Quaternary Science Reviews 28 (2009) 1831–1849
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Quaternary Science Reviews
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Modeling ice sheets from the bottom up
T. Hughes*
Department of Earth Sciences, Climate Change Institute, University of Maine, Bryand Global Sciences Center, Grove Street Extension, Orono, ME 04469-5790, USA
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 6 November 2008
Received in revised form
25 May 2009
Accepted 6 June 2009
Three facts should guide ice-sheet modeling. (1) Ice height above the bed is controlled by the strength of
ice-bed coupling, reducing ice thickness by some 90 percent when coupling vanishes. (2) Ice-bed
coupling vanishes along ice streams that end as floating ice shelves and drain up to 90 percent of an ice
sheet. (3) Because of (1) and (2), ice sheets can rapidly collapse and disintegrate, thereby removing ice
sheets from Earth’s climate system and forcing abrupt climate change. The first model of ice-sheet
dynamics was developed in Australia and applied to the present Antarctic Ice Sheet in 1970. It treated
slow sheet flow, which prevails over some 90 percent of the ice sheet, but is the least dynamic
component. The model made top-down calculations of ice velocities and temperatures, based on known
surface conditions and an assumed basal geothermal heat flux. In 1972, Joseph Fletcher proposed a sixstep research strategy for studying dynamic systems. The first step was identifying the most dynamic
components, which for Antarctica are fast ice streams that discharge up to 90 percent of the ice. Ice-sheet
models developed at the University of Maine in the 1970s were based on the Fletcher strategy and
focused on ice streams, including calving dynamics when ice streams end in water. These models
calculated the elevation of ice sheets based in the strength of ice-bed coupling. This was a bottom-up
approach that lowered ice elevations some 90 percent when ice-bed coupling vanished. Top-down
modeling is able to simulate changes in the size and shape of ice sheets through a whole glaciation cycle,
provided the mass balance is treated correctly. Bottom-up modeling is able to produce accurate changes
in ice elevations based on changes in ice-bed coupling, provided the force balance is treated correctly.
Truly holistic ice-sheet models should synthesize top-down and bottom-up approaches by combining
the mass balance with the force balance in ways that merge abrupt changes in stream flow with slow
changes in sheet flow. Then discharging 90 percent of the ice by ice streams mobilizes 90 percent of the
area so ice sheets can self-destruct, and thereby terminate a glaciation cycle.
Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction
This review primarily traces the trajectory of my glaciological
career, which began in 1968. Consequently, those who influenced
my career the most are cited prominently. My apologies to other
prominent glaciologists. A half-century ago, glaciology was being
converted from a descriptive branch of geology to an analytical
branch of physics. Analytical reconstructions of ice sheets began
with the parabolic profile of an ice sheet having a constant basal
shear stress on a horizontal bed (Nye, 1951). Next, the basal shear
stress was allowed to vary with ice velocity determined by
a constant surface accumulation rate and whether ice moved by
creep over a frozen bed (Haefeli, 1961) or by sliding over a thawed
bed (Nye, 1959), using the newly published flow law (Glen, 1955)
and sliding law (Weertman, 1957a) of ice. These treatments
* Tel.: þ1 207 581 2198; fax: þ1 207 581 1203.
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0277-3791/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.quascirev.2009.06.004
produced elliptical ice-sheet profiles on a horizontal bed. Ablation
rates were added and both accumulation and ablation rates were
allowed to vary in later refinements (see Hughes, 1998, Figure 5.10).
In all these treatments, gravitational ice motion was resisted by
a basal shear stress proportional to the product of ice height above
the bed and ice surface slope. The resulting ice surface was high and
convex, even when moderate bed topography was included. Their
dependence on the surface mass balance made them top-down
models that produced nearly steady-state ice sheets. The ice sheets
of Antarctica and Greenland today are nearly in steady state overall,
within the accuracy of the surface mass balance. These ice sheets
have high convex surfaces where slow sheet flow prevails, as
assumed in the analytical models. The Antarctic Ice Sheet often
ends as floating ice shelves because ice accumulation over virtually
its entire surface allows it to advance into the sea, where iceberg
calving provides the primary ablation mechanism. Weertman
(1957b) provided the first analytical derivation of the low and
essentially flat surface of a floating ice shelf. In his derivation,
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T. Hughes / Quaternary Science Reviews 28 (2009) 1831–1849
gravitational ice motion is resisted by a longitudinal tensile stress
proportional to the height of ice floating above sea level.
2. Modeling ice sheets from the top down
Numerical ice-sheet modeling was inaugurated by William
Budd, Richard Jenssen, and Uwe Radok in 1971. They developed
a steady-state flowline model which they applied to the Antarctic
Ice Sheet in order to derive variations of temperature, stress, and
velocity with depth, using measured ice heights above the bed, ice
elevations above sea level, ice surface accumulation rates, and ice
surface temperatures (Budd et al., 1971). From these data, their
model plotted ice trajectories and timelines with depth along
surface flowlines, and calculated either basal ice temperatures
below the melting point or basal ice melting rates at the melting
point for specified rates of the basal geothermal heat flux. Doubling
the geothermal heat flux converted a ubiquitously frozen bed into
a largely thawed bed. Widespread changes from a frozen to
a thawed bed also resulted from moderate changes in conditions at
the ice surface. An outer basal freezing zone was introduced beyond
the inner basal melting zone in subsequent applications of the
model to prevent widespread ice-bed decoupling as the basal water
layer thickened (Sugden, 1977).
Budd and Radok were meteorologists who saw interactions of
the ice surface with the atmosphere as the critical boundary
condition in modeling ice sheets. Budd et al. (1971) specified
surface conditions in order to determine basal conditions. Theirs
was a top-down model in which the surface mass balance combines
with the force balance to offset gravitational motion with basal drag
that resists motion. By that constraint, their model applied only to
slow sheet flow. This is known as the ‘‘shallow-ice’’ approximation
(Hutter, 1983). Their pioneering work set the stage for developing
gridpoint ice-sheet models that were three dimensional and time
dependent. Time-dependent modeling showed that present basal
thermal conditions are determined primarily by past surface
conditions, not present conditions, even if surface changes from
past to present are only moderate. These models also simulate only
slow sheet flow, which prevails over some 90 percent of ice sheets,
past and present. In sheet flow, gravitational flow is resisted
primarily by basal drag, as quantified by the basal shear stress.
Since past surface conditions are poorly known for present ice
sheets, and unknown for former ice sheets, top-down models
cannot deliver reliable basal conditions for 90 percent of the bed
beneath ice sheets. For example, when a state-of-the-art three
dimensional time dependent top-down model was applied to the
Antarctic (Huybrechts, 1990, 1992) and Greenland (Huybrechts,
1994, 1996) ice sheets, it was unable to generate the amount and
distribution of basal water that has been mapped by radar sounding
in both Antarctica (Siegert et al., 1996) and Greenland (Oswald and
Gogineni, 2008), unless the model used a distribution of basal
geothermal heat flux that forced a fit. Basal water controls ice-bed
coupling, and therefore the height and stability of ice sheets. Basal
water cannot support a basal shear stress, so gravitational flow is
not resisted by basal drag when basal ice is no longer in contact
with the bed. As a consequence, progressive reduction of ice-bed
coupling by basal water converts the high convex surface of
a grounded ice sheet into the low and flat surface of a floating ice
shelf. The ice sheet has destroyed itself when the ice shelf disintegrates into icebergs. Disintegration of an ice shelf is also
a consequence of eliminating ice-bed coupling where the ice shelf
is grounded laterally in a confining embayment and where the ice
shelf is pinned locally to the sea floor, producing ice rumples or ice
rises on the ice-shelf surface above each pinning point. Confined
and pinned ice shelves are common where the Antarctic Ice Sheet
advances into the sea and becomes afloat.
The top-down models for sheet flow by Budd et al. (1971) and
later top-down models were incompatible with important field
data from Antarctica, much of it collected by tractor-train traverses
during the International Geophysical Year (IGY) in 1958 and
beyond. The traverses measured ice elevations, temperatures, and
accumulation rates at the surface and ice heights above the bed
along traverse routes. The data, traverse routes, and geographical
features appeared on the 1970 map, Antarctica, published by the
American Geographical Society. Contoured bed topographic data
showed that most of the West Antarctic Ice Sheet was grounded
below sea level on the Antarctic continental shelf (Bentley and
Ostenso, 1961), leading Mercer (1970) to propose that it was an
inherently unstable ‘‘marine’’ ice sheet. Contoured surface elevation data showed the East Antarctic Ice Sheet had the convex
surface produced by steady-state models of sheet flow, but the
West Antarctic Ice Sheet had a concave surface. Perhaps the West
Antarctic Ice Sheet was far from steady state and in fact was in an
advanced stage of gravitational collapse that produced the low
floating ice shelves surrounding it. My response to this possibility
appeared in four monographs, in 1972, 1973, 1974, and 1975, under
the acronym ISCAP (Ice Streamline Cooperative Antarctic Project),
all of which posed the question, ‘‘Is the West Antarctic Ice Sheet
disintegrating?’’ Was the West Antarctic Ice Sheet not only
collapsing into ice shelves, but would the ice shelves then disintegrate into icebergs, thereby removing the West Antarctic Ice
Sheet from the global climate system, and flooding the world ocean
with icebergs that, in melting, would cool ocean surface water and
therefore reduce the ocean-to-atmosphere heat exchange that
drives atmospheric circulation? Could a new glaciation cycle then
begin?
3. The Fletcher memorandum
Incorporated in my ISCAP bulletins was a research strategy for
studying dynamic systems proposed by Joseph Fletcher in an
internal memorandum when he headed the Office of Polar
Programs at the National Science Foundation (Fletcher, 1972).
Fletcher recommended research that answered six questions
directed at how any dynamic system operates. His six questions and
my answers for the Antarctic Ice Sheet that also apply to all ice
sheets are:
1. What are its most dynamic parts? Answer: ice streams,
including their calving fronts when ice streams end grounded
in water or as floating ice tongues often imbedded in ice
shelves.
2. What factors force motion in these parts? Answer: gravity
resisted by ice-bed coupling and atomic bonding in ice.
3. Which of these factors vary over time? Answer: ice-bed
coupling and breaking atomic bonds during iceberg calving
events.
4. What physical processes cause the time variations? Answer:
processes that weaken or strengthen ice-bed coupling and that
lead to and cause calving of ice.
5. Can these processes be quantified theoretically? Answer: yes,
but the processes are poorly understood and the theories must
be holistic, including transitions from sheet flow to stream flow
to shelf flow and the dynamics of calving.
