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ARTICLE IN PRESS
K. Lambeck et al. / Quaternary Science Reviews 23 (2004) 1567–1598
and (5–30) Â 1021 Pa s for the lower-mantle viscosity
(mlm). The range of predicted values for these effective
model parameters are shown in Fig. 2(c)–(e) for the
ENEA core locality (site 1). The major variation in this
parameter range occurs for the lower mantle viscosity
(Fig. 2d) reflecting the role of deep mantle flow towards
the former areas of glaciation during the deglaciation
phase. But the dependence on upper mantle viscosity is
also important, even within the relatively narrow range
of values with which this parameter is defined in
rebound analyses. Models of low viscosity—for either
the lower or upper mantle—yield predictions that lie
higher than those for high viscosity models, and the
comparison of results in Figs. 2c and d indicate some of
the trade-offs that can occur at sites, with low mlm
models leading to similar predictions at Versilia as low
mum models. These trade-offs change with location from
north to south but for the restricted positional range full observed values where the former are represented by the
separation of parameters may not be achieved and in
this case we adopt mlm values determined from more
global analyses where such separation has been more
effective (Lambeck et al., 1998).
The ice-volume-equivalent sea-level function (or
eustatic function in the absence of any other contribu-
tion to ocean volume change) is taken from Lambeck
et al. (2002) for epochs from the LGM to 7 ka, Lambeck
(2002) for the last 7 ka, and Lambeck and Chappell
(2001) for the period before the LGM. The contribu-
tions to the uncertainty of the sea-level prediction
arising from the limitations of the individual ice models
are estimated in the same way as in Lambeck and Bard
(2000); using a range of different ice models for North
America and Europe to predict the sea levels at the
Italian sites. For North America two models have been
used that represent upper and lower limits to the ice
models that are consistent with sea-level data from that
region. One is based on the Licciardi et al. (1998) model
and the second is based on a modified version of ICE-1
from Peltier and Andrews (1976). For the European ice
sheet, the isostatic corrections have been predicted for
three different models that span the permissible range in
so far as agreement with the rebound data from
Scandinavia is concerned (Lambeck et al., 1998). The
influence of the uncertainty of the ice model is then
estimated from the range of the sea-level predictions at
the individual sites using different combinations of ice-
sheet models. The precision of the global equivalent sea-
level function is based on the root-mean-square scatter
obtained from the combination of the isostatically
corrected sea-level data from far-field sites discussed in
Lambeck et al. (2002).
The different model errors are added in quadrature to
provide an estimate of the total prediction uncertainty
spred for each locality and for each epoch. Fig. 2f
illustrates the total prediction uncertainty for two
localities (1, 15). (These estimates tend to be conserva-
1583
tive because they ignore the trade-off that occurs
between some of the parameters.) At both, the
maximum values are reached for TB14 ka and the error
functions are representative for the other Italian sites as
well. For convenience we use a spatially averaged spred
for all sites within the Italian Peninsula of
spred ¼ À0:13 þ 0:24T þ 0:012T2; 1 > T > 14 ka; ð2Þ
spred ¼ 0:12T ; To1 ka:
5. Comparison of predicted and observed sea levels
5.1. Tectonically stable sites
The most comprehensive data set is from the
tectonically stable Versilia Plain (1) and Fig. 3a
illustrates the comparison between the predicted and
upper and lower limits defined by spred. With the
exception of the single point at 7.87 ka BP, agreement
between the observed and predicted values is within the
combined observational and model uncertainties and
the model describes well the observed sea-level change in
the time interval spanned by the data. The exception
corresponds to one of three samples of very similar age
(Table 1), but with the other two corresponding to a
higher horizon. The sediments and some foraminifera of
the 7.81 ka BP sample are indicative of a lagoonal
environment and provide a more precise indicator than
the infralittoral shells at 7.87 ka which can live in deeper
water, although they do occur here in association with
other shallow-water species.
The Argentarola Island data (3) display greater
discrepancies between observations and predictions
(Fig. 3b). The five ages for samples from À18.5 m indi-
cate that the terrestrial speleothem ages, corresponding
to a time before emergence, are significantly older than
the two ages of the encrusted serpulid at the same
position. Thus the hiatus between the two types of
samples may be as long as 2000 years and we do not use
the terrestrial ages when serpulid or lithophaga ages are
available. But the serpulid ages also exhibit some
anomalies, with the sample at 21.5 m depth giving an
older age than the terrestrial speleothem sample from
the same location, and possibly the ages are too old
because of contamination by older carbon from the
speleothems.
Agreement between observations and predictions for
the archaeological data from the four tectonically stable
sites from the northern Tyrrhenian coast (2, 4, 7, 8) is
generally satisfactory. The two younger data points
from Anzio and T. Astura lie higher than the predicted
values by about 0.2–0.5 m (Fig. 3c), consistent with the
functions of the two piscinae being filled at highest tidal
levels.