PALEOCEANOGRAPHY,
VOL. 1, NO. 3, PAGES313-337,
PALEOCLIMATIC
CONSTRAINTS
SEPTEMBER1986
ON THE
MAINTENANCE OF POSSIBLE
ICE-SHELF
COVER
IN THE NORWEGIAN AND GREENLAND SEAS
Dean R. Lindstrom
Department
University
and Douglas R. MacAyeal
of Geophysical
Sciences
of Chicago, Illinois
Abstract.
We examine
the
controver-
existence
of
ice
shelf
cover
in
the
sial issue of whether or not an integrated ice shelf existed
in the Norwegian
and Greenland seas during glacial
events
Norwegian and Greenland
seas are possible
through a comparison of the sedimentary
record
of
of
shelf
flow
the
Pleistocene.
Our
method
consists
of testing
for equilibrium
ice shelf
configurations
with the use of a finite
element model that predicts
ice shelf
evolution
under a variety
of atmospheric
and oceanic forcing
conditions.
Ice flow
at the margins of the simulated
hypothetical
ice
shelf
is
determined
Denton and Hughes' (1981)
from
one
of
reconstructions
of continental
glaciation
applicable
to
the last glacial
maximum.
Our results
suggest
that
the
existence
of
the
ice
ponding
to an area-average
basal
,
corres-
melting
rate of 0.50 m a-1 (ice equivalent),
near the upper limit
equilibrium.
Greater
to
cause
an
initial
is
allowing
ice shelf
heat flux is found
450-m-thick
ice
shelf
to rapidly
collapse.
The equilibrium
ice
shelf configurations
examined provide
effective
buttressing
support for the
marine ice sheet grounded in the Barents
Sea 18 kyr B.P.
Tests confirming
the
Copyright
1986
by the American Geophysical
Paper
number
6P0296.
0883-8305/86/006P-0296510.00
deduced
with
ice
from
our
sim-
ulations.
INTRODUCTION
An integrated,
floating
ice shelf
bridging
the Arctic
Ocean and the
Norwegian and Greenland
seas constitutes
a hypothetical
element of certain
reconstructions
of Pleistocene
glaciations
[Thomson, 1888; Mercer,
1970; Broecker,
during
the
last
(approximately
1977].
glacial
Its
existence
maximum
18 kyr B.P.),
for
example,
is proposed as a logical,
but by no means
necessary,
consequence of glaciated
continental
shelves
of
the
Arctic
Ocean
[Denton and Hughes, 1981; Grosswald,
1980].
If such an ice cover ever existed
during the past,
it would have created
substantially
different
climatic
and
glaciological
conditions
than those associated
with an expanded,
wind-driven
sea ice pack commonly reconstructed
for
the Arctic
Ocean during glacial
episodes
[Manabe and Broccoli,
1985; Manabe and
Hahn, 1977].
A thick
Union.
debris
patterns
1975; Hughes et al.,
shelf,
and possibly
surrounding
marinebased ice •heets,
depends most sensitively
on oceanic heat flux.
A heat flux
of approximately 4 ß 80 J m-2 s-!
ice-rafted
ice
shelf
cover
such
as
exists
today in the Ross and Weddell seas of the
Antarctic
would eliminate,
for example,
air-sea
heat exchange that occurs in pack
ice by conduction
and through small-scale
314
Lindstrom and MacAyeal:
leads
tions
and polynyas.
Ice
to brine rejection
seasonal
nate
sea
local
as that
Arctic
1981].
ice
formation
thermohaline
which
shelf restricassociated
with
could
elimi-
circulation
presently
such
maintains
the
Ocean halocline
[Aagaard et al.,
One would also expect ice shelf
cover to modify large-scale
thermohaline
circulations
such as those which today
transport
heat into the Norwegian and
Greenland
seas
from
the
North
Atlantic.
The northern
limit
of poleward heat flux
due to large-scale
meridional
overturning
in the North Atlantic
is apparently
de-
termined by the sea ice margin [Manabe
and Bryan, 1985].
An ice shelf would
presumably
from
its
push this
otherwise
position,
margin
"normal"
as is
the
Ross Sea [Zwally
case
the
Arctic
Ocean.
ice
in
iceberg-calving
An
Arctic
ice
Without
sheets
mix
climatic
sediment
present
at
shelf,
coastlines.
into
sheets
saddles
of
the
be ultimately
the North Atlantic
shelves
deposited
during
into
aphotic
events (T. B. Kellogg,
personal
terns,
and
characteristic
better
Arctic
interpret
time
ice
shelf
scales
cover
the geologic
OUR
continen-
discharged
[Hughes et al.,
CONTRIBUTION
We put
the
cerned with
controversial
issue
the interpretation
geologic record aside and simply investi-
marine
seas at
and Kara seas
to
exist
in
[Grosswald,
the
Barents
1980].
con-
of the
gate what atmospheric
and oceanic
tions are required to support ice
sheets
of
to
record.
1977].
In addition,
ice shelf restrictions
to continental
ice sheet drainage
might be a factor
permitting
stable
ice
could
or
and
domes
ice shelf
hypothetical
of
ice
units
ice
foraminifera
communication,
1986; M. M. Monaghan,
personal communication,
1986).
It would
be useful to know more quantitatively
the
climatological
constraints,
flow pat-
terminate
eliminate
than
foraminiferal
"gaps" in the
record would not necessarily
be
expected because bioturbation,
low sedimentation
rates,
and the possibly
short
which
the
rather
However,
sediment
could
length of this terminus
and
that ice accumulation
north
the
abundance
over
restrict
the
would require
tal
foraminiferal
complete absences,
and this evidence
is
used as an argument against
the existence
of an Arctic
ice shelf [Andrews, 1983].
periods
an ice
would
in
communication,
1986].
however,
reflect
minima
existed
would
fronts
shelf
Kellogg,
personal
These depletions,
time
1983].
on Ice Cover
sediment cores from the Norwegian Sea and
North Atlantic;
notably at the 18 kyr
B.P. glacial
maximum and at previous
glacial
isotopic stages [Kellogg, 1975;
1986; Mcintyre
et al.,
1972; T. B.
have
Ice shelf
cover could additionally
have modified
glaciological
conditions
in the continental
regions
surrounding
continental
Constraints
southward
for
et al.,
Paleoclimatic
cover in the Arctic
any time
condishelf
Ocean and neighboring
during
This investigation
the
Pleistocene.
was performed using
CONTROVERSY
a time-dependent finite
element computer
model of ice shelf dynamics normally used
The question
of whether such an Arctic
ice shelf did exist at times during the
tion [MacAyeal and Thomas, 1986].
simplify the preliminary analysis,
Pleistocene
concentrate
in
is
a matter
of
considerable
debate.
While there are sound glacial
dynamic reasons for suggesting
ice shelf
cover accompanying marine ice sheet for-
mation during glacial
maxima [Weertman,
1974; Denton and Hughes, 1981], the deepsea sediment
record,
not provide
clear-cut
in our opinion,
evidence
either
verifying
or denying
such an ice
existence
during
any period
of
does
shelf's
the
Pleistocene.
Marine micropaleontologists
generally
agree that large-scale
ice shelf cover
would be detected
by planktonic
foraminiferal
depletions
consistent
with the
ical
studies
ice
of
Antarctic
ice
on the portion
shelf
cover
in
shelf
evolu-
To
we
of hypothet-
the
Greenland
and
Norwegian seas as depicted by Denton and
Hughes' [1981] and Hughes' [1985] reconstructions
of the glacial
maximum at
18
kyr B.P. shown in Figure 1. The analysis
is further simplified by considering atmospheric and oceanic conditions during
the time period of the last glacial maximum. These results,
however, could be
equally applicable to other time periods.
Our method consists of simulating the
time evolution of this hypothetical
ice
shelf from an arbitrary
initial
condition
to see if
equilibrium
ice
thickness
and
aphotic sub-ice-shelf
environment (T. B.
Kellogg, personal communication, 1986).
conditions.
