= Solution
For the first year's increase, the forcing increment is
$$
\Delta F_1=5.4\ln\!\left(\frac{417.5}{415}\right)
=0.0324325\ \mathrm{W\,m^{-2}}.
$$
Using linear superposition of the supplied one-year <aerosol> calibration,
$$
\boxed{m_1=\frac{0.0324325}{1.37\times10^{-5}}
=2.367\times10^3\ \mathrm{tons\ of\ SO_2}.}
$$
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.
Back to article page
