# If the polar ice caps were to melt .

1. Aug 2, 2011

### warfreak131

If the polar ice caps were to melt.....

wouldn't the sea levels decrease?

Water ice is less dense than liquid water, so the volume (and displacement of liquid water) is greater when its frozen. But when you melt that, the volume decreases, and some of the water that was initially displaced by the ice would flow back to its original position.

2. Aug 2, 2011

### Dotini

Re: If the polar ice caps were to melt.....

You must remember that the ice at Greenland and Antarctica is mostly sitting on continental crust, and not floating.

Respectfully submitted,
Steve

3. Aug 2, 2011

### SW VandeCarr

Last edited: Aug 2, 2011
4. Aug 2, 2011

### billiards

Re: If the polar ice caps were to melt.....

No. As already mentioned the most important point is that the ice is not floating.

However you have misunderstood the physics, if the water and the ice have the same composition then the water level will not change when the ice melts. However, if floating ice of fresh water composition melts in a denser saline solution the water level will RISE.

Consider a mass of ice floating in sea water. Archimedes principle states that the ice displaces its own weight in sea water. When the ice melts it converts all of its weight into fresh water which is less dense than sea water -- this is the key point -- the same weight of fresh water takes up more volume than seawater. This causes the sea level to rise slightly. This effect is mostly ignored in sea level budgets, however, it is not a negligible effect.

5. Aug 2, 2011

### Andre

Re: If the polar ice caps were to melt.....

There are several more factors to consider, for instance the change in gravity patterns as the ice sheets are still a big mass that adhere to Newtons law. Furthermore there is supposed to be isostacy/eustacy, the land previously below the ice sheets, rebouncing. But imo it's more complicated.

6. Aug 2, 2011

### SW VandeCarr

Re: If the polar ice caps were to melt.....

When land based water or water ice enters the sea, it is adding mass to the sea and sea levels will rise, discounting evaporation. The floating ice (of any composition) is part of the mass of ocean and displaces a volume of water equal to its weight. So its melting does not cause the water level to rise.

You can do a simple experiment: The water level in a glass of water that already contains a floating ice cube will not change as the ice melts. If you add an ice cube to a glass of water, the water level will of course rise.

Last edited: Aug 2, 2011
7. Aug 2, 2011

### Staff: Admin

Re: If the polar ice caps were to melt.....

So the concern comes from say the Greenland and Arctic ice caps?

8. Aug 2, 2011

### SW VandeCarr

Re: If the polar ice caps were to melt.....

From the Greenland ice cap, but not the floating Arctic ice pack. By far, the biggest mass of land based ice is the Antarctic ice cap.

9. Aug 2, 2011

### 256bits

Re: If the polar ice caps were to melt.....

In that case, ice, or an iceberg, will float higher up in saline seawater. And when the ice melts the sea level will rise proportionally. I guess the extreme experiment to prove this would be to float an ice cube in a glass of liquid mercury ( denser than the ice). The liquid level ( mercury/water ) when the ice melted would be higher than the liquid level ( mercury ) with the ice floating on top.

10. Aug 2, 2011

### billiards

Re: If the polar ice caps were to melt.....

Agree, and never expressed otherwise.

No you're overlooking the fact that the density of fresh water is less than the density of sea water. It turns out to be important, for shelf ice at least.

If a floating body of ice has mass $m$ we can do some simple calculations to consider the implications to sea level if it melts.

These relations are trivial and yet hidden within them is the truth.

$$m=\rho_{ice}V_{ice}$$

Upon melting to fresh water the mass remains the same.

$$m=\rho_{freshwater}V_{freshwater}$$

By Archimedes' principle, the weight of the ice is equal to the weight of the displaced sea water.

$$mg=\rho_{seawater}V_{displaced seawater}g$$

Divide by g.

$$m=\rho_{seawater}V_{displaced seawater}$$

Bring together the fresh water and seawater terms.

$$m=\rho_{freshwater}V_{freshwater}=\rho_{seawater}V_{displaced seawater}$$

Rearrange:

$$V_{freshwater}=\frac{\rho_{seawater}}{\rho_{freshwater}}V_{displaced seawater}$$

If seawater is 5% denser than freshwater then.

$$V_{freshwater}=1.05V_{displaced seawater}$$

Sea level is related to the volume of water in the basin such that the greater the volume of water in the basin the greater the sea level.

$$V_{filledbasin}(beforemelting) = datum + V_{displaced sea water}$$

$$V_{filledbasin} (aftermelting) = datum + V_{fresh water}$$

$$V_{filledbasin} (aftermelting) = datum + 1.05 * V_{displaced sea water}$$

Therefore:

$$V_{filledbasin} (beforemelting) < V_{filledbasin} (aftermelting)$$

Last edited: Aug 2, 2011
11. Aug 2, 2011

### SW VandeCarr

Re: If the polar ice caps were to melt.....

