The Global Warming Potential (GWP) is a widely used single-number metric used to compare the climate change effects of various greenhouse gases. Although GWP has an established role in international climate agreements, it is unphysical, unintuitive, arbitrary, ignores the time dependence of emission sources, and is in some cases misleading. The same doubts have been expressed by the convening lead author of the relevant chapter in the First Assessment Report of the Intergovernmental Panel on Climate Change, in which GWP was introduced. GWP and the related CO2-equivalent methodology have no place in describing the effects of climate change mitigation strategies beyond a 20 year horizon. An important element of sound policy making is the quantitative analysis of policy interventions. This work argues for the broader use of temperature change trajectories in educating policymakers and the public about greenhouse gas control. Modeling tools include general circulation models, related reduced complexity models, and simpler models of global mean temperature change. Examples are presented illustrating the misleading nature of GWP and the CO2-equivalent methodology. These include the greenhouse gas impacts of (1) single year and multiyear emissions of methane, (2) natural gas and coal use in the electric power sector, (3) pipeline and LNG transport of natural gas, (4) natural gas flaring, and (5) livestock herd reduction. Responding to climate change is likely to require global investments measured in trillions of dollars. Clear and accurate communication among and between scientists, policy makers. and the general public is essential. GWP is a crude, inaccurate tool that and the general public is essential. GWP is a crude, inaccurate tool that played a constructive role in the formulation of international agreements. Using better modeling tools can help make climate policy discussions more scientifically rigorous while demystifying the criteria upon which policy choices are made.