6. What experiments will test the theories? Answer: experiments
designed to gather broad comprehensive data over the
Antarctic Ice Sheet, especially in West Antarctica and relying
heavily on satellite technology, combined with field studies
that include deep drilling and are concentrated on ice streams
and their calving fronts where rapid changes in behavior are
observed, with all data being input to computer models
T. Hughes / Quaternary Science Reviews 28 (2009) 1831–1849
designed to replicate observed behavior and to project
behavior into the future when internal and external forcing
may change.
The ISCAP bulletins applied my answers to Fletcher’s questions
in a research strategy for the Antarctic Ice Sheet as a dynamic
system that was changing most noticeably in West Antarctica. My
answers were based on glaciological, geophysical, and geological
field studies in Antarctica during and after the International
Geophysical Year in 1958. Much of the glaciological and geophysical
research was directed by Charles R. Bentley and published in
Volume 16 of the Antarctic Research Series of the American
Geophysical Union (Crary, 1971). Because ice streams discharge 90
percent of Antarctic ice, instabilities in ice streams make the entire
Antarctic Ice Sheet inherently unstable and subject to rapid
collapse, collapse that was largely complete in its marine West
Antarctic sector that has a concave surface and is mostly grounded
below sea level. Field studies of glacial and marine geology in the
Dry Valleys of the Ross Sea embayment by Denton et al. (1968,
1971), on East Antarctic outlet glaciers through the Transantarctic
Mountains into the embayment by Mercer (1968, 1972), and in the
Weddell Sea embayment by Anderson (1972) confirmed collapse of
former marine ice sheets in these parts of West Antarctica. Field
studies of surface lowering along the Byrd Station Strain Network in
the center of West Antarctica by Whillans (1972, 1973) provided
direct evidence that collapse was still underway.
Newly developed airborne radar sounding technology was
applied to the West Antarctic Ice Sheet, showing that the concave
surface was a consequence of major ice streams (Robin et al., 1970a)
and that basal water was abundant where these ice streams had
a nearly flat surface, as though here the ice streams were afloat,
making these portions ‘‘pseudo ice shelves’’ (Robin et al., 1970b).
Concave ice streams draining the West Antarctic Ice Sheet supplied
floating ice shelves, so ice streams seemed to be the vehicles by
which gravitational collapse converted the high convex surface of
nearly steady-state sheet flow into the low flat surface of shelf flow.
The ISCAP bulletins were designed to test this hypothesis. Their
contents were subsequently published in refereed journals
(Hughes, 1973, 1975, 1977) and as a book chapter (Hughes, 1998,
Chapter 3). They presented a case for studying ongoing gravitational collapse of the West Antarctic Ice Sheet.
Glaciologists began studying the ice streams mapped by Robin
et al. (1970a). Early results were presented at a conference sponsored by the American Association for the Advancement of Science
(AAAS) at the University of Maine on 8–10 April 1980, as recorded
by Horne (1980). These studies led to The West Antarctic Ice Sheet
Initiative (WAIS) funded by the U.S. National Science Foundation
(NSF) as a long-term investigation of this possibility (Bindschadler,
1991). Results over the next decade were presented at a Chapman
Conference sponsored by the American Geophysical Union (AGU)
and held at the University of Maine on 13–18 September 1998
(Bindschadler and Borns, 1998). More recent results are presented
in Volume 77 of the AGU Antarctic Research Series (Alley and
Bindschadler, 2001). WAIS workshops have been held annually
since 1993.
The ISCAP bulletins explored two mechanisms for gravitational
collapse. The first mechanism was gravitational collapse progressing inward from marine margins of the West Antarctic Ice Sheet.
Collapse was triggered by rising sea level, beginning 18,000 years
ago, and accelerated by disintegration of floating ice shelves formed
during collapse. Ross Ice Shelf occupies a confining embayment and
is pinned to the sea floor at places identified by ice rumples and ice
rises on the surface (Hughes, 1972, 1973). Surface velocities along
the north–south leg of the Ross Ice Shelf Survey (Dorrer et al., 1969)
were less than velocities for ice entering the Ross Ice Shelf from
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West Antarctica, based on mass-balance measurements available at
the time (Bull, 1971). Perhaps a confined and pinned ice shelf can
buttress the ice streams supplying it. Then, if the ice shelf disintegrated, perhaps ice streams would rapidly downdraw the
remaining ice sheet until it became afloat. If the bed under these ice
streams sloped downward into the ice sheet, retreat of the ice-shelf
grounding line would force ice streams to retreat. Weertman (1974)
published the essence of this retreat mechanism (Fig. 1) and
Thomas (1977) quantified the processes driving retreat (Fig. 2).
Thomas and Bentley (1978) applied the mechanism to model
collapse on the former marine ice sheet in the Ross Sea Embayment
when ice-bed uncoupling began 18,000 years ago with rising global
sea level. They assumed the convex surface of sheet flow extended
to the grounding line of Ross Ice Shelf, as it does for ice ridges
between ice streams. De Angleis and Skvarka (2003) documented
retreat when part of Larsen Ice Shelf disintegrated.
In the second mechanism for gravitational collapse, heads of
concave ice streams retreat and drag the marine ice-shelf
grounding lines with them (Hughes, 1974, 1975). This seemed
possible, based on the theory for cyclic surging mountain glaciers
developed by Robin and Weertman (1973), applied to account for
nearly flat sections, ‘‘pseudo ice shelves,’’ of West Antarctic ice
streams reported by Robin et al. (1970b). Ice-bed uncoupling by
deepening basal water under the flat sections would migrate
upstream if the pressure gradient of basal water decreased upslope,
causing the maxima in surface slope between each flat section to
migrate upslope. This process may now be underway in West
Antarctic ice streams (Bindschadler, 1997) and it causes the ice
streams to retreat. In both cases, collapse of the ice sheet is determined by conditions at the bed, specifically ice-bed uncoupling. To
capture these mechanisms, which depart radically from steadystate conditions, models should be constructed from the bottom up.
4. Reconstructing former ice sheets for CLIMAP
The International Decade of Ocean Exploration (IDOE), 1970–
1980, was underway when my ISCAP bulletins were circulating and
Fig. 1. The marine ice instability at marine ungrounding lines of ice sheets (Weertman,
1974). Top left: the base of right-triangles are equal basal ice and water pressures, the
heights of these triangles are heights of ice and water above the base, the areas of these
triangles are opposing longitudinal gravitational driving forces in ice and water per
unit transverse width, the pulling force is the difference between these areas, shown as
the dashed triangle. Top right: the longitudinal pulling force is the area of the dashed
triangles and is proportional to the square of ice thickness. Bottom: as the ungrounding
line retreats, the pulling force increases on a downsloping bed and decreases on an
upsloping bed because the floating ice thickness increases and then decreases.
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T. Hughes / Quaternary Science Reviews 28 (2009) 1831–1849
Fig. 2. Processes triggering gravitational collapse of marine portions of an ice sheet
(Thomas, 1977). The ungrounding line migrates across basal sills due to (a) ice thinning
during an ice-stream surge, (b) lowering the sill due to glacial erosion or ongoing bed
depression under the weight of ice, (c) rising sea level that lifts floating ice, (d) melting
the upper or lower surfaces of floating ice, and (e) accelerated calving causing a calving
bay to migrate up the ice stream.
an awareness was taking root that ice sheets may be the most
vulnerable component of Earth’s climate system (Hollin, 1972). A
major part of IDOE was CLIMAP (Climate: Long-range Investigation,
Mapping, and Prediction). CLIMAP provided glaciologists with an
opportunity to become part of the large scientific community
engaged in documenting and understanding global climate change.
George Denton at the University of Maine (UM) was charged
primarily with reconstructing ice sheets at the Last Glacial
Maximum (LGM) for 18 ka BP, but also with disintegrating the
marine West Antarctic Ice Sheet during the preceding Eemian
Interglacial at the Last Interglacial Maximum (LIM) for 125 ka BP.
Denton recruited me for these tasks. The top-down model of ice
sheets developed by Budd et al. (1971) was not suited to the CLIMAP tasks, so I developed a bottom-up approach for reconstructing
and disintegrating ice sheets. James Fastook and David Schilling
contributed mightily to this effort. We incorporated the marine ice
instability (Weertman, 1957a,b; Thomas, 1977) in conducting the
LIM experiment.
The primitive models of atmospheric circulation used by CLIMAP required three boundary conditions that only ice sheets could
provide. These models needed (1) the areal extent of ice sheets (and
sea ice) as albedo input, (2) the volume of ice sheets to obtain the
reduced ocean surface area in the ocean-to-atmosphere heat
exchange, and (3) the elevation of ice sheets to obtain the surface
topography that may re-direct surface winds and the jet stream. As
a glacial geologist, Denton could provide the areal extent of ice
sheets, but he needed a glaciologist to determine their volume and
elevation at the LGM, and a mechanism to collapse the West
Antarctic Ice Sheet to obtain the Eemian sea level 6 m higher than
at present at the LIM. The only numerical model for ice sheets
available at that time was the flowline model Budd et al. (1971) had
developed for the Antarctic Ice Sheet. My ISCAP bulletins highlighted defects in that modeling approach, the primary defect being
theirs was a top-down model of sheet flow in which the amount
and distribution of basal water was very sensitive to the surface
temperature and accumulation rates and the basal geothermal heat
flux. None of this information was available for former ice sheets to
be reconstructed for CLIMAP. However, these data are of minor
importance in reconstructing former ice sheets because the
primary result CLIMAP needed was ice elevations above the bed.
That depends on the strength of ice-bed coupling, which could be
determined from the glacial geology Denton was providing,
a bottom-up approach.
Bottom-up modeling requires distinguishing between ‘‘firstorder’’ and ‘‘second-order’’ glacial geology. First-order glacial
geology consists of a glacial imprint on the deglaciated landscape
that becomes more pronounced with each cycle of Quaternary
glaciation due to repeated processes of nearly steady-state glacial
erosion and deposition. Second-order glacial geology is produced
over time during the last glacial retreat. It overprints first-order
glacial geology. Most glacial geologists at that time were mapping
and dating second-order glacial geology. For this reason, our icesheet reconstructions based on first-order glacial geology were
rejected when we presented them at the International Symposium
on Dynamics of Large Ice Masses, sponsored by the International
Glaciological Society and held in Ottawa, Canada, in 1978. We
subsequently published our CLIMAP work in book form, The Last
Great Ice Sheets (Denton and Hughes, 1981). It is necessary to
present the rationale for our bottom-up approach based on firstorder glacial geology that determines ice-bed coupling and therefore ice elevations above the bed. In the bottom-up approach, the
unknown surface conditions and basal geothermal heat flux at the
LGM and LIM, and the previous history of an ice sheet, are virtually
irrelevant in determining the size and shape of former ice sheets.
