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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Fred Haynie said,
March 22, 2008 at 5:28 am
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?
zac said,
March 22, 2008 at 8:35 am
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?
mohammad said,
May 17, 2008 at 3:01 pm
“applecation of math” please
zac said,
May 17, 2008 at 3:36 pm
Hi Mohammad
I’ve never seen that spelling for “application” before!