Page 4 - Sea-level change_2004

ARTICLE IN PRESS
1972 K. Lambeck, A. Purcell / Quaternary Science Reviews 24 (2005) 1969–1988

models for the isostatic response functions and for sea- andLambeck, 2004), andNorth America (unpublished).
level change. Mountain glacier models have been adopted using
known ice margins andvolume changes given by
2.2. Ice-volume equivalent sea-level (esl) function Denton andHughes (1981) with melting assumed
to be in phase with the global deglaciation. The
Far from the former ice sheets, sea levels are subject difference between the esl function for the northern
to isostatic corrections Dz I that are typically 10–15% of hemisphere andmountain glaciations andthe ‘observed’
the amplitude of the eustatic change. They are function is usedto define the history of the change
dependent largely on the total ice volumes, as expressed in Antarctic ice volume DV ant ðtÞ. The distribution
by Dz esl ðtÞ, andon the hydro-isostatic contribution of ice across the continent, the ice margin retreat and
Dz I-h ðj; tÞ. Observations during the glacial cycle can ice-thickness change, is basedon an interpolation
therefore be correctedwith some certainty to establish between a scaled Denton andHughes (1981) LGM
an estimate of the esl function as reconstruction andthe present ice sheet such that the
total Antarctic ice mass is consistent with DV ant ðtÞ. If the
Dz esl ðtÞ¼ Dz o ðj; tÞ fDz I ðj; tÞþ Dz T ðj; tÞg, (5)
testing of this model against rebound data for the
where Dz o ðj; tÞ is the observedvalue at ðj; tÞ. Either Antarctic margin leads to a need to modify the ice sheet,
data from tectonically stable regions are used (e.g. the then the sequence of analyses will be repeatedin a next
Sunda Shelf (Hanebuth et al., 2000) or the Bonaparte iteration.
Gulf (Yokoyama et al., 2000)), in which case The ice sheet models for the pre-LGM period are
Dz T ðj; tÞ¼ 0, or the elevations of known interglacial much more primitive than for the more recent time, and
shorelines are usedto correct for any tectonic effect (e.g. the current models used here assume that if at any pre-
0
Barbados (Bardet al., 1990) or Huon Peninsula LGM time t the esl value is equal to that for a post-
00
0
(Chappell andShackleton, 1986)). For the present LGM epoch t 00 then DV i ðt Þ¼ DV i ðt Þ. Tests with
purpose, the esl function of Lambeck andChappell alternative hypotheses about the pre-LGM ice sheet
(2001) is usedfor the interval from MIS 5.5 to MIS 2, indicate that this simple assumption is adequate only if
andof Lambeck et al. (2002) for the Last Glacial the predictions are restricted to the LGM and post-
Maximum (LGM) and post-LGM period. Two different LGM period.
representations for the Late Holocene will be used: (i) In the case of the Mediterranean, the dominant ice
the nominal model in which all melting has ceased by sheets contributing to the isostatic components of sea-
6.8 ka BP, and(ii) a model in which some Antarctic level change are the European ice sheet (Scandinavia,
melting has continueduntil more recent time. Barents-Kara, andEurasia) andthe western hemisphere
ice sheets (Laurentide, Cordilleran, Arctic Canada, and
2.3. Ice sheet models Greenland). The Antarctic glacio-isostatic contribution
is small andvaries slowly across the region andthe main
The global esl functions provide the boundary contribution from this continent’s ice volume change is
conditions for the total ice that can be contained within through the water loading. Thus details of the Antarctic
the sum of the individual ice sheets. The procedure we ice distribution are not important in this context and the
adopt for distributing this volume between the ice sheets preliminary model is adequate.
is an iterative one in which glaciologically-derived ice Complete ice models take into consideration
models are used as a starting point, scaled such that the realistic time and spatial dependence of the ice
their total volume is equal to the global esl function. In a loads on the continents and includes grounded ice
secondstep, sea-level data from sites far from the ice on the shelves. Each of the northern ice sheets is
sheets—far-fieldsites—are usedto estimate global defined at discrete time intervals, typically at 1000-year
mantle rheology parameters. In the thirdstep, rebound intervals, as prisms of 0.251 latitude by 0.51 longitude
data from former glaciated regions are used to establish ( 25 25 km) horizontal dimensions (this avoids
improvedice sheets, subject to the global mass the overlaps andcreation of voids that occurs with
constraint, as well as improvedrheological parameters. disc representations). The Antarctic ice sheet is
In a fourth step, the far-fieldisostatic corrections are re- similarly defined but on a coarser 11 11 grid.
evaluatedusing the new ice models anda new esl Melting of every prism at any location is assumed
function is estimated. The previous steps are then to be linear within each interval (Nakada and Lambeck,
repeateduntil convergence is reached. 1987).
This process has been followedover several iterations
with new ice sheets developed successively for the British 2.4. Earth models
Isles (Lambeck, 1993), Barents-Kara Sea (Lambeck,
1995a), Fennoscandinavia and Eurasia (Lambeck et al., The time dependence of the earth’s response appears
1998; Lambeck andPurcell, 2003), Greenland(Fleming to be well representedby simple models in which the