Does melting sea ice raise sea level?

[Graeme M]

On a climate change blog I recently had a brief exchange in relation to melting sea ice. I argued that melting sea ice must add to sea level rise. Others maintained that floating sea ice cannot add to sea level when it melts because it displaces the same weight of water as it weighs itself. I wonder if people who know more about the physics of buoyancy etc can explain which view is correct? I have done some research and come across arguments in both directions but many seem to view buoyancy in a way fundamentally different from how I look at it. One caveat - I know nothing about sea ice, but I assume that it floats, and that some portion is proud of the sea surface. I don't know how much but that it does is why we have ice-breakers.

 

My understanding is that buoyancy and displacement are related but not the same thing. Buoyancy is the extent to which an object in water is prevented by the buoyant force from being accelerated down by gravity. The buoyant force is due to the pressure differential between the top and bottom of an object and can be considered equivalent to the weight of the volume of water displaced by the object. Displacement is the volume of water displaced by that volume of an object which is submerged.

 

The density of an object will determine whether it floats or not, given sufficient body of water.

 

In the case of fresh or pure water, an ice block in the shape of a cube should float with its top surface flush with the water surface (assuming no impurities, or air trapped in the block). It cannot do otherwise as the buoyant force will be exactly equal to its weight once it is completely submerged. When we do an experiment at home along these lines various other factors come into play, such as air trapped in the cube or accuracy of measurement at such small scale, however generally speaking we should find that a melting ice cube doesn't have any appreciable effect on the water level in a container.

 

I expect that the internal molecular structure must have some influence, for example a block of ice might be slightly less dense than the equivalent volume of water, but I don't actually know how the structure is affected by being frozen. I suspect however that at the macro level the difference is negligible - a body of water is of mass X whether it's liquid or solid and the relative densities are almost the same.

 

However, sea water is salty and has various impurities. As I understand it, frozen sea water (sea ice) is fresher as the salt precipitates out as it freezes, and this process continues over time. Older sea ice is thus more 'fresh' than new sea ice which is itself more 'fresh' than sea water. For this reason, sea ice floats.

 

That is, a volume of sea water is denser than an equivalent volume of sea ice - it has additional mass from the presence of salts and other impurities. Looked at another way, the molecules of salt etc are more dense (have more mass) than water molecules, so a given volume of sea water weighs more than an equivalent volume of fresh water. Equally however, equivalent volumes of each should have different quantities of actual water - the sea water has less water per volume than fresh water.

 

When sea ice forms, it is fresher than sea water, and hence less dense, and therefore floats. The buoyant force is equal to the weight of the volume of water it displaces. If for example a sheet of sea ice is 5 metres thick, it may be that 4.5 metres is below the surface, and .5 metres above the surface. The volume of sea water displaced by the volume of ice beneath the surface is less than the total volume of the ice sheet, but its weight is sufficient (by way of its greater density) to offset the weight of the whole ice sheet.

 

This means that the mass of the displaced sea water is equivalent to the mass of the whole sea ice sheet, but its volume is less. When the sea ice melts, the total mass of water plus now melted ice remains the same but the volume of the sea water increases and the sea level must rise. I imagine the effect to be quite small, but nonetheless I believe it must be a positive value.

 

Am I right or wrong?

[swansont]

Sea ice floats not only because seawater is more dense than fresh water, but also because ice is less dense than water for fresh water — it expands by around 10% when it becomes ice. Ice floats better in seawater — more of it protrudes — because of the higher density of the water. It doesn't look like you are accounting for the reduction in volume of the water when the ice melts.

 

If you have 1 kg of water, it has a volume of 1L. 1 kg of ice will displace 1L of water, but the ice will take up a volume of around 1.1 L. If this is in a pool of 9L of fresh water, then the water line will be at the 10L mark, and that won't move as the ice melts. (I'm ignoring changes due to temperature, which is a separate effect)

 

What you need to do is apply that to a pool of salt water, using the density of salt water, which for the ocean surface is 2-3% higher than fresh water. A wrinkle in that is the change in salinity, but that will be a much smaller effect in the oceans than in the example I described, because the ratio of ice to water is markedly different.

[fiveworlds]

The problem is that while the ice is in the water it melting isn't a problem. The problem is the ice that is on land and will fall into the sea when it melts.

[Graeme M]

Interesting. I hadn't realised ice is 10% larger by volume, I'd assumed the effect would be very small. That is a lot. I did however dig around and find this:

http://www.skepticalscience.com/Sea-level-rise-due-to-floating-ice.html

 

Which refers to a paper by Noerdlinger and Brower ( http://www.ingentaconnect.com/content/bsc/gji/2007/00000170/00000001/art00010).

 

I tried to think through the whole thing but got too confused, however I do think melting sea ice will add volume even if only a very small amount. I guess I think of it from a practical perspective. A volume of ice floating in seawater should ride higher than in freshwater due to the greater density of the sea water. If I push the ice down into the sea water to the same level as it would ride in fresh water, it must displace some volume of water. It follows that when it melts it must add volume. But then I think, hang on, the water will then become denser. That's when I get confused!

 

Either way, it's been an interesting thing to think about.

Edited December 5, 2015 by Graeme M

[swansont]

Interesting. I hadn't realised ice is 10% larger by volume, I'd assumed the effect would be very small. That is a lot. I did however dig around and find this:

http://www.skepticalscience.com/Sea-level-rise-due-to-floating-ice.html

 

Which refers to a paper by Noerdlinger and Brower ( http://www.ingentaconnect.com/content/bsc/gji/2007/00000170/00000001/art00010).

 

I tried to think through the whole thing but got too confused, however I do think melting sea ice will add volume even if only a very small amount. I guess I think of it from a practical perspective. A volume of ice floating in seawater should ride higher than in freshwater due to the greater density of the sea water. If I push the ice down into the sea water to the same level as it would ride in fresh water, it must displace some volume of water. It follows that when it melts it must add volume. But then I think, hang on, the water will then become denser. That's when I get confused!

 

Either way, it's been an interesting thing to think about.

You have to remember that the water contracts as it melts.

[reasonmclucus]

Keep in mind that increasing the area covered by liquid water will increase evaporization of the water. Although ice can subllime and go from a frozen state to a gas, the rate of vaporization is slower than for liquid water.

[Alan Watson]

Hi reasonmclucus

 

Are you saying that melting ice will ultimately lead to a disproportionate increase in the amount of atmospheric water?

 

I find that interesting in the context of all these extreme weather events we have been experiencing in recent years.