ARTICLE IN PRESS
Quaternary Science Reviews 23 (2004) 1053–1077
Constraints on the Greenland Ice Sheet since the Last Glacial
Maximum from sea-level observations and glacial-rebound models
Kevin Fleminga,*, Kurt Lambeckb
a
GeoForschungsZentrum Potsdam, Department 1: Geodesy and Remote Sensing, Telegrafenberg, D-14473, Potsdam, Germany
b
Research School of Earth Sciences, Australian National University, Canberra, ACT, 0200, Australia
Received 1 August 2002; accepted 8 November 2003
Abstract
Geomorphological descriptions of changes in the extent of the Greenland Ice Sheet (GIS) have been combined with glacialisostatic-adjustment models to reproduce the sea-level history of Greenland since the Last Glacial Maximum (LGM). The
contribution to past sea-level change around Greenland due to ice-load changes outside of that region has been considerable (7 10’s
of meters), while still contributing a rise of several mm yr1 today. The isostatic contribution to relative sea level around Greenland
from changes in the GIS is found by iteratively perturbing preliminary ice models with different LGM extents and deglaciation
starting times. The resulting first-order model that provides the best agreement between observed and predicted sea level contributes
3.1 and 1:9 m water-equivalent of additional ice relative to present-day ice volumes at the LGM and Younger Dryas, respectively.
The GIS in most areas does not appear to have extended far onto the continental shelf, the exceptions being southern-most
Southwest Greenland and northern East Greenland, as well as at the coalescence of the Northwest Greenland and Innuitian Ice
Sheets. Changes in ice thickness since the LGM were > 500 m along the present-day outer coast and > 1500 m along some parts of
the present-day ice margin. The observed mid- to late-Holocene fall in sea level to below the present-day level and the subsequent
transgression seen in some areas implies that the GIS retreated behind the present-day margin by distances of the order of 40 km
before readvancing.
r 2003 Elsevier Ltd. All rights reserved.
1. Introduction
A consequence of the deglaciation of the expanded
continental ice sheets after the Last Glacial Maximum
(LGM, ca 18 ka BP in the radiocarbon ð14 CÞ timescale,
21 ka BP in the calendar (cal) timescale) is the vertical
rebound of the formerly ice-covered parts of the Earth’s
surface. This resulted in the numerous raised shorelines
that are observed within such areas, for example Arctic
Canada, Scandinavia and the region of interest to this
paper, Greenland. The Greenland Ice Sheet (GIS) was
substantially larger during the LGM, as evident by the
just mentioned raised shorelines as well as by recessional
moraines. Studies of the ice-sheet and sea-level history
of Greenland since the LGM include those dealing with
the GIS itself (e.g. Ten Brink and Weidick, 1974; Kelly,
!
1980; Ingolfsson
et al., 1994; van Tatenhove et al., 1996;
.
Zreda et al., 1999; Bennike and Bjorck,
2002), local sea*Corresponding author. Tel.: +49-331-288-1449.
E-mail address: [email protected] (K. Fleming).
0277-3791/$ - see front matter r 2003 Elsevier Ltd. All rights reserved.
doi:10.1016/j.quascirev.2003.11.001
level change, especially during the Holocene (e.g. Rasch
and Jensen, 1997; Hjort, 1997; Long et al., 1999;
Bennike and Weidick, 2001) and assessments of the
isostatic contribution to sea-level change (e.g. Kelly,
1973; Ten Brink, 1974; Weidick, 1996; Bennike et al.,
2002; Tarasov and Peltier, 2002).
In this paper we use observations of relative sea-level
change and predictions from realistic glacial-isostaticadjustment (GIA) models to place constraints on the
primary characteristics of the GIS’s past behaviour; its
extent during the LGM, the timing of deglaciation and
the spatial changes in ice thickness. Such a methodology
for resolving glacial histories is well established (e.g.
Peltier and Andrews, 1976; Lambeck et al., 1990) and is
particularly important where geomorphological constraints on the ice sheet are limited, as in the BarentsKara Seas (e.g. Lambeck, 1995).
The interest in resolving the history of the GIS is two
fold. Firstly, the GIS is the sole northern hemisphere ice
sheet to have survived the Last Glacial-Interglacial
Transition (LGIT), despite being in a region of vigorous
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K. Fleming, K. Lambeck / Quaternary Science Reviews 23 (2004) 1053–1077
1054
climatic change (Funder et al., 1998). Secondly, the GIS
today contains around 7 m water-equivalent of ice, if
evenly distributed over the present-day oceans (Letre! guilly et al., 1991), and is therefore an important factor
when considering contemporary sea-level change (e.g.
Oerlemans, 1993; Krabill et al., 2000). There is also the
fact that the GIS is still reacting to past climate changes
(e.g. Abe-Ouchi et al., 1994) and so resolving its former
extent will assist in predicting its future behaviour.
The radiocarbon timescale is used throughout this
work because most observational evidence related to
sea-level change and ice-sheet evolution is constrained
by radiocarbon dating. The effects of minor nonlinearities in the 14 C timescale are insignificant when
compared to the ice- and earth-model uncertainties.
2. Methodology
Relative sea level ðDzrsl Þ at a time t and location f
may be expressed schematically as (Lambeck, 1993):
Dzrsl ðt; fÞ ¼ Dzesl ðtÞ þ Dzice ðt; fÞ þ Dzwat ðt; fÞ;
ð1Þ
Dzesl is the ice-volume equivalent sea level or simply
equivalent sea level, representing the amount of ice/water
exchanged between the oceans and land-based ice sheets
over time (when all other effects are ignored, this value
is also referred to as the eustatic sea level). Dzice and
Dzwat are the ice- (glacio-isostatic) and water- (hydroisostatic) load components. Eq. (1) is a simplified
description of the changes in sea level that arise from
GIA, and the complete formulation used includes the
interactions between the various components (e.g.
Lambeck et al., 2003; Mitrovica, 2003). For example,
Dzesl is a function of the shape of the ocean basins,
which are in turn affected by surface-load changes and
by the collapse of marine-based ice sheets.
For several ice sheets, ðJÞ; and incorporating observations, Eq. (1) may be rewritten as
Dzo ðt; fÞ þ eo ðt; fÞ
¼ Dzesl ðtÞ þ
J
X
bj ½Dzjice ðt; fÞ þ Dzjwat ðt; fÞ;
ð2Þ
j¼1
where Dzo is an observation’s elevation relative to
present-day sea level, eo is the correction required to
relate the imperfect observation to mean sea level, Dzjice
and Dzjwat are the ice- and water-load components of the
jth ice sheet and bj is a scaling parameter for the jth ice
sheet’s isostatic contribution (Lambeck et al., 1990).
Since only the GIS is considered, Eq. (2) is rewritten
as
non
Dzo ðt; fÞ þ eo ðt; fÞ ¼ Dzesl ðtÞ þ Dznon
iso ðt; fÞ þ dziso ðt; fÞ
gis
þ bgis ½Dzgis
ice ðt; fÞ þ Dzwat ðt; fÞ
þ dzgis
iso ðt; fÞ:
ð3Þ
Here, Dznon
iso is the isostatic contribution of the nonGreenland ice sheets, i.e. those located outside of
Greenland (specifically North America, Europe and
gis
Antarctica), Dzgis
ice and Dzwat are the ice- and water-load
gis
contributions of the GIS, while dznon
iso and dziso are the
uncertainties associated with the non-Greenland and
GIS isostatic contributions. bgis is the scaling factor for
the GIS isostatic contribution that leads to a minimum
in the variance, s2 ; defined as
s2 ¼
2
S Dzs Dzs
X
1
o
pred
:
ðS 1Þ s¼1
sso
ð4Þ
The superscript s refers to the sth observation ðDzso Þ and
prediction ðDzspred Þ; of a total of S data, where Dzpred is
the predicted change given by the right-hand side of
Eq. (3) without the uncertainty parts. sso is the total
uncertainty associated with the sth observation. It
results from combining the correction required to relate
the observation to mean sea level, eo ; which in this work
is set to a constant value of 5 m; and the isostatic
contributions of the non-Greenland ðdznon
iso Þ and Greenland ðdzgis
)
ice
sheets,
and
is
written
as
iso
gis 2 1=2
2
so ¼ ½e2o þ ðdznon
;
iso Þ þ ðdziso Þ ð5Þ
s2 is therefore a measure of the misfit between the scaled
predictions and observations. If the ice- and earth-model
parameters employed are correct (i.e. give results that
are within the uncertainty in the observations) and the
observational uncertainties have a normal distribution,
then the expected value of s2 is 1. However, since such
conditions are rarely satisfied, a range of preliminary ice
models incorporating different assumptions about the
past conditions of the GIS are used, with the scaled
model that best reproduces Greenland’s sea-level history
selected. Because the reliability of the initial models will
vary over the study area, analyses are carried out over
various spatial scales, with the likelihood that different
preliminary models will be preferred for different areas.