Such depletions
termine (1) whether a steady state ice
are
observed
in
deep-sea
flow is attainable
for given climatic
The study thus seeks to de-
Lindstrom
and MacAyeal:
Paleoclimatic
Constraints
7
on Ice
40•
Cover
315
30øE
20øE
4oø
10øE
8
0o
oøw
4
9
3
Iceland
-
Faeroe
Rise•14'
13
1oøw
40øW
5oOw
20øW
oøw
70øN
w
Fig. 1.
w
Reconstruction of glacial
Greenland Sea region after
cover at 18 kyr B.?. for the Norwegian and
Denton and Hughes [1981].
clude the ice shelf front (notched line),
grounded ice (heavy solid
line),
Features
illustrated
in-
the boundary between ice shelf and
ice sheet surface elevation
contours (solid
lines broken by elevation in meters), the boundary of the ice shelf drainage
basin (dashed and two-dotted line), subdivisions of the drainage basin used
for flux determinations (dashed and three-dotted line).
The heavy dashed line
defines the area included in the model grid, and stippled areas represent the
present subaerial
land surface.
basin
for
subdivision
reference
Numbers 1 to 15 are assigned to each drainage
from
shelf
can exist
and (2) what the ice
thickness
and flow regime would be so as
to provide more detailed
information
useful for interpreting
geologic
evidence
for or against
the ice shelf hypothesis.
Transient
ice shelf configurations
and
time
evolution
sed in
portant
scenarios
are
not
addres-
this paper,
but are considered
imissues to be investigated
later.
Table
3.
Climatic
tion
conditions
are
input
for
each
as boundary
simula-
condition
parameters and include (1) basal melting
or freezing
rates,
(2) surface accumulation or melting rates,
(3) basal and surface temperatures,
and (4) ice flux into
the shelf from the surrounding grounded
ice
of
sheets,
snow
determined
accumulation
from
over
assumed
the
ice
rates
shelf's
316
Lindstrom
snow
catchment
basins.
were
designed
to test
the
ice
these
shelf
to
The
the
combinations
A 46 x 50 element
(of 50-km resolution),
total
representing
for
sea region
the
Norwegian
(see Figure
of
stepped
forward
intervals
lapsed
450
until
(thinned
m.
accumulation
tures
consistent
of
the
grid
a
and Greenland
1).
The
model
through
time
the
shelf
ice
was
in
then
col-
below 20 m) or reached
a mass equilibrium
condition
in which
total
mass input as snow and from continental
ice sheet discharge
matched total
mass output
through basal melting
and ice
front
calving
(model integration
was
when the maximum thickness
at all
points was less than 0.01 m a-l).
METHOD
change
VERIFICATION:
PRESENT-DAY
SHELVES
One
of
the
most
crucial
elements
in
our research
is to verify
our method for
predicting
equilibrium
ice shelf compatibility
with climatic
conditions.
Under
ideal
circumstances,
this
would be accomplished
by demonstrating
that our method
could successfully
ice shelf existence
predict
during
patterns
with
and
equilibrium
a geologic
Cover
and tempera-
those
observed
Filchner-Ronne
terns
[Giovinetto
results
of
ice
on
shelves
and Bentley,
this
test
1985].
simulation
of
West Antarctica
are presented
in the appendix along with other details
of the
model input.
Clearly,
the performance of our equilibrium
ice shelf
prediction
method is
satisfactory
in that it produces an equilibrium
ice
shelf
cover
Weddell seas (Figures
halted
ICE
Ross
on Ice
[Thomas et al.,
1984; Robin et al.,
1983]
were applied
as climatic
constraints;
and
ice flux from the surrounding
grounded
portions
of the West Antarctic
and East
Antarctic
ice sheets were specified
consistently
with present-day
ice flux patThe
25-year
either
Constraints
basal
Each individual
model run began with
entire
ice shelf having an arbitrary
thickness
Paleoclimatic
of
area of 5.75 x 106 km2, was con-
structed
the
simulations
sensitivity
various
parameters.
and MacAyeal:
in
the
Ross
and
A2, A3, and A4).
Our model does not, however, successfully
predict
the existence
of the present
grounded ice sheet between the Ross and
Filchner-Ronne
ice shelves,
nor does it
predict
that the ice fronts
presently
occur within
the continental
shelf
region
rather
than at its outer edge.
These defects
are not considered
germane to the
issue of demonstrating
predict
the existence
shelf
cover.
However,
basal melting
rates in
West
Antarctic
ice
our ability
to
of equilibrium
ice
had we varied
the
our simulation
of
shelf
cover
an
ice
shelf
thickness
could have been produced
sufficient
to ground in the region
of the
present
grounded ice sheet.
Similarly,
had we required
a larger minimum thick-
time period
when its occurrence
is independently
verified.
For the Arctic
region this
is not possible
because of the
obvious lack of independent
geological
evidence.
We have performed
this test,
however,
in the context
of using our
method to predict
the existence
of
present-day
ice shelf
cover in Antarctica
West
(see appendix).
method may tend to "overestimate"
As a demonstration
of the validity
of
our methods,
we decided
to simulate
the
time evolution
of an ice shelf
covering
West Antarctica
to see if we could predict the present-day
existence
of the
extent
of ice shelf
cover when it is applied to the Norwegian and Greenland
seas.
This is not a serious difficulty
because of the geographic
differences
be-
Ross
region.
The Norwegian and Greenland seas
are abyssal ocean basins,
whereas the
grounded portions
of West Antarctica
that
we incorrectly
predicted
as an ice shelf
are a relatively
shallow continental
shelf.
Thus the only major region in the
Norwegian and Greenland
seas in which we
might predict
an ice shelf when grounded
ice would prevail
is over the Iceland-
be
and
Filchner-Ronne
consistent
with
ice
the
shelves.
technical
To
details
of our treatment
of the Norwegian and
Greenland
seas, we used the same 50-km
spatial
resolution
and time step size.
We emplaced an arbitrary
initial
ice
shelf,
450 m thick,
in the regions of
West Antarctica
where the present,
obser-
ved subglacial
topography (not corrected
for isostatic
depression) exceeds 400 m.
The
not
of
seaward
limits
allowed
to extend
the
continental
of
the
ice
shelf
were
beyond the margins
shelves.
Surface
and
ness
for
fronts
an ice
could
positions
It is
West
Faeroe
present
500
m.
Barents
to
eroded
exist,
the
back
to
ice
the
in which they are found today.
possible
to conclude from our
Antarctic
tween
shelf
have
demonstration
Antarctica
Rise
and
and
the
depths
It
also
is
the
Denmark
water
and Kara
that
are
this
the
Arctic
sea
Strait,
where
approximately
assumed
seas were
that
the
covered
by
Lindstrom
and MacAyeal:
Paleoclimatic
Constraints
on Ice
Cover
317
I START
L
Ji=i+]LJ
I
Temperature
I
boundary
condition
Analytic
STOP
HAS
ICE
SHELF
Y•
EQUILIBRIUM
temp.-depth
profile
Adjust
for
element
ice shelf
collapse
Stress
balance
Flow
ice
law
sheet
-
ice
boundary thickness
Boundary condition
or
shelf
changes
NO
Does
steady
ICE SHELF
DOES NOT EXIST
COLLAPSED?
state
STOP
EQUILIBRIUM
exist?
ICE SHELF
EXISTS.
Hass conservation
Boundary condition
time step size
•.• Hi+l]
Fig. 2.
Flow chart showing relationship
between parameters,
equation,
and boundary conditions
of the time-dependent
ice
in this study.
continental
glaciation,
considering
the possible
Arctic
shelf
ice
over
regions.
however,
the
shelf
those
respectively,
not
extension
of an
continental
subject
tutive relation
Paterson,
1981,
to
the
ice
given by [Glen,
p. 34]
consti-
1955;
This would be possible,
in a future
Arctic
so we are
governing
shelf model used
study considering
Ocean and surrounding
seas
ß
as
n-1
z = 'r
B-
1
(3)
T
a whole.
