2010). It is also useful for the canonical 1% peryr experiment, so we can set TCR = F2X/(β + γ), where F2X equals the forcing due to doubling of CO2. We can then use the same proportionality constant, 1/(β + γ), to interpret 20th century warming and 21st century projections given only the evolution of the forcing F over time. As an example, Gregory and Forster (2008) show how the same proportionality constant between forcing and global mean temperature holds in a particular GCM for all of the 21st century forcing scenarios utilized by the AR4 and pictured in Figure 3.3 (IPCC, 2007c). The lack of separation of these different scenarios in the first half of the 21st century is not primarily due to some inertia in the physical climate system, but rather to the fact that the net radiative forcings in the various scenarios do not substantially diverge until the latter half of the century.
FIGURE 3.3 In stabilization scenarios, such as A1B (green) and B1 (blue) after 2100, or the “constant composition commitment” (yellow) in which the forcing is held fixed at the values in 2000, the warming grows slowly despite the constant forcing. Rescaling the TCR by the forcing will underestimate the surface warming in the stabilization period by an amount that grows with time, as the system slowly makes its transition to its equilibrium response. The average ratio of TCR to the equilibrium sensitivity in the models utilized by the AR4 (using values in Table 8.2 in Chaper 8 of the WG1 report) is 0.55. So the slow growth in the stabilization period, in which the forcing is somehow maintained at a constant level, continues for many centuries beyond that indicated in this figure, until the additional warming in these periods becomes comparable to that in the preceding periods of increasing forcing.