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OCR for page 73
4
Glacial Isostatic Adjustment and
Relative Sea-Leve! Change
W. RICHARD PELTIER
University of Toronto
ABSTRACT
Secular trends of relative sea level revealed on tide-gauge records have recently been interpreted as
requiring some eustatic increase of sea level to have occulted during the past century. Although
allowance in interpreting these data is usually made for a contribution due to thermal expansion of
ocean volume, it is not generally recognized that the continuing influence of glacial isostatic
disequilibrium also contributes significantly to the observed secular trends. The eastern seaboard of
the continental United States is a geographical region in which this source of "contamination" is
especially large. This fact is discussed in illustration of a global model of deglaciation-induced
relative sea-level change, which may be employed to filter the isostatic signal from the tide-gauge
data. The same geophysical model has also been successfully employed to explain certain anomalies
of the Earth's rotation that have been previously invoked to support the notion that a eustatic increase
of sea level must be occurring at present. The anomalies consist of the ongoing wander of the
rotation pole toward Hudson Bay at a rate near 1° per million years, and the so-called nontidal
component of the Earth's acceleration of rotation that has recently been observed with the LAGEOS
satellite. Both anomalies are explicable as memories of the most recent deglaciation event of the
current ice age.
INTRODUCTION
The purpose of this chapter is to review results of re-
search conducted over the past decade concerning the nature
of relative sea-level (RSL) variations forced by disintegra-
tion of the huge continental ice sheets that covered Can-
ada, Northwestern Europe, and West Antarctica at Wurm-
Wisconsin maximum 18,000 years ago (18 ka). The melt-
ing of these ice sheets was essentially complete by 7 ka
73
and resulted in a net rise of mean sea level over the global
ocean of about 130 m. The rate of eustatic rise during the
glacial-interglacial transition was therefore approximately
10 mm/yr. In spite of the fact that melting has been
complete for so many millennia, RSL continues to vary in
response to this cause due to the extremely high value of
the effective viscosity of the planetary mantle that governs
the rate of return to isostatic (gravitational) equilibrium.
To fix orders of magnitude it is useful to recall that pres
OCR for page 74
74
~1_~_~
W. RICHARD PELTIER
~I' ...
.
1 . _._ .-....
_:
_
.~.,,~. ~:~.,,,~:~''~"''"''' 'I
.,,x,, ,;,
{ ~.'.' '"-,."''L''''''' :~"'"'-"'~'w'~ 't^""'''''''''''''1' ~ ~
.. , A , ,,, ~ .~ . . ..
, . i .. . ~ .. ~ ... ~.~ ... .. .' ~ ~ ~ :
FIGURE 4.1 (a) This photograph shows a flight of raised beaches
that are located in the Richmond Gulf on the southeast shore of
Hudson Bay near the center of postglacial rebound. (b) The
relative sea-level (RSL) curve from the Richmond Gulf beaches
shown in (a). The age of individual horizons is determined by
~4C dating of relict beach material.
ent-day rates of RSL fall in the three regions that were
previously ice covered are approximately 1 cm/yr. The
main observational data that have been employed to dem-
onstrate this fact consist of ~4C-controlled RSL histories in
the age range O to 12 ka. These data are obtained from
flights of raised beaches such as those shown in Figure
4. 1 a, which are located in the Richmond Gulf on the south-
east shore of Hudson Bay near the center of postglacial
30c
200
IOC
CC
O i 1 ~
, ,~,
8 7 6 5 4 3 2 1 o
1000 YEARS BP
rebound. Individual relict beaches in the sequence may be
dated using the radiocarbon method and their heights above
present-day sea level plotted as a function of their age to
obtain a local history of relative sea level such as that
shown in Figure 4.1b for the Richmond Gulf sequence.
Such data make up the primary geophysical database for
the inference of mantle viscosity, a physical parameter
that is fundamental to the understanding of continental
OCR for page 75
GLACIAL ISOSTATIC ADJUSTMENT AND RELATIVE SEA-LEVEL CHANGE
drift and many other geodynamic processes. A recent
review of solid-earth geophysical applications of RSL data
is provided in Pettier (1982~.
Although radiocarbon data on raised beaches, such as
those shown in Figure 4.1, demonstrate that the surface of
the solid earth has been rising monotonically with respect
to the geoid since glaciation was complete at sites that
were once ice covered, the opposite sense of RSL vari-
ation has persisted in the regions immediately peripheral
to the margins of the major ice sheets. That this should be
the case is simply understandable on the basis of the prin-
ciple of conservation of mass. At glacial maximum, the
Earth is depressed under the weight of the ice, approxi-
mately by the amount required for the buoyant restoring
force due to the surface deflection (the Archimedes force)
to balance the weight of the load. The material that must
be removed from beneath the ice sheet to accommodate
the sinking of the Earth flows viscously into the immedi-
ately peripheral region where the land is elevated. This
region will subsequently be referred to as the peripheral
bulge. When the ice sheet disintegrates, this process re-
verses and the land rises with respect to sea level in places
that were once ice covered, and beaches such as those
shown on Figure 4.1 are cut into the land where it contacts
the sea, thus constituting a history of the recovery process.
In the peripheral region, however, the land sinks with
respect to sea level and relict beaches are drowned. An
excellent example of a drowned coast produced by glacial
peripheral bulge collapse is provided by the east coast of
the continental United States, all of which is peripheral to
the huge Laurentide ice mass that covered Canada 18 ka.
An illustrative set of '4C-controlled RSL data from sites
along this coast is shown in Figure 4.2. Inspection of these
2
4
1 1 _
12
13
= f /~
,8. of hiss /
61~\/pi,
, / ~ ,,/
I 11
10 9 87
,:~;
,,
6 5 4 3 2 1 0
TIME (Kyr BPJ
FIGURE 4.2 Relative sea-level data from a number of sites
along the east coast of the United States. Adapted from Bloom
(1967~.
75
data demonstrates that the rate of sea-level rise at some
sites along the coast (e.g., Barnstable, Massachusetts) is in
excess of 1 mm/yr. Although this rate is an order of mag-
nitude less than the rate of sea-level fall that obtains within
the central Laurentide depression, it is nevertheless a rate
that is rather significant from several points of view.