Variables
fined
MODEL EQUATIONS
The equilibrium
tions
ice
shelf
sought are defined
time and (2)
budgets in
stationary
flow regimes consistent
shelf
stress
model
cover
used
must
balance
to
simulate
solve
the
mass
in
--
V ß T - p g •
ice
and
= 0
(1)
(2_)
are
de-
m;
m a-1
snow-accumulation
tion rate,
with
equations
•__H
+ Vm
ß (uH)- i- • = 0
8t
Arctic
above equations
ice velocity,
surface
stress equilibrium
and the non-Newtonian
ice rheology.
Accordingly,
the finite
element
the
ice thickness,
time,
s;
configura-
to have (1)
balanced mass conservation
which the ice thickness
is
in
as:
basal
or
abla-
m a-1 water equivalent;
melting
or freezing
rate,
m a-1 water equivalent;
(VHß) horizontal divergence operator
(Vß)
full
T
stress
divergence
tensor,
operator
Pa;
p
ice density, kg m-3;
g
gravitational
m s-2.
unit vector
•
ß
z
z
acceleration,
orthogonal
geoid (pointing
strain
9.81
to the
upward);
rate tensor, s 1.
318
Lindstrom
and MacAyeal:
Paleoclimatic
Constraints
on Ice
Cover
(0.5 TijTij) 'õ second
invariantof
the
stress
tensor;
power law flow exponent relationship (set in our study equal to
three)
icestiffness
parameter,
Nm-2s
1/3
A flow chart summary of the numerical
model and the procedure
used to seek
equilibrium
ice shelf configurations
is
presented
in Figure
2.
The equations
are subject
to mass,
stress,
and temperature
boundary conditions on the ice shelf.
Mass gains or
losses at the top and botto• surfaces are
specified
by values of the A and B parameters,
respectively.
Mass flux is
specified
at lateral
ice shelf margins;
but not ice thickness
or normal velocity
(which are allowed to change during the
simulations).
At the narrow gap between
Greenland and Spitsbergen
which separates
the Norwegian-Greenland
Sea and Arctic
Ocean components of the ice shelf,
depicted in Figure 8-1 of Denton and Hughes
[1981],
This
mass flux
amounts
channel
is set equal to zero.
to assuring
constitutes
that
a natural
in our equilibrium
tion.
Certainly,
also exist,
as is
this
narrow
ice
divide
ice shelf configuraa nonzero flux could
depicted
in Figure 8-2
of Denton and Hughes [1981];
but this
scenario
Ice
is
not
considered.
flux
through other lateral
except the ice front,
ice shelf margins,
is specified
through
of
ment
consideration
basin
the
ice
of
the
shelf.
ice
This
the
sheets
basin
snow catchthat
is
feed
[1981].
The mass flux through the
grounded ice/ice
shelf boundary
(grounding line) of each subsystem is set
to the
onto the subsystem's catchment
thereby maintaining
mass equilib-
rium for
cipitation
tion are
statistics
precipitation
and
section.
At
shelf/open
amount which
the grounded regions.
rates
used in this
acquired
from climate
are
the
described
seaward
Snow prespecificamodel
in
ice
the
front
":'::::::::::F
.......
Fig. 3.
Precipitation
for 18 kyr B.P. over
pattern
predicted
the ice sheet region
that
Greenland
drains
Norwegian
illustrated
into
the
seas.
are
1 except
Symbols
the
same
that
for
as
contour
and
features
those
for
numbers
represent isopleths (centimeter
per annum
ice equivalent)
after Hughes [1985].
into 15 parts shown in Figures 1 and 3
according
to the ice sheet flow regime
reconstructed
by Denton and Hughes
falls
area,
==========================================
Figure
subdivided
equal
===================================================
next
(ice
ocean boundary) extending
and at the seaward ice front,
seawater pressure
is applied.
ice shelf/grounded
hydrostatic
For the
ice junctions,
veloci-
ties normal to the boundary are specified
as was described
above, but tangential
velocities
are arbitrarily
set to zero.
At the ice divide
boundary between Greenland and Spitsbergen,
the normal velocity
is set equal to zero, but free tangential
slip
is allowed.
These conditions
on
boundary velocity
allow the numerical
along the northern
boundary of the North
Atlantic
Ocean, balance is required
between iceberg
calving
and ice advection.
Stress boundary conditions
are applied
model to compute the stress regime (or
"back stress") compatible with steady
on
Boundary thicknesses are initially
set
equal to 450 m. At the end of each time
step, the average thickness of nodes
all
surfaces
of
the
ice
shelf.
On
the
top, wind force is assumed to be negligi.ble and is set to zero.
At the bottom
state mass balance
complex.
of
the
entire
glacial
Lindstrom and MacAyeal:
TABLE 1.
Paleoclimatic
Constraints
on Ice Cover
Summaryof Parameter Values Specified
Surface
for Each Simulation
Surface
Temperature,
Simulation
319
Basal Melting
Accumulation
Rate, m a- 1•
Rate, m a- 1'
Oc
-19.0
-19.0
-19.0
-19.0
-11.0
0.00
0.25
0.50
0.60
0.50
Oceanic Heat
Needed,J s- 1
0.225
0.225
0.225
0.225
0.225
5.82
1.17
1.40
1.17
0.00
x 1012
x 1013
x 1013
x 1013
*Ice equivalent
within
the ice shelf adjacent
to the
boundary node is computed.
The boundary
node thickness
is then changed to this
value if the computed average value is
greater
than 450 m. Computed average
values of less than 450 m imply grounding
line retreat
and would require
expansion
of our ice shelf grid.
Conditions
of
grounding
line retreat
were disregarded
in this study,
and when necessary,
boundary thicknesses
greater
than or equal
to 450 m were artificially
maintained.
calculation
of
the
ice
stiffness
transfer.
steady
zontal
His
solution
is
Treatment
of
horizontal
heat
for
hori-
advection
distribution.
The
finite
variables
The
element
spatial
time
method
variations
was
of
the
used
to
model
[MacAyeal and Thomas, 1982].
derivative
in equation
an implicit
of
the
ice
it
is
that
collapse
driven
each
to
ice
be
shelf
less
than
assumed that
the ice shelf
particular
element will
and become part
ocean (still
possibly
sea
of
the
open
covered by wind-
ice).
ORGANIZATION
OF MODEL
BOUNDARY
CONDITIONS
identify
straints
of this
study is to
atmospheric
and oceanic conon the maintenance of equili-
brium ice shelf cover in the Norwegian
and Greenland seas.
The boundary condition values that correspond to these
straints,
and which must be specified
gions
thickness
(1) is accounted for by using
time step [MacAyeal, 1985].
and the adjoining
of the grounded
ice
basal melting
or freezing
heat
the
flux)
shelf,
was not possible
in our study because of
computational
limitations.
We do not expect, however,
our results
to be substantially
influenced
by this short cut.
The
temperature-depth
profile
was recalculated using Crary's
formula at every time
step.
It therefore
is assumed to vary
quasi-statically
with the ice thickness
treat
20 m,
within
for
determined
of the ice shelf
valid
state
ice thickness
in which
heat advection
is negligible.
is
conto
run the model,
include
the mean annual
snow accumulation
(mass) over the surface
parameter B is derived from Crary's
[1961] analytic
solution for ice shelf
heat
thickness
The objective
Temperature
values
are specified
at
the top and bottom of the ice shelf.
The
temperature
at the base is given as the
pressureand salinity-dependent
freezing
temperature.
The temperature-depth
profile
within
the ice shelf necessary
for
the
average
element
at
bottom
and the surface
summary of
the
sheet,
rate
of
rethe
(oceanic
the
ice
temperature.
parameter
values
A
used
for
each model simulation
is presented in
Table 1. A comparison of these parameter
values with their present-day values and
other estimates of their 18 kyr B.P.
values
studies
Mean
in
a number
is
presented
annual
snow
of
climate
model
in Table
2.
accumulation
rates
over the ice shelf
and over the adjoining
grounded
area
ice
sheet
which
flows
into
the ice shelf were estimated from precipitation
and ablation
isopleths
presented
in Figure 1 of Hughes [1985].