Ice-bed coupling weakens when a frozen bed becomes thawed
beneath an ice sheet. For slow sheet flow, basal thawing lowers the
ice surface by about 20 percent. Thawing begins in bed hollows,
from which progressive thawing expands and eventually envelops
bed hills as ice flows across a melting bed. When ice flows across
a freezing bed, hilltops are frozen first and hollows last. Complete
freezing raises the ice surface by about 25 percent and restores the
surface above a frozen bed. Therefore, melting and freezing beds
consist of a mosaic of frozen and thawed patches which are
determined primarily by bed topography. Ice surfaces above both
frozen and thawed beds are high and convex. Melting and freezing
zones along an ice-sheet flowline produce respectively more steep
and less steep ice surface slopes in the flow direction, but the
overall ice surface remains convex (Fig. 3).
Once the bed is wholly thawed, continued basal melting will
submerge the wet bed, first in hollows but progressive submergence eventually envelops hills as well. Since bed topography
includes linear channels formed by tectonic activity or by subaerial
and submarine erosion processes before the ice sheet existed,
drowning of the bed will preferentially occur along channels. The
resulting ice-bed decoupling will allow overlying ice to move faster
along these channels because resistance to gravitational motion is
T. Hughes / Quaternary Science Reviews 28 (2009) 1831–1849
Fig. 3. Response of ice elevation and ice trajectories to ice-bed coupling linked to basal
thermal conditions (Denton and Hughes, 1981, Chapter 5). For sheet flow, the ice
surface lowers 20 percent as a frozen bed thaws and rises 25 percent as a thawed bed
freezes (broken surface lines). Frozen beds are white. Thawed beds are black. Basal
shear stresses sO are higher for creep (sO)C over a frozen bed and lower for sliding (sO)S
over a thawed bed (broken tau lines). Top: ice elevations and trajectories as ice moves
from a frozen bed on an upland plateau across melting and freezing beds to a frozen
bed under a surface ablation zone on land. Bottom: ice elevations and trajectories as ice
moves from a thawed bed in a marine embayment across freezing and melting beds to
a thawed bed under a marine ice stream that becomes afloat. Melting and freezing
beds are shown as a mosaic of thawed (black) and frozen (white) patches.
weakened by the deepening basal water. Fast currents of ice in
these channels will become ice streams imbedded in the ice sheet,
especially toward ice margins where thinning sheet flow is forced
to increasingly conform with bed topography. Ultimately, up to 90
percent of ice in an ice sheet is discharged by ice streams. It is
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unclear whether stream flow begins when basal water submerges
hills lower than a critical size, supersaturates till or sediments to
a critical depth, or drowns bedrock bumps up to a ‘‘controlling
obstacle size’’ in the Weertman (1957a) theory of basal sliding.
Progressive reduction of ice-bed coupling along channels where
basal water progressively drowns the topography of a hard bed,
mobilizes the till or sediments of a soft bed, or both, will produce
the lowering concave surface of ice streams that ends with the low
flat surface of ice tongues in water or as the low convex surface of
ice lobes on land. Basal water draining around the perimeter of an
ice lobe allows partial ice-bed recoupling and gives the lobe its low
convex surface. If ice tongues enter an embayment, they can merge
to become a floating ice shelf that is grounded along the sides of the
embayment or at basal pinning points within the embayment. In
this way partial ice-bed coupling continues into the embayment,
and allows the ice shelf to buttress the ice streams (Thomas,
1973a,b). Most West Antarctic ice streams enter the Ross Sea and
Weddell Sea marine embayments, where their floating ice tongues
merge to become the buttressing Ross and Ronne–Filchner ice
shelves.
The former LGM ice sheets of North America and Eurasia were
centered on Hudson Bay in North America and over the Gulf of
Bothnia, Barents Sea, and (in my opinion) Kara Sea in Eurasia, all
isostatically depressed by the weight of overlying ice. Postglacial
raised beaches and negative gravity anomalies are first-order
features that locate these centers of ice spreading at the LGM when
the ice load was greatest. They are first-order glacial features. Being
marine water bodies originally, the ice domes that formed above
them probably rested on a largely thawed bed in the deepest water.
From these centers, ice moved across exposed Precambrian crystalline shields from which the remaining overlying layer of sedimentary rock has been removed by Quaternary glacial erosion, after
eons of subaerial erosion. Since these shields are spattered with
lakes, which would have been thawed patches under the ice, the ice
sheets moved across a freezing bed that was a mosaic of thawed
and frozen patches. These eroded shields are first-order glacial
features. Beyond the shields, rock and regolith eroded from the
thawed patches are deposited over the largely un-eroded sedimentary rock cover, producing looping end moraines. This band of
depositional moraines is a first-order glacial feature. The biggest
looping moraines lie beyond troughs eroded in the sedimentary
rock cover. Today, these troughs are often occupied by linear lakes
on land (notably the Great Lakes in North America). Along marine
ice margins, the troughs are linear straits and inter-island channels
today. The troughs were occupied by ice streams at the LGM and are
first-order glacial features. Fast stream flow produced a melting bed
that cut across the freezing bed between ice streams. Each cycle of
Quaternary glaciation reinforced the imprint of these first-order
glacial features on the deglaciated landscape (Hughes, 1981a;
Hughes et al., 1981). In North America, the Laurentide Ice Sheet
centered on Hudson Bay merged with a Cordilleran Ice Sheet which
had a frozen bed beneath ice divides along the crests of mountain
ranges and a thawed bed in valleys on the flanks of these ranges,
giving an overall melting bed from ice divides to ice margins as
a first-order glacial feature.
In the CLIMAP Eemian modeling experiment at the LIM, the
Thomas (1977) marine instability mechanism at ice-stream
ungrounding lines was applied to the CLIMAP West Antarctic Ice
Sheet at the LGM (Stuiver et al., 1981). Rising sea level since the
LGM triggered the marine instability, causing ungrounding lines to
retreat up the concave CLIMAP ice streams (Fig. 4). The ice sheet
collapsed into ice shelves on its eastern and western flanks,
producing the Weddell Sea embayment occupied by the Ronne–
Filchner Ice Shelf and the Ross Sea embayment occupied by the
Ross Ice Shelf. Subsequent collapse occurred on its northern flank,
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T. Hughes / Quaternary Science Reviews 28 (2009) 1831–1849
Fig. 4. : Gravitational collapse of the West Antarctic Ice Sheet during Terminations of Quaternary glaciation cycles modeled for CLIMAP at the LIM (Denton and Hughes, 1981,
Chapter 10). Ice is downdrawn by progressive ice-bed uncoupling along ice streams occupying the shaded submarine troughs. Stages of collapse proceed from the glacial maximum
(A), to progressive collapse in marine embayments of the Ross, Weddell, and Amundsen seas (B and C), to collapse of the central West Antarctic Ice Sheet (D), to disintegration of
buttressing ice shelves produced during collapse (E).
T. Hughes / Quaternary Science Reviews 28 (2009) 1831–1849
producing an equally large embayment in the Amundsen Sea when
ungrounding lines migrated up Thwaites and Pine Island glaciers
into the heart of West Antarctica. Pine Island Bay is the beginning of
that embayment today. Final collapse occurred following disintegration of the confined and pinned ice shelves that formed as
ungrounding lines retreated. These ice shelves had buttressed the
retreating ice streams. This LIM experiment could apply equally to
the present Holocene Interglacial, and projects ongoing collapse of
the West Antarctic Ice Sheet into the future. Collapse is entirely due
to ice-bed uncoupling that progresses up lowering concave ice
streams and allows calving bays to discerp the downdrawn ice.
Ice-bed uncoupling can also proceed from the interior of ice
sheets along ice streams to ice margins, as had been modeled for
the Laurentide Ice Sheet in Hudson Bay and its ice stream in Hudson
Strait (MacAyeal, 1993; Calov et al., 2002). When a frozen bed
thaws, ice-bed coupling is largely lost in these models, and the icesheet collapses and spreads until surface lowering brings cold
interior ice into contact with the bed, causing the bed to freeze so
surface ice accumulation can restore the original ice elevation.
These ‘‘binge/purge’’ cycles can be tuned to mimic Heinrich (1988)
events for quasi-periodic rapid discharges of icebergs from the
Laurentide Ice Sheet. No changes in ice surface temperature and
accumulation rates are required, not even changes linked to the
lowering ice surface. Changing surface conditions take millennia to
affect the basal thermal regime (Whillans, 1981), so surface changes
have little effect on these essentially bottom-up processes linked to
abrupt ice-bed decoupling and recoupling.
The CLIMAP bottom-up approach to ice-sheet modeling focused
attention on ice streams. Since ice streams discharge up to 90
percent of ice from past and present ice sheets, modeling icestream dynamics correctly can generate changes in the size and
shape of ice sheets that are big enough and fast enough to trigger
rapid changes in global climate and sea level. Changes of this kind
are well documented for former ice sheets (Denton and Hughes,
1981; Mayewski et al., 1997), and even now are becoming manifest
in present ice streams in Antarctica (Thomas et al., 2004) and
Greenland (Thomas, 2004). Top-down models controlled by the
surface mass balance are often unable to advance the Laurentide Ice
Sheet below the Great Lakes at the Last Glacial Maximum (LGM),
which did happen, without also advancing the Cordilleran Ice Sheet
almost to Mexico, which didn’t happen. This is because ice elevations at the center of the Laurentide Ice Sheet over Hudson Bay
must be high enough, from a positive mass balance, to force sheet
flow across the Great Lakes. With ice streams occupying the deep
troughs of the Great Lakes, the southern Laurentide margin is
rapidly advanced by greatly reducing ice-bed coupling when
summer meltwater in the surface ablation zone reaches the bed,
probably through crevasses (Zwally et al., 2002). This process
would be greatly accelerated by heavy summer rainfall over the
southern Laurentide ablation zone (Bromwich et al., 2004).
The ablation zone, not the accumulation zone, controls advance of
the ice margin by controlling ice-bed decoupling. In the ablation,
zone, therefore, surface conditions can directly influence basal
conditions, with no time lag. Such is not the case in the accumulation
zone.
5. The Peltier challenge
The CLIMAP reconstructions of ice sheets at the LGM were used
by climate modelers throughout the decade of the 1980s until 1994,
when W. Richard Peltier presented another approach to reconstructing LGM ice sheets in his paper, ‘‘Ice Age Paleotopography’’
(Peltier, 1994). He had developed models of global isostasy in which
the lengths of Earth radii changed as the load of ice and water over
Earth’s surface changed during glaciation cycles. His radii had
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a viscous response in the mantle and an elastic response in the
lithosphere to changing surface loads. This allowed him to determine mantle viscosities and lithosphere flexures which he then
used, in a circular way, to calculate the changing height (calculated
ice load) of ice at the end of these radii from the known changing
areal extent of ice sheets and changing sea level (measured water
load) during the last deglaciation. Glaciologists weren’t needed. He
published his ice elevations on the Internet at precisely the locations climate modelers preferred in their General Circulation
Models (GCMs) of Earth’s atmosphere. In my view, Peltier’s challenge has been good for glaciology. Competition is always good, and
his approach compels glaciologists to examine more critically the
defects in their approach to ice-sheet modeling.