Most important for our purposes is the fact that this rate
of RSL rise is close to that which has been inferred on the
basis of tide-gauge observations of secular sea-level trends
and interpreted in terms of implications for climate change
(e.g., Hansen et al., 1981~. Recent analyses of these data
(reviewed by Barnett, Chapter 1, this volume) reinforce
the conclusions of earlier workers to the effect that on a
global basis the data suggest that RSL is currently rising at
a rate of 1 to 2 mm/yr. Gornitz et al. (1982), for example,
concluded that the tide-gauge data imply a global increase
of RSL at a rate near 1 mm/yr. The most straightforward
interpretation of this observation, assuming that the claim
made for its global validity is justified, is that the volume
of water in the global ocean is currently increasing. Al-
though this could, in principle, be caused by thermal ex-
pansion of the water column (a process discussed in detail
by Roemmich, Chapter 13, this volume), the estimate by
Gornitz et al. (1982) of the possible contribution owing to
this effect suggests that it is able to explain no more than
50 percent of the observed rate of RSL rise. If this is a
valid upper bound, it implies that the mass of water in the
oceans must also be increasing and, therefore, that water
"normally" stored in continental ice complexes is being
returned to the oceanic reservoir, this being the only con-
ceivable source for the amounts of water required to bal-
ance the observation. Hansen et al. (1981) suggested that
this implied wastage of continental ice masses could be
the first indication of the global climate amelioration that
is expected as a result of the increasing atmospheric con-
centrations of carbon dioxide and other "greenhouse" gases.
Meier (1984) recently discussed the compatibility of this
hypothesis of a current retreat of continental ice with the
available glaciological evidence. His conclusion (also
discussed in Chapter 10, this volume) is that although
there is no evidence supporting the possibility of a signifi-
cant ongoing reduction of either Greenland or Antarctic
ice, there is strong evidence to the effect that a reduction in
volume of the small ice sheets and glaciers of the world is
occurring, which could very well provide the mass re-
quired to balance the RSL analyses of Gornitz et al. (1982~.
The possible climatological implications of the secular
variation of RSL, discussed above, that has been extracted
from the tide-gauge data, are clearly important. They do
hinge crucially, however, on the assumption that the secu-
lar trend of 1 to 2 mm/yr is a number that is globally
representative. Unfortunately, and as discussed at length
by Barnett (Chapter 1, this volume), the existing network
OCR for page 76
76
of tide gauges does not provide uniform coverage over the
globe so that a severe sampling problem exists. Further-
more, many of the most heavily instrumented coastlines of
the world, such as the west coast of the North American
continent and coastal Japan, are strongly influenced by
local tectonic processes and, therefore, are unlikely to
provide any reliable information on eustatic water rise. At
these locations, the vertical motions of the solid earth
associated with the dominantly strike-slip earthquakes that
mark the San Andreas Fault and the dip-slip earthquakes
associated with active subduction in the Japan trench are
expected to obscure the eustatic signal. Other heavily
instrumented coastlines such as the passive continental
margins of the east coast of North America and northwest-
ern Europe might be considered more likely regions to
provide a signal that is free of such tectonic contamina-
tion. These coastlines are however located, respectively,
on the forebulges of the ancient Laurentian and Fenno-
scandian ice sheets so that, as discussed above, sea level in
these regions will appear to be rising as a consequence of
the sinking of the land with respect to the geoid that
accompanies the isostatic readjustment of the surface fol-
lowing deglaciation. If it were possible to correct these
passive margin data for the influence of glacial isostatic
disequilibrium, the residual trends so obtained might be
particularly useful as constraints on the current rate of
eustatic water rise (fall) cause by steric and ice-sheet dis-
integration effects.
Over the past decade a geophysical model has been
developed that is ideally suited to the task of filtering from
the RSL record, at any tide-gauge station on the Earth's
surface, the contribution to the secular change of RSL
resulting from current glacial isostatic disequilibrium. This
model is based on the mathematical analysis of the defor-
mation of a viscoelastic Earth produced by surface mass
loads originally presented in Peltier (1974~. It was first
employed by Peltier and Andrews (1976) to predict vari-
ations of RSL forced by Pleistocene deglaciation; their
calculations were based on the assumption that the water
produced by ice-sheet melting could be assumed to be
distributed uniformly over the ocean basins. Farrell and
Clark (1976) showed how this mathematical analysis could
be extended to determine the way in which the meltwater
must be distributed within and among the ocean basins
such that the instantaneous geoid remained an equipoten-
tial surface at all times during and subsequent to the ice-
sheet disintegration event. The first predictions of ex-
pected RSL variations with the complete theory were
described in Clark et al. (1978) and Peltier et al. (1978~.
By comparing these predictions with t4C-controlled RSL
observations such as those illustrated in Figure 4.1, it was
demonstrated that a large fraction of the variance in the
global RSL record over the age range 0 to 18 ka could be
W. RICHARD PELTIER
explained. In particular the previously enigmatic observa-
tion of raised beaches at sites in the southern ocean at
times subsequent to 6 ka (e.g., Russell, 1961) was shown
to be a natural consequence of the global-scale viscoelas-
tic adjustment process following a deglaciation that ended
about 7 ka.
Although one other global model of RSL change has
also been produced (Cathles, 1975), it suffers from two
crucial flaws. First, it is not gravitationally self-consistent
and so does not accurately predict far-field RSL data;
second, it does not incorporate a surface lithosphere and so
cannot accurately predict RSL data in the near field. All
of the discussion to be presented here will therefore be
based on the more accurate model.
In the past few years several additional geophysical
observations have been shown to be explicable in terms of
extensions of the same theory developed in the papers
cited above to explain deglaciation-induced RSL change.