These
values
are
equilibrium
structed.
those needed
for the ice
to maintain
mass
sheets he recon-
At the end of each time step,
a check is
performed
to determine
if either
a steady
m a-1 (ice equivalent) was chosen for the
state
entire
condition
has collapsed.
is
continued.
exists
If
In
not,
or
the
ice
shelf
model integration
addition,
if
the
ice
A precipitation
shelf.
The
rate
values
of 0.225
used
for
the grounded ice sheet region are presented in Figure 3. Assuming mass equili-
320
Lindstrom
TABLE 2.
and MacAyeal:
Paleoclimatic
Summary of Estimated Precipitation
for the Greenland and Norwegian
and Temperature
Sea Regions
Present
Kut zbach
on Ice Cover
Values
18 kyr B.P.
Surface
Surface
Temperature,
øC
Study
Constraints
Precipitation,
(P-E),
m a -1
Temperature,
m a -1
øC
Precipitation,
(P-E),
ma - 1
ma - 1
and
Guetter
[1986] a
Kut zbach
-18.8
Y
0.62
Y
0.33
Y
-26.2
Y
0.48
Y
0.26
Y
-15.1
Y
0.72
Y
0.34
Y
-24.5
Y
0.54
Y
0.31
Y
and
Guetter
[1986] b
Manabe
and
Broccoli
-10.6c Y
[1985]
Manabe
0.51d S
-37.3e W
0.29f Y
and
Hahn
[1977]g
Hughes
0.63
S
[1985] h
0.48
S
0.27
Y
Gates
0.33i S
[1976]
2j
S
0.13i S
"Y" denotes yearly average, "S" denotes summeraverage, and "W" denotes winter average.
avalueis zonal averagefor 60ø N - 90ø N. Theyearly averagevaluewasdetermined
from the mean of January and July values,
(personal correspondence, 1985).
which were provided to us by J. E. Kutzbach
bValue
is zonalaverage
for60ø N- 73.2
ø N. Theyearlyaverage
value
wasdetermined
by the mean of January and July values, which were provided to us by J. E. Kutzbach
(personal correspondence, 1985).
CValueis zonalaveragefor 60ø N - 73ø N, estimatedfromFigure4 of Manabe
and
Broccoli
[1985].
dAverage
valuefor theregion
covered
bytheGreenland
andNorwegian
seas,estimated
from Figure
27 of Manabe and Broccoli
[1985].
evalueis averagefor 60ø N - 73ø N for the regionwithin the samelongitudeas
the North Atlantic,
estimated
from Figure
7 of Manabe and Broccoli
[1985].
fAverage
valuefortheregion
covered
bytheGreenland
andNorwegian
seas,estimated
from Figure
28 of Manabe and Broccoli
[1985].
gvalueis zonalaverage
for 60ø N - 73ø N (including
landandsea)fromFigure5 of
Manabe and Hahn
[1979].
hAverage
valueestimated
from
Figure
1 of Hughes
[1985]
for theGreenland
and
Norwegian
Sea region.
•Value
is zonalaverage
for60ø N- 73ø N, determined
from
Figure
25of Gates
[1976].
3Value
estimated
for theGreenland
andNorwegian
seasfromFigure7 of Gates[1976].
brium over the grounded ice sheet,
mass of ice entering
the ice shelf
the
from
(Figure
each subglacial
drainage region
1 and Figure 3) is set equal to the
amount of precipitation
the subsystem.
Values
specified
to enter
which falls
on
of the mass of ice
through each subsystem
per
year
are
presented
in
Table
3.
As
can be seen in Table 2, the precipitation
values used are comparable with other estimates, an exception being the study by
Gates [1976], who predicts a substantially
The
lower
mass
value.
of
ice
added
due
to
surface
Lindstrom
and MacAyeal:
TABLE 3.
Paleoclimatic
Constraints
on Ice
Cover
321
Mass Fluxes off Grounded Ice Sheets Surrounding
and Greenland Seas at 18 kyr B.P.
the
Norwegian
Glacial
Subdivision*
Mass Ice
Mass Ice Flux x 10!3 kg a-!
Flux
1
4.036
4.401
2
3.183
3.471
3
7.241
7.896
4
14.250
15.540
5
6.365
6.941
6
6.969
7.600
7
2.553
2. 784
8
2.358
2.571
6.569
9
6.024
10
5.342
5.825
11
13.440
14.656
12
3.599
3.925
13
6.146
6.702
14
0.350
0.382
15
0.249
0.271
TOTAL
82. 105
89. 534
x 1010 m3 a -1
*See Figure 1 for subdivision locations.
precipitation
and flux
from the
sides
approximately 13.25 x 1014 kg a-1.
is
When
a mass equilibrium
condition
is reached,
this addition
is counterbalanced
by an
equal loss due to basal melting and
iceberg calving
into the sea at the
shelf's
edge.
If no calving were to occur, an equilibrium
state would be obtained
if
the
entire
form mass basal
ice
melting
shelf
had
rate
a uni-
of 543 kg
suming that it was below the limiting
threshold
value, we performed four model
simulations
with
heat
flux
values
of
0 00, 2 39, 4 79, and 5 75 J m-2 s-1
which correspond
to mass basal
melting
rates of 0.0, 0.25, 0.50, and 0.60 m a-!
(ice
equivalent),
respectively.
The zonal average 18-kyr B.P. surface
temperature
for the latitude
belt which
contains
the Norwegian and Greenland seas
m-2 a-1 (approximately 0.6 m a-1 ice
was
equivalent),
which corresponds to an
oceanic surface heat flux of 5.78 J m-2
ulations
by Kutzbach and Guetter [1986]
to be approximately -24.5øC.
Because
s-1.
much
If
the heat flux were higher,
it
estimated
of
this
from
numerical
latitude
climate
belt
covered
sheets
survive.
tions,
we decided
Present-day
estimates
of the heat flux
through the ocean surface determined by
Worthington [1970] and by Hibler and
shelf
-19.0øC)
to account
for its
tion.
In one run,
however,
Bryan [1984] are 99.48 J m-2 s-1 and
higher
58 50 J m-2 s-1
proximately
the present-day
average temperature
for the latitude
belt which the
ice shelf covers [Naumienko, 1968].
This
was performed
to determine
how sensitive
the ice shelf would have been to changes
in surface
temperature.
for
the
ice
respectively,
shelf
to
and are
above the limiting
threshold
allowing
ice
shelf existence.
These large values are
primarily
due to the flow of the North
Atlantic
Current
into
the
region.
From
microfossil
analysis [Ruddiman and
Mcintyre,
1981], however, it is deduced
that at the glacial
maximum this current
was restricted
to more southerly
latitudes.
It is thus entirely
possible
that
the 18 kyr B.P. oceanic heat flux was reduced to, or below, the critical
value
of 5.78 J m-2 s-1.
influence
of
this
To investigate
oceanic
heat
flux,
the
as-
DERIVED
high
was
by ice
would be impossible
having
sim-
to
increase
surface temperature
temperature,
ICE
SHELF
surface
the
elevaice
by 5øC (to
lower
elevaa
we chose
-11øC, which is ap-
CHARACTERISTICS
Our numerical
simulations
produced a
variety
of equilibrium
ice shelf
configurations
whenever the basal melting
rate
(assumed spatially
uniform)
to be less than 0.60 m a-1.
was specified
This upper
322
Lindstrom
and MacAyeal:
Paleoclimatic
!
..... •
• '• ½ •
Fig.
Fig.
4.
Ice thickness
distributions
!
•
Constraints
I\•
•
x
on Ice
x..........
-.:.:'-'.'•i:i
.-:'•'"'
.....'..'..." '..•i...................
4a
(in meters)
for trials
with
surface
tem-
peratures of -19øC and basal melting rates of (a) 0 0 m a-1 (b) 0 25 m a-1
and (c) 0.50 m a-1. In Figure 4a the solid line is contoured at 25-m
ß
intervals,
the
toured
25-m
and the dashed
solid
at
line
is
100-m intervals;
intervals,
line
contoured
and the
at
is
contoured
50-m
line
limit
of basal melting
nearly
balances
the total
mass gain due to ice shelf precipitation
and flux from the bordering
grounded ice sheets.
