Uncertainty in carbon budget estimates due to internal climate variability

Remaining carbon budget specifies the cap on global cumulative CO(2)emissions from the present-day onwards that would be in line with limiting global warming to a specific maximum level. In the context of the Paris Agreement, global warming is usually interpreted as the externally-forced response to anthropogenic activities and emissions, but it excludes the natural fluctuations of the climate system known as internal variability. A remaining carbon budget can be calculated from an estimate of the anthropogenic warming to date, and either (i) the ratio of CO2-induced warming to cumulative emissions, known as the Transient Climate Response to Emissions (TCRE), in addition to information on the temperature response to the future evolution of non-CO(2)emissions; or (ii) climate model scenario simulations that reach a given temperature threshold. Here we quantify the impact of internal variability on the carbon budgets consistent with the Paris Agreement derived using either approach, and on the TCRE diagnosed from individual models. Our results show that internal variability contributes approximately +/- 0.09 degrees C to the overall uncertainty range of the human-induced warming to-date, leading to a spread in the remaining carbon budgets as large as +/- 50 PgC, when using approach (i). Differences in diagnosed TCRE due to internal variability in individual models can be as large as +/- 0.1 degrees C/1000 PgC (5%-95% range). Alternatively, spread in the remaining carbon budgets calculated from (ii) using future concentration-driven simulations of large ensembles of CMIP6 and CMIP5 models is estimated at +/- 30 PgC and +/- 40 PgC (5%-95% range). These results are important for model evaluation and imply that caution is needed when interpreting small remaining budgets in policy discussions. We do not question the validity of a carbon budget approach in determining mitigation requirements. However, due to intrinsic uncertainty arising from internal variability, it may only be possible to determine the exact year when a budget is exceeded in hindsight, highlighting the importance of a precautionary approach.