Conversion factors for ice and water mass and volume
Mass and volume units for water and ice
One gigatonne is one billion metric tonnes ( 1 Gt = 1 x 109 tonnes)
One metric tonne is 1000 kilograms (1 tonne = 1000 kg)
One metric tonne of water has a volume of one cubic meter (1 tonne water ≡ 1 m³)
One gagatonne of water has a volume of one billion cubic meters, or one cubic kilomter.(1 Gt water ≡ 1 km³)Of course, one gigatonne of ice has a greater volume than one gigatonne of water. But it will still have a volume of 1 km³ when it melts.
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How much does one Gigatonne of melted ice (1 km³ of water) raise the oceans?
The oceans occupy 361 million square kilometers ( 361 x 106 km²) of the Earth’s surface.
If one cubic kilometer of water (i.e., one gigatonne of water) is spread evenly over the entire 361 million square kilomters, the thickness of the new layer of water will be given by:
1 km³ / 361 x 106 km² = 2.78 x 10-6 meters = 2.78 microns.
Or, in terms of gigatonnes:
1 Gt x (1 km³/Gt) / 361 x 106 km² = 2.78 x 10-6 meters = 2.78 microns / Gt
That is, one cubic kilometer of water (i.e., one gigatonne of water) will add less than 3 millionths of a meter to the oceans!
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How many gigatonnes of ice must melt to raise the oceans one millimeter (10-3 meters)?
The number of gigatonnes of water that must be added to the oceans to raise the sea level 1 millimeter is given by:
1 mm / (2.78 microns / Gt) = 10-3 m / (2.78 x 10-6 m / Gt) = 360 Gt
Similarly, 360 km³ of water will raise the oceans 1 mm.
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How many gigatonnes of ice must melt to raise the oceans one inch?
1 inch = 25.4 mm = 2.54 x 10-2 meters
The number of gigatonnes of water that must be added to the oceans to raise the sea level 1 inch is given by:
1 inch x (2.54 x 10-2 m / inch) / (2.78 x 10-6 m / Gt) = 9137 Gt
Similarly, 9137 km³ of water will raise the oceans 1 inch.
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How many gigatonnes of ice must melt each year to raise the oceans one foot per decade?
1 foot = 305 mm = 3.05 x 10-1 meters
1 foot per decade = 3.05 x 10-2 meters / yr = 30.5 mm / yr
The number of gigatonnes of water that must be added to the oceans to raise the sea level 1 foot per decade is the same as the number of gigatonnes required to raise the oceans 30.5 mm/yr, and is given by:
360 Gt/mm x 30.5 mm/yr = 10,980 Gt/yr
Similarly, 10,980 km³ of water per year will raise the oceans 1 foot per decade.
RSS
Please answer these questions: how many GT of ice are there in the world and how many feet will the oceans rise if one half of all the ice melts, and if all of it melts? THEN we will have an idea of the actual magnitude of the problem, instead of going “gee a whole GT only raises the oceans a teeny bit so we must not need to worry”. HOW MANY TOTAL GTs ARE WE TALKING ABOUT AND HOW MUCH WOULD HALF AND ALL OF IT MELTING INUNDATE US?
Dear DancesWithFascists,
Thank you for your impassioned comments.
I will first answer your specific questions about melting half or all of the ice on the planet.
The volume of ice in Antarctica is approximately 25,000,000 km3. The volume of ice in Greenland is about approximately 2,500,000 km3. The rest of the landed ice is small compared to these two, so I think it is fair to round up and say the total is about 30,000,000 km3.
The world’s oceans have an area of about 335,000,000 km2. So, simply speaking, if half of the ice in Antarctica and Greenland were to melt, then the oceans would rise about 45 meters (about 150 feet). All of the ice melting would raise the oceans 90 meters (or 300 feet). Of course, you are correct that this would be a devastating effect.
But remember, the above conclusion requires that 30,000,000 km2 of ice must melt.
How fast is ice actually melting? There are conflicting numbers resulting from various methods of measuring. Velicogna (Science, vol 311, 2006) used time varying gravity measurements from the GRACE satellites estimated that Antarctica was losing 152 km3 of ice per year. She concludes that this “is equivalent to 0.4 millimeters of global sea-level rise per year.” This is the same result you would get by multiplying the number of km3 of ice by 2.7 microns as I suggested in my blog. One hundred years at this rate would contribute a whopping 4cm (about one and a half inches) to the oceans.
In the same journal, Davis (Science, vol 308, 2005) concluded that Antarctica was actually gaining ice.
You may be able to find studies reported in the literature that claim faster rates of ice loss in the Antarctic than claimed by Velicogna. For example, Eric Rignot, (Rignot, et. al., “Recent Antarctic ice mass loss from radar interferometry and regional climate modeling,” Nature Geoscience, 2008) of the California Institute of Technology used satellite interferometric synthetic-aperture radar observations to show that the ice losses in the East Antarctic were essentially zero, while the West Antarctic and the Antarctic Peninsula had combined losses of about 190 gigatonnes per year. This results in a stunning 0.5 mm ocean rise per year, or about 2 inches in a hundred years.
