  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.
