# 0h for two, melting sea ice and GW alarmism

Two common assertions: melting sea ice has no effect on global sea level, and alarmists will grasp at every straw in trying to scare us all.

It turns out that they are both wrong.

Robert Grumbine has the details on why melting sea ice does in fact raise sea levels. In a nutshell, what is frozen and what it floats in are not the same. Fresh water is less dense than sea water.

Now the effect is small, but if the scientists who are aware of this are truly just out to scare us out of our research funding, shouldn’t they be scrambling to correct this common misconception?

Just wondering…

1. #1 Ben
April 16, 2009

I am confused. If the fresh water is less dense, does it become more dense after melting and take up less space? That would be weird.

2. #2 coby
April 16, 2009

Being less dense, fresh water takes up more space than salt water per litre, so results in an overall increase in ocean volume when mixed. Robert has a good conceptualization imagining the melted ice burgh remained as a block and noting that this would mean, like the frozen form, it would float with a little sticking out above the ware level. An ice burgh is around 10% above water, a “fresh meltwater burgh” would stick up 2.7%. Since it won’t stay together of course, you can imagine that that 2.7% would actually spread out and raise the level.

HTH…

3. #3 Vernon
April 16, 2009

Coby,

That is a disingenuous argument. Yes it works fine if you mix two equal quantities but fails remarkably fast when you actually do the math for the real world. Taking the facts presented in the paper:

Facts:
Specific gravity of water is 1 at 4C
Specific gravity of saltwater is 1.029
Average temperature of sea water globally ~20C
From paper: volume arctic sea ice is 700,000km3
Volume of total seawater is 1.37 billionkm3

The author stated the difference in volume is going to be the displacement of the 10 percent that is above the seawater level, or 70,000km3.

The average global seawater temperature causes an expansion that changes the specific gravity to 1.025, but I will go with the 1.029 as a worse case.

The additional water added to the sea from the melting sea ice is:

70,000*.029=2030km3

The addition of the melted sea ice 1.37E+11 + 2.03E3 =1.37E+11

The actual change is 0.00000001482% increase in volume. There would be detectible sea level rise.

That is why your presentation and that paper fall into the factual but misleading category.

4. #4 Vernon
April 16, 2009

Opps, forgot the no. Next to last line should read:

There would be no detectible sea level rise.

5. #5 Vernon
April 16, 2009

Coby,

I got to thinking, what if we dont use the papers numbers but use the actual one’s from the government sites.

Doing that total volume of sea ice is 15,200,000km3
Since ice has a sg of .912, then the sea ice is displacing 13,471,720km3 of seawater
The melted ice (pure water, no salt – worse case) has a
volue of 13,862,400km3.
The resulting difference has a volume of 390,679.9km3.

Adding 390,679.9km3 to 1,300,000,000km3 of seawater is a .0003 percent increase in volume.

There would be no detectible rise in sea level if all the sea ice melted.

This is quite a bit less that the paper indicated.

6. #6 coby
April 16, 2009

Hi Veron,

I’m not sure about your approach in seperating and only working with the 10% of floating ice that is above the water line, it doesn’t seem right to me.

Regardless, I think we all agree it is a very small matter, but it is there. If your calculations are at odds with the cited article, it might be a useful exercise to find a flaw in their approach. Why not head over to Rob Grumbine’s site and take it up there? I’m afraid I just don’t have the time…

7. #7 Patrick
April 17, 2009

Its the melted water running off Antarctica that makes the seas rise guys. Thinking about the floating ice is like thinking you only have to dodge VWs on the freeway.

8. #8 Vernon
April 17, 2009

Patrick,

I agree, if there was a possibility of Antarctic warming enough to melt the ice cape, then that would be a problem. The only thing is that the Antarctic is cooling and has been for the last 35+ years. 35+ years cooling, that is climate, right.

April 17, 2009

Vernon –

The only thing is that the Antarctic is cooling and has been for the last 35+ years.

It’s true that the interior of the continent seems to be cooling, but the perimeter of the continent has largely warmed in the same time.
http://earthobservatory.nasa.gov/IOTD/view.php?id=6502

Besides, if you’re referring to this paper (Doran, 2002)
http://www.nature.com/nature/journal/v415/n6871/abs/nature710.html

Let’s see what the author himself has to say about it.
http://www.nytimes.com/2006/07/27/opinion/27doran.html?_r=1

“Our study did find that 58 percent of Antarctica cooled from 1966 to 2000. But during that period, the rest of the continent was warming. And climate models created since our paper was published have suggested a link between the lack of significant warming in Antarctica and the ozone hole over that continent. These models, conspicuously missing from the warming-skeptic literature, suggest that as the ozone hole heals — thanks to worldwide bans on ozone-destroying chemicals — all of Antarctica is likely to warm with the rest of the planet.”

“Also missing from the skeptics’ arguments is the debate over our conclusions. Another group of researchers who took a different approach found no clear cooling trend in Antarctica.”

10. #10 Geof
April 17, 2009

Vernon, the oceans are about 4km deep. .0003% of that works out to about 1.2 cm, which is in approximate agreement with the paper.

11. #11 Vernon
April 18, 2009

Geof,

Yes it does, but what is not considered all the factors. He took a simple experiment of equal amounts of ice and salt water. Here is what I found.
I used 2000 numbers and got a sea ice volume of 42,500km3. I then took the total volume of sea water globally, 1,320,000,000km3.