The large-scale negative free-air gravity anomalies ob-
served over the three main centers of postglacial rebound
have been shown to be compatible with the same visco-
elastic model that fits the RSL data (Peltier, 1980, 1981;
Peltier and Wu, 1982; Wu and Peltier, 1983~. Also, the
large misfits between predicted and observed RSL data
(Peltier et al., 1978; Clark et al., 1978) at sites in the
peripheral bulge regions have been shown to be due to the
neglect of the influence of the surface lithosphere (Peltier,
1984b). Finally, two rather important and previously
unexplained anomalies in the Earth's rotation, namely, the
true wander of the rotation pole toward Hudson Bay at a
rate near 1°/106 yr, which is revealed in the International
Latitude Service path, and the so-called nontidal compo-
nent of the acceleration of the axial rate of rotation, which
has recently been observed using the LAGEOS satellite,
have also been shown to be consistent with the same
viscoelastic Earth structure (Sabadini and Peltier, 1981;
Peltier, 1982, 1983, 1984a, 1985a; Peltier and Wu, 1983;
Wu and Peltier, 1984~. That the latter effect might be due
to glacial isostatic adjustment was first suggested by Dicke
(1969), who suggested that it could be employed to con-
strain mantle viscosity a notion that was later investi-
gated in more quantitative fashion by O'Connell (1971~.
The former observation is particularly important as it was
originally invoked by Munk and Revelle (1952) in support
of the notion that some current retreat of the Earth's major
ice sheets must be occurring to account for it. Their
argument has been resurrected in the recent literature on
the secular variation of RSL seen on tide gauges, in sup-
port of the same idea (e.g., Barnett, 1983~. The analysis
first reported in Peltier (1982) demonstrated that the theo-
retical argument employed by Munk and Revelle is incor-
rect, however. When the radial variations of viscoelastic
structure of the real Earth are properly taken into account,
OCR for page 77
GLACIAL ISOSTATIC ADJUSTMENT AND RELATIVE SEA-LEVEL CHANGE
it is shown that the observed polar wander toward Hudson
Bay can be explained entirely as an ongoing effect due to
the deglaciation event that ended about 7 ka. No current
wastage of continental ice is therefore required to under-
stand this observation, and the data may in fact be con-
strued as arguing against this possibility.
The remainder of this chapter provides a more detailed
discussion of the evidence cited above to the effect that
this viscoelastic model does in fact fit the wide range of
geophysical data. Since the model does fit, in particular,
the observed RSL record in the age range 0 to 18 ka rather
well, it may reasonably be employed to predict the pres-
ent-day rate of RSL variation that should be occurring at
any site at which a tide gauge is located. This is the
secular change that a tide gauge should record if glacial
isostatic disequilibrium were the only source of RSL change
at the site in question. The viscoelastic model is then
employed to predict the present-day rate of vertical motion
with respect to the geoid of the surface of the land every-
where on the North American continent. A map of this
field is presented. This demonstrates that present-day
rates of RSL rise along the U.S. east coast caused by
glacial isostatic disequilibrium may be as high as 2 mm/yr.
The field theory is then employed to filter this effect from
the secular trends observed on all tide gauges located
along both the east and west coasts of the continental
United States. The average of the residual trends at U.S.
East Coast sites is still significantly different from zero
and has a value near 1 mm/yr. However, variations about
the mean are extreme on rather small spatial scales and
indicate contributions to the residual from sources other
than eustatic water rise. In conclusion, a brief summary
and discussion of future prospects for further applications
of the isostatic adjustment model of RSL change reviewed
here is presented.
THE GLOBAL MODEL OF GLACIAL ISOSTASY
The mathematical structure of the global model of gla-
cial isostatic adjustment has been reviewed in Pettier (1982),
to which the interested reader is referred for details and for
a much more complete review of the history of this subject
than could be presented here. In this model the planetary
interior is assumed to be radially stratified with an elastic
structure fixed by observations of the frequencies of the
elastic gravitational normal modes of free oscillation as
described, for example, by Gilbert and Dziewonski (1975~.
The rheology of the interior is assumed to be linearly
viscoelastic and of the "Maxwell" type, in which the initial
response to an applied shear stress is Hookean elastic, but
the final response is Newtonian viscous. The depth-de-
pendent viscosity in the model is therefore the only pa-
rameter that one can vary in order to fit RSL data, such as
77
those shown in Figure 4.1. In the actual prediction of such
RSL variations, one assumes a melting history for all of
the surface ice loads that exist at glacial maximum and
then computes, in a gravitationally self-consistent fashion,
the manner in which the meltwater must be distributed
over the global ocean in order to ensure that the instanta-
neous surface of the new ocean is maintained as an equi-
potential surface at all times. This operation requires in-
version of an integral equation at every instant during and
subsequent to the deglaciation, and results in a direct pre-
diction of the time-dependent separation of the geoid and
the surface of the solid earth at any point on the Earth's
surface where ocean and land meet. In the model the
geography of oceans and continents is realistically de-
scribed and the full effects of gravitation are accounted for
including the gravitational attraction of the water by the
ice and the self-attraction of the water. The integral equa-
tion is inverted using a finite-element discretization of the
surface, and a Green's function formalism is employed to
describe the gravitational interactions between the aqua-
sphere, cryosphere, and solid-earth components of the
model that are fundamental to the determination of sea-
level change. It is important to be able to make a reason-
ably accurate a priori estimate of the deglaciation history
subsequent to 18 ka since we would not otherwise be in a
good position to invert the predictions of the model to
recover the radial variation of mantle viscosity. Pettier
and Andrews (1976) described the way in which i4C-age-
controlled terminal moraine data can be combined with
far-field observations of RSL and ice-mechanical consid-
erations to develop first-order models of the glacial chro-
nology. Their initial model, called ICE-1, has since been
improved by Wu and Pettier (1983), who have called the
new model ICE-2. This model is illustrated in Figure 4.3.
The forward problem for RSL prediction takes as input
this glaciation history and a model of the planet's radial
viscoelastic structure and produces as output a prediction
of the RSL variation that should be observed at any site of
interest. These predictions are illustrated in the following
subsections.
