Now THAT is a big number - 10 cu km of ice lost in a MONTH!!!
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So little? Why is this a piece of news?
Glaciers and large continental ice packs contribute to the sea level rise some 450 cubic kilometres a year, that is an average of 9 cubic kilometres a week, with peaks during both boreal and austral summers. This is just "contribution to sea level rise", as actual melting rates peak many times those figures as most of the ice is going to be replenish during the cold seasons.
Ice in floating shelves like Ross, Larsen, Fischer-Ronne, Amery, Wilkins, and many more, including shelf-like ice floating in Greenland's fiords and nearby, is not going to contribute to sea level rise -read further-, but it is also lost at a comparable rate. These events are not so seasonal as they involve ice structures with structural features, and they develop with a chaotic component, so exactly like earthquakes, but less predictable than simple melting. These events are also important, now and then -like an earthquake-. Petermann Glacier lost some 250 square kilometres (30 cubic kilometres?) of ice, all at one, back in 2010 or 2011. Back in 2007?2008? a much much much larger chunk of ice was broken in the Antarctic Peninsula, but fortunately most of it moved and stranded elsewhere, though the definitive loss was much important.
Jakobshavn Glacier losses at least 40 cubic kilometres of ice a year. Why is this specially relevant? Was there any doubt global warming continues? Is there any doubt the Arctic gets most of its heat from lower latitudes, even during July? Was it necessary that story of tropical warm waters reaching the ice and sneakily melting it from below, sort of a thermal McCarthyism?
Can we put all this ice ... sheet thing to a rest?
I propose you to take, say 1,000 km3 of sea ice, 0% salt, only 890 km3 of it below sea surface, and 100,000 km3 of sea water, 3.5% salt, all at 0°C, all at sea level -for the sake of a straightforward calculation-, and crunch the final variation of volume and sea level -remember 110 km3 of ice were above sea level-. You only need a table or figure of seawater densities at 0°C when salinity varies.
Let's solve the problem.
We have a sea area of one million square kilometres and 100 metres deep, that is, 100,000 cubic kilometres of water and a sea level of 100 metres. That water is all at 0°C and it all has a salinity of 35 grams per litre. We have floating there a volume of 1,000 cubic kilometres of ice, free of brine or any salt content, and also at even 0°C. Some heat is added, the exact heat to melt the ice and have it all at 0°C. What happens with our 100-metre level?
Let's start. Fresh water density: (pure water) Ice density at 0°C : 0.9167 g/cm3 (
source). Sea water density at 0°C, 1 atm and salinity of 35 g/litre:
I'm using the approximation given by this document offered by MIT faculty through MIT Open Access Articles:
http://dspace.mit.edu/handle/1721.1/69157 , formula (6) page 48 (in print,49 in downloadable pdf). It's a little old, but it has a maximum error of 1/10,000th, that is not in the part of the range we are using, and even better, it has a web version in this page:
http://www.csgnetwork.com/h2odenscalc.html . For those sceptics like me, you are encourage to read the code and verify it follows that formula. Here's the chunk of javascript, for those sceptic but lazy:
function rhoscalc (rho,conc,temp) { // temp and conc dependent density
var rhos, A, B, temp;
A = 0.824493 - 0.0040899*temp + 0.000076438*Math.pow(temp,2)-0.00000082467*Math.pow(temp,3) + 0.0000000053675*Math.pow(temp,4);
B = -0.005724 + 0.00010227*temp - 0.0000016546*Math.pow(temp,2);
rhos = rho + A*conc + B*Math.pow(conc,(3/2)) + 0.00048314*Math.pow(conc,2);
return rhos;
}
For our sea ice, it gives 1,028.131 kg/m3.
So, our ice (1000 km3 *0.9167 g/cm3 = 916.7 GT) must displace 916.7 GT / 1,028.131 kg/m3 = 891.618 km3 of sea water, that means:
We have 891.618 km3 of ice submerged in the sea water; we have 108.382 km3 of ice (1000-891.618) protruding above sea level; we have 99108.382 km3 of sea water (100000-891.618), and that salty water weighs 101,896.4 GT (99108.382 * 1.028131) of which 3468,793 GT are salts (99108.382 * 35/1000) and 98,427.607 GT are water (101896.4-3468.793). Water then totals 99344,307 GT (98427.607+916.7).
All melts, and now we have a mess of 99344.307+3468.793 = 102813.1 GT of sea water with a salinity of 3468.793/102813.1 = 33.739 g per kilogram (and not litre). How do we follow now? By iteration. If it were 33.739 per litre, its density would be -using link above- 1027.113 kg/m3, so, one litre must contain 33.739 g/kg * 1.027113 kg/litre = 34.654 g/litre. Back to the link, the density for that is 1027.852 kg/m3, so 33.739 multiplied by that gives 34.679. Repeating the cycle: 1027.872, 34,679 -round to the same decimal-. Let's check: we have sea water with a salinity of 34.679 g/litre and a density of 1027.872 kg/m3, which means 34.679/1.027872 = 33.739 g of salts per kilogram, the same value we started from.
And here is the question. What's the volume of water? Its 102813.1 GT of sea water divided 1.027872 kg/litre of density, that is 100,025.2 km3, what means, the sea level has risen 25.2 mm. That is for an ice loss of 1,000 km3 and an ocean of one million square kilometres. For an ice loss of 650 and a global ocean of 360, the rise is 25.2*.65/360 = 45 microns a year
Conclusions:
Formation and melting of ice each year drive important seasonal changes in sea level both in the Arctic and Antarctic (we're talking of 15/18,000 km3 of ice in just 6 months) and it even should account for unbalances in ocean currents.
Changes in salinity all around the ocean drive a change of sea level known as its halosteric component that has been in recent years much stronger and opposite in sign to the sea-level change estimated above. In this case, also temperature but mostly the forgotten element, pressure, do this.
The sea level continue to rise about 1.25 mm a year because of the melting of glaciers and ice packs, and this has an upwards trend.
These three elements alone render this conclusion: for any practical end we can dismiss any variation of sea level coming from melting sea ice as irrelevant. The bit "yearly loss of sea ice doesn't contribute to sea level rise" stands.
Uffa! If I added the estimation of sea ice loss from other sources, I would have had a paper with this recommendation: models need to include a yearly variation of 45 microns a year in sea level coming from loss of sea ice. Wait! Some other did it. Rush! We're running out of obvious or irrelevant things to publish!