## Results for climate feedback parameter (λ, horizontal axis), effective vertical thermal diffusivity (κ_{v}, vertical axis), and fraction of climate change (contours) realized (a) 10 years and (b) 100 years after a step-function quadrupling of atmospheric CO_{2} content; results shown here were derived by using the one-dimensional model described in the text, which can differ from the other curve fits by about 5%

**Figure 4.** Results for climate feedback parameter (λ, horizontal axis), effective vertical thermal diffusivity (κ_{v}, vertical axis), and fraction of climate change (contours) realized (a) 10 years and (b) 100 years after a step-function quadrupling of atmospheric CO_{2} content; results shown here were derived by using the one-dimensional model described in the text, which can differ from the other curve fits by about 5%. Crossed lines indicate 95% confidence intervals. Numeric values are listed in SOM tables S1 and S2 (available at stacks.iop.org/ERL/8/034039/mmedia).

**Abstract**

The temperature response of atmosphere–ocean climate models is analyzed based on atmospheric CO_{2} step-function-change simulations submitted to phase 5 of the Coupled Model Intercomparison Project (CMIP5). From these simulations and a control simulation, we estimate adjusted radiative forcing, the climate feedback parameter, and effective climate system thermal inertia, and we show that these results can be used to predict the temperature response to time-varying CO_{2} concentrations. We evaluate several kinds of simple mathematical models for the CMIP5 simulation results, including single- and multiple-exponential models and a one-dimensional ocean-diffusion model. All of these functional forms, except the single-exponential model, can produce curves that fit most CMIP5 results quite well for both continuous and step-function CO_{2}-change pathways. Choice of model for any particular application would include consideration of factors such as the number of free parameters to be constrained and the conception of the underlying mechanistic model. Smooth curve fits to the CMIP5 simulation results realize approximately half (range 38%–61%) of equilibrium warming within the first decade after a CO_{2} concentration increase, but approximately one quarter (range 14%–40%) of equilibrium warming occurs more than a century after the CO_{2} increase. Following an instantaneous quadrupling of atmospheric CO_{2}, fits to four of the 20 simulation results reach 4 ° C of warming within the first decade, but fits to three of the 20 simulation results require more than a century to reach 4 ° C. These results indicate the need to reduce uncertainty in the temporal response of climate models and to consider this uncertainty when evaluating the risks posed by climate change.