Postglacial Variations of Relative Sea Level
Typical examples of observed and predicted RSL vari-
ations at a number of sites on the North American conti-
nent are illustrated on Figure 4.4 for six locations, three at
sites that were once ice covered (a, b, and c) and three for
sites along the east coast of the continental United States
in the peripheral region of monotonic subsidence (d, e, and
f). The Earth model employed to make these predictions
has elastic structure 1066B of Gilbert and Dziewonski
(1975), an upper mantle viscosity of 102 Pa s, and a lower
mantle viscosity beneath 670 km of 2 x 102~ Pa s. On
OCR for page 78
78
FIGURE 4.3 Time slices through the ICE-
2 deglaciation chronology of Wu and
Peltier (1983~. Ice thickness is shown at
three times for both the Laurentian and
Fennoscandian ice sheets.
(e) 8,000 B. ~
Figure 4.4, comparisons are shown for three different
models that differ from one another only in terms of their
lithospheric thicknesses. Inspection of these comparisons
shows that the RSL data at sites inside the ice margin are
reasonably well fit by the theoretical model and that the
RSL variations at these sites are rather insensitive to changes
of lithospheric thickness. This is entirely expected as the
spatial scale of the Laurentian ice sheet (Figure 4.3) is so
large that the lithosphere is transparent to the response at
locations that were once under the ice-sheet center. At
sites in the peripheral region, on the other hand, the re-
sponse is extremely sensitive to lithospheric thickness as
the deformation at such sites is significantly affected by
relatively short horizontal wavelengths that see the litho-
sphere clearly. This sensitivity was first exploited (Peltier,
1984b) to measure lithospheric thickness, and a relatively
high value in excess of 200 km was obtained. As reviewed
(o ) 18,000
(c) 12,000 B.P
W. RICHARD PELTIER
( b ) 18,000 B. ~
(d) 12,000 B.P
~3: ~
,_ i.:::.:
mxi.-...-...'.'..-...22,'
a.:.. ....
.........
... ..
. ,::::::: ::
...........
.. .......
.........
. .........
&,, . ,.~,.' a.,
/' ''', ','
~ .
At' ^ ~("2:
(f) 8,000 B.P
in Peltier (1982), the totality of i4C-controlled RSL data
also requires an almost uniform profile of mantle viscosity
with little variation between the upper and lower mantles.
Weertman (1978) commented on this result from the point
of view of theoretical ideas concerning the microphysical
basis of solid-state creep in the Earth and suggested that it
might be taken to imply that the relaxation of the lower
mantle that occurs in postglacial rebound is controlled by
transient creep rather than the steady-state creep, which is
assumed in the Maxwell analogue. This possibility may
be tested using the simple Burger's body rheology derived
in Peltier et al. (1981), which includes the transient com-
ponent of the response via a single Debye peak governed
by two additional physical constants. An analysis of the
asymptotic properties of the Burger's body rheology,
however, demonstrates that when the elastic defect is large
and the short- and long-time-scale viscosities sufficiently
OCR for page 79
GLACIAL ISOSTATIC ADJUSTMENT AND RELATIVE SEA-LEVEL CHANGE
different, the Burger body rheology again behaves like a
Maxwell solid but with a viscosity equal to that which
governs the short-time-scale transient response. Under
these circumstances the lower mantle viscosity inferred by
analysis of rebound data based on the Maxwell analogue
would be the transient viscosity as originally suggested by
Weertman (19781.
The Free-Air Gravity Anomaly over Centers of
Post-Glacial Rebound
Figure 4.5 shows maps of the free-air gravity anomalies
over the present-day centers of postglacial rebound in
Canada [Figure 4.5(a)] and Fennoscandia fFigure 4.5(b)~.
Comparison of these maps with those for ice thickness at
80C
60C
40C
-
~n 200
O
_
-200
450:
350
-
~ 250
-
J
150
50
o
-50
25
Ol
-
~ -25
J
- 50
-75k
1066B NULM = 2 x 10
- -- L =245.4 km
L ~ 195.6 km
L= 120 7km
._ .
-100
- 18 - 14
- 10 - 6
-2 2
CHURCHILL
800
60C
40C
20C
20C
25
o
-25
-50
-75
-100
1066B NULM = 2 x 10
- L = 245.4 km
- ~L=195.6km
. ~L = 120. 7 km
If,
SOUTHAMPTON IS.
'I
1066B NULM = 2 x 10
hi, - -- L = 245.4 km
L=195.6km
Nt --- L=120.7km
1 1 1 1 1
. BRIGANTINE N.J.
~-
,~ ""
25
o
-25
-50
-75
_ -100 _
_ -18
TIME (kyrs)
OTTAWA IS.
........ 1
=:~. 1066B NULM - 2 x 102
-- ~ L = 245.4 km
it;. L=195.6km
\~;L L - 120. 7 km
1 1
N.Y. CITY
A
\ ~ Hi.
........ ~ _
AL,_ hi,, .
·'l.lit ...
t 1 ~
1066B NULM = 2 x 10
- - - L = 245.4 km
- L = ! 95 .6 km
L- 120 7km
1 1 1 1 1
DELAWARE
~T ~ / .-
~/
,.....
... ... . ~ 1066B NULM = 2 x 102
--- L =245.4km
L = 1 95 .6 km
L = 120 7km
~,1
-14 -10 -6 -2 2
79
glacial maximum, shown previously in Figure 4.3, demon-
strates a high degree of correlation between these two
fields and provides strong support for the hypothesis that
the observed free-air anomalies are to be interpreted as
measures of the currently existing degree of isostatic dis-
equilibrium of these two regions. Figure 4.6 shows a
comparison of observed and predicted present-day peak
free-air anomalies for Laurentia and Fennoscandia for a
number of Earth models having fixed lithospheric thick-
ness of 120.7 km, and an upper mantle viscosity of 102~ Pa
s as required by the sea-level data discussed previously.
The Earth models employed differ from one another only
in terms of their elastic structures, and lower mantle vis-
cosity is varied through the same sequence of values for
all models. As described in the figure caption, four of the
FIGURE 4.4 Observed RSL histories at 6
North American sites and predictions based
on the ICE-2 melting chronology coupled
with an Earth model having 1066B elastic
structure, an upper-mantle viscosity of 102'
Pa s, and a lower-mantle viscosity of 2 x
102' Pa s. Theoretical predictions are shown
for models that differ only in their
lithospheric thicknesses. The response is
sensitive to this parameter only at the last
three sites (d, e, and f), which are located
in the peripheral bulge region south of the
ice sheet margin along the U.S. east coast.
