphometry) and to test numerical models that predict esker spacing (e.g. Boulton et al, 2009;Hewitt, 2011).…”

On the reconstruction of palaeo-ice sheets: Recent advances and future challenges

“…More generally, the imprint of meltwater drainage recorded on the bed of former ice sheets is a potentially useful test of numerical models that predict the configuration of the subglacial hydrological system (e.g. Hewitt, 2011;Werder et al, 2013), but which has generally been under-used.…”

Effects of ice deformation on Röthlisberger channels and implications for transitions in subglacial hydrology

“…the bed slope in the idealised ice stream, or the local surface slope in the flat-bedded mountain glacier; Fig. 1; Table 1), A c is the cross-sectional area, and R h is the hydraulic radius, which is defined as R h ≡ A c /P r for the wetted perimeter P r (Henderson, 1966;Clarke, 2003). For a semicircular channel, we follow Weertman (1972) and write the flow rate as a function of the channel diameter D as…”