Conditions for Instability in the Climate-Carbon Cycle System

Abstract. The climate and carbon cycle interact in multiple ways. An increase in carbon dioxide in the atmosphere warms the climate through the greenhouse effect, but also leads to uptake of CO₂ by the land and ocean sink, a negative feedback. However, the warming associated with a CO₂ increase is also expected to suppress carbon uptake, a positive feedback. This study addresses the question: ‘under what circumstances could the climate-carbon cycle system become unstable?’ It uses both a reduced form model of the climate-carbon cycle system as well as the complex land model JULES, combined with linear stability theory, to show that: (i) the key destabilising loop involves the increase in soil respiration with temperature; (ii) the climate-carbon system can become unstable if either the climate sensitivity to CO₂ or the sensitivity of soil respiration to temperature is large, and (iii) the climate-carbon system is stabilized by land and ocean carbon sinks that increase with atmospheric CO₂, with CO₂-fertilization of plant photosynthesis playing a key role. For central estimates of key parameters, the critical equilibrium climate sensitivity (ECS) that would lead to instability at current atmospheric CO₂ lies between about 11 K (for large CO₂ fertilization) and 6K (for no CO₂ fertilization). The latter value is close to the highest ECS values amongst the latest Earth Systems Models. Contrary to a previous study that did not include an interactive ocean carbon cycle sink, we find that the stability of the climate-carbon system increases with atmospheric CO₂, such that the glacial CO₂ concentration of 190 ppmv would be unstable even for ECS greater than around 4.5 K in the absence of CO₂ fertilization of land photosynthesis.