OCR for page 80
80
FIGURE 4.5 Observed free-air gravity
anomalies over (a) Canada and (b) Fenno-
scandia. The locations of these anomalies
should be compared with the ice-sheet
topographic maxima shown on Figure 4.3.
models are flat, homogeneous, layered approximations to
the 1066B elastic structure that have either one or two
internal discontinuities of elastic parameters within the
mantle at 420 km and/or 670 km depth corresponding to
the depths to the olivine ~ spinet and spinet ~ post-
spinel phase boundary horizons. The remaining two curves
7()~
60 _
so
~ 30
cr
(a ~ cAuRENT'a
sex
//'
10 21 lo2
LOWER MANTLE VISCOSITY (10 Pas)
FIGURE 4.6 Observed (hatched regions) and predicted peak
free-air gravity anomalies for both Laurentia and Fennoscandia.
Predictions of the peak free-air anomaly are shown as a function
of lower mantle viscosity with the upper mantle value held fixed
at 102' Pa s and the lithospheric thickness fixed at 120 km. The
individual curves are predictions for models that differ only in
their elastic structures: (x) 1066B; (O) PREM; (+) flat
W. RICHARD PELTIER
are for the seismically realistic models 1066B of Gilbert
and Dziewonski (1975) and PREM of Dziewonski and
Anderson (19811. In these models, all of the radial vari-
ation of density is treated as though it were nonadiabatic.
Inspection of these results shows that fitting the observed
free-air gravity anomalies with a model with weak radial
7OI
( b ~ FENNOSCAND'A
n,(
50 _
-
~ 40
-
cr
,9
loo 101 lo2
LOWER MANTLE VISCOSITY (10 Pas)
incompressible approximation to 1066B with a single internal
density discontinuity with 12 percent increase at 670 km depth:
(V) same as (+) but having a 6 percent increase at 670 km depth
and a 3 percent increase at 420 km depth; (/\) same as (+) but
having only a 6 percent increase of density at 670 km depth; and
( CJ) same as (+) but having no internal density discontinuities in
the mantle. See text for discussion.
OCR for page 81
GLACIAL ISOSTATIC ADJUSTMENT AND RELATIVE SEA-LEVEL CHANGE
variation of viscosity requires the presence in the model of
significant internal buoyancy associated with a density
structure that behaves nonadiabatically on the time scales
of glacial rebound. This requires at least that the density
variations across the phase boundaries at 420 and 670 km
depth behave in this fashion, which is possible only to the
extent that these transitions may be considered univariant
(e.g., O'Connell, 1976; Mareschal and Gangi, 1977~. Al-
though such behavior is not inconceivable, it may also
prove possible to reconcile these data by appealing to
other physical effects. This is clearly an extremely impor-
tant issue insofar as the problem of mantle convection is
concerned (Peltier, 1985b). In any event, the demonstra-
tion that the incorporation of internal buoyancy of the
mantle allows the essentially isoviscous model preferred
by the sea-level data to simultaneously reconcile the large
observed free-air anomalies does rather strongly under-
mine the claim of Walcott (1970, 1980) that these anoma-
lies require that the viscosity of the lower mantle be high.
PLEISTOCENE DEGLACIATION AND
EARTH ROTATION
From about 1900 until 1982 the location of the Earth's
north pole of rotation was carefully monitored by the ILS
using a global network of photo-zenith tubes equipped
observatories. Since 1982 this observing system has been
replaced by the much more accurate VLBI-based network
of the IRIS Earth-orientation monitoring system that rou-
tinely determines the pole position at 5-day intervals with
a verified accuracy of 2 milliseconds of arc (Carter and
Robertson, 1985~. Although these new data will quickly
replace the old as the industry standard, the duration of the
time series is still sufficiently short that the ILS data remain
the best source of information on the secular motion of the
pole. These data are shown in Figure 4.7 as x and y
components of the displacement relative to the axes shown
on the inset polar projection. The origin of the coordinate
system corresponds to the Conventional International Origin
(CIO). Inspection of these data, which are based on the
reduction by Vincente and Yumi (1969, 1970), demon-
strates that the dominant oscillatory signal, which consists
of a 7-yr periodic beat generated by the interference be-
tween the 14-month Chandler and 12-month annual
wobbles, is superimposed on a secular drift at the rate of
0.95° + 0.15°/106 yr toward Hudson Bay. The direction of
this drift is shown by the arrow on the inset polar projec-
tion of Figure 4.7.
In 1952, Munk and Revelle interpreted this observed
secular drift of the rotation pole as requiring some present-
day variation of surface mass load and suggested that the
cause of the apparently required variation might be found
in the melting of ice on Greenland and/or Antarctica. Their
inference that such an effect was required to explain the
81
data was, however, based on a dynamical model in which
it was assumed that the Earth could be treated as a homo-
geneous viscoelastic sphere insofar as its rotational re-
sponse to surface loading was concerned. To the extent
that this approximation is valid, the inference of Munk and
Revelle is completely correct since the theory then shows
that the pole must be fixed at any instant of time in which
the surface load is steady. As demonstrated by Peltier
(1982), this holds true for homogeneous Earth models,
since in this limit the isostatic adjustment and rotational
contributions to the rotational forcing exactly annihilate
one another. For radially stratified models, however, the
dynamical symmetry that underlies this cancellation is
broken and polar wander can occur even at a time when
the surface load is steady. It therefore becomes plausible
that the secular drift of the rotation pole shown on Figure
4.7 could simply be an effect due to the influence of
planetary deglaciation that began 18 ka and ended about 7
ka. In Peltier (1982), Peltier and Wu (1983), Peltier (1984a),
and Wu and Peltier (1984), it was in fact demonstrated that
both the observed rate and direction of drift were just as
expected if the Earth has the viscoelastic stratification
required by the previously discussed RSL and free-air
gravity data, and if the only forcing to which the system
has been subject is that due to a glaciation-deglaciation
cycle that ended about 7 ka.