The Achilles’ heel in Peltier’s approach was threefold: (1) his
model depends on the rheology of Earth’s interior, a rheology
which can never be known as accurately as the rheology of ice
sheets, (2) only vertical motion in the mantle and lithosphere is
treated, and (3) only a slow isostatic response is delivered for
changes in ice sheets when rapid climatic responses to rapid
changes in ice sheets are of most interest. In (1), Peltier treats ice
sheets as a purely static load on Earth’s surface. As a consequence of
ignoring ice-sheet modeling, his ice sheets tend to be too thin to
account for the known lowered sea level at the LGM and, contrary
to the glacial geological record, his ice sheets are more like ice slabs
of nearly constant thickness than even the idealized elliptical ice
sheets permit for constant accumulation rates. In (2), adding the
linear viscous radial extensions in Earth’s mantle to linear elastic
flexures in Earth’s lithosphere allows Peltier to use Green functions
to generate spherical harmonics on Earth’s surface that could be
linked to known changing sea levels worldwide as the loads of ice
and water changed during the last deglaciation. A more robust
model would allow elastic–viscoplastic lithosphere flexure, allow
lateral variations in nonlinear mantle viscosity as surface loads
changed, and allow nonlinear viscoplastic mantle creep to vary
laterally and interact with moving lithosphere plates and mantle
convection currents (Koons and Kirby, 2007). In (3), Peltier
provided no mechanisms for controlling ice elevations by specifying the strength of ice-bed coupling, coupling that weakens
drastically as basal ice melts and ultimately allows ice sheets to
destroy themselves. Rapid changes in the size and shape of ice
sheets in response to basal decoupling are not possible in Peltier’s
model, so it cannot be used in studying causes of abrupt climate
change. Peltier has modified his old approach to include mechanisms for ice-bed decoupling, based on glacial geology (Peltier,
2004; Tarasov and Peltier, 2004).
The CLIMAP ice sheets also had an Achilles’ heel. The gravitational driving stress for sheet flow in ice sheets is proportional to
the product of ice height above the bed and ice surface slope. This
driving stress was equated with the basal shear stress resisting
gravitational motion in the CLIMAP ice sheets. Generating the
concave CLIMAP ice streams by letting the basal shear stress
decrease along ice streams also made the gravitational driving
stress decrease, because both ice height above the bed and ice
surface slope decrease along a concave ice stream. That was unrealistic because marine ice streams typically end as floating ice
tongues which may or may not be imbedded in confined and pinned ice shelves. For floating ice, the gravitational driving stress is
proportional to ice height above water and it is equated with the
longitudinal tensile stress in an ice tongue (Weertman, 1957b). This
tensile stress is reduced when the ice tongue is imbedded in an ice
shelf confined laterally and pinned locally to the bed (Thomas,
1973a,b). Therefore, resistance to gravitational motion in an ice
stream should allow a downstream transition from basal shear to
longitudinal tension, with the tensile stress actually reaching up ice
streams and pulling ice out of the ice sheet. Including this stress in
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T. Hughes / Quaternary Science Reviews 28 (2009) 1831–1849
the longitudinal force balance introduced the ‘‘pulling power’’ of ice
streams.
6. The ‘‘pulling power’’ of ice streams
The bed was not only fully thawed under the CLIMAP ice
streams, basal water progressively drowned bed topography
downstream. Progressive drowning would produce a ‘‘floating
fraction’’ of ice that increased downstream. In hollows it might
even produce the ‘‘pseudo ice shelves’’ along West Antarctic ice
streams reported by Robin et al. (1970b). When ice was fully afloat,
the ice stream would become an ice shelf. Therefore, the concave
surface profiles of ice streams were bottom-up reflections of major
ice-bed uncoupling as the floating fraction increased from essentially zero under the high convex surface of sheet flow to essentially
one under the low flat surface of shelf flow. The Achilles’ heel in the
CLIMAP ice streams could be ‘‘healed’’ by making the floating
fraction of ice the primary variable in modeling stream flow. Sheet
flow alone cannot collapse an ice sheet and terminate a glaciation
cycle. Stream flow can because most of the ice, up to 90 percent, is
pulled out by ice streams. In his treatment of ice shelves, Weertman
(1957b) showed that the tensile gravitational ‘‘pulling’’ stress in
a flat ice shelf is determined by the height of ice floating above
water, not by the product of ice thickness and ice surface slope,
which is zero for a flat ice shelf. So as the floating fraction of ice
increases along an ice stream, the gravitational driving stress
changes from being determined by the product of ice thickness and
surface slope (which applies to sheet flow) to being determined by
the height of ice floating above water (which applies to shelf flow).
Gravitational thinning in Weertman’s ice shelf is resisted by
a longitudinal tensile stress that is a ‘‘pulling stress’’ on the ice
streams that supply an ice shelf. If stream flow is transitional
between sheet flow and shelf flow, this pulling stress should extend
up ice streams and ‘‘pull’’ ice out of ice sheets. Linking the floating
fraction of ice along an ice stream to the decrease in basal shear
stress that resists sheet flow and the increase in longitudinal
pulling stress that resists shelf flow quantifies how ice streams pull
ice out of ice sheets. I called this ‘‘the pulling power of ice streams,’’
pulling power being the product of the longitudinal gravitational
pulling force and the longitudinal ice velocity (Hughes, 1992).
Bottom-up ice-sheet modeling linked to the pulling power of ice
streams has been developed further since then (Hughes, 1998,
2003, 2009a,b). It remains a work in progress. The pulling power
concept is now being applied to ice streams in Greenland and
Antarctica that have suddenly increased their ice discharge in
recent years, behavior for which conventional glaciology theory
had no explanation solely in terms of sheet flow resisted by basal
drag. Those working on this problem all take the pulling power of
shelf-like flow into account, including the acceleration of marine
ice streams when a buttressing ice shelf disintegrates (e.g., Van der
Veen, 1985, 1987; MacAyeal, 1989; Hulbe and MacAyeal, 1999;
Hindmarsh and LeMeur, 2001; Marshall et al., 2002; MacAyeal
et al., 2003; Hulbe et al., 2004; Thomas, 2004; Thomas et al., 2004;
Dupont and Alley, 2005a,b; Marshall, 2005; Schoof, 2007; Hofstede,
2008).
In my approach to pulling power, as it exists now, ice-bed
uncoupling produces a floating fraction of ice under ice streams
that increases from being essentially zero for a frozen bed or small
for a thawed bed where sheet flow predominates, to unity or close
to unity as stream flow develops, and remains at or close to unity
when ice streams merge with floating ice tongues or confined and
pinned ice shelves, but decreases toward zero when ice streams
end as ice lobes grounded on land and beneath which basal water
can escape (Hughes, 2009a,b). All stresses in the direction of ice
flow depend on the floating fraction of ice. These stresses are basal
and side shear and longitudinal tension and compression. Basal
shear dominates in slow sheet flow, longitudinal tension dominates
in unconfined shelf flow, but all stresses appear in stream flow and
confined shelf flow. The floating fraction of ice is the part of the ice
overburden that is supported by basal water and for which longitudinal gravitational motion is resisted by longitudinal tension in
the ice. The remaining part is supported by the bed, so that longitudinal gravitational motion is resisted by basal and side shear and
longitudinal compression, all of which occur along ice streams and
in confined or pinned ice shelves.
Physically, the floating fraction of ice can be an ambiguous
quantity at the bed. Is it the submerged fraction of rolling bed
topography, supersaturated regions of basal sediments or till, the
drowned fraction of bedrock bumps that are smaller than the
controlling obstacle size in theories of basal sliding, or all of these?
The important point is that the floating fraction is linked to parts of
the bed that are unable to resist longitudinal gravitational motion
by generating basal or side shear or longitudinal compression.
Perhaps the best way to illustrate the floating fraction of ice is
with a cartoon that shows areas of wet thawed or drowned beds in
black and areas of dry frozen beds in white, with flow radiating
from both marine and terrestrial ice domes, including vertical
longitudinal cross-sections along selected flowline transects that
show ice trajectories (Fig. 5). In slow sheet flow, the bed is generally
wet under a marine ice dome over an embayment and dry under
a terrestrial ice dome over a plateau. Ice streams begin near the
marine dome but begin far from the terrestrial dome. Ice streams
moving landward end as ice lobes and ice streams moving seaward
end as ice shelves. Between ice streams, a freezing zone surrounds
the marine dome and a melting zone surrounds the terrestrial
dome, with these zones consisting of a mosaic of wet and dry
patches. Wet patches become elongated lakes or marine channels
in flow directions as ice velocity increases. Dry patches that thaw
become elongated drumlins or roches moutonees as velocity
increases. Eskers form in the braided drainage systems near ice
margins and under ice lobes.
7. Modeling a glaciation cycle from the bottom up
Bottom-up ice-sheet modeling allows reconstructing a full
glaciation cycle based on first-order glacial geology (Hughes, 1996).
This was presented at a symposium honoring Johannes Weertman
when he turned seventy. Since the symposium volume did not
reach many glaciologists, the work was presented again in Ice
Sheets (Hughes, 1998), which described the glacial geology on pages
239–250 in Chapter 9 and produced the reconstructed ice sheets on
pages 307–317 in Chapter 10. In these reconstructions, the basal
shear stress balanced gravitational forcing in sheet flow, but in
stream flow the basal shear stress was gradually replaced by the
longitudinal tensile stress along ice streams as providing primary
resistance to gravitational forcing. Northern Hemisphere ice sheets
were reconstructed for six stages in a generalized Quaternary
glaciation cycle based on the last cycle: (1) the initial advance of ice
sheets, (2) their extent during interstadials, (3) their advance from
interstadial to stadial positions, (4) their extent during stadials, (5)
their retreat from stadial to interstadial positions, and (6) their
collapse during Termination of the glaciation cycle. Ice elevations
above the bed depend mainly on ice-bed coupling assigned to each
stage.
Pleistocene ice sheets were nucleated at high northern latitudes
in both terrestrial and marine environments where permafrost is
continuous, even on broad Arctic continental shelves (Hughes,
1986a). Therefore these ice sheets had a high height-to-area ratio
during their initial advance because a frozen bed maximized icebed coupling.
