Why Do Melting Antarctic Ice Caps Cause Sea Levels to Rise?

[davies65]

When I freeze water in an ice cube tray in my freezer they expand slightly. Their weight remains the same therefore density has reduced. When I put these ice cubes in a glass of water they float because of the lower density. A small portion of the cube rises above the surface of the water.

Is the volume of the cube which is below the surface equal to the volume of the original thawed water? And if so, why do people say melting antartic ice caps cause sea levels to rise? Wouldn't the ice simply melt and occupy the same volume as the frozen portion which is below the surface therefore sea levels would remain exactly the same?

Cheers

 

[paisiello2]

Yes, by Archimedes principle the weight of the volume of water displaced must be equal to the total weight of the floating object.

As far as the melting ice caps go, you have to be aware of the two types of ice under consideration: sea ice and land ice. The former is floating in the arctic and antartic seas and varies considerably up and down over the year. The latter are the ice masses and glaciers that have built up over a long time on land. It is the melting of land ice that contributes to the rise in sea levels.

And as a passing note, it is currently the arctic sea ice melting while the antartic sea ice has been actually increasing. However, the large majority of land ice on the planet has been steadily decreasing.

 

[davies65]

Ok thanks

 

[dauto]

Also note that thermal expansion of ocean waters may lead to sea level rise even if no ice melts.

 

[Buckleymanor]

When I freeze water in an ice cube tray in my freezer they expand slightly. Their weight remains the same therefore density has reduced. When I put these ice cubes in a glass of water they float because of the lower density. A small portion of the cube rises above the surface of the water.

Is the volume of the cube which is below the surface equal to the volume of the original thawed water? And if so, why do people say melting antartic ice caps cause sea levels to rise? Wouldn't the ice simply melt and occupy the same volume as the frozen portion which is below the surface therefore sea levels would remain exactly the same?

Cheers

The volume of the cube which is below the surface is less than the volume of the original thawed water.
The total volume of the cube which includes the ice above the surface is equal to the volume of the original thawed water.

 

[Buckleymanor]

Also note that thermal expansion of ocean waters may lead to sea level rise even if no ice melts.

Doubtfull as water is at it's densest at 4 degrees so the oceans will contract before they expand if no ice melts.

 

[DrewD]

The volume of the cube which is below the surface is less than the volume of the original thawed water.
The total volume of the cube which includes the ice above the surface is equal to the volume of the original thawed water.

Unless I am misunderstanding you, this is not correct. Ice does indeed expand when it freezes, so the volume of an ice cube will be greater than the same cube when melted.

 

[paisiello2]

The volume of the cube which is below the surface is less than the volume of the original thawed water.
The total volume of the cube which includes the ice above the surface is equal to the volume of the original thawed water.

This is just not correct. Water expands something around 10% in volume when it transitions to ice.

Let V1 and V2 be the volumes of water and ice cube respectively.

Let V3 be the portion of the ice cube submerged below the water line.

By definition:

V2 = 1.1*V1

The weight of the ice cube is the same as the water before it froze = gamma*V1

By Archimedes principle, the buoyant force acting on the ice cube = gamma *V3

In order to be floating the buoyant force must be equal to the weight of the ice cube:

gamma*V3 = gamma*V1

which means that V3 = V1
= V2 / 1.1

Therefore, the submerged volume V3 is equal to the volume of water V1 and is less than the volume of the ice cube V2.

 

[paisiello2]

Doubtfull as water is at it's densest at 4 degrees so the oceans will contract before they expand if no ice melts.

Not correct. We are talking about sea water whose maximum density is close to its freezing point which in turn depends on the salinity and pressure.

 

[dauto]

Doubtfull as water is at it's densest at 4 degrees so the oceans will contract before they expand if no ice melts.

The ocean's temperature is mostly above 4 C. Any warming will lead to expansion, not contraction.

Note that we're talking about temperature near the surface (where warming is currently happening, not about deep ocean waters which are indeed below 4 C but are not currently changing.

 

[Buckleymanor]

Unless I am misunderstanding you, this is not correct. Ice does indeed expand when it freezes, so the volume of an ice cube will be greater than the same cube when melted.

