indicates that thick ice must have extended out to the edge
of the continental shelf before the formation of the oldest
sea-level signals at ~20,000 years ago. The record from
the Vestfold Hills, East Antarctica, is of shorter duration
than that of Andøya, but the fall in level during the past
6,000 years is similar and indicative of this area having
been extensively glaciated. Further outside the ice margins
as in southern England, sea-level has continued to rise up
to the present as a result of the subsidence of the crust
beyond the ice margins, and the spatial variability of this
rise provides information on the mantle response function.
At the far-field continental margin site of Orpheus Island,
Australia, sea-level has been falling for the past 6,000 or
so years, reflecting the Earth’s response to the water loading, and the spatial variability of this highstand provides a
measure of the Earth’s response as well as any changes in
ocean volume during this period. Far-field observations
from the time of the LGM, such as the Bonaparte Gulf
(Australia) or Sunda Shelf (Southeast Asia), provide a first
approximation estimate of the total change in ice volume
that has occurred since the LGM, and records from the late
glacial period, such as from Barbados, constrain in a first
approximation the timing and rate of melting of the global
ice sheets. Second approximation solutions require that
these observations be corrected for the isostatic (and,
where relevant, the tectonic) contributions to the local
sea-level change.
Inversion of sea-level data for geophysical and
glaciological parameters
From this brief global survey, it should be evident that
geophysical inversion of global data sets should be able
to provide constraints on both the Earth’s rheology and
on ice sheet histories. There are often a number of caveats
to such models concerning the distribution of the sea-level
data, the parameterization of the rheology function,
assumptions about the role of tectonics, or the nature of
independent constraints on the location of former ice margins and on ice thickness through time.
The resolution for the radial dependence of mantle viscosity is limited in these inversions (Paulson et al., 2007)
in part because of the limiting nature of the distribution
of field data and in part because of uncertainties in the
knowledge of the ice sheets, but solutions do point to an
increase in mantle viscosity from the average upper mantle value to the average lower mantle value by a factor of
50–100 or more, consistent with independent –
geodynamically reasoned – estimates (e.g., Mitrovica
and Forte, 2004; Čížková et al., 2012).
Limitations in the knowledge of the past ice sheets are
particularly severe in their impact on the inferred rheologies. The usual assumption is that the ice margin history
is known, and the ice thickness through time is treated as a
partially known function. Of the major past ice sheets, the
Fennoscandian ice models is best constrained from
rebound analyses because of an extensive and reliable
database of both sea-level change within its former maximum margin and of the ice margin history. The North
American ice sheet is less well constrained, and the Antarctic ice sheet remains largely unconstrained. Recent ice
models obtained from sea-level data inversions include
Peltier (2004) for a global model, Lambeck et al. (2010)
for northern Europe, Fleming and Lambeck (2004) for
Greenland, and Whitehouse et al. (2012) for Antarctica.
Generally, the models provide a good description of the
observational evidence (Figure 2) and a basis for predictive models for the evolution of coastlines and water
depths from the LGM to the present, provided that the
model parameters are from consistent Earth-ice solutions
because of the trade-offs that can occur between them
through incomplete a priori information of the ice sheets.
Figure 3 provides one such example for the Mediterranean
where the contours provide lines of constant sea-level
change from the LGM to the present. Of note is that these
contours follow closely the coastline, indicative of the
importance of the water loading within the Mediterranean
basin. The influence of the local Alpine ice sheet is
restricted to the northern Adriatic and Gulf of Genoa. Less
visibly evident is the longer wavelength influence of the
North American and Eurasian ice sheets consisting of a
north–south gradient across the region. Results such as
these are model-parameter dependent and can be, and
have been, tested against local independent sea-level data,
but they provide useful starting points for discussing
Glacio(hydro)-isostatic Adjustment, Figure 1 Representative sea-level curves from different localities around the world from the
time of the Last Glacial Maximum to the present. Note the different time and sea-level change scales. The A ˚ ngerman result, from
central Sweden, is representative of a location near the center of a former ice sheet, with crustal rebound exceeding the increase in
ocean volume throughout the melting and post-glacial phase. The Andøya result, from the northwest coast of Norway, and the
Nanortalik result, from southern Greenland, are representative of sites near the edge of an ice sheet. Initially, the rebound dominates,
followed by a period when the increase in ocean volume dominates and a later phase when the rebound is again dominant. In the
case of the Greenland signal, a major contributor to the sea-level change is from the North American deglaciation. The East Antarctic
site of Vestfold Hills is similar to that of Andøya indicating that substantial changes in ice volume occurred here before the area
became ice-free. The southwest England result is representative of locations outside of the ice sheet where the crustal rebound after
the onset of melting is one of subsidence. The signal is initially dominated by the increase in ocean volume and later by the crustal
response. The Sunda Shelf and Barbados locations are far-field sites, and the sea-level signal is dominated by the change in ocean
volume, modulated by glacio-hydro-isostatic contributions. The North Queensland site is representative of far-field continental
margins where a small-amplitude highstand forms in Late Holocene time due to the water-loading component. At the mid-ocean
island site of Kiritimati, the change in sea-level is virtually constant for 5,000 years due to a cancellation out of the various isostatic
contributions to sea-level change.
