letters to nature
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Stabilizing feedbacks in glacier-bed
erosion
R. B. Alley1, D. E. Lawson2, G. J. Larson3, E. B. Evenson4 & G. S. Baker5
1
Department of Geosciences and EMS Environment Institute, Pennsylvania State
University, University Park, Pennsylvania 16802, USA
2
Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire
03755, USA
3
Department of Geological Sciences, Michigan State University, East Lansing,
Michigan 48824, USA
4
Department of Earth and Environmental Sciences, Lehigh University, Bethlehem,
Pennsylvania 18015, USA
5
Department of Geology, University at Buffalo, Buffalo, New York 14260, USA
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Glaciers often erode, transport and deposit sediment much more
rapidly than nonglacial environments1, with implications for the
evolution of glaciated mountain belts and their associated sedimentary basins. But modelling such glacial processes is difficult,
partly because stabilizing feedbacks similar to those operating in
rivers2,3 have not been identified for glacial landscapes. Here we
combine new and existing data of glacier morphology and the
processes governing glacier evolution from diverse settings to
reveal such stabilizing feedbacks. We find that the long profiles of
beds of highly erosive glaciers tend towards steady-state angles
opposed to and slightly more than 50 per cent steeper than the
overlying ice–air surface slopes, and that additional subglacial
deepening must be enabled by non-glacial processes. Climatic or
glaciological perturbations of the ice–air surface slope can have
large transient effects on glaciofluvial sediment flux and apparent
glacial erosion rate.
Geomorphologists have long used the concept of a graded river,
in which “…any change in any of the controlling factors will cause a
displacement of the equilibrium in a direction that will tend to
absorb the effect of the change”2. For example, increased sediment
supply or decreased water supply to a segment of a river initially in
steady state causes sediment supply to exceed sediment transport
there; the resulting sediment accumulation steepens the river bed in
the downstream direction, increasing transport to restore balance.
Graded rivers are a consequence of the coupling of mass conservation with a slope-dependent mass-transport law. Nearly complete independence of ice flow from bed slope has prevented a
similar concept for glaciers. However, a thermodynamic effect
introduces dependence of subglacial transport on a combination
of surface and bed slope, stabilizing beds of terminal regions of
highly erosive glaciers at a slope just sufficient to cause supercooling
of subglacial waters. Process understanding motivates this ‘graded
glacier’ hypothesis, which is supported by data indicating widespread supercooling, and both increase and decrease of bed slopes of
different glaciers towards the equilibrium condition.
Considering processes first, rapid glacial geomorphic activity
appears to be restricted to glaciers with abundant surface meltwater
flowing along their beds, especially if those glaciers are large and
slide rapidly1,4,5. The sediment discharge from such highly erosive
glaciers is dominated by material carried in subglacial streams6–8. In
the absence of such drainage, any rapid erosion would quickly
produce a till (the equivalent of a fault gouge) that would protect
bedrock from the ice and greatly limit further erosion9–11. (Widespread and sustained entrainment of sediment to basal ice sufficiently
rapidly to balance the faster rates of glacial erosion is thermodynamically difficult and has not been observed (see review8)).
Rapid subglacial erosion produces overdeepenings, with the
glacier bed rising in the direction of ice flow. Overdeepenings may
form in cirques near glacier heads or anywhere along the length of a
glacier12, but are prominent in downglacier reaches, probably owing
758
to the downglacier increase in surface meltwater reaching the bed
and its critical role in erosion13.
The work done in moving subglacial water is partitioned between
heat generation from viscous dissipation, and increase in potential
energy of the water during ascent from any overdeepening(s)14–16.
Some heat is required to warm the water as the melting point rises in
response to falling pressure along water flow. For beds decreasing in
elevation or increasing only gradually in the direction of ice and
water flow, the potential-energy term is small or negative, heat
production from viscous dissipation exceeds that needed to maintain water at the pressure-melting temperature, most of the excess
heat melts the ice walls of water channels, and the associated channel
expansion produces lower water pressure. Heat is generated
throughout the channel cross-sectional area, which increases with
channel radius more rapidly than does the perimeter being melted;
thus, melting is faster and produces lower pressure in larger
channels, in turn favouring downglacier convergence of water
flow14. Because sediment-transport capacity increases more rapidly
than water flux3,8, convergent water flow favours erosion and
transport, accelerating local deepening of the glacier bed and
formation and steepening of the downglacier sides of overdeepenings (Fig. 1a).