The sensitivity
of
the ice shelf
to the basal melting
rate
was explored by performing
four simulations with basal melting
rates of 0.0,
0.25, 0.50, and 0.60 m a-1 (ice equivalent) with a surface temperature of
-19.0øC (see Table 1), referred
to below
as runs 1 to 4, respectively.
To analyze
the effect
of surface
temperature,
we ran
the model with a surface
temperature
of
-11øC and a basal melting
m a-1,
referred
rate
of 0.50
to below as run 5, and
compared the results
with
those
of run
3 (which also had a 0.50 m a -1 basal
melting rate).
The effects
of basal melting
on the
equilibrium
ice shelf configurations
can
be seen by comparing the ice thickness,
at
intervals,
and in Figure
dashed
Cover
is
•
100-m intervals;
and the
4c the solid
contoured
at
velocity,
displayed
sults
ß
dashed
line
50-m
is
in Figure
line
is
•
4b
con-
contoured
at
intervals.
and flow of runs 1, 2, and 3
in Figures 4, 5, and 6. Re-
from
run
no equilibrium
4 are
ice
not
shown
shelf
because
configuration
was possible for the 0.60 m a-1 basal
melting rate.
The simulation
was carried
out anyway to verify
that the initial
ice
shelf would eventually
collapse.
As a
rule,
increased
basal
melting
tends
to
(1) decrease basin-averaged
ice thickness, (2) decrease the ice front flow
velocity,
and (3) increase the ice
velocity
of
the
straits.
averaged
over
Iceland-Faeroe
These
the
and
results
regions
north
Denmark
can
be
in simple terms by considering
petition
between ice discharge
understood
the comby iceberg
calving and basal melting.
For run 1 the
large positive
mass flux into the ice
shelf must be balanced entirely
by iceberg calving.
This means that the ice
J
•-
_•
/
• ••• /
•_ • •
•
•
x
•
_
•
••
. .............
.......
.:::::?
..::•:•:•:•:•:•:•:•:•:•:•:•:•:.
======================================
..::•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•
..::•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:
................................
.................................
........................................
.........................................
.........................................
..........................................
....................................................................................
.....................................................................................
...........................................
.............................................
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
...........................................................................................
I
' •
•) •.•::•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:•:
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
...............................................................
.............................................................................................................................
.............................................................................................................................
...............................................................
...............................................................
................................................................................................................................
.................................................................
.................................................................
..................................................................
...................................................................
...................................................................
........................................................................................................................................
.........................................................................................................................................
...........................................................................................................................................
•.:c.•:.:.:.:.:.:.:.:..•c.:..zcc•.:.:.:.:.:.:c.:.•................................................................................
500
324
Lindstrom
and MacAyeal:
Paleoclimatic
Constraints
on Ice Cover
II I
Fig.
Fig.
5.
Equilibrium
velocity
5a
distributions
(in meters per annum) for trials
with surface temperatures of -19øC and basal melting rates of (a) 0.0 m a-1
(b) 0 25 m a-1 and (c) 0 50 m a-1
In Figure 5a the solid line is contoured
at 100 m a-1 intervals,
and the dashed line is contoured at 1000 m a-1 intervals; in Figure 5b the solid line is contoured at 50 m a-1 intervals, and the
dashed line is contoured at 250 m a-1 intervals; and in Figure 5c the solid
line is contoured at 25 m a-1 intervals,
and the dashed line is contoured at
50 m a -1
intervals.
thickness and seaward velocity
large at the relatively
short
in
the
tain
Iceland-Faeroe
this
shelf
high
must
Strait.
seaward
have
the
ice
thickness
(~1100 m, Figure 4a) and driving stress
(proportional to thickness [MacAyeal et
al., 1986]) to resist the large resistive
stresses
Faeroe
associated
and
Denmark
with
the
Iceland-
straits.
With increasing
basal melt rates,
the
iceberg calving
rate must decrease for
an equilibrium
configuration.
This re-
lationship
is borne out by runs 2 and 3,
which
both show substantial
decreases
ice
thicknesses
and ice
front
velocities
over run 1 (Figures 4 and 5).
within
the interior
basin,
Iceland-Faeroe
Strait,
is
crease in our simulations
To main-
flux,
sufficient
ity
the
must be
ice front
in
Although
the ice front velocity
must decrease with
increasing
basal melting,
the ice veloc-
north of
seen to in-
(Figure
5).
This increase
is primarily
associated
with our constant
ice flux boundary condition
applied
at grounding line ice
boundaries.
As basal melting
reduces the
ice shelf thickness
along the grounding
lines,
grounding line ice velocities
must
increase
to deliver
the same equilibrium
mass
flux
"Ice
into
the
ice
shelf.
stream" grounding line
discharge
velocities
typical
for West Antarctic
ice
streams are achieved only by our runs in
which the basal melting
rate is high and
the ice shelf is relatively
thin (Figure
5).
This suggests that evidence for ice
streams
Barents
in the seabed topography of the
and Kara seas would also support
Fig.
5b
200
•,•, •,\•;ix
•l .t
:::::::::::::::::::::::::::::::::::::::::::
,.:.:..:..:..:..:..:..:..:..:..:..:..:..:..:..
=================================================================
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Fig.
5c
Lindstrom
and MacAyeal:
Paleoclimatic
Constraints
on Ice
Cover
327
.:i:i:
:-:
...
:::.:
....
.-.-.....v.
Fig. 7. Distribution
of equilibrium
result from a change in temperature
rate of 0.5 m a-1 (ice equivalent).
thickness
from-11øC
(in meters) differences
which
to -19øC for a basal melting
The contour interval
a relatively
thin ice shelf with a high
basal melting rate [Grosswald, 1980].
The flow line patterns
of runs 1 to
3 indicate
that basal melting determines
rected
the degree and location
of ice convergence within
the equilibrium
ice shelf.
Figure 6a shows that in the absence of
velops in the Denmark-Faeroe
Strait.
For
run 1 the thickness
changes by 300 m in
basal melting,
flow lines
Iceland-Faeroe
Strait.
converge in the
Ice
divides
are
also evident near the SpitsburgenGreenland passage and near the Denmark
Strait.
vergence
This example of flow line contoward
the ice front
is explained by the required
balance between
mass flux off the grounded ice sheets and
toward
is 5 m.
the
ice
shelf
interior
to
counterbalance
local basal melting.
Perhaps the most striking
feature
runs
1 to
3 is
the
"ice
300 km on a section
to the flow through
strait.
This
though large,
the analagous
Filchner-Ronne
fall"
that
of
de-
extending parallel
the middle of the
ice thickness
gradient,
alis small in comparison with
present-day
ice fall
on the
Ice
Shelf
between
Korff
and Henry ice rises [Robin et al.,
One possibility
not considered
1983].
in the
iceberg calving.
For the higher basal
melting rate of run 3 (Figure 6c), flow
lines converge on an axis that transects
present
study is that of ice shelf
grounding
in the straits
leading
out of
the Greenland and Norwegian seas.
Presently,
ocean depths in these straits
the
are
ice
shelf
basin
from
the
Iceland-
Faeroe Strait
to the SpitsbergenGreenland passage.
The ice divide off
Spitsbergen
is also shifted
to the south.
This more distinct
pattern
of convergence
indicates
how
grounded ice
the
flux
sheets
of
ice
off
must primarily
the
be di-
less
than
~550
Iceland-Greenland
m as
Rise
a result
and
the
of
the
Iceland-
Faeroe Rise.
During the glacial
maximum,
sea level was approximately
120 m lower.
Our simulations
for basal melting
rates
of less than 0.5 m a-1 imply ice shelf
grounding
in these
straits.
We did not
328
Lindstrom
and MacAyeal:
Paleoclimatic
Constraints
on Ice
Cover
Fig. 8. Distribution
of equilibrium velocity (in meters per annum) differences which result from a change in temperature from-11øC
to -19øC for a
basal melting rate of 0.5 m a-1 (ice equivalent). The solid line represents
a contour interval of -25 m a-1 and the dashed line represents a contour interval
of -100
analyze the effects
cause,
at
present,
m a -1.
of this grounding beour
model
does
not
ad-
dress grounded ice dynamics.
