The oceanic origin of path-independent carbon budgets

Virtually all Earth system models (ESM) show a near proportional relationship between cumulative emissions of CO2 and change in global mean temperature, a relationship which is independent of the emissions pathway taken to reach a cumulative emissions total. The relationship, which has been named the Transient Climate Response to Cumulative CO2 Emissions (TCRE), gives rise to the concept of a 'carbon budget'. That is, a finite amount of carbon that can be burnt whilst remaining below some chosen global temperature change threshold, such as the 2.0 degrees C target set by the Paris Agreement. Here we show that the path-independence of TCRE arises from the partitioning ratio of anthropogenic carbon between the ocean and the atmosphere being almost the same as the partitioning ratio of enhanced radiative forcing between the ocean and space. That these ratios are so close in value is a coincidence unique to CO2. The simple model used here is underlain by many assumptions and simplifications but does reproduce key aspects of the climate system relevant to the path-independence of carbon budgets. Our results place TCRE and carbon budgets on firm physical foundations and therefore help validate the use of these metrics for climate policy.