Simple question about ice melting

Zaph0d

Ice is about 10% less dense than liquid water. Hence, the observation that only 10% of an iceberg is visible above the surface of the water. So, if the iceberg melts, you would expect that the 90% portion below the water will reduce in size by 10%, reducing the water level by 9% of the iceberg's volume. Meanwhile the 10% portion above the water will also reduce in size by 10% but will be added to the sea water below, increasing the water level by 9% of the icebergs volume.

So I must have this wrong somewhere because it seems to me that when an iceberg melts the overall water level remains constant.

However this couldn't be true because it would invalidate global warming.

Where am I going wrong?

dudara

the total mass of the ice present remains constant throughout. therefore if you start with 1 kg of ice, at the end you will have 1 kg of water.

density = mass/volume, so if density changes (ice -> water), and the mass is to remain constant, then the volume must change accordingly.

Zaph0d

dudara wrote:

the total mass of the ice present remains constant throughout. therefore if you start with 1 kg of ice, at the end you will have 1 kg of water.

yes, mass is constant.

dudara wrote:

density = mass/volume, so if density changes (ice -> water), and the mass is to remain constant, then the volume must change accordingly.

yes, as density increases, volume decreases.

I was asking what happens to the overall water level when a lump of floating ice melts in a container of water.

cajun_tiger

i like your thinking.... makes you wonder.... but i think the global warming also has an effect on the ice cliffs which is out of the sea and when that melts it falls in to the sea raising the water level... but i do think that your right with ice in container....

dudara

Ok, i get you now.

Maths wise, a 1kg lump of ice (specific density 0.92) has a volume of 0.00108 cubic metres. The corresponding 1 kg of water (s.d = 1) has a volume of 0.001 cubic metres.

But we must only consider the volume of water displaced by the ice. 92% of the ice is below water, ie 0.92*(0.00108) = 0.001 cubic metres.

Thus when the ice melts, 0.001 m3 below water disappears and is replaced by water from the whole ice lump with volume 0.001 m3. So there is no drop in the water levels. Now this calculation changes every so slightly when the densities used are replaced by those for salt ice and salt water.

I only just thought this through, so if anyone has anything to add, please do.

Zaph0d

dudara wrote:

...Thus when the ice melts, 0.001 m3 below water disappears and is replaced by water from the whole ice lump with volume 0.001 m3. So there is no drop in the water levels...

OK, so that would mean that when icebergs melt, the water level stays constant. I think the North Pole is one big iceberg (is it?). So the whole north pole could melt and sea levels wouldn't rise.

Now cajun tiger talked about ice cliffs melting and I guess she was referring to big lumps of ice on land such as on Greenland or on the south pole, melting and sliding into the sea. So is this what environmentalists are talking about when they say sea levels will rise following global warming?

cajun_tiger

i dont know i'm no brain when it comes to this but i kinda thought that this could be the case

dudara

I did that calculation using values for fresh water and fresh water ice. The density values will change for salt water and ice. (salt water is more dense at 1025 kg m^-3 and I couldn't easily find a value for salt water ice).

I presume that if you repeat the calculation with those values, you'll find that there will be a slight increase overall. Multiply that by however many kg are in an iceberg and the extra volume could increase significantly.

One problem with ice cliffs collapsing into the ocean rather than melting gradually is that they possess the risk of creating shock waves when impacting the water surface, thus possibly causing tsunamis.

does that help?

cajun_tiger

well if it was salt water to salt ice and back again
and
fresh water to fresh ice to fresh water
would it not be the same....

even though salt water to fresh water would be different

would the difference still be the same

dudara

the values of the densities used will affect the results.

cajun_tiger

ye but what i mean is you say with fresh water from fresh ice it will be x amount wouldn't it be the same method just different answer but same difference ie sa difference between fresh water and fresh ice is .24
would the difference between salt water and salt ice be .24


or am i compleetly off track

Capt'n Midnight

Zaph0d wrote:

Ice is about 10% less dense than liquid water.

No it's not, Icebergs can have air trapped in them from falling snow so 90% is a very rough rule of thumb and not too accurate.

So I must have this wrong somewhere because it seems to me that when an iceberg melts the overall water level remains constant.

Eureka !
a floating iceberg won't affect the water level, except by thermal expansion of water around it. water is denseist at 4 degrees C

However this couldn't be true because it would invalidate global warming.

Where am I going wrong?

couple of things
average depth of the sea is 2 miles / 3 Km - a 0.03% exansion of water would cause a 9m increase in sea level ( thermometers work on the priciple that liquids expand )
and the ice cap on greenland, and antartica is held back by floating icebergs, if they melt or float away those ice caps (several miles thick in places) would flow faster into the sea and melt. there are also glaciers in siberia, norway canada and alaska that would do similar

Steven

Basically

Icebergs melting = no increase in sea level

Ice on land (glaciers and ice caps) melting = increase of somewhere around 70 m ("Waterworld" exaggerated a teeny bit)

Not entirely sure of the height because it's a long time since I watched that documentary, but it's within 10m of that.

Zaph0d

Thanks for the replies.

Here's a link about how sea water density is influenced by salinity and temperature.
http://geosun1.sjsu.edu/~dreed/130/lab10/7.html

This would seem to suggest that the melting of icebergs could reduce the salinity of the sea and reduce the density of water, lowering sea levels.

So there seem to be two scenarios:
1. temperature of seawater rises a couple of degrees leading to sealevels rising a few metres, causing worldwide coastal flooding.
2. ambient temperatures rise to the point where ice caps slide into the sea and sea levels rise massively

I don't think "salt ice" exists. If you freeze sea water, I think the ice and salt get separated.

Finally what about evaporation? If average ambient temperatures rise a couple of degrees, does that not mean that a lot more water will evaporate, mitigating the sea level rise?

Capt'n Midnight

salt ice exists, the older the ice the less salt in it - the clear blue stuff would have least ice. even though pure ice freezes first a small amount of salt will get trapped.

Re evaporation: the atmosphere is equilivant to 10m of water maybe at most 1% will be water vapour ( where are steam tables when you need them ) also many areas are drier - so evaporation would hold maybe 10cm of water , rivers lakes and groundwater will hold more water but permafrost will melt so would probably have more water realeased in to the sea.

re dry, by looking at the way soil grains have settled it's been shown that there has been no discernable rainfall in the dry valleys of antartica in the last two million years !!!

in the permian age there were glaciers within 10 degrees of the equator and sea levels at other times were up to 300m above present levels (though continanets were different places)

now the real cutie
if the temperature of the sea floor raises above 4 degrees then methane hydrates keep intact by cold and pressure will decompose releasing methane into the atmosphere which is a greenhouse gas and there is a LOT of methane down there.