Depends if the water talked about is liquid or solid.
I probably misunderstood davies was the cube thawed or not.

 

[paisiello2]

Depends if the water talked about is liquid or solid.
I probably misunderstood davies was the cube thawed or not.

Yeah, it doesn't really depend on that if we are talking about seawater as the OP was doing. I think you probably misunderstood that he wasn't talking about pure water but rather was talking about sea ice and how its melting would affect sea levels (which it doesn't).

 

[Buckleymanor]

Yeah, it doesn't really depend on that if we are talking about seawater as the OP was doing. I think you probably misunderstood that he wasn't talking about pure water but rather was talking about sea ice and how its melting would affect sea levels (which it doesn't).

Actualy I am not sure about the misunderstanding which the OP could clear up.
What he said.

Is the volume of the cube which is below the surface equal to the volume of the original thawed water?

If he had said water instaid of thawed water then there would be no misunderstanding on my part.
By mentioning that the water was thawed could mean that he is talking about volume of the cube when it has melted and the amount of melted water above and below the surface.

 

[Buckleymanor]

Not correct. We are talking about sea water whose maximum density is close to its freezing point which in turn depends on the salinity and pressure.

We are also talking about ice which when melts or does not is at it's densest at 4 degrees.

 

[Buckleymanor]

Not correct. We are talking about sea water whose maximum density is close to its freezing point which in turn depends on the salinity and pressure.

Are we not also talking about the melting of ice and sea ice which is still at it's maximum density at around 4 degrees.
The freezing point of sea ice is lower than freshwater ice due to salinity and pressure also has an effect.
But salts in the ice can be excluded when it freezes so it becomes fresher won't this fresh water behave like normal ice when it thaws becoming denser at 4 degrees?
http://www.britannica.com/EBchecked/topic/531121/seawater/301668/Density-of-seawater-and-pressure

 

[craigi]

When I freeze water in an ice cube tray in my freezer they expand slightly. Their weight remains the same therefore density has reduced. When I put these ice cubes in a glass of water they float because of the lower density. A small portion of the cube rises above the surface of the water.

Is the volume of the cube which is below the surface equal to the volume of the original thawed water? And if so, why do people say melting antartic ice caps cause sea levels to rise? Wouldn't the ice simply melt and occupy the same volume as the frozen portion which is below the surface therefore sea levels would remain exactly the same?

Cheers

The Antarctic (and Greenland) have land ice, which will contribute to the sea level rise. This ice isn't floating on water.

There's no land under the Arctic ice cap, where your argument is relevant.

A major component of sea level rise will be thermal expansion of water. Incidentally, hot water is also an essential factor in the formation of hurricanes.

One reason that the receding of the ice caps is relevant is that it's a measure of warming.

Another reason is that snow and ice reflect heat much more than water, meaning that the lower the surface area that they cover, the more of the heat from the sun is absorbed by the earth, which contributes to warming, in a positive feedback loop. Positive feedback loops lead to instabilties.

That's just the physics (and a little bit of geography) of it. Sadly Climate Change is a banned topic on these forums so we have to be careful, but I guess it's still ok to talk about the physics.

 

[paisiello2]

We are also talking about ice which when melts or does not is at it's densest at 4 degrees.

There are two different issues:

1) The OP was talking about sea ice which has salt in it. The OP just made analogy of an ice cube since the physics of buoyancy is the same for pure water and sea water but the density and melting points are not.

2) You brought up the issue of the density of water being a maximum at 4 degrees and assumed that it was the same as ocean sea water, which it is not.

 

[paisiello2]

Are we not also talking about the melting of ice and sea ice which is still at it's maximum density at around 4 degrees.
But salts in the ice can be excluded when it freezes so it becomes fresher won't this fresh water behave like normal ice when it thaws becoming denser at 4 degrees?
http://www.britannica.com/EBchecked/topic/531121/seawater/301668/Density-of-seawater-and-pressure

Not true, again. Look at your own referenced link. It shows the maximum density of sea water with a salinity of 10 or more is actually at 0 degrees, not 4 degrees.

