Page 2 - Sea-level change_2004

ARTICLE IN PRESS
1970 K. Lambeck, A. Purcell / Quaternary Science Reviews 24 (2005) 1969–1988

physical properties of the solidplanet, primarily the 2. Theory and model requirements
mantle viscosity, andinto the changes in global ice
volume through time. If the rheological andice 2.1. Theory
dependence can be established, predictive models for
glacially-driven sea-level change can then be developed The theory for glacio-hydro-isostasy used here has
andusedas reference for estimating vertical rates and been developed over a period of years by Nakiboglu et
scales of surface tectonic processes or for predicting al. (1983), Nakada and Lambeck (1987), Johnston
shoreline migrations. (1993, 1995), Lambeck andJohnston (1998),and
The Mediterranean margins and islands have pro- Lambeck et al. (2003), with successive models represent-
vided a fruitful area for such studies for a number of ing improvements in theory, computational methods,
reasons. First, because the area is a small tidal-range andmodel-parameter estimation. There has been some
environment, the observational evidence can often be discussion on aspects of the theory that we use
relatedprecisely to mean sea level. Second, there is a concerning the distribution of the glacial melt water
wide range of geological and archaeological evidence into the deformable ocean basins (Peltier, 2002) but
available from most of the region. While this data according to Mitrovica andMilne (2003), the theory
remains inadequate to construct a purely empirical usedhere represents, along with that of Milne (1998),
model for sea-level change that has predictive capabil- the most complete andrigorous available (see also
ities across the region, it does provide a significant Mitrovica, 2003).
database for testing and calibrating the quantitative We do not discuss the theory in detail since this is
models of change during a glacial cycle. The Mediterra- given in the above references. Instead, we express
nean region is particularly useful in that older inter- relative sea-level change Dz rsl ðj; tÞ schematically as
glacial shorelines are preservedin many locations so that
Dz rsl ðj; tÞ¼ Dz esl ðtÞþ Dz I ðj; tÞþ Dz T ðj; tÞ (1a)
it becomes possible to examine whether changes in
tectonic rates have occurredon time scales from years to with
5
10 years. Third, there are a number of active tectonic
Dz I ðj; tÞ¼ Dz I-g ðj; tÞþ Dz I-h ðj; tÞ (1b)
processes whose understanding would be considerably
aided if rates of vertical movement can be measured where Dz rsl ðj; tÞ represents the change at location j of
5
0
over a range of time scales of 10 –10 years. Finally, the sea surface relative to landat time t comparedto its
once successful models for sea-level change have been present position at time t P . The first term on the right-
developed, it is also possible to predict past and future handside of Eq. (1a) represents the ice-volume
shoreline migrations andto address, for example, equivalent sea-level contribution (esl), the secondterm,
questions about the functions of coastal archaeological Dz I ðj; tÞ, is the isostatic contribution, andthe last term
structures or help in exploring the submarine environ- is a tectonic contribution for tectonically active areas.
ment for past sites of human activity. The isostatic term is schematically divided into two
In this paper, we are concernedwith the eustatic and contributions: the glacio-isostatic part Dz I-g ðj; tÞ,and
glacio-hydro-isostatic contributions to sea level across the hydro-isostatic part Dz I-h ðj; tÞ.
the Mediterranean basin, with a focus on change The ice-volume equivalent term is defined as
since the endof the last glaciation about 20,000 r Z 1
years ago. Over the past decade a number of studies Dz esl ðtÞ¼ i dV i dt. (2)
have been undertaken to establish regional predictive r o t A o ðtÞ dt
models (Lambeck, 1996; Lambeck andBard, 2000; V i is the ice volume at time t, A o ðtÞ is the ocean surface
Sivan et al., 2001, 2004; Lambeck et al., 2004a, b). area at time t, and r , r are the average densities of ice
i o
Here, we attempt a basin-wide study that integrates andocean water. In the absence of any other factors
some of these results. Emphasis is on demonstrating the that leadto changes in ocean volume, the ice-volume
nature of the spatially andtemporally variable level equivalent sea-level is equal to eustatic sea level. In our
across the Mediterranean basin and on assessing how formulation, the ice loadis evaluatedfrom the integral
this variability can be exploitedto establish optimum over the ice mass on the continents andgroundedon
parameters for modeling sea-level change through time. continental shelves. The water loadis then definedby
Preliminary comparisons with observational evidence the shoreline at the epoch in question andby the
are made to test the essential correctness of the model. grounding line of any ice on the shelves. Thus the ice
In a follow-up paper, this model will be compared more volume V i in (2) refers to all ice out to the grounding
rigorously with observational evidence from across the line andthe surface area A o is defined by this line and by
region, with the objective of estimating improved the coastline.
rheological parameters andwith providing an improved The glacio-isostatic term Dz I-g in Eq. (1b) is the
reference surface for measuring rates of tectonic uplift response of the sea surface to the changing ice loadand
andsubsidence. the hydro-isostatic term Dz I-h is the response to the