However, if the bed rises at a sufficiently steep angle in the
direction of flow, then enough of the work done in moving water is
stored as potential energy that viscous dissipation is not sufficient to
warm the water along the pressure-melting curve. The critical angle,
or ‘supercooling threshold’, is ,20–70% steeper than and opposed
to the ice–air surface slope, with the range arising from uncertainty
about maintenance of air-saturation of the water under changing
pressure12,14,17. Beds steeper than the threshold cause supercooling
and ice growth, releasing latent heat. Some of the ice grows on
channel walls, constricting channels, raising water pressure, and
causing divergent water flow into a distributed ice-contact drainage
system; the resulting decrease in sediment-transport capacity along
flow favours deposition. This will eliminate local erosion, trap
sediment transported from upglacier (Fig. 1b), and so prevent
further local deepening of the glacier bed and steepening of the
slope on the downglacier side of the overdeepening5,18.
Process understanding thus shows that erosion faster than in the
proglacial environment by a large, meltwater-rich glacier can continue until the slope of the downglacier side of a terminal overdeepening steepens across the supercooling threshold, interfering
with further erosion and sediment evacuation. Steepening of the
ice–air surface slope will allow additional erosional steepening of
the subjacent bed slope, and flattening of the ice–air surface slope
will tend to trap sediment transported from upglacier, thus maintaining weak supercooling and ice growth near the supercooling
threshold. Averaged over an appropriately long interval, which will
depend on the nonsteadiness of climate and on the response time of
the glacial-geomorphic system, further downcutting beneath terminal regions of a glacier near the supercooling threshold should
depend on the ability of the proglacial environment to erode
downward or on isostatic or tectonic tilting. Proglacial erosion
rates or tectonic processes thus should control subglacial downcutting by long-lived, highly erosive glaciers. Additional glacial
erosion would also remain possible through headward growth of
cirques19, valley widening4, and downcutting of portions of the
valley not yet at the supercooling threshold, including formation or
upglacier extension of terminal or of upglacier overdeepenings
(which have slopes on their downglacier sides that probably also
tend to the supercooling threshold13).
Our compilation of new and existing data from diverse glacial
settings to test this graded-glacier hypothesis provides much support. First, supercooling is active beneath many glaciers, including
some in Sweden15, Alaska, USA18, and Iceland20.
Additionally, steepening of glacier beds to stabilize near the
supercooling threshold is illustrated by the recent history of the
© 2003 Nature Publishing Group
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letters to nature
Taku and Muir glaciers in Alaska. Both experienced post-Little Ice
Age retreats along fjords that left the glaciers without large proglacial morainal shoals21–23. Both then discharged very large quantities of sediment into their proglacial fjords, rapidly building
prominent moraine shoals with upglacier slopes that evolved to
angles just steep enough to cause supercooling5,21,24, and exhibiting
evidence that supercooling was active5. Erosion of overridden sediments of 3 m yr21 beneath Taku21 and proglacial sedimentation of
30 m yr21 at the nearby, similar Riggs glacier in Alaska25 illustrate the
spectacular rates at which sediment can be moved as overdeepenings
form and steepen towards the supercooling threshold; even for
erosion into bedrock, rates of 10 mm yr21 or more may be possible1.
Rapid reduction of the ice–air surface slope can shift a glacier far
into the supercooling condition. Evidence from Matanuska glacier,
Alaska, indicates that in response to such a slope reduction,
sedimentation is filling overdeepenings and reducing bed slopes
Figure 1 Cartoons of sediment-transport capacity and sediment load in subglacial
streams, for a glacier lacking supercooling (a), and for a glacier far into the supercooling
field (b). In each case, a moraine or moraine shoal has developed, so that the terminal
overdeepening is in part a sediment-floored feature. In a, load is less than capacity in
upglacier regions owing to the difficulty of eroding bedrock, but load rises to match
capacity on the overridden and easily erodible sediments, as erosion steepens the
upglacier slope of the sediments. In b, ice growth from supercooling of streams flowing up
the overly steep face of the moraine shoal causes transport capacity to drop below load
delivered, producing deposition (shown as a negative erosion rate in the lower panel of b)
to fill the overdeepening back towards the supercooling threshold. Were the proglacial
environment able to remove all the sediment delivered but not able to erode bedrock as
rapidly as the glacier, then the upper panel of b could also be drawn with ice wholly on
bedrock, and subglacial erosion lowering the glacier bed below the proglacial
environment.
