Abstract

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 pre-industrial control simulations of the CMIP5 archive. Two distinct regimes are found. On sub-decadal frequencies, the surface temperature and the outgoing short-wave flux are in quadrature, with the short-wave acting as a stochastic forcing of surface temperature. The long-wave flux is linearly related to temperature, and acts as a negative feedback on temperature perturbations. On longer time-scales the outgoing short-wave and long-wave fluxes are both linearly related to temperature, with the long-wave continuing to act as a negative feedback and the short-wave 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 co-efficients. The frequency-dependent regression co-efficients for the total cloudy-sky flux on time-scales of 2.5 to 3 years are found to be strongly (r^2 >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 explanation of these results.