Melting the polar caps

[Dragonrock]

I was wondering if anyone knew of where or how I could get information about how long it would take to melt the antarctic ice cap? I'm asking this because a few co-workers were talking about the move AI and they asked me about the scene showing the city under hundreds of feet of water. I said that it would take more than the 100 years depicted by the movie to melt the south pole enough to raise the oceans that much. Then I realized that while I had read this, I didn't know how they came up with that information.

I figured based on 29 million cubic kilometers of sea ice at an average temp of -14c with a melting point of sea water of -2c that it would take 34.8 *10E22 calories to melt all off the antarctic ice cap, so how do I convert this to joules and how much energy does the earth get from the sun each day?

 

[patnray]

1 calorie = 4.19 joules should work.

Unit Converter

 

[Dragonrock]

Okay, so now I have 1.45 * 10E24 joules to melt the entire ice cap. I've been trying to find how much energy the earth recieves from the sun.

 

[Soapy Sam]

Dragonrock-
I should imagine a large enough solar flare could melt the southern icecap in a matter of hours. Possibly minutes. (The difference would be of academic interest only!) I'm sure that's not what you mean, but I'm not really sure what you DO mean.

Temperature is not the only variable- albedo, humidity, precipitation rate, would be involved- and there would be negative feedback effects too- eg, if all that ice starts melting , sea temperatures drop. Icebergs move further north. Ocean currents change direction. Humidity increases. Cloud and fog increase. Albedo increases. Insolation energy drops. Temperature drops. Snow falls. Ice starts accumulating.

I don't think you will find a simple energy in water out model that has any real applicability.

 

[Dragonrock]

Sam,

What I am trying to do is find some type of real world model to explain how much time and energy would be required to raise sea level like the global warming alarmists claim is happening. Something fairly concise that would make sense without getting too long. You know, something for our "sound bite" culture such as, "if all the energy of the sun that reaches the earth were concentrated on the south pole it would take 50 years to melt the ice." I'm not disputing global warming, just the timeline put forth in most movies.

 

[Soapy Sam]

Hmm. That's a LOT of latent heat requirement.
I bet the net temperature effect of melting the ice cap would be a dramatic global chilling.

 

[Cecil]

The Sun produces 4x10^26 J/s of energy.

Assuming a mean distance to the Earth of 1.5x10^8 km, this energy is spread out on the surface of a sphere with area 4pir^2 = 2.83*10^17 km^2. So at 1AU, the energy density is 1.4*10^9 J/s km^2

The cross-sectional area of the Earth is 3.14*10^8 km^2, so the Earth intercepts 4.4*10^17 J/s of the Sun's energy.

Given 1.45*10^24 J to melt the ice cap, it will take 3.3*10^6 = 3300000 s = 38 days.

This of course assumes that all the energy intercepted is absorbed and concentrated into melting the ice, none of it being reflected by clouds or radiated back into space.

 

[Dragonrock]

Well, that's much shorter than 50 years. So, I guess I'm a bit off in my idea. Oh well, it was worth a try. Thanks everyone.

 

[Capsid]

I've heard arguments that if the polar caps did melt then the sea level would not rise because water expands when it freezes and shrinks when it thaws. One simple experiment I saw was a glass full of water with ice cubes in it, the cubes melted but no water overflowed. Is this a valid experiment to support this view? Would sea levels rise or not?

 

[Bjorn]

I've heard arguments that if the polar caps did melt then the sea level would not rise because water expands when it freezes and shrinks when it thaws. One simple experiment I saw was a glass full of water with ice cubes in it, the cubes melted but no water overflowed. Is this a valid experiment to support this view? Would sea levels rise or not?

Your glass of water with ice cubes is relevant for the North Pole, since the ice there is floating in the ocean.

The South Pole, however, is solid land - the ice there would definately add water to the oceans if it melted.

 

[Ladewig]

The arctic ice is "floating" and as such would not raise ocean levels by melting. However the antarctic ice rests on top of a large land mass. So if that ice melted, then it would run off the land and raise ocean levels appreciably.


National Science Foundation

The essence of Antarctica is glacial ice cover. The ice, which has accumulated over millions of years, is up to 3 miles deep and covers about 5.3 million square miles, or about 97.6 percent of the continent. This volume of ice amounts to about 6 million cubic miles — if it were returned to the oceans, it would raise global sea level about 200 feet.

Melting just the Greenland ice sheet would raise the mean sea level over 20 feet.
Map showing southern Florida with a 20' rise in sea level.

 

[Keneke]

The cross-sectional area of the Earth is 3.14*10^8 km^2, so the Earth intercepts 4.4*10^17 J/s of the Sun's energy.

This of course assumes that all the energy intercepted is absorbed and concentrated into melting the ice, none of it being reflected by clouds or radiated back into space.

And since the side of the earth facing the sun is hemispherical, not flat (as if it were cross-sectional) absorbed and deflected energy would be much more prevalent. On the other hand, it's not order-of-magnitude different, so double- or possibly triple-digit length of days would still be feasible.

 

[pupdog]

from Capsid:

I've heard arguments that if the polar caps did melt then the sea level would not rise because water expands when it freezes and shrinks when it thaws. One simple experiment I saw was a glass full of water with ice cubes in it, the cubes melted but no water overflowed. Is this a valid experiment to support this view? Would sea levels rise or not?

In studies of rising sea level due to global warming, one of the significant factors is thermal expansion--warming water (not ice) expands, adding to the rate of sea-level rise. But it's only (don't qute me now) on the order of centimeters per decade or century or so. Head for the hills!

 

[DangerousBeliefs]

The arctic ice is "floating" and as such would not raise ocean levels by melting. However the antarctic ice rests on top of a large land mass. So if that ice melted, then it would run off the land and raise ocean levels appreciably.


National Science Foundation


Melting just the Greenland ice sheet would raise the mean sea level over 20 feet.
Map showing southern Florida with a 20' rise in sea level.

220 feet??? But what about WaterWorld? Damn you Kevin Cosner!

 

[Ladewig]

220 feet??? But what about WaterWorld? Damn you Kevin Cosner!

No. That fits with the explanation of the film given to me. The sea level rises 220 feet and all the characters in the movie are Californians who are too narcissistic or too oblivious to seek out anyone else.

 

[patnray]

I've heard arguments that if the polar caps did melt then the sea level would not rise because water expands when it freezes and shrinks when it thaws. One simple experiment I saw was a glass full of water with ice cubes in it, the cubes melted but no water overflowed. Is this a valid experiment to support this view? Would sea levels rise or not?

Yes and no. As water cools it contracts until around 4 degrees centigrade. Upon further cooling it expands (probably due to weakening of hydrogen bonds) until it freezes.