Several problems may arise with this method. Firstly,
a fundamental assumption is that the former ice margins
are correctly defined and that only the ice thickness
needs to be modified. The method will therefore break
down when this is not the case, the result sometimes
being that the ice model needs to be scaled by an
implausible amount to improve the fit (i.e. decrease s2 )
between the observations and predictions (e.g. Lambeck, 1995). Therefore, preliminary models with differing ice-margin locations need to be tested. Another
problem concerns biases that may arise from the spatial
and temporal distribution of the observations. For
example, if some areas are more densely sampled than
others, the resulting bgis and s2 values will be more
representative of those localities, as opposed to the
entire region under consideration.
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K. Fleming, K. Lambeck / Quaternary Science Reviews 23 (2004) 1053–1077
Table 1
Upper and lower limits for the effective earth-model parameters
considered in this work. The last column gives nominal parameter
values that are suitable for Greenland
Parameter
Lower Upper Nominal
limit
limit
Lithosphere thickness Hlith (km)
50
Upper mantle viscosity Zum ð1020 Pa sÞ 2
5
Lower mantle viscosity Zlm ð1021 Pa sÞ
100
5
20
80
4
10
The Earth’s rheology is described by a three-layer
earth model incorporating an elastic lithosphere with a
thickness Hlith ; an upper mantle extending to the seismic
discontinuity at 670 km depth described by its viscosity
Zum ; and a lower mantle extending until the core-mantle
boundary described by its viscosity Zlm : The mantle is
assumed to be a Maxwell viscoelastic body, meaning
that at low frequencies it acts as a viscous fluid while at
high frequencies it responds elastically. While this is a
comparatively simple description of the Earth, it is
adequate for our purposes given the uncertainties
involved in the ice model. Hence, the values assigned to
the earth-model parameters are termed effective values.
Uncertainties associated with the modelled isostatic
contribution to sea-level change arise from two sets of
unknowns. The first involves our incomplete knowledge
of the Earth’s rheology. The uncertainty in the predictions from this part of the problem is accommodated by
using a number of earth models that include upper and
lower limits of the effective values from previous GIA
studies (Table 1, e.g. Nakada and Lambeck, 1989;
Mitrovica, 1996; Lambeck et al., 1998; Nakada et al.,
2000). Also listed in Table 1 is a nominal earth model,
whose values are preferred for regions such as Greenland that are made up of very old cratonic units (e.g.
Lambeck et al., 1998). The second source of uncertainty
is from the ice models used to describe not only the GIS,
but also the other major areas of glaciation. For the
non-GIS, this is dealt with by using variants of the
nominal ice models that contain 90% or 110% of
the nominal’s ice volume (i.e. 710%). This assumes that
the uncertainties in the spatial distribution of the changes
in these ice sheets are of negligible importance by
distances from their centres of loading such as Greenland.
The computer programs and ice models used in this
work were developed progressively at the Research
School of Earth Sciences (RSES), the Australian
National University, and have been applied to many
GIA and sea-level change studies (e.g. Nakada and
Lambeck, 1987; Lambeck et al., 1990; Johnston, 1993;
Lambeck, 1995; Fleming et al., 1998; Lambeck et al.,
1998; Johnston and Lambeck, 1999; Yokoyama et al.,
2000). The computer programs accommodate moving
coastlines, transitions between grounded and floating ice
and changes in the Earth’s rotation tensor.
1055
3. Sea-level change around Greenland since the LGM
The dominant contribution to sea-level change
around Greenland since the LGM is glacio-isostatic
emergence resulting from the Earth’s response to the
retreat of the expanded GIS. The manner in which this
emergence varied about the island, itself a function of
the extent to which the GIS expanded, is well described
by the spatial variability of the local marine limits.
Marine limits are the occurrence at a given locality of
the highest indication of past sea level (e.g. Funder and
Hansen, 1996), as shown for Greenland in Fig. 1. Such
diagrams are not descriptions of relative sea level for a
given epoch, since the timing of the marine limits’
formation varies from site to site, depending upon each
locality’s glacial history. There is also the problem that
most marine limits lack suitable fossil material to allow
the dating of their formation. Therefore, interpolations
from lower, younger events are often used, with a
subsequent loss of accuracy (Section 6). This point will
be discussed further in Section 6. Despite these
limitations, marine limits are still a useful qualitative
tool in that they provide upper/lower limits when
comparing predictions with observations.
The Greenland marine limits resemble elongated
domes lying approximately parallel to the present-day
coastline. Holocene emergence around Greenland is
generally less than 100 m relative to present-day sea
level, although three areas display prominent higher
limits; Kong Frederik IXs Land in West Greenland,
where the limits reach up to 140 m, Scoresby Sund in
East Greenland (ca 135 m) and Northwest Greenland
around Hall Land (ca 120 m). A fourth area may exist in
Peary Land, North Greenland, but the available data
does not allow a definite statement to be made (Weidick,
1976; Funder, 1989; Funder and Hansen, 1996). These
areas also correspond to the more extensive expanses of
ice-free land, where the retreat of the LGM ice sheet (i.e.
change in ice loading) was the greatest. For example, in
Kong Frederik IXs Land (Fig. 1) the ice-free area
extends for 150–200 km between the current GIS margin
and the present-day coastline. On the other hand, less
extensive ice-free areas record a smaller Holocene
emergence. For example, the Frederiksha( b and
Julianeha( b districts of Southwest Greenland have
marine limits between 40 and 60 m with ice-free zones
of ca 50 km (Weidick, 1975; Kelly, 1977).
Fig. 1 also presents several examples of local sea-level
curves from around Greenland. The dominance of the
glacial-rebound contribution is apparent from the
observed emergence/recession. Holocene transgressive/
regressive events may have interrupted the general trend
of falling sea level in some areas (e.g. Jameson Land,
.
East Greenland, Bjorck
et al., 1994) although evidence
for such events is not definitive. Most local sea-level
curves from other localities show the same general
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K. Fleming, K. Lambeck / Quaternary Science Reviews 23 (2004) 1053–1077
Fig. 1. Location map of Greenland showing the spatial variation in the elevation (metres above sea level, a.s.l.) of local marine limits (from Funder
and Hansen, 1996). Also shown are representative relative sea-level curves: 1. Outer Disko (Rasch and Jensen, 1997), 2. Arveprinsen Ejland (Long
et al., 1999), 3. Central Hall Land (Kelly and Bennike, 1992), 4. Central Scoresby Sund (Funder, 1978), 5. Ingolf Land (Hjort, 1997).
tendencies, with coastal areas exhibiting earlier, smaller
emergence than sites further inland (e.g. Weidick, 1996).
Some variation in the timing and rate of emergence is
apparent around the island, however the available
observations generally lack the precision required to
allow more detailed discussions. In most areas, sea level
appears to have been close to the present-day level
between ca 4–2 14 C ka (Kelly, 1985), although in other
localities this occurred much earlier (e.g. South Greenland, ca 9 14 C ka; Bennike et al., 2002), after which it
fell to below the present-day level before a late-Holocene
transgression. During this period, the GIS in some areas
readvanced from its Holocene minimum position, which
was sometimes located behind the current ice margin.
This period is termed the neoglaciation and was the
result of a cooling trend in the climate (e.g. Kelly, 1980).
More recent evidence for sea-level fluctuations include
the inundation of Eskimo and Viking sites and repeated
geodetic surveys of water markers (e.g. Saxov, 1958,
1961; Weidick, 1996; Rasch and Jensen, 1997; Kuijpers
et al., 1999).
Fig. 2 shows the distribution of relative sea-level data
for Greenland that are considered useful for this work.
Details of these data and a complete reference list is
available on a website (see the Acknowledgments).
