A range of different climate pollutants contribute to anthropogenic climate change [1]. Emissions of different climate pollutants are often described using a common metric, generally scaled relative to carbon dioxide (CO 2 ); hence non-CO 2 emissions are typically communicated (and aggregated) as carbon dioxide equivalent (CO 2 -e) quantities.

The most widely used CO 2 equivalence metric is the Global Warming Potential (GWP), defined as the integrated change in radiative forcing (the perturbation of the Earth's atmospheric energy balance, which leads to warming) over a specified time-period following an emission pulse of a given climate pollutant, relative to the same quantity of CO 2 . Emissions of a given climate pollutant (E) can thus be converted to a CO 2 -e emission ( ) quantity by multiplying by the appropriate GWP conversion factor, for the specified time-horizon (H):

The 100-year variant of the Global Warming Potential (GWP 100 ) has been formally adopted in international climate policy (currently as established in the Kyoto Protocol, and in the draft text of the Paris Agreement [2]) and standardised Life Cycle Assessment (LCA)/carbon-footprinting approaches [3]). Subsequently, GWP 100 has become the de facto standard for expressing emissions in the scientific literature and general media, and has essentially become shorthand for the relative climate impacts of a given product or activity. Despite its ubiquity, the relationship between aggregate CO 2 -e emissions calculated using GWP 100 and global warming itself is ambiguous.

This has been a significant and long-standing criticism of the GWP (e.g. [4–7]). Fundamentally, many of the shortcomings of the GWP as a universal climate metric arise because it cannot sufficiently differentiate the contrasting impacts of long- and short-lived climate pollutants (SLCPs), and it is this element that we focus on here.

A large fraction of anthropogenic CO 2 emissions will persist in the atmosphere for millennia without active, large-scale efforts to remove them [8, 9]. Consequently, continued emissions add cumulatively to the atmospheric stock, and so within this millennial time period temperatures will increase indefinitely for as long as emissions are maintained, then remain approximately fixed at this level for centuries once emissions cease [10]. For greenhouse gases with relatively short atmospheric lifespans (or, more broadly, SLCPs) such as methane (CH 4 ), however, natural atmospheric removals limit indefinite increases in their atmospheric concentrations for stable emission rates, as an equilibrium can be established where emissions and removals are approximately balanced. GWP 100 , or indeed any pulse-based metric treating long- and short-lived climate pollutants in the same way, cannot capture these contrasting dynamics.

Following these behaviours, sustained emissions of an SLCP therefore result in a similar impact to a one-off release of a fixed amount of CO 2 : both lead to a relatively stable long-term increase in radiative forcing. Thus an alternative means of equivalence can be derived, relating a change in the rate of emissions of SLCPs to a fixed quantity of CO 2 ([7, 11–13], and see [14] for a recent elaboration on this equivalence concept). Allen et al [15] demonstrated that this can be achieved using GWP conversion factors (and thus based on the same basic atmospheric properties incorporated in the GWP), where a change in the emissions rate of an SLCP (ΔE SLCP ) is equivalent to a one-off release or sequestration of ΔE SLCP × GWP H × H tonnes of CO 2 . This alternative application of GWPs is termed GWP*, and as the means of defining equivalence is better associated with temperature change contribution, can be considered a 'CO 2 warming equivalent (CO 2 -w.e.)', in contrast to a per-emission CO 2 -e [16]. (For the rest of this letter we will use CO 2 -w.e. to report equivalents derived using GWP*, CO 2 -e for equivalents from conventional application of GWP 100 , and 'CO 2 -equivalents' as a generic term to describe either means of deriving equivalents). GWP* was further refined in Allen et al [17], showing that specifying a time-period (Δt) of 20 years over which to assess the change in SLCP emission rates (ΔE SLCP ), and scaling the CO 2 -w.e. per year of this period (i.e. /Δt) provides a good fit for modelled warming, and a means of annualising the reported emissions.

Recent work by Cain et al [16] further improved the accuracy of GWP*. Sustained SLCP emissions result in stable forcing. Eventually, if maintained indefinitely, this results in no additional warming, but since most SLCP emission sources originated within the past century, there is a slow adjustment even to perfectly constant emissions due to the delayed response to past forcing increases [18]. For CO 2 , this slower temperature adjustment is approximately balanced by medium-term carbon cycle dynamics, particularly ocean CO 2 absorption [19]. GWP* was consequently redefined to include a smaller component that also treats SLCPs as a 'stock' pollutant (similarly to conventional GWP 100 usage) to account for this delayed response to past increases in SLCP emissions:

where r represents the weighting given to the impacts of changing the rate of SLCP emissions, and s the weighting given to the impacts of the current emissions rate.

These two weighting factors are scenario dependent (as they will vary based on the historical legacy of emissions, and hence how much of the slow warming component is already experienced), but using the GWP 100 and a combination of r and s of 0.75 and 0.25 respectively was found to give a good approximation of the historical and projected warming impacts of methane over a range of emission trajectories [16], and we use these parameter values in this letter.

Using the values suggested above, under all scenarios except near-constant emissions the equation is dominated by (0.75 × 100 = 75) the rate-based component, with much less weight (0.25) assigned to the stock component. Both components are then multiplied by the GWP 100 to provide a CO 2 warming-equivalent quantity of emissions. Alternatively, if CO 2 -equivalent emissions are pre-computed using GWP 100 , they can be combined using the part of equation (2) in parentheses: hence GWP* is compatible with emissions reporting under the Paris Rulebook agreed at COP24, provided cumulative and SLCPs are reported and aggregated separately in emissions reporting and nationally determined contributions. The rule-book does not explicitly state that gases must be reported individually, although it is near-universal practice in reporting of emissions inventories to specify gases separately in terms of CO 2 -e. Separate reporting and aggregation of cumulative and short-lived pollutants in all communications between parties and the UNFCCC would substantially enhance the transparency of the UNFCCC process and ensure climatically important information is not lost.

With these suggested parameters, the GWP* equation can also be simplified further to:

where E SLCP(t) is the current SLCP emission rate, and E SLCP(t − 20) the rate of SLCP emissions 20 years ago, highlighting that GWP* requires only two values, which are already calculated and reported within the UNFCCC. This version of the equation can be thought of as representing that any 'new' methane emissions have a very strong climate impact, 4 times greater than reported by GWP 100 , but after 20 years much of the warming caused is automatically reversed.

Longer-lived climate pollutants (those with a lifespan longer than H, i.e. 100 years), will also display cumulative behaviours over this timeframe, and so their GWP* CO 2 -w.e. follows conventional use of GWP as in (1). Note, however, that this is in the context of formulating near-to-medium term climate policy, and is not meant to suggest that, for example, nitrous oxide (N 2 O) is directly equivalent to CO 2 either; the impact of our emissions on the carbon cycle means that CO 2 is unique, and the gas is uniquely long-lived [1, 7]. Whether a given climate pollutant is defined as short- or long-lived depends on the timescale being considered, and GWP* could potentially be applied using longer GWP time-horizons than 100 years to also treat longer-lived gases than methane as 'short-lived' (i.e. their impacts depend on the ongoing emissions rate, rather than cumulative total emissions, as for CO 2 ). Further elaboration comparing different timeframes and climate pollutants is shown for related approaches, the combined global warming potential (CGWP) and combined global temperature-change potential (CGTP) in [14]. For this letter we focus exlusively on methane, as the most important SLCP, which must be treated as a non-cumulative pollutant to anticipate the impacts of ambitious emission reduction scenarios even over the next few decades.