If such
grounding were to be accounted for, we
estimate that ice thicknesses upstream
of the straits
would increase signifi-
cantly both (1) to maintain a driving
stress
able
the straits
to
resist
basal
traction
be understood in terms of changes of the
depth-averaged
ice strength parameter
which appears in equation (3).
As the
value of this parameter is reduced by
higher depth-averaged
temperatures,
ice
velocity
is increased for a given ice
thickness.
in
and (2) in response to the
reduction
of oceanic
heat flux
from the
North Atlantic.
On the basis
of this
To maintain
a constant
ice
flux, such increases would require ice
thickness changes roughly proportional
to the "original"
thickness
thickness
of either
(e.g.,
the
run 3 or run 5),
with
idea alone, an extremely thick ice shelf
cover as suggested by Broecker [1975] ap-
and downstream of the west Barents Trough
pears
reasonable.
The effects
of
locity
perature
are displayed
tends
to
changes
(subdivision
increased
surface
tem-
by comparison of
runs 3 and 5. Figures 7 and 8 display
the velocity and thickness differences,
respectively.
In general, warmer temperature
largest
reduce
increase ice velocity.
ice
thickness
and
This tendency can
is
least
front
the
local
6 in Figure 1).
changes are largest
sensitive
cosity.
crease
over
confined
to
and
changes
are
in
ice
Ice ve-
where the flow
therefore
ice
shelf
The largest
ice velocity
occurs,
for example, near
(Figure
counterbalanced
8).
domes
This increase
by a decrease
most
vis-
inthe ice
is
of ice
Lindstrom
and MacAyeal:
Paleoclimatic
Constraints
on Ice
Cover
329
evidence
concerning
the Arctic
hypothesis
and related
issues.
ice shelf
Our dis-
cussion here focuses on two aspects:
(1)
the implications
of how possible
ice
shelf cover may have modified
deep-sea
sediment organization,
distribution,
and
transport
our
and (2)
previous
cover
ice
is
needed
sheets
the consistency
claims
that
to
Arctic
buttress
covering
the
between
ice
the
shelf
marine
Barents
and Kara
between
sedimen-
seas.
One
basic
difference
tation
resulting
from ice shelf cover and
that resulting
from iceberg
drift
concerns the pattern
of sediment transport,
or "ice
Fig. 9a.
found
on
General division
the
eastern
of rock types
coast
of
Greenland
[after
Henriksen and Higgins,
1976;
Bridgwater et al.,
1976] and Iceland,
Spitsbergen,
the Faeroe Islands,
and the
western coast of Norway [International
Geological Congress, 1971].
In Figure 9a,
the different
rock types are denoted by
capital
letters
as follows:
A, Archaean
gneisses;
B, Tertiary
basalts;
C,
gneissic,
migmatic,
and sedimentary
complexes;
D, mid-Precambrian
sedimentary
rocks;
E, sea bottom sediments;
F, mixture
of upper Precambrian
schists
and
Pleistocene
volcanics;
G, mixture
of rock
types deposited in the Barents Sea basin
from surrounding
land regions;
H,
Paleozoic
metamorphics;
I, Paleozoic
granites;
J, Paleozoic
and Precambrian
metamorphic schists;
K, mixture of rock
types; L, volcanics
from the Faeroe
Islands;
and M, Icelandic
volcanics.
The
extension
of
sediments
derived
Barents Sea (type G) into
from
the
the ice shelf
portrays
the region where its sediments
would predominate
if the ice shelf had a
basal melting rate of 0.25 m a-1 (distribution
derived
of Figure
6b).
cation
the
of
and Duplessy
thickness
from
core
aid
line
pattern
denotes the loby Grousset
[1983].
(Figure
EVIDENCE
flow
analyzed
7) at the ice front
that the net iceberg
stantly
maintained.
FIELD
the
The star
calving
rate
is
so
con-
INTERPRETATION
Our ice shelf simulations
provide
for interpreting
geological
field
an
rafting",
prior
to deposition.
For iceberg
transport,
one would expect
ice-rafting
patterns
associated
with
oceanic circulation.
Such patterns
could
range from areal homogeneity,
if iceberg
drift
during melting
were purely random,
to patterns
reflecting
areal assymetry
as would occur if iceberg
drift
were
driven by a large-scale
gyre circulation.
Sediment deposition
patterns
associated
with ice shelf transport
would reflect
characteristics
of ice shelf
flow,
which
would be entirely
different
from that of
oceanic
circulation.
In particular,
Arctic
ice shelf
flow
would organize
sediments derived
from the
various
subglacial
erosional
provinces
of the surrounding
continents
into distinct
depositional
regimes associated
with ice shelf
flow lines
[Anderson et
al.,
1984].
Precisely
where the deposi-
tion occurs along any particular
flow
line would be determined
by the basal
melting
pattern
and by the amount and
distribution
of
sediment
contained
within
ice shelf•
absent•_
homogeneous
sedimentation
iceshelf•J
present
I.1,
iceshelf
absent
q homogeneous
sedimentation
t
Fig.
9b.
tern
of
t'
Idealized
sedimentation
cross-sectional
fot
the
t-t'
patline
of Figure 9a.
Before and after
the ice
shelf existence,
sedimentation
is controlled
by iceberg transport,
resulting
in a homogeneous sediment-type
distribution.
During the period of ice shelf
presence,
the sediment type of any point
at the bed is dictated
by the region from
which the ice flowing over it originally
became ungrounded.
330
Lindstrom and MacAyeal:
the
ice.
rafted
The organization
debris
would
Paleoclimatic
Constraints
on Ice Cover
of ice-shelf-
thus
result
from
the
combined effects of the ice shelf flow,
the amount of sediment within the ice,
and the oceanic heat flux regime.
As a demonstration of a possible difference
between
ice-shelf-rafted
sedimen-
tation
and iceberg-rafted
sedimentation,
we constructed
two imaginary
surface
sediment records of the Norwegian and
Greenland seas.
of
used
To construct
ice-shelf-rafted
the
ice
the example
sedimentation,
flow
lines
derived
we
from
our
0.25 m a-1 simulation (Figure 6b) to project the transport
of erosional
products
from the various bedrock regimes of the
continents
surrounding
the Greenland
and
Norwegian seas.
We do not apply an assumed pattern
of basal melting
to the ice
shelf,
nor do we estimate
the vertical
distribution
of englacial
debris within
the
ice
column
as
it
enters
the
ice
shelf
from the grounded ice sheets.
Our construction
thus only delineates
the broad
regions
where the various
sediments
could
be found and suggests where certain
sediment types should be mutually
exclusive
in the geologic
record.
For constructing
the example of iceberg rafting,
we assumed a counterclockwise oceanic gyre similar
to that produced today in response to positive
wind
stress
tern
of
curl
[Aagaard,
1970].
circulation
is
ocean
This patalso
consis-
tent with results
atmosphere
general
ulations
that
of coupled oceancirculation
model simpredict
the response to
lower atmospheric C02 thought to prevail
during the glacial
maximum [Manabe and
Bryan, 1985].
In addition
to the oceanic
gyre, we assume considerable
ocean eddy
circulation
consistent
with the presentday circulation.
This additional
assumption requires
that iceberg
drift
trajectories
have a stochastic
component.
Sediment deposition
from such iceberg
rafting
is thus assumed to be virtually
random and should produce no organized
pattern
in the geologic
record.
Subglacial
bedrock regimes used in
both
constructions
were
derived
from
Fig.
10.
Representation
pattern
which
would
shelf
did
exist
in
not
These drift
an ice
and
periods.
are consistent
[Aagaard,
GCMsimula-
tions [Manabeand Bryan, 1985].
on icebergs represent
Symbols
rock types contained
within them (see Figure 9 for symbolic interpretations).
The sediment distribution
will be more homogeneous than that for the
ice shelf scenario illustrated
in Figure
9.
ranging
from
Pleistocene
volcanics
in
Iceland to Paleozoic schists and granites
in Europe and gneisses and basalts along
the
eastern
coast
of
Greenland.