When sea water freezes (around -2 degrees) the salinity remains in the ice, it does not fall out of the solution. But, even if it did, it would be irrelevant to the OP's question and it is also irrelevant to your false statement about the density of sea ice being at 4 degrees.

 

[paisiello2]

Sadly Climate Change is a banned topic on these forums so we have to be careful, but I guess it's still ok to talk about the physics.

Why is it banned? (I can guess the reasons but just want to know the official reasons for this censorship.)

 

[Buckleymanor]

Not true, again. Look at your own referenced link. It shows the maximum density of sea water with a salinity of 10 or more is actually at 0 degrees, not 4 degrees.

When sea water freezes (around -2 degrees) the salinity remains in the ice, it does not fall out of the solution. But, even if it did, it would be irrelevant to the OP's question and it is also irrelevant to your false statement about the density of sea ice being at 4 degrees.

So even if it salt did fall out of the solution and became fresh water ice it would not become densest at 4 degrees when it thaws.
How come? Fresh water is fresh water even if it had salt in it at any time.

Can you drink melted sea ice?
New ice is usually very salty because it contains concentrated droplets called brine that are trapped in pockets between the ice crystals, and so it would not make good drinking water. As ice ages, the brine eventually drains through the ice, and by the time it becomes multiyear ice, nearly all of the brine is gone. Most multiyear ice is fresh enough that someone could drink its melted water. In fact, multiyear ice often supplies the fresh water needed for polar expeditions. See Salinity and Brine in the Characteristics section for more information.

 

[dauto]

Why is it banned? (I can guess the reasons but just want to know the official reasons for this censorship.)

The forum administrators claim they don't have the expertize needed to properly moderate that topic.

 

[dauto]

So even if it salt did fall out of the solution and became fresh water ice it would not become densest at 4 degrees when it thaws.
How come? Fresh water is fresh water even if it had salt in it at any time.

Once it melts it does mix with salty water again, doesn't it?

 

[craigi]

Why is it banned? (I can guess the reasons but just want to know the official reasons for this censorship.)

It's a politically charged area of science regardless of its validity so becomes difficult to moderate. You can find the long and incredibly tedious discussion about this in the Earth Sciences forum.

Allow me to preempt your next question. Politics in science is a banned topic too.

 

[paisiello2]

So even if it salt did fall out of the solution and became fresh water ice it would not become densest at 4 degrees when it thaws.
How come? Fresh water is fresh water even if it had salt in it at any time.

We are talking about sea ice the majority of which only lasts for the winter season not multiple years like land ice. So most of it will be salty.

But again it's irrelevant to the OP's original question and it is irrelevant to your false claim about the density of sea water.

 

[paisiello2]

It's a politically charged area of science regardless of its validity so becomes difficult to moderate. You can find the long and incredibly tedious discussion about this in the Earth Sciences forum.

Allow me to preempt your next question. Politics in science is a banned topic too.

I don't see it as politically charged anymore than an area like evolution or cold fusion. But someone felt it was I guess.

 

[Buckleymanor]

We are talking about sea ice the majority of which only lasts for the winter season not multiple years like land ice. So most of it will be salty.

But again it's irrelevant to the OP's original question and it is irrelevant to your false claim about the density of sea water.

No we are talking about the Artic allthough originaly confused with the Antarctic and it's complete melting.
50% of which remains frozen through out the winter.
You made the accusation that I was claiming sea ice was densist at 4 degrees,could you please point out where as all I can find is my assertion that fresh water when thawed from ice becomes densest at 4 degrees.I can't pinpiont where I say sea ice or sea water.

 

[paisiello2]

The whole point is that you claimed in post #6 that sea level rise caused by thermal expansion was doubtful because water was densest at 4 deg and therefore should contract first. I corrected you with the fact that oceans are not fresh water but sea water and have different density-temperature relationships. So whether you meant to or not you were actually talking about sea water.

And then you went on again in post #15 to claim sea ice was still at a maximum density of 4 deg. I showed you that this was incorrect using your own supplied reference.