There are large areas where no useful observations are
available, e.g. the southeast coast adjacent the Danmark
Strait and the west coast along Melville Bugt, hence few
comments can be made about the glacial and sea-level
histories of these areas using the procedure followed in
this work. The potential for biases arising from the
uneven distribution of data is also apparent, with areas
such as Scoresby Sund and Disko Bugt being more
densely sampled that most parts. Fig. 3 presents for each
of the regional subdivisions the temporal distribution of
the data. There is a relatively well-defined time from
when observations are available (ca 10 14 C ka), marking
when the present-day coastal areas became ice free.
Therefore, like those areas without observations, few
conclusions can be drawn about Greenland’s sea-level
and glacial histories prior to this date. All together, just
over 600 data have been used in this work, the vast
majority of which are fossil molluscs ð> 80%Þ; that
mostly provide only a lower limit for sea level (Kelly,
1973; Bennike and Weidick, 2001). However, in recent
years additional data from isolation basins have become
available, allowing sea-level histories to be better
.
constrained (e.g. Bjorck
et al., 1994; Anderson and
Bennike, 1997; Long et al., 1999; Bennike et al., 2002).
4. Isostatic effect of ice sheets outside of Greenland
Changes in ice loading outside of Greenland affects
local relative sea level in two ways (Eq. (3)). The first is
the Dzesl contribution from those ice sheets. The second
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K. Fleming, K. Lambeck / Quaternary Science Reviews 23 (2004) 1053–1077
1057
Peary Land
Jùrgen Brùnlund Fjord
Kap Kùbenhavn
Nyeboe Land
Danmark Fjord
Hall Land
Holm Land
North
North
Iterluk
Northeast
Blþsù
South
Thule
Northwest
Hvalrosodden
North
South
Central north
Waltershausen Gletscher
Mester Vig
East Central central
Central south
Arveprinsen Ejland
Central West Disko
South
Jameson Land
North
Central north
Holsteinsborg
Inner Sùndre Strùmfjord
Middle Sùndre Strùmfjord
Southwest
Central south
South
Kap Farvel
Fig. 2. The spatial distribution of relative sea-level data (filled red circles) used in this work. Also marked are the regional (black lines, bold font) and
sector (grey lines, blue font) subdivisions, listed in Tables 2 and 3. The localities where predicted sea-level curves have been compared with
observations in Figs. 10–13 are labeled in italics (green-filled circles).
is the associated isostatic response, Dznon
iso ; with an
uncertainty, dznon
iso ; that arises from unknowns in the
imperfectly defined ice and earth models. Fig. 4 presents
for several sites around Greenland time-series curves of
the isostatic response since the LGM arising from such
ice-load changes. The curves were calculated using
nominal ice models representing the North American,
European and Antarctic ice sheets, the response from
the sum of these ice masses, and the nominal earth
model (Table 1). The contribution from the expanded
Icelandic Ice Sheet has been neglected owing to its small
size and because its response is restricted to the
immediate vicinity of the island due to the much thinner
lithosphere and underlying low-viscosity zone (e.g. Wolf
et al., 1997).
The dominance of the North American isostatic
contribution, owing to the great size and proximity of
these ice sheets, is the most obvious result, especially
when its contribution is compared with the summed
non-Greenland response. There is a relatively large
spatial variation in this part of the signal, for example
Hall Land (Fig. 4d) experiences an isostatic response
from the North American ice sheets of ca 33 m at
18 14 C ka; decreasing to o1 m at 10 14 C ka; while at
Jameson Land (Fig. 4b), these values are 26 and 7 m;
respectively. The European ice sheets also contribute,
with noticeable spatial variability between, for example,
Jameson Land and Claushavn (Fig. 4c). Another feature
of these modelled curves, especially the North American
and European results, is the complex temporal variation. The earlier positive values are heavily influenced by
the direct gravitational attraction of the ice sheets, while
the later negative values are a consequence of the
collapse of the peripheral forebulges surrounding the ice
sheets. Little spatial dependence is found in the
Antarctic results because Greenland is in the far-field
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K. Fleming, K. Lambeck / Quaternary Science Reviews 23 (2004) 1053–1077
1058
Southwest
East
30
30
N = 221
N = 161
10
10
Number
20
Number
20
0
0
14
12
10
8
6
4
2
0
14
12
10
8
6
Age (14C ka)
Age (14C ka)
Northwest
Northeast
4
2
0
15
15
N = 89
N = 154
5
5
Number
10
Number
10
0
14
0
12
10
8
6
4
2
Age (14C ka)
0
14
12
10
8
6
Age (14C ka)
4
2
0
Fig. 3. The temporal distribution of relative sea-level data for the regional datasets (Fig. 2).
relative to Antarctica. Most variation in the Antarctic
contribution is a function of the water load, which is in
turn dependent upon each site’s location relative to the
coast. The combined effect of these ice sheets is such
that, in the absence of changes in the GIS, all of
Greenland would today be experiencing a rise in sea
level of the order of several mm yr1 (e.g. Tarasov and
Peltier, 2002).
The total isostatic contribution, Dznon
iso ; of these ice
sheets for several epochs is shown in Fig. 5. The spatial
and temporal variability in this response is now clear,
where at 18 14 C ka (Fig. 5a), Dznon
iso ranges between ca 0
and 25 m across Disko and Disko Bugt (west to east),
and ca 45–30 m along Scoresby Sund (west to east),
while reaching up to 100 m in the northwest. By
10 14 C ka (Fig. 5b), Dznon
iso is between ca 35 and
15 m around Disko Bugt and between ca 10 and 0 m
along the east coast. At 6 14 C ka (Fig. 5c), it is ca 40 m
for Disko Bugt and 10 m for Scoresby Sund, with
between ca 12 to 4 m; west to east across the island,
still remaining by 2 14 C ka (Fig. 5d). As described in
Section 2, the uncertainty associated with the nonGreenland response, dznon
iso ; is found using a series of
earth- and ice-model parameters (Table 1) with dznon
iso set
to equal one third of the range (1 sigma) between the
maximum and minimum results.
5. Preliminary Greenland ice models
Four preliminary models of the GIS are used. These
are divided between maximum and minimum versions,
where maximum and minimum refers to the extent of
the GIS during the LGM. For each of these, two
different deglaciation starting times are considered; (i)
18 14 C ka; corresponding to deglaciation beginning
immediately after the LGM and (ii) 14 14 C ka; which
corresponds to the time from when deglaciation is
believed to have started in West Greenland (Kelly,
1985). The minimum and maximum reconstructions of
Denton and Hughes (1981) are used to define the extent
of the GIS during the LGM. These are based on the flow
equations of Hughes (1981), taking into account bedrock topography, isostatic displacement and different
basal conditions. The minimum models employ the
assumption that the Arctic ice sheets were out of phase
with the more southernly ice masses and hence deprived
of moisture during the maximum glaciation, while the
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D
North America
Europe
Antarctica
All non-Greenland
B
C
A
18
15
15
12
9
6
C Claushavn
3
0 18
15
12
9
6
Age (14C ka)
Age (14C ka)
D Hall Land
E Kap Morris Jessup
12
9
6
0
3
Age (14C ka)
0 18
15
12
9
6
3
3
0
0
50
40
30
20
10
0
-10
-20
-30
-40
-50
∆ζ iso (m)
50
40
30
20
10
0
-10
-20
-30
-40
-50
18
15
3
50
40
30
20
10
0
-10
-20
-30
-40
-50
∆ζ iso (m)
∆ζ iso (m)
∆ζ iso (m)
B Jameson Land
50
40
30
20
10
0
-10
-20
-30
-40
-50
18
12
9
6
Age (14C ka)
50
40
30
20
10
0
-10
-20
-30
-40
-50
∆ζiso (m)
A Narssaq
E
Age (14C ka)
Fig. 4. Time-series of the isostatic response from the separate non-Greenland ice models and the nominal earth model (Table 1) for various sites
around Greenland.
maximum models assume that the Arctic ice sheets were
in phase with those in the south. The minimum GIS
expanded to the edge of the present-day coastline during
the LGM, while the maximum reached the edge of the
continental shelf. For the purpose of this work, the
actual mass-loss mechanisms (melting, calving) are
irrelevant and only the fact that the GIS retreated and
thinned is of concern.
