The relationship between climate models’ internal variability and their response to external forcings is investigated. Frequency-dependent regressions are performed between the outgoing top-of-atmosphere (TOA) energy fluxes and the global-mean surface temperature in the preindustrial control simulations of the CMIP5 archive. Two distinct regimes are found. At subdecadal frequencies the surface temperature and the outgoing shortwave flux are in quadrature, while the outgoing longwave flux is linearly related to temperature and acts as a negative feedback on temperature perturbations. On longer time scales the outgoing shortwave and longwave fluxes are both linearly related to temperature, with the longwave continuing to act as a negative feedback and the shortwave acting as a positive feedback on temperature variability. In addition to the different phase relationships, the two regimes can also be seen in estimates of the coherence and of the frequency-dependent regression coefficients. The frequency-dependent regression coefficients for the total cloudy-sky flux on time scales of 2.5 to 3 years are found to be strongly (r² > 0.6) related to the models’ equilibrium climate sensitivities (ECSs), suggesting a potential “emergent constraint” for Earth’s ECS. However, O(100) years of data are required for this relationship to become robust. A simple model for Earth’s surface temperature variability and its relationship to the TOA fluxes is used to provide a physical interpretation of these results.
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