This
large variation
suggests that a test of
the Arctic ice shelf hypothesis should
be possible
because
less
variation
would
imply homogeneoussedimentation patterns
regardless of the sediment transport
mechanism.
The two alternative
sedimentation pat-
terns are displayed
in Figures 9 and 10.
The ice shelf pattern
is seen to be or-
ganized into mutually exclusive provinces
distinguished by sediment type, whereas
the iceberg pattern
is seen to be purely
random.
exception
most regions
controlled
for Iceland,
Spitsbergen,
the Faeroe
Islands,
and Western Europe.
These regimes, shown in Figure 9, represent
only
the gross features
of the geologic conditions.
A large variation
occurs,
trajectories
if
Greenland
with present-day circulation
1970] and with paleoclimatic
[International
Congress, 1971]
result
the
Norwegian seas during glacial
Henriksen and Higgins [1976] for
Greenland and from a geologic map of
Europe and the Mediterranean
region
Geological
of the iceberg
drift
A possible
positional
isolation
subject
deposition
to the com-
one would expect for
to
ice-shelf-
is the Iceland-
Faeroe Ridge, over which flow strongly
converges from all regions.
This effect
suggests that the region of the Iceland-
Faeroe Ridge would not be a good place
to test the ice shelf hypothesis using
Lindstrom
the
and MacAyeal:
sedimentary
course,
would
Paleoclimatic
record.
Constraints
The pattern,
be much different
of
for
the
case of a high basal melting
rate,
where
a high percentage
of the ice is melted
instead
of calving.
Figure 6c suggests
that for this case, a large amount of
sediment should be deposited
in the region of the ice shelf slightly
north of
on Ice
Cover
buttressing
the
force
marine
using
ice
our
is
defined
stress
periods
in which
in steady
state.
the
At
ice shelf
would be
other
times,
such
as during ice shelf growth or collapse,
the sedimentation
patterns
could be entirely
different.
An example of a deep-sea
sediment
analysis
relevant
to the possible
test
of the Arctic
ice shelf hypothesis
was
carried
out by Grousset and Duplessy
[1983].
taken
They analyzed a sediment core
from the waters
Iceland
(the
by a star
just
location
in Figure
of
north
which
denoted
9 ) and found that
before the glacial
maximum period
kyr B.P.,
the sediments deposited
derived
from
Icelandic
of 18
were
however,
located
in
Greenland
of
and
this
type
associated
Duplessy
from
latitudes
If
[1983]
that
which
of
suggest that
ice-rafted
debris
in
the
where
region
in
a
core
convergence to have occurred
6c for
core
where
ß
the
x direction
is
shelf
where
vertical
shear
sumed negligible).
by equation
stresses
located
predict
flow
(see Figure
(3)
of strain
rate
flow law given
[MacAyeal and Thomas,
-1
-z
-n )
v = •z '0.5 [0.5e..e..]-0.5(1
lj
lj
alone
•z
whether
this
with
the
total
is
equal
depth-averaged
from seawater presto:
The difference
is
a measure
ice
shelf
(6)
between Txxz and TxxZsw
of
the
degree
buttresses
the
to which
marine
the
ice
sheets, because •xx z sw is the lower bound
of
the
buttressing
stress.
over a 150-km length
line were calculated
line
(subdivision
the
of the grounding
for the grounding
6 in Figure
location
of
1) which
the
west
6 of
Grosswald
[1980]).
We chose this
location because it may have been a site of
ANALYSIS
our
(5)
= 0.5pig(Oi/Ow)
H
sw
represents
pothesized Arctic ice shelf [Hughes et
al.,
1977; Denton and Hughes, 1981].
To
tent
as-
The values of TxxZ and TXX z SW averaged
The necessity
for ice shelf
buttressing of marine
ice sheets in the Barents
and Kara seas provides
one of the
strongest
arguments
in support
of the hy-
determine
are
The depth-averaged
viscosity
is a function
and is derived
from the
amount
location).
FORCE
(4)
perpendicular
Barents Trough (see also Figure
BOUNDARY
and
(upstream) to the grounding line, the y
direction
is parallel
(to the right of--Z
upstream) to the grounding line, and v
is the depth-averaged ice viscosity
(see
MacAyeal [1985] for a development of this
xx
an ice
large
we would
shelf
•zxx = -2• (2exx + eyy ) + 0.5 0igh
sure
and
cover was made by Ruddiman [1977],
of
ß
ice
is correct,
Grousset
an exceptionally
--Z
the
stress Txx z resulting
was present
in the region
until
the
18 kyr B.P. glacial
maximum, after
which
it collapsed
in a relatively
short period
of time.
An example of an observation
which might support
a thin
ice shelf
he noted
stress
within
For comparison,
is
circulation
our analysis
results
force
depth-averaged
rocks
of
Sedimentation
with
oceanic
10).
the
derived
Scandanavia.
agrees
with
(Figure
then,
were
the higher
Following
1986]:
basalts.
This agrees with our ice shelf deposition pattern
presented
in Figure
9.
Sediments deposited
between 18 and 10 kyr
B.P.,
given
equation;
of
is
data.
of
Sea
to the material
plane defined
by the
grounding
line.
This stress
is related
to the glaciostatic
stress
and the de-
by:
to
Barents
•xx z (in pascals) acting perpendicular
is
only
the
the buttressing
as the
viatoric
refer
on portions
in
simulation
ice
deposition
acting
sheet
MacAyeal [1985],
the center,
where much of the flow converges.
We remark
that
our estimates
of
shelf
331
results
argument,
are
consis-
we calculate
the
ice
stream
flow
and
enhanced
ice
sheet
discharge [Grosswald, 1980].
The calculated depth averaged stress and ice
thickness
simulation
are
listed
of
Table
in
Table
1 which
4
was
for
each
able
to
support an equilibrium
ice shelf configuration.
These values are comparable
to
those calculated
for present-day
ice
332
Lindstrom
TABLE 4.
Calculated
values
and MacAyeal:
of
the buttressing
provided by the ice shelf
Basal
Melting
Paleoclimatic
force
Constraints
for
the West Barents
for simulations
Surface
on Ice
Cover
Trough
1 to 4
Buttressing
Stress
temperature, øC
0.00
-19
5. 355 x 10 6
5. 354 x 10 6
0.25
0.50
0.50
-19
-19
-11
4. 922 x 10 6
2.874 x 10 6
2.443 x 10 6
4. 905 x 10 6
2.813 x 10 6
2.387 x 10 6
For comparison,
streams
which
the total
flow
into
depth-averaged
Antarctic
shelves
[Thomas and MacAyeal,
Thus
conclude
we
equilibrium
Greenland
adequately
that
ice
1982].
stresses
within
an
ice shelf cover over the
and Norwegian seas would have
buttressed
the surrounding
ice
Force, Pa
From
Rate, m a-1
stress
due to seawater
derived
The oceanic heat flux,
through its
control
of ice shelf
thickness,
appears
to be the greatest
factor
in determining
the strength
of marine ice sheet buttres-
cally
sing.
The strong reduction
heat
flux
of TxxZ when
is at 4.79
J m-2
s-1 suggests that a possible increase of
oceanic
heat
glacial
trigger
marine
flux
at
the
end
of
the
last
in
from
our
is also
simulations
more restrictive
which
showed
given.
an
ice
that
shelf
this
is
under
dramati-
conditions
exists.
We further
restrictive
stress
re-
gime is reduced to its minimum value
(corresponding to removal of the ice
shelf) by a small change in oceanic heat
flux relative
to its present value.
If
the grounded marine ice sheet in the
Barents
maximum would be sufficient
to
catastrophic
collapse
of the
ice sheet covering
the Barents
alone
tional
support in favor of the controversial
ice shelf hypothesis
if the flux
was approximately
13 times lower during
glacial
times than it presently
is.
The
stress regime at the margin of continental glaciation
on the Barents Sea shelf
sheets.
the oceanic
Seawater, Pa
Sea
strictive
was
stress
sensitive
to
regime,
this
re-
as was suggested
by Weertman [1974] and Denton and Hughes
[1981],
Sea.
sitive
CONCLUSION
Our results
have illustrated
the range
of climatic
conditions
under which equilibrium
ice shelf
cover could persist
over the Greenland
and Norwegian
seas
during the last glacial
maximum.
