A New Method for Characterising Carbon Cycle Sensitivities in Earth System Models

Carbon cycle feedbacks play a key role in past climate variations and may also have a significant impact on future climate. However, it was not until the early 2000s that general circulation models (GCMs) of the climate started to include carbon cycle feedbacks on climate change. The results of the first two climate-carbon GCMs were compared in a paper published in Tellus. Following those first model runs, many other such ‘Earth System Models (ESMs)’ have been developed and compared as part of the Coupled Climate-Carbon Cycle Model Intercomparison project (C⁴MIP). Modelled changes in global land and ocean carbon storage have been routinely compared using a simple formalism that assumes a linear dependence of global land and ocean carbon storage on both atmospheric CO₂ increase and global warming. This 𝛽-𝛾 formulation has been very helpful to identify the zeroth-order reasons for differences between ESM projections, but it is unable to reproduce the saturating time-evolution of global land and ocean carbon storage as simulated by the C⁴MIP models. In this paper, we summarise work to date on modelling the coupled climate-carbon cycle system, and suggest an update to the 𝛽–𝛾 formulation to include a representation of sink saturation as well as the timescale dependencies of land and ocean carbon uptake. Our new approach adds half-saturation constants, 𝜅, for quasi-equilibrium land and ocean carbon increases with CO₂, and land and ocean timescales, 𝜏, that approximate how quickly this quasi-equilibrium is approached. This new ‘𝛽–𝛾–𝜅–𝜏’ formulation reproduces the C⁴MIP results with much greater accuracy than the existing 𝛽–𝛾 formulation, without requiring any additional ESM runs to be analysed.