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The approximate proportional relationship between cumulative carbon emissions and instantaneous global temperature rise (the carbon budget approximation) has proven to be a useful concept to translate policy-relevant temperature objectives into CO 2 emissions pathways. However, when non-CO 2 forcing is changing along with CO 2 forcing, errors in the approximation increases. Using the GCAM model to produce an ensemble of∼ 3000 scenarios, we show that linked changes in CO 2 forcing, aerosol forcing, and non-CO 2 greenhouse gas (GHG) forcing lead to an increase in total non-CO 2 forcing over the 21st century across mitigation scenarios. This increase causes the relationship between instantaneous temperature and cumulative CO 2 emissions to become more complex than the proportional approximation often assumed, particularly for low temperature objectives such as 1.5 C. The same linked …