Finally, the OP specifically mentioned Antarctic where the sea ice almost 100% melts each summer. If you now specifically want to talk about the portion of Artic sea ice that doesn't melt each summer and claim it has no salinity content then I can only say it is still completely irrelevant to the OP's original question. Their original question was about sea ice melting causing sea level rising (which it doesn't).

It is also completely irrelevant regarding thermal expansion of sea water causing sea level rising (which it does).

 

[Buckleymanor]

The whole point is that you claimed in post #6 that sea level rise caused by thermal expansion was doubtful because water was densest at 4 deg and therefore should contract first. I corrected you with the fact that oceans are not fresh water but sea water and have different density-temperature relationships. So whether you meant to or not you were actually talking about sea water.

And then you went on again in post #15 to claim sea ice was still at a maximum density of 4 deg. I showed you that this was incorrect using your own supplied reference.

Finally, the OP specifically mentioned Antarctic where the sea ice almost 100% melts each summer. If you now specifically want to talk about the portion of Artic sea ice that doesn't melt each summer and claim it has no salinity content then I can only say it is still completely irrelevant to the OP's original question. Their original question was about sea ice melting causing sea level rising (which it doesn't).

It is also completely irrelevant regarding thermal expansion of sea water causing sea level rising (which it does).

I corrected you to show that sea ice can become freshwater ice and has the same properties with regards density when melting.

With respect to the OP's specifications we both realize that you regarded his comments were directed at the Artic and not the Antarctic.Never the less if you insist that it was the Antarctic which is what is wrote, then examine the first post there is no mention of sea ice,what is mentioned is ice caps and those are made of freshwater.

 

[paisiello2]

I corrected you to show that sea ice can become freshwater ice and has the same properties with regards density when melting.

Which maybe is true only if we are talking about the portion of arctic sea ice that doesn't melt every year. But that is irrelevant anyway because once a fresh water iceberg melts (at whatever temperature you want it to) it mixes with the ocean and becomes ...sea ice. And sea ice is what causes the sea level to rise from thermal expansion.

With respect to the OP's specifications we both realize that you regarded his comments were directed at the Artic and not the Antarctic.Never the less if you insist that it was the Antarctic which is what is wrote, then examine the first post there is no mention of sea ice,what is mentioned is ice caps and those are made of freshwater.

Not true. I took the OP's comments at face value. I expanded upon it to include the arctic just to be complete.

And yet again, even if you take all sea ice in the world to be fresh water (which it's not) it is completely irrelevant as to what causes the sea level to rise.

 

[Buckleymanor]

Which maybe is true only if we are talking about the portion of arctic sea ice that doesn't melt every year. But that is irrelevant anyway because once a fresh water iceberg melts (at whatever temperature you want it to) it mixes with the ocean and becomes ...sea ice. And sea ice is what causes the sea level to rise from thermal expansion.


Not true. I took the OP's comments at face value. I expanded upon it to include the arctic just to be complete.

And yet again, even if you take all sea ice in the world to be fresh water (which it's not) it is completely irrelevant as to what causes the sea level to rise.

So it does not sink, you don't get an overturn with denser water?

If you took the OP's comments at face value you would have mentioned the ice caps and less of the none sense about sea ice and that would have been mainly the Artic because we both know the north polar ice cap is what he was describeing.

 

[paisiello2]

So it does not sink, you don't get an overturn with denser water?.

Don't know what you are referring to but whatever it is you're probably wrong about it.

If you took the OP's comments at face value you would have mentioned the ice caps and less of the none sense about sea ice and that would have been mainly the Artic because we both know the north polar ice cap is what he was describeing.

Thought I did mention it and sea ice was an important consideration in fully answering his question.

And again it doesn't matter what he was describing or what you think he meant to describe because the question and answer applies to both Arctic and Antarctic.

 

[Buckleymanor]

Don't know what you are referring to but whatever it is you're probably wrong about it.


Thought I did mention it and sea ice was an important consideration in fully answering his question.

And again it doesn't matter what he was describing or what you think he meant to describe because the question and answer applies to both Arctic and Antarctic.