NATURE | VOL 424 | 14 AUGUST 2003 | www.nature.com/nature
back towards the supercooling threshold. The best-studied, prominent terminal overdeepening of Matanuska glacier now has a bed
slope opposed to and typically several times steeper than the ice–air
surface slope, producing extensive supercooling of subglacial
waters18. (The ice–air surface slope is even locally reversed over
the upglacier end of this overdeepening, causing lakes to form on
the ice.) Average ice–air surface slope overlying the overdeepening
has probably decreased over time in response to changing climate;
observations of Matanuska glacier in 1954 and photographs taken
in 1898 have been used26 to demonstrate that considerable thinning
but little horizontal retreat had occurred in downglacier reaches
over the 56-yr interval (subsequent retreat has shifted the active ice
margin a few hundred metres from its former moraine).
Common cobbles on an outwash surface with its head graded to
the former moraine show that abundant bed load was discharged in
the past, probably through subglacial channels that have been
disrupted during the subsequent surface-slope reduction into the
supercooling field. The metres-thick silt-bearing basal ice that has
accreted to Matanuska glacier from supercooled subglacial discharge18,27 occasionally contains evidence of basal or near-basal
water channels plugged by radial growth of ice crystals from channel
walls28. Dye-tracing and other data sets from the best-characterized
overdeepening indicate a distributed, high-pressure, low-velocity
basal water system despite water entering the glacier in vigorous
streams at large moulins18.
Such a distributed water system would not be expected to carry
much coarse sediment. Consistent with this, observations during
one summer at two prominent vents29 found almost zero discharge
of coarse-grained bed load (,1% of total load versus subequal
suspended and bed loads for typical glaciers6). Subaqueous fan
deposits at these vents, observed in the autumn after melting slowed
before snowfall, probably contained the coarsest material discharged during the entire melt season, yet were fine-grained, with
pebble-sized or larger clasts being rare.
Suppression of erosion beneath the terminal region may contribute to this lack of bed load; however, most of the glacier is at higher
elevations than the terminal overdeepenings (the glacier is about
45 km long, with 3,000 m of vertical relief, and an unglaciated area
of 185 km2 in the drainage basin potentially contributing much
coarse material by inwash or infall to the 380 km2 glacier18), so it is
highly likely that cobble-sized and coarser clasts are being generated
and delivered to the terminal overdeepening. Furthermore, coarse
clasts are present in the terminal overdeepening, as shown by
limited cobbles in the silt-rich basal accretion ice and by the clastbearing, although fine-grained, till that is frozen to the glacier sole
by ice-marginal wintertime conductive cooling and exposed by
thrusting of the ice margin27. And, abundant cobbles were discharged to the outwash surface before the decrease in ice–air surface
slope shifted the glacier so far into the supercooling field.
The total effect of the supercooling on the sediment budget is
difficult to estimate, in large part because we lack pre-supercooling
sediment-discharge data for Matanuska glacier, and because the
subglacial sediment trapping does not appear to be fast enough for
easy direct measurement. In light of the common dominance of
stream discharge in sediment budgets (for example, ref. 7), typically
with subequal bedload and suspended load6, the nearly total lack of
Matanuska bedload discharge may indicate a supercooling-caused
reduction in sediment discharge of the order of 50%. The suspended
sediment still discharging through subglacial water is equivalent to
roughly 1 mm yr21 of bedrock erosion averaged over the complete
glacier area30. Setting the trapped bed load equal to this discharged
suspended load, and assuming that terminal overdeepening(s)
occupy ,10% of the glacier area, we infer sedimentation in
terminal overdeepening(s) of order 10 mm yr21 or more, tending
to return the bed slope closer to the supercooling threshold.