The LGM part of these models was digitised from the
ice-thickness maps presented in Hughes et al. (1981).
These maps were then compared with the present-day
GIS (Simon Ekholm, pers. com., National Survey and
Cadastre, Denmark, Ekholm, 1996) to determine the
change in ice thickness. For all models, the 10 14 C ka
margin is located approximately around the present-day
coastline, using the results of Andersen (1981) and
Funder and Hansen (1996). The ice margin is defined to
have reached its current position in all areas by
7 14 C ka: The ice margins between the LGM and 10
ka were linearly interpolated; 16, 14 and 12 ka for
deglaciation starting at 18 14 C ka; and 12 ka for the
14 14 C ka starting date, with the LGM ice sheet used
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1060
10
0
25
50
40
50
60
100
-10
20
10
30
40
- 10
30
0
0
30
20
10
-60
50
-20
-60
20 10
-10
40
50
0
30
0
40
-40
0
30
-20
-10
10
-20
20
-10
40
10
10
30
-40
0
40
0 -10
-20
-40
30
0
(a)
(b)
-20
0
0
-2
-4
-20
-15
-4
-10
-6
-15
-10
-15
-4
-20
-8
-30
-10
-40
-6
-8
-10
-40
-15
-20
-60
-70
-6
-50
-80
-4
-15
5
-20
-1
-30
-15
-70
-10
-50
-60
(c)
(d)
Fig. 5. The isostatic contribution (Dznon
iso ; Eq. (3)) from the sum of the nominal non-Greenland ice models and the nominal earth model (Table 1) for;
(a) 18 14 C ka; (b) 10 14 C ka; (c) 6 14 C ka and (d) 2 14 C ka: Contours are metres relative to the present-day sea level.
between 18 and 14 ka: Similarly, the ice margins for 9
and 8 ka were interpolated between the 10 and 7 ka
margin, with some modifications from Andersen (1981).
The final models after gridding have a resolution of
0:25 latitude and 0:5 longitude (ca 25 km) and are
denoted as; (i) MIN1 and MIN2, which are the
minimum models with 18 14 C and 14 14 C ka start-ofdeglaciation times, respectively, and (ii) MAX1 and
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0
0.0
-1
0.4
-2
0.8
-3
1.2
MIN1
MIN2
MAX1
MAX2
-4
1.6
-5
Change in ice volume (km3)
∆ζesl (m)
K. Fleming, K. Lambeck / Quaternary Science Reviews 23 (2004) 1053–1077
2.0
18
16
14
12
10
8
Age (14C ka)
6
4
2
0
Fig. 6. The equivalent sea-level curves (Dzesl ; Eq. (1)) and changes in
ice volume for the preliminary Greenland ice models.
MAX2, which are the corresponding maximum models.
Two important simplifications are; (i) no readvances or
pauses in deglaciation are included and (ii) ice-margin
retreat associated with the neoglaciation is not considered. This deglaciation chronology is relatively simple
compared to the present state of knowledge (e.g.
.
Bennike and Bjorck,
2002), but is believed to reflect
those primary characteristics of the expanded GIS to
which the relative sea-level signal is sensitive.
Fig. 6 shows the Dzesl and change-in-ice-volume
curves for each model and Fig. 7 presents the changes
in ice thickness. The largest change in ice thickness
occurs in those areas with the higher marine limits
(compare Fig. 7 with Fig. 1). It is also seen that in some
regions, the maximum model actually leads to a smaller
change in ice thickness than the minimum model. This is
due to ice streams being more important in the
formulation of the maximum models than in the
minimum, resulting in ice flowing around the coastal
mountains. Another difference between the minimum
and maximum models is the incorporation of the
coalescence of the Innuitian Ice Sheet and the northwest
GIS in the maximum models, while in the minimum
models these ice sheets remain separate. While the
question of whether this occurred has been the topic of
much debate, the consensus today is for a model that is
closer to the maximum description (e.g. England, 1999).
6. Comparisons between predictions and observations of
sea-level change
Table 2 presents the statistical results found when
comparing the sea-level observations with predictions
(Eq. (3)), using the preliminary GIS models (Section 5)
and the ice and earth models discussed in Section 4.
Listed are the initial variances for the unscaled predictions (s2b¼1 ; Eq. (4)), the bgis values that lead to a
minimum variance between observations and predictions, and the resulting s2 values after scaling for each
1061
dataset subdivision (Fig. 2). For most combinations of
datasets and GIS models, a reduction in the change in
ice thickness as defined by the preliminary GIS models is
necessary. The minimum models require a proportionally larger reduction, remembering that in some areas,
the changes in ice thickness defined in the minimum
models are greater than in the maximum. For all
datasets, the 14 14 C ka start-of-deglaciation option
results in smaller variances, while the minimum model
better represents most areas. As expected from the
discussion in Section 2, a single scaling parameter for the
entire ice sheet is inappropriate, with different bgis values
and preliminary models better suiting each area. For
example, when considering the full Greenland dataset
(Table 2, line 1), the single-parameter scaled maximum
models better describe Greenland’s sea-level history (i.e.
lower s2 ), but when the northwest dataset is excluded
(Table 2, line 2), the minimum models lead to smaller
variances.
These results are described further by Fig. 8, where
predictions from the MIN2 (Fig. 8a) and MAX2 (Fig.
8b) models, scaled by factors derived using the regional
datasets (Table 2, lines 3, 8, 14 and 17), are compared
with observations. Despite the large scatter, regional
differences can be identified. The most obvious are for
the northwest dataset, with MAX2 giving the better fit.
Fig. 9 presents the residuals between the observations
and scaled predictions, again for MIN2 (Fig. 9a) and
MAX2 (Fig. 9b). In general, the modelled isostatic
responses are too small at earlier times (ca 10 14 C ka)
and excessive at later epochs (ca 8–6 14 C ka), especially
for East Greenland. This suggests that temporal, as well
as spatial, scaling factors are required.
6.1. Southwest Greenland
Fig. 10 compares the observations of sea-level change
and marine limits at representative sites for Southwest
Greenland (Fig. 2) with the corresponding predicted
curves. The predictions were found using the isostatic
response from the preliminary models after applying the
sector-derived bgis values (Table 2, lines 4–7). The
converging of results from all models indicates that the
methodology is correcting the initial predictions in a
way that improves the fit with observations. However,
the lack of data from earlier epochs prevents constraints
to be placed on the glacial histories for those periods.
For example, sites such as Middle and Inner S^ndre
Str^mfjord (Figs. 10b and c) and Arveprinsen Ejland
(Fig. 10f), where similar Holocene sea levels are
predicted, display quite different LGM and early postglacial relative sea levels (ca 18–12 14 C ka).
As discussed in Section 3, sea-level regression
dominants the period covered by the available data,
which in general has been reproduced by the models.
The sudden change in the modelled rate of sea-level
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1000
500
0
00
10
100
0
1000
0
1000
500
500
50
50 0
50
50
0
1500
10
00
500
0
1
15 000
00
1500
1000
500
10
00
500
50
0
1000
100
1500
500
0
100
0
100
2000
500
500
0
50
0
15
500
500
50
0
500
0
(a)
(b)
50
500
500
500
500
00
500
0
10
50
0
0
10
00
50
1000
0
50
50
0
500
500
500
500
0
50
00
10
00
10
500
(c)
(d)
0
500
1000
1500
2000
Change in ice thickness (m)
2500
Fig. 7. The change in ice thickness relative to the present day as defined by the (a, c) minimum (MIN1) and (b, d) maximum (MAX1) Greenland ice
models at (a, b) 18 and (c, d) 10 14 C ka: The 14 14 C ka start-of-deglaciation models are not shown since the difference between the 10 14 C ka models
associated with each starting-time option is small.
