= Solution
For the <albedo-to-forcing conversion>, Earth intercepts sunlight over a disk but distributes the global mean over its full sphere, giving incident mean flux $S_0/4$. The absorbed shortwave flux is $F_{\rm abs}=(1-A)S_0/4$, and hence
$$
\boxed{\Delta F_{\rm abs}=-\frac{1370}{4}(4\times10^{-8})
=-1.37\times10^{-5}\ \mathrm{W\,m^{-2}}.}
$$
The cooling magnitude is $1.37\times10^{-5}\ \mathrm{W\,m^{-2}}$ for the assumed one-year effect of one <mass> unit of injection. <Albedo> does not change the sunlight incident at the top of the atmosphere; it changes the absorbed/net incoming flux. The minus sign therefore accompanies the <radiative cooling>.
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