Water at 4 degrees sinks.

Ice sheets and ice caps melting lowers the temperature of sea water makeing it more dense this in turn lowers the volume of water within the oceans unless Archimedes was wrong.

 

[paisiello2]

Water at 4 degrees sinks.

So what? And how does it keep a constant temperature anyway? Not that it is relevant to anything.

Ice sheets and ice caps melting lowers the temperature of sea water makeing it more dense this in turn lowers the volume of water within the oceans unless Archimedes was wrong.

Wrong and double wrong. The ice sheets and ice caps do not lower the temperature of the ocean. The ocean is a huge heat sink and would never be affected by this small amount of ice. It would be like saying adding a bucket of ice to an Olympic sized swimming pool would change it's temperature.

The ocean temperatures have been measured and shown to be absorbing a large amount of heat energy from the sun, causing a steady and gradual increase in temperature.

And you are confused about Archimedes principle which describes the buoyant force on a submerged object. It has nothing to do with how temperature affects density.

 

[Buckleymanor]

So what? And how does it keep a constant temperature anyway? Not that it is relevant to anything.


Wrong and double wrong. The ice sheets and ice caps do not lower the temperature of the ocean. The ocean is a huge heat sink and would never be affected by this small amount of ice. It would be like saying adding a bucket of ice to an Olympic sized swimming pool would change it's temperature.

The ocean temperatures have been measured and shown to be absorbing a large amount of heat energy from the sun, causing a steady and gradual increase in temperature.

And you are confused about Archimedes principle which describes the buoyant force on a submerged object. It has nothing to do with how temperature affects density.

They would lower the temperature if they melted.

Archimedes principle has everything to do with temperature as temperature effects density why does your ice float in the first place!
Here is a quote from you.
Yes, by Archimedes principle the weight of the volume of water displaced must be equal to the total weight of the floating object.

Now it's churlish to say the least to use Archimedes to support your argument with regards ice which only floats because lowering the temperature of water causes it to expand and become a floating partly submerged body.
Archimedes principle still applies to objects with different temperatures. two objects of the same weight and same material displace different quantities of water if submerged they have unequal buoyancy.

 

[paisiello2]

They would lower the temperature if they melted.

No, you're wrong. They wouldn't lower the temperature to anything we could ever measure.

Archimedes principle has everything to do with temperature as temperature effects density why does your ice float in the first place!

Wrong yet again because I didn't say that. What I said was that Archimedes principle doesn't have anything to do with how temperature affects density which your post said it did. And your post was (what else?) wrong.

So you're still wrong no matter how much you try.

 

[Buckleymanor]

No, you're wrong. They wouldn't lower the temperature to anything we could ever measure.


Wrong yet again because I didn't say that. What I said was that Archimedes principle doesn't have anything to do with how temperature affects density which your post said it did. And your post was (what else?) wrong.

So you're still wrong no matter how much you try.

Better leave it to Mr Right.

 

[paisiello2]

Better leave it to the facts.

 

[D H]

Better leave it to the facts.

Buckleymanor, you are wrong.

The fact is that ice floats because it is less dense than water. Measure the volume of a chunk of ice, melt it, and measure the volume of the water. The volume of the melt will be less than the volume of the chunk of ice.

The density of liquid water does vary with temperature, reaching a maximum at some above point where water (how much above varies with salinity), but this variation is small compared to the much larger difference in density between liquid water and ice.
This sidetrack has left a key question raised in the original post unanswered.

And if so, why do people say melting antartic ice caps cause sea levels to rise? Wouldn't the ice simply melt and occupy the same volume as the frozen portion which is below the surface therefore sea levels would remain exactly the same?

Consider two experiments involving melting ice surrounded by water. The goal is to determine whether the level of the level of the water rises, falls, or remains the same.

In experiment #1 we'll float a chunk of ice in some water. We'll measure the level of the water immediately after adding that chunk of ice, and then later when the ice has melted. Except for small variations due to the fact that the density of water varies with temperature, the level of the water will remain pretty much the same.