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1063
Table 2
Statistics for comparisons between observations and predictions (Eqs. (3) and (4)) of relative sea-level change arising from the four preliminary
Greenland ice models. The listed datasets are subdivisions of the main Greenland dataset (Fig. 2)
Dataset (number of observations)
MIN1
s2b¼1
MAX1
bgis
s
2
s2b¼1
MIN2
bgis
s
2
s2b¼1
MAX2
bgis
s
2
s2b¼1
bgis
s2
14.8
8.7
0.90
0.85
14.3
7.5
12.7
9.5
1.09
1.02
12.4
9.5
15.5
10.1
0.82
0.78
13.8
7.2
11.8
9.3
1.00
0.93
11.8
9.0
3
4
5
6
7
Southwest (221)
South (47)
Central south (58)
Central north (50)
North (66)
10.2
31.3
4.6
5.4
4.2
0.92
1.19
0.91
0.81
0.98
9.9
30.7
4.2
3.1
4.2
12.1
31.1
10.6
5.6
5.4
1.21
1.85
1.34
1.07
1.12
10.7
24.3
6.8
5.4
4.9
10.8
30.3
5.7
7.6
4.4
0.85
1.11
0.83
0.74
0.90
9.6
30.1
4.0
2.9
3.9
10.7
29.1
8.3
5.2
4.5
1.10
1.70
1.22
0.98
1.01
10.3
23.6
6.4
5.1
4.5
8
9
10
11
12
13
East (161)
South (25)
Central south (51)
Central central (27)
Central north (26)
North (32)
10.0
8.9
12.1
12.2
4.7
11.2
0.82
0.81
0.72
0.79
0.84
1.44
7.4
5.5
4.1
7.6
2.8
5.2
6.9
10.8
7.8
9.9
3.6
3.8
0.85
0.81
0.80
0.87
0.92
0.99
5.2
6.9
3.9
8.3
3.2
3.8
12.1
11.6
16.9
15.1
6.5
8.5
0.75
0.74
0.66
0.72
0.77
1.31
6.9
5.0
3.7
6.9
2.6
5.0
9.1
14.2
11.2
11.5
4.9
4.3
0.77
0.73
0.72
0.79
0.84
0.86
4.6
6.3
3.6
7.5
2.8
3.2
14
15
16
Northeast (154)
North (65)
South (89)
5.4
5.1
5.7
0.82
0.80
0.85
3.7
2.6
4.6
8.7
10.1
7.7
1.22
1.45
1.08
7.3
4.9
7.5
7.0
7.2
7.0
0.75
0.73
0.77
3.5
2.4
4.3
7.5
8.1
7.2
1.11
1.34
0.98
7.1
4.8
7.1
17
18
19
Northwest (89)
South (43)
North (46)
52.1
67.0
39.3
1.89
0.00
1.90
40.0
0.0
15.4
32.4
35.3
30.4
1.95
2.86
1.79
12.9
12.7
7.4
48.5
66.4
32.8
1.74
0.00
1.75
39.1
0.0
14.3
27.2
31.3
23.9
1.78
2.52
1.64
11.9
11.9
7.1
120
120
100
100
80
80
60
60
40
40
20
20
0
0
-20
-20
-40
βgis scaled predictions (m)
Full (625)
Excluding Northwest (536)
βgis scaled predictions (m)
1
2
-40
Southwest
East
-60
-60
Northeast
Northwest
-80
-80
-100
-100
0
(a)
20
40
60
∆ζo (m)
80
100
120
0
(b)
20
40
60
80
100
120
∆ζo (m)
Fig. 8. Comparisons of observed and scaled-predicted relative sea-level change resulting from the; (a) MIN2 and (b) MAX2 preliminary Greenland
models. The predictions are scaled using bgis (Eq. (3)) derived from the regional datasets (Table 2, lines 3, 8, 14 and 17). The straight line represents
the 1:1 relationship between observations and predictions.
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1064
120
Southwest
∆ζo - βgis scaled predictions (m)
100
East
80
Northeast
60
Northwest
40
20
0
-20
-40
-60
-80
-100
14
13
12
11
10
9
(a)
8
7
6
5
Age (14C ka)
4
3
2
1
0
120
∆ζo - βgis scaled predictions (m)
100
80
60
40
20
6.2. East Greenland
0
-20
-40
-60
-80
-100
14
(b)
interpretations need to be treated with caution. At Inner
S^ndre Str^mfjord, the modelled curves are higher than
the observations during the mid-Holocene, consistent
with the observations being lower limits. However, as
discussed above, the retreat of the GIS to behind its
current margin would improve these results. Holsteinsborg (Fig. 10d) also suggest an inadequate change in
local ice loading after scaling, a result that is repeated at
West Central Disko (Fig. 10e). The ice sheet’s profile in
these areas either needs to be modified as for Kap
Farvel, or/and, incorporate more ice some distance
offshore, but not as far as the shelf edge. Arveprinsen
Ejland shows a similar pattern as Inner S^ndre
Str^mfjord. The intersection of the recessional part of
the modelled curves with the marine limit at Inner
S^ndre Str^mfjord and Arveprinsen Ejland provides
estimates for the age of these features, although it is still
possible that they formed during an earlier period of
relatively stable sea level.
13
12
11
10
9
8
7
6
5
4
3
2
1
0
Age (14C ka)
Fig. 9. Comparisons of the residuals between observed and scaledpredicted relative sea-level change resulting from the; (a) MIN2 and (b)
MAX2 preliminary Greenland models. The predictions are scaled
using bgis derived from the regional datasets (Table 2, lines 3, 8, 14
and 17).
change at 714 C ka is due to the deglaciation of the GIS
being completed at that time, as defined by the
preliminary models. If a neoglacial component is
considered, then the curves from 7 14 C ka onward
would be displaced downwards, hence providing a
better fit at several sites for mid- to late-Holocene times,
e.g. Inner S^ndre Str^mfjord and Arveprinsen Ejland.
The change in ice thickness around the southern-most
site, Kap Farvel (Fig. 10a) is clearly underestimated,
with the predicted curves being much lower than the
observations. Because the continental shelf in this area is
fairly close to the present-day coastline (ca 50 km), the
models’ profiles need to incorporate a greater change in
ice thickness towards the seaward end of the ice. This
area is also believed to have deglaciated at a faster rate
than has been defined in the preliminary models
(Bennike et al., 2002). For Middle S^ndre Str^mfjord,
an increase in the change in ice thickness is required
since the curves do not reach the two higher observations and barely meet the marine limit. However, this
area is prone to the upward displacement of marine
material by glacial action (Sugden, 1972), and such
Fig. 11 compares scaled predictions and observations,
including marine limits, from selected East Greenland
sites (Fig. 2, Table 2, lines 9 to 13). The previously
discussed temporal dependence observed in the residuals
(Fig. 9) becomes more obvious. For example, at Mesters
Vig (Fig. 11b), the predictions at ca 7 14 C ka are above
the observations, but the earlier epoch results, ca
9 14 C ka; lie below them. Following the same trend as
Southwest Greenland, a greater change in ice thickness
along coastal areas and/or extra ice offshore is required
(e.g. Mesters Vig) while sites closer to the present-day
margin (e.g. Waltershausen Gletscher, Fig. 11c) appear
adequately described.
As mentioned in Section 3, some areas show evidence
for transgressive/regressive events during the Holocene.
While glacial readvancements are often proposed to
explain such events, another possibility is that they are a
result of the relative importance of the isostatic response
due to both local and non-Greenland load changes and
the equivalent sea-level rise. Such events are seen to be
theoretically possible using these models (e.g. Jameson
Land, Fig. 11a).
The northern sector (e.g. Hvalrosodden, Fig. 11d)
displays a different behaviour to much of East Greenland, with the maximum models being preferred (Table
2, line 13, Fig. 11d). It has been proposed that this area
experienced a later deglaciation than other parts of
Greenland, with the GIS expanding some distance
offshore, since the shelf in this area extends ca 300 km
(Bennike and Weidick, 2001). There is also a recently
discovered island (Tobias Øer) that may have formed a
.
base for additional ice buildup (Bennike and Bjorck,
2002). Our results add support to that hypothesis, also
considering that in the northern part of this sector is the
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140
60
120
40
100
20
80
0
60
-20
40
-40
20
-60
0
-20
-80
16
14
12
10
8
6
4
2
0
14
(a)
18
16
14
12
6
4
2
0
14
Inner Søndre Strømfjord
∆ζrsl (m)
8
Age ( C ka)
(b)
Age ( C ka)
10
Holsteinsborg
140
140
120
120
100
100
80
80
60
60
40
40
20
20
0
0
-20
-20
18
16
14
12
10
8
6
4
2
0
14
(c)
18
16
14
12
10
8
6
4
2
0
14
(d)
Age ( C ka)
Age ( C ka)
Central West Disko
Arveprinsen Ejland
140
140
120
120
MIN1
MAX1
MIN2
MAX2
100
∆ζrsl (m)
∆ζrsl (m)
18
80
100
80
60
60
40
40
20
20
0
0
-20
-20
18
(e)
∆ζrsl (m)
Middle Søndre Strømfjord
80
∆ζrsl (m)
∆ζrsl (m)
Kap Farvel
1065
16
14
12
10
8
14
Age ( C ka)
6
4
2
0
18
(f)
16
14
12
10
8
6
4
2
0
14
Age ( C ka)
Fig. 10. Comparisons of observations and scaled-predicted relative sea-level curves (Table 2, lines 4–7) for various sites around Southwest Greenland
(Fig. 2). Dark-grey shading indicates the estimated local marine limits (Fig. 1). Symbols: triangles—lower limits, diamonds—mean sea level, inverted
triangles—upper limits.
