Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2021 / Interdisciplinary paper IDP1 / 3 / b / iv / Solution

If “steady temperature in 2050” means preventing the next annual increase relative to the climate at the delayed start, the relevant forcing increment isIts smaller value follows from $dF/dC=5.4/C$: the same additional ppm gives less incremental forcing at a higher baseline.

That interpretation must be separated from the earlier objective of holding temperature at the original reference climate. To cancel the accumulated increase from $415$ to $500$ ppm requiresThis annual versus accumulated radiative forcing distinction is essential: the first box offsets just the further year's growth; the second is the equivalent one-year aerosol inventory needed for the accumulated forcing. In subsequent years that inventory must be replaced as particles disappear and increased as carbon dioxide rises. A delayed start does not erase the earlier warming merely because the annual incremental requirement is smaller.