1. Breaking Cold Ice How Surface Water Reaches the Bed R.B. Alley, T.K. Dupont, B.R. Parizek and S. Anandakrishnan Penn State

2. 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).

3. Zwally et al., 2002, Science

5. 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).

6. Zwally et al., Science, 2002

7. 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.

8. 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).

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

10. 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.

11. 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.

12. 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;

13. 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).

14. 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) 3 M/(48  y ’d  ).

15. 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 ’.

17. 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

18. 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.

19. 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.

20. 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.

21. 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…

24. Zwally et al., Science, 2002