Flowline D

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co 0

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¡53^

(LGM)

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-- melted bed ■■■ . . .

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1000 shelf"

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Figure 71.3 Last Glacial Maximum (22.1 ka) and modern ice-sheet reconstructions with isotherms and basal melting indicated for flowlines C (with grounding-line forcing) and D (without grounding-line forcing). (Based on fig. 2 in Parizek et al., 2002, 2003.)

71.2 Numerical Simulations

In an attempt to reconcile localized basal-freezing tendencies amidst ongoing fast-glacier flow, Parizek et al. (2002, 2003)

conducted numerical studies of the basal heat budget. Using a two-dimensional (vertical and along-flow) thermomechanical flowline model, a wide range of parameter space (sensitivity to accumulation rate, geothermal heat-flux density and basal resis tance to flow) was tested along the four flowlines (A-D; down Mercer, Whillans, Kamb and Bindschadler Ice Streams, respectively) displayed in Fig. 71.1. The boundary conditions for the coupled ice-sheet and bedrock model include a temperature gradient from the geothermal heat-flux density, slip/no-slip basal conditions and variable basal-resistance parameterizations for 'sheet', 'stream' and 'shelf' zones (see Fig. 71.3), and forcings for surface temperature from the Byrd ice core, sea level from SPECMAP, accumulation rate following Huybrechts (1992), and specified grounding-line evolution (along flowlines A-C) following Conway et al. (1999). Throughout forty-one 130-kyr reconstructions, the basal heat budget was calculated as the difference between the heat flow into the ice-bedrock interface (from geothermal and frictional-heating sources) and the conductive heat flow out of the interface and into the ice. Locally, excess heat generates basal melting, whereas a deficit indicates basal freezing. A positive (negative) 'total' heat budget indicates that there is (not) sufficient up-glacier basal melting to buffer down-glacier freeze-on. Figure 71.2 illustrates four such 'total' balances along the four flowlines assuming the inland 'sheet' region is twice as wide as the 'stream' region based on modern observations (Joughin et al., 1999). Last Glacial Maximum (LGM) and modern reconstructions for the same parameterizations along flowlines C and D are displayed in Fig. 71.3.

71.3 Results

For today, all of the flowlines are simulated to have excess heat (Fig. 71.2). Supporting the observations of Engelhardt & Kamb (1998) and Kamb (2001), meltwater from beneath thick inland ice and in bedrock lows (Fig. 71.3) is driven in a throughgoing hydrological system to the ice streams, where it locally freezes to their cold bases without exhausting the flow. Hence, subglacial tills do not need to supply water for freeze-on, and rapid ice flow can continue.

Data (Conway et al. 1999) show that grounding-line retreat of as much as 1300 km began ca. 13ka after most of the post-glacial sea-level rise was completed. As shown in Fig. 71.2, this is when simulated thermal budgets became positive in several of the model runs. Hence, Parizek et al. (2002, 2003) suggested that slightly thicker, colder LGM ice streams were little affected by sea-level rise, that post-glacial warming increased basal lubrication allowing speed-up, thinning, flotation and grounding-line retreat, and that this retreat can continue. The mismatch between the short time constant of the subglacial water and the slower ice response may help explain the short-term variability of the persistent ice streams.

71.4 Discussion and conclusions

These results were generated with a thermal code coupled to an ice-dynamics code that utilizes a diffusion formulation of the thin-ice approximation (Hutter, 1983) in which only the vertical shear stress drives ice deformation. At the scale used in the studies, longitudinal stresses are negligible in the force balance (Whillans & van der Veen, 1993). However, a possible bias is introduced by neglect of ice-stream sides, because modern ice streams dissipate much of their potential energy as heat within the ice at their sides (e.g. Raymond, 2000). The simulated ice streams also have less advection of cold ice than indicated by observations, reducing calculated basal temperature gradients to 5-7% below observed values in ice streams. To offset these unavoidable problems of the reduced-dimensional simulations, basal 'slipperiness' was chosen to produce thinner inland ice and flatter ice streams than observed, reducing, on average, the mechanically generated heating rate per unit area below that modelled in other studies (e.g. Raymond, 2000; Joughin et al., 2002). Taking these difficulties and corrections together, the simulated flowline beds are probably slightly colder than in reality, yet have excess water. Thus, although these two-dimensional studies are not the final word and three-dimensional modelling will certainly improve upon the preliminary results, the regional conclusions indicating continuation of rapid ice flow and thermal ties to the onset of deglaciation are likely robust and highlight the need to account for the basal thermal and water balances when studying the dynamic evolution of the WAIS.

The practice ofglaciology

Power Table For Energy Changes

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