Implications of non-linearities between cumulative CO2emissions and CO2-induced warming for assessing the remaining carbon budget

To determine the remaining carbon budget, a new framework was introduced in the Intergovernmental Panel on Climate Change's Special Report on Global Warming of 1.5 degrees C (SR1.5). We refer to this as a 'segmented' framework because it considers the various components of the carbon budget derivation independently from one another. Whilst implementing this segmented framework, in SR1.5 the assumption was that there is a strictly linear relationship between cumulative CO(2)emissions and CO2-induced warming i.e. the TCRE is constant and can be applied to a range of emissions scenarios. Here we test whether such an approach is able to replicate results from model simulations that take the climate system's internal feedbacks and non-linearities into account. Within our modelling framework, following the SR1.5's choices leads to smaller carbon budgets than using simulations with interacting climate components. For 1.5 degrees C and 2 degrees C warming targets, the differences are 50 GtCO(2)(or 10%) and 260 GtCO(2)(or 17%), respectively. However, by relaxing the assumption of strict linearity, we find that this difference can be reduced to around 0 GtCO(2)for 1.5 degrees C of warming and 80 GtCO(2)(or 5%) for 2.0 degrees C of warming (for middle of the range estimates of the carbon cycle and warming response to anthropogenic emissions). We propose an updated implementation of the segmented framework that allows for the consideration of non-linearities between cumulative CO(2)emissions and CO2-induced warming.