Emission pathways that are consistent with meeting the Paris Agreement goal of holding global mean temperature rise well below 2 °C often assume a temperature overshoot. In such overshoot scenarios, a given temperature limit is first exceeded and later returned to, under the assumption of large‐scale deliberate carbon dioxide removal from the atmosphere. Here we show that although such strategy might result in a reversal of global mean temperature, the carbon cycle exhibits path dependence. After an overshoot, more carbon is stored in the ocean and less on land compared to a scenario with the same cumulative CO₂ emissions but no overshoot. The near‐path independence of surface air temperature arises despite the path dependence in the carbon cycle, as it is offset by path dependence in the thermal response of the ocean. Such behavior has important implications for carbon budgets (i.e. the total amount of CO₂ emissions consistent with holding warming to a given level), which do not differ much among scenarios that entail different levels of overshoot. Therefore, the concept of a carbon budget remains robust for scenarios with low levels of overshoot (up to 300 Pg C overshoot considered here) but should be used with caution for higher levels of overshoot, particularly for limiting the environmental change in dimensions other than global mean temperature rise. Plain Language Abstract

Many of the CO₂ emission pathways that are consistent with the 1.5 and 2 °C temperature limit in the long term are based on an assumption that emitting CO₂ and removing it later from the atmosphere leads to the same state of the climate system. Such removal of excess carbon dioxide (CO₂) from the atmosphere is possible, in principle, by the implementation of technologies that deliberately remove CO₂ from the atmosphere (referred to as CDR), resulting in net‐negative emissions. Here we study climate response to overshoot scenarios, where a given temperature level is temporarily exceeded and then restored by carbon dioxide removal from the atmosphere. We show that carbon cycle responses depend on the CO₂ emission pathway, and the magnitude of the overshoot. However, the global mean temperature response is reversible and independent of CO₂ emission pathway. This has important implications for carbon budgets (i.e., the total amount of CO₂ emissions that can be emitted to limit global mean warming to a given level). We show that carbon budgets do not differ much among scenarios whereby a given target is reached after temporary overshoot, and nonovershoot scenarios.