In experiment #2 we'll first put a big rock in the water, with the rock big enough so that the top pokes out of the water. Then we'll put our chunk of ice on top of the rock. Once again, we'll measure the level of the water immediately after adding that chunk of ice, and then later when the ice has melted. Now the water level will indeed rise.

Experiment #1: That represents the sea level rise that would result from the ice in the Arctic melting (not much). Experiment #2: That represents the sea level rise that would result if the ice in the Antarctic melts (a considerable rise).

The Arctic is an ocean covered with floating sea ice during the winter. Antarctica is a continent, a big rock whose top sits above sea level. Note also that the ice covering Greenland isn't floating. Melting the ice covering Greenland would similarly contribute to a rise in sea level.

 

[jbriggs444]

Then we'll put our chunk of ice on top of the water.

I think you intended to put your second chunk of ice on top of the rock.

 

[D H]

I think you intended to put your second chunk of ice on top of the rock.

Indeed I did. Thanks. I fixed my post.

 

[paisiello2]

This sidetrack has left a key question raised in the original post unanswered.

I believe it was all answered in post #2.

 

[Buckleymanor]

Buckleymanor, you are wrong.




Consider two experiments involving melting ice surrounded by water. The goal is to determine whether the level of the level of the water rises, falls, or remains the same.

In experiment #1 we'll float a chunk of ice in some water. We'll measure the level of the water immediately after adding that chunk of ice, and then later when the ice has melted. Except for small variations due to the fact that the density of water varies with temperature, the level of the water will remain pretty much the same.

In experiment #2 we'll first put a big rock in the water, with the rock big enough so that the top pokes out of the water. Then we'll put our chunk of ice on top of the rock. Once again, we'll measure the level of the water immediately after adding that chunk of ice, and then later when the ice has melted. Now the water level will indeed rise.

Experiment #1: That represents the sea level rise that would result from the ice in the Arctic melting (not much). Experiment #2: That represents the sea level rise that would result if the ice in the Antarctic melts (a considerable rise).

The Arctic is an ocean covered with floating sea ice during the winter. Antarctica is a continent, a big rock whose top sits above sea level. Note also that the ice covering Greenland isn't floating. Melting the ice covering Greenland would similarly contribute to a rise in sea level.

Experiment 1 and 2 are representative of what happens over a long period of melting . For these events to happen the temperature would have to increase by a substantial amount.As mentioned the seas would contract before any melting of the Antarctic cap.
The Antarctic cap is surrounded by sea ice which would first have to melt before the ice cap thawed causing an increase in sea density.
Additional to that the Arctic cap melts and recovers at a faster rate than the Antartic cap.
This melting of the Antarctic sea ice, the Arctic cap and sea will lower the temperature of the seas and increase density.
So unless the laws of physics have changed the seas will contract before there is any thermal expansion and the Antarctic ice cap melts.

 

[D H]

When sea water freezes (around -2 degrees) the salinity remains in the ice, it does not fall out of the solution.

Minor correction: The salinity does drop out of the solution. However, freshly frozen sea ice remains rather salty because as the ice forms, the salt forms pockets of liquid brine (extremely salty water) that are intermixed with the solid ice.

Now it's churlish to say the least to use Archimedes to support your argument with regards ice which only floats because lowering the temperature of water causes it to expand and become a floating partly submerged body.

Major correction: This is completely wrong, and it is the source of your confusion. Ice floats because it is considerably less dense than water. The density of liquid water (pure, not salty) at 0° C is 0.9998 g/cm³, or 0.02% less than the density of water at 4° C. The density of ice at 0° C is 0.9162 g/cm³, or 8.36% less than the density of water at 0° C.

You are making a mountain of the tiny molehill of variations in density of liquid water as a function of temperature and are at the same time ignoring the huge mountain that represents the significant difference in density between liquid water and solid ice.

The Antarctic cap is surrounded by sea ice which would first have to melt before the ice cap thawed causing an increase in sea density.

This is false as well. The ice cap is melting *now*. This has been verified by satellites such as GRACE. The volume of land ice on the Antarctic continent is falling. Some of that melt enters the seas that surround Antarctic as liquid water, but a whole lot more enters those seas as ice from glaciers flowing from the Antarctic plateaus and mountains into the sea.

