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It has been suggested that global warming will lead to increased precipitation in parts of Antarctica. This would sequester water in the ice sheet, preventing sea level rise.

However, the slope (and thus the height and volume) of continental ice sheets is limited by ice properties. What if the ice sheet is already at its maximum slope/height/volume (is this known)? Wouldn't adding more ice just cause more flow to the sea?

According to "Ice Sheet Modeling"

ice behaves as a deformable plastic material, which means that there is a critical shear stress, below which no strain (deformation or flow) will occur ... If the slope is too low, the basal shear stress will not match the critical shear stress, ... but as snow piles up, ... flow will begin. ... The result of this is that a glacier has an equilibrium profile

I am presuming that the ice sheets are already slightly above their equilibrium profile (since they are flowing). Since the profile depends on the area and shape of the base (which is shrinking due to melting around the edges), they are already holding as much ice as possible, and adding more snow to any region will just accelerate the flow. I don't know on what timescale this occurs. (I have not tried the computer models described in the paper.)

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There is some scope for continuing debate because quantifying the various components of the ice/snow/water balance are fraught with difficulty, and many of the estimates have error bounds which approach the magnitude that is being measured. However, a good best estimate, subject to continuing research, is given in:Is Antarctica losing or gaining ice? This cites the following two graphs:

enter image description here

Clearly there are important regional differences, with East Antarctica gaining slightly, but not enough to compensate for the ice loss in west Antarctica.

It is true that the amount of fresh snow in the Antarctic is increasing, but it still doesn't amount to much. Antarctica is still the driest continent, by far, and much more so than Australia. The controlling factor is not the amount of snow on the land, but the fate of the sea ice around the perimeter. Notwithstanding climate deniers, there is abundant evidence that the oceans' sea surface temperatures are warming, including the Southern Ocean. This reduces the seasonal extent and thickness of sea ice, which lowers the oceanic albedo, and increases near-surface heat absorbtion. It is a well-documented feedback process. Overall the warmer ocean around Antarctic destabilizes the shelf ice, thereby unlocking the glacial ice which would have been held back. So we have two opposing non-linear processes, mobilization of coastal land ice (mass loss), vs increased snowfall (mass gain). At present, and for the forseable future, the mass-loss is winning. I'm guessing this will continue to be the case because the negative feedback is very powerfull. I don't think there are any reliable forward projections about how precipitation in the Antarctic will evolve.

(Later) In view of the comments, maybe it would be helpful to visualize the daily precipitable moisture around the world. This is available at El Dorado Weather.

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    $\begingroup$ I think you mean positive feedback in the third to last line. $\endgroup$ – bon Aug 31 '16 at 7:40
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    $\begingroup$ Many don't consider how cold it is at the poles. As such, much precipitation happens before air masses actually reach the "poles", falling in the oceans/seas rather than over any land mass. Hence some of the relative dryness of Antarctica itself. $\endgroup$ – user2338816 Aug 31 '16 at 8:23
  • $\begingroup$ Good stuff, but my question is about the theory of equilibrium profile, which implies that ice fields have a maximum non-flowing height proportional to the square root of the width. So even if we do get more precipitation, the icefield will be unstable and will flow to the equilibrium shape. On the other hand, if precipitation were to stop, this suggests that the icefield would shrink to the equilibrium shape and then stop flowing. Is this theory a good way of thinking about icefield behavior? It might not be if the relaxation time is very long, but I can't find anything about that. $\endgroup$ – Keith McClary Sep 7 '16 at 19:11
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Drifting into what-if territory (and apologies for the lousy units) : Let's pick a rough rule of thumb that 30 inches of ( cold temperature) snow is equivalent to one inch of water. The land area of Antarctica is 5.4 million square miles. The world's major oceans' total area is roughly 140 million square miles (all data from Wikipedia). Thus, to reduce sea level by one inch, you'd need to dump 26 inches of water onto Antarctica, or maybe 620 inches of snow. To drop sea level by, say two feet, then, you'd need 19000 inches, aka 1560 feet, or 5.2 football fields, of snowfall.
Since some ice will break back into the sea, we'll need more snow to fall than is lost to icebergs -- but so long as the snowfall exceeds lost ice by any amount, the sea level will decrease (albeit slowly :-) ).

I do want to emphasize that this is a what-if answer (without the funny drawings or velociraptors), not a suggestion of what could possibly happen in the real world.

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I want to support other arguments with the historical one.

All we know that since the Last Ice Age the Sea Level has increased by .. 120 meters

enter image description here

For some reason (I guess explained by now: it is too small and experiencess net loss of ice instead of build up), Antarctica did not stop the raise. Antarctica never hampered the sea level rise and fall along with the global temperature. Which magic do you expect to turn the tide? Why should antropogenic nature of the human-induced warming should revert the trend?

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    $\begingroup$ Argumentative and severely lacking in accuracy (and poorly written - it's hard even to figure out what you are claiming) $\endgroup$ – Carl Witthoft Aug 31 '16 at 18:50

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