Figure 4.8 illustrates the nature of the fit to the ob-
served polar-wander speed as a function of the viscoelastic
model employed to make the prediction. Observations of
oxygen-isotope composition in deep-sea sedimentary cores
(e.g., Peltier, 1982) are employed to constrain the cyclic
variation of planetary ice cover that has occurred over the
past 106 yr. These data demonstrate that the major conti-
nental ice masses have appeared and disappeared in a
highly periodic fashion with a time interval of 105 yr
separating successive interglacials. Individual glaciation
pulses in the sequence are each observed to have a sawtooth
form with a slow glaciation period lasting about 9 x 104 yr
followed by a fast collapse lasting 104 yr. The calculations
illustrated in Figure 4.8 are based on the assumption that
seven such cycles have occurred and the observed polar-
wander speed of about 1°/106 yr is shown at a time 6000 yr
following the last 104-yr disintegration event. Again this
choice gives a best fit of the simple glaciation history
model to the oxygen isotope data. Polar-wander speed
predictions are shown on this figure for six different vis-
coelastic models of the interior, each of which has the
same lithospheric thickness L = 120 km. The prediction
denoted by LOF (no core) is for the homogeneous model
and verifies that the predicted speed following the end of
the last glaciation phase of the load cycle is essentially
identically zero in accord with the theory of Munk and
Revelle (19521. However, as radial structure is added to
the model, the symmetry that enforces the null response in
OCR for page 82
FIGURE 4.7 Position of the rotation pole _ 470
relative to the CIO since 1900. See text 1900
for discussion.
the homogeneous model is broken, and the speeds pre-
dicted for times subsequent to the last glacial-deglacial
pulse differ from zero. The effect of adding an inviscid
high-density core to the model is illustrated by the calcu-
lation denoted LOF for which the elastic structure of the
mantle is taken to be the average of model 1066B, and the
mantle viscosity is assumed to have the value 102~ Pa s.
Model L1F includes, in addition, the influence of the density
jump at 670 km depth in the Earth based on the assump-
tion that this discontinuity is capable of inducing a buoy-
ant restoring force when it is displaced from equilibrium
by the applied surface loads. The effect of this internal
buoyancy in the mantle is to further increase the speed
prediction in the model with 102i Pa s uniform mantle
viscosity. Adding a second density discontinuity at 420
km depth (model L2F with uniform viscosity) does not
produce a significant further increase in the speed predic-
tion, however. The final calculation illustrated on Figure
W. RICHARD PELTIER
C
.470" ~\
~ \
I c LAUliNTlD~ ,_ ~ ASIA
\ATI ANTIC OCEAN ~NDM )/
~ 1
(X)
YEAR
1975
4.8, denoted L2F (VLM = 3 x 1021 Pa s), demonstrates that
the predicted speed can be reduced to the observed speed
simply by elevating the viscosity of the lower mantle to
the same value required by the free-air gravity and RSL
data discussed previously. As discussed in Wu and Pettier
(1984), this model also correctly predicts the observed
direction of polar wander. These results establish that the
data shown in Figure 4.7 cannot be construed as requiring
any currently ongoing variation in surface load due to ice-
sheet disintegration on Greenland and Antarctica. Rather,
they are entirely explicable as a memory of the planet of
the last deglaciation event of the current ice age, an event
that was complete by about 7 ka.
A second effect of deglaciation on Earth's rotation
addressed here concerns its influence on rotation rate and,
therefore, on the so-called length of day (l.o.d.~. Although
the most important ongoing change in l.o.d. is the decel-
eration of the rate of rotation due to the gravitational
OCR for page 83
GLACIAL ISOSTATIC ADJUSTMENT AND RELATIVE SEA-LEVEL CHANGE
interaction between Earth and Moon through the agency of
the lunar semidiurnal tide in the oceans, it has been known
for some time that at least one other source of l.o.d. vari-
ation must exist. Analysis of ancient eclipse data (e.g.,
Muller and Stephenson, 1975) demonstrated that if one
assumes that the lunar-tidal torque has been constant over
the past few thousands of years and uses this assumption
to predict the times and locations in the past of total
eclipses of the Sun and Moon, then as one goes further
back into the past, one makes an increasingly large sys-
tematic error in the predictions, which is such as to imply
the action of a nontidal acceleration of rotation that is
working in opposition to the tidal effect. Lambeck (1980)
summarized such estimates and concluded that the best
available from such data is the number (CO/CO)NT = (6.9 +
2.6) x 10-~/yr. A recent confirmation of this number has
been provided through analysis of 5.5 yr of laser-ranging
data to the LAGEOS satellite that has delivered an esti-
mated of (~/CO)NT = (7.1 + 0.6) x 10-~/yr (Yoder et al.,
1983~. Pettier (1982, 1983) demonstrated that this ob-
served rate of nontidal acceleration was also predicted as
an effect of the last deglaciation event of the current ice
age. In this analysis, exactly the same model as that
employed to fit the secular drift of the pole revealed in the
ILS data was employed to predict (CO/CO)NT, and the results
are shown on Figure 4.9. The three calculations illustrated
~ T------ .q
\
>L \ ~L2F(/M,~ncomp.lith.)
~ \~ / ~ LIF (~M . no 420 km disc
~ \\
· ~
PO LAR WANDER SPEED
L =120 km
\
\\E ;~)
-
L~: L O F ( n o core ) ~ _
O _1 ~ 1 ~ 1 ~
0 2 4 6 8 10
TIME (kyrs)
FIGURE 4.8 Predictions of polar-wander speed for several
different viscoelastic models discussed in the text. The observed
speed obtained from the secular rate of drift visible on Figure 4.7
is shown as the cross.
83
1.25~
1.00
o
x 0 75
-
~r
- 0.50
.31c:
025
1°7
/W _
/ ~ \
.. ,, ,
22 23 24
L0G'o ( z,~( poise ) )
0.6
0.5
o
0.4 -O
X
0.3 ~
_
Cal
.=
0.2
_ 0.1
O
FIGURE 4.9 Observed nontidal acceleration of rotation, (Cl)/C,))NT,
and equivalent J2 obtained from the analysis of laser-ranging data
to the LAGEOS satellite. Predictions are shown as a function of
lower mantle viscosity for models with 1066B elastic structure
and for models that include only one ice sheet (L), two ice sheets
(L + F), and three ice sheets (L + F + A). See text.
