Time-scale dependence of airborne fraction and underlying climate-carbon cycle feedbacks for weak perturbations in CMIP5 models

Abstract. The response of the global climate-carbon cycle system to anthropogenic perturbations happens differently at different time scales. The unraveling of the memory structure underlying this time-scale dependence is a major challenge in climate research. Recently the widely applied α-β-γ framework proposed by Friedlingstein et al. (2003) to quantify climate-carbon cycle feedbacks has been generalized to account also for such internal memory. By means of this generalized framework, we investigate the time-scale dependence of the airborne fraction for a set of Earth System Models that participated in CMIP5 (Coupled Model Intercomparison Project Phase 5); the analysis is based on published simulation data from C⁴MIP-type experiments with these models. Independently of the considered scenario, the proposed generalization describes at global scale the reaction of the climate-carbon system to sufficiently weak perturbations. One prediction from this theory is how the time-scale resolved airborne fraction depends on the underlying feedbacks between climate and carbon cycle. These feedbacks are expressed as time-scale resolved functions depending solely on analogues of the α, β, and γ sensitivities, introduced in the generalized framework as linear response functions. In this way a feedback-dependent quantity (airborne fraction) is predicted from feedback-independent quantities (the sensitivities). This is the key relation underlying our study. As a preparatory step, we demonstrate the predictive power of the generalized framework exemplarily for simulations with the MPI Earth System Model. The whole approach turns out to be valid for perturbations up to about 100 ppm CO₂ rise above pre-industrial level; beyond this value the response gets nonlinear. By means of the generalized framework we then derive the time-scale dependence of the airborne fraction from the underlying climate-carbon cycle feedbacks for an ensemble of CMIP5 models. Our analysis reveals that for all studied CMIP5 models (1) the total climate-carbon cycle feedback is negative at all investigated time scales; (2) the airborne fraction generally decreases for increasing time scales; and (3) the land biogeochemical feedback dominates the model spread in the airborne fraction at all these time scales. Qualitatively similar results were previously found by employing the original α-β-γ framework to particular perturbation scenarios, but our study demonstrates that, although obtained from particular scenario simulations, they are characteristics of the coupled climate-carbon cycle system as such, valid at all considered time scales. These more general conclusions are obtained by accounting for the internal memory of the system as encoded in the generalized sensitivities, which in contrast to the original α, β, and γ are scenario-independent.