I agree that 1 kg of fresh water occupies a larger volume than 1 kg salt water, other things being equal. The issue is whether the ocean level rises when floating ice melts. When fresh water ice enters the ocean, it will raise the ocean level immediately by displacing whatever volume based on its density. If liquid fresh water enters the ocean, it would "float" because it is less dense and raise the ocean level. So, as far as I can tell, there is no difference between a given amount of floating fresh water ice melting in the ocean and an equivalent amount of fresh water entering the ocean in liquid form. That's the point I was making.

EDIT: I did find some articles that agree with you, but they don't appear to be from peer reviewed journals. On one hand, it seems that as a large mass of floating fresh water ice melts, the released fresh water would occupy a larger volume than the salt water mass it displaces. In part, this would be compensated by the decreased volume of salt water displacement by the melting ice mass. In any case, how long does the melt water remain "fresh"? It seems that the fresh melt water would quickly lose its characteristics as it is dispersed in the much larger volume of salt water. The salinity of the oceans is maintained by a balance between evaporation and fresh water infusions.

Could you find a peer reviewed article that supports your argument?

Last edited: Aug 3, 2011
12. Aug 2, 2011

### Jack23454

Re: If the polar ice caps were to melt.....

If the ice is floating it is only displacing it's equal weight. If submerged it is displacing volume. If it has trapped air in the ice, the volume will decrease when it melts and the air is no longer contained. In that case the water level would be less. To answer the question empirically; submerge an ice cube with a magnet frozen in the center. Hold it in place near the bottom with a magnet. When the ice melts see if the water level changes, assuming evaporation is not a noticeable factor.

13. Aug 2, 2011

### Nik_2213

Re: If the polar ice caps were to melt.....

Uh, IMHO, the relative expansions of salt and fresh water is a minor detail compared to the way the additional free water will arrange itself on the globe.

Also, you'll get 'primary isostatic rebound' as the land masses and associated 'moat' depressed by those huge ice-caps gradually pop up a kilometre or two, displacing more water, then 'secondary' effects as areas beyond the 'moat' sink slower...

14. Aug 3, 2011

### SW VandeCarr

Re: If the polar ice caps were to melt.....

When you say "concern", yes there is concern about the melting floating Arctic ice pack because of its predicted effect on Arctic ecology and the world climate, but not because of its potential to add to rising sea levels. Rising sea levels will be mostly due to the melting of land based ice and the redistribution of water due to continental rebound as the ice melts.

The article I linked to treated rising sea levels is a long term issue, but that position has been disputed. Many worry about the possible instability of the Greenland and Antarctic ice sheets and that these ice sheets could become mobile if liquid water accumulates underneath them. That means that large volumes of ice could be dumped into the ocean in a relatively short time. It's just one of the several proposed theories.

http://www.sciencedaily.com/releases/2010/01/100116103350.htm

Last edited: Aug 3, 2011
15. Aug 3, 2011

### billiards

Re: If the polar ice caps were to melt.....

It won't "float" in the sense of the ice, which clearly has some of it's head above the water. The fresh water will redefine sea level. When it is ice it redefines sea level by displacing saline sea water; when it melts it redefines sea level using its own fresh water. < That's the key.

I fully acknowledge that it is a small effect. But it is one that is almost always overlooked. It can safely be overlooked when we consider sea ice because sea ice is derived from the ocean itself and melts and forms every year, it cannot be safely overlooked for shelf ice which is the floating portion of the continental ice sheets. The point is that the melting of the shelf ice will act to slightly increase sea level by the effect I have described, it is not a zero contribution as is often assumed.

Haven't looked. But the point is that it is widely ignored, which is why I bring it up. I would be interested to see if someone here can debunk it.

Good point. We can include this in the maths quite simply.