T. Hughes / Quaternary Science Reviews 28 (2009) 1831–1849
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Fig. 5. : The flow regime linked to ice-bed coupling for an idealized ice sheet (Hughes, 1998, Chapter 9). Left: surface ice flowlines (solid lines) and the surface equilibrium line
(dashed line) linked to wet bed conditions where ice-bed coupling is weakened in sheet flow (mosaics of black patches) and largely lost in stream flow (solid black areas). Right:
flowline transects along the main ice divide (AA), from the main ice saddle (BB), from an ice dome above a marine embayment (CC), and from an ice dome above a highland plateau
(DD), showing ice trajectories (solid lines) for beds that are wet (W), dry (D), freezing (F), and melting (M), and regions of debris-charged refrozen basal ice (shaded areas).
Initial advance was primarily over Precambrian shields studded
with lakes. These lakes would have been thawed patches under the
spreading ice sheet. The largest lakes arc around the edges of the
shields and are furthest from centers of ice spreading, so they
would be interconnected pro-glacial lakes during interstadials
when the advancing ice sheets halted long enough to produce an
isostatically depressed trough along their landward margins at the
edge of the shields.
Beyond the shields and surrounding the centers of ice spreading
are straits and inter-island channels extending seaward and the arc
of large linear lakes extending landward. These linear troughs
would have been occupied by ice streams that advanced the icesheet margins during transitions from interstadials to stadials.
These transitions are triggered when complete thawing of the bed
takes place under the centers of spreading on the shields. Thawing
occurs because the increasing ice overburden finally crushes
basal ice into water, causing reduced ice-bed coupling (crushing is
physically observed as a reduction in ice volume and melting
temperature). The resulting partial gravitational collapse shot ice
streams into the surrounding troughs during stadials. The exposed
shields have ubiquitous erosion features produced by ice sliding over
a wholly thawed bed. This proves that thawed patches originally
confined to the smattering of lakes on the shields expanded over
the entire shield at glacial stadials, causing general ice-sheet
lowering and spreading, without a great change in ice mass.
As ice over the shields lowered, colder ice would move toward
the bed and restore the previous pattern of thawed patches in
a frozen matrix. That would shut down the ice streams and allow
interior ice to thicken. Rock and rubble eroded from shields and
along the linear troughs when these areas were wholly thawed were
deposited as ice-rafted sediments after icebergs calved from marine
ice streams, and were deposited as looped moraines at the lobate
termini of terrestrial ice streams. Successive recessional moraines
would form after terrestrial ice streams shut down and their lobes
retreated during transitions from stadials to interstadials.
When ice lowered sufficiently, calving bays would migrate up
stagnating marine ice streams and eventually carve out marine
embayments that were formerly centers of ice spreading. Calving
bays carve out the heart of the accumulation zone of an ice sheet,
and forcedforcedtermination of the glaciations cycle. Calving also
discerps terrestrial ice margins ending in proglacial lakes.
Following deglaciation, sites of greatest isostatic rebound and of
strongly negative gravity anomalies would identify sites of major
domes at the glacial maximum, as distinct from the last remaining
ice domes on land after final gravitational collapse of ice saddles in
marine embayments.
These then constitute the first-order features useful in modeling
a glaciation cycle: (1) the present distribution of permafrost, (2) the
present distribution of lakes on Precambrian shields, (3) troughs
radiating seaward and landward from these shields, (4) the areal
extent of ubiquitous glacial scouring on shields that over time
exposes the shields, (5) lobate recessional moraines at the ends of
landward troughs beyond the shields, and (6) centers of greatest
postglacial isostatic rebound. Each of these six features is associated
with a particular stage of a glaciation cycle, and they should
therefore guide ice-sheet modeling of the cycle from the bottom up.
In this modeling activity, ice-bed coupling deduced from these
features is the primary control on ice elevations above the bed.
Surface temperatures and accumulation rates, which are largely
unknown, are very much secondary controls on ice elevations. If
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T. Hughes / Quaternary Science Reviews 28 (2009) 1831–1849
the first-order glacial geology and geomorphology that controls
each stage of the glaciation cycle are converted into correct variations in ice-bed coupling, the resulting elevations of the ice sheets
above the bed will be correct, regardless of conditions at the ice
surface, prior changes in the size and shape of the ice sheets, or the
pattern of the geothermal heat flux over the glaciated landscape
under the ice sheets.
The key to bottom-up modeling of ice sheets is linking glacial
geology and geomorphology to ice-bed coupling that dominates
each stage of the glaciation cycle. In addition to identifying which
first-order features of the glaciated landscape control a given stage,
second-order glacial features can be ‘‘peeled off’’ the first-order
landscape in layers that ‘‘stack’’ these features in a time transgressive manner from the youngest to the oldest (Boulton et al.,
1985; Boulton and Clark, 1990; Hughes, 1998, Figures 9.24, 9.25,
and 9.26). Joan Kleman of Stockholm University has taken this
approach to a new level by developing a time–space topology that
peers into the past along all flowline transects of former ice sheets
until that ‘‘look’’ is blocked by more recent events of glacial erosion
or deposition that erase the older features (Fig. 6). These secondorder features are often glacial lineations of various kinds that align
in directions of ice flow at the time the lineations were imprinted
on the landscape. They show whether the bed was frozen, thawed,
or a mosaic of frozen and thawed patches that correlate with basal
freezing and melting zones. By applying time–space topology to
various parts of the former Scandinavian and Laurentide ice sheets,
Kleman has taken the concept of ice-bed coupling under former ice
sheets at various times in their history to a new level (Kleman,
1990, 1992, 1994a,b, 2008; Kleman et al., 1992, 1994, 1997, 2008;
Kleman and Borgstrom, 1996; Kleman and Stroeven, 1997; Kleman
and Hattestrand, 1999; Kleman and Glasser, 2007; De Angelis and
Kleman, 2008; Clark and Stokes, 2001; Stokes et al., 2007; Stokes
et al., 2009).
With this bottom-up approach, there is no need to know the
past climate history that determines the surface temperatures and
accumulation rates, and partly determines the basal geothermal
heat flux, at a given stage in the glaciation cycle. Top-down models
that trace their pedigrees to Budd et al. (1971) depend critically on
all these conditions. Yet it remains true that the changing size and
shape of ice sheets during a full glaciation cycle cannot be modeled
without using the top-down approach.
8. Combining top-down and bottom-up modeling strategies
Modeling ice sheets needs the top-down approach because that
approach employs the mass-balance equation that controls how ice
sheets advance and retreat over time. When snow precipitation
accumulates year by year over highland plateaus or on sea ice, so
surface snow is compressed into ice at depth, the ice eventually
becomes thick enough to thin and spread under its own weight.
Merger of these ice spreading centers can produce an ice sheet with
terrestrial and marine portions (Hughes, 1986a, 1998, Figure 1.9).
Marine portions formed initially from sea ice are necessary for
grounded ice to occupy marine embayments so terrestrial portions
formed initially in highlands will not end by calving along marine
shorelines. Gravitational thinning of ice is more than compensated
by continued surface accumulation of snow, so spreading ice
advances until landward ice margins melt and marine or lacustrine
ice margins calve as fast or faster than ice moves forward. This is the
first-order effect of the mass balance. A bottom-up modeling
approach is not useful until an ice sheet is already in place, so icebed coupling can be treated as a first-order effect in controlling ice
elevations above the bed.
A bottom-up application of the top-down University of Maine
Ice Sheet Model (UMISM) developed by James Fastook (Fastook,
1987, 1992, 2009) is used by Canadian and Scandinavian glacial
geologists to provide a glaciological explanation for glacial geology
they map that was produced by the Laurentide and Scandinavian
ice sheets during the last glaciation cycle. Since I am familiar with
UMISM, I will use it as an example of the advantages of combining
top-down and bottom-up modeling approaches. UMISM generates
ice sheets in the map plane, using specified surface temperatures
and accumulation or ablation rates as model input, obtained by
direct measurement for present ice sheets and as output from
models of atmospheric circulation or by other means for past ice
sheets. In this sense it is a standard top-down model. Temperatures
at depth are calculated vertically from specified surface temperatures and accumulation or ablation rates, and are linked to vertically averaged horizontal ice velocities by way of the flow law of ice,
such that mass and energy are conserved. The temperature field is
used to determine if the bed is frozen or thawed and, if thawed, to
calculate basal melting and freezing rates. For a thawed bed, sliding
velocities can be calculated from a variety of sliding laws modified
to convert the calculated amount of basal water into a water depth
that progressively drowns bedrock bumps or supersaturates
deformable till and sediments. Both processes decouple ice from
the bed. The combined velocities of basal sliding, a mobilized
deformable bed, and vertically averaged creep in ice become the
horizontal ice velocity in the mass-balance equation. A positive or
negative mass balance at model gridpoints requires ice to thicken
or thin at these sites to sustain mass continuity. Ice thickening or
thinning rates over time are obtained from the difference between
the surface accumulation or ablation rates of ice (and basal freezing
or melting rates) and thickening or thinning rates of ice due to
convergence or divergence of ice flow caused by gravitational
motion. The rheology of a soft deforming bed is not included in
UMISM, but it is generally included in other top-down models
(Marshall, 2005). Treatments of deforming beds under West
Antarctic ice streams appear in Volume 77 of the AGU Antarctic
Research Series (Alley and Bindschadler, 2001), which includes
a comprehensive study of wet deforming till by Kamb (2001). Also
see discussion by Hooke (2005, Chapters 7 and 8).
UMISM and other top-down models based on the shallow ice
approximation progressively add velocities obtained from flow and
sliding laws to get the cumulative mass-balance velocity and the ice
thickness profile used in the mass balance for transporting ice in
the direction of the downsloping ice surface, for prescribed rates of
surface ice accumulation and ablation entered as model input. As
noted by Van der Veen (1987) and Hofstede (2008), however, the
concave profile of ice streams introduces reduced velocities in the
flow and sliding laws which depend on a gravitational driving
stress proportional to the product of ice height above the bed and
ice surface slope in the shallow ice approximation. For a positive
surface accumulation rate, the mass-balance ice velocity increases
as the driving stress decreases, because both ice thickness and slope
decrease along an ice stream as the surface goes from convex for
sheet flow to concave for stream flow. This introduces negative
longitudinal strain rates that reduce ice velocities based on the
driving stress, whereas ice velocities based on the mass balance
increase continuously for the calculated downslope ice thickness
profile. Poorly known quantities in the flow and sliding laws,
especially in sliding laws, can be ‘‘tuned’’ to force the two velocities
to match. This problem points to a breakdown in the shallow ice
approximation that may be corrected by gradually replacing
resistance by basal drag with resistance by longitudinal tension,
both linked to the flotation height of ice through the longitudinal
gravitational force (Hughes, 2009a,b). The amount of basal water
calculated in UMISM and a version of the Johnson (2002) model of
subglacial hydrology are used to move basal water from sources to
sinks. The gravitational driving stress, proportional to the product
Fig. 6. Geomorphic systems associated with an ice sheet (Kleman, 1994a,b, Figure 7, reproduced with permission). Top: an ice sheet is sectioned to show velocity profiles for creep
over a frozen (dry) bed and sliding over a thawed (wet) bed, flowline trajectories, the surface mass-balance regime, and the basal thermal regime. Dry bed, wet bed, and marginal
meltwater geomorphic systems are shown for one-dimensional symmetry. Bottom: a demonstration of how time–space histories can be deduced by observing geomorphic
landforms along transects such as I–II. The actual history is shown in (a), the line-of-sight along a given transect is shown in (b), what can be seen along all possible lines-of-sight is
shown in (c), and what can be seen in sectors A, B, C, and D is shown in (d).
