The stabilization and overshoot pathways were derived from the cost-effective calculation method described above. We allow the model to determine the abatement levels of three gases over time under the abatement constraints (i.e., first- and second-derivative constraints, as well as the upper limits of abatement levels) to arrive at a pathway that meets a policy objective while minimizing the global total costs of mitigation. Two temperature target levels (2° and 1.5°C) and three temperature pathway profiles [non-overshoot, medium overshoot (till 2100), and high overshoot (till 2150)] were considered. Temperature overshoot emerges as a consequence of how the temperature target is implemented: The target is assumed effective only after a certain point in time in the future.

It should be noted that the reference pathways against which the additional costs of using metrics were calculated are not identical to the illustrative pathways in Fig. 2. All metric cost calculations in our study did not use the abatement constraints, that is, the first- and second-derivative constraints, as well as the upper limits of abatement levels, which were used to derive the illustrative pathways. These constraints influence the metric cost calculations and, in some cases, make the pathway infeasible because they can be too restrictive when applied together with metrics. To maintain consistency, the abatement constraints were also not used in the reference pathways to derive the cost of metrics. However, the overall pathways and mitigation costs without the use of abatement constraints are not substantially different from those with the use of such constraints, except for cases with high overshoot. Another exception is the periods when the mitigation starts and when the target is met (table S2 and figs. S12 to S16). In such periods, particularly under the overshoot pathways, abatement levels can change drastically in the absence of the abatement constraints, requiring careful interpretation.

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