Combining temperature rate and level perspectives in emission metrics

Abstract. The ultimate goal of the United Framework Convention on Climate Change, which is reconfirmed by the Paris Agreement, is to stabilize the climate change at level that prevents dangerous anthropogenic interference, and it should be achieved within a time frame that allow the natural systems to adapt. Numerous emission metrics have been developed and applied in relation to the first target, while very few metrics have focused on the second target regarding rate of change. We present here a simple and analytical physical emission metric based on the rate of global temperature change and link that to a metric based on a target for the temperature level. The rate of change perspective either can supplement the level target or can be considered together in one commitment that needs one combined metric. Both emission metrics depend on assumptions on a temperature baseline scenario. We give some illustrations on how this framework can be used, such as different temperature rate and level constraints based on the Representative Concentration Pathways. The selection of the time horizon, for what time period and length the rate constraint is binding, and how to weight the rate and level metrics are discussed. For a combined metric, the values for short-lived climate forcers are larger in periods where the critical rate is binding, with larger temporal increases during the rate constraint period as the atmospheric perturbation timescale of the species becomes shorter. Global CO₂ emissions remain the most important, or among the most important, drivers of temperature rates even during periods of binding rate constraints.