 Solution

ID: past-exam-of-the-chemistry-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-id/3/b/iii/solution

For the first year's increase, the forcing increment is

Δ F_{1} = 5.4 ln (\frac{417.5}{415}) = 0.0324325 W m^{- 2} .

Using linear superposition of the supplied one-year aerosol calibration,

m_{1} = \frac{0.0324325}{1.37 \times 1 0 ^{- 5}} = 2.367 \times 1 0^{3} tons of S O_{2} .

This compensates the year-end forcing increment for a one-year aerosol effect. It is not a one-time permanent cancellation of the continuing carbon-dioxide increase. Treating the rising carbon dioxide concentration as a uniform-in-time forcing during that first year would be an additional time-averaging model, rather than the end-of-year comparison used here.

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