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Modeling the Subglacial Hydrology of the James Lobe of the Laurentide Ice Sheet

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Modeling the Subglacial Hydrology of the James Lobe of the Laurentide Ice Sheet ARTICLE IN PRESS Quaternary Science Reviews 26 (2007) 1384–1397 Modeling the subglacial hydrology of the James Lobe of the Laurentide Ice Sheet Anders E. Carlsona,Ã, John W. Jensonb, Peter U. Clarka aDepartment of Geosciences, Oregon State University, Corvallis, OR 97331, USA bWERI, University of Guam, Mangilao, GU 96923, USA Received 22 February 2006; received in revised form 9 January 2007; accepted 29 January 2007 Abstract To investigate the drainage conditions that might be expected to develop beneath soft-bedded ice sheets, we modeled the subglacial hydrology of the James Lobe of the Laurentide Ice Sheet from Hudson Bay to the Missouri River. Simulations suggest the James Lobe had little effect on regional groundwater flow because the poorly conductive Upper-Cretaceous shale that occupies the upper layer of the bedrock would have functioned as a regional aquitard. This implies that general northward groundwater flow out of the Williston Basin has likely persisted throughout the Quaternary. Moreover, the simulations indicate that the regional aquifer system could not have drained even the minimum amount of basal meltwater that might have been produced from at the glacier bed. Therefore, excess drainage must have occurred by some sort of channelized drainage network at the ice–till interface. Using a regional groundwater model to determine the hydraulic conductivity for an equivalent porous medium in a 1-m thick zone between the ice and underlying sediment, and assuming conduit dimensions from previous theoretical work, we use a theoretical karst aquifer analog as a heuristic approach to estimate the spacing of subglacial conduits that would have been required at the ice–till interface to evacuate the minimum water flux. Results suggest that for conduits assumed to be on the order of a tenth of a meter deep and up to a meter wide, inter-conduit spacing must be on the order of tens–hundreds of meters apart to maintain basal water pressures below the ice overburden pressure while evacuating the hypothesized minimum meltwater flux. r 2007 Elsevier Ltd. All rights reserved. 1. Introduction caused the discharge of large quantities of icebergs to the ocean and affected continental runoff with attendant The rapid fluctuations of the James, Des Moines, Green consequences for ocean circulation (see review in Clark Bay and Lake Michigan Lobes draining the southern et al., 1999). The occurrence and importance of basal margin of the Laurentide Ice Sheet (LIS) (Fig. 1)(Clayton sliding and/or subglacial sediment deformation to ice sheet and Moran, 1982; Mickelson et al., 1983) under relatively motion are linked to the subglacial hydrology of the ice low driving stresses (Mathews, 1974; Clark, 1992; Hooyer sheet. Of particular importance is the ability of the regional and Iverson, 2002) require a significant component of ice aquifer to drain meltwater (Alley, 1989), and the ability of motion by basal sliding and/or subglacial sediment whatever basal drainage system that might develop to deformation (Alley, 1991; Clark, 1994; Hooyer and discharge excess meltwater that cannot be accommodated Iverson, 2002). These processes of bed dynamics have by the regional aquifer. broader implications for interpretations of global and The absence of modern analogs to the mid-latitude, abrupt climate change where rapid changes in ice sheet terrestrial paleo-ice lobes of the LIS and the limited access dimensions may have influenced the 100-ka ice age cycle, to the ice streams of the West Antarctic Ice Sheet, which are the most closely related modern analogs (e.g. Patterson, 1998), have necessitated the use of numerical model ÃCorresponding author. Currently at: Department of Geology and Geophysics, Woods Hole Oceanographic Institution, Woods Hole, MA simulations to investigate the subglacial hydrology of ice 02540, USA. Tel.: +1 508 289 3976; fax: +1 508 457 2175. sheets and lobes. Previous modeling studies have found E-mail address: [email protected] (A.E. Carlson). that subglacial aquifers were unable to drain meltwater at 0277-3791/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.quascirev.2007.02.002 ARTICLE IN PRESS A.E. Carlson et al. / Quaternary Science Reviews 26 (2007) 1384–1397 1385 still crucial, however, because although such conduits may occupy only a small fraction of the aquifer volume or even of the total porosity, they would be the dominant mechanism for regional flow. This dilemma is familiar to karst modelers, however. A well-known approach in modeling karst systems is to treat the aquifer as an equivalent porous medium (EPM), in which ‘‘the relevant physical properties (e.g., frequency, diameter, and tortuosity of tubes for capillary tube models; frequency and aperture width for parallel-fracture models) are combined so that discharge per unit hydraulic gradient is equivalent to that produced by Darcy’s Law’’ (Vacher and Mylroie, 2002). The EPM approach has