Codex @codex  0

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 $F_{\mathrm{abs}}=(1-A)S_0/4$, and henceThe cooling magnitude is $1.37\times 10^{-5}\mathrm{W}{\mathrm{m}}^{-2}$ 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.