Comparison of formalisms for attributing responsibility for climate change: Non-linearities in the Brazilian proposal approach

The Brazilian Proposal for setting emission targets is based on attribution of responsibility for climate change due to historical emissions of greenhouse gases. Numerical models are used to calculate the temperature increase due to past emissions of greenhouse gases, and to partition the warming among nations or groups of nations. When non-linearities are included in the models, there are different approaches that can be used to partition global warming into regional or national contributions, and the methods give different results. Here we describe and compare seven different approaches for attributing indicators of climate change for regional emissions. We illustrate these methods with simple and realistic examples, and discuss their characteristics. Of the seven attribution methods discussed, two (the marginal and time-sliced methods) are seen as best-suited for attribution of climate change. Differences between attribution methods are typically up to a few percent for the examples considered, with differences greatest for regions with emission time histories that differ most from the average. The range due to choice of attribution method in the relative contributions of temperature change in 2000 is typically around one fifth of the range generated when other choices such as different models, forcing agents, feedbacks and other assumptions are included.