FIXED GROUNDING LINE
5.1. EXPERIMENTAL SETUP
5.2.1. The present reference state
In order to investigate the points rnentioned above, a reference state has to be defined. This is accornplished in two steps. First, the coupled velocity and ternperature fields are run forward in time for 100000 years in a diagnostic way (thus keeping present ice thickness and grounding line position fixed) until an approxirnate steady solution is reached. Following this, the position of the grounding line is still prescribed but ice thickness is allowed to relax to steady state for another 100000 years.
This defines the reference run and a comparison between observed and modelled ice thicknesses is shown in fig. 5.1. In general, rnodelled ice thicknesses appear to be within 5-10% or so of reality, which is certainly acceptable. Nevertheless, sornewhat larger deviations do occur in several places. However, this does not necessarily have to mean that the model is in error. Alternative explanations could be that bedrock data coverage is
Ice thickness [m]
300 - 1000 BELOW 300
ABOVE 31 00 2400 1700 1000 300 BELOW
flg.5.1: A comparison between observed ice thicknesses and those produced by the model in the reference run. upper panel: observations: lower panel: model.
insufficient in these areas andlor the fact that the ice sheet is just not in steady state. In this respect, it is interesting to note that the rnodel produces substantial thicker ice in the Pine Island and Thwaites Glacier catchrnent areas (approx. 1 OOOW) in West Antarctica. This happens to be an area which is considered to be very sensitive to grounding line instability, because the ice streams flowing into Pine Island Bay are presently unimpeded by a buttressing ice shelf (cf.
9
3.3.4.). Indeed, there is independent evidence that the Pine Island ice stream may at present be in the process of drawing its drainage basin down (Lindstrorn and Hughes, 1984; Kellogg and Kellogg, 1987a). As a consequence, steady state ice thicknesses under 'normal conditions' are likely to be larger than the present day values. The rnodel seerns to confirrn this.The overprediction of ice Cover in the Antarctic Peninsula, on the other hand, must be attributed to the poor quality of the bedrock data. The SPRI map West Antarctica, no further atternpts have been rnade to irnprove this situation.
Although less obvious, insufficient bedrock data coverage may also be the reason for the thicker ice produced by the rnodel upstrearn the Shackleton Range in Dronning Maud Land (30-40°W EAIS). In this area, bedrock elevation contours are based on only a few rneasurements (Drewry, 1983, sheet 3).
The associated (depth-averaged) velocity and basal ternperature fields (relative to pressure rnelting) are displayed in figs. 5.2
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5.3 and provide an additional check on overall rnodel performance. As far as can be judged from available data, the velocity field looks reasonable, with very low velocities over central East Antarctica, typically around 200 rnly at the grounding line and up to 1500 rnly along central portions of the three rnajor floating ice regions, narnely the Ronne-Fiichner, Amery and ROSS ice shelves. These rnodelled ice shelf velocities are certainly of the right rnagnitude, although they tend to be sornewhat higher than the observations: the Ronne and Filchner ice shelves flow at a rnaxirnum rate of  1500 rnly (Robin et al., 1983);Velocity rnagnitude [rn/y]
ABOVE 500 - 100
-
20 - 5
-
1 - BELOW
flg.5.2: Calculated speed of ice flow. Shown are depth-averaged values. The corresponding surface velocities in the grounded ice sheet are 5-10 O/o larger, depending On the ternperature conditions in the bottorn layers and the arnount of basal sliding.
Basal ternperature relative to prnp [deg. C]
EQUALTO -0 -5
-
-0-10
-
-5-15 - -10 -25 - -15 BELOW -25
fig.5.3: Bottorn ternperatures produced by the rnodel. They have been corrected for the dependence of ternperature On pressure. Yellow areas are areas where basal rnelting occurs.
the ROSS ice shelf at  ± 100 rnly (Thomas et al., 1984); and the Amery ice shelf at ±I30 rnly (Budd et al., 1982). This discrepancy rnay be due to the neglect of basal rnelting in the rnass balance of the ice shelf. As a consequence, the rnodel probably overpredicts the rnass outflow and, since the thicknesses agree much better, this results in sornewhat higher velocities.
Although ice strearns and outlet glaciers (discharging an irnportant fraction of the ice rnass into the ice shelves and the ocean) are not explicitly included in the calculations, they are apparent in the results and are characterized by velocities of 500 rnly or rnore (fig.5.2). This is essentially a consequence of the fine grid used. Despite anticipated difficulties rnentioned earlier (cf. Â 4.1), also the rnajor ice strearns discharging into the Ronne- Filchner and ROSS ice shelves can be clearly identified. This is an encouraging result and is largely because of basal sliding.
According to the rnodel, bottorn ice at pressure rnelting point is dominant over rnost of the Antarctic Peninsula and is widespread in West Antarctica. In East Antarctica, basal rnelting is confined to the thick interior regions (because of the insulating effect of ice) and the fast flowing regions at the rnargin (fig.5.3).
This temperature field can be reconciled with independent evidence for the locations of temperate ice frorn radio-echo sounding, where sub-ice lakes in central areas have been found to obscure reflections (Oswald and Robin, 1973). The coolest basal layers are found above the Garnburtsev Mountains, where the ice is relatively thin (1500
-
2000rn), arid along the fringing rnountain ranges, where both thin ice and cold ice advection frorn above play an important role.The distribution of pressure rnelting as obtained here deviates frorn the calculation presented in Herterich (1988) with a similar rnodel. Despite a lower value for the geotherrnal heat flux used in his study, Herterich's rnap shows basal rnelting to be substantially rnore widespread. This disagreernent seerns to be prirnarily the consequence of a different experimental setup.
Herterich derived the vertical velocity cornponent from the flux divergence of the horizontal flow field. However, since the shape of his ice sheet was fixed, the horizontal velocity field was not in internal equilibriurn with the ice thickness distribution. This disequilibriurn rnay indicate a real world imbalance (as assurned by Herterich) but it rnay also just reflect shortcomings in the
rnodel physics. Uncertainties in the flow law parameters and in the ice thickness distribution rnay easily lead to changes in the diagnostic velocity field by up to an order of magnitude. His velocity components, which are needed for the advective terrns in the heat equation, therefore do not necessarily correspond to a balanced stationary state. Also the use of a fixed vertical coordinate in the Herterich rnodel rnay introduce nurnerical errors when values are interpolated to the actual upper and lower ice surfaces.