of sufficient magnitude and duration to trigger significant effects from slow climate system feedbacks.
The climate system responds differently to perturbations in radiative forcing on different time scales. It is of special importance to carefully distinguish between the “equilibrium climate sensitivity” and the “transient climate response.” The concept of equilibrium climate sensitivity and its alternative definitions have been discussed in Section 3.2. The transient climate response is of special relevance for climate change over the 20th and 21st centuries.
The transient climate response, or TCR, is traditionally defined in a model using a particular experiment in which the atmospheric CO2 concentration is increased at the rate of 1% per year. The increase in global mean temperature in a 20-year period centered at the time of doubling (year 70) is defined as the TCR (Cubasch, 2001). The upper tens of meters of the ocean, the atmosphere, and the land surface are all strongly coupled to each other on time scales greater than a decade, and are expected to warm coherently with a well-defined spatial pattern during a period of increasing radiative forcing. (This pattern is discussed in Section 4.1.) On these time scales, the rate of change of the heat stored in oceanic surface layers, as well as the atmosphere and land surface, can be ignored to first approximation, and we can think of global mean temperature as determined by the energy balance between the radiative forcing F, the change in the radiative flux at the top of the atmosphere U, and the flux of energy D into the deeper layers of the ocean that are far from equilibrium: F = U + D.
On long enough times scales, as long as a millennium by some estimates (e.g., Stouffer, 2004), the heat flux into the deep ocean D tends to zero, and the climate response approaches its equilibrium value determined by the balance between F and U. On the shorter times scales at which the changes in the deep ocean are still small, the heat uptake grows in time roughly proportional to the global mean temperature perturbation, D = γT (Gregory and Mitchell, 1997; Raper et al., 2002; Dufresne and Bony, 2008), similar to the more familiar linear approximation to the radiative flux response, U = βT. The implication is that on these time scales we can use the simple approximation T = F/(β + γ).
This approximation is useful on a limited range of time scales—longer than a decade but shorter than the centuries required for the heat uptake by the oceans to begin to saturate (Gregory and Forster, 2008; Held et al.,