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ARTICLE IN PRESS
K. Lambeck, A. Purcell / Quaternary Science Reviews 24 (2005) 1969–1988 1977
Table 1 define the model NA-2. Compared with NA-1, this
Summary of parameters for the three-layeredmantle model
model is characterized by a multi-domed ice sheet, a
larger ice volume at the time of the LGM, advanced
Earth model Lithospheric Upper mantle Lower mantle
thickness (km) viscosity viscosity melting for the early deglaciation stage, and delayed
20
22
( 10 Pa s) ( 10 Pa s) melting during the late stage of deglaciation.
Fig. 6 illustrates the comparisons of the glacio-
El 65 2 1
E2 (nominal) 65 3 1 isostatic terms at 6 and12 ka BP, along the same profiles
E3 65 4 1 as before. The amplitude of the isostatic signal in the
E4 50 3 1 Mediterranean basin due to the northern European ice
E5 80 3 1 sheet, for example, is 6% of the total change at the
E6 65 3 0.5 LGM and 10% at 12 ka BP anduncertainties in the ice
E7 65 3 2
volumes of the order of 10–20% should not introduce
E2 is the nominal model and the other models represent the range of major uncertainties into the glacio-isostatic predictions.
parameters that are consistent with reboundanalyses in the This is indeed the case, with the maximum differences
Mediterranean region and elsewhere.
resulting from either the two European models or the
two North American models not exceeding 1 m at
6 ka BP and 2 m at 12 ka BP. We therefore adopt the
andas estimates of precision we use the root-mean- nominal models NE-2, NA-2 and use the differences in
square of the predicted variability, relative to the model predictions between NE-2 and NE-1 and NA-2
nominal solution, for the models defined in Table 1. andNA-1 as a measure of uncertainty. This gives the
Figs. 4e andf illustrate these precision estimates for the results illustratedin Figs. 6e andf for the two profiles
two transects at 6, 12, and20 ka. andat three epochs. In most cases, the uncertainty
introduced from this source is less than observational
4.2. Ice-model dependence uncertainties for the same epochs.
Uncertainties in the ice sheet models enter into the
4.3. Equivalent sea-level dependence
sea-level predictions through both the esl function and
through the isostatic terms. The latter follows from
The nominal esl function is basedon Eq. (5), using
comparisons of predictions for different representations
data from a number of far-field localities around the
of the ice sheets. For northern Europe, including the
world. For each observed data point, the accuracy of the
Barents-Kara region, two ice models are used. The first,
inferredesl value is based on the observational accuracy
NE-1, from Lambeck et al. (2000), is characterizedby a
andon the precision of the isostatic correction
thick LGM ice sheet that experienceda rapidreduction
(Lambeck et al., 2002). The esl-reduced observations
in thickness at 19 ka BP. The second, NE-2, is the
can then be combined into a time-dependent esl function
nominal northern European model used above. It is the
whose precision is estimatedfrom the scatter of results.
result of more recent iterative inversions in which
additional field data have been used, including con- The resulting error function (Lambeck et al., 2004a)is
illustratedin Fig. 7a andthe precision estimates range
straints on ice thickness during the late stages of from 0.4 m at 6 ka BP to 5 m at the LGM.
deglaciation of Sweden as well as information from
the drainage history of the Baltic (Lambeck andPurcell,
2003). The principal difference between the two is that in 4.4. Precision of sea-level predictions
NE-2 there is less ice during both the LGM and the late
stages of deglaciation compared with NE-1 (Fig. 5). The variances of the predicted sea levels are estimated
Two different ice models have been used for the as the sum of the variances of the three principal
North American ice sheet. NA-1, is basedon the contributions: earth model, ice sheet, and esl function
original ICE-1 model of Peltier andAndrews (1976) uncertainties. The resulting spatially variable estimates
but scaledin amplitude so that when combined with the are illustratedin Figs. 7b andc for the two Mediterra-
other ice sheets, the resulting esl function is consistent nean profiles at the epochs 6, 12 and20 ka BP. The
with the observedvalues (Lambeck et al., 2002). NA-2, dominant contribution to these estimates comes from
the nominal model used above, is based on inversions of the esl function, a consequence of which is that the
observeddata compiled by Tushingham andPeltier uncertainty of the relative sea-level predictions are
(1992) andtwo glaciologically-based starting models of primarily time dependent. Their magnitudes, 1, 3.5,
Peltier andAndrews (1976) and Licciardi et al. (1998). and5.5 m at 6, 12, and 20 ka, respectively, are
Model features common to the different inversion comparable to the uncertainties of much of the
solutions, that are independent of the starting ice-sheet observational evidence for the region and the model
models and are consistent with observational data, predictions should provide a sound basis for modeling