Now to be fair I assumed that all sea ice was pure water, no salt, and when frozen had a specific gravity of .912, further since this is for a global rise in sea level, I adjusted the specific gravity for sea water from 1.029 to 1.025 to adjust for thermal expansion. The average global sea temperature is ~20C. I then did the following calculations:

42500km3 Total volume of arctic sea ice
1320000000km3 Total volume of sea water

0.912 Specific Gravity Sea Ice

37814.65km3 Displacement of the sea ice
38760km3 Displacement of melted sea ice
945.4km3 Additional volume above sea ice when melted

1320000945km3 Increase in Sea water volume
0.000072% Volume increase expressed as a percentage

361000000km2 Surface area of the Sea
3.656509695km Average depth
0.002618742m Increase in average depth

However, when we figure in the mixing of fresh water to saltwater into a homogeneous mixture, the specific gravity goes from 1.029 to 1.028999 which is not much. What it means is that there is an initial rise until the mixing is complete and then the difference in sea level height is .000085 meters, or with modern equipment unmeasurable.

So while technically his presentation is correct, the presentation falls into the factual but wrong. There will be almost no measurable sea level rise if all the sea ice in the Arctic melts. An example with equal ice and sea water does not reflect the real world.

12. #12 Vernon
April 18, 2009

Sorry, second paragraph is something else I am working on for surface water. The paragraph should read:

Now to be fair I assumed that all sea ice was pure water, no salt, and when frozen had a specific gravity of .912.

13. #13 alufelgi
April 19, 2009

In my opinion the largest threat for California are cataclysms and ecological catastrophes. Not important is how many money we have because one tragedy can us take all.

14. #14 Thom
April 21, 2009

The answer is 4 cm! Not my answer, but Dr. Peter Noerdlinger of Nova Scotia has calculated that if all “sea ice” the stuff that floats not the stuff on land, were to melt the result would be an increase in sea level of 4 cm.

XXXX://www.physorg.com/news5619.html

15. #15 Vernon
April 21, 2009

Actually he is half right. I did make an error the first time. Should have known better to do this in excel, oh well. Anyway actually I agree that there is a problem with Archimedes principle, namely that ice is fresh water and the sea is salt water. A study by Peter D. Noerdlinger and Kay R. Brower, in The Geophysical Journal International, 170, pp. 145-150, 2007 “The melting of floating ice raises the ocean leve”l says it does but I think there is an error. I could be wrong but here is what I think actually happens. I am not addressing grounded ice. I used 2000 numbers Arctic sea ice and got a sea ice volume of 42,500km3. I then took the total volume of sea water globally, 1,320,000,000km3. Now to be fair I used the numbers from the study. I then did the following calculations:

42500km3 Total volume of arctic sea ice
1320000000km3 Total volume of sea water

1.026 Specific Gravity Sea water
0.919 Specific Gravity Sea Ice

38067.74km3 Displacement of the sea ice
46245.92km3 Displacement of melted sea ice
8178.18km3 Additional volume above sea ice when melted

1320008178km3 Increase in Sea water volume
0.00062% Volume increase expressed as a percentage
361000000km2 Surface area of the Sea
3.656509695km Average depth
0.02265m Increase in average depth or 2.27cm

However, when we figure in the mixing of fresh water to saltwater into a homogeneous mixture, the specific gravity goes from 1.026 to 1.025999089 which is not much.

1320001172km3 expansion due to lower specific gravity
38067.72km3 volume of the ice at the new specific gravity

As you can see, the new volume of the melted ice once mixed is only 0.0338km3 greater than the displacement.

The increase in sea level is 0.00325m or 3.25mm.

What it means is that there is an initial rise until the mixing is complete and then the difference in sea level height is 3.25mm. Now I could have looked up the Antarctic numbers for sea ice but since the preponderance is in the Arctic, I did not bother. Take a look, I dont see where I am wrong but maybe you’ll spot something.

16. #16 humorix
April 23, 2009

So that it justify there an increase in the level of waters, still it is necessary that there is an increase in temperatures. And, the différenciel kept in theoretical has anything has see with the climatic modifications which would be in order. (Steam of fresh water). Adequacy is not kept.More just would be to keep (understand) the new training of glaciers, snow, rains, rivers which would follow from it.

Pour qu’il y ait une hausse du niveau des eaux, encore faut-il qu’il y ait une hausse des températures. Or, le différentiel retenu en théorique n’a rien a voir avec les modifications climatiques qui s’en suivraient. (Vapeur d’eau douce). L’adéquation n’est pas retenue. Plus juste serait de retenir (comprendre) la nouvelle formation de glaciers, neige, pluies, rivières qui en découlerait.

17. #17 Vernon
April 23, 2009

I really do not see that happening. The surface sea temperature in the Arctic is just above 0C. The energy needed to melt all the ice is 3.392E+18Kj. The fact is that as soon as the Arctic sea water started warming, it would start sinking, moving away from the sea ice.

18. #18 humorix
April 24, 2009

@ Vernon
Say to me if I make a mistake.
To me, the volume of an icicle is the UPPER in its volume in water. If the ice melts, the level of see water GOES DOWN.
It is also necessary to take into account surrounding hygrometry and volume of water kept by the soil and by clouds.

Dites moi si je me trompe. Chez moi, le volume d’un glaçon est SUPERIEUR à son volume en eau. Si la glace fond, le niveau de l’eau des mers BAISSE.
Il faut aussi prendre en compte l’hygrométrie ambiante et le volume d’eau retenu par le sol et par les nuages.

19. #19 Vernon
April 24, 2009

humorix,

Ice has a specific gravity of 0.919 from the Noerdlinger et al paper, which is why it floats. Water or Sea water have their greatest specific gravity at 4C. I used all the Arctic sea ice as the example but when it melts but before it mixes, there is a ~2.3cm rise in sea level, however once it mixes, the sea level drops to ~3.3mm. At least that is what my numbers show. I could be wrong but no one has pointed out what I got wrong yet.