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Mesters Vig
120
120
100
100
80
80
60
60
40
40
20
20
0
0
-20
-20
18
16
14
12
10
8
6
4
2
Age (14C ka)
(a)
0 18
16
14
12
10
8
6
4
2
0
Age (14C ka)
(b)
Walterhausen Glacier
Hvalrosodden
120
120
MIN1
MAX1
MIN2
MAX2
100
∆ζrsl (m)
80
100
80
60
60
40
40
20
20
0
0
-20
∆ζrsl (m)
∆ζrsl (m)
Jameson Land
∆ζrsl (m)
1066
-20
18
16
(c)
14
12
10
8
6
4
2
Age (14C ka)
0 18
16
(d)
14
12
10
8
6
4
2
0
Age (14C ka)
Fig. 11. Comparisons of observations and scaled-predicted relative sea-level curves (Table 2, lines 9–13) for various sites around East Greenland
(Fig. 2). Dark-grey shading indicates the estimated local marine limits (Fig. 1). Symbols: triangles—lower limits, diamonds—mean sea level, inverted
triangles—upper limits.
outlet for the Northeast Ice Stream (Fahnestock et al.,
1993; Thomsen et al., 1997), which exhibits frequent
fluctuations in the extent of the surrounding outlet
glaciers (Higgins, 1991).
6.3. Northeast Greenland
Fig. 12 presents the predictions, observations and
marine limits for Northeast Greenland (Fig. 2, Table 2,
lines 15 and 16). J^rgen Br^nlund Fjord and Kap
K^benhavn (Figs. 12b and c) are best represented by
these predictions, while the results are less favourable
for Peary Land and Holm Land (Figs. 12a and e). As
with the previous regions’ results, the models include a
deficiency in the change in ice volumes required along
the present-day coast (e.g. Peary Land and Holm Land).
Predictions for areas closer to the present-day margin
have either an excessive change in ice loading (e.g.
Danmark Fjord and Bla( so, Figs. 12d and f) or are
adequately described (e.g. J^rgen Br^nlund Fjord).
Overall, the minimum ice models appear to best serve
this region. This is consistent with work that describes
how the LGM margin was close to the present-day coast
along Holm Land (Hjort, 1997), although as discussed
previously, the LGM margin to the south was possibly
located further offshore (north East Greenland,
Fig. 11d). On the other hand, ice shelves are believed
to have existed off East Peary Land and Johannes V.
Jensen Land in the Wandal Sea, suggesting a greater ice
loading, which would be better for sites such as Peary
Land (Funder and Hjort, 1980).
6.4. Northwest Greenland
Modelled sea-level curves from selected Northwest
Greenland sites (Fig. 2) are compared with observations
and local marine limits in Fig. 13 (Table 2, lines 18
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Peary Land
1067
Jørgen Brønlund Fjord
140
140
MIN1
MAX1
MIN2
MAX2
100
80
80
60
60
40
40
20
20
0
0
-20
-20
16
14
12
10
8
6
4
2
0
18
16
14
12
14
(a)
8
6
4
2
0
14
Age ( C ka)
Age ( C ka)
(b)
Kap København
∆ζrsl (m)
10
Danmark Fjord
140
140
120
120
100
100
80
80
60
60
40
40
20
20
0
0
-20
-20
18
16
14
12
10
8
6
4
2
0
14
(c)
Age ( C ka)
18
16
14
12
∆ζrsl (m)
10
8
6
4
2
0
14
Age ( C ka)
(d)
Holm Land
Blåsø
140
140
120
120
100
100
80
80
60
60
40
40
20
20
0
0
-20
-20
18
(e)
∆ζrsl (m)
18
∆ζrsl (m)
∆ζrsl (m)
100
120
∆ζrsl (m)
120
16
14
12
10
8
6
4
2
0
18
14
Age ( C ka)
16
14
12
10
8
6
4
2
0
14
(f)
Age ( C ka)
Fig. 12. Comparisons of observations and scaled-predicted relative sea-level curves (Table 2, lines 15 and 16) for various sites around Northeast
Greenland (Fig. 2). Dark-grey shading indicates the estimated local marine limits (Fig. 1). Symbols: triangles—lower limits, diamonds—mean sea
level, inverted triangles—upper limits.
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Thule
Iterluk
100
100
MIN1
MAX1
MIN2
MAX2
60
40
40
20
20
0
0
-20
-20
-40
-40
-60
-60
18
16
14
12
10
8
6
4
2
0
Age (14C ka)
(a)
18
16
14
12
8
6
4
2
0
Age (14C ka)
(b)
Hall Land
∆ζrsl (m)
10
Nyeboe Land
140
140
120
120
100
100
80
80
60
60
40
40
20
20
0
0
-20
-20
18
(c)
∆ζrsl (m)
∆ζrsl (m)
60
80
∆ζrsl (m)
80
16
14
12
10
8
6
4
2
0
Age (14C ka)
18
16
(d)
14
12
10
8
6
4
2
0
Age (14C ka)
Fig. 13. Comparisons of observations and scaled-predicted relative sea-level curves (Table 2, lines 18 and 19) for various sites around Northwest
Greenland (Fig. 2). Dark-grey shading indicates the estimated local marine limits (Fig. 1). Symbols: triangles—lower limits, diamonds—mean sea
level, inverted triangles—upper limits.
and 19). The minimum-model results for Thule (Fig.
13a) and Iterluk (Fig. 13b) are completely inadequate
and are not included since the resulting scaling factors
are meaningless (Table 2, line 18). This supports the
current view that the Innuitian and Northwest Greenland ice masses coalesced during the LGM (e.g.
England, 1998, 1999; Zreda et al., 1999). However, the
fits between the observations and maximum model
results are also poor, and require significant modifications to the spatial and temporal characteristics of the
models. In these later models, the present-day coastline
was cleared of ice by 10 14 C ka; whereas the more likely
deglaciation chronology involved a largely latitudinal
movement of the ice margin through either end of Nares
Strait (Fig. 1). This started ca 10:1 14 C ka in the north
and 9 14 C ka in the south, producing a clear ocean way
by 7:5 14 C ka (England, 1999).
Regarding the northern-sector sites, Hall Land
(Fig. 13c) and Nyeboe Land (Fig. 13d), the scaled
maximum models produce reasonable fits with the
observations, although still underestimating the response required at ca 8 14 C ka: It must also be
remembered that the non-GIS, especially the Innuitian
Ice Sheet, have a significant influence in this area (see
Fig. 6d). Hence, future GIS models will require the local
glacial history to be examined in conjunction with that
of the Canadian Arctic (e.g. Dyke, 1999).