Upon melting to fresh water the mass remains the same except for the component of trapped air which escapes.

$$m=\rho_{freshwater}V_{freshwater}+\rho_{air}V_{trappedair}$$

Bring together the fresh water and seawater terms.

$$m=\rho_{freshwater}V_{freshwater}+\rho_{air}V_{trappedair}=\rho_{seawater}V_{displaced seawater}$$

Rearrange:

$$V_{freshwater}=\frac{\rho_{seawater}}{\rho_{freshwater}}V_{displaced seawater}-\frac{\rho_{air}}{\rho_{freshwater}}V_{trappedair}$$

Consider sea water 1% denser than fresh water, and freshwater 500 times denser than the trapped air (conservative numbers) and rearrange:

$$1.01V_{displaced seawater}-V_{freshwater}=0.002V_{trappedair}$$

Now how much trapped air would we need such that the volume of released fresh water is equal to the displaced sea water?

If $V_{displaced seawater}=V_{freshwater}$
then $0.01V_{freshwater}=0.002V_{trappedair}$
that is $5V_{freshwater}=V_{trappedair}$

Now the volume of freshwater is increased by about 10% when it freezes to ice.

$$5V_{freshwater}=5.5V_{ice}=V_{trappedair}$$

So on the back of an envelope I estimate conservatively that you need air to occupy 2 parts of volume for every 11 parts of volume occupied by ice (air occupies at least 15% of the total volume) such that when the ice melts in sea water the released fresh water does not raise sea level. Of course, the ice would need to be greater than 15% air for the sea level to drop, any less than 15% and the sea level will rise.

Now what is the volume of air as a percentage of the antarctic ice shelf?

16. Aug 3, 2011

### Studiot

Re: If the polar ice caps were to melt.....

@Billiards

When considering the ice melting you need to include the dilution effect of the meltwater in your calculations.

The resultant seawater will be somewhat less saline due to the addition of fresh water.

This will change its density.

go well

17. Aug 3, 2011

### SW VandeCarr

Re: If the polar ice caps were to melt.....

You didn't address my point that even if fresh water is released, it will be dispersed in the much larger volume of salt water so that its true effect in raising sea levels is negligible, even for large Antarctic icebergs. Many factors affect ocean salinity which reflects the balance between of fresh water input from all sources vs evaporation. That's why I asked for peer reviewed sources support the position that this is not merely a theoretical argument.

I think a much more important effect from major fresh water sources such as from a large river, is that it raises the freezing point of seawater over a large area since, being less dense, the fresh water will tend to remain on the surface. It's demonstrably true that sea ice forms regularly in the Gulf of St Lawrence, which is at the lowest latitude for seasonal sea ice formation in the North Atlantic.

Last edited: Aug 3, 2011
18. Aug 3, 2011

### billiards

Re: If the polar ice caps were to melt.....

Why?

Yes, but this is after the effect has already established itself.

I don't see how diffusion of salt will change the volume.

19. Aug 3, 2011

### Studiot

Re: If the polar ice caps were to melt.....

Consider a beaker of salt water, density p1

add a quantity of pure water, density p0

This results in a quantity of salt water, density p2

Since density is a function of salinity

p1 > p2 > p0

Whether this effect is significant depends upon the relative quantities of original saline and meltwater.

go well

20. Aug 3, 2011

### billiards

Re: If the polar ice caps were to melt.....

I agree it is a small effect.

To put it into perspective consider the sea level, $z$ in relation to the volume of the basin, $V$ and the area, $A$ of the basin $V=Az$.

$$V_{new}=V_{old}+\Delta V$$

$$Az_{new}=Az_{old}+\Delta V$$

Change in sea level is denoted $\Delta z$

$$\Delta z=z_{new}-z_{old}=\Delta V/A$$

$$\Delta z=(V_{freshwater}-V_{displaced seawater})/A$$

If for example $V_{freshwater}=1.05V_{displacedseawater}$, then
$$\Delta z=0.05V_{displaced seawater}/A$$

and $V_{displaced seawater}=\frac{\rho_{ice}}{\rho_{seawater}}V_{ice}\approx0.9V_{ice}$

$$\Delta z=0.045V_{ice}/A$$

So for example with these numbers a 1000 km3 volume of ice melting in a 100 million km2 expanse of ocean basin will contribute about .45mm of sea level rise. Not much but I would not call this negligible.

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