Measuring change in an ice sheet

With a surface area of around 12 million km2, the grounded Antarctic Ice Sheet is the single largest control on world sea level. The East Antarctic Ice Sheet holds the equivalent of 52 m of global sea-level rise, and the West Antarctic Ice Sheet, which rests on rock that lies considerably below sea level and is inherently less stable, contains the equivalent of 5 m of sea-level rise (Lythe et al., 2001).

More than 50% of the outflow from the continental ice sheet passes through the largest 40 outlet glaciers and ice streams (hereafter collectively termed ice streams). It is these ice streams that are the most important control on the dynamics and volume of the ice sheet. Assuming that ice flow is generally in a downslope direction, it is relatively easy to define the portion of the ice sheet that feeds each glacier, i.e. its drainage basin (Fig. 42.2). And as each drainage basin operates largely independently of its neighbours, it makes sense to try to understand the evolution of the ice sheet in terms of these basins.

Our understanding of the evolution of the glacier basins in the Antarctic Ice Sheet (indeed any ice sheet, ice cap or glacier) is built

Figure 42.2 Drainage basins for 30 of the most significant glaciers in Antarctica. Within the basins for the significant glaciers the tone indicates the calculated balance flux (taken from Bamber et al., 2000), with the lighter tones indicating faster flow. Areas of the ice sheet not drained by these significant glaciers are shaded grey and ice shelves are unshaded.

Figure 42.2 Drainage basins for 30 of the most significant glaciers in Antarctica. Within the basins for the significant glaciers the tone indicates the calculated balance flux (taken from Bamber et al., 2000), with the lighter tones indicating faster flow. Areas of the ice sheet not drained by these significant glaciers are shaded grey and ice shelves are unshaded.

around the concept of steady-state ice flow. Ice is driven to flow downslope by gravity, and this gravitational driving stress is controlled by surface slope and ice thickness. Thus as thickness increases so does ice flow. An ice sheet is said to have reached steady-state when it has thickened enough to cause sufficient flow at every point to remove all the snow accumulating between that point and the ice divide. After that, so long as the accumulation rate remains the same, and the relationship between driving stress and ice-flow velocity remains constant, a drainage basin should achieve something close to a steady-state. In reality, it is implausible that any major glacier drainage basin will ever reach a precise steady-state, because long before it is reached, some change (perhaps in snowfall or temperature) will have occurred, altering the accumulation rate or the way in which ice flow responds to stress. Having said this, that a true steady-state is implausible, we find that most drainage basins are actually surprisingly close to steady-state, and imbalances (known as the mass balance of the basin) have proved difficult to measure. Because any deviation from steady-state implies an immediate contribution to sea-level change, however, this remains an important measurement for glaciologists to make.

Estimates of the mass balance of the Antarctic Ice Sheet and its basins began very soon after the basic techniques for measuring accumulation rate, thickness and ice-flow velocity were established. These early assessments tended to use a credit/debit approach, in which the amount of snow accumulating over a particular domain, usually a complete drainage basin, was estimated, together with the flux of ice leaving this domain. Many such calculations have been published, but until quite recently, every one has been hindered by an unfavourable error budget. After all, the credit/debit approach relies on taking the difference between two

Figure 42.3 (a) The drainage basins of the principal outlet glaciers and ice streams in Antarctica, derived from a digital elevation model (Bamber & Bindschadler, 1997). (b) Map of surface elevation change in the period 1992-1996 derived from ERS-1,2 satellite altimetry. (Reproduced from Wingham et al. (1998), courtesy of American Association for the Advancement of Science.)

Figure 42.3 (a) The drainage basins of the principal outlet glaciers and ice streams in Antarctica, derived from a digital elevation model (Bamber & Bindschadler, 1997). (b) Map of surface elevation change in the period 1992-1996 derived from ERS-1,2 satellite altimetry. (Reproduced from Wingham et al. (1998), courtesy of American Association for the Advancement of Science.)

large numbers that contain substantial uncertainty. A 10% uncertainty in the mean accumulation rate across the basin (which would be a particularly precise estimate) means that even with ice flux known precisely the mass balance can only ever be found to ±10%. Not surprisingly, the credit/debit approach has rarely resulted in a statistically significant measurement of imbalance.

So although many, including myself, have tried to use the credit/debit method to measure change in the Antarctic Ice Sheet, these efforts were mired in uncertainty and the credit/debit approach has failed to provide a useful answer for most of the basins in the ice sheet (e.g. Jacobs et al., 1992). This impasse remained until satellite altimetry finally came of age.

The idea has existed for many years to use satellite altimetry data to make a different kind of assessment of mass balance in ice sheets: a direct measurement of the rate of change in the surface elevation over a sufficiently long period to be able to observe mass imbalance directly. Notable efforts in both Antarctica and Greenland using several satellite altimeters (Zwally et al., 1989; Lingle & Covey, 1998) were published, but only as improved satellite orbit determinations became available in the late 1990s did the technology finally come of age and creditable assessments become possible. The first entirely convincing assessment was published by Wingham et al. (1998; see Fig. 42.3). Although satisfactory altimetry could still not be retrieved from steep coastal zones, the area beyond the satellite's orbital range (south of 81.5°S), or those portions of the ice sheet where the satellites were out of range of ground receiving stations, this study produced estimates of change over 63% of the continental ice sheet. Somewhat surprisingly, it showed that between 1992 and 1996 there was little evidence for any surface elevation change exceeding ca. 10 cmyr-1 over the majority of basins. Owing to the limitations of the technique, small-scale changes could not be ruled out but most of the individual basins appeared to be close to balance. There was, however, one substantial region that showed a spatially coherent change: the drainage basins feeding Pine Island, Thwaites and Smith glaciers in West Antarctica, which appeared to be thinning at a rate of >10 cmyr-1. Given the high snowfall rates in these basins, it was not possible for Wingham et al. (1998) to be certain whether this change was due to unusual snowfall or a dynamic imbalance in the glacial flow, but it was clear that unique and substantial changes were occurring in this area.

Later in this chapter we will return to the successful credit/debit assessments (section 42.4.2) and to glacier basins identified by Wingham et al. (1998) (section 42.5), but first we will discuss changes that have been observed elsewhere in Antarctica, which illustrate some of the causes of change that could lead to basin-wide imbalance.

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