 

[Buckleymanor]

This is false as well. The ice cap is melting *now*. This has been verified by satellites such as GRACE. The volume of land ice on the Antarctic continent is falling. Some of that melt enters the seas that surround Antarctic as liquid water, but a whole lot more enters those seas as ice from glaciers flowing from the Antarctic plateaus and mountains into the sea.

Not according to NASA
http://wattsupwiththat.com/2013/10/22/nasa-announces-new-record-growth-of-antarctic-sea-ice-extent/
The point was that the Arctic sea ice old and new will melt first before the Antarctic sea ice and cap. Thus lowering the mean temperature of the sea and it's density before the main bulk of land ice on the Antarctic melts. We will fry before any substantial sea levell rise.

 

[russ_watters]

Not according to NASA
http://wattsupwiththat.com/2013/10/22/nasa-announces-new-record-growth-of-antarctic-sea-ice-extent/

That link is clearly about sea ice, not land ice.

The point was that the Arctic sea ice old and new will melt first before the Antarctic sea ice and cap.

The link you posted also explicitly states that the cap itself is melting.

Thus lowering the mean temperature of the sea and it's density before the main bulk of land ice on the Antarctic melts. We will fry before any substantial sea levell rise.

HOW MUCH?

The volumes of the oceans and ice can easily be found with a Google. Assuming it could be done adiabatically(which it can't), this is a simple mixing problem with a thermal contraction. You should be able to show the math behind your claim.

(Edit) Hint: I just did the math and the impact of the temperature change falls out as a rounding error if you don't keep enough sig figs.

 

[Buckleymanor]

Major correction: This is completely wrong, and it is the source of your confusion. Ice floats because it is considerably less dense than water. The density of liquid water (pure, not salty) at 0° C is 0.9998 g/cm³, or 0.02% less than the density of water at 4° C. The density of ice at 0° C is 0.9162 g/cm³, or 8.36% less than the density of water at 0° C.

You are making a mountain of the tiny molehill of variations in density of liquid water as a function of temperature and are at the same time ignoring the huge mountain that represents the significant difference in density between liquid water and solid ice.

Ice does not have to be considerably less dense than water to float it just happens to be so.
Like wise water at 4 degrees is denser than water at 0 degrees and is only marginaly denser.
That won't stop it from sinking and occupying less space than warmer water.
The average temperature of the sea is 3.5 degrees C so any additional cooling or warming causes thermal contraction or expansion.

 

[russ_watters]

the average temperature of the sea is 3.5 degrees c so any additional cooling or warming causes thermal contraction or expansion.

How much?

 

[Buckleymanor]

How much?

That depends on depth and the rise in temperature on the land. For every degree of temperature rise on land it will translate to about 0.2 degree temperature rise in the sea but only to a certain depth say 25 meters.That will result in the expansion of the oceans by around 2.5 millimeters in hight.

 

[russ_watters]

That depends on depth and the rise in temperature on the land. For every degree of temperature rise on land it will translate to about 0.2 degree temperature rise in the sea but only to a certain depth say 25 meters.That will result in the expansion of the oceans by around 2.5 millimeters in hight.

That's not the totality of your claim. You claimed that the melting of the ice caps would lower the sea level, not raise it. Please show us the calculation that supports your claim.

 

[Buckleymanor]

That's not the totality of your claim. You claimed that the melting of the ice caps would lower the sea level, not raise it. Please show us the calculation that supports your claim.

Only to the point of floating ice if the presumption is that the Arctic cap and sea ice melts first and then the sea ice in the Antarctic melts before the main cap (which it probably will).
Land ice melt in the main Antarctic cap will eventualy raise the sea level though until that happens the sea level would lower.
Fresh melting sea ice at 0 degrees would mix with warmer water at whatever temperature, the result would be that the warmer water will end up cooler than it's original temperature.
Sea water becomes more and more dense right down to it's freezing point so the result would be a more dense and lower sea.