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I often hear people claim "global warming will cause the ice-caps to melt, and that will cause the water levels in the ocean to rise, and that will cause major world-wide flooding."

Now, ignoring the question "are ice cap melting", I am still wondering how it is possible for melting ice-caps to cause water levels to rise.

Here is why I am skeptical:
    According to the law of displacement, the volume of an immersed object will be exactly equal to the volume of the displaced fluid. Therefor, if an icecap is floating in water, the displacement of the water would be based on the volume of the icecap, not it's shape, and the levels should be the same regardless of whether or not it is melted.

In fluid mechanics, displacement occurs when an object is immersed in a fluid, pushing it out of the way and taking its place. The volume of the fluid displaced can then be measured, as in the illustration, and from this the volume of the immersed object can be deduced (the volume of the immersed object will be exactly equal to the volume of the displaced fluid).
[....]
In the case of an object that floats, the amount of fluid displaced will be equal in weight to the displacing object.

The icecap will have the same weight, regardless of whether it is in ice form, or liquid form.

So how is it that people claim that melting ice caps can cause floods? Shouldn't water level stay exactly the same?

Icecaps includes polar ice, and smaller icecaps.

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@kotekzot In the case of an object that floats, the amount of fluid displaced will be equal in weight to the displacing object. - The icecap will have the same weight, regardless of whether it is in ice form, or liquid form. –  Ephraim May 3 '12 at 20:41
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There's land at the South Pole, so there's a lot of ice that isn't floating on water - en.wikipedia.org/wiki/Antarctica –  Tom77 May 3 '12 at 20:56
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According to Wikipedia (en.wikipedia.org/wiki/Current_sea_level_rise) it seems one is worried about land-based ice (Greenland and Antarctica). –  UncleBens May 3 '12 at 21:02
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In fact, most of the ice is not floating, but land-bound. Melt it, and it now quickly becomes seawater. –  user3344 May 3 '12 at 21:45
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Ice caps, by definition are not floating. –  Flimzy May 4 '12 at 3:23
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4 Answers

Antarctica contains 70% of the world's ice and the vast majority of this is on land, so there is no displacement confusion - if it melts it will pour off the land into the sea, thus raising the sea level.

The thickness of ice on the Antarctic continent (from this paper at RD Springer) averaged 2.2km in the East Antarctic Ice Sheet!

From The Physics Factbook (which is based on USGS ice caps area and thickness data) the maximum sea level rise potential globally is 73.44 m:

Geographic region: Antarctica

  • Volume: 30,109,800 km3
  • Maximum sea level rise potential: 73.44 m
  • Area: 13,586,400 km2"
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Aren't all the continents floating on liquid rock? Are fluid dynamics of lava different than water? –  user1873 May 4 '12 at 1:44
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@user1873 Yes but (1) The density of the liquid rock is much high than that of water so you get less motion (2) to first order it would only be Antartica and Greenland that rose on that account and (3) the mantle is visco-elastic rather than properly fluid and the relaxation times can be pretty long on the human scale. –  dmckee May 4 '12 at 2:00
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In addition to Rory Alsop's excellent point about Antarctica, water expands as it is heated. Even if the ice was all floating, global warming would still cause the sea level to rise. –  DJClayworth May 4 '12 at 3:30
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73m did not match my intuition at all. Surely there's not that much ice. So, I checked the reference. The ice caps are up to 5km thick? FIVE KILOMETRES. Staggering! –  Oddthinking May 4 '12 at 8:50
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@Oddthinking: So much for intuition :-) –  Hendrik Vogt May 4 '12 at 9:48
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Yes, they are already doing so

Here is what the IPCC has to say about this:

During recent years (1993–2003), for which the observing system is much better, thermal expansion and melting of land ice each account for about half of the observed sea level rise, although there is some uncertainty in the estimates.

FAQ 5.1 Is Sea Level Rising?

In other words, as the ocean warms up it expands and as the land ice melts, it pours into the ocean. At the moment the contributions are 50% each.

The following graph shows the past/present/future of sea levels according to the IPCC:

sea rise

Time series of global mean sea level (deviation from the 1980-1999 mean) in the past and as projected for the future.

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In other words, according to IPCC melting ice caps will be responsible for about 4 to 8 inches of sea level rise by 2100? –  vartec May 4 '12 at 9:16
    
@vartec Did you do the conversion wrong? 200 mm in in ~= 8 in, 500 mm in in ~= 20 in. That's about a foot in 2100. –  Tacroy May 4 '12 at 16:42
    
@Tacroy but only 50% would be due to the melting ice caps. –  Sklivvz May 4 '12 at 19:00
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@Sklivvz Ohhh right, I missed the due to "melting ice caps" bit. You can't really extend that out, though - the percentage contribution of expanding water vs melting icecaps will change over time. –  Tacroy May 4 '12 at 20:34
    
Only about 50% of sea level rise in the open ocean is due to melting ice, the rest is from thermal expansion. But that's untrue at the coasts. At the coasts, thermal expansion does not affect sea level significantly, because when water in the upper layer of the ocean warms and expands it rises up IN PLACE, like a very stubby iceberg. Its displacement is measured in units of mass, and doesn't change. It gets deeper where it warms, by a (small) percentage of its previous depth. A percentage of zero is zero, so at the coasts, where the depth is near zero, the rise is negligible. –  Dave Burton Jun 5 '13 at 20:32
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While the melting of Arctic sea ice may have little direct effect on sea level rise, it will substantially reduce the albedo of the Arctic ocean as sunlight will be absorbed by the dark ocean water, rather than being reflected back into space from the bright ice. This is likely to result in a general warming of the Arctic region, which is likely in turn to result in melting of the Greenland ice sheet, which would result in a very substantial rise in global sea levels over the course of a thousand years or so. This means there is a good reason to be concerned about the loss of summer (when albedo really matters) Arctic sea ice from a sea level rise perspective.

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Actually, my read of various recent refs indicates that the sea level rise projected by IPCC in 2007, as shown in the graph above, was more than 70% due to thermal expansion of sea water and the rest due to non-polar glacier melt. Polar ice cap melt was ignored at that point because it was not well understood. Recent advances in understanding increase the expected global sea level rise by year 2100 to as much as 2 meters, largely due to melt and stable glacier flow from the Greenland and West Antarctica ice caps. Were those two ice caps to destabilize, glacier flow would accelerate and sea level rise increase even more.

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You mention “various recent refs”. Please put them in your answer because otherwise this answer does not fulfil the requirements on this site that every claim needs to be properly referenced. –  Konrad Rudolph Oct 8 '12 at 18:09
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