Emission metrics, a crucial tool in setting effective equivalences between greenhouse gases, currently require a subjective, arbitrary choice of time horizon. Here, we propose a novel framework that uses a specific temperature goal to calculate the time horizon that aligns with scenarios satisfying that temperature goal. We analyze the Intergovernmental Panel on Climate Change Special Report on Global Warming of 1.5 C Scenario Database 1 to find that justified time horizons for the 1.5 C and 2 C global warming goals of the Paris Agreement are 22 +/- 1 and 55 +/- 1 years respectively. We then use these time horizons to quantify time-dependent emission metrics. Using methane as an example, we find that emission metrics that align with the 1.5 C and 2 C warming goals respectively (using their associated time horizons) are 80 +/- 1 and 45 +/- 1 for the Global Warming Potential, 62 +/- 1 and 11 +/- 1 for the Global Temperature change Potential, and 89 +/- 1 and 50 +/- 1 for the integrated Global Temperature change Potential. Using the most commonly used time horizon, 100 years, results in underestimating methane emission metrics by 40-70% relative to the values we calculate that align with the 2 C goal.
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