Breaking Cold IceHow Surface Water Reaches the Bed

R.B. Alley, T.K. Dupont, B.R. Parizek and S. Anandakrishnan

Penn State

Water penetrates >1 km of cold ice in Greenland:

• Clean water goes down moulins, dirty water comes out the front;

• When seasonal melting starts, moulin-drained ice near Swiss Camp speeds up (Zwally et al., 2002).

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Zwally et al., 2002, Science

Water penetrates >1 km of cold ice in Greenland:

• Clean water goes down moulins, dirty water comes out the front;

• When seasonal melting starts, moulin-drained ice near Swiss Camp speeds up (Zwally et al., 2002).

Zwally et al., Science, 2002

Can warming move Greenland meltwater access to bed inland?

• If yes, could speed flow by:Thawing frozen regions (latent heat);Lubricating thawed regions (pressurized

water);

• Causing faster ice-sheet melting and sea-level rise than currently modeled.

Moulins form by fracture, then Walder localization of flow:

• Physical understanding (surface water can’t drill through 1 km ice);

• Observations on glaciers (Larsen B ice shelf, Matanuska Gl., etc.);

• Analogy to volcanic eruptions (fire curtains from fissures).

Kilauea, Hawaii in eruption, 1983, NOAA NGDC Slide Set

But, isn’t easy for a water-filled crevasse to get through:

• Water inflow must exceed freezing:New crack initially narrow, so water inflow

slow, but below top few meters, Greenland ice cold when first broken, so freezes;

• Water inflow must keep crack water-filled to reach bed and allow Walder instability:If water scarce or inflow slow, won’t work.

If crack deep enough and remains water-filled:

• Deeper crack is wider allowing more water inflow so doesn’t freeze closed as easily;

• Deeper crack opened more easily by larger excess of water pressure over ice pressure;

• So deep enough crack should propagate to bed, but shallower cracks should “fail”;

• We calculate that “deep enough” is order of tens of meters.

Equations (we do have some):

• We think/hope they are mostly right;• Reviewers didn’t yell very loudly;• Closely follow Rubin (1995, Ann. Rev.

Earth Planet Sci.) for cracks in magmatic systems;

• Lots of uncertainties, may eventually need numerical treatment;

Some equations:

• Freezing rate decreases as square-root of time since opening, crack-volume growth increases with depth d and deepening rate u;

• Freezing equals opening at:

u=[y’)]2/d

with far-field stress y’ (are thermal, M elastic parameters).

Some equations:

• Water inflow rate increases with crack width (2w)3, which increases with depth d and stress y’;

• Pressure gradient G driving water inflow from crack-tip pressure drop to just allow propagation;

• Water inflow (with viscosity balances crack growth for u=-G(2w)3M/(48 y’d ).

So, for moulin formation:

• Water-filled crack must reach glacier bed; hence,• Water inflow must exceed crack-opening rate; and• Water inflow must exceed freezing rate;• As shown in next diagram, far-field longitudinal-

deviatoric tensile stress magnitude must exceed some minimum value y_min’ .

Some equations:

• Calculating that minimum stress magnitude -y_min’for crack reaching the bed, we have lots of uncertainties, but get 9 bars for a 1-m-deep crack and 4 bars for a 10-m-deep crack, dropping through zero as the crack becomes deeper;

• As expected, small cracks have troubles, and big cracks can go if they tap a big enough water reservoir

How to “nucleate” a crack:

• Multiple fracture-heal at a place to warm the ice?• Really high glaciogenic stresses?• We especially like lakes on the surface:

Help warm the ice (must freeze before winter cooling);

Supply big water reservoir to keep crack full;Supply extra driving stress for crack

propagation.

How to grow a lake:

• Localized ablation?• Partially healed crevasses? Ogives?• We especially like surface-slope reversals:

Require large longitudinal-deviatoric stress to “raft” ice over bumps or lubrication changes;

Observed in marginal regions, sometimes inland (Lake Vostok has one);

Observed with Greenland lakes.

So, our models suggest:

• Hard to start moulins in cold ice; shallow cracks freeze or run out of water; easier with higher tensile stress, warmer ice;

• Lakes help by warming, forcing, and supplying water; may be required in Greenland;

• In warming world, meltwater access to bed to thaw and lubricate may follow lakes inland;

• So modeling surface-slope reversals as well as surface melt will help in projecting future of Greenland ice sheet.

So, why is this at WAIS?

• Well, I hope it is interesting;• More important, not that far from regional

Antarctic summertime surface melting, which may start in future;

• Suppose surface meltwater reaches bed and thaws an inter-ice-stream ridge--flow speed-up not now modeled would follow…

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Zwally et al., Science, 2002