Towards a time-explicit climate–carbon feedback framework for Earth system stability analysis

Climate sensitivity and stability analysis so far rely on two separate concepts: climate and carbon feedbacks. The climate feedback framework allows the separation of two components of Earth’s radiative budget: forcing and temperature feedbacks. The carbon feedback concept helps to diagnose the strength with which oceanic and terrestrial systems buffer anthropogenic carbon emissions to the atmosphere and respond to changes in temperature. Both, albeit limited in their interpretation by temperature pathway and time dependence, play major roles in our current understanding of the Earth’s capacity to withstand anthropogenic pressures, but have been used and treated separately in large parts of the literature.However, two approaches that serve a more holistic grasp of Earth system stability have been pursued. One is simple climate modelling as a prognostic tool that—often by tuning idealized response functions—captures a net response to emissions that inherently includes both carbon and climate feedbacks. The other, a diagnostic framework by Gregory et al. (2009), combines climate and carbon feedbacks for a specific set of climate model simulations under the assumption of constant parameters. A combined climate–carbon feedback framework that represents Earth system stability and the role of warming-induced carbon emissions in a more comprehensive and flexible manner, however, is still lacking.We present an attempt at Earth system stability analysis that mitigates pathway and time dependence by combining methods from traditional feedback analysis and simple climate modelling: time-explicit feedback functions constructed from linear response theory like initiated by Torres Mendonça et al., (2021) in a diagnostic framework, now for climate and carbon feedbacks. We apply our analysis to flat10MIP-style Earth system model simulations, which provide the necessary statistical foundation and allow us to test sensitivity and robustness with respect to applications to observational evidence. This approach could ultimately support assessments of present and past Earth system stability particularly under temperature overshoot scenarios as well as high-level model evaluation on the effects of warming-induced carbon emissions. Gregory, J. M., C. D. Jones, P. Cadule, and P. Friedlingstein, 2009: Quantifying Carbon Cycle Feedbacks. J. Climate, 22, 5232–5250, https://doi.org/10.1175/2009JCLI2949.1.Torres Mendonça, G. L., Pongratz, J., and Reick, C. H., 2021: Identification of linear response functions from arbitrary perturbation experiments in the presence of noise – Part 1: Method development and toy model demonstration, Nonlin. Processes Geophys., 28, 501–532, https://doi.org/10.5194/npg-28-501-2021.