On this figure are for loading models that include only the
Laurentian ice sheet (L), one that also includes the effect
of the Fennoscandian ice sheet (L + F), and one that adds
the effect of the West Antarctic ice sheet melting to that of
the other two (L + F + A). The influence of the latter is
clearly much more important as a source of forcing for
rotation rate than as a source of forcing for polar wander.
_ All speed predictions are shown as a function of lower
mantle viscosity VIM with the upper mantle value held
; fixed at 1021 Pa s. Again, the preferred value of V! M is near
l 3 x 102~ Pa s. As mentioned previously, the lower-mantle
I viscosity could very well be associated with the transient
component of the response rather than with the steady
state component that would govern the long-time scale
thermal circulation. The manner in which the interpreta
tions of both of these rotational data are influenced by
small ice sheets and glaciers has been discussed in detail
by Pettier (19881.
SECULAR VARIATIONS OF RELATIVE SEA
LEVEL WITH GLACIAL ISOSTASY REMOVED
Given that the global model of glacial isostasy, de-
scribed above, is able to explain much of the observed
variability in the record of RSL change over the past 104
yr, it is natural to employ it to filter from the recent
historical record of tide-gauge observations of secular sea-
level change that component which is due to this cause.
OCR for page 84
W. RICHARD PELTIER
. ~ _ ~ ~ ~ i, k:
|~=.8mmyr~l tN: ~ 'A /''
FIGURE 4.10 Continent scale maps of the predicted rate of
vertical motion of the surface of the solid earth relative to the
geoid using a "best" viscoelastic model with parameters fixed by
fitting to the data of postglacial rebound and the ICE-2 deglaciation
history shown on Figure 4.3: (a) is for North America and (b) for
One simply employs the data in the long-time scale rec-
ords of RSL history (controlled by ]4C dating) to constrain
the viscous component of mantle rheology. One then
employs this Earth structure to predict the present-day rate
of sea-level rise and fall that should be observed at any
location at which a tide gauge is installed, subtracts this
prediction from the secular trend observed on the tide
gauge, and analyzes the filtered data so produced.
As a preliminary to this procedure, it is useful to first
illustrate the continent-scale variability of present-day RSL
variation that is predicted by the isostatic adjustment model.
Figure 4.10 shows the present-day rate of sea-level rise
and fall predicted for North America and northwestern
Europe using an Earth model with 1066B elastic structure.
The viscous component of themodel is one that has a litho-
spheric thickness of 200 km, an upper-mantle viscosity of
102i Pa s, and a lower-mantle viscosity of 2 x 102' Pa s.
This model provides a reasonably good fit to the 14C record
of RSL rise along the U.S. east coast when employed in
conjunction with the ICE-2 deglaciation history of Wu and
Pettier (19831. The rates shown in the continental interior
(where no ocean exists) represent the rates of separation
between the surface of the solid earth and the geoid at such
locations. (The geoid is an imaginary surface continued
inland from the oceans, on which the gravitational poten
Europe. Dashed contours are in regions in which the land is
currently rising out of the sea and solid contours are in regions
that are currently submerging. Rates of vertical motion are in
units of millimeters per year and the contour intervals are shown
on the individual maps.
tial has the same value as that obtained on the sea surface.)
Notable on these maps is the fact, mentioned above, that
the present-day maximum rates of RSL fall in the regions
that were once ice covered are near 1 cm/yr. Surrounding
each of the two main Northern Hemisphere centers of
postglacial rebound, however, are ring-shaped regions in
which RSL is predicted to be rising at rates that may be as
high as 2 mm/yr, a maximum calculated along the passive
continental margin of the U.S. east coast. The variation
with position along the coast is fairly extreme, however,
with very low calculated values obtaining both to the north
and to the south of the maximum. Notable also on this
map is the fact that the predicted rates of glacial isostatic
submergence along the U.S. west coast are rather different
from those on the east coast. The former region is much
further distant from the main Laurentian ice mass and is
also quite strongly influenced by the separate Cordilleran
ice sheet that existed west of the Canadian Rocky Moun-
tains. As a consequence of these effects, the predicted
variations of the rate of present-day RSL change along this
active continental margin are more complex.
Examination of Figure 4.10(b) illustrates a similar de-
gree of complexity of the pattern of present-day RSL change
predicted by the model for northwestern Europe. The
maximum present-day rates of RSL fall near the center of
OCR for page 85
GLACIAL ISOSTATIC ADJUSTMENT AND RELATIVE SEA-LEVEL CHANGE
uplift in the Gulf of Bothnia are again near 1 cm/yr.
Surrounding this central region of uplift is the region of
peripheral submergence. Again the latter region is very
strongly asymmetric with respect to the former, just as in
North America, a consequence of the geometric complex-
ity of the distribution of water and land. One important
feature of these results is the fact that rates of present-day
sea-level rise are predicted to be much lower along the
coast of France, which extends to the southwest away
from the center of uplift in Fennoscandia, than those along
the east coast of the United States, which is similarly
located with respect to the larger Laurentian ice mass.
Perhaps the most interesting aspect of the predictions
discussed above of the rates of present-day RSL variation
induced by the most recent deglaciation, is that they may
be compared directly to tide-gauge observations of these
rates at any point on the Earth's surface that may be of
interest. Figure 4.1 1 summarizes the comparisons. The
tide-gauge observations employed to construct this figure
consist of the secular trends extracted from the individual
U S EAST COAST INFER
~ (a
4 _
85
time series of observations at each gauge over the time
interval 1940 to 1980 as published in the recent catalogue
of the National Ocean Service (19831. Figure 4.11(a)
shows the results of the analysis for sites along the U.S.
east coast. Each cross represents the secular trend at a
specific gauge corrected for the secular trend expected
from the influence of glacial isostatic adjustment. These
corrected data are plotted as a function of the distance (in
radians) of each gauge from the station at Key West,
Florida, which is the southernmost station along the coast.