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of ice thickness and surface slope, is balanced only by the local basal
shear stress in the shallow ice approximation. Therefore, UMISM is
a sheet-flow model even thought the mass balance and subglacial
hydrology combine to concentrate ice motion along linear basal
depressions that generate stream flow. To introduce longitudinal
tension that allows ice streams to pull ice out of ice sheets, UMISM
has a parameter called a ‘‘Weertman’’ that represents the pulling
power of marine ice streams at their (un)grounding lines, with
values increasing from zero to unity down an ice stream or as
a buttressing ice shelf disintegrates, with unity providing the
pulling force for an unconfined ice shelf, following Weertman
(1957b). The ‘‘Weertman’’ generates concave ice-stream profiles in
UMISM, and thereby aleviates the problem of negative longitudinal
strain rates noted by Van der Veen (1987) and Hofstede (2008). A
more complete treatment of this problem requires solution of the
full momentum/equilibrium equation, as Sargent (2009) has done.
Her solution can be imbedded in UMISM for stream flow and
confined or pinned shelf flow.
Glacial geology, often undated, reveals changing directions of ice
flow and changing basal thermal conditions before and after the
LGM. These data are then used as ‘‘targets’’ that UMISM attempts to
‘‘hit’’ by adjusting variables in the model within acceptable limits.
These variables are parameters in the flow and sliding laws of ice,
conditions at the ice surface (temperatures and rates of ice accumulation or ablation), and conditions at the bed (temperatures,
water volume and distribution, rates of basal freezing or melting,
and the geothermal heat flux). For a Scandinavian application, see
Näslund et al. (2003a,b). For Laurentide applications, see Clarhall
(2002) and De Angelis (2007). In this way, the concept of first-order
and second-order glacial geology developed for CLIMAP is used by
UMISM to target basal processes and understand the glacial history
of former ice sheets.
MacAyeal (1992) developed the first model for turning West
Antarctic ice streams on and off in an irregular way, as basal till
thaws and loses its cohesion under thickening ice and refreezes to
regain cohesion under thinning ice. In top-down models, changes
in ice-bed coupling are determined primarily by changing the
amount and distribution of basal water that is produced by changes
in the surface temperature and mass balance over time, for a given
distribution of the basal geothermal heat flux. Modeling changes in
the size and shape of ice sheets over time must employ a top-down
approach, because bottom-up modeling calculates ice elevations
sustained by ice-bed coupling anchored to basal thermal conditions. These conditions ultimately depend on surface conditions for
a specified pattern of the basal geothermal heat flux. Surface
conditions change during a glaciation cycle, so the basal thermal
conditions will also change, including the geothermal heat flux,
which changes as the insulating ice thickness changes over time.
For rapid surface lowering of the kind modeled for Termination of
a glaciation cycle, these long-term effects are less important than
repeating episodes of basal freeze–thaw processes of the MacAyeal
(1992) kind or episodes of repeating discharge of impounded basal
water, as proposed by Erlingsson (1994, 2006, 2008) for rapid
drainage of subglacial lakes. Sudden drainage of this kind has been
reported by Stearns et al. (2008) at the head of Byrd Glacier in East
Antarctica, with a rapid increase in ice velocity, probably as discharged water causes additional ice-bed uncoupling to propagate
down the ice stream.
Gravity easily thins thick ice after it loses contact with the bed,
so a grounded ice sheet 3 km thick under its interior ice domes is
only 300 m thick after it becomes afloat, for the same surface mass
balance. This is because, for the same ice thickness, the longitudinal
tensile stress for floating ice is ten times larger than the basal shear
stress for grounded ice, so reducing ice thickness by a factor of 10
equates the two stresses that resist gravitational spreading. Any
reduction of ice thickness for grounded ice results in a rise in global
sea level. To accomplish this surface lowering by way of ice streams,
resistance to gravitational spreading has to change from being
dominated by the basal shear stress for sheet flow at the head of ice
streams to being dominated by the longitudinal ‘‘pulling’’ stress
when ice streams become afloat as shelf flow.
9. Modeling basal thermal conditions under
present ice sheets
Nearly all studies of ice streams have been in West Antarctica,
where the bed is largely below sea level (Alley and Bindschadler,
2001). These ice streams lie on soft deforming marine sediments
mobilized into till. Maintaining ice streams of this kind requires
a continual supply of soft sediments if the ice streams remain
largely in place. West Antarctic ice streams are believed to be
retreating along submarine troughs from positions near the
continental shelf edge at the LGM (Fig. 3), with soft marine sediments occupying the troughs (Anderson, 1999). This may have
strongly biased our understanding of ice-stream dynamics. Many if
not most Antarctic and Greenland ice streams today pass through
fjords as outlet glaciers, and may remain in place in their fjords
even as ice margins advance and retreat. This was also the case for
many ice streams draining former ice sheets. For such ice streams,
soft marine sediments should have been removed by glacial
erosion. Without mechanisms for resupplying sediments, these
would be rock-floored ice streams. Very little fieldwork has focused
on these ice streams. The study of a former rock-floored stream by
Stokes and Clark (2003) on the Dubawnt swarm should inform
fieldwork; also see De Angelis (2007). Our concepts of ice-stream
dynamics may need major revisions when these studies are done.
Essential data for studying ice streams in their full complexity
include gridded seismic sounding of the kind being done for Rutford Ice Stream in West Antarctica (Smith and Murray, 2009), and
applications of seismic streamer technology to ice streams. Equally
important is deep radar sounding capable of mapping the amount
and extent of basal water, and therefore of ice-bed coupling and
perhaps even the geothermal heat flux, as has been done along
radar flightlines crisscrossing the northern Greenland Ice Sheet
(Oswald and Gogineni, 2008). Jakobshavn Isbrae, Kangerdlugssuaq
Glacier, and Helheim Glacier are probable rock-floored ice streams
that occupy Greenland fjords and have doubled their velocities in
recent years (Stearns and Hamilton, 2007; Joughin et al., 2008).
These should be mapped by seismic and radar sounding, and
monitored continually by satellite sensors. Deep drilling to the bed,
as done for West Antarctic ice streams, is possible (Engelhardt and
Kamb, 1997, 1998).
Basal thermal regimes can be mapped under present ice sheets
by linking ice elevations to ice-bed coupling. Using this linkage,
basal thermal zones (frozen, freezing, melting, and thawed conditions at the bed) were mapped under the Antarctic Ice Sheet where
surface and bed topography were known with sufficient accuracy
along flowbands in sheet flow, taking variable flowband widths and
surface accumulation rates into account (Wilch and Hughes, 2000).
Martin Siegert compared places where the bed was determined to
be wholly thawed with the known locations of subglacial lakes
detected by radar, and found a strong match (Siegert, 2001). The
geothermal heat flux was not needed in this approach.
Johnson (2002) developed a finite-element map-plane model of
subglacial hydrology, based on a solution of the Manning equation,
that he coupled to UMISM to map flow of basal water from sources
to sinks beneath the Antarctic Ice Sheet for various rates of the
geothermal heat flux. His model generated subglacial lakes that
matched those detected using radar (Siegert, 2001), and located
where other subglacial lakes would be, with some subsequently
T. Hughes / Quaternary Science Reviews 28 (2009) 1831–1849
found. His model also drove subglacial water toward bed channels,
resulting in enhanced ice-bed decoupling so stream flow developed
in ice above the channels. Pulses in discharge of impounded
subglacial water generated pulses in stream flow.
Linking ice elevations to ice-bed coupling for stream flow was
used to map the floating fraction of ice beneath Byrd Glacier, one of
the fastest East Antarctic ice streams with the biggest ice drainage
basin (Reusch and Hughes, 2003). Surface wave-like undulations
having the appearance of stacked terraces correlated with the
floating fraction of ice along the bed, after correcting for variations
of bed topography. As with sheet flow, surface elevations in stream
flow are primarily determined by the degree of ice-bed coupling.
The relatively level portions of the wave-like surface of Byrd Glacier
were matched with the greatest floating fraction of ice, thereby
quantifying the concept of ‘‘pseudo ice shelves’’ for the level
portions of West Antarctic ice streams proposed by Robin et al.
(1970b) and based on radar sounding. This correlation remained
after a ‘‘bookkeeping’’ error was corrected (Hughes, 2009b).
Hofstede (2008) applied the ice-bed coupling concept to model
recent lowering of Jakobshavn Isbrae in Greenland, following
disintegration of a buttressing ice shelf in Jakobshavn Isfjord in
2002. He used a flowline version of the flowband model that
partitions a geometrical representation of the longitudinal gravitational driving force among local basal and side shear stresses,
longitudinal tensile stresses upstream, and longitudinal compressive stresses downstream, all resisting gravitational flow and all
linked to the floating fraction of ice (Hughes, 2009a,b). The flowline
was along a flightline down the center of Jakobshavn Isbrae that
delivered surface and bed radar reflections. Side shear stresses
vanish along the center of ice streams, so the effects of side and
basal drag were assigned to the basal shear stress. Hofstede’s
model was able to reproduce the known thinning of Jakobshavn
Isbrae after its ice shelf disintegrated. An increase in the floating
fraction of ice accompanied surface lowering, giving a direct link
between a reduction of ice thickness and a reduction of ice-bed
coupling over time.
Aitbala Sargent, a doctoral student advised by James Fastook,
has modified the MacAyeal/Morland equations for ice shelves to
include a basal shear stress to get equations that also apply to ice
streams. This amounts to a solution of the full equilibrium/
momentum equations that modelers have long sought, since the
ice-shelf application already includes stresses in the map plane for
side shear and for longitudinal and transverse tension and
compression (Sargent, 2009; Sargent and Fastook, 2008). The Sargent equations apply to ice streams in a standard top-down icesheet model. Resistance to gravitational stream flow is reduced in
a bottom-up application that increases the ‘‘Weertman’’ floating
fraction under ice streams and eliminates basal pinning points
under ice shelves. This solution is being imbedded in UMISM.
Among innovative ways of thinking, may I include thermal
convection below the density inversion of the Antarctic and
Greenland ice sheets as the origin of ice streams (Hughes, 2009c)?
A gravitational buoyancy force below the density inversion generates a buoyancy stress that is about one-third the gravitational
driving stress for advective sheet flow. The buoyancy stress is
therefore theoretically large enough to cause thermal convective
flow in ice below the density inversion. When superimposed on
advective flow, the pattern of convective flow would be aligned in
the direction of advective flow. The most efficient pattern would be
for warm basal ice to rise in narrow curtains that would be the
lateral shear zones of ice streams, with ice sinking slowly in the ice
stream between shear zones. That lowers the surface of ice streams
and allows basal water to flow toward ice streams, thereby further
decoupling ice from the bed and increasing stream flow. The cycling
convective flow would spiral downstream at a rate controlled by
1843
the advective ice flow, but it could be measured in principle. If it is
found to occur and to be significant, then thermal convection
should be included in ice-sheet models.
10. Modeling West Antarctic collapse from the bottom up
The six kinds of first-order features useful in modeling ice sheets
from the bottom up to capture stages in past glaciation cycles are
also useful in capturing basal conditions for the Greenland and
Antarctic ice sheets at present. The present size of these ice sheets
should be close to stage 5, when the ice sheets are in recession from
forward positions during the LGM. Whether these ice sheets
continue recession to stage 6 and a full Termination remains an
open question. The West Antarctic Ice Sheet is the leading candidate for this event.
In stage 5, interior ice has lowered, bringing cold upper ice into
contact with the bed and partly freezing a ubiquitously thawed bed
at state 4 so that isolated thawed patches remain, most prominently as subglacial lakes in bedrock hollows. That this condition
now exists beneath the Greenland Ice Sheet has been demonstrated
from basal radar data (Oswald and Gogineni, 2008). Subglacial
lakes, also located by radar sounding, are widespread beneath the
Antarctic Ice Sheet (Siegert et al., 1996). Johnson (2002) developed
a model of subglacial hydrology coupled to UMISM that generated
numerous known subglacial Antarctic lakes. Robin Bell, in a lecture
at the Center for Remote Sensing of Ice Sheets (CReSIS) at the
University of Kansas on 1 November 2006 titled, ‘‘East Antarctica:
An Ice Sheet Controlled By Lakes and Mountains,’’ explored the
implications of these bed conditions for ice-sheet stability if
subglacial lakes can link up and generate ice streams. Stearns et al.
(2008) presented evidence from precision ice elevation changes
mapped by Earth-orbiting satellites showing that subglacial lakes
linking up under Byrd Glacier right now are causing a substantial
increase in ice velocity.
With these new methods for mapping the amount and extent
of basal water, including linked subglacial lakes (‘‘pseudo ice
shelves’’), it now becomes possible for top-down models to use
basal water as bottom-up input and calculate the geothermal heat
flux as output, as Koons and Kirby (2007) have done for tectonic
systems. Then sites of high geothermal heating can be used as
sources for basal water in bottom-up modeling of subglacial
instabilities which, coupled to models of subglacial hydrology,
allow basal water to ‘‘carry’’ the overlying ice at accelerating rates.
Transport of basal water from geothermal sources to sinks at iceshelf grounding lines should generate stream flow in overlying
ice. Ice streams, therefore, become the primary vehicles for
transporting subglacial water from sources to sinks, sinks being
both marine ice tongues, possibly imbedded in ice shelves, and
terrestrial ice lobes from which basal water drains away. This
demonstrates that ice streams must be modeled correctly.
The best natural laboratory for modeling the interaction
between top-down and bottom-up process is the West Antarctic Ice
Sheet, which is in an advanced stage of gravitational collapse, and is
underlain by a Cenozoic volcanic province in its central subglacial
highlands. A probable high geothermal heat flux in the highlands
would provide the source of subglacial water that enters ice
streams moving toward sinks for that water (Blankenship et al.,
2001). Long fast concave ice streams drain West Antarctic ice on
three sides, east, west, and north (Fig. 7). Again, modeling ice
streams and subglacial hydrology correctly becomes paramount.
Both require modeling basal processes correctly. Data input from
the bed is as important as data input from the surface.
The West Antarctic Ice Sheet was one-third of the Antarctic Ice
Sheet at the LGM (Fig. 1), but after Holocene gravitational collapse
of its Ross Sea and Weddell Sea sectors, it is only one-tenth of the
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T. Hughes / Quaternary Science Reviews 28 (2009) 1831–1849
Fig. 7. : The Antarctic Ice Sheet today. Broken lines show ice drainage divides for Pine Island Glacier (P) and Thwaites Glacier (T) draining West Antarctic ice into Pine Island Bay,
Foundation Ice Stream (F) and Mercer Ice Stream (M) draining East Antarctic ice through the Bottleneck into Ronne–Filchner and Ross ice shelves, Byrd Glacier (B) draining East
Antarctic ice into Ross Ice Shelf, and Lambert Glacier (L) draining East Antarctic ice into Amery Ice Shelf. Heavy dashed lines show projected retreat routes of Pine Island and
Thwaites glaciers through the Bottleneck into East Antarctica as they downdraw and collapse the West Antarctic Ice Sheet.
Antarctic Ice Sheet today (Fig. 7). During collapse, ice poured into
both the Ross Sea and Weddell Sea sectors from three sides, south,
east, and west, and left from the remaining side, north. Today, East
Antarctic ice enters only through the Bottleneck and ice leaves West
Antarctica on its north, east, and west flanks. It has gone from
gaining ice on three sides and losing ice on one side to gaining ice
on one side and losing ice on three sides. This has to be an unstable
situation, and today the West Antarctic Ice Sheet is in an advanced
stage of gravitational collapse. Ice leaving on the east and west sides
is buttressed by the respective Ronne–Filchner and Ross ice shelves,
but ice leaving on the north side enters the ice-free Pine Island Bay
polynya in the Amundsen Sea, which provides no buttressing. For
this reason Pine Island Bay may be ‘‘the weak underbelly of the
West Antarctic Ice Sheet’’ (Hughes, 1981b).
How much of the remaining West Antarctic Ice Sheet will
collapse and how soon? How high and how fast will global sea
level rise? How much East Antarctic ice will pour through the
Bottleneck as West Antarctic ice lowers? The Bottleneck (60 W–
135 W at 84 S) is the junction connecting the grounded east and
west components of the Antarctic Ice Sheet (Fig. 7). Thiel Mountains in the middle of the Bottleneck diverts most East Antarctic ice
into Ronne–Filchner Ice Shelf by way of Foundation Ice Stream on
the east and into Ross Ice Shelf by way of Mercer Ice Stream on the
west. Little East Antarctic ice now enters West Antarctica, so the
West Antarctic Ice Sheet can be considered as losing ice on three
sides and gaining ice only from the top. The rise in sea level will be
3–5 m if the ice sheet collapses to sea level, depending on whether
buttressing ice shelves disintegrate (Fig. 1). This is not the worstcase scenario.
If the West Antarctic Ice Sheet collapses into Pine Island Bay, as
anticipated, two giant ice streams, Pine Island Glacier and Thwaites
Glacier, will retreat and may eventually reach the two entrances to
the Bottleneck on the east and west sides of Thiel Mountains
(Fig. 7). Then they may merge with Foundation and Mercer ice
streams and continue to migrate into East Antarctica and discharge
an unknown amount of East Antarctic ice (Fig. 8). In the worst-case
scenario, they could throw the entire East Antarctic Ice Sheet into
a negative mass balance that may put it on the road to total gravitational collapse and a 65 m rise in sea level. That answers the
‘‘how high’’ question.
An answer to the ‘‘how fast’’ question depends on what happens
to the ice shelves that buttress the West Antarctic Ice Sheet as it
continues to collapse. Holocene collapse began about 7000 BP
(Anderson and Shipp, 2001), apparently continues today, and
produced the huge Ross and Ronne–Filchner ice shelves that
buttress most of the remaining grounded one-third of the ice sheet.
If Pine Island Bay remains an ice-free polynya as it opens to the
south, following downdrawn retreat of Pine Island and Thwaites
glaciers, these ice streams should continue to move at their present
velocities of several kilometers per year, and may even speed up as
they merge with Foundation and Mercer ice streams, pass through
the Bottleneck, and tap into much higher East Antarctic ice. As they
pull out East Antarctic ice, discharge of East Antarctic ice by other
ice streams supplying Ronne–Filchner and Ross ice shelves should
diminish and may even stop, if these ice streams through the
Transantarctic Mountains have high fjord-like headwalls, as does
Byrd Glacier, the largest ice stream (Hughes, 1998, Figure 3.20). In
that case, the Ronne–Filchner and Ross ice shelves will be deprived
of ice input from these ice streams and the resulting negative mass
balance may lead to catastrophic ice-shelf disintegration. The ice
streams that remain active will then be unbuttressed and can pull
out even more East Antarctic ice.
T. Hughes / Quaternary Science Reviews 28 (2009) 1831–1849
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Fig. 8. : Possible partial gravitational collapse of the East Antarctic Ice Sheet. Present ice elevations are contoured every 0.5 km. Broken contour lines show possible ice elevations
before partial gravitational collapse of East Antarctic ice into Amery Ice Shelf, and after partial gravitational collapse of East Antarctic ice through the Bottleneck into an ice-free West
Antarctica. Heavy black lines enclose possible collapsed portions of the East Antarctic Ice Sheet. Collapse obtained using Equation 11.34 in Hughes (2009b).
Far fetched? Look at Byrd Glacier, the largest of these ice streams
through the Transantarctic Mountains (Fig. 7). It has a huge
drainage basin, as large as the West Antarctic Ice Sheet, drawing ice
from the three highest interior ice domes of East Antarctica. Glacier
erratics and scoured bedrock that can be dated using cosmogenic
nuclides are found all along its fjord through the mountains at
elevations 1000 m above Byrd Glacier. So Byrd Glacier has thinned
and lowered by at least 1000 m, and that is why it has acquired such
a vast ice drainage basin. Yet it is still buttressed by Ross Ice Shelf.
The ‘‘how fast’’ question is answered by removing buttressing ice
shelves. Calving bays accomplish this task most rapidly (Thomas,
1977; Hughes, 2002; MacAyeal et al., 2003; Hulbe et al., 2004).
11. Calving bays
Lambert Glacier lies across the East Antarctic ice divide opposite
the Bottleneck (Fig. 7). Lambert Glacier discharges into Amery Ice
Shelf, which has a drainage basin even larger and much lower than
the drainage basin of Byrd Glacier. Ice may have lowered 3000 m
where Lambert Glacier enters Amery Ice Shelf (Fig. 8). If we treat
Amery Ice Shelf as a giant ice stream that has lost contact with its
bed, retaining partial basal contact only along Lambert Glacier and
other tributary ice streams, then it enters an ice-free polynya in the
Indian Ocean. Like Pine Island and Thwaites glaciers, and unlike
Byrd Glacier, it is then unbuttressed and can pull out much more ice
as a result. That would explain why it has such a broad and low ice
drainage basin, and that is what could happen across the East
Antarctic ice divide if Pine Island and Thwaites glaciers passed,
unbuttressed, through the Bottleneck and into East Antarctica.
