The melting Arctic – a disturbing application of math
The article Maths and climate change: the melting Arctic is from the Millennium Mathematics Project people.
It features the work of Peter Wadhams, Professor of Ocean Physics and Head of the Polar Ocean Physics Group at University of Cambridge.
Wadhams outlines the seriousness of an Arctic meltdown:
“As the ice area decreases you’re replacing an area of white, which reflects about 90% of the solar radiation, by open water, which reflects less than 10%. As the sea ice retreats you’re absorbing a lot more radiation and this increases the rate of warming at high latitudes.” This effect can raise the global average rate of warming by 20%.
Image source.
The article goes on to describe a simple ice growth model that involves differentiation (from calculus) and vectors. The model predicts that the growth of ice (thickness, h) over time is proportional to the square root of the elapsed time:
h(t) = k√t (where k is a constant).
This means that when ice is thin, it grows quickly, but as time goes on the rate of growth decreases.
Then Wadham goes on to model the movement of ice that is floating on water and is being acted on by the wind and by the Coriolis force.
This is mathematics that I wish we didn’t have to concern ourselves so much with. But we do…
Check out the full Plus Magazine article.
[Thanks to Li-sa, one of my loyal readers, for the link to Plus Magazine.]
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22 Mar 2008 at 5:28 am Link to this comment
Warming sea water is the major source of CO2. The solubility of CO2 decreases as temperature increases. Conversely. Cold sea water at high latitudes is a strong sink. When sea ice forms and covers the cold water, much of the major sink is lost and atmospheric CO2 levels rise. Sea ice is also a weak source. When the global SST rises, we should expect atmospheric concentrations of CO2 to rise. Ice core data confirms that. It also falls as SST falls. The positive feedback proposed by CO2 contributing significantly to global warming thus suggests that CO2 warms the oceans, producing more CO2 which inturn makes it even warmer until we end up like Venus. In any case, the contribution of anthropogenic sources becomes relatively less and less. So with what bullet are you going to kill either?
22 Mar 2008 at 8:35 am Link to this comment
Thanks for your insights, Fred. You have become rather fatalistic – are you saying that in your view, it is too late to do anything?
Please note: Fred’s final question is in response to my challenge in Earth killer where I asked…
…it is a chicken and egg thing, but in terms of a solution, which should we kill – the chicken?
17 May 2008 at 3:01 pm Link to this comment
“applecation of math” please
17 May 2008 at 3:36 pm Link to this comment
Hi Mohammad
I’ve never seen that spelling for “application” before!
6 Dec 2008 at 6:02 am Link to this comment
Uhhh, maybe it was true that Artic ice did go decrease a couple of years ago, but as of this year Artic ice has grown by 40%! It appears that it fluctuates over time. Granted, if the ice did melt in such fashion we would be in trouble, but so far such doomsday scenarios have held very little validity.
I think that the changes in ice are due to natural factors, especially the Sun.
And by the way, CO2 isn’t Venus’s problem, its way too close to the Sun!
6 Dec 2008 at 6:05 am Link to this comment
And Fred, where’s the evidence? I don’t want something from the IPCC either…THere are charts that conclusively show that the increase in C02 has done nothing to increase sea levels…
Sea levels are increasing very slowly, and they have been increasing for the last 5,000 years or as long as recorded history goes. Sealevels have not changed their level of ascent because Joe decided to use his car instead of his bicycle to go to work…