A very detailed global viscoelastic theory of the process of glacial isostatic adjustment (GIA) has been developed. Application of this theory to the prediction of postglacial relative sea level histories has demonstrated that most 14C-dated observations, from all sites in the global data base, are well explained by a spherically symmetric viscoelastic model whose elastic structure is fixed to that of PREM and whose radial viscosity profile is that of the VM2 model. Of course, there are exceptions to this general rule concerning the goodness of fit of the predictions of the spherically symmetric model to the observations. For example, at locations such as the Huon Peninsula of Papua New Guinea, where the entire coastline is being uplifted coseismically, the predictions of the GIA model fail to explain the observations (see Peltier, 1998a,d). It is expected that at other tectonically active locations similar misfits of the spherically symmetric theory to the observations should also be evident. Examples of such regions would certainly include the Mediterranean Sea region, Japan, and perhaps also the Pacific Northwest of North America where the Cordilleran ice sheet played a strong role in controlling the local history of relative sea level change but which is also influenced by active subduction.

These regions of misfit to the RSL predictions of the global viscoelastic theory of postglacial sea level change not withstanding, the extent to which this global spherically symmetric theory has been successful in reconciling the vast majority of the observations is satisfying, especially because only a very small subset of the observations has been employed to tune the model's radial profile of mantle viscosity. As discussed in greater detail in Peltier (1998b), these observations consisted of the set of wavenumber-dependent relaxation times determined by McConnell (1968) as characterizing the relaxation of Fennosandia following removal of its LGM ice load (the validity of which has recently be reconfirmed by Wieczerkowski et al., 1999, as previously mentioned), a set of 23 site-specific relaxation times from locations in both Canada and Fennoscandia, and the observed nontidal rate of the acceleration of axial rotation. The VM2 viscosity model that was determined on the basis solely of these data, using the formal procedure of Bayesian inference with the simple four-layer VM1 model as a starting model, was thereafter (Peltier

1996) shown to immediately reconcile the dramatic misfits of the starting model to the high-quality data set of 14C-dated RSL histories that is available from the east coast of the continental United States (see also Peltier, 1998a). Because these data were not employed to constrain the radial viscosity structure, this is an extremely meaningful test of the validity of the model. That the new model also very well reconciles relative sea level data from far field sites throughout the equatorial Pacific Ocean has also been demonstrated explicitly in this chapter (see Figs. 4.9 and 4.10). The observations from the latter region offer a means by which we may strongly constrain the rate of mass loss from the great polar ice sheets on Antarctica and Greenland that may have been occurring continuously since mid-Holocene time. Our analysis demonstrates that the extent to which this influence could be contributing to the present-day observed rate of global sea level rise is negligibly small, a conclusion that is inconsistent with the claim to the contrary by Flemming et al. (1998).

Application of the global theory of the glacial isostatic adjustment process to filter this influence from the tide gauge data is clearly justified by the high-quality fits that the model delivers to the (widely distributed in space) observations of RSL variability on geological timescales over which 14C dating may be employed to accurately determining sample age. As demonstrated through the analyses summarized in Tables 4.1 and 4.2, application of the GIA filter sharply reduces the standard deviation of the individual tide gauge measurements of the rate of RSL rise from their mean value, demonstrating the importance of this step in the analysis procedure. As demonstrated in Table 4.2, application of the filter to an aggregated set of tide gauge data, in which sites are lumped together if they are close in geographical location, also leads to an increase in the estimated global rate of RSL rise. In either case (Table 4.1 or Table 4.2) the best estimate we have been able to produce of the global rate of RSL rise that could be related to ongoing climate change in the Earth system is between 1.91 and 1.84 mm/yr.

An important additional result that follows from the results listed in Table 4.1 concerns the comparison between the GIA-corrected rates of RSL rise on tide gauges located along the east coast of the continental United States that would be obtained by least-squares fitting a straight line to the geological data over a period of 3-4 kyr and the result that is obtained by using the geological rate that obtains over the same time period over which RSL is sampled by the tide gauges. This has been investigated by using the GIA-predicted rates as proxy for the actual geological data and computing the GIA-corrected rates listed in the column labeled LSQ in Table 4.1. Comparing the results in this column with the average of those in the -0.5 and +0.5 kyr columns for all U.S. east coast sites will show that the procedure of least-squares fitting a straight line to the geological data over a period of 3-4 kyr will significantly overestimate the magnitude of the GIA-related signal and therefore its use will lead to a significant underestimate of the filtered tide gauge result. This fact very directly explains the reason for the approximately

0.4 mm/yr difference between the GIA-corrected rates for the U.S. east coast determined by Peltier (1996b) and those previously determined by Gornitz (1995), the former result being near 1.9 mm/yr and the latter near 1.5 mm/yr.

In concluding discussion of the analyses presented in this chapter, it is useful to reflect upon their implications concerning the relative importance of the various sources that might be contributing to the inferred global rate of relative sea level rise whose magnitude has been herein implied to be somewhat in excess of 1.8 mm/yr (between 1.91 and 1.84 mm/yr). The most recent estimates of the contribution from small ice sheets and glaciers (Meier and Bahr, 1996) are that this source has a strength of 0.3 ± 0.1 mm/yr. The influence of permafrost melting is expected to be even smaller with a strength of 0.1 ± 0.1 mm/yr. I have argued herein that the contribution due to continuing late Holocene melting of polar ice from either Antarctica or Greenland is bounded above by 0.1 mm/yr. Since the most recent estimate of the terrestrial storage term (Chapter 5) suggests this to be -0.9 ± 0.5 mm/yr (note that this is revised from the previous estimate of -0.3 ± 0.15 mm/yr obtained by Gornitz et al. 1997) there is clearly a residual that requires explanation in terms of significant contributions from either Greenland and/or Antarctica and/or from the thermal expansion of the oceans. Since the geophysical constraint through Earth rotation observations (Peltier 1998a, 1999) appears to require the former to be less than 0.5 mm/yr, the implication of these arguments would appear to be that the current rate of global sea level rise due to thermal expansion of the oceans might be significantly larger than the rate usually assumed to best represent this contribution (0.6 ± 0.2 mm/yr). In connection with the latter contribution, however, it is not at all clear that the current generation of coupled atmosphere-ocean models, the results from which provide a primary basis for this estimate, are capable of accurately gauging the significance of this steric effect. Clearly much further effort, especially in strengthening the observational constraint on the steric signal and in more precisely estimating the contribution due to terrestrial storage will be required before we shall be in any position to be confident as to which of these conventionally considered influences is more important. If terrestrial storage were entirely unimportant, then the observed present day rate of rsl rise would be within the upper bound defined by the net influence of the other contributions. However, if the (negative) influence of terrestrial storage is as large as the most recent estimate (see Chapter 5), then the influence of thermal expansion (or one of the other contributions) would have to be considerably larger than the above stated estimates in order that the inferred global rate of rsl rise be successfully explained.

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