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zonation and accounts for the radial increase in ice velocity outward from the cen-
tral zone of ice accumulation to the abrasion maximum near the ice terminus. In our
models, abrasion increases up to a point and then possibly decreases due to over-
whelming of the abrasive content that reduces basal sliding velocity by increased
basal friction. Ice boundaries thus control concentric changes of the erosion rates.
This broad pattern provides a regional context for further refinements. The main
refinement in the erosion pattern is caused by fast-flowing ice streams near the
glacial margins that have an enhanced capacity for erosion (Fig. 3.2 ) . Ice streams
move at high velocities under low driving stresses in a basal zone environment
mostly because their base is lubricated (see discussion in Marshall et al. 1996 ,
Tulaczyk et al. 2000 , Stokes and Clark 2001 , Kamb 2001 , Bougamont and Tulaczyk,
2003 , Hall and Glasser 2003 ) .
The bedrock surface determines the topography of ice streams with profound
erosion capacity. The location of bedrock troughs or elongated lowlands was ini-
tially controlled or at least influenced by the bedrock topography. Domination of
elongated landforms of smaller scale is taken to indicate zones of faster ice flow.
The elongation ratio of bedrock forms and megascale lineations are known to be a
useful proxy for ice velocity (Anderson and Shipp 2001 ) . Long subglacial bedforms
(length:width ratios 10:1) are indicative of fast ice flows (Stokes and Clark 2002 ) .
The geological-geomorphological impact of ice streams cannot be underestimated,
since modern ones literally control ice discharge. For example, over 90% of ice dis-
charging from the West Antarctic Ice Sheet into the Ross Ice Shelf (Joughin and
Tulaczyk 2002 ) is carried by ice streams.
Bedrock surface forms may also suggest very low ice velocities and erosion.
Areas with abundant distribution of relict landforms indicate slow ice. Special grid
filtering to emphasize outliers with a relevant search window can identify these areas
best. In zones adjacent to weathered bedrock, possible frozen-bed conditions and
weak erosional capacity can be manually input as constraints.
3.3 Methods
The preceding section suggests what must be taken into account by any glacial
erosion analysis. Not discussed thus far is that the mass of glacial sediments must
equal the mass of material eroded. We compile a huge quantity of published seis-
mic and sedimentological data and make our best estimates of the total sediments
deposited across the Quaternary. This provides a bound on the total Quaternary
erosion. We use denudation surfaces to estimate the erosion directly. This stage of
analysis is essentially an automation of traditional methods (Riis and Jensen 1992 ) .
Surfaces capture stages of Tertiary uplift and erosion (Amantov 2007 ) . The surfaces
connect isolated summit outcrops, patches of exhumed peneplains, and etchplains.
Surfaces emerging from under sedimentary cover can be extrapolated and correlated
with onshore saprolites and (or) remnants of cover so that the grids measure miss-
ing volumes. The surfaces can also illustrate past geological conditions. Regional
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