RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 7, ES5004, doi:10.2205/2005ES000180, 2005
[47] Reconstructing the Okhotsk Ice Sheet presents challenges not encountered in previous reconstructions of Pleistocene ice sheets using the geometrical force balance [e.g., Grosswald and Hughes, 1995, 2002; Hughes, 1995, 1998; Hughes and Hughes, 1994]. As we envision it, based on evidence provided here, the Okhotsk Ice Sheet is a marine ice sheet in which flow begins along a highland arc that rings the Sea of Okhotsk on the east and north, transgresses onto the Asian mainland to the west, and ends along the Kuril Island Arc to the south. Did the ice sheet form as glaciers from these highlands advanced onto the shallow continental shelf in the Sea of Okhotsk during lowering sea level at the beginning of Quaternary glaciation cycles? Or did sea ice thicken and ground in the Sea of Okhotsk and cause snowlines to lower to sea level in surrounding mountains, thereby allowing the mountain glaciers to advance and merge with the grounded sea ice to produce the marine ice sheet that ended as a floating ice shelf? How far did the mountain glaciation extend to the north of the highland arc? Did the precipitation shadow cast by the Okhotsk Ice Sheet confine these highland glaciers to the northern mountain slopes, or did they merge with a marine ice sheet in the East Siberian Sea that transgressed onto the Siberian coastal plain? Was there a connection to the east with a largely marine Beringian Ice Sheet that originated in the Chukchi Sea, poured through Bering Strait into the Bering Sea, and ended as an ice shelf calving along the Aleutian Island Arc? If any of these connections existed, when did they exist? If none of these ice sheets existed, what are we to make of the evidence presented here?
[48] In the geometrical force balance [Hughes, 1992, 1998], the surface slope along an ice-sheet flowband of width wI is given by the expression:
![]() | (1) |
Surface slope
Dh/Dx is the incremental
increase in ice elevation
Dh
in incremental horizontal
distance
Dx measured upslope along an
ice flowline from
x = 0 at the ice margin. Densities are
rI for
ice,
rW for water, and
rR for Earth's mantle. Isostatic
sinking beneath the ice load lowers ice elevation
h on an
undepressed bed of height or depth
hR relative to sea level.
Lowered ice elevation
h
lies on
a depressed bed lowered from
hR to
hR
, with
r defined
as
r = (hR - hR
)/(h
- hR ) such that
hR = hG remains constant at an ice-shelf
grounding line. For grounded ice,
r = r0 [1 - exp (-t/t0)] during
time
t of ice-sheet advance and
r = ra exp (-t/t0) during time
t of ice sheet retreat, where
t0 is the relaxation time of Earth's
mantle to the ice load,
r = r0 = rI/(rR - rI) for isostatic equilibrium at
t=
, and
r = ra for
t = 0 at the glacial maximum. Assuming present-day isostatic
equilibrium, present-day bed topographies can be used for
hR along
flowlines of a former ice sheet. Transitions from sheet flow to
stream flow to shelf flow downslope along ice flowlines are
controlled by basal buoyancy factor
PW/PI, where
PW = rW g hW is the basal water pressure that supports water of height
hW above
the bed,
PI = rI g hI is the ice overburden pressure for ice
of thickness
hI,
g is gravity acceleration,
PW/PI
0 for sheet flow in which
hW = 0 for a frozen bed and
hW
hI for a thawed bed,
PW/PI = 1 for shelf flow because
hI = (rW/rI) hW for floating ice, and
PW/PI increases from nearly zero to nearly
unity downslope along ice streams, which
are fast currents of ice that drain most of a marine ice sheet.