7. The first-order Greenland ice model—GREEN1
A first-order model for the GIS has been produced in
an interactive process, based on the analysis described in
Section 6. The first step involves defining for each sector
the preliminary model that results in the lowest s2 after
scaling (Table 2). We find that the 14 14 C ka start-ofdeglaciation results in the smallest variances, with the
scaled MIN2 model best reproducing the sea-level
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1069
Table 3
The preliminary ice models and scaling factors that make up the intermediate and first-order (GREEN1) Greenland ice models. The listed datasets
are subdivisions of the main Greenland dataset (Fig. 2)
Datasets
Ice model
Scale
Full Dataset
Intermediate
GREEN1
s2b¼1
bgis
5.5
1.00
2
s2b¼1
bgis
5.5
5.4
1.00
5.4
s
s2
Southwest
South
Central south
Central north
North
MAX2
MIN2
MIN2
MIN2
1.70
0.83
0.74
0.90
6.7
15.3
4.9
3.7
4.7
1.02
1.11
1.00
0.93
1.11
6.6
14.9
4.9
3.4
4.3
6.3
13.8
5.1
4.0
4.1
1.00
1.05
1.00
0.92
1.06
6.3
13.7
5.1
3.7
4.0
East
South
Central south
Central central
Central north
North
MIN2
MAX2
MIN2
MIN2
MAX2
0.74
0.72
0.72
0.77
0.86
5.1
6.6
4.7
8.7
3.0
3.9
0.99
1.06
0.95
1.00
0.98
1.04
5.1
6.4
4.5
8.7
2.9
3.8
5.1
6.4
4.7
8.9
3.0
3.7
0.99
1.04
0.95
1.01
0.99
1.01
5.1
6.3
4.6
8.9
3.0
3.7
Northeast
North
South
MIN2
MIN2
0.73
0.77
4.9
3.5
6.0
0.98
1.03
0.94
4.9
3.5
5.8
5.0
3.4
6.3
0.99
1.03
0.97
5.0
3.4
6.3
Northwest
South
North
MAX2
MAX2
2.52
1.64
4.3
3.6
5.0
0.99
0.92
1.03
4.3
3.4
4.9
4.3
4.0
4.7
1.00
1.01
1.00
4.3
4.0
4.7
history for most areas. The exceptions are Northwest
Greenland, southern-most Southwest Greenland and
parts of East Greenland, all of which are better
represented by the scaled MAX2 model. The corresponding bgis values are applied to the appropriate
preliminary model, and these new sector models are
combined to produce an ‘‘intermediate’’ ice model.
Predictions from the intermediate model are then
compared with observations, with the resulting bgis
values applied to each sector of the intermediate model
to produce the first-order model, GREEN1 (Table 3).
The appropriate model for the centre of the GIS and
coastal areas without observations is found by comparing the observations with predictions based on iterations
of GREEN1 incorporating MIN2 and MAX2 portions
of those areas, scaled by 1.0, 0.9, etc. Based on these
comparisions, we select the MIN2 model’s portion,
scaled by 0.7 although we noted little difference for
values of 0.8–0.6. The final bgis values that result from
the use of GREEN1 tend to be around unity (Table 3),
indicating; (i) if another iteration were carried out, the
improvement would be minimal and, (ii) this model
provides the optimum agreement between predictions
and observations, given the available datasets and
assumptions made about the Earth’s rheology.
Fig. 14 shows the GREEN1 model for; (a) the LGM
(18–14 14 C ka) and (b) 10 14 C ka; and the resulting
topography after considering sea-level change for; (c)
the LGM (18 14 C ka) and (d) 10 14 C ka: The change in
ice thickness since the LGM along the present-day
coastline in most areas is of the order of 500 m; with
changes of over 1500 m in some parts adjacent to the
present-day margin. From 10 14 C ka; changes adjacent
to the present-day margin are still > 1000 m in areas
with highly raised shorelines. The GREEN1 ice-volume
changes are equivalent to a eustatic sea-level contribution of 3:1 m at the LGM and 1:9 m at 10 14 C ka; within
the range predicted by recent thermomechanical icesheet modelling (Huybrechts, 2002).
8. Discussion
Fig. 15 presents the modelled Dzrsl (Eq. (1)) over
Greenland resulting from GREEN1 and the other
model parameters used in the previous sections. We
see that the general spatial form of the areas of
maximum sea-level recession correspond very well to
the higher marine limits (Fig. 1). We however note
discrepancies in the modelled elevations. For example,
in the southeast and along Melville Bugt, no Holocene
recession is reproduced whereas marine limits with
elevations up to 20 m are found, although the marinelimit estimates in that area may be unreliable (Bennike,
pers. com.). Likewise, the highest predicted sea levels in
areas such as Disko Bugt and Scoresby Sund are lower
than the observed marine limits.
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Fig. 14. (a, b) The first-order Greenland ice model, GREEN1, showing the change in ice thickness since; (a) 18 14 C ka and (b) 10
topography of Greenland, accommodating the changes in ice thickness and sea level at (c) 18 14 C ka and (d) 10 14 C ka:
14
C ka: (c, d) The
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K. Fleming, K. Lambeck / Quaternary Science Reviews 23 (2004) 1053–1077
50
50
25
0
5
-50
-100
-50
0
12
0
50
100
25
15025
1
0
15
25
200
50
25
0
-5
0
25
0
25 0
10
50
-50
25
-1
0
-5
-1
-50 00
0
1071
-50
0
0
50
125
25
-50
50
25
0
-10
0
50
-125
-100
-125
-100
100
0
-100
5
-100 -12
-50
0
-5
-50
-100
-125
25
100
-50
(a)
0
25
50
50
25
0
0
50
-50
25 0
-50
-50
25
0
-50
(b)
-20
-5
5
40
20
0
0
60
0
0
40
5
5
0
10
-5
-20
20
0
-5
0
-5
0
5
-15
-5
-10
(c)
-20
0
-40 -60
-20
-20
40
-5
0
-20
20
0
20
-20
-15
-60
0
5
0
-10
0
20
-40
-5
-20
-20
-5
20
0
0
-2
20
(d)
Fig. 15. Relative sea-level change (Dzrsl ; Eq. (1)) resulting from the GREEN1 (Fig. 15) and nominal non-Greenland ice and earth models (Fig. 5,
Table 1) for; (a) 18 14 C ka; (b) 10 14 C ka; (c) 6 14 C ka and (d) 2 14 C ka: Contours are in metres relative to the present day.
In Fig. 16, the range in Dzrsl is presented for
representative sites selected from Figs. 10–13. Large
uncertainties occur for earlier times (between ca 18 and
9 14 C ka), of the order of 720 m; emphasizing the low
resolution for the early epochs where the sea-level data
is of an uncertain quality. Also of note is that the
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K. Fleming, K. Lambeck / Quaternary Science Reviews 23 (2004) 1053–1077
Arveprinsen Ejland
140
120
120
100
100
80
80
60
60
40
40
20
20
0
0
-20
-20
16
14
12
10
8
6
4
2
0
18
16
14
14
(a)
10
8
6
4
2
0
14
Age ( C ka)
Age ( C ka)
(b)
Mesters Vig
∆ζrsl (m)
12
Walterhausen Glacier
120
120
100
100
80
80
60
60
40
40
20
20
0
0
-20
-20
18
16
14
12
10
8
6
4
2
0
14
(c)
Age ( C ka)
18
16
14
12
10
8
6
4
2
0
14
Age ( C ka)
(d)
Jørgen Brønlund Fjord
Nyeboe Land
140
140
120
120
100
100
80
80
∆ζrsl (m)
∆ζrsl (m)
18
60
60
40
∆ζrsl (m)
∆ζrsl (m)
Inner Søndre Strømfjord
140
∆ζrsl (m)
1072
40
20
20
0
0
-20
-20
-40
18
(e)
16
14
12
10
8
14
Age ( C ka)
6
4
2
0
18
(f)
16
14
12
10
8
6
4
2
0
14
Age ( C ka)
Fig. 16. Comparisons of observations and the range in predicted relative sea level using the GREEN1 model and a series of non-Greenland ice and
earth models (Table 1) for various locations around Greenland. The 71s uncertainty (light-grey shading) is plotted over the nominal results. Darkgrey shading indicates the estimated local marine limit (Fig. 1). Symbols: triangles—lower limits, diamonds—mean sea level, inverted triangles—
upper limits.
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observed sea levels below the present-day level are not
reproduced by the model. To investigate this later point,
a series of order-of-magnitude calculations have been
made using an axisymmetric GIA model (e.g. Johnston,
1993; Bennike et al., 2002) in which the present-day ice
model has the same area and equivalent-water content
as the current GIS. The expanded ice sheet is
constrained by the GREEN1 Dzesl values, with the icesheet profiles being simple parabolas. A standard model
that excludes a neoglacial component is compared with
three other models; (i) NEO1, where the GIS retreats to
behind the present-day margin between 7 and 6 14 C ka
by 10 km; readvancing to the present-day margin
between 3 14 C ka and today, (ii) NEO2, which has the
same timing but a 20 km movement and (iii) NEO3,
which has a 20 km movement but readvances from
1 14 C ka:
Fig. 17 presents the results of these tests for; (a) the
axisymmetric ice models at different epochs and (b) the
associated change in ice loading relative to the present
day. Figs. 17c and d shows the predicted Dzgis
iso curves
(Eq. (3)) arising from these ice models using the nominal
earth model (Table 1) at two locations; (c) the presentday ice margin and (d) the present-day coastline. The
neoglacial contribution is shown in Figs. 17e and f
where (e) is the present-day ice margin and (f) the
present-day coastline. The downward displacement of
sea level at late-Holocene times by the neoglacial
contribution demonstrates that such ice-sheet behaviour
is a possible mechanism for the observed fall in sea level
to below the present-day level and subsequent transgression.
