Professor Stewart's Hoard of Mathematical Treasures by Ian Stewart

Author:Ian Stewart [Stewart, Ian]
Language: eng
Format: epub, pdf
Tags: Mathematics, General
ISBN: 0465017754
Google: 6_7nH3pHxD4C
Amazon: B003GYEGIY
Publisher: Basic Books
Published: 2009-01-02T08:00:00+00:00

Here temperature is forced periodically (the sin t term) which models the changing heat coming from the Sun. Moreover, any change in C produces a proportionate change in T (the 0.25C term), and any change in T produces a proportionate change in C (the 0.1T term). So my model is set up so that higher temperatures cause more CO2, and more CO2 causes higher temperatures, just like the real world. Since 0.25 is bigger than 0.1, temperature responds faster to changes in CO2 than CO2 does to changes in temperature. Finally, I subtract 0.01T2 and 0.01C2 to mimic the cut-off effects known to occur.

I now solve these equations on my computer, and see what I get. Here are three pictures of how T (black curve) and C (grey curve) change over time. I have plotted 4y - 60 rather than y to move the two curves close enough together to see the relationship.

• When the system is free-running, both T and C fluctuate periodically, and C lags behind T. This is the paradoxical time delay, which according to the TV programme means that rising CO2 does not cause rising temperatures. But, in our model, rising CO2 does cause rising temperatures, thanks to the 0.25C term in the first equation, yet we still see that time delay. The time delay is a consequence of non-linear effects in the model, not delays in what affects what.

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