Page 15 - 23

ARTICLE IN PRESS 1581
K. Lambeck et al. / Quaternary Science Reviews 23 (2004) 1567–1598
contribution is the Earth’s response to the loading and
unloading of the Northern Hemisphere ice sheets.
During loading, a broad and shallow bulge develops
out to several thousand kilometers from the centres of
the ice sheets and this subsides during the deglaciation
phase (cf. Lambeck, 1995; Lambeck and Johnston,
1995). Like much of the Mediterranean, Italy is located
on this bulge and relative sea levels here rise during the
Holocene even after ice volumes have stabilized. The
principal hydro-isostatic effect is the changing load on
the sea floor as ice sheets grow or shrink, with the
consequence that the sea floor subsides during and after
deglaciation while larger land bodies tend to be uplifted.
To these effects must be added lesser isostatic compo-
nents that result from the global changes in the planetary
shape, rotation and gravity during the glacial cycle.
Numerical models with high resolution have been
developed over recent years that give realistic represen-
tations of the spatial variability of the sea-level change
and shoreline evolution if the history of the ice sheets
through time is known (Lambeck and Johnston, 1998;
Lambeck et al., 2003). One unknown in these models is
the rheological response function of the Earth. This is
usually inferred from observations of sea-level change
themselves. Likewise, the hypothesis that the ice model
is adequately known can be tested by comparing
observed and predicted sea levels. However, such
comparisons require that any land uplift or subsidence
from non glacio-hydro-isostatic causes is not important
or, if it is, that it can be independently assessed. As
illustrated by the above examples, the assumption of
zero tectonic contributions cannot be justified for many
segments of the Italian coast. But, if the predictions can
be calibrated with observational data from stable sites,
we can use the model to infer the tectonic rates at the
unstable localities. We use, as discussed above, the
observation of the position of the Last Interglacial
shoreline (MIS 5.5) to assess whether a section of the
coast is likely to be tectonically stable or not. The so-
calibrated model can then be used as an interpolation
devise to estimate tectonic rates from uplifting or
subsiding regions where we do not have satisfactory
independent estimates of vertical tectonic rates or to test above prediction have previously been found to give a
the hypothesis of uniform rates of vertical movement.
The isostatic model allows for a high-spatial and
temporal resolution of the ice–water load with a
rigorous definition of the distribution of the meltwater
into the oceans to include:
(i) Conservation of water–ice mass and the require–
ment that the ocean surface remains an equipoten-
tial (Farrell and Clark, 1976).
(ii) The global deformation of the sea floor and its
associated redistribution of ocean water during the
glacial cycle (Nakada and Lambeck, 1987; Mitro-
vica and Peltier, 1991).
(iii) Migration of shorelines as sea levels rise and fall
(Lambeck and Nakada, 1990).
(iv) Rigorous treatment of ice on the shelves as it
changes from being grounded to floating as it thins
or as sea levels rise (Lambeck and Johnston, 1998;
Lambeck et al., 2003; Mitrovica and Milne, 2003).
(v) Contributions from glaciation-induced changes in
the Earth’s rotation (Milne and Mitrovica, 1998).
As previously demonstrated, the spatial variability of
sea level around the Italian coast is significant (Lambeck
and Johnston, 1995) and it will generally not be
permissible to combine data from different localities
into a single sea-level curve without first establishing
that such variability is less than the observational
accuracy. This is illustrated in Fig. 2a for predictions
at sites at different distances from the former Scandi-
navian ice sheet. Compare, for example, the predictions
for sites 29, 1, 7, 15 (the numbers refer to the site
numbers in Section 3). Here the differences for Early
Holocene time are of the order of 15 m, with the
northern sites yielding systematically higher sea levels
than the southern sites. Within smaller regions, the
spatial variability is also not wholly negligible as is
shown by the results in Fig. 2b for localities in Sardinia.
These results represent differences in prediction from
their mean value for the 12 individual sites within the
observation group 20. Differences here never exceed
0.5 m for the last 14 ka but they become larger when
Orosei, on the east coast of Sardinia, is included. Thus,
rather than combining observational data into single
sea-level curves when we compare the observations and
predictions, the comparisons are made for the location
of each observation. Of note is that the predicted levels
for all Italian sites never rise above present sea level at
any time during the Lateglacial and Holocene intervals.
Thus any observations of Holocene shorelines higher
than present sea level provide an immediate diagnostic
for tectonic uplift.
The earth- and ice-model parameters used in the
good description of the sea-level change in the Medi-
terranean region and have been defined by Lambeck
et al. (2002). Estimates of the accuracy of these
predictions are based on the accuracy of the earth-
and ice-model parameters where the latter include (i) the
uncertainty arising from the descriptions of the indivi-
dual ice loads, and (ii) the uncertainty of the ice-volume
equivalent sea-level function describing the globally
averaged sea-level change. The earth-model uncertainty
is estimated by predicting sea levels at the measurement
sites for a range of earth models that encompass the
probable values and calculating the root-mean-square
values of the departures from the mean. The adopted
range is 50–80 km for the lithospheric thickness (Hl),
(2–4) Â 1020 Pa s for the upper-mantle viscosity (mum)