We apply a new identification method to derive the response functions that characterize the sensitivity of the land carbon cycle to CO₂ perturbations in an Earth system model. By means of these response functions, which generalize the usually employed single-valued sensitivities, we can reliably predict the response of the land carbon to weak perturbations. Further, we demonstrate how by this new method one can robustly derive and interpret internal spectra of timescales of the system.