obvious limitations. First, it can only characterize aquifers in terms of general, large-scale properties, most notably, regional hydraulic conductivity. Second, there is some uncertainty associated with the fact that flow within conduits is generally turbulent flow, while the application of Darcy’s Law inherently assumes laminar flow. Inferring specific characteristics such as the types and dimensions of porosity from the general properties of an EPM, such as hydraulic conductivity or effective porosity, is therefore problema- tical. Nevertheless, such heuristic approaches can be useful for placing quantitative boundaries on unknown and unobservable properties, as long as the limitations of the approach are explicitly acknowledged (cf., Scanlon et al., 2003). Here we simulate the interaction between the James Lobe of the LIS (Fig. 1) and the regional aquifer system extending from the Hudson Bay Lowland south to the terminus of the James Lobe in South Dakota. Based on known characteristics of the regional aquifer and hypothe- tical minimum subglacial meltwater production rates, we Fig. 1. Map of the James Lobe (west) and neighboring Des Moines Lobe find that, as in other studies, a subglacial drainage network (east) margins (solid black line) and model domain (white line) overlain on would have been necessary to prevent ice flotation. We a 50-m DEM. Precambrian Shield is exposed in the area bounded by the then use an EPM model, in combination with other large dashed lines. Small dashed line is the location of the cross-section in previous theoretical work, to infer the range of effective Fig. 2. Latitude north and longitude west are indicated. Inset map shows porosity, in terms of conduit spacing or ‘‘conduit density’’ the LIS Last Glacial Maximum ice margin (Dyke et al., 2003) and the box denotes the location of 50 m DEM. of a drainage network that could have maintained basal water pressures near the ice load while evacuating a minimum meltwater flux. Until more rigorous models are the ice–till interface without the development of a basal available, this heuristic approach offers a useful first drainage system such as a laminar film (Alley et al., 1989; approximation of the properties a basal drainage system Breemer et al., 2002), a channelized system (Brown et al., at the ice–till interface for an ice lobe. 1987; Walder and Fowler, 1994; Ng, 2000), or periodic outburst floods (Piotrowski, 1997a, b) to maintain stable 2. Model configuration ice flow. However, as Breemer et al. (2002) recognized, because films are unstable (Walder, 1986; Engelhardt and 2.1. Boundary conditions and parameters Kamb, 1997), they would most likely be only an idealized hydrological equivalent of a channelized network such as The James Lobe was the westernmost of the distinctive the system of shallow subglacial conduits predicted from lobes that drained the southern margin of the LIS. Ice flow the theoretical work of Walder and Fowler (1994) and Ng feeding the lobe originated in the Hudson Bay Lowland (2000). Detailed modeling of a system of such conduits, (Fig. 1). Clark (1992) calculated that the lobe had a driving predicted to be on the order of only meters wide but stress of 1.0 kPa. It reached its maximum extent in South distributed over a region on the order of 100s of kilometers Dakota 20 14C ka BP with subsequent margin fluctua- wide, is beyond the state of the art for current models and tions before retreating at 14 14CkaBP (Clayton and computing power. Accounting for their overall effects is Moran, 1982). ARTICLE IN PRESS 1386 A.E. Carlson et al. / Quaternary Science Reviews 26 (2007) 1384–1397 Fig. 2. Simplified hydrostratigraphic bedrock cross-section used in the model (northeast to south). Location is indicated on Fig. 1. See Table 1 for abbreviations and hydraulic conductivities. The till layer is not included on this cross-section but rests on top of all the bedrock layers and thickens towards the south from 1 to 15 m. Table 1 to 15 m, towards the south is added atop these layers. We The grouping of rock units into hydrostratigraphic layers (Downey, 1986; use the term till in the broad sense to describe Quaternary Downey and Dinwiddie, 1988), with hydraulic conductivities (Stephenson sediment that is actually a combination of basal till, et al., 1988; Lennox, 1993) supraglacial debris flows, glaciofluvial sand and gravel, and Layer Rock units K (m sÀ1) Unit type glaciolacustrine sediment. These types of glacial units have K values that range over 8 orders of magnitude (Stephen- Till Quaternary drift 3 Â 10À8–3 Â 10À6 Aquifer U–K Upper K shale 3 Â 10À10 Aquitard son et al., 1988). We thus group them into a sediment À7 À1 L–K Lower K sandstone 3 Â 10À5 Aquifer hydrostratigraphic unit assigned a K of 3 Â 10 ms , J–P Jurassic through Pennsylvanian units 3 Â 10À12 Aquitard which is at the upper end of unweathered basal till, the À7 M Madison Limestone 3 Â 10 Aquifer average of weathered basal till, and the lower end of S–D Silurian–Devonian limestone and shale 3 Â 10À12 Aquitard C–O Cambrian–Ordovician sandstone 3 Â 10À6 Aquifer glaciofluvial sediment (Stephenson et al., 1988).
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