10.6.3.2 Dynamic Response and Feedback on Mass Balance
As glacier volume is lost, glacier area declines so the ablation decreases. Oerlemans et al. (1998) calculate that omitting this effect leads to overestimates of ablation of about 25% by 2100. Church et al. (2001), following Bahr et al. (1997) and Van de Wal and Wild (2001), make some allowance for it by diminishing the area A of a glacier of volume V according to V ∝ A1.375. This is a scaling relation derived for glaciers in a steady state, which may hold only approximately during retreat. For example, thinning in the ablation zone will steepen the surface slope and tend to increase the flow. Comparison with a simple flow model suggests the deviations do not exceed 20% (van de Wal and Wild, 2001). Schneeberger et al. (2003) find that the scaling relation produced a mixture of over- and underestimates of volume loss for their sample of glaciers compared with more detailed dynamic modelling. In some regions where G&IC flow into the sea or lakes there is accelerated dynamic discharge (Rignot et al., 2003) that is not included in currently available glacier models, leading to an underestimate of G&IC mass loss.
The mean specific surface mass balance of the glacier or ice cap will change as volume is lost: lowering the ice surface as the ice thins will tend to make it more negative, but the predominant loss of area at lower altitude in the ablation zone will tend to make it less negative (Braithwaite and Raper, 2002). For rapid thinning rates in the ablation zone, of several metres per year, lowering the surface will give enhanced local warmings comparable to the rate of projected climatic warming. However, those areas of the ablation zone of valley glaciers that thin most rapidly will soon be removed altogether, resulting in retreat of the glacier. The enhancement of ablation by surface lowering can only be sustained in glaciers with a relatively large, thick and flat ablation area. On multi-decadal time scales, for the majority of G&IC, the loss of area is more important than lowering of the surface (Schneeberger et al., 2003).
The dynamical approach (Oerlemans et al., 1998; Schneeberger et al., 2003) cannot be applied to all the world’s glaciers individually as the required data are unknown for the vast majority of them. Instead, it might be applied to a representative ensemble derived from statistics of size distributions of G&IC. Raper et al. (2000) developed a geometrical approach, in which the width, thickness and length of a glacier are reduced as its volume and area declines. When applied statistically to the world population of glaciers and individually to ice caps, this approach shows that the reduction of area of glaciers strongly reduces the ablation during the 21st century (Raper and Braithwaite, 2006), by about 45% under scenario SRES A1B for the GFDL-CM2.0 and PCM AOGCMs (see Table 8.1 for model details). For the same cases, using the mass-balance sensitivities to temperature of Oerlemans (2001) and Oerlemans et al. (2006), G&IC mass loss is reduced by about 35% following the area scaling of Van de Wal and Wild (2001), suggesting that the area scaling and the geometrical model have a similar effect in reducing estimated ablation for the 21st century. The effect is greater when using the observationally derived mass balance sensitivity (Section 10.6.3.1), which is larger, implying faster mass loss for fixed area. The uncertainty in present-day glacier volume (Table 4.4) introduces a 5 to 10% uncertainty into the results of area scaling. For projections, the area scaling of Van de Wal and Wild (2001) is applied, using three estimates of world glacier volume (see Table 4.4 and Appendix 10.A). The scaling reduces the projections of the G&IC contribution up to the mid-21st century by 25% and over the whole century by 40 to 50% with respect to fixed G&IC area.