Sea-Rise Algebra
Who’s up for a little climate algebra?
Greenland lost 11 billion tons of ice the other day. What contribution did this single event make to sea-level rise?
First, let’s calculate the approximate surface area of the ocean, which, as it’s spherical, goes as 4 pi r2 where r is 7000 km or 7*106 m, so we have 0.7 (fraction of the Earth’s surface that is ocean) 4 pi (7*106)2 = 400*1012 m2 or 4*1014 m2.
Now, let’s calculate the volume that is 11*109 tons of ice, or 1.1*1012 kg = 1.1*1015 g, divided by 0.9 (density of ice in g/cc) = 1.2*1015 cc or 1.2*109 m3.
So now we have the surface of the ocean times the additional height caused by the ice melt (call it x) = the volume of the new water.
4*1014 m2 * X m = 1.1*109 m3 = 1.1*1012 mm.
About 1/250 of a millimeter. Not huge, but happening steadily through the summer, and increasing exponentially as time goes on.
Craig,
WTF ? the world oceans are a huge and complex dynamic consisting of thousands of known and unknown factors.
By treating the worlds oceans as a sort of bath tub, with only one influence you have reached a new low in rationale ! Even for a “true believer” this is kinda silly.
No accurate measurement of the volume of the woulds oceans exists.
This is due to the enormity of the task. At the best, scientist can take an approximation, but with so many unknown facts and dynamics there can be no real accuracy.
Despite millions of papers and masses of media coverage, the is no real evidence of any rise in sea levels apart from the belief by pundits.
In fact the consequences of sea level rises and falls remain elusive and conjectural.
You ended up being off by about 7.5fold. There were a few issues that I spotted, and otherwise I believe you lost an order of magnitude somewhere.
🙂
First: The size of the Earth.
The Earth has an equatorial diameter of 12,756 km, or a radius of 6,378, and . Since we are dealing with the square of the radius, the extra 10% that you tacked on increases your result by 21%.
Because the Earth is not a perfect sphere, the true result of the surface area of the Earth is ~510 million km2.
The measured surface area of the world oceans (to the 4th significant digit) is ~361.9 million km2.
The second error is that you used the density of ice… But we’re discussing ice melt. We aren’t dealing with ice anymore, we’re dealing with water. Upon melting, we have ~11 GT of water. Cold water has a density of ~0.997 tonnes/m3, or ~997 million tonnes/km3.
So 11 billion tons easily approximates to ~11 km3. Divide 11 km3/361 million km2, and you get ~0.03 mm.
While it doesn’t seem like much, what’s important to get a handle on is that the melt-off of the Greenland Ice Sheet is accelerating at a non-linear rate.
In the 80’s, Greenland was loosing an average of ~50 GT/year. In the 2010’s, Greenland will average a loss of ~290+ GT/year. That’s a ~6-fold increase in rate of loss in 3 decades.
Were that acceleration in loss rate to continue, we’d see ~~1.8 TT of loss per year by 2050, and ~~10.8 TT/year by 2080(!!!)
That’s not projected to happen, thankfully… The system is more complex than that and it’s unlikely that the rate of accelerating ice loss will continue along such a perfectly simplistic trajectory… But at this rate of acceleration it will take very little time before the losses from Greenland alone start becoming extremely significant.