Similar conflicting, but small, results hold for Greenland.
The bottom line is that at current rates of ice melt it would take about 200,000 years for all the ice to melt in the Antarctic. And even this scenario is ridiculously unlikely, because if the pattern of the last 2 million years continues, then the next 200,000 years should contain two ice ages, each about 100,000 years long. (If this conclusion surprises you, just look at Al Gore’s presentation, which shows the repeating glacial/interglacial pattern of 100,000/15,000 years during the Quaternary.)
Again, thank you for your comment.
Best Regards,
Tom
The entire surface area of the oceans works real well if you have a none moving bath tub. Take a tennis ball get it wet and start spinning it the water goes to the edge. Now take the gravitational pull of the moon that causes high tide / low tide and give it a few more gigatonnes of water to move around about 300 more gigatonnes per year. No one really knows what’s going to happen they are given it there best guess but if you look at the whole picture it doesn’t look good.
Gary,
The effect you are talking about is seen in the oblateness of the Earth. (Note that “a” and “c” in the given link refer to the radius of the oblate spheroid at the equator and at the pole, respectively.)
The second order gravitational moment,J2, for the earth is about 0.001. See the plot here of variations in J2 due to redistribution of water in the oceans, soil and atmosphere. Notice that the changes in J2 are on the order of 10E-10 (0.0000000001).
The actual oblateness of the Earth is about 0.003 (about 1/300th). Adding water to the oceans may change the oblateness of the Earth, but not by much. The best first approximation would be that the oblateness remains essentially unchanged. So if the oceans rose by one meter on the average, then it might be 1.003 meters at the equator. A small effect.
In the long run, I suspect other things, like glacial isostatic adjustment, have had a much greater impact on spatial variation of sea level rise since the last ice age. This would probably continue to be true.
Best regards,
Tom
[...] blog suggests there’s nothing to worry about, but I don’t have the time to work out the [...]
dont forget that most ice is floating. Ice is at a minimum 10 percewnt more volume than water. when ice melts, water levels will decrese.
[...] in 2005 that must have been 0.9 mm greater than the sea level rise rate in 1995 (320 Gt/year x 2.7 microns/Gt = 0.9 [...]
Tom, thanks for the numbers.
Some time ago I read an impassioned headline about 48 cubic miles of ice melting each year and the ominous result that would occur if that much ice were lost each year. I did my own calculations which demonstrated that the total sea level rise after 100 years from such a scenario would be less than 2.25 inches.
Sea level rise is one of the great — and obviously untrue — scare stories of CAGW.
Frank, I don’t think anyone in the AGW crowd (unless they are really out to lunch) is talking about sea ice. Every last bit of the sea ice could melt and it would not cause an increase in sea levels. The question is how much land-based ice will melt.
HMMMMMMMMMM………
The flaw in your argument is that you can’t dismiss the ice floating in the sea.
If you put ice into a glass of fresh water and leave it to melt the level will not change because the ice displaces a volume equivalent to its mass. It will melt and fill the space it displaced exactly.
However, icebergs are fresh water floating on salt water. Salt water is denser than fresh water and so less of it is displaced by the ice to balance the weight of the ice. But when the ice melts it takes up as much room as before. (i.e. for the same mass the salt water has less volume than fresh water). So the level of the water will rise.
Can’t give you figures on it though…
Dear “younearlypersuededme”
There is nothing controversial in my calculations, and I an not making an “argument.”
If you read carefully, I say things like “The number of gigatonnes of water that must be added to the oceans to raise the sea level 1 millimeter is given by…” It is stated explicitly that the water is “added” to the ocean. Floating ice that melts does not add anything to the ocean – it was already there. I assumed this was understood.
Your concern about freshwater from floating ice melting into salt water of the ocean is a triviality in this context. I have also ignored issues of the thermal expansion of water ,which is zero at about 4 degrees C, so that the volume of a given mass of water increases for temperatures above and below 4 degrees C.
Thank you for you comment.
Tom
I think it would be useful to point out that Davis coauthors the rignot paper… and that davis et al. 2005 uses radar altimetry which has an upwards trending bias in regions of high slopes and rugged terrain, thus resulting in lower than actual mass losses in the WAIS… Also it should be noted that the Velicogna measurements have been corrected for since then with an adjustment for glacial isostatic rebound which is more appropriate and the result is mass declines. Check out Allison et al. 2009 for the most comprehensive summary of the ice sheet contributions since clearly your papers that are being cited are outdated. Velicogna’s 2009 paper is a good read and so is Pritchard et al. 2009 also if you want to learn a bit.
But overall the net loss is anywhere between -100 Gt and -300 Gt depending on the paper and method of either Altimetry (rarely used), Grace or InSar
Dear Robert,
The math is still very simple. Even at 300 Gt per year, the oceans rise a tiny 0.85 mm per year. Too bad, no cities under water I guess.
Best Regards,
ClimateSanity
this really helped with my science test
this really helped with my science test,:)