February 2016 Articles

Climate Math

The Mathematics of Climate Change


  1. Arctic ice in September 1988 was 7.5 million square kilometers; in 1998, 6.5 million km2; and in 2008, 4.65 million km2. The units are in square kilometers measured in millions. The overall trend in the amount of sea ice was to decrease.
  2. The line of best fit is given by y = -0.091t + 190.12.
  3. The slope of this line is m = -0.0921.
  4. The units are million km2 per year. Each year, the amount of sea ice in September will be 0.09 million km2 less than the year before.
  5. If present trends continue, there will be 4.08 million km2 of Arctic sea ice in September 2020, and the Arctic will be ice-free in September 2064.
  6. The data in the last three years are all below the line of best fit, with the most recent values of 2012 being significantly below the line. So the best fit line could be a poor predictor of the future because it weights earlier years equally with recent years. But the recent years suggest that the behavior of the sea ice is changing. The positive feedback loop might be accelerating the melting. The problem of sea ice melt is very complex due to the non-linear feedbacks involved; the scientific community has not reached consensus on when they think the ice-free stage will arrive.
  7. Some pros of having an ice-free passage through the Arctic sea: it will make shipping through the Northwest Passage possible, which will reduce cost and travel time for goods. It might also give access to more natural resources. Cons include that it will make it difficult for polar bears to survive. And it is also an indicator that serious climate changes are taking place on the earth and these changes will have far-reaching consequences.

Comments on “Climate Math”

  1. Curve fitting three data points does not make sense and the problem does not look like it should be linear.

  2. Absolutely correct – although we suggested a linear fit for simplicity, a quadratic function would
    provide a better fit and is indicative of the non-linear feedback of the dark open ocean absorbing more
    heat and causing the melting to speed up.