Does feedback temperature dependence influence the slow mode of the climate response?
Abstract. Atmosphere-Ocean General Circulation models (AOGCMs) are a necessary tool to understand climate dynamics on centennial timescales for which observations are scarce. We explore to which degree the temperature dependence of the climate radiative feedback influences the slow mode of the surface temperature response. We question whether long-term climate change is described by a single e-folding mode with a constant timescale which is commonly assumed to be independent of temperature or forcing and the evolution of time. To do so, we analyze AOGCM simulations which have an integration time of 1000 years and are forced by atmospheric CO2 concentrations ranging from 2 times (2X) to 8 times (8X) the preindustrial level. Our findings suggest that feedback temperature dependence strongly influences the equilibrium temperature response and adjustment timescale of the slow mode. The magnitude and timescale of the slow mode is approximately reproduced by a zero-dimensional energy balance model that has a constant effective heat capacity and incorporates a background feedback parameter and a coefficient for feedback temperature dependence. However, the effective heat capacity of the slow mode increases over time, which makes the adjustment timescale also time-dependent. The time-varying adjustment timescale can be approximated by a multiple timescale structure of the slow temperature response, or vice versa, a multiple timescale structure of the slow temperature response is described by a time-dependent timescale. The state-dependence and time-dependence of the adjustment timescale of long-term climate change puts into question common eigenmode decomposition with a fast and a slow timescale in the sense that the slow mode is not well described by a single linear e-folding mode with a constant timescale. We find that such an eigenmode decomposition is valid at a certain forcing level only, and an additional mode or a multiple mode and timescale structure of the slow adjustment is necessary to reproduce the details of AOGCM simulated long-term climate change.