Figure 4.10 shows a location map for a large number of equatorial Pacific island locations from which relative sea level information is available for the Holocene epoch of Earth history. Figure 4.11 presents comparisons of the predictions of the same ICE-4G (VM2) model of the relative sea level history that should be observed at each of these island locations (shown as the solid line) together with the data available from each site as recently quality ensured in the paper of Grossman et al. (1998). From most of these oceanic islands there is usually only a single high-quality sea level datum available, often consisting of a 14C-dated "notch" cut in coral that is currently observed to be located above local MSL. On each frame of this figure is also shown the predictions for two modifications of the Northern Hemisphere-constrained ICE-4G ( VM2) model as well as for this base model itself. These modifications consist of adding to ICE-4G a continuous "melting tail" that continues to add meltwater to the oceans following the time at which the déglaciation event is assumed to have ended in ICE-4G, namely at 4 kyr BP. For the first of these modifications to the ICE-4G model, for which results are shown by the dotted lines on Fig. 4.11, the rate of eustatic sea level rise associated with late Holocene melting has been assumed to be equal to 0.25 mm/yr and all melting is assumed to derive from the Antarctic ice sheet. The second modification to ICE-4G, RSL results for which are shown as the dashed lines on Fig. 4.11, consists of a continuing eustatic sea level rise of strength 0.5 mm/yr, also assumed to be due to ongoing Antarctic melting.
Inspection of the intercomparison of observations and theory shown in Fig. 4.11 demonstrates immediately that the strength of any late Holocene meltwater addition to the global oceans due to sustained melting of the Greenland ice sheet is strongly constrained by the elevation of the mid-Holocene highstand of sea level that is observed at essentially all islands in the equatorial Pacific Ocean from which actual shoreline elevation observations are available. This constraint is sufficiently tight that even continuous melting at the modest rate of 0.25 mm/yr leads to such a sharp reduction in the theoretically predicted amplitude of the highstand, to approximately 1 m rather than the observed 2 m, that it is ruled out by the observations. This same conclusion follows when the continuing melting of polar ice is assumed to derive from Greenland rather than from Antarctica (results not shown). With a rate of late Holocene melting of 0.5 mm/yr, the observed mid-Holocene highstand is entirely eliminated at all locations, as will be clear by inspection of Fig. 4.11. On this basis it would seem that the recent claim by Flemming et al. (1998) to the effect
Figure 4.11 Comparisons of the predictions of the version of the gravitationally self-consistent theory of postglacial relative sea level history that neglects rotational feedback with the observations of many of the island locations shown in Fig. 4.10. All three of the time series shown at each site have been computed using the VM2 viscosity model but differ from one another in that they correspond to three variations on the ICE-4G déglaciation history. In particular the solid lines are the RSL predictions delivered by ICE-4G itself, the dotted lines are for a déglaciation
history that is identical to ICE-4G from LGM until 4 kyr BP. following which it is assumed that Antarctic melting continues to deliver water to the global ocean at an eustatic rate of 0.25 mm/ yr. The dashed RSL curves are for a model that is identical to that which produces the dotted RSL curves but for which the post-4-kyr BP "melting tail" is of strength 0.5 mm/yr. It will be noted that neither of the models that include late Holocene melting from Antarctica is able to fit any of the data.
that continuing late Holocene melting of the polar ice caps on Greenland and Antarctica might be contributing significantly to the tide gauge inferred modern rate of global sea level rise of 1.8 mm/yr, is untenable. They suggest that as much as 0.5 mm/yr of this signal could be due to such continuing polar ice sheet instability. Clearly this rate, or any significant fraction of it, would rule out the existence of the mid-Holocene highstand of sea level that is observed at both Pacific island locations and at virtually all coastal locations in the far field of the ice sheets (results not shown).
Since it is the existence of the GIA-related mid-Holocene highstand of sea level and the subsequent fall to modern levels that leads to the increase in the tide gauge rates of relative sea level rise at far field sites when the tide gauge rate is corrected for the influence of glacial isostatic adjustment (see the results for individual gauges shown in Table 4.1), we may also usefully express the impact of the late Holocene melting postulated by Flemming et al. (1998) in the form of global maps of the predicted present-day rate of RSL rise due to the GIA process. Figure 4.12 (see color plate) provides a useful demonstration of the utility of a presentation of this kind. The top of this figure shows the predicted present-day rate of RSL rise for the standard ICE-4G (VM2) model, whereas the middle and bottom respectively show equivalent predictions for the models that incorporate the influence of Antarctica derived "melting tails" of global strength 0.25 and 0.50 mm/yr. Clearly, when the strength of late Holocene melting is taken to be the larger value, the sign of the present-day rate of GIA-related RSL rise in the far field is no longer negative but is positive, as the highstand has been entirely eliminated.
On the basis of these analyses of the implications of the observed mid-Holocene highstand of sea level at sites distant from the polar ice sheets, it should be clear that the existence of this ubiquitous feature places strong constraints upon the extent to which these ice sheets may have continued to supply meltwater to the sea from mid-Holocene time onward. Based upon the analysis of these data discussed herein, I would therefore suggest that an upper bound on the rate of sustained mass loss from these systems should be taken to be no more than 0.1 mm/yr. This is clearly an insignificant fraction of the global rate of sea level rise of 1.8 mm/yr that we are required to explain. If the polar ice sheets are making a significant contribution to this global rate, then this contribution must have been activated only recently and could therefore plausibly be related to modern climate change. Even if we consider such contributions to be of relatively recent vintage, however, their magnitude is still rather strongly constrained by other geophysical observations. In particular, it has been demonstrated in Peltier (1998a, 1999) that Earth rotation observations of the nontidal acceleration of the rate of axial rotation and the speed and direction of true polar wander strongly constrain the present-day rate of mass loss from these polar locations. These analyses suggest that the maximum rate of collective mass loss from Greenland and Antarctica that could be accommodated by these observations is 0.5 mm/yr and this would be possible only under very special circumstances. In particular, Greenland would have to be the primary source of melting and the contributions from GIA and from the melting of small ice sheets and glaciers (e.g., Meier, 1984) would have to be most accommodating. If these constraints on the RSL contributions from the large polar ice sheets are correct, then we are clearly obliged to look elsewhere for explanation of the 1.8 mm/yr global sea level rise signal that the GIA-corrected tide gauge data reveal.
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