Why is global warming proportional to cumulative carbon dioxide emissions?

Abstract:

Climate models consistently show that global mean warming is closely proportional to cumulative CO₂ emissions, with little sensitivity to emissions pathway. This result was a high profile assessment finding of the IPCC Fifth Assessment Report, and leads directly to the concept of cumulative emissions budgets for CO₂, to which emissions must be limited in order to avoid exceeding a particular temperature threshold. This proportionality requires two distinct properties of the climate system. The first is that the global mean temperature response to a pulse emission of CO₂ is independent of the background CO₂ concentration or emissions scenario. This property is well known, and has been explained by the balance between an approximately logarithmic dependence of radiative forcing on changes in CO₂ concentration, leading to a smaller change in radiative forcing per unit change in atmospheric CO₂ concentration at higher ambient CO₂, balanced by an increasing airborne fraction at higher ambient CO₂, owing to a saturation of CO₂ sinks. The second distinct property required is that temperatures are proportional to cumulative CO₂ emissions over time under a step change in radiative forcing, such as in an instantaneous CO2 doubling experiment, or equivalently under any other arbitrary type of scenario. The first property implies that if proportionality of warming to emissions occurs for one type of scenario, it will apply to all others. It has been argued that the second property arises because heat and carbon are mixed into the ocean by the same physical processes and are hence proportional to one another. Here we show that this argument is not generally true, and additional conditions are required for proportionality of warming to emissions. We evaluate these conditions analytically, and assess to what extent they hold in output from an earth system model.