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Radio-echo sounding measurements made in 1994 across the divide of Siple Dome, West Antarctica (Raymond et al. 1995; Scambos and Nereson 1995), reveal internal reflecting horizons to about 70 percent of total depth [1,009±6 meters (m) at the summit]. These layers are asymmetric about the divide; layers to the north are deeper than layers to the south. Within 2 kilometers (km) of the divide, the internal layers are warped convex up along the divide with maximum displacement of about 50 m ( figure). The variation in the shape of these layers along the divide ridge is minimal, so that the layer shapes are largely two-dimensional (Jacobel, Fisher, and Sundell, Antarctic Journal, in this issue). Examination of these layers shows that the axis of maximum warping is not vertical but tilted to the north toward ice stream D by about 60° (figure).
The warped layers beneath the divide may arise from a local low in accumulation over the divide and/or the special ice-flow field associated with the presence of a divide (Raymond 1983; Hvidberg 1996). Regardless of what causes layer warping observed at Siple Dome, it is likely an effect associated with the presence of the divide, and therefore, the tilted axis of the up-warping is suggestive of recent divide migration northward toward ice stream D.
We have used a two-dimensional finite element model (FEM) (Raymond 1983) to predict the shapes of isochrones under steady-state conditions at Siple Dome. The model assumes
a nonlinear flow rheology (n=3),
a frozen bed,
a constant accumulation rate of 10 centimeters per year (cma-1) ice-equivalent, and
a steady-state temperature profile following Firestone, Waddington, and Cunningham (1990) (see Nereson et al. 1996).
We find that the predicted warping of isochrones by the FEM is larger than the observed warping by a maximum of 50 m. We suspect that this difference is at least partially due to migration of the divide zone.
To simulate the effect of divide migration on isochrone layer shapes, we construct a kinematic flow model from the FEM flow field and move this flow field through a grid of ice particles in time. We track the path of these particles as they flow through the migrating flow field and map the shape of the resulting isochrones. We also simulate the effect of spatial accumulation gradients by assuming constant ice thickness and by scaling the FEM flow field to the surface accumulation rates, so that continuity is satisfied.
To compare the predicted layer shapes to the observed layer shapes, we define a mismatch parameter, J:
where N is the number of points,
mi are the depth positions of points along the modeled layers and
di are depth positions of points along the observed layers,
si is the expected combined error from the model and the data, and
wi is a weighting factor that depends on depth.
We define a set of parameters to represent divide migration and a simple spatial accumulation rate pattern, and find the set of parameters that minimize J. We consider two cases:
case 1 includes the special flow field associated with an ice divide so that the isochrone warping is caused by a
case 2 assumes no special divide flow field so that the warped layers are caused solely by accumulation scouring on the divide
For the first case, we assume a linear accumulation gradient on either side of the divide defined by two slopes. The spatial pattern looks like a hinge, centered at the divide. This pattern is divide-specific and moves as the divide migrates. We find the combination of three parameters, migration rate, and the two accumulation rate slopes, which minimizes J. This minimization gives a migration rate of 3±1 times the reference accumulation rate, or about 30 cma-1.
For the second case, we define the accumulation scouring and redeposition as one cycle of a sinusoid superimposed on the "hinge" pattern given by the above minimization. We position the low of the sinusoid over the divide (scouring) with the rest of the cycle north of the divide (deposition). In this case, the migration rate, the amplitude of the sinusoid, and its wavelength are adjusted. The resulting minimization gives a migration rate of 2±1 times the reference accumulation rate, or about 20 cma-1.
In both cases, the modeled layers match the observed layers to within 0.10 of the amplitude of the up-warping. It appears as though the migration rate inferred from this minimization scheme is only slightly sensitive to the prescribed cause of isochrone warping. Based on the regularity of the layer shapes, we expect that the divide has been migrating toward ice stream D for at least the past 5,000 years. Migration of the divide is important to the selection of the deep ice core at Siple Dome. It indicates effects from nonsteady processes possibly including changing activity of ice streams C and D and evolution of the accumulation pattern. Continuing investigations with the aid of new radio-echo sounding data from the south flank of Siple Dome to be collected in 1996 aim to place constraints on the time evolution of the spatial accumulation pattern, divide migration, and adjacent ice stream activity.
This work was supported by a National Science Foundation grant OPP 93-16807. We also gratefully acknowledge other members of the 1994 field team: H. Conway, A. Gades, R. Jacobel, and T. Scambos.
References
Firestone, J., E. Waddington, and J. Cunningham. 1990. The potential for basal melting under Summit, Greenland. Journal of Glaciology, 36(123), 163-168.
Hvidberg, C.S. 1996. Steady state thermo-mechanical modelling of ice flow near the centre of large ice sheets with the finite element technique. Annals of Glaciology, 23, 116-123.
Jacobel, R.W., A.J. Fisher, and N.M. Sundell. 1996. Internal stratigraphy from ground-based radar studies at Siple Dome summit. Antarctic Journal of the U.S., 31(2).
Nereson, N.A., E.D. Waddington, C.F. Raymond, and H.P. Jacobsen. 1996. Predicted age-depth scales for Siple Dome and inland WAIS ice cores in West Antarctica. Geophysical Research Letters, 23(22), 3163-3166.
Raymond, C., N. Nereson, A. Gades, H. Conway, R. Jacobel, and T. Scambos. 1995. Geometry and stratigraphy of Siple Dome, Antarctica. Antarctic Journal of the U.S., 30(5), 91-93.
Raymond, C.F. 1983. Deformation in the vicinity of ice divides, Journal of Glaciology, 29(103), 357-373.
Scambos, T., and N. Nereson. 1995. Satellite image and global positioning system study of the morphology of Siple Dome, Antarctica. Antarctic Journal of the U.S., 30(5), 87-89.