In addition,
our results
display
the thickness
and flow configuration
for use in interpretation
of geologic
evidence.
The
single most important
factor
in determin-
then it
to
the
must also
oceanic
heat
have been senflux.
This
constitutes
a direct
coupling
between
grounded continental
glaciation
and the
ocean that could possibly
account for
rapid
disintegration
of northern
hemisphere glaciation
in response to relatively
minor changes in orbital
parameters
(see also Saltzman et al.
proposed in the Denton and Hughes [1981]
[1982]).
The properties
of a possible
Arctic
ice shelf during different
stages of its
disintegration
are therefore
of interest
in understanding
the earth's
climatic
record and could be investigated
using
the methods developed here.
Such an investigation
relating
to the disintegration of the ice shelf and surrounding
ice
reconstruction
sheets
ing
the outcome of our simulations
oceanic
heat
melting
rate.
if
an Arctic
flux
and
This
ice
result
shelf
of
associated
suggests
did
18 kyr
is
exist,
B.P.
the
basal
that
as was
Arctic
gla-
ciation,
then increases
of the oceanic
heat flux into the Norwegian
and
study.
Greenland
APPENDIX
would
rapid
seas
from
the
North
Atlantic
be a leading
factor
in triggering
glacial
collapse
during the
Holocene.
We suggest that the sensitivity
of the
ice shelf
configurations
examined here
to oceanic heat flux may provide
addi-
will
be
dealt
with
in
a
future
The geographic
region represented
by
our West Antarctic
grid comprises an area
of 8.82 x 10 6 km2 and is illustrated
in
Figure A1.
We have attempted
to make
parameter
specifications
comparable to
Lindstrom
and MacAyeal:
Paleoclimatic
Constraints
on Ice
Cover
333
an ice shelf cover or which is part of
the sea overlying
the continental
shelf
are initially
specified
to be part of the
ice shelf.
Grid elements representing
part of the present
grounded ice sheet
Ronne
IceShelf
are specified
as being either
(1)
grounded if the present bed [Drewry,
Filchner
Ice
1983]
is
less
than
400 m below
or (2) an ice shelf
is less
the ice
tion
Ice
Strea
sea
level
the present
bed
than this depth.
Mass gain to
shelf occurs by snow precipita-
on the shelf's
from surrounding
Rutfo
if
surface
grounded
and by flux
regions.
A
precipitation
rate of 0.20 m a-1 was
specified
the
for
entire
region.
For simplicity,
area and precipitation
ponents
which
of
drain
the
into
East
the
Antarctic
West
be the same as that for
presented
by Giovinetto
[1985].
total
West
Antarctic
we assumed the
rates
of the comIce
to
the present
and Bentley
as
Using these assumptions,
mass input
to the
Sheet
Antarctic
ice
shelf
the
from
Ross
Ice
Shelf
Fig.
A1.
West
Antarctic
Grid
representation
Ice
Shelf
used for
the
simulation.
Stipled
areas represent
open or sea-icecovered water,
and solid areas represent
grounded regions
where the bed is less
than 400 m below sea level;
the remainder
is an ice shelf cover.
Present-day
ice
shelf
cover (checkerboard
pattern)
is
superimposed
upon the grid for aid in determining
the geographic
region
covered.
For current
ice sheet/ocean
boundaries,
please refer
to maps of Antarctica
such
as sheet 2 of Drewry [1983].
those for our Norwegian-Greenland
Sea reconstruction
so a comparison
of the simulations
can be as valid
as possible.
Grid
elements
are
a
combination
of
squares and triangles
having short sides
equal to 50 km. At the beginning
of our
run,
the
ness
of
ice
450
shelf
m and
had a uniform
extended
to
the
thickconti-
nental
shelf margin.
All grid elements
which represent
a region presently
having
Fig.
A2.
Steady state
flow
of the West Antarctic
Ice
with
a surface
accumulation
line
Shelf
rate
pattern
simulation
of 0.20
m a-1 and a basal melting rate of 0.12
ma-1.
334
Lindstrom
precipitation
and flux
and MacAyeal:
Paleoclimatic
Constraints
on Ice
Cover
from the grounded
regions is 1.8 x 1014 kg a-1.
Mass is lost from the ice shelf
melting at its base and by calving
seaward
front.
We specified
by
at its
a basal
melting rate of 0.12 m a-1.
This value
was
of
chosen
so
that
the
ratio
total
mass input
to mass loss from basal
melting
would be the same as for the
Norwegian-Greenland
Sea simulation
having
a basal melting rate of 0.25 m a-1.
was specified
The
surface
temperature
-11øC.
This temperature is considerably
warmer
than
the observed
so as
for
the lower
surface
elevation.
Mass equilibrium
was attained
a computer simulated
to
to be
account
after
time of 1700 years
Fig. A4.
Steady state velocity
distribution (in meters per annum) of the West
Antarctic
surface
Ice
Shelf
simulation
accumulation
rate
with
a
of 0.20 m a -1
and a basal melting rate of 0.12 m a-1.
The contour interval
is 100 m a -1.
using 25-year
time steps.
The resulting
flow line,
thickness,
and velocity
distributions
are shown in Figures A2, A3,
and A4, respectively.
Unlike
the Arctic
simulation
with a basal melting
rate of
0.25 m a-1, most of the ice shelf tends
to
Fig. A3.
Steady state thickness
(in meters)
of the West Antarctic
pattern
Ice
Shelf
accumu-
lation
simulations
rate
with
of 0.20
a
melting rate of 0.12 m-1.
interval
is
50
m.
surface
m a -1 and a basal
The contour
thin
from
its
initial
thickness.
This
difference
is accounted
for by the larger
ice shelf
front
length of West
Antarctica,
which permits
a greater
iceberg calving
flux at lower overall
driving
stress.
Even though thickening
of the ice
shelf does not occur to any great extent
in
not
the
interior
retreat
and
from the
the
ice
shelf
continental
does
margin,
Lindstrom
and MacAyeal:
Paleoclimatic
Constraints
there are a number of striking
similarities with the present-day
ice cover.
First,
regions where velocity
and thickness gradients
are a maximum correspond
almost exactly
with the present grounding
line
positions
for the Ross and FilchnerRonne ice shelves.
In addition,
the ice
velocities
in the grounding region for
the Ross Ice Shelf compare favorably
with
current
measured velocities.
Second,
the
thicknesses
at the present
edge of the
Ross
and
Filchner-Ronne
ice
shelves
are
approximately
equal to those determined
by the model for the same geographic
region.
Finally,
regions of maximum
thickness
correspond
favorably
with
present-day
ice-sheet
divides
for the
West
Antarctic
Ice
Sheet.
These similarities
method is capable of
favorable
large
to
ice-shelf
thickening
suggest
detecting
that our
conditions
existence.
of the ice
A
shelf's
in-
terior
region would probably
have occurred if the simulation
had been performed
using a smaller
basal melting
rate.
A
more realistic
calving
front position
would also have resulted
if we had specified a larger
thickness
for the minimum
ice shelf
thickness
and/or
included
a
treatment
of ice-shelf-calving
dynamics
in
the
model.
Acknowledgments.
This
work was sup-
ported by NSF grant DPP-8401016 and by
NASA grant NAG-5394.
Computer time on
the NASA/GSFC High-Speed Vector Processing facility
was provided
through the
kind
efforts
of
Bindschadler.
R.
The
H.
Thomas
Technical
Group (TAG) provided
and
R.
A.
Assistance
valuable
consulting
services
in helping
us adapt our model
to the NASA computer.
We thank G. York
for typing the manuscript
and editorial
assistance
and G. H.
Denton,
T.
J.
Hughes, K. Bryan, Jr.,
J. T. Andrews, T.
B. Kellogg,
M. M. Monaghan, and J.
Anderson for many helpful
suggestions
and
encouragement
throughout
the span of this
project.
We also thank S. Manabe and J.
E. Kutzbach
for providing
us with detailed
results
of their
paleoclimatic
model simulations
of the Arctic
region.
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