These neoglacial results are now combined with the
GREEN1 model for the case of Arveprinsen Ejland,
West Greenland, a site whose sea-level history is
reasonably well described by GREEN1 (Figs. 10f and
17b). Long et al. (1999) comment that sea level at
2:5 14 C ka in this area was ca 5 m; while the predicted
value from GREEN1 is ca 6 m: Since the NEO2 model
predicted a downward shift in sea level at this time of ca
5 m; results from an axisymmetric ice model that
incorporates an ice-margin movement of 40 km with
the readvance starting at 2:5 14 C ka are combined with
those from the GREEN1 model. These results are
shown in Fig. 18; (a) the predictions from the GREEN1
model, (b) the effect of the new neoglacial description
with respect to the standard model and (c) the sum of
the initial predictions and neoglacial response. The fall
in sea level to below today’s level and the subsequent
transgression are reproduced, but the early-Holocene
predictions are now less representative of the observations. Hence, the introduction of a neoglacial component in the GREEN1 model impacts on the solution for
the ice model for earlier epochs. Nonetheless, the
estimated neoglacial ice-margin movement is consistant
with studies based on moraine dating (10’s of km of ice
1073
margin movement, vanTatenhove et al., 1996) and
vertical motion observed by GPS measurements (ca
50 km; Wahr et al., 2001a, b).
9. Conclusions
This paper deals with the development of a first-order
model of the ice-load history of the GIS since the LGM.
The first part is an assessment of the contribution to
Greenland’s sea-level history of changes in the ice sheets
located outside of Greenland. The findings of this
section are:
*
*
*
Changes in these ice sheets contributed a complex
spatial and temporal signal to Greenland’s sea-level
history, of the order of metres to 10’s of metres (Figs.
4 and 5).
The North American ice sheets are the dominant part
of this signal, especially the Innuitian Ice Sheet’s
influence on Northwest Greenland.
The ongoing isostatic contribution of these ice-load
changes, if treated in isolation, causes an ongoing rise
in sea level around Greenland today of the order of
several mm yr1 :
Inversions of sea-level change along the Greenland
coast are made using different initial GIS ice models
(Figs. 6 and 7) and scaling parameters (bgis ; Eq. (4)) that
minimise the variance (s2 ; Eq. (5)) between predictions
and observations of relative sea level. We find that:
*
*
*
*
A single scaling parameter for all of Greenland is
inappropriate, hence requiring the spatial subdivision
of the observational dataset (Table 2).
A deglaciation that started at 14 14 C ka provides
better results (smaller s2 ) than an earlier (18 14 C ka)
date.
The scaled minimum (MIN2) models better reproduced Greenland’s sea-level history for most areas.
The exceptions are southern-most Southwest Greenland, parts of East Greenland and Northwest Greenland. The coalescence of the Greenland and Innuitian
ice sheets is reaffirmed.
The LGM ice sheet extended some distance offshore,
but not usually as far as the shelf edge. However, this
probably did occur in some areas, namely southernmost West Greenland, northern East Greenland and
Northwest Greenland.
The resulting first-order Greenland ice
GREEN1, has the following characteristics:
*
*
model,
A deglaciation starting at 14 14 C; although a single
starting date for the entire island would be too
simplistic.
LGM and 10 14 C ka equivalent sea-level contributions of 3.1 and 1:9 m; respectively.
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1074
3500
1750
1250
1000
750
2000
500
LGM
10 14C ka
7 14C ka/Present
10 km retreat
20 km retreat
1500
1000
500
250
0
-250
-500
0
-750
0
1
2
(a)
3
4
5
Distance (degrees)
6
7
8
0
(b)
1
2
3
4
5
Distance (degrees)
6
7
8
60
60
50
45
40
50
45
40
35
35
30
30
25
25
20
20
15
15
10
10
5
5
0
0
-5
-5
8
7
6
5
4
3
2
1
0
14
(c)
Age ( C ka)
8
7
6
5
4
3
2
1
0
14
(d)
Age ( C ka)
10
10
NEO1-standard
8
NEO2-standard
∆ζiso
neo
4
4
2
2
0
0
-2
-2
-4
-4
-6
-6
-8
-8
8
(e)
(m)
6
NEO3-standard
stan
- ∆ζiso
stan
(m)
6
- ∆ζiso
8
neo
∆ζiso (m)
55
standard
NEO1 10 km, 314C ka
NEO2 20 km, 314C ka
NEO3 20 km, 114C ka
∆ζiso (m)
55
∆ζiso
Ice thickness (m)
2500
Change in ice thickness (m)
1500
3000
7
6
5
4
14
Age ( C ka)
3
2
1
0
8
(f)
7
6
5
4
3
2
1
0
14
Age ( C ka)
Fig. 17. Effect of a neoglacial contribution on glacial-isostatic rebound in Greenland. See the text for model descriptions. (a, b) Profiles at various
epochs of; (a) ice-sheet heights and (b) changes in ice thickness. (c, d) Isostatic response for sites located at; (c) the present-day ice margin and (d) the
present-day coastline. (e, f) Differences between results with and without neoglaciation at; (e) the present-day ice margin and (f) the present-day
coastline.
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1075
90
14
80
12
8
∆ζrsl (m)
60
6
50
4
40
2
30
0
-2
20
-4
10
Neoglacial correction (m)
10
70
-6
0
a
-8
b
-10
-10
10
8
6
4
2
0
10
8
Age (14C ka)
6
4
2
0
Age (14C ka)
90
80
70
∆ζrsl (m)
60
50
40
30
20
10
0
c
-10
10
8
6
4
2
0
Age (14C ka)
Fig. 18. Comparisons of observations with modelled relative sea-level change for Arveprinsen Ejland, West Greenland. (a) The range in predicted
relative sea-level change (see Fig. 16). (b) The neoglacial correction term (see text for details). (c) The sum of (a) and (b). The 71s uncertainty (lightgrey shading) is plotted over the nominal results. Dark-grey shading indicates the estimated local marine limit (Fig. 1). Symbols: triangles—lower
limits, diamonds—mean sea level.
*
Changes in ice thickness of the order of 500 m along
the present-day coast and > 1500 m adjacent to the
current margin in areas of major ice retreat.
The resulting sea-level histories from the use of this
model are characterised by:
*
*
The spatial form of the marine limits have been
reproduced (compare Figs. 1 and 15). However, the
observed limit elevations are not always reached,
although there are doubts as to the reliability of some
marine limits.
Mid- to late-Holocene sea levels below today’s level
are not reproduced (Fig. 16).
Regarding the last point, to reproduce sea levels that are
below the present day’s and the subsequent late-
Holocene transgression, a neoglacial component where
the GIS retreated ca 40 km behind its present-day
margin and readvanced over the last few thousand years
is required (Fig. 18). Such a contribution, if included in
an ice model, would also affect predictions for earlier
times.
Acknowledgements
We would like to thank Prof. Svend Funder and Dr.
Ole Bennike for providing their datasets for this study.
We would also like to thank Dr. Bennike and an
anonymous reviewer for their comments that greatly
improved this work. The completion of this work was
assisted by the support of the SEAL (Sea Level Change)
ARTICLE IN PRESS
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K. Fleming, K. Lambeck / Quaternary Science Reviews 23 (2004) 1053–1077
project of the Hermann von Helmholtz Association of
German Research Centres. Thanks also to Mr. Hans
Kuhn
.
and Mr. Volker Klemann of GFZ and Dr. Herb
McQueen of RSES for assistance with the necessary
computing facilities. A complete listing of the relative
sea-level observations and relevant references can be
found on the webpage of Kevin Fleming (www.gfzpotsdam.de/pb1/pg3/index S13d.html).
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