GLACIO(HYDRO)-ISOSTATIC ADJUSTMENT
297
of the continental shelf before the formation of the oldest
sea-level signals at ~20,000 years ago. The record from
the Vestfold Hills, East Antarctica, is of shorter duration
than that of Andøya, but the fall in level during the past
6,000 years is similar and indicative of this area having
been extensively glaciated. Further outside the ice margins
as in southern England, sea-level has continued to rise up
to the present as a result of the subsidence of the crust
beyond the ice margins, and the spatial variability of this
rise provides information on the mantle response function.
At the far-field continental margin site of Orpheus Island,
Australia, sea-level has been falling for the past 6,000 or
so years, reflecting the Earth’s response to the water loading, and the spatial variability of this highstand provides a
measure of the Earth’s response as well as any changes in
ocean volume during this period. Far-field observations
from the time of the LGM, such as the Bonaparte Gulf
(Australia) or Sunda Shelf (Southeast Asia), provide a first
approximation estimate of the total change in ice volume
that has occurred since the LGM, and records from the late
glacial period, such as from Barbados, constrain in a first
approximation the timing and rate of melting of the global
ice sheets. Second approximation solutions require that
these observations be corrected for the isostatic (and,
where relevant, the tectonic) contributions to the local
sea-level change.
Inversion of sea-level data for geophysical and
glaciological parameters
From this brief global survey, it should be evident that
geophysical inversion of global data sets should be able
to provide constraints on both the Earth’s rheology and
on ice sheet histories. There are often a number of caveats
to such models concerning the distribution of the sea-level
data, the parameterization of the rheology function,
assumptions about the role of tectonics, or the nature of
independent constraints on the location of former ice margins and on ice thickness through time.
The resolution for the radial dependence of mantle viscosity is limited in these inversions (Paulson et al., 2007)
in part because of the limiting nature of the distribution
of field data and in part because of uncertainties in the
knowledge of the ice sheets, but solutions do point to an
increase in mantle viscosity from the average upper mantle value to the average lower mantle value by a factor of
50–100 or more, consistent with independent –
geodynamically reasoned – estimates (e.g., Mitrovica
and Forte, 2004; Čížková et al., 2012).
Limitations in the knowledge of the past ice sheets are
particularly severe in their impact on the inferred rheologies. The usual assumption is that the ice margin history
is known, and the ice thickness through time is treated as a
partially known function. Of the major past ice sheets, the
Fennoscandian ice models is best constrained from
rebound analyses because of an extensive and reliable
database of both sea-level change within its former maximum margin and of the ice margin history. The North
American ice sheet is less well constrained, and the Antarctic ice sheet remains largely unconstrained. Recent ice
models obtained from sea-level data inversions include
Peltier (2004) for a global model, Lambeck et al. (2010)
for northern Europe, Fleming and Lambeck (2004) for
Greenland, and Whitehouse et al. (2012) for Antarctica.
Generally, the models provide a good description of the
observational evidence (Figure 2) and a basis for predictive models for the evolution of coastlines and water
depths from the LGM to the present, provided that the
model parameters are from consistent Earth-ice solutions
because of the trade-offs that can occur between them
through incomplete a priori information of the ice sheets.
Figure 3 provides one such example for the Mediterranean
where the contours provide lines of constant sea-level
change from the LGM to the present. Of note is that these
contours follow closely the coastline, indicative of the
importance of the water loading within the Mediterranean
basin. The influence of the local Alpine ice sheet is
restricted to the northern Adriatic and Gulf of Genoa. Less
visibly evident is the longer wavelength influence of the
North American and Eurasian ice sheets consisting of a
north–south gradient across the region. Results such as
these are model-parameter dependent and can be, and
have been, tested against local independent sea-level data,
but they provide useful starting points for discussing
Glacio(hydro)-isostatic Adjustment, Figure 1 Representative sea-level curves from different localities around the world from the
time of the Last Glacial Maximum to the present. Note the different time and sea-level change scales. The A ˚ ngerman result, from
central Sweden, is representative of a location near the center of a former ice sheet, with crustal rebound exceeding the increase in
ocean volume throughout the melting and post-glacial phase. The Andøya result, from the northwest coast of Norway, and the
Nanortalik result, from southern Greenland, are representative of sites near the edge of an ice sheet. Initially, the rebound dominates,
followed by a period when the increase in ocean volume dominates and a later phase when the rebound is again dominant. In the
case of the Greenland signal, a major contributor to the sea-level change is from the North American deglaciation. The East Antarctic
site of Vestfold Hills is similar to that of Andøya indicating that substantial changes in ice volume occurred here before the area
became ice-free. The southwest England result is representative of locations outside of the ice sheet where the crustal rebound after
the onset of melting is one of subsidence. The signal is initially dominated by the increase in ocean volume and later by the crustal
response. The Sunda Shelf and Barbados locations are far-field sites, and the sea-level signal is dominated by the change in ocean
volume, modulated by glacio-hydro-isostatic contributions. The North Queensland site is representative of far-field continental
margins where a small-amplitude highstand forms in Late Holocene time due to the water-loading component. At the mid-ocean
island site of Kiritimati, the change in sea-level is virtually constant for 5,000 years due to a cancellation out of the various isostatic
contributions to sea-level change.
GLACIO(HYDRO)-ISOSTATIC ADJUSTMENT
297