Annual versus accumulated radiative forcing

For $F(C)-F(C_0)=a\ln (C/C_0)$, a further annual concentration increment produces $a\ln [(C+\Delta C)/C]$, whereas the accumulated forcing from the original baseline is $a\ln (C/C_0)$. The former can decrease as $C$ rises while the latter increases. Maintaining a short-lived compensating aerosol burden also requires replacement, not only compensation of the next increment.