Accumulation rate
a along an ice flowline is taken as constant, and
ice thickness changes at a rate
dhI/dt that is positive for
a thickening ice sheet and negative for a thinning ice sheet. Ice
thickness is
h
I = h
- hG across an ice-shelf
grounding line, where
h
I = hI and ice velocity
uG is negative for
x positive upslope. Stresses in equation (1) are
tS for side shear in stream flow and shelf flow,
t0 for basal shear
in sheet flow and stream flow, and
sT for longitudinal tension and
its gradient
DsT/Dx, expressed in terms of
PW/PI and
D(PW/PI)/Dx, and linked to the mass balance through
longitudinal extending strain rate
eT, ice hardness parameter
A, and ice viscoplastic parameter
n in the flow law
eT (sT/A)n for creep in ice. The quantity
tS(PW/PI) allows a
reduction in resistance from side shear as basal shear increases due
to decreasing
PW/PI.
[49] In the geometrical force balance,
t0 is determined by the
ice surface slope
Dh/Dx and by the ice thickness
hI
- hW
(rW/rI) that is supported by the bed, not by basal water pressure:
![]() | (2) |
and
sT is determined by the ice thickness
hW (rW/rI) that is supported by basal water pressure,
not by the bed, where
sT appears in longitudinal tensile force
FT given by:
![]() | (3) |
so that:
![]() | (4) |
Therefore, t0 decreases as sT increases, and vice versa. The controlling variable is PW/PI.
[50] The decrease of PW/PI upslope from an ice-shelf grounding line is a consequence of progressive loss of hydraulic continuity as the ice overburden becomes increasingly supported by the bed, not by basal water pressure. In ice streams, this loss is accompanied by side shear and basal shear which contribute to a back-force FB that becomes progressively larger with distance x upslope from the calving front of an ice shelf. For floating ice, the back force is also due to average water pressure PW = 12 PW = 12 rW ghW exerted on cross-sectional area wI hW for a flowband of width wI at x = 0. The back stress sB for both grounded and floating ice at any distance x is given by the negative term in equation (3):
![]() | (5) |
For right-hand terms in equation (5), the first term is the back force exerted by water at the calving front of an ice shelf where x = 0, the second term is the increase of the water back force due to ice-shelf thickening over floating length L from the calving front to the grounding line of the ice shelf, the third term is the average side shear force along x due to average side shear stress tS acting on average ice thickness hI for PW/PI veraged over x, and the fourth term is the average basal shear force along x due to average basal shear stress t0 acting on average flowband width wI.
[51] In applying equations (1) through (5) to flowlines of the Okhotsk
Ice Sheet, ice-shelf buttressing is virtually complete because floating
ice over Kuril Basin would have been grounded along Kuril Island Arc.
Therefore floating ice would have had a nearly constant thickness, so
the second term in equation (5) can be ignored. An average side shear stress
of
tS = 250 kPa can be applied, taking measurements along West
Antarctic ice streams
[Raymond et al., 2001].
An average basal shear stress can be determined from equation (2)
for average values of
hI, PW/PI, and
Dh
/Dx,
using an iterative procedure for successive steps of
Dx = 20 km
along ice flowlines. In the first iteration,
PW/PI = 1 for floating
ice and
PW/PI = (1 - x/Ls)c for grounded ice, with
Ls being
the length of the grounded flowline and
c ranging from 2 to 5 such
that all flowlines have comparable heights at the interior ice divide.
For the first
Dx step,
t0 = 100 kPa is taken for ice
margins grounded on land or in water, assuming the ice shelf is grounded
at the calving front along the Kuril Island Arc. A frozen bed is assumed
for ice flowlines north of the interior ice divide, so
PW/PI = 0 and
t0 = 100 kPa are taken along these flowlines. In the flow law of ice,
n = 3 and
A = 231
10 kPa a1/3 were used, assuming an average ice
temperature of
- 20oC. In adition,
r = r0, a = 0.2 m a-1 and
dhI/dt = 0 were assumed, with
rR = 3200 kg m-3,
rI = 917 kg m-3,
rW = 1020 kg m-3, and
g = 980 m s-2.
Present-day topography and bathymetry were used for
hR, with
hG = 1000 m
and
uG determined from mass-balance conservation.
![]() |
Figure 7 |
Citation: 2005), "Back-arc" marine ice sheet in the Sea of Okhotsk, Russ. J. Earth Sci., 7, ES5004, doi:10.2205/2005ES000180.
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