Because the divergent water flow from ice growth clogging
subglacial streams is expected to reduce suspended-load as well as
© 2003 Nature Publishing Group
759
letters to nature
bedload transport capacity8, Matanuska glacier might be trapping
fine-grained as well as coarse-grained sediment subglacially. This is
consistent with the observed fine-grained character of the subglacial
tills, and would mean that subglacial sedimentation is faster than
estimated above. However, estimates are complicated by sediment
trapped in the ice accreted to the base of the glacier and
then discharged by ice-marginal melting (which may transport
0.1–1 mm yr21 of erosion averaged over the glacier area), as well
as by any sediment transport through subglacial till deformation.
Certainly, given the very high sediment fluxes from some glaciers,
and the possibility that supercooling can trap a substantial fraction
of the sediment flux in spatially restricted overdeepenings, geomorphically and glaciologically important sedimentation rates in
those basins seem likely.
We thus hypothesize that beds of highly erosive glaciers tend to
evolve to an equilibrium angle close to but slightly steeper than the
supercooling threshold, which is 20–70% steeper than and opposed
to the ice–air surface slope. Additional data are clearly desirable, but
this hypothesis is supported by our understanding of processes, by
the widespread occurrence of overdeepenings with supercooling,
and by evidence indicating evolution of both too-gradual and toosteep bed slopes towards the supercooling threshold. Some supercooling is likely at equilibrium to suppress the tendency for
continued excavation of overdeepenings; the exact equilibrium
slope should depend on several factors including the supply to
terminal overdeepenings of sediment that must be moved in steady
state, whether the sediment is from nonglacial sources, from valley
widening or headward extension, or from downcutting in regions
not yet at the supercooling threshold.
Our hypothesis implies that, over sufficiently long times, the bed
profiles of terminal regions of highly erosive glaciers will be
controlled by the ability of proglacial regions to downcut, or by
tectonic or isostatic tilting. Over shorter times, perturbations to the
surface slope can greatly affect sediment transport and erosion (by
twofold to perhaps an order of magnitude or more), with interesting
corollaries such as the possibility that kinematic waves in the ice
could serve as sediment pumps. Proglacial sediments should thus be
sensitive recorders of climatic and glaciological changes, but interpreting that record will require careful consideration of the glacial
sedimentary system.
A
Received 16 February; accepted 23 June 2003; doi:10.1038/nature01839.
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4. Montgomery, D. R. Valley formation by fluvial and glacial erosion. Geology 30, 1047–1050 (2002).
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(Geol. Soc. Am. Spec. Pap. 337, Boulder, CO, 1999).
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Acknowledgements We thank K. Cuffey for advice and for comments on this manuscript,
including help with the third paragraph. We thank our many colleagues in studying the
Matanuska glacier system, including S. Arcone, S. Kopczynski, R. Bigl, J. Denner, S. Ensminger,
T. Johnston and J. Strasser, and we thank R. Hooke for suggestions. Discussions with B. Hallet,
G. Clarke, T. Creyts, S. Tulaczyk and other colleagues helped clarify our ideas. We thank NSF and
CRREL for funding.
Author contributions R.B.A. led collaborative theory development and writing, D.E.L., G.J.L. and
E.B.E. provided extensive data and insights on glacier processes, and G.S.B. produced new
geophysical data at Matanuska glacier.
Competing interests statement The authors declare that they have no competing financial
interests.
Correspondence and requests for materials should be addressed to R.B.A. ([email protected]).
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Intense equatorial flux spots on the
surface of the Earth’s core
Andrew Jackson
School of Earth Sciences, University of Leeds, Leeds LS2 9JT, UK
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A large number of high-accuracy vector measurements of the
Earth’s magnetic field have recently become available from the
satellite Oersted, complementing previous vector data from the
satellite Magsat, which operated in 1979/80. These data can be
used to infer the morphology of the magnetic field at the surface
of the fluid core1, ,2,900 km below the Earth’s surface. Here I
apply a new methodology to these data to calculate maps of the
magnetic field at the core surface which show intense flux spots in
equatorial regions. The intensity of these features is unusually
large—some have intensities comparable to high-latitude flux
patches near the poles, previously identified as the major component of the dynamo field2. The tendency for pairing of some of
these spots to the north and south of the geographical equator
suggests they might be associated with the tops of equatorially
symmetric columnar structures in the fluid, or their antisymmetric equivalents. The drift of the equatorial features may
represent material flow or could represent wave motion; discrimination of these two effects based on future data could
provide new information on the strength of the hidden toroidal
magnetic field of the Earth.
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