When ice downdrawn by ice streams become afloat, water-filled
bottom crevasses can extend upward close to sea level and air-filled
top crevasses can extend downward close to sea level. Floating ice
calves when they meet (Kenneally and Hughes, 2006). This is the
case in an arid polar environment and it is an essentially bottom-up
process because bottom crevasses fracture up to 90 percent of the
ice thickness. If surface melting is extensive, water-filled top
crevasses can propagate through the whole ice thickness. Johannes
Weertman was first to treat both cases (Weertman, 1973, 1980).
These and other processes are active in calving bays (Thomas, 1977;
Hughes, 2002; MacAyeal et al., 2003).
Jakobshavn Isbrae drains about seven percent of the Greenland
Ice Sheet, has long been the fastest known ice stream, and becomes
afloat in Jakobshavn Isfjord. A calving bay has migrated some 30 km
up the fjord since 1850 AD, the end of the Little Ice Age (Weidick
and Bennike, 2007). Several seasons of observations suggested
a series of positive feedback mechanisms called the Jakobshavn
Effect (Hughes, 1986b). The ‘‘pulling power’’ of an ice stream in
extending flow produces ubiquitous surface crevasses which
absorb much more solar energy than does smooth surface ice,
thereby enhancing surface melting so surface meltwater can reach
the bed by way of the ubiquitous crevasses, accelerate basal sliding
and, once ice becomes afloat, accelerate the calving rate. These
processes have accelerated in recent years. The calving bay has
carved away the ice shelf and the unbuttressed ice stream is
moving nearly twice as fast (Thomas, 2004; Joughin et al., 2008).
Jay Zwally and five colleagues first observed the connection
between increased midday summer melting and increased ice
velocity on the smooth ice surface just north of Jakobshavn Isbrae
(Zwally et al., 2002). This is now called the Zwally Effect and it
should accelerate most Greenland ice streams. It may have caused
rapid advance of the southern margin of the Laurentide Ice Sheet at
the LGM, where a climate simulation generated heavy summer
rainfall (Bromwich et al., 2004). The Zwally Effect is unlikely in the
cold Antarctic environment, but other positive feedbacks in the
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T. Hughes / Quaternary Science Reviews 28 (2009) 1831–1849
Jakobshavn Effect should be active if a calving bay follows Pine
Island and Thwaites glaciers into the Bottleneck. As East Antarctica
ice pouring through the Bottleneck lowers, the calving bay may
migrate up Pine Island and Thwaites glaciers and begin to carve out
the heart of the East Antarctic Ice Sheet. The heart of the Laurentide
Ice Sheet was carved out 8000 years ago when a calving bay
migrated up a giant ice stream in Hudson Strait and entered Hudson Bay (Hughes et al., 1977; Denton and Hughes, 1981, Figure 8.8).
With most of its accumulation zone gone, the Laurentide Ice Sheet
collapsed in 200 years, leaving three isolated ice caps on land above
sea level.
All aspects of the above scenario take place with no change in
surface temperatures and accumulation or ablation rates except
those associated with the lowering ice surface. Therefore, the
scenario is controlled by conditions at the base of ice and bottomup modeling is required to capture the ice-sheet response to
changing these conditions. For the floating ice shelves, changing
basal conditions by enhanced basal melting frees basal ice from
pinning points that enable the ice shelves to buttress ice streams
supplying them with ice. Enhanced basal melting is now widespread under Antarctic ice shelves (Jacobs et al., 1996; Rignot and
Jacobs, 2002).
Calving bays can remove the pinning points by removing the ice
shelves, which is what triggered the doubled discharge from
Jakobshavn Isbrae in Greenland after its ice shelf disintegrated in
2002. This was first demonstrated by NASA glaciologist, Robert
Thomas (Thomas, 2004). Hofstede (2008) used a bottom-up
approach to model the same observations.
As basal melting allows ice streams to pull more Antarctic ice
into the sea, the resulting rise in sea level can also float Antarctic ice
shelves free from their basal pinning points. Basal conditions that
would allow ice streams to discharge more ice center around
expanding the supply of water under the ice streams. This would
allow the ice streams to both widen and lengthen. Even without
expanding the water supply, glacial erosion of a till or sediment
blanket, and then of bedrock pinning points that project up into
basal ice, will free overlying ice to slide more swiftly over whatever
basal water is available.
If an ice stream joins an ice shelf at a bedrock sill, retreat of the
ice-shelf grounding line over the sill increases the ice thickness, and
therefore the height of ice floating above sea level. The ‘‘pulling’’
force of the ice shelf on the ice stream increases as the square of this
height, so more ice is pulled out and the grounding line may retreat
even faster if the bed continues to deepen (Fig. 1). This retreat over
sills can be caused by a surging ice stream that thins ice upstream,
by lowering of the sill due to delayed isostatic sinking and glacial
erosion, by rising sea level, and by melting basal ice, all with no
change in surface conditions unrelated to surface lowering (Fig. 2).
These are the processes that give ice sheets a measure of independence from other components of Earth’s climate system, yet
allow ice sheets to control the system by discharging enormous
amounts of ice into the ocean in a short time. It takes eighty degrees
of sensible heat in ocean surface water to supply latent heat needed
to melt one gram of an iceberg, and these icebergs can be tens to
thousands of cubic kilometers in volume, weighing billions of
metric tons. If they are discharged by the hundreds to thousands in
a few centuries, they may trigger sustained global cooling over that
time (Hughes, 2004). The heat needed to bring these icebergs up to
the melting point, and then melt them, is supplied primarily by
ocean surface water to the depth of the draft of the icebergs. This
heat is then unavailable to sustain the ocean-to-atmosphere heat
exchange that drives global climate. Rapid disintegration of ice
shelves (MacAyeal et al., 2003; Hulbe, et al., 2004) and calving of
giant icebergs (Kenneally and Hughes, 2006) should become
a major focus of glaciological research. Ice shelves may also be
discerped by large oceans swells that are known to pass under
Antarctic ice shelves (MacAyeal et al., 2006). These mechanisms
allow ice sheets to trigger rapid changes in the ocean and atmosphere. The West Antarctic Ice Sheet is where all these interacting
top-down and bottom-up processes can be studied and then
modeled to simulate its ongoing gravitational collapse.
12. Discussion
This review is based primarily on my own experiences in
glaciology in a career now spanning four decades. It began at The
Ohio State University in 1968. I had no knowledge of glaciology.
Paterson (1969), in his first edition of The Physics of Glaciers,
provided my initial education. In 1970 the American Geographical
Society published its map, Antarctica, which changed my perspective forever. The first-order concave profile of the West Antarctic Ice
Sheet, in sharp contrast to the overall convex profiles of the East
Antarctic Ice Sheet and the Greenland Ice Sheet, led me to suspect
that it was in an advanced stage of gravitational collapse. If so, was
collapse ongoing? The Fletcher (1972) memorandum provided the
anchor for answering that question. I composed and circulated four
ISCAP bulletins designed to address the question, using a quantum
jump in data from Antarctic meteorology, geophysics, glaciology,
glacial geology, and marine geology, dating from the International
Geophysical Year in 1958.
My bulletins led to my move to the University of Maine in 1974,
where I was given the task of reconstructing global ice sheets at the
LGM and to model total gravitational collapse of the West Antarctic
Ice Sheet at the LIM as part of CLIMAP during the 1970–1980
International Decade of Ocean Exploration (Denton and Hughes,
1981). To accomplish that task, I had to develop a way to reconstruct ice sheets from the bottom up, based on ice-bed coupling
deduced from glacial geology at the LGM, rather than employ a topdown model that depended on unknown surface conditions.
Simulating total collapse of the West Antarctic Ice Sheet at the LIM
brought James Fastook into glaciology, and began a collaboration
that continues to this day. Fastook developed his University of
Maine Ice Sheet Model (UMISM), which combines the essentials of
top-down and bottom-up modeling.
Peltier (1994) inspired me to more forcefully re-direct my
thinking from the CLIMAP view that ice sheets at the LGM and the
LIM defined boundary conditions bracketing maximum perturbations of a fundamentally stable global climate. After CLIMAP, I
began to view ice sheets as fundamentally unstable and able to
control climate change, especially rapid climate change, through
the instabilities inherent in ice sheets. I found these instabilities as
residing primarily in the periphery of ice sheets, allowing the icesheet interiors to remain relatively stable until the instabilities
were able to penetrate the core regions and Terminate a glaciation
cycle, thereby warming global climate. This led me to assign
particular features of first-order glacial geology and related
geomorphic features on a deglaciated landscape to specific stages
of a glaciation cycle, not just to the LGM (Hughes, 1996, 1998). Then
ice-bed decoupling under the central core lowered the interior ice
surface and shot out ice streams at the LGM without a large change
in ice volume, whereas in the CLIMAP ice sheets, an increase in ice
volume caused the ice sheets to advance to the LGM ice margins.
I now believe the CLIMAP simulation of gravitational collapse of
the West Antarctic Ice Sheet, in order to account for sea level 6 m
higher at the LIM, should have been allowed to propagate through
the Bottleneck into the East Antarctic Ice Sheet. This propagation
can also take place during the present interglacial, with an
unknown increase in sea level. Rapid collapse of sectors of the
Greenland and Antarctic ice sheets is the focus of my contribution to
CReSIS. This is a new problem to solve that will draw on insights
T. Hughes / Quaternary Science Reviews 28 (2009) 1831–1849
gained from both top-down and bottom-up modeling strategies.
Future models should include the dynamics of calving bays to
complete the destruction of ice sheets, as was the case for the
Laurentide Ice Sheet and may become possible for the East Antarctic
Ice Sheet with prolonged climate warming. A central part of this
strategy should be coupling the isostatic response to rapid lowering
of ice sheets to a holistic model that treats the lithosphere and
mantle as one coupled system in which both lateral and vertical
deformation interact with thermal convective flow driving plate
tectonics and with the dynamics of Earth’s oceans, atmosphere, and
ecology. The rheology should include nonlinear flow laws linking
strain rates to driving stresses, so that the effective viscosity can
change by orders of magnitude laterally, not just vertically. The
resulting synthesis will be truly holistic for all dynamic process in
the Fletcher (1972) research strategy.
Acknowledgements
Extended discussions with James Fastook, Robert Thomas, and
Kees van der Veen demonstrated the need for this review. Beverly
Hughes processed the manuscript. Johan Kleman provided a very
useful review. Support was provided by NSF and NASA through the
Center for Remote Sensing of Ice Sheets (CReSIS), University of
Kansas.
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