The northernmost data point is for the gauge at Eastport,
Maine. Also shown on this figure is the secular drift that
has been subtracted from the raw data to make the correc-
tion for isostatic disequilibrium. This correction attains a
maximum near 2 mm/yr about midway along the coast
with very small rates obtaining at sites in Florida and
Maine to the south and north of the maximum, respec-
tively. To give some indication of the error in the model
predicted rates, the predictions are shown not only for the
present (18,000 yr after glacial maximum) but also for
it'
U S. WEST COAST 1066 B
( b ) AV. RATE 17- 19 KYRS
AV. RaTE 17- 18 HIS
---- AV. RATE 18- 19 KYRS
1~
11 1 1 1 1 1 1 11 1 1 1 1 1 -3
00 0! 02 03 0.4 05 06 00 0 1 0.2 03 04 05 06
GAMMA (RADIANS) GAMMA (RADIANS)
FIGURE 4.11 Tide-gauge secular trends of RSL rise along the
(a) U.S. east coast and (b) west coast that have been corrected for
the glacial isostatic motions shown on Figure 4.10 are shown as
individual data points with the cross through the points indicating
the error assigned to these data by the National Ocean Service
(1983~. The magnitude of the correction that was applied to the
raw data is shown as a function of distance along each coast
measured positive to the north of the southernmost tide gauge,
which on the east coast is at Key West and on the west coast is
-2
rrl
C
I D
r
On
rrl
r
O r
- 1
11
at San Diego. Some indication of the error that might be involved
in making the correction is provided by the three estimates of the
isostatic rates computed at 500-yr separation through model
"present." The solid line through the corrected data on (a) is the
average secular rate of rise that remains after glacial isostatic
contamination has been removed. No similar average was
computed for the west coast data as the scatter is so extreme as
to imply that the average would be meaningless physically.
OCR for page 86
86
17.5 ka and 18.5 ka. Noticeable on these predicted curves
are the several locations at which the predicted rates devi-
ate from the smooth variation of rate with distance that
otherwise obtains. These are sites at which errors due to
the finite-element discretization occur (see Wu and Pettier,
1983, for a detailed discussion of the finite-element dis-
cretization employed to solve the sea-level equation).
The main point to note by inspection of the data shown
on Figure 4.1 lta) is that the correction, due to the influ-
ence of glacial isostasy, of the secular rate of RSL rise
along the U.S. east coast accounts for as much as 100
percent of the observed rate of rise at some sites. That is,
at some sites along the U.S. east coast, all of the observed
secular rates of rise are explicable in terms of the influence
of glacial isostatic adjustment. In general, however, there
is a systematic misfit between the predicted and the ob-
served rates such that the observed rate of rise exceeds that
predicted by the glacial isostatic adjustment model that
fits the long-time scale, ~4C-controlled RSL histories. At
no tide gauge along the U.S. east coast is the observed rate
of rise significantly slower than that predicted by the ad-
justment model. The average of the reduced rates of RSL
rise at sites in this region is also shown on Figure 4.1 lfa)
and is near 1.1 mm/yr. The interpretation of this average
in terms of a eustatic increase of sea level (either of steric
or nonsteric origin) is clearly made rather difficult by
virtue of the fact that the residual trends vary erratically as
a function of distance along the coast. Other physical
processes must be contributing substantially to the secular
variations of RSL that individual gauges are recording.
An identical treatment of the tide-gauge data from the
U.S. west coast is shown on Figure 4.11(b). Here, the
corrected tide-gauge-observed rates of RSL rise are shown
as a function of position, measured positive, north from
the southernmost gauge, which in this case is the one
located at San Diego. The observations along this active
continental margin are much more erratically scattered
than those along the passive east coast continental margin,
demonstrating the severe contamination of this record (for
our present purposes) that is presumably associated with
local tectonic activity. Furthermore, the corrected data are
scattered about zero and show no systematic bias toward
positive rates as is evident for east coast sites. It would
clearly be unreasonable to employ these data to make any
inference whatsoever concerning eustatic sea-level vari-
ations.
CONCLUSIONS
The analysis of RSL variations presented in the previ-
ous sections of this chapter demonstrate that effects due to
the most recent deglaciation of the current ice age con-
tinue in the modern record of sea-level change even though
W. RICHARD PELTIER
Wurm-Wisconsin ice had disappeared from the continents
by about 7 ka. In regions that were once ice covered, RSL
is currently falling at a rate near 1 cm/yr due to this cause.
In the immediately peripheral region of the collapsing
forebulge, sea level would appear to be rising at rates in
excess of 1 mm/yr due to the same process of glacial
isostatic adjustment, if this were the only effect operative.
The east coast of the continental United States is perhaps
the best location illustrating this "drowning" effect, which
is responsible for many of the unique features of its near-
shore environment, including the extensive occurrence of
salt marshes. A global model of glacial isostatic adjust-
ment was described that has been employed to filter from
the tide-gauge records of RSL change the influence of this
effect. Although it is especially useful along the U.S. east
coast, the model may also be applied to filter the global
data base before these data are employed to draw conclu-
sions concerning eustatic sea-level variations. An initial
attempt to perform such a global analysis has been pre-
sented by Pettier and Tushingham (1989), whose analysis
of all of the records in the data base (Permanent Service
for Mean Sea Level, Bidston Observatory, Birkenhead,
Mercyside, England) has led them to conclude that cor-
recting the observed secular sea-level trends for the influ-
ence of glacial isostasy reveals a global eustatic signal
with much increased coherence of strength of 2.4 + 0.9
mm/yr. It is noteworthy that the secular drift of the rota-
tion pole evident in the ILS pole path, which was previ-
ously interpreted by Munk and Revelle ( 1952) as requiring
some ongoing decrease in surface ice load and thus a
present-day increase in eustatic sea level, is also fully
explicable as a rotational memory of the Earth of the most
recent deglaciation of the current ice age, an event that
ended about